{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy and NumPy Cheat Sheet\n",
    "The core libraries in Python are NumPy, SciPy, Matplotlib and Pandas. NumPy provides homogeneous multidimensional arrays, SciPy provides functions and operators for mathematical computation\n",
    "Matplotlib can be used to plot functions and Pandas is used for non-homogeneous data manipulation and reading and writing files."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Python built-in data structures\n",
    "Python offers the following built-in data structures: tutple, list, dictionary and set. We will discuss the array data structure in a following sextion about the NumPy numerical package. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tuple\n",
    "A tutple is an immutable collection of mutable or immutable items that can be of different types: int, float, bool, string. A tuple provides few operators such as count() and index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of occurrences: 2\n",
      "Index of 1st occurrence: 2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "t = 1, 2.6, 'New York', 'New York'\n",
    "c = t.count('New York') \n",
    "i = t.index('New York')\n",
    "print(\"Number of occurrences: {0:d}\\nIndex of 1st occurrence: {1:d}\\n\".format(c, i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set\n",
    "A set in Python is a mutable unordered collection of unique keys. Several operation can be performed on sets, for instance union and intersection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "s1 = {1, 2, 3, 'a', 'b'}\n",
    "s2 = {'Rome', 'Paris', 1, 3}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Union of two sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 2, 3, 'Paris', 'Rome', 'a', 'b'}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s3 = s1 | s2\n",
    "s3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Intersection of two sets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1, 3}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s4 = s1 & s2\n",
    "s4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List\n",
    "A Python list is a mutable collection of mutable items that can be of different types. In other words, a list can be expanded and reduced and its items are mutable. The functions used to expand a list are: append(), extend(), insert(). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 5]\n",
      "1\n"
     ]
    }
   ],
   "source": [
    "alist = [1,2,5]\n",
    "print(alist) # prints the list\n",
    "print(alist[0]) # prints the 1st element of the list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add one item at a time to the end of the list using append()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 5, 7]\n"
     ]
    }
   ],
   "source": [
    "alist.append(7)\n",
    "print(alist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use extend() to add more items"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 5, 7, 8, 3, 2]\n"
     ]
    }
   ],
   "source": [
    "alist.extend([8, 3, 2])\n",
    "print(alist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can add an element at a certain index in the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 'New York', 2, 5, 7, 8, 3, 2]\n"
     ]
    }
   ],
   "source": [
    "alist.insert(1, 'New York')\n",
    "print(alist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can remove the 1st occurrence of an item that contains a particular value from the list "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 5, 7, 8, 3, 2]\n"
     ]
    }
   ],
   "source": [
    "alist.remove('New York')\n",
    "print(alist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also return an item with a certain index value and remove it from the list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = alist.pop(3)\n",
    "v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 2, 5, 8, 3, 2]\n"
     ]
    }
   ],
   "source": [
    "print(alist)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can slice a tuple or a list to select subsets of those collections"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 8]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alist[2:4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look for an item in a list of strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "cities = ['Rome', 'Paris', 'London', 'Berlin', 'Madrid', 'Athens']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_item(list, item):\n",
    "    if (item in list):\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_item(cities, 'Madrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Multi-dimensional list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.1, 2], [3, 4]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.1"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alist2d = [[0.1, 2], [3, 4]]\n",
    "print(alist2d)\n",
    "alist2d[0][0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### List comprehension\n",
    "List comprehension can be used to apply a function to a list of objects, as with a for loop, like a map() function or a lambda function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "families = [\"Pippo/Pluto\", \"Qui/Quo/Qua\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define a function that splits the tokens in a string and extracts the last element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def leaf(family):\n",
    "    length = len(family.split(\"/\"))\n",
    "    leaf = family.split(\"/\")[length - 1]\n",
    "    return leaf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we apply the function to a list of strings using a list comprehension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Pluto', 'Qua']"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[leaf(family) for family in families]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can achieve the same result with the following line, kind of lambda function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Pluto', 'Qua']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[family.split(\"/\")[len(family.split(\"/\")) -1] for family in families ]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can easily create nested list comprehension that work similarly to nested for loops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[(1, 1), (1, 2), (1, 3), (1, 4)],\n",
       " [(2, 1), (2, 2), (2, 3), (2, 4)],\n",
       " [(3, 1), (3, 2), (3, 3), (3, 4)],\n",
       " [(4, 1), (4, 2), (4, 3), (4, 4)]]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[[(i,j) for j in range(1,5)] for i in range(1,5)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Functional programming\n",
    "We can get the same result by applying the leaf() function to each object in the families list using the map() function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Pluto', 'Qua']"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(leaf, families))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dictionary\n",
    "A dictionary is a symbol table: a collection of objects in which each object is associated to a key. The collection can be expanded and reduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "cartoon_characters = {\"Pippo\":    5,\n",
    "                      \"Pluto\":    4,\n",
    "                      \"Topolino\": 2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: Pippo, score: 5\n",
      "Name: Pluto, score: 4\n",
      "Name: Topolino, score: 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[None, None, None]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[print(\"Name: \" + name + \", score: \" + str(score)) for name, score in cartoon_characters.items()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can print the objects' keys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Pippo', 'Pluto', 'Topolino']"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(cartoon_characters.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 4, 2]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(cartoon_characters.values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A dictionary can be created from two or more lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "character_names = ['Pippo', 'Pluto', 'Paperino']\n",
    "character_score = [5, 8, 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "character_score_dict = {'Name': character_names, 'Score': character_score}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "def find_score(name, dict):\n",
    "    score = -1\n",
    "    for i in range(len(dict)): \n",
    "        if (dict['Name'][i] == name):\n",
    "            score = dict['Score'][i]\n",
    "    return score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_score('Pluto', character_score_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NumPy \n",
    "A list can be used as an array: a collection of mutable objects of the same type: chars, integers or float or bool. Let's import the NumPy library"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A NumPy array can be created from a list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 2 4]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l = [1, 2, 4]\n",
    "array = np.array(l)\n",
    "print(array)  # prints the full array\n",
    "type(array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or from a range of number with start, end and step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8]\n"
     ]
    }
   ],
   "source": [
    "arange = np.arange(0, 9, 1) # an array from 0 to 9 with increment 1\n",
    "print(arange)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Python array is an object, an instance of a class, that contains a list of data of the same type and offers many functions to transform the data. We can write the data into a file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = 'physics/data/myarray.txt'\n",
    "with open(path, 'wb') as f:\n",
    "    arange.tofile(f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can read the file and put the data into a new array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8]\n"
     ]
    }
   ],
   "source": [
    "with open(path, 'rb') as f:\n",
    "    c = np.fromfile(f, dtype='int')\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute the sum, the mean, and the standard deviation of the elements in the array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sum: 36.0\n",
      "Mean: 4.0\n",
      "Standard deviation: 2.582\n"
     ]
    }
   ],
   "source": [
    "s = c.sum()\n",
    "m = c.mean()\n",
    "e = c.std()\n",
    "print(\"Sum: {0:.1f}\\nMean: {1:.1f}\\nStandard deviation: {2:.3f}\".format(s, m, e))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bi-dimensional array\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "array2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "print(array2d) # prints the 2D array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's print the element in the 3rd row and 2nd column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "print(array2d[2, 1]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An n-dimensional array is used to represent a transformation into an n-dimesional space. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Array dimension: 2\n"
     ]
    }
   ],
   "source": [
    "d = array2d.ndim # dimension of the array \n",
    "print(\"Array dimension: {0:d}\".format(d))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each dimension consists of a tuple of numbers that represents its shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array2d.shape # shape of the multidimensional array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute the sum of the values of the array along one dimension or axix, for example along the columns "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 15, 18])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array2d.sum(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or along the rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6, 15, 24])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array2d.sum(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may want to initialize an array with zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 0. 0.]\n",
      " [0. 0. 0.]\n",
      " [0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "zeros2d = np.zeros((3,3))\n",
    "print(zeros2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or with ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 1. 1.]\n",
      " [1. 1. 1.]\n",
      " [1. 1. 1.]]\n"
     ]
    }
   ],
   "source": [
    "ones2d = np.ones((3, 3))\n",
    "print(ones2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "or we might need an identity matrix, a square matrix whose diagonal values are ones and all the rest zeros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sometimes we need a sample of real numbers from an interval that are equally spaced. The linspace() function can be used to create such samples. It takes as input the two endpoints of the interval and the number of sample data points equally spaced within that interval. It is similar to range() but instead of setting the step we set the number of data points in the sample. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.linspace(0., 1., 11)\n",
    "x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Reshaping\n",
    "The data points to be represented in a matrix, or in another multi-dimesional array, may come from a sequence so that once they are in a unidimensional array we have to change its shape adding the missing dimensions and putting the data points in the right place. After a reshaping operation The number of elements will stay the same but the shape of the array will be different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 5 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "l = 1, 2, 3, 4, 5, 6, 7, 8, 9\n",
    "m1 = np.array(l)\n",
    "m2 = m1.reshape(3,3) # this is the same array but represented as a 3x3 matrix\n",
    "print(m2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also flatten the data back to its original shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m2.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As said at the beginning of this section an array contains mutable object, that is, each object can change value (not type)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2 3]\n",
      " [4 0 6]\n",
      " [7 8 9]]\n"
     ]
    }
   ],
   "source": [
    "m2[1, 1] = 0\n",
    "print(m2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resizing\n",
    "We may need to create a new array, for example the column vectors from a matrix, by resizing an array. After the risizing the shape will be different but the dimensions will stay the same so to create a column vector we have to create a nwe array and copy the values of the resized (or of the original matrix) into it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 3.])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_shape = 3\n",
    "v1 = np.resize(m2, (v_shape, 1))\n",
    "v1\n",
    "v2 = np.zeros(3)\n",
    "for i in range(0, 3):\n",
    "    v2[i] = v1[i];\n",
    "v2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Boolean arrays\n",
    "We can apply logical operators to arrays as well as to numbers. We apply a logic operator to a random matrix, a matrix whose elements are a sample of pseudo-random numbers from a uniform distribution in the interval [0, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[False,  True,  True],\n",
       "       [ True,  True,  True],\n",
       "       [False, False, False]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R = np.random.rand(3, 3)\n",
    "A = R > 0.5\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of representing the logical values with True or False we can represent them with the integers 1 and o respectively"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 1],\n",
       "       [1, 1, 1],\n",
       "       [0, 0, 0]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can filter the elements of an array according to the logical rule defined before"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.66377115, 0.70955479, 0.96854003, 0.76779624, 0.77286988])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R[A]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply different rules on the array elements depending on the result of the logical operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ True, False, False],\n",
       "       [False, False, False],\n",
       "       [ True,  True,  True]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(R > 0.5, R - 0.5, R + 0.5) > 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: total: 1.11 s\n",
      "Wall time: 1.13 s\n"
     ]
    }
   ],
   "source": [
    "I = 5000\n",
    "%time mat = np.random.standard_normal((I, I))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Concatenation\n",
    "Let's say we have four 2x2 matrices A, B, C and D and we want to concatenate them in one 4x4 matrix M\n",
    "\n",
    "$$ M = \\begin{bmatrix} A & B \\\\ C & D \\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1, 2],\n",
       "        [3, 4]]),\n",
       " array([[5, 6],\n",
       "        [7, 8]]),\n",
       " array([[0., 0.],\n",
       "        [0., 0.]]),\n",
       " array([[1., 1.],\n",
       "        [1., 1.]]))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2], [3, 4]])\n",
    "B = np.array([[5, 6], [7, 8]])\n",
    "C = np.zeros([2, 2])\n",
    "D = np.ones([2, 2])\n",
    "A, B, C, D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 5., 6.],\n",
       "       [3., 4., 7., 8.],\n",
       "       [0., 0., 1., 1.],\n",
       "       [0., 0., 1., 1.]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M_up = np.concatenate([A, B], axis=1)\n",
    "M_down = np.concatenate([C, D], axis=1)\n",
    "M = np.concatenate([M_up, M_down], axis=0)\n",
    "M"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vectorized operators\n",
    "An important feature of Python arrays is that mathematical operators on arrays do not need to use loops, an operator is applied to all members of an operand array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.,  8., 11., 14., 17., 20., 23., 26., 29.])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.arange(0., 9., 1)\n",
    "y = 3 * x + 5\n",
    "y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "vectorization is even more useful for multi-dimensional arrays "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6, 3, 3],\n",
       "       [3, 1, 0],\n",
       "       [8, 5, 0]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.random.randint(0, 10, (3, 3))\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9, 1, 9],\n",
       "       [0, 5, 2],\n",
       "       [8, 5, 1]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.random.randint(0, 10, (3, 3))\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can compute the sum of two matrices with one single statement without loops. The operator is apüplied to an element of the first matrix and the corresponding element in the second matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[15,  4, 12],\n",
       "       [ 3,  6,  2],\n",
       "       [16, 10,  1]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A + B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Broadcasting\n",
    "Broadcasting allows to use an operator with operands of different shapes, for example a matrix and a scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  4, 12],\n",
       "       [ 3,  8,  5],\n",
       "       [11,  8,  4]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B + 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[18,  2, 18],\n",
       "       [ 0, 10,  4],\n",
       "       [16, 10,  2]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 * B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two matrices A and B can be used as operand of an operator O if the matrix with the smaller shape can be broadcasted over the bigger one by moving it along one index or both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array((1, 2, 3))\n",
    "B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly we can move B over A one row at a time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4,  9],\n",
       "       [ 4, 10, 18],\n",
       "       [ 7, 16, 27]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Broadcasting doesn't change the associative rule of the operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  4,  9],\n",
       "       [ 4, 10, 18],\n",
       "       [ 7, 16, 27]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B * A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binning\n",
    "NumPy provides functions that can be used for common tasks, one of these is binning, a function to associate a number to a specific interval. We define an interval [0, 10] that we split in 4 bins. We have an array x whose values are within the interval and we want to associate the values to the intervals they belong to."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 2, 3, 3, 3, 4, 4, 4])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins = np.array([0.0, 1.0, 3.0, 7.0, 10.0])\n",
    "x = np.array([0.2, 1.2, 1.5, 1.8, 3.0, 3.7, 6.4, 8.7, 8.9, 8.3])\n",
    "inds = np.digitize(x, bins)\n",
    "inds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 <= 0.2 < 1.0 belongs to class 1\n",
      "1.0 <= 1.2 < 3.0 belongs to class 2\n",
      "1.0 <= 1.5 < 3.0 belongs to class 2\n",
      "1.0 <= 1.8 < 3.0 belongs to class 2\n",
      "3.0 <= 3.0 < 7.0 belongs to class 3\n",
      "3.0 <= 3.7 < 7.0 belongs to class 3\n",
      "3.0 <= 6.4 < 7.0 belongs to class 3\n",
      "7.0 <= 8.7 < 10.0 belongs to class 4\n",
      "7.0 <= 8.9 < 10.0 belongs to class 4\n",
      "7.0 <= 8.3 < 10.0 belongs to class 4\n"
     ]
    }
   ],
   "source": [
    "for i in range(x.size):\n",
    "    interval = inds[i]\n",
    "    interval_low = bins[inds[i] - 1]\n",
    "    interval_up = bins[inds[i]]\n",
    "    value = x[i]\n",
    "    print('{:.1f} <= {:.1f} < {:.1f} belongs to class {:d}'.format(interval_low, value, interval_up, interval))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -2],\n",
       "       [ 5, -9]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C = np.array([[1, -2], [5, -9]])\n",
    "C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-9,  2],\n",
       "       [-5,  1]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.array([[-9, 2], [-5, 1]])\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0],\n",
       "       [0, 1]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C @ D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since D is the inverse of C, that is $D = C^{-1}$ then CD = DC = I, where I is the identity matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0],\n",
       "       [0, 1]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D @ C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can apply an operator C to a vector x in two ways: directly or through their transpose $\\hat{C}\\vec{x} = \\vec{x}^T\\hat{C}^T$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1, -4])"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1, 1])\n",
    "C @ x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1, -4])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.T @ C.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Matrix multiplication for collaborative filtering\n",
    "A case is the computation of item similarities. Given an interaction matrix A where the rows are users and the columns represent\n",
    "items, a 1 represent an interaction between a user and an item. A similarity measure between items can be computed from the interaction matrix A as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3, 2, 1, 2],\n",
       "       [2, 2, 1, 1],\n",
       "       [1, 1, 1, 0],\n",
       "       [2, 1, 0, 2]])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,1,0,1], [1,1,1,0], [1,0,0,1]]) # 3 users and 4 items\n",
    "AT = A.transpose()\n",
    "S = AT.dot(A) # S is symmetric\n",
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also consider the ratings of the users on the items, e.g. on a scale from 1 to 5 (0 means not rated) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[50, 15, 12, 17],\n",
       "       [15,  9,  0,  6],\n",
       "       [12,  0,  9,  3],\n",
       "       [17,  6,  3,  6]])"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[5,3,0,2], [4,0,3,1], [3,0,0,1]])\n",
    "AT = A.transpose()\n",
    "S = AT.dot(A)\n",
    "S"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now recommend items to a user by multiplying the user's ratings by the similarity matrix. The output is a vector of values that represent how much the user should rate each item. We will have to remove from the list the items that have been already rated by the user in order to recommend previously unseen items."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[329 114  66 115]\n"
     ]
    }
   ],
   "source": [
    "u1 = A[0] # user 1 interactions\n",
    "r1 = S.dot(u1)\n",
    "print(r1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "66 (array([2], dtype=int64),)\n"
     ]
    }
   ],
   "source": [
    "u1_nr = (u1 == 0) # find items not rated by user 1\n",
    "item_i = np.where(u1_nr) # find the index of the 1st not rated item\n",
    "print(r1.dot(u1_nr), item_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[253  66  78  83]\n"
     ]
    }
   ],
   "source": [
    "u2 = A[1]\n",
    "r2 = S.dot(u2)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1329 (array([1], dtype=int64),)\n"
     ]
    }
   ],
   "source": [
    "u2_nr = (u2 == 0)\n",
    "item_i = np.where(u2_nr)\n",
    "print(r2.dot(u2), item_i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([167,  51,  39,  57])"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u3 = A[2]\n",
    "S.dot(u3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Record array\n",
    "A record array can contain objects of different types in different colums, e.g. all integers in a column and all strings in another column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0., b'') (0, 0., b'')]\n"
     ]
    }
   ],
   "source": [
    "recarray = np.zeros((2,), dtype=[('Integers','i4'),('Float','f4'),('Strings','a10')]) # a record array of two empty records (dtype is optional)\n",
    "print(recarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([1, 2]), array([1.5, 2.5]), array(['Rome', 'Paris'], dtype='<U5')]\n",
      "['Rome' 'Paris']\n"
     ]
    }
   ],
   "source": [
    "# prepare three arrays each of the same type: integer, float, string\n",
    "column1 = np.array((1,2), dtype='int')\n",
    "column2 = np.array((1.5,2.5), dtype='float')\n",
    "column3 = np.array(('Rome','Paris'), dtype='str')\n",
    "recarray = [column1, column2, column3] # puts together the three arrays in a record array \n",
    "print(recarray[:])\n",
    "print(recarray[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[b'New York' b'Moscow']\n"
     ]
    }
   ],
   "source": [
    "# another way of creating a record array\n",
    "recarray2 = np.rec.array([(1,1.5,'New York'),(2,3.7,'Moscow')],dtype=[('Integers','i4'),('Float','f4'),('Strings','a10')])\n",
    "print(recarray2.Strings) # prints all the values in column 'Strings'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.75]\n",
      " [1.75]\n",
      " [0.75]]\n",
      "[[12.]\n",
      " [-2.]\n",
      " [10.]]\n"
     ]
    }
   ],
   "source": [
    "# Solve the linear system AX = B\n",
    "A = np.array([[3, 6, -5],   \n",
    "[1, -3, 2],\n",
    "[5, -1, 4]])\n",
    "\n",
    "B = np.array([[12],\n",
    "[-2],\n",
    "[10]])\n",
    "\n",
    "Ainv = np.linalg.inv(A) # inverse of A\n",
    "\n",
    "X = Ainv.dot(B)  # X = A^(-1)B\n",
    "print(X)\n",
    "\n",
    "print(A.dot(X)) # returns B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-2.0\n",
      "[ 1.  2. -1.]\n"
     ]
    }
   ],
   "source": [
    "# Determinant of a squared matrix\n",
    "#     1 2 3\n",
    "# S = 0 2 1\n",
    "#     0 0 -1\n",
    "\n",
    "S = np.array([[1,2,3],\n",
    "              [0,2,1],\n",
    "              [0,0,-1]])\n",
    "det = np.linalg.det(S)\n",
    "print(det)\n",
    "l = np.linalg.eigvals(S) # eigenvalues\n",
    "print(l)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histograms"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "mu, sigma = 0.0, 1.0  # mean value and standard deviation\n",
    "sample_size = 10000\n",
    "v = np.random.normal(mu,sigma, sample_size) # Normal distribution\n",
    "fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(5, 5))\n",
    "n = ax.hist(v, bins=100) # n contains the number of samples in each bin, the one-dimensional grid values and the plot object"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SciPy\n",
    "Let's import the SciPy library and the Matplotlib library for visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.99569401 2.03516151]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2bd49935130>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a linear function to model and create data\n",
    "def linearfunc(x, a, b):\n",
    "    return a * x + b\n",
    "\n",
    "x = np.linspace(0, 10, 100) # start = 0, stop = 0, samples = 100\n",
    "y = linearfunc(x, 1, 2) # linear function defined in [0,10]\n",
    "plt.figure()\n",
    "plt.plot(x, y)\n",
    "# Adding noise to the data\n",
    "yn = y + 0.9 * np.random.normal(size=len(x))\n",
    "plt.plot(x,yn)\n",
    "# Executing curve_fit on noisy data\n",
    "popt, pcov = curve_fit(linearfunc, x, yn) # estimates the parameters of the linear function a, b\n",
    "print(popt)\n",
    "yfit = linearfunc(x,popt[0],popt[1]) # the fitted linear function overlaps with the original one\n",
    "plt.plot(x,yfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gaussian fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.97061079  5.08490729 -2.02934528]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2bd49dbbf70>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tPazc1jmi56AlLyVX25/iXstPiCRMfK/mRp6ffCnCYqeuzE53OEYwbfBIRR6Hr3XKzK3C6YtCSVs9/JLdbA200E1HIAImExx8BbfufSctohbzAxfCcz+EeOa+9BbJ+j71MNaCKeWU2S15E7fxhMQfiTOlwpH3/PoikHT2UmKsWFaMLZTgK0rKdx/5gK/e996InoPX286d9t8y/4Nf8mLiAO5ccDfPdE5lr0naQqtJZZqIt3aHcyZQ6YIfjsXpCccKVsn0hivZ1iB76pUvGEUIKHPkVv1Uu20Z83LXJRr4uvv/YNkX4LWbtDLOnlT3WI/dgsUkjJCOXqFTX+5gVp07b0hHb6egC35/E7fp1Tlqpe7YRAm+omR0BaKs2NbJrq4g4dgIJfa82/nsR1dwtFgJJ/6cm+t+xL8+9uMNRJk7SVs8VZcU/JbuUI7Dr3RZ8QajdPq1xwfi8E0mgcuWO9fWG4xS7rDmdNcEqHLb6EiruOkMRPB43HDqb+DMW6HpHbj9KNjzAaB12UxvoKaHserK7Myqded1+HrCdmqF1oO/v4Kf/n7UAPWxiRJ8Rcl4aX0L8WQ5ZKGRfUPKjrfhT8dQFW3mhurr4BNXcdDsGjYkWyrMrdcEf1JyIVVL0uFbkgINKYff7u+9SqYv8rVIztcpU6faZc1w+B3+aCphvPgCuPRZLZZy13LYoMX1q1xW48LU4gtR7rDgsJqZVetONorLusNICv6UyqTD72cMXzn8sY8SfEXJ0OevAmxvD/Sy5RCw9nG4+1SwefiS85fsrj0UIKOnzFw9pFOeGdKpcFqNVsnlTiuRWIJdXi0mPlDBz9ciWeuFX2AhlTuzgVqnP5IZTpqyCL74AlTPhnvPhbf/lGygpsfww0wq14R8Vq0bKWF7Vq8dvXHalKTD769op1/AVGnm2EQJvqIkROMJXl7XwtH7aENrssVmSFnxZ3jgszB5f7jsBVb21Bou/sCZmuCX2S3UJ4W+2mXDbBJGSCc9iao78C1t2l3BwB1+7tSrfK2RdWrcNnrCMcIxrQKmI5CncVr5VPj8UzD3RHjyf/hs6B5j6lVLd9jITcyu1e5kNme1WNAbp02tHHwMX4V0xiZK8BUlYcXWTnyhGJ9ZNg2n1cy24XD4UsLL/wePfx3mHAsXP4bfUoE/EjdcfLXbxj71Zew9ucxw8SaToNZjo8WnOfx0EdbFf0ubdv4DKcsEbZB5tqD6glEqC62cNVo1R/Enh7DkXeVr98Bn/g5LLuI079+4tOdWSCRo9oUMwZ9Z60q+h0zB94UyHX5/QzrpdwQqpDM2Ud0yFSXhhbXN2Mwmjti7junVrqF3+FLC8z+G134LC8+DM24Gs5XWpMjVpTU1u+n8xZhEZqJ0UpnDiOGnu/iU4GudNfOVUBaDx25hjy+U8Zg3EKHCmf8rp4t7hz9CJLkgqtCiK8wWOP1m3tqd4Nw99yL/eQXt3WcwqXwKAGUOK3VlduMuRUd3+PXlDoQYQFlmWDn8sY4SfEVJeOHjFg6eXY3HbmF6jWtoY/hSwjPfgzdv0coWT/61Vr9OqjxRd/gA8yaX5+xiUpmd3V0h/JEYs2pTLRJSgu+nypU7r7ZYspO20XgCbzBKTYGqH13c0wW/17sLIXhv3rd4eUeM73zwAP8nttHs/r3xdL5KHT2GX+6w4LFZ6O5vlY5y+GMeFdJRDJpNrT1safNz3Px6AMPhD8lqTCnhyW9rYn/wlXDKjYbYQ6o8cVKelsbp1JXZDYefEcNProJt9oULO+wicNstGXX4Hf4IUqZKQrOpThN8vU1yX8evctu4JX4mGxdfy6nmt1i+7vsQ11z87DyC3x2K4rKZsZhNvQ5aL4SK4Y99lOArBs2LyeqcY+drg0CmV7sIRuO0JhuAlQwp4envwjt/gkO/AstvgKxQjb7itJCw6kwqs9PuD2vTrvLE8GHgCVsAd1YdfnqdfD70Y3UGIkZ5ZqFOnTp6PuCFqnO5LnoRDbuehYe+APEos2rdtPVEMton+0LaOgAAj6PwoPVC+MMxYyKXqtIZm5RE8IUQy4UQ64QQG4UQ1+Z5vkII8W8hxPtCiDVCCDXTdhzxxuZ29prkobFKSxZOT/aIL2lYR0p4/kfw1q1wyFVw/HU5Yg9aSMdqFka/+ELUlTuQUpt+lS7yZQ6LsduBJmxBc/jBaNxoU9yX4Ovlmh3+iFGe2afDTwr+uuZu7oyfTNvhP9Yma/3rS8ys0e5wtqa5/O5QzFjlm30HUgyBSByP3YLNYiIQVSGdscigBV8IYQb+AJwELADOF0IsyNrsKuAjKeUitGHnvxZCDPzbpBhVtPsjTK10Gr/rQ7pLmrh96QatxcCyS+HEn+UVe9CEtc5jNypyCpGe1E2v0jGZhOGCBxPS8WR1zDQEP8+ELACL2USF00qHP0JnIILZJCjP04IhHf2itr5ZG85uP/xqOO7H8MGDHPThdYDMWADnC6Uqkjx2Mz2haPYue8UfjuG2mXHbzBkJXMXYoRRJ24OAjVLKzQBCiPuBM4CP0raRQJnQvoUeoANQFmGc0B2K0liVEvzGKidCULrSzNdvhpdvgMUXwcm/Kij2oDn8vsI5kJnUzV4Mpa+2HazDB00kyx1WI7zV27lVJxdfReOSKpetz4uWfkHa0NyD02rWLjKHfwPCPVT991f8wOKlqWOesX13KGaEjjx2C23dkbz7LUQgEsdltyCEUEnbMUopQjoNwI6035uSj6VzMzAf2AV8AHxNSpm33Z4Q4nIhxAohxIrW1tZ8myhGGb5gLMON2i1mppQ72FEKh7/qPnj2/9E05QSCy3+TkaDNR4svRF0fCVtINVCD3NJL/fdBxfCNqVcph19m11ofFKLabTNi+MU0bdMvVOFYgvrytLuaY74PB3+JSy1Psde624ztfcFUDN+dZyVwX/gjmsN32cwqaTtGKYXg57Mh2eUZJwKrgKnAYuBmIURurRwgpbxdSrlMSrmsrq6uBKenGGq605KBOtNrXGwbrOCvewr56FWsti3hmC0X8tCq3X2+pLU7nOHeC5E+fLzCVXrBT0290oSxtafvO48ql40Of5SOIgevWMwmIyafUZUkBCy/nudtx3Ds7j/ByruBzBh+2QAEPxCO47JZtMZwSvDHJKUQ/CZgWtrvjWhOPp3PA49IjY3AFmAeijFPJJYgHEvktPwdyOKreELyzJo9rNrhJbTpNRIPXMI6MZuL/V8Fs51NLfmHeuhE4wk6ApGCcfJ0HFZzRg/8dPQLwOAcfmZP/NbuMLV9CH6120qHP0xHIFL0sfULQ132RU4IHpx6DW9blsLj30Cu/XdGDF8vy+xP6aw/EsNtN+OyWQY99SqekLy+sW1Q+1D0n1II/jvAXCHErGQi9jzgsaxttgPHAggh6oF9gM0lOLZihNFXb5ZlOfwZNW5au8P9uvV/Y1M7V/xtJd+85UGCfz2XbbFKrkhcy22XHsW8KWVsKjDFSae9R6t1L8bhQyqsUyikM5DxhjrZU6/aisgtVLltdOoOv2jB1851Up59T6ku46ro15BTD4CHLmVRYq1xYfY4LMT6OeYwENEcvttuzinL7PRH+vz3SeeVDa1ccMdbfLzHV/RrFINn0IIvpYwBVwPPAGuBB6SUa4QQVwohrkxudh1wqBDiA+AF4Boppbq8jwP0/izZDn/aACp12v1h6vDyaMWN2G02Hpp/E3d+eTkHz65hTp2nT4ev1+D3tehKp67Mjs1swpkVV9cFv6aXAeZ9kT3XVq8e6o1qlzaAvKMfoxX1Wvx877mxyklr2ILv7HuIlzfyJ9uNNMaagMJjGHujJ6w5fKdNKzlN5zfPr+fMP7xmTMXqC72Pf3tP/xLHisFRkjp8KeWTUsq9pZRzpJQ/Sz52m5TytuTPu6SUJ0gp95dS7iel/HspjqsYeXSHnx3DnzEAwQ90d3Gn7f/wxLy4LnmIb5+3nL2SQ0vm1LnZ1RXKEBQpJZf9ZQWPva9FEPuqdc9mcrmDSpc1pxpm7iQPNW5bwTYIxeC2paZehaJxusOxPs8rPYxT7N1Fbw6/IVkquyPkpOnkvxHHxLHvXg09rbhtScHvRwO1QDimOfw8w12afSG6QzGeWN13ngVSq3a7+1kaqhgcaqWtYlB0F3D4ei3+tvbcyUt5ScQ5ZNU17Cu2Ej3rDmhYmvH0nLrclr9NnUGeX9vMdY9/RDAST/XRKVLwrzpmL3597qKcx89a0sCb3zvWGPY9ENJj+H3V4OukC36xMXzD4ecJY+kL4Zo6g3Tap3JZ5H9whFvhvvMot2hCW6zDTyQkgWgct82MM0+Vjjc5resf7+zI9/Icgobgq/LO4UQJvmJQFIrhV7qslDksxZdmPvdDZrW/ws8SF2Pb95Scp+cknX56nPiDnV2A5uz//uY2WnyasNYWkbQF7SJyxNzcSjAhBFbz4L4aLpvZ6EhZTA0+ZC70Kj6GXzik05BcG7HTG8QXirFK7sWWo26CnStZsvK7CBJF99MJxeJICS67BbfNgj+SmfDtSs7rXbGtk40t3X3uT88BKMEfXpTgKwaF3oEx2+ELIZheXWRp5jt3whs381rNOTxmPy3vJjNqXJgEbEpz+KuburCaBQfPqubWlzexrd1Plcs6KGdeKoQQRk/8YkNN6b1z+uqjozO33kOZ3WKIezpVLitOq5mdnUHjwiz3OQVO+Cm125/im5aHinb4ukDrDj8hyUj4egNRjtlnEhaTKMrl660Z+lsaqhgcI//NUIxp9Dmp+SY5Ta8uok3yphe17pdzT+S+6ispL9Av3m4xM63aleXwvcybXM41J82jwx/h0fd3FZ2wHQ60apZ+CL4n3eEX14f/pP0m8873jzOSsOkIIWisctLUGUi7MFvhE1fRteBCvmL5F5UbHinqOHruRI/ha4+lwjreYIQ5kzwcv6Ceh9/dabR4LkRQxfBHBCX4ikGh35LnE5y5kzxsbfcXdnFtG+CBS6BuHpxzJ12hRE7yN530Sh0pJaubuti/sYIDpldxzLxJxBOy6JLM4cBtt+CPxGntDiNE33H5MrsFS7IbZbExfCFEr6t3G6qc7PSmHH650wJCEDzuF7weX8Di934A297Ied3vXtjAf9alZhQbDj9Zh689pv27hqJxQtEEFU4r5x44jQ5/hOfXNvd63vrFQjn84UUJvmJQ+EJRPHaL0TY3naUzq0lIWLXdm/vCYCfcdx6YrXDB/WAvwxeKFZz5ClqlzpY2P/GEZFt7gO5QjIUNFQB88/i9gb4To8OJJ7m4qbUnTLXL1mdeQAhBlduG3ZJbKjpQGpOC7wtFMZuEsV+P28mXol+n2zEF/nEReLcbr5FScutLm/jnuzuNx9IdvivZNkIvzdRbMFe6rBw5t44pFQ7+/uY2o1NoPnSH71Mx/GFFCb5iUKQv18/mgOmVmAS8s7Uj84l4DB68BDq3afNZK6cn9xUtuC/QHH44lmCXN8jqZMJ2YWMlAPs1VPDzs/bn4kNnDvYtlQy3zWKEdIotFa122ah29904rVgaKl14A1F2d4WSrZ+1/bqsZrrw8M99fqUNTbnvAghrd0894RjBaJy2tHkGeisFt91slHTqDl+v0Kl0asPhLzl0Jq9vaueMP7zK+zu8ec9Lv4CopO3wogR/ArOlzT/oqVT5+ujolDmszJ9Sniv4z34fNr8Ep90EMz5hPKw1YevF4ScrdTa29vBBkxe7xcTceo/x/AUHT2fRtMoBv5dSo/ecb+sJF105VOOxDWrBVzZ6Mnft7u6Mv63JJPDYLewwT4Nz7oKWNfCvKyGRMMpb0wU/EE45fGcyhq+7dH0RVWVyTcDlR87m5guW0OILc+Ytr3H9k2tzzku/gPS3RbNicCjBn6Bsbw/wyV+9xIMrmwa1n94cPsCBM6t5b7uXaDyZxHvv78khJl+GJRdmbKv1eund4QNsaulhdVMXC6aWD7p8cihJT9oW6/C/s3wePzgle5zEwNHbVm9s6c75d3LbzfSEozD3OG2gzNp/w8u/MMpb29JWwRoO32ZJOXxd8JMhHX2FshCCUxdO5YVvHcXyfSfzx1c2Z0zeAlWHP1KM3m+LYkhp7dHaEPz5ta2Dcvm+PsIwB86sJhiN89EuH+x4Bx7/Bsw+WhOYNELROJFY70nbareNKpeVjS09fLizy4jfj1b0BmX9EfzF0yo5eHZNyc6hMbnaNhqXOX9bLceQrLT5xFWw6AJ4+QbM6x4HtHGLseSF2ojh282Gw9cf6wqkYvjplDmsHL2Pts4hOzmrv1YlbYcXJfgTAH1kXjr6eLu1u32s3NY54H1395FoXTazCoA16z7WkoPlU+GcP4M58yKhO72+pjzNrvPw4sct+CNx9k/G70crHruFjkCEcCwxYsnkWo/WLwhy10p40lskCwGn/gYalrJ45bXMFU1IiTFQPVWHbzF6/QcMh6+HdHJDUdldQ3WUwx8ZlOCPc25/ZRMHXPdczorX9C/gX9/YNuD99xXSqS93MKfKyiHvfB3C3XDefeCqztmut3r+dObUuY0Y88LGUe7wbRb0m6diHX6pMZmEEcfP/tvmDEGxOuAzfydicvAn66+poMeYihWIxDAJcFhNuKy5SVuLSRj1+dnHgDwOP5oqy0z0Us2jKC1K8McxK7d18Iun1wFac6t09C/gcfPreerD3cbioP4gpUxW1vQi0lLyc/vdzA6vRZ51K9Tnj0/7gvmbsGWjx/GdVrPx82hFd8IwcoIPqSZq+Rx+TmuF8qncMeUnTBVt/N76e9p8mlHwh+O4bVqVT07SNhjN24QOtLUFkNukLRCJYzVr2/eocYnDhhL8cUqnP8JX7n0v9aXKdljJ3688ajbRuOT+t7fn7KMvQtEE0bjs1eGz4k4O9j7B72NnsqXu2IKb6fXYvSVtISX4+zWU5639H02kL0YbScHXE7f5Yvj5Qipvx+fyC9NlHGn+gPqVvwI0h6/X39ssJqxmYSRtuwLRnJkCOvlCOrF4gkgsYayKVmGd4UMJ/jhESsn/PPg+rT1hfnrm/kCu4Otf1v0aKjhibi33vr3dSNAVS6HWyAbb3oCnrsE//Rh+EzuHFVsL5wr63FcSvTRz/4bKfp3rSOBOE/xiyzKHgoIO32HJO4y8pTvMuoZPcW/sGPbZ8CdY8y/8kbhRnQNkTL3yBiN54/eQv+++Hs7RV0X3p0WzYnAowR+HPLNmDy983ML3Tp7PJ+ZoFR/Zt+494RgWk8BuMfHZQ2awuyvEf9b1b2h8oeEn2pO74IHPQeV0XOffRaXbwdvZ9fjpm6f3eumF6dUuPnvIDM5Z2tivcx0JdLGzmIQxcHwk6DWGH8odc9jiCzG7zs3P+Dw73fvBv75MZfdGw+EDGXNtvYFowfeXz+HroaB6w+GrWvzhQgn+OETvKHn+QdPxJF1Z9m2zPxzDbddiskfvMwmzSbC6yduv4xR05bGwJvYRP5x3L8JZxbIZVbywtpnL/7qCs295jc/d9XaqNp/0pG3vIR2zSXDdmfuxYGp5v851JNDFrtZjxzSC4Sd9+lh22MVjzx1zGIrG8YViTCqzU+nx8Kep/wt2D19u/iG1llQeyJXWE98biOYMgtfR8xjpQ8/16h7d4Xer0sxhoySCL4RYLoRYJ4TYKIS4tsA2RwshVgkh1gghXi7FcRX5ae0OU+aw4LCaU1+4rBmkWhIuFZOdVuXMGC5SDAUd/tPXQtM7cOYfYNJ8AE5bNBWbxcS29gC+UIxX1rey25sSEF9Qq/QoVQ+Z0YAr+fcdyfg9wNLpVfz8rP05au/M3v/5wi2txhAZB7UeG5vD5XDuX6mLN/N1368goV0ctMZwyTr8YJRKZ/6Qjt1ixmY2ZRgOvQa/vlzF8IebQQu+EMIM/AE4CVgAnC+EWJC1TSVwC3C6lHJf4NODPa6iMK09qYU+FrMJh9WUE6vVHb7OnDpPv4ZQQ5rDT3eO7/4NVtwFh30N9j3LePi0RVN563vH8cw3juRHp2kfj+buUNq+tHr+UvWQGQ3ogjrSgm8yCS44eHpOV8184RZjLnC5nRqPnbbuMEw/hFvsl7I4+Ca8/AtAq5IKROJE4wl6wrGcRVeZx8kciag7fP3vokI6w0cpHP5BwEYp5WYpZQS4Hzgja5sLgEeklNsBpJQtKIaM7IHZ+aox/JFMwZ+d1omyWHLGG+5cCU98S1tJe8wPC75Or85ILxXta8XuWET/+46mDp7p5HP4elsF3eHr/XTukyeyonI5vHwDrHsKt91CIBLL6JRZCHdW+acu+LrDV0nb4aMUgt8ApI+4aUo+ls7eQJUQ4iUhxEohxOdKcFxFAdq6w9SWZQp+vqStJ8vh650oiyVjvGFPK/zjc+Cph0/dlbOSNp36ZOy22Zeq/fcFCzdhG6voF7CRdviF8OSpkTfmApfbqfXYafdHSCQk/kicp2deA1MWwSOXM53dBMJxo1NmobJM/Tg9GUlb7edajw2TUCGd4aQUgp/vHjzbJlqApcApwInAD4QQe+fdmRCXCyFWCCFWtLb2r2pEoZHt8HNWVAKBcDxjYdBsvTFZP8I6vqC2+tJtkfDQ5yHQBp/5G7h77wVT4dTGELZ0pzv8WJ8J27GGw2rm+rP35zMHThvpU8mLx6E3QUt9Npp9ISwmQbXLRq3HTjwh8QajBCJx7E6X1s7aZOHK3T9Ehnvo6qWtgk56vB9SDt9ts+RcDBRDSykEvwlI/0Q3ArvybPO0lNIvpWwDXgEW5duZlPJ2KeUyKeWyurrcAdOK3glF43SHYxmuMt+Xqiccy6irnlPnBjJnxvaFvspWvPC/sPW/Wi+WqYv7fJ0QgvpyuxE+gPHp8EGrlNKrZEYbnuQFvzvL4etVRfpd4i5vkFhCapOuKqfDOXcyKbyNa6I34032aeqt7NSTLP/U0QXfZTNT5rAaFVqKoacUgv8OMFcIMUsIYQPOAx7L2uZR4AghhEUI4QIOBnKbZCsGTb75qdlfOMiN4Ve7bVQ4rWzuh8PvDsU4w/ImvP57OPAyWHxB0a+tL3NkxPD76smjKD0euybS6RVcLd1ho1yyNtmXf3uyD5PRK2fOMbwy7Uss5w3qPrgd6D2GnxvS0Y7ntJkpc+R+NhVDx6AFX0oZA64GnkET8QeklGuEEFcKIa5MbrMWeBpYDbwN3CGl/HCwx1bk0tqTR/DzrKjMrtIRQjCnzt2vkE6Zbz3fi94M0w6BE6/v13nWlztykrbj0eGPZvQLbPqgkxZfiElluuBr/9+WHETvSvu8fDjzEp6MH8R+a3/DoaYPC5Zlgl6lk7qo+NPGJRZq76AYGkpiqaSUTwJPZj12W9bv/wf8XymOpyiM4fCzYvjpSdtwLE40Lo1bep3ZdR5eWV9k3iTo5Ut7fkjQ5MJx7l/A0r8pTZPK7byyXjvXaDxBIBLvs1OmorS47Rb2rvdkTCRr7Q6zZLrW0loX/O0dWpgvo7WC3cq3o1ewzN3CzfJ3lIXOA9eMgsfJXmlrt5gwmwRlDothUhRDj1ppO87IF9Ipy3JRgbAeQ8283s+p89DSHe67LjqRgEcupzbewh/rfwxlk/t9nvXlDrrDMfzhWNG98BWl59A5tbyztYNILEE0nqDdHzEcfqXTitkk0hx+yiC47Wb8OLmp9sdYRRzTg5+DaP4KL4/dQk8k1cIhEIkbi9LKHFYV0hlGlOCPM1q7wwihxeR13HYL4eQXGlJ11+llmaDV4gN9r7h96XrY8Aw3WS+lpXLxgM5TF5X0C4xy+MPPJ+bUEIomeG97pxHa0WP4JpOgxm1Li+GnPi/O5M/v+Wv5uf0bsHuVtgYjz/Q0j12bC6AnazXB117vcaiQznCiBH+c0dYTptply5j1mr2iUo+huu25Dh/6KM38+Al45Zew+CL+Gj1uwIlWfdFNsy9UdOM0Rek5ZHYNJgGvb2rPWHSlU+uxG2szXGkDTvQE7u6uIB+VHQZHXQur7oF37sg5RvbnLxiNGT31yxwW1UtnGFGCP87INz+1LGtFpf7Fc2fF8KdXuzCbRGGH37oeHrkCpi5BnvIrusO9jzfsjdTiq1CqcZoK6Qw7FU4r+zVU8Mam9tSiq7TPT22ZHX3xdbpB0AW7MxClwmWDo66BvZdrfZS2vZ5xjOwVvf5wWkjHbiESSxCOZfZ6UgwNSvDHGa094Zze69lj5vSKieyQjs1iYnq1K7/DD3XB/ReAxQ6f+Tv+hJWELNAauQgmJR1+iy+cmnalQjojwifm1PDejk62tWsXej2kA1CbHhrMcPipf/dKpxVMJjj7dqiaqXVK7dqZ2tZw+NrnLpgVwwfVXmG4UII/Avzx5U2s3e0bkn3nc/jGisosh5+dtAVtAVaOw08kNGffuQXO/QtUNGa2VRgAZXYLTquZZl8olbRVgj8iHDanlmhc8uQHuxEic1hLeouO9LLM9PCOUYPvqIDP3KMlbx/4LES1slv9TlI3HIFoLBXDt+dv360YGpTgDzOxeILrn/qYf723s++N+4mUMr/gG1+41OBo7fFcwZ9d52FLe1YTtZdvgPVPwfIbYObhQPrAkoE5fH21bXN32AjpqIVXI8OymVVYzYJ3t3tz8j/64isgo3V1uvhnrLKdNA/Oui3ZSO+bIGVOSCcQiWfE8EEJ/nChBH+Y0QdBDMVy8p5wjHAskdOdUV9Rqd82F4rhg+bwI7EEOzuTJXZr/621xF18kbaaNkmxIwl7Y1Jy8ZUvGEUIjGEtiuHFZbOwZJpWe59tFnS377SaM2YIu9LEvyK7j87807SY/qp74O3bDcE3kraRuPF6/Q6xO6zaKwwHSvCHGf1Dr7eVLSX5avAhbeqQUaWTbF5VwOFDslKn+SP455XQsBRO+TWk9arPaY08ACaV2WnxhfCFYpTZLSM6FWqic+heWsM7Pbeiowt+tjlIr8nP20fnqGthn5Ph6e9S1fwmkOnwXcrhjwhK8IeZQGToBT87aWvESdNi+ObkPNts9NLMjzdvhfvOA5tH65BozRQC3yBj+KCVZrZ0a0lbFb8fWQ6dUwtkVuhA6rOUne+xmU1YkhfovH10TCY4649QsxeVT3yRRtFiGI5AJGbU8euCr5K2w4MS/GFGj6PrMfBSkq+PDuSpww/HcNvMeadLVbttHL9PNUve+gaye7cm9uVTc7bzGYnWgTv8+nI7gUicXV1BVYM/wiyeVkmtx8be9Z6Mx/UYfnqSFrQcjB6HL9g4zVEO598HMs4d1l8TCXQRjSeIxqVR8ZNK2qqQznCgBH+YCYxASMdqNmG3mIxb6p5wPG/CVufGygc5RHzIn6u+jmxclnebUsTw9cVXG1t6VA3+CGOzmPjP/xzNpYfPzni82m1DiPzhP700s6KXxmnUzEF8+m7miiaOW/cjAslYvTO7LFMtvhoWlOAPMz1DKPhtPWEsJpE3plrmsKTFUGN5v8AArLybsvfvZHXjhfykaTHPrGnOu1l3KIbVnD8sVCz6is62nogK6YwCyhzWjMQsaDORq1y2HIcPKdffW2tkAOYcw02WzzPf+wrml29Ivlb7/NksmhlRMfzhQQn+MKP3E+kORUn0Mj/2b29u44F3dhR8Ph+tacMrsnGn9cTvCRcQ/C3/1fqh7HUc8y/+LfMml/Hjx9bkvd02hp8MYuh4fdoCH9UaefQyq9bNlApHzuN64ra38YY6TzhP5/Xyk/C8dSOnmV7PuICUOSxGiFAxtCjBH2Z0l52Q0BMp/CG/69UtPPxuU7/23dodprYs/+11+lxbrRd+lmPr2KwtlqmeA+fchdVq4/qz96e5O8Rdr27N2Z8vGBt0GCa9ImS8jTccT9x58TJ+eNq+OY+7rFo/+/S6/UJ4HFburLga/+SD+JX1j0zuTo3DKHNYVUhnmFCCP8wE0kS+K5A/rBNPSJo6A4RjiX7tu7UnnFODr5M+19YfjmcsjSfohXvP036+4H5txSSwZHoV8yeXs2JbB9noDn8weOwWI5egkrajl0qXLW/Ox2U3F+XuQfv8eSMm1h11C82ykgNe/zJ0aYZGG4KikrbDgRL8YaYnbfJPocVXu7xBonFJKNq/hlL5VtnqlKUJfk84lvoCx6Pw4CXQsQnO/RtUZybt9p1azke7fEYvc51SjSTUywBV0nbsccjsGj45r7i50/oQFJ+pgkuj38YcD2smI9yjxhwOI0rwh5lA2q1rocSt3n880g+Hn0hI2nsiBQU/feqQkbSVEp78Nmz+D5x2E8w6Iud1+zVU0O6PsCdtHKGUkq3tASbniev2F71Rl0rajj2uPGoOPz1z/6K21Q1HMBJng2xk53F/gJY18PCllNuFStoOEyURfCHEciHEOiHERiHEtb1sd6AQIi6EOKcUxx2LpM+W9RUQfH3CUH9COt5glFhCFh3ScdnN8MYfYOWf4fBvwpKL8r5u36nlAKzZmWr2tr0jQFtPmKUzqoo+v0LopZkqaTu+0Q2HXrQg9zoOTvolrH+aC7x/VDH8YWLQgi+EMAN/AE4CFgDnCyEWFNjuF2jDzics/nAcW7KUsdDiq23JGaL96RFurLItFNJJlmVGYgki8QQLff+FZ78PC86AY35QcL/zp5QjBHy4q8t4bOW2TgCWzagu+vwKkRJ8FdIZz2iCHyeQDFM6bWY46ItwyFUc2fEwp4YeG+EznBiUwuEfBGyUUm6WUkaA+4Ez8mz3FeBhoKUExxyz+MMxo8StYEgn6fBD0eIdfr7h5em4bRZC0QRdwShLxAZOXPd9aFwGZ96mLYMvgNtuYVatmzW7Ug5/xbZOyhwW5k7yFHxdsRgxfBXSGdd47GYi8QRdgQiQ1qrhhOvYWH0k35F3k1j7xKCP8+fXtgxJJ9rxQikEvwFILxhvSj5mIIRoAM4CbutrZ0KIy4UQK4QQK1pbW0tweqMLfyTGpDI7JlFY8FMhnX44/B4txl4ohq/3xPc2fcwdtl8RdNTD+feDzdXnvvebWsGanSmH/+62Tg6YXlWSZmfakn47jVXOQe9LMXrR133oxsRotWwy88r+1/OBnIV4+FJoWjHgYzyzZg//+++PuOGpj3td4zKRKYXg5/vWZ/+1fwtcI6XsU8GklLdLKZdJKZfV1RVXATCW8CfbGpQ7rXmrdKSURtI2GpeZfel7oa+QjsduphofDU98FoB3Dr8d3LVF7XvfqeXs6grR4Y/QFYyyrrm7JPF7gGUzq1nx/eOozG6xqxhX6FVhrT1hHFZTxopep7ucyyLfJu6eBPeeC+2b+r3/HR0Bvv3g+3jsFvb4QqxOMyiKFKUQ/CZgWtrvjcCurG2WAfcLIbYC5wC3CCHOLMGxxxz+SAyX3UKF05rX4Xf4I/SEY0aoo9hKnRZfGKfVbMyvzabCHOEu2y+xBfbwxci3EDVzij7n/Rq0uvw1u7pYtcOLlLCsRIKvmBh40hx+dudNj91CGxU0nfw3rXLs75+CnuLv7qPxBF+57z2khHu/eDBmk+CZNXtKev5DTSSW6HcZ9kAoheC/A8wVQswSQtiA84CMDIyUcpaUcqaUcibwEPBlKeW/SnDsMYc/HMNjs1DuyC/425Lufu/6MoCiPwQt3WEmldvztzqIRzno7a+zn9jKE/v8nHfl3r02T8vGqNTZ5WPl1g5MAhZNqyz69QqFHtJp6Q5nTM6CVIvkdsd0uOAB6N4D95wD4e6i9v3rZ9ezaoeXGz61kIWNlRwyu5pnx5jg//jfa7j4rreH/DiDFnwpZQy4Gq36Zi3wgJRyjRDiSiHElYPd/3gjkCyJrHBa85Zl6gnbuck2tcWWZjb7QtSX5amLTyTg0aup3vNfvhe7lDetBwOZQ6j7otJlo6HSyYc7u1i5vZP5U8oLN19TKPJgCL4vnNOITU/Y+4JRmHagNjd5zwdw/4UQC/e57wdW7OCk/SZzysIpAJywYDKbWv1sbOkp8bsYOtbs8mlDh4aYktThSymflFLuLaWcI6X8WfKx26SUOUlaKeUlUsqHSnHcsYaUEn9EW+VaKKSzrT2AEDB3kubwi03ctnaHqSvPit9LCc/+P1h9P60HfpsH4p+kJbmAqj8OH2C/hnJWN3WxartXhXMU/Ub/vAWj8RzBr3Vrn9u25DwH9j4RzvgDbHkZHvkiJAp/B7qCUTr8kYw7zhP2rQfg2Y/Gjsvf5Q3S4Y8UnbMbKGql7TASiiZISK0krdxpoStPHf62Dj+Tyx1Gj5JiSzPzOvyXfwlv3gIHf4nQId/QtuvWBN+VZ55tb+w7tYLtHQH8kTgHKMFX9BNP2jqL7Bi+3vCvrSeSenDx+XDCz+CjR41h6PnY2qatWZlZ4zYem1LhZFFjRcHW3qONcCxOa3eYhITOQKTvFwwCJfjDiL6a0GM3F6zS2d4eYHq1y+gzX4zD7wnH8EfiRpsCAN68DV76OSy+EE78OWXJC0izL5w8h/47fJ1lMwe/4EoxsUgfUJ/t8F02C06rOeXwdQ69Go74Fqy8W1skmEf0t7Zrgj+r1p3x+An7Tub9HV72dIVyXjPaSD/H9h4l+OMGvVOmy6aFdPJl5rd1BJhR48Ju1QW/b4evh2mM/vLv/R2evgbmnQqn/Q5MJiOG2tYTLjjPtjf2napV6kwudzC1BD10FBOL9HbczjzDVGrLbLmCD9oq8IMuhzdu1u5Ys9japuW8ZtRkric5MRnWeW4MhHV2eoPGz+35/gYlRAl+kfjDMd7ZmtsmuD/oDt9ttxi9Y9Lj+IFIjNbuMDNq3Ngt2pciXERIR3ftk8ocsPpBePRqmP1J+NSdYNaEXh9zKCUF59n2xqQyO1MqHBw0q3pQQ08UExNL8vMHuQ4ftGHped2tELD8F9qd6ks/h9d/n/H01nY/UyscOLIqf+bUeZhd6+a5taN/Yf8ub8rhtyrBHx08/G4Tn77tjYyrcX/RG0e50/qIp1fq6Auuple7cCQdfjFlmS3JuPzs1ufgn1fAzMPhvHvBmunE9TDOQCpshBDc+8VD+NFpOW2SFIqi0D9/2TF80AQ/r8MHrfXHab+Dfc/SQjtv3mo8taXNz4wad85LhBAsnVHF2t2+nOdGG7syHL4K6YwKOvzaP8TbW9oHvI90h68LfrrD11sqzKhxpRx+USGdMCeY3mHyc1dD44EFWyboibOBllTOqnVTU6BXj0LRF/rnL29IpzfBB+1O9ew/wfzT4Olr4e0/AZrDn1mbK/gAcyZ5aO0OF5w7MVrY5Q1S67FhNgna/crhjwp0d/72loGHdQLJ4Sdum8WoPU4XfL0Gf0a1u19J26ptT/MH6+9g6hK48EGw529qptfeqxp6xUhgfP7yCH6dx9Z3WaLZCp+6C/Y5BZ78HwKv3YY3EGVWbf5+ULOTF4LNrf7Bn/wQstMbpKHKRY3bRlu3cvijAt2dvzUIwfcbDj8tpJPmPrZ1+KlwWqlwWYtP2q75J2dt+n98bJ6LuOgRcJQX3FS/pfb0syRToSgF+ufPmSekU+Oxk5CpO+mCWGzw6bthn5NxPXcNXzA/lVGSmc7sOs34bB6GBU2DYac3SEOlgxqPXTn80YIu1ptb/Uajsn7vI6KXZaaFdAKZIR292sCRDOn0GsNf/SA8dCkbbPP5Ze3PehV7SAvp9GOVrUJRKvRKnUJJW6D3sI6OxQaf/gs7p5zAD61/44Add+fdbHq1C7NJjGqHL6VklzfI1AontR5b5lqEIUAJfpH4w3GsZq06ZaDVOvpFw2WzGP1D0hdfpSeg+nT4K+7SViHOOJRvWn9AeWXftfHuQSRtFYrB4jaStvkEX1t8VXTS0mLjwVn/y6PxQ6l983r4z/U5dfo2i4np1S42t41eh98ZiBKKJpha6dQqlZTDHx34wzH2nVqB02oecBzfH4ljM5uwWUxYzSbcNrMR0ukORWnqDDJvstZSodeyzFd/C49/A+aeABc+yPYek9FdszdSVToqpKMYfnSTk908DVJtvYty+Em2dIT5leubsPgiePkGLZmbyPy+zK51j2qHr1foTK10DksMX1m9IvFHYlS5bCydUTXgOL4/HMtoaZDeT+fjPVpnwPlTNME3mwRWs8hM2koJL/wEXr0R9j0bzr6dnpigJxwzRgX2hh67Vw5fMRL0VjTQr5BOkq1tfqbXlcHpvwdHBbz5Bwh64YybtQQvMLvOzasb20gkZEkG9pQavcy7odLJFo+dYDROIBLLW7paCpTDLxJ/WGt6dtCsaj7e48uIvRe/j3hG/Lw8XfCT9cLzJqfi8HaLOdVLJx6FR6/SxH7pJfCpO8BsNVbZFufwtS+BR8XwFSOA2164LLPcYcFmNhW98EhKyZY2v5awNZngxJ/BMd+H1ffDPy6CiObqZ9d5CMcSRa+fkQV69gwVusNvqHL2P6w1AJTgF4k/HMdtN3PQrGqkhBXb+u/y/eFYRjilPK1F8ke7u6lwWo15twB2i0lz+BE/3Hc+rLoHjv4unPpbMGn7aUkmkItx+EbSTDl8xQjg6SWGL4SgxlN8SKMzEMUXiqV66AgBR34bTrkRNjwLd58KPa3MSVbq9NV6OJGQ/PLpjznk+heMXNtwsMsbxGE1UeWyDugup78owS8Sf/I2a/G0Smxm04Di+P5ILON2Nj2ks3a3j/lTyjLaFtgtJmzBFrj7FNj0Apx2Exx9rfbhTtLcL4evyjIVI4demVaocV+fi6/S0Jum5ZRkHngpfOYeaFkLdx7HXmatl05vcfxILMG3HnyfW17aRLMvbOx7ONjlDTG10mlc8IAhrdRRgl8EUkojpOOwmlk0rWJAcXx/OJYZ0nFoDj+RkKzb050RzgFYYNrOVzdfAa3rtVYJSy/J2adeIjqpmBj+IFfaKhSD4ZSFU/jd+UtorMq/UKrWYyu6SsVoi5xvle28k+Hif0O4m6r7TuYYx7qClTo94RiX/uUd/vneTk5fNBWAnZ0Db5/SX5q8QRoqnQDGKvahbKCmBD+LW17ayGm/fzXjMb2PvS6UB82q5oOdXf2+9QtE4hkhnQqnFV8oxraOAMFonAVT0gR/3dP8LvhdLVH7hadhn5Py7rPZF8JuMVHu6FvEVVmmYiRx2y2GqOaj1mMvOqSztc2PSWi19nmZdiBc9jzCXcft/JQZWx/Mu9nNL27ktY1t/PKchfz49H0BaBpGwddr8AFq3MkYfl+LzwZBSQRfCLFcCLFOCLFRCHFtnucvFEKsTv73uhBiUSmOOxSs3d3NuubMWZr6gildrPdvqCSekP0u9+rJcvgVTis94Rgf7OwCYN6UMk3gX/kV3HceuywN/Kj+9zBlYcF9tnSHqS93FNXBcr+pFRwyu9qYUatQjCZqy7Q6dD1xKqXk729uy7vQcUt7gIYqJ7be2nxXz4bLnmejeylf9N4ET10L8ZRJk1Ly+OpdHLl3Hecum0aVy4rTah5Ug8T+oA8+mZp0+A6rmTK7ZcALO4th0IIvhDADfwBOAhYA5wshslsqbgGOklIuBK4Dbh/scYcKbyCS06feaImQFOtp1do/0I7OQL/2rTn89Cod7ee3t7RjErB3lYAHL4YXr4P9PsWPa39Fs+x9ulSzL1RU/B6grszO/Zd/QmujrFCMMmo9dqJxaeS1NrT08P1/fcjjq3flbLtVr9DpC0cFLy79PX+OnQhv3Qp/OxN6WgFY3dRFU2eQk/fXZuEKIWioctLUz+/1QNEHn0ytTH0fazy2Ue/wDwI2Sik3SykjwP3AGekbSClfl1J2Jn99E2gswXH7zaOrdvLy+tZet9F7eXSHUk4gvcslYMQg+/vB6MlThw/w1uYOjqr24rj7RFj7bzjhp/CpOzDZ3H320mnxhYuq0FEoRju1RtJSc7irdniBVOPCdJo6A4XDOVnMqqvgf2MX03T0b6DpHbj9KGhayRMf7MZqFpy4YLKxbWOVc9gcfnoNvo42F2AUO3ygAdiR9ntT8rFCXAo8VYLj9gt/OMZ3H/mAG576uNftvMn6+vSmZul97EET6nKHpV+xvmg8QSSWyKiB1wV/ftuz3Bb4Jvhb4KKH4dCvgNCmUvXVD7+lO0xdkQ5foRjN6GWJrck4/uomL0DeXFlPOGZ8f/piziStNHNl5Ylw6bNgMiPvOhHnu3/i8Dk1VLhS+2modA5b0lYffNJQlRL8Go9t1Nfh5wse5129IIT4JJrgX1NwZ0JcLoRYIYRY0drauxvvD8+s2UMgEmftbh+dvdwy6UOEe3P4oLn8HR3FO3y9NXJ6DXyFNc5PLXfyO9vNtJfNgytfhTnHGM/bLSYivTh8fzhW9CpbhWK0owu+Xqnz/g4tt5Xt8COxBNG4LLr4YEaNC5OATa1+mLIILn8ZX+NRfCN2Jz8N3wCBVMVdY5WLzkB0WGrx9UVXkyvSQzrFl6YOhFIIfhMwLe33RiAn6CaEWAjcAZwhpSw4RURKebuUcpmUclldXV0JTk/jkXd3Gj3m3yowxCQUjRsfrvRJVNkxfNBu/frj8FOdMpMhnd2r2f+J07nI8gK3xU5j/fJ7oTyzgsFhNfca0kktulIOXzH2MUI63WFC0bgxrUqfBa2Tmg1d3HoSu8VMY5Ur1SbZVc3Nk37Cz+KfZWrrf+GPR8JWrTJPd9vDEdbZ5Q1SV2Y3+maBdtHrCPQxF2AQlELw3wHmCiFmCSFswHnAY+kbCCGmA48An5VSri/BMfvFnq4Qr21q49LDZ+G0mnljU37B96a1S8gI6YQzQzoA06pdNHUGi16KbXTKtJrg9ZvhjmOxRHxcGPkuN8TOZ5+G3G6XfYV0UouulMNXjH2qXNrUp7aeCB/t9hFLip4/y+Hrv/enzffsOjcrt3WyvrkbKSVPftjMpjkXI77wjNZ35+5T4dkf0FimSeJwJG63tvuNCh2dWo8NKVORhlIzaMGXUsaAq4FngLXAA1LKNUKIK4UQVyY3+yFQA9wihFglhFgx2OP2h3+t2omUcO6yaSybWcUbm/MLfvof2RfMDel47JkOPxiNF51R90fizBB7OOLVi+HZ/wd7HU/ki6/yWmJ/Kl1WJucJy9gtyuErJg4mk6DabaOtJ8zqZMK2rsxOMEvwA7p56seK8UsOnYk/HGP5b1/hir+tZKc3WZ3TuBSu+K+2qPH137H/k2exr9gy5HH8rkCUFVs7OWR2ptGrceuLr0ap4ANIKZ+UUu4tpZwjpfxZ8rHbpJS3JX++TEpZJaVcnPxvWSmOW+S58fDKJpbOqGJmrZtPzKlhfXNP3jhZuuB3h3JDOi5bZgwfilykkYhTvupPPG27Fo9vPZx5G5x3D46KOmxmE/Mml+Wto7dbTb2OOGxRDl8xzqhJCv77TV1MKrMzq9adE0/XHX6xIR2Ao/eZxMvf/iSf+8RMXvi4BZvZxPEL6rUn7R447bdw/j+whDp41PYD5qy+EaKhUr2tHJ5b20wsITl5vykZj9dkVSqVmnG/0nbNLh8bWno4a4lWOPSJ2TUAvJnH5Xf684d00vvY6+i1+H3e+u1aBXccy+yVP+X1xL5sPOd5WHw+CIEQgv0bKzhq70l5X+qwmInGZcF43ke7fbhsZqOeX6EY69SV2WntifD+Di+LplXitplzkraBPAasGKrcNn58+r48940jue/yQ3KrfPZZjrjqTZ6zfpJDd/8F/ngEbPnvoN5PIZ76YDcNlU4WNlZkPD7UDdTGveA/8u5ObGYTpy7UrqT7N1TgsVvyxvF1hy9EZkgnu8slpGpnd3QUcPihLnj6u/CnT0LXTt5e+n9cGv0f7NWZSxAe/tKhfOnoOXl3kZp6levyd3QEeGzVLj69tLGoVbYKxVig1mNnW7ufzW1+Fk+rxGW35CRtBxLDT2d2nYelMwosaHRWcc/ka/hRxU8hFoK/nAqPXA7dzQB0BaNc9pcVg0rqdoei/HdDG8v3m5zz3R3qFsnjXvCfX9vMkXvXUenS/pAWs4kDC8TxvUnBn1zuyAnpZLuJMoeVSpc11+En4vDuX+H3S+HNW2Hp5+Hqd1hfdyIg+jVtSq8qyjf16uYXN2IyCb509F5F70+hGO3UemxG8cSixkpc1jwOP9L/GH5/aKh08oR/Plz1Nhz5HVjzT7j5QHj997y5bhfPr23mnQEOQQJ48eMWIvEEJ+8/Oee5cocVi0kohz9Q2nrCzKzJXJH3iTk1bG71G1UuOp2BKC6bmRqPDV9aHb4/Esvb0nValSszhr/5Zc3RP/YVqJ4Dl/8HTr0RnJV5Szv7whhzmJW43d4e4KF3m7jgoOkZNbwKxVhHD2kA7N9YgdtuyYnhBwbp8PuiscpJW0+YEDY45v/Bl96AaQfBs9/noKdO5kTT24NaDfvkB7upL7ezZFruXYbJJIZ08dW4FvxwTKurr0p2odM5dE4tkBvH7/RHqHLZjLbFOvrwk2waq5xaP53dq+FvZ8NfTwd/O3zqTq3D5dQlafuIIUT+eZ6FcBQI6fz+xQ1YTKJgKEihGKvogj+71k2F04rTZiaYVZrsH0CVTn/IqcWv3QsuegguepieuJk/2n7L8rc+N6D4vj8c46V1rSzfd3LBkYs17qEbZj6uBV8fQ5idnJk/pZxyR24cvzMQocpt1QQ/I2kby7uq7wD7Tr7T9TMtubPrXTjhZ/CVlbD/ORlDSrR9xHFZzf2aq6k7/FBaSGdrm59H3tvJBQdPVytsFeMOvUpl0bRKANw2rXAhfcW57vBd/TBP/UGvwMsuzYzPPpZTItdzbfQyPOE9Wnz/r2fCjrd73V8iIUkkCy/+s66FcCzBSftPKbh9jcc2ZENQxnV5hzfp0itdmYJvNgmWTK9idVNXxuOdgajm8J2WjNYK/nCM+vTSx53vwqs38sW1/8YnnPgP+Qbuo74OzsqC56Ilfvv35zZi+GkO/69vbMNsEnzpKOXuFeMPvS+UXr2i586CkbhRJeePxLBZTFjMQ+NXdYefXXK9ubUHXwTu5xh6Gs/h5rkrtRnTdx4Ps47URizOPCLH7J196+t8tNunrd2JxKn12DhwZu5CS51aj50tbUMzdWt8C37S4Vc6bTnPTat2Gt34UttHmFbtoixPSMdlM8GG5+C1m2Drf8FezpZ9r+KMlYv48/wTWNqL2IPm8Psr+A5rbgx/d1eQGdWuoiZcKRRjjfmTy/n+KfP51FKtmk2vtfdHYkaTs0A4jrsfNfj9pb7Mjtkk2OnNLMjQ9aLWY6clBBx6NSz7PKz4M7z+O/jLaTD1AO3x+WeA2UJPOMaqHV4OmllNjcdGU2eQMxZPxdzLnf7SGVWYhqjybpwLvnZblO3wARoqXXQFo/SEUwnZDn+EapcW0vFH4sTiCSzRHk4N/5vLNj8Pa7dD2VQ4/jpYegmxLoFv5Ss0dQYKl3klyVfa2RdGWWZaSMcXilJeZJdAhWKsYTIJLjtitvG73mwwvTRTny89VFjMJqZUOHIc/vtNXjx2C0tnVKaGH9ncmsAfeBms+ju8cQs89AWomAbLvsCmutMAuPzI2RynL/Tqg4sOmcFFh8wo6XvSGeeCnz+kA2mJmc4g+0wuIxZP4AvFqHTZKHeYWSQ2En/0a1g+foTvyh52WfaFk/8I+54NFu2OocGkfQiLWW2bPc+2GPSQTno/HV8wZtTqKhTjHd3Jp5dmBgoUUZSSfG2S39/RxcLGCmo8dlZu68x8gdWhif7SL8D6p+HNW+CF/2U/8XN+az2QhbFvQaIOTCObNh3XSVtvUHf4uQKpL5zSb9u6glEm087hLfdy9luf5lH7D7F+9ADxeadxRvgnPLL0L7DoPEPsQYsv1rhtRTVaKpT47Y18ZZnK4SsmEk49pBNOE/xofEgdPmiJ23Qjp3fvXDStkhq3jc5A1EjEZmAyaUPUL3kcvvwWb9eeyTGmVUx65FPwu8Xw0g3QsXlIz703xr3Dt5hE3nhfY9Lht+/ZAd2P43zvQV63v4lpg6SreiHfi17KRRd/gymT6nn/7ec4s4BYN1a7inL4gXAcd21/Y/i5SVtfMEq5Qwm+YmKg3xUHo6mQTmAA4dH+0lDlpLk7RCSWwGYxsTbZvXNRYyW7vEHiCYkvFM1rJg0mzeM3lksxTTqf+49oh1X3aIL/0vVarH+/s2HBmVA5rfA+Ssz4FvxglEqXNXP5spTQtp66dc/wsO3vHPDSekAiymfx29inOPysK0lUz+be29/k1LiTsjzDT9JprHLy0S5fn+eiDTDvZww/y+FLKfGFYqp3jmLC4Mrj8P151taUmsYqJ1JqU7eWzazm/WTCdtG0CiPE2uGP9Cr4UkrW7enmlIVTYOGxsPBc8O6ANY/Ah4/As9/X/puyCOadCvucBPX75VT5lJJxrRzeQESrwQ92agMONr+kVdp4t2ECKiwzeaLqYk499wr+21rF7/7+LsdP3tvIoPtCMWNwSaH4e2OVk+fWNJNIyF5r7LMHmBdDdgw/EIkTT0jl8BUThnxJ20Ak1q9OmQPhuPn1TKlw8LX7V/Ho1YcZ3TsnlzuMi02HP8LsXmY07fGF6ApGmTe5LPVg5TQ47Gvaf+2btBnWHz8B//k5/Odn4JkMex0Hex0LC84AU2nf5/gUfH87bH+DU3c9zDfDH8AvN4FMgNUNMw+Hw74Kc0/gRw/tIhCJc2r9ArzbtbG86QleXyhqOItCt5DTqlxE4glausMF2xxIKbUYfj8/pNllmfpiMBXDV0wU8iVttTLpoZWuareN2z+7jHNue50v//1dmrtDLJpWiRCCmjTB742P93QDsE99Wf4NaubA4V/X/utuho3Pw8bn4ON/w6YXYd+zSviONMaf4MfCcOM8iEc4DitbHPPhsG/D7KOhYVlG0rWhspOX1mlzczuSJZxVbpvRjtgXTM22zNdLB2BWrRuAtbt9BQU/EIkjZeGwUCFsWc3T9A6eyuErJgrOfFU6AzBPA2H/xgp+ec5Cvnb/KkAboAQYDr+vqVTrkoI/b3J53wcrq4clF2r/xWPQtWNIQjvjT/AtdjjtJqiezQn3dLF09mR+/clFeTdtqHTR0h0mHIvTGYhgM5tw28xImWyRHIrlHX6SztIZVbhsZp5f28wn5+Xva6/P5pxe7cr7fCHMJoHVLIykbcrhj79/NoUiHzazCYtJGN/DREISiMSNUM9Qc8biBtbu7ua2lzdxwHRtrU11Mm7f17S7dXu6mVzuMBaMFY3ZAtWzBnS+fTE+yzIXXwDTD6E1KPPW4Ovotfi7vSG8/lSC12QSeOwWukNRo/d2IYfvsJo5au86nl/bnL9MC3hlQxsmkWra1h/sFrPRS0df/ascvmKiIITAlTYEJRTTO2UOvcPX+c6J+/DPLx9qjCN02sw4rCY6+xD8tbt9zJtSIJwzQpRE8IUQy4UQ64QQG4UQ1+Z5Xgghfpd8frUQ4oBSHLc3IrGEls3vTfArU13xOgNap0wdrWNmrKjOfMfNr6fZF+aDnV15n//vhlYWNlb2/0qPVpqZ6/CV4CsmDi5bagiKnlMbLocP2urfJdOrMqr9atx2OtIm5GUTjSfY1NrDPpPHmeALIczAH4CTgAXA+UKIBVmbnQTMTf53OXDrYI/bF/qiq4peyqYa01bbdgYiGXcDZQ6LlrSN9B7DBzhm3iTMJsFzHzXnPNcVjPL+Di9Hzu2/u4fMQeZ6Q7cyhwrpKCYOLnvK4QeMqrnhc/j5qHJb6eilhfGWNj/RuMys0BkFlMLhHwRslFJullJGgPuBM7K2OQP4q9R4E6gUQhTuD1oCuozGaYXd8OQKByYBTd4gnYEo1Wm1veVOq5G0NZuEUSKZjyq3jWUzqvIK/hub2khIOHxuL/VbvWC3mIyyTD2kowRfMZFw2yyG4BsOf6QF32WjI1DY4acqdIpI2A4jpRD8BmBH2u9Nycf6uw0AQojLhRArhBArWltbB3xShVojp2M1m6gvd9DUGcAbyFxEUe6w0h2KJUvAzH3OjT1+QT3rmrvZ3p7ZZuGVDW24bWaWTK8c0PuwWUxpZZkxHFaTsSBLoZgIOG1mI7RqjDcc4rLMvqh223qN4X+824fFJJgzyT2MZ9U3pRD8fEqYnb0sZhvtQSlvl1Iuk1Iuq6sbmCsGjH+MfK2R02modNLUGUz2wk9dHMr1kE44/3jDbE5YoM2nfPajPRmPv7qhjU/MqcU6wN7dDmsqpKPaKigmIu60qVfGAPMhbq3QF30J/ro93cyuc486c1YKwW8C0ptBNAK7BrBNSSnG4YNWqbNuTzfxhMxM2uohnSKbnk2vcbFPfRnPr02Fdba1+9neEeCIAcbvQQvphKOppK1K2ComGi5baq5toI8y6eGi2mWjOxzLGT8K2kLLj/d0s08x9ffDTCkE/x1grhBilhDCBpwHPJa1zWPA55LVOocAXVLK3SU4dkG6emmNnE5jlZOu5MUhvT9HuUMbXtAdKn6Rx/EL6nlna6cx4PiVDW0AgxN8q5lQLLXwqlzF7xUTDJfNTDCS5fBHWPB1rfDmieP/a9VOdnqDHLHXwL/3Q8WgBV9KGQOuBp4B1gIPSCnXCCGuFEJcmdzsSWAzsBH4E/DlwR63L7zBCOZkPX1vNFSmFkNlhHScVhISWrvDRa+QPWXhFKSUnH7za7z4cTOvbmilodJprMYdCA7l8BUTHLfdYgh9MNJ3mfRwUKi9Qqc/wnWPr2XxtEpjatdooiSXSSnlk2iinv7YbWk/S+CqUhyrWLyBKJVOa5/JVn3xFWT2zdcrYXZ5g0wrcoXs/Cnl/OOKT/DdRz7gC3evwCS05dh9nUNv2K1mY4CzLxhlZs3oSgIpFEON02ZO1eGPMoefLfg/f3ItvmCU68/ev9cxhiPF+FxpS1Lwi1jopC++giyHn0yO+voR0gE4cGY1T3z1cL55/N64bRZOWzS1H2ediz2rSke1VVBMNNw2M9G4JBJLEAjHECI1K2KkqM4j+K9vauPBlU1cdsRs5k8ZffF7GI+9dJJ4g733qtZJF/zsOnydgUyq+uqxc/nqsXP79br8+9Lq8KWUqkpHMSHRE7TBSBx/JI7L2neZ9FCjF3joDdTiCcn3//kh06tdfK0E3/uhYnw7/CLi3U6bmRq3DZPI7FGT/nN/Bb+U6GWZwWicWEKqGL5iwmEMQYnEtF74I/h91NGjAe09muCv2dXF5jY/Xzt2rtHhczQyrgW/2N41DVVOKpzWjAEm6atZRzJeqIV04kZbBeXwFRON1BCUOP5wfMTbKgBYzCYqnFbD4b+2sR2AI/YefZU56Yz8pXKI6ApG+1x0pbPXJA8JmbkOLDOkM3IfMLtFi1/qHyzVVkEx0XBZ9Z74SYc/wglbnWq3zYjhv76pjb3rPUwqyz8TY7QwOv5yJSYSS9ATjvXaKTOdH522r1H6qJPh8EfwFtKeTE61dmu1/Sqko5ho6CWYgUg8OSp05B0+aGGdDn+EcCzOO1s7OO/A6SN9Sn0yLkM6XUWustWpcFqZVJ55ZbaaTUbscERj+JYswVcOXzHB0EOqgUhMS9qOGodvp8Mf4d1tXkLRBIeNwoVW2YxTwe+7NXIx6C7fM5IhneTtrHL4iomKkbQNxwmEY6PG4Ve7tRj+65u0AUcHJwekjGbGpeB7i2iNXAx6gnQkHYU9x+ErwVdMLPSkbTAZ0nFaR4fDr3Lb6PRHeW1jGwsbK8fEd3NcCn5nkX10+kJ308V0yxwqHEmH35IUfJW0VUw03GllmVozw1Hi8F02IvEE7+3wctheNSN9OkUxLgXfm6xoqRpkSEePl49o0jbN4dstJuMCoFBMFPS69kAkTiA8mmL4mr5ICYcNYF71SDAuBV9P2g5khmw6ZclbtJGs+9X7abf2hFX8XjEhsZlNWEyCrmCUSDwxKurwISX4douJA2ZUjfDZFMe4FHxvIIrZJCgbpDPX+9aMlrJMVaGjmIgIIXDazLQl246PhpW2kGqgtmxm1Zi58x6fgh+MUFFEp8y+qHbbsZlNOEfwH9ORdPhdQdUaWTFxcdsstCXbGIwWh1/nsQNw6BgJ58A4XXjVWWSnzL645NCZHL5XbUbLheHGntYVcCxUASgUQ4HLbjYq1UaLw59W7eJ35y/hmHmTRvpUimZ0/OVKTFeRjdP6otpt46BZI1tbqydtQVXoKCYuLpuZPV1JwR9F4ZPTB9n+fLgZtyGdYlojjwXShyCrkI5iouKyWejw6w5/9Aj+WGN8Cn6JHP5owKFCOgoFbpuZhNR/Vne6A2VQgi+EqBZCPCeE2JD8f05tkhBimhDiP0KItUKINUKIrw3mmMXQn9bIo51Mh68+6IqJSXrt/WhZeDUWGazDvxZ4QUo5F3gh+Xs2MeBbUsr5wCHAVUKIBYM8bkGklHzp6DljKpHSG+kxfOXwFRMVV1plzmhZeDUWGexf7gzg6OTPfwFeAq5J30BKuRvYnfy5WwixFmgAPhrksfMihOCqT+41FLseEUwmgc1sIhJPqBi+YsKSvhZGhXQGzmAdfn1S0HVh79VWCyFmAkuAt3rZ5nIhxAohxIrW1tZBnt74QHf5auGVYqKSPjZwNI8QHO30qSBCiOeByXme+n/9OZAQwgM8DHxdSukrtJ2U8nbgdoBly5bJQttNJOxWE91hVaWjmLjoi62sZoHNMi5rTYaFPgVfSnlcoeeEEM1CiClSyt1CiClAS4HtrGhif4+U8pEBn+0ERU/cqhi+YqLiTIZxVPx+cAz2UvkYcHHy54uBR7M3EFp/gzuBtVLKGwd5vAmJvtpWVekoJiq6wx8tbRXGKoMV/BuA44UQG4Djk78jhJgqhHgyuc1hwGeBY4QQq5L/nTzI404olMNXTHT0dgqjpa3CWGVQfz0pZTtwbJ7HdwEnJ39+FRi5ZjTjALvFhE31wldMYPR2CsrhDw6V/RgDOKwmVaGjmNDo7RRUDH9wKMEfA9gtZhXOUUxo9Np7tcp2cKjL5RjgyL3rjNawCsVERF9pqxz+4FB/vTHApYfPGulTUChGFCNpq2L4g0KFdBQKxahHT9oqhz84lOArFIpRj560VTH8waEulwqFYtRjt5j57knzxk0X3JFCCb5CoRgTXHHUnJE+hTGPCukoFArFBEEJvkKhUEwQlOArFArFBEEJvkKhUEwQlOArFArFBEEJvkKhUEwQlOArFArFBEEJvkKhUEwQhJSjd064EKIV2DbAl9cCbSU8nbGAes/jn4n2fkG95/4yQ0pZl++JUS34g0EIsUJKuWykz2M4Ue95/DPR3i+o91xKVEhHoVAoJghK8BUKhWKCMJ4F//aRPoERQL3n8c9Ee7+g3nPJGLcxfIVCoVBkMp4dvkKhUCjSUIKvUCgUE4RxJ/hCiOVCiHVCiI1CiGtH+nyGGiHENCHEf4QQa4UQa4QQXxvpcxouhBBmIcR7QojHR/pchgMhRKUQ4iEhxMfJf+9PjPQ5DTVCiG8kP9cfCiHuE0I4RvqcSo0Q4i4hRIsQ4sO0x6qFEM8JITYk/19VimONK8EXQpiBPwAnAQuA84UQC0b2rIacGPAtKeV84BDgqgnwnnW+Bqwd6ZMYRm4CnpZSzgMWMc7fuxCiAfgqsExKuR9gBs4b2bMaEu4Glmc9di3wgpRyLvBC8vdBM64EHzgI2Cil3CyljAD3A2eM8DkNKVLK3VLKd5M/d6OJQMPIntXQI4RoBE4B7hjpcxkOhBDlwJHAnQBSyoiU0juiJzU8WACnEMICuIBdI3w+JUdK+QrQkfXwGcBfkj//BTizFMcab4LfAOxI+72JCSB+OkKImcAS4K0RPpXh4LfAd4DECJ/HcDEbaAX+nAxj3SGEcI/0SQ0lUsqdwK+A7cBuoEtK+ezIntWwUS+l3A2aqQNKMr19vAm+yPPYhKg7FUJ4gIeBr0spfSN9PkOJEOJUoEVKuXKkz2UYsQAHALdKKZcAfkp0mz9aScatzwBmAVMBtxDiopE9q7HNeBP8JmBa2u+NjMNbwGyEEFY0sb9HSvnISJ/PMHAYcLoQYita2O4YIcTfR/aUhpwmoElKqd+9PYR2ARjPHAdskVK2SimjwCPAoSN8TsNFsxBiCkDy/y2l2Ol4E/x3gLlCiFlCCBtaguexET6nIUUIIdDiumullDeO9PkMB1LK70opG6WUM9H+jV+UUo5r5yel3APsEELsk3zoWOCjETyl4WA7cIgQwpX8nB/LOE9Up/EYcHHy54uBR0uxU0spdjJakFLGhBBXA8+gZfTvklKuGeHTGmoOAz4LfCCEWJV87HtSyidH7pQUQ8RXgHuSZmYz8PkRPp8hRUr5lhDiIeBdtGq09xiHbRaEEPcBRwO1Qogm4EfADcADQohL0S58ny7JsVRrBYVCoZgYjLeQjkKhUCgKoARfoVAoJghK8BUKhWKCoARfoVAoJghK8BUKhWKCoARfoVAoJghK8BUKhWKC8P8BV2nrmx0ET+AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creating a Gaussian function to model and create data\n",
    "def gaussfunc(x, a, b, c):\n",
    "    return a*np.exp(-(x-b)**2/(2*c**2))\n",
    "\n",
    "# Generating clean data\n",
    "x = np.linspace(0, 10, 100)\n",
    "y = gaussfunc(x, 1, 5, 2)\n",
    "\n",
    "# Adding noise (gaussian) to the data (also gaussian)\n",
    "yn = y + 0.2 * np.random.normal(size=len(x))\n",
    "plt.figure()\n",
    "plt.plot(x,yn) # plot the gaussian function with random noise - red color\n",
    "# Executing curve_fit on noisy data\n",
    "popt, pcov = curve_fit(gaussfunc, x, yn) # estimates the parameters of the gaussian function a, b, c\n",
    "print(popt)\n",
    "yfit = gaussfunc(x,popt[0],popt[1],popt[2]) # plot the fitted gaussian\n",
    "plt.plot(x,yfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve equations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.]\n",
      "[2.]\n"
     ]
    }
   ],
   "source": [
    "from scipy.optimize import fsolve\n",
    "curve = lambda x: (x - 1)*(x - 2)\n",
    "solution1 = fsolve(curve, 0)\n",
    "print(solution1)\n",
    "solution2 = fsolve(curve,3)\n",
    "print(solution2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Univariate interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2bd49efe0a0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.interpolate import interp1d\n",
    "x = np.linspace(0, 3*np.pi, 10)\n",
    "y = np.sin(x)\n",
    "\n",
    "# create a linear interpolation function\n",
    "linearfunc = interp1d(x, y, kind='linear')\n",
    "# create a quadratic interpolation function\n",
    "quadraticfunc = interp1d(x, y, kind='quadratic')\n",
    "# interpolate on a grid of 1,000 points\n",
    "x_interp = np.linspace(0, 3*np.pi, 100)\n",
    "linear_interp = linearfunc(x_interp)\n",
    "quadratic_interp = quadraticfunc(x_interp)\n",
    "# plot the results\n",
    "plt.figure() # new figure\n",
    "plt.plot(x, y,'o') # plot the data points\n",
    "plt.plot(x_interp, linear_interp, x_interp, quadratic_interp); # plot the linear and quadratic interpolations\n",
    "plt.legend(['data', 'linear', 'quadratic'], loc='best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2bd4af4fbb0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interpolation of noisy data\n",
    "from scipy.interpolate import UnivariateSpline\n",
    "sample = 30\n",
    "x = np.linspace(0.5, 10*np.pi, sample)\n",
    "y = np.cos(x) + np.log10(x) + np.random.randn(sample) / 10\n",
    "linearfunc = interp1d(x, y, kind='linear')\n",
    "splinefunc = UnivariateSpline(x, y, s=1)\n",
    "x_interp = np.linspace(0.5, 10*np.pi, 1000)\n",
    "linear_interp = linearfunc(x_interp)\n",
    "spline_interp = splinefunc(x_interp)\n",
    "plt.figure()\n",
    "plt.plot(x,y,'o')\n",
    "plt.plot(x_interp, linear_interp, x_interp, spline_interp)\n",
    "plt.legend(['data', 'linear', 'spline'], loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multivariate Interpolation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def func(x, y):\n",
    "    return np.sqrt(x**2 + y**2)+np.sin(x**2 + y**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# creates a 2D grid of 1000x1000 points with coordinates values from 0 to 5 for both x and y\n",
    "grid_x, grid_y = np.mgrid[0:5:100j, 0:5:100j]  \n",
    "\n",
    "# sample data points\n",
    "xy = np.random.rand(1000, 2)\n",
    "z = func(xy[:,0]*5, xy[:,1]*5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.interpolate import griddata\n",
    "# interpolating data\n",
    "grid_z0 = griddata(xy*5, z, (grid_x, grid_y), method='cubic')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Interpolated')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.imshow(func(grid_x, grid_y).T, extent=(0,1,0,1), origin='lower') # shows the image generated on the grid points \n",
    "plt.plot(xy[:,0], xy[:,1], 'k.', ms=1) # print the ramdom sample points\n",
    "plt.title('Original')\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.imshow(grid_z0.T, extent=(0,1,0,1), origin='lower') # shows the interpolated image\n",
    "plt.title('Interpolated')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2D contour plot\n",
    "In a contour plot we want to show a slice of a function, e.g. z = f(x, y). In order to plot a function that depends on two variables, we need to define a regular grid with the set of coordinate values of the function's domain, e.g. -5 < x < 5 and -5 < y < 5. We also have to set the spacing between the grid nodes, e.g. 25 so that the total number of nodes in each dimension is 250 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-5.0, 5.0, 250)\n",
    "y = np.linspace(-5.0, 5.0, 250)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "Z1 = np.exp(-2 * np.log(2) * ((X - 0.5) ** 2 + (Y - 0.5) ** 2) / 1 ** 2)\n",
    "Z2 = np.exp(-3 * np.log(2) * ((X + 0.5) ** 2 + (Y + 0.5) ** 2) / 2.5 ** 2)\n",
    "Z = 10.0 * (Z2 - Z1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '2D contour plot')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "cs = ax.contour(X, Y, Z)\n",
    "ax.set_xlabel('X')\n",
    "ax.set_ylabel('Y')\n",
    "ax.clabel(cs, fontsize=10)\n",
    "ax.set_title('2D contour plot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x, y):\n",
    "    return np.exp(-(x*x + y*y) / 1.0)\n",
    "    #return 1 / (1 + np.exp(-5*x - 4*y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, 100)\n",
    "y = np.linspace(-1, 1, 100)\n",
    "X, Y = np.meshgrid(x, y) # generates a grid from one-dimensional arrays\n",
    "z = f(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.contour.QuadContourSet at 0x215ea2bfc40>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "ax.contour3D(X, Y, z, 100, cmap='binary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D grids\n",
    "We may need to create scatter plots or grids in 3D "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimensions: 2\n",
      "Shape: (1000, 16)\n"
     ]
    }
   ],
   "source": [
    "random = np.random.normal(size=(1000, 16))\n",
    "print('Dimensions: {:d}\\nShape: {}'.format(random.ndim,random.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimensions: 3\n",
      "Shape: (10, 10, 10)\n"
     ]
    }
   ],
   "source": [
    "random3d = np.random.normal(size=(10, 10, 10))\n",
    "print('Dimensions: {:d}\\nShape: {}'.format(random3d.ndim,random3d.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0, 10)\n",
    "y = np.arange(0, 10)\n",
    "z = np.arange(0, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import itertools\n",
    "S = 10\n",
    "S_range = list(range(0, S + 1)) \n",
    "triplets = list(itertools.product(S_range, repeat=3)) # list of (x,y,z) coordinates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of triplets: 1331\n"
     ]
    }
   ],
   "source": [
    "print('Number of triplets: {:d}'.format(len(triplets)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 9, 1)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "triplets[100]  # one triplet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = [t[0] for t in triplets]  # x coordinates\n",
    "y = [t[1] for t in triplets]  # y coordinates\n",
    "z = [t[2] for t in triplets]  # z coordinates"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We plot the grid points in the plane y = 5 and x = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D \n",
    "fig = plt.figure(figsize=(5, 5)) \n",
    "ax = fig.add_subplot(111, projection='3d') \n",
    "ax.set_xlabel('x')\n",
    "ax.set_ylabel('y')\n",
    "ax.scatter(x, 5, z, s = 5)\n",
    "ax.scatter(5, y, z, s = 1, c='red')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x25749d7c350>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IJMQimLbbofD9Ab5c8GNjYxEVFYXExETWjg1cuV7idukNpqen0dfXh9LSUpSWlnq9uERFRdG1C4qioNfraVKanJwEAJqQyI7c07H5tLDx5VrckZAjxGIxTTaA83bw+Ph4u847X9XB+ZiOC2XLOCElrVaL+Pj4kFwD1xBIiAX4YrvtCCKDE2ibLEVRmJqawsDAAL3gnz59mvVUn7fpOCIFJJfLnTZD+GpLERcXh7i4OKxZs4ZOE6lUKshkMrqexCSlq7WexDYCiTzctYOPjIxAp9P5rA5OOuP4QtJAcCMhZ6Aoim6tvxohkFCACNT3xxtlA08wm83o6emBWq1GfX090tLS6GOznfrxhoSIER5R4g60GcLZNZA0UXFxMaxWK5aWlqBSqTAxMYGenh4kJCTQpMRc/PiQCuPDNRD4Egl5gjft4J7UwfnWGQfwY3hWp9MJkZCA1fDHdtsRgZLQ0tISpFIp4uPjsW3bNrsIgIumB08kND8/j+7ubjsjPK4hkUjorjrgSj3JcfFLTk6GzWZDTEwMLxYVvuz02SQhR/ijDs63GSGAHySk1WqRkJAQ0mvgCgIJ+YFAbLcd4ThU6ss1TE5OYnBwEGVlZSgpKXHa/h2sSMhms2FgYAAzMzOorq6mFx53189VRBAVFYXs7GxkZ2cDAF1PmpychEajwdmzZ5GSkkKn7uLi4oI+C8MXcElCjnBUB3fWDh4fHw+KoqDRaDhvB/cWoU7HWa1WGAwGgYQEXIE3sz++wB8SYrY7NzQ00IViR/jTyeYJzo5pMBjo4dPm5mbepQ1iY2ORn58PnU4HiqKQm5sLlUoFuVyO4eFhREZG2tWTAu3w8gZ8WFyB0OnGuWoHn52dxcrKCi5fvsx5O7i3CHUkpNFoAECoCV3r8GX2xxeQ43hLFiT9lpCQQLc7uwIX6TjH6EqhUKCzsxOZmZmorKwM6Y7RG4hEIiQmJiIxMRFFRUV0Pcmxw4sp+BkRwe7XhG+REB8IkdT5LBYLFhcX0dTUxHk7uLcIdSSk1WoBQIiErmU42m6z3b3jjYgpRVGYmJjA0NAQ1q5di+LiYq9akrlKx1EUhZGREYyNjaGiogJr1qxh9TxcwfF+MOtJZWVlMJvNdIpoaGgIBoMBSUlJ9HsSExNDXh9gE3whIQJSE3JsB7dYLE43C4G0g/tyTaEmoZiYGN5v8PyFQEIeQJoPzp07h/r6ek5SAp4iFpPJhO7ubiwvL7tNv/l6XH8gEolgtVrR2toKnU6HLVu2ICkpidVzhBKRkZHIyspCVlYWgC+L6SqVCtPT07DZbPTCl5aW5lc9iU8LP5+uBXCd+oqIiHDaDq5SqfxuB/flmrgiOG/Ap/oYFxBIyAUcZ3+0Wi1naRR3ZLG4uAipVIrExESP6TdHcFET0uv1WFpaQmZmJpqbm0P65fQV/kSGjsV0jUazSsaGKcIarBQRW+BbS7S39Rc22sG9BR/ScXFxcSE7P9cQSMgJnM3+cCGvQ+CMhJhin+vWrUNRUZHPOyE2u+NIN97o6Ciio6NRU1Nz1e7MXIFZTyosLKRlbFQqFWZmZtDf34/Y2FialFJTU13Wk/hy7/gWCfl7Pf60g3t7nlA3JpD2bD59TmxCICEHuJr94cp8DlhNQiaTCV1dXVhZWUFjYyPtmhnocf0F0aJTq9UoKyuDXC4P+AtxNXyhHOsWjikivV6PxMREup6UlJTESdt8IOAbCbG14HvTDu6tOjgfIiG+dZyyCYGE/v/wNPsTrEhIrVajo6MDSUlJ2LZtW0DpLjYaE4gTK7GCWFxchEwmC+iYoQSXBOCYIjIYDHQ9qbu7G1arFSkpKYiOjmZFqokN8OEamOAi6nCnDq5QKDyqg/MlErpaIZAQvJPe4ToSslgsGB0dxcjIiN/pN2fHDeSaZ2Zm0Nvbi+LiYqxdu5buCuTTTp7PiImJQW5uLnJzc+nduEqlwsLCAvR6Pc6dO2fX5MC2vJE34BsJBaNG5as6uMViCXkkJNSErmK4st12hEQi4SwSAoCxsTFYrVY0NTUhOTmZlWP6S0JWqxX9/f2Yn59HTU0NvbMH2Gv7DtWAZKjA3I3HxcVheHgYGzZsgEqlohe+2NhYO727YDR98E0mJxTX46kdXKvVYnBwEGq1mvN2cGcQIqGrFI6zP56UD7gyn1OpVFheXkZ8fDxaWlpYfbj9IQydTgepVAqRSISWlpZVLelcdNxdixCLxUhJSaHrfWRIU6VSYXR01K7lmJj6cREh8C0SCnXqC1jdDn7u3Dnk5eXBZDJx3g7uDAIJXYUgygdMGXtPX0S2IyGKojA6OorR0VHExcUhLy+P9d2Vr3UsmUyGzs5O5OXlYcOGDU4XAzYL66FY/PiQSnR2DREREcjIyKAtL4xGI+2f1NPTQ3d3kc47trqlBBLyDJvNhvT0dHoejst2cGcQ0nFXEZjSO/74/rAVARiNRnR2dkKv16OpqQljY2OcLI7eRi02mw1DQ0OYnJxEdXU1cnNz3R6TDwt5uMPTcxcdHW1XT9LpdDQpjY2N0SkkpqmfP+AbCfFtbglYTYzMdnCKouwaUGZmZugGFH/awZ1Bq9UiPz+fjT+Fl7hmSChQ3x+2IiGlUonOzk6kpqaitrYWERERnKX6vIlaDAYDOjo6YDab0dzc7DHsF0gocPh6/0QiEeLj4xEfH4+CggLYbDba1I/Uk2JiYuzmk7yNqvlGQqGWyHEE2bi6uiaRSORTO7g/KhtCOu4qgD+2244IlCiYWmvl5eUoKCigr4NLEnJ3XKVSiY6ODmRkZKC+vt4roc5wJiE+LbaBQCwWIzk5GcnJySgpKaHrSSRK6u7upueTSHrI1SLKRxLikwoHaaX3NjpzbAe32WzQaDRQqVRetYM7w9Xsqgpc5SQUiO22IwKJhJjpN2daa1yRkCvCoCgKY2NjGBkZwYYNG7BmzRqv70s4kxDAj5oQwC4hOqsnkZ14X18fzGYzkpOTaVJipof4SEJ8SseR76W/0ZlYLLZzAfbUDu5MHfxqrwnx59NmGST9xobxHOD/sKpSqcS5c+cQFRWFlpYWp2KfXM0gOSM3s9mMtrY2TE1NoampyS4i8/eY/oBEp9ciuCZCUrOoqKhAS0sLGhsbkZmZSduAnDlzBl1dXZiZmYHRaOQVCfGtJsRM37MBUssrLS1FfX09tm/fjvLyckRGRmJqagrnzp3DxYsXMTg4iK6uLsjlcrobzxOOHDmCkpISxMTEoL6+HmfOnHH53rm5OXzjG99AeXk5xGIxDh065PR9R48eRWVlJaKjo1FZWYljx465POZTTz0FkUjk8liucFVGQt7O/vgCiUTi06JJURSGh4cxPj7uMdoQi8WcLMiOjQmOXkT+pD3YiIT0ej3a29uxvLyMhIQEWtbGXdroakOwFn5mPWnNmjV0PUmtVmNhYQGLi4sQi8Xo7++nd+K+iOSyDb7OLXF1Tc7UwUkU+5vf/AZvvvkmIiIi8Mc//hEpKSm47rrrnEr4vPnmmzh06BCOHDmCbdu24fnnn8fu3bvR29uLwsLCVe83Go3IzMzEY489hl/84hdOr+3ChQvYv38/fvSjH2Hfvn04duwY7rrrLpw9exZbtmyxe++lS5fwwgsvYNOmTT7fA/5sOVgAiX6cab8FCl8iIYPBgEuXLmF+fh5bt271GG1w3ZhAxEe/+OILFBQUoK6uzu+8e6AkpFQqcf78eSQlJWHr1q0oLCyE2WxGX18fzpw5A6lUSttwc+GFxAeEMiVI6knFxcWoq6tDWVkZEhMTERERgYmJCZw9exZffPEFhoeHoVQqOR3Qdga+peMCqSP7A2IlUl5ejueffx5SqRTx8fHQ6/X4zne+g9TUVDzwwAOrfu/nP/857rnnHnz7299GRUUFnnnmGRQUFODZZ591ep7i4mL88pe/xN///d+7HI5/5pln8Nd//dc4fPgwNmzYgMOHD+OGG27AM888Y/c+jUaDb37zm3jxxRe9tplh4qqJhNi23XaEtykz4jSakZGBuro6r4r9XJKQ1WpFV1cXFAoF6uvrkZaWFtAxmaZ2vtxfZh2qoqKCHv6Li4ujW11JGzIZ2CQ2CeRfKHfoVytEIhGio6Oxdu1aAFfEc0m7cX9/P0wmE11PIqZ+XC7IfCOhUF9PUVERAOA//uM/0NDQgLGxMSwuLtq9x2QyobW1FY8++qjd6zfeeCPOnz/v97kvXLiAhx9+2O61Xbt2rSKh+++/HzfffDO++tWv4sc//rHP5wl7EiItlHNzc5DJZKisrOTkS+IpErLZbBgeHsbExITPTqNckZDJZMLy8jKtfsCGNpk/99ZisaCrqwtLS0u0LJHj3+usDZnYJBAnTTZSd3xoTOBTM4DjtURFRSE7OxvZ2dmgKMrO1G9ychIA7PTuYmNjWf1b+HRvgNAraANfdseJRCKUlpau+rlCoYDVakV2drbd69nZ2Zifn/f7vPPz8x6P+cYbb6CtrQ2XLl3y+zxhTULM2R+z2UwvuFzAXSTk66yNI7ggobm5OQwODiIiIgKNjY2sFlYB7xcLjUaD9vZ2WoXb22iGqedVVlZmt0MnHV9EQSAtLe2qdp7kEu4+R5FIhLi4OMTFxSE/P59Wn1apVJDL5RgeHkZkZKSdqV+g0WqoIw9HhPp6SHnBm8YEx8+RDUJ3d8ypqSk89NBDOHHiREAb3LAlIcfZn8jISE7z164iIblcjs7OTmRlZaGiosKr9Ju3x/YHNpsN/f39mJ2dRUlJCRYWFlj9EpEH0Jsv5/z8PLq6ulBUVIR169YF9IVw3KGHe+qOL4TpSyMAU326uLgYVqvVabTKFGH1NYoI9aLviFAPz2o0GgBw6yeUkZEBiUSyKuqRyWSrIhlfkJOT4/aYra2tkMlkqK+vp39utVrx2Wef4Te/+Q2MRqNX9y7sSMjV7A/XKteOkRBT6qaysjIgWQ22IiG9Xg+pVAqKotDS0gKdThdQOO4MzPkSVyD3ZmpqCps2bQroi+DqGvxJ3fFl4edDSpAgkN2yRCKh7zFwJf1LRFiJplpycjJNSomJiR4Jho8t2qH2EgLck1BUVBTq6+tx8uRJ7Nu3j3795MmT2LNnj9/nbm5uxsmTJ+3qQidOnEBLSwsA4IYbbkBXV5fd79x9993YsGEDvv/973tN3mFFQu6kd7gmIWa0otfr0dHRAYvF4lf6zdmxA12YSESWk5ODDRs2QCKRwGAwsJ7m80RCJpMJUqkUJpMJW7duDYrciLepOwI+1B1CfX4CNu9FVFQUsrKykJWVBeDK94To3U1PT8Nms9np3TmTr+Fji3aoSSguLs7jgv7II4/gwIEDaGhoQHNzM1544QVMTk7ivvvuAwAcPnwYMzMzeOWVV+jfkUqlAK5EW3K5HFKpFFFRUaisrAQAPPTQQ9ixYweefvpp7NmzB8ePH8fHH3+Ms2fPAgASExNRXV1tdx3x8fFIT09f9bo7hA0JubLdJghGJGS1WiGTydDV1YXs7GxUVFSwEqoHko5jziM5RmRc2C64I6HFxUVIpVKkpKR43RnIBVyl7mZmZmgzObKDdzahzjWulkjIE2JjY5Gfn0/Xk5jyNaSexCSl6OjokC/6jgh1YwKx9vb0Ge3fvx9KpRJPPvkk5ubmUF1djffff5/urpubm6MbSwhqa2vp/25tbcVrr72GoqIijI+PAwBaWlrwxhtv4PHHH8cTTzyBsrIyvPnmm6tmhAIF70nIk+02ASEJrr5UIpEIJpMJHR0dqKqqQl5eHmvH9jcdR+SADAYDtm7duqp4yabtAgGzJsTE1NQU+vv7sXbtWhQXF/NmN8tM3VmtVmg0GuTn57PedefPdfEBwYoKRSIREhMTkZiYiKKiIlitViwvL9t9DvHx8XSDUXx8fMg2MUyEmhR9kew5ePAgDh486PRnv/vd71a95s3acMcdd+COO+7w6vwAcOrUKa/fSxD6T9kNfJn9IQsHF4VEvV6Pnp4e2Gw2bN++3W1+1h/4Q0JqtRpSqdROjZuN43qCo8W31WpFX18fZDIZ6urq6MlvvkIkEtml7sxmM93gEKyuO75FQqFYZCUSyarPgXgnTU1NYXh4GElJSXSUlJSUFJLrDHUkpNForvrOT16SENP3h+zUvDGdA9h/aBYWFtDd3Y2MjAz6gWAbvpAFRVEYHx/H8PAw1q9fj8LCQrcttlz5FJEZkvb2dlbnkLiEs/sUGRnpsutubGyMLr6TtFGwU3dcgw/1MeBLpYCenh7U1NRAJBLR8jWknsQ09QvWwsyHSOhqtnEAeEhCjrbb3uo2kQeFzVbngYEBzMzMoKqqCqmpqZibm+PkofSWhMxmM7q7u7G0tITGxka7Ynsgx/UVZIEYGBighTL5lMd3B3ek7K7rbnp6Gn19fQG3IDPPxQfwhYQAe9uEmJiYVR49ZHPAtEMgpMTVBogPJMTFxpdP4BUJOdpu+/Lhs9mmrdPp0NHRAYqi0NzcTOeqyTWy/VB6Iwm0vLwMqVSKuLg4r4c+mdpxbC005Hi9vb2orKz0SRki3ODYdcdM3fX399MWCenp6T5ZbvMtHccXEnL1vWd69BQWFtrZIczMzKC/vx+xsbF2pn5s1ZOsVmtIo1+BhIIEtnx/2CCh+fl5dHd3Iy8vD+Xl5fROlxlpsV0w9UQWZBdeUlKCsrIyn4YLAfYWGiK/Y7PZsHHjxrCzHA70HrhK3REzOVLnIPUkd4sXXxZ+PpEQIWdPmzzm5qC0tBQWi4VO3Y2MjECv168y9fN348iHSEhIx3GMQG23mQiEhJhKA9XV1cjJybH7OXkQuRIaJcdmpnesVit6e3shk8lQW1tLm5b5c9xAv0hM+Z2oqChWdmektsSXRdAXuEvdzczMoK+vD/Hx8TQhMVN3fIuE+JJKJd8tX5+HiIgIZGZmIjMzE8AVGS0yJzY7OwuLxWKnd+dLPSnUjQkCCXEMT7M/vsJfEtLpdPTgVktLi9OWSJFIxKq8DhPOSEir1UIqlUIikWDbtm1+5bzZIk5H+Z3Tp0+zspCGKwE5A3N3DnzpC6NUKu1Sd2lpaTCZTLwhIj59Bv6k4Z0hJiYGubm5yM3NpetJhJTGxsYgFovtmk3cfbf4EAkJ6TgO4O3sj6/wh4RI+i0/P592GXR3fK4jIeY1rVmzBuvXr/f7S+CNxI472Gw2DA4OYnp62k5+J5wtvoN13aTbKysri+4kJPUkpVIJAOjp6fEqdccl+EZCbBvIMetJJGIl80nEXjs2Ntau2YTptcUHEvI1AxJuCAkJiUQiTnx/fCEhq9WK/v5+zM3NYePGjV7pm3GlykD+frPZjLGxMUxPTztNCfp7XH8HYTs6OmAymejmDOZxw5WEQgGmGvWaNWswPj4OlUqF2NhYj6k7rsEnEgpGalAsFiMlJYXuLLVYLLTe3ejoKLRaLZKSkmhSslgsQjqOY4QsHcfFB+stSZBUl1gsdpl+cwYuW55FIhE6OzvtOvLYOq6vhLG4uIj29nakpqY6ld/hQg4oGODLYkuM5EpLS1FaWkqn7ojwp6ORnLddd/6AT1ptobiWiIgIZGRk0NGG0WikP4uenh6YTCaMj49Dr9dz/lk4g06n88rGIZwR8sYENuENCc3NzaG7uxsFBQU+p7q4ioSUSiUoikJMTAw2b97MKkH7Ogg7NTWFgYEBrFu3DkVFRU6/cEIkFBgc75271N34+Dhdw+AidcenSCjUqS8AiI6ORk5ODu32e+7cOaSkpGBpaYn+LJjzSbGxsZxejy+yPeGKq46EyJCrI4i8zMLCAjZv3kwr/foCtiMhiqIwOjqK0dFRSCQSlJaWsh4henvNpBNPLpd7tAFnQ5OOLwsf3+CYumPWMLhI3Qkk5BrkvmRnZ9NuwMTUb35+HgMDA4iJibEjJWY9iQ1oNBohEuIKXDz4riIVjUaDjo4OSCQStLS0+L17YTMSMplM6OzshE6nw5YtW9DW1sZZqs8TYZDuQJKe9NSJx1YkFIrFjw8RnC8LP7OG4Sx1ZzQa7bTufE0X8YmE+NQuTsDsWBWLxUhOTkZycjJKSkpgsVjotvzx8XF0d3cjMTGRJqVAxXBJZ5/QHRdGcEYSs7Oz6OnpQWFhIdatWxfQQ85WizaxPEhOTkZzczMiIyM5qzd5Oq5CoUBHRwdyc3OxYcMGr+6PkI4LHdhO3fGJhPhUnyJwZ2oXERGB9PR0WrTXZDLRw8tEDNfR1M/Xv0+n0wmNCeEEiUQCo9EIwD79VlNTQw+yBXr8QIiCoihMTk5icHBwleVBsEmImQr01Rk2XEmITwscG9fiKXXX39+PuLg4t6k7vpEQnyIhomLibTQTFRVlV09imvoRLx/HepKney9EQhyCy3ScRqOBVCpFRESE34OezhBIJGSxWNDd3Q21Wo2GhgZ6qJF57GCl48xmM7q6urCysoItW7YgKSnJp2Oyca0GgwHj4+O0lw/buXQ+gysC9yd1J5CQazDHSHyFsw0CMfVbWFjA4OAgoqOj7UjJmR6kVqu96mtC/PnEWYBEIoFWq8WFCxeQlZWFpqYmVtV1/Y2EVlZWcOHCBZjNZrS0tKwioECO7QmOhEGuxWazobm52WcCAgKPhNRqNS5cuICVlRWMjY3h7NmzaG1txdjYGJaXlzmNssIxgvMXJHW3YcMGNDc3Y8uWLcjMzMTS0hLa2tpw9uxZWuLGYDCE+nJ5RYgAewoO5BhJSUkoLi5GXV0dduzYgfLyckRGRmJiYgJnz57FF198geHhYSiVSlgsFphMJlgsFo8kdOTIEZSUlCAmJgb19fU4c+aMy/fOzc3hG9/4Bj2Yf+jQIafvO3r0KCorKxEdHY3KykocO3bM7udPPfUUGhsbkZiYiKysLOzduxcDAwM+3xfgKkrHWSwWzM7OQqvVoq6ujpX0myP8iYRITaq4uBhr1651+SXjMhIixyXt6Z6uxZtj+rOYM1vAy8vLkZWVBZFIBKPRSCsJTE1NQSQScdaSzAeEYrF1lbrr7OyEUqnE9PS0x9Qd17iaIiFPkEgkq+pJzKj1u9/9Lv2M9PX1ITMz06lw8ptvvolDhw7hyJEj2LZtG55//nns3r0bvb29KCwsXPV+o9GIzMxMPPbYY/jFL37h9NouXLiA/fv340c/+hH27duHY8eO4a677sLZs2dpa+/Tp0/j/vvvR2NjIywWCx577DHceOONtEOuLxBRIdoaUhQFk8nEyrFWVlZo7TeRSITrrruOleM6YmBgAFarFZWVlR7fSxQZ5ufnsWnTJo+k2NraiszMTKcPTiD4/PPPUVhYiKWlJczMzGDTpk1+tacz0dbWhvT0dNq/3hvYbDZajLWmpgapqan0589ckEkbrFKphEqlwvLyMp2yS09PD0gReWZmBgqFAps3b/br99nCyMgILBYLysvLQ3odAHD+/HlUVFQgISGBXgRVKhWMRiM9MJuenh6UIc2pqSmo1Wps2rSJ0/N4C61Wi0uXLmHnzp1BPS+xSnnjjTfwy1/+EqmpqbDZbPjKV76Cf/mXf7Fb37Zs2YK6ujo8++yz9GsVFRXYu3cvnnrqKbfn2blzJ2pqavDMM8/Yvb5//34sLy/jgw8+oF/72te+htTUVLz++utOjyWXy5GVlYXTp09jx44dPv29YR0JURRFz04UFxcjOTnZ75DQG4jFYq+Ik7Q8E8dRb1rCuYqEgCuLnkgkYlWJwZe9i8FgQHt7O60GERsb6/L3mW2wpK5BoqSenh5YrVY7u4SrfZCPa5C2aGbXHQA7m4qJiQm7IU1Pop+BXgtf4KhqHyyIRCJUVVXh61//Ol566SUsLCygo6MDH3/8sV00ZDKZ0NraikcffdTu92+88UacP3/e7/NfuHABDz/8sN1ru3btWkVWTCwtLQGA2/lCVwhbErJYLOjp6YFSqaRtDlQqFSeKBgTe1G1kMhk6OzuRl5fndcszwA0JqdVqLC0tISkpCY2Njaz5IPlCQmq1GlKpFOnp6aiqqvL5S+3o4aPVaqFUKiGXyzE0NISYmBh6t56SksK61xMX4FNdylVq0DF1R6LT2dlZWvSTEFJqaiorizXfWrTdtWcHA0QtISIiAg0NDWhoaLD7uUKhgNVqXaV7mZ2djfn5eb/POz8/79MxKYrCI488guuuuw7V1dU+n4//31gnIOm36Ohou+FKrmR1CNzVhGw2G4aGhjA5OYnq6mrk5ub6fGy2SIhZe4mLi0NeXh6ri7O31zo1NYX+/n63EkC+gKmIXFRUBKvVSqeQhoaGYDAYaKdTV4ObfCEAviy23tSnnEWnRPRzcHDQLnXn7zwMwL+aUKgiIQJv27OdPeNsfNe8PeY///M/o7OzE2fPnvXrXGHVok1RFKanp9Hf3++0uM41CbmKhIxGI6RSKcxmM5qbm/0aLmNrENZqtaKnpwcKhQL19fWYmJhgfeH1FAkRg8C5uTnU1dXRxVe2IZFI7MQn9Xo9XUsaHx+HRCKxa3DgC/hChIB/C1ZkZKSdiZxOp6M3A4Gk7vhGQqGOhDQajVsDvoyMDEgkklURikwm88oVwBVycnK8PuYDDzyAd999F5999hnWrFnj1/lCGgn5ktZhztm4WtgiIiJgs9k46z5yRnIqlQodHR1IS0tDfX293xEHG5GQTqdDe3s7LU8UExODycnJoJIQIWSr1eqxHsb20GtsbCzWrFlDp5CIpMrk5CR6e3vpxXBxcRFJSUkhXWDCKRLyBJK6y8/Pt9NXY/r1MLvuXH1H+FgTCuX1eFJLiIqKQn19PU6ePIl9+/bRr588eRJ79uzx+7zNzc04efKkXV3oxIkTaGlpof8/RVF44IEHcOzYMZw6dQolJSV+ny8s0nHLy8uQSqWIjY1FS0uLy5Zd8sBYrVZOagNMoqAoCmNjYxgZGUF5eTkKCgoC+jIHGgnJ5XJ0dnaukt/hotbkijzI/ElaWhqqq6tDmspgOp2WlZXBZDJhZGQESqUSXV1dsNlsdlES12rIfAXbGzZn+mrOUqbOUnehTn85ItTW3hqNxmPjzSOPPIIDBw6goaEBzc3NeOGFFzA5OYn77rsPAHD48GHMzMzglVdeoX+HdBJrNBrI5XJIpVJERUXRXb8PPfQQduzYgaeffhp79uzB8ePH8fHHH9ul2+6//3689tprOH78OBITE+nIKTk52efvEq9JiFnbIN4r7r4whHi4IiESCTEVB5qampCcnBzwsb3tvHMERVEYGRnB2NgYqqqqkJeXZ/dzLrx/nB1zZmYGvb29q+SI+IKoqCgkJyfDYDCgpqaG3q2T6XWyWycNDlwuPnwayuT6WiIiIuxSd0ytu8nJSYhEIjp1ZzabeaWcEepIyBtDu/3790OpVOLJJ5/E3Nwcqqur8f7779PjE3Nzc7RkEEFtbS39362trXjttddQVFSE8fFxAEBLSwveeOMNPP7443jiiSdQVlaGN998k54RAkC3hDu2r7/88sv41re+5dPfydt0nNlsRk9PD9RqtUdrAebxmK6tbEMsFsNsNuP8+fNISEhAc3OzU6kNf4/tK1mYzWZ0dnZCo9G4lN9hw3bBEczPzWazYWBgALOzs3SXIt8hEomQlJRET7CT3bpSqaRN5ZjyNu7y8oFcQ6hBtNGCeS2xsbHIz893mrpbWlpCZGQkLBaLx9RdMBDqyMxbV9WDBw/i4MGDTn/2u9/9btVr3qwHd9xxB+644w6XP2dzTeFlJLS0tASpVIq4uDi36TdHiEQizpoTKIqCQqGA0WjE+vXrUVJSwnoawxcSWllZQXt7O+Lj49HS0uJyB8lFOo6kDk0mE6RSKW0BHq4zO8zdOkVR9IwMsXyOjIykoyQ2PGP40phAriNUhOiYuuvs7ERERAQoivKYugsGQt2YcC2IlwI8IyGmyrQ36Tdn4IKELBYLbfgmFotRWlrK6vEB38iCSAGVlJSgrKzM7T3iQvGaSO2cP38eKSkpTi3A+QhvniWRSIT4+HjEx8ejoKAAVqsVS0tLUCqVGBsbQ09PDxITE+k28KSkJL8WRr5EQgA/roUgMTERBQUFAFan7gDY1fG4GJhlgg/puKtdvBTgEQmZzWZ0d3djcXHRqcq0t2CbhIgid2RkJOrq6nDp0iXWjs2ENyREUl8zMzNe21OQFCKbIAXNdevWsR4Rcg1fCZnZ5g1cUX8gC+PU1BSALxfG9PT0sNK54xsJOS767lJ3vnTd+YtQNyZotVqf5w3DESGvCQFfpt8SEhKwbdu2gOosbJIQEfwkhnhGo5GzFnBPagyk9dlisaClpcXr1BebjQk2mw2Dg4NQKBRITU3lJCLkO2JiYpCXl4e8vDxQFEX79xAlgbi4ODpKSklJcbqTFtJxzuEu8gik6y6Q6wllo4SQjgsCKIrC+Pg4hoaGWOuqYoOEmBHH5s2baT0tsiviomDpLhIKRPqGrcYEk8mEjo4OGI1GFBQUsCY+G84QiUR2CyPx71EqlbSzJun8Sk9Pp03M+NIdxzcS8uW+eOq6A76MUImBnK+wWq2cp/zcQafTCSTENQYHBzE9PR1Q+s0RgZKQXq+HVCoFRVGrIg7mHFIwSIhZI1u/fj0KCwt9XjDYaExYWVlBW1sbkpKSUFtbi6mpKdrBNlAEc0Hm+jyO1ttarRYqlQoKhQIjIyOIiopCeno6DAYDL1qR+UZCgdRgmKk7ZoQaSOqODzWhq93aGwgxCRUVFaGwsJC1NmcgMBIiA5/Z2dmoqKhYRTTMSIhtOJIFkd9RKpUBkXSgjQkkJclsFAlXe+9ggqlzV1hYCKvVisXFRSiVSiwvL0OtVmN5eTmoVgmOuJpIiAnHCJWZuhseHoZer0dSUhJ9712l7gQSCg5CSkKxsbGwWCysHtMfEqIoCsPDwxgfH0dlZSXy8/Odvo/LOSQmCRH5nYiICDQ3NweUEvA3EqIoCoODg5iamrJLSQLcdNwFC6G6bqaJmcViQUREBOLj4+301siimJaWxurGzBVIFMoXEuJKtsdd6o40lzC17kjqLpSNCWRUQCChMISvJERqHXq9Hlu3bvXYEsm1DbdcLkdHRwfy8/NpC142jusLzGaz3T1x/CKEMwnxBZGRkXadX8vLy7SzbG9vLxITE+lFMRAjP3fgS22KIFhWDo6pO2JTMT8/j8HBQdoexGg0hvQ512g0AglxjWCJjLoCKfinpqaitrbWqzwxV8OwIpEIZrMZUqnUqfxOIMf15YvEHILdunWr09oFF1JA1xIcF3+xWIyUlBSkpKTQOndkp97d3Q2bzYbU1FQ6SmJL546PJBTs9BdTPYOk7ohNhcFgoNXgyYbA37kwfyCk48IUEonE41wMRVGYmJjA0NCQzwV/tiwXmDCbzejv74fNZsO2bdtYHVDzJRJaWFhAZ2enU5sMJsI1EuLTgusOUVFRyMnJQU5ODiiKgkajgVKpXKVzF6ihnEBCqxEREUHbgyiVSpSUlMBms3lM3bEN0tgikFAYQiKRwGAwuPw5GYpdWlpCY2MjUlJSfD4+m1EA6TwjDzPbE9LeRC3MmtimTZs8epFwoUd3rcHbxV8kEiExMRGJiYl2OndMQ7mUlBQ6SvJF545vJMRHK4fY2FgkJyfTc2GOwrckdUc2BGwNzBoMBthsNoGEuEaw03GOlhD+FH/ZjISY8jv5+fk4ffo067tBT4RBRFC1Wq1XNTEgfCMhgB+DooFcg6POHSmyK5VKjI6OIiIigiaktLQ0t63gfCMhvtt7OxO+Jam7kZERu647MjDr73dZq9UCgEBC4QhXJDQ9PY2+vj6v9NY8HT/QSIjpPErkd8jwJxck5Op6NRoN2tvbERsbi+bmZq9nV9ggIZFIBJVKRU/C82nxCQbY+HtFIhFtKEeM/MiiODExYdfgkJ6evqqewScSIorefIuE3F0PM3UHOJd08jd1p9FoIBaLrwmfq6uehKxWK/r6+rCwsMCK1UCgkZDBYKCdR5nK0+RhD5YBnUwmQ2dnJwoKCrB+/XqfFqNASYiQ8OzsLL3wBKM9mU8LLhcg95Ho3BmNRjpKmp6eBmAvAMqnyIM893whIYqifFZGcZR0CiR1R9QS+PL5cImrOh2n1WohlUohkUiwbds2ViQ4AomE3MnvcEVCjpEQ0wSvurraL4HEQFQYmPYPTU1NiIiIoAvvxIabOUgYzG6kYCIYf1N0dDRyc3ORm5tr14pMVASio6NhsVigUqmQnJwcUrFOQsx8IaFASTHQ1J1Go7lmSIgfnziLICS0sLCACxcuIC0tDU1NTaxpQPkTCRGNvMuXL6OsrAwbN25c9YXnkoTIF9xisUAqlWJmZgZbt271W6HX30hoZWUFFy5cQEREBLZu3YrY2Fi6PbmsrAxNTU3Ytm0b8vPzodPp0NHRgbNnz6Knpwfz8/Os6NXxoSYUCpBFsaSkBPX19bjuuuuQnZ0NiqLQ19eHM2fOoKOjA1NTU9BqtUG/T+S558uiS66HLWImqbv169dj69ataG5uRm5uLrRaLf2cd3V1YWZmBmNjY16Llx45cgQlJSWIiYlBfX09zpw54/K9c3Nz+MY3vkHPHx46dMjp+44ePYrKykpER0ejsrISx44dC+i8nhDydBzbRW6RSASDwYCuri5UV1cjJyeHtWMDvkdCFosFPT09UKlUHuV3uBiEJd1xWq0W7e3tiI6ODtgR1p/PjKT/ioqK6PZvZ630zN27syHOqyFK4gMRRkZGIjk5GQqFAk1NTdDpdFAqlVAqlbTOHdPIj2u/KL6l48hGk6vrcZW6m5ycxK233kpHQcePH8dXvvIVJCcnrzrGm2++iUOHDuHIkSPYtm0bnn/+eezevRu9vb0oLCxc9X6j0YjMzEw89thj+MUvfuH0ui5cuID9+/fjRz/6Efbt24djx47hrrvuwtmzZ2l7b1/P6wkiKsTfCJPJxNqX0mAwoLW1FSsrK9i+fTsnCrS9vb2QSCQoLy/3+F6y8EdGRqKmpsaj18wnn3yCxsZGpzbd/kKj0eD8+fMQi8VYs2YN1q9fH/AXS6VSoaurC9dff73H91IUhbGxMYyMjKxK/1ksFlgsFq+vh1njUKlUEIlEPtWS5HI5xsfH0djY6NX5uEJnZyfS0tKwZs2akF6HXC7H2NgYmpqa7F4nOnfkXpPUEbnPXDic6nQ6XLx4EV/5yldYPa6/0Ol0+OKLL7Bz586gn3txcRFPPvkk/vSnPyElJQVDQ0PYsmUL/vCHP6C4uJh+35YtW1BXV4dnn32Wfq2iogJ79+7FU0895fYcO3fuRE1NDZ555hm71/fv34/l5WV88MEH9Gtf+9rXkJqaitdffz3g8zpDyCMhtqBUKtHR0YGUlBSsrKxwJoHubT2E7Px9kd9h24qboihMT0/DZrOhuro66CoMVqsV3d3dUKvVaGpqWrWb83Xz4RglkRoHU+qG6LPxOUriQyQEuO6OY+rcrVu3DgaDgSb+yclJmvzJPzaM/PjWGRdKa++UlBRUVlZiYmICJ06cwOTkJE6ePGmX1TGZTGhtbcWjjz5q97s33ngjzp8/7/e5L1y4gIcfftjutV27dtFkxcV5Q05CgabjKIrC6OgoRkdHUVFRgfT0dMhkMs6mryUSiVsbA+bgp6+FfzZJyGKx0AQAgFWHRm+u02AwoL29HSKRCM3Nzaw7jjJNzkpLS2Eymeh00vT0tN1CmZ6eHhRBUF/AB4L0tkU7JiZmlc6dSqWixx4SEhLoKMlfnTs+deoBoVdvYNaECgsLcc8999j9XKFQwGq1rhosz87Oxvz8vN/nnZ+fd3tMLs4bchIKBCaTCZ2dndDpdNiyZQuSkpLoOgNXD5G7BZh5Pd4Ofnp7bF+g0+nQ1taGqKgoNDQ04Ny5c6zOhHjaOCwuLqK9vR0ZGRmoqqoKypc5KirKaZREFsrExERatZ1P8zGhhD/3galzR8ifzMb09PTAarXazcZ46wAc6kXfEXyw9vZmUNXx82Pj2fbmmGyeN2xJaHFxEVKpFElJSXaDluTBIXL5bMPVMOzy8jLa29uRmJjo0+AnE2yQkEKhQEdHB/Ly8lBeXk5bZbDd/OHqeEQFYt26dSgqKgrJYu8qSpqdnYVer8eZM2foCCkUURKf0nGBLvzOdO5UKhVkMhmGhobo2Zj09HS3ZnJ8I6FQX4+n7riMjAxIJJJV0YdMJvMou+UOOTk5bo/JxXlDTkK+LlJMt1FnluBisZgzzx9yfEeimJmZQW9vr53xG1vH9hakDXx4eNjOE4nZ+s3Wzs4ZCTH9h4gKBF9AoqTIyEiMjIxgw4YNq6KkYNeS+BCJsR0RMnXuioqK6NkYpVKJoaEhGAwGJCcn06k7ppEf32pCbH5f/IFWq3XbSRsVFYX6+nqcPHkS+/bto18/efIk9uzZ4/d5m5ubcfLkSbu60IkTJ9DS0sLZeUNOQr6AWeeor6+nJ8MdwZXnDzk2IThn8juBwF8SIg0AKpVqVQMAF/NHjqKoFosFHR0dtP4cn/WumK6bzChJpVKho6MDADiPkvgUCXFJho6yNjqdjk7djY+PQyKR2Ck88IGYCULZmABcuVcFBQVu3/PII4/gwIEDaGhoQHNzM1544QVMTk7ivvvuAwAcPnwYMzMzeOWVV+jfkUqlAK50zcrlckilUkRFRaGyshIA8NBDD2HHjh14+umnsWfPHhw/fhwff/wxzp496/V5fUXYkBDROYuOjkZLS4vbQrdEImHdsZWADKsS+R2bzWYnv8PGsX2BXq9He3s7JBKJ0/vC3GmyBWYkpNVq0dbWhpiYGL/TkKEEs5ZEURQ9l8SMkphzSWwtTHxYcINdG3PUuVtaWqKVMohW2ujoKO3bE0oS4EMk5KnDd//+/VAqlXjyyScxNzeH6upqvP/++ygqKgJwZTh1cnLS7ndqa2vp/25tbcVrr72GoqIijI+PAwBaWlrwxhtv4PHHH8cTTzyBsrIyvPnmm/SMkDfn9RVhQUKkzlBUVIR169Z5/OJwZTxHjm0ymXD+/HlkZmaisrKStYfV10hIqVRCKpUiNzcXGzZscPqlJfbNbEZC5DyO9SdfF41QLMTuyNhZlERmZbq6ukBRlN1ckr8df9dKJOQOYrEYqampdMppenoaU1NT0Ov19L0mDQ7p6emsKZ54i1BHQt4qJhw8eBAHDx50+rPf/e53q17z5tm74447cMcdd/h9Xl8RchJy9yWwWq3o7+/H/Py8T+kurkiIoijI5XLo9XpUVlaioKCA1S+xtyTENOXbsGGDx7CdKyfUtrY2VFZWhnzokis4Ft1JlDQzM2PXmsx2lBQs8KktWiKRIDo6GlVVVXYKAsRyOzY2lib/lJQUzqMUPjQm8DmtzSZCTkKuoNPpIJVKIRKJ0NLS4pOkORckROpRSqUSUVFRfslTeII3JGS1WtHT0wOlUulRBoh5XLZ23zabDYODgwCA+vp6pKens3LcYCCQBZfNKIkvLeJ8uQ7AftF3Jv5Jakn9/f0wm81ISUmh73dcXBzrf0e4tGhfDeAlCclkMnR1dblNM7kD2yRE5HeioqKwadMmdHZ2snZsJjyREKn/iMViNDc3e52iYGv+yGQyob29nZ7FcqZn5Qv4sgD6A8coicwlhVOUxFcSckRERASysrKQlZUFiqLoBgdi5BcZGWmnc8dGXTKUkRD5GwUSChKYXwKbzYbh4WFMTEygqqrKb5mZiIgI1kiIyO8Q3TWdTsdp552rY6tUKkilUmRlZaGystKnLwgbIrErKytobW1FSkoKampq8Omnn3J2H7gEF/UY5s69pKTEZZREFkryO6EGn0jI2xZtkUiE+Ph4xMfHo6CgwE7nbmxsDD09PXYit/7q3NlsNs5FW91BiIRCAKPRiI6ODhiNRjQ3Nwf0AbBhwU1RFIaGhjAxMWEnv0OOzcUX2FnthqIoTE1NYWBgAOXl5X7VoQKNhBYWFtDZ2Um70pKFnC8Fdr7BVZQ0OzuLgYEBiEQiLCwsIDo6OqRREp9IyN/6FFPnDljtbioSiZCamupzM4nVag2p1JNAQkEGmdFIS0tDXV1dwDuQQNNx7uR3SJ6Yiy+wWCy2ay232Wzo7e2FTCbzuv7jDP42JjB1+TZu3LjKFiNQEiKWzsFCKBZcxyjJbDbj8uXLsFgsdl1gZCFlW2PPHfhGQmyQMdMigSnfxEyTkqg0JSXF5TlDnY4TSCiIWFpaQmtrq9+7fGcIhISWlpYglUpdyu8QEuKihZO0fwNfCoACV3r3A2lR9acxwWq1oqurC4uLi7QuHwEXs0fXCiIjIxEREYE1a9YgMzNzVZQUHx8fsBiot7gaSYgJR/kms9lMR0m9vb2wWq1ISUmh7zdz1i+UjQk6nQ4URQkkFCwkJyejpaWFVeuFiIgIt0rXrkAGFMvKylBSUuL0C0q+KFarlfXBTJI2c2cDHshxvQVzANaVAjZbZoShHgoMJZxFSaSW1N3dDZvNZqfewHaUxCcSCoZsT2RkJLKzs2lHWa1WC5VKBblcjqGhIURHR9OEFMo5Ia1WCwACCQULpNDIJnyNhGw2G/r6+jA/P4/a2lpaZsQZiDYdF0V5sVgMjUaDy5cvY/369SgsLGRlkfCFMNRqNdrb2z02QAR6DyiKomtrJpMJYrGY/sclfCFO0dAQxGNjsJWWglq7ltXrcPa5Oi6SzqIkQkpsREkURfFmAxDszYhIJEJCQgISEhJQWFgIq9UKtVoNlUqFkZER6HQ6mEwmmEwmpKen2+nccQ2tVouIiIigpmZDCV6QENvwpTGBpL0oivJ6HomNxgdH2Gw2LCwsQKPRoKGhgdX5G28jIRIJekOAgURChICALzsCyT9yvUTpISS7UZUKsffcg4hPPqFfstxwA/T/8z+An3U5Jry5b8GIkvgUCdlstpBKPkkkEjudu88//xwpKSlYXl7GxMSEnc6dNy6+gUCr1SIuLo6Xbf1cIOQkxAW8bdEmbqxZWVmoqKjweifGtkCq0WiEVCqFXq+nVYbZhCcSstlsGBgYwOzsrMdIkHlMf0iISTgSiYRuQrHZbLBarbDZbKAoir5eQkRsEJK3C27sPfdAcuqU3WuSU6cQ+4//CP2xYwFdg6/XQuAqSpqbm8PAwADi4uJoQvI2SuIbCfFt0c3MzER6ejqtc0c67oiLLxeagsAVncxrJRUH8ISE2KovEHhKxzFtD7yRvXEEm5HQ0tIS2trakJaWhvz8fMzMzLByXCbc3V+z2YyOjg7o9Xps3brV69Sor58Z6YQj940QCwEzFUeIiJAS814z38fFoiUaGrKLgOjXrVZEfPIJRMPDAafmAn3W3UVJxFiOOZfkqqmFTyTENysHZmMCU+eurKxs1RwYiUrJP1/UXZzBW924qwW8ICG24Y6EiPzO4uIiGhsbkZKS4tfx2YiESPqL+CItLCxwonnnKhIiCthxcXHYunWrT+kQX0iIWf8hv+tu8SOLEVkEHKMk0sbuT5Tk6ZrFY2Pufz46CivL9aFA4RglaTQaKJVKWnfNVZTEJxLik44d4D4yc2bkp1QqsbCwQOvcMY38fK11ERLi0/3gEtcUCWk0Gto/o6Wlxe+8bqCRkKv0F1vyOo5w1kQgl8vR0dGBgoICrF+/3ucH3lsSIqk18qX254vlGCUx/zmLkgLZUdtKStz/vLTU72MzwdUCwzSWKy4udhslWSwW3ix0fEvHedso4Xi/LRYL3eAwMDAAk8lkZ+TnDbkIkVAIEIx03MLCArq6ulBQUIB169YF9MAHEgkR/TWLxbLKh4grEmLWb5gK3IFII3nTHcdMqflLQI5wlrYjhBRolAQA1Lp1sNxwAySnTkHEeIYoiQTWnTtZ6ZIL5nyVuyhpaWkJKysrdAcY13NJ7sCndBx5bv25noiICGRmZiIzMxMURUGv19Omid7q3F1rJMSPT51lMEmI2E53dnaiurraL98bR/gbCS0tLeH8+fOIjo7Gli1bVhnhcUlCZKHu7u7G2NgYGhsb/SYgckx3iykzhcYWATm7BolEgsjISERHRyMqKgqRkZF2A8UWiwUmkwkWi8XrxV//P/8D686ddq9Zd+680h3HEkKl3kB27PX19bRSg9lsRk9PD86cOYPOzk7MzMzAYDAE9dr4lI4jz0mgLeMikQhxcXEoKCjA5s2bsX37dlRUVCAyMhJjY2M4e/YsLl++jLGxMSwtLdHn9bYx4ciRIygpKUFMTAzq6+tx5swZt+8/ffo06uvrERMTg9LSUjz33HN2PzebzXjyySdRVlaGmJgYbN68GR9++KHdeywWCx5//HGUlJQgNjYWpaWlePLJJwNat3gRCbENQkImkwkdHR0wGAwB69E5Ht/Xm06M+TwNwnKVjjObzfjiiy9oJ9hATcJcRa+eGhC4hKvmBnJNBoMBFEXBbDa7j5JSU6E/dgyi4WGIR0dZnxPii9IEaXDIz893W0vyJHHDBviUjmM+u2yC2ea9du1aGI1GOkqampqCTCbDH/7wB1AU5bFW/eabb+LQoUM4cuQItm3bhueffx67d+9Gb2+vU5uZsbEx3HTTTbj33nvx6quv4ty5czh48CAyMzNx++23AwAef/xxvPrqq3jxxRexYcMGfPTRR9i3bx/Onz9PO7I+/fTTeO655/C///u/qKqqwuXLl3H33XcjOTkZDz30kF/3hRckxPYiJZFIQFEUzp8/j+TkZDQ3N7OqiOtLJET8d6anpz0a87Hd+k1gsVgwNzeHrKwsVFdXszIU6IyEmOk30nwQSudO4MvdrEwmw9DQEIqLiwHAq1oStXYtZ00IfNj1MxsTnNWS1Go1lEolLXHD1Lhj2+mUTyTEnFfjEtHR0bTOHUVRGB4exqVLl/B///d/UKlU2LhxI772ta9h165duOGGG+yemZ///Oe455578O1vfxsA8Mwzz+Cjjz7Cs88+i6eeemrVuZ577jkUFhbimWeeAQBUVFTg8uXL+P/+v/+PJqHf//73eOyxx3DTTTcBAP7pn/4JH330Ef7rv/4Lr776KgDgwoUL2LNnD26++WYAQHFxMV5//XVcvnzZ7/vACxJiG/Pz8wCA/Px8rF27lhOS84YsSCRGlME95Xm5UGKYn5/HwsICkpOTsWnTJtbuhSMJORIQXxYUAJicnMTw8DCqqqqQnZ29qgU82IOyfImE3HXHRUZG2nn4OHaAxcXF2XWAsaHewJdnxmq1Bv0ZFolEWLduHZ5++mno9XrEx8fj+uuvx4cffoh///d/xw033EC/12QyobW1FY8++qjdMW688UacP3/e6fEvXLiAG2+80e61Xbt24aWXXoLZbEZkZCSMRuOqzUVsbCzOnj1L///rrrsOzz33HAYHB7F+/Xp0dHTg7NmzNLn5g6uKhIjq9MLCAgCwbr9N4E0ktLy8jPb2diQlJaG2ttarSIyk49honSU7q/HxcWRlZSE6OprVe8EkTC4aENgAqQfOzc2hrq6OTnF4agHnYlCWj/D2OXPWAUY67hyjJH/nZPhUEwp1VKbValFSUoI777wTd95556qfKxQKWK1WZGdn272enZ1Nb8AdMT8/7/T9FosFCoUCubm52LVrF37+859jx44dKCsrwyeffILjx4/brXXf//73sbS0hA0bNtBlj5/85Cf4+te/7vffywsSYuPh0+v1kEqlAK6oTp85c4aTmRvA8zDs3Nwcuru7UVpaitLSUq//PrZsIohNwPLyMrZu3Yr5+Xm/BF3dgTQm8JWAiAq4VqtFU1PTqiYQJnwdlGVjgeLDffL3OXN0OtVqtavmZEjaztsoKdQLPxOhFtXV6/Vun1cCx8/O0+fp7P3M13/5y1/i3nvvxYYNGyASiVBWVoa7774bL7/8Mv07b775Jl599VW89tprqKqqglQqxaFDh5CXl4d/+Id/8PpvZIIXJBQonMnvsG3xzYSj7w8B2XlPTU1h8+bNyMrK8vm4QGBfSJ1Oh/b2dkRGRqK5uRlRUVFYWFjgpNZks9no+8AnAjIajWhvb0dERASampp8GsLlclCWIBzScd6CKQRaVFRkFyX19fXBYrEgNTWVTt25ipL4REKhVNAGPHfHZWRkQCKRrIp6ZDLZqmiHICcnx+n7IyIiaJmwzMxMvPPOOzAYDFAqlcjLy8Ojjz6KEsbs3Pe+9z08+uij+Nu//VsAwMaNGzExMYGnnnrq2iQhpvxORUUF1qxZQ/+MSxKSSCSrIgtH+Rt/OvGYJOQPVCoV2tvbkZubiw0bNtjJ27C58JHFS61WIzk5GbGxsbwhII1Gg/b2dqSmpvpsg+4MXA3K8uF+cVGHcRUlkcYQV1ESn2pCoY6EPBnaRUVFob6+HidPnsS+ffvo10+ePIk9e/Y4/Z3m5ma89957dq+dOHECDQ0NqzZpMTExyM/Ph9lsxtGjR3HXXXfRP9PpdKs+p0AbqnhBQv58IUnKaWlpCU1NTUhOTrb7OdckxLzpKysraG9vR3x8vM/yN0wEQkJTU1Po7+9HeXn5qhZNNlu/SaoqPz8fk5OTOH/+PBISEpCRkYHMzEwkJSWFbIFVKpXo7OxEYWGhT2lQb8HWoOzVFAm5g6coyWw207Uk0gzAB4Q6EtLpdB43sY888ggOHDiAhoYGNDc344UXXsDk5CTuu+8+AMDhw4cxMzODV155BQBw33334Te/+Q0eeeQR3Hvvvbhw4QJeeuklvP766/QxL168iJmZGdTU1GBmZgb/8R//AZvNhn/913+l33PrrbfiJz/5CQoLC1FVVYX29nb8/Oc/xz/+4z/6/ffygoR8BdntxsTEuJTf4TodR449Pz+Prq4uFBcXB9yJR7qyfCEMm82G/v5+uvjuTIGbLUUKZq0kOzsbOTk5MJlMUCqVkMvlaGtrg0gkogkpPT2d1dZ4d5iensbAwAAqKyuRm5vL+flcpe0IMXmKkviw4AZbO85dlAQAHR0dyMjIoOeSQhWNhIO19/79+6FUKvHkk09ibm4O1dXVeP/991FUVATgSl16cnKSfn9JSQnef/99PPzww/jv//5v5OXl4Ve/+hXdng1csbV5/PHHMTo6ioSEBNx00034/e9/bzez9Otf/xpPPPEEDh48CJlMhry8PHznO9/Bv/3bv/n9N4soHmzLbDYbzGazV++dn59Hd3e3R82zixcvoqCgICBVAFeYnp7G7OwsUlNTMT4+jk2bNrnMxfqKkydPej1Yy2wBr6urc1nMnJqawsLCAhoaGvy+Lm8aEIjkvVwuh0KhgE6nQ2pqKu3TwoUUCekCnJ6exubNm5GWlsb6OXyF46Asc1MhEonw+eefY+PGjX6J57KJCxcuYMOGDUhlwSMpEFitVpw+fRobNmzA8vIylEqlXZTkrpbEBWZmZiCXy1FTUxO0cxJQFIW1a9fi3XffxdatW4N+/lAgbCIhm82GoaEhTE1NYePGjR4XfYlE4rR5gA1QFIXl5WXWlRgA7wdhNRoN2trakJCQgK1bt7qNOAKZPyIdcN6IkDIl79evXw+dTgeFQgGFQkHXAwghpaamBrzbtFqt6OnpwfLyMpqamnijt+UuSlpaWqKfS7PZTKfsQrHz5ouKNtkHZ2Vl0YObzmpJgShT+4JQN0l4EwldTeAFCXn6IjDld7wt+nOlPqDRaDA8PAzgSrGPbTdIb+o3RAG7sLAQ69at83j//G1MYJIPOY4vi1ZcXBwKCwtRWFhI1wMUCgW6u7thtVqRnp6OzMxMZGRk+KxobjKZ6Jb8pqYmTp0uAwUhGblcjq6uLqxduxaJiYkhd5Tly2wOcy6L/K9jLYmoN/T393MeJTG9hIINm80GnU7Hmw1VMMALEnKHpaUltLe3+yy/w0VNSCaTobOzExkZGVheXubEjtgdCTG7Aaurq72uffjTmODoARToouhYD1hZWYFcLsfU1BR6enqQnJxMR0mJiYluF0etVksPAldVVYW0k8lbzMzMYGBggFZtIAjloCxfIiFPMjmOytRarRYqlQpyuZyTKCmUkZBWqwUAJCYmhuT8oQCvSYh0fBHTN1++MGym4yiKwsjICMbGxrBx40ZERUWhq6uLlWM7whVhkNSTUql02g3o6Zi+uqByOYDKdAYtKyuD0Wik03bj4+OIiIigCSk9Pd1uUVGr1ejo6OBMkoltUBSF0dFRTE5OoqamZlXNKhSDssxr48P9Y2oNegIzSiIRtqsoKS0tzauhT2fXE6qNDSEhIRIKMhwfPqvVir6+PshkMpcdX57AViRksVjQ2dmJlZUVbN26FYmJiVhaWuK0886RhAwGA9rb2wHALwVsX2pCzAgoWAOo0dHRyM/PR35+Pmw2G9RqNRQKBQYHB2E0GpGamorMzEzYbDYMDw+jvLzcbiaMryCdiwqFAo2NjR7TyMxaEvm82B6UZYIvJBTIjJBjlKTT6ehuzaGhIcTExNjNJXlDLqFMx+l0OkRFRSE6Ojok5w8FeEFCTOj1erS3t0MkEqG5udnvfK9EIvG6484VSNonOjqaVh8AuLNccHbspaUltLW1IT093e/Uk7fXy6xRhEoBQSwW04sGaW6Qy+UYHx+HwWBATEwM9Ho9PSjLlwFHR1itVnR2dkKv16OpqcnnjQNz0BjgxlGWLyTEVm1KJBIhPj4e8fHxdlES0+WUqd7gKkqy2WycpNq9gUajQVxcHC8+l2CBNyQkEonogntOTg4qKioCWmACjYTItaxZswbr16+3uxauZ5AIYRAPIn/SkUx4mhMKtAGBK4hEIsTGxkKj0QAAGhsbYTAYoFAo0NHRAQBIT0+nU3ehWjgcQZomRCIRGhsbWbkutgZlmeATCXGxmXAVJSkUCgwPD7uMkkIZCWk0mmsqFQfwhIRIzWVkZGSV/I6/8JcoKIrC2NgYRkZGXNpfkxoLF18e0qI9ODhI1xHceRB5e0x3zQ5sNiCwCSKFZLFY0NTURKcocnJy6HZnUkcizQ2k2y4+Pj4kC6xer0dbWxsSExM5a5oIdFCWgC8kFAzJHmdR0uLiIpRKJR0lpaSk0E6zoWxMSEhI4MXnEizwgoQA0GrHvhTc3cEfErJYLOju7sbi4iK2bNmCpKQkl8cGuNnBiUQiTE5Owmaz+a1B5+yYzkjI2/mfUECn00EqlSIuLg61tbWrFnORSISUlBSkpKRg7dq1MBgM9JDsyMgIoqKiaEJKTU0Nys6W2Hfk5OS4HaRmG+6aG1y1gDPboUONUHSjMZtfHKMktVoNjUYDvV6PtLS0oD0/wJXn3p9minAGL0hIJBJh8+bNrNZZfCUhnU6HtrY2REVFuZQCIiBfGKvVyqosjU6nw+LiIqKiolidQXLWHcdXCwYAWFxchFQqRW5urteLeUxMDAoKClBQUACr1UrPJPX19cFkMtml7dh2BQW+VHIvLS1FUVERbxxlXbWA80AohUao55Uco6TLly8jOTkZNtsVV2RmlETmkri6Xk8K2lcjeEFCXMAXEiI1hry8PJSXl3vclQWqdu0MSqUSUqkU0dHRyM3NZbW+4ZiO40MDgissLCzQdTBHIVZvIZFI7GoBGo0GCoUCs7Oz6O/vR0JCAh0lsSG4Ojs7i76+vqDp1vkCV1HS9PQ0vTkxmUx27wt2VBJqhQJHUBSF5ORkeqZNp9PRwqvDw8OIjo6mCYntKEmr1Qo1oasF3pAQc/izsrIS+fn5Xh2bFH3Zak6YnJzEwMAAKioqsLi4yPoulTQmME3oAP40IABXPouJiQmMjo5i48aNAdfBCJiuoCUlJXaCq5OTkxCLxXYzSb5EtuT5GR8fR01NjV+jBMEEIZ2JiQlMTEygtrYW0dHRnLWAews+2TgA9o0JzCiJRNlkLskxSiJzSYF8p641yR6ARyTE9mIYERHhliSsViu6u7uhVqv9qkWxIQtks9nQ19dHi4umpqZieXmZ9fZvsvgwh3e9HQ4MBsg8jVwuR0NDg8taHBuIiopCbm4ucnNzYbPZsLi4SNeRurq6aMHVzMxMt7l5iqIwMDBAf3bhMOFOTBfn5+dXXTMXLeDeItTpOEe4i8wkEoldLUmv10OpVEKpVNK1yECiJCESuorgLlIhHUwRERFobm72azAs0EjIZDKhvb0dFovFbh6Kixkk8gVXqVRIS0vj1a6TDAMbjUZs2bKFk3qNK4jFYqSlpSEtLc1OcJUpB0MIiWnARjYwpJkmmArP/sJms6G3txeLi4tobGxcRbBctID7cm18eia9VUwQiUSIi4tDXFwca1GSQEJXEUg6zrENldReHN1H/Tm+v2SxsrKCtrY2JCUlob6+3i4FJBaLYTKZ/DquM5BUR25uLrq7uwEgJH4/zkCUIKKjo9HY2BjSawGcC64S0VGbzUbvbmdnZ1mdAeIaZHDWYDCgsbHR46bLWXMDl1ES30jIX1M7NqIkrVbLmi1MuIA3nzwX6Tjgy+YBkr9va2vD+vXrA7Z+9jcSWlhYwOeff478/HzU1NSsWnjZjISY8yNVVVW4/vrrsXnzZkRHR2NkZASnTp1Ca2srJicnodfrWTmnt1heXsbFixeRnJzs9D6EGkRwtaqqCjt27EBdXR2ioqIwODiI5eVlUBSFqakprKys8KrTzBFmsxltbW2wWCxoaGjwO+qPiIhAVFQU/U8ikdileU0mE8xmM92J5wv4VhNigxRJlFRQUICamhps376d7vQcGhrCZ599hvb2dkxOTkKr1dLPkDc1oSNHjqCkpAQxMTGor6/HmTNn3L7/9OnTqK+vR0xMDEpLS/Hcc8/Z/dxsNuPJJ59EWVkZYmJisHnzZnz44YerjjMzM4O/+7u/o9Umampq0Nra6uOdWQ1+ffNZBHP6GQAt/tnY2MiKmZivkRARsiSF95ycHKfvY4OE3DUgEL+fdevW0ZI4MpkMg4ODiI+Pp7vGkpOTOcvTk+gi1O3M3oKknoiTZElJCT1TwhRczczMRFpaGm9UvY1GI9ra2hATE4NNmzaxcl1sDcoywaeaEEk/sv0ZMqMkAPRcklKpxOjoKPr7+3Hx4kUMDw+jrq7O5XHefPNNHDp0CEeOHMG2bdvw/PPPY/fu3ejt7XXaTTo2NoabbroJ9957L1599VWcO3cOBw8eRGZmJu2q+vjjj+PVV1/Fiy++iA0bNuCjjz7Cvn37cP78edTW1gK4Ihy8bds2fOUrX8EHH3yArKwsjIyMsLKW8sJZFbhCFmya0FEUhY8++ghbtmxBX18fxGIxampqWKs5XLx4EWvWrPGqo85qtaKrqwuLi4uoq6tzW3gfHx+HSqVy+yC6g6MCgrcNCGazme4aUygUdNcYWVjZilQmJycxPDy8ytKAz1CpVOjo6EBxcfEq+SQiuErum9FoRFpaGr3ghKpepNfr0draiuTkZFRVVQXNn4g5f8ZcWtx5JY2OjsJoNKKiooLza/QEi8WCzz77DNu3bw9aqtVqteLixYt4+eWX8c4778BqtWLnzp3YvXs3br75ZpSXl9Pv3bJlC+rq6vDss8/Sr1VUVGDv3r146qmnVh37+9//Pt5991309fXRr913333o6OjAhQsXAAB5eXl47LHHcP/999Pv2bt3LxISEvDqq68CAB599FGcO3fOY9TlD3gTCXFhFyAWi9HW1obs7OyA02+O8HYOyWAwoK2tDWKx2KsmiEAioUAGUCMjI5GTk4OcnBy6a4wU6A0GA61knZmZ6ReRk86subk51NXVhdza2lvMz8+jp6cHFRUVLiWcSJ6fzJTI5XIsLCxgYGAA8fHxNJlzGV0yodFo0NraiuzsbJSXlwdVuQHwPCjr2NzAp5oQucZgRrMSiQQtLS1oaWnB8PAwvvnNbyIiIgIffPABpFIpXnnlFQBXmplaW1vx6KOP2v3+jTfeiPPnzzs99oULF3DjjTfavbZr1y689NJLMJvNiIyMhNFoXPWdjo2NxdmzZ+n//+6772LXrl248847cfr0aeTn5+PgwYO49957A/77eUNCbILk6202G4qLi7F+/XrWz+FNOm5xcRHt7e3IzMz0mgT9JSE2FRCYXWPl5eXQarWQy+WYn5/HwMAAEhIS6IXVm2FPEgmSbrJwkSUZHx/H6OgoNm/eTKdR3IE5U1JcXExHlwqFgnaBZc4kcbHTJs9cUVERSkpKQprm8tYryWq18iYdR64rVNej0+lQWlqKPXv24IEHHrCLJhUKBaxW66oMQnZ2Nubn550eb35+3un7LRYLFAoFcnNzsWvXLvz85z/Hjh07UFZWhk8++QTHjx+3+4xGR0fx7LPP4pFHHsEPfvADfPHFF3jwwQcRHR2Nv//7vw/ob77qSIi0ospkMkRFRXm1ePgDT40JMzMz6O3txbp163yqe/hDQlwrIDAXVuawJ4nwSITkrB5iNBrR3t6OiIgINDU1hUU3meM8jb9zS8zokgiuyuVyjI2Nobu7GykpKTQpsSG4qlAo0NnZiXXr1qGgoCCgY7ENV1GSwWCASqVCdnY2TCZT0AdlHUHas0NBQsQ1ljm/5ew6HF/zJETr7P3M13/5y1/i3nvvxYYNGyASiVBWVoa7774bL7/8Mv07NpsNDQ0N+OlPfwoAqK2tRU9PD5599tmrh4TY+NCZ5m8tLS24fPkyZ5YLriIhMsQ4MzOD2tpan0nQl4aHUCggOA57EgO6gYEBuh5CSMlsNqO9vR2pqamsp0O5gs1mQ3d3N5aXl53O0/gLpuDqunXroNfraTfZkZERREdH09Flamqqz/eKpA35KB3kDGQUobOzE0lJSSgqKgIAv5sb2IK/7dlswV13XEZGBiQSyaqoRyaTuayv5uTkOH1/REQErfCRmZmJd955BwaDAUqlEnl5eXj00UdRUlJC/05ubi4qKyvtjlNRUYGjR4/6/Dc6gjckFCjUajWkUikyMjJQWVkJiUTCue+P47GJ9YBer8fWrVv9GjrzNhJy9AAKhQICsx6yfv16Om1HtNSAK914BQUFvEm3uAP5/KxWK5qamtyK2AaK2NjYVYKrcrkcPT09sFgsdoKrnuqIU1NTGBoa8jptyAeQxom0tDRUVFTQz0ewB2UdEer6lE6nc0lCUVFRqK+vx8mTJ7Fv3z769ZMnT2LPnj1Of6e5uRnvvfee3WsnTpxAQ0PDqqxETEwM8vPzYTabcfToUdx11130z7Zt24aBgQG79w8ODtKbh0BwVZDQ1NQU+vv7sX79ehQWFtIPNJck5HhsrVaLtrY2xMbGYuvWrX6nnbwhIWZuPVRpC0eIRCIkJCQgISEBkZGRWF5eRl5eHsxmM1pbWxEZGWm30+dLGzMBiaJjYmKcWkdwCWeCq3K5HDMzM+jr60NiYiJNSMwaHGn7n5ycDKtmD61WSzdOOKqkc9EC7gtCaWhntVqh1+vdbl4feeQRHDhwAA0NDWhubsYLL7yAyclJ3HfffQCAw4cPY2Zmhm5muO+++/Cb3/wGjzzyCO69915cuHABL730El5//XX6mBcvXsTMzAxqamowMzOD//iP/4DNZsO//uu/0u95+OGH0dLSgp/+9Ke466678MUXX+CFF17ACy+8EPDfHdYkRLTX5ufnUVdXt0pAkutIiCgbEBVu4sIaaFOAOxLiswUDRVEYHh7G9PQ06urqkJaWBuDK58S0VjCbzXZpOy4jDm+g0WjQ1taGjIyMgFQ02ABTcLW0tBQmk4lO2zkKrpLaXLho1wFfqoXk5+ejrKzM4/PrqrnBWSaAjSgplJEQcRB291nu378fSqUSTz75JObm5lBdXY3333+fjkjm5uYwOTlJv7+kpATvv/8+Hn74Yfz3f/838vLy8Ktf/YqeEQKubMAef/xxjI6OIiEhATfddBN+//vf221qGhsbcezYMRw+fBhPPvkkSkpK8Mwzz+Cb3/xmwH83b+aEgCtFbF/e297eDpvNhtraWqfzGFKpFMnJyXa5TbYwOjqK5eVlpKSkYGhoyCcVbndYWlpCa2sr/uqv/mrVz/hMQFarFT09PVheXkZtba3L3Rxzpy+Xy7GysoKkpCR6SDbYrpIkjVtYWIjS0lJe3VNHMFvnZ2ZmYLVakZKSguzsbGRkZPC+63BpaQltbW0oLi5m5TvpGCU5zsb5EyXNz89jZmYG9fX1AV+fr5iZmUFFRQWMRmPIN2bBBK8iIWI54AmkDTUtLQ3V1dUuw2cuIyGRSITFxUWo1WrWVBgA55EQaUDgqweQyWSiW5A91VIcd/pGo5EWDR0dHaUdUf0t0PsC4l20fv16VizluYZYLEZycjImJiYQGxuLiooKLC8vQy6XY3BwEHFxcXSUxBRc5QMI2ROVDDbgrgXclaOsN+oNobpvOp0O0dHRvJOw4hph99dOT0+jr68Pa9euXTW97giuSMhoNGJqagoWiwXXXXcdq8rPjg0PjmkHvhGQVqtFe3s7kpKSUFVV5XM+PTo6Gvn5+cjPz3dZoCdREpu7Q6LcwKZ3Edcwm8002ZPCckpKCi24SmaSmIKrRKg2lDtr4jrLJdn7OyjrCG8VtLmARqNhpVU/3BA2JEQ8Z+bm5rxufeaChJaXl9HW1obo6GhERUWxbj1ARCFJRMiU4OHTzha4srvt6OhAfn4+1q5dG/CXx7FAv7KyQpvP9fb2Ijk5mSYkf7+spG5FUi6++kiFCp504CIiIpCdnY3s7GxQFIXl5WUoFApMTEygp6cnZClPohNYUVER1NZxbwdlHZsbQtmiTUjoWgOvSMhVOs5oNEIqldLeO97mviUSCau2CPPz87TwZlxcHMbHx1k7NoEzTxe+RT/AlQJob28vysvLOdndikQiJCUlISkpCWVlZTAYDHTajszVEMLyNvVks9nQ09ODpaUlNDY2hs0XXqfToa2tDSkpKV7NW4lEIiQnJyM5Odnu3ikUCoyNjdGdihkZGZwKrpLZperq6pDqBDKjJOZsnbMWcIvFEjISIjNCfPuucw1ekZAzLC0tob29HSkpKau8dzyBrUiIoiiMjIxgbGwMmzZtQnZ2NmQyGSepPvIFMJvNtFw+nx5KZltwMC2tY2JisGbNGqxZswZWq9Vl6ikjI8Npe7zFYkFHRwfMZrNXnjp8Aekmy8nJ8bvz0vHeORswJu3zbEX2s7Oz6O/v593skmNtyNEnaXl5GbGxsTCZTEEflNXpdLxvLuECvCah2dlZ9PT0oKyszC8dLDZIyGKxoKurC8vLy9i6dSvdPsmGvbcjiPyGSCRCd3c3srKyeNHCTEAkkUgzhiffE64gkUiQlZWFrKwsOvUkl8sxPj6Onp4eWg4nMzMT8fHxdCdlVFQUGhoawqbwy4UOnKPxmlarhUKhoHUB2bDzIMOzNTU1dJs+X0FIhqT7TSYTKioq7LySgOAMymo0mpB9p0IJXn4bbTYbBgcHMT09jZqaGr8Lx4GSELEBj4yMRHNzsx0ZsF1vYraZNjU1QS6XY2pqCn19fUhOTqYJKVQ7JaImYLFY0NTUxJtIgpl6Wrt2LS2HI5fLMTw8jJiYGJhMJiQnJ2PTpk1hQ0DB0IFjDhgzBVflcrnfgqvj4+MYGxsLq+FZItWk0WhQX19PP9vBHpS9Fq29AZ6RkEgkgslkQkdHB4xGI5qbmwP6UAIhCrVajfb2dmRnZ9M7IybYdEB19AByrIWQmZqhoSHExcXRtZBgWQPodDpIpVLExcUFXU3AVzDlcEhXVmxsLFZWVnD27FnOVazZAKm3VVVVuTQ/5AKOdh4kwnQUXCWbIeazR9K0U1NTqK+v91v0NdggBKTVatHQ0GC30eSiBdwd3En2XM3gFQktLy/j8uXLSEpKQm1tbcC7Vn9JiLSBl5eXO3UrDOTYjvA0/xMTE0MvqqQNVyaTob293aOCNRtYXFyEVCpFbm5uwGoQwYRMJkN3dzcdSTBVrEdHR9Hd3U17JPFp0JMvOnBisdip4KpjYwiZSRoZGcHc3BwaGhrCZiG12Wzo6uqCTqdDfX2927Q3Wy3g7iB0x/EACwsLWLNmDWuT6xKJxCe3VpvNhoGBAczOzjqVAWKCREKeZNTdwVcFBGYbLnN6nuSyyS6VrZkaMsy5du1al2TMR0xPT2NwcBDV1dXIysoCsFrFWqfT0YsqGfQMdoTJBN914NwJrhILhtLSUt5Gl47whYCcwdcWcPLf7iCk43iA9evXs2rx7UvzABkEJGlATztj5o7InwgkUA8gpvHc+vXraSmcqakpu5marKwsn3f5FEVhYmICo6OjYTXMSboYp6amPC7kcXFxKCwsRGFhoUvzOTLoyXUdidh/LCwshLThw1uQea709HT09PRArVYjOzubjpKI4GpmZiYSExN5Fz0TAtLr9X4RkCM8RUneNjdotVpWpL/CDbwiIbbhbcqMCFjGx8dj69atXi06zOE2X0iICw8gRykcZh1peHjYp10+6RIiwpjhlNvv6+uDSqXyeSF3rIWQtN3IyAi6urposdWMjAynGoWBXjeZXWpqamL9+FyBWczfsmULXcx3JrhK7l1aWlrIG0NsNhs6OzthMBhQV1fHSeepY5Tk2Abu+D7yXp1OJ0RCVxsICblLmcnlcnR0dKCwsBDr1q3zmhCYux5v4diAwFWrp791JIvFgs7OThiNRmzZsoV1NQiuwLzuxsbGgK5bLBYjNTUVqamptEeSQqHAwsKCXQuzt9bm7mC1WukFMZxml8h1G43GVcX8qKgo5OXlIS8vzy5lPDQ0BL1ebzeTFGzCtdlsdNNTfX19UFKHjoQEwGWUtLi4KJBQqMF22E4WWKvVumoHRlEUxsfHMTw8jKqqKuTl5fl0bNIN421zQqgESL2tIyUmJqK7uxvR0dFobGwM+Y7VW5hMJto+3JlRV6Ag1uZFRUUwm810HYlYmzPTdr5ExM504MIBVqsVUqkUVqvV40LOTBmXl5fThO4ouEoidC6HQkNBQI5wrA0xIySZTIYLFy5wovjPd4THSuMnXEUrxHZAqVSiqanJb/0wb2tOfLFgcFVHGh8fh1arRVRUFHJycmAymcKChIicTXJyMqqqqjifbI+MjLSzNieEPjg4aGdtnpGR4TYa86QDx1dYLBa0t7dDJBKhrq7O52eESehMwdWOjg5QFGXXPs9mmoxEbiaTKWQE5AwkSlIqlbjjjjvwla98Bf/5n/8Z6ssKOvi/0gQAsihZLBb6oSYLAHDF+jaQ1I03NadAGxC4AqkjGQwGjI+Po6SkBNHR0XQtJNTdYp5A5Jzy8vJ8SqOyBUdCJ7v8ubk59Pf3IyEhgb5/zOK8rzpwfIHZbKYHtzdv3hwwcToTXJXL5bTganJysp3qhb+fr9VqpeWa6urqeENABIuLi9izZw+Ki4vx1ltv8UYdJZjgFQmxvZCIRCI7oiALV1paml+2A45wtF1ggosGBLZB7AyqqqpogUlmHUkulwdtHskXEGXmsrIy1rxpAoGj8gCzOD8xMYGIiAhavXp0dDTsZq7Ixi0uLg4bN25knTgdVS+YgqvEY8ofa3hCQBaLhZcEtLy8jL179yI7Oxv/93//d00SEMAzZ1WKolhVvQaAv/zlL6irq4Ner0d3d7dXPkTe4uzZsygvL1/VwuzYgEDqR3wBRVEYHBzE3Nwcampq3LYyM9NOMpmMk3kkXzAzM4P+/v6gqwn4C5vNBrVajenpachkMohEIlpsNTMzk/fNCAaDAa2trbRfVLAjN6bgqlwuh8lk8irtySSg2tpa3hGQRqPB3r17ERcXh/feey9suiK5wFVPQqdOnUJqairkcjk2b97M6szL+fPnUVpaarcYMnWm+Bj9WK1WekivpqbGpxkiZ9bcZB6JpE24AnOYc/PmzbwXxmSCRG5r165FWloaff+Wl5eRmJhI3z++yfjrdDq0trYiPT0dFRUVIb82puCqXC7H0tISEhIS6E0R6VZkNk/4U7viGlqtFrfffjtEIhH+/Oc/834ujGvwioSAK6E/W7BYLPj0008RERHByRDgxYsXUVBQQHfW8aUBwRWImnRERAQ2b94c8O6QOY+kUqk4qyOR2SWFQoG6urqw+tK604EzmUyQy+VQKBRQKpWIjIy0m6kJZb1Iq9WitbUV2dnZvE0dkm5F8o9EmRqNBhKJhJcEpNfrcdddd8FgMODDDz+kVfmvZVy1JEQKwAaDAeXl5ZwoEV+6dAk5OTkoKCjgbQMCgUajQXt7O1JTUzkpiDPrSHK5nLU6Euls0uv1qKurC5vZJeDLmtumTZs86sCRtBO5f1xam3vCysoKWltbsWbNGpSVlfHuWXYGkvbs7e2FyWQCRVFITU2lO+74MH9jNBrx9a9/HWq1GidOnAgbV1+uwTsSIg9QIFCpVGhvb0dubi5WVlaQn5/PiftnW1sb0tLSUFhYSDcg8K3+AwBKpRKdnZ0oLCxkTZfPHZh1JLlcDqPRiPT0dGRlZfm0oJpMJkilUohEItTU1PAur+8KzNRhbW2tzzpwztKexJ470G4xT1haWkJbWxuKi4vDambFarWivb0dFEWhtrbWbqZLrVYjJiaGJqTU1NSgR5kmkwkHDhzAzMwMPv7447BKJ3ONq46EJicnMTAwgA0bNqCgoACtra3IyMjgpItKKpUiISEBhYWFNPnwjYCmp6cxMDCAyspK5ObmBv38/taRiJdTQkICqqurQ96R5y2IDpxMJmMtdWg0Gu3SntHR0XbdYmwtqGq1GlKpFGVlZWElWEsICABqampWpeCYTrwKhSLoUabZbMbdd9+N4eFh/OUvf+GV0ywfcNWQEKkbzM/P2zk6SqVSJCUlobS0lNXrpCgK3d3dWFpawpo1a5CVlcWrTieKojA8PEwbA6ampob6kgB4V0daXl6mvZzKy8t5R+yuwNSBq6+v56TjialgLZfL7azNAxnyJN5L69ev5yRrwBWYA7TeeF1RFIWVlRWakJaXl5GUlERHSWwLrlosFtx7773o6urCqVOnaFV3AV+CdyRkNpt9NosjaRsykMb88hMpmnXr1rF2jaQBwWAwYH5+nu50CkS5mk0QRYjl5WXU1tbyIh/uDM7qSImJiVCr1SgpKWHN0joYIC3BJpMJtbW1QdmQkCFPknbSaDR+dSuS7r2KioqQRMv+ghCQWCxGTU2NX9Gy0Wikn0GlUknPdBHlhkAicKvVioMHD+KLL77AqVOnwureBhNhT0IrKytoa2tDUlISNm7cuCoU7+3thVgsxoYNG1i5PlcdcCRlIpPJoFKpaKHLrKysoMrZE0IGrqQmwmUAzmazYWRkBOPj44iMjITVavWrjhQKmM1mejceytoViTIVCgVUKhVdB8nMzERKSorTtN38/Dx6enqwcePGsNqls0FAjiDNDYTUjUajnfGhL5GtzWbDgw8+iM8++wyffvopZxbtVwPCmoRkMhk6OztRVFSEtWvXOl3oBwYGYLFYUFVVFdB1OSoguKv/EH8amUwGhUJBt95mZWW5XAzYgFarRXt7Oz1YGE51lPHxcYyPj2PTpk1IS0sL2TySr+CrDhypgxBSstlsdmKrkZGRmJ2dRX9/v1fde3yCxWJBW1sbJBIJawTkDGQmSaFQQK1W06njjIwMt4KrNpsN3/3ud/Hhhx/i1KlTKC4u5uT6rhbwjoQsFotHPTaKojA2NoaRkRFs3LjR7eT8yMgItFotNm3a5Pc1MRWwAd864Gw2G1QqFWQyGeRyOS3UmJWVFXC4z4RKpUJHRwfWrFnjkpD5CKahW11dndO5CSLjQqJMvujahYsOHFObTS6XQ6vVIjY2Fnq9HlVVVWGVJgoWATnCbDbTtTiFQmEnuJqRkUFHvzabDYcPH8Y777yDTz/9FGvXrg3K9YUzwo6ErFYruru7oVarUVdX59F0bXx8HGq1GrW1tX5dD5seQBRFYWlpCTKZDDKZzK51OTMz0+80DhmILC8vD6uiMvksNRrNqlqeKzirIxFSD6auHUkD5+Tk8HaY0xWGhoYwOTmJhIQErKys2O3wU1JSePu3kLQnGbYOVdTJJHWFQgGNRoPXXnsNubm5UCgU+Pjjj3Hq1CmUl5eH5PrCDWFFQgaDwa4Txpvi79TUFBYWFtDQ0ODztXCpgEAkSAghaTQaOv/sreEXcx5l06ZNSE9PZ+36uAbx06Eoyu/alat5JHIPuaojkVbm4uJi1nQIgwHyvBD786SkJDtSVygUAIJrbe4t2FbxZhMGgwHPPfccnnvuOUxNTSEvLw/79u3DLbfcgp07d4bVgHUowI8nzAssLi6ivb0dGRkZPgkpemvx7QiuJXiYysulpaXQ6/X0Yjo4OIiEhARkZWUhKyvL6XCizWZDb28v1Go1J5JEXEKv16O9vZ1WZfZ3QXFmpyCTyTA9PY2+vj5O6kikkyzcWpkpisLQ0BDm5ubQ0NBAPy+OlgqO1ua+boy4ACGgqKgoXtXdCKKjo2E2m6HT6XDx4kUolUr86U9/wne+8x28/PLL+Ku/+qtQXyKvwbtIyGq10pa3BLOzs+jp6cG6detQVFTkEyEsLCxgZGQELS0tXr2fNCCEUoKHWAGQ3Wl0dDRNSMnJybBYLHYKwXyaT/KElZUVtLe3IzMzExs2bODs3nJRR3KnA8dnUBRFa+/V19d7PT6g0+noZ1CtVtMdn6QwH4zvBZOANm/ezLu6G0VR+NWvfoWf/exnOHnyJOrr6+1+RlEU766Zb+A1CRHLgampKdTU1PjVwaNQKNDX14ft27d7fG8gDQhcgdnlJJfLAVy5zri4OF56pLgDaZ4oKioK6gyQY8pJJBL5XEciOnCbN28Oq7QniZgXFxcDGqAlHZ/kHjKtzdPS0jhJ25nNZrS2tiI6Opq3BPTss8/ixz/+MT766CNs2bIl1JcUluAtCZHdvk6nQ11dnd/pFLVajY6ODuzcudPt+9hsQOAKarUa7e3tiI2NhcVigdlstuu04zMhkXmUiooKWnU8FPC1jsSso3jyXuIbbDYb3fhRX1/PWsRM7iGJ1g0Gg13ajo0aCCEg0vrOt+8jRVF46aWX8MQTT+D999/Htm3bQn1JYQvekRB5wNva2hAbGxuw5cDy8jIuXbqEG264weV7+G7BAFxJK/b09GDt2rUoLCyk5UdI67dWq0VaWhrdacenFN3ExARGRkZ4N49CmkPIkLHjPFJcXBzrOnDBAlEfNxqNqKur43TYl9xDdx4/vsBkMtnNXvGRgH7/+9/je9/7Ht577z2PG1wB7sE7ElIqlbh48SLy8/NZ0Q3TarU4d+4cbrzxRqc/pyiKTv/xIf3mCIqiMDExgdHRUWzcuNGlKZ9Op6MJaWlpCUlJSTQhhWq4k6RTiZ4f36XrSR2J6NqR56GyshJZWVm8ezZcgWnqFmxXUaZ6tVKp9NnSw2QyobW1lTMr8UBBURRef/11HDp0CMePH3e7uRXgHXhHQnq9HvPz86ylbAwGA06dOoVdu3Y57TDjswcQEWWVy+Wora31OBNFwFRdViqViIuLownJn52pPyCpoOXlZdTV1YVUS89XkEVcp9MhKSkJarWariOR1mW+dWgRkNZ3IiEUyhZrZzI4xJrbWbTOdwICgLfeegsHDx7EH//4R+zevTvUl3NVgHckxLbFt9lsxieffIKvfvWr9BeSjw0IjrBYLHQ6pba21u88OynKEwkhiURCExJXvipmsxkdHR30TpzPum+OcKYDF6p5JF9hMpnQ3t7Oy1ZmZuqTaW1OiD06OhptbW28JqDjx4/j29/+Nl5//XXcdtttob6cqwZXPQnZbDacOHECX/nKVxAdHR0WDQhkKDc6OhqbNm1ibTdLdqZkQNZms9ELaUZGBiuLFrl2vmmpeQNy7bGxsS7nlzzVkUKV+iQadnxexJlgjiEolUrYbDbExMRg/fr1vIw0//znP+Nb3/oWXnnlFdx+++2hvpyrClc9CQHARx99hO3btyM2NhY2mw1Wq5WX6TcAtJcOmaPhajEh0iOEkAwGg11jgz+7e2IhnpaWhoqKCt4vhEz4qwPnWEeKiYmh72GwZmkMBgNaW1uRnJzMaw07ZzAajbh8+TKioqKQkJAAhUIBs9lsl7YLdaR58uRJfPOb38SLL76Ir3/96yG9lqsRvCMh4MqDySY+/vhjNDU1IS4ujrf1H+DLafzS0lKfh3IDBVNCaGVlBSkpKbTytzezJUTKJlgW4myCLR04V/NIXNaRdDodWltbkZ6ejoqKirC670ajEa2trUhMTKRVUJhOvEzTORKtJyQkBPVvPHXqFO666y4cOXIEBw4cCKv7Gy64Jkjo008/xcaNG5GUlMRbAiLDkFVVVcjOzg7ptRBfGplMBrVajYSEBJqQnC0CpH083KRsAO504IJRR9JqtWhtbUV2dnbYiag6IyBX72Om7aKiouh7yFVNk+Ds2bO4/fbb8Ytf/AL33HNPWN3fcAIvSchfi29HENmMtrY2qNVqerAzIyODN8KMpI15bm6Ol8OQpOVWJpPZLQLEG2lqagrDw8Nu28f5imDpwHFRR1pZWUFrayvWrFmDsrKysFogSQouOTkZVVVVXl87sTYnpGSxWGhiZ9v48PPPP8e+ffvw05/+FAcPHgyr+xtuuGpJiNmAwAzxZTIZ9Ho90tLSkJ2dHZCFQqCwWq3o6uqCTqdDTU0N79uYySJA5pHI/V27di0KCgp4V0x2B6IDV11dHfTIk9lC708daWlpCW1tbSguLkZJSUmQrpodMOtXvhCQI8iwNrmPTGvzjIwMp6K/3qK1tRW33norfvjDH+LBBx8UCIhjXJUkRFqwXTUgkPrHwsICbaFABEKDpTRgNBrtvFH4LLnjCJvNhp6eHqhUKqSnp0OtVsNsNtvZcfP57+GTDpwzKwUSITmrI5H0YVlZGQoLC0NxyX6DEBBp/mBzcXdsEImOjqbvoy9uxh0dHbj55ptx+PBhfPe73xUIKAjgJQn5YvHtCF8lePR6PV2QZyoNZGVlcRaZkC6y1NTUsOtmIpp+ZrOZVvAmkSaJkJjEzpaWGBugKAojIyOYnp5GbW0t7xQcPNWRVlZW0NHREZa1N4PBgMuXL9PPPJeLOxH9JaRks9ns0nauNkjd3d246aabcOjQITz22GMCAQUJVxUJBaqAQNIkRP7fk6ePP1Aqlejs7AzLLjISvZFhSFd1NULscrkci4uLSExMtLuPoQCxM5DL5WGhA+c43Lm0tAQAyM7ORllZWcjuoz8IJgE5wpm1Oen8JGk7AOjr68NNN92E73znO/jhD38YVt/LcMdVQUKk7kPM69hQQGAW5BUKBZ23z8rK8lv6Znp6GgMDA6isrERubm5A1xdsaLVatLW1+Ry9mUwmOwkhNu6jryASQisrK17biPMJ8/Pz6O7uRn5+PgwGA11HIg0iwZpH8gd6vR6tra307Fior1Ov19MRUnd3N37yk5+goaEBp0+fxj333IOnn346rDITVwN4SULuLL4d4aiAwIUEj9VqtSOkiIgIeiFNSUnxeD6KojA8PIzp6WnU1NQgNTWV1evjGouLi5BKpcjPz8fatWv9vr/kPhJSEovF9H3kqt3WarWio6MDJpOJczVpLjAzM4OBgQE7BXJf60ihAt8IyBHLy8t48cUX8dOf/hQikQixsbHYvXs3br31Vtx+++1+ddAeOXIEP/vZzzA3N4eqqio888wzLr3M5ubm8C//8i9obW3F0NAQHnzwQTzzzDOr3nf06FE88cQTGBkZQVlZGX7yk59g3759To/51FNP4Qc/+AEeeughp8fiI/jRp+wngmXBIJFIaAtkm81Gd4h1dHQAAL2QpqWlrVpIrVYrenp6sLy8jKamprBKowCATCZDd3c31q1bh4KCgoCO5Xgf1Wo15HI5enp6YLVa7byR2GihJzpwYrEYDQ0NvGnL9xZTU1MYGhpCTU0N0tLS6NeZltw2mw1LS0uQyWQYHBzkja6dXq/H5cuXkZGRwamDbiBQq9X47W9/i7vvvhu//OUvcfnyZbz33nt4/vnnceedd/p8vDfffBOHDh3CkSNHsG3bNjz//PPYvXs3ent7nTaRGI1GZGZm4rHHHsMvfvELp8e8cOEC9u/fjx/96EfYt28fjh07hrvuugtnz55dZaJ36dIlvPDCC9i0aZPP1x5KhG0kxAcPIFJIJo0NzIU0IyODVmMGgJqamrDbhU9PT2NwcBDV1dXIysri7DzMvD2zhd6V2rI38EYHjs8YHx/H2NgYamtrvZ4dcyYSGgpLj3AgoJmZGezatQs33HADnn/+eVai8C1btqCurg7PPvss/VpFRQX27t2Lp556yu3v7ty5EzU1Nauil/3792N5eRkffPAB/drXvvY1pKam4vXXX6df02g0qKurw5EjR/DjH//Y6bH4Cl5uDT09tHyxYBCLxUhLS0NaWhrKy8tpLbbh4WF0d3cDABISErB58+awIiDSRTY1NYXa2lrO04cikQjJyclITk7G2rVr6YV0dnYW/f399PyHtx2LRMomHDXsmE6u9fX1Xtt3AFfuY0JCAhISElBSUmI3jzQyMhKUOhIhoMzMTFb8wLjA/Pw8br75Zmzfvh3PPfccK88HsaF49NFH7V6/8cYbcf78eb+Pe+HCBTz88MN2r+3atWsVwdx///24+eab8dWvfhU//vGP/T5fKMBLEnIFxwYEPknwMBfStLQ0dHR0IDExERaLBWfPnqXFQbOysnhNSDabDX19fVCpVGhsbAxJF1l8fDzi4+NRXFxs17E4PDyM+Ph4eiFNTExc9fkTHbjc3FysW7eON8+HN6AoCkNDQ5ibm0NDQ0PA9z46Ohpr1qzBmjVr7OpIJDpnu45EyJ/PBCSTyXDLLbegoaEBL730EmsRskKhgNVqXTX4nJ2djfn5eb+POz8/7/GYb7zxBtra2nDp0iW/zxNKhA0JhYMHEPDlJH55eTk9y0FcT5k7e6LWwKdOLaaHUWNjIy/me5gLqdlspr2RLl++jMjISDsJoaWlJU504IIB0kKuUCjQ2NjI+owa13UkQkBZWVm81bFTKpW47bbbUFlZif/93//lpEbo+HdTFBXwvXB3zKmpKTz00EM4ceIEL76v/iAsSIhZ/xGJRLxMr5A0yuTkJGpqauwm8ePi4uiFkSkOOjg4yIsZGuBLQzSJRIKGhgZeKh5ERkYiJycHOTk5dg0iXV1d9PORn5+PwsJCXi6CrmCz2dDb24vFxUU0NDRwvjERi8VITU1Famoq1q9fT6c/Z2Zm0NfX53MdSafT4fLly7wWUlWr1dizZw9KSkrw2muvsf58Ez8ux6hHJpMFJAuVk5Pj9pitra2QyWSor6+nf261WvHZZ5/hN7/5DYxGI+/robwkIeZDzIcGBE8gi4harfaYwoqJiUFBQQEKCgpoY6+FhQWMjo4iNjaWJiRnqSauQLx0iJ4XH0neEWKxGBkZGcjIyKAXz/T0dCiVSpw6dYq2UAilNqA3IDNMGo0GjY2NQZONIvC2jkTkb5xJYLW2tiInJ4e36c+lpSXs3bsX2dnZ+L//+z9O0uFRUVGor6/HyZMn7dqnT548iT179vh93ObmZpw8edKuLnTixAm0tLQAAG644QZ0dXXZ/c7dd9+NDRs24Pvf/z7vCQjgKQkRhAMBEStri8WCpqYmnxaRqKgo5OXlIS8vDxaLhZ5FIiZfhJC4HEZcWlpCe3s78vLyeLuIuAPRgautrUV6ejrdISaTyTA5OYne3l6kpqbSaTs+pSysViud/mxoaOBFrdCxjuQ4jsCsIxEtOD4T0MrKCm6//XYkJyfj7bff5pTkH3nkERw4cAANDQ1obm7GCy+8gMnJSdx3330AgMOHD2NmZgavvPIK/TukPkcElqVSKaKiolBZWQkAeOihh7Bjxw48/fTT2LNnD44fP46PP/4YZ8+eBQAkJiaiurra7jri4+ORnp6+6nW+gpct2larFSaTiRcdcO6g0+kglUppS2W2dh2OatUikYiToU5iZVBWVoaioiJWjhkseKsDp9fr6Z098UZiW4rJH5D2favVitraWl5HawDoOhJJJRuNRlAUhbS0NFRWVvKK3Am0Wi1uv/12iMVi/PnPfw5KuvvIkSP4z//8T8zNzaG6uhq/+MUvsGPHDgDAt771LYyPj+PUqVP0+509f0VFRRgfH6f//1tvvYXHH38co6Oj9LDq3/zN37i8Blft3nwFL0nov//7v6FWq7F3714UFxfzMj1EVARyc3M5zYOToU4yi2Sz2ehdfSBdTTMzM+jv70dVVRVycnJYvmpu4a8OHEl/EqWB6OjooESbjjCbzZBKpRCJRKipqQm7IVqNRoPLly8jPj6envEi7qehrm0S6PV63HnnnTCZTPjggw+QmJgY6ksS4AK8JKE//vGPeOGFF3D69GlUVVVh79692LNnD29CfuIkunbt2qDK6VMURXc1yWQymEwmn436KIrC2NgYJiYmsHnzZrtJ/HAAWzpwRGmZSDGJRCJ6EXWmfMEWTCYT2traEB0djU2bNoVFzp4JjUaD1tZW5Ofn02Z6zvyR3NWRuIbBYMDXv/51LC0t4aOPPuKdWroAe/CShIAri6VKpcI777yDo0eP4pNPPsH69euxZ88e7N27NyRaVBRFYWJiAqOjoyF3EmXaJ8hkMmi1WtrPx1Wbrc1mo9uAa2trw253yJUOHFP5Qi6Xw2w220kIsZUqMxqNaGtro9O3fIzw3cEZATnCkdyB4OramUwm/N3f/R3m5ubw8ccfh51O47UI3pIQEyQCePfdd3H06FGcOHECRUVFuO2227Bv376gfKHJAi6Xy1FbW+vTJHswQIrxxD7a0c+H6eJaV1fHyxy+OzB14LhMYRHHTkJIWq2WHjT2V0IIsHcUDTcPKeBLAlqzZo3XFiQURdH+SKSORO5lRkYG600CZrMZ3/rWtzA6OopPPvmEFnwVwG+EBQk5Ynl5GX/+859x9OhRfPjhh8jOzqYJqa6ujvUvOHOIs7a2lvcLOCnGy2QyLC4uIiEhAWazGZGRkaivr+d9EdwRBoPBLoIIZgqLDBoTTx9/tNjIIGd6ejov1aQ9gdSACgoKUFZW5tcxXOnaMeWYArkvFosF3/72t9HT04NPP/2UU61DAewiLEmICa1Wiw8++ABvv/02/vznPyMlJQW33XYb9uzZgy1btgS8YBEhTJLDD7ciMlERAK7sFOPj4+lifEJCAu8XROJjxAcdOGbtQ6lUIi4ujiYkV95IZI6Gz4Oc7rCysoLW1taACMgZ2KwjWa1W/NM//RMuXbqEU6dOhZ1X17WOsCchJvR6PU6ePImjR4/ivffeQ0xMDG677Tbs3bsXLS0tPhPI8vIy2tvbkZmZiQ0bNoRdCoVcf3Z2NsrLy+1mkdgy6uMS5Pr5qANHtNjIvZRIJDQhkTZ6soCvWbPGZQ2FzyDXT1yAuQKpIxFSAryvI9lsNjzwwAM4c+YMPv3004DtRgQEH1cVCTFhMpnwySef4OjRozh+/DhEIhFuvfVW7N27Fzt27PCYkiIzNKWlpSgqKgq7BUSpVKKjo8Pl9TMLyHK5nF5EiQ5bqAlXrVZDKpWipKQExcXFIb0WT3DWRp+cnAy1Wo3i4mJWI4hggRBQUVERSkpKgnZeV3UkZ7YeNpsN//Iv/4ITJ07g008/5f1zIsA5rloSYsJiseD06dP44x//iOPHj8NkMuGWW27Bnj178JWvfGVVgZRM4VdVVQWk+xQqzM7Ooq+vz2sbcaYOm1wuB0VRdrNIwSYksgFYv349LQIbLqAoirZxj4iIgNVq5YXJnC9YXl5GW1tb0AnIEc7qSLGxsfjwww+xd+9evPHGG3j33Xdx6tSpsCR6AVcQXvklPxEREYEbbrgBzz33HKanp/H2228jKSkJDz30EEpKSnDPPffgvffew8rKCu6991689NJLqKurCzsCIjNAAwMDqKmp8To3TnTYKisrsWPHDmzevBkRERHo7+/HqVOn0NXVhYWFBVgsFo7/gisE2tnZiaqqqrAjIABQqVQYGhpCRUUFdu7ciS1btiA5ORnT09P47LPPcPnyZUxMTECv14f6Up1ieXk5JBGQMxBdu5KSEjQ1NWH79u2Ii4vDxYsXsXPnTjz//PO48cYbMTs769EE0xOOHDmCkpISxMTEoL6+HmfOnHH53rm5OXzjG99AeXk5xGIxDh065PR9R48eRWVlJaKjo1FZWYljx47Z/fypp55CY2MjLWK8d+9eDAwMBPR3hCOuCRJiQiKR4Prrr8evf/1rTExM4P3330dubi6+//3vIz8/H++8847Xg598AkVRGBgYwOTkJOrr6+1UvH2BSCRCamoqysvLcd1119GqzsPDwzh9+jSkUilmZ2dhNptZ/guAiYkJ9Pf3o6amJuw2AMAVdWOpVIqKigrk5+cDAL2IbtmyBddddx2ys7OhUChw7tw5fP755xgZGcHKygr4kJAgBFRSUhJyAnKG6Oho1NTUYPv27UhPT8fPf/5z2Gw2/M3f/I1TtWlvQWy5H3vsMbS3t2P79u3YvXs3Jicnnb6facu9efNmp+8httwHDhxAR0cHDhw4gLvuugsXL16k33P69Gncf//9+Pzzz3Hy5ElYLBbceOON0Gq1fv0d4YprIh3nCXNzc7j11lsBANu2bcMHH3yA6elp/PVf/zX27NmDm266iXdzQUxYrVZaiTkQFQFPYA7HajQaVuZnAO914PiM+fl59Pb2em2Fbjab6SYRpVKJqKgoO2+kYNcgl5aW0NbWxusaHEVR+NnPfobf/OY3+Mtf/oJNmzYBuPL8X7p0CVu2bPHrvoXSlpsJuVyOrKwsnD59mtabuxYQXtt9DkBRFPbt24eqqiq8+OKLiIqKwi9+8Qt0dXXhrbfewn/913/h4MGDuOGGG3DbbbfhlltuCcki4QpEh4yiKDQ2NnJacyCS/6WlpdDr9ZDJZJibm6ON+khjgy8kyNSBY8NNNBSYmZnBwMAANm3a5PWAZGRkJHJzc5Gbm2snWMtUqyYSQlzPRRECIk0sfARFUfjlL3+JX/3qVzh58iRNQMCV7MbWrVv9Om6obbmZWFpaAoCwk9IKFNc8CYlEIrz99tvIzc2liUUsFmPz5s3YvHkznnzySfT19eGtt97Cs88+iwceeAA7d+7Enj17cMsttyAjIyNkhKTX69He3h6SIc7Y2FgUFRWhqKgIRqORjpCGhobslKrdkQpTB66xsZFXLrPeYnJyEiMjI6ipqfF78ZBIJHTjAukOk8lk6O/vh9lspuWYMjIyWB80JgRUVlYWVB1EX0BRFI4cOYKf/exn+Oijj+wM3AJFKG25maAoCo888giuu+66sLFgYAvXPAkBQF5ensufiUQiVFZW4t/+7d/wxBNPYHh4GG+99RZ+97vf4dChQ7juuuuwZ88e3HbbbcjOzg4aIa2srKC9vR0ZGRkhn2GKjo6mjfrMZjPdXjs2NubSqI+oUJhMJs4jOK4wPj6OsbEx1NXVsZZCJDU54npKUqATExPo6elZJccUCBYXF9He3s57Avrtb3+LH//4x3j//ffR1NTEyXmCbcvtiH/+539GZ2cn7RN0LUEgIR8gEomwbt06HD58GI8++ijGx8dx9OhR/PGPf8T3vvc9bNmyBXv27MGePXuQn5/PGSGpVCp0dHTQHUx8SQ0CV9JMTKM+Mot0+fJlREZG0imm0dFR2ko8HJtASA2roaGBMyFYkUiExMREJCYmoqysjE6BLiwsYGBgICBreEJAa9eu5e2AJ0VReOWVV/D444/jvffew7Zt21g/R6hsuZl44IEH8O677+Kzzz4Ly47QQCE0JrAAiqIwMzODt99+G0ePHsX58+dRV1dHW1CwOew6Pz+Pnp4ebNiwge7ACgfYbDYolUrMzc1hYWEBIpEIubm5yMnJYdWoj2tQFIXBwUHMz8+jvr4+ZDUsk8lkJyHki/pFuBDQa6+9hocffhjHjx/HDTfcwNm5tmzZgvr6ehw5coR+rbKyEnv27AmoMWFlZQXvv/8+/dru3buRkpJCNyZQFIUHHngAx44dw6lTp7Bu3Tr2/qgwgkBCLIOiKMzPz9MWFKdPn8bGjRtpC4q1a9f6TUgTExMYGRnxqQDOJxAduNTUVOTk5NDdYVarlRWjPq5BmigUCgXq6+sRFxcX6ksC8KWEECElUmNy5sSrVqvR3t6OdevW8ZaAgCueYvfffz/++Mc/Yvfu3Zye680338SBAwfw3HPP0bbcL774Inp6elBUVOTWlvvb3/42ysvL8b3vfc/Olvv8+fPYsWMHfvKTn9C23I8//jjOnj2LLVu2AAAOHjyI1157DcePH0d5eTl97OTk5LCsj/oLgYQ4BEVRUCqVOH78ON566y385S9/QXl5Oa1n562iMtl9z83NhW0LsysdOOLMSdJMRqOR9vLJzMzkTarOZrOht7cXS0tLnLbBBwoiIUTqclarlb6fEokEnZ2dvFeieOedd3Dvvffi9ddfx2233RaUc4bCltvVd//ll1/Gt771LVb+rnCAQEJBAul6Ip5IJ0+eRHFxMW1BUV1d7TQlRTrIlpeXUVdXx5vdty/wVgfOH6O+YMBms9l5MbHtg8MVCMHL5XLMzc3BYDAgISEBBQUFyMrK4mUzyJ/+9CfcfffdeOWVV3D77beH+nIEBAECCYUIy8vL+NOf/kR7IuXm5tKEVFtbC7FYDIVCgU8//RSFhYWora3l5aLhCTKZDN3d3SgvL/e5hkW8fGQyGZaXl5GSkkLXPYLl6WS1WmkvKTbdXIMJlUoFqVSK4uJiiMVi+n4mJyfb+fmEGh999BEOHDiA3/72t/jbv/3bUF+OgCBBICEeQKPR2HkipaWl4frrr8fHH3+MTZs24c033+RNWsoXECHV6urqgGV4DAYDTUiLi4sBdYZ5C4vFgo6ODlitVtTW1oadGSDwJQE5bgKIn49MJoNKpaJ9pjIzM+1a6YOFTz/9FPv378eRI0dw4MABXnV8CuAWAgnxDHq9Hi+99BK+//3vw2w2IyMjg2779scTKVQgTRSBDHG6AukMI5I3XBj1ETtxiURCC7qGGwgBbdiwwe0snNlstvNGIq30xGCO687FM2fO4I477sAzzzyDf/zHfxQI6BqDQEI8w9mzZ3HbbbfhgQcewOHDh/GXv/yF9kSSSCS45ZZbsG/fPmzfvp2XO/Ng68A5GvVFRUXRhJScnOzXgmYymdDW1ka76fK1W88diJ+UJwJyhCtbD28M5vzBhQsXsG/fPvy///f/8E//9E8CAV2DEEiIZ3jttdewsrKC73znO3avm81mnD59Gm+99RbeeecdmM1m3HLLLdi7dy927tzJi2I5RVHo6+ujW5i5SpO5AhtGfUajEW1tbbQUUrjMLzFBCKiioiIgq2uKorC0tESnQUnnIiGlQDdBly9fxm233YYf/vCHePDBBwUCukYhkFAYwmKx4OzZszQhaTQa3HTTTdi7dy9uuOGGkLQPM3Xg+NDC7Oh2yjTqcyUKajAY0NraiuTkZFRWVoYlASkUCnR2dgZMQI4gBnNMFfXU1FT6nvraKCKVSnHzzTfjBz/4Ab773e8KBHQNQyChMIfVasXnn3+Oo0eP4tixY1Aqldi1axf27t2LG2+8MSjRCCngWywWXnbxkR39wsICZDIZXWsjoqARERHQ6XRobW1Fenq61/NbfANXBOQMer2eHo5Vq9V2orXx8fFu7193dzd2796NRx55BD/4wQ/C8l4LYA8CCV1FsNlsuHz5Mk1IMzMztCfS7t27OfFEMplMkEqlYVPApygKKysr9I5er9cjOTkZKysryM7ODlsCIpbolZWVyMnJCeq5TSaTnTdSdHS0y7pcX18fdu/ejfvuuw8//OEPw/JeC2AXAgldpbDZbOjs7MRbb72Ft99+G6Ojo/jqV7+K2267DTfffDMrnkgGgwFtbW2Ij49HdXV1WBbwZTIZurq6EBERAbPZTKtUZ2Vl8aLO5g3kcjltiR5sAnIEsy6nUCggEokwMDCAlJQU2ijuH/7hH/DTn/40LNOdAtiH8BRcpRCLxaipqcGPf/xj9PT0oLW1FY2NjThy5AhKSkqwb98+/O53v4NCofDLWlqr1eLSpUtITk4O2w6ypaUl9PT0oLS0FNdffz22bduGjIwMzM/P48yZM/jiiy8wPj4OvV4f6kt1CUJA1dXVIScgAHQzSHV1NXbs2IGNGzdiamoK3/3ud9Hc3IzExERs2rQJKysrAZ+LPMsxMTGor6/HmTNnXL53bm4O3/jGN1BeXg6xWIxDhw45fd/Ro0dRWVmJ6OhoVFZW4tixYwGdV4BnCCR0DUAkEqGqqgr//u//jvb2dnR3d2Pnzp14+eWXUVZWhltuuQUvvvgi5ufnvSKk5eVlXLp0CTk5OaisrAzLlIparabN3EpKSgB8adTX2NiI7du3Iy8vDyqVCufOncPnn3+O0dFRaDQav0ibCzAJKNBhYC4gFouRlpaGb3/724iNjcXtt9+O/fv346mnnkJmZib+/d//3e9jv/nmmzh06BAee+wxtLe3Y/v27di9ezcmJyedvt9oNCIzMxOPPfYYNm/e7PQ9Fy5cwP79+3HgwAF0dHTgwIEDuOuuu3Dx4kW/zyvAM4R03DUMiqIwNjZG15AuXbqErVu30sOxeXl5qwiGeBl50oHjM0gLs7dSQmaz2W4WyRfbBK5A0oh8JSCCmZkZ7Nq1C1/96lfx3HPP0Sm44eFh6HQ6O5tuX7BlyxbU1dXh2WefpV8j6b5A7BeWl5fxwQcf0K997WtfQ2pqKm2/EMh5BTiHEAldwxCJRCgtLcX3vvc9nDt3DqOjo7jjjjvw3nvvoaKiAjfccAN++ctfYnx8HBRF4Q9/+ANefPFFrF+/PmwJSCaT0TM03mrZRUZGIjc3F5s3b8bOnTuxdu1auh529uxZDAwMQK1WBy1CIgS0ceNGXhPQ/Pw8brrpJuzYsQPPPvusXQ1o7dq1fhOQyWRCa2srbrzxRrvXb7zxRpw/f97v671w4cKqY+7atYs+JlfnvdbB71YmAUGDSCRCQUEBHnroITz44IOYn5/HsWPHcPToUfzbv/0b8vLyMDs7iyeeeMKnCXw+YX5+Hr29vaiurkZWVpZfx5BIJMjOzkZ2dradukBHRwcA0BFSWloaJ4X3hYUFdHd3Y+PGjX7/DcGATCbDzTffjKamJvz2t79ltWaoUChgtVpXEXB2dvYqN1NfMD8/7/aYXJ33WgfvIyFfi4CnT59GfX09YmJiUFpaiueee87u52azGU8++STKysoQExODzZs348MPP1x1nJmZGfzd3/0d0tPTERcXh5qaGrS2trL6t/EVxPX04MGD+Pjjj/HEE09AJpNh06ZN+MlPfoLm5mY89dRT6Ovr4019xBNmZmbQ29uLTZs2sbZ4i8ViZGRkoLKyEtdffz02bdoEsViM3t5enD59Gl1dXVhYWIDVamXlfISA2PwbuIBCocCtt96K6upq/O53v+Osbd8xDUpRVMCpUW+OycV5r2XwmoR8LQKOjY3hpptuwvbt29He3o4f/OAHePDBB3H06FH6PY8//jief/55/PrXv0Zvby/uu+8+7Nu3D+3t7fR71Go1tm3bhsjISHzwwQfo7e3Ff/3XfyElJYXrP5l3+OlPf4pf//rXOHPmDC5fvoy5uTk88sgjkEql2LZtGxoaGvDkk0+iq6sLNpst1JfrFJOTkxgcHERtbS1njrQikQhpaWnYsGEDtm/fjrq6OsTExGB4eBinTp1CR0cH5ubmYDab/To+k4AyMzNZvnr2oFarsWfPHpSWluIPf/gDJ/qGGRkZkEgkq6IPmUwWUHoyJyfH7TG5Ou+1Dl43JvhaBPz+97+Pd999F319ffRr9913Hzo6OnDhwgUAQF5eHh577DHcf//99Hv27t2LhIQEvPrqqwCARx99FOfOnRNaLwGcO3cOGRkZdvbDBEtLS/jTn/6Et99+m/ZE2rNnD/bt24eamhpezIGMjY1hfHwcdXV1IXGkdSZ3k5aWRqftvFGXmJ+fR09PD+8JaGlpCbfeeiuysrJw7NgxTuestmzZgvr6ehw5coR+rbKyEnv27AmoMWFlZQXvv/8+/dru3buRkpJi15jg73kFOAdva0KkCPjoo4/ave6uCOiqsPjSSy/BbDYjMjISRqNxlc5VbGwszp49S///d999F7t27cKdd96J06dPIz8/HwcPHsS9997L0l8XPti2bZvLnyUnJ+Ob3/wmvvnNb0Kj0eD999/H22+/jZtuuglpaWm0jXljY2PQ54iYat4NDQ1ITEwM6vkJRCIREhISkJCQgNLSUtqob3Z2Fv39/UhOTkZ2djYyMzOd6u2ROtbmzZs5i+LYwMrKCv7mb/4GqampOHr0KOeDvo888ggOHDiAhoYGNDc344UXXsDk5CTuu+8+AMDhw4cxMzODV155hf4dqVQK4Ip/l1wuh1QqRVRUFCorKwEADz30EHbs2IGnn34ae/bswfHjx/Hxxx/brQ2ezivAd/CWhPwpAroqLBK5/9zcXOzatQs///nPsWPHDpSVleGTTz7B8ePH7fL2o6OjePbZZ2ltqy+++AIPPvggoqOj8fd///fs/7FXARISEnDXXXfhrrvugk6nw4kTJ3D06FHcfvvtiI+Px2233YY9e/agubmZc2kfiqIwODiIhYUFNDQ0ICEhgdPz+YK4uDgUFxejuLgYBoOB9kUaHBxcZdQ3NzeHvr4+bNq0idcEpNVqceeddyI6OhrvvPNOUMRr9+/fD6VSiSeffBJzc3Oorq7G+++/j6KiIgBXhlMd0/a1tbX0f7e2tuK1115DUVERxsfHAQAtLS1444038Pjjj+OJJ55AWVkZ3nzzTWzZssXr8wrwHbxNx83OziI/Px/nz59Hc3Mz/fpPfvIT/P73v0d/f/+q31m/fj3uvvtuHD58mH7t3LlzuO666zA3N4ecnBzI5XLce++9eO+99yASiVBWVoavfvWrePnll6HT6QAAUVFRaGhosIu4HnzwQVy6dIlO6wnwDgaDAZ988gmOHj2Kd999FxEREbQn0nXXXcd6zYCiKPT399N2EnywrfYGRH9tYWEBKpUKkZGRMJlMKC8vx5o1a3hb+Nbr9bjzzjthMpnwwQcfhCziFBC+CH3S3gX8KQK6KixGREQgPT0dAJCZmYl33nkHWq0WExMT6O/vR0JCAj01DwC5ubl0iE5QUVEhTEX7gZiYGNx88834n//5H8zNzeH3v/89JBIJ7rnnHpSVleHgwYM4ceIETCZTwOey2Wzo6emBSqVCY2Nj2BAQcGXjk5eXh9raWqxfvx4mkwkpKSkYGhrCuXPnMDg4iMXFRV51IxoMBnzjG9+ATqfDn//8Z4GABPgF3pJQVFQU6uvrcfLkSbvXT548iZaWFqe/09zcvOr9J06cQENDw6odd0xMDPLz82GxWHD06FHs2bOH/tm2bdswMDBg9/7BwUEh5A4QkZGR+Ou//ms8//zzmJ6exltvvYWEhATcf//9KC4uxr333os//elPMBgMPh/bZrOhq6sLKysraGho8Nnfhi+YnZ3F0NAQamtr0dDQgOuvvx7l5eUwm82QSqX47LPP0NfXB6VSGdJuRJPJhL//+7+HQqHABx98EJKmDwFXB3ibjgOutGgfOHAAzz33HF0EfPHFF9HT04OioqJVxcexsTFUV1fjO9/5/7V3/1FR1ekfwN+TMPw0V5EyKxBZlOGIMQNmayKeNhVhCzxuICrr711wVX5kgPnjmCKSGWGrwELkWpKywrgoFBkpkIqIDGABKQIDNCKW1hrZEjDP948O9+sIGODADPC8zplz5HM/9975zD3HZ+bez+d5/oY1a9agoKAAAQEBOHLkCBYuXAgAKCwshEqlgpOTE1QqFbZv347a2looFAphCnZRURFmzJiBN954Az4+Prh48SLWrFmDxMRELFmyRFcfx5DV3t6OgoICIX3Q7du34e7uDm9vb8yZM+c3ayK1t7fj8uXLaGlpgUwm07t6Rj3VMVnByckJY8aM6bT9/kJ9arVaKCrXH6W3u9Pa2oply5ahtrYWp0+fFu4yMNYXeh2EgF8Xq+7Zs0d4CPjOO+9g1qxZAIDly5dDqVQiNzdX6J+Xl4eQkBCUl5dj/PjxCA8P15i5kpeXh8DAQNTU1MDc3BweHh6Ijo7ulAUgMzMTmzZtQlVVFWxsbBAaGjosZ8cNNLVajaKiIiEgXb9+HXPnzhVqIt1/y6ejoF57ezukUmm/rEsZCCqVCleuXOk2AN3v/tLbv/zyS6dCff2hra0Nq1atQkVFBc6cOaPXi2bZ4KD3QYgNX2q1GmVlZUJNJKVSqVETqa2tDWvXrsXatWvh6uo6KMtJAMA333yDq1ev9jgA3Y+I0NzcLASku3fvCmuRLC0ttfbLsL29HQEBASguLkZubq5elI5ggx8HITYoEBHKy8uRlpaG48ePo7KyEmKxGOPGjUNmZiaefvppvZ1B9iAdAUgqlWL06NFaOea9i2N//PFHoVCfpaVln5+Vtbe3Y/369Th37hxyc3N7nPyVsd+itxMT9JUuctm1tbVhy5YtsLGxgYmJCSZOnIgdO3bobZqc/iASiTBlyhRs374d2dnZwlqbkSNHwtHRES+99BLee+89NDU16dUMsgfpjwAEAGZmZrCxscH06dPx/PPPw9LSEk1NTTh79qxQqK9jOUJPqNVqvPrqq8jLy0NOTg4HIKZVHIR6QVe57N58800kJCRg//79qKysxJ49e/DWW2/hH//4R7+PWd/cvn0bbm5ueO6551BaWgqFQoGvv/4a7u7uOHLkCOzs7DB//nzEx8dDpVLpbUBqaGhAVVUVZDKZVgPQ/UxMTGBlZQUXFxfMmjVLKNR3/vx5FBQUoLq6+oGF+tRqNSIiIpCdnY2cnByeIcq0jm/H9YKuctn96U9/wuOPP47k5GShz8KFC2FqaooPP/xQ6+PUZ0SEf//733jllVc65aYjIjQ0NEAul0Mul+P8+fOYNm2aUKTPyspKL27ZNTQ04Nq1a5BKpTpLituTQn1qtRpbt25FamoqcnNzMWnSJJ28Vza08S+hHupLQavuctldunRJyKbck1x2M2fOxOeff46rV68CAMrKynD27Fl4eHg89LgGG5FIBF9f3y6To4pEIlhZWSE4OBh5eXmor6/H0qVLcerUKUydOhVubm54++23ce3aNZ39Qqqvr9d5AAI6F+qzs7NDS0sLFAoFPDw8sHLlSqxYsQIpKSnIycnRWgDi29msE2I9olKpCACdO3dOo33Xrl00adKkLvexs7OjXbt2abSdO3eOAND169eJiMjPz48cHBzo6tWr1N7eTqdOnSITExMSi8XCPmq1miIiIkgkEpGBgQGJRCKKiorS8giHLrVaTTdv3qR//vOfNHfuXDI0NKSpU6fS1q1bqbi4mJqbm+mnn37q91dlZSVlZmaSSqUakPP15fXjjz/S4cOHSSKRkEgkotGjR9Pq1avp448/pv/9738PdR2OHj1KhoaGlJSURBUVFRQUFERmZmZUV1fXZf+amhoyNTWloKAgqqiooKSkJDI0NKS0tDShT1hYGI0fP56ysrKourqa4uLiyNjYmBQKhdAnMjKSLCwsKDMzk2pra+nYsWNkbm5OsbGxDzUeph38S6iXelvQqqv+97bv27cPdnZ2sLe3h1gsxrp167BixQqN6capqak4fPgwPvroIygUChw6dAh79+7FoUOHtDWsIU0kEsHS0hJ//etfkZ2djRs3biA4OBgKhQIzZszAtGnTsHPnTnz11Vf99u24rq4O1dXVkMlkel2XSiQSQalU4saNGygsLERGRgbMzc0REBCA6Ojohzp2TEwMVq1ahdWrV0MikSA2NhZPP/20xu3teyUkJMDKygqxsbGQSCRYvXo1Vq5cib179wp9PvzwQ7z++uvw8PDAxIkTERgYiHnz5uHtt98W+hQUFMDLywuenp6YMGEC/vznP2Pu3Lm4dOnSQ42HaQcHoR7SZS671157DREREVi0aBEcHR3h7++PkJAQrl/SBx3F51asWIHMzEw0NTXh9ddfx5UrVzB79mxIpVJs27YNCoVCawGprq4ONTU1Oqtp1FNEhAMHDmDv3r3Izs7GtGnT4OrqinfeeQdKpRLh4eF9Pjbfzmbd4SDUQ7rMZXf37t1Oz0BGjBjB97S1YNSoUVi6dCnkcjmampoQGRmJhoYGzJ8/H46Ojti0aRMKCwv7/FkrlcpBE4CSkpKwa9cuZGVl4dlnn9XYLhKJHiofX3+UZgEglGapqqqCWq3GZ599hoyMDDQ2Ngr7hIeHw8/PD/b29jA0NIRUKkVwcDD8/Pz6PB6mPRyEeiE0NBTvvfce3n//fVRWViIkJKRTIa176w0FBASgrq4OoaGhqKysxPvvv4/k5GRs3LhR6FNYWAi5XI6amhp88cUXcHd3h1qtRlhYmNDnpZdeEv5zUCqVOH78OGJiYrBgwYKBG/wwMHLkSPj6+iI1NRVNTU2IiYnBrVu3sGDBAkgkEmzcuBFnz57VqD31IEqlErW1tXB2dtb7AHTo0CFs27YNJ06c6PZLlTbw7WzWiQ6fRw1KBw4cIGtraxKLxSSTySgvL0/YtmzZMnJzc9Pon5ubS1KplMRiMU2YMIHi4+M7bZdIJGRkZEQWFhbk7+9PKpVKo8+dO3coKCiIrKysyNjYmCZOnEibN2+mlpaWfhsn+38///wznTx5kpYvX05jxoyhcePG0erVqykrK4t++OGHLh/wl5eXU1ZWFjU2Nup8ssGDXs3NzZSYmEjm5ub0+eef99tn2NLSQiNGjCC5XK7RvmHDBpo1a1aX+7i6utKGDRs02uRyORkYGNAvv/yi0f7zzz/TN998Q2q1msLCwsjBwUHY9tRTT9H+/fs1+u/cuZMmT578MENiWsLrhBjrhdbWVpw5cwZpaWnIyMiAWq2Gp6cnFixYADc3N4jFYkRHR+P3v/895s2bp9c1dogIx44dw7p165CWlgZ3d/d+Pd/06dPh7OyMuLg4oc3BwQFeXl7drrM7efIkKioqhLbAwECUlpZ2W1yytbUVEokEPj4+iIqKAgBYWFggMjISgYGBQr/du3fj4MGDwnMipkM6DoKMDVqtra10+vRpWrt2LY0fP55+97vfkYODA5mYmFB2drbOf+X81islJYVMTU3pxIkTA/J5dUzRTk5OpoqKCgoODiYzMzNSKpVERBQREUH+/v5C/44p2iEhIVRRUUHJycmdpmhfuHCB0tPTqbq6mvLz8+mFF14gGxsb+v7774U+y5YtoyeffFKYoi2Xy2ns2LEUFhY2IONmD8ZBaJA7cOAATZgwgYyMjEgmk1F+fn63fa9fv05+fn40adIkEolEFBQU1GW/tLQ0kkgkJBaLSSKRdLqF0tvzDgdtbW20atUqMjY2pscff5weffRR8vHxoZSUFPr22291HnDuf6WmppKpqSmlp6cP6OfEt7PZ/TgIDWK9XfxXW1tLGzZsoEOHDpGTk1OXQej8+fM0YsQIioqKosrKSoqKiiIDAwO6cOFCn887HGzfvp3Gjh1Lly9fpvb2diooKKCNGzeSra0tmZmZkbe3N/3rX/+iGzdu6DwAyeVyMjU1paNHj+r6Y2OMnwkNZr3NZXev2bNnw8nJCbGxsRrtvr6+uHPnDj755BOhzd3dHaNHj8aRI0ce+rxD1d69e+Hu7o4pU6ZotKvVapSWlgo1kerq6vDiiy/Cy8sLHh4eGDVq1IDmszt9+jQWLVqE+Ph4LF26VC9y6bHhjadoD1J9WfzXE90tEOw4Zn+dd7DbuHFjpwAEAI888ghkMhmioqJQWVmJixcvQiaT4d1334WNjQ0WLlyIDz74ALdu3er3fHb5+fnw8/PDvn37OAAxvcFBaJDqy+K/nuhugWDHMfvrvMOBSCSCo6Mj3njjDZSVlaGsrAyurq5ISkqCra0tXn75ZSQnJ+PmzZtaD0gFBQXw8fHBnj17sHLlSg5ATG9wEBrkerv4T1vH7I/zDicikQj29vbYvHkzLl26hMrKSsydOxcpKSlCTaSEhARcv379oQNSUVERFi5ciMjISAQEBPB1YnqFg9Ag1Zdcdj3RXb67jmP213mHM5FIBFtbW4SHh6OgoADXrl3DggULcPz4cdjb22POnDl49913UV9f3+uAVFJSAm9vb2zZsgXr16/nAMT0DgehQaovuex6ort8dx3H7K/zsl+JRCJYW1sjJCQE+fn5qKurw+LFi/Hpp5/C0dERbm5uiImJQXV19W8GpC+//BIvv/wyXnvtNbz66qscgJh+0tW0PPbwerv4j4iopKSESkpKyNnZmRYvXkwlJSVUXl4ubD937hyNGDGCoqOjqbKykqKjo7udot3deZn2qdVqunHjBiUkJNCcOXOEmkjbtm0jhULRqSZSUVERjR07lrZt20ZqtVrXb5+xbnEQGuR6u/gPQKeXtbW1Rp9jx47R5MmTydDQkOzt7btc0Pig87L+pVar6bvvvqPk5GTy9PQkIyMjcnBwoE2bNtHFixdJoVDQuHHjKCIiggMQ03u8ToixQe6HH37AyZMnIZfLkZ2djba2NqxatQpxcXFdlkFnTJ9wEGJsCLlz5w7eeustbN++XaOcAWP6ir8mMa2Ki4uDjY0NjI2N4ezsjC+++KLbvo2NjVi8eDEmT56MRx55BMHBwV32S09Ph4ODA4yMjODg4IDjx49rbN+9ezemTZuGkSNH4rHHHoO3tzeuXLmizWENGo8++ih27typtQDUm+sJAHl5eXB2doaxsTEmTpyIhIQEje2tra3YsWMHbG1tYWxsjGeeeQbZ2dmdjqNSqbB06VJYWFjA1NQUTk5OKC4u1sqYmJ7R7d1ANpToKpfdvHnz6ODBg/TVV19RaWkpeXp6kpWVFTU3N/fXUIeF3l7PjqzXQUFBVFFRQUlJSZ2yXoeFhdH48eMpKyuLqqurKS4ujoyNjUmhUAh9bt++TdbW1rR8+XIqLCyk2tpaysnJoWvXrvX7mNnA4yDEtObZZ5+lgIAAjTZ7e3uKiIj4zX3d3Ny6DEI+Pj7k7u6u0TZv3jxatGhRt8e6efMmAeDJEg+pt9czLCyM7O3tNdr+9re/0XPPPSf8/cQTT3QqMOfl5UVLliwR/g4PD6eZM2c+7NtngwTfjmNaoatcdl3573//CwAYM2ZMn8873PXlenZ3rS5duoTW1lYAQEtLC4yNjTX6mJiY4OzZs8LfJ06cgIuLC1555RU89thjkEqlSEpK0sawmB7iIMS0Qle57O5HRAgNDcXMmTO7TCjKeqYv17O7a9XW1obvvvsOwK9BKSYmBlVVVVCr1fjss8+QkZGBxsZGYZ+amhrEx8fDzs4On376KQICArBhwwZ88MEHWh4l0wcGun4DbGjRVS67DuvWrcPly5c1vlmzvuvt9eyq/73t+/btw5o1a2Bvby+kK1qxYgUOHjwo7KNWq+Hi4iKU55ZKpSgvL0d8fDz+8pe/aGVcTH/wLyGmFbrKZXev9evX48SJEzhz5gyeeuqpPp+T9e16dnetDAwMYGFhAQCwtLTEf/7zH/z000+oq6vD119/DXNzc9jY2Aj7PPHEE3BwcNA4jkQiQX19vTaGxvQMByGmFbrKZQf8+m173bp1kMvlOH36tMZ/aKxv+nI9u7tWLi4uMDQ01Gg3NjbGk08+iba2NqSnp8PLy0vY9vzzz3eaYn/16lVYW1s/zJCYvtLlrAg2tOgql11gYCCNGjWKcnNzqbGxUXjdvXt3YAY+RPX2enZM0Q4JCaGKigpKTk7uNEX7woULlJ6eTtXV1ZSfn08vvPAC2djY0Pfffy/0uXjxIhkYGNCuXbuoqqqKUlJSyNTUlA4fPjxgY2cDh4MQ0ypd5LLr6hgA6ODBg/00yuGjt9czNzeXpFIpicVimjBhAsXHx3faLpFIyMjIiCwsLMjf359UKlWn8548eZKmTJlCRkZGZG9vT4mJif0yPqZ7nLaHMcaYzvAzIcYYYzrDQYgxxpjOcBBiQ54ukqrea/fu3RCJRN0ei7HhjIMQG9JSU1MRHByMzZs3o6SkBK6urpg/f363a05aWlpgaWmJzZs345lnnumyT0FBAXx9feHv74+ysjL4+/vDx8cHhYWFnfoWFRUhMTERU6dO1eq4GBsqeGICG9KmT58OmUyG+Ph4oU0ikcDb2xu7d+9+4L6zZ8+Gk5MTYmNjNdp9fX1x584dfPLJJ0Kbu7s7Ro8ejSNHjghtzc3NkMlkiIuLQ2RkZJfHYmy4419CbMjSdVLVv//97/D09MSLL77Y53MxNtRx7jg2ZOkyqerRo0ehUChQVFTU5/MwNhxwEGJD3kAnVW1oaEBQUBBOnTrVqWwBY0wTByE2ZOkqqWpxcTFu3rwJZ2dnYXt7ezvy8/Oxf/9+tLS0aK38NmODHT8TYkOWrpKq/vGPf8SXX36J0tJS4eXi4oIlS5agtLSUAxBj9+BfQmxICw0Nhb+/P1xcXPCHP/wBiYmJqK+vR0BAAABg06ZNUKlUGgXTSktLAfw6u+3bb79FaWkpxGKxUF4gKCgIs2bNwptvvgkvLy9kZGQgJydHqGE0cuTITgX1zMzMYGFhwYX2GLsPByE2pPn6+uLWrVvYsWMHGhsbMWXKFHz88cdCWYDGxsZOa4akUqnw7+LiYnz00UewtraGUqkEAMyYMQNHjx7Fli1bsHXrVtja2iI1NRXTp08fsHExNlTwOiHGGGM6w8+EGGOM6QwHIcYYYzrDQYgxxpjOcBBijDGmMxyEGGOM6QwHIcYYYzrDQYgxxpjOcBBijDGmMxyEGGOM6QwHIcYYYzrDQYgxxpjO/B/eM5IJQcnpYwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "x1 = 0.1\n",
    "y1 = 0.1\n",
    "z1 = 0.1\n",
    "ax.scatter(x1, y1, z1, c='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}