Creating fresh checkpoint for puzzle 034720009608000250700900003910000765020300800070009300080001504001003000509402030
Conversation started at: 2023-12-09 20:38:22.269010
Turn number: 1
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Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - user: <output>
first_row: [0,3,4,7,2,0,0,0,9]
second_row: [6,0,8,0,0,0,2,5,0]
third_row: [7,0,0,9,0,0,0,0,3]
fourth_row: [9,1,0,0,0,0,7,6,5]
fifth_row: [0,2,0,3,0,0,8,0,0]
sixth_row: [0,7,0,0,0,9,3,0,0]
seventh_row: [0,8,0,0,0,1,5,0,4]
eighth_row: [0,0,1,0,0,3,0,0,0]
ninth_row: [5,0,9,4,0,2,0,3,0]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [0,3,4,7,2,0,0,0,9]
RowTwo = [6,0,8,0,0,0,2,5,0]
RowThree = [7,0,0,9,0,0,0,0,3]
RowFour = [9,1,0,0,0,0,7,6,5]
RowFive = [0,2,0,3,0,0,8,0,0]
RowSix = [0,7,0,0,0,9,3,0,0]
RowSeven = [0,8,0,0,0,1,5,0,4]
RowEight = [0,0,1,0,0,3,0,0,0]
RowNine = [5,0,9,4,0,2,0,3,0]

# Columns
ColumnOne = [0,6,7,9,0,0,0,0,5]
ColumnTwo = [3,0,0,1,2,7,8,0,0]
ColumnThree = [4,8,0,0,0,0,0,1,9]
ColumnFour = [7,0,9,0,3,0,0,0,4]
ColumnFive = [2,0,0,0,0,0,0,0,0]
ColumnSix = [0,0,0,0,0,9,1,3,2]
ColumnSeven = [0,2,0,7,8,3,5,0,0]
ColumnEight = [0,5,0,6,0,0,0,0,3]
ColumnNine = [9,0,3,5,0,0,4,0,0]

# Blocks
BlockOne:
[[0,3,4],
[6,0,8],
[7,0,0]]
BlockOne = [0,3,4,6,0,8,7,0,0]
BlockTwo:
[[7,2,0],
[0,0,0],
[9,0,0]]
BlockTwo = [7,2,0,0,0,0,9,0,0]
BlockThree:
[[0,0,9],
[2,5,0],
[0,0,3]]
BlockThree = [0,0,9,2,5,0,0,0,3]
BlockFour:
[[9,1,0],
[0,2,0],
[0,7,0]]
BlockFour = [9,1,0,0,2,0,0,7,0]
BlockFive:
[[0,0,0],
[3,0,0],
[0,0,9]]
BlockFive = [0,0,0,3,0,0,0,0,9]
BlockSix:
[[7,6,5],
[8,0,0],
[3,0,0]]
BlockSix = [7,6,5,8,0,0,3,0,0]
BlockSeven:
[[0,8,0],
[0,0,1],
[5,0,9]]
BlockSeven = [0,8,0,0,0,1,5,0,9]
BlockEight:
[[0,0,0],
[0,0,3],
[4,0,2]]
BlockEight = [0,0,0,0,0,3,4,0,2]
BlockNine:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockNine = [5,0,4,0,0,0,0,3,0]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([0,3,4,7,2,0,0,0,9]) = [1,5,6,8]
CandidatesRowOne = [1,5,6,8]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([6,0,8,0,0,0,2,5,0]) = [1,3,4,7,9]
CandidatesRowTwo = [1,3,4,7,9]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([7,0,0,9,0,0,0,0,3]) = [1,2,4,5,6,8]
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,0,0,0,0,7,6,5]) = [2,3,4,8]
CandidatesRowFour = [2,3,4,8]
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([0,2,0,3,0,0,8,0,0]) = [1,4,5,6,7,9]
CandidatesRowFive = [1,4,5,6,7,9]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([0,7,0,0,0,9,3,0,0]) = [1,2,4,5,6,8]
CandidatesRowSix = [1,2,4,5,6,8]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,0,0,1,5,0,4]) = [2,3,6,7,9]
CandidatesRowSeven = [2,3,6,7,9]
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([0,0,1,0,0,3,0,0,0]) = [2,4,5,6,7,8,9]
CandidatesRowEight = [2,4,5,6,7,8,9]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([5,0,9,4,0,2,0,3,0]) = [1,6,7,8]
CandidatesRowNine = [1,6,7,8]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([0,6,7,9,0,0,0,0,5]) = [1,2,3,4,8]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([3,0,0,1,2,7,8,0,0]) = [4,5,6,9]
CandidatesColumnTwo = [4,5,6,9]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([4,8,0,0,0,0,0,1,9]) = [2,3,5,6,7]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([7,0,9,0,3,0,0,0,4]) = [1,2,5,6,8]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([2,0,0,0,0,0,0,0,0]) = [1,3,4,5,6,7,8,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,0,0,9,1,3,2]) = [4,5,6,7,8]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([0,2,0,7,8,3,5,0,0]) = [1,4,6,9]
CandidatesColumnSeven = [1,4,6,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([0,5,0,6,0,0,0,0,3]) = [1,2,4,7,8,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([9,0,3,5,0,0,4,0,0]) = [1,2,6,7,8]
CandidatesColumnNine = [1,2,6,7,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([0,3,4,6,0,8,7,0,0]) = [1,2,5,9]
CandidatesBlockOne = [1,2,5,9]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([7,2,0,0,0,0,9,0,0]) = [1,3,4,5,6,8]
CandidatesBlockTwo = [1,3,4,5,6,8]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([0,0,9,2,5,0,0,0,3]) = [1,4,6,7,8]
CandidatesBlockThree = [1,4,6,7,8]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,0,0,2,0,0,7,0]) = [3,4,5,6,8]
CandidatesBlockFour = [3,4,5,6,8]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,3,0,0,0,0,9]) = [1,2,4,5,6,7,8]
CandidatesBlockFive = [1,2,4,5,6,7,8]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,0,0,3,0,0]) = [1,2,4,9]
CandidatesBlockSix = [1,2,4,9]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,0,0,1,5,0,9]) = [2,3,4,6,7]
CandidatesBlockSeven = [2,3,4,6,7]
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,0,0,3,4,0,2]) = [1,5,6,7,8,9]
CandidatesBlockEight = [1,5,6,7,8,9]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockNine = [1,2,6,7,8,9]

# Index of all zeros, by row
RowOne = [0,3,4,7,2,0,0,0,9]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 0
RowOne[1] = 3
RowOne[2] = 4
RowOne[3] = 7
RowOne[4] = 2
RowOne[5] = 0
RowOne[6] = 0
RowOne[7] = 0
RowOne[8] = 9
IndexOfAll0ElementsInRowOne => [0,5,6,7]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [1,6,7,8]
EmptyColumnNamesRowOne = [ColumnOne,ColumnSix,ColumnSeven,ColumnEight]

RowTwo = [6,0,8,0,0,0,2,5,0]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 6
RowTwo[1] = 0
RowTwo[2] = 8
RowTwo[3] = 0
RowTwo[4] = 0
RowTwo[5] = 0
RowTwo[6] = 2
RowTwo[7] = 5
RowTwo[8] = 0
IndexOfAll0ElementsInRowTwo => [1,3,4,5,8]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [2,4,5,6,9]
EmptyColumnNamesRowTwo = [ColumnTwo,ColumnFour,ColumnFive,ColumnSix,ColumnNine]

RowThree = [7,0,0,9,0,0,0,0,3]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 7
RowThree[1] = 0
RowThree[2] = 0
RowThree[3] = 9
RowThree[4] = 0
RowThree[5] = 0
RowThree[6] = 0
RowThree[7] = 0
RowThree[8] = 3
IndexOfAll0ElementsInRowThree => [1,2,4,5,6,7]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [2,3,5,6,7,8]
EmptyColumnNamesRowThree = [ColumnTwo,ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]

RowFour = [9,1,0,0,0,0,7,6,5]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 9
RowFour[1] = 1
RowFour[2] = 0
RowFour[3] = 0
RowFour[4] = 0
RowFour[5] = 0
RowFour[6] = 7
RowFour[7] = 6
RowFour[8] = 5
IndexOfAll0ElementsInRowFour => [2,3,4,5]
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = [3,4,5,6]
EmptyColumnNamesRowFour = [ColumnThree,ColumnFour,ColumnFive,ColumnSix]

RowFive = [0,2,0,3,0,0,8,0,0]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 0
RowFive[1] = 2
RowFive[2] = 0
RowFive[3] = 3
RowFive[4] = 0
RowFive[5] = 0
RowFive[6] = 8
RowFive[7] = 0
RowFive[8] = 0
IndexOfAll0ElementsInRowFive => [0,2,4,5,7,8]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [1,3,5,6,8,9]
EmptyColumnNamesRowFive = [ColumnOne,ColumnThree,ColumnFive,ColumnSix,ColumnEight,ColumnNine]

RowSix = [0,7,0,0,0,9,3,0,0]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 0
RowSix[1] = 7
RowSix[2] = 0
RowSix[3] = 0
RowSix[4]= 0
RowSix[5] = 9
RowSix[6] = 3
RowSix[7] = 0
RowSix[8] = 0
IndexOfAll0ElementsInRowSix => [0,2,3,4,7,8]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [1,3,4,5,8,9]
EmptyColumnNamesRowSix = [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]

RowSeven = [0,8,0,0,0,1,5,0,4]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 0
RowSeven[1] = 8
RowSeven[2] = 0
RowSeven[3] = 0
RowSeven[4] = 0
RowSeven[5] = 1
RowSeven[6] = 5
RowSeven[7] = 0
RowSeven[8] = 4
IndexOfAll0ElementsInRowSeven => [0,2,3,4,7]
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = [1,3,4,5,8]
EmptyColumnNamesRowSeven = [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight]

RowEight = [0,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 0
RowEight[1] = 0
RowEight[2] = 1
RowEight[3] = 0
RowEight[4] = 0
RowEight[5] = 3
RowEight[6] = 0
RowEight[7] = 0
RowEight[8] = 0
IndexOfAll0ElementsInRowEight => [0,1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [1,2,4,5,7,8,9]
EmptyColumnNamesRowEight = [ColumnOne,ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowNine = [5,0,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 5
RowNine[1] = 0
RowNine[2] = 9
RowNine[3] = 4
RowNine[4] = 0
RowNine[5] = 2
RowNine[6] = 0
RowNine[7] = 3
RowNine[8] = 0
IndexOfAll0ElementsInRowNine => [1,4,6,8]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [2,5,7,9]
EmptyColumnNamesRowNine = [ColumnTwo,ColumnFive,ColumnSeven,ColumnNine]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 4 + 5 + 6 + 4 + 6 + 6 + 5 + 7 + 4 = 47

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 20

PART TWO, CELL CANDIDATES
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnOne,ColumnSix,ColumnSeven,ColumnEight]
Note, the last empty column of the RowOne is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 20
Up to ColumnOne in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnOne means BlockOne
import CandidatesRowOne, CandidatesColumnOne, CandidatesBlockOne
CandidatesRowOne = [1,5,6,8]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockOne = [1,2,5,9]
Finding Common Elements:
CommonElementsOfRowOneAndColumnOne => [1,5,6,8] & [1,2,3,4,8] = [1,8]
CommonElementsOfRowOneAndColumnOneAndBlockOne => [1,8] & [1,2,5,9] = [1]
CellCandidates = [1]
Length = 1
FOUND RowOne, ColumnOne, BlockOne

### 2 of 20
Up to ColumnSix in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnSix means BlockTwo
import CandidatesRowOne, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowOne = [1,5,6,8]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnSix => [1,5,6,8] & [4,5,6,7,8] = [5,6,8]
CommonElementsOfRowOneAndColumnSixAndBlockTwo => [5,6,8] & [1,3,4,5,6,8] = [5,6,8]
CellCandidates = [5,6,8]
Length = 3
Not 1

### 3 of 20
Up to ColumnSeven in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnSeven means BlockThree
import CandidatesRowOne, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowOne = [1,5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockThree = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnSeven => [1,5,6,8] & [1,4,6,9] = [1,6]
CommonElementsOfRowOneAndColumnSevenAndBlockThree => [1,6] & [1,4,6,7,8] = [1,6]
CellCandidates = [1,6]
Length = 2
Not 1

### 4 of 20
Up to ColumnEight in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Last column of current row
The next row is RowTwo
RowOne and ColumnEight means BlockThree
import CandidatesRowOne, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowOne = [1,5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnEight => [1,5,6,8] & [1,2,4,7,8,9] = [1,8]
CommonElementsOfRowOneAndColumnEightAndBlockThree => [1,8] & [1,4,6,7,8] = [1,8]
CellCandidates = [1,8]
Length = 2
Not 1

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnTwo,ColumnFour,ColumnFive,ColumnSix,ColumnNine]
Note, the last empty column of the RowTwo is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 5 of 20
Up to ColumnTwo in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnTwo means BlockOne
import CandidatesRowTwo, CandidatesColumnTwo, CandidatesBlockOne
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnTwo => [1,3,4,7,9] & [4,5,6,9] = [4,9]
CommonElementsOfRowTwoAndColumnTwoAndBlockOne => [4,9] & [1,2,5,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowTwo, ColumnTwo, BlockOne

### 6 of 20
Up to ColumnFour in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFour means BlockTwo
import CandidatesRowTwo, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFour => [1,3,4,7,9] & [1,2,5,6,8] = [1,4]
CommonElementsOfRowTwoAndColumnFourAndBlockTwo => [1,4] & [1,3,4,5,6,8] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

### 7 of 20
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [1,3,4,7,9] & [1,3,4,5,6,7,8,9] = [1,3,4,7,9]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [1,3,4,7,9] & [1,3,4,5,6,8] = [1,3,4]
CellCandidates = [1,3,4]
Length = 3
Not 1

### 8 of 20
Up to ColumnSix in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnSix means BlockTwo
import CandidatesRowTwo, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnSix => [1,3,4,7,9] & [4,5,6,7,8] = [4,7]
CommonElementsOfRowTwoAndColumnSixAndBlockTwo => [4,7] & [1,3,4,5,6,8] = [4]
CellCandidates = [4]
Length = 1
FOUND RowTwo, ColumnSix, BlockTwo

### 9 of 20
Up to ColumnNine in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Last column of current row
The next row is RowThree
RowTwo and ColumnNine means BlockThree
import CandidatesRowTwo, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnNine => [1,3,4,7,9] & [1,2,6,7,8] = [1,7]
CommonElementsOfRowTwoAndColumnNineAndBlockThree => [1,7] & [1,4,6,7,8] = [1,7]
CellCandidates = [1,7]
Length = 2
Not 1

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnTwo,ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Note, the last empty column of the RowThree is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 10 of 20
Up to ColumnTwo in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnTwo means BlockOne
import CandidatesRowThree, CandidatesColumnTwo, CandidatesBlockOne
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnTwo => [1,2,4,5,6,8] & [4,5,6,9] = [4,5,6]
CommonElementsOfRowThreeAndColumnTwoAndBlockOne => [4,5,6] & [1,2,5,9] = [5]
CellCandidates = [5]
Length = 1
FOUND RowThree, ColumnTwo, BlockOne

### 11 of 20
Up to ColumnThree in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnThree means BlockOne
import CandidatesRowThree, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesBlockOne = [1,2,5,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnThree => [1,2,4,5,6,8] & [2,3,5,6,7] = [2,5,6]
CommonElementsOfRowThreeAndColumnThreeAndBlockOne => [2,5,6] & [1,2,5,9] = [2,5]
CellCandidates = [2,5]
Length = 2
Not 1

### 12 of 20
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,2,4,5,6,8] & [1,3,4,5,6,7,8,9] = [1,2,4,5,6,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,2,4,5,6,8] & [1,3,4,5,6,8] = [1,2,4,5,6,8]
CellCandidates = [1,2,4,5,6,8]
Length = 6
Not 1

### 13 of 20
Up to ColumnSix in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnSix means BlockTwo
import CandidatesRowThree, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSix => [1,2,4,5,6,8] & [4,5,6,7,8] = [4,5,6,8]
CommonElementsOfRowThreeAndColumnSixAndBlockTwo => [4,5,6,8] & [1,3,4,5,6,8] = [4,5,6,8]
CellCandidates = [4,5,6,8]
Length = 4
Not 1

### 14 of 20
Up to ColumnSeven in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnSeven means BlockThree
import CandidatesRowThree, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockThree = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSeven => [1,2,4,5,6,8] & [1,4,6,9] = [1,4,6]
CommonElementsOfRowThreeAndColumnSevenAndBlockThree => [1,4,6] & [1,4,6,7,8] = [1,4,6]
CellCandidates = [1,4,6]
Length = 3
Not 1

### 15 of 20
Up to ColumnEight in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Last column of current row
The next row is RowFour
RowThree and ColumnEight means BlockThree
import CandidatesRowThree, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnEight => [1,2,4,5,6,8] & [1,2,4,7,8,9] = [1,2,4,8]
CommonElementsOfRowThreeAndColumnEightAndBlockThree => [1,2,4,8] & [1,4,6,7,8] = [1,4,8]
CellCandidates = [1,4,8]
Length = 3
Not 1

## RowFour Candidates
EmptyColumnNamesRowFour: [ColumnThree,ColumnFour,ColumnFive,ColumnSix]
Note, the last empty column of the RowFour is ColumnSix
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFour and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFour and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFour and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 16 of 20
Up to ColumnThree in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnSix
Not the last column of current row
RowFour and ColumnThree means BlockFour
import CandidatesRowFour, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowFour = [2,3,4,8]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesBlockFour = [3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnThree => [2,3,4,8] & [2,3,5,6,7] = [2,3]
CommonElementsOfRowFourAndColumnThreeAndBlockFour => [2,3] & [3,4,5,6,8] = [3]
CellCandidates = [3]
Length = 1
FOUND RowFour, ColumnThree, BlockFour

### 17 of 20
Up to ColumnFour in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnSix
Not the last column of current row
RowFour and ColumnFour means BlockFive
import CandidatesRowFour, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowFour = [2,3,4,8]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockFive = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFour => [2,3,4,8] & [1,2,5,6,8] = [2,8]
CommonElementsOfRowFourAndColumnFourAndBlockFive => [2,8] & [1,2,4,5,6,7,8] = [2,8]
CellCandidates = [2,8]
Length = 2
Not 1

### 18 of 20
Up to ColumnFive in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnSix
Not the last column of current row
RowFour and ColumnFive means BlockFive
import CandidatesRowFour, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFour = [2,3,4,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFive => [2,3,4,8] & [1,3,4,5,6,7,8,9] = [3,4,8]
CommonElementsOfRowFourAndColumnFiveAndBlockFive => [3,4,8] & [1,2,4,5,6,7,8] = [3,4,8]
CellCandidates = [3,4,8]
Length = 3
Not 1

### 19 of 20
Up to ColumnSix in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnSix
Last column of current row
The next row is RowFive
RowFour and ColumnSix means BlockFive
import CandidatesRowFour, CandidatesColumnSix, CandidatesBlockFive
CandidatesRowFour = [2,3,4,8]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockFive = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnSix => [2,3,4,8] & [4,5,6,7,8] = [4,8]
CommonElementsOfRowFourAndColumnSixAndBlockFive => [4,8] & [1,2,4,5,6,7,8] = [4,8]
CellCandidates = [4,8]
Length = 2
Not 1

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnOne,ColumnThree,ColumnFive,ColumnSix,ColumnEight,ColumnNine]
Note, the last empty column of the RowFive is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 20 of 20
Up to ColumnOne in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnOne means BlockFour
import CandidatesRowFive, CandidatesColumnOne, CandidatesBlockFour
CandidatesRowFive = [1,4,5,6,7,9]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockFour = [3,4,5,6,8]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnOne => [1,4,5,6,7,9] & [1,2,3,4,8] = [1,4]
CommonElementsOfRowFiveAndColumnOneAndBlockFour => [1,4] & [3,4,5,6,8] = [4]
CellCandidates = [4]
Length = 1
FOUND RowFive, ColumnOne, BlockFour

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnOne, BlockOne
2: FOUND RowTwo, ColumnTwo, BlockOne
3: FOUND RowTwo, ColumnSix, BlockTwo
4: FOUND RowThree, ColumnTwo, BlockOne
5: FOUND RowFour, ColumnThree, BlockFour
6: FOUND RowFive, ColumnOne, BlockFour
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnOne, BlockOne):
CandidatesRowOne = [1,5,6,8]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnTwo, BlockOne):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnSix, BlockTwo):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]

cell(RowThree, ColumnTwo, BlockOne):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowFour, ColumnThree, BlockFour):
CandidatesRowFour = [2,3,4,8]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesBlockFour = [3,4,5,6,8]

cell(RowFive, ColumnOne, BlockFour):
CandidatesRowFive = [1,4,5,6,7,9]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockFour = [3,4,5,6,8]

</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 20:46:23.475664
Turn number: 2
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - user: <output>
first_row: [0,3,4,7,2,0,0,0,9]
second_row: [6,0,8,0,0,0,2,5,0]
third_row: [7,0,0,9,0,0,0,0,3]
fourth_row: [9,1,0,0,0,0,7,6,5]
fifth_row: [0,2,0,3,0,0,8,0,0]
sixth_row: [0,7,0,0,0,9,3,0,0]
seventh_row: [0,8,0,0,0,1,5,0,4]
eighth_row: [0,0,1,0,0,3,0,0,0]
ninth_row: [5,0,9,4,0,2,0,3,0]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: One
3: FOUND RowTwo, ColumnSix, BlockTwo
4: FOUND RowThree, ColumnTwo, BlockOne
5: FOUND RowFour, ColumnThree, BlockFour
6: FOUND RowFive, ColumnOne, BlockFour
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnOne, BlockOne):
CandidatesRowOne = [1,5,6,8]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnTwo, BlockOne):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnSix, BlockTwo):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]

cell(RowThree, ColumnTwo, BlockOne):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowFour, ColumnThree, BlockFour):
CandidatesRowFour = [2,3,4,8]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesBlockFour = [3,4,5,6,8]

cell(RowFive, ColumnOne, BlockFour):
CandidatesRowFive = [1,4,5,6,7,9]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockFour = [3,4,5,6,8]

</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnOne):
CandidatesRowOne = [1,5,6,8]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnTwo):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowTwo, ColumnSix):
CandidatesRowTwo = [1,3,4,7,9]
CandidatesColumnSix = [4,5,6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8]

cell(RowThree, ColumnTwo):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnTwo = [4,5,6,9]
CandidatesBlockOne = [1,2,5,9]

cell(RowFour, ColumnThree):
CandidatesRowFour = [2,3,4,8]
CandidatesColumnThree = [2,3,5,6,7]
CandidatesBlockFour = [3,4,5,6,8]

cell(RowFive, ColumnOne):
CandidatesRowFive = [1,4,5,6,7,9]
CandidatesColumnOne = [1,2,3,4,8]
CandidatesBlockFour = [3,4,5,6,8]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowOne, ColumnOne):
CandidatesRowOne.length = 4
CandidatesColumnOne.length = 5
CandidatesBlockOne.length = 4

shortest_list = CandidatesBlockOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowOne and CandidatesColumnOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [1,5,6,8], broken into CandidatesRowOneLow = [1,5] and CandidatesRowOneHigh = [6,8]
CandidatesColumnOne = [1,2,3,4,8], broken into CandidatesColumnOneLow = [1,2,3,4] and CandidatesColumnOneHigh = [8]
CandidatesBlockOne = [1,2,5,9], broken into CandidatesBlockOneLow = [1,2,5] and CandidatesBlockOneHigh = [9]

Checking digits in CandidatesBlockOneLow = [1,2,5] against: CandidatesRowOneLow = [1,5] and CandidatesColumnOneLow = [1,2,3,4]
1: [1,5].count(1) = 1, [1,2,3,4].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE
2: [1,5].count(2) = 0, [1,2,3,4].count(2) = 1, TotalCount(2) = 1
5: [1,5].count(5) = 1, [1,2,3,4].count(5) = 0, TotalCount(5) = 1

Checking digits in CandidatesBlockOneHigh = [9] against: CandidatesRowOneHigh = [6,8] and CandidatesColumnOneHigh = [8]
9: [6,8].count(9) = 0, [8].count(9) = 0, TotalCount(9) = 0

Confirmed candidates found for cell(RowOne, ColumnOne): [1]

## Cell 2 of 6
cell(RowTwo, ColumnTwo):
CandidatesRowTwo.length = 5
CandidatesColumnTwo.length = 4
CandidatesBlockOne.length = 4

shortest_list = CandidatesColumnTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [1,3,4,7,9], broken into CandidatesRowTwoLow = [1,3,4] and CandidatesRowTwoHigh = [7,9]
CandidatesColumnTwo = [4,5,6,9], broken into CandidatesColumnTwoLow = [4,5] and CandidatesColumnTwoHigh = [6,9]
CandidatesBlockOne = [1,2,5,9], broken into CandidatesBlockOneLow = [1,2,5] and CandidatesBlockOneHigh = [9]

Checking digits in CandidatesColumnTwoLow = [4,5] against: CandidatesRowTwoLow = [1,3,4] and CandidatesBlockOneLow = [1,2,5]
4: [1,3,4].count(4) = 1, [1,2,5].count(4) = 0, TotalCount(4) = 1
5: [1,3,4].count(5) = 0, [1,2,5].count(5) = 1, TotalCount(5) = 1

Checking digits in CandidatesColumnTwoHigh = [6,9] against: CandidatesRowTwoHigh = [7,9] and CandidatesBlockOneHigh = [9]
6: [7,9].count(6) = 0, [9].count(6) = 0, TotalCount(6) = 0
9: [7,9].count(9) = 1, [9].count(9) = 1, TotalCount(9) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnTwo): [9]

## Cell 3 of 6
cell(RowTwo, ColumnSix):
CandidatesRowTwo.length = 5
CandidatesColumnSix.length = 5
CandidatesBlockTwo.length = 6

shortest_list = CandidatesRowTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnSix and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [1,3,4,7,9], broken into CandidatesRowTwoLow = [1,3,4] and CandidatesRowTwoHigh = [7,9]
CandidatesColumnSix = [4,5,6,7,8], broken into CandidatesColumnSixLow = [4,5] and CandidatesColumnSixHigh = [6,7,8]
CandidatesBlockTwo = [1,3,4,5,6,8], broken into CandidatesBlockTwoLow = [1,3,4,5] and CandidatesBlockTwoHigh = [6,8]

Checking digits in CandidatesRowTwoLow = [1,3,4] against: CandidatesColumnSixLow = [4,5] and CandidatesBlockTwoLow = [1,3,4,5]
1: [4,5].count(1) = 0, [1,3,4,5].count(1) = 1, TotalCount(1) = 1
3: [4,5].count(3) = 0, [1,3,4,5].count(3) = 1, TotalCount(3) = 1
4: [4,5].count(4) = 1, [1,3,4,5].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowTwoHigh = [7,9] against: CandidatesColumnSixHigh = [6,7,8] and CandidatesBlockTwoHigh = [6,8]
7: [6,7,8].count(7) = 1, [6,8].count(7) = 0, TotalCount(7) = 1
9: [6,7,8].count(9) = 0, [6,8].count(9) = 0, TotalCount(9) = 0

Confirmed candidates found for cell(RowTwo, ColumnSix): [4]

## Cell 4 of 6
cell(RowThree, ColumnTwo):
CandidatesRowThree.length = 6
CandidatesColumnTwo.length = 4
CandidatesBlockOne.length = 4

shortest_list = CandidatesColumnTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,5,6,8], broken into CandidatesRowThreeLow = [1,2,4,5] and CandidatesRowThreeHigh = [6,8]
CandidatesColumnTwo = [4,5,6,9], broken into CandidatesColumnTwoLow = [4,5] and CandidatesColumnTwoHigh = [6,9]
CandidatesBlockOne = [1,2,5,9], broken into CandidatesBlockOneLow = [1,2,5] and CandidatesBlockOneHigh = [9]

Checking digits in CandidatesColumnTwoLow = [4,5] against: CandidatesRowThreeLow = [1,2,4,5] and CandidatesBlockOneLow = [1,2,5]
4: [1,2,4,5].count(4) = 1, [1,2,5].count(4) = 0, TotalCount(4) = 1
5: [1,2,4,5].count(5) = 1, [1,2,5].count(5) = 1, TotalCount(5) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnTwoHigh = [6,9] against: CandidatesRowThreeHigh = [6,8] and CandidatesBlockOneHigh = [9]
6: [6,8].count(6) = 1, [9].count(6) = 0, TotalCount(6) = 1
9: [6,8].count(9) = 0, [9].count(9) = 1, TotalCount(9) = 1

Confirmed candidates found for cell(RowThree, ColumnTwo): [5]

## Cell 5 of 6
cell(RowFour, ColumnThree):
CandidatesRowFour.length = 4
CandidatesColumnThree.length = 5
CandidatesBlockFour.length = 5

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnThree and CandidatesBlockFour

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [2,3,4,8], broken into CandidatesRowFourLow = [2,3,4] and CandidatesRowFourHigh = [8]
CandidatesColumnThree = [2,3,5,6,7], broken into CandidatesColumnThreeLow = [2,3,5] and CandidatesColumnThreeHigh = [6,7]
CandidatesBlockFour = [3,4,5,6,8], broken into CandidatesBlockFourLow = [3,4,5] and CandidatesBlockFourHigh = [6,8]

Checking digits in CandidatesRowFourLow = [2,3,4] against: CandidatesColumnThreeLow = [2,3,5] and CandidatesBlockFourLow = [3,4,5]
2: [2,3,5].count(2) = 1, [3,4,5].count(2) = 0, TotalCount(2) = 1
3: [2,3,5].count(3) = 1, [3,4,5].count(3) = 1, TotalCount(3) = 2 FOUND A CANDIDATE
4: [2,3,5].count(4) = 0, [3,4,5].count(4) = 1, TotalCount(4) = 1

Checking digits in CandidatesRowFourHigh = [8] against: CandidatesColumnThreeHigh = [6,7] and CandidatesBlockFourHigh = [6,8]
8: [6,7].count(8) = 0, [6,8].count(8) = 1, TotalCount(8) = 1

Confirmed candidates found for cell(RowFour, ColumnThree): [3]

## Cell 6 of 6
cell(RowFive, ColumnOne):
CandidatesRowFive.length = 6
CandidatesColumnOne.length = 5
CandidatesBlockFour.length = 5

shortest_list = CandidatesColumnOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowFive and CandidatesBlockFour

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [1,4,5,6,7,9], broken into CandidatesRowFiveLow = [1,4,5] and CandidatesRowFiveHigh = [6,7,9]
CandidatesColumnOne = [1,2,3,4,8], broken into CandidatesColumnOneLow = [1,2,3,4] and CandidatesColumnOneHigh = [8]
CandidatesBlockFour = [3,4,5,6,8], broken into CandidatesBlockFourLow = [3,4,5] and CandidatesBlockFourHigh = [6,8]

Checking digits in CandidatesColumnOneLow = [1,2,3,4] against: CandidatesRowFiveLow = [1,4,5] and CandidatesBlockFourLow = [3,4,5]
1: [1,4,5].count(1) = 1, [3,4,5].count(1) = 0, TotalCount(1) = 1
2: [1,4,5].count(2) = 0, [3,4,5].count(2) = 0, TotalCount(2) = 0
3: [1,4,5].count(3) = 0, [3,4,5].count(3) = 1, TotalCount(3) = 1
4: [1,4,5].count(4) = 1, [3,4,5].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnOneHigh = [8] against: CandidatesRowFiveHigh = [6,7,9] and CandidatesBlockFourHigh = [6,8]
8: [6,7,9].count(8) = 0, [6,8].count(8) = 1, TotalCount(8) = 1

Confirmed candidates found for cell(RowFive, ColumnOne): [4]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnOne): [1]
[1].length = 1
length is 1, Passes

cell(RowTwo, ColumnTwo): [9]
[9].length = 1
length is 1, Passes

cell(RowTwo, ColumnSix): [4]
[4].length = 1
length is 1, Passes

cell(RowThree, ColumnTwo): [5]
[5].length = 1
length is 1, Passes

cell(RowFour, ColumnThree): [3]
[3].length = 1
length is 1, Passes

cell(RowFive, ColumnOne): [4]
[4].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnOne): [1]
cell(RowTwo, ColumnTwo): [9]
cell(RowTwo, ColumnSix): [4]
cell(RowThree, ColumnTwo): [5]
cell(RowFour, ColumnThree): [3]
cell(RowFive, ColumnOne): [4]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowTwo, RowThree, RowFour, RowFive

RowOne: [0,3,4,7,2,0,0,0,9]
cell(RowOne, ColumnOne): [1]

RowTwo: [6,0,8,0,0,0,2,5,0]
cell(RowTwo, ColumnTwo): [9]
cell(RowTwo, ColumnSix): [4]

RowThree: [7,0,0,9,0,0,0,0,3]
cell(RowThree, ColumnTwo): [5]

RowFour: [9,1,0,0,0,0,7,6,5]
cell(RowFour, ColumnThree): [3]

RowFive: [0,2,0,3,0,0,8,0,0]
cell(RowFive, ColumnOne): [4]

RowSix: [0,7,0,0,0,9,3,0,0]

RowSeven: [0,8,0,0,0,1,5,0,4]

RowEight: [0,0,1,0,0,3,0,0,0]

RowNine: [5,0,9,4,0,2,0,3,0]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowOne, ColumnOne): [1]
RowOne = [0,3,4,7,2,0,0,0,9]
The ColumnOne element of RowOne needs to be updated to [1]

ColumnOne: 0
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 9

Now replacing ColumnOne with the element to update [1], such that ColumnOne = 1
Redoing column list like we just did, but with ColumnOne set to 1

ColumnOne: 1
ColumnTwo: 3
ColumnThree4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 9

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnOne.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnOne it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnOne (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnOne does Not appear on this list!!! The ONLY time you don't is if ColumnOne is ColumnOne, in which case the list is empty.):
PreCellColumnsList = []
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnOne:
PreCellColumnsList.length => [].length = 0
Now the elements of the columns in PreCellColumnsList, which is the first 0 elements of RowOne:
PreCellList = []

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 0 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [1,3,4,7,2,0,0,0,9]

## Updating 2 of 6
cell(RowTwo, ColumnTwo): [9]
RowTwo = [6,0,8,0,0,0,2,5,0]
The ColumnTwo element of RowTwo needs to be updated to [9]

ColumnOne: 6
ColumnTwo: 0
ColumnThree: 8
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Now replacing ColumnTwo with the element to update [9], such that ColumnTwo = 9
Redoing column list like we just did, but with ColumnTwo set to 9

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnTwo.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnTwo it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnTwo (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnTwo does Not appear on this list!!! The ONLY time you don't is if ColumnTwo is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnTwo:
PreCellColumnsList.length => [ColumnOne].length = 1
Now the elements of the columns in PreCellColumnsList, which is the first 1 elements of RowTwo:
PreCellList = [6]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [9] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(9) = [6,9]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [6,9,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 1 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [6,9,8,0,0,0,2,5,0]

## Updating 3 of 6
cell(RowTwo, ColumnSix): [4]
RowTwo = [6,9,8,0,0,0,2,5,0]
The ColumnSix element of RowTwo needs to be updated to [4]

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Now replacing ColumnSix with the element to update [4], such that ColumnSix = 4
Redoing column list like we just did, but with ColumnSix set to 4

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 0
ColumnFive: 0
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSix.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSix it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSix (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSix does Not appear on this list!!! The ONLY time you don't is if ColumnSix is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSix:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
Now the elements of the columns in PreCellColumnsList, which is the first 5 elements of RowTwo:
PreCellList = [6,9,8,0,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [6,9,8,0,0,4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [6,9,8,0,0,4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 5 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [6,9,8,0,0,4,2,5,0]

## Updating 4 of 6
cell(RowThree, ColumnTwo): [5]
RowThree = [7,0,0,9,0,0,0,0,3]
The ColumnTwo element of RowThree needs to be updated to [5]

ColumnOne: 7
ColumnTwo: 0
ColumnThree: 0
ColumnFour: 9
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnTwo with the element to update [5], such that ColumnTwo = 5
Redoing column list like we just did, but with ColumnTwo set to 5

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 0
ColumnFour: 9
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnTwo.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnTwo it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnTwo (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnTwo does Not appear on this list!!! The ONLY time you don't is if ColumnTwo is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnTwo:
PreCellColumnsList.length => [ColumnOne].length = 1
Now the elements of the columns in PreCellColumnsList, which is the first 1 elements of RowThree:
PreCellList = [7]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [5] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(5) = [7,5]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [7,5,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 1 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [7,5,0,9,0,0,0,0,3]

## Updating 5 of 6
cell(RowFour, ColumnThree): [3]
RowFour = [9,1,0,0,0,0,7,6,5]
The ColumnThree element of RowFour needs to be updated to [3]

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 0
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Now replacing ColumnThree with the element to update [3], such that ColumnThree = 3
Redoing column list like we just did, but with ColumnThree set to 3

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnThree.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnThree it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnThree (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnThree does Not appear on this list!!! The ONLY time you don't is if ColumnThree is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnThree:
PreCellColumnsList.length => [ColumnOne,ColumnTwo].length = 2
Now the elements of the columns in PreCellColumnsList, which is the first 2 elements of RowFour:
PreCellList = [9,1]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [3] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(3) = [9,1,3]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [9,1,3,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 2 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [9,1,3,0,0,0,7,6,5]

## Updating 6 of 6
cell(RowFive, ColumnOne): [4]
RowFive = [0,2,0,3,0,0,8,0,0]
The ColumnOne element of RowFive needs to be updated to [4]

ColumnOne: 0
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnOne with the element to update [4], such that ColumnOne = 4
Redoing column list like we just did, but with ColumnOne set to 4

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnOne.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnOne it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnOne (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnOne does Not appear on this list!!! The ONLY time you don't is if ColumnOne is ColumnOne, in which case the list is empty.):
PreCellColumnsList = []
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnOne:
PreCellColumnsList.length => [].length = 0
Now the elements of the columns in PreCellColumnsList, which is the first 0 elements of RowFive:
PreCellList = []

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 0 + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [4,2,0,3,0,0,8,0,0]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [1,3,4,7,2,0,0,0,9]
UpdatedRowTwo = [6,9,8,0,0,4,2,5,0]
UpdatedRowThree = [7,5,0,9,0,0,0,0,3]
UpdatedRowFour = [9,1,3,0,0,0,7,6,5]
UpdatedRowFive = [4,2,0,3,0,0,8,0,0]

The rows to update are RowOne, RowTwo, RowThree, RowFour, RowFive
Using the contents of UpdatedRowOne, UpdatedRowTwo, UpdatedRowThree, UpdatedRowFour, UpdatedRowFive
Printing Sudoku:
UpdatedRowOne: [1,3,4,7,2,0,0,0,9]
UpdatedRowTwo: [6,9,8,0,0,4,2,5,0]
UpdatedRowThree: [7,5,0,9,0,0,0,0,3]
UpdatedRowFour: [9,1,3,0,0,0,7,6,5]
UpdatedRowFive: [4,2,0,3,0,0,8,0,0]
RowSix: [0,7,0,0,0,9,3,0,0]
RowSeven: [0,8,0,0,0,1,5,0,4]
RowEight: [0,0,1,0,0,3,0,0,0]
RowNine: [5,0,9,4,0,2,0,3,0]

# STEP_SEVEN: Shifting the Rows of the Sudoku
UpdatedRowFour: [9,1,3,0,0,0,7,6,5]
UpdatedRowFive: [4,2,0,3,0,0,8,0,0]
RowSix: [0,7,0,0,0,9,3,0,0]
RowSeven: [0,8,0,0,0,1,5,0,4]
RowEight: [0,0,1,0,0,3,0,0,0]
RowNine: [5,0,9,4,0,2,0,3,0]
UpdatedRowOne: [1,3,4,7,2,0,0,0,9]
UpdatedRowTwo: [6,9,8,0,0,4,2,5,0]
UpdatedRowThree: [7,5,0,9,0,0,0,0,3]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [9,1,3,0,0,0,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,0]
RowThree: [0,7,0,0,0,9,3,0,0]
RowFour: [0,8,0,0,0,1,5,0,4]
RowFive: [0,0,1,0,0,3,0,0,0]
RowSix: [5,0,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,0,0,0,9]
RowEight: [6,9,8,0,0,4,2,5,0]
RowNine: [7,5,0,9,0,0,0,0,3]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 20:57:40.972877
Turn number: 3
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,0,0,0,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,0]
RowThree: [0,7,0,0,0,9,3,0,0]
RowFour: [0,8,0,0,0,1,5,0,4]
RowFive: [0,0,1,0,0,3,0,0,0]
RowSix: [5,0,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,0,0,0,9]
RowEight: [6,9,8,0,0,4,2,5,0]
RowNine: [7,5,0,9,0,0,0,0,3]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [9,1,3,0,0,0,7,6,5]
RowTwo = [4,2,0,3,0,0,8,0,0]
RowThree = [0,7,0,0,0,9,3,0,0]
RowFour = [0,8,0,0,0,1,5,0,4]
RowFive = [0,0,1,0,0,3,0,0,0]
RowSix = [5,0,9,4,0,2,0,3,0]
RowSeven = [1,3,4,7,2,0,0,0,9]
RowEight = [6,9,8,0,0,4,2,5,0]
RowNine = [7,5,0,9,0,0,0,0,3]

# Columns
ColumnOne = [9,4,0,0,0,5,1,6,7]
ColumnTwo = [1,2,7,8,0,0,3,9,5]
ColumnThree = [3,0,0,0,1,9,4,8,0]
ColumnFour = [0,3,0,0,0,4,7,0,9]
ColumnFive = [0,0,0,0,0,0,2,0,0]
ColumnSix = [0,0,9,1,3,2,0,4,0]
ColumnSeven = [7,8,3,5,0,0,0,2,0]
ColumnEight = [6,0,0,0,0,3,0,5,0]
ColumnNine = [5,0,0,4,0,0,9,0,3]

# Blocks
BlockOne:
[[9,1,3],
[4,2,0],
[0,7,0]]
BlockOne = [9,1,3,4,2,0,0,7,0]
BlockTwo:
[[0,0,0],
[3,0,0],
[0,0,9]]
BlockTwo = [0,0,0,3,0,0,0,0,9]
BlockThree:
[[7,6,5],
[8,0,0],
[3,0,0]]
BlockThree = [7,6,5,8,0,0,3,0,0]
BlockFour:
[[0,8,0],
[0,0,1],
[5,0,9]]
BlockFour = [0,8,0,0,0,1,5,0,9]
BlockFive:
[[0,0,0],
[0,0,3],
[4,0,2]]
BlockFive = [0,0,0,0,0,3,4,0,2]
BlockSix:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockSix = [5,0,4,0,0,0,0,3,0]
BlockSeven:
[[1,3,4],
[6,9,8],
[7,5,0]]
BlockSeven = [1,3,4,6,9,8,7,5,0]
BlockEight:
[[7,2,0],
[0,0,4],
[9,0,0]]
BlockEight = [7,2,0,0,0,4,9,0,0]
BlockNine:
[[0,0,9],
[2,5,0],
[0,0,3]]
BlockNine = [0,0,9,2,5,0,0,0,3]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,0,0,0,7,6,5]) = [2,4,8]
CandidatesRowOne = [2,4,8]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,0,8,0,0]) = [1,5,6,7,9]
CandidatesRowTwo = [1,5,6,7,9]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([0,7,0,0,0,9,3,0,0]) = [1,2,4,5,6,8]
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,0,0,1,5,0,4]) = [2,3,6,7,9]
CandidatesRowFour = [2,3,6,7,9]
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,1,0,0,3,0,0,0]) = [2,4,5,6,7,8,9]
CandidatesRowFive = [2,4,5,6,7,8,9]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([5,0,9,4,0,2,0,3,0]) = [1,6,7,8]
CandidatesRowSix = [1,6,7,8]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,0,0,0,9]) = [5,6,8]
CandidatesRowSeven = [5,6,8]
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,0,0,4,2,5,0]) = [1,3,7]
CandidatesRowEight = [1,3,7]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([7,5,0,9,0,0,0,0,3]) = [1,2,4,6,8]
CandidatesRowNine = [1,2,4,6,8]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([9,4,0,0,0,5,1,6,7]) = [2,3,8]
CandidatesColumnOne = [2,3,8]
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([1,2,7,8,0,0,3,9,5]) = [4,6]
CandidatesColumnTwo = [4,6]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([3,0,0,0,1,9,4,8,0]) = [2,5,6,7]
CandidatesColumnThree = [2,5,6,7]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([0,3,0,0,0,4,7,0,9]) = [1,2,5,6,8]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,0,0,0,2,0,0]) = [1,3,4,5,6,7,8,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([0,0,9,1,3,2,0,4,0]) = [5,6,7,8]
CandidatesColumnSix = [5,6,7,8]
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([7,8,3,5,0,0,0,2,0]) = [1,4,6,9]
CandidatesColumnSeven = [1,4,6,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([6,0,0,0,0,3,0,5,0]) = [1,2,4,7,8,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([5,0,0,4,0,0,9,0,3]) = [1,2,6,7,8]
CandidatesColumnNine = [1,2,6,7,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,0,7,0]) = [5,6,8]
CandidatesBlockOne = [5,6,8]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,3,0,0,0,0,9]) = [1,2,4,5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,0,0,3,0,0]) = [1,2,4,9]
CandidatesBlockThree = [1,2,4,9]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,0,0,1,5,0,9]) = [2,3,4,6,7]
CandidatesBlockFour = [2,3,4,6,7]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,0,0,3,4,0,2]) = [1,5,6,7,8,9]
CandidatesBlockFive = [1,5,6,7,8,9]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockSix = [1,2,6,7,8,9]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,0]) = [2]
CandidatesBlockSeven = [2]
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([7,2,0,0,0,4,9,0,0]) = [1,3,5,6,8]
CandidatesBlockEight = [1,3,5,6,8]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([0,0,9,2,5,0,0,0,3]) = [1,4,6,7,8]
CandidatesBlockNine = [1,4,6,7,8]

# Index of all zeros, by row
RowOne = [9,1,3,0,0,0,7,6,5]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 9
RowOne[1] = 1
RowOne[2] = 3
RowOne[3] = 0
RowOne[4] = 0
RowOne[5] = 0
RowOne[6] = 7
RowOne[7] = 6
RowOne[8] = 5
IndexOfAll0ElementsInRowOne => [3,4,5]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [4,5,6]
EmptyColumnNamesRowOne = [ColumnFour,ColumnFive,ColumnSix]

RowTwo = [4,2,0,3,0,0,8,0,0]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 4
RowTwo[1] = 2
RowTwo[2] = 0
RowTwo[3] = 3
RowTwo[4] = 0
RowTwo[5] = 0
RowTwo[6] = 8
RowTwo[7] = 0
RowTwo[8] = 0
IndexOfAll0ElementsInRowTwo => [2,4,5,7,8]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [3,5,6,8,9]
EmptyColumnNamesRowTwo = [ColumnThree,ColumnFive,ColumnSix,ColumnEight,ColumnNine]

RowThree = [0,7,0,0,0,9,3,0,0]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 0
RowThree[1] = 7
RowThree[2] = 0
RowThree[3] = 0
RowThree[4] = 0
RowThree[5] = 9
RowThree[6] = 3
RowThree[7] = 0
RowThree[8] = 0
IndexOfAll0ElementsInRowThree => [0,2,3,4,7,8]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [1,3,4,5,8,9]
EmptyColumnNamesRowThree = [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]

RowFour = [0,8,0,0,0,1,5,0,4]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 0
RowFour[1] = 8
RowFour[2] = 0
RowFour[3] = 0
RowFour[4] = 0
RowFour[5] = 1
RowFour[6] = 5
RowFour[7] = 0
RowFour[8] = 4
IndexOfAll0ElementsInRowFour => [0,2,3,4,7]
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = [1,3,4,5,8]
EmptyColumnNamesRowFour = [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight]

RowFive = [0,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 0
RowFive[1] = 0
RowFive[2] = 1
RowFive[3] = 0
RowFive[4] = 0
RowFive[5] = 3
RowFive[6] = 0
RowFive[7] = 0
RowFive[8] = 0
IndexOfAll0ElementsInRowFive => [0,1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [1,2,4,5,7,8,9]
EmptyColumnNamesRowFive = [ColumnOne,ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowSix = [5,0,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 5
RowSix[1] = 0
RowSix[2] = 9
RowSix[3] = 4
RowSix[4] = 0
RowSix[5] = 2
RowSix[6] = 0
RowSix[7] = 3
RowSix[8] = 0
IndexOfAll0ElementsInRowSix => [1,4,6,8]
ColumnPositionOfAll0ElementsRowSix=> map(element+1, IndexOfAll0ElementsInRowSix) = [2,5,7,9]
EmptyColumnNamesRowSix = [ColumnTwo,ColumnFive,ColumnSeven,ColumnNine]

RowSeven = [1,3,4,7,2,0,0,0,9]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 1
RowSeven[1] = 3
RowSeven[2] = 4
RowSeven[3] = 7
RowSeven[4] = 2
RowSeven[5] = 0
RowSeven[6] = 0
RowSeven[7] = 0
RowSeven[8] = 9
IndexOfAll0ElementsInRowSeven => [5,6,7]
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = [6,7,8]
EmptyColumnNamesRowSeven = [ColumnSix,ColumnSeven,ColumnEight]

RowEight = [6,9,8,0,0,4,2,5,0]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 6
RowEight[1] = 9
RowEight[2] = 8
RowEight[3] = 0
RowEight[4] = 0
RowEight[5] = 4
RowEight[6] = 2
RowEight[7] = 5
RowEight[8] = 0
IndexOfAll0ElementsInRowEight => [3,4,8]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [4,5,9]
EmptyColumnNamesRowEight = [ColumnFour,ColumnFive,ColumnNine]

RowNine = [7,5,0,9,0,0,0,0,3]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 7
RowNine[1] = 5
RowNine[2] = 0
RowNine[3] = 9
RowNine[4] = 0
RowNine[5] = 0
RowNine[6] = 0
RowNine[7] = 0
RowNine[8] = 3
IndexOfAll0ElementsInRowNine => [2,4,5,6,7]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [3,5,6,7,8]
EmptyColumnNamesRowNine = [ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 3 for each EmptyColumnNamesRowOne + 5 for each EmptyColumnNamesRowTwo + 6 for each EmptyColumnNamesRowThree + 5 for each EmptyColumnNamesRowFour + 7 for each EmptyColumnNamesRowFive + 4 for each EmptyColumnNamesRowSix + 3 for each EmptyColumnNamesRowSeven + 3 for each EmptyColumnNamesRowEight + 5 for each EmptyColumnNamesRowNine = 41

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 20

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnFour,ColumnFive,ColumnSix]
Note, the last empty column of the RowOne is ColumnSix
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 20
Up to ColumnFour in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnSix
Not the last column of current row
RowOne and ColumnFour means BlockTwo
import CandidatesRowOne, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowOne = [2,4,8]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnFour => [2,4,8] & [1,2,5,6,8] = [2,8]
CommonElementsOfRowOneAndColumnFourAndBlockTwo => [2,8] & [1,2,4,5,6,7,8] = [2,8]
CellCandidates = [2,8]
Length = 2
Not 1

### 2 of 20
Up to ColumnFive in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnSix
Not the last column of current row
RowOne and ColumnFive means BlockTwo
import CandidatesRowOne, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowOne = [2,4,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnFive => [2,4,8] & [1,3,4,5,6,7,8,9] = [2,4,8]
CommonElementsOfRowOneAndColumnFiveAndBlockTwo => [2,4,8] & [1,2,4,5,6,7,8] = [2,4,8]
CellCandidates = [2,4,8]
Length = 3
Not 1

### 3 of 20
Up to ColumnSix in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnSix
Last column of current row
The next row is RowTwo
RowOne and ColumnSix means BlockTwo
import CandidatesRowOne, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowOne = [2,4,8]
CandidatesColumnSix = [5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnSix => [2,4,8] & [5,6,7,8] = [8]
CommonElementsOfRowOneAndColumnSixAndBlockTwo => [8] & [1,2,4,5,6,7,8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowOne, ColumnSix, BlockTwo

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnThree,ColumnFive,ColumnSix,ColumnEight,ColumnNine]
Note, the last empty column of the RowTwo is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 4 of 20
Up to ColumnThree in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnThree means BlockOne
import CandidatesRowTwo, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [5,6,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnThree => [1,5,6,7,9] & [2,5,6,7] = [5,6,7]
CommonElementsOfRowTwoAndColumnThreeAndBlockOne => [5,6,7] & [5,6,8] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 5 of 20
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [1,5,6,7,9] & [1,3,4,5,6,7,8,9] = [1,5,6,7,9]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [1,5,6,7,9] & [1,2,4,5,6,7,8] = [1,5,6,7]
CellCandidates = [1,5,6,7]
Length = 4
Not 1

### 6 of 20
Up to ColumnSix in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnSix means BlockTwo
import CandidatesRowTwo, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnSix = [5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnSix => [1,5,6,7,9] & [5,6,7,8] = [5,6,7]
CommonElementsOfRowTwoAndColumnSixAndBlockTwo => [5,6,7] & [1,2,4,5,6,7,8] = [5,6,7]
CellCandidates = [5,6,7]
Length = 3
Not 1

### 7 of 20
Up to ColumnEight in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnEight means BlockThree
import CandidatesRowTwo, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,2,4,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnEight => [1,5,6,7,9] & [1,2,4,7,8,9] = [1,7,9]
CommonElementsOfRowTwoAndColumnEightAndBlockThree => [1,7,9] & [1,2,4,9] = [1,9]
CellCandidates = [1,9]
Length = 2
Not 1

### 8 of 20
Up to ColumnNine in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Last column of current row
The next row is RowThree
RowTwo and ColumnNine means BlockThree
import CandidatesRowTwo, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,2,4,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnNine => [1,5,6,7,9] & [1,2,6,7,8] = [1,6,7]
CommonElementsOfRowTwoAndColumnNineAndBlockThree => [1,6,7] & [1,2,4,9] = [1]
CellCandidates = [1]
Length = 1
FOUND RowTwo, ColumnNine, BlockThree

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]
Note, the last empty column of the RowThree is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 9 of 20
Up to ColumnOne in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnOne means BlockOne
import CandidatesRowThree, CandidatesColumnOne, CandidatesBlockOne
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnOne = [2,3,8]
CandidatesBlockOne = [5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnOne => [1,2,4,5,6,8] & [2,3,8] = [2,8]
CommonElementsOfRowThreeAndColumnOneAndBlockOne => [2,8] & [5,6,8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowThree, ColumnOne, BlockOne

### 10 of 20
Up to ColumnThree in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnThree means BlockOne
import CandidatesRowThree, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnThree => [1,2,4,5,6,8] & [2,5,6,7] = [2,5,6]
CommonElementsOfRowThreeAndColumnThreeAndBlockOne => [2,5,6] & [5,6,8] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 11 of 20
Up to ColumnFour in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFour means BlockTwo
import CandidatesRowThree, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFour => [1,2,4,5,6,8] & [1,2,5,6,8] = [1,2,5,6,8]
CommonElementsOfRowThreeAndColumnFourAndBlockTwo => [1,2,5,6,8] & [1,2,4,5,6,7,8] = [1,2,5,6,8]
CellCandidates = [1,2,5,6,8]
Length = 5
Not 1

### 12 of 20
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [1,2,4,5,6,7,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,2,4,5,6,8] & [1,3,4,5,6,7,8,9] = [1,2,4,5,6,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,2,4,5,6,8] & [1,2,4,5,6,7,8] = [1,2,4,5,6,8]
CellCandidates = [1,2,4,5,6,8]
Length = 6
Not 1

### 13 of 20
Up to ColumnEight in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnEight means BlockThree
import CandidatesRowThree, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,2,4,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnEight => [1,2,4,5,6,8] & [1,2,4,7,8,9] = [1,2,4,8]
CommonElementsOfRowThreeAndColumnEightAndBlockThree => [1,2,4,8] & [1,2,4,9] = [1,2,4]
CellCandidates = [1,2,4]
Length = 3
Not 1

### 14 of 20
Up to ColumnNine in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Last column of current row
The next row is RowFour
RowThree and ColumnNine means BlockThree
import CandidatesRowThree, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,2,4,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnNine => [1,2,4,5,6,8] & [1,2,6,7,8] = [1,2,6,8]
CommonElementsOfRowThreeAndColumnNineAndBlockThree => [1,2,6,8] & [1,2,4,9] =[1,2]
CellCandidates = [1,2]
Length = 2
Not 1

## RowFour Candidates
EmptyColumnNamesRowFour: [ColumnOne,ColumnThree,ColumnFour,ColumnFive,ColumnEight]
Note, the last empty column of the RowFour is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFour and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFour and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFour and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 15 of 20
Up to ColumnOne in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnOne means BlockFour
import CandidatesRowFour, CandidatesColumnOne, CandidatesBlockFour
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnOne = [2,3,8]
CandidatesBlockFour = [2,3,4,6,7]
Finding Common Elements:
CommonElementsOfRowFourAndColumnOne => [2,3,6,7,9] & [2,3,8] = [2,3]
CommonElementsOfRowFourAndColumnOneAndBlockFour => [2,3] & [2,3,4,6,7] = [2,3]
CellCandidates = [2,3]
Length = 2
Not 1

### 16 of 20
Up to ColumnThree in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnThree means BlockFour
import CandidatesRowFour, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockFour = [2,3,4,6,7]
Finding Common Elements:
CommonElementsOfRowFourAndColumnThree => [2,3,6,7,9] & [2,5,6,7] = [2,6,7]
CommonElementsOfRowFourAndColumnThreeAndBlockFour => [2,6,7] & [2,3,4,6,7] = [2,6,7]
CellCandidates = [2,6,7]
Length = 3
Not 1

### 17 of 20
Up to ColumnFour in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnFour means BlockFive
import CandidatesRowFour, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockFive = [1,5,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFour => [2,3,6,7,9] & [1,2,5,6,8] = [2,6]
CommonElementsOfRowFourAndColumnFourAndBlockFive => [2,6] & [1,5,6,7,8,9] = [6]
CellCandidates = [6]
Length = 1
FOUND RowFour, ColumnFour, BlockFive

### 18 of 20
Up to ColumnFive in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnFive means BlockFive
import CandidatesRowFour, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,5,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFive => [2,3,6,7,9] & [1,3,4,5,6,7,8,9] = [3,6,7,9]
CommonElementsOfRowFourAndColumnFiveAndBlockFive => [3,6,7,9] & [1,5,6,7,8,9] = [6,7,9]
CellCandidates = [6,7,9]
Length = 3
Not 1

### 19 of 20
Up to ColumnEight in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Last column of current row
The next row is RowFive
RowFour and ColumnEight means BlockSix
import CandidatesRowFour, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFourAndColumnEight => [2,3,6,7,9] & [1,2,4,7,8,9] = [2,7,9]
CommonElementsOfRowFourAndColumnEightAndBlockSix => [2,7,9] & [1,2,6,7,8,9] = [2,7,9]
CellCandidates = [2,7,9]
Length = 3
Not 1

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnOne,ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]
Note, the last empty column of the RowFive is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 20 of 20
Up to ColumnOne in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnOne means BlockFour
import CandidatesRowFive, CandidatesColumnOne, CandidatesBlockFour
CandidatesRowFive = [2,4,5,6,7,8,9]
CandidatesColumnOne = [2,3,8]
CandidatesBlockFour = [2,3,4,6,7]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnOne => [2,4,5,6,7,8,9] & [2,3,8] = [2,8]
CommonElementsOfRowFiveAndColumnOneAndBlockFour => [2,8] & [2,3,4,6,7] = [2]
CellCandidates = [2]
Length = 1
FOUND RowFive, ColumnOne, BlockFour

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnSix, BlockTwo
2: FOUND RowTwo, ColumnNine, BlockThree
3: FOUND RowThree, ColumnOne, BlockOne
4: FOUND RowFour, ColumnFour, BlockFive
5: FOUND RowFive, ColumnOne, BlockFour
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnSix, BlockTwo):
CandidatesRowOne = [2,4,8]
CandidatesColumnSix = [5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]

cell(RowTwo, ColumnNine, BlockThree):
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,2,4,9]

cell(RowThree, ColumnOne, BlockOne):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnOne = [2,3,8]
CandidatesBlockOne = [5,6,8]

cell(RowFour, ColumnFour, BlockFive):
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockFive = [1,5,6,7,8,9]

cell(RowFive, ColumnOne, BlockFour):
CandidatesRowFive = [2,4,5,6,7,8,9]
CandidatesColumnOne = [2,3,8]
CandidatesBlockFour = [2,3,4,6,7]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:05:53.198940
Turn number: 4
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,0,0,0,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,0]
RowThree: [0,7,0,0,0,9,3,0,0]
RowFour: [0,8,0,0,0,1,5,0,4]
RowFive: [0,0,1,0,0,3,0,0,0]
RowSix: [5,0,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,0,0,0,9]
RowEight: [6,9,8,0,0,4,2,5,0]
RowNine: [7,5,0,9,0,0,0,0,3]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant:  [2]
Length = 1
FOUND RowFive, ColumnOne, BlockFour

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnSix, BlockTwo
2: FOUND RowTwo, ColumnNine, BlockThree
3: FOUND RowThree, ColumnOne, BlockOne
4: FOUND RowFour, ColumnFour, BlockFive
5: FOUND RowFive, ColumnOne, BlockFour
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnSix, BlockTwo):
CandidatesRowOne = [2,4,8]
CandidatesColumnSix = [5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]

cell(RowTwo, ColumnNine, BlockThree):
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,2,4,9]

cell(RowThree, ColumnOne, BlockOne):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnOne = [2,3,8]
CandidatesBlockOne = [5,6,8]

cell(RowFour, ColumnFour, BlockFive):
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockFive = [1,5,6,7,8,9]

cell(RowFive, ColumnOne, BlockFour):
CandidatesRowFive = [2,4,5,6,7,8,9]
CandidatesColumnOne = [2,3,8]
CandidatesBlockFour = [2,3,4,6,7]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnSix):
CandidatesRowOne = [2,4,8]
CandidatesColumnSix = [5,6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8]

cell(RowTwo, ColumnNine):
CandidatesRowTwo = [1,5,6,7,9]
CandidatesColumnNine = [1,2,6,7,8]
CandidatesBlockThree = [1,2,4,9]

cell(RowThree, ColumnOne):
CandidatesRowThree = [1,2,4,5,6,8]
CandidatesColumnOne = [2,3,8]
CandidatesBlockOne = [5,6,8]

cell(RowFour, ColumnFour):
CandidatesRowFour = [2,3,6,7,9]
CandidatesColumnFour = [1,2,5,6,8]
CandidatesBlockFive = [1,5,6,7,8,9]

cell(RowFive, ColumnOne):
CandidatesRowFive = [2,4,5,6,7,8,9]
CandidatesColumnOne = [2,3,8]
CandidatesBlockFour = [2,3,4,6,7]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 5
cell(RowOne, ColumnSix):
CandidatesRowOne.length = 3
CandidatesColumnSix.length = 5
CandidatesBlockTwo.length = 8

shortest_list = CandidatesRowOne = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnSix and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [2,4,8], broken into CandidatesRowOneLow = [2,4] and CandidatesRowOneHigh = [8]
CandidatesColumnSix = [5,6,7,8], broken into CandidatesColumnSixLow = [5] and CandidatesColumnSixHigh = [6,7,8]
CandidatesBlockTwo = [1,2,4,5,6,7,8], broken into CandidatesBlockTwoLow = [1,2,4,5] and CandidatesBlockTwoHigh = [6,7,8]

Checking digits in CandidatesRowOneLow = [2,4] against: CandidatesColumnSixLow = [5] and CandidatesBlockTwoLow = [1,2,4,5]
2: [5].count(2) = 0, [1,2,4,5].count(2) = 1, TotalCount(2) = 1
4: [5].count(4) = 0, [1,2,4,5].count(4) = 1, TotalCount(4) = 1

Checking digits in CandidatesRowOneHigh = [8] against: CandidatesColumnSixHigh = [6,7,8] and CandidatesBlockTwoHigh = [6,7,8]
8: [6,7,8].count(8) = 1, [6,7,8].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowOne, ColumnSix): [8]

## Cell 2 of 5
cell(RowTwo, ColumnNine):
CandidatesRowTwo.length = 5
CandidatesColumnNine.length = 5
CandidatesBlockThree.length = 4

shortest_list = CandidatesBlockThree = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesColumnNine

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [1,5,6,7,9], broken into CandidatesRowTwoLow = [1,5] and CandidatesRowTwoHigh = [6,7,9]
CandidatesColumnNine = [1,2,6,7,8], broken into CandidatesColumnNineLow = [1,2] and CandidatesColumnNineHigh = [6,7,8]
CandidatesBlockThree = [1,2,4,9], broken into CandidatesBlockThreeLow = [1,2,4] and CandidatesBlockThreeHigh = [9]

Checking digits in CandidatesBlockThreeLow = [1,2,4] against: CandidatesRowTwoLow = [1,5] and CandidatesColumnNineLow = [1,2]
1: [1,5].count(1) = 1, [1,2].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE
2: [1,5].count(2) = 0, [1,2].count(2) = 1, TotalCount(2) = 1
4: [1,5].count(4) = 0, [1,2].count(4) = 0, TotalCount(4) = 0

Checking digits in CandidatesBlockThreeHigh = [9] against: CandidatesRowTwoHigh = [6,7,9] and CandidatesColumnNineHigh = [6,7,8]
9: [6,7,9].count(9) = 1, [6,7,8].count(9) = 0, TotalCount(9) = 1

Confirmed candidates found for cell(RowTwo, ColumnNine): [1]

## Cell 3 of 5
cell(RowThree, ColumnOne):
CandidatesRowThree.length = 6
CandidatesColumnOne.length = 3
CandidatesBlockOne.length = 3

shortest_list = CandidatesColumnOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,5,6,8], broken into CandidatesRowThreeLow = [1,2,4,5] and CandidatesRowThreeHigh = [6,8]
CandidatesColumnOne = [2,3,8], broken into CandidatesColumnOneLow = [2,3] and CandidatesColumnOneHigh = [8]
CandidatesBlockOne = [5,6,8], broken into CandidatesBlockOneLow = [5] and CandidatesBlockOneHigh = [6,8]

Checking digits in CandidatesColumnOneLow = [2,3] against: CandidatesRowThreeLow = [1,2,4,5] and CandidatesBlockOneLow = [5]
2: [1,2,4,5].count(2) = 1, [5].count(2) = 0, TotalCount(2) = 1
3: [1,2,4,5].count(3) = 0, [5].count(3) = 0, TotalCount(3) = 0

Checking digits in CandidatesColumnOneHigh = [8] against: CandidatesRowThreeHigh = [6,8] and CandidatesBlockOneHigh = [6,8]
8: [6,8].count(8) = 1, [6,8].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowThree, ColumnOne): [8]

## Cell 4 of 5
cell(RowFour, ColumnFour):
CandidatesRowFour.length = 5
CandidatesColumnFour.length = 5
CandidatesBlockFive.length = 6

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFour and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [2,3,6,7,9], broken into CandidatesRowFourLow = [2,3] and CandidatesRowFourHigh = [6,7,9]
CandidatesColumnFour = [1,2,5,6,8], broken into CandidatesColumnFourLow = [1,2,5] and CandidatesColumnFourHigh = [6,8]
CandidatesBlockFive = [1,5,6,7,8,9], broken into CandidatesBlockFiveLow = [1,5] and CandidatesBlockFiveHigh = [6,7,8,9]

Checking digits in CandidatesRowFourLow = [2,3] against: CandidatesColumnFourLow = [1,2,5] and CandidatesBlockFiveLow = [1,5]
2: [1,2,5].count(2) = 1, [1,5].count(2) = 0, TotalCount(2) = 1
3: [1,2,5].count(3) = 0, [1,5].count(3) = 0, TotalCount(3) = 0

Checking digits in CandidatesRowFourHigh = [6,7,9] against: CandidatesColumnFourHigh = [6,8] and CandidatesBlockFiveHigh = [6,7,8,9]
6: [6,8].count(6) = 1, [6,7,8,9].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE
7: [6,8].count(7) = 0, [6,7,8,9].count(7) = 1, TotalCount(7) = 1
9: [6,8].count(9) = 0, [6,7,8,9].count(9) = 1, TotalCount(9) = 1

Confirmed candidates found for cell(RowFour, ColumnFour): [6]

## Cell 5 of 5
cell(RowFive, ColumnOne):
CandidatesRowFive.length = 7
CandidatesColumnOne.length = 3
CandidatesBlockFour.length = 5

shortest_list = CandidatesColumnOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowFive and CandidatesBlockFour

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [2,4,5,6,7,8,9], broken into CandidatesRowFiveLow = [2,4,5] and CandidatesRowFiveHigh = [6,7,8,9]
CandidatesColumnOne = [2,3,8], broken into CandidatesColumnOneLow = [2,3] and CandidatesColumnOneHigh = [8]
CandidatesBlockFour = [2,3,4,6,7], broken into CandidatesBlockFourLow = [2,3,4] and CandidatesBlockFourHigh = [6,7]

Checking digits in CandidatesColumnOneLow = [2,3] against: CandidatesRowFiveLow = [2,4,5] and CandidatesBlockFourLow = [2,3,4]
2: [2,4,5].count(2) = 1, [2,3,4].count(2) = 1, TotalCount(2) = 2 FOUND A CANDIDATE
3: [2,4,5].count(3) = 0, [2,3,4].count(3) = 1, TotalCount(3) = 1

Checking digits in CandidatesColumnOneHigh = [8] against: CandidatesRowFiveHigh = [6,7,8,9] and CandidatesBlockFourHigh = [6,7]
8: [6,7,8,9].count(8) = 1, [6,7].count(8) = 0, TotalCount(8) = 1

Confirmed candidates found for cell(RowFive, ColumnOne): [2]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnSix): [8]
[8].length = 1
length is 1, Passes

cell(RowTwo, ColumnNine): [1]
[1].length = 1
length is 1, Passes

cell(RowThree, ColumnOne): [8]
[8].length = 1
length is 1, Passes

cell(RowFour, ColumnFour): [6]
[6].length = 1
length is 1, Passes

cell(RowFive, ColumnOne): [2]
[2].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnSix): [8]
cell(RowTwo, ColumnNine): [1]
cell(RowThree, ColumnOne): [8]
cell(RowFour, ColumnFour): [6]
cell(RowFive, ColumnOne): [2]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowTwo, RowThree, RowFour, RowFive

RowOne: [9,1,3,0,0,0,7,6,5]
cell(RowOne, ColumnSix): [8]

RowTwo: [4,2,0,3,0,0,8,0,0]
cell(RowTwo, ColumnNine): [1]

RowThree: [0,7,0,0,0,9,3,0,0]
cell(RowThree, ColumnOne): [8]

RowFour: [0,8,0,0,0,1,5,0,4]
cell(RowFour, ColumnFour): [6]

RowFive: [0,0,1,0,0,3,0,0,0]
cell(RowFive, ColumnOne): [2]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 5
cell(RowOne, ColumnSix): [8]
RowOne = [9,1,3,0,0,0,7,6,5]
The ColumnSix element of RowOne needs to be updated to [8]

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 0
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Now replacing ColumnSix with the element to update [8], such that ColumnSix = 8
Redoing column list like we just did, but with ColumnSix set to 8

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 0
ColumnFive: 0
ColumnSix: 8
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSix.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSix it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSix (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSix does Not appear on this list!!! The ONLY time you don't is if ColumnSix is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSix:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
Now the elements of the columns in PreCellColumnsList, which is the first 5 elements of RowOne:
PreCellList = [9,1,3,0,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [9,1,3,0,0,8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [9,1,3,0,0,8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 5 + 1 = 6 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [9,1,3,0,0,8,7,6,5]

## Updating 2 of 5
cell(RowTwo, ColumnNine): [1]
RowTwo = [4,2,0,3,0,0,8,0,0]
The ColumnNine element of RowTwo needs to be updated to [1]

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnNine with the element to update [1], such that ColumnNine = 1
Redoing column list like we just did, but with ColumnNine set to 1

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 1

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about theelement just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnNine.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnNine it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnNine (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnNine does Not appear on this list!!! The ONLY time you don't is if ColumnNine is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnNine:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight].length = 8
Now the elements of the columns in PreCellColumnsList, which is the first 8 elements of RowTwo:
PreCellList = [4,2,0,3,0,0,8,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [4,2,0,3,0,0,8,0,1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [4,2,0,3,0,0,8,0,1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 8 + 1 = 9 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [4,2,0,3,0,0,8,0,1]

## Updating 3 of 5
cell(RowThree, ColumnOne): [8]
RowThree = [0,7,0,0,0,9,3,0,0]
The ColumnOne element of RowThree needs to be updated to [8]

ColumnOne: 0
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 0
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnOne with the element to update [8], such that ColumnOne = 8
Redoing column list like we just did, but with ColumnOne set to 8

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 0
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnOne.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnOne it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnOne (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnOne does Not appear on this list!!! The ONLY time you don't is if ColumnOne is ColumnOne, in which case the list is empty.):
PreCellColumnsList = []
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnOne:
PreCellColumnsList.length => [].length = 0
Now the elements of the columns in PreCellColumnsList, which is the first 0 elements of RowThree:
PreCellList = []

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 0 + 1 = 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [8,7,0,0,0,9,3,0,0]

## Updating 4 of 5
cell(RowFour, ColumnFour): [6]
RowFour = [0,8,0,0,0,1,5,0,4]
The ColumnFour element of RowFour needs to be updated to [6]

ColumnOne: 0
ColumnTwo: 8
ColumnThree: 0
ColumnFour: 0
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Now replacing ColumnFour with the element to update [6], such that ColumnFour = 6
Redoing column list like we just did, but with ColumnFour set to 6

ColumnOne: 0
ColumnTwo: 8
ColumnThree: 0
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFour.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFour it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFour (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFour does Not appear on this list!!! The ONLY time you don't is if ColumnFour is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFour:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree].length = 3
Now the elements of the columns in PreCellColumnsList, which is the first 3 elements of RowFour:
PreCellList = [0,8,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [0,8,0,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [0,8,0,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 3 + 1 = 4 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [0,8,0,6,0,1,5,0,4]

## Updating 5 of 5
cell(RowFive, ColumnOne): [2]
RowFive = [0,0,1,0,0,3,0,0,0]
The ColumnOne element of RowFive needs to be updated to [2]

ColumnOne: 0
ColumnTwo: 0
ColumnThree: 1
ColumnFour: 0
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnOne with the element to update [2], such that ColumnOne = 2
Redoing column list like we just did, but with ColumnOne set to 2

ColumnOne: 2
ColumnTwo: 0
ColumnThree: 1
ColumnFour: 0
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnOne.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnOne it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnOne (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnOne does Not appear on this list!!! The ONLY time you don't is if ColumnOne is ColumnOne, in which case the list is empty.):
PreCellColumnsList = []
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnOne:
PreCellColumnsList.length => [].length = 0
Now the elements of the columns in PreCellColumnsList, which is the first 0 elements of RowFive:
PreCellList = []

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [2] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(2) = [2]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [2,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 0 + 1 = 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [2,0,1,0,0,3,0,0,0]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [9,1,3,0,0,8,7,6,5]
UpdatedRowTwo = [4,2,0,3,0,0,8,0,1]
UpdatedRowThree = [8,7,0,0,0,9,3,0,0]
UpdatedRowFour = [0,8,0,6,0,1,5,0,4]
UpdatedRowFive = [2,0,1,0,0,3,0,0,0]

The rows to update are RowOne, RowTwo, RowThree, RowFour, RowFive
Using the contents of UpdatedRowOne, UpdatedRowTwo, UpdatedRowThree, UpdatedRowFour, UpdatedRowFive
Printing Sudoku:
UpdatedRowOne: [9,1,3,0,0,8,7,6,5]
UpdatedRowTwo: [4,2,0,3,0,0,8,0,1]
UpdatedRowThree: [8,7,0,0,0,9,3,0,0]
UpdatedRowFour: [0,8,0,6,0,1,5,0,4]
UpdatedRowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,0,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,0,0,0,9]
RowEight: [6,9,8,0,0,4,2,5,0]
RowNine: [7,5,0,9,0,0,0,0,3]

# STEP_SEVEN: Shifting the Rows of the Sudoku
UpdatedRowFour: [0,8,0,6,0,1,5,0,4]
UpdatedRowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,0,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,0,0,0,9]
RowEight: [6,9,8,0,0,4,2,5,0]
RowNine: [7,5,0,9,0,0,0,0,3]
UpdatedRowOne: [9,1,3,0,0,8,7,6,5]
UpdatedRowTwo: [4,2,0,3,0,0,8,0,1]
UpdatedRowThree: [8,7,0,0,0,9,3,0,0]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [0,8,0,6,0,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,0,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,0,0,0,9]
RowFive: [6,9,8,0,0,4,2,5,0]
RowSix: [7,5,0,9,0,0,0,0,3]
RowSeven: [9,1,3,0,0,8,7,6,5]
RowEight: [4,2,0,3,0,0,8,0,1]
RowNine: [8,7,0,0,0,9,3,0,0]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:14:27.990468
Turn number: 5
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [0,8,0,6,0,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,0,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,0,0,0,9]
RowFive: [6,9,8,0,0,4,2,5,0]
RowSix: [7,5,0,9,0,0,0,0,3]
RowSeven: [9,1,3,0,0,8,7,6,5]
RowEight: [4,2,0,3,0,0,8,0,1]
RowNine: [8,7,0,0,0,9,3,0,0]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [0,8,0,6,0,1,5,0,4]
RowTwo = [2,0,1,0,0,3,0,0,0]
RowThree = [5,0,9,4,0,2,0,3,0]
RowFour = [1,3,4,7,2,0,0,0,9]
RowFive = [6,9,8,0,0,4,2,5,0]
RowSix = [7,5,0,9,0,0,0,0,3]
RowSeven = [9,1,3,0,0,8,7,6,5]
RowEight = [4,2,0,3,0,0,8,0,1]
RowNine = [8,7,0,0,0,9,3,0,0]

# Columns
ColumnOne = [0,2,5,1,6,7,9,4,8]
ColumnTwo = [8,0,0,3,9,5,1,2,7]
ColumnThree = [0,1,9,4,8,0,3,0,0]
ColumnFour = [6,0,4,7,0,9,0,3,0]
ColumnFive = [0,0,0,2,0,0,0,0,0]
ColumnSix = [1,3,2,0,4,0,8,0,9]
ColumnSeven = [5,0,0,0,2,0,7,8,3]
ColumnEight = [0,0,3,0,5,0,6,0,0]
ColumnNine = [4,0,0,9,0,3,5,1,0]

# Blocks
BlockOne:
[[0,8,0],
[2,0,1],
[5,0,9]]
BlockOne = [0,8,0,2,0,1,5,0,9]

BlockTwo:
[[6,0,1],
[0,0,3],
[4,0,2]]
BlockTwo = [6,0,1,0,0,3,4,0,2]

BlockThree:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockThree = [5,0,4,0,0,0,0,3,0]

BlockFour:
[[1,3,4],
[6,9,8],
[7,5,0]]
BlockFour = [1,3,4,6,9,8,7,5,0]

BlockFive:
[[7,2,0],
[0,0,4],
[9,0,0]]
BlockFive = [7,2,0,0,0,4,9,0,0]

BlockSix:
[[0,0,9],
[2,5,0],
[0,0,3]]
BlockSix = [0,0,9,2,5,0,0,0,3]

BlockSeven:
[[9,1,3],
[4,2,0],
[8,7,0]]
BlockSeven = [9,1,3,4,2,0,8,7,0]

BlockEight:
[[0,0,8],
[3,0,0],
[0,0,9]]
BlockEight = [0,0,8,3,0,0,0,0,9]

BlockNine:
[[7,6,5],
[8,0,1],
[3,0,0]]
BlockNine = [7,6,5,8,0,1,3,0,0]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,6,0,1,5,0,4]) = [2,3,7,9]
CandidatesRowOne = [2,3,7,9]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([2,0,1,0,0,3,0,0,0]) = [4,5,6,7,8,9]
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([5,0,9,4,0,2,0,3,0]) = [1,6,7,8]
CandidatesRowThree = [1,6,7,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,0,0,0,9]) = [5,6,8]
CandidatesRowFour = [5,6,8]
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,0,0,4,2,5,0]) = [1,3,7]
CandidatesRowFive = [1,3,7]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([7,5,0,9,0,0,0,0,3]) = [1,2,4,6,8]
CandidatesRowSix = [1,2,4,6,8]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,0,0,8,7,6,5]) = [2,4]
CandidatesRowSeven = [2,4]
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,0,8,0,1]) = [5,6,7,9]
CandidatesRowEight = [5,6,7,9]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([8,7,0,0,0,9,3,0,0]) = [1,2,4,5,6]
CandidatesRowNine = [1,2,4,5,6]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([0,2,5,1,6,7,9,4,8]) = [3]
CandidatesColumnOne = [3]
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([8,0,0,3,9,5,1,2,7]) = [4,6]
CandidatesColumnTwo = [4,6]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([0,1,9,4,8,0,3,0,0]) = [2,5,6,7]
CandidatesColumnThree = [2,5,6,7]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([6,0,4,7,0,9,0,3,0]) = [1,2,5,8]
CandidatesColumnFour = [1,2,5,8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,2,0,0,0,0,0]) = [1,3,4,5,6,7,8,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([1,3,2,0,4,0,8,0,9]) = [5,6,7]
CandidatesColumnSix = [5,6,7]
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([5,0,0,0,2,0,7,8,3]) = [1,4,6,9]
CandidatesColumnSeven = [1,4,6,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([0,0,3,0,5,0,6,0,0]) = [1,2,4,7,8,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([4,0,0,9,0,3,5,1,0]) = [2,6,7,8]
CandidatesColumnNine = [2,6,7,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([0,8,0,2,0,1,5,0,9]) = [3,4,6,7]
CandidatesBlockOne = [3,4,6,7]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([6,0,1,0,0,3,4,0,2]) = [5,7,8,9]
CandidatesBlockTwo = [5,7,8,9]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockThree = [1,2,6,7,8,9]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,0]) = [2]
CandidatesBlockFour = [2]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([7,2,0,0,0,4,9,0,0]) = [1,3,5,6,8]
CandidatesBlockFive = [1,3,5,6,8]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([0,0,9,2,5,0,0,0,3]) = [1,4,6,7,8]
CandidatesBlockSix = [1,4,6,7,8]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,0]) = [5,6]
CandidatesBlockSeven = [5,6]
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([0,0,8,3,0,0,0,0,9]) = [1,2,4,5,6,7]
CandidatesBlockEight = [1,2,4,5,6,7]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,0,1,3,0,0]) = [2,4,9]
CandidatesBlockNine = [2,4,9]

# Index of all zeros, by row
RowOne = [0,8,0,6,0,1,5,0,4]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 0
RowOne[1] = 8
RowOne[2] = 0
RowOne[3] = 6
RowOne[4] = 0
RowOne[5] = 1
RowOne[6] = 5
RowOne[7] = 0
RowOne[8] = 4
IndexOfAll0ElementsInRowOne => [0,2,4,7]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [1,3,5,8]
EmptyColumnNamesRowOne = [ColumnOne,ColumnThree,ColumnFive,ColumnEight]

RowTwo = [2,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 2
RowTwo[1] = 0
RowTwo[2] = 1
RowTwo[3] = 0
RowTwo[4] = 0
RowTwo[5] = 3
RowTwo[6] = 0
RowTwo[7] = 0
RowTwo[8] = 0
IndexOfAll0ElementsInRowTwo => [1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [2,4,5,7,8,9]
EmptyColumnNamesRowTwo = [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowThree = [5,0,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 5
RowThree[1] = 0
RowThree[2] = 9
RowThree[3] = 4
RowThree[4] = 0
RowThree[5] = 2
RowThree[6] = 0
RowThree[7] = 3
RowThree[8] = 0
IndexOfAll0ElementsInRowThree => [1,4,6,8]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [2,5,7,9]
EmptyColumnNamesRowThree = [ColumnTwo,ColumnFive,ColumnSeven,ColumnNine]

RowFour = [1,3,4,7,2,0,0,0,9]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 1
RowFour[1] = 3
RowFour[2] = 4
RowFour[3] = 7
RowFour[4] = 2
RowFour[5] = 0
RowFour[6] = 0
RowFour[7] = 0
RowFour[8] = 9
IndexOfAll0ElementsInRowFour => [5,6,7]
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = [6,7,8]
EmptyColumnNamesRowFour = [ColumnSix,ColumnSeven,ColumnEight]

RowFive = [6,9,8,0,0,4,2,5,0]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 6
RowFive[1] = 9
RowFive[2] = 8
RowFive[3] = 0
RowFive[4] = 0
RowFive[5] = 4
RowFive[6] = 2
RowFive[7] = 5
RowFive[8] = 0
IndexOfAll0ElementsInRowFive => [3,4,8]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [4,5,9]
EmptyColumnNamesRowFive = [ColumnFour,ColumnFive,ColumnNine]

RowSix = [7,5,0,9,0,0,0,0,3]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 7
RowSix[1] = 5
RowSix[2] = 0
RowSix[3] = 9
RowSix[4] = 0
RowSix[5] = 0
RowSix[6] = 0
RowSix[7] = 0
RowSix[8] = 3
IndexOfAll0ElementsInRowSix => [2,4,5,6,7]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [3,5,6,7,8]
EmptyColumnNamesRowSix = [ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]

RowSeven = [9,1,3,0,0,8,7,6,5]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 9
RowSeven[1] = 1
RowSeven[3,4,5,6,7,8]
RowSeven[2] = 3
RowSeven[3] = 0
RowSeven[4] = 0
RowSeven[5] = 8
RowSeven[6] = 7
RowSeven[7] = 6
RowSeven[8] = 5
IndexOfAll0ElementsInRowSeven => [3,4]
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = [4,5]
EmptyColumnNamesRowSeven = [ColumnFour,ColumnFive]

RowEight = [4,2,0,3,0,0,8,0,1]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 4
RowEight[1] = 2
RowEight[2] = 0
RowEight[3] = 3
RowEight[4] = 0
RowEight[5] = 0
RowEight[6] = 8
RowEight[7] = 0
RowEight[8] = 1
IndexOfAll0ElementsInRowEight => [2,4,5,7]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [3,5,6,8]
EmptyColumnNamesRowEight = [ColumnThree,ColumnFive,ColumnSix,ColumnEight]

RowNine = [8,7,0,0,0,9,3,0,0]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 8
RowNine[1] = 7
RowNine[2] = 0
RowNine[3] = 0
RowNine[4] = 0
RowNine[5] = 9
RowNine[6] = 3
RowNine[7] = 0
RowNine[8] = 0
IndexOfAll0ElementsInRowNine => [2,3,4,7,8]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [3,4,5,8,9]
EmptyColumnNamesRowNine = [ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 4 + 6 + 4 + 3 + 3 + 5 + 2 + 4 + 5 = 36

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 20

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnOne,ColumnThree,ColumnFive,ColumnEight]
Note, the last empty column of the RowOne is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 20
Up to ColumnOne in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnOne means BlockOne
import CandidatesRowOne, CandidatesColumnOne, CandidatesBlockOne
CandidatesRowOne = [2,3,7,9]
CandidatesColumnOne = [3]
CandidatesBlockOne = [3,4,6,7]
Finding Common Elements:
CommonElementsOfRowOneAndColumnOne => [2,3,7,9] & [3] = [3]
CommonElementsOfRowOneAndColumnOneAndBlockOne => [3] & [3,4,6,7] = [3]
CellCandidates = [3]
Length = 1
FOUND RowOne, ColumnOne, BlockOne

### 2 of 20
Up to ColumnThree in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnThree means BlockOne
import CandidatesRowOne, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowOne = [2,3,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [3,4,6,7]
Finding Common Elements:
CommonElementsOfRowOneAndColumnThree => [2,3,7,9] & [2,5,6,7] = [2,7]
CommonElementsOfRowOneAndColumnThreeAndBlockOne => [2,7] & [3,4,6,7] = [7]
CellCandidates = [7]
Length = 1
FOUND RowOne, ColumnThree, BlockOne

### 3 of 20
Up to ColumnFive in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Not the last column of current row
RowOne and ColumnFive means BlockTwo
import CandidatesRowOne, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowOne = [2,3,7,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowOneAndColumnFive => [2,3,7,9] & [1,3,4,5,6,7,8,9] = [3,7,9]
CommonElementsOfRowOneAndColumnFiveAndBlockTwo => [3,7,9] & [5,7,8,9] = [7,9]
CellCandidates = [7,9]
Length = 2
Not 1

### 4 of 20
Up to ColumnEight in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Last column of current row
The next row is RowTwo
RowOne and ColumnEight means BlockThree
import CandidatesRowOne, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowOne = [2,3,7,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowOneAndColumnEight => [2,3,7,9] & [1,2,4,7,8,9] = [2,7,9]
CommonElementsOfRowOneAndColumnEightAndBlockThree => [2,7,9] & [1,2,6,7,8,9] = [2,7,9]
CellCandidates = [2,7,9]
Length = 3
Not 1

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]
Note, the last empty column of the RowTwo is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 5 of 20
Up to ColumnTwo in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnTwo means BlockOne
import CandidatesRowTwo, CandidatesColumnTwo, CandidatesBlockOne
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnTwo = [4,6]
CandidatesBlockOne = [3,4,6,7]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnTwo => [4,5,6,7,8,9] & [4,6] = [4,6]
CommonElementsOfRowTwoAndColumnTwoAndBlockOne => [4,6] & [3,4,6,7] = [4,6]
CellCandidates = [4,6]
Length = 2
Not 1

### 6 of 20
Up to ColumnFour in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFour means BlockTwo
import CandidatesRowTwo, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFour = [1,2,5,8]
CandidatesBlockTwo = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFour => [4,5,6,7,8,9] & [1,2,5,8] = [5,8]
CommonElementsOfRowTwoAndColumnFourAndBlockTwo => [5,8] & [5,7,8,9] = [5,8]
CellCandidates = [5,8]
Length = 2
Not 1

### 7 of 20
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [4,5,6,7,8,9] & [1,3,4,5,6,7,8,9] = [4,5,6,7,8,9]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [4,5,6,7,8,9] & [5,7,8,9] = [5,7,8,9]
CellCandidates = [5,7,8,9]
Length = 4
Not 1

### 8 of 20
Up to ColumnSeven in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnSeven means BlockThree
import CandidatesRowTwo, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnSeven => [4,5,6,7,8,9] & [1,4,6,9] = [4,6,9]
CommonElementsOfRowTwoAndColumnSevenAndBlockThree => [4,6,9] & [1,2,6,7,8,9] = [6,9]
CellCandidates = [6,9]
Length = 2
Not 1

### 9 of 20
Up to ColumnEight in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnEight means BlockThree
import CandidatesRowTwo, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnEight => [4,5,6,7,8,9] & [1,2,4,7,8,9] = [4,7,8,9]
CommonElementsOfRowTwoAndColumnEightAndBlockThree => [4,7,8,9] & [1,2,6,7,8,9] = [7,8,9]
CellCandidates = [7,8,9]
Length = 3
Not 1

### 10 of 20
Up to ColumnNine in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Last column of current row
The next row is RowThree
RowTwo and ColumnNine means BlockThree
import CandidatesRowTwo, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnNine => [4,5,6,7,8,9] & [2,6,7,8] = [6,7,8]
CommonElementsOfRowTwoAndColumnNineAndBlockThree => [6,7,8] & [1,2,6,7,8,9] = [6,7,8]
CellCandidates = [6,7,8]
Length = 3
Not 1

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnTwo,ColumnFive,ColumnSeven,ColumnNine]
Note, the last empty column of the RowThree is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 11 of 20
Up to ColumnTwo in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnTwo means BlockOne
import CandidatesRowThree, CandidatesColumnTwo, CandidatesBlockOne
CandidatesRowThree = [1,6,7,8]
CandidatesColumnTwo = [4,6]
CandidatesBlockOne = [3,4,6,7]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnTwo => [1,6,7,8] & [4,6] = [6]
CommonElementsOfRowThreeAndColumnTwoAndBlockOne => [6] & [3,4,6,7] = [6]
CellCandidates = [6]
Length = 1
FOUND RowThree, ColumnTwo, BlockOne

### 12 of 20
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,6,7,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,6,7,8] & [1,3,4,5,6,7,8,9] = [1,6,7,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,6,7,8] & [5,7,8,9] = [7,8]
CellCandidates = [7,8]
Length = 2
Not 1

### 13 of 20
Up to ColumnSeven in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnSeven means BlockThree
import CandidatesRowThree, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowThree = [1,6,7,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSeven => [1,6,7,8] & [1,4,6,9] = [1,6]
CommonElementsOfRowThreeAndColumnSevenAndBlockThree => [1,6] & [1,2,6,7,8,9] = [1,6]
CellCandidates = [1,6]
Length = 2
Not 1

### 14 of 20
Up to ColumnNine in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Last column of current row
The next row is RowFour
RowThree and ColumnNine means BlockThree
import CandidatesRowThree, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowThree = [1,6,7,8]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnNine => [1,6,7,8] & [2,6,7,8] = [6,7,8]
CommonElementsOfRowThreeAndColumnNineAndBlockThree => [6,7,8] & [1,2,6,7,8,9] = [6,7,8]
CellCandidates = [6,7,8]
Length = 3
Not 1

## RowFour Candidates
EmptyColumnNamesRowFour: [ColumnSix,ColumnSeven,ColumnEight]
Note, the last empty column of the RowFour is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFour and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFour and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFour and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 15 of 20
Up to ColumnSix in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnSix means BlockFive
import CandidatesRowFour, CandidatesColumnSix, CandidatesBlockFive
CandidatesRowFour = [5,6,8]
CandidatesColumnSix = [5,6,7]
CandidatesBlockFive = [1,3,5,6,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnSix => [5,6,8] & [5,6,7] = [5,6]
CommonElementsOfRowFourAndColumnSixAndBlockFive => [5,6] & [1,3,5,6,8] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 16 of 20
Up to ColumnSeven in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnSeven means BlockSix
import CandidatesRowFour, CandidatesColumnSeven, CandidatesBlockSix
CandidatesRowFour = [5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockSix = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnSeven => [5,6,8] & [1,4,6,9] = [6]
CommonElementsOfRowFourAndColumnSevenAndBlockSix => [6] & [1,4,6,7,8] = [6]
CellCandidates = [6]
Length = 1
FOUND RowFour, ColumnSeven, BlockSix

### 17 of 20
Up to ColumnEight in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Last column of current row
The next row is RowFive
RowFour and ColumnEight means BlockSix
import CandidatesRowFour, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowFour = [5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockSix = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowFourAndColumnEight => [5,6,8] & [1,2,4,7,8,9] = [8]
CommonElementsOfRowFourAndColumnEightAndBlockSix => [8] & [1,4,6,7,8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowFour, ColumnEight, BlockSix

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnFour,ColumnFive,ColumnNine]
Note, the last empty column of the RowFive is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 18 of 20
Up to ColumnFour in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnFour means BlockFive
import CandidatesRowFive, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowFive = [1,3,7]
CandidatesColumnFour = [1,2,5,8]
CandidatesBlockFive = [1,3,5,6,8]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFour => [1,3,7] & [1,2,5,8] = [1]
CommonElementsOfRowFiveAndColumnFourAndBlockFive => [1] & [1,3,5,6,8] = [1]
CellCandidates = [1]
Length = 1
FOUND RowFive, ColumnFour, BlockFive

### 19 of 20
Up to ColumnFive in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnFive means BlockFive
import CandidatesRowFive, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFive = [1,3,7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,3,5,6,8]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFive => [1,3,7] & [1,3,4,5,6,7,8,9] = [1,3,7]
CommonElementsOfRowFiveAndColumnFiveAndBlockFive => [1,3,7] & [1,3,5,6,8] = [1,3]
CellCandidates = [1,3]
Length = 2
Not 1

### 20 of 20
Up to ColumnNine in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Last column of current row
RowFive and ColumnNine means BlockSix
import CandidatesRowFive, CandidatesColumnNine, CandidatesBlockSix
CandidatesRowFive = [1,3,7]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockSix = [1,4,6,7,8]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnNine => [1,3,7] & [2,6,7,8] = [7]
CommonElementsOfRowFiveAndColumnNineAndBlockSix => [7] & [1,4,6,7,8] = [7]
CellCandidates = [7]
Length = 1
FOUND RowFive, ColumnNine, BlockSix

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnOne, BlockOne
2: FOUND RowOne, ColumnThree, BlockOne
3: FOUND RowThree, ColumnTwo, BlockOne
4: FOUND RowFour, ColumnSeven, BlockSix
5: FOUND RowFour, ColumnEight, BlockSix
6: FOUND RowFive, ColumnFour, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnOne, BlockOne):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnOne = [3]
CandidatesBlockOne = [3,4,6,7]

cell(RowOne, ColumnThree, BlockOne):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [3,4,6,7]

cell(RowThree, ColumnTwo, BlockOne):
CandidatesRowThree = [1,6,7,8]
CandidatesColumnTwo = [4,6]
CandidatesBlockOne = [3,4,6,7]

cell(RowFour, ColumnSeven, BlockSix):
CandidatesRowFour = [5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFour, ColumnEight, BlockSix):
CandidatesRowFour = [5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFive, ColumnFour, BlockFive):
CandidatesRowFive = [1,3,7]
CandidatesColumnFour = [1,2,5,8]
CandidatesBlockFive = [1,3,5,6,8]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:23:02.752886
Turn number: 6
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [0,8,0,6,0,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,0,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,0,0,0,9]
RowFive: [6,9,8,0,0,4,2,5,0]
RowSix: [7,5,0,9,0,0,0,0,3]
RowSeven: [9,1,3,0,0,8,7,6,5]
RowEight: [4,2,0,3,0,0,8,0,1]
RowNine: [8,7,0,0,0,9,3,0,0]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: ting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnOne, BlockOne
2: FOUND RowOne, ColumnThree, BlockOne
3: FOUND RowThree, ColumnTwo, BlockOne
4: FOUND RowFour, ColumnSeven, BlockSix
5: FOUND RowFour, ColumnEight, BlockSix
6: FOUND RowFive, ColumnFour, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnOne, BlockOne):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnOne = [3]
CandidatesBlockOne = [3,4,6,7]

cell(RowOne, ColumnThree, BlockOne):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [3,4,6,7]

cell(RowThree, ColumnTwo, BlockOne):
CandidatesRowThree = [1,6,7,8]
CandidatesColumnTwo = [4,6]
CandidatesBlockOne = [3,4,6,7]

cell(RowFour, ColumnSeven, BlockSix):
CandidatesRowFour = [5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFour, ColumnEight, BlockSix):
CandidatesRowFour = [5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFive, ColumnFour, BlockFive):
CandidatesRowFive = [1,3,7]
CandidatesColumnFour = [1,2,5,8]
CandidatesBlockFive = [1,3,5,6,8]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnOne):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnOne = [3]
CandidatesBlockOne = [3,4,6,7]

cell(RowOne, ColumnThree):
CandidatesRowOne = [2,3,7,9]
CandidatesColumnThree = [2,5,6,7]
CandidatesBlockOne = [3,4,6,7]

cell(RowThree, ColumnTwo):
CandidatesRowThree = [1,6,7,8]
CandidatesColumnTwo = [4,6]
CandidatesBlockOne = [3,4,6,7]

cell(RowFour, ColumnSeven):
CandidatesRowFour = [5,6,8]
CandidatesColumnSeven = [1,4,6,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFour, ColumnEight):
CandidatesRowFour = [5,6,8]
CandidatesColumnEight = [1,2,4,7,8,9]
CandidatesBlockSix = [1,4,6,7,8]

cell(RowFive, ColumnFour):
CandidatesRowFive = [1,3,7]
CandidatesColumnFour = [1,2,5,8]
CandidatesBlockFive = [1,3,5,6,8]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowOne, ColumnOne):
CandidatesRowOne.length = 4
CandidatesColumnOne.length = 1
CandidatesBlockOne.length = 4

shortest_list = CandidatesColumnOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowOne and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [2,3,7,9], broken into CandidatesRowOneLow = [2,3] and CandidatesRowOneHigh = [7,9]
CandidatesColumnOne = [3], broken into CandidatesColumnOneLow = [3] and CandidatesColumnOneHigh = []
CandidatesBlockOne = [3,4,6,7], broken into CandidatesBlockOneLow = [3,4] and CandidatesBlockOneHigh = [6,7]

Checking digits in CandidatesColumnOneLow = [3] against: CandidatesRowOneLow = [2,3] and CandidatesBlockOneLow = [3,4]
3: [2,3].count(3) = 1, [3,4].count(3) = 1, TotalCount(3) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnOneHigh = [] against: CandidatesRowOneHigh = [7,9] and CandidatesBlockOneHigh = [6,7]
No high digits to check.

Confirmed candidates found for cell(RowOne, ColumnOne): [3]

## Cell 2 of 6
cell(RowOne, ColumnThree):
CandidatesRowOne.length = 4
CandidatesColumnThree.length = 4
CandidatesBlockOne.length = 4

shortest_list = CandidatesRowOne = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnThree and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [2,3,7,9], broken into CandidatesRowOneLow = [2,3] and CandidatesRowOneHigh = [7,9]
CandidatesColumnThree = [2,5,6,7], broken into CandidatesColumnThreeLow = [2,5] and CandidatesColumnThreeHigh = [6,7]
CandidatesBlockOne = [3,4,6,7], broken into CandidatesBlockOneLow = [3,4] and CandidatesBlockOneHigh = [6,7]

Checking digits in CandidatesRowOneLow = [2,3] against: CandidatesColumnThreeLow = [2,5] and CandidatesBlockOneLow = [3,4]
2: [2,5].count(2) = 1, [3,4].count(2) = 0, TotalCount(2) = 1
3: [2,5].count(3) = 0, [3,4].count(3) = 1, TotalCount(3) = 1

Checking digits in CandidatesRowOneHigh = [7,9] against: CandidatesColumnThreeHigh = [6,7] and CandidatesBlockOneHigh = [6,7]
7: [6,7].count(7) = 1, [6,7].count(7) = 1, TotalCount(7) = 2 FOUND A CANDIDATE
9: [6,7].count(9) = 0, [6,7].count(9) = 0, TotalCount(9) = 0

Confirmed candidates found for cell(RowOne, ColumnThree): [7]

## Cell 3 of 6
cell(RowThree, ColumnTwo):
CandidatesRowThree.length = 4
CandidatesColumnTwo.length = 2
CandidatesBlockOne.length = 4

shortest_list = CandidatesColumnTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,6,7,8], broken into CandidatesRowThreeLow = [1] and CandidatesRowThreeHigh = [6,7,8]
CandidatesColumnTwo = [4,6], broken into CandidatesColumnTwoLow = [4] and CandidatesColumnTwoHigh = [6]
CandidatesBlockOne = [3,4,6,7], broken into CandidatesBlockOneLow = [3,4] and CandidatesBlockOneHigh = [6,7]

Checking digits in CandidatesColumnTwoLow = [4] against: CandidatesRowThreeLow = [1] and CandidatesBlockOneLow = [3,4]
4: [1].count(4) = 0, [3,4].count(4) = 1, TotalCount(4) = 1

Checking digits in CandidatesColumnTwoHigh = [6] against: CandidatesRowThreeHigh = [6,7,8] and CandidatesBlockOneHigh = [6,7]
6: [6,7,8].count(6) = 1, [6,7].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowThree, ColumnTwo): [6]

## Cell 4 of 6
cell(RowFour, ColumnSeven):
CandidatesRowFour.length = 3
CandidatesColumnSeven.length = 4
CandidatesBlockSix.length = 5

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnSeven and CandidatesBlockSix

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [5,6,8], broken into CandidatesRowFourLow = [5] and CandidatesRowFourHigh = [6,8]
CandidatesColumnSeven = [1,4,6,9], broken into CandidatesColumnSevenLow = [1,4] and CandidatesColumnSevenHigh = [6,9]
CandidatesBlockSix = [1,4,6,7,8], broken into CandidatesBlockSixLow = [1,4] and CandidatesBlockSixHigh = [6,7,8]

Checking digits in CandidatesRowFourLow = [5] against: CandidatesColumnSevenLow = [1,4] and CandidatesBlockSixLow = [1,4]
5: [1,4].count(5) = 0, [1,4].count(5) = 0, TotalCount(5) = 0

Checking digits in CandidatesRowFourHigh = [6,8] against: CandidatesColumnSevenHigh = [6,9] and CandidatesBlockSixHigh = [6,7,8]
6: [6,9].count(6) = 1, [6,7,8].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE
8: [6,9].count(8) = 0, [6,7,8].count(8) = 1, TotalCount(8) = 1

Confirmed candidates found for cell(RowFour, ColumnSeven): [6]

## Cell 5 of 6
cell(RowFour, ColumnEight):
CandidatesRowFour.length = 3
CandidatesColumnEight.length = 6
CandidatesBlockSix.length = 5

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnEight and CandidatesBlockSix

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [5,6,8], broken into CandidatesRowFourLow = [5] and CandidatesRowFourHigh = [6,8]
CandidatesColumnEight = [1,2,4,7,8,9], broken into CandidatesColumnEightLow = [1,2,4] and CandidatesColumnEightHigh = [7,8,9]
CandidatesBlockSix = [1,4,6,7,8], broken into CandidatesBlockSixLow = [1,4] and CandidatesBlockSixHigh = [6,7,8]

Checking digits in CandidatesRowFourLow = [5] against: CandidatesColumnEightLow = [1,2,4] and CandidatesBlockSixLow = [1,4]
5: [1,2,4].count(5) = 0, [1,4].count(5) = 0, TotalCount(5) = 0

Checking digits in CandidatesRowFourHigh = [6,8] against: CandidatesColumnEightHigh = [7,8,9] and CandidatesBlockSixHigh = [6,7,8]
6: [7,8,9].count(6) = 0, [6,7,8].count(6) = 1, TotalCount(6) = 1
8: [7,8,9].count(8) = 1, [6,7,8].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowFour, ColumnEight): [8]

## Cell 6 of 6
cell(RowFive, ColumnFour):
CandidatesRowFive.length = 3
CandidatesColumnFour.length = 4
CandidatesBlockFive.length = 5

shortest_list = CandidatesRowFive = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFour and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [1,3,7], broken into CandidatesRowFiveLow = [1,3] and CandidatesRowFiveHigh = [7]
CandidatesColumnFour = [1,2,5,8], broken into CandidatesColumnFourLow = [1,2,5] and CandidatesColumnFourHigh = [8]
CandidatesBlockFive = [1,3,5,6,8], broken into CandidatesBlockFiveLow = [1,3,5] and CandidatesBlockFiveHigh = [6,8]

Checking digits in CandidatesRowFiveLow = [1,3] against: CandidatesColumnFourLow = [1,2,5] and CandidatesBlockFiveLow = [1,3,5]
1: [1,2,5].count(1) = 1, [1,3,5].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE
3: [1,2,5].count(3) = 0, [1,3,5].count(3) = 1, TotalCount(3) = 1

Checking digits in CandidatesRowFiveHigh = [7] against: CandidatesColumnFourHigh = [8] and CandidatesBlockFiveHigh = [6,8]
7: [8].count(7) = 0, [6,8].count(7) = 0, TotalCount(7) = 0

Confirmed candidates found for cell(RowFive, ColumnFour): [1]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnOne): [3]
[3].length = 1
length is 1, Passes

cell(RowOne, ColumnThree): [7]
[7].length = 1
length is 1, Passes

cell(RowThree, ColumnTwo): [6]
[6].length = 1
length is 1, Passes

cell(RowFour, ColumnSeven): [6]
[6].length = 1
length is 1, Passes

cell(RowFour, ColumnEight): [8]
[8].length = 1
length is 1, Passes

cell(RowFive, ColumnFour): [1]
[1].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnOne): [3]
cell(RowOne, ColumnThree): [7]
cell(RowThree, ColumnTwo): [6]
cell(RowFour, ColumnSeven): [6]
cell(RowFour, ColumnEight): [8]
cell(RowFive, ColumnFour): [1]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowThree, RowFour, RowFive

RowOne: [0,8,0,6,0,1,5,0,4]
cell(RowOne, ColumnOne): [3]
cell(RowOne, ColumnThree): [7]

RowTwo: [2,0,1,0,0,3,0,0,0]

RowThree: [5,0,9,4,0,2,0,3,0]
cell(RowThree, ColumnTwo): [6]

RowFour: [1,3,4,7,2,0,0,0,9]
cell(RowFour, ColumnSeven): [6]
cell(RowFour, ColumnEight): [8]

RowFive: [6,9,8,0,0,4,2,5,0]
cell(RowFive, ColumnFour): [1]

RowSix: [7,5,0,9,0,0,0,0,3]

RowSeven: [9,1,3,0,0,8,7,6,5]

RowEight: [4,2,0,3,0,0,8,0,1]

RowNine: [8,7,0,0,0,9,3,0,0]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowOne, ColumnOne): [3]
RowOne = [0,8,0,6,0,1,5,0,4]
The ColumnOne element of RowOne needs to be updated to [3]

ColumnOne: 0
ColumnTwo: 8
ColumnThree: 0
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Now replacing ColumnOne with the element to update [3], such that ColumnOne = 3
Redoing column list like we just did, but with ColumnOne set to 3

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 0
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnOne.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnOne (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = []
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [].length = 0
Now the elements of the columns in PreCellColumnsList, which is the first 0 elements of RowOne:
PreCellList = []

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [3] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(3) = [3]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [3,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the restof the row:
UpdatedRowOne = [3,8,0,6,0,1,5,0,4]

## Updating 2 of 6
cell(RowOne, ColumnThree): [7]
RowOne = [3,8,0,6,0,1,5,0,4]
The ColumnThree element of RowOne needs to be updated to [7]

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 0
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Now replacing ColumnThree with the element to update [7], such that ColumnThree = 7
Redoing column list like we just did, but with ColumnThree set to 7

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 7
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnThree.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnThree (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [ColumnOne,ColumnTwo].length = 2
Now the elements of the columns in PreCellColumnsList, which is the first 2 elements of RowOne:
PreCellList = [3,8]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [7] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(7) = [3,8,7]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [3,8,7,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [3,8,7,6,0,1,5,0,4]

## Updating 3 of 6
cell(RowThree, ColumnTwo): [6]
RowThree = [5,0,9,4,0,2,0,3,0]
The ColumnTwo element of RowThree needs to be updated to [6]

ColumnOne: 5
ColumnTwo: 0
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 0
ColumnEight: 3
ColumnNine: 0

Now replacing ColumnTwo with the element to update [6], such that ColumnTwo = 6
Redoing column list like we just did, but with ColumnTwo set to 6

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 0
ColumnEight: 3
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnTwo.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnTwo (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [ColumnOne].length = 1
Now the elements of the columns in PreCellColumnsList, which is the first 1 elements of RowThree:
PreCellList = [5]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [5,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [5,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [5,6,9,4,0,2,0,3,0]

## Updating 4 of 6
cell(RowFour, ColumnSeven): [6]
RowFour = [1,3,4,7,2,0,0,0,9]
The ColumnSeven element of RowFour needs to be updated to [6]

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 9

Now replacing ColumnSeven with the element to update [6], such that ColumnSeven = 6
Redoing column list like we just did, but with ColumnSeven set to 6

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 6
ColumnEight: 0
ColumnNine: 9

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSeven.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSeven (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
Now the elements of the columns in PreCellColumnsList, which is the first 6 elements of RowFour:
PreCellList = [1,3,4,7,2,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [1,3,4,7,2,0,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [1,3,4,7,2,0,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [1,3,4,7,2,0,6,0,9]

## Updating 5 of 6
cell(RowFour, ColumnEight): [8]
RowFour = [1,3,4,7,2,0,6,0,9]
The ColumnEight element of RowFour needs to be updated to [8]

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 6
ColumnEight: 0
ColumnNine: 9

Now replacing ColumnEight with the element to update [8], such that ColumnEight = 8
Redoing column list like we just did, but with ColumnEight set to 8

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 6
ColumnEight: 8
ColumnNine: 9

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowFour:
PreCellList = [1,3,4,7,2,0,6]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [1,3,4,7,2,0,6,8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [1,3,4,7,2,0,6,8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [1,3,4,7,2,0,6,8,9]

## Updating 6 of 6
cell(RowFive, ColumnFour): [1]
RowFive = [6,9,8,0,0,4,2,5,0]
The ColumnFour element of RowFive needs to be updated to [1]

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 0
ColumnFive: 0
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Now replacing ColumnFour with the element to update [1], such that ColumnFour = 1
Redoing column list like we just did, but with ColumnFour set to 1

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 1
ColumnFive: 0
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFour.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFour (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree].length = 3
Now the elements of the columns in PreCellColumnsList, which is the first 3 elements of RowFive:
PreCellList = [6,9,8]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [6,9,8,1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [6,9,8,1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = PreCellListWithCandidateElementAppended.length, the same as PreCellColumnsList.length + 1 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [6,9,8,1,0,4,2,5,0]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [3,8,7,6,0,1,5,0,4]
UpdatedRowThree = [5,6,9,4,0,2,0,3,0]
UpdatedRowFour = [1,3,4,7,2,0,6,8,9]
UpdatedRowFive = [6,9,8,1,0,4,2,5,0]

The rows to update are RowOne, RowThree,RowFour, RowFive
Using the contents of UpdatedRowOne, UpdatedRowThree, UpdatedRowFour, UpdatedRowFive
Printing Sudoku:
RowOne: [3,8,7,6,0,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,6,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,0,6,8,9]
RowFive: [6,9,8,1,0,4,2,5,0]
RowSix: [7,5,0,9,0,0,0,0,3]
RowSeven: [9,1,3,0,0,8,7,6,5]
RowEight: [4,2,0,3,0,0,8,0,1]
RowNine: [8,7,0,0,0,9,3,0,0]

# STEP_SEVEN: Shifting the Rows of the Sudoku
RowFour: [1,3,4,7,2,0,6,8,9]
RowFive: [6,9,8,1,0,4,2,5,0]
RowSix: [7,5,0,9,0,0,0,0,3]
RowSeven: [9,1,3,0,0,8,7,6,5]
RowEight: [4,2,0,3,0,0,8,0,1]
RowNine: [8,7,0,0,0,9,3,0,0]
RowOne: [3,8,7,6,0,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,6,9,4,0,2,0,3,0]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,0,6,8,9]
RowTwo: [6,9,8,1,0,4,2,5,0]
RowThree: [7,5,0,9,0,0,0,0,3]
RowFour: [9,1,3,0,0,8,7,6,5]
RowFive: [4,2,0,3,0,0,8,0,1]
RowSix: [8,7,0,0,0,9,3,0,0]
RowSeven: [3,8,7,6,0,1,5,0,4]
RowEight: [2,0,1,0,0,3,0,0,0]
RowNine: [5,6,9,4,0,2,0,3,0]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:32:28.588105
Turn number: 7
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,0,6,8,9]
RowTwo: [6,9,8,1,0,4,2,5,0]
RowThree: [7,5,0,9,0,0,0,0,3]
RowFour: [9,1,3,0,0,8,7,6,5]
RowFive: [4,2,0,3,0,0,8,0,1]
RowSix: [8,7,0,0,0,9,3,0,0]
RowSeven: [3,8,7,6,0,1,5,0,4]
RowEight: [2,0,1,0,0,3,0,0,0]
RowNine: [5,6,9,4,0,2,0,3,0]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [1,3,4,7,2,0,6,8,9]
RowTwo = [6,9,8,1,0,4,2,5,0]
RowThree = [7,5,0,9,0,0,0,0,3]
RowFour = [9,1,3,0,0,8,7,6,5]
RowFive = [4,2,0,3,0,0,8,0,1]
RowSix = [8,7,0,0,0,9,3,0,0]
RowSeven = [3,8,7,6,0,1,5,0,4]
RowEight = [2,0,1,0,0,3,0,0,0]
RowNine = [5,6,9,4,0,2,0,3,0]

# Columns
ColumnOne = [1,6,7,9,4,8,3,2,5]
ColumnTwo = [3,9,5,1,2,7,8,0,6]
ColumnThree = [4,8,0,3,0,0,7,1,9]
ColumnFour = [7,1,9,0,3,0,6,0,4]
ColumnFive = [2,0,0,0,0,0,0,0,0]
ColumnSix = [0,4,0,8,0,9,1,3,2]
ColumnSeven = [6,2,0,7,8,3,5,0,0]
ColumnEight = [8,5,0,6,0,0,0,0,3]
ColumnNine = [9,0,3,5,1,0,4,0,0]

# Blocks
BlockOne:
[[1,3,4],
[6,9,8],
[7,5,0]]
BlockOne = [1,3,4,6,9,8,7,5,0]
BlockTwo:
[[7,2,0],
[1,0,4],
[9,0,0]]
BlockTwo = [7,2,0,1,0,4,9,0,0]
BlockThree:
[[6,8,9],
[2,5,0],
[0,0,3]]
BlockThree = [6,8,9,2,5,0,0,0,3]
BlockFour:
[[9,1,3],
[4,2,0],
[8,7,0]]
BlockFour = [9,1,3,4,2,0,8,7,0]
BlockFive:
[[0,0,8],
[3,0,0],
[0,0,9]]
BlockFive = [0,0,8,3,0,0,0,0,9]
BlockSix:
[[7,6,5],
[8,0,1],
[3,0,0]]
BlockSix = [7,6,5,8,0,1,3,0,0]
BlockSeven:
[[3,8,7],
[2,0,1],
[5,6,9]]
BlockSeven = [3,8,7,2,0,1,5,6,9]
BlockEight:
[[6,0,1],
[0,0,3],
[4,0,2]]
BlockEight = [6,0,1,0,0,3,4,0,2]
BlockNine:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockNine = [5,0,4,0,0,0,0,3,0]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,0,6,8,9]) = [5]
CandidatesRowOne = [5]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,1,0,4,2,5,0]) = [3,7]
CandidatesRowTwo = [3,7]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([7,5,0,9,0,0,0,0,3]) = [1,2,4,6,8]
CandidatesRowThree = [1,2,4,6,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,0,0,8,7,6,5]) = [2,4]
CandidatesRowFour = [2,4]
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,0,8,0,1]) = [5,6,7,9]
CandidatesRowFive = [5,6,7,9]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([8,7,0,0,0,9,3,0,0]) = [1,2,4,5,6]
CandidatesRowSix = [1,2,4,5,6]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,6,0,1,5,0,4]) = [2,9]
CandidatesRowSeven = [2,9]
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([2,0,1,0,0,3,0,0,0]) = [4,5,6,7,8,9]
CandidatesRowEight = [4,5,6,7,8,9]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([5,6,9,4,0,2,0,3,0]) = [1,7,8]
CandidatesRowNine = [1,7,8]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([1,6,7,9,4,8,3,2,5]) = [0]
CandidatesColumnOne = [0]
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([3,9,5,1,2,7,8,0,6]) = [4]
CandidatesColumnTwo = [4]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([4,8,0,3,0,0,7,1,9]) = [2,5,6]
CandidatesColumnThree = [2,5,6]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([7,1,9,0,3,0,6,0,4]) = [2,5,8]
CandidatesColumnFour = [2,5,8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([2,0,0,0,0,0,0,0,0]) = [1,3,4,5,6,7,8,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([0,4,0,8,0,9,1,3,2]) = [5,6,7]
CandidatesColumnSix = [5,6,7]
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([6,2,0,7,8,3,5,0,0]) = [1,4,9]
CandidatesColumnSeven = [1,4,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([8,5,0,6,0,0,0,0,3]) = [1,2,4,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([9,0,3,5,1,0,4,0,0]) = [2,6,7,8]
CandidatesColumnNine = [2,6,7,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,0]) = [2]
CandidatesBlockOne = [2]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([7,2,0,1,0,4,9,0,0]) = [3,5,6,8]
CandidatesBlockTwo = [3,5,6,8]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([6,8,9,2,5,0,0,0,3]) = [1,4,7]
CandidatesBlockThree = [1,4,7]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,0]) = [5,6]
CandidatesBlockFour = [5,6]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,8,3,0,0,0,0,9]) = [1,2,4,5,6,7]
CandidatesBlockFive = [1,2,4,5,6,7]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,0,1,3,0,0]) = [2,4,9]
CandidatesBlockSix = [2,4,9]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,2,0,1,5,6,9]) = [4]
CandidatesBlockSeven = [4]
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([6,0,1,0,0,3,4,0,2]) = [5,7,8,9]
CandidatesBlockEight = [5,7,8,9]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockNine = [1,2,6,7,8,9]

# Index of all zeros, by row
RowOne = [1,3,4,7,2,0,6,8,9]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 1
RowOne[1] = 3
RowOne[2] = 4
RowOne[3] = 7
RowOne[4] = 2
RowOne[5] = 0
RowOne[6] = 6
RowOne[7] = 8
RowOne[8] = 9
IndexOfAll0ElementsInRowOne => [5]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [6]
EmptyColumnNamesRowOne = [ColumnSix]

RowTwo = [6,9,8,1,0,4,2,5,0]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 6
RowTwo[1] = 9
RowTwo[2] = 8
RowTwo[3] = 1
RowTwo[4] = 0
RowTwo[5] = 4
RowTwo[6] = 2
RowTwo[7] = 5
RowTwo[8] = 0
IndexOfAll0ElementsInRowTwo => [4,8]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [5,9]
EmptyColumnNamesRowTwo = [ColumnFive,ColumnNine]

RowThree = [7,5,0,9,0,0,0,0,3]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 7
RowThree[1] = 5
RowThree[2] = 0
RowThree[3] = 9
RowThree[4] = 0
RowThree[5] = 0
RowThree[6] = 0
RowThree[7] = 0
RowThree[8] = 3
IndexOfAll0ElementsInRowThree => [2,4,5,6,7]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [3,5,6,7,8]
EmptyColumnNamesRowThree = [ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]

RowFour = [9,1,3,0,0,8,7,6,5]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 9
RowFour[1] = 1
RowFour[2] = 3
RowFour[3] = 0
RowFour[4] = 0
RowFour[5] = 8
RowFour[6] = 7
RowFour[7] = 6
RowFour[8] = 5
IndexOfAll0ElementsInRowFour => [3,4]
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = [4,5]
EmptyColumnNamesRowFour = [ColumnFour,ColumnFive]

RowFive = [4,2,0,3,0,0,8,0,1]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 4
RowFive[1] = 2
RowFive[2] = 0
RowFive[3] = 3
RowFive[4] = 0
RowFive[5] = 0
RowFive[6] = 8
RowFive[7] = 0
RowFive[8] = 1
IndexOfAll0ElementsInRowFive => [2,4,5,7]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [3,5,6,8]
EmptyColumnNamesRowFive = [ColumnThree,ColumnFive,ColumnSix,ColumnEight]

RowSix = [8,7,0,0,0,9,3,0,0]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 8
RowSix[1] = 7
RowSix[2] = 0
RowSix[3] = 0
RowSix[4] = 0
RowSix[5] = 9
RowSix[6] = 3
RowSix[7] = 0
RowSix[8] = 0
IndexOfAll0ElementsInRowSix => [2,3,4,7,8]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [3,4,5,8,9]
EmptyColumnNamesRowSix = [ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]

RowSeven = [3,8,7,6,0,1,5,0,4]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 3
RowSeven[1] = 8
RowSeven[2] = 7
RowSeven[3] = 6
RowSeven[4] = 0
RowSeven[5] = 1
RowSeven[6] = 5
RowSeven[7] = 0
RowSeven[8] = 4
IndexOfAll0ElementsInRowSeven => [4,7]
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = [5,8]
EmptyColumnNamesRowSeven = [ColumnFive,ColumnEight]

RowEight = [2,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 2
RowEight[1] = 0
RowEight[2] = 1
RowEight[3] = 0
RowEight[4] = 0
RowEight[5] = 3
RowEight[6] = 0
RowEight[7] = 0
RowEight[8] = 0
IndexOfAll0ElementsInRowEight => [1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [2,4,5,7,8,9]
EmptyColumnNamesRowEight = [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowNine = [5,6,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 5
RowNine[1] = 6
RowNine[2] = 9
RowNine[3] = 4
RowNine[4] = 0
RowNine[5] = 2
RowNine[6] = 0
RowNine[7] = 3
RowNine[8] = 0
IndexOfAll0ElementsInRowNine => [4,6,8]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [5,7,9]
EmptyColumnNamesRowNine = [ColumnFive,ColumnSeven,ColumnNine]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 1 for each EmptyColumnNamesRowOne + 2 for each EmptyColumnNamesRowTwo + 5 for each EmptyColumnNamesRowThree + 2 for each EmptyColumnNamesRowFour + 4 for each EmptyColumnNamesRowFive + 5 for each EmptyColumnNamesRowSix + 2 for each EmptyColumnNamesRowSeven + 6 for each EmptyColumnNamesRowEight + 3 for each EmptyColumnNamesRowNine = 30

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 20

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnSix]
Note, the last empty column of the RowOne is ColumnSix
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 20
Up to ColumnSix in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnSix
Last column of current row
RowOne and ColumnSix means BlockTwo
import CandidatesRowOne, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowOne = [5]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]
Finding Common Elements:
CommonElementsOfRowOneAndColumnSix => [5] & [5,6,7] = [5]
CommonElementsOfRowOneAndColumnSixAndBlockTwo => [5] & [3,5,6,8] = [5]
CellCandidates = [5]
Length = 1
FOUND RowOne, ColumnSix, BlockTwo

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnFive,ColumnNine]
Note, the last empty column of the RowTwo is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 2 of 20
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [3,7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [3,5,6,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [3,7] & [1,3,4,5,6,7,8,9] = [3,7]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [3,7] & [3,5,6,8] = [3]
CellCandidates = [3]
Length = 1
FOUND RowTwo, ColumnFive, BlockTwo

### 3 of 20
Up to ColumnNine in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Last column of current row
The next row is RowThree
RowTwo and ColumnNine means BlockThree
import CandidatesRowTwo, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowTwo = [3,7]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,4,7]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnNine => [3,7] & [2,6,7,8] = [7]
CommonElementsOfRowTwoAndColumnNineAndBlockThree => [7] & [1,4,7] = [7]
CellCandidates = [7]
Length = 1
FOUND RowTwo, ColumnNine, BlockThree

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnThree,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Note, the last empty column of the RowThree is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 4 of 20
Up to ColumnThree in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnThree means BlockOne
import CandidatesRowThree, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnThree = [2,5,6]
CandidatesBlockOne = [2]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnThree => [1,2,4,6,8] & [2,5,6] = [2,6]
CommonElementsOfRowThreeAndColumnThreeAndBlockOne => [2,6] & [2] = [2]
CellCandidates = [2]
Length = 1
FOUND RowThree, ColumnThree, BlockOne

### 5 of 20
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [3,5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,2,4,6,8] & [1,3,4,5,6,7,8,9] = [1,2,4,6,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,2,4,6,8] & [3,5,6,8] = [6,8]
CellCandidates = [6,8]
Length = 2
Not 1

### 6 of 20
Up to ColumnSix in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnSix means BlockTwo
import CandidatesRowThree, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSix => [1,2,4,6,8] & [5,6,7] = [6]
CommonElementsOfRowThreeAndColumnSixAndBlockTwo => [6] & [3,5,6,8] = [6]
CellCandidates = [6]
Length = 1
FOUND RowThree, ColumnSix, BlockTwo

### 7 of 20
Up to ColumnSeven in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnSeven means BlockThree
import CandidatesRowThree, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,4,7]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSeven => [1,2,4,6,8] & [1,4,9] = [1,4]
CommonElementsOfRowThreeAndColumnSevenAndBlockThree => [1,4] & [1,4,7] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

### 8 of 20
Up to ColumnEight in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Last column of current row
The next row is RowFour
RowThree and ColumnEight means BlockThree
import CandidatesRowThree, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [1,4,7]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnEight => [1,2,4,6,8] & [1,2,4,7,9] = [1,2,4]
CommonElementsOfRowThreeAndColumnEightAndBlockThree => [1,2,4] & [1,4,7] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

## RowFour Candidates
EmptyColumnNamesRowFour: [ColumnFour,ColumnFive]
Note, the last empty column of the RowFour is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFour and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFour and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFour and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 9 of 20
Up to ColumnFour in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnFive
Not the last column of current row
RowFour and ColumnFour means BlockFive
import CandidatesRowFour, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowFour = [2,4]
CandidatesColumnFour = [2,5,8]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFour => [2,4] & [2,5,8] = [2]
CommonElementsOfRowFourAndColumnFourAndBlockFive => [2] & [1,2,4,5,6,7] = [2]
CellCandidates = [2]
Length = 1
FOUND RowFour, ColumnFour, BlockFive

### 10 of 20
Up to ColumnFive in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnFive
Last column of current row
The next row is RowFive
RowFour and ColumnFive means BlockFive
import CandidatesRowFour, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFour = [2,4]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFive => [2,4] & [1,3,4,5,6,7,8,9] = [2,4]
CommonElementsOfRowFourAndColumnFiveAndBlockFive => [2,4] & [1,2,4,5,6,7] = [2,4]
CellCandidates = [2,4]
Length = 2
Not 1

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnThree,ColumnFive,ColumnSix,ColumnEight]
Note, the last empty column of the RowFive is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 11 of 20
Up to ColumnThree in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnEight
Not the last column of current row
RowFive and ColumnThree means BlockFour
import CandidatesRowFive, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowFive = [5,6,7,9]
CandidatesColumnThree = [2,5,6]
CandidatesBlockFour = [5,6]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnThree => [5,6,7,9] & [2,5,6] = [5,6]
CommonElementsOfRowFiveAndColumnThreeAndBlockFour => [5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 12 of 20
Up to ColumnFive in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnEight
Not the last column of current row
RowFive and ColumnFive means BlockFive
import CandidatesRowFive, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFive = [5,6,7,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFive => [5,6,7,9] & [1,3,4,5,6,7,8,9] = [5,6,7,9]
CommonElementsOfRowFiveAndColumnFiveAndBlockFive => [5,6,7,9] & [1,2,4,5,6,7] = [5,6,7]
CellCandidates = [5,6,7]
Length = 3
Not 1

### 13 of 20
Up to ColumnSix in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnEight
Not the last column of current row
RowFive and ColumnSix means BlockFive
import CandidatesRowFive, CandidatesColumnSix, CandidatesBlockFive
CandidatesRowFive = [5,6,7,9]
CandidatesColumnSix = [5,6,7]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnSix => [5,6,7,9] & [5,6,7] = [5,6,7]
CommonElementsOfRowFiveAndColumnSixAndBlockFive => [5,6,7] & [1,2,4,5,6,7] = [5,6,7]
CellCandidates = [5,6,7]
Length = 3
Not 1

### 14 of 20
Up to ColumnEight in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnEight
Last column of current row
The next row is RowSix
RowFive and ColumnEight means BlockSix
import CandidatesRowFive, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowFive = [5,6,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockSix = [2,4,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnEight => [5,6,7,9] & [1,2,4,7,9] = [7,9]
CommonElementsOfRowFiveAndColumnEightAndBlockSix => [7,9] & [2,4,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowFive, ColumnEight, BlockSix

## RowSix Candidates
EmptyColumnNamesRowSix: [ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]
Note, the last empty column of the RowSix is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSix and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowSix and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowSix and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 15 of 20
Up to ColumnThree in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnThree means BlockFour
import CandidatesRowSix, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowSix = [1,2,4,5,6]
CandidatesColumnThree = [2,5,6]
CandidatesBlockFour = [5,6]
Finding Common Elements:
CommonElementsOfRowSixAndColumnThree => [1,2,4,5,6] & [2,5,6] = [2,5,6]
CommonElementsOfRowSixAndColumnThreeAndBlockFour => [2,5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 16 of 20
Up to ColumnFour in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnFour means BlockFive
import CandidatesRowSix, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowSix = [1,2,4,5,6]
CandidatesColumnFour = [2,5,8]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFour => [1,2,4,5,6] & [2,5,8] = [2,5]
CommonElementsOfRowSixAndColumnFourAndBlockFive => [2,5] & [1,2,4,5,6,7] = [2,5]
CellCandidates = [2,5]
Length = 2
Not 1

### 17 of 20
Up to ColumnFive in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnFive means BlockFive
import CandidatesRowSix, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowSix = [1,2,4,5,6]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockFive = [1,2,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFive => [1,2,4,5,6] & [1,3,4,5,6,7,8,9] = [1,2,4,5,6]
CommonElementsOfRowSixAndColumnFiveAndBlockFive => [1,2,4,5,6] & [1,2,4,5,6,7] = [1,2,4,5,6]
CellCandidates = [1,2,4,5,6]
Length = 5
Not 1

### 18 of 20
Up to ColumnEight in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnEight means BlockSix
import CandidatesRowSix, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowSix = [1,2,4,5,6]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockSix = [2,4,9]
Finding Common Elements:
CommonElementsOfRowSixAndColumnEight => [1,2,4,5,6] & [1,2,4,7,9] = [1,2,4]
CommonElementsOfRowSixAndColumnEightAndBlockSix => [1,2,4] & [2,4,9] = [2,4]
CellCandidates = [2,4]
Length = 2
Not 1

### 19 of 20
Up to ColumnNine in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Last column of current row
The next row is RowSeven
RowSix and ColumnNine means BlockSix
import CandidatesRowSix, CandidatesColumnNine, CandidatesBlockSix
CandidatesRowSix = [1,2,4,5,6]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockSix = [2,4,9]
Finding Common Elements:
CommonElementsOfRowSixAndColumnNine => [1,2,4,5,6] & [2,6,7,8] = [2,6]
CommonElementsOfRowSixAndColumnNineAndBlockSix => [2,6] & [2,4,9] = [2]
CellCandidates = [2]
Length = 1
FOUND RowSix, ColumnNine, BlockSix

## RowSeven Candidates
EmptyColumnNamesRowSeven: [ColumnFive,ColumnEight]
Note, the last empty column of the RowSeven is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSeven and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowSeven and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowSeven and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 20 of 20
Up to ColumnFive in EmptyColumnNamesRowSeven
The last empty column of EmptyColumnNamesRowSeven is ColumnEight
Not the last column of current row
RowSeven and ColumnFive means BlockEight
import CandidatesRowSeven, CandidatesColumnFive, CandidatesBlockEight
CandidatesRowSeven = [2,9]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockEight = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowSevenAndColumnFive => [2,9] & [1,3,4,5,6,7,8,9] = [9]
CommonElementsOfRowSevenAndColumnFiveAndBlockEight => [9] & [5,7,8,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowSeven, ColumnFive, BlockEight

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnSix, BlockTwo
2: FOUND RowTwo, ColumnFive, BlockTwo
3: FOUND RowTwo, ColumnNine, BlockThree
4: FOUND RowThree, ColumnThree, BlockOne
5: FOUND RowThree, ColumnSix, BlockTwo
6: FOUND RowFour, ColumnFour, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnSix, BlockTwo):
CandidatesRowOne = [5]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnFive, BlockTwo):
CandidatesRowTwo = [3,7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnNine, BlockThree):
CandidatesRowTwo = [3,7]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,4,7]

cell(RowThree, ColumnThree, BlockOne):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnThree = [2,5,6]
CandidatesBlockOne = [2]

cell(RowThree, ColumnSix, BlockTwo):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowFour, ColumnFour, BlockFive):
CandidatesRowFour = [2,4]
CandidatesColumnFour = [2,5,8]
CandidatesBlockFive = [1,2,4,5,6,7]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:41:45.399683
Turn number: 8
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,0,6,8,9]
RowTwo: [6,9,8,1,0,4,2,5,0]
RowThree: [7,5,0,9,0,0,0,0,3]
RowFour: [9,1,3,0,0,8,7,6,5]
RowFive: [4,2,0,3,0,0,8,0,1]
RowSix: [8,7,0,0,0,9,3,0,0]
RowSeven: [3,8,7,6,0,1,5,0,4]
RowEight: [2,0,1,0,0,3,0,0,0]
RowNine: [5,6,9,4,0,2,0,3,0]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant:  of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnSix, BlockTwo
2: FOUND RowTwo, ColumnFive, BlockTwo
3: FOUND RowTwo, ColumnNine, BlockThree
4: FOUND RowThree, ColumnThree, BlockOne
5: FOUND RowThree, ColumnSix, BlockTwo
6: FOUND RowFour, ColumnFour, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnSix, BlockTwo):
CandidatesRowOne = [5]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnFive, BlockTwo):
CandidatesRowTwo = [3,7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnNine, BlockThree):
CandidatesRowTwo = [3,7]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,4,7]

cell(RowThree, ColumnThree, BlockOne):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnThree = [2,5,6]
CandidatesBlockOne = [2]

cell(RowThree, ColumnSix, BlockTwo):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowFour, ColumnFour, BlockFive):
CandidatesRowFour = [2,4]
CandidatesColumnFour = [2,5,8]
CandidatesBlockFive = [1,2,4,5,6,7]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnSix):
CandidatesRowOne = [5]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnFive):
CandidatesRowTwo = [3,7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9]
CandidatesBlockTwo = [3,5,6,8]

cell(RowTwo, ColumnNine):
CandidatesRowTwo = [3,7]
CandidatesColumnNine = [2,6,7,8]
CandidatesBlockThree = [1,4,7]

cell(RowThree, ColumnThree):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnThree = [2,5,6]
CandidatesBlockOne = [2]

cell(RowThree, ColumnSix):
CandidatesRowThree = [1,2,4,6,8]
CandidatesColumnSix = [5,6,7]
CandidatesBlockTwo = [3,5,6,8]

cell(RowFour, ColumnFour):
CandidatesRowFour = [2,4]
CandidatesColumnFour = [2,5,8]
CandidatesBlockFive = [1,2,4,5,6,7]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowOne, ColumnSix):
CandidatesRowOne.length = 1
CandidatesColumnSix.length = 3
CandidatesBlockTwo.length = 4

shortest_list = CandidatesRowOne = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnSix and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [5], broken into CandidatesRowOneLow = [5] and CandidatesRowOneHigh = []
CandidatesColumnSix = [5,6,7], broken into CandidatesColumnSixLow = [5] and CandidatesColumnSixHigh = [6,7]
CandidatesBlockTwo = [3,5,6,8], broken into CandidatesBlockTwoLow = [3,5] and CandidatesBlockTwoHigh = [6,8]

Checking digits in CandidatesRowOneLow = [5] against: CandidatesColumnSixLow = [5] and CandidatesBlockTwoLow = [3,5]
5: [5].count(5) = 1, [3,5].count(5) = 1, TotalCount(5) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowOneHigh = [] against: CandidatesColumnSixHigh = [6,7] and CandidatesBlockTwoHigh = [6,8]
No digits to check in CandidatesRowOneHigh.

Confirmed candidates found for cell(RowOne, ColumnSix): [5]

## Cell 2 of 6
cell(RowTwo, ColumnFive):
CandidatesRowTwo.length = 2
CandidatesColumnFive.length = 8
CandidatesBlockTwo.length = 4

shortest_list = CandidatesRowTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [3,7], broken into CandidatesRowTwoLow = [3] and CandidatesRowTwoHigh = [7]
CandidatesColumnFive = [1,3,4,5,6,7,8,9], broken into CandidatesColumnFiveLow = [1,3,4,5] and CandidatesColumnFiveHigh = [6,7,8,9]
CandidatesBlockTwo = [3,5,6,8], broken into CandidatesBlockTwoLow = [3,5] and CandidatesBlockTwoHigh = [6,8]

Checking digits in CandidatesRowTwoLow = [3] against: CandidatesColumnFiveLow = [1,3,4,5] and CandidatesBlockTwoLow = [3,5]
3: [1,3,4,5].count(3) = 1, [3,5].count(3) = 1, TotalCount(3) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowTwoHigh = [7] against: CandidatesColumnFiveHigh = [6,7,8,9] and CandidatesBlockTwoHigh = [6,8]
7: [6,7,8,9].count(7) = 1, [6,8].count(7) = 0, TotalCount(7) = 1

Confirmed candidates found for cell(RowTwo, ColumnFive): [3]

## Cell 3 of 6
cell(RowTwo, ColumnNine):
CandidatesRowTwo.length = 2
CandidatesColumnNine.length = 4
CandidatesBlockThree.length = 3

shortest_list = CandidatesBlockThree = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesColumnNine

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [3,7], broken into CandidatesRowTwoLow = [3] and CandidatesRowTwoHigh = [7]
CandidatesColumnNine = [2,6,7,8], broken into CandidatesColumnNineLow = [2] and CandidatesColumnNineHigh = [6,7,8]
CandidatesBlockThree = [1,4,7], broken into CandidatesBlockThreeLow = [1,4] and CandidatesBlockThreeHigh = [7]

Checking digits in CandidatesBlockThreeLow = [1,4] against: CandidatesRowTwoLow = [3] and CandidatesColumnNineLow = [2]
1: [3].count(1) = 0, [2].count(1) = 0, TotalCount(1) = 0
4: [3].count(4) = 0, [2].count(4) = 0, TotalCount(4) = 0

Checking digits in CandidatesBlockThreeHigh = [7] against: CandidatesRowTwoHigh = [7] and CandidatesColumnNineHigh = [6,7,8]
7: [7].count(7) = 1, [6,7,8].count(7) = 1, TotalCount(7) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnNine): [7]

## Cell 4 of 6
cell(RowThree, ColumnThree):
CandidatesRowThree.length = 5
CandidatesColumnThree.length = 3
CandidatesBlockOne.length = 1

shortest_list = CandidatesBlockOne = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesColumnThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,6,8], broken into CandidatesRowThreeLow = [1,2,4] and CandidatesRowThreeHigh = [6,8]
CandidatesColumnThree = [2,5,6], broken into CandidatesColumnThreeLow = [2,5] and CandidatesColumnThreeHigh = [6]
CandidatesBlockOne = [2], broken into CandidatesBlockOneLow = [2] and CandidatesBlockOneHigh = []

Checking digits in CandidatesBlockOneLow = [2] against: CandidatesRowThreeLow = [1,2,4] and CandidatesColumnThreeLow = [2,5]
2: [1,2,4].count(2) = 1, [2,5].count(2) = 1, TotalCount(2) = 2 FOUND A CANDIDATE

Checking digits in CandidatesBlockOneHigh = [] against: CandidatesRowThreeHigh = [6,8] and CandidatesColumnThreeHigh = [6]
No digits to check in CandidatesBlockOneHigh.

Confirmed candidates found for cell(RowThree, ColumnThree): [2]

## Cell 5 of 6
cell(RowThree, ColumnSix):
CandidatesRowThree.length = 5
CandidatesColumnSix.length = 3
CandidatesBlockTwo.length = 4

shortest_list = CandidatesColumnSix = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,6,8], broken into CandidatesRowThreeLow = [1,2,4] and CandidatesRowThreeHigh = [6,8]
CandidatesColumnSix = [5,6,7], broken into CandidatesColumnSixLow = [5] and CandidatesColumnSixHigh = [6,7]
CandidatesBlockTwo = [3,5,6,8], broken into CandidatesBlockTwoLow = [3,5] and CandidatesBlockTwoHigh = [6,8]

Checking digits in CandidatesColumnSixLow = [5] against: CandidatesRowThreeLow = [1,2,4] and CandidatesBlockTwoLow = [3,5]
5: [1,2,4].count(5) = 0, [3,5].count(5) = 1, TotalCount(5) = 1

Checking digits in CandidatesColumnSixHigh = [6,7] against: CandidatesRowThreeHigh = [6,8] and CandidatesBlockTwoHigh = [6,8]
6: [6,8].count(6) = 1, [6,8].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE
7: [6,8].count(7) = 0, [6,8].count(7) = 0, TotalCount(7) = 0

Confirmed candidates found for cell(RowThree, ColumnSix): [6]

## Cell 6 of 6
cell(RowFour, ColumnFour):
CandidatesRowFour.length = 2
CandidatesColumnFour.length = 3
CandidatesBlockFive.length = 6

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFour and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [2,4], broken into CandidatesRowFourLow = [2,4] and CandidatesRowFourHigh = []
CandidatesColumnFour = [2,5,8], broken into CandidatesColumnFourLow = [2,5] and CandidatesColumnFourHigh = [8]
CandidatesBlockFive = [1,2,4,5,6,7], broken into CandidatesBlockFiveLow = [1,2,4,5] and CandidatesBlockFiveHigh = [6,7]

Checking digits in CandidatesRowFourLow = [2,4] against: CandidatesColumnFourLow = [2,5] and CandidatesBlockFiveLow = [1,2,4,5]
2: [2,5].count(2) = 1, [1,2,4,5].count(2) = 1, TotalCount(2) = 2 FOUND A CANDIDATE
4: [2,5].count(4) = 0, [1,2,4,5].count(4) = 1, TotalCount(4) = 1

Checking digits in CandidatesRowFourHigh = [] against: CandidatesColumnFourHigh = [8] and CandidatesBlockFiveHigh = [6,7]
No digits to check in CandidatesRowFourHigh.

Confirmed candidates found for cell(RowFour, ColumnFour): [2]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnSix): [5]
[5].length = 1
length is 1, Passes

cell(RowTwo, ColumnFive): [3]
[3].length = 1
length is 1, Passes

cell(RowTwo, ColumnNine): [7]
[7].length = 1
length is 1, Passes

cell(RowThree, ColumnThree): [2]
[2].length = 1
length is 1, Passes

cell(RowThree, ColumnSix): [6]
[6].length = 1
length is 1, Passes

cell(RowFour, ColumnFour): [2]
[2].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnSix): [5]
cell(RowTwo, ColumnFive): [3]
cell(RowTwo, ColumnNine): [7]
cell(RowThree, ColumnThree): [2]
cell(RowThree, ColumnSix): [6]
cell(RowFour, ColumnFour): [2]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowTwo, RowThree, RowFour

RowOne: [1,3,4,7,2,0,6,8,9]
cell(RowOne, ColumnSix): [5]

RowTwo: [6,9,8,1,0,4,2,5,0]
cell(RowTwo, ColumnFive): [3]
cell(RowTwo, ColumnNine): [7]

RowThree: [7,5,0,9,0,0,0,0,3]
cell(RowThree, ColumnThree): [2]
cell(RowThree, ColumnSix): [6]

RowFour: [9,1,3,0,0,8,7,6,5]
cell(RowFour, ColumnFour): [2]

RowFive: [4,2,0,3,0,0,8,0,1]

RowSix: [8,7,0,0,0,9,3,0,0]

RowSeven: [3,8,7,6,0,1,5,0,4]

RowEight: [2,0,1,0,0,3,0,0,0]

RowNine: [5,6,9,4,0,2,0,3,0]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowOne, ColumnSix): [5]
RowOne = [1,3,4,7,2,0,6,8,9]
The ColumnSix element of RowOne needs to be updated to [5]

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 0
ColumnSeven: 6
ColumnEight: 8
ColumnNine: 9

Now replacing ColumnSix with the element to update [5], such that ColumnSix = 5
Redoing column list like we just did, but with ColumnSix set to 5

ColumnOne: 1
ColumnTwo: 3
ColumnThree: 4
ColumnFour: 7
ColumnFive: 2
ColumnSix: 5
ColumnSeven: 6
ColumnEight: 8
ColumnNine: 9

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSix.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSix (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSix does Not appear on this list!!! The ONLY time you don't is if ColumnSix is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSix:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
Now the elements of the columns in PreCellColumnsList, which is the first 5 elements of RowOne:
PreCellList = [1,3,4,7,2]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [5] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(5) = [1,3,4,7,2,5]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [1,3,4,7,2,5,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 5 + 1 = 6 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [1,3,4,7,2,5,6,8,9]

## Updating 2 of 6
cell(RowTwo, ColumnFive): [3]
RowTwo = [6,9,8,1,0,4,2,5,0]
The ColumnFive element of RowTwo needs to be updated to [3]

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 1
ColumnFive: 0
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Now replacing ColumnFive with the element to update [3], suchthat ColumnFive = 3
Redoing column list like we just did, but with ColumnFive set to 3

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 1
ColumnFive: 3
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowTwo:
PreCellList = [6,9,8,1]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [3] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(3) = [6,9,8,1,3]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [6,9,8,1,3,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [6,9,8,1,3,4,2,5,0]

## Updating 3 of 6
cell(RowTwo, ColumnNine): [7]
RowTwo = [6,9,8,1,3,4,2,5,0]
The ColumnNine element of RowTwo needs to be updated to [7]

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 1
ColumnFive: 3
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 0

Now replacing ColumnNine with the element to update [7], such that ColumnNine = 7
Redoing column list like we just did, but with ColumnNine set to 7

ColumnOne: 6
ColumnTwo: 9
ColumnThree: 8
ColumnFour: 1
ColumnFive: 3
ColumnSix: 4
ColumnSeven: 2
ColumnEight: 5
ColumnNine: 7

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnNine.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnNine (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnNine does Not appear on this list!!! The ONLY time you don't is if ColumnNine is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnNine:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight].length = 8
Now the elements of the columns in PreCellColumnsList, which is the first 8 elements of RowTwo:
PreCellList = [6,9,8,1,3,4,2,5]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [7] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(7) = [6,9,8,1,3,4,2,5,7]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [6,9,8,1,3,4,2,5,7,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 8 + 1 = 9 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [6,9,8,1,3,4,2,5,7]

## Updating 4 of 6
cell(RowThree, ColumnThree): [2]
RowThree = [7,5,0,9,0,0,0,0,3]
The ColumnThree element of RowThree needs to be updated to [2]

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 0
ColumnFour: 9
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnThree with the element to update [2], such that ColumnThree = 2
Redoing column list like we just did, but with ColumnThree set to 2

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnThree.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnThree (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnThree does Not appear on this list!!! The ONLY time you don't is if ColumnThree is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnThree:
PreCellColumnsList.length => [ColumnOne,ColumnTwo].length = 2
Now the elements of the columns in PreCellColumnsList, which is the first 2 elements of RowThree:
PreCellList = [7,5]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [2] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(2) = [7,5,2]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [7,5,2,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 2 + 1 = 3 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [7,5,2,9,0,0,0,0,3]

## Updating 5 of 6
cell(RowThree, ColumnSix): [6]
RowThree = [7,5,2,9,0,0,0,0,3]
The ColumnSix element of RowThree needs to be updated to [6]

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnSix with the element to update [6], such that ColumnSix = 6
Redoing column list like we just did, but with ColumnSix set to 6

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 0
ColumnSix: 6
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSix.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSix (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSix does Not appear on this list!!! The ONLY time you don't is if ColumnSix is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSix:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
Now the elements of the columns in PreCellColumnsList, which is the first 5 elements of RowThree:
PreCellList = [7,5,2,9,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [7,5,2,9,0,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [7,5,2,9,0,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 5 + 1 = 6 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [7,5,2,9,0,6,0,0,3]

## Updating 6 of 6
cell(RowFour, ColumnFour): [2]
RowFour = [9,1,3,0,0,8,7,6,5]
The ColumnFour element of RowFour needs to be updated to [2]

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 0
ColumnFive: 0
ColumnSix: 8
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Now replacing ColumnFour with the element to update [2], such that ColumnFour = 2
Redoing column list like we just did, but with ColumnFour set to 2

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 2
ColumnFive: 0
ColumnSix: 8
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFour.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFour (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFour does Not appear on this list!!! The ONLY time you don't is if ColumnFour is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFour:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree].length = 3
Now the elements of the columns in PreCellColumnsList, which is the first 3 elements of RowFour:
PreCellList = [9,1,3]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [2] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(2) = [9,1,3,2]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [9,1,3,2,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 3 + 1 = 4 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [9,1,3,2,0,8,7,6,5]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [1,3,4,7,2,5,6,8,9]
UpdatedRowTwo = [6,9,8,1,3,4,2,5,7]
UpdatedRowThree = [7,5,2,9,0,6,0,0,3]
UpdatedRowFour = [9,1,3,2,0,8,7,6,5]

The rows to update are RowOne, RowTwo, RowThree, RowFour
Using the contents of UpdatedRowOne, UpdatedRowTwo, UpdatedRowThree, UpdatedRowFour
Printing Sudoku:
UpdatedRowOne: [1,3,4,7,2,5,6,8,9]
UpdatedRowTwo: [6,9,8,1,3,4,2,5,7]
UpdatedRowThree: [7,5,2,9,0,6,0,0,3]
UpdatedRowFour: [9,1,3,2,0,8,7,6,5]
RowFive: [4,2,0,3,0,0,8,0,1]
RowSix: [8,7,0,0,0,9,3,0,0]
RowSeven: [3,8,7,6,0,1,5,0,4]
RowEight: [2,0,1,0,0,3,0,0,0]
RowNine: [5,6,9,4,0,2,0,3,0]

# STEP_SEVEN: Shifting the Rows of the Sudoku
UpdatedRowFour: [9,1,32,0,8,7,6,5]
RowFive: [4,2,0,3,0,0,8,0,1]
RowSix: [8,7,0,0,0,9,3,0,0]
RowSeven: [3,8,7,6,0,1,5,0,4]
RowEight: [2,0,1,0,0,3,0,0,0]
RowNine: [5,6,9,4,0,2,0,3,0]
UpdatedRowOne: [1,3,4,7,2,5,6,8,9]
UpdatedRowTwo: [6,9,8,1,3,4,2,5,7]
UpdatedRowThree: [7,5,2,9,0,6,0,0,3]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,0,8,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,1]
RowThree: [8,7,0,0,0,9,3,0,0]
RowFour: [3,8,7,6,0,1,5,0,4]
RowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,6,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,0,6,0,0,3]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 21:51:46.388609
Turn number: 9
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,0,8,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,1]
RowThree: [8,7,0,0,0,9,3,0,0]
RowFour: [3,8,7,6,0,1,5,0,4]
RowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,6,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,0,6,0,0,3]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [9,1,3,2,0,8,7,6,5]
RowTwo = [4,2,0,3,0,0,8,0,1]
RowThree = [8,7,0,0,0,9,3,0,0]
RowFour = [3,8,7,6,0,1,5,0,4]
RowFive = [2,0,1,0,0,3,0,0,0]
RowSix = [5,6,9,4,0,2,0,3,0]
RowSeven = [1,3,4,7,2,5,6,8,9]
RowEight = [6,9,8,1,3,4,2,5,7]
RowNine = [7,5,2,9,0,6,0,0,3]

# Columns
ColumnOne = [9,4,8,3,2,5,1,6,7]
ColumnTwo = [1,2,7,8,0,6,3,9,5]
ColumnThree = [3,0,0,7,1,9,4,8,2]
ColumnFour = [2,3,0,6,0,4,7,1,9]
ColumnFive = [0,0,0,0,0,0,2,3,0]
ColumnSix = [8,0,9,1,3,2,5,4,6]
ColumnSeven = [7,8,3,5,0,0,6,2,0]
ColumnEight = [6,0,0,0,0,3,8,5,0]
ColumnNine = [5,1,0,4,0,0,9,7,3]

# Blocks
BlockOne:
[[9,1,3],
[4,2,0],
[8,7,0]]
BlockOne = [9,1,3,4,2,0,8,7,0]

BlockTwo:
[[2,0,8],
[3,0,0],
[0,0,9]]
BlockTwo = [2,0,8,3,0,0,0,0,9]

BlockThree:
[[7,6,5],
[8,0,1],
[3,0,0]]
BlockThree = [7,6,5,8,0,1,3,0,0]

BlockFour:
[[3,8,7],
[2,0,1],
[5,6,9]]
BlockFour = [3,8,7,2,0,1,5,6,9]

BlockFive:
[[6,0,1],
[0,0,3],
[4,0,2]]
BlockFive = [6,0,1,0,0,3,4,0,2]

BlockSix:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockSix = [5,0,4,0,0,0,0,3,0]

BlockSeven:
[[1,3,4],
[6,9,8],
[7,5,2]]
BlockSeven = [1,3,4,6,9,8,7,5,2]

BlockEight:
[[7,2,5],
[1,3,4],
[9,0,6]]
BlockEight = [7,2,5,1,3,4,9,0,6]

BlockNine:
[[6,8,9],
[2,5,7],
[0,0,3]]
BlockNine = [6,8,9,2,5,7,0,0,3]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,2,0,8,7,6,5]) = [4]
CandidatesRowOne = [4]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,0,8,0,1]) = [5,6,7,9]
CandidatesRowTwo = [5,6,7,9]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([8,7,0,0,0,9,3,0,0]) = [1,2,4,5,6]
CandidatesRowThree = [1,2,4,5,6]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,6,0,1,5,0,4]) = [2,9]
CandidatesRowFour = [2,9]
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([2,0,1,0,0,3,0,0,0]) = [4,5,6,7,8,9]
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([5,6,9,4,0,2,0,3,0]) = [1,7,8]
CandidatesRowSix = [1,7,8]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,5,6,8,9]) = []
CandidatesRowSeven = []
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,1,3,4,2,5,7]) = []
CandidatesRowEight = []
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([7,5,2,9,0,6,0,0,3]) = [1,4,8]
CandidatesRowNine = [1,4,8]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([9,4,8,3,2,5,1,6,7]) = []
CandidatesColumnOne = []
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([1,2,7,8,0,6,3,9,5]) = [4]
CandidatesColumnTwo = [4]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([3,0,0,7,1,9,4,8,2]) = [5,6]
CandidatesColumnThree = [5,6]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([2,3,0,6,0,4,7,1,9]) = [5,8]
CandidatesColumnFour = [5,8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([0,0,0,0,0,0,2,3,0]) = [1,4,5,6,7,8,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([8,0,9,1,3,2,5,4,6]) = [7]
CandidatesColumnSix = [7]
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([7,8,3,5,0,0,6,2,0]) = [1,4,9]
CandidatesColumnSeven = [1,4,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([6,0,0,0,0,3,8,5,0]) = [1,2,4,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([5,1,0,4,0,0,9,7,3]) = [2,6,8]
CandidatesColumnNine = [2,6,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,0]) = [5,6]
CandidatesBlockOne = [5,6]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([2,0,8,3,0,0,0,0,9]) = [1,4,5,6,7]
CandidatesBlockTwo = [1,4,5,6,7]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,0,1,3,0,0]) = [2,4,9]
CandidatesBlockThree = [2,4,9]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,2,0,1,5,6,9]) = [4]
CandidatesBlockFour = [4]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([6,0,1,0,0,3,4,0,2]) = [5,7,8,9]
CandidatesBlockFive = [5,7,8,9]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockSix = [1,2,6,7,8,9]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,2]) = []
CandidatesBlockSeven = []
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([7,2,5,1,3,4,9,0,6]) = [8]
CandidatesBlockEight = [8]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([6,8,9,2,5,7,0,0,3]) = [1,4]
CandidatesBlockNine = [1,4]

# Index of all zeros, by row
RowOne = [9,1,3,2,0,8,7,6,5]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 9
RowOne[1] = 1
RowOne[2] = 3
RowOne[3] = 2
RowOne[4] = 0
RowOne[5] = 8
RowOne[6] = 7
RowOne[7] = 6
RowOne[8] = 5
IndexOfAll0ElementsInRowOne => [4]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [5]
EmptyColumnNamesRowOne = [ColumnFive]

RowTwo = [4,2,0,3,0,0,8,0,1]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 4
RowTwo[1] = 2
RowTwo[2] = 0
RowTwo[3] = 3
RowTwo[4] = 0
RowTwo[5] = 0
RowTwo[6] = 8
RowTwo[7] = 0
RowTwo[8] = 1
IndexOfAll0ElementsInRowTwo => [2,4,5,7]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [3,5,6,8]
EmptyColumnNamesRowTwo = [ColumnThree,ColumnFive,ColumnSix,ColumnEight]

RowThree = [8,7,0,0,0,9,3,0,0]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 8
RowThree[1] = 7
RowThree[2] = 0
RowThree[3] = 0
RowThree[4] = 0
RowThree[5] = 9
RowThree[6] = 3
RowThree[7] = 0
RowThree[8] = 0
IndexOfAll0ElementsInRowThree => [2,3,4,7,8]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [3,4,5,8,9]
EmptyColumnNamesRowThree = [ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]

RowFour = [3,8,7,6,0,1,5,0,4]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 3
RowFour[1] = 8
RowFour[2] = 7
RowFour[3] = 6
RowFour[4] = 0
RowFour[5] = 1
RowFour[6] = 5
RowFour[7] = 0
RowFour[8] = 4
IndexOfAll0ElementsInRowFour => [4,7]
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = [5,8]
EmptyColumnNamesRowFour = [ColumnFive,ColumnEight]

RowFive = [2,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 2
RowFive[1] = 0
RowFive[2] = 1
RowFive[3] = 0
RowFive[4] = 0
RowFive[5] = 3
RowFive[6] = 0
RowFive[7] = 0
RowFive[8] = 0
IndexOfAll0ElementsInRowFive => [1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [2,4,5,7,8,9]
EmptyColumnNamesRowFive = [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowSix = [5,6,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 5
RowSix[1] = 6
RowSix[2] = 9
RowSix[3] = 4
RowSix[4] = 0
RowSix[5] = 2
RowSix[6] = 0
RowSix[7] = 3
RowSix[8] = 0
IndexOfAll0ElementsInRowSix => [4,6,8]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [5,7,9]
EmptyColumnNamesRowSix = [ColumnFive,ColumnSeven,ColumnNine]

RowSeven = [1,3,4,7,2,5,6,8,9]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 1
RowSeven[1] = 3
RowSeven[2] = 4
RowSeven[3] = 7
RowSeven[4] = 2
RowSeven[5] = 5
RowSeven[6] = 6
RowSeven[7] = 8
RowSeven[8] = 9
IndexOfAll0ElementsInRowSeven => []
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = []
EmptyColumnNamesRowSeven = []

RowEight = [6,9,8,1,3,4,2,5,7]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 6
RowEight[1] = 9
RowEight[2] = 8
RowEight[3] = 1RowEight[4] = 3
RowEight[5] = 4
RowEight[6] = 2
RowEight[7] = 5
RowEight[8] = 7
IndexOfAll0ElementsInRowEight => []
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = []
EmptyColumnNamesRowEight = []

RowNine = [7,5,2,9,0,6,0,0,3]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 7
RowNine[1] = 5
RowNine[2] = 2
RowNine[3] = 9
RowNine[4] = 0
RowNine[5] = 6
RowNine[6] = 0
RowNine[7] = 0
RowNine[8] = 3
IndexOfAll0ElementsInRowNine => [4,6,7]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [5,7,8]
EmptyColumnNamesRowNine = [ColumnFive,ColumnSeven,ColumnEight]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 1 for each EmptyColumnNamesRowOne + 4 for each EmptyColumnNamesRowTwo + 5 for each EmptyColumnNamesRowThree + 2 for each EmptyColumnNamesRowFour + 6 for each EmptyColumnNamesRowFive + 3 for each EmptyColumnNamesRowSix + 0 for each EmptyColumnNamesRowSeven + 0 for each EmptyColumnNamesRowEight + 3 for each EmptyColumnNamesRowNine = 24

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 20

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnFive]
Note, the last empty column of the RowOne is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 20
Up to ColumnFive in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnFive
Last column of current row
RowOne and ColumnFive means BlockTwo
import CandidatesRowOne, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowOne = [4]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowOneAndColumnFive => [4] & [1,4,5,6,7,8,9] = [4]
CommonElementsOfRowOneAndColumnFiveAndBlockTwo => [4] & [1,4,5,6,7] = [4]
CellCandidates = [4]
Length = 1
FOUND RowOne, ColumnFive, BlockTwo

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnThree,ColumnFive,ColumnSix,ColumnEight]
Note, the last empty column of the RowTwo is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 2 of 20
Up to ColumnThree in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnEight
Not the last column of current row
RowTwo and ColumnThree means BlockOne
import CandidatesRowTwo, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnThree = [5,6]
CandidatesBlockOne = [5,6]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnThree => [5,6,7,9] & [5,6] = [5,6]
CommonElementsOfRowTwoAndColumnThreeAndBlockOne => [5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 3 of 20
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnEight
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [5,6,7,9] & [1,4,5,6,7,8,9] = [5,6,7,9]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [5,6,7,9] & [1,4,5,6,7] = [5,6,7]
CellCandidates = [5,6,7]
Length = 3
Not 1

### 4 of 20
Up to ColumnSix in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnEight
Not the last column of current row
RowTwo and ColumnSix means BlockTwo
import CandidatesRowTwo, CandidatesColumnSix, CandidatesBlockTwo
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnSix = [7]
CandidatesBlockTwo = [1,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnSix => [5,6,7,9] & [7] = [7]
CommonElementsOfRowTwoAndColumnSixAndBlockTwo => [7] & [1,4,5,6,7] = [7]
CellCandidates = [7]
Length = 1
FOUND RowTwo, ColumnSix, BlockTwo

### 5 of 20
Up to ColumnEight in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnEight
Last column of current row
The next row is RowThree
RowTwo and ColumnEight means BlockThree
import CandidatesRowTwo, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [2,4,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnEight => [5,6,7,9] & [1,2,4,7,9] = [7,9]
CommonElementsOfRowTwoAndColumnEightAndBlockThree => [7,9] & [2,4,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowTwo, ColumnEight, BlockThree

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnThree,ColumnFour,ColumnFive,ColumnEight,ColumnNine]
Note, the last empty column of the RowThree is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 6 of 20
Up to ColumnThree in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnThree means BlockOne
import CandidatesRowThree, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnThree = [5,6]
CandidatesBlockOne = [5,6]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnThree => [1,2,4,5,6] & [5,6] = [5,6]
CommonElementsOfRowThreeAndColumnThreeAndBlockOne => [5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 7 of 20
Up to ColumnFour in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFour means BlockTwo
import CandidatesRowThree, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnFour = [5,8]
CandidatesBlockTwo = [1,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFour => [1,2,4,5,6] & [5,8] = [5]
CommonElementsOfRowThreeAndColumnFourAndBlockTwo => [5] & [1,4,5,6,7] = [5]
CellCandidates = [5]
Length = 1
FOUND RowThree, ColumnFour, BlockTwo

### 8 of 20
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,2,4,5,6] & [1,4,5,6,7,8,9] = [1,4,5,6]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,4,5,6] & [1,4,5,6,7] = [1,4,5,6]
CellCandidates = [1,4,5,6]
Length = 4
Not 1

### 9 of 20
Up to ColumnEight in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnEight means BlockThree
import CandidatesRowThree, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [2,4,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnEight => [1,2,4,5,6] & [1,2,4,7,9] = [1,2,4]
CommonElementsOfRowThreeAndColumnEightAndBlockThree => [1,2,4] & [2,4,9] = [2,4]
CellCandidates = [2,4]
Length = 2
Not 1

### 10 of 20
Up to ColumnNine in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Last column of current row
The next row is RowFour
RowThree and ColumnNine means BlockThree
import CandidatesRowThree, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnNine = [2,6,8]
CandidatesBlockThree = [2,4,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnNine => [1,2,4,5,6] & [2,6,8] = [2]
CommonElementsOfRowThreeAndColumnNineAndBlockThree => [2] & [2,4,9] = [2]
CellCandidates = [2]
Length = 1
FOUND RowThree, ColumnNine, BlockThree

## RowFour Candidates
EmptyColumnNamesRowFour: [ColumnFive,ColumnEight]
Note, the last empty column of the RowFour is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFour and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFour and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFour and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 11 of 20
Up to ColumnFive in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Not the last column of current row
RowFour and ColumnFive means BlockFive
import CandidatesRowFour, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFour = [2,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowFourAndColumnFive => [2,9] & [1,4,5,6,7,8,9] = [9]
CommonElementsOfRowFourAndColumnFiveAndBlockFive => [9] & [5,7,8,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowFour, ColumnFive, BlockFive

### 12 of 20
Up to ColumnEight in EmptyColumnNamesRowFour
The last empty column of EmptyColumnNamesRowFour is ColumnEight
Last column of current row
The next row is RowFive
RowFour and ColumnEight means BlockSix
import CandidatesRowFour, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowFour = [2,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFourAndColumnEight => [2,9] & [1,2,4,7,9] = [2,9]
CommonElementsOfRowFourAndColumnEightAndBlockSix => [2,9] & [1,2,6,7,8,9] = [2,9]
CellCandidates = [2,9]
Length = 2
Not 1

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]
Note, the last empty column of the RowFive is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 13 of 20
Up to ColumnTwo in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnTwo means BlockFour
import CandidatesRowFive, CandidatesColumnTwo, CandidatesBlockFour
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnTwo = [4]
CandidatesBlockFour = [4]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnTwo => [4,5,6,7,8,9] & [4] = [4]
CommonElementsOfRowFiveAndColumnTwoAndBlockFour => [4] & [4] = [4]
CellCandidates = [4]
Length = 1
FOUND RowFive, ColumnTwo, BlockFour

### 14 of 20
Up to ColumnFour in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnFour means BlockFive
import CandidatesRowFive, CandidatesColumnFour, CandidatesBlockFive
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnFour = [5,8]
CandidatesBlockFive = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFour => [4,5,6,7,8,9] & [5,8] = [5,8]
CommonElementsOfRowFiveAndColumnFourAndBlockFive => [5,8] & [5,7,8,9] = [5,8]
CellCandidates = [5,8]
Length = 2
Not 1

### 15 of 20
Up to ColumnFive in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnFive means BlockFive
import CandidatesRowFive, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFive => [4,5,6,7,8,9] & [1,4,5,6,7,8,9] = [4,5,6,7,8,9]
CommonElementsOfRowFiveAndColumnFiveAndBlockFive => [4,5,6,7,8,9] & [5,7,8,9] = [5,7,8,9]
CellCandidates = [5,7,8,9]
Length = 4
Not 1

### 16 of 20
Up to ColumnSeven in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnSeven means BlockSix
import CandidatesRowFive, CandidatesColumnSeven, CandidatesBlockSix
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnSeven => [4,5,6,7,8,9] & [1,4,9] = [4,9]
CommonElementsOfRowFiveAndColumnSevenAndBlockSix => [4,9] & [1,2,6,7,8,9] = [4,9]
CellCandidates = [4,9]
Length = 2
Not 1

### 17 of 20
Up to ColumnEight in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnEight means BlockSix
import CandidatesRowFive, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnEight => [4,5,6,7,8,9] & [1,2,4,7,9] = [4,7,9]
CommonElementsOfRowFiveAndColumnEightAndBlockSix => [4,7,9] & [1,2,6,7,8,9] = [7,9]
CellCandidates = [7,9]
Length = 2
Not 1

### 18 of 20
Up to ColumnNine in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Last column of current row
The next row is RowSix
RowFive and ColumnNine means BlockSix
import CandidatesRowFive, CandidatesColumnNine, CandidatesBlockSix
CandidatesRowFive = [4,5,6,7,8,9]
CandidatesColumnNine = [2,6,8]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnNine => [4,5,6,7,8,9] & [2,6,8] = [6,8]
CommonElementsOfRowFiveAndColumnNineAndBlockSix => [6,8] & [1,2,6,7,8,9] = [6,8]
CellCandidates = [6,8]
Length = 2
Not 1

## RowSix Candidates
EmptyColumnNamesRowSix: [ColumnFive,ColumnSeven,ColumnNine]
Note, the last empty column of the RowSix is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSix and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowSix and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowSix and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 19 of 20
Up to ColumnFive in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnFive means BlockFive
import CandidatesRowSix, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowSix = [1,7,8]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFive => [1,7,8] & [1,4,5,6,7,8,9] = [1,7,8]
CommonElementsOfRowSixAndColumnFiveAndBlockFive => [1,7,8] & [5,7,8,9] = [7,8]
CellCandidates = [7,8]
Length = 2
Not 1

### 20 of 20
Up to ColumnSeven in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnNine
Not the last column of current row
RowSix and ColumnSeven means BlockSix
import CandidatesRowSix, CandidatesColumnSeven, CandidatesBlockSix
CandidatesRowSix = [1,7,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockSix = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowSixAndColumnSeven => [1,7,8] & [1,4,9] = [1]
CommonElementsOfRowSixAndColumnSevenAndBlockSix => [1] & [1,2,6,7,8,9] = [1]
CellCandidates = [1]
Length = 1
FOUND RowSix, ColumnSeven, BlockSix

Finished printing 20 of 20 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnFive, BlockTwo
2: FOUND RowTwo, ColumnSix, BlockTwo
3: FOUND RowTwo, ColumnEight, BlockThree
4: FOUND RowThree, ColumnFour, BlockTwo
5: FOUND RowThree, ColumnNine, BlockThree
6: FOUND RowFour, ColumnFive, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnFive, BlockTwo):
CandidatesRowOne = [4]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnSix, BlockTwo):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnSix = [7]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnEight, BlockThree):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [2,4,9]

cell(RowThree, ColumnFour, BlockTwo):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnFour = [5,8]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowThree, ColumnNine, BlockThree):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnNine = [2,6,8]
CandidatesBlockThree = [2,4,9]

cell(RowFour, ColumnFive, BlockFive):
CandidatesRowFour = [2,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:00:00.835484
Turn number: 10
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,0,8,7,6,5]
RowTwo: [4,2,0,3,0,0,8,0,1]
RowThree: [8,7,0,0,0,9,3,0,0]
RowFour: [3,8,7,6,0,1,5,0,4]
RowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,6,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,0,6,0,0,3]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: ## Collating Results, Six Max
1: FOUND RowOne, ColumnFive, BlockTwo
2: FOUND RowTwo, ColumnSix, BlockTwo
3: FOUND RowTwo, ColumnEight, BlockThree
4: FOUND RowThree, ColumnFour, BlockTwo
5: FOUND RowThree, ColumnNine, BlockThree
6: FOUND RowFour, ColumnFive, BlockFive
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnFive, BlockTwo):
CandidatesRowOne = [4]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnSix, BlockTwo):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnSix = [7]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnEight, BlockThree):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [2,4,9]

cell(RowThree, ColumnFour, BlockTwo):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnFour = [5,8]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowThree, ColumnNine, BlockThree):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnNine = [2,6,8]
CandidatesBlockThree = [2,4,9]

cell(RowFour, ColumnFive, BlockFive):
CandidatesRowFour = [2,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnFive):
CandidatesRowOne = [4]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnSix):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnSix = [7]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowTwo, ColumnEight):
CandidatesRowTwo = [5,6,7,9]
CandidatesColumnEight = [1,2,4,7,9]
CandidatesBlockThree = [2,4,9]

cell(RowThree, ColumnFour):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnFour = [5,8]
CandidatesBlockTwo = [1,4,5,6,7]

cell(RowThree, ColumnNine):
CandidatesRowThree = [1,2,4,5,6]
CandidatesColumnNine = [2,6,8]
CandidatesBlockThree = [2,4,9]

cell(RowFour, ColumnFive):
CandidatesRowFour = [2,9]
CandidatesColumnFive = [1,4,5,6,7,8,9]
CandidatesBlockFive = [5,7,8,9]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowOne, ColumnFive):
CandidatesRowOne.length = 1
CandidatesColumnFive.length = 7
CandidatesBlockTwo.length = 5

shortest_list = CandidatesRowOne = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [4], broken into CandidatesRowOneLow = [4] and CandidatesRowOneHigh = []
CandidatesColumnFive = [1,4,5,6,7,8,9], broken into CandidatesColumnFiveLow = [1,4,5] and CandidatesColumnFiveHigh = [6,7,8,9]
CandidatesBlockTwo = [1,4,5,6,7], broken into CandidatesBlockTwoLow = [1,4,5] and CandidatesBlockTwoHigh = [6,7]

Checking digits in CandidatesRowOneLow = [4] against: CandidatesColumnFiveLow = [1,4,5] and CandidatesBlockTwoLow = [1,4,5]
4: [1,4,5].count(4) = 1, [1,4,5].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowOneHigh = [] against: CandidatesColumnFiveHigh = [6,7,8,9] and CandidatesBlockTwoHigh = [6,7]

Confirmed candidates found for cell(RowOne, ColumnFive): [4]

## Cell 2 of 6
cell(RowTwo, ColumnSix):
CandidatesRowTwo.length = 4
CandidatesColumnSix.length = 1
CandidatesBlockTwo.length = 5

shortest_list = CandidatesColumnSix = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [5,6,7,9], broken into CandidatesRowTwoLow = [5] and CandidatesRowTwoHigh = [6,7,9]
CandidatesColumnSix = [7], broken into CandidatesColumnSixLow = [] and CandidatesColumnSixHigh = [7]
CandidatesBlockTwo = [1,4,5,6,7], broken into CandidatesBlockTwoLow = [1,4,5] and CandidatesBlockTwoHigh = [6,7]

Checking digits in CandidatesColumnSixLow = [] against: CandidatesRowTwoLow = [5] and CandidatesBlockTwoLow = [1,4,5]

Checking digits in CandidatesColumnSixHigh = [7] against: CandidatesRowTwoHigh = [6,7,9] and CandidatesBlockTwoHigh = [6,7]
7: [6,7,9].count(7) = 1, [6,7].count(7) = 1, TotalCount(7) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnSix): [7]

## Cell 3 of 6
cell(RowTwo, ColumnEight):
CandidatesRowTwo.length = 4
CandidatesColumnEight.length = 5
CandidatesBlockThree.length = 3

shortest_list = CandidatesBlockThree = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesColumnEight

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [5,6,7,9], broken into CandidatesRowTwoLow = [5] and CandidatesRowTwoHigh = [6,7,9]
CandidatesColumnEight = [1,2,4,7,9], broken into CandidatesColumnEightLow = [1,2,4] and CandidatesColumnEightHigh = [7,9]
CandidatesBlockThree = [2,4,9], broken into CandidatesBlockThreeLow = [2,4] and CandidatesBlockThreeHigh = [9]

Checking digits in CandidatesBlockThreeLow = [2,4] against: CandidatesRowTwoLow = [5] and CandidatesColumnEightLow = [1,2,4]
2: [5].count(2) = 0, [1,2,4].count(2) = 1, TotalCount(2) = 1
4: [5].count(4) = 0, [1,2,4].count(4) = 1, TotalCount(4) = 1

Checking digits in CandidatesBlockThreeHigh = [9] against: CandidatesRowTwoHigh = [6,7,9] and CandidatesColumnEightHigh = [7,9]
9: [6,7,9].count(9) = 1, [7,9].count(9) = 1, TotalCount(9) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnEight): [9]

## Cell 4 of 6
cell(RowThree, ColumnFour):
CandidatesRowThree.length = 5
CandidatesColumnFour.length = 2
CandidatesBlockTwo.length = 5

shortest_list = CandidatesColumnFour = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,5,6], broken into CandidatesRowThreeLow = [1,2,4,5] and CandidatesRowThreeHigh = [6]
CandidatesColumnFour = [5,8], broken into CandidatesColumnFourLow = [5] and CandidatesColumnFourHigh = [8]
CandidatesBlockTwo = [1,4,5,6,7], broken into CandidatesBlockTwoLow = [1,4,5] and CandidatesBlockTwoHigh = [6,7]

Checking digits in CandidatesColumnFourLow = [5] against: CandidatesRowThreeLow = [1,2,4,5] and CandidatesBlockTwoLow = [1,4,5]
5: [1,2,4,5].count(5) = 1, [1,4,5].count(5) = 1, TotalCount(5) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnFourHigh = [8] against: CandidatesRowThreeHigh = [6] and CandidatesBlockTwoHigh = [6,7]
8: [6].count(8) = 0, [6,7].count(8) = 0, TotalCount(8) = 0

Confirmed candidates found for cell(RowThree, ColumnFour): [5]

## Cell 5 of 6
cell(RowThree, ColumnNine):
CandidatesRowThree.length = 5
CandidatesColumnNine.length = 3
CandidatesBlockThree.length = 3

shortest_list = CandidatesBlockThree = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesColumnNine

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,2,4,5,6], broken into CandidatesRowThreeLow = [1,2,4,5] and CandidatesRowThreeHigh = [6]
CandidatesColumnNine = [2,6,8], broken into CandidatesColumnNineLow = [2] and CandidatesColumnNineHigh = [6,8]
CandidatesBlockThree = [2,4,9], broken into CandidatesBlockThreeLow = [2,4] and CandidatesBlockThreeHigh = [9]

Checking digits in CandidatesBlockThreeLow = [2,4] against: CandidatesRowThreeLow = [1,2,4,5] and CandidatesColumnNineLow = [2]
2: [1,2,4,5].count(2) = 1, [2].count(2) = 1, TotalCount(2) = 2 FOUND A CANDIDATE
4: [1,2,4,5].count(4) = 1, [2].count(4) = 0, TotalCount(4) = 1

Checking digits in CandidatesBlockThreeHigh = [9] against: CandidatesRowThreeHigh = [6] and CandidatesColumnNineHigh = [6,8]
9: [6].count(9) = 0, [6,8].count(9) = 0, TotalCount(9) = 0

Confirmed candidates found for cell(RowThree, ColumnNine): [2]

## Cell 6 of 6
cell(RowFour, ColumnFive):
CandidatesRowFour.length = 2
CandidatesColumnFive.length = 7
CandidatesBlockFive.length = 4

shortest_list = CandidatesRowFour = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFour = [2,9], broken into CandidatesRowFourLow = [2] and CandidatesRowFourHigh = [9]
CandidatesColumnFive = [1,4,5,6,7,8,9], broken into CandidatesColumnFiveLow = [1,4,5] and CandidatesColumnFiveHigh = [6,7,8,9]
CandidatesBlockFive = [5,7,8,9], broken into CandidatesBlockFiveLow = [5] and CandidatesBlockFiveHigh = [7,8,9]

Checking digits in CandidatesRowFourLow = [2] against: CandidatesColumnFiveLow = [1,4,5] and CandidatesBlockFiveLow = [5]
2: [1,4,5].count(2) = 0, [5].count(2) = 0, TotalCount(2) = 0

Checking digits in CandidatesRowFourHigh = [9] against: CandidatesColumnFiveHigh = [6,7,8,9] and CandidatesBlockFiveHigh = [7,8,9]
9: [6,7,8,9].count(9) = 1, [7,8,9].count(9) = 1, TotalCount(9) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowFour, ColumnFive): [9]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnFive): [4]
[4].length = 1
length is 1, Passes

cell(RowTwo, ColumnSix): [7]
[7].length = 1
length is 1, Passes

cell(RowTwo, ColumnEight): [9]
[9].length = 1
length is 1, Passes

cell(RowThree, ColumnFour): [5]
[5].length = 1
length is 1, Passes

cell(RowThree, ColumnNine): [2]
[2].length = 1
length is 1, Passes

cell(RowFour, ColumnFive): [9]
[9].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnFive): [4]
cell(RowTwo, ColumnSix): [7]
cell(RowTwo, ColumnEight): [9]
cell(RowThree, ColumnFour): [5]
cell(RowThree, ColumnNine): [2]
cell(RowFour, ColumnFive): [9]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowTwo, RowThree, RowFour

RowOne: [9,1,3,2,0,8,7,6,5]
cell(RowOne, ColumnFive): [4]

RowTwo: [4,2,0,3,0,0,8,0,1]
cell(RowTwo, ColumnSix): [7]
cell(RowTwo, ColumnEight): [9]

RowThree: [8,7,0,0,0,9,3,0,0]
cell(RowThree, ColumnFour): [5]
cell(RowThree, ColumnNine): [2]

RowFour: [3,8,7,6,0,1,5,0,4]
cell(RowFour, ColumnFive): [9]

RowFive: [2,0,1,0,0,3,0,0,0]

RowSix: [5,6,9,4,0,2,0,3,0]

RowSeven: [1,3,4,7,2,5,6,8,9]

RowEight: [6,9,8,1,3,4,2,5,7]

RowNine: [7,5,2,9,0,6,0,0,3]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowOne, ColumnFive): [4]
RowOne = [9,1,3,2,0,8,7,6,5]
The ColumnFive element of RowOne needs to be updated to [4]

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 2
ColumnFive: 0
ColumnSix: 8
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Now replacing ColumnFive with the element to update [4], such that ColumnFive = 4
Redoing column list like we just did, but with ColumnFive set to 4

ColumnOne: 9
ColumnTwo: 1
ColumnThree: 3
ColumnFour: 2
ColumnFive: 4
ColumnSix: 8
ColumnSeven: 7
ColumnEight: 6
ColumnNine: 5

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowOne:
PreCellList = [9,1,3,2]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [9,1,3,2,4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [9,1,3,2,4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [9,1,3,2,4,8,7,6,5]

## Updating 2 of 6
cell(RowTwo, ColumnSix): [7]
RowTwo = [4,2,0,3,0,0,8,0,1]
The ColumnSix element of RowTwo needs to be updated to [7]

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 0
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 1

Now replacing ColumnSix with the element to update [7], such that ColumnSix = 7
Redoing column list like we just did, but with ColumnSix set to 7

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 1

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSix.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSix it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSix (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSix does Not appear on this list!!! The ONLY time you don't is if ColumnSix is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSix:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
Now the elements of the columns in PreCellColumnsList, which is the first 5 elements of RowTwo:
PreCellList = [4,2,0,3,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [7] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(7) = [4,2,0,3,0,7]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [4,2,0,3,0,7,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 5 + 1 = 6 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [4,2,0,3,0,7,8,0,1]

## Updating 3 of 6
cell(RowTwo, ColumnEight): [9]
RowTwo = [4,2,0,3,0,7,8,0,1]
The ColumnEight element of RowTwo needs to be updated to [9]

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 0
ColumnNine: 1

Now replacing ColumnEight with the element to update [9], such that ColumnEight = 9
Redoing column list like we just did, but with ColumnEight set to 9

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 9
ColumnNine: 1

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnEight it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnEight does Not appear on this list!!! The ONLY time you don't is if ColumnEight is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnEight:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowTwo:
PreCellList = [4,2,0,3,0,7,8]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [9] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(9) = [4,2,0,3,0,7,8,9]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [4,2,0,3,0,7,8,9,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 7 + 1 = 8 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [4,2,0,3,0,7,8,9,1]

## Updating 4 of 6
cell(RowThree, ColumnFour): [5]
RowThree = [8,7,0,0,0,9,3,0,0]
The ColumnFour element of RowThree needs to be updated to [5]

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 0
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnFour with the element to update [5], such that ColumnFour = 5
Redoing column list like we just did, but with ColumnFour set to 5

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFour.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFour it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFour (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFour does Not appear on this list!!! The ONLY time you don't is if ColumnFour is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFour:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree].length = 3
Now the elements of the columns in PreCellColumnsList, which is the first 3 elements of RowThree:
PreCellList = [8,7,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [5] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(5) = [8,7,0,5]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [8,7,0,5,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 3 + 1 = 4 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [8,7,0,5,0,9,3,0,2]

## Updating 5 of 6
cell(RowThree, ColumnNine): [2]
RowThree = [8,7,0,5,0,9,3,0,0]
The ColumnNine element of RowThree needs to be updated to [2]

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnNine with the element to update [2], such that ColumnNine = 2
Redoing column list like we just did, but with ColumnNine set to 2

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 2

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnNine.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnNine it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnNine (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnNine does Not appear on this list!!! The ONLY time you don't is if ColumnNine is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnNine:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight].length = 8
Now the elements of the columns in PreCellColumnsList, which is the first 8 elements of RowThree:
PreCellList = [8,7,0,5,0,9,3,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [2] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(2) = [8,7,0,5,0,9,3,0,2]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [8,7,0,5,0,9,3,0,2,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 8 + 1 = 9 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [8,7,0,5,0,9,3,0,2]

## Updating 6 of 6
cell(RowFour, ColumnFive): [9]
RowFour = [3,8,7,6,0,1,5,0,4]
The ColumnFive element of RowFour needs to be updated to [9]

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 7
ColumnFour: 6
ColumnFive: 0
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Now replacing ColumnFive with the element to update [9], such that ColumnFive = 9
Redoing column list like we just did, but with ColumnFive set to 9

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 7
ColumnFour: 6
ColumnFive: 9
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowFour:
PreCellList = [3,8,7,6]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [9] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(9) = [3,8,7,6,9]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFourStartingElements = [3,8,7,6,9,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFour = [3,8,7,6,9,1,5,0,4]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [9,1,3,2,4,8,7,6,5]
UpdatedRowTwo = [4,2,0,3,0,7,8,9,1]
UpdatedRowThree = [8,7,0,5,0,9,3,0,2]
UpdatedRowFour = [3,8,7,6,9,1,5,0,4]

The rows to update are RowOne, RowTwo, RowThree, RowFour
Using the contents of UpdatedRowOne, UpdatedRowTwo, UpdatedRowThree, UpdatedRowFour
Printing Sudoku:
UpdatedRowOne: [9,1,3,2,4,8,7,6,5]
UpdatedRowTwo: [4,2,0,3,0,7,8,9,1]
UpdatedRowThree: [8,7,0,5,0,9,3,0,2]
UpdatedRowFour: [3,8,7,6,9,1,5,0,4]
RowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,6,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,0,6,0,0,3]

# STEP_SEVEN: Shifting the Rows of the Sudoku
UpdatedRowFour: [3,8,7,6,9,1,5,0,4]
RowFive: [2,0,1,0,0,3,0,0,0]
RowSix: [5,6,9,4,0,2,0,3,0]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,0,6,0,0,3]
UpdatedRowOne: [9,1,3,2,4,8,7,6,5]
UpdatedRowTwo: [4,2,0,3,0,7,8,9,1]
UpdatedRowThree: [8,7,0,5,0,9,3,0,2]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [3,8,7,6,9,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,6,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:13:50.737064
Turn number: 11
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [3,8,7,6,9,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,6,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [3,8,7,6,9,1,5,0,4]
RowTwo = [2,0,1,0,0,3,0,0,0]
RowThree = [5,6,9,4,0,2,0,3,0]
RowFour = [1,3,4,7,2,5,6,8,9]
RowFive = [6,9,8,1,3,4,2,5,7]
RowSix = [7,5,2,9,0,6,0,0,3]
RowSeven = [9,1,3,2,4,8,7,6,5]
RowEight = [4,2,0,3,0,7,8,9,1]
RowNine = [8,7,0,5,0,9,3,0,2]

# Columns
ColumnOne = [3,2,5,1,6,7,9,4,8]
ColumnTwo = [8,0,6,3,9,5,1,2,7]
ColumnThree = [7,1,9,4,8,2,3,0,0]
ColumnFour = [6,0,4,7,1,9,2,3,5]
ColumnFive = [9,0,0,2,3,0,4,0,0]
ColumnSix = [1,3,2,5,4,6,8,7,9]
ColumnSeven = [5,0,0,6,2,0,7,8,3]
ColumnEight = [0,0,3,8,5,0,6,9,0]
ColumnNine = [4,0,0,9,7,3,5,1,2]

# Blocks
BlockOne:
[[3,8,7],
[2,0,1],
[5,6,9]]
BlockOne = [3,8,7,2,0,1,5,6,9]

BlockTwo:
[[6,9,1],
[0,0,3],
[4,0,2]]
BlockTwo = [6,9,1,0,0,3,4,0,2]

BlockThree:
[[5,0,4],
[0,0,0],
[0,3,0]]
BlockThree = [5,0,4,0,0,0,0,3,0]

BlockFour:
[[1,3,4],
[6,9,8],
[7,5,2]]
BlockFour = [1,3,4,6,9,8,7,5,2]

BlockFive:
[[7,2,5],
[1,3,4],
[9,0,6]]
BlockFive = [7,2,5,1,3,4,9,0,6]

BlockSix:
[[6,8,9],
[2,5,7],
[0,0,3]]
BlockSix = [6,8,9,2,5,7,0,0,3]

BlockSeven:
[[9,1,3],
[4,2,0],
[8,7,0]]
BlockSeven = [9,1,3,4,2,0,8,7,0]

BlockEight:
[[2,4,8],
[3,0,7],
[5,0,9]]
BlockEight = [2,4,8,3,0,7,5,0,9]

BlockNine:
[[7,6,5],
[8,9,1],
[3,0,2]]
BlockNine = [7,6,5,8,9,1,3,0,2]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,6,9,1,5,0,4]) = [2]
CandidatesRowOne = [2]
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([2,0,1,0,0,3,0,0,0]) = [4,5,6,7,8,9]
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([5,6,9,4,0,2,0,3,0]) = [1,7,8]
CandidatesRowThree = [1,7,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,5,6,8,9]) = []
CandidatesRowFour = []
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,1,3,4,2,5,7]) = []
CandidatesRowFive = []
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([7,5,2,9,0,6,0,0,3]) = [1,4,8]
CandidatesRowSix = [1,4,8]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,2,4,8,7,6,5]) = []
CandidatesRowSeven = []
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,7,8,9,1]) = [5,6]
CandidatesRowEight = [5,6]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([8,7,0,5,0,9,3,0,2]) = [1,4,6]
CandidatesRowNine = [1,4,6]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([3,2,5,1,6,7,9,4,8]) = []
CandidatesColumnOne = []
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([8,0,6,3,9,5,1,2,7]) = [4]
CandidatesColumnTwo = [4]
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([7,1,9,4,8,2,3,0,0]) = [5,6]
CandidatesColumnThree = [5,6]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([6,0,4,7,1,9,2,3,5]) = [8]
CandidatesColumnFour = [8]
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([9,0,0,2,3,0,4,0,0]) = [1,5,6,7,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([1,3,2,5,4,6,8,7,9]) = []
CandidatesColumnSix = []
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([5,0,0,6,2,0,7,8,3]) = [1,4,9]
CandidatesColumnSeven = [1,4,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([0,0,3,8,5,0,6,9,0]) = [1,2,4,7]
CandidatesColumnEight = [1,2,4,7]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([4,0,0,9,7,3,5,1,2]) = [6,8]
CandidatesColumnNine = [6,8]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,2,0,1,5,6,9]) = [4]
CandidatesBlockOne = [4]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([6,9,1,0,0,3,4,0,2]) = [5,7,8]
CandidatesBlockTwo = [5,7,8]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([5,0,4,0,0,0,0,3,0]) = [1,2,6,7,8,9]
CandidatesBlockThree = [1,2,6,7,8,9]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,2]) = []
CandidatesBlockFour = []
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([7,2,5,1,3,4,9,0,6]) = [8]
CandidatesBlockFive = [8]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([6,8,9,2,5,7,0,0,3]) = [1,4]
CandidatesBlockSix = [1,4]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,0]) = [5,6]
CandidatesBlockSeven = [5,6]
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([2,4,8,3,0,7,5,0,9]) = [1,6]
CandidatesBlockEight = [1,6]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,9,1,3,0,2]) = [4]
CandidatesBlockNine = [4]

# Index of all zeros, by row
RowOne = [3,8,7,6,9,1,5,0,4]
Now finding the index of Each 0 element in RowOne
RowOne[0] = 3
RowOne[1] = 8
RowOne[2] = 7
RowOne[3] = 6
RowOne[4] = 9
RowOne[5] = 1
RowOne[6] = 5
RowOne[7] = 0
RowOne[8] = 4
IndexOfAll0ElementsInRowOne => [7]
ColumnPositionOfAll0ElementsRowOne => map(element+1, IndexOfAll0ElementsInRowOne) = [8]
EmptyColumnNamesRowOne = [ColumnEight]

RowTwo = [2,0,1,0,0,3,0,0,0]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 2
RowTwo[1] = 0
RowTwo[2] = 1
RowTwo[3] = 0
RowTwo[4] = 0
RowTwo[5] = 3
RowTwo[6] = 0
RowTwo[7] = 0
RowTwo[8] = 0
IndexOfAll0ElementsInRowTwo => [1,3,4,6,7,8]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [2,4,5,7,8,9]
EmptyColumnNamesRowTwo = [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]

RowThree = [5,6,9,4,0,2,0,3,0]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 5
RowThree[1] = 6
RowThree[2] = 9
RowThree[3] = 4
RowThree[4] = 0
RowThree[5] = 2
RowThree[6] = 0
RowThree[7] = 3
RowThree[8] = 0
IndexOfAll0ElementsInRowThree => [4,6,8]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [5,7,9]
EmptyColumnNamesRowThree = [ColumnFive,ColumnSeven,ColumnNine]

RowFour = [1,3,4,7,2,5,6,8,9]
Now finding the index of Each 0 element in RowFour
RowFour[0] = 1
RowFour[1] = 3
RowFour[2] = 4
RowFour[3] = 7
RowFour[4] = 2
RowFour[5] = 5
RowFour[6] = 6
RowFour[7] = 8
RowFour[8] = 9
IndexOfAll0ElementsInRowFour => []
ColumnPositionOfAll0ElementsRowFour => map(element+1, IndexOfAll0ElementsInRowFour) = []
EmptyColumnNamesRowFour = []

RowFive = [6,9,8,1,3,4,2,5,7]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 6
RowFive[1] = 9
RowFive[2] = 8
RowFive[3] = 1
RowFive[4] = 3
RowFive[5] = 4
RowFive[6] = 2
RowFive[7] = 5
RowFive[8] = 7
IndexOfAll0ElementsInRowFive => []
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = []
EmptyColumnNamesRowFive = []

RowSix = [7,5,2,9,0,6,0,0,3]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 7
RowSix[1] = 5
RowSix[2] = 2
RowSix[3] = 9
RowSix[4] = 0
RowSix[5] = 6
RowSix[6] = 0
RowSix[7] = 0
RowSix[8] = 3
IndexOfAll0ElementsInRowSix => [4,6,7]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [5,7,8]
EmptyColumnNamesRowSix = [ColumnFive,ColumnSeven,ColumnEight]

RowSeven = [9,1,3,2,4,8,7,6,5]
Now finding the index of Each 0 element in RowSeven
RowSeven[0] = 9
RowSeven[1] = 1
RowSeven[2] = 3
RowSeven[3] = 2
RowSeven[4] = 4
RowSeven[5] = 8
RowSeven[6] = 7
RowSeven[7] = 6
RowSeven[8] = 5
IndexOfAll0ElementsInRowSeven => []
ColumnPositionOfAll0ElementsRowSeven => map(element+1, IndexOfAll0ElementsInRowSeven) = []
EmptyColumnNamesRowSeven = []

RowEight = [4,2,0,3,0,7,8,9,1]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 4
RowEight[1] = 2
RowEight[2] = 0
RowEight[3] = 3
RowEight[4] = 0
RowEight[5] = 7
RowEight[6] = 8
RowEight[7] = 9
RowEight[8] = 1
IndexOfAll0ElementsInRowEight => [2,4]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [3,5]
EmptyColumnNamesRowEight = [ColumnThree,ColumnFive]

RowNine = [8,7,0,5,0,9,3,0,2]
Now finding the index ofEach 0 element in RowNine
RowNine[0] = 8
RowNine[1] = 7
RowNine[2] = 0
RowNine[3] = 5
RowNine[4] = 0
RowNine[5] = 9
RowNine[6] = 3
RowNine[7] = 0
RowNine[8] = 2
IndexOfAll0ElementsInRowNine => [2,4,7]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [3,5,8]
EmptyColumnNamesRowNine = [ColumnThree,ColumnFive,ColumnEight]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 1 for each EmptyColumnNamesRowOne + 6 for each EmptyColumnNamesRowTwo + 3 for each EmptyColumnNamesRowThree + 0 for each EmptyColumnNamesRowFour + 0 for each EmptyColumnNamesRowFive + 3 for each EmptyColumnNamesRowSix + 0 for each EmptyColumnNamesRowSeven + 2 for each EmptyColumnNamesRowEight + 3 for each EmptyColumnNamesRowNine = 18

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 18

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowOne Candidates
EmptyColumnNamesRowOne: [ColumnEight]
Note, the last empty column of the RowOne is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowOne and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowOne and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowOne and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 18
Up to ColumnEight in EmptyColumnNamesRowOne
The last empty column of EmptyColumnNamesRowOne is ColumnEight
Last column of current row
RowOne and ColumnEight means BlockThree
import CandidatesRowOne, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowOne = [2]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowOneAndColumnEight => [2] & [1,2,4,7] = [2]
CommonElementsOfRowOneAndColumnEightAndBlockThree => [2] & [1,2,6,7,8,9] = [2]
CellCandidates = [2]
Length = 1
FOUND RowOne, ColumnEight, BlockThree

## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnTwo,ColumnFour,ColumnFive,ColumnSeven,ColumnEight,ColumnNine]
Note, the last empty column of the RowTwo is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 2 of 18
Up to ColumnTwo in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnTwo means BlockOne
import CandidatesRowTwo, CandidatesColumnTwo, CandidatesBlockOne
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnTwo = [4]
CandidatesBlockOne = [4]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnTwo => [4,5,6,7,8,9] & [4] = [4]
CommonElementsOfRowTwoAndColumnTwoAndBlockOne => [4] & [4] = [4]
CellCandidates = [4]
Length = 1
FOUND RowTwo, ColumnTwo, BlockOne

### 3 of 18
Up to ColumnFour in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFour means BlockTwo
import CandidatesRowTwo, CandidatesColumnFour, CandidatesBlockTwo
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFour = [8]
CandidatesBlockTwo = [5,7,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFour => [4,5,6,7,8,9] & [8] = [8]
CommonElementsOfRowTwoAndColumnFourAndBlockTwo => [8] & [5,7,8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowTwo, ColumnFour, BlockTwo

### 4 of 18
Up to ColumnFive in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnFive means BlockTwo
import CandidatesRowTwo, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [5,7,8]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnFive => [4,5,6,7,8,9] & [1,5,6,7,8] = [5,6,7,8]
CommonElementsOfRowTwoAndColumnFiveAndBlockTwo => [5,6,7,8] & [5,7,8] = [5,7,8]
CellCandidates = [5,7,8]
Length = 3
Not 1

### 5 of 18
Up to ColumnSeven in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnSeven means BlockThree
import CandidatesRowTwo, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnSeven => [4,5,6,7,8,9] & [1,4,9] = [4,9]
CommonElementsOfRowTwoAndColumnSevenAndBlockThree => [4,9] & [1,2,6,7,8,9] = [4,9]
CellCandidates = [4,9]
Length = 2
Not 1

### 6 of 18
Up to ColumnEight in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Not the last column of current row
RowTwo and ColumnEight means BlockThree
import CandidatesRowTwo, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnEight => [4,5,6,7,8,9] & [1,2,4,7] = [4,7]
CommonElementsOfRowTwoAndColumnEightAndBlockThree => [4,7] & [1,2,6,7,8,9] = [7]
CellCandidates = [7]
Length = 1
FOUND RowTwo, ColumnEight, BlockThree

### 7 of 18
Up to ColumnNine in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnNine
Last column of current row
The next row is RowThree
RowTwo and ColumnNine means BlockThree
import CandidatesRowTwo, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnNine = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnNine => [4,5,6,7,8,9] & [6,8] = [6,8]
CommonElementsOfRowTwoAndColumnNineAndBlockThree => [6,8] & [1,2,6,7,8,9] = [6,8]
CellCandidates = [6,8]
Length = 2
Not 1

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnFive,ColumnSeven,ColumnNine]
Note, the last empty column of the RowThree is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 8 of 18
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,7,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [5,7,8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,7,8] & [1,5,6,7,8] = [1,7,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,7,8] & [5,7,8] = [7,8]
CellCandidates = [7,8]
Length = 2
Not 1

### 9 of 18
Up to ColumnSeven in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Not the last column of current row
RowThree and ColumnSeven means BlockThree
import CandidatesRowThree, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowThree = [1,7,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSeven => [1,7,8] & [1,4,9] = [1]
CommonElementsOfRowThreeAndColumnSevenAndBlockThree => [1] & [1,2,6,7,8,9] = [1]
CellCandidates = [1]
Length = 1
FOUND RowThree, ColumnSeven, BlockThree

### 10 of 18
Up to ColumnNine in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnNine
Last column of current row
The next row is RowSix
RowThree and ColumnNine means BlockThree
import CandidatesRowThree, CandidatesColumnNine, CandidatesBlockThree
CandidatesRowThree = [1,7,8]
CandidatesColumnNine = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnNine => [1,7,8] & [6,8] = [8]
CommonElementsOfRowThreeAndColumnNineAndBlockThree => [8] & [1,2,6,7,8,9] = [8]
CellCandidates = [8]
Length = 1
FOUND RowThree, ColumnNine, BlockThree

## RowSix Candidates
EmptyColumnNamesRowSix: [ColumnFive,ColumnSeven,ColumnEight]
Note, the last empty column of the RowSix is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSix and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowSix and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowSix and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 11 of 18
Up to ColumnFive in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Not the last column of current row
RowSix and ColumnFive means BlockFive
import CandidatesRowSix, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowSix = [1,4,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [8]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFive => [1,4,8] & [1,5,6,7,8] = [1,8]
CommonElementsOfRowSixAndColumnFiveAndBlockFive => [1,8] & [8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowSix, ColumnFive, BlockFive

### 12 of 18
Up to ColumnSeven in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Not the last column of current row
RowSix and ColumnSeven means BlockSix
import CandidatesRowSix, CandidatesColumnSeven, CandidatesBlockSix
CandidatesRowSix = [1,4,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockSix = [1,4]
Finding Common Elements:
CommonElementsOfRowSixAndColumnSeven => [1,4,8] & [1,4,9] = [1,4]
CommonElementsOfRowSixAndColumnSevenAndBlockSix => [1,4] & [1,4] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

### 13 of 18
Up to ColumnEight in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Last column of current row
The next row is RowEight
RowSix and ColumnEight means BlockSix
import CandidatesRowSix, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowSix = [1,4,8]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockSix = [1,4]
Finding Common Elements:
CommonElementsOfRowSixAndColumnEight => [1,4,8] & [1,2,4,7] = [1,4]
CommonElementsOfRowSixAndColumnEightAndBlockSix => [1,4] & [1,4] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

## RowEight Candidates
EmptyColumnNamesRowEight: [ColumnThree,ColumnFive]
Note, the last empty column of the RowEight is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowEight and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowEight and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowEight and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 14 of 18
Up to ColumnThree in EmptyColumnNamesRowEight
The last empty column of EmptyColumnNamesRowEight is ColumnFive
Not the last column of current row
RowEight and ColumnThree means BlockSeven
import CandidatesRowEight, CandidatesColumnThree, CandidatesBlockSeven
CandidatesRowEight = [5,6]
CandidatesColumnThree = [5,6]
CandidatesBlockSeven = [5,6]
Finding Common Elements:
CommonElementsOfRowEightAndColumnThree => [5,6] & [5,6] = [5,6]
CommonElementsOfRowEightAndColumnThreeAndBlockSeven => [5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 15 of 18
Up to ColumnFive in EmptyColumnNamesRowEight
The last empty column of EmptyColumnNamesRowEight is ColumnFive
Last column of current row
The next row is RowNine
RowEight and ColumnFive means BlockEight
import CandidatesRowEight, CandidatesColumnFive, CandidatesBlockEight
CandidatesRowEight = [5,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [1,6]
Finding Common Elements:
CommonElementsOfRowEightAndColumnFive => [5,6] & [1,5,6,7,8] = [5,6]
CommonElementsOfRowEightAndColumnFiveAndBlockEight => [5,6] & [1,6] = [6]
CellCandidates = [6]
Length = 1
FOUND RowEight, ColumnFive, BlockEight

## RowNine Candidates
EmptyColumnNamesRowNine: [ColumnThree,ColumnFive,ColumnEight]
Note, the last empty column of the RowNine is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowNine and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowNine and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowNine and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 16 of 18
Up to ColumnThree in EmptyColumnNamesRowNine
The last empty column of EmptyColumnNamesRowNine is ColumnEight
Not the last column of current row
RowNine and ColumnThree means BlockSeven
import CandidatesRowNine, CandidatesColumnThree, CandidatesBlockSeven
CandidatesRowNine = [1,4,6]
CandidatesColumnThree = [5,6]
CandidatesBlockSeven = [5,6]
Finding Common Elements:
CommonElementsOfRowNineAndColumnThree => [1,4,6] & [5,6] = [6]
CommonElementsOfRowNineAndColumnThreeAndBlockSeven => [6] & [5,6] = [6]
CellCandidates = [6]
Length = 1
FOUND RowNine, ColumnThree, BlockSeven

### 17 of 18
Up to ColumnFive in EmptyColumnNamesRowNine
The last empty column of EmptyColumnNamesRowNine is ColumnEight
Not the last column of current row
RowNine and ColumnFive means BlockEight
import CandidatesRowNine, CandidatesColumnFive, CandidatesBlockEight
CandidatesRowNine = [1,4,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [1,6]
Finding Common Elements:
CommonElementsOfRowNineAndColumnFive => [1,4,6] & [1,5,6,7,8] = [1,6]
CommonElementsOfRowNineAndColumnFiveAndBlockEight => [1,6] & [1,6] = [1,6]
CellCandidates = [1,6]
Length = 2
Not 1

### 18 of 18
Up to ColumnEight in EmptyColumnNamesRowNine
The last empty column of EmptyColumnNamesRowNine is ColumnEight
Last column of current row
RowNine and ColumnEight means BlockNine
import CandidatesRowNine, CandidatesColumnEight, CandidatesBlockNine
CandidatesRowNine = [1,4,6]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockNine = [4]
Finding Common Elements:
CommonElementsOfRowNineAndColumnEight => [1,4,6] & [1,2,4,7] = [1,4]
CommonElementsOfRowNineAndColumnEightAndBlockNine => [1,4] & [4] = [4]
CellCandidates = [4]
Length = 1
FOUND RowNine, ColumnEight, BlockNine

Finished printing 18 of 18 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnEight, BlockThree
2: FOUND RowTwo, ColumnTwo, BlockOne
3: FOUND RowTwo, ColumnFour, BlockTwo
4: FOUND RowTwo, ColumnEight, BlockThree
5: FOUND RowThree, ColumnSeven, BlockThree
6: FOUND RowThree, ColumnNine, BlockThree
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnEight, BlockThree):
CandidatesRowOne = [2]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowTwo, ColumnTwo, BlockOne):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnTwo = [4]
CandidatesBlockOne = [4]

cell(RowTwo, ColumnFour, BlockTwo):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFour = [8]
CandidatesBlockTwo = [5,7,8]

cell(RowTwo, ColumnEight, BlockThree):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnSeven, BlockThree):
CandidatesRowThree = [1,7,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnNine, BlockThree):
CandidatesRowThree = [1,7,8]
CandidatesColumnNine = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:22:55.127729
Turn number: 12
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [3,8,7,6,9,1,5,0,4]
RowTwo: [2,0,1,0,0,3,0,0,0]
RowThree: [5,6,9,4,0,2,0,3,0]
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: # Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowOne, ColumnEight, BlockThree
2: FOUND RowTwo, ColumnTwo, BlockOne
3: FOUND RowTwo, ColumnFour, BlockTwo
4: FOUND RowTwo, ColumnEight, BlockThree
5: FOUND RowThree, ColumnSeven, BlockThree
6: FOUND RowThree, ColumnNine, BlockThree
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowOne, ColumnEight, BlockThree):
CandidatesRowOne = [2]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowTwo, ColumnTwo, BlockOne):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnTwo = [4]
CandidatesBlockOne = [4]

cell(RowTwo, ColumnFour, BlockTwo):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFour = [8]
CandidatesBlockTwo = [5,7,8]

cell(RowTwo, ColumnEight, BlockThree):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnSeven, BlockThree):
CandidatesRowThree = [1,7,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnNine, BlockThree):
CandidatesRowThree = [1,7,8]
CandidatesColumnNine = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowOne, ColumnEight):
CandidatesRowOne = [2]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowTwo, ColumnTwo):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnTwo = [4]
CandidatesBlockOne = [4]

cell(RowTwo, ColumnFour):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnFour = [8]
CandidatesBlockTwo = [5,7,8]

cell(RowTwo, ColumnEight):
CandidatesRowTwo = [4,5,6,7,8,9]
CandidatesColumnEight = [1,2,4,7]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnSeven):
CandidatesRowThree = [1,7,8]
CandidatesColumnSeven = [1,4,9]
CandidatesBlockThree = [1,2,6,7,8,9]

cell(RowThree, ColumnNine):
CandidatesRowThree = [1,7,8]
CandidatesColumnNine = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowOne, ColumnEight):
CandidatesRowOne.length = 1
CandidatesColumnEight.length = 4
CandidatesBlockThree.length = 6

shortest_list = CandidatesRowOne = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnEight and CandidatesBlockThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowOne = [2], broken into CandidatesRowOneLow = [2] and CandidatesRowOneHigh = []
CandidatesColumnEight = [1,2,4,7], broken into CandidatesColumnEightLow = [1,2,4] and CandidatesColumnEightHigh = [7]
CandidatesBlockThree = [1,2,6,7,8,9], broken into CandidatesBlockThreeLow = [1,2] and CandidatesBlockThreeHigh = [6,7,8,9]

Checking digits in CandidatesRowOneLow = [2] against: CandidatesColumnEightLow = [1,2,4] and CandidatesBlockThreeLow = [1,2]
2: [1,2,4].count(2) = 1, [1,2].count(2) = 1, TotalCount(2) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowOneHigh = [] against: CandidatesColumnEightHigh = [7] and CandidatesBlockThreeHigh = [6,7,8,9]
No digits to check in CandidatesRowOneHigh.

Confirmed candidates found for cell(RowOne, ColumnEight): [2]

## Cell 2 of 6
cell(RowTwo, ColumnTwo):
CandidatesRowTwo.length = 6
CandidatesColumnTwo.length = 1
CandidatesBlockOne.length = 1

shortest_list = CandidatesColumnTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [4,5,6,7,8,9], broken into CandidatesRowTwoLow = [4,5] and CandidatesRowTwoHigh = [6,7,8,9]
CandidatesColumnTwo = [4], broken into CandidatesColumnTwoLow = [4] and CandidatesColumnTwoHigh = []
CandidatesBlockOne = [4], broken into CandidatesBlockOneLow = [4] and CandidatesBlockOneHigh = []

Checking digits in CandidatesColumnTwoLow = [4] against: CandidatesRowTwoLow = [4,5] and CandidatesBlockOneLow = [4]
4: [4,5].count(4) = 1, [4].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnTwoHigh = [] against: CandidatesRowTwoHigh = [6,7,8,9] and CandidatesBlockOneHigh = []
No digits to check in CandidatesColumnTwoHigh.

Confirmed candidates found for cell(RowTwo, ColumnTwo): [4]

## Cell 3 of 6
cell(RowTwo, ColumnFour):
CandidatesRowTwo.length = 6
CandidatesColumnFour.length = 1
CandidatesBlockTwo.length = 3

shortest_list = CandidatesColumnFour = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [4,5,6,7,8,9], broken into CandidatesRowTwoLow = [4,5] and CandidatesRowTwoHigh = [6,7,8,9]
CandidatesColumnFour = [8], broken into CandidatesColumnFourLow = [] and CandidatesColumnFourHigh = [8]
CandidatesBlockTwo = [5,7,8], broken into CandidatesBlockTwoLow = [5,7] and CandidatesBlockTwoHigh = [8]

Checking digits in CandidatesColumnFourLow = [] against: CandidatesRowTwoLow = [4,5] and CandidatesBlockTwoLow = [5,7]
No digits to check in CandidatesColumnFourLow.

Checking digits in CandidatesColumnFourHigh = [8] against: CandidatesRowTwoHigh = [6,7,8,9] and CandidatesBlockTwoHigh = [8]
8: [6,7,8,9].count(8) = 1, [8].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnFour): [8]

## Cell 4 of 6
cell(RowTwo, ColumnEight):
CandidatesRowTwo.length = 6
CandidatesColumnEight.length = 4
CandidatesBlockThree.length = 6

shortest_list = CandidatesColumnEight = digits to search
The shortest list will be checked against the other two lists: CandidatesRowTwo and CandidatesBlockThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [4,5,6,7,8,9], broken into CandidatesRowTwoLow = [4,5] and CandidatesRowTwoHigh = [6,7,8,9]
CandidatesColumnEight = [1,2,4,7], broken into CandidatesColumnEightLow = [1,2,4] and CandidatesColumnEightHigh = [7]
CandidatesBlockThree = [1,2,6,7,8,9], broken into CandidatesBlockThreeLow = [1,2] and CandidatesBlockThreeHigh = [6,7,8,9]

Checking digits in CandidatesColumnEightLow = [1,2,4] against: CandidatesRowTwoLow = [4,5] and CandidatesBlockThreeLow = [1,2]
1: [4,5].count(1) = 0, [1,2].count(1) = 1, TotalCount(1) = 1
2: [4,5].count(2) = 0, [1,2].count(2) = 1, TotalCount(2) = 1
4: [4,5].count(4) = 1, [1,2].count(4) = 0, TotalCount(4) = 1

Checking digits in CandidatesColumnEightHigh = [7] against: CandidatesRowTwoHigh = [6,7,8,9] and CandidatesBlockThreeHigh = [6,7,8,9]
7: [6,7,8,9].count(7) = 1, [6,7,8,9].count(7) = 1, TotalCount(7) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowTwo, ColumnEight): [7]

## Cell 5 of 6
cell(RowThree, ColumnSeven):
CandidatesRowThree.length = 3
CandidatesColumnSeven.length = 3
CandidatesBlockThree.length = 6

shortest_list = CandidatesRowThree = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnSeven and CandidatesBlockThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,7,8], broken into CandidatesRowThreeLow = [1] and CandidatesRowThreeHigh = [7,8]
CandidatesColumnSeven = [1,4,9], broken into CandidatesColumnSevenLow = [1,4] and CandidatesColumnSevenHigh = [9]
CandidatesBlockThree = [1,2,6,7,8,9], broken into CandidatesBlockThreeLow = [1,2] and CandidatesBlockThreeHigh = [6,7,8,9]

Checking digits in CandidatesRowThreeLow = [1] against: CandidatesColumnSevenLow = [1,4] and CandidatesBlockThreeLow = [1,2]
1: [1,4].count(1) = 1, [1,2].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowThreeHigh = [7,8] against: CandidatesColumnSevenHigh = [9] and CandidatesBlockThreeHigh = [6,7,8,9]
7: [9].count(7) = 0, [6,7,8,9].count(7) = 1, TotalCount(7) = 1
8: [9].count(8) = 0, [6,7,8,9].count(8) = 1, TotalCount(8) = 1

Confirmed candidates found for cell(RowThree, ColumnSeven): [1]

## Cell 6 of 6
cell(RowThree, ColumnNine):
CandidatesRowThree.length = 3
CandidatesColumnNine.length = 2
CandidatesBlockThree.length = 6

shortest_list = CandidatesColumnNine = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,7,8], broken into CandidatesRowThreeLow = [1] and CandidatesRowThreeHigh = [7,8]
CandidatesColumnNine = [6,8], broken into CandidatesColumnNineLow = [] and CandidatesColumnNineHigh = [6,8]
CandidatesBlockThree = [1,2,6,7,8,9], broken into CandidatesBlockThreeLow = [1,2] and CandidatesBlockThreeHigh = [6,7,8,9]

Checking digits in CandidatesColumnNineLow = [] against: CandidatesRowThreeLow = [1] and CandidatesBlockThreeLow = [1,2]
No digits to check in CandidatesColumnNineLow.

Checking digits in CandidatesColumnNineHigh = [6,8] against: CandidatesRowThreeHigh = [7,8] and CandidatesBlockThreeHigh = [6,7,8,9]
6: [7,8].count(6) = 0, [6,7,8,9].count(6) = 1, TotalCount(6) = 1
8: [7,8].count(8) = 1, [6,7,8,9].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowThree, ColumnNine): [8]

# STEP_THREE Checking the number of elements in each cell
cell(RowOne, ColumnEight): [2]
[2].length = 1
length is 1, Passes

cell(RowTwo, ColumnTwo): [4]
[4].length = 1
length is 1, Passes

cell(RowTwo, ColumnFour): [8]
[8].length = 1
length is 1, Passes

cell(RowTwo, ColumnEight): [7]
[7].length = 1
length is 1, Passes

cell(RowThree, ColumnSeven): [1]
[1].length = 1
length is 1, Passes

cell(RowThree, ColumnNine): [8]
[8].length = 1
length is 1, Passes

## Passing Cells
cell(RowOne, ColumnEight): [2]
cell(RowTwo, ColumnTwo): [4]
cell(RowTwo, ColumnFour): [8]
cell(RowTwo, ColumnEight): [7]
cell(RowThree, ColumnSeven): [1]
cell(RowThree, ColumnNine): [8]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowOne, RowTwo, RowThree

RowOne: [3,8,7,6,9,1,5,0,4]
cell(RowOne, ColumnEight): [2]

RowTwo: [2,0,1,0,0,3,0,0,0]
cell(RowTwo, ColumnTwo): [4]
cell(RowTwo, ColumnFour): [8]
cell(RowTwo, ColumnEight): [7]

RowThree: [5,6,9,4,0,2,0,3,0]
cell(RowThree, ColumnSeven): [1]
cell(RowThree, ColumnNine): [8]

RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowOne, ColumnEight): [2]
RowOne = [3,8,7,6,9,1,5,0,4]
The ColumnEight element of RowOne needs to be updated to [2]

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 7
ColumnFour: 6
ColumnFive: 9
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 0
ColumnNine: 4

Now replacing ColumnEight with the element to update [2], such that ColumnEight = [2]
Redoing column list like we just did, but with ColumnEight set to [2]

ColumnOne: 3
ColumnTwo: 8
ColumnThree: 7
ColumnFour: 6
ColumnFive: 9
ColumnSix: 1
ColumnSeven: 5
ColumnEight: 2
ColumnNine: 4

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnEight it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnEight does Not appear on this list!!! The ONLY time you don't is if ColumnEight is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnEight:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowOne:
PreCellList = [3,8,7,6,9,1,5]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [2] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(2) = [3,8,7,6,9,1,5,2]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowOneStartingElements = [3,8,7,6,9,1,5,2,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 7 + 1 = 8 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowOne = [3,8,7,6,9,1,5,2,4]

## Updating 2 of 6
cell(RowTwo, ColumnTwo): [4]
RowTwo = [2,0,1,0,0,3,0,0,0]
TheColumnTwo element of RowTwo needs to be updated to [4]

ColumnOne: 2
ColumnTwo: 0
ColumnThree: 1
ColumnFour: 0
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnTwo with the element to update [4], such that ColumnTwo = [4]
Redoing column list like we just did, but with ColumnTwo set to [4]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 0
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnTwo.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnTwo it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnTwo (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnTwo does Not appear on this list!!! The ONLY time you don't is if ColumnTwo is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnTwo:
PreCellColumnsList.length => [ColumnOne].length = 1
Now the elements of the columns in PreCellColumnsList, which is the first 1 elements of RowTwo:
PreCellList = [2]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [2,4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [2,4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 1 + 1 = 2 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [2,4,1,0,0,3,0,0,0]

## Updating 3 of 6
cell(RowTwo, ColumnFour): [8]
RowTwo = [2,4,1,0,0,3,0,0,0]
The ColumnFour element of RowTwo needs to be updated to [8]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 0
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnFour with the element to update [8], such that ColumnFour = [8]
Redoing column list like we just did, but with ColumnFour set to [8]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFour.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFour it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFour (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFour does Not appear on this list!!! The ONLY time you don't is if ColumnFour is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFour:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree].length = 3
Now the elements of the columns in PreCellColumnsList, which is the first 3 elements of RowTwo:
PreCellList = [2,4,1]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [2,4,1,8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [2,4,1,8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 3 + 1 = 4 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [2,4,1,8,0,3,0,0,0]

## Updating 4 of 6
cell(RowTwo, ColumnEight): [7]
RowTwo = [2,4,1,8,0,3,0,0,0]
The ColumnEight element of RowTwo needs to be updated to [7]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 0

Now replacing ColumnEight with the element to update [7], such that ColumnEight = [7]
Redoing column list like we just did, but with ColumnEight set to [7]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnEight it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnEight does Not appear on this list!!! The ONLY time you don't is if ColumnEight is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnEight:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowTwo:
PreCellList = [2,4,1,8,0,3,0]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [7] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(7) = [2,4,1,8,0,3,0,7]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [2,4,1,8,0,3,0,7,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 7 + 1 = 8 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [2,4,1,8,0,3,0,7,0]

## Updating 5 of 6
cell(RowThree, ColumnSeven): [1]
RowThree = [5,6,9,4,0,2,0,3,0]
The ColumnSeven element of RowThree needs to be updated to [1]

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 0
ColumnEight: 3
ColumnNine: 0

Now replacing ColumnSeven with the element to update [1], such that ColumnSeven = [1]
Redoing column list like we just did, but with ColumnSeven set to [1]

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 1
ColumnEight: 3
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSeven.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSeven it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSeven (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSeven does Not appear on this list!!! The ONLY time you don't is if ColumnSeven is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSeven:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
Now the elements of the columns in PreCellColumnsList, which is the first 6 elements of RowThree:
PreCellList = [5,6,9,4,0,2]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [5,6,9,4,0,2,1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [5,6,9,4,0,2,1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 6 + 1 = 7 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [5,6,9,4,0,2,1,3,0]

## Updating 6 of 6
cell(RowThree, ColumnNine): [8]
RowThree = [5,6,9,4,0,2,1,3,0]
The ColumnNine element of RowThree needs to be updated to [8]

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 1
ColumnEight: 3
ColumnNine: 0

Now replacing ColumnNine with the element to update [8], such that ColumnNine = [8]
Redoing column list like we just did, but with ColumnNine set to [8]

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 1
ColumnEight: 3
ColumnNine: 8

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnNine.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnNine it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnNine (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnNine does Not appear on this list!!! The ONLY time you don't is if ColumnNine is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnNine:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight].length = 8
Now the elements of the columns in PreCellColumnsList, which is the first 8 elements of RowThree:
PreCellList = [5,6,9,4,0,2,1,3]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [5,6,9,4,0,2,1,3,8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [5,6,9,4,0,2,1,3,8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 8 + 1 = 9 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [5,6,9,4,0,2,1,3,8]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowOne = [3,8,7,6,9,1,5,2,4]
UpdatedRowTwo = [2,4,1,8,0,3,0,7,0]
UpdatedRowThree = [5,6,9,4,0,2,1,3,8]

The rows to update are RowOne, RowTwo, RowThree
Using the contents of UpdatedRowOne, UpdatedRowTwo, UpdatedRowThree
Printing Sudoku:
RowOne: [3,8,7,6,9,1,5,2,4]
RowTwo: [2,4,1,8,0,3,0,7,0]
RowThree: [5,6,9,4,0,2,1,3,8]
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]

# STEP_SEVEN: Shifting the Rows of the Sudoku
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,0,6,0,0,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,0,3,0,7,8,9,1]
RowNine: [8,7,0,5,0,9,3,0,2]
RowOne: [3,8,7,6,9,1,5,2,4]
RowTwo: [2,4,1,8,0,3,0,7,0]
RowThree: [5,6,9,4,0,2,1,3,8]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
RowThree: [7,5,2,9,0,6,0,0,3]
RowFour: [9,1,3,2,4,8,7,6,5]
RowFive: [4,2,0,3,0,7,8,9,1]
RowSix: [8,7,0,5,0,9,3,0,2]
RowSeven: [3,8,7,6,9,1,5,2,4]
RowEight: [2,4,1,8,0,3,0,7,0]
RowNine: [5,6,9,4,0,2,1,3,8]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:30:50.919258
Turn number: 13
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
RowThree: [7,5,2,9,0,6,0,0,3]
RowFour: [9,1,3,2,4,8,7,6,5]
RowFive: [4,2,0,3,0,7,8,9,1]
RowSix: [8,7,0,5,0,9,3,0,2]
RowSeven: [3,8,7,6,9,1,5,2,4]
RowEight: [2,4,1,8,0,3,0,7,0]
RowNine: [5,6,9,4,0,2,1,3,8]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [1,3,4,7,2,5,6,8,9]
RowTwo = [6,9,8,1,3,4,2,5,7]
RowThree = [7,5,2,9,0,6,0,0,3]
RowFour = [9,1,3,2,4,8,7,6,5]
RowFive = [4,2,0,3,0,7,8,9,1]
RowSix = [8,7,0,5,0,9,3,0,2]
RowSeven = [3,8,7,6,9,1,5,2,4]
RowEight = [2,4,1,8,0,3,0,7,0]
RowNine = [5,6,9,4,0,2,1,3,8]

# Columns
ColumnOne = [1,6,7,9,4,8,3,2,5]
ColumnTwo = [3,9,5,1,2,7,8,4,6]
ColumnThree = [4,8,2,3,0,0,7,1,9]
ColumnFour = [7,1,9,2,3,5,6,8,4]
ColumnFive = [2,3,0,4,0,0,9,0,0]
ColumnSix = [5,4,6,8,7,9,1,3,2]
ColumnSeven = [6,2,0,7,8,3,5,0,1]
ColumnEight = [8,5,0,6,9,0,2,7,3]
ColumnNine = [9,7,3,5,1,2,4,0,8]

# Blocks
BlockOne:
[[1,3,4],
[6,9,8],
[7,5,2]]
BlockOne = [1,3,4,6,9,8,7,5,2]

BlockTwo:
[[7,2,5],
[1,3,4],
[9,0,6]]
BlockTwo = [7,2,5,1,3,4,9,0,6]

BlockThree:
[[6,8,9],
[2,5,7],
[0,0,3]]
BlockThree = [6,8,9,2,5,7,0,0,3]

BlockFour:
[[9,1,3],
[4,2,0],
[8,7,0]]
BlockFour = [9,1,3,4,2,0,8,7,0]

BlockFive:
[[2,4,8],
[3,0,7],
[5,0,9]]
BlockFive = [2,4,8,3,0,7,5,0,9]

BlockSix:
[[7,6,5],
[8,9,1],
[3,0,2]]
BlockSix = [7,6,5,8,9,1,3,0,2]

BlockSeven:
[[3,8,7],
[2,4,1],
[5,6,9]]
BlockSeven = [3,8,7,2,4,1,5,6,9]

BlockEight:
[[6,9,1],
[8,0,3],
[4,0,2]]
BlockEight = [6,9,1,8,0,3,4,0,2]

BlockNine:
[[5,2,4],
[0,7,0],
[1,3,8]]
BlockNine = [5,2,4,0,7,0,1,3,8]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,5,6,8,9]) = []
CandidatesRowOne = []
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,1,3,4,2,5,7]) = []
CandidatesRowTwo = []
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([7,5,2,9,0,6,0,0,3]) = [1,4,8]
CandidatesRowThree = [1,4,8]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,2,4,8,7,6,5]) = []
CandidatesRowFour = []
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,0,7,8,9,1]) = [5,6]
CandidatesRowFive = [5,6]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([8,7,0,5,0,9,3,0,2]) = [1,4,6]
CandidatesRowSix = [1,4,6]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,6,9,1,5,2,4]) = []
CandidatesRowSeven = []
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([2,4,1,8,0,3,0,7,0]) = [5,6,9]
CandidatesRowEight = [5,6,9]
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([5,6,9,4,0,2,1,3,8]) = [7]
CandidatesRowNine = [7]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([1,6,7,9,4,8,3,2,5]) = []
CandidatesColumnOne = []
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([3,9,5,1,2,7,8,4,6]) = []
CandidatesColumnTwo = []
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([4,8,2,3,0,0,7,1,9]) = [5,6]
CandidatesColumnThree = [5,6]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([7,1,9,2,3,5,6,8,4]) = []
CandidatesColumnFour = []
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([2,3,0,4,0,0,9,0,0]) = [1,5,6,7,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([5,4,6,8,7,9,1,3,2]) = []
CandidatesColumnSix = []
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([6,2,0,7,8,3,5,0,1]) = [4,9]
CandidatesColumnSeven = [4,9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([8,5,0,6,9,0,2,7,3]) = [1,4]
CandidatesColumnEight = [1,4]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([9,7,3,5,1,2,4,0,8]) = [6]
CandidatesColumnNine = [6]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,2]) = []
CandidatesBlockOne = []
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([7,2,5,1,3,4,9,0,6]) = [8]
CandidatesBlockTwo = [8]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([6,8,9,2,5,7,0,0,3]) = [1,4]
CandidatesBlockThree = [1,4]
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,0]) = [5,6]
CandidatesBlockFour = [5,6]
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([2,4,8,3,0,7,5,0,9]) = [1,6]
CandidatesBlockFive = [1,6]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,9,1,3,0,2]) = [4]
CandidatesBlockSix = [4]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,2,4,1,5,6,9]) = []
CandidatesBlockSeven = []
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([6,9,1,8,0,3,4,0,2]) = [5,7]
CandidatesBlockEight = [5,7]
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([5,2,4,0,7,0,1,3,8]) = [6,9]
CandidatesBlockNine = [6,9]

# Index of all zeros, by row
RowThree = [7,5,2,9,0,6,0,0,3]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 7
RowThree[1] = 5
RowThree[2] = 2
RowThree[3] = 9
RowThree[4] = 0
RowThree[5] = 6
RowThree[6] = 0
RowThree[7] = 0
RowThree[8] = 3
IndexOfAll0ElementsInRowThree => [4,6,7]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [5,7,8]
EmptyColumnNamesRowThree = [ColumnFive,ColumnSeven,ColumnEight]

RowFive = [4,2,0,3,0,7,8,9,1]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 4
RowFive[1] = 2
RowFive[2] = 0
RowFive[3] = 3
RowFive[4] = 0
RowFive[5] = 7
RowFive[6] = 8
RowFive[7] = 9
RowFive[8] = 1
IndexOfAll0ElementsInRowFive => [2,4]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [3,5]
EmptyColumnNamesRowFive = [ColumnThree,ColumnFive]

RowSix = [8,7,0,5,0,9,3,0,2]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 8
RowSix[1] = 7
RowSix[2] = 0
RowSix[3] = 5
RowSix[4] = 0
RowSix[5] = 9
RowSix[6] = 3
RowSix[7] = 0
RowSix[8] = 2
IndexOfAll0ElementsInRowSix => [2,4,7]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [3,5,8]
EmptyColumnNamesRowSix = [ColumnThree,ColumnFive,ColumnEight]

RowEight = [2,4,1,8,0,3,0,7,0]
Now finding the index of Each 0 element in RowEight
RowEight[0] = 2
RowEight[1] = 4
RowEight[2] = 1
RowEight[3] = 8
RowEight[4] = 0
RowEight[5] = 3
RowEight[6] = 0
RowEight[7] = 7
RowEight[8] = 0
IndexOfAll0ElementsInRowEight => [4,6,8]
ColumnPositionOfAll0ElementsRowEight => map(element+1, IndexOfAll0ElementsInRowEight) = [5,7,9]
EmptyColumnNamesRowEight = [ColumnFive,ColumnSeven,ColumnNine]

RowNine = [5,6,9,4,0,2,1,3,8]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 5
RowNine[1] = 6
RowNine[2] = 9
RowNine[3] = 4
RowNine[4] = 0
RowNine[5] = 2
RowNine[6] = 1
RowNine[7] = 3
RowNine[8] = 8
IndexOfAll0ElementsInRowNine => [4]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [5]
EmptyColumnNamesRowNine = [ColumnFive]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 3 for each EmptyColumnNamesRowThree + 2 for each EmptyColumnNamesRowFive + 3 for each EmptyColumnNamesRowSix + 3 for each EmptyColumnNamesRowEight + 1 for each EmptyColumnNamesRowNine = 12

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 12

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnFive,ColumnSeven,ColumnEight]
Note, the last empty column of the RowThree is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 12
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1,4,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [8]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1,4,8] & [1,5,6,7,8] = [1,8]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1,8] & [8] = [8]
CellCandidates = [8]
Length = 1
FOUND RowThree, ColumnFive, BlockTwo

### 2 of 12
Up to ColumnSeven in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnEight
Not the last column of current row
RowThree and ColumnSeven means BlockThree
import CandidatesRowThree, CandidatesColumnSeven, CandidatesBlockThree
CandidatesRowThree = [1,4,8]
CandidatesColumnSeven = [4,9]
CandidatesBlockThree = [1,4]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnSeven => [1,4,8] & [4,9] = [4]
CommonElementsOfRowThreeAndColumnSevenAndBlockThree => [4] & [1,4] = [4]
CellCandidates = [4]
Length = 1
FOUND RowThree, ColumnSeven, BlockThree

### 3 of 12
Up to ColumnEight in EmptyColumnNamesRowThreeThe last empty column of EmptyColumnNamesRowThree is ColumnEight
Last column of current row
The next row is RowFive
RowThree and ColumnEight means BlockThree
import CandidatesRowThree, CandidatesColumnEight, CandidatesBlockThree
CandidatesRowThree = [1,4,8]
CandidatesColumnEight = [1,4]
CandidatesBlockThree = [1,4]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnEight => [1,4,8] & [1,4] = [1,4]
CommonElementsOfRowThreeAndColumnEightAndBlockThree => [1,4] & [1,4] = [1,4]
CellCandidates = [1,4]
Length = 2
Not 1

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnThree,ColumnFive]
Note, the last empty column of the RowFive is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 4 of 12
Up to ColumnThree in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnFive
Not the last column of current row
RowFive and ColumnThree means BlockFour
import CandidatesRowFive, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowFive = [5,6]
CandidatesColumnThree = [5,6]
CandidatesBlockFour = [5,6]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnThree => [5,6] & [5,6] = [5,6]
CommonElementsOfRowFiveAndColumnThreeAndBlockFour => [5,6] & [5,6] = [5,6]
CellCandidates = [5,6]
Length = 2
Not 1

### 5 of 12
Up to ColumnFive in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnFive
Last column of current row
The next row is RowSix
RowFive and ColumnFive means BlockFive
import CandidatesRowFive, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowFive = [5,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [1,6]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnFive => [5,6] & [1,5,6,7,8] = [5,6]
CommonElementsOfRowFiveAndColumnFiveAndBlockFive => [5,6] & [1,6] = [6]
CellCandidates = [6]
Length = 1
FOUND RowFive, ColumnFive, BlockFive

## RowSix Candidates
EmptyColumnNamesRowSix: [ColumnThree,ColumnFive,ColumnEight]
Note, the last empty column of the RowSix is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSix and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowSix and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowSix and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 6 of 12
Up to ColumnThree in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Not the last column of current row
RowSix and ColumnThree means BlockFour
import CandidatesRowSix, CandidatesColumnThree, CandidatesBlockFour
CandidatesRowSix = [1,4,6]
CandidatesColumnThree = [5,6]
CandidatesBlockFour = [5,6]
Finding Common Elements:
CommonElementsOfRowSixAndColumnThree => [1,4,6] & [5,6] = [6]
CommonElementsOfRowSixAndColumnThreeAndBlockFour => [6] & [5,6] = [6]
CellCandidates = [6]
Length = 1
FOUND RowSix, ColumnThree, BlockFour

### 7 of 12
Up to ColumnFive in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Not the last column of current row
RowSix and ColumnFive means BlockFive
import CandidatesRowSix, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowSix = [1,4,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [1,6]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFive => [1,4,6] & [1,5,6,7,8] = [1,6]
CommonElementsOfRowSixAndColumnFiveAndBlockFive => [1,6] & [1,6] = [1,6]
CellCandidates = [1,6]
Length = 2
Not 1

### 8 of 12
Up to ColumnEight in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnEight
Last column of current row
The next row is RowEight
RowSix and ColumnEight means BlockSix
import CandidatesRowSix, CandidatesColumnEight, CandidatesBlockSix
CandidatesRowSix = [1,4,6]
CandidatesColumnEight = [1,4]
CandidatesBlockSix = [4]
Finding Common Elements:
CommonElementsOfRowSixAndColumnEight => [1,4,6] & [1,4] = [1,4]
CommonElementsOfRowSixAndColumnEightAndBlockSix => [1,4] & [4] = [4]
CellCandidates = [4]
Length = 1
FOUND RowSix, ColumnEight, BlockSix

## RowEight Candidates
EmptyColumnNamesRowEight: [ColumnFive,ColumnSeven,ColumnNine]
Note, the last empty column of the RowEight is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowEight and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowEight and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowEight and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 9 of 12
Up to ColumnFive in EmptyColumnNamesRowEight
The last empty column of EmptyColumnNamesRowEight is ColumnNine
Not the last column of current row
RowEight and ColumnFive means BlockEight
import CandidatesRowEight, CandidatesColumnFive, CandidatesBlockEight
CandidatesRowEight = [5,6,9]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [5,7]
Finding Common Elements:
CommonElementsOfRowEightAndColumnFive => [5,6,9] & [1,5,6,7,8] = [5,6]
CommonElementsOfRowEightAndColumnFiveAndBlockEight => [5,6] & [5,7] = [5]
CellCandidates = [5]
Length = 1
FOUND RowEight, ColumnFive, BlockEight

### 10 of 12
Up to ColumnSeven in EmptyColumnNamesRowEight
The last empty column of EmptyColumnNamesRowEight is ColumnNine
Not the last column of current row
RowEight and ColumnSeven means BlockNine
import CandidatesRowEight, CandidatesColumnSeven, CandidatesBlockNine
CandidatesRowEight = [5,6,9]
CandidatesColumnSeven = [4,9]
CandidatesBlockNine = [6,9]
Finding Common Elements:
CommonElementsOfRowEightAndColumnSeven => [5,6,9] & [4,9] = [9]
CommonElementsOfRowEightAndColumnSevenAndBlockNine => [9] & [6,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowEight, ColumnSeven, BlockNine

### 11 of 12
Up to ColumnNine in EmptyColumnNamesRowEight
The last empty column of EmptyColumnNamesRowEight is ColumnNine
Last column of current row
The next row is RowNine
RowEight and ColumnNine means BlockNine
import CandidatesRowEight, CandidatesColumnNine, CandidatesBlockNine
CandidatesRowEight = [5,6,9]
CandidatesColumnNine = [6]
CandidatesBlockNine = [6,9]
Finding Common Elements:
CommonElementsOfRowEightAndColumnNine => [5,6,9] & [6] = [6]
CommonElementsOfRowEightAndColumnNineAndBlockNine => [6] & [6,9] = [6]
CellCandidates = [6]
Length = 1
FOUND RowEight, ColumnNine, BlockNine

## RowNine Candidates
EmptyColumnNamesRowNine: [ColumnFive]
Note, the last empty column of the RowNine is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowNine and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowNine and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowNine and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 12 of 12
Up to ColumnFive in EmptyColumnNamesRowNine
The last empty column of EmptyColumnNamesRowNine is ColumnFive
Last column of current row
RowNine and ColumnFive means BlockEight
import CandidatesRowNine, CandidatesColumnFive, CandidatesBlockEight
CandidatesRowNine = [7]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [5,7]
Finding Common Elements:
CommonElementsOfRowNineAndColumnFive => [7] & [1,5,6,7,8] = [7]
CommonElementsOfRowNineAndColumnFiveAndBlockEight => [7] & [5,7] = [7]
CellCandidates = [7]
Length = 1
FOUND RowNine, ColumnFive, BlockEight

Finished printing 12 of 12 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowThree, ColumnFive, BlockTwo
2: FOUND RowThree, ColumnSeven, BlockThree
3: FOUND RowFive, ColumnFive, BlockFive
4: FOUND RowSix, ColumnThree, BlockFour
5: FOUND RowSix, ColumnEight, BlockSix
6: FOUND RowEight, ColumnFive, BlockEight
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowThree, ColumnFive, BlockTwo):
CandidatesRowThree = [1,4,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [8]

cell(RowThree, ColumnSeven, BlockThree):
CandidatesRowThree = [1,4,8]
CandidatesColumnSeven = [4,9]
CandidatesBlockThree = [1,4]

cell(RowFive, ColumnFive, BlockFive):
CandidatesRowFive = [5,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [1,6]

cell(RowSix, ColumnThree, BlockFour):
CandidatesRowSix = [1,4,6]
CandidatesColumnThree = [5,6]
CandidatesBlockFour = [5,6]

cell(RowSix, ColumnEight, BlockSix):
CandidatesRowSix = [1,4,6]
CandidatesColumnEight = [1,4]
CandidatesBlockSix = [4]

cell(RowEight, ColumnFive, BlockEight):
CandidatesRowEight = [5,6,9]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [5,7]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:39:35.728161
Turn number: 14
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
RowThree: [7,5,2,9,0,6,0,0,3]
RowFour: [9,1,3,2,4,8,7,6,5]
RowFive: [4,2,0,3,0,7,8,9,1]
RowSix: [8,7,0,5,0,9,3,0,2]
RowSeven: [3,8,7,6,9,1,5,2,4]
RowEight: [2,4,1,8,0,3,0,7,0]
RowNine: [5,6,9,4,0,2,1,3,8]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: ] = [7]
CellCandidates = [7]
Length = 1
FOUND RowNine, ColumnFive, BlockEight

Finished printing 12 of 12 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowThree, ColumnFive, BlockTwo
2: FOUND RowThree, ColumnSeven, BlockThree
3: FOUND RowFive, ColumnFive, BlockFive
4: FOUND RowSix, ColumnThree, BlockFour
5: FOUND RowSix, ColumnEight, BlockSix
6: FOUND RowEight, ColumnFive, BlockEight
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowThree, ColumnFive, BlockTwo):
CandidatesRowThree = [1,4,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [8]

cell(RowThree, ColumnSeven, BlockThree):
CandidatesRowThree = [1,4,8]
CandidatesColumnSeven = [4,9]
CandidatesBlockThree = [1,4]

cell(RowFive, ColumnFive, BlockFive):
CandidatesRowFive = [5,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [1,6]

cell(RowSix, ColumnThree, BlockFour):
CandidatesRowSix = [1,4,6]
CandidatesColumnThree = [5,6]
CandidatesBlockFour = [5,6]

cell(RowSix, ColumnEight, BlockSix):
CandidatesRowSix = [1,4,6]
CandidatesColumnEight = [1,4]
CandidatesBlockSix = [4]

cell(RowEight, ColumnFive, BlockEight):
CandidatesRowEight = [5,6,9]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [5,7]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowThree, ColumnFive):
CandidatesRowThree = [1,4,8]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockTwo = [8]

cell(RowThree, ColumnSeven):
CandidatesRowThree = [1,4,8]
CandidatesColumnSeven = [4,9]
CandidatesBlockThree = [1,4]

cell(RowFive, ColumnFive):
CandidatesRowFive = [5,6]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockFive = [1,6]

cell(RowSix, ColumnThree):
CandidatesRowSix = [1,4,6]
CandidatesColumnThree = [5,6]
CandidatesBlockFour = [5,6]

cell(RowSix, ColumnEight):
CandidatesRowSix = [1,4,6]
CandidatesColumnEight = [1,4]
CandidatesBlockSix = [4]

cell(RowEight, ColumnFive):
CandidatesRowEight = [5,6,9]
CandidatesColumnFive = [1,5,6,7,8]
CandidatesBlockEight = [5,7]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowThree, ColumnFive):
CandidatesRowThree.length = 3
CandidatesColumnFive.length = 5
CandidatesBlockTwo.length = 1

shortest_list = CandidatesBlockTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesColumnFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,4,8], broken into CandidatesRowThreeLow = [1,4] and CandidatesRowThreeHigh = [8]
CandidatesColumnFive = [1,5,6,7,8], broken into CandidatesColumnFiveLow = [1,5] and CandidatesColumnFiveHigh = [6,7,8]
CandidatesBlockTwo = [8], broken into CandidatesBlockTwoLow = [] and CandidatesBlockTwoHigh = [8]

Checking digits in CandidatesBlockTwoHigh = [8] against: CandidatesRowThreeHigh = [8] and CandidatesColumnFiveHigh = [6,7,8]
8: [8].count(8) = 1, [6,7,8].count(8) = 1, TotalCount(8) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowThree, ColumnFive): [8]

## Cell 2 of 6
cell(RowThree, ColumnSeven):
CandidatesRowThree.length = 3
CandidatesColumnSeven.length = 2
CandidatesBlockThree.length = 2

shortest_list = CandidatesColumnSeven = digits to search
The shortest list will be checked against the other two lists: CandidatesRowThree and CandidatesBlockThree

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1,4,8], broken into CandidatesRowThreeLow = [1,4] and CandidatesRowThreeHigh = [8]
CandidatesColumnSeven = [4,9], broken into CandidatesColumnSevenLow = [4] and CandidatesColumnSevenHigh = [9]
CandidatesBlockThree = [1,4], broken into CandidatesBlockThreeLow = [1,4] and CandidatesBlockThreeHigh = []

Checking digits in CandidatesColumnSevenLow = [4] against: CandidatesRowThreeLow = [1,4] and CandidatesBlockThreeLow = [1,4]
4: [1,4].count(4) = 1, [1,4].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Checking digits in CandidatesColumnSevenHigh = [9] against: CandidatesRowThreeHigh = [8] and CandidatesBlockThreeHigh = []
9: [8].count(9) = 0, [].count(9) = 0, TotalCount(9) = 0

Confirmed candidates found for cell(RowThree, ColumnSeven): [4]

## Cell 3 of 6
cell(RowFive, ColumnFive):
CandidatesRowFive.length = 2
CandidatesColumnFive.length = 5
CandidatesBlockFive.length = 2

shortest_list = CandidatesRowFive = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [5,6], broken into CandidatesRowFiveLow = [5] and CandidatesRowFiveHigh = [6]
CandidatesColumnFive = [1,5,6,7,8], broken into CandidatesColumnFiveLow = [1,5] and CandidatesColumnFiveHigh = [6,7,8]
CandidatesBlockFive = [1,6], broken into CandidatesBlockFiveLow = [1] and CandidatesBlockFiveHigh = [6]

Checking digits in CandidatesRowFiveLow = [5] against: CandidatesColumnFiveLow = [1,5] and CandidatesBlockFiveLow = [1]
5: [1,5].count(5) = 1, [1].count(5) = 0, TotalCount(5) = 1

Checking digits in CandidatesRowFiveHigh = [6] against: CandidatesColumnFiveHigh = [6,7,8] and CandidatesBlockFiveHigh = [6]
6: [6,7,8].count(6) = 1, [6].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowFive, ColumnFive): [6]

## Cell 4 of 6
cell(RowSix, ColumnThree):
CandidatesRowSix.length = 3
CandidatesColumnThree.length = 2
CandidatesBlockFour.length = 2

shortest_list = CandidatesColumnThree = digits to search
The shortest list will be checked against the other two lists: CandidatesRowSix and CandidatesBlockFour

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowSix = [1,4,6], broken into CandidatesRowSixLow = [1,4] and CandidatesRowSixHigh = [6]
CandidatesColumnThree = [5,6], broken into CandidatesColumnThreeLow = [5] and CandidatesColumnThreeHigh = [6]
CandidatesBlockFour = [5,6], broken into CandidatesBlockFourLow = [5] and CandidatesBlockFourHigh = [6]

Checking digits in CandidatesColumnThreeLow = [5] against: CandidatesRowSixLow = [1,4] and CandidatesBlockFourLow = [5]
5: [1,4].count(5) = 0, [5].count(5) = 1, TotalCount(5) = 1

Checking digits in CandidatesColumnThreeHigh = [6] against: CandidatesRowSixHigh = [6] and CandidatesBlockFourHigh = [6]
6: [6].count(6) = 1, [6].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowSix, ColumnThree): [6]

## Cell 5 of 6
cell(RowSix, ColumnEight):
CandidatesRowSix.length = 3
CandidatesColumnEight.length = 2
CandidatesBlockSix.length = 1

shortest_list = CandidatesBlockSix = digits to search
The shortest list will be checked against the other two lists: CandidatesRowSix and CandidatesColumnEight

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowSix = [1,4,6], broken into CandidatesRowSixLow = [1,4] and CandidatesRowSixHigh = [6]
CandidatesColumnEight = [1,4], broken into CandidatesColumnEightLow = [1,4] and CandidatesColumnEightHigh = []
CandidatesBlockSix = [4], broken into CandidatesBlockSixLow = [4] and CandidatesBlockSixHigh = []

Checking digits in CandidatesBlockSixLow = [4] against: CandidatesRowSixLow = [1,4] and CandidatesColumnEightLow = [1,4]
4: [1,4].count(4) = 1, [1,4].count(4) = 1, TotalCount(4) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowSix, ColumnEight): [4]

## Cell 6 of 6
cell(RowEight, ColumnFive):
CandidatesRowEight.length = 3
CandidatesColumnFive.length = 5
CandidatesBlockEight.length = 2

shortest_list = CandidatesBlockEight = digits to search
The shortest list will be checked against the other two lists: CandidatesRowEight and CandidatesColumnFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowEight = [5,6,9], broken into CandidatesRowEightLow = [5] and CandidatesRowEightHigh = [6,9]
CandidatesColumnFive = [1,5,6,7,8], broken into CandidatesColumnFiveLow = [1,5] and CandidatesColumnFiveHigh = [6,7,8]
CandidatesBlockEight = [5,7], broken into CandidatesBlockEightLow = [5] and CandidatesBlockEightHigh = [7]

Checking digits in CandidatesBlockEightLow = [5] against: CandidatesRowEightLow = [5] and CandidatesColumnFiveLow = [1,5]
5: [5].count(5) = 1, [1,5].count(5) = 1, TotalCount(5) = 2 FOUND A CANDIDATE

Checking digits in CandidatesBlockEightHigh = [7] against: CandidatesRowEightHigh = [6,9] and CandidatesColumnFiveHigh = [6,7,8]
7: [6,9].count(7) = 0, [6,7,8].count(7) = 1, TotalCount(7) = 1

Confirmed candidates found for cell(RowEight, ColumnFive): [5]

# STEP_THREE Checking the number of elements in each cell
cell(RowThree, ColumnFive): [8]
[8].length = 1
length is 1, Passes

cell(RowThree, ColumnSeven): [4]
[4].length = 1
length is 1, Passes

cell(RowFive, ColumnFive): [6]
[6].length = 1
length is 1, Passes

cell(RowSix, ColumnThree): [6]
[6].length = 1
length is 1, Passes

cell(RowSix, ColumnEight): [4]
[4].length = 1
length is 1, Passes

cell(RowEight, ColumnFive): [5]
[5].length = 1
length is 1, Passes

## Passing Cells
cell(RowThree, ColumnFive): [8]
cell(RowThree, ColumnSeven): [4]
cell(RowFive, ColumnFive): [6]
cell(RowSix, ColumnThree): [6]
cell(RowSix, ColumnEight): [4]
cell(RowEight, ColumnFive): [5]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowThree, RowFive, RowSix, RowEight

RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
RowThree: [7,5,2,9,0,6,0,0,3]
cell(RowThree, ColumnFive): [8]
cell(RowThree, ColumnSeven): [4]
RowFour: [9,1,3,2,4,8,7,6,5]
RowFive: [4,2,0,3,0,7,8,9,1]
cell(RowFive, ColumnFive): [6]
RowSix: [8,7,0,5,0,9,3,0,2]
cell(RowSix, ColumnThree): [6]
cell(RowSix, ColumnEight): [4]
RowSeven: [3,8,7,6,9,1,5,2,4]
RowEight: [2,4,1,8,0,3,0,7,0]
cell(RowEight, ColumnFive): [5]
RowNine: [5,6,9,4,0,2,1,3,8]

# STEP_FIVE: Applying Cell Updates to Rows
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.

## Updating 1 of 6
cell(RowThree, ColumnFive): [8]
RowThree = [7,5,2,9,0,6,0,0,3]
The ColumnFive element of RowThree needs to be updated to [8]

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 0
ColumnSix: 6
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnFive with the element to update [8], such that ColumnFive = 8
Redoing column list like we just did, but with ColumnFive set to 8

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 8
ColumnSix: 6
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowThree:
PreCellList = [7,5,2,9]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [8] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(8) = [7,5,2,9,8]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [7,5,2,9,8,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [7,5,2,9,8,6,0,0,3]

## Updating 2 of 6
cell(RowThree, ColumnSeven): [4]
RowThree = [7,5,2,9,8,6,0,0,3]
The ColumnSeven element of RowThree needs to be updated to [4]

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 8
ColumnSix: 6
ColumnSeven: 0
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnSeven with the element to update [4], such that ColumnSeven = 4
Redoing column list like we just did, but with ColumnSeven set to 4

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 8
ColumnSix: 6
ColumnSeven: 4
ColumnEight: 0
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSeven.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSeven it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSeven (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSeven does Not appear on this list!!! The ONLY time you don't is if ColumnSeven is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSeven:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
Now the elements of the columns in PreCellColumnsList, which is the first 6 elements of RowThree:
PreCellList = [7,5,2,9,8,6]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [7,5,2,9,8,6,4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [7,5,2,9,8,6,4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 6 + 1 = 7 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [7,5,2,9,8,6,4,0,3]

## Updating 3 of 6
cell(RowFive, ColumnFive): [6]
RowFive = [4,2,0,3,0,7,8,9,1]
The ColumnFive element of RowFive needs to be updated to [6]

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 0
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 9
ColumnNine: 1

Now replacing ColumnFive with the element to update [6], such that ColumnFive = 6
Redoing column list like we just did, but with ColumnFive set to 6

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 6
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 9
ColumnNine: 1

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowFive:
PreCellList = [4,2,0,3]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [4,2,0,3,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [4,2,0,3,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [4,2,0,3,6,7,8,9,1]

## Updating 4 of 6
cell(RowSix, ColumnThree): [6]
RowSix = [8,7,0,5,0,9,3,0,2]
The ColumnThree element of RowSix needs to be updated to [6]

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 0
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 2

Now replacing ColumnThree with the element to update [6], such that ColumnThree = 6
Redoing column list like we just did, but with ColumnThree set to 6

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 6
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 2

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnThree.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnThree it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnThree (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnThree does Not appear on this list!!! The ONLY time you don't is if ColumnThree is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnThree:
PreCellColumnsList.length => [ColumnOne,ColumnTwo].length = 2
Now the elements of the columns in PreCellColumnsList, which is the first 2 elements of RowSix:
PreCellList = [8,7]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [8,7,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowSixStartingElements = [8,7,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 2 + 1 = 3 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowSix = [8,7,6,5,0,9,3,0,2]

## Updating 5 of 6
cell(RowSix, ColumnEight): [4]
RowSix = [8,7,6,5,0,9,3,0,2]
The ColumnEight element of RowSix needs to be updated to [4]

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 6
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 0
ColumnNine: 2

Now replacing ColumnEight with the element to update [4], such that ColumnEight = 4
Redoing column list like we just did, but with ColumnEight set to 4

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 6
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 4
ColumnNine: 2

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnEight it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnEight does Not appear on this list!!! The ONLY time you don't is if ColumnEight is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnEight:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowSix:
PreCellList = [8,7,6,5,0,9,3]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [4] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(4) = [8,7,6,5,0,9,3,4]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowSixStartingElements = [8,7,6,5,0,9,3,4,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 7 + 1 = 8 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowSix = [8,7,6,5,0,9,3,4,2]

## Updating 6 of 6
cell(RowEight, ColumnFive): [5]
RowEight = [2,4,1,8,0,3,0,7,0]
The ColumnFive element of RowEight needs to be updated to [5]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 0
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 0

Now replacing ColumnFive with the element to update [5], such that ColumnFive = 5
Redoing column list like we just did, but with ColumnFive set to 5

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 5
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowEight:
PreCellList = [2,4,1,8]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [5] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(5) = [2,4,1,8,5]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowEightStartingElements = [2,4,1,8,5,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first 4 + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowEight = [2,4,1,8,5,3,0,7,0]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowThree = [7,5,2,9,8,6,4,0,3]
UpdatedRowFive = [4,2,0,3,6,7,8,9,1]
UpdatedRowSix = [8,7,6,5,0,9,3,4,2]
UpdatedRowEight = [2,4,1,8,5,3,0,7,0]

The rows to update are RowThree, RowFive, RowSix, RowEight
Using the contents of UpdatedRowThree, UpdatedRowFive, UpdatedRowSix, UpdatedRowEight
Printing Sudoku:
RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
UpdatedRowThree: [7,5,2,9,8,6,4,0,3]
RowFour: [9,1,3,2,4,8,7,6,5]
UpdatedRowFive: [4,2,0,3,6,7,8,9,1]
UpdatedRowSix: [8,7,6,5,0,9,3,4,2]
RowSeven: [3,8,7,6,9,1,5,2,4]
UpdatedRowEight: [2,4,1,8,5,3,0,7,0]
RowNine: [5,6,9,4,0,2,1,3,8]

# STEP_SEVEN: Shifting the Rows of the Sudoku
RowFour: [9,1,3,2,4,8,7,6,5]
UpdatedRowFive: [4,2,0,3,6,7,8,9,1]
UpdatedRowSix: [8,7,6,5,0,9,3,4,2]
RowSeven: [3,8,7,6,9,1,5,2,4]
UpdatedRowEight: [2,4,1,8,5,3,0,7,0]
RowNine: [5,6,9,4,0,2,1,3,8]
RowOne: [1,3,4,7,2,5,6,8,9]
RowTwo: [6,9,8,1,3,4,2,5,7]
UpdatedRowThree: [7,5,2,9,8,6,4,0,3]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,4,8,7,6,5]
RowTwo: [4,2,0,3,6,7,8,9,1]
RowThree: [8,7,6,5,0,9,3,4,2]
RowFour: [3,8,7,6,9,1,5,2,4]
RowFive: [2,4,1,8,5,3,0,7,0]
RowSix: [5,6,9,4,0,2,1,3,8]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,8,6,4,0,3]
</output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:44:45.971883
Turn number: 15
----
Entry 1/5 - system: You are going to analyze the sudoku you've just been given. When printing, follow the requested formats Exactly as given by the prompt, with no additions, omissions, or shortcuts.
- For each section, start by printing the section heading, which are lines beginning with #, ##, or ###.
- Lines beginning with a dash are instructions, '- {instructions to follow}'.
- All other lines are to be printed. They are to be printed Verbatim, with nothing changed except for filling in values surrounded by curly brackets {values to replace are given like this}, or filling in list elements when asked [the elements of {list_name}].
- When asked to perform calculations, do so Carefully and with Full Accuracy.
- When asked to use a value from a previous section, fetch and use the Already Existing Value, Do Not recalculate it. It was calculated accurately already.
- Many sections require printing the contents multiple times, such as once for each instance in a list (or similar). Do this when asked, making sure to print the contents the Full requested number of items, once for each item.
- Some sections are, themselves, meant to be printed multiple times. These are:
    - The '## {row_name} Candidates' section, for rows with empty elements.
    - And the '### {current_cell_count} of {MaxCells}' section, for empty cells (cells with a value of 0).
- The value of MaxCells will be calculated either as 20, or a number less than 20. MaxCells determines how many times the following sections are repeated, these are:
    - The '### {current_cell_count} of {MaxCells}' section is printed Exactly {MaxCells} times, NEVER less than that. The Only time it is printed less than 20 times is when ALL empty cells in the Entire sudoku have been processed, otherwise it is printed the Full 20 times.
    - The '## {row_name} Candidates' section is printed however many times is required for the '### {current_cell_count} of {MaxCells}' section to be printed the Full and Correct number of times. So if the '### {current_cell_count} of {MaxCells}' section has not yet been printed {MaxCells} times when a row ends, then the '## {row_name} Candidates' section must be printed again for the next required row.
- When a section is repeated, it should always use the next required value or item (the items to iterate over are described in the section).
- Go through the sections in the given order, following the given instructions exactly for each.
- If a section header is marked by '(this section is not printed)', then do not print that section.
- Each must be done section In Full.

Some notes on specific sections:
- In the '# Index of all zeros, by row' section, you Must get the index of Every 0 element in each row. It is Vital to get this correct, so the row elements are checked one by one for each row. The index of any 0 digit of a row found by checking one by one, is then added to a single list to be converted to column names for that row.
- In each '### {current_cell_count} of {MaxCells}' section, when fetching the block name, you Must use the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct block name.
- Also in the '### {current_cell_count} of {MaxCells}' section, take care to use the Correct Candidates lists for the current Row, Column, and Block. The Correct list elements Must be fetched and printed to be used for calculations.

Do not use spaces in lists anywhere, just use commas without spaces to separate elements.

Entry 2/5 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,4,8,7,6,5]
RowTwo: [4,2,0,3,6,7,8,9,1]
RowThree: [8,7,6,5,0,9,3,4,2]
RowFour: [3,8,7,6,9,1,5,2,4]
RowFive: [2,4,1,8,5,3,0,7,0]
RowSix: [5,6,9,4,0,2,1,3,8]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,8,6,4,0,3]
</output>

Entry 3/5 - assistant: Awaiting instructions.

Entry 4/5 - user: - You are going to analyze the sudoku you've just been given.
- All lists should have comma separated elements Without spaces.

- First print the title:
PART ONE, GROUPS AND CANDIDATES

- Then begin.
# Rows
- Display the board state in terms of the rows.
- Use (almost) the exact format as the sudoku given in the output tags, using 'Row{row_number}' for the row names (for example, 'RowOne').
- The only difference is you write '{row_name} = [the elements of {row_name}]' instead of '{row_name}: [the elements of {row_name}]' for each row.
- Do all rows.


# Columns
- Display the board state in terms of the columns.
- Use the same format as in the '# Rows' section, using 'Column{column_number}' for the column names.
- Do all columns.


# Blocks
- Display the board state in terms of the blocks.
- Do all blocks.
- Use 'Block{block_number}' for the block names.
- Give each in a 3x3 matrix, followed immediately by the same Block and elements as a standard list, using the format:
Block{block_number}:
[[a,b,c],
[d,e,f],
[g,h,i]]
Block{block_number} = [a,b,c,d,e,f,g,h,i]


# Row Candidates
- Now produce the row candidates.
- Do all rows, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each row in '# Rows', write out the digits NOT in the row using the following format:
Candidates{row_name} => AllDigits.difference({row_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {row_name}] from '# Rows') = [digits from AllDigits (1 to 9) not in {row_name}]
Candidates{row_name} = [the Candidates{row_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Row, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Column Candidates
- Now produce the column candidates.
- Do all columns, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each column in '# Columns', write out the digits NOT in the column using the following format:
Candidates{column_name} => AllDigits.difference({column_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {column_name} from '# Columns']) = [digits from AllDigits (digits 1 to 9) not in {column_name}]
Candidates{column_name} = [the Candidates{column_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Column, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Block Candidates
- Now produce the block candidates.
- Do all blocks, one at a time.

- First write out AllDigits for reference:
AllDigits = [1,2,3,4,5,6,7,8,9]

- For each block in '# Blocks', write out the digits NOT in the block using the following format:
Candidates{block_name} => AllDigits.difference({block_name}) => [1,2,3,4,5,6,7,8,9].difference([the elements of {block_name} from '# Blocks']) = [digits from AllDigits (digits 1 to 9) not in {block_name}]
Candidates{block_name} = [the Candidates{block_name} elements you just calculated at the end of the previous line]
- You Must write out both lines for each Block, first the calculation line, followed Immediately by the second more concise line. This is Required.


# Index of all zeros, by row
- Do all rows, one at a time.

- For each row in '# Rows', carefully calculate the index of Every 0 element in {row_name}, using the format below for each row.
- First each element {row_name}[0 to 8] is checked.
- Then the index of each 0 element is put into one list.
- Then add one to each index to turn them into column positions.
- Then convert the column positions to column names.
- Do this for all rows.
{row_name} = [list the elements of {row_name} from '# Rows']
Now finding the index of Each 0 element in {row_name}
{row_name}[0] = {the element at {row_name}[0]}
{row_name}[1] = {the element at {row_name}[1]}
{row_name}[2] = {the element at {row_name}[2]}
{row_name}[3] = {the element at {row_name}[3]}
{row_name}[4] = {the element at {row_name}[4]}
{row_name}[5] = {the element at {row_name}[5]}
{row_name}[6] = {the element at {row_name}[6]}
{row_name}[7] = {the element at {row_name}[7]}
{row_name}[8] = {the element at {row_name}[8]}
IndexOfAll0ElementsIn{row_name} => [the index of every 0 element found in {row_name}, from the elements just checked]
ColumnPositionOfAll0Elements{row_name} => map(element+1, IndexOfAll0ElementsIn{row_name}) = [elements of IndexOfAll0ElementsIn{row_name} with all elements incremented by 1]
EmptyColumnNames{row_name} = [Column{column_number as a Word} for column_number in ColumnPositionOfAll0Elements{row_name}]


# Calculate the number of empty cells in each row in '# Rows'
- Use the following as a format:
total_empty_cells = {Length{row_name} as a number} for each EmptyColumnNames{row_name} = {total sum}
- This will look like:
total_empty_cells = {number} + {number} + {number}, + {number} + {number} + {number}, + {number} + {number} + {number} = {total sum}


# Calculate MaxCells:
- Cap the number of cells to list:
MaxCells => min({total_empty_cells}, 20) = (the lower of 20 or {total_empty_cells})


PART TWO, CELL CANDIDATES
# Cell Candidates
- Calculate the cell candidates of the empty cells, up to MaxCells.
- Iterate through the empty cells from, stopping immediately after processing all {MaxCells} cells.
- To ensure only empty cells are processed, print the '## {row_name} Candidates' section when beginning each row.

- When you get to the start of a new row (and have not yet reached MaxCells), print the following to use as a reference (elements of EmptyColumnNames{row_name}, note on last empty column of the row, note on digits in lists, the row and column to block reference title, then Exactly three Row and Column to Block reference lines).
- Do this at the start of Each row when you get to it (until MaxCells). Then proceed with processing the empty cells in that row.
- Everything MUST be printed using the formats provided. This is Required.
## {row_name} Candidates
- Print the EmptyColumnNames for the current row, with the format:
EmptyColumnNames{row_name}: [list the column_names in EmptyColumnNames{row_name} from '# Index of all zeros, by row']
- Then print the following notes, with the format:
Note, the last empty column of the {row_name} is {EmptyColumnNames{row_name}[-1]}
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
- Then print the title for the block_name reference (Must be printed):
Reference: Row and Column to Block
- Then print EXACTLY AND ONLY THREE of the following reference lines. These are the Row and Column to Block reference table and Must be printed as is (only filling in the row_name). Change NOTHING about the lines other than filling in 'Row{row_number}' to the current row_name. You MUST print all three lines and leave the columns and blocks unchanged in each.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine
- end of the '## {row_name} Candidates' format

- For each empty cell in EmptyColumnNames{row_name}, up to a maximum of {MaxCells}, calculate the cell candidates using the format below.
- (List out the elements of a list when instructed).
- (Everything MUST be printed using the formats provided. This is Required).
### {current_cell_count} of {MaxCells}
Up to {column_name} in EmptyColumnNames{row_name}
The last empty column of EmptyColumnNames{row_name} is {EmptyColumnNames{row_name}[-1]}
- if {column_name} is the last empty column of EmptyColumnNames{row_name}:
    print("Last column of current row")
    - And If it is NOT the last cell of the section ({current_cell_count} != {MaxCells}), Also add:
        print("The next row is {next row_name with empty columns})
- else:
    print("Not the last column of current row")
{row_name} and {column_name} means {use the current Row and Column with the 'Reference: Row and Column to Block' table from the '## {row_name} Candidates' section of the current row to get the correct {block_name}}
import Candidates{row_name}, Candidates{column_name}, Candidates{block_name}
- You MUST use the already calculated Candidate elements for the current Row, Column, and Block (it is Required to use the already existing Candidates lists). You Must reprint the elements here to refresh them.
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
Finding Common Elements:
- Use the following format to calculate the elements common to both the current row, and the current column.
CommonElementsOf{row_name}And{column_name} => [the elements of Candidates{row_name}] & [the elements of Candidates{column_name}] = [element if element in Candidates{row_name} and if element in Candidates{column_name}]
- Use the following format to calculate the elements common to both the results of the previous line (the common row and column elements), and the current block.
CommonElementsOf{row_name}And{column_name}And{block_name} => [the elements of CommonElementsOf{row_name}And{column_name}] & [the elements of Candidates{block_name}] = [element if element in CommonElementsOf{row_name}And{column_name} and if element in Candidates{block_name}]
CellCandidates = [list the calculated elements of CommonElementsOf{row_name}And{column_name}And{block_name} exactly as they appear at the end of the previous line, and with No Spaces]
Length = {CellCandidates.length}
- If Length == 1, print the line:
FOUND {row_name}, {column_name}, {block_name}
- Else, print the line:
Not 1
{at the end of each cell, print a newline}
- then move to the next empty cell until All {MaxCells} empty cells are done.
- end of the '### {current_cell_count} of {MaxCells}' format

- Calculate the candidates for all {MaxCells} cells starting from the top (though never more than 20 cells, that is the max).
- As soon as you have finished processing all {MaxCells} of {MaxCells} cells, Stop Listing Cells, and print:
Finished printing {MaxCells} of {MaxCells} cells
- This is ONLY when {current_cell_count} == {MaxCells}, NEVER before.


PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
- For every (up to six) empty cell which had only one element in CellCandidates, marked by "FOUND", find and output all of the FOUND cells (up to a Maximum of 6 FOUND cells) in one place using the same format as the `FOUND {row_name}, {column_name}, {block_name}` line:
{count from 1 to (at most) 6}: FOUND {row_name}, {column_name, {block_name}}
- If there were six or more cells with only one CellCandidates, print the following As Soon as you have printed six cells (the max) (if less than six, skip to the Else If below), and then don't print the rest:
Printed The Max Of Six FOUND Cells
- Else If you have printed all FOUND cells, but there were less than six, at the end of the FOUND cells print:
Printed all {number_of_FOUND_cells (when Less than 6 are found)} FOUND cells
- Make sure to list all of the ones you found up to a max of six (if there were less than six, just print the ones you found).
- If there where none, instead print "There were no empty cells with only one cell candidate"

## Unbiased Results
- You MUST print the '## Unbiased Results' section heading, so it can be picked up by the system.
- For every cell in the '## Collating Results' section (up to a MAX of 6), list them in the format:
cell({row_name}, {column_name}, {block_name}):
Candidates{row_name} = [the elements of Candidates{row_name} from '# Row Candidates']
Candidates{column_name} = [the elements of Candidates{column_name} from '# Column Candidates']
Candidates{block_name} = [the elements of Candidates{block_name} from '# Block Candidates']
{newline}
- Surround the entire list of cells with <analysis output></analysis output> tags.
- If there were no found cells, output the <analysis output></analysis output> tags containing only the phrase "There were no empty cells with only one cell candidate"
- (Do not put anything after the closing analysis output tag).


- # Final Notes (this section is not printed)
- You Must Finish All Sections In Full. Do not stop until All Sections are Fully Finished.
- Print the provided headers when appropriate.
- Use these instructions to analyze the sudoku.
- Begin.

Entry 5/5 - assistant: PART ONE, GROUPS AND CANDIDATES
# Rows
RowOne = [9,1,3,2,4,8,7,6,5]
RowTwo = [4,2,0,3,6,7,8,9,1]
RowThree = [8,7,6,5,0,9,3,4,2]
RowFour = [3,8,7,6,9,1,5,2,4]
RowFive = [2,4,1,8,5,3,0,7,0]
RowSix = [5,6,9,4,0,2,1,3,8]
RowSeven = [1,3,4,7,2,5,6,8,9]
RowEight = [6,9,8,1,3,4,2,5,7]
RowNine = [7,5,2,9,8,6,4,0,3]

# Columns
ColumnOne = [9,4,8,3,2,5,1,6,7]
ColumnTwo = [1,2,7,8,4,6,3,9,5]
ColumnThree = [3,0,6,7,1,9,4,8,2]
ColumnFour = [2,3,5,6,8,4,7,1,9]
ColumnFive = [4,6,0,9,5,0,2,3,8]
ColumnSix = [8,7,9,1,3,2,5,4,6]
ColumnSeven = [7,8,3,5,0,1,6,2,4]
ColumnEight = [6,9,4,2,7,3,8,5,0]
ColumnNine = [5,1,2,4,0,8,9,7,3]

# Blocks
BlockOne:
[[9,1,3],
[4,2,0],
[8,7,6]]
BlockOne = [9,1,3,4,2,0,8,7,6]

BlockTwo:
[[2,4,8],
[3,6,7],
[5,0,9]]
BlockTwo = [2,4,8,3,6,7,5,0,9]

BlockThree:
[[7,6,5],
[8,9,1],
[3,4,2]]
BlockThree = [7,6,5,8,9,1,3,4,2]

BlockFour:
[[3,8,7],
[2,4,1],
[5,6,9]]
BlockFour = [3,8,7,2,4,1,5,6,9]

BlockFive:
[[6,9,1],
[8,5,3],
[4,0,2]]
BlockFive = [6,9,1,8,5,3,4,0,2]

BlockSix:
[[5,2,4],
[0,7,0],
[1,3,8]]
BlockSix = [5,2,4,0,7,0,1,3,8]

BlockSeven:
[[1,3,4],
[6,9,8],
[7,5,2]]
BlockSeven = [1,3,4,6,9,8,7,5,2]

BlockEight:
[[7,2,5],
[1,3,4],
[9,8,6]]
BlockEight = [7,2,5,1,3,4,9,8,6]

BlockNine:
[[6,8,9],
[2,5,7],
[4,0,3]]
BlockNine = [6,8,9,2,5,7,4,0,3]

# Row Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesRowOne => AllDigits.difference(RowOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,2,4,8,7,6,5]) = []
CandidatesRowOne = []
CandidatesRowTwo => AllDigits.difference(RowTwo) => [1,2,3,4,5,6,7,8,9].difference([4,2,0,3,6,7,8,9,1]) = [5]
CandidatesRowTwo = [5]
CandidatesRowThree => AllDigits.difference(RowThree) => [1,2,3,4,5,6,7,8,9].difference([8,7,6,5,0,9,3,4,2]) = [1]
CandidatesRowThree = [1]
CandidatesRowFour => AllDigits.difference(RowFour) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,6,9,1,5,2,4]) = []
CandidatesRowFour = []
CandidatesRowFive => AllDigits.difference(RowFive) => [1,2,3,4,5,6,7,8,9].difference([2,4,1,8,5,3,0,7,0]) = [6,9]
CandidatesRowFive = [6,9]
CandidatesRowSix => AllDigits.difference(RowSix) => [1,2,3,4,5,6,7,8,9].difference([5,6,9,4,0,2,1,3,8]) = [7]
CandidatesRowSix = [7]
CandidatesRowSeven => AllDigits.difference(RowSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,7,2,5,6,8,9]) = []
CandidatesRowSeven = []
CandidatesRowEight => AllDigits.difference(RowEight) => [1,2,3,4,5,6,7,8,9].difference([6,9,8,1,3,4,2,5,7]) = []
CandidatesRowEight = []
CandidatesRowNine => AllDigits.difference(RowNine) => [1,2,3,4,5,6,7,8,9].difference([7,5,2,9,8,6,4,0,3]) = [1]
CandidatesRowNine = [1]

# Column Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesColumnOne => AllDigits.difference(ColumnOne) => [1,2,3,4,5,6,7,8,9].difference([9,4,8,3,2,5,1,6,7]) = []
CandidatesColumnOne = []
CandidatesColumnTwo => AllDigits.difference(ColumnTwo) => [1,2,3,4,5,6,7,8,9].difference([1,2,7,8,4,6,3,9,5]) = []
CandidatesColumnTwo = []
CandidatesColumnThree => AllDigits.difference(ColumnThree) => [1,2,3,4,5,6,7,8,9].difference([3,0,6,7,1,9,4,8,2]) = [5]
CandidatesColumnThree = [5]
CandidatesColumnFour => AllDigits.difference(ColumnFour) => [1,2,3,4,5,6,7,8,9].difference([2,3,5,6,8,4,7,1,9]) = []
CandidatesColumnFour = []
CandidatesColumnFive => AllDigits.difference(ColumnFive) => [1,2,3,4,5,6,7,8,9].difference([4,6,0,9,5,0,2,3,8]) = [1,7]
CandidatesColumnFive = [1,7]
CandidatesColumnSix => AllDigits.difference(ColumnSix) => [1,2,3,4,5,6,7,8,9].difference([8,7,9,1,3,2,5,4,6]) = []
CandidatesColumnSix = []
CandidatesColumnSeven => AllDigits.difference(ColumnSeven) => [1,2,3,4,5,6,7,8,9].difference([7,8,3,5,0,1,6,2,4]) = [9]
CandidatesColumnSeven = [9]
CandidatesColumnEight => AllDigits.difference(ColumnEight) => [1,2,3,4,5,6,7,8,9].difference([6,9,4,2,7,3,8,5,0]) = [1]
CandidatesColumnEight = [1]
CandidatesColumnNine => AllDigits.difference(ColumnNine) => [1,2,3,4,5,6,7,8,9].difference([5,1,2,4,0,8,9,7,3]) = [6]
CandidatesColumnNine = [6]

# Block Candidates
AllDigits = [1,2,3,4,5,6,7,8,9]
CandidatesBlockOne => AllDigits.difference(BlockOne) => [1,2,3,4,5,6,7,8,9].difference([9,1,3,4,2,0,8,7,6]) = [5]
CandidatesBlockOne = [5]
CandidatesBlockTwo => AllDigits.difference(BlockTwo) => [1,2,3,4,5,6,7,8,9].difference([2,4,8,3,6,7,5,0,9]) = [1]
CandidatesBlockTwo = [1]
CandidatesBlockThree => AllDigits.difference(BlockThree) => [1,2,3,4,5,6,7,8,9].difference([7,6,5,8,9,1,3,4,2]) = []
CandidatesBlockThree = []
CandidatesBlockFour => AllDigits.difference(BlockFour) => [1,2,3,4,5,6,7,8,9].difference([3,8,7,2,4,1,5,6,9]) = []
CandidatesBlockFour = []
CandidatesBlockFive => AllDigits.difference(BlockFive) => [1,2,3,4,5,6,7,8,9].difference([6,9,1,8,5,3,4,0,2]) = [7]
CandidatesBlockFive = [7]
CandidatesBlockSix => AllDigits.difference(BlockSix) => [1,2,3,4,5,6,7,8,9].difference([5,2,4,0,7,0,1,3,8]) = [6,9]
CandidatesBlockSix = [6,9]
CandidatesBlockSeven => AllDigits.difference(BlockSeven) => [1,2,3,4,5,6,7,8,9].difference([1,3,4,6,9,8,7,5,2]) = []
CandidatesBlockSeven = []
CandidatesBlockEight => AllDigits.difference(BlockEight) => [1,2,3,4,5,6,7,8,9].difference([7,2,5,1,3,4,9,8,6]) = []
CandidatesBlockEight = []
CandidatesBlockNine => AllDigits.difference(BlockNine) => [1,2,3,4,5,6,7,8,9].difference([6,8,9,2,5,7,4,0,3]) = [1]
CandidatesBlockNine = [1]

# Index of all zeros, by row
RowTwo = [4,2,0,3,6,7,8,9,1]
Now finding the index of Each 0 element in RowTwo
RowTwo[0] = 4
RowTwo[1] = 2
RowTwo[2] = 0
RowTwo[3] = 3
RowTwo[4] = 6
RowTwo[5] = 7
RowTwo[6] = 8
RowTwo[7] = 9
RowTwo[8] = 1
IndexOfAll0ElementsInRowTwo => [2]
ColumnPositionOfAll0ElementsRowTwo => map(element+1, IndexOfAll0ElementsInRowTwo) = [3]
EmptyColumnNamesRowTwo = [ColumnThree]

RowThree = [8,7,6,5,0,9,3,4,2]
Now finding the index of Each 0 element in RowThree
RowThree[0] = 8
RowThree[1] = 7
RowThree[2] = 6
RowThree[3] = 5
RowThree[4] = 0
RowThree[5] = 9
RowThree[6] = 3
RowThree[7] = 4
RowThree[8] = 2
IndexOfAll0ElementsInRowThree => [4]
ColumnPositionOfAll0ElementsRowThree => map(element+1, IndexOfAll0ElementsInRowThree) = [5]
EmptyColumnNamesRowThree = [ColumnFive]

RowFive = [2,4,1,8,5,3,0,7,0]
Now finding the index of Each 0 element in RowFive
RowFive[0] = 2
RowFive[1] = 4
RowFive[2] = 1
RowFive[3] = 8
RowFive[4] = 5
RowFive[5] = 3
RowFive[6] = 0
RowFive[7] = 7
RowFive[8] = 0
IndexOfAll0ElementsInRowFive => [6,8]
ColumnPositionOfAll0ElementsRowFive => map(element+1, IndexOfAll0ElementsInRowFive) = [7,9]
EmptyColumnNamesRowFive = [ColumnSeven,ColumnNine]

RowSix = [5,6,9,4,0,2,1,3,8]
Now finding the index of Each 0 element in RowSix
RowSix[0] = 5
RowSix[1] = 6
RowSix[2] = 9
RowSix[3] = 4
RowSix[4] = 0
RowSix[5] = 2
RowSix[6] = 1
RowSix[7] = 3
RowSix[8] = 8
IndexOfAll0ElementsInRowSix => [4]
ColumnPositionOfAll0ElementsRowSix => map(element+1, IndexOfAll0ElementsInRowSix) = [5]
EmptyColumnNamesRowSix = [ColumnFive]

RowNine = [7,5,2,9,8,6,4,0,3]
Now finding the index of Each 0 element in RowNine
RowNine[0] = 7
RowNine[1] = 5
RowNine[2] = 2
RowNine[3] = 9
RowNine[4] = 8
RowNine[5] = 6
RowNine[6] = 4
RowNine[7] = 0
RowNine[8] = 3
IndexOfAll0ElementsInRowNine => [7]
ColumnPositionOfAll0ElementsRowNine => map(element+1, IndexOfAll0ElementsInRowNine) = [8]
EmptyColumnNamesRowNine = [ColumnEight]

# Calculate the number of empty cells in each row in '# Rows'
total_empty_cells = 1 for each EmptyColumnNamesRowTwo + 1 for each EmptyColumnNamesRowThree + 2 for each EmptyColumnNamesRowFive + 1 for each EmptyColumnNamesRowSix + 1 for each EmptyColumnNamesRowNine = 6

# Calculate MaxCells:
MaxCells => min(total_empty_cells, 20) = 6

PART TWO, CELL CANDIDATES
# Cell Candidates
## RowTwo Candidates
EmptyColumnNamesRowTwo: [ColumnThree]
Note, the last empty column of the RowTwo is ColumnThree
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowTwo and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowTwo and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowTwo and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 1 of 6
Up to ColumnThree in EmptyColumnNamesRowTwo
The last empty column of EmptyColumnNamesRowTwo is ColumnThree
Last column of current row
The next row is RowThree
RowTwo and ColumnThree means BlockOne
import CandidatesRowTwo, CandidatesColumnThree, CandidatesBlockOne
CandidatesRowTwo = [5]
CandidatesColumnThree = [5]
CandidatesBlockOne = [5]
Finding Common Elements:
CommonElementsOfRowTwoAndColumnThree => [5] & [5] = [5]
CommonElementsOfRowTwoAndColumnThreeAndBlockOne => [5] & [5] = [5]
CellCandidates = [5]
Length = 1
FOUND RowTwo, ColumnThree, BlockOne

## RowThree Candidates
EmptyColumnNamesRowThree: [ColumnFive]
Note, the last empty column of the RowThree is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowThree and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
RowThree and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
RowThree and ColumnSeven, ColumnEight, or ColumnNine means BlockThree

### 2 of 6
Up to ColumnFive in EmptyColumnNamesRowThree
The last empty column of EmptyColumnNamesRowThree is ColumnFive
Last column of current row
The next row is RowFive
RowThree and ColumnFive means BlockTwo
import CandidatesRowThree, CandidatesColumnFive, CandidatesBlockTwo
CandidatesRowThree = [1]
CandidatesColumnFive = [1,7]
CandidatesBlockTwo = [1]
Finding Common Elements:
CommonElementsOfRowThreeAndColumnFive => [1] & [1,7] = [1]
CommonElementsOfRowThreeAndColumnFiveAndBlockTwo => [1] & [1] = [1]
CellCandidates = [1]
Length = 1
FOUND RowThree, ColumnFive, BlockTwo

## RowFive Candidates
EmptyColumnNamesRowFive: [ColumnSeven,ColumnNine]
Note, the last empty column of the RowFive is ColumnNine
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowFive and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowFive and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowFive and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 3 of 6
Up to ColumnSeven in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Not the last column of current row
RowFive and ColumnSeven means BlockSix
import CandidatesRowFive, CandidatesColumnSeven, CandidatesBlockSix
CandidatesRowFive = [6,9]
CandidatesColumnSeven = [9]
CandidatesBlockSix = [6,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnSeven => [6,9] & [9] = [9]
CommonElementsOfRowFiveAndColumnSevenAndBlockSix => [9] & [6,9] = [9]
CellCandidates = [9]
Length = 1
FOUND RowFive, ColumnSeven, BlockSix

### 4 of 6
Up to ColumnNine in EmptyColumnNamesRowFive
The last empty column of EmptyColumnNamesRowFive is ColumnNine
Last column of current row
The next row is RowSix
RowFive and ColumnNine means BlockSix
import CandidatesRowFive, CandidatesColumnNine, CandidatesBlockSix
CandidatesRowFive = [6,9]
CandidatesColumnNine = [6]
CandidatesBlockSix = [6,9]
Finding Common Elements:
CommonElementsOfRowFiveAndColumnNine => [6,9] & [6] = [6]
CommonElementsOfRowFiveAndColumnNineAndBlockSix => [6] & [6,9] = [6]
CellCandidates = [6]
Length = 1
FOUND RowFive, ColumnNine, BlockSix

## RowSix Candidates
EmptyColumnNamesRowSix: [ColumnFive]
Note, the last empty column of the RowSix is ColumnFive
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowSix and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
RowSix and ColumnFour, ColumnFive, or ColumnSix means BlockFive
RowSix and ColumnSeven, ColumnEight, or ColumnNine means BlockSix

### 5 of 6
Up to ColumnFive in EmptyColumnNamesRowSix
The last empty column of EmptyColumnNamesRowSix is ColumnFive
Last column of current row
The next row is RowNine
RowSix and ColumnFive means BlockFive
import CandidatesRowSix, CandidatesColumnFive, CandidatesBlockFive
CandidatesRowSix = [7]
CandidatesColumnFive = [1,7]
CandidatesBlockFive = [7]
Finding Common Elements:
CommonElementsOfRowSixAndColumnFive => [7] & [1,7] = [7]
CommonElementsOfRowSixAndColumnFiveAndBlockFive => [7] & [7] = [7]
CellCandidates = [7]
Length = 1
FOUND RowSix, ColumnFive, BlockFive

## RowNine Candidates
EmptyColumnNamesRowNine: [ColumnEight]
Note, the last empty column of the RowNine is ColumnEight
Note, digits in lists will Only consist of subsets of AllDigits = [1,2,3,4,5,6,7,8,9]
Reference: Row and Column to Block
RowNine and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
RowNine and ColumnFour, ColumnFive, or ColumnSix means BlockEight
RowNine and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

### 6 of 6
Up to ColumnEight in EmptyColumnNamesRowNine
The last empty column of EmptyColumnNamesRowNine is ColumnEight
Last column of current row
RowNine and ColumnEight means BlockNine
import CandidatesRowNine, CandidatesColumnEight, CandidatesBlockNine
CandidatesRowNine = [1]
CandidatesColumnEight = [1]
CandidatesBlockNine = [1]
Finding Common Elements:
CommonElementsOfRowNineAndColumnEight => [1] & [1] = [1]
CommonElementsOfRowNineAndColumnEightAndBlockNine => [1] & [1] = [1]
CellCandidates = [1]
Length = 1
FOUND RowNine, ColumnEight, BlockNine

Finished printing 6 of 6 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowTwo, ColumnThree, BlockOne
2: FOUND RowThree, ColumnFive, BlockTwo
3: FOUND RowFive, ColumnSeven, BlockSix
4: FOUND RowFive, ColumnNine, BlockSix
5: FOUND RowSix, ColumnFive, BlockFive
6: FOUND RowNine, ColumnEight, BlockNine
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowTwo, ColumnThree, BlockOne):
CandidatesRowTwo = [5]
CandidatesColumnThree = [5]
CandidatesBlockOne = [5]

cell(RowThree, ColumnFive, BlockTwo):
CandidatesRowThree = [1]
CandidatesColumnFive = [1,7]
CandidatesBlockTwo = [1]

cell(RowFive, ColumnSeven, BlockSix):
CandidatesRowFive = [6,9]
CandidatesColumnSeven = [9]
CandidatesBlockSix = [6,9]

cell(RowFive, ColumnNine, BlockSix):
CandidatesRowFive = [6,9]
CandidatesColumnNine = [6]
CandidatesBlockSix = [6,9]

cell(RowSix, ColumnFive, BlockFive):
CandidatesRowSix = [7]
CandidatesColumnFive = [1,7]
CandidatesBlockFive = [7]

cell(RowNine, ColumnEight, BlockNine):
CandidatesRowNine = [1]
CandidatesColumnEight = [1]
CandidatesBlockNine = [1]
</analysis output>

----
Conversation ended.

Conversation started at: 2023-12-09 22:52:34.790890
Turn number: 16
----
Entry 1/9 - system: Follow ALL instructions METHODICALLY and IN FULL. Your task is to calculate the possible candidate elements for the given cells using the given information, then to update the non-rejected cells of the given sudoku using the calculated candidate elements, then to shift the rows, and finally to output the updated and shifted sudoku. Once you begin you must complete ALL of these tasks BEFORE stopping. After receiving the full instructions you have ONLY one message to finish the task, as soon as you stop responding the final section of your response is sent to the next part of the process. Thus the final text you write MUST be the updated and shifted Sudoku, in the correct format, after ALL other sections have been completed. Do not use spaces in lists, only use commas without spaces to separate elements. Begin as soon as you receive the full instruction set.

Entry 2/9 - user: Respond to this message with "Awaiting instructions." and nothing else. When you receive the current sudoku in <output> tags, say only "Awaiting instructions." and nothing else. You will then receive the last few hundred characters of the previous analysis results. When you receive the previous results say "Awaiting instructions." and nothing else. You will then receive instructions. When you receive the instructions, you may begin.

Entry 3/9 - assistant: Awaiting instructions.

Entry 4/9 - assistant:  and Outputting the Sudoku
<output>
RowOne: [9,1,3,2,4,8,7,6,5]
RowTwo: [4,2,0,3,6,7,8,9,1]
RowThree: [8,7,6,5,0,9,3,4,2]
RowFour: [3,8,7,6,9,1,5,2,4]
RowFive: [2,4,1,8,5,3,0,7,0]
RowSix: [5,6,9,4,0,2,1,3,8]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,8,6,4,0,3]
</output>

Entry 5/9 - assistant: Awaiting instructions.

Entry 6/9 - assistant: BlockNine = [1]
Finding Common Elements:
CommonElementsOfRowNineAndColumnEight => [1] & [1] = [1]
CommonElementsOfRowNineAndColumnEightAndBlockNine => [1] & [1] = [1]
CellCandidates = [1]
Length = 1
FOUND RowNine, ColumnEight, BlockNine

Finished printing 6 of 6 cells

PART THREE, OUTPUT
# Outputting FOUND Cells
## Collating Results, Six Max
1: FOUND RowTwo, ColumnThree, BlockOne
2: FOUND RowThree, ColumnFive, BlockTwo
3: FOUND RowFive, ColumnSeven, BlockSix
4: FOUND RowFive, ColumnNine, BlockSix
5: FOUND RowSix, ColumnFive, BlockFive
6: FOUND RowNine, ColumnEight, BlockNine
Printed The Max Of Six FOUND Cells

## Unbiased Results
<analysis output>
cell(RowTwo, ColumnThree, BlockOne):
CandidatesRowTwo = [5]
CandidatesColumnThree = [5]
CandidatesBlockOne = [5]

cell(RowThree, ColumnFive, BlockTwo):
CandidatesRowThree = [1]
CandidatesColumnFive = [1,7]
CandidatesBlockTwo = [1]

cell(RowFive, ColumnSeven, BlockSix):
CandidatesRowFive = [6,9]
CandidatesColumnSeven = [9]
CandidatesBlockSix = [6,9]

cell(RowFive, ColumnNine, BlockSix):
CandidatesRowFive = [6,9]
CandidatesColumnNine = [6]
CandidatesBlockSix = [6,9]

cell(RowSix, ColumnFive, BlockFive):
CandidatesRowSix = [7]
CandidatesColumnFive = [1,7]
CandidatesBlockFive = [7]

cell(RowNine, ColumnEight, BlockNine):
CandidatesRowNine = [1]
CandidatesColumnEight = [1]
CandidatesBlockNine = [1]
</analysis output>

Entry 7/9 - assistant: Awaiting instructions.

Entry 8/9 - user: - My previous message contains the last few hundred characters of a Sudoku analysis.
- You are examining the text between the <analysis output></analysis output> tags in the '## Unbiased Results' section of my previous message. Ignore any text appearing before the opening <analysis output> tag, as it was part of the working out and should be ignored.
- The cells given inside analysis output tags are cells which were found to have only one possible candidate.
- However, the process which found the given cells sometimes made mistakes, due to having to check so many cells at once.
- Your task is to use the given instructions to perform a Thorough Independent Verification or Rejection of the given cells, then updating the sudoku with the verified ones.
- Detailed instructions are provided below, but an overview is as follows:
    - Calculate the possible candidate elements for each cell using the Thorough method given below.
    - If a cell has multiple candidates, reject that cell as a mistake made by the previous process.
    - Update and rotate the Sudoku, then output it.
- Complete all steps starting at STEP_ONE.

- Note: Block names from the Row name and Column name.
- (don't print this table, it's just here for reference).
- In order to not get confused by the block names, here is a reference table.
- These three for RowOne, RowTwo, or RowThree
Row{row_number == One|Two|Three} and ColumnOne, ColumnTwo, or ColumnThree means BlockOne
Row{row_number == One|Two|Three} and ColumnFour, ColumnFive, or ColumnSix means BlockTwo
Row{row_number == One|Two|Three} and ColumnSeven, ColumnEight, or ColumnNine means BlockThree
- OR these three for RowFour, RowFive, or RowSix
Row{row_number == Four|Five|Six} and ColumnOne, ColumnTwo, or ColumnThree means BlockFour
Row{row_number == Four|Five|Six} and ColumnFour, ColumnFive, or ColumnSix means BlockFive
Row{row_number == Four|Five|Six} and ColumnSeven, ColumnEight, or ColumnNine means BlockSix
- OR these three for RowSeven, RowEight, or RowNine
Row{row_number == Seven|Eight|Nine} and ColumnOne, ColumnTwo, or ColumnThree means BlockSeven
Row{row_number == Seven|Eight|Nine} and ColumnFour, ColumnFive, or ColumnSix means BlockEight
Row{row_number == Seven|Eight|Nine} and ColumnSeven, ColumnEight, or ColumnNine means BlockNine

- Note: Possible values and lengths for PreCellColumnsList.
- (don't print this table, it's just here for reference).
- These (in general) are the possible values and associated lengths for PreCellColumnsList in STEP_FIVE.
- Note that (except for the ColumnOne list which is empty and has length 0), these all have length implied by the element BEFORE the current column_name. That is, the accurate length is the length implied by The Last Column in each list (which is the column Before column_name).
When column_name == ColumnOne: [].length = 0
When column_name == ColumnTwo: [ColumnOne].length = 1
When column_name == ColumnThree: [ColumnOne,ColumnTwo].length = 2
When column_name == ColumnFour: [ColumnOne,ColumnTwo,ColumnThree].length = 3
When column_name == ColumnFive: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
When column_name == ColumnSix: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive].length = 5
When column_name == ColumnSeven: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
When column_name == ColumnEight: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
When column_name == ColumnNine: [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven, ColumnEight].length = 8


- Begin at STEP_ONE
# STEP_ONE Extracting Previous Results
- Extract the results of the <analysis output></analysis output> tag in the '# Unbiased Results' section of my previous message. ONLY use the extracted results, nothing else from that message. If you can see any of the working above you MUST ignore it and do YOUR OWN calculations using ONLY the Unbiased Results.
- When printing the cell names, use Almost the same format, but do not include the {block_name}, so the cell name format you print should be `cell({row_name}, {column_name})`. You Still Need to print the Row, Column, AND Block candidates for each.
- If you do not see the '# Unbiased Results' header or the opening analysis output tag, that means they were cut off when the results were extracted. In that case, make sure the message ends in the closing analysis output tag and take the last six COMPLETE cells given. Make sure NOT to take a partial cell, always look for each the starting word 'cell' of each cell.
- There should only be a maximum of six cells given in my previous message. If there are more than that, take ONLY a Maximum of SIX CELLS, as that's all the system can handle.
- Print the extracted text from the analysis output tag under the current heading '# STEP_ONE Extracting Previous Results'. Do not print the heading or the tags from the previous message, just the required contents.
- These cells will be used in STEP_TWO.


# STEP_TWO Calculating the candidates of each cell
- For each cell from STEP_ONE, use the following method to calculate the candidates of that cell.
- Find the shortest list out of the row, column, or block.
- Break up each of the Candidates lists into two lists each:
    - '{list_name}Low' containing only the {list_name} digits up to 5 (the 'Low' digits)
    - '{list_name}High' containing only the {list_name} digits 6 or higher (the 'High' digits)
- For each cell:
    - Loop through the digits of the shortest {list_name}, first {list_name}Low, then {list_name}High, to cover the whole {list_name}. The candidates are a subset of each of the three {list_name} lists, and the shortest list gives the least digits to search.
    - For each digit, count the number of times that digit appears in each appropriate list using list.count(digit).
    - After that on the same line, sum the counts that line to get the TotalCount.
    - Most importantly, if the TotalCount is 2, immediately print "FOUND A CANDIDATE".
- At the end of each cell, find all the digits which had a TotalCount of 2 (marked by 'FOUND A CANDIDATE') and list them as the candidates of that cell.
- Then move to the next cell until all are done.
- If there are more than 6 cells, cap the number to check at 6.

- At the start of this section (After the '# STEP_TWO Calculating the candidates of each cell' heading, but Before the first '## Cell 1 of {number of cells}' heading) print DigitsLow and DigitsHigh for reference:
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

- For each cell in STEP_ONE, use the following format to calculate the Candidates of that cell:
## Cell {current_cell_count, starts at 1, capped at 6} of {number of cells, capped at 6}
cell({row_name}, {column_name}):
Candidates{row_name}.length = {the number of elements in Candidates{row_name}}
Candidates{column_name}.length = {the number of elements in Candidates{column_name}}
Candidates{block_name}.length = {the number of elements in Candidates{block_name}}

shortest_list = Candidates{row_name|column_name|block_name, whichever has the smallest length} = digits to search
The shortest list will be checked against the other two lists: Candidates{name of one of the remaining lists} and Candidates{name of the other remaining list}

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
Candidates{row_name} = [the elements of Candidates{row_name}], broken into Candidates{row_name}Low = [only the digits from Candidates{row_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{row_name}High = [only the digits from Candidates{row_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{column_name} = [the elements of Candidates{column_name}], broken into Candidates{column_name}Low = [only the digits from Candidates{column_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{column_name}High = [only the digits from Candidates{column_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]
Candidates{block_name} = [the elements of Candidates{block_name}], broken into Candidates{block_name}Low = [only the digits from Candidates{block_name} that are in DigitsLow, that is only digits <= 5 (note that the lists are already sorted)] and Candidates{block_name}High = [only the digits from Candidates{block_name} that are in DigitsHigh, that is only digits >= 5 (note that the lists are already sorted)]

- You Must check both the Low digits And the High digits from the shortest_list, starting with Low, then High.
- You must always check the Low digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}Low = [the elements of Candidates{shortest_list}Low] against: Candidates{one of the remaining lists}Low = [the elements of Candidates{one of the remaining lists}Low] and Candidates{the other remaining list}Low = [the elements of Candidates{the other remaining list}Low]
- For each digit in Candidates{shortest_list}Low, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}Low].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}Low].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

- You must always check the High digits from shortest_list. The following line must Always be printed.
Checking digits in Candidates{shortest_list}High = [the elements of Candidates{shortest_list}High] against: Candidates{one of the remaining lists}High = [the elements of Candidates{one of the remaining lists}High] and Candidates{the other remaining list}High = [the elements of Candidates{the other remaining list}High]
- For each digit in Candidates{shortest_list}High, print the following:
{current_digit}: [the elements of Candidates{one of the remaining lists}High].count({current_digit}) = {the correct count, 0 or 1}, [Candidates{the other remaining list}High].count({current_digit}) = {the correct count, 0 or 1}, TotalCount({current_digit}) = {the sum of both counts for the current_digit, 0 or 1 or 2} {IF the sum of both counts == 2, print " FOUND A CANDIDATE" here, else move on to the next digit}

Confirmed candidates found for cell({row_name}, {column_name}): [the elements which were in all of the candidates lists, marked by " FOUND A CANDIDATE" while checking digits]
- Then move on to the next cell
{end of cell candidates format}

- For reference, here is an example of breaking up Candidates lists into Low and High digits, to clarify the process:
- CandidatesExampleRowName = [1,2,4,6,7,9], broken into CandidatesExampleRowNameLow = [1,2,4] and CandidatesExampleRowNameHigh = [6,7,9]
- CandidatesExampleColumnName = [1,3,4,5,6,9], broken into CandidatesExampleColumnNameLow = [1,3,4,5] and CandidatesExampleColumnNameHigh = [6,9]
- CandidatesExampleBlockName = [2,3,6,8,9], broken into CandidatesExampleBlockNameLow = [2,3] and CandidatesExampleBlockNameHigh = [6,8,9]


# STEP_THREE Checking the number of elements in each cell
- For each cell, count the number of elements in the candidates of that cell using .length().
- After each length, either print "length is 1, Passes" if the length is 1, or print "length is {length}, not 1, Rejected" if the length is Not one.
- Example (shows both forms, a rejection and passing cells):
cell({row_name_A}, {column_name_A}): [f,i]
[f,i].length = 2
length is 2, not 1, Rejected

cell({row_name_B}, {column_name_B}): [h]
[h].length = 1
length is 1, Passes

cell({row_name_C}, {column_name_C}): [e]
[e].length = 1
length is 1, Passes

- After doing this for all the cells, list the cells which Passed, making sure Not to list any Rejected cells.
- Example:
## Passing Cells
cell({row_name_B}, {column_name_B}): [h]
cell({row_name_C}, {column_name_C}): [e]


# STEP_FOUR: Grouping Cells with Corresponding Rows
- Group each cell from the "Passing Cells" in STEP_THREE with their corresponding row from the current Sudoku. Do not update them yet.
- If there are no passing cells to update, print "There are no cells to update" and move to the next step.
- List All rows from RowOne to RowNine
- List all Passing Cells from '## Passing Cells' in your STEP_THREE, each cell Must be Directly Underneath the Correct row.

- First, list the rows that have Passing Cells.
Rows with Passing Cells: {list the rows of the passing cells. For the example this would be `RowOne, RowTwo`, but use your Own passing cells}
{newline}

- Then print all rows (starting with {RowOne}), printing the cells-to-update for each row underneath that row (if the row has cells-to-update).
- Use the following format:
(- For each row, if the row from the previous sudoku output (Not updated)):
{row_name}: [the elements of {row_name}, from the previous output]
(- if the row has no cells-to-update, move on the next row):
(- However if the given row Does have cells-to-update, list the row followed immediately by the cells to update for the current row):
cell({row_name}, {column_name}): [candidate element]

- Make sure to list all rows from the previous sudoku (not yet updated), and all cells-to-update from '## Passing Cells'.


# STEP_FIVE: Applying Cell Updates to Rows
- The best way to ensure accuracy when updating an element is to be methodical.
- For each cell-to-update, print out each column by name, along with the element currently in that column.
- Then after printing all column names and the element in it, identify the column to update.
- Then, and this is important, Reprint the column list with {column_name} updated to the candidate element (and all other columns the same).
- Finally, print the updated Row.
- Do this for all cells-to-update.

- First print this Vital Note at the start of STEP_FIVE (just under STEP_FIVE heading), printed with Nothing Changed:
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList ends with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
- This note is So important that it must be repeated, in full and WITHOUT CHANGE in Every cell update (at the appropriate section). It MUST NOT be modified.

- Use the format below for each Passing Cell:
## Updating 1 of {number_of_cells_to_update}
cell({row_name}, {column_name}): [candidate element]
{row_name} = [the elements of {row_name}]
The {column_name} element of {row_name} needs to be updated to [candidate element]

ColumnOne: {element[0]}
ColumnTwo: {element[1]}
ColumnThree: {element[2]}
ColumnFour: {element[3]}
ColumnFive: {element[4]}
ColumnSix: {element[5]}
ColumnSeven: {element[6]}
ColumnEight: {element[7]}
ColumnNine: {element[8]}

Now replacing {column_name} with the element to update {candidate element}, such that {column_name} = {candidate element}
Redoing column list like we just did, but with {column_name} set to {candidate element}

{all columns and their elements fully listed as above, now with {column_name} set to the candidate element}

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE {column_name}.
VITAL NOTE Printed Verbatim: When listing all column names Before {column_name} it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...{the column BEFORE column_name}], except when column_name is ColumnOne, that is the only exception.
First list all column names Before {column_name} (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! {column_name} does Not appear on this list!!! The ONLY time you don't is if {column_name} is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [list all column names BEFORE {column_name}, DON'T FORGET to end with the column BEFORE {column_name}, and DON'T put {column_name} on the list!!!]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in {column_name}:
PreCellColumnsList.length => [the elements of PreCellColumnsList].length = {PreCellColumnsList.length}
Now the elements of the columns in PreCellColumnsList, which is the first {PreCellColumnsList.length} elements of {row_name}:
PreCellList = [Column Element for Column in PreCellColumnsList]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) {candidate element} to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append({candidate element}) = {ALL elements of PreCellList, followed Afterwards by {candidate element} (as the last appended element)}
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
Updated{row_name}StartingElements = [the elements of PreCellListWithCandidateElementAppended, followed by ..., to make it clear what the updated list starts with]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first {PreCellColumnsList.length} + 1 = {PreCellListWithCandidateElementAppended.length, the same as {PreCellColumnsList.length} + 1} elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
Updated{row_name} = [the already calculated elements of the updated {row_name}, from the column list you just printed, which starts with ALL of the elements of PreCellListWithCandidateElementAppended WITHOUT EXCEPTION]
- And move on to the next cell_to_update, until all are done.


# STEP_SIX: Printing the Updated Sudoku
- The output Must Not have spaces in the list. So directly underneath the STEP_SIX heading you must print:
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

-Print all updated rows, to be sure we don't confuse them with the original rows.
- Make sure to print the Exact updated rows you calculated in STEP_FIVE.
- Start by printing:
Updated Rows:
- Then print each of the updated rows in the form:
Updated{row_name} = [the elements of Updated{row_name} from STEP_FIVE]

- Now print the Sudoku using the updated rows.
- Print the Sudoku with spaces in the lists, only using commas to separate digits.
- Specify the rows to update first to be sure they aren't forgotten. Do not include any rejected cells.

- Example, follow the following format but using Your Own Rows:
- First print:
The rows to update are {row_names to update}
Using the contents of {the rows to update as Update{row_name}}
Printing Sudoku:
- Print each Row or UpdatedRow. Each should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`:
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]


# STEP_SEVEN: Shifting the Rows of the Sudoku
- Before you output the Sudoku, the top three rows(RowOne, RowTwo, and RowThree) need to shifted to the bottom, like cutting a deck of cards.
- This will shift the rows to the following order from top to bottom: Four, Five, Six, Seven, Eight, Nine, One, Two, Three.
- Make sure to use the Sudoku from STEP_SIX

- Each row should either look like `{row_name}: [the elements of {row_name}]` or `Updated{row_name}: [the elements of Updated{row_name}]`.
- Format:
{RowFour or UpdatedRowFour}: [RowFourElements or UpdatedRowFourElements]
{RowFive or UpdatedRowFive}: [RowFiveElements or UpdatedRowFiveElements]
{RowSix or UpdatedRowSix}: [RowSixElements or UpdatedRowSixElements]
{RowSeven or UpdatedRowSeven}: [RowSevenElements or UpdatedRowSevenElements]
{RowEight or UpdatedRowEight}: [RowEightElements or UpdatedRowEightElements]
{RowNine or UpdatedRowNine}: [RowNineElements or UpdatedRowNineElements]
{RowOne or UpdatedRowOne}: [RowOneElements or UpdatedRowOneElements]
{RowTwo or UpdatedRowTwo}: [RowTwoElements or UpdatedRowTwoElements]
{RowThree or UpdatedRowThree}: [RowThreeElements or UpdatedRowThreeElements]


# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
- WITHOUT moving the rows of the Sudoku, standardize the row names.
- Make sure to use the Sudoku from STEP_SEVEN (with standardized names).
- Also surround the Sudoku in output tags to clearly mark it as the output.
- Do not write ANYTHING after the closing output tag, as it will interfere with the system extracting your output.

- Example:
<output>
RowOne: [RowFourElements]
RowTwo: [RowFiveElements]
RowThree: [RowSixElements]
RowFour: [RowSevenElements]
RowFive: [RowEightElements]
RowSix: [RowNineElements]
RowSeven: [RowOneElements]
RowEight: [RowTwoElements]
RowNine: [RowThreeElements]
</output>


# Final notes
- Ensure all sections and subsections are clearly labeled using the simple headers provided in the instructions. Especially each STEP_NUMBER section.
- Stop ONLY after completing STEP_EIGHT, writing NOTHING ELSE after you write the final closing output tag.
- Begin

Entry 9/9 - assistant: # STEP_ONE Extracting Previous Results
cell(RowTwo, ColumnThree):
CandidatesRowTwo = [5]
CandidatesColumnThree = [5]
CandidatesBlockOne = [5]

cell(RowThree, ColumnFive):
CandidatesRowThree = [1]
CandidatesColumnFive = [1,7]
CandidatesBlockTwo = [1]

cell(RowFive, ColumnSeven):
CandidatesRowFive = [6,9]
CandidatesColumnSeven = [9]
CandidatesBlockSix = [6,9]

cell(RowFive, ColumnNine):
CandidatesRowFive = [6,9]
CandidatesColumnNine = [6]
CandidatesBlockSix = [6,9]

cell(RowSix, ColumnFive):
CandidatesRowSix = [7]
CandidatesColumnFive = [1,7]
CandidatesBlockFive = [7]

cell(RowNine, ColumnEight):
CandidatesRowNine = [1]
CandidatesColumnEight = [1]
CandidatesBlockNine = [1]

# STEP_TWO Calculating the candidates of each cell
DigitsLow = [1,2,3,4,5]
DigitsHigh = [6,7,8,9]

## Cell 1 of 6
cell(RowTwo, ColumnThree):
CandidatesRowTwo.length = 1
CandidatesColumnThree.length = 1
CandidatesBlockOne.length = 1

shortest_list = CandidatesRowTwo = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnThree and CandidatesBlockOne

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowTwo = [5], broken into CandidatesRowTwoLow = [5] and CandidatesRowTwoHigh = []
CandidatesColumnThree = [5], broken into CandidatesColumnThreeLow = [5] and CandidatesColumnThreeHigh = []
CandidatesBlockOne = [5], broken into CandidatesBlockOneLow = [5] and CandidatesBlockOneHigh = []

Checking digits in CandidatesRowTwoLow = [5] against: CandidatesColumnThreeLow = [5] and CandidatesBlockOneLow = [5]
5: [5].count(5) = 1, [5].count(5) = 1, TotalCount(5) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowTwoHigh = [] against: CandidatesColumnThreeHigh = [] and CandidatesBlockOneHigh = []

Confirmed candidates found for cell(RowTwo, ColumnThree): [5]

## Cell 2 of 6
cell(RowThree, ColumnFive):
CandidatesRowThree.length = 1
CandidatesColumnFive.length = 2
CandidatesBlockTwo.length = 1

shortest_list = CandidatesRowThree = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockTwo

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowThree = [1], broken into CandidatesRowThreeLow = [1] and CandidatesRowThreeHigh = []
CandidatesColumnFive = [1,7], broken into CandidatesColumnFiveLow = [1] and CandidatesColumnFiveHigh = [7]
CandidatesBlockTwo = [1], broken into CandidatesBlockTwoLow = [1] and CandidatesBlockTwoHigh = []

Checking digits in CandidatesRowThreeLow = [1] against: CandidatesColumnFiveLow = [1] and CandidatesBlockTwoLow = [1]
1: [1].count(1) = 1, [1].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowThreeHigh = [] against: CandidatesColumnFiveHigh = [7] and CandidatesBlockTwoHigh = []

Confirmed candidates found for cell(RowThree, ColumnFive): [1]

## Cell 3 of 6
cell(RowFive, ColumnSeven):
CandidatesRowFive.length = 2
CandidatesColumnSeven.length = 1
CandidatesBlockSix.length = 2

shortest_list = CandidatesColumnSeven = digits to search
The shortest list will be checked against the other two lists: CandidatesRowFive and CandidatesBlockSix

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [6,9], broken into CandidatesRowFiveLow = [] and CandidatesRowFiveHigh = [6,9]
CandidatesColumnSeven = [9], broken into CandidatesColumnSevenLow = [] and CandidatesColumnSevenHigh = [9]
CandidatesBlockSix = [6,9], broken into CandidatesBlockSixLow = [] and CandidatesBlockSixHigh = [6,9]

Checking digits in CandidatesColumnSevenLow = [] against: CandidatesRowFiveLow = [] and CandidatesBlockSixLow = []

Checking digits in CandidatesColumnSevenHigh = [9] against: CandidatesRowFiveHigh = [6,9] and CandidatesBlockSixHigh = [6,9]
9: [6,9].count(9) = 1, [6,9].count(9) = 1, TotalCount(9) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowFive, ColumnSeven): [9]

## Cell 4 of 6
cell(RowFive, ColumnNine):
CandidatesRowFive.length = 2
CandidatesColumnNine.length = 1
CandidatesBlockSix.length = 2

shortest_list = CandidatesColumnNine = digits to search
The shortest list will be checked against the other two lists: CandidatesRowFive and CandidatesBlockSix

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowFive = [6,9], broken into CandidatesRowFiveLow = [] and CandidatesRowFiveHigh = [6,9]
CandidatesColumnNine = [6], broken into CandidatesColumnNineLow = [] and CandidatesColumnNineHigh = [6]
CandidatesBlockSix = [6,9], broken into CandidatesBlockSixLow = [] and CandidatesBlockSixHigh = [6,9]

Checking digits in CandidatesColumnNineLow = [] against: CandidatesRowFiveLow = [] and CandidatesBlockSixLow = []

Checking digits in CandidatesColumnNineHigh = [6] against: CandidatesRowFiveHigh = [6,9] and CandidatesBlockSixHigh = [6,9]
6: [6,9].count(6) = 1, [6,9].count(6) = 1, TotalCount(6) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowFive, ColumnNine): [6]

## Cell 5 of 6
cell(RowSix, ColumnFive):
CandidatesRowSix.length = 1
CandidatesColumnFive.length = 2
CandidatesBlockFive.length = 1

shortest_list = CandidatesRowSix = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnFive and CandidatesBlockFive

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowSix = [7], broken into CandidatesRowSixLow = [] and CandidatesRowSixHigh = [7]
CandidatesColumnFive = [1,7], broken into CandidatesColumnFiveLow = [1] and CandidatesColumnFiveHigh = [7]
CandidatesBlockFive = [7], broken into CandidatesBlockFiveLow = [] and CandidatesBlockFiveHigh = [7]

Checking digits in CandidatesRowSixLow = [] against: CandidatesColumnFiveLow = [1] and CandidatesBlockFiveLow = []

Checking digits in CandidatesRowSixHigh = [7] against: CandidatesColumnFiveHigh = [7] and CandidatesBlockFiveHigh = [7]
7: [7].count(7) = 1, [7].count(7) = 1, TotalCount(7) = 2 FOUND A CANDIDATE

Confirmed candidates found for cell(RowSix, ColumnFive): [7]

## Cell 6 of 6
cell(RowNine, ColumnEight):
CandidatesRowNine.length = 1
CandidatesColumnEight.length = 1
CandidatesBlockNine.length = 1

shortest_list = CandidatesRowNine = digits to search
The shortest list will be checked against the other two lists: CandidatesColumnEight and CandidatesBlockNine

Breaking up the Candidates lists into Low digits [1,2,3,4,5] and High digits [6,7,8,9]:
CandidatesRowNine = [1], broken into CandidatesRowNineLow = [1] and CandidatesRowNineHigh = []
CandidatesColumnEight = [1], broken into CandidatesColumnEightLow = [1] and CandidatesColumnEightHigh = []
CandidatesBlockNine = [1], broken into CandidatesBlockNineLow = [1] and CandidatesBlockNineHigh = []

Checking digits in CandidatesRowNineLow = [1] against: CandidatesColumnEightLow = [1] and CandidatesBlockNineLow = [1]
1: [1].count(1) = 1, [1].count(1) = 1, TotalCount(1) = 2 FOUND A CANDIDATE

Checking digits in CandidatesRowNineHigh = [] against: CandidatesColumnEightHigh = [] and CandidatesBlockNineHigh = []

Confirmed candidates found for cell(RowNine, ColumnEight): [1]

# STEP_THREE Checking the number of elements in each cell
cell(RowTwo, ColumnThree): [5]
[5].length = 1
length is 1, Passes

cell(RowThree, ColumnFive): [1]
[1].length = 1
length is 1, Passes

cell(RowFive, ColumnSeven): [9]
[9].length = 1
length is 1, Passes

cell(RowFive, ColumnNine): [6]
[6].length = 1
length is 1, Passes

cell(RowSix, ColumnFive): [7]
[7].length = 1
length is 1, Passes

cell(RowNine, ColumnEight): [1]
[1].length = 1
length is 1, Passes

## Passing Cells
cell(RowTwo, ColumnThree): [5]
cell(RowThree, ColumnFive): [1]
cell(RowFive, ColumnSeven): [9]
cell(RowFive, ColumnNine): [6]
cell(RowSix, ColumnFive): [7]
cell(RowNine, ColumnEight): [1]

# STEP_FOUR: Grouping Cells with Corresponding Rows
Rows with Passing Cells: RowTwo, RowThree, RowFive, RowSix, RowNine

RowOne: [9,1,3,2,4,8,7,6,5]
RowTwo: [4,2,0,3,6,7,8,9,1]
cell(RowTwo, ColumnThree): [5]
RowThree: [8,7,6,5,0,9,3,4,2]
cell(RowThree, ColumnFive): [1]
RowFour: [3,8,7,6,9,1,5,2,4]
RowFive: [2,4,1,8,5,3,0,7,0]
cell(RowFive, ColumnSeven): [9]
cell(RowFive, ColumnNine): [6]
RowSix: [5,6,9,4,0,2,1,3,8]
cell(RowSix, ColumnFive): [7]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
RowNine: [7,5,2,9,8,6,4,0,3]
cell(RowNine, ColumnEight): [1]

# STEP_FIVE: Applying Cell Updates to Rows
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

## Updating 1 of 6
cell(RowTwo, ColumnThree): [5]
RowTwo = [4,2,0,3,6,7,8,9,1]
The ColumnThree element of RowTwo needs to be updated to [5]

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 0
ColumnFour: 3
ColumnFive: 6
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 9
ColumnNine: 1

Now replacing ColumnThree with the element to update [5], such that ColumnThree = 5
Redoing column list like we just did, but with ColumnThree set to 5

ColumnOne: 4
ColumnTwo: 2
ColumnThree: 5
ColumnFour: 3
ColumnFive: 6
ColumnSix: 7
ColumnSeven: 8
ColumnEight: 9
ColumnNine: 1

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnThree.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnThree it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnThree (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnThree does Not appear on this list!!! The ONLY time you don't is if ColumnThree is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnThree:
PreCellColumnsList.length => [ColumnOne,ColumnTwo].length = 2
Now the elements of the columns in PreCellColumnsList, which is the first 2 elements of RowTwo:
PreCellList = [4,2]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [5] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(5) = [4,2,5]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowTwoStartingElements = [4,2,5,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 3 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowTwo = [4,2,5,3,6,7,8,9,1]

## Updating 2 of 6
cell(RowThree, ColumnFive): [1]
RowThree = [8,7,6,5,0,9,3,4,2]
The ColumnFive element of RowThree needs to be updated to [1]

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 6
ColumnFour: 5
ColumnFive: 0
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 4
ColumnNine: 2

Now replacing ColumnFive with the element to update [1], such that ColumnFive = 1
Redoing column list like we just did, but with ColumnFive set to 1

ColumnOne: 8
ColumnTwo: 7
ColumnThree: 6
ColumnFour: 5
ColumnFive: 1
ColumnSix: 9
ColumnSeven: 3
ColumnEight: 4
ColumnNine: 2

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowThree:
PreCellList = [8,7,6,5]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [8,7,6,5,1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowThreeStartingElements = [8,7,6,5,1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowThree = [8,7,6,5,1,9,3,4,2]

## Updating 3 of 6
cell(RowFive, ColumnSeven): [9]
RowFive = [2,4,1,8,5,3,0,7,0]
The ColumnSeven element of RowFive needs to be updated to [9]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 5
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 0

Now replacing ColumnSeven with the element to update [9], such that ColumnSeven = 9
Redoing column list like we just did, but with ColumnSeven set to 9

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 5
ColumnSix: 3
ColumnSeven: 9
ColumnEight: 7
ColumnNine: 0

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnSeven.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnSeven it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnSeven (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnSeven does Not appear on this list!!! The ONLY time you don't is if ColumnSeven is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnSeven:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix].length = 6
Now the elements of the columns in PreCellColumnsList, which is the first 6 elements of RowFive:
PreCellList = [2,4,1,8,5,3]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [9] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(9) = [2,4,1,8,5,3,9]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [2,4,1,8,5,3,9,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 7 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [2,4,1,8,5,3,9,7,0]

## Updating 4 of 6
cell(RowFive, ColumnNine): [6]
RowFive = [2,4,1,8,5,3,0,7,0]
The ColumnNine element of RowFive needs to be updated to [6]

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 5
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 0

Now replacing ColumnNine with the element to update [6], such that ColumnNine = 6
Redoing column list like we just did, but with ColumnNine set to 6

ColumnOne: 2
ColumnTwo: 4
ColumnThree: 1
ColumnFour: 8
ColumnFive: 5
ColumnSix: 3
ColumnSeven: 0
ColumnEight: 7
ColumnNine: 6

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnNine.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnNine it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnNine (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnNine does Not appear on this list!!! The ONLY time you don't is if ColumnNine is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnNine:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven,ColumnEight].length = 8
Now the elements of the columns in PreCellColumnsList, which is the first 8 elements of RowFive:
PreCellList = [2,4,1,8,5,3,0,7]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [6] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(6) = [2,4,1,8,5,3,0,7,6]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowFiveStartingElements = [2,4,1,8,5,3,0,7,6,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 9 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowFive = [2,4,1,8,5,3,0,7,6]

## Updating 5 of 6
cell(RowSix, ColumnFive): [7]
RowSix = [5,6,9,4,0,2,1,3,8]
The ColumnFive element of RowSix needs to be updated to [7]

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 0
ColumnSix: 2
ColumnSeven: 1
ColumnEight: 3
ColumnNine: 8

Now replacing ColumnFive with the element to update [7], such that ColumnFive = 7
Redoing column list like we just did, but with ColumnFive set to 7

ColumnOne: 5
ColumnTwo: 6
ColumnThree: 9
ColumnFour: 4
ColumnFive: 7
ColumnSix: 2
ColumnSeven: 1
ColumnEight: 3
ColumnNine: 8

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnFive.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnFive it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnFive (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnFive does Not appear on this list!!! The ONLY time you don't is if ColumnFive is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnFive:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour].length = 4
Now the elements of the columns in PreCellColumnsList, which is the first 4 elements of RowSix:
PreCellList = [5,6,9,4]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [7] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(7) = [5,6,9,4,7]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowSixStartingElements = [5,6,9,4,7,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 5 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowSix = [5,6,9,4,7,2,1,3,8]

## Updating 6 of 6
cell(RowNine, ColumnEight): [1]
RowNine = [7,5,2,9,8,6,4,0,3]
The ColumnEight element of RowNine needs to be updated to [1]

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 8
ColumnSix: 6
ColumnSeven: 4
ColumnEight: 0
ColumnNine: 3

Now replacing ColumnEight with the element to update [1], such that ColumnEight = 1
Redoing column list like we just did, but with ColumnEight set to 1

ColumnOne: 7
ColumnTwo: 5
ColumnThree: 2
ColumnFour: 9
ColumnFive: 8
ColumnSix: 6
ColumnSeven: 4
ColumnEight: 1
ColumnNine: 3

Before we print the row, we need to ensure it will have no mistakes, being Especially careful about the element just before the updated cell.
Counting number of columns (and thus number of elements) BEFORE ColumnEight.
VITAL NOTE Printed Verbatim: When listing all column names Before ColumnEight it is [] if column_name is ColumnOne, it is [ColumnOne] if column_name is ColumnTwo, it is [ColumnOne,ColumnTwo] if column_name is ColumnThree, ect. Every PreCellColumnsList end with [...the column BEFORE column_name], except when column_name is ColumnOne, that is the only exception.
First list all column names Before ColumnEight (See VITAL NOTE Printed Verbatim above, start at ColumnOne and DON'T FORGET TO END WITH the column BEFORE the current column_name!!! ColumnEight does Not appear on this list!!! The ONLY time you don't is if ColumnEight is ColumnOne, in which case the list is empty.):
PreCellColumnsList = [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven]
Then the number of columns in PreCellColumnsList (which Never includes the current column). This list has length implied by the last column name in the list, which is the column BEFORE the current column, and is One Less than the number version of the column number in ColumnEight:
PreCellColumnsList.length => [ColumnOne,ColumnTwo,ColumnThree,ColumnFour,ColumnFive,ColumnSix,ColumnSeven].length = 7
Now the elements of the columns in PreCellColumnsList, which is the first 7 elements of RowNine:
PreCellList = [7,5,2,9,8,6,4]

The candidate element goes in the position directly AFTER PreCellList. So we first make the start of the updated row by appending (APPENDING!!!) [1] to PreCellList (this will have length PreCellColumnsList.length + 1):
PreCellListWithCandidateElementAppended => PreCellList.append(1) = [7,5,2,9,8,6,4,1]
Now we print this list again, but with ,... at the end (such as [element,element,...]), to make it clear what the updated row starts with:
UpdatedRowNineStartingElements = [7,5,2,9,8,6,4,1,...]
Finally, print the updated row, which WITHOUT EXCEPTION starts with All the elements of PreCellListWithCandidateElementAppended (the first PreCellColumnsList.length + 1 = 8 elements of the updated row). No adjustments are made, this is just the PreCellListWithCandidateElementAppended elements, followed by the rest of the row:
UpdatedRowNine = [7,5,2,9,8,6,4,1,3]

# STEP_SIX: Printing the Updated Sudoku
Reminder: Removing Spaces From The Sudoku Rows, so it can be correctly picked up by the system.

Updated Rows:
UpdatedRowTwo = [4,2,5,3,6,7,8,9,1]
UpdatedRowThree = [8,7,6,5,1,9,3,4,2]
UpdatedRowFive = [2,4,1,8,5,3,9,7,6]
UpdatedRowSix = [5,6,9,4,7,2,1,3,8]
UpdatedRowNine = [7,5,2,9,8,6,4,1,3]

The rows to update are RowTwo, RowThree, RowFive, RowSix, RowNine
Using the contents of the rows to update as UpdatedRowTwo, UpdatedRowThree, UpdatedRowFive, UpdatedRowSix, UpdatedRowNine
Printing Sudoku:
RowOne: [9,1,3,2,4,8,7,6,5]
UpdatedRowTwo: [4,2,5,3,6,7,8,9,1]
UpdatedRowThree: [8,7,6,5,1,9,3,4,2]
RowFour: [3,8,7,6,9,1,5,2,4]
UpdatedRowFive: [2,4,1,8,5,3,9,7,6]
UpdatedRowSix: [5,6,9,4,7,2,1,3,8]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
UpdatedRowNine: [7,5,2,9,8,6,4,1,3]

# STEP_SEVEN: Shifting the Rows of the Sudoku
RowFour: [3,8,7,6,9,1,5,2,4]
UpdatedRowFive: [2,4,1,8,5,3,9,7,6]
UpdatedRowSix: [5,6,9,4,7,2,1,3,8]
RowSeven: [1,3,4,7,2,5,6,8,9]
RowEight: [6,9,8,1,3,4,2,5,7]
UpdatedRowNine: [7,5,2,9,8,6,4,1,3]
RowOne: [9,1,3,2,4,8,7,6,5]
UpdatedRowTwo: [4,2,5,3,6,7,8,9,1]
UpdatedRowThree: [8,7,6,5,1,9,3,4,2]

# STEP_EIGHT Fixing the Row Names and Outputting the Sudoku
<output>
RowOne: [3,8,7,6,9,1,5,2,4]
RowTwo: [2,4,1,8,5,3,9,7,6]
RowThree: [5,6,9,4,7,2,1,3,8]
RowFour: [1,3,4,7,2,5,6,8,9]
RowFive: [6,9,8,1,3,4,2,5,7]
RowSix: [7,5,2,9,8,6,4,1,3]
RowSeven: [9,1,3,2,4,8,7,6,5]
RowEight: [4,2,5,3,6,7,8,9,1]
RowNine: [8,7,6,5,1,9,3,4,2]
</output>

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Conversation ended.

1: 134720009698004250750900003913000765420300800070009300080001504001003000509402030
2: 134720009698004250750900003913008765420300801870009300080601504201003000509402030
3: 134720689698104250750900003913008765420300801870009300387601504201003000569402030
4: 134725689698134257752906003913208765420300801870009300387601504201003000569402030
5: 134725689698134257752906003913248765420307891870509302387691504201003000569402030
6: 134725689698134257752906003913248765420307891870509302387691524241803070569402138
7: 134725689698134257752986403913248765420367891876509342387691524241853070569402138
8: 134725689698134257752986413913248765425367891876519342387691524241853976569472138
Done. Elapsed time:8591.1851272583 Estimated cost:8.151720000000001 Prompt tokens:400077 Output tokes:138365 Total tokens:538442