{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import sympy as sy\n", "import fractions as fr\n", "import matplotlib.pyplot as plt\n", "import scipy as sp\n", "import scipy.special\n", "from texttable import Texttable\n", "import scipy.stats\n", "import scipy.special\n", "import numpy as np\n", "import pandas as pd\n", "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "plt.style.use(\"fivethirtyeight\")\n", "np.set_printoptions(precision=4)\n", "np.set_printoptions(suppress=True) # suppress scientific notation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To proceed with inferential statistics, there is no way to circumvent **probability theory** and it's undoubtedly the most important mathematical subject should you ever know in your life. Once probability view deeply implanted in your mind, you would have a revolutionary world view.\n", "\n", "Here we will review the probability theory in a textbook style, i.e. start from defining sets." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Basic Concepts Refresh" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A set is a collection of _distinct elements_, for instance, $(1, 2, 3)$ is a set, but $(2, 2, 3)$ isn't. Here we will demonstrate a bit of **SymPy** library, only scratching the surface. SymPy is an extremely powerful library, there are extensive examples in the **Linear Algebra With Python** training sessions.\n", "\n", "We'll start from defining sets then basic operations. ```sy.``` is alias of ```sympy```." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{2, 3, 4, 5, 6\\right\\}$" ], "text/plain": [ "{2, 3, 4, 5, 6}" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = sy.FiniteSet(2, 3, 4, 5, 6)\n", "s" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{0.5, \\frac{1}{2}, 2, 8\\right\\}$" ], "text/plain": [ "{0.5, 1/2, 2, 8}" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s1 = sy.FiniteSet(2, 1 / 2, fr.Fraction(1, 2), 8)\n", "s1 # Fraction subject can keep the fraction format" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check if $2$ is in the set $S_1$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2 is in the set!\n" ] } ], "source": [ "x = 2\n", "if x in s1:\n", " print(\"{} is in the set!\".format(x))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Convert a list into a set, the list needs unpacking with $*$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{1, 3, 5, 7, 8\\right\\}$" ], "text/plain": [ "{1, 3, 5, 7, 8}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s3_list = [1, 3, 5, 7, 8]\n", "s3 = sy.FiniteSet(*s3_list)\n", "s3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Subsets, Supersets and Power Sets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now define two sets, $a$ is a **superset** of $b$ ($a\\supseteq b$), then $b$ is called a **subset** of $a$ ($b\\subseteq a$). " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "a = sy.FiniteSet(1, 2, 3, 4, 5)\n", "b = sy.FiniteSet(2, 3, 4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example, $a$ is a **proper superset** of $b$ denoted as $a\\supset b$, $b$ is a **proper subset** of $a$ denoted as $b\\subset a$.\n", "\n", "The methods ```is_subset``` and ```is_superset``` are doing exactly as their names say." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.is_subset(a)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.is_superset(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **powerset** is set contains all subsets, including the empty set and itself." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{\\emptyset, \\left\\{2\\right\\}, \\left\\{3\\right\\}, \\left\\{4\\right\\}, \\left\\{2, 3\\right\\}, \\left\\{2, 4\\right\\}, \\left\\{3, 4\\right\\}, \\left\\{2, 3, 4\\right\\}\\right\\}$" ], "text/plain": [ "FiniteSet(EmptySet, {2}, {3}, {4}, {2, 3}, {2, 4}, {3, 4}, {2, 3, 4})" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.powerset()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Any sets are their own subset, but not their proper subset." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.is_subset(b)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "b.is_proper_subset(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Set Operations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Define two sets again." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{1, 2, 3\\right\\}$" ], "text/plain": [ "{1, 2, 3}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\left\\{2, 3, 4\\right\\}$" ], "text/plain": [ "{2, 3, 4}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a = sy.FiniteSet(1, 2, 3)\n", "b = sy.FiniteSet(2, 3, 4)\n", "display(a)\n", "display(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Union** and **intersection** are sympy object methods, the same as we've learned in high school." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{1, 2, 3, 4\\right\\}$" ], "text/plain": [ "{1, 2, 3, 4}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\left\\{2, 3\\right\\}$" ], "text/plain": [ "{2, 3}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(a.union(b))\n", "display(a.intersect(b))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Python Built-in Sets And Operations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sets operations are fairly common in general programming, therefore Python has built-in operations for sets. Here are examples using built-in function. \n", "\n", "We define sets in Python with ```{}```, which are the same for the dictionaries." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "a = {1, 3, 5, 7, 9}\n", "b = {1, 7, 10}" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "set" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "type(a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Union operation." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1, 3, 5, 7, 9, 10}" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a | b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1, 3, 5, 7, 9, 10}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.union(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Intersection." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1, 7}" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a & b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{1, 7}" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.intersection(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set difference." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{3, 5, 9}" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a - b" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{3, 5, 9}" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a.difference(b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cartesian Product" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The famous **Cartesian product** is defined mathematically as below.\n", "\n", "Two sets multiply each other, the result presents all the possible ordered paired, the first element from $A$, the second element from $B$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "A\\times B=\\{(a,b)\\mid a\\in A\\ {\\mbox{ and }}\\ b\\in B\\}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A visual example would be helpful. Define two sets, then compute the Cartesian product by multiplication." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{1, 2, 3, 4, 5\\right\\} \\times \\left\\{2, 3, 4, 5, 6\\right\\}$" ], "text/plain": [ "ProductSet({1, 2, 3, 4, 5}, {2, 3, 4, 5, 6})" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sy.FiniteSet(*list(range(1, 6)))\n", "y = sy.FiniteSet(*list(range(2, 7)))\n", "z = x * y # Cartesian producet\n", "z" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(7, 7))\n", "\n", "for i in z:\n", " ax.scatter(i[0], i[1], s=100)\n", "\n", "ax.grid(True)\n", "ax.set_title(\"Cartesian Product\", size=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a more concrete example of Cartesian product, suppose H&M has a type of dress with different parameters, a Cartesian product will show them all combinations they could have. For instance, a dress with parameters $( 'blue', 'polyester')$." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left\\{black, blue, red, white\\right\\} \\times \\left\\{cotton, polyester, wool\\right\\}$" ], "text/plain": [ "ProductSet({black, blue, red, white}, {cotton, polyester, wool})" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "colours = sy.FiniteSet(\"red\", \"black\", \"blue\", \"white\")\n", "material = sy.FiniteSet(\"wool\", \"cotton\", \"polyester\")\n", "colours * material" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Probability and Event" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After demonstrating so many sets theory, but how are they used in probability theory?\n", "\n", "Dice rolling problem never gets old. To answer the question: _what is the probability of rolling an odd number_? We will show how to answer the question with set operations." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = sy.FiniteSet(1, 2, 3, 4, 5, 6)\n", "odd = sy.FiniteSet(1, 3, 5)\n", "p = len(odd) / len(s)\n", "p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is vastly intuitive, just the proportion of odd sides over all sides." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two Dice Problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two dice problem is slightly more complicated. Now we are asking: _what's the probability of getting a $7$ while rolling them together_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create a dictionary to hold the Cartesian product of two dice and its sum. The ```.update``` function is for adding elements in the dictionary if the updated key didn't exist." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{(1, 1): 2,\n", " (1, 2): 3,\n", " (1, 3): 4,\n", " (1, 4): 5,\n", " (1, 5): 6,\n", " (1, 6): 7,\n", " (2, 1): 3,\n", " (2, 2): 4,\n", " (2, 3): 5,\n", " (2, 4): 6,\n", " (2, 5): 7,\n", " (2, 6): 8,\n", " (3, 1): 4,\n", " (3, 2): 5,\n", " (3, 3): 6,\n", " (3, 4): 7,\n", " (3, 5): 8,\n", " (3, 6): 9,\n", " (4, 1): 5,\n", " (4, 2): 6,\n", " (4, 3): 7,\n", " (4, 4): 8,\n", " (4, 5): 9,\n", " (4, 6): 10,\n", " (5, 1): 6,\n", " (5, 2): 7,\n", " (5, 3): 8,\n", " (5, 4): 9,\n", " (5, 5): 10,\n", " (5, 6): 11,\n", " (6, 1): 7,\n", " (6, 2): 8,\n", " (6, 3): 9,\n", " (6, 4): 10,\n", " (6, 5): 11,\n", " (6, 6): 12}" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dice_cartesian = {}\n", "for i in range(1, 7):\n", " for j in range(1, 7):\n", " dice_cartesian.update({(i, j): i + j})\n", "dice_cartesian" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Python dictionary has a method ```.items()``` that lists all key-value pairs in tuples. We'll make use of this method in the loop below." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "dict_items([((1, 1), 2), ((1, 2), 3), ((1, 3), 4), ((1, 4), 5), ((1, 5), 6), ((1, 6), 7), ((2, 1), 3), ((2, 2), 4), ((2, 3), 5), ((2, 4), 6), ((2, 5), 7), ((2, 6), 8), ((3, 1), 4), ((3, 2), 5), ((3, 3), 6), ((3, 4), 7), ((3, 5), 8), ((3, 6), 9), ((4, 1), 5), ((4, 2), 6), ((4, 3), 7), ((4, 4), 8), ((4, 5), 9), ((4, 6), 10), ((5, 1), 6), ((5, 2), 7), ((5, 3), 8), ((5, 4), 9), ((5, 5), 10), ((5, 6), 11), ((6, 1), 7), ((6, 2), 8), ((6, 3), 9), ((6, 4), 10), ((6, 5), 11), ((6, 6), 12)])" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dice_cartesian.items()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use ```defaultdict``` from ```collections``` module, it creates a dictionary which doesn't report errors and suitable for counting. We pass ```list``` as the _default factory_, meaning initialising values as lists whenever the key is given. " ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "defaultdict(list,\n", " {2: [(1, 1)],\n", " 3: [(1, 2), (2, 1)],\n", " 4: [(1, 3), (2, 2), (3, 1)],\n", " 5: [(1, 4), (2, 3), (3, 2), (4, 1)],\n", " 6: [(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)],\n", " 7: [(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)],\n", " 8: [(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)],\n", " 9: [(3, 6), (4, 5), (5, 4), (6, 3)],\n", " 10: [(4, 6), (5, 5), (6, 4)],\n", " 11: [(5, 6), (6, 5)],\n", " 12: [(6, 6)]})" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from collections import defaultdict\n", "\n", "dice_count = defaultdict(list)\n", "for i, j in dice_cartesian.items():\n", " dice_count[j].append(i)\n", "dice_count" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create another dictionary holding all sums of dice and corresponding probabilities." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{2: 0.0278,\n", " 3: 0.0556,\n", " 4: 0.0833,\n", " 5: 0.1111,\n", " 6: 0.1389,\n", " 7: 0.1667,\n", " 8: 0.1389,\n", " 9: 0.1111,\n", " 10: 0.0833,\n", " 11: 0.0556,\n", " 12: 0.0278}" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Prob = {i: round(len(j) / 6**2, 4) for i, j in dice_count.items()}\n", "Prob" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The example above actually is more about Python techniques, it also can be conveniently solved without making a fuss, as below:" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "def dice_prob(number):\n", " dice1, dice2 = list(range(1, 7)), list(range(1, 7))\n", " cartesian_dice = [\n", " (i, j) for i in dice1 for j in dice2\n", " ] # list comprehension to create Cartesian product\n", " ocurrence = 0\n", " for element in cartesian_dice:\n", " if np.sum(list(element)) == number:\n", " ocurrence += 1\n", " print(\n", " \"The probability of {} while rolling two dice is {:.2f}%\".format(\n", " number, ocurrence / 6**2 * 100\n", " )\n", " )" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of 7 while rolling two dice is 16.67%\n" ] } ], "source": [ "dice_prob(7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Combination And Permutation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, high school skills, two question to help differentiate them. \n", "
    \n", "
  1. Pick 3 letters from English alphabet, how many ways to choose? Use combination.
  2. \n", "
  3. Pick 3 letters from English alphabet to construct a word (doesn't have to be meaningful), how many ways to choose? Use permutation.<\\li>\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Just remember: whenever needs certain order, use permutation, like the second question above, 'dog' and 'god' are different words though letters are the same. We don't need to memorise formula, but still FYI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "_nC_N = \\frac{N!}{n!(N-n)!}\\\\\n", "_nP_N = \\frac{N!}{(N-n)!}\n", "$$" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2600.0" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scipy.special.comb(26, 3) # combination" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "15600.0" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "scipy.special.perm(26, 3) # permutation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Conditional Probability, Multiplication Law and Independence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All above are just warm-up, from here on comes the real deal of probability theory." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The probability of A given B, so called **conditional probability**, defined as:\n", "\n", "\\begin{equation}\n", "\\frac{P(A\\cap B)}{P(B)}=P(A|B)\n", "\\end{equation}\n", "\n", "It is best to be demonstrated by a joint probability table, which is essentially a discrete numeric form of 3D distribution. \n", "\n", "Here I want to introduce a module of draw text-style table, particular useful when you working on shells. Install in jupyter with ```conda install -c conda-forge texttable```." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+------------------+------------+---------+\n", "| | Have Ht. Disease | Not Have | Total |\n", "+=======+==================+============+=========+\n", "| Male | 0.450 | 0.060 | 0.510 |\n", "+-------+------------------+------------+---------+\n", "| Femal | 0.360 | 0.130 | 0.490 |\n", "+-------+------------------+------------+---------+\n", "| Total | 0.810 | 0.190 | 1 |\n", "+-------+------------------+------------+---------+\n" ] } ], "source": [ "table = Texttable()\n", "table.set_cols_align([\"l\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [\n", " [\"\", \"Have Ht. Disease\", \" Not Have \", \" Total \"],\n", " [\"Male\", 0.45, 0.06, 0.51],\n", " [\"Femal\", 0.36, 0.13, 0.49],\n", " [\"Total\", 0.81, 0.19, 1],\n", " ]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Marginal probability** is the key concepts, which got its name because located on the margin of a table, it is the sum of all probabilities from the same column or row.\n", "\n", "The marginal probability of having heart disease is $81\\%$ and marginal probability of not having is $19\\%$. \n", "\n", "Here is the question: _what is the probability of not having heart disease given the person is a woman_? Because the condition is that _the person must be a woman_. So the first step is to narrow down the table." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+------------------+------------+---------+\n", "| | Have Ht. Disease | Not Have | Total |\n", "+=======+==================+============+=========+\n", "| Femal | 0.360 | 0.130 | 0.490 |\n", "+-------+------------------+------------+---------+\n" ] } ], "source": [ "table = Texttable()\n", "table.set_cols_align([\"l\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [[\"\", \"Have Ht. Disease\", \" Not Have \", \" Total \"], [\"Femal\", 0.36, 0.13, 0.49]]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So the conditional probability of a woman not having heart disease is\n", "$$\n", "\\frac{P(A\\cap B)}{P(B)} = \\frac{.13}{.49}\n", "$$" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of not having heart disease given the person is a woman is 26.53%\n" ] } ], "source": [ "P_female = 0.49 # the marginal prob of being a women, this is P(B)\n", "P_female_no_disease = 0.13\n", "P_con = P_female_no_disease / P_female\n", "print(\n", " \"The probability of not having heart disease given the person is a woman is {0:.2f}%\".format(\n", " P_con * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From conditional probability it is straightforward to deduct **multiplication law**, simply rearrange the formula\n", "$$\n", "P(A|B)P(B)=P(A\\cap B)\\\\\n", "P(B|A)P(A)=P(B\\cap A)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Two events $A$ and $B$ are independent if \n", "$$\n", "P(A|B)=P(A)\\\\\n", "P(B|A)=P(B)\n", "$$\n", "\n", "Otherwise, the events are dependent.\n", "\n", "Then the **independent multiplication law** indicates\n", "$$\n", "P(A)P(B)=P(A\\cap B)\\\\\n", "P(B)P(A)=P(B\\cap A)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will not dive deep into probability problems for now, there will be a full-round training session on
**Probability Theory**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Distributions That You Should Know" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These are most important probability distributions that you should know by heart. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Binomial Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first one is binomial distribution, we will give a it more extensive coverage, other distributions have similar functions in Python.\n", "\n", "A binomial experiment has 4 features:\n", "* A sequence of $n$ identical trials, e.g. throwing darts\n", "* Only two outcomes are possible: _success_ or _failure_, e.g. hitting bullseye or not\n", "* The probability of success $p$ does not change from trial to trial\n", "* Trials are independent events, e.g. first throw doesn't affect the second throw" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **probability mass function(PMF)** of binomial distribution is \n", "\n", "

\n", "$$\n", "f(k,n,p)=_nC_k p^kq^{n-k}\n", "$$\n", "

\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
parametersmeaning
$n$number of trials
$k$number of specific outcome
$p$probability of success
$q$probability of failure
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a simple example.\n", "\n", "A personal banker might meet 50 people enquiring for loan monthly, empirically 30% of them has bad credit history. So calculate probability from 1 to 50 people has bad credit history, meaning calculate 1 person out of 50 has bad credit, 2 persons out of 50 have bad credit, so on so forth till 50 persons (all of them)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Start from a single number could be more intuitive, what's probability that a personal banker to encounter exact $14$ persons of bad credit history in a month?" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The prob of meeting 14 persons who has bad credit history is 11.89%.\n" ] } ], "source": [ "n = 50\n", "k = 14 # what is the prob that exact 14 ppl she met had bad credit history?\n", "b = scipy.special.comb(50, 14)\n", "p = 0.3\n", "f_binomial = b * p**k * (1 - p) ** (n - k)\n", "print(\n", " \"The prob of meeting {0} persons who has bad credit history is {1:.2f}%.\".format(\n", " k, f_binomial * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use ```scipy.stats.binom.pmf``` to get an array of PMF." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "

" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 50\n", "p = 0.3\n", "bad_credit_person = np.arange(1, 51)\n", "prob = sp.stats.binom.pmf(bad_credit_person, n, p)\n", "fig, ax = plt.subplots(figsize=(12, 4))\n", "ax.plot(bad_credit_person, prob, lw=3, color=\"r\", alpha=0.5)\n", "ax.set_ylim([0, 0.13])\n", "ax.set_title(\n", " \"The probability that from 1 to 50 persons who have bad credit history\",\n", " size=16,\n", " x=0.5,\n", " y=1.02,\n", ")\n", "ax.set_xlabel(\"Number of Person Who Has Bad Credit History\", size=12)\n", "ax.set_ylabel(\"Probability\", size=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We could interpret the plot with straightforward observation:\n", "
  • Most likely the personal banker would encounter $10$ to $20$ persons who have bad credit history.
  • \n", "
  • Encountering less than $5$ or more than $25$ person are less likely.
  • \n", "
  • The highest possibility is to encounter $50\\times .03 = 15$ persons with bad credit.
  • " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next example we can formulate a question by using **cumulative probability distribution**, the SciPy function is ```scipy.stats.binom.cdf```. \n", "\n", "If a stock trader trades $n$ times a month, he has a $p%$ chance of winning the trade, find out the probability that he can win less than $k$ trades a month." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "If a trader's winning rate is 55%, the probability of winning less than 12 times is 74.8% if he trades 20 per month.\n", "If a trader's winning rate is 55%, the probability of winning more than 12 times is 25.2% if he trades 20 per month.\n", "If a trader's winning rate is 55%, the probability of winning between 14 and 4 times is 94.3% if he trades 20 per month.\n" ] } ], "source": [ "n = 20\n", "p = 0.55\n", "k = 12\n", "k1, k2 = 14, 4\n", "\n", "win_less = sp.stats.binom.cdf(k, n, p)\n", "win_more = 1 - sp.stats.binom.cdf(k, n, p)\n", "win_betw = sp.stats.binom.cdf(14, n, p) - sp.stats.binom.cdf(4, n, p)\n", "\n", "print(\n", " \"If a trader's winning rate is {:.0f}%, the probability of winning less than {} times is {:.1f}% if he trades {} per month.\".format(\n", " p * 100, k, win_less * 100, n\n", " )\n", ")\n", "print(\n", " \"If a trader's winning rate is {:.0f}%, the probability of winning more than {} times is {:.1f}% if he trades {} per month.\".format(\n", " p * 100, k, win_more * 100, n\n", " )\n", ")\n", "print(\n", " \"If a trader's winning rate is {:.0f}%, the probability of winning between {} and {} times is {:.1f}% if he trades {} per month.\".format(\n", " p * 100, k1, k2, win_betw * 100, n\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or present in the text table." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+----------+------------+----------------+\n", "| Win Less | Win More | Win btw 4~14 |\n", "+==========+============+================+\n", "| 0.748 | 0.252 | 0.943 |\n", "+----------+------------+----------------+\n" ] } ], "source": [ "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [[\"Win Less\", \" Win More \", \" Win btw 4~14 \"], [win_less, win_more, win_betw]]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What if the probability of wining changing from 0.1 to 0.8, what is the probability that he wins less than 6 trades, assuming every month he trades 20 times." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
    \n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
    win_ratewin_less
    00.100.997614
    10.150.978065
    20.200.913307
    30.250.785782
    40.300.608010
    50.350.416625
    60.400.250011
    70.450.129934
    80.500.057659
    90.550.021414
    100.600.006466
    110.650.001521
    120.700.000261
    130.750.000030
    140.800.000002
    \n", "
    " ], "text/plain": [ " win_rate win_less\n", "0 0.10 0.997614\n", "1 0.15 0.978065\n", "2 0.20 0.913307\n", "3 0.25 0.785782\n", "4 0.30 0.608010\n", "5 0.35 0.416625\n", "6 0.40 0.250011\n", "7 0.45 0.129934\n", "8 0.50 0.057659\n", "9 0.55 0.021414\n", "10 0.60 0.006466\n", "11 0.65 0.001521\n", "12 0.70 0.000261\n", "13 0.75 0.000030\n", "14 0.80 0.000002" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "win_rate = np.arange(0.1, 0.81, 0.05)\n", "win_less = sp.stats.binom.cdf(6, 20, win_rate)\n", "\n", "data_dict = {\n", " \"win_rate\": win_rate,\n", " \"win_less\": win_less,\n", "} # I am using annotation in matplotlib, so Pandas is used for easy tracking data points\n", "df = pd.DataFrame(data_dict)\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "According to the table above, if the trader has at least $60\\%$ winning rate, merely $0.6\\%$ probability that he wins less then $6$ trades. Marginally higher winning rates are even important for traders in the short run." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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dzcKFC1m7di2HDh3i8uXL+Pn5ERISQoMGDejcuTP16tXL1oUTExMpU6YMH330EZ07d3aVjx49mn379rFixYp0x0RERNC0aVNef/11evXqRWxsLGPGjOHAgQP8/PPPmV4rPDw8W7GJiIiISP6pXr16ltvdWsjAarXSp08f+vTpkytBAURGRmKz2ShZsmSa8pIlS3LmzJkMjwkNDeWbb77hqaeeYvTo0djtdurVq8eiRYuyvNa1KiG3hIeH59m1bmSqx5xTHeac6jB3qB5zTnWYO1SPOVeQ6jDfl5I1DCPNa4fDka4s1enTpxk2bBiPPfYYP//8M9999x0BAQE89dRT2O32vAhXbmIR0Un0XxvFA9+fpf/aKCKik/I7JBERkZvSdS0lmxuCg4Mxm83pWlvPnTuXrlU21axZs/D39+eVV15xlX344YfUrl2bLVu20KJFC4/GLDeviOgkOq+M5Ei0zVW2/WwiS9oHE2q15GNkIiIiN598a4H19vamQYMGrFmzJk35mjVraNasWYbHxMXFuQZvpUp9rRZY8aSJO6PTJK8AR6JtTNwZnU8RiYiI3LzytQvB0KFDmTdvHp9//jkHDhzg2Wef5dSpU/Tu3RuACRMm0KlTJ9f+7dq147fffuP111/n0KFD7N69m6FDh1K+fHkaNGiQT3chN4OTsbYMy09lUi4iIiKek29dCAAeeughoqKieOONNzh9+jRhYWEsWLCAihUrAnDq1CmOHDni2r9t27bMnj2bd999l6lTp+Lr60vjxo1ZtGgRRYoUya/bkJtAGX9zhuUhmZSLiIiI5+RrAgvQr18/+vXrl+G2GTNmpCt7+OGHefjhhz0dlkgaLzS0sv1sYppuBJWtZl5oaM3HqERERG5O2U5go6OjOXHiBOfPn8fhSD+FbKtWrXIlMJGCJNRqYUn7YCbujOZUrI0Qf2fyqgFcIiIiec/tBPbChQuMGTOGb775Bpstfb+/1OmvoqKicjVAkYIi1GphVtvi+R2GiIjITc/tBPY///kP3333Hf3796dVq1YEBQV5MCwRERERkYy5ncCuWrWKgQMHMmnSJE/GIyIiIiKSJben0fL29qZq1aqejEVERERE5JrcTmAffPBBfvrpJ0/GIiIiIiJyTW4nsMOGDePUqVMMGjSIbdu2cerUKc6ePZvuS0RERETEk9zuA9uoUSMMw2D37t0sWLAg0/00C4GIiIiIeJLbCeyYMWMwDMOTsYiIiIiIXJPbCey4ceM8GYeIiIiIiFvc7gMrIiIiIlIQZHsp2a1bt7J7924uXryI3W5Ps80wDMaMGZNrwYmIiIiIXM3tBPbixYs89thjbNmyxbVsrMPhAHD9XwmsiIiIiHia210Ixo8fz65du/jggw/YtWsXDoeDxYsXs2PHDnr16kW9evX466+/PBmriIiIiIj7CewPP/xAr1696NatG4GBgc6DTSaqVKnCO++8Q5kyZXjuuec8FqiIiIiICGQjgY2KiqJOnToAWCwWAC5fvuzafs8997Bq1apcDk9EREREJC23E9hSpUpx5swZAKxWK1arlfDwcNf28+fPY7PZcj9CEREREZEruD2Iq3HjxmzYsIHRo0cDcPfddzN16lRCQkKw2+1Mnz6dpk2beixQERERERHIRgvsgAEDqF69OvHx8QC8+uqrFC9enEGDBjFkyBCKFy/O66+/7rFARUREREQgGy2wLVq0oEWLFq7X5cqVY8uWLfz++++YzWZuueUWvLyyPa2siIiIiEi25CjjNAyDunXr5lYsIiIiIiLXlO0E9sCBAxw9epTz58+7FjK4Uvfu3XMlMBERERGRjLidwEZERDBw4EC2bt2aYeIKzhZZJbAiIiIi4kluJ7AjR45kz549TJo0iVatWhEUFOTBsEREREREMuZ2Artp0yaGDx/O4MGDPRmPiIiIiEiW3J5Gq2jRogQHB3syFhERERGRa3I7ge3RowdLlizxYCgiIiIiIteWaReCHTt2pHndrl071qxZQ8eOHenduzfly5fHbDanO65Ro0a5H6WIiIiISIpME9i7774bwzDSlKXOPrBhw4Z0+zscDgzDICoqKpdDFBERERH5V6YJ7LRp0/IyDhERERERt2SawPbo0SMv4xARERERcYvbg7g6duzI2rVrM92+bt06OnbsmCtBiYiIiIhkxu0E9tdff+XMmTOZbj937lyGfWNFRERERHKT2wnstfz9998UKVIkt04nIiIiIpKhLFfiWr58OStWrHC9/vTTT/nll1/S7XfhwgXWrl2rKbRERERExOOyTGD//PNPvv76awAMw2Dbtm3p5oc1DAN/f3+aN2/O66+/7rlIRURERES4RgI7evRoRo8eDUCxYsWYNm0aXbt2zZPAREREREQykmUCe6Xz5897Mg4REREREbfk2iAuEREREZG8oARWRERERAoVJbAiIiIiUqgogRURERGRQkUJrIiIiIgUKjlOYLdu3cqPP/7I5cuXcyMeEREREZEsuZ3A/u9//6NLly5pyh599FHuvfdeHnvsMZo2bcqxY8dyPUARERERkSu5ncAuWbKEWrVquV6vWLGCH3/8kREjRjB79mwSExP53//+55EgReTmZV6/nqJBQRQNCsK8fn2O98trfoMHUzQoCGvduvkdyg0t9XvvM3lygbi2cfQo/g89RGDFihQNCiKgdetsnzf1vVO3U6fcDDdHLHPnuu7XiIjwyDX0mfmX6iJzbiewJ06coHr16q7X3377LVWrVuXll1/moYceol+/fqxdu9YjQYrIjcdat67rF2FmX9lJRhxWK8mNG5PcuDEOq9WDkWePvXJlkhs3xlavXraP1S+vtPIieYLs/zGU+r6zlyvnKvN77jksP/8MsbEk33orttq1Mz0+P5Pv7HKUKOG6X3x8PHKNnHxm8pMn3p+eqAvvWbNccVqrVEm33fL11wTcdhuBISFYK1XCv1cvTIcP/7vD5cv4DRmCtUoVrJUr4zdkCMTGujYbEREEli2L9wcf5FrMGXF7JS4Am83m+v/atWvp2LGj63XZsmU5e/Zs7kUmIjc0W7162EuXBsD0zz+Y/vnHWV63Lo6UX4xXJgTXYm/QgMurVuV+oDmUMGYMCWPG5HcY4kEZve9M+/cDkNyhA7GffZbXIXlMcvv2JLdv79FrFKjPTGIieHvn2+Vzuy5M+/fj+9JLmW63fP45/sOHA2APDcU4fx7LsmWYN20i5tdfAfB5+228583j8tdfg91Oka5dsZctS8ILLwDgN2oUtrAwEgcMyLW4M7wXd3esVq0ay5cvB2DVqlWcOnWKu+++27X977//JigoKNcDFJEbU+zcuVxetYrLq1aR+MQTrvLLX3zhKk/q1SvNMaaTJ/Hv2ZPAsmWx1quH5fPPXdsyajUzzpzBb8AArDVrEliqFNZq1Shy331Y5s/PNK7U8zRu0gTL3Ln4P/KIsyWidm28P/44zb7G8eP4DRyI9ZZbCCxRAmtYGH4jRmBc8cd8Rq2oqa3PfgMH4vPaa1hr1CAwNBS/AQMgOtq1j/eXXzrv+/jxa7YIXtn647VsGUVuv53AkBD8O3fGOHUKy8KFWOvXJ7BiRfz693ddBwCHA+9Zswho1YrAkBACK1bE/7HHXEkYgHHsGP6PPIK1dm3nPiEhBLRogff06eBwZHpv9e69N929AXitWkWR9u0JDA111m+9evj37Ilx9GiG9+c3eDD+Q4e6XgfWr59xq2VSEr7PPedsHapWDd9nn4XkZNdm3xdfJKB5cwIrVnR+z2rWxG/QIIxTpwDwmTyZgCsaZwI6dnTez+DBGcYFaVtQjYgI5/cppcXKsnRppsenvtdcsU2ZkmmLu9eKFQQ0a0Zg2bIUue8+TOHhabf//DNFOnYksEIFAkNCKHLXXXh9/32mMQMU6dDBGdvTTzsLoqMJDA52xr9xI/Bva11gxYpgt2fYynjle9xryRICmjTJMM7r2S+VO58ZAC5exK9/fwLLlcN6yy34TJmC36BBbnXFSL0v3xdfxG/wYOfnoHdvZ0wDBhDQsCGB5csTWLIk1jp18B0zBi5dcsWc5fszMRGf//2PgMaNnT+LKlfGr18/jL//zjKmjOoiu58dl8RE/Pv3x+HrS3Lbthlu950wAYCkTp2I/u03ordswWG1Yjp7Fp+33gLAvGcPAMlt2pB8223Osr17AbAsXIjX2rXEvfcemDw70ZXbZx82bBi//PILoaGhdO/enVtuuYU77rjDtX3t2rXU1WMuEfEgvxEjnD8ovbwwHTuG33/+g+mvvzLff9QovBcswIiOxh4WBn5+mLdswSulJeGa1/vvfzEdPIjD3x/T33/j99//4vXjjwAYZ88S0K4d3vPnY1y8iL1aNYxz5/D+7DOK3HsvxMRc8/yWxYvxmTEDfH0xLl7Ee8ECfN55B0hpoQ4OBsDh7Z2t7hH+AwdixMZCQgKWX36hyIMP4vf00zgsFoxLl/BeuNB1HQDfMWPwe+YZzH/8gT00FIevL5YffiCgXTvXL0VTZCSWlJZG+y234LBaMf/5J37PPYf37NmZ3pvDxyfdvRmRkfj36IFXyi9He7VqEB2NZflyTCdPZnhP9sqVsVWq5Hptq1s33WN7AJ8ZM7B8+SX4+mI6dw6fmTOxzJ3r2u61ahWmf/7BXr489ipVME6fxvurr/Dv0cN5nXLlsNWo8e91atRwXqdy5WvWuzMAH+f3KaXVzh4cnOnxqd1eXPdYtmyGj4st5845EymHA+Li8Nq06d+kE/BauhT/hx/Ga/16HIGB2MuWxWvHDmcdL12aaajJKf1yzVu2OM+zdStGypNWr02bnNs2b3bu27LlNRMS4+RJ/Pv3B8PIMM7s7peRrD4z4PwZ4b1wIcblyzisVnymTcPy7bdunTuV98yZWJYuxV6+vOtpkGX5cowLF7BXqoS9XDlMJ07g8+GH+A8bBlz7/en/xBP4vvYapsOHne93hwPvRYsIaN8eLlxwO7br+eyk8p0wAfPevcS9+y72smXTbTfv3IkpMhJwJrAAjjJlXO9Rr59/dt5byvvTa/16vNatc92vcf48vuPGkTB8OPYsuszkFrcT2C5durB48WJ69uzJf//7X5YtW4aXl7MHwvnz5wkODqbXVa0lIiK5Kfmee4j+7TdiVqwAwLDbs0xGTYcOARD31lvErF1L9N69RIeHk+Dmo62kBx8kZvduonftwl6+PIDrl6X3rFmYTp7EYRhc/v57YjZvJjalxdR86BDeVyRNmfL1JXrLFqJ37SL51lsB8EoZSxA7dy7J7doB4Chd2tUqbW/Q4JqnTRg1ipitW0nq2tUZz4EDxE2dSsz27SS3aJHmOkZEhCsBjX3nHWK2bCF6715sYWEYly7h+3//B4CtcmUu/fYb0X/8Qcy6dUQfOOBManAmFZnd295vvkl3b8bx4xiJiTisVqK3biXm11+JPnKE6F9/xX7FWIs09zRmDAnPPON6ndpSf3UrvaNUKaJ37yZ6507sZcqkuS5A7KxZXDp6lJiNG4nZupW4d9917rNzJ6YjR0jq1Yu4N9907R/35ptcXrXK7ce4jpAQLq9ahSOle0xyu3aZHn91t5fEJ57g8qpVxF713jElJRH76afEbN1KYkpLrteWLRAXB4DfSy9hOBwkdu1K9O+/E7NzJ4m9emE4HK4WtYwkt2kDgDk8HOPcOcwpSasjMNCVuKYmssluDEIzkpOJ/fzzTOPM7n4ZyuIzYzpyBO8lSwBI6N+fmB07iN62Dbyy1VvS+b7cto2YjRuJmzULgJjvvyf68GFifv2VmN27iR892nnt5cshPj7L96d5wwYsK1cCELtoETEbNxK9ezf24GBnIpzBH4CZuZ7PDoD5l1/wnj6dxF69SM6kJdp0RWuwvWTJf+sj5f+mEycASBg5ksQePfDr1w+/AQNI7NGDhP/+F9/nn8dRtChJXbs6BzCGhhLQqhVea9a4fX/Zka3v6u23387tt9+errxYsWJ88cUXuRWTiFyniOgkJu6M5vA5H6r8E8ULDa2EWi35HVauSezWDQwDe82arjLjzJlM90+6917M+/bhN2QIPq+/jr16dWzNmpH41FNuXS8pderAokVJuvtufD79FNOffwJg3rULAHuVKtgaNgQg+e67sQcFYbpwwbU9K8lt2uBIaQmxV68Ou3ZhyuJ+3JV0773Oc1asmL4sNBQ2bXJdx7xrF0ZKFwD///wH/vOfNOcyb9/u/I/Fgs9772FZuRLj1CmMKx7LGxm0/LjuLTw83b3Za9bEVqkS5qNHCaxe3VmHYWEkt29PUg5bbpLuuw+KFnXdq+nkyTR1av79d/yHDsV08CDGVfOXGydPgrstrXkoOSCA5PvuA8B25Xv/7Fnw98eU8ijfe+FCvBcuTHOs+fBhjKgoHMWLpzuvrUkTHL6+GPHxzicTmzdjq1wZe926eP3yC6YjR1x901OT3aw4AgMzjdNxxXvR3f0yrIssPjOpn02ApEcecV6rdGmS27TB8t1314zfdWynTjhSW/bNZsCZJHsPHIjpyBGM+Ph/Y05Oxjh3DkfKH7gZMe/Y4fp/kYceSr992za3Y7uuz87ly/gPHoy9alXishooeEVXoCwVKULc9Olpisxr12L58ksuL12K37BhmA8cIPazz/CZOBH/Xr2I3r0bR8oTpdzidgIbFxfH5cuXKVGihKvs3LlzfP7551y4cIHOnTvTMOWHeHbMnj2b9957j9OnT1OzZk0mT55My5S/6jPicDiYMWMGn3zyCRERERQrVozu3bszfvz4bF9b5EYSEZ1E55WRHIm2AWZ2XIpj+9lElrQPvmGSWEdKYpKmRSWLH7oJL76IrVkzvFavxvznn3ht3ozlp5+wfPMNMRs2ZOvaRmbXMYxsnedKrvsB1y9Kt3+JZHXe1G4GqecECAx0/psab8p1rrwvW506OHx9054rJAQAv3Hj8E7pc2yrWhVHsWLOBCcy0vXYOc1xWd2bry8xv/yC9/z5mHfswLx/P5aFC/FesIC4U6dIvKIvYXZldV3zpk34DR6M4XBgL14cW40aGJcvYz5wIKUC0t9HQWC7stvIld9ThyPN+8UeGpqm5cwlKSnjE/v4YGvSxPkoeP16zDt3kvTgg9jq1sWybBneH33kvEzRotjd6CKYYd2nxnkd+7l9jYyOy8nnslSpNK8tCxbg9+KLANhDQrCVK4cRGYk5tc/ptd43V8SX3KhRutjsFSq4H9x1fHaMc+ecT4ssFgJvucVZmJAAgCkqisBy5Yj96CPXUyYA09mzpN5Vap/+TAfVxsfjN3IkST17Yrv1Vry2bSPpgQdIvuMOTAcO4DV2LOatW11/tOQWtxPYkSNH8ueff7qmyrp8+TJ33XWXa/GCGTNm8O2339K8eXO3L7548WLGjh3LW2+9RfPmzZk9ezZdu3Zl8+bNVMjkG/r888+zcuVKXnnlFWrXrs3Fixc5ffq029cUuVFN3Bmdkrz+60i0jYk7o5nVNn3ry83AvHkzya1auUZNW776Cv9BgzD/8UemrVJXsixd6vyhGx3t6v9lDwsDwHbrrVh++gnToUOYd+7E1rChs39lSn82W8rjzZxw+Ps7/xMX5/wlmINfyplJvvVWHIbhfAT9yCMkXtECa9q9GyPlF11qS2zSnXcSu3gxxMcTcPfdkNJnLlsuXcIcHu4cpZxyT0U6dcJr3Tq81q3LPIFNrQ/AiI0lu6m+eft2V8Ies3EjjpAQfN5+G/PVj9mvuo6nOfz8MOLirutajpIlsVesiOnYMWxhYcTOmQMW5x+sxvHjmPfscXVnyEhy69Z4rV+P97x5GLGxJLdo4erj6P3pp859WrXy+ICc3GCrVcv1XrYsXYqtaVOM06fxyuG80KktpA6rlejffgMfH3z/+1/MVw3qzOz9abuicS9x6FCSUlthHQ7MGzemTcqv5Xo/O4CRlJThHzPG5cuQnIytYUPsxYtjiorCsmwZSY88gnHyJF4pn/3ku+7K8Lw+//sfRnQ0cRMnupL11D7gqe9FV6wdOuC1YQPJrVpxOWVigOvl9jty8+bN3HdF9rxo0SKOHTvGokWLOHDgADVq1ODNK/oNuWPatGn06NGDJ598kho1avDGG29QunRpPr76TZEiPDycDz/8kHnz5tGhQwcqVapE/fr1aZfST0zkZnYyNuNWgFOZlN8MfCdMILBKFQJuvZWAtm3xGzkScLYkOIoVu+bxlm+/JaBBA6z162M6fhyAhBEjAEjs3x97SAiGw0GR++4joEUL/Lt3B8BWpQqJPXvmOP7UPm2mc+cIaNKEInff7V4/wWxwVKpEYp8+APiNH4+1Th0CWrXCWqkS1ttv/3fgRsrjScvPPxPQuDHW2rWvOYI6M6Zz5wi45x6slSsT0LIlAU2a/DsYpE6dTI+zXdHHr0jnzhS5+25XX0132K84d0DLlgQ0bYr3e++l369yZRwpv3j9Bg2iyN13ZzkYKqdSv8/eM2dS5I478HnllWwdH5/yBNLyww9Ya9QgoE0brDVrYq1XD5+rHvVeLbVrgJEymt7WrBn2unVxBARgpAxEdKf/a0HgqFSJpAcfBMBn2jTn+7RJk8xboN2U+p40oqOxpvw8sHzzTfr9Mnl/2tq0IemeewDw79OHgEaNCGjZksCKFQno0AHzb7+5Hcv1fHYcoaFcvHAhzVdiys8qe/HiXLxwgeQHHgBvb+JTptiyLFuGtX59rM2aOQfBBgeTkPLzM008f/yBz9SpxE+ZAkFBEBhIcuPGeG3Z4vzj4ccfcVit2K4YrJhb3E5gT58+Tbkrmo+///57mjZtyl133UWpUqXo2bMne1KmVnBHYmIiu3fv5s4770xTfuedd7IlZUTk1VasWEGlSpVYtWoV9evXp27dugwaNEjzz4oAZfzNGZaHZFJ+M0jq0gVbo0YYMTGY9u3DERBA0v33c3nhQrdaM+Pefht7jRoYcXHYy5Yl7o03XK25jpIlifnpJxIffRRH0aKYwsNxlChBYq9eXF65EgICchx/4uOPO/vjBQZiPnjQ2RLigcfc8W+8QdyUKdjq1HE+bjx2DEdICAl9+7pGI8dPmkTS/fe7EpuE4cNJTulXm1324sVJ7NkTR0gIpuPHMR0/jq1yZeL/8x8Snn028+Pq1CH+mWewlyqF6fRpvLZvx8jGCO7kO+4gbsIE7GXKYMTHY69enfiUQWpXchQvTvyUKdjLl8e4cAGv7dsxefBJX9yUKdhSVrr02rUL88GD2To+6aGHuLxoEcm33YaRlOScmcPHh6TOnUlIGSWfGVvjxjj8/ADn98V+yy1gNpPcpIlrn8KSwALEvfsuiV274ihSBOPCBRIGDnS1HNqvc+GFpCeeIGHoUOzBwRgxMSS3bk3Cc8+l2y+r92fsF18QP24ctltucb7n//4be2goCU8/na36vd7Pjtv3+tRTxH74oXNWgZSp5ZIeeIDLK1fiSBkU+W8wdvxGjCD5jjv+bVUG4j78EHuVKlgbNsQUEUHsJ5/gSOl+apw/D5Dlwh7uMi5cuODWU5hq1aoxYsQIhg0bRnJyMlWqVGHw4MGMGzcOgE8//ZRx48Zx8hrTOKQ6efIkYWFhLF++nFatWrnKp0yZwsKFC9meOnDgCiNHjmTevHnUqVOHV155BcMweDGlX8pPP/2EKZNHHOFXzZcnciP6O87g6T98OBH/7+egvK+d92snUM4v5/0qbxbWHTuoMWgQAAc++IDoRo3yOSIRcZfl1CmSixVzTX/ldeECtR99FEtUFJHt23Nk4sR8jvDmZb54kQb33ENS8eL8sXBh2r7dGaiexawKkI0+sLfeeitz5szhtttu4/vvvycmJoZ7r/jr+8iRI5S6quOzO4yrWkEcDke6slR2u52EhARmzpxJtWrVAJg5cyaNGzdm586dNM6kifpalZBbwsPD8+xaNzLV4/WpDiyvnDILQWQMVYIDbrhZCPKCOaXVAaBcuXJpHgtK9unznHOqQ/d5//QTPv/7H7YGDcDbG/PWrZguXMAREMDJp55SPeZQTt6LXt99h+FwkPzGG1S5jkH/6c7n7o4vvPACXbp04Y477sDhcNCpUyduvWKQwnfffUezZs3cvnBwcDBms5kzV00Zc+7cOUpmNIoSKF26NF5eXq7kFaBq1ap4eXlx4sSJTBNYkZtFqNXCrLbFCQ+PpHr1rKejERG50dhq18ZerRpeO3dCbKyzW88jj5AwejTx5pu3O1VBkPzAA1zMRpefa3E7ga1fvz7btm1jy5YtWK1W2lwxJ9yFCxfo169fmq4A1+Lt7U2DBg1Ys2YNnTt3dpWvWbOGTplMstu8eXOSk5M5cuQIlVPm6jt69CjJycmZzlogIpIdtjZtuHjhglq9RAohW9u2XM5omVQAdSe8oWRrIYPg4GDuv//+dOVBQUEMzmKd6MwMHTqUgQMH0qhRI5o1a8bHH3/MqVOn6J2y9vCECRPYsWMHy5YtA5wLKdSvX5+hQ4cyOWUy3nHjxtG4ceM0rcEiIiIicuPKVgJrs9n4+uuvWbduHWfPnuXFF1+kTp06XLhwgTVr1tCiRQtCUia9dsdDDz1EVFQUb7zxBqdPnyYsLIwFCxZQMWUljlOnTnHkyBHX/iaTifnz5/Pss8/SoUMHfH19ueOOO5g0aVKmA7hERERE5MbidtZ38eJF2rVrx8CBA1m6dCk//fQTkSkTWFutVp5//nk+/PDDbAfQr18/9u7dy5kzZ1i7dm2abggzZsxg7969afYPCQnhs88+48SJExw8eJBZs2Zd1+AxESlcLHPnUjQoiKJBQRgpS2cWNIUhRnf5TJ7supfckHoun6yWssxgP/P69a4yc8qE9LkdW055rVlDQOvWBJYuTdGgIHzHjs21c/sNHkzjJk2wurES1vWy1q1L0aAg/K7jSer1yuj7KpIdbiewEyZMYP/+/SxcuJDdu3fjuGJpNLPZTMeOHfnpp588EqSI3DyKdOhA0aAginTokN+hZKowxFhYJTduTHLjxpkvW4lzIYrU/VLlW1Jrt+PXuzfm338HHx9n7BVzbwClvXJlYurUca2O5Qm2evWccaeMLREpDNzuQrB8+XIGDBjA3XffTVRUVLrtVatWZf78+bkanIiI5KLEREhd4rGAurxq1TX3SerVi6RevfIgmmszTp1yLR8c/+KLJPbvn6vnTxgzhvAuXTw6oDB27lyPnVvEU9xugb1w4YJr5H9GHA4HiYmJuRKUiNycigYF4bVhAwBeGzZk+jje/NdfFOnYkcCQEOdSij/8kGa76eBB/Pr0wVqtGoElSxLQsKFzyVC73bWP67HpwIH4vPYa1ho1CAwNxW/AAIiOLhAxZnb9okFB+Iwfj++oUQSGhhJYsSK+zzzjTFCv2s/3xRfxGzyYwIoV8U8ZIGucP4/vM89grVOHwBIlsFarhl/fvpiuGHOQ5l42bybgttsILF2agFatMG/c+O997N5NkU6dnPVXqhSBZctS5I47sGTWoJGUhO+zz2KtVCnLuLPqanB1a2uRDh3wnTIl3Tksn3+OtXZtV325XL5MYJkyFA0KwvuTTzK9zrXqyTJ3LoEpK2gB+D3zjPO6GSWE8fGuLgaWr74CwGvlSooGBREYEuKqA/8nn6RoUBD+jz7qPGcGXQjcfe9me7+ULgRGRISrDr2nTsVvwAACy5fHGhaGzxtvpLkt059/UuS++5zvjSZN8Pr22xx1STDv3In/o4863x+lShHQsiWWL75Is49l/nzn+7FCBQLLliWgUSP8+vSBixedMR08iH/PnlirVyewVCmsNWtS5MEHCdy0KdvxSMHldgJbsWJF9u3bl+n2DRs2pJmfVUQku5IbN8aRsjqLw2r99zHxVUtA+vfqhfHPP2AYmMPD8e/f37VEoenwYQLuugvvxYsxkpKw33ILpqNH8XvpJXwzWGrRsngxPjNmgK8vxsWLeC9YgM877xSoGDPiM2MGliVLcBQtinHpEj6zZuGbwSpD3jNnYlm6FHv58s7VieLjKdKhAz6zZmGcPIm9WjWMmBi8v/6aInffjfH33+nOUaRrV0hIcN7LH39QpFs3jJQlvE0REZh//RW8vbHXrInD2xuvXbvwHzgQr5Ur08c9cyaWRYsgMDDLuLPDVrMm9rJlXa9TvyeO0qVJfOopZz18+SUkJwNg+fFHjLg4HL6+JHbpkvFJ3agnR4kS2K5ILG2VKjmvm7JsZhq+vq714M0py6WbN28GwIiPx7xrV5qy5CumqsyMu+/d7L7H04T9yit4rVuHw8cH08mT+E6ahNeaNf/WUdeueG3a5Fzi2GTCf8AAjKvmd3eXecsWitx7L5aVK8FiwV6lCuZ9+/B/+mm8p04FwPT77/gNGoR5zx7sJUpgr1QJ09mzzs9STAwA/n37Ylm+HJKSsIeFgcmE19q1FMkih5HCx+0EtmvXrnz++edsSGl5gH9X0Zo5cybfffcdPXr0yP0IReSmcXnVKldfP1u9elxetYrLq1bhuGp2k8Q+fYjZsYPYjz4CwIiOxrxjBwA+b72FcfEitmrVuPT778Rs2EDcBx8A4P3RRxgnTqS9qK8v0Vu2EL1rF8kp0/F5rV1bsGLMgL1iRaL37CH6t99IeuAB57EffgixsWn2c1itRG/bRszGjcTNmoVl0SLMKb/IYz/+mJjNm4n5+WccZjOmyEh8pk9Pd624SZOI2bKFmB9+wGEYzkRu1ixnHTRrRvT+/UTv3UvMunVE79+PrUoVACxff50+7rJl3Yo7O+LfeovEJ55wvU79niS3b0/ik0/i8PZ2rk3/448AeKVMzZh0//2QSZ9Zd+opuX17Ll/ROpjwzDOu62YkNSn1SklSvTZvxhEYCDgTV9Phw5hOn3bu27r1tW/c3fduNt/jV7I1aED0nj3EbN2Kw+Jc1c+ccqxl4UJMKe/V2I8+ImbLFmK/+AIjIcGtc6cLc+JEjMREklu2JHrfPmI2byb+hRec2/73P4iPx3ToEIbDga1qVWJ27CBm40YuHT1KzKpVOIoVA8B06JAzpnnziFm7luh9+7j0xx9E3XXXdcUlBZPbCezIkSNp3bo1nTp14r777sMwDMaOHUvNmjUZO3Ys999/PwMHDvRkrCIiACSmPF6116zpKktt9UlNEs0HD1K0QgXn49gBA5z72O2u7amS27TBUbYsmEzYU/oZmq6zBclTMWYkuV07KFIEDIOklMVgjPj4dN0Akjp1wpE6IMpsdrX0Oby9SU5ZNMZeqxb22rWdu6RsT3OOlFZKe4MG2KtWde7355/OjSYTvi+8gLVmTQKDgykaEoL58GHnpiuW5c1u3LnFUaoUSSn36f3FFxAfjyVlwHFS9+6ZHnc99XQtqUmpaf9+jNOnMe/aRdKDD2IPDsZr0yZX1wxH0aLY3Ri05e57Nyfv8aQuXcDbG0dwMI6UVTJTj019D1xZR8l33YX9OgfSpb7vvTZupGjJks4uMCmt80Z0NKb9+7E1b449KAjzoUMEVqpEkTvuwG/4cOfTDX9/Z8wpy9wXefBBAho3xr9HDyxLl5KkGYtuKG4P4rJYLCxYsICFCxeyZMkSDMMgOTmZ+vXr89BDD9GtWzdXi6yIiCc5ihZ1/nvl0pCpM6Ok/GsvXhx7SktgGn5+GZ4LgNTzXTHLSkGI8doXyzxeR2a/tK/35/VV1/IbMADLL7/gMAzsNWrgCAjAfOAARnS087FyNs7lKYl9++K9aBFeP/6I97x5GDEx2ENCSL7zzmsfnIu/12xNmuDw88OIi8N75kyM+HiSmzfHiIzEvGkTjuLFAUhu2RLcmNvc3fduTt7jbh1rGLlaT/YyZTKehcIwcJQuTczmzVjmz8e8axfmP//E+4sv8P7iCy7PmUNyx47EffAByffdh/nXXzHv34/Xzz9jWbGCyrfdBimt71L4ZWshA3B2JejatWu68l27drFlyxYGDRqUK4GJyM3JkdKKcr2PlG0NG2I+cAD8/Yn96qt/+yNeuoTlu++cLYA3QIxeP/0Ezz8Pfn5Yvv3WGZev7zWnQrKlPEI2EhLwWraM5AcfxLRvH6Y//kiz/UqWJUtIeuIJTHv2YEppXbWFhTnj2L4dgMQnnyT+nXcwzp8noEULZwKbi3Ffi+t7AnD5srOVN/WeW7TAVqcO5t9/x/fFFwFI6tbt34QsA9dTT9fk44OtcWO81q/HZ/ZsV2xGVBSWFSuwpCRX7vR/LQhsKQPYjIQEvL7/nuT77sNr9WrXrAzZPt+tt+K1YQP2kBAuL13q+h4a587htXYt9vr1MU6exIiMJHHECNdxAbfeivnIEbzWrSO5Y0fMGzeS9MADJD38MAA+//sfvq+9RuD27cTk7JalAMm15atWr17Nc889l1unE5GbVOojTq9duwho2RL/lF9C7koYNQpHYCCmEyew1q1LQJs2WOvXJ7BKFfyHDLlhYjT9/TfWevWw1q/vSnwS+/d3PUbNTNIjj7gSD/8+fQho3pyAu+7CsNmwBweTkMH1/Z5/3rlf+/YYDgeOIkVI7NcPAFvKI3Xvzz8noHlzrA0aQHx8rsd9LfYrppmyNm/uHGh19KirLCElXuPyZec1rzFm43rqyR2pyalx6RL2UqWwV6mCrUULZ1nKICS3+r8WAEmPPIK9fHnAOWgxoHlz/Hv2dA4WvA7xL7yAw2LBa9cuAmvWdH4u6tTBesst+KbMImE6cABr69ZYq1UjoHVrrPXrY07pfmKrU8cZy6BBBFaqREDjxgS0aeOaOSFOA81vKFp/VUQKlIRhw0i6/Xbno+h9+7Ld19BerRoxq1eT+PDDOAICMO3fD4mJJLduTdw1VoEqTDEmDBzobGG6dAlHYCAJffu6BrxkydeXy8uXk9C/P46QEEwHD+Lw9yfxoYecg9EyeHR7ef585/yxNhu2WrW4PH++q2tC3PTpzqTM1xcjNpa4yZNd/URzNe5rSL73XhKffBJ78eKYjh/Ha/t2jCtayJO6dnUNmEq+9dY0fZMzdB315FacV7Su2po1c/5bv76rBdkeFIQ9JREr8Hx9ubxwIcktWji7ECQmEjtzJo6AAAAc2ewKY2vRgsvff09S+/bOwXIHDgDOftPxzz8PgL1SJRIfeQRH0aKYDh/GOHcOW82axI0f75obOLFnT2y1amFERWHavx9HiRIkduvGoUmTcvHmJb8ZFy5cyJVOSG+++SavvfZahosc3CzCw8M9Otn0zUL1mHOqw5wrqHWYOvdp/LPPkjBuXP4G44aCVI8BLVti3rePuDffdLUgFwYFqQ6vZjp0yNmPO6UPrHnDBgJSVqiLfecdklKmMSsICnI9FhYFqQ6z3QdWRESkMPEdNw7z7t2Y9+3DXrLkNbsPiPt8X3wR8969zhbP2FjMKYsF2GrUcPYzFvEQJbAiInJDs3z3HcY//2CrVYu4t9/OcX9b+VdymzaYDh3Ca/16SE7GXrEiyffdR/wzz6iexaOyTGDfffddt0+0SUu0iYh43MXrHOF9M4veuze/Q7hhJQ4eTOJ1LBkrklNZJrDjr1w72g2aB1ZEREREPC3LBPa3337LqzhERLJkmTsX/6FDAbj02284QkPzOaKCz4iIILB+fQBip00jqWdPj17Pb/BgvL/8EnuFCmr1FBGPynIarYoVK2b7S0QkJ4p06EDRoCCKpIxkLqiM48fxe/pprGFhBJYsibVqVfy7dMFIWRs+w2MiIigaFETRoCAsc+fmYbR5w165MsmNG2NzYxnUrHh9/z3+PXtirVePwDJlsFapQpH77sNrxYo0+/lMnuyqz6u/SE527nT5Mn5DhmCtUgVr5cr4DRmSZgEKIyKCwLJl8f7ggxzFLCJ5S4O4RESyyXT4MEXuuQdTZCQOb2/s1aqBw4HXpk2Yzp7FljK5e44lJjrnXy0kEsaMIWHMmByfx7JsGZbly51zolaujOmvv/DatAmvTZu4/OmnJHfunGZ/e3Bw+pW8Urq0+bz9Nt7z5nH566/BbqdI167Yy5YlIWXuWb9Ro7CFhZE4YECO4xaRvKOFDESkwCgaFITXhg0AeG3Y4GpNMyIi0uxn/usvinTsSGBICAFNmuD1ww+ubcaxY/g/8gjW2rUJDAlx7tOiBd7Tp6dZw91aty5Fg4LwGzgQn9dew1qjBoGhofgNGACZLIOaynfMGEyRkdhq1SJ6715iNm0iZvNmLh075lq96WqWuXNdj/MB/IcOTdPSfGXLs/c772CtWZPAlPkWvadOda46VKkSgSVKYK1WDf/HH8d08GCaa3h9+y0BjRoRWLo0Re67z7lcbQZMBw/i16cP1mrVCCxZkoCGDfF+7z2w2/8916pVFGnfnsDQUAJDQrDWq4d/z55pVre6mt/gwRQNCsJat66rLHDjxmyfJ7lFC2J++onoo0eJ2biRyz/9hMPk/HXlPX9++v3btePyqlVpvlKXiTXv2ePcp00bkm+7zVmW0r3BsnAhXmvXEvfee2DSr0ORwkSfWBEpMJIbN8ZhtQLgsFpJbtyY5MaN4aqlKf179cL45x8wDMzh4fj3749x/jwApshILKtWAWC/5RYcVivmP//E77nn8E5Zf/5KlsWL8Zkxw7mS1MWLeC9YgM8772Qe5IULeK1e7Tx/uXIUefBBAsuVI6BNG7y+/z5drKkcJUpguyKxs1Wq5HzcftWKUOZt2/B99VUcRYviSFm0wOvXXzEdOYKjdGnst9yCcf48lu++o0jnzq5lW01//IH/U09hPnQIvL0xzp3Dv3fvdHGYDh8m4K678F68GCMpCfstt2A6ehS/l17C99lnATAiI/Hv0QOvLVtwWK3OFuboaCzLl2M6eTLzurmKERlJtdGjs32epF69sDVp8m9d1a8Pqas7ZVC/lm+/dSbHNWrg360bpivGb6R2Z/Bavx6vdeucZXXrYpw/j++4cSQMH57lymEiUjApgRWRAuPyqlWuhMNWr56rNc0REpJmv8Q+fYjZsYPYjz4CwIiOxrxjh/O4ypW59NtvRP/xBzHr1hF94ADJLVsCzmQ1HV9fordsIXrXLpJvvRUAr7VrM43RfOgQRkpLruWnnzCio51J8t69FHnyyTStwVdKbt+ey1984Xqd8MwzXF61ivi33kqzn5GYSOz8+cRs2UL0zp0AxI8fz6WjR4nZssXZIvn11wCYTpzAvGULAD5Tp2LYbDgCAojevJmYbdtIyGB6I5+33sK4eBFbtWpc+v13YjZsIC6l/6f3Rx9hnDiBcfw4RmIiDquV6K1bifn1V6KPHCH611+xZ2MVHuP4cUxJSTk+j2XePIxLl3AYBolXJeUOsxl7qVLYK1bEdPo0lh9/JKBdO1cSmzByJIk9euDXrx9+AwaQ2KMHCf/9L77PP4+jaFGSunbF/6GHCAwNJaBVK7zWrHE7LhHJP0pgRaTQSXz0UYA069kbZ844/2Ox4PPee1jr1CGwRAmKFi+O18aNzn0yaPVLbtMGR9myYDK5kipT6rkykjo4CLCFhRG9ezfRu3djr1ABAO9Zs3J0b7bq1Um++27ni5TH4KYTJ5xdJipUILBYMQKu6AOa2pJp3rfPGV7TpjjKlQMgqUuXdOdPTfTNBw9StEIFigYF4Z/S/9Ow2zHv2IG9Zk1slSphREcTWL06AW3a4DdgAOYDB3AEB7t9L/aaNYkvVy5H5/H+8EP8RozAYRjET56MrW1b17akrl2JPniQmJ07idm61ZXYGwkJ+KS2thcpQtz06c7E+cgR4qZPx7xtG5YvvyTu7bfxGzYMr+3bif30Uxy+vs7W/chIt+9RRPKHBnGJSKHjKFrU+W9Kgud84WwV9Rs3Du/PPwfAVrUqjmLFMB05gikyEsNmy/RcgCthvLKv7NXsZcq4/m+rXRssFrBYsNWqhen4cUzHjl3vbTkvXapUmtfG0aPOPqMpLaK2Bg0wkpNd/TjJ4J7+PVkG95FSZi9e3LmG/dX8/MDXl5hffsF7/nzMO3Zg3r8fy8KFeC9YQNypUySmTGd2Tb6+/DlnDjW3bcv+eWw2fMeOxWfWLBze3sS9/z5J3bun2cVerVqa18l33YW9eHFMUVGZzwYRH4/fyJEk9eyJ7dZb8dq2jaQHHiD5jjswHTiA19ixmLduJfm++9y7RxHJF24nsF9++WWW2w3DwNfXl7Jly9KgQQO8C9HIWREpOBypy09eMdVRdpi3bwcg6c47iV28GOLjCbj7bsilVjVHxYrYqlXDfPAg5j/+cLbI2myY//wTAHvVqpkffMXSmoab92f+7TeMxEQALn/9NbamTbF8/TX+ffum2c8WFoZ5zx68tm7FOHkSR5kyWJYuTXc+W8OGzsFd/v7EfvUVjhIlnBsuXcLy3Xckt2sHly5hDg93jsxPGc1fpFMnvNatw2vdOvcT2EuX8D16NPvnuXQJ/969saxejb1YMWLnzMHWunW63bzfeYekhx/GkdL67bVmDaaoKMD5fcqIz//+hxEdTdzEia5k3pH6+8picf6bEqvfwIGYd+7E1rAhcTNnunfPIpIn3E5ghwwZ4lppy3HVX/VXlhuGgdVqZfTo0QwbNiwXQxWRm4G9enX46Se8du0ioGVL7GXKEJvyaNgdttq1Me/bh+Xnnwlo3Ng5uOuK0fW5IX7CBPwffxzzn39ibdAAkpMxnTqFw2IhYdSoTI9zlCjhaiH0nTABy1dfkdStG4kDB2Z6jD0sDIfZjGGzUeSRR7CXL49x+nS6/RKefhrLwoUYMTFYmzbFXqYMpqtmbwBIGDXKOYjqxAmsdetir1YN49IljL//xkhO5mKPHpjOnSPgnnuwBwU5u1ckJWEODwfAVqeO2/VkOneOsD59sP/3v9k6j+/LL2NJGShHkSL4XrEqpK1+fVe/YZ+PPsJ3wgQc5cvj8PfH9NdfADiKFMmw/6/pjz/wmTrVmYymDJBLbtwYry1bME6fxuvHH52t3I0bO/c/cQJzeHi6VnERyX9u94H99ddfqVOnDq1ateLTTz/l119/Zf369Xz66ae0bNmSevXqsXLlSj777DPq1KnDyy+/zOcpj/FERNyVMGwYSbffjiMgAPO+fZh37crW8fGTJpF0//04AgIwYmJIGD6c5HvvzdUYkzt0IHb+fJKbNME4dw5sNpLuuYeY1avTjJ5PxzCIe/ddbFWqQFwcXjt2YDp+PMtr2W+5hbj338ceGgqJiTiKF3cNXkuzX926xH7yifPcCQk4AgOJzWDWBXu1asSsXk3iww/jCAjAtH8/JCaS3Lo1cZMnO/cpXpzEnj1xhIQ4u0UcP46tcmXi//MfElJmKnCHvXhxznXsmO3zGCkzK4AzifTavt31Zd6/37UtftQoktu2haQkTEeP4qhQgcRu3Yj55Zc0/aOdwdjxGzGC5DvuIOmhh1zFcR9+iL1KFawNG2KKiCD2k0/+bZUWkQLLuHDhQuadva4wYsQIIiIi+Oabb1wtrqnsdjtdunShcuXKvPPOO9jtdu655x4SEhL49ddfPRJ4QRQeHk71bIyslYypHnNOdZhzqsPcoXrMOdVh7lA95lxBqkO3W2C//fZbHnjggXTJK4DJZOKBBx5g2bJlrtedO3fm0KFDuRepiIiIiAjZSGATExM5nsWjrmPHjpGYMtAAwNfXF0tqh3gRERERkVzidgJ7++23M3PmTJZmMKp1yZIlzJo1i9tvv91VtmvXLipmMgpUREREROR6uT0LwZQpU+jYsSO9e/emVKlSVK5cGYAjR45w5swZQkNDmTJlCgDx8fGcOXOGJ554wjNRi4iIZOHiRbhyil8RubG4ncCWK1eODRs28PHHH7N69WpXd4JatWoxfPhwnnrqKfxT5jj09fVl0aJFnolYREQkE3Y7fPqpNzExMHx44rUPEJFCKVsrcfn5+TF06FCGujuJtYiISB45eNDEhx9606NHIg0a5O7cvyJSsGgpWRERKdSSk2HWLG+Sk2HSpHg0fljkxpetBPaXX37hs88+4+jRo5w/fz7DFbl2796dm/GJiIhkat8+E5984k3v3onUqqVWV5GbhdsJ7IwZM3j++ecpUaIEjRs3JiwszJNxiYiIZCopCT74wBuLBSZPjsdLzxNFbipuf+SnTZtGq1at+Prrr/H29vZkTCIiIpnavdvE3LneDByYSLVqanUVuRm5ncBGRkYyatQoJa8iIpIv4uNh2jQfihVzMGVKPCa3ZzIXkRuN2wlsgwYNOHbsmCdjERERydDWrWa+/trCkCEJhIY6rn2AiNzQ3P77ddKkScybN49169Z5Mh4RERGX2Fh4/XUf/vrLxOuvxyt5FREgGy2wkydPJjAwkM6dO1O1alUqVKiA2WxOs49hGCxYsCDXgxQRkZvP+vVmVqywMGxYAmXLKnEVkX+5ncDu378fwzAoX748CQkJHDx4MN0+hmHkanAiInLzuXQJ3nvPhxo17Lz2Wjz61SIiV3M7gd27d68n4xAREWHVKi9++cWL4cMTKFVKra4ikjGN4RQRkXx34QKMH+9DbCxMnBiv5FVEsqSpn0VEJF8tX+7F1q1ejBiRQPHiSlxF5NoyTWCLFSuGyWTi5MmTeHt7U6xYsWv2cTUMg8jIyFwPUkREbjznzhm8+64PrVsnM2FCfH6HIyKFSKYJ7JgxYzAMA6+U9flSX4uIiOSEwwHffGNh3z4To0fHU7RofkckIoVNpgnsuHHjsnwtIiKSXadOGbz3ng/t2yfxwgtJ+R2OiBRS6gMrIiIe53DAV19ZOHrUxHPPxRMQkN8RiUhhlq0E1maz8fPPP3P06FHOnz+Pw5G2s71hGIwZMyZXAxSRG0tEdBITd0ZzMtZGGX8zLzS0Emq15HdY4kHHjxu8/74PnTsn0b27Wl1FJOfcTmD37NnD448/zokTJ9IlrqmUwIpIViKik+i8MpIj0TZX2faziSxpH6wk9gZkt8M335TAMLwZPz4eP7/8jkhEbhRuJ7CjR48mJiaGOXPm0KpVK4KCgjwYlojciCbujE6TvAIcibYxcWc0s9oWz6eoxBMOHzbxwQfetGwZS+fOCfkdjojcYLLVAjtu3Dg6dOjgyXhE5AZ2MtaWYfmpTMql8LHZ4KOPvImLcy5IEBERm98hicgNyO2VuEqVKuWaUis3zZ49m3r16lG6dGnatm3Lxo0b3Tru0KFDlC9fnnLlyuV6TCLiGWX8zRmWh2RSLoXLgQMmxo71pUWLZEaMSMTbO78jEpEbldsJ7IABA/jqq69ISsq9DviLFy9m7NixjBo1inXr1tG0aVO6du3K8ePHszwuMTGRPn360LJly1yLRUQ874WGVipb0yarla3OgVxSeCUlwbRp3qxa5cXkyfHUrWvP75BE5AbndpNq2bJl8fLyokWLFjz++OOUL18eszl9q0mXLl3cvvi0adPo0aMHTz75JABvvPEGq1ev5uOPP+bll1/O9LiXX36Z2rVr06pVKzZs2OD29UQkf4VaLSxpH8zEndGcirURolkICr09e0zMmeNNv36J1KihxFVE8obbCWzfvn1d/58wYUKG+xiG4XYCm5iYyO7duxk2bFia8jvvvJMtW7ZketzKlStZuXIla9euZdmyZW5dS0QKjlCrRQO2bgAJCTB9ug8BAQ5efz2eDNozREQ8xu0E9ttvv83VC0dGRmKz2ShZsmSa8pIlS3LmzJkMjzl16hQjRoxgzpw5WK3uP3IMDw/PUazZkZfXupGpHnNOdZhzqsOM/fFHEb7/vjiPPXaM8uUTOHw46/1VjzmnOswdqsecy6s6rF69epbb3U5gW7duneNgMmIYRprXDocjXVmqAQMG0KdPH5o0aZKta1yrEnJLeHh4nl3rRqZ6zDnVYc6pDtOLi4P33/ehdGk7M2YkYTJVvOYxqsecUx3mDtVjzhWkOsy3pWSDg4Mxm83pWlvPnTuXrlU21bp169iwYQNTpkwBnMmu3W4nODiYt956i6eeesrTYYuI3JQ2bTKzdKmFoUMTqFAh48VsRETySrYS2F9++YXPPvssy6Vkd+/e7da5vL29adCgAWvWrKFz586u8jVr1tCpU6cMj7l6iq0VK1bw1ltvsXr1asqWLZudWxERETfExMB77/lQpYqdyZPjyeQBmYhInnI7gZ0xYwbPP/88JUqUoHHjxoSFheX44kOHDmXgwIE0atSIZs2a8fHHH3Pq1Cl69+4NOAeL7dixwzVYq1atWmmO37VrFyaTKV25iIjk3C+/mPnxRwvDhycQEqJWVxEpONxOYKdNm0arVq34+uuv8c6l2akfeughoqKieOONNzh9+jRhYWEsWLCAihWd/apOnTrFkSNHcuVaIiLinosX4d13fahb186kSWp1FZGCx+0ENjIyklGjRuVa8pqqX79+9OvXL8NtM2bMyPLYnj170rNnz1yNR0TkZvbDD15s3OjF8OEJlCihVlcRKZjcXomrQYMGHDt2zJOxiIhIPomKMnj5ZV/sdnjllXglryJSoLndAjtp0iS6d+/OHXfcwW233ebJmEREJA8tXerFb7+ZGTkynqCg/I5GROTa3E5gJ0+eTGBgIJ07d6Zq1apUqFAh3VKyhmGwYMGCXA9SRERy35kzBu++68NddyXz0ksJ+R2OiIjb3E5g9+/fj2EYlC9fnoSEBA4ePJhun8wWIBARkYLD4YCFCy389ZeJsWPjycbChiIiBYLbCezevXs9GYeIiOSBv/82mDrVhwceSKJbt6T8DkdE5Lrk20pcIiKSdxwO+OILCydPmnjppXj8/fM7IhGR66cEVkTkBnf0qMH06T507ZrEE0+o1VVECr9ME9hixYphMpk4efIk3t7eFCtW7Jp9XA3DIDIyMteDFBGR7LPb4ZNPvLl40eDVV+Px8cnviEREckemCeyYMWMwDAMvL680r0VEpOA7eNDEzJnePP54IvXr2/M7HBGRXJVpAjtu3LgsX4uISMGTnAwffuiNzQavvRaPxZLfEYmI5D63+8DGxsbir17/IiIF1h9/mPj0U2/69EkkLEytriJy43I7ga1YsSL169enZcuWtGjRgpYtWxKkJVtERPJdYiJ88IE3Pj7w+uvxXLXGjIjIDcftBPb5559n06ZNfP7557z//vuYTCZq1KhBy5YtXUltmTJlPBmriIhcZfduE3PnejNoUCJVq6rVVURuDm4nsCNHjmTkyJE4HA5+++03Nm7cyKZNm1i6dCkff/wxAJUqVWLnzp0eC1ZERJzi4+H9930IDnYwZUo8JlN+RyQikneyPQ+sYRg0aNCAevXq0aJFC3799VfmzJlDeHg4R48e9UCIIiJypS1bzCxebGHIkARCQx35HY6ISJ5zO4FNTExk27ZtbNq0iY0bN7Jt2zYuX75MxYoVad68OU8//TQtW7b0ZKwiIje1y5dh6lQfKlSw8/rr8WhmQxG5WWVrEFdSUhI1atSgefPm9OjRg5YtW1K2bFlPxiciIsC6dWa+/97CsGEJlC2rVlcRubm5ncDa7XYcDucPTbPZ7PoSERHPuXQJ3nvPh7AwO6+9plZXERHIRgJ77NixNF0IvvzyS2JjY6lcubJrJoKWLVsSGhrqyXhFRG4aP/3kxdq1XowYkUDJkmp1FRFJ5XYC6+vrS5s2bWjTpg0ANpuN3bt3s3HjRubMmcPcuXMxDIPIyEiPBSsicjM4f97g3Xe9adTIxsSJ8fkdjohIgZPtWQgA9u7dy8aNG11TaZ09exZA/WFFRHLou++82L7dzIgRiRQrplZXEZGMuJ3ATp06lV9//ZUtW7Zw6dIlHA4HVatW5d5773UtZKDuAyIi1+fsWYN33/Whbdtkxo9PyO9wREQKNLcT2PHjx1OrVi0effRRV3/XkiVLejI2EZEbnsMBixdb+PNPE2PGxBMYmN8RiYgUfG4nsIcPH6Zo0aKejEVE5KZy8qTBe+/5cO+9SbzwQlJ+hyMiUmi4ncAqeRURyR0OB8ybZ+H4cRMvvBBPkSL5HZGISOFyXYO4RETk+hw7ZjBtmg8PPZREz55qdRURuR5KYEVE8oDdDp9/biEy0sSECfH4+uZ3RCIihZcSWBERDzt82MSMGd706JHErbeq1VVEJKeUwIqIeIjNBrNne5OQAJMmxePtnd8RiYjcGEyZbShevDgLFy50vR46dCjbt2/Pk6BERAq7/ftNjB3rS+vWyQwfnqjkVUQkF2WawHp5eZGU9O+jrnnz5nHkyJE8CUpEpLBKSoKpU71Zs8aLyZPjqV3bnt8hiYjccDLtQlClShUWLlxI/fr1CUyZWTsqKorjx49necIKFSrkboQiIoXEnj0m5szxZsCARKpXV+IqIuIpmSawo0ePZvDgwbRp0wYAwzAYN24c48aNy/KEUVFRuRuhiEgBl5AA06f7EBjo4PXX4zGb8zsiEZEbW6YJ7COPPELjxo3ZuHEjZ8+eZfz48Tz00EPUrVs3L+MTESkwDh40Ua1a2pbV7dvNLFhgYciQBCpVcuRTZCIiN5csZyGoVKkSlSpVAuCjjz7i4Ycf5v7778+LuERECpT4ePj0U28mTowHIDYWpk71oWxZO1OmxGMY+RygiMhNxO1ptPbs2ePJOERECrRZs7zp1y8BgA0bzHz7rYWnn06gfHm1uoqI5LVszQNrs9mYN28eP/74I8eOHQOgYsWKtG/fnu7du2NWxy8RuQH9/bdBcrJBcLCDSZN8qFbNzuTJanUVEckvbiewly5d4qGHHmLnzp0EBARQqVIlHA4Ha9euZfny5Xz22WcsXrwYq9XqyXhFRPLchx/60KxZMpMn+zJiRAKlS6vVVUQkP7mdwE6cOJFdu3bx2muv0adPH7xTZuVOSkri448/5rnnnmPixIlMmTLFY8GKiHhaRHQSE3dGc/icD1X+ieL2i8XZvdtEUJCJZs2SWbTIwsWLBj4+MHJkAqZMZ9MWERFPcTuB/e677+jduzeDBg1KU26xWBg4cCB//fUX3377rRJYESm0IqKT6LwykiPRNsDMjktxrNqYwJOtzISFGZQvb6dt22SKFkXdB0RE8pHbbQeRkZGEhYVlur1WrVpERkbmSlAiIvlh4s7olOT1X+dbnuPvZme5995k6tSxExSk5FVEJL+5ncBWqFCBNWvWZLp9zZo1WoVLRAq1k7G2DMtPZVIuIiL5w+0E9vHHH2f58uUMHjyYP//8k6SkJJKSkti3bx9Dhw5lxYoV9OrVy5Oxioh4VBn/jGdSCcmkXERE8ofbfWBHjBhBREQEn376KfPnz8dIeYbmcDhwOBz07t2b4cOHeyxQERFPe6Ghle1nE9N0I6hsNfNCQ82uIiJSkLidwBqGwdtvv82AAQNYuXJlmnlg27VrR61atTwWpIhIXgi1WljSPtg5C0FkDFWCA3ihoZVQqyW/QxMRkStkayEDgLCwsCwHc4mIFGahVguz2hYnPDyS6tUr5nc4IiKSAc1gKCIiIiKFihJYERERESlUlMCKiIiISKGiBFZEREREChUlsCIiIiJSqLidwHbs2JG1a9dmun3dunV07NgxV4ISEREREcmM2wnsr7/+ypkzZzLdfu7cOTZs2JArQYmIiIiIZCbXuhD8/fffFClSJNvHzZ49m3r16lG6dGnatm3Lxo0bM913/fr1dO/enRo1alCmTBlatmzJnDlzchK2iIiIiBQyWS5ksHz5clasWOF6/emnn/LLL7+k2+/ChQusXbuWRo0aZeviixcvZuzYsbz11ls0b96c2bNn07VrVzZv3kyFChXS7b9161Zq167NiBEjCAkJYfXq1fznP//B19eXrl27ZuvaIiIiIlI4ZZnA/vnnn3z99deAcynZbdu2sWPHjjT7GIaBv78/zZs35/XXX8/WxadNm0aPHj148sknAXjjjTdYvXo1H3/8MS+//HK6/UeNGpXmdd++fVm/fj3Lli1TAisiIiJyk8gygR09ejSjR48GoFixYkybNi3XEsXExER2797NsGHD0pTfeeedbNmyxe3zREdHU7Zs2VyJSUREREQKviwT2CudP38+Vy8cGRmJzWajZMmSacpLliyZ5WCxK/3www+sXbuWlStXZrlfeHj4dceZXXl5rRuZ6jHnVIc5pzrMHarHnFMd5g7VY87lVR1Wr149y+1uJ7CeYhhGmtcOhyNdWUY2b95M//79mTJlyjX73l6rEnJLeHh4nl3rRqZ6zDnVYc6pDnOH6jHnVIe5Q/WYcwWpDjNNYOvVq4fJZGLbtm1YLBbq1at3zcTSMAx2797t1oWDg4Mxm83pWlvPnTuXrlX2aps2baJbt26MGzeOvn37unU9EREREbkxZJrAtmrVCsMwMJlMaV7nFm9vbxo0aMCaNWvo3Lmzq3zNmjV06tQp0+M2bNjAo48+yrPPPsuQIUNyLR4RERERKRwyTWBnzJiR5evcMHToUAYOHEijRo1o1qwZH3/8MadOnaJ3794ATJgwgR07drBs2TLAOQ/so48+St++fenWrRunT58GwGw2U6JEiVyPT0REREQKnnztA/vQQw8RFRXFG2+8wenTpwkLC2PBggVUrFgRgFOnTnHkyBHX/vPmzSM2NpapU6cydepUV3mFChXYu3dvnscvIiIiInkv0wT2+PHj13XCjBYgyEq/fv3o169fhtsyagX2REuwiIiIiBQeWQ7iup4+r1FRUTkKSEREREQkK5kmsO+//36uDtoSEREREckNmSawPXv2zMs4RERERETcYsrvAEREREREsiPTFtgvv/wSgMceewzDMFyvr6V79+65E5mIiIiISAYyTWCHDBmCYRg8/PDDeHt7u7VogGEYSmBFRERExKMyTWB/++03wLli1pWvRURERETyU6YJbOpiApm9FhERERHJD9e1Etfvv//uWuigQoUK1K5dW1NuiYiIiEieyFYC+/XXX/Pyyy/zzz//pCkvW7YsL7/8Ml27ds3V4EREREREruZ2Ajt37lyefvppqlevzoQJE6hWrRoOh4NDhw7x+eefM3DgQBITEzV/rIiIiIh4lNsJ7P/93//RqFEjvvvuO3x9fdNs69+/P/fffz//93//pwRWRERERDzK7YUM/v77b7p27ZoueQXw9fXl0UcfTde1QEREcl9EdBL910bxwPdn6b82iojopPwOSUQkT7ndAluzZk1OnjyZ6fZ//vmHGjVq5EpQIiKSsYjoJDqvjORItM1Vtv1sIkvaBxNqteRjZCIiecftFthXXnmFzz77jG+++Sbdtq+//prPP/+cV199NVeDExGRtCbujE6TvAIcibYxcWd0PkUkIpL3Mm2BzWhGgeDgYPr27cvYsWOpXLkyhmFw+PBhzp49S9WqVZk6dSpt2rTxaMAiIjezk7G2DMtPZVIuInIjyjSB3b9/f4Zzu5YvXx7A1d/Vx8eH8uXLk5CQwIEDBzwUpoiIAJTxN2dYHpJJuYjIjSjTBHbv3r15GYeIiLjhhYZWtp9NTNONoLLVzAsNrfkYlYhI3rqulbhERCR/hFotLGkfzMSd0ZyKtRHi70xeNYBLRG4m15XARkdHc+nSJex2e7ptFSpUyHFQIiKSuVCrhVlti+d3GCIi+SZbCeznn3/Oe++9x+HDhzPdJyoqKsdBiYiIiIhkxu1ptObMmcOIESOoUKECL7zwAg6Hg8GDBzNy5EhKlSpF3bp1mTp1qidjFRERERFxP4GdMWMGbdq04ZtvvuGpp54CoF27drz44ots3ryZCxcucOnSJU/FKSIiIiICZCOBPXz4MA888IDzIJPzsKQk5/KFQUFB9OrVi9mzZ3sgRBERERGRf7mdwBYpUgSHwwFAQEAAZrOZU6dOubYXL17cNTesiIiIiIinuJ3AVq9enX379gHg5eVF3bp1+eqrr0hKSiI+Pp758+cTGhrqsUBFRERERCAbsxB06NCBGTNmEB8fj6+vL6NHj+aJJ56gUqVKGIbB5cuX+eCDDzwZq4iIiIiI+wnssGHDGDZsmOt1hw4dWLFiBUuWLMHLy4t7772X1q1beyRIEREREZFUOVqJq3nz5jRv3jy3YhERERERuaZsJ7DR0dGsX7+e48ePA1CxYkVatWpFYGBgrgcnIiIiInK1bCWwb7/9Nm+++SZxcXGuGQkA/Pz8GDVqFKNGjcr1AEVEREREruR2Avvuu+/yyiuv0Lp1a/r160e1atVwOBwcOnSI2bNnM2nSJLy8vBgxYoQn4xURERGRm5zbCeysWbO44447WLx4cZryOnXq0KlTJ7p06cKsWbOUwIqIiIiIR7k9D2xUVBT3339/htsMw+CBBx4gKioq1wITEREREcmI2wls/fr12b9/f6bb//zzTxo0aJAbMYmIiIiIZMrtLgRvvPEGDz/8MBUqVKBv374EBAQAEBMTw+zZs1m+fDlff/21xwIVEZHCIyI6iYk7ozl8zocq/0TxQkMroVZLfoclIjeITBPYZs2apSszDIMJEybw6quvUqpUKQzD4PTp09jtdkqVKkXfvn3ZvHmzRwMWEZGCLSI6ic4rIzkSbQPM7LgUx/aziSxpH6wkVkRyRaYJbIkSJTAMI01ZyZIlqVatWpqyypUreyYyEREplCbujE5JXv91JNrGxJ3RzGpbPJ+iEpEbSaYJ7PLly/MyDhERuUGcjLVlWH4qk3IRkexyexCXiIiIO8r4mzMsD8mkXEQku7K1EpfNZmPevHn8+OOPHDt2DHAuJdu+fXu6d++O2awfTiIiN7sXGlrZfjYxTTeCylYzLzS05mNUInIjcbsF9tKlS7Rv354RI0awdu1aHA4HdrudtWvXMnz4cO69916io6M9GauIiBQCoVYLS9oH07WKH42K2uhaxU8DuEQkV7mdwE6cOJFdu3bx2muvcfDgQdatW8f69es5dOgQkydPZufOnUycONGTsYqISCERarUwq21xPqibwKy2xZW8ikiucjuB/e677+jduzeDBg3C29vbVW6xWBg4cCBPPfUU3377rUeCFBERERFJ5XYCGxkZSVhYWKbba9WqRWRkZK4EJSIiIiKSGbcT2AoVKrBmzZpMt69Zs4YKFSrkSlAiIiIiIplxO4F9/PHHWb58OYMHD+bPP/8kKSmJpKQk9u3bx9ChQ1mxYgW9evXyZKwiIiIiIu5PozVixAgiIiL49NNPmT9/vmuVLofDgcPhoHfv3gwfPtxjgYqIiOSmiOgkJu6M5mSsjTL+zmm+NNhMpHBwO4E1DIO3336bAQMGsHLlyjTzwLZr145atWp5LEgREZHcFBGdROeVkWnmqt1+NlHTfYkUEm4lsHFxcXTr1o1HH32Uxx9/PMvBXCIiIgXdxJ3RaZJXgCPRNibujGZW2+L5FJWIuMutPrB+fn789ttv2Gxax1pERAq/k7EZ/z47lUm5iBQsbg/iat26NRs3bvRkLCIiInmijH/GS5+HZFKeHyKik+i/NopBe3zovzaKiOik/A5JpMBwO4GdMmUKO3fu5MUXX+To0aPY7XZPxiUiIuIxLzS0UtmaNlmtbHUO5CoIUvvoLjwcx45LZhYejqPzykglsSIp3E5gmzRpwrFjx5g2bRoNGzakVKlSlClTJs1X2bJlsx3A7NmzqVevHqVLl6Zt27bXbOX9448/uP/++wkJCSEsLIwpU6bgcDiyfV0REbl5hVotLGkfTNcqfrQJ8aZrFb8CNYArqz66BUlqK/ED358tsK3EBb0lW3V4fdyehaBLly6uqbNyy+LFixk7dixvvfUWzZs3Z/bs2XTt2pXNmzdnuCjCpUuX6NKlCy1btuTnn38mPDycoUOH4u/vz7Bhw3I1NhERubGFWi0FdsBWYeijWxhmckgbo5kdl+IKVIyqw+vndgI7Y8aMXL/4tGnT6NGjB08++SQAb7zxBqtXr+bjjz/m5ZdfTrf/woULiYuLY8aMGfj5+VGrVi3++usvpk+fztNPP53rCbaIiEh+KAx9dAvDTA4FPcaCHh8U3BivmcAmJCSwYsUKjh49SnBwMO3atSMkJCTHF05MTGT37t3pWk7vvPNOtmzZkuExW7dupUWLFvj5+bnK7rrrLiZNmkRERASVKlXK8Ljw8PAcx+uuvLzWjUz1mHOqw5xTHeYO1WP29SxmsMnXhxPx//b0K+9rp2exKMLDI/Mxsn8dPucDpE+oD0fGKEY3FfT4IP9irF69epbbs0xgT58+zf3338+RI0dc/Uz9/f1ZsGABrVq1ylFgkZGR2Gw2SpYsmaa8ZMmSnDlzJsNjzpw5k66fberxZ86cyTSBvVYl5Jbw8PA8u9aNTPWYc6rDnFMd5g7V4/WpDiyv7Fwp7HBkDFWCAwrcSmFV/olix6W49OXBAVSvXjEfIkqvoMdY0OODghtjloO4Jk6cyNGjRxkyZAjz589n8uTJ+Pr6MmbMmFwL4OrH/g6HI8uuABntn1G5iIhIYZbaR/eDugnMalu8QCWvUPBncoCCH2NBjw8KboxZtsD+/PPPdO/enYkTJ7rKSpUqRb9+/fj7778pV67cdV84ODgYs9mcrrX13Llz6Vplr7x2RvsDmR4jIiIiuS91JoeJO6M5FWsjxN9c4FqJr4yxILZkqw6v3zW7EDRr1ixNWfPmzXE4HJw4cSJHCay3tzcNGjRgzZo1dO7c2VW+Zs0aOnXqlOExTZs2Zfz48cTHx+Pr6+vav0yZMoSGhl53LCIiIpJ9BXkmh1SpMYaHRxaYx/JXUh1enyy7ENhsNleimCr1dXx8fI4vPnToUObNm8fnn3/OgQMHePbZZzl16hS9e/cGYMKECWmS2UceeQQ/Pz+GDBnCvn37WLZsGe+88w5DhgxRFwIRERGRm8Q1ZyE4evQoO3bscL2+dOkS4OyYHxAQkG7/Ro0auX3xhx56iKioKN544w1Onz5NWFgYCxYsoGJFZ3Z/6tQpjhw54tq/aNGifPPNN4wePZo77riDoKAghg4dytNPP+32NUVERESkcDMuXLiQ6TJWxYoVy7BlM6OBVqllUVFRuR9lIaHRtrlD9ZhzqsOcUx3mDtVjzqkOc4fqMecKUh1m2QI7bdq0vIpDRERERMQtWSawPXr0yKs4RERERETckuUgLhERERGRgkYJrIiIiIgUKkpgRURERKRQUQIrIiIiIoWKElgRERERKVSynAdWRERERKSgUQusiIiIiBQqSmBFREREpFBRAisiIiIihYoSWBEREREpVJTAioiIiEihogRWRERERAoVJbDZMHv2bOrVq0fp0qVp27YtGzduzHTf+Ph4Bg8eTMuWLSlRogQdOnTIw0gLtuzU4/r16+nevTs1atSgTJkytGzZkjlz5uRhtAVTdupw//79PPDAA1SvXp3SpUtTv359XnnlFRITE/Mw4oInO3V4pUOHDlG+fHnKlSvn4QgLh+zUY0REBEFBQem+Vq1alYcRFzzZfS86HA6mT59OkyZNKFWqFDVq1GD8+PF5E2wBlZ06nDx5cobvw6CgIM6ePZuHURc82X0vrl69mnvuuYfy5ctTpUoVunfvzsGDB/MkViWwblq8eDFjx45l1KhRrFu3jqZNm9K1a1eOHz+e4f42mw1fX18GDBhAu3bt8jjagiu79bh161Zq167NZ599xqZNm+jbty//+c9/WLhwYR5HXnBktw69vb3p3r07ixcvZtu2bUyePJk5c+YwceLEPI684MhuHaZKTEykT58+tGzZMo8iLdiutx6//vprDhw44Pq67bbb8ijigud66vD555/no48+Yvz48WzdupUFCxbc1O/J7NbhsGHD0rz/Dhw4QKtWrWjdujUlS5bM4+gLjuzW49GjR+nRowctWrRg3bp1LFmyhPj4eLp27Zon8WohAzfddddd1K5dm/fee89V1rBhQx588EFefvnlLI995pln2LdvH8uXL/d0mAVeTuox1VNPPYXNZrtpW2Jzow6fe+45tm3bxk8//eSpMAu0663DcePGcfHiRVq1asWYMWP4+++/8yLcAiu79RgREUH9+vVZs2YNt956a16GWmBltw7Dw8Np0aIFGzZsoEaNGnkZaoGV05+JJ06coF69esycOTPPkq+CKLv1uHTpUnr37s3Zs2cxm80ArFu3jk6dOnHo0CGCg4M9Gq9aYN2QmJjI7t27ufPOO9OU33nnnWzZsiWfoip8cqseo6OjCQoKyuXoCofcqMPDhw+zevVqWrVq5YkQC7zrrcOVK1eycuVKpkyZ4ukQC4WcvBefeOIJqlWrRvv27Vm6dKknwyzQrqcOV6xYQaVKlVi1ahX169enbt26DBo06KZ99J0bPxPnzJlD0aJF6dSpkydCLBSupx4bNGiAxWLh888/x2azER0dzZdffknDhg09nryCEli3REZGYrPZ0j1aKFmyJGfOnMmnqAqf3KjHH374gbVr1/LUU095IMKCLyd12K5dO0qXLk3Dhg1p3rw5L730kidDLbCupw5PnTrFiBEjmDlzJlarNS/CLPCupx4DAgJ49dVX+eSTT1i4cCG33XYbvXv3Zv78+XkRcoFzPXV49OhRjh8/zuLFi5k+fTozZ84kPDycxx57DLvdnhdhFyg5/b1it9uZO3cujz32GD4+Pp4Ks8C7nnoMDQ3lm2++YfLkyZQqVYqKFSuyb9++PPs8K4HNBsMw0rx2OBzpyuTarrceN2/eTP/+/ZkyZQqNGjXyVHiFwvXU4ccff8zatWuZPXs2P/30E++8844HIyz4slOHAwYMoE+fPjRp0iQvQitUslOPwcHBDBs2jCZNmnDrrbfy/PPP07t3b9599928CLXAyk4d2u12EhISmDlzJq1ataJly5bMnDmTHTt2sHPnzrwIt0C63t8rP/74IydOnKBXr16eCq1QyU49nj59mmHDhvHYY4/x888/89133xEQEMBTTz2VJ39MeXn8CjeA4OBgzGZzur9Czp07d1N3+M6unNTjpk2b6NatG+PGjaNv376eDLNAy0kdli9fHoCaNWtis9kYPnw4w4cPx8vr5voxcD11uG7dOjZs2ODqPuBwOLDb7QQHB/PWW2/dlE8EcuvnYqNGjZg7d25uh1coXE8dli5dGi8vL6pVq+Yqq1q1Kl5eXpw4cYLGjRt7NOaCJqfvw88++4xmzZoRFhbmqRALheupx1mzZuHv788rr7ziKvvwww+pXbs2W7ZsoUWLFh6NWS2wbvD29qZBgwasWbMmTfmaNWto1qxZPkVV+FxvPW7YsIGuXbsyZswYhgwZ4ukwC7Tcei/a7XaSk5Ox2Wy5HWKBdz11uHHjRtavX+/6eu655/Dz82P9+vV07tw5D6IueHLrvbh3715Kly6d2+EVCtdTh82bNyc5OZkjR464yo4ePUpycjIVKlTwaLwFUU7ehydPnuTHH39U6yvXV49xcXGuwVupUl+rBbYAGTp0KAMHDqRRo0Y0a9aMjz/+mFOnTtG7d28AJkyYwI4dO1i2bJnrmP3795OYmEhkZCSXL19mz549ANSrVy9f7qEgyG49rl+/nkcffZS+ffvSrVs3Tp8+DTg/JCVKlMi3+8hP2a3Dr776Cl9fX2rVqoW3tze7du3ilVde4cEHH7xp+3xltw5r1aqV5vhdu3ZhMpnSld9ssluP8+bNw2KxUK9ePUwmEz/88AOzZ8++qecwzW4d3n777dSvX5+hQ4cyefJkwDk7RuPGjW/amR2u5/czwBdffEGRIkXo0qVLfoRd4GS3Htu1a8f06dN5/fXX6dq1K9HR0bz66quUL1+eBg0aeDxeJbBueuihh4iKiuKNN97g9OnThIWFsWDBAipWrAg4B3lc+RcxkG7+tNS5Di9cuJBncRc02a3HefPmERsby9SpU5k6daqrvEKFCuzduzfP4y8IsluHXl5e/N///R+HDx/G4XBQoUIF+vXrd1O3Zl/P51nSu556fPPNNzl+/Dhms5mqVavy/vvv8+ijj+ZH+AVCduvQZDIxf/58nn32WTp06ICvry933HEHkyZNwmS6OR+qXs/70OFwMGfOHLp27Yq/v39+hF3gZLce27Zty+zZs3n33XeZOnUqvr6+NG7cmEWLFlGkSBGPx6t5YEVERESkULk5/1wTERERkUJLCayIiIiIFCpKYEVERESkUFECKyIiIiKFihJYERERESlUlMCKiIiISKGiBFZEJAsREREEBQV5fLnTvLqOiMiNQAmsiNywli1bRlBQEIsWLUq3rWPHjlluCw0NxeG4eabJ7tChA0FBQa6vkJAQWrZsyfTp0697Wch9+/YxefJkIiIicjlaEbnZaSUuEblhtWjRAoBNmzbxyCOPuMqTk5PZsWMHXl5emW5r06YNhmFQsWJFTp06hcVi8WiseXWdrISEhDBhwgQAIiMjWbRoEc899xznzp3jpZdeyvb5/vzzT6ZMmULr1q0JDQ3N7XBF5CamBFZEblglS5akatWqbNq0KU35b7/9RmxsLN26dct0W/PmzQEwDANfX1+Px5pX18mK1WpNs6xrnz59aNKkCbNmzeL555/HbDbnY3QiIv9SFwIRuaG1aNGC/fv3c+HCBVfZ5s2bKVOmDI8++miG21KPg4z7pk6ePJmgoCAOHTrEyJEjqVy5MuXKlePJJ58kKioqzfXr1q3Lww8/zI4dO7j33nsJCQmhdu3aTJ8+Pc1+Ob2Ow+HgzTffpHbt2pQpU4Z27dqxdetWOnToQIcOHa6r7nx9fWnYsCHR0dGcPXvWVf77778zePBgGjRoQOnSpalatSp9+/blxIkTrn3mzp1L3759gX+7a1x9f7t27eLRRx+lYsWKhISEcOedd/LDDz9cV6wicnNRAisiN7TmzZtjt9vZunWrq2zz5s00a9aMJk2aAKTb5uvry6233nrNc/ft25d//vmH559/nl69evHdd98xZsyYdPtFRETw2GOP0axZMyZNmkSlSpV47rnn+Pnnn926B3eu8+qrrzJx4kRq1qzJK6+8QsOGDenWrRv//POPW9fIzLFjxzAMg6JFi7rK1qxZQ3h4ON26deN///sfjz/+OD/99BMdO3YkLi4OgFatWtG/f38ARo0axcyZM5k5cyatWrUC4Ndff+Xee+/lzJkzPPPMM0yYMAFvb2+6d+/OsmXLchSziNz41IVARG5oqS2pmzdvpl27dgBs2bKFkSNHEhgYSM2aNdNtu/XWW/Hx8bnmuW+55RY+/PBD12uHw8GsWbN466230iR8Bw8eZMmSJdx+++0APP7449SpU4fPPvuMO++8M8fXOXv2LFOnTqVdu3bMnz8fwzAAqFWrFsOHD6ds2bLXvAaAzWYjMjISgKioKObMmcOuXbu4//778fPzc+3Xt29fhg0blubYe++9l/vuu49vv/2Wbt26UalSJZo3b86sWbO4/fbbadOmTZr4R44cSdOmTVm6dCkmk7MtpX///rRv356XXnqJTp06uRWziNyc1AIrIje0qlWrUrp0aVdf10OHDnHmzBlXH9fmzZun29ayZUu3zp36iDxVq1atsNlsaR6lp8aQmrwC+Pj40LhxY44ePZor1/nll19ISkqiX79+ruQVoEePHmkS6Ws5fPgwVatWpWrVqjRp0oT33nuPTp06pevu4O/v7/p/TEwMUVFR3HLLLRQtWpTdu3df8zp79+51teCeP3+eyMhIIiMjOX/+PHfffTdHjx7l2LFjbsctIjcftcCKyA2vWbNm/PjjjyQmJrJ582b8/f2pW7eua9u8efNc2wBXcnstFSpUSPM6KCgIgPPnz2e5X+q+f/zxR65c5/jx44AzUb6Sl5dXtkb/ly9fnvfffx+73c7hw4f5v//7vwxnRrhw4QLjx49n6dKl6e714sWL17zOoUOHABg2bFi6ltxU586do2LFim7HLiI3FyWwInLDa968OcuWLWPXrl1s3ryZRo0a4eXl/PHXrFkz4uPjXdtMJhNNmzZ167yZjcq/ev5Yd/fL6XVycg0APz8/V0vxnXfeSYsWLWjbti2vvPIKU6ZMce3Xp08fNm7cyNNPP029evWwWq0YhkGfPn3cmjM2dZ/x48fToEGDDPepVq2a23GLyM1HCayI3PBSuwRs3ryZzZs307lzZ9e2SpUqERIS4tpWu3btbD12LwhSW2gPHTqUphU2OTmZY8eOUadOnes6b+3atenevTsff/wxQ4cOpWLFily4cIGff/6ZsWPHMnbsWNe+8fHxaWZzANJ0Z7hS5cqVAQgICEjTtUJExF3qAysiN7y6desSEBDA8uXLCQ8PT9dFoFmzZpluKwxuv/12vLy8mD17dpoW13nz5rn1SD8rw4cPJzk5malTpwK4Blxd3bKb0YpdqX1lr05sGzRoQNWqVZk6dWqG8Z07dy5HMYvIjU8tsCJywzObzTRu3JhffvkFk8lE48aN02xv1qwZzz33HIDbA7gKkpIlS/L000/zzjvv8Mgjj3Dvvfdy+PBhvvrqKypXrpxpS6g7qlevTvv27fniiy8YM2YMJUuWpHXr1rz33nskJSVRoUIFNm3axMaNGylevHiaY+vXr4/JZOLtt9/m4sWL+Pn50ahRIypVqsT777/Pww8/TPPmzenZs6drJbJt27Zx/PhxV39kEZGMqAVWRG4KqdNphYWFpesicGWra2FsgQV46aWXeO655/jzzz958cUX2bFjBwsWLKBo0aI5XuFr2LBhxMXFuWYjmD17Nu3bt+eTTz7hpZde4uLFiyxbtowiRYqkOa5MmTK88847XLhwgREjRtC3b182bNgAOL8fq1evpnnz5nz66aeMHj2azz77DJPJxLhx43IUr4jc+IwLFy6438NfREQKDZvNRrVq1ejYsSPvvfdefocjIpJr1AIrInIDSF0B60pz587l/Pnz3HbbbfkQkYiI56gPrIjIDWDx4sV89tlntG/fnmLFirFr1y7mzp1LnTp1tKqViNxwlMCKiNwAateujb+/P9OnT+fixYuUKFGCXr168eKLL+Lt7Z3f4YmI5Cr1gRURERGRQkV9YEVERESkUFECKyIiIiKFihJYERERESlUlMCKiIiISKGiBFZERERECpX/B/LQtjcaCV5vAAAAAElFTkSuQmCC\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 6))\n", "ax.scatter(win_rate, win_less)\n", "txt = \"This point means that if the winning rate is 40%,\\n then the probability of winning less\\n than 6 trades is 25%.\"\n", "ax.annotate(\n", " txt,\n", " xy=(df.iloc[6][0], df.iloc[6][1]),\n", " xytext=(0.35, 0.5),\n", " weight=\"bold\",\n", " color=\"r\",\n", " size=14,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\", color=\"b\"),\n", ")\n", "ax.set_xlabel(\"Winning Rate\")\n", "ax.set_ylabel(\"Probabilit of winning Less than 6 trades\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Binomial Random Variable Generator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Scipy library, every distribution has a random variable generator named ```.rvs```, we set parameters, the generator will return the randomly generated numbers." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "n = 100\n", "p = 0.3\n", "bino = sp.stats.binom.rvs(n, p, size=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red vertical line in the graph below is the mean, because binomial distribution is a symmetric distribution, thus the mean should theoretically have the highest draw as well." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "txt = \"This line is the $y =p \\cdot n$ \\n and where theoretical highest draw should be.\"\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(bino, bins=160)\n", "ax.axvline(p * n, color=\"r\", ls=\"--\", lw=3)\n", "ax.annotate(\n", " txt,\n", " xy=(p * n, h.max() * 0.4),\n", " xytext=(p * n, h.max() * 0.7),\n", " weight=\"bold\",\n", " color=\"r\",\n", " size=14,\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\", color=\"b\"),\n", ")\n", "ax.set_title(\"Generated Binomial R.V.s\", size=18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But how to interpret the histogram? \n", "\n", "A concrete example: you are trying to shoot basketball into the basket, your chances of success is $30\\%$, what each day you can shoot $100$ rounds, but in the long run, you are mostly like to have $30$ successes each day, and it would be extremely unlikely that you would land a $50$-success." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Moments of Binomial Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To return moments, use ```.stats``` functions with moments = `msvk`, it is short for _mean_, _skewness_, _variance_ and _kurtosis_." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------+------------+------------+-----------+\n", "| mean | variance | skewness | kurtosis |\n", "+======+============+============+===========+\n", "| 30 | 21 | 0.087 | -0.012 |\n", "+------+------------+------------+-----------+\n" ] } ], "source": [ "n = 100\n", "p = 0.3\n", "bino_stats = sp.stats.binom.stats(n, p, moments=\"mvsk\")\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [\n", " [\"mean\", \" variance \", \" skewness \", \"kurtosis \"],\n", " [bino_stats[0], bino_stats[1], bino_stats[2], bino_stats[3]],\n", " ]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When $n\\rightarrow\\infty$ and $p\\rightarrow0$,a binomial distribution approaches a **Poisson distribution** asymptotically, i.e. when $n$ is large and $p$ is small, we can use Poisson to approximate Binomial.\n", "\n", "Again with trader's example, if a trader has $1/1000$ probability to encounter a 'wiped-out' in each trade (assume each trade is independent, actually not), and trades $20$ times per month, what is the probability that the trader will encounter twice 'wiped-out' within 5 years?\n", "\n", "This problem can be solved by Binomial, the formulation as below\n", "\n", "$$\n", "\\text{trades} = 20\\times 12\\times 5=1200\\\\\n", "P(x=2) = \\binom{1200}{2}\\Big(\\frac{1}{1000}\\Big)^2\\Big(\\frac{999}{1000}\\Big)^{1198}\n", "$$" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.2169828095260339" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.special.comb(1200, 2) * 1 / 1000**2 * (999 / 1000) ** 1198" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The result tells that if a trader keep a frequency of $20$ trades per month, there $21\\%$ possibility that he/she gets wiped out twice in next $5$ years." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we mentioned, Poisson is the limit version of Binomial, it is a suitable case to use, calculate $\\lambda$\n", "\n", "\\begin{equation}\n", "\\lambda = np = 1200 \\times \\frac{1}{1000} = 1.2\n", "\\end{equation}\n", "\n", "it means every 5 years, there is in average 1.2 times of chance to get wiped out.\n", "\n", "\\begin{equation}\n", "P(x=2)=\\frac{\\lambda^ke^{-\\lambda}}{k!}=\\frac{1.2^2e^{-1.2}}{2!}\n", "\\end{equation}\n", "\n", "\n", "Formulate in Python" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of having 2 wiped-out shock(s) in a span of 5 years is 21.69%.\n" ] } ], "source": [ "k = 2\n", "n = 20 * 12 * 5 # 20 times per month, and 5 years span\n", "p = 1 / 1000\n", "lambdaP = p * n # lambda in Poisson\n", "p = sp.stats.poisson.pmf(k, lambdaP)\n", "print(\n", " \"The probability of having {0} wiped-out shock(s) in a span of 5 years is {1:.2f}%.\".format(\n", " k, p * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You probably have notices that Binomial and Poisson provide the same answer.\n", "\n", "Similarly what's the probability of having more than $k$ times wiped-out?" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of having more than 2 BS shock in 5 years is 12.051%.\n" ] } ], "source": [ "k = 2\n", "prob = 1 - sp.stats.poisson.cdf(k, lambdaP)\n", "print(\n", " \"The probability of having more than %1.0f BS shock in 5 years is %3.3f%%.\"\n", " % (k, prob * 100)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Poisson Random Variable Generator" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use the parameters $\\lambda = 1.2$, we generate a frequency distribution with ```sp.stats.poisson.rvs``` function." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lambdaP = 1.2\n", "poisson = sp.stats.poisson.rvs(lambdaP, size=1000)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(poisson, bins=10)\n", "ax.set_title(\"Generated Poisson R.V. Distribution\", size=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Moments of Poisson Distribution" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+------------+------------+-----------+\n", "| mean | variance | skewness | kurtosis |\n", "+=======+============+============+===========+\n", "| 1.200 | 1.200 | 0.913 | 0.833 |\n", "+-------+------------+------------+-----------+\n" ] } ], "source": [ "lambdaP = 1.2\n", "poiss_stats = sp.stats.poisson.stats(\n", " lambdaP, moments=\"mvsk\"\n", ") # mean, variance, skewness, kurtosis\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [\n", " [\"mean\", \" variance \", \" skewness \", \"kurtosis \"],\n", " [poiss_stats[0], poiss_stats[1], poiss_stats[2], poiss_stats[3]],\n", " ]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geometric Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PMF of **Geometric Distribution** is \n", "$$\n", "f(k)=p(1-p)^k\n", "$$\n", "\n", "where $k \\in \\mathbb{Z}^+$ is a number of failures before first success, and $p$ is the probability of success.\n", "\n", "Geometric Distribution is to model the solutions to questions: '_How many times you have to fail in order to embrace the initial success?_'\n", "\n", "If you are shooting basketball to the basket, your success rate is $30\\%$, what's the probability of first success after $k$ times of trials?" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of observing exact 5 times of failures trials before first success is 5.04%.\n" ] } ], "source": [ "k = 5\n", "p = 0.3\n", "\n", "geo_dist = (1 - p) ** k * p\n", "print(\n", " \"The probability of observing exact {} times of failures trials before first success is {:.2f}%.\".format(\n", " k, geo_dist * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "```sp.stats.geom.pmf``` function will do the same trick." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.07202999999999998" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.geom.pmf(k, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, you have noticed the same parameters didn't produce the same result. That's because Scipy has a slightly different definition of parameter, $k$ in Scipy means the total number of trials, therefore $k+1$ would work the same." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.05042099999999998" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.stats.geom.pmf(k + 1, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, CDF could answer the a question: _What's the probability of observing $k$ or less than $k$ times of failure before the first success?_" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of observing 5 or fewer than 5 times of failure before a first success is 88.235%.\n" ] } ], "source": [ "geom_cdf = sp.stats.geom.cdf(k + 1, p)\n", "print(\n", " \"The probability of observing %1.0f or fewer than %1.0f times of failure before a first success is %3.3f%%.\"\n", " % (k, k, geom_cdf * 100)\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Geometric Distribution Moments and Generator" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+---+-------+------------+------------+------------+\n", "| p | k | mean | variance | skewness | kurtosis |\n", "+=======+===+=======+============+============+============+\n", "| 0.300 | 5 | 3.333 | 7.778 | 2.032 | 6.129 |\n", "+-------+---+-------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.geom.stats(p, moments=\"mvsk\")\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [\n", " [\"p\", \"k\", \"mean\", \" variance \", \" skewness \", \" kurtosis \"],\n", " [p, k, mean, var, skew, kurt],\n", " ]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "geometric = sp.stats.geom.rvs(p, size=10000)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(geometric, bins=30)\n", "ax.set_title(\"Generated Geometric R.V. Distribution\", size=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hypergeometric Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The main difference between hypergeometric and binomial is that the former's sampling is not independent of each other, i.e. the sampling is **without replacement**. \n", "\n", "The PMF of hypergeometric is \n", "\n", "$$\n", "f(x) =\\frac{{K\\choose k} {N-K \\choose n-k}}{{N\\choose n}} \n", "$$\n", "\n", "Read the PMF with this example: $100$ people live in a building, $20$ of them are stashing drugs, $80$ are clean, but we don't have information who is clean or not. In one field operation, police took away $5$ persons form the building, what is the probability of having exact $2$ persons .are drug stasher?\n", "\n", "Solution:\n", "$$\n", "\\frac{{20\\choose2}{80\\choose3}}{{100\\choose5}}\n", "$$\n", "To solve it:" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability of getting 2 drug stashers by taking 5 persons away is 20.73%.\n" ] } ], "source": [ "k = 2\n", "n = 5\n", "K = 20\n", "N = 100\n", "hyper_geo = (\n", " sp.special.comb(K, k) * sp.special.comb(N - K, n - k) / sp.special.comb(N, n)\n", ")\n", "print(\n", " \"The probability of getting {} drug stashers by taking {} persons away is {:.2f}%.\".format(\n", " k, n, hyper_geo * 100\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or use SciPy function" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.20734379349990603" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# pmf(x, M, N, n, loc=0)\n", "hgeo = sp.stats.hypergeom.pmf(\n", " k, N, K, n, loc=0\n", ") # the argurment order the same as MATLAB, quite confusing\n", "hgeo" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A histogram would provide some intuitions of geometric distribution." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "hgeo_rv = sp.stats.hypergeom.rvs(100, 20, 5, size=10000)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(hgeo_rv, density=True)\n", "ax.set_title(\"Generated Hypergeometric R.V. Distribution\", size=16)\n", "s = \"\"\" It can be interpreted as: if 100 persons in the building, \n", " 20 are drug stasher, take 5 out of 100.\n", " \n", " The probability of getting from 1 to 5 drug stashers, \n", " is shown in the chart.\n", " \n", " As we can see it is nearly impossible \n", " to get 4 or 5 drugs stasher. \n", " But getting one is the most possible outcome.\"\"\"\n", "\n", "ax.text(1.6, 0.5, s, fontsize=14, color=\"red\")\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-----+---+------+------------+------------+------------+\n", "| N | k | mean | variance | skewness | kurtosis |\n", "+=====+===+======+============+============+============+\n", "| 100 | 2 | 1 | 0.768 | 0.629 | -0.010 |\n", "+-----+---+------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.hypergeom.stats(N, K, n, moments=\"mvsk\")\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [\n", " [\"N\", \"k\", \"mean\", \" variance \", \" skewness \", \" kurtosis \"],\n", " [N, k, mean, var, skew, kurt],\n", " ]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discrete Uniform Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Rolling a die is the simplest **discrete uniform distribution** generator from $1$ to $6$." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "unif_d = sp.stats.randint.rvs(low=0, high=6, size=1000)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(unif_d, bins=6, ec=\"k\")\n", "ax.set_title(\"Discrete Uniform Frequency Distribution\", size=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discrete Probability Mass Function" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.arange(0, 8)\n", "l, h = 1, 7\n", "unif_pmf = sp.stats.randint.pmf(x, low=l, high=h)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "ax.scatter(\n", " x, unif_pmf, s=100, color=\"green\", label=\"Low = {}, High = {}\".format(l, h - 1)\n", ")\n", "ax.plot(x, unif_pmf, lw=3, color=\"k\")\n", "ax.legend(fontsize=18, loc=\"center\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Continuous Uniform Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDF of *Continuous uniform distribution** is \n", "\n", "\\begin{equation}\n", "f(x)=\\frac{1}{b-a}\n", "\\end{equation}\n", "\n", "And its r.v. generator is one of the most commonly used function in NumPy." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "unif = np.random.rand(10000)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(unif, density=True, bins=30)\n", "ax.set_title(\"Continous Uniform Frequency Distribution\", size=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CDF and PDF of Continuous Uniform Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The CDF and PDF of uniform distribution are ```sp.stats.uniform.cdf``` and ```sp.stats.uniform.pdf``` accordingly." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# pdf(x, loc=0, scale=1)\n", "# cdf(x, loc=0, scale=1)\n", "x = np.linspace(-0.2, 1.2, 100)\n", "unif_pdf = sp.stats.uniform.pdf(x)\n", "unif_cdf = sp.stats.uniform.cdf(x)\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 6))\n", "ax[0].plot(x, unif_pdf, lw=4, label=\"PDF of Continous Uniform Distribution\")\n", "ax[0].set_xlim([-0.1, 1.1])\n", "ax[0].set_ylim([0, 2])\n", "ax[0].legend(fontsize=16)\n", "\n", "ax[1].plot(x, unif_cdf, lw=4, label=\"CDF of Continous Uniform Distribution\")\n", "ax[1].set_xlim([-0.2, 1.2])\n", "ax[1].set_ylim([0, 2])\n", "ax[1].legend(fontsize=16)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+-------+------------+------------+------------+\n", "| mean | variance | skewness | kurtosis |\n", "+=======+============+============+============+\n", "| 0.500 | 0.083 | 0 | -1.200 |\n", "+-------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.uniform.stats(moments=\"mvsk\")\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [[\"mean\", \" variance \", \" skewness \", \" kurtosis \"], [mean, var, skew, kurt]]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **normal distribution** is the king of all distributions, there are extensive discussions in my Linear Algbra Notes. The PDF of Normal distribution is\n", "$$\n", "f(x)=\\frac{1}{\\sigma \\sqrt{2 \\pi}} e^{-\\frac{1}{2}\\left(\\frac{x-\\mu}{\\sigma}\\right)^{2}}\n", "$$\n", "Below are the plots of CDF and PDF." ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu = 2\n", "sigma = 1\n", "x = np.arange(-2, 6, 0.1)\n", "norm_pdf = sp.stats.norm.pdf(x, mu, sigma)\n", "norm_cdf = sp.stats.norm.cdf(x, mu, sigma)\n", "\n", "fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 6))\n", "ax[0].plot(x, norm_pdf, lw=4, label=\"PDF of Normal Distribution\", ls=\"--\")\n", "ax[0].legend(fontsize=16, loc=\"lower left\", framealpha=0.2)\n", "\n", "ax[1].plot(x, norm_cdf, lw=4, label=\"CDF of Normal Distribution\")\n", "ax[1].legend(fontsize=16, fancybox=True, framealpha=0.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Inverse Normal CDF" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is a useful plot that you might have known by heart. The light blue area cover $95\\%$ of area under the bell curve, darker blue area on either side covers $2.5\\%$ respectively. If we want to search the point where $2.5\\%$ area is on its left, we simply need a inverse function of CDF, in SciPy ```.ppf``` (point percentage function) can provide us the location of any percentage that we specify." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_95_r = sp.stats.norm.ppf(\n", " 0.975\n", ") # ppf mean point percentage function, actually inverse CDF\n", "norm_95_l = sp.stats.norm.ppf(0.025)\n", "\n", "x = np.linspace(-5, 5, 200)\n", "y = sp.stats.norm.pdf(x)\n", "\n", "xl = np.linspace(-5, norm_95_l, 100)\n", "yl = sp.stats.norm.pdf(xl)\n", "xr = np.linspace(norm_95_r, 5, 100)\n", "yr = sp.stats.norm.pdf(xr)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "ax.plot(x, y, lw=4, label=\"PDF of Normal Distribution\", ls=\"-\", color=\"#CC4845\")\n", "ax.set_ylim([0, 0.45])\n", "\n", "ax.fill_between(x, y, 0, alpha=0.6, color=\"#2E86C3\")\n", "ax.fill_between(xl, yl, 0, alpha=0.9, color=\"#2E86C3\")\n", "ax.fill_between(xr, yr, 0, alpha=0.9, color=\"#2E86C3\")\n", "\n", "ax.text(-0.2, 0.15, \"95%\", fontsize=20)\n", "ax.text(-2.3, 0.015, \"2.5%\", fontsize=12, color=\"white\")\n", "ax.text(2.01, 0.015, \"2.5%\", fontsize=12, color=\"white\")\n", "\n", "ax.annotate(\n", " \"±%.4f\" % norm_95_r,\n", " xy=(norm_95_r, 0),\n", " xytext=(-0.4, 0.05),\n", " weight=\"bold\",\n", " color=\"#CC4845\",\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\", color=\"#757516\"),\n", " fontsize=16,\n", ")\n", "ax.annotate(\n", " \"±%.4f\" % norm_95_r,\n", " xy=(norm_95_l, 0),\n", " xytext=(-0.4, 0.05),\n", " weight=\"bold\",\n", " color=\"#CC4845\",\n", " arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3\", color=\"#757516\"),\n", " fontsize=16,\n", ")\n", "\n", "ax.set_title(\"Normal Distribution And 2.5% Shaded Area\", size=20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Normal Random Variable Generator" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# rvs(loc=0, scale=1, size=1, random_state=None)\n", "norm_rv = sp.stats.norm.rvs(mu, sigma, size=5000)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "h, bins, patches = ax.hist(norm_rv, density=True, bins=50)\n", "ax.set_title(\"Normal Frequency Distribution\", size=16)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "+------+------------+------------+------------+\n", "| mean | variance | skewness | kurtosis |\n", "+======+============+============+============+\n", "| 2 | 1 | 0 | 0 |\n", "+------+------------+------------+------------+\n" ] } ], "source": [ "mean, var, skew, kurt = sp.stats.norm.stats(mu, sigma, moments=\"mvsk\")\n", "table = Texttable()\n", "table.set_cols_align([\"c\", \"c\", \"c\", \"c\"])\n", "table.set_cols_valign([\"m\", \"m\", \"m\", \"m\"])\n", "table.add_rows(\n", " [[\"mean\", \" variance \", \" skewness \", \" kurtosis \"], [mean, var, skew, kurt]]\n", ")\n", "print(table.draw())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bivariate Normal Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The most prevalent _multivariate normal distribution_ is **bivariate normal distribution**\n", "\n", "\\begin{equation}\n", "f_\\boldsymbol{X}(x_1,x_2)=\\frac{1}{\\sqrt{(2\\pi)^2|\\Sigma|}}\\exp{\\Big(-\\frac{(X-\\mu)^T\\Sigma^{-1}(X-\\mu)}{2}\\Big)}\n", "\\end{equation}\n", "\n", "
    " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are two ways of formulating a multivariate normal distribution in Python, use any one you see fit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1st Method of Plotting Formulation" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu_x = 0\n", "sigma_x = 2\n", "\n", "mu_y = 0\n", "sigma_y = 2\n", "\n", "# Create grid and multivariate normal\n", "x = np.linspace(-10, 10, 500)\n", "y = np.linspace(-10, 10, 500)\n", "X, Y = np.meshgrid(x, y)\n", "pos = np.empty(X.shape + (2,))\n", "pos[:, :, 0] = X\n", "pos[:, :, 1] = Y # more technical than next one\n", "norm = sp.stats.multivariate_normal(\n", " [mu_x, mu_y], [[sigma_x, 0], [0, sigma_y]]\n", ") # frozen\n", "\n", "# Make a 3D plot\n", "fig, ax = plt.subplots(figsize=(7, 7), subplot_kw={\"projection\": \"3d\"})\n", "ax.plot_surface(X, Y, norm.pdf(pos), cmap=\"viridis\", linewidth=0)\n", "ax.set_xlabel(\"X axis\")\n", "ax.set_ylabel(\"Y axis\")\n", "ax.set_zlabel(\"Z axis\")\n", "ax.set_title(\"Bivariate Normal Distribution\", size=22, y=1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2st Method of Plotting Formulation" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parameters to set\n", "mu_x = 0\n", "sigma_x = 7\n", "\n", "mu_y = 0\n", "sigma_y = 15\n", "\n", "x = np.linspace(-10, 10, 500)\n", "y = np.linspace(-10, 10, 500)\n", "X, Y = np.meshgrid(x, y)\n", "\n", "position = np.array([X.flatten(), Y.flatten()]).T # more intuitive than former one\n", "\n", "binormal_obj = sp.stats.multivariate_normal([mu_x, mu_y], [[sigma_x, 0], [0, sigma_y]])\n", "\n", "fig, ax = plt.subplots(figsize=(7, 7))\n", "ax.contourf(X, Y, binormal_obj.pdf(position).reshape(500, 500), cmap=\"viridis\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beta Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDF of **Beta distribution** is \n", "\n", "\\begin{equation}\n", "f(x, a, b)=\\frac{\\Gamma(a+b) x^{a-1}(1-x)^{b-1}}{\\Gamma(a) \\Gamma(b)}\n", "\\end{equation}\n", "\n", "where $0\\leq x \\leq 1$ and $a>0$, $b>0$, $\\Gamma$ is the Gamma function, and $a$ and $b$ decide the shape of Beta PDF." ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "\n", "fig = plt.figure(figsize=(7, 7))\n", "ax = fig.add_subplot(111)\n", "\n", "a = [0.5, 5, 1, 2, 2, 3, 1] # these are values of parameter a\n", "b = [0.5, 1, 5, 2, 3, 2, 1]\n", "\n", "for parameter in zip(a, b):\n", " beta_pdf = sp.stats.beta.pdf(x, parameter[0], parameter[1])\n", " ax.plot(\n", " x, beta_pdf, lw=3, label=\"$a = %.1f, b = %.1f$\" % (parameter[0], parameter[1])\n", " )\n", " ax.legend()\n", "\n", "ax.set_title(\"PDF of Beta Distribution\", size=20)\n", "ax.axis([0, 1, 0, 3])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 1, 100)\n", "\n", "fig = plt.figure(figsize=(7, 7))\n", "ax = fig.add_subplot(111)\n", "\n", "a = [0.5, 5, 1, 2, 2, 3, 1] # these are values of parameter a\n", "b = [0.5, 1, 5, 2, 3, 2, 1]\n", "\n", "for parameter in zip(a, b):\n", " beta_pdf = sp.stats.beta.cdf(x, parameter[0], parameter[1])\n", " ax.plot(\n", " x, beta_pdf, lw=3, label=\"$a = %.1f, b = %.1f$\" % (parameter[0], parameter[1])\n", " )\n", " ax.legend()\n", "ax.set_title(\"CDF of Beta Distribution\", size=20)\n", "ax.axis([0, 1, 0, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Beta distribution is mostly useful as **prior distribution** in Bayesian estimation, because it is bounded in $[0, 1]$, that is perfect for modeling the _probability distribution of probabilities_. In Bayesian estimation, we only care about the proportion between prior and posterior, by adjusting $a$ and $b$ we can use Beta distribution to express any kinds of prior beliefs including normal, uniform, exponential distribution and etc.\n", "\n", "\\begin{equation}\n", "f(x, a, b)\\propto x^{a-1}(1-x)^{b-1}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\chi^2$ Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\chi^2$ distribution is closely connected with normal distributions, if $z$ has the standard normal distribution, then $z^2$ has the $\\chi^2$ distribution with $d.f.=1$. And further,if\n", "\n", "\\begin{equation}\n", "z_1, z_2, ..., z_k \\sim i.i.d. N(0, 1)\n", "\\end{equation}\n", "\n", "Then summation has a $\\chi^2$ distribution of $d.f. = k$:\n", "\n", "\\begin{equation}\n", "\\sum_{i=0}^k z_i^2 \\sim \\chi^2(k)\n", "\\end{equation}\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will see in later chapters how $\\chi^2$ distribution is referred when performing hypothesis testing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### $\\chi^2$ PDF and CDF " ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "k = 1\n", "x = np.linspace(0, 5, 100)\n", "chi_pdf = sp.stats.chi2.pdf(x, k)\n", "\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "ax.plot(x, chi_pdf, lw=3, c=\"r\", label=\"$\\chi^2$ distribution with d.f. = 1\")\n", "ax.legend(fontsize=18)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(10, 6))\n", "for i in range(1, 6):\n", " x = np.linspace(0, 5, 100)\n", " chi_pdf = sp.stats.chi2.pdf(x, i)\n", " ax.plot(x, chi_pdf, lw=3, label=\"$\\chi^2$ distribution with d.f. = %.0d\" % i)\n", " ax.legend(fontsize=12)\n", " ax.axis([0, 5, 0, 1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## F Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $U_1$ has a $\\chi^2$ distribution with $\\nu_1$ d.f. and $U_2$ has a $\\chi^2$ distribution with $\\nu_2$ d.f., then\n", "\n", "\\begin{equation}\n", "\\frac{U_1/\\nu_1}{U_2/\\nu_2}\\sim F(\\nu_1, \\nu_2)\n", "\\end{equation}\n", "\n", "We are using $F$ distribution for ratios of variances." ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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3kfge4+Pjad++fZ2vC3kxkKIoAW1VVascO+Ho0aNMmTKFP/zhD/zwww988cUXxMbGctNNN+H1euvcSRFZe3O2UWovAiA2KoFOaT2buEeabu36kpbUAQCX28nyzd/UcoUQQojmpF+/fsyYMUNvL1u2jFGjRtGmTRsSExMbZTrdhx9+SGJiYpX/qpv+V1cnv0do/Pe5e/du7rnnHoYNG0ZycjJXXnlltedu27aNyy67jNatW9OjRw+eeuopPB5PxPpWa0YzJSUFo9FYJXt5/PjxKlnOE95++22io6N58skn9WP/+Mc/yMzMZOXKlZx99tkN7LYIJ//V5r3Tz8JgaB5VrxRF4by+l/GfH/8OwMpt33Fu7980ahF5IYQQ9VNcXMy+ffvo3bs3oE3FGz9+PKNHj2b69OlYrdYap9OF2/z584mKitLb6enpDb7nye8RmuZ9bt26lYULFzJo0CBcLle15xUWFnLFFVfQvXt35syZw549e3jsscdQVZXHHnssIn2rNdC0WCz069ePRYsWccUVV+jHFy1axGWXXRb0moqKCoxGY8CxE23JaDYvHq+bLfvW6O3G2ts8VL06DiQ1oQ25RYdxuOz8unMp52Re1NTdEkIIUYuNGzeiqqoehC1dupS8vDymT59Oy5YtG70/AwYMIDY2Nqz3PPk9QtO8z7Fjx3LJJZcAMH78eHJzc4OeN2vWLCoqKpg9ezbx8fGMHDmSkpISZsyYwd133018fHzQ6xoipNTV5MmTmTNnDu+//z7bt2/nwQcfJCcnh4kTJwIwbdq0gKDzwgsvZP369cyYMYNdu3axbt06Jk+eTLt27ejXr1/Y34Sov8N5+7A7ywGIj06mXWqXJu5RIINi4OxeF+rtldu+x6vKP1aEEKI5KS4u5t577yU9PZ3OnTvz8ssvs2HDBuLj40lPT+fiiy/mqquuAqBbt24kJiZy5MiRJu513dT2HoEme5+hjkQuXLiQ0aNHBwSUV111FRUVFSxbtiwifas1o3miE/n5+Tz33HMcPXqUnj178vHHH9OhgzZ/Licnhz17fKuUzzvvPN555x1efvllXn31VWw2G4MGDWLu3LnExMiwZ3Oy7+h2/XWn1j2qnXfblPp2Podv13yM3VVOfslRdh3aREa7rKbulhBCCLSh4nHjxlFaWsqLL76oT52rqKggMzMTgJkzZ/LEE09gt9t58sknURSF1q1bh3R/VVVDmkNoMtUc0vTv35/8/Hw6derE5MmT9WRZKEJ5j9A83mdNsrOzGTFiRMCx9u3bEx0dTXZ2NmPHjq33vasTcm9vueUWbrnllqA/e+ONN6ocGzduHOPGjat/z0Sj2OsXaKa36t6EPamexWxlQMZwlm/RFgOt2PadBJpCiNOW5ZN/Yfn0vUZ/rvOKCdjHXlvn61566SV27tzJ2rVrSU5OBiAhIYGxY8dywQUXAJCVlUVubi6jR49m8ODBdbr/nDlzmDx5cq3nFRYWBj2elpbGo48+ysCBA/F4PMydO5d7772X8vLykO4Lob1HaNr3GYrCwkISEhKqHE9MTGzQfWtS/7BYnPK8qpd9R31ljTo200AT4Kweo/VAM/vgBvKLjzZxj4QQQng8Ht566y0mTZqkB2AAnTp1AqBPH23zD7fbzY4dO7j77rv1c+677z6++uorjhw5UmOQM3bsWBYtWlTvPo4ePZrRo0fr7TFjxuB0Onn++ee58847ax12DvU9QtX3efDgQe666y5ycnIwGAxceOGFTJs2LejoYUPfZ6iCPbumSkINJYHmGexYwUF9fmaMLZ4W8WlN3KPqpcS3IqNtFtmHNqCismr7D3RJHNTU3RJCiDPa5s2byc/PZ+TIkQHH9+/fD/iCsB07duB0OgOGmceNG8dDDz1Et27danxGUlJS2BepXH755XzyySfs37+/1tXnob5HqPo+TSYT06ZNo3///jidTq644grmz5/P5ZdfXuU5kXifJ0tMTKSoqKjK8eLi4qCZznCQQPMM5p/NTG/VvVnOz/Q3tOcFZB/aAMDa7MV0HNC3iXskhBDh57xyIs4rQ58/GFZ13E3m6FFtdKldu3YBx7///nuMRiM9evQAtGDNbDYHBJXDhg0L6RmNMaRck1DfI1R9n2lpaaSlaUkci8VCZmYmhw4dCvqcxnifGRkZVXbwOnjwIGVlZRHbcEECzTNYwPzMtOY7bH5C17Z9SIpLpaAkF7uznD25m+jZo1dTd0sIIc5YJ4aSd+/eTceOHQHIz8/n7bffJiMjQ69buWnTJjIyMjCbzXV+RiSGlOfPn09KSoq+qLkmob5HqPl95ufns2DBAubNmxf0OY0xdD5mzBheeeUVSkpKiIuLA+CTTz4hKioq5MC/riTQPEOpqhoQaHZsWfPQRXNgUAwM6XEBX6/+CIBtOWsYq17T7DOxQghxuurduzdt27blwQcfZOrUqbhcLmbOnEl5eXlAbcnNmzcHtOsiOTk5YG5kXd14440MHDiQzMxMPB4P8+bNY968eTz77LP6/MwlS5Zw6aWX8vnnnzN8+PB6vUeo/n06HA7Gjx/PHXfcQffuwRM7DXmf5eXlLFy4EIAjR45QVFTEZ599BmjBZXR0NAA333wzb731FjfeeCP33HMPe/fuZcaMGUyePDliw/bNYwsY0ejyS45SWqHN07CZo2mVVPf9S5vCgK7DMZssABSUHWX/sexarhBCCBEpVquV9957D4vFwsSJE5k+fTq33XYbycnJVQJN//mZjSkjI4MPPviA8ePHc9NNN7F9+3befPNNbr/9dv2ciooKgKA7Hob6HiH4+/R4PNx6661kZWUxZcqUCLxDyM3NZcKECUyYMIHVq1ezY8cOve1fvD0xMZHPPvsMj8fDH/7wB5555hnuvPNOHn744Yj0C0ApLCxUI3b3Zio7OzticxFOFWuzF/Ppsn8C2p7iN15wXxP3KHSfLf8Xa3b8CGhbZv7+/NDKU4jmSf48nh7ke6y7oqKiiC3AqC+73Y7NZmvUZ0aytE6onn76aZYvX84XX3wR9ntPmTIFj8fDa6+91mgjcJH4Huv7+yoZzTPUvpzmXz+zOkN6+MpUbNm3luKy/CbsjRBCiPqYMmUKvXpp8+x79eoVsWxfKFatWhVyTc26WLFiBbNnz2bdunUMHz6cc889lzfffDPsz2nOZI7mGSpgfmaQQLPA4eVf28vYVeyma7yJPslm+iSbaRVtrHJuY0tL7kB6q+7sPbodr+ph9Y4fGd3/qqbulhBCiDp49dVXm7oLuk8//TQi9x06dGiTZ2ubmgSaZ6CisnwKSrU5G2ajhTYp6frPCh1eXttcyltbSil2VZ1VkWoz0CfZzPltrNzWMxabqWkW4gzpeYEeLK/Z8SPn970Mo0F+nYUQQojmRP5mPgP572/evmVXTEYThQ4vr28p5c3NwQPME3LtXn447OCHww7m7q5g1vlJdE2oe7mKhurZYQBR5lgqXKWUVhSx4+AGenYY0Oj9EEIIIUT1ZI7mGShw2Lwb7+8oI2tuDjPXlQQEmd0STEwdGM+kHjGclWoh5qTs5YZ8F+fPz+U/u8obre8nGA0murTy7Xe+dsdPjd4HIYQQQtRMMppnIP9AM8/QibuXFQb8PCPBxAN947iqUxRGgy+49Koqe4o9LNhfwV9/KcbphVK3yu2LC1h8xMHMIQnEmBvv3y5dW/Zj08HlAOw4tJ7isnziY+pfa00IIYQQ4SUZzTNMmb2E3MLDABgUI49uTNJ/1jnOyD9GJLHiipZc0yU6IMjUzlfokmBiSp84Fv42lS7xvoVBH2aXM+rzXDbnuxrnjQDxUcl0StO2/lJVlV93LWu0ZwshhBCidhJonmH89zcvNrbjmFNLaqdFGfjmklR+FyTADKZvioUfL2vJ77r4tt7aXuTmoi9z2ZDnDH/HqzEw4zz99drsn/Cq3kZ7thBCCCFqJoHmGcZ/IdB2l7Znq0GBd85PJjWqbqWL4swG3hqexGvnJhJdOX+z1K3yh+/yOFzmCV+na9Cr4yBsFm1rrYKSXPbmbGuU5wohhBCidhJonmH852ceJh2AR/rHc26atV73UxSF6zNi+PaSVOLNWrB5uNzLH77Lo9QV+eyi2WShb+dz9Pba7MURf6YQQgghQiOB5hnE7qzgSN4+AFRV4TAdGdnGyn1ZsQ2+d+9kM++NTMZYOeq+Id/FLT8V4PFGfofTgRkj9Ndb9q6h3FEa8WcKIYQQonYSaJ5B9h7NRkUL/I6TRnJUDP8YkYQhTHuvjmxr48WzE/X21wfsPLq6KCz3rknrlI560Xm318WG3T9H/JlCCCGEqJ0EmmeQjzdu1F8fUdLrNS+zNhO6x/DH3r4M6Ztbynh7a+QzjP6Lgtbs+AlVjXwmVQghhBA1k0DzDFHs9HLgmG/F+dD0XvWel1mbJwbFc1lHm95+cGUR3x6wR+RZJ2R1HorZaAHgaMEBDuftjejzhBBC1K5fv37MmDFDby9btoxRo0bRpk0bEhMTycvLa5R+/O9//2PEiBG0bduWnj17cvvtt3PkyJGw3Pvk9wiN/z53797NPffcw7Bhw0hOTubKK68Met6HH35IYmJilf9mzZoVsb5JoHmG+DC7lGTV94fqjkGZEXuWQVF4a0QyA1toW1N6VbhtcT5HyiO3Et1miSYzfbDelp2ChBCiaRUXF7Nv3z569+4NgNPpZPz48XTt2pW5c+fy/fffk5KSEvF+LFiwgEmTJjFkyBDmzJnD1KlTWb58Ob///e/xehu2aPXk9whN8z63bt3KwoUL6dq1K127dq31/Pnz57Nw4UL9v0svvTRifZOdgc4AHq/KB5sPMEpxAGAwxZIY4R10okwKH12QwqjPczlY5qHQqXLP8kL+PToZJUxzQk82sNt5rKss2r5hzwouHnwtFnNksrZCCCFqtnHjRlRV1YOwpUuXkpeXx/Tp02nZsmWj9WPu3Ln07duX5557Tj8WFxfHddddR3Z2Nt27d6/3vU9+j9A073Ps2LFccsklAIwfP57c3Nwazx8wYACxsQ1fCBwKyWieAb49aMdedlBvd2jRIWLBnr+WUUbeGO7beeibA3Y+2hm5fdE7tuxGSnwaAA5XBZv3rY7Ys4QQQvgUFxdz7733kp6eTufOnXn55ZfZsGED8fHxpKenc/HFF3PVVVcB0K1bNxITE8M2dF0bl8tFfHx8wLGEhASAOs3nr+09Ak32Pg2G5hvOSUbzDPDmljJa4PtFb5vSodGePby1ldt6xvCPrWUAPLSqiPPa2GgbE95FSKDV9BzU7Ty+WfMfQNspqH/Xc8P+HCGEED5Op5Nx48ZRWlrKiy++SHR0NE8++SQVFRVkZmrTtGbOnMkTTzyB3W7nySefRFEUWrduHdL9VVXF46l96pXJFDykueGGG7j++uv56KOPuOSSSzh27BjTp09n+PDh9OjRI2zvsanfZ13079+f/Px8OnXqxOTJk5k4cWKD71kdCTRPc5vzXfx0xMElfoFmWnLjBZoATwyM57uDdnaXeCh2qty9rIC5Y1IiklXt12UYC9f+F6/qZd/RHeQXHyU5vlXYnyOEEJHi3D0b194PG/255vTroc01db7upZdeYufOnaxdu5bkZG1aVkJCAmPHjuWCCy4AICsri9zcXEaPHs3gwYNrul0Vc+bMYfLkybWeV1hYGPT4RRddxOuvv86UKVO48847ARgyZAizZ88OuQ+hvEdo2vcZirS0NB599FEGDhyIx+Nh7ty53HvvvZSXl4f07PqQQPM091ZlaaEW5OjH0pI74HXk4S3chKdwI57CTaj2oxjiu2NqORxT6rkoloSw9SHGbOC14Un8ZsFxVOD7Qw5mZ5czvltM2J5xQmxUAhlts9h+cB0Av+5axuj+V4X9OUIIIcDj8fDWW28xadIkPQAD6NSpEwB9+vQBwO12s2PHDu6++279nPvuu4+vvvqKI0eO1Bg8jR07lkWLFtW7j4sXL+a+++7jjjvu4IILLiA3N5cZM2Zwww038Nlnn2E01jzCFup7hKrv8+DBg9x1113k5ORgMBi48MILmTZtWtBES0PfZyhGjx7N6NGj9faYMWNwOp08//zz3HnnnREZgpdA8zSWZ/fw8a5yrJQTrxQCYFQUYrY+QYX9cJXzvQXrcBasw7njNYxJ/TC2HIEpdRiKOa7BfTm7lZW7MmN5bbMW+D66qojz21jpEBv+X8F+Xc/VA811u5Yxst8VGJTmO39FCCFOVZs3byY/P5+RI0cGHN+/fz/gC8J27NiB0+kMGGYeN24cDz30EN26davxGUlJSVXmWNbFY489xtixY5k2bZp+rE+fPgwePJgvv/ySyy67rMbrQ32PUPV9mkwmpk2bRv/+/XE6nVxxxRXMnz+fyy+/POzvs74uv/xyPvnkE/bv36/PNQ0nCTRPY+9uL8fugbZ+2cwWJicGe37NF6pePPm/4Mn/BeeO17B0vglT+6saPNT92IB4vjlgZ2exmxKXypSlhXx6UfiH0Hu070eUJYYKZxmFpcfZl7OdTq17hvUZQggRKZbON2LpfGOTPNtur1vN46NHjwLQrl27gOPff/89RqNRnwO5efNmzGZzQFA5bNiwkJ7R0CHl7Oxsrr766oBjGRkZREVFsXfv3lrvG+p7hKrvMy0tjbQ0bZGqxWIhMzOTQ4cOBX1OYwydNwUJNE9TLq/KO9u07GFv4xaoLBXW0uLWXhjMGOJ7YEzMwpjYGyUqDc/xlbiPLcZbtMV3I68L58638RTvwNrzXhSjjfqKMim8MTyJixbk4lXhpyMO3t1ezsQe4R1CNxnNZHUeyspt3wPw686lEmgKIUQEnBhK3r17Nx07dgQgPz+ft99+Ww/mADZt2kRGRgZms7nOz2jokHL79u1Zv359wLHt27dTUVFBhw61r1kI9T1Cze8zPz+fBQsWMG/evKDPaYyh82Dmz59PSkpKSJ9FfUigeZr6bG8FR8q99LPs5lLzT2wv137pW1kVrH2ewJgyEMVgCbjG0P4KzO2vwGvPxXNsMa4jC1HL9gLgOfYTFWX7sPV5HEN0m3r3a3BLC1MyY3l5kxYET1tbxOXpNpJt4V2F3q/ruXqguXnfai4ZeiNWc/2DZCGEEFX17t2btm3b8uCDDzJ16lRcLhczZ86kvLw8oLbk5s2bA9p1kZycHDA3sq4mTpzII488QlpaGmPGjOHYsWPMnDmTDh06MGbMGACWLFnCpZdeyueff87w4cPr9R6h+vfpcDgYP348d9xxR7V1OxvyPsvLy1m4cCEAR44coaioiM8++wzQ5mFGR0cDcOONNzJw4EAyMzPxeDzMmzePefPm8eyzz0asRJJMXDtNvbmllMHWbP7d6gUKXL7j7TInYUo9u0qQ6c9gS8XcYRxRg1/F1PYS/bhatpeKNVNwH1/ZoL493D+e9DgtsCx0qjz9a0mD7hdM25ROpCZqAbHT7WDLvjVhf4YQQpzprFYr7733HhaLhYkTJzJ9+nRuu+02kpOTqwSa/vMzG9Mdd9zB888/z6JFi7juuut44okn6NOnD/PnzycmRhtRq6ioACA1NbXK9aG+Rwj+Pj0eD7feeitZWVlMmTIlIu8xNzeXCRMmMGHCBFavXs2OHTv0tn/x9oyMDD744APGjx/PTTfdxPbt23nzzTe5/fbbI9IvAKWwsDD0aqWniezsbDIyMpq6GxGz+piTqd8v5t3UV7AqTl440BIv2jzIR659nShr3YaqXYe/wbnj7+D1RazmTjdgTr++3vMrv9xXwfU/aHNFDQr8dFlL+iTXbUiltu9x6aYFek3NTmk9uPnih+vVVxFZp/ufxzOFfI91V1RUpBcOby7sdjs2W+OO/iQmJjb5vMOnn36a5cuX88UXX4T93lOmTMHj8fDaa681ymYpEJnvsb6/r5LRPA0t3rGO91JfJtrgJM9l0oPMxJgWdQ4yAcxtLsI24AUUq+9feq49H+Da/W69+/ibDjZGttG2h/Sq8NDKwjrt0BCKvp3P0f9Q78nZRkFJzVtyCSGEaDxTpkyhV69eAPTq1Sti2b5QrFq1KiJ1JFesWMHs2bNZt24dw4cP59xzz+XNN98M+3OaM5mjeZrxej2MKJtFlFnLPh72JOo/a0ihdmN8N6IGv4p98wy8BesAcO37D4o1FXO739b5foqi8MyQBIZ9egyPCstynHy2184VnaJqvzhEcdGJdG3Th+xDGwBfqSMhhBBN79VXX23qLug+/fTTiNx36NChTZ6tbWqS0TzN7N29iF7mvQDYVTOFiefpP2vdwB2BFEsitr5PYUwZoh9z7ngdd+7P9bpfj0Qzt/b0ZVgfW11EudvboD6ezH8Lyl93LsWrhvf+QgghhKieBJqnEdXrxHbwfb29xDCWY6W+mplpye0b/AzFYMTa+2EMcSfmYnlxbJ6Bp2hbve73UL94Uqzar+HBMg+vbCxtcB/99WjfH5tFW21XUJrL/qM7wnp/IYQQQlRPAs3TiPvQAhK8xwAo8MTgbXs1R/L36T9vndwxLM9RjDZsfZ9EsWlFaPE6sG94Am951d2GapNoNfCXgb6dEF7eWMqBUndY+glgNlno08mXgf1159Kw3VsIIYQQNZNA8zShustw7Jmjt18p/i2DUg1UOMoAsJqjSIxtEbbnKZYkbP2mg7kySHQVYV//GKqzsM73ujEjmqzKFecVHpXHVxeHrZ8A/bv6aqJt2rsap8sR1vsLIYQQIjgJNE8Trn0fo7i1AG2/uwVboy6iovSg/vO05PZhL6tgiG6HLWsqVNbkVCsOY98wFdXrrNN9jAaFGUN8JRM+2VvBspzwBYPtWnSmRUJrAJxuO1v2S01NIYQQojFIoHka8DqO4zrwqd5+tuBKLmgfx5H8/fqxcA2bn8yY0Atr5oNQWULJW7wN56736nyfc9KsjPNbcf7EmqKwlTtSFIX+XQIXBQkhhBAi8iTQPA24ds8Gr5YB3ODoyGflZ3FRexs5foFmWlLDFwJVx5Q6DEvXW/S2+8D/cOfVPWv4xKB4LJW/kWtyXXyx3x6uLtK3yzkolcHwniNbKSrLC9u9hRBCCBGcBJqnOG/pXtxHFurtpwqvpkOsme4JJnIK/ALNBpY2qo2p/VUYUwbrbefWF1CdBXW6R4dYE7f4lTv669pi3N7wZDUTYpLp3ForDKyisn5X/UoyCSGEECJ0Emie4py7/gVotSEXVfRmqb0XF7W34XTbyS/WVqAbFAMtE9tGtB+KomDteT+KJQkA1VmAY8sLqHWsW3l/VhzxZi3zuKPIzZyd5WHrY7+uw/TXv+5aGvadiIQQQggRSALNU5ineDuevJUAeFWFpwuuBuDi9jaOFhxERQukWiS0xmyyRLw/iiURS88/+fqXvwa339zRUKTYjEzpHau3Z/xaTIU7PAFhrw6DsJi0bS+PFx3hUN6esNxXCCGEEMFJoHkKc+d8r7/+tPwstrjaE2NSGJZmDZyfGeFhc3+mlIGYO4zT285ds/CU7KzTPe7KjKVllParebjcy9tbw1PE3WK2ktnRN7y/ThYFCSGEEBElgeYpSvV6cB9drLc/KhkBwMg2VqxG5aQV540XaAKYO9/k2zlIdePYPAPVE/rCnhizgQf6xuntFzeUUOgIz9aR/fy2pNywZwVuT/iKwwshhAjUr18/ZsyYobeXLVvGqFGjaNOmDYmJieTlRX5h5u7du7nnnnsYNmwYycnJXHLJJVXO+fDDD0lMTKzy36xZs8LWj+bwWQD873//Y8SIEbRt25aePXty++23c+TIkYg9TwLNU5SnYB24CgHIVxNZ4egGwEXtbQDk5B/Qz23MjCaAYjBjzXwIjFpf1PKDOHe8Wad7TOgeQ6c4IwCFTpWXN5aEpW/pad1JiEkGoMJRxo6D68NyXyGEEIGKi4vZt28fvXv3BsDpdDJ+/Hi6du3K3Llz+f7770lJSYl4P7Zu3crChQvp2rUrXbt2rfHc+fPns3DhQv2/Sy+9NCx9aC6fxYIFC5g0aRJDhgxhzpw5TJ06leXLl/P73/8erzc8CZ2TmSJyVxFxnqOL9Nf/KxmMt/LfDBe2s+H1ejla4BdoJjVuoAlgiG6LpdtdOLe+CID7yNeYWo3AmDwgpOvNBoXHBsQz6Sdt5fqbW8q4rVcsraONDeuXYqBvl2Es3vA5AOt2LaVXx4ENuqcQQoiqNm7ciKqqenC1dOlS8vLymD59Oi1btmy0fowdO1bPYo4fP77GzOGAAQOIjY2t9uf11Vw+i7lz59K3b1+ee+45/VhcXBzXXXcd2dnZdO/ePezPlIzmqcLpwLjlF4zrV2JYtxT30SX6j7YeaweqyoAWZlpFG8krOYrLo+3OExeVSGxUfHV3jShT2hiMqb6hase2V+o0hH5lp6iArSmf/TU8W1P26+Jbfb7j4HrK7OHJlgohxJmquLiYe++9l/T0dDp37szLL7/Mhg0biI+PJz09nYsvvpirrroKgG7dupGYmBjR4Vp/BkPjhjrN+bNwuVzExwfGBAkJ2s58karEIhnNU4Bx4yqs78zEUHgcAHtHA5yvrSI3Fnn5YNkb3Bv7NVsuuBHUkU22EOhkiqJg6XYXFQXrwF2Kas/BuXs21oxbQ7reoChMHRTPVd9q//qcnV3O//WOpWuCuUH9Sk1oTbsWXTh4fBcer4eNe1YwtOeYBt1TCCHOVE6nk3HjxlFaWsqLL75IdHQ0Tz75JBUVFWRmZgIwc+ZMnnjiCex2O08++SSKotC6deuQ7q+qKh6Pp9bzTKaGhzT9+/cnPz+fTp06MXnyZCZOnFin65vLZ1GdG264geuvv56PPvqISy65hGPHjjF9+nSGDx9Ojx496n3fmkig2Zw5KrD85y0s338acNjeyTd8bNvjRQEGle5h0KdP4tk4l6NDfL8sacmR2xEoFAZrMpaut+HcVjmEfuATbQg9PrT0/Mg2Vka0trL4iAOPCjPXlfCP85Ib3K9+XYdx8PguANbtWiaBphCi2fjh109YtP7TRn/uyL5XcE7PsXW+7qWXXmLnzp2sXbuW5GTt/88JCQmMHTuWCy64AICsrCxyc3MZPXo0gwcPrul2VcyZM4fJkyfXel5hYWGd+35CWloajz76KAMHDsTj8TB37lzuvfdeysvLQ3r2Cc3ls8jJyQl6/KKLLuL1119nypQp3HnnnQAMGTKE2bNn16kfdSGBZjNl2LUF21tPYzh6UD+mxiXg6tIVR/stUFkj85e8zgw27CHK6wLAuGsL+VG5kBoNQKvEdo3e95OZWo/BffQHvAXrAC/ObX/DNuhVFEPtv36KovDYgDgu/FLbYvO/uyu4v6+L7okNy2r26TSEr1Z9iMfr4dDxPRwrPEzLxDYNuqcQQpxpPB4Pb731FpMmTdIDK4BOnToB0KdPHwDcbjc7duzg7rvv1s+57777+Oqrrzhy5EiNQeLYsWNZtGhRtT8Ph9GjRzN69Gi9PWbMGJxOJ88//zx33nlnSMPv9f0sDh48yF133UVOTg4Gg4ELL7yQadOmoShKlWc09LNYvHgx9913H3fccQcXXHABubm5zJgxgxtuuIHPPvsMo7Fh6yCCkUCzuXG7scx/H/PnH6D4rQBzDzgXx8T7cZauhm2bAcg1dmJU18do3b6AWUULuGDHQhS3i2PRvq81bcM66Hw2BPmFbSyKomDtfjcVq+4ErwNv6R5c++diSf9DSNef1dLKmLZWFh5yoAIzfi3hXyMbltWMtsbSvX1/tuzT9mRft2spFw78XYPuKYQQZ5rNmzeTn5/PyJEjA47v369N4ToRXO3YsQOn06kPHwOMGzeOhx56iG7dutX4jKSkpCrzChvD5ZdfzieffML+/ftJT0+v9fz6fhYmk4lp06bRv39/nE4nV1xxBfPnz+fyyy+v8oxQPwu3O3jpvscee4yxY8cybdo0/VifPn0YPHgwX375JZdddlmt964rCTSbGeu/nsO89Bu9rdqicdwwBfe5F4Oi4N7l+5fMIvfZAByxJpF95WTOSbkJ4+fvc9y7QT+n3ef/xVBYgWP8H8HYdF+3IboNls434tz5DgCuvR9iSh2GISa0of2H+8ez8FAuAJ/sreD+fBfWBvapX5dheqC5ftfPXND/6kafNC6EECcb1f9KRvW/skmebbeHvmAT4OjRowC0axc4evb9999jNBr1eX+bN2/GbDYHBJXDhg0jFI0xdB4O9f0s0tLSSEtLA8BisZCZmcmhQ4eCPqOhQ+fZ2dlcffXVAccyMjKIiopi7969td63PiTQbEaMG1cHBJme7n2x3/oQaqo2SdjryMNbcKLuo8I7x31leQanWlCTYsi58gY8nzwIQKLdjdWjwo+foxTkYr/rcbBFN9r7OZmp3ZW4j/6EtyQbvC4c217GNmAmilJ7cDcg1cLY9ja+OqD9T3DGr8U80cB1Thlts4i2xlHuKKG4PJ89OVvp0iaz9guFEEIA6EPEu3fvpmPHjgDk5+fz9ttv6wEMwKZNm8jIyMBsrvu0p8YYOg9m/vz5pKSk0KFDaH/ZhOOzyM/PZ8GCBcybNy/oMxr6WbRv35716wPrR2/fvp2KioqQ32ddSaDZXDgdWN97SW+6hozEccdjYPDNl/AcWwJow+nOuN5s3pcIQLxFoXui9lXmFh3Wz29hiQe0fxWZ1q8g6ul7sN/3DGpi5IvCBqMYjFh63IN9zRRQvXiLNuE+/BXmtlV3aQjm4f5xeqD5xX47v09WyGhAf0xGE1mdh7Ji60IAft25VAJNIYSog969e9O2bVsefPBBpk6disvlYubMmZSXl+s1I0HL4vm36yI5OTlgzmNdlZeXs3Ch9v/5I0eOUFJSwmeffQZoczGjo6O58cYbGThwIJmZmXg8HubNm8e8efN49tlnA0a6lixZwqWXXsrnn3/O8OHDA57T0M/C4XAwfvx47rjjjmrrWYb6WVSXmZ44cSKPPPIIaWlpjBkzhmPHjjFz5kw6dOjAmDGRWRQr44TNhGX+bAy5WpCoRsfivH5KQJAJ4PYr0r7N7BtyGNTCgqFyDmZesS9dntLzbJyX3qC3jft2EPXXu1AO74vIewiFMa4L5g7X6G3nrn+hOotCujYrxcJlHW16+619lgb3x7+m5pb9a3C4Khp8TyGEOFNYrVbee+89LBYLEydOZPr06dx2220kJydXCa7852c2ptzcXCZMmMCECRNYvXo127Zt09u5udqUrIyMDD744APGjx/PTTfdxPbt23nzzTe5/fbbA+5VUaH9HZGamlrlOQ35LDweD7feeitZWVlMmTIl3B+B7o477uD5559n0aJFXHfddTzxxBP06dOH+fPnExMTE5FnKoWFhZGp0NmMZWdnk5HRkFxYeCmH9xH92CSUyn237Tfdj3tk4LZX3vLDVKy4ufICE89a3+CV7dq/Ex7sF8fD/bXJwZ8s+ye/ZGt7oF8y5AaG9hyDadHnWN9/SV9cpMbGU/7Y31FbN02NTdXjoGLlHah2rUCtqfXFWHveE9K1WwtcnPPpMU780n7321QGpdY/4FRVlb9/9ijHCrXM75XDJjEgY0S97yfqrrn9eRT1I99j3RUVFenFspsLu92OzWar/cQwSkxMbPL5laF6+umnWb58OV988UVY7ztlyhQ8Hg+vvfZa0NXmdRWJ77G+v6+S0Wxqqort3Rf1INPTtTfu86oOJftnM40pA/npuG8pzFktfYHWcf+h8wRtbqd75KXY73ka1ar90imlxUQ9/wBKYfXbcEWSYrRi6XaH3nYf+RpP0baQru2ZZGZc5yi9/fQvDdstSFEU+nf17V70685lDbqfEEKI0EyZMoVevXoB0KtXr4hm8sJl1apVdaqrGYoVK1Ywe/Zs1q1bx/Dhwzn33HN58803w/qMpiRzNJuYacnXGLdrE3NVoxHHTffBSSufVVXFffQnve1JOZ9Nv7j09sAW/oGmb+g8NcG304Cn71AqHnyRqBn3oTjtGI7nYHvpYSoe/luTLBAytRiCu8UQPMdXAuDc8Rq2QX9DUWqv4fVgvzjm7anAq8IPhx38fNTB2a3qvwa9b+dz+Hbtx6iqyt6j2ygoySUpruqwiBBCiPB59dVXm7oLdfbpp5+G/Z5Dhw49ZTK69SEZzaZUUoj1P2/oTddFv8PbvnOV09SKI6jlldtKGqysVwbgqRw77pFoItGqfY1l9hLKHaUAWExW4qKTAu7j7dIL++THUStXeRv37sD22jTwBK+3FWmWjDvAoK2685Zk4z78dUjXZSSY+V0Ys5px0Yl0beObP7Nul2Q1hRBCiHAIOdB85513yMrKolWrVpx33nksX768xvNVVeX1119n8ODBtGzZku7duzN16tSG9ve0Yv33myilWpDkbdEK5xXjg57nKfTVxTQmZbHyuO9rG5zqn808or9ukZCGIUjZIE+/c3BMuEdvmzas1Fa7q40/VdcQ1Rpzx9/r7bosDHqwXzzGypmaS3KcLM1xNKgv/bv6Vg+u27UMtQk+DyGEEOJ0E1KgOW/ePB566CHuv/9+Fi9ezFlnncU111zDgQMHqr3m0Ucf5Z///CdTp05l1apVfPzxx5xzzjlh6/ipzrB9A+alvgye48Z7wBoV9FxPga/mlSExi1XHnHp7sN/8TP/SRinxvmHzk7lHXhawGt3805eY50dun9OamDtcg2JLq+xYKc7d74Z0Xad4E5e08ujtZ39tWFazR/v+2MzaFIL8kmPsP5bdoPsJIYQQIsRA87XXXuO6665jwoQJdO/eneeee45WrVoxa9asoOdnZ2fzj3/8gzlz5nDJJZeQnp5O3759ufDCC8Pa+VOZ5du5+mv3oBF4+p0d9DxVVfEWbtTbhsQ+rM71BZqBC4GCz88MxjluEq5hF+lt67xZmJaGNnQdTlUWBh3+Gk/x9pCundjehbFycV5Ds5pmk4Xenc7S27/uXFrvewkhhBBCU2ug6XQ6WbduHaNGjQo4PmrUKFauXBn0mgULFpCens53331H37596dOnD3fccYder+qMV1aCcd3PetMxblK1p6oVh1Edx7WGMZoDdOK4XStTlGBR6JbgW88VOHRec6CJouC4+U+4M327C1n/9QKGPaEFeeFkajEUY8qQypaKc/vfUVVPjdcAtLOpXNvVt5CpoVlN/9Xnm/auwulu2HC8EEIIcaarddV5Xl4eHo+nSnHS1NRUjh07FvSavXv3cuDAAebNm8frr7+Ooij85S9/4Q9/+AMLFy6sdj/p7OzGG65szGedLPnXJcS6tVXj5a07sqPMCdX0J7p0GYmVr+3mTszfdAgqd/nuGe1m186d+rmHj/sKsZcXuUJ6j4bfTKBbbg5Rxw6huF0YX3qEnbf8BU9UZAq3VsdouZiWrEXBjbckm8PrZlMeW/s+uOMS8vgIGx4UluQ4+c+aXQxI8NarD6qqEmdLpsSej8NVwaJVC+icWr+dLETdNOWfRxE+8j3WjcViwWKxhKVuYjjVdb9z0TyF83tUVZXCwsKgcV9t9XNDLm908h8EVVWr/cPh9XpxOBy89dZbdO3aFYC33nqLQYMG8csvvzBo0KCg1zVWsd+mLixsm/ua/tp4/m9r7It98/84kduLb3cOBw4lA2UAnJ+eSEaGVqjd7XFRurwQAAWF/r0HYzGFVvLHe/+zqFNvR6kow1qUR6/v/4P9j09VKbMUWRk4rb/HtfdDABJLv6JNn2tQTNUHvNnZ2Yzs05Vriwr4ILscgA+PJ/D7QS3q3YuzKs7n+1+1PWZzSndy0TlX1vteIjRN/edRhId8j3XndrspKSkhMTGx2QSbTVGwXYRfOL/HE0Fm27ZtMZnqXhWz1itSUlIwGo1Votjjx48H3YIJoFWrVphMJj3IBOjSpQsmk4mDBw9WG2ieCZT8Y766mYoB99BR1Z6rqireAt+Kc0NiFqt+DT4/M7/kmL5SOiE2JeQgE0BNa4f9lgeJevVxAEzrfsa84CNcv70+5HuEg7njNbiPfIvqyAVXEc49c7Bm3FrrdX/qG8dHO8vxqLD4iINlOQ6GpdWvrma/LsP0QHPXkc0Ul+UTH1P/PXaFEKI6JpOJuLg4iosbNu0nnIqLi4mPj2/qbogGCvf3GBcXV68gE0IINC0WC/369WPRokVcccUV+vFFixZx2WWXBb1m6NChuN1u9uzZQ6dOnQBtON3tdtO+fft6dfR0YVrxA0plQOjp1R81MaXac9Xyg6jO/MoLY7Db0tlcoAX8CjAw1X/Fud/8zBpWnFfHM2gEzot/h+XrjwGwzP0n3i698PTsX+d71ZditGHpeguOzc8A4D74KeY2F2OIqfl3Jj3OxB+6RvNhZVbz2XUlzL+4foFmYmwLOqX1ZE/OVlRVZd3unxnRp+pOTUIIEQ4mk6lZbUN57NixM/7v6dNBc/oeQxobnTx5MnPmzOH9999n+/btPPjgg+Tk5DBx4kQApk2bFhB0nn/++fTt25fJkyezfv161q9fz+TJkxk0aBD9+zde4NIcmZYv1F+7zxlT47kB9TMTe/NLnlcv1N4z0USCxff1+S8Eqm3FeXWc19yGJ0Obk6ioXqxvPNno21QaW47AkJCpNVQPzp1vh3Tdn7Li9BXoJ7Ka9eW/KGjdzqVSU1MIIYSop5ACzauuuopnnnmG5557juHDh7NixQo+/vhjOnToAEBOTg579uzx3dRg4D//+Q+pqalccskljBs3jrZt2zJnzpxqFwKdCQwHd2M8sAsA1WzBPXB4jed7CvwDzb4BZY3862dCHVecV8dkwn7XE3jjtR2FDEUF2F5/slF3DlIUpbLckRY1evJW4c5bU+t1neK1rOYJz64rqXcfenUcpE89yC06zMHju+t9LyGEEOJMFnLUd8stt7Bx40aOHTvGTz/9xLBhvhXBb7zxBhs3bgw4Py0tjffee4+DBw+yc+dO3n77bVq2bBm+np+CTMu/01+7+w+DGlZ2a/Uz/eZnJmWxsppC7RCejCaAmpyK447HfNtUbl+PZd6/6n2/+jDGZWBq7au56sx+C9Vbe7Abrqym1WwjM32w3v41e0m97iOEEEKc6c7c9GJj83ox/ewXaNYybK6WH0B1FmgNUyxKTCfW+AWaZ/nNz1RVNXCOZgMCTQBP5kCcV03U2+Yv52DYtq5B96wrS5ebwKhlKNXyA7gPfVHrNeHMag7w25Jy456VuNzOGs4WQgghRDASaDYSw46NGPK1hTxqTDyePoNrPD9w2LwPe0pU8hxafchEi0JXv0LtpRVFOFwVAFjNUcRGNXxiueu31+vF3BVVxfbW01BW/8CtrhRLEpZO1+lt557ZqM7CWq87Oau5vJ5ZzY6tupMc1woAu6ucLfvX1us+QgghxJlMAs1GYvbPZp51PpjMNZ7vKfTtb25M6ssq//mZqRYMfjXXTh42D0s9NoMBxy0PocZo5REM+cewvvcSNOLCGFO7y1Gi2moNdxnOPbXvx94p3sTvuzQ8q6koSsCioF+yF9frPkIIIcSZTALNxuByYlr9o695zgU1nq6qakBG05CYxeoa5mf6D5unJKQ1sLN+/UhOxX7zn/S2eeUPAavmI00xmLFk3Ka33Ye+wlta+8KcP/X1ZTV/OuLg56P1y2r27zoMpXJR0p4jWyksPV6v+wghhBBnKgk0G4Fxw0qUymFnb4s0vF1r3tZQLdsHriKtYYrDEJsekNE8q8aFQG3C1GuNZ9AIXCN+o7et7/8NJfdIDVeElzHlLIzJAypbXhzZ/6i13FDnMGU1E2JS6NJG+65UVH7dubRe9xFCCCHOVBJoNoKAYfOzL6h1a8eA+plJfSh3w5YCbW90BRjQ4qRAszh8C4GCcVz/f3hbaUPYir0c21tPNVrJI0VRsHS9DSpXwXsL1uHJW1nrdf5ZzR8PO1hRz6zmgAzfoqBfdi7Bq9ZvH3UhhBDiTCSBZqSVl2Jct1xvus6uedgcqtbP3FroxluZxMtIMBFvCfzacsNU2qhatmjstz+KWhkgG7M3Yf5iTvifUw1DbDqmNr6sqjP7bVSvq8ZrOseb+F0Yspo92vfHZtHuU1h6nL052+t1HyGEEOJMJIFmhJk2rkZxaUGRp0NX1LbpNZ6vql48hb6apMakLDbn+4Kq3smBi4icbgdFpdruPYqikBwXmVql3i69cF5xk962fPouhl1bI/KsYCydbgSTVndUrTiE++DntV7zZ7+s5qJ6ZjXNJgt9O5+tt3/ZKYuChBBCiFBJoBlhhmxf0Ojpd3YNZ2oC5meaE1BiOrKpwBdoZiYFBpp5xUdR0dKdSbEtMRlrXs3eEK5Lr/dtUen1Ynv7aXDWf6vHulAsCVjSr9fbzr0fYvCU1nhN53gT13SO0tv1zWr296upuWXvGuzO8nrdRwghhDjTSKAZYcYdfoFmtz61nn9y/UxFMQRkNDOTTQHnh2tHoJAYjNoQuk0L3gxHDmCZ+05kn+nH1O7SgHJHccULar3mz33jMfhlNVfWI6vZJiWdVkntAHB5nGzau6rO9xBCCCHORBJoRlJFOYb9lXubKwqeLr1qvSRwIVAWqqqy2S+j2fukjGbgHufhK21UHTW1NY5rJ+tt87dzG23XIMVgxtL1Fr0dXboMb+neGq/pkmDidw3MaiqKErBT0C+yJaUQQggREgk0I8i4ewtK5Splb/vOEB1b6zXeom2+6xOzOFTmocipDY0nWBTaxhgDzg/n1pOhcp93Ce4+ZwGVuwa9PQMqGmc42dhiKIakftqz8eLcWXu5I/+s5g/1zGr27XIOBkX77A/k7uRY4eE630MIIYQ400igGUEBw+YZtQ+bex35qE5tYQ8GK0pMezYX+MoIZSaZq+z6k1ccuRqa1VIUHDf/GbUycDYcz8H67zca6dEK1ozbOPGr68n/BU/e6hqv6ZIQOFdzRj2ymjG2eLq376e3f90pWU0hhBCiNhJoRpAhe5P+2ptRc5F2AG/pLt+1cV1QFCObAuZnBg6be1Vvk2Q0Qds1yDH+Hr1t/vFzjBtqr28ZDobYzpjaXKS3nTv/geqtua7nAyfN1azPCnT/mprrdi7DU8szhRBCiDOdBJqR4nFj3LnZ1wxhIZC3ZKf+2hDXFaDG+Zkl5QW43NqOQVHWGGJscQ3qcl25h47GPWiE3rb+8zkoq9/K7rqydJ6AV7EBoJYfxH3oixrPP3mu5jO/1r2fGW2ziItOBKDUXsS2A+vqfA8hhBDiTCKBZoQYDuxGcdgB8Canoqa0qvWagEAztjLQrCGjGfFC7bVRFOwT7sMbnwSAofA41tkvN86jLYmUxPtlNfd8gOoqrvGaB/rFB+yBviynbllNo8EYsCho7Y4f63S9EEIIcaaRQDNC6jo/E6pmNO1ulexibXhWAXokBpY2yi8+qr9OiYv8ivOg4hNx3HSf3jT//B3GNY0zf7Es7jwUW2WA7S7FueeDGs/vHG/iD119uwU982vNgWkwAzPO01/vPLSJwspi+UIIIYSoSgLNCKnr/EzVVYJqrwwcFTOGmA5sK3TpW092ijMSaw78uvJKjumvk+Nrz5hGimfgcFzDfNlF63svQklh5B+smLFk+ModuQ99gbdsf42X/LlvHKbKrObSHCeLj9Qtq5kUl0qX1pkAqKj8ki07BQkhhBDVkUAzElS1zoXaA4fN01EMpsD5mclVd/wJyGg2YaAJ4Lj+//AmtgDAUFyAdfYrjfJcY4tzMCRmaQ3Vi3Pn2zWenx5n4tqTspq1lUc62cBuvqzmLzsX4/V663S9EEIIcaaQQDMClOM5GAqPA6DaorUamrXwBFkIVNOKc4B8/4xmhPY4D1lMHI6b/6Q3zSt/wLj6x4g/VlEULBl3oE0uAE/eaty1lDv6k19W8+ejdc9q9uwwgGirtvCqqCyfnYc31nKFEEIIcWaSQDMCArKZXTPBYKzhbE3wFeeBNTQDzle9zSvQBDx9h+IaPlZvW9/7GxQXRvy5xrjOmNpcrLed2W/XWO6oY5yJGzL8s5oldcpqmoxm+ncdprfX7Pipjj0WQgghzgwSaEaA0W9+pieE+ZkA3tLAQFNV1YCM5slD5yXlhbg92s+jrbFEWWMa0uWwcVx7F97kVAAMJYVY3/9bozzX0nk8GLXgUS3fj/twzfug3983jhNTXlccc/Lj4bplNf0XBW0/sI6S8sI6XS+EEEKcCSTQjABDti+jGdJCIHcZavkhraEYMMR04miFl3yHNvcv1qTQITYwK9rcspm6mDgcN/9Zb5pX/4hp5aKIP1axJGFOv1ZvO3fPRnVVXyuzfayJGzN8wfnTdZyrmZrYho6tugHgVT38unNpPXothBBCnN4k0Ay3shIMh/YCoBoMeLr0rPUSb8lu/bUhpiOK0RKwEKhXkhnDSVtP+i8EasoV58F4+pyF67xL9Lb1/ZdQivIj/lxz+8v9yh2V4Nwzu8bz78uKxVL5J2B1rouFB+uf1Vyb/RNeVRYFCSGEEP4k0Awz484tKJWZMW+HrmCLruWKk4bNgxZqN1W5Jq/EL9BsThnNStoQutYvpbQY63svQR1Xd9eVYrBg6TpJb2vljvZVe367WBMTuvmymk/VMauZmT4Ym1n7fvNLjrE3Z3s9ei2EEEKcviTQDDNjdt3KGkHwhUA1zc+EwKHzpi5tFFRUDI5bHtCbprVLMK34IeKPNaYOCyh35NjxVo3B4/1947BVzkpYn+fi8332kJ9lMVnp2+Vsvb1GdgoSQgghAkigGWYBgWaIOwIFLW3kN3R+8opzgPziZjpH048ncxCukZfpbevsv6EURnYnHUVRsHa7gxO/2t6CX/AcX1Ht+WnRRm7tGau3n/61GI839KzmwG7n66+37FtDub20zn0WQgghTlcSaIaT24Vh11a9GdJCII8dtexAZUvBENsZp0dlR6GvPE/PkwJNVVXJDxg6b4YZzUqO39+Bt4W2PaZSVoL1Xy9EfAjdENsZU9vf6G3nzn+gep3Vnn9Pn1hiKwtrbit0M3dPRcjPap3cgbYtOgHg8bpZt0sWBQkhhBAnSKAZRoZ92SguLaDxprZGTWpR6zXe0j2AtohEiW6HYopiR5Ebd2Us1iHWSIIl8Gsqs5fgcGlDvFazjRhbXPjeRLhFReO45UG9aVq3HNOybyP+WEvn8WDSMpVqxRFcBz6t9twUm5E7M31ZzRm/FuOqQ1ZzkF9Wc9X2RXXeaUgIIYQ4XUmgGUYBhdpDHDYPXqi9lmFzv/mZSXEtUU5akd7ceHr2x3nBlXrb+uErKPm5EX2mYo7H0ulGve3a+xFeR/XD9pMzY0m0aJ/jnhIPc7LLQ35WVqezsZqjAMgrzmH3kS317LUQQghxepFAM4wCCrV3C7FQu1+gaYwLtuI8WKDpt8d5Mx429+f83W14U9sAoJSXYZ31XMSH0E1tf4sS01FreCpw7fpXtecmWg3c3ceXGZ65rgS7O7T+WcxW+nc9V2+v2h75RU9CCCHEqUACzXBRVQw76laoHWrPaPYOktHMC6ih2TwXAlVhjcJ+60OoldlX08ZVmBbXvHtPQykGI9aM2/W2O+c7PEXbqj3/9p4xpNq0PxKHyj28u6Ms5GcN7j5Sf71t/y8Ul0W+bqgQQgjR3EmgGSZKfi6GkkIA1OgYvG3Sa71G9ToD6jwaYrsAgaWNgtXQDChtdIpkNAG83bNwjRmnt61zXkPJO1rDFQ1nTB6AscU5etuZ/SZqNYXVY8wG7s3yZTVf3FBCmSu0IuwtE9vSKa0HoO1DL/ufCyGEEBJoho3h8F79tbddZzDU/tF6y/aBqq0uV2ytUcyx5FZ4OFqhBTdRRoXOcUECzVOgtFF1nFffgrdVOwAUeznWd54Fb2R31LF0vQUULTPsLd6GO+f7as+9uXsMbaK17+5YhZe3t9YlqzlKf70m+0c8XncNZwshhBCnPwk0w8RwyJeZDCWbCScPm2vZzC1+w+Y9k0wYDVUX+gSUNmqOxdprYrVVDqFrv3qmLb9g/v7TiD7SEN0Gc4er9LZr1yxUd/AA0mZS+HPfeL39t40lFDpCC4R7dhhIbFQCACXlhWzb/2sDei2EEEKc+iTQDJOAjGbbjiFd4y3Z5bteL9Tuy4IFW3Fe4Sij3KEVBTcZzcRFJ9ajt03Lm9Eb19jf623Lx2+h5ByM6DPNHf+AYtXKTanOApx7Pqj23Bu6RZMep20XVOhUeWVTSUjPMBlNAfufy6IgIYQQZzoJNMOk4RnNUFec+5c2SsWgnJpfofOqiXjaaYXOFacD29vPgNcTsecppigsXW/V2+6Dn+Et3Rv0XLNB4bEBvqzmG5vLOFIeWt8Gdz9fLze1+8gWcouO1L/TQgghxCnu1IxSmhtVDcxotqk9o6l6PXhLd+ttY5AV571qqaF5Ki0EqsJswXHbI6hGLXNo3LkZ84J/R/SRxpYjTtoH/fVqi6tf1SmKPpWBfoVHZea64pCekRCTQvd2/fX2aslqCiGEOINJoBkGSlE+Srk2nK1GxYS0I5BafgAqt0VUrKkolkS8qkp2kW/ovFdS1YVAgaWNTuFAE/B2zMB5+QS9bZn3Lwz7d9VwRcNo+6DfBZVZYG/hBjzHFgc916AoPDHQl9V8f0c5O4tcQc892ZAevkVBv+5citPtaECvhRBCiFOXBJphYDi0V3/tbdMRQtipxxNk2PxwmYfyyiLhSVaFFGvVr6cgIKN5aq04D8b12+vwdO4JgOJxY337aXCHFtDVhyE2HVO7y/W2c+fbqO7ge5uPbmvl3DQLAB4Vpv8S2lzNzm0y9WoAdmc5G/esbGCvhRBCiFOTBJphYDjsPz8zxIVApf4LgbQV5/7ZzG4J5qBbS+b5rzg/DQJNjCZtFbpZC+iM+3dh+fS9iD7S0ukGFEsSAKrjOK69HwU9T1EUpg5K0Nuf7q3g1+POWu9vUAyc5VfqaPU2GT4XQghxZpJAMwyqZDRDoAYUatcWxezwCzQzEqoOm8NJNTRP8aHzE9Q2HXH+7ja9bf5iDoadmyP2PMUUg7nLJL3tOjAPb9mBoOcOSrVwaUeb3p62NrS5mv27Dsdk0OZ4Hsrbw4HcyE0JEEIIIZorCTTDICCj2TY9pGu8Zft910d3AE7OaFYNNJ0uByUVhdo1ipGEmJR69LZ5cl1wFe6e2iIaRfVie+spsJdH7HmmtFEYEnppDdWNM/uNahcG/WVAPCfKmf542MGPh+213j/aFkufzkP09s9bvm1wn4UQQohTjQSaYVDnFefuMlTHca2hmFCiWgO1ZzTzS33ZzMTYFhgNxnr2uBkyGHDc8iBqVIzWPHYY65zXIvY4RTFg6XYXJ/4IePJ/wZO7LOi53RLN3JARrbenrinGW01Q6m9ozwv115v3rpb9z4UQQpxxJNBsqOJClJIiAFSLDTWl9uFsb7mvOLkS3RbFoAWV2X6rmrslBClt5LfiPCX+NJifeRK1RRqOG/+ot80/fYnxl6URe54xriumtr/R287sN1HdwbOoD/WLx1YZ16/Lc/HZ3uALiPy1SelIeqvuAHhVjxRwF0IIccaRQLOBAhcCdQh9j/MT10e3B6DY6eVIubbVocUAHeOqZiv9a2gmn8o1NGvgPmcMriEj9bZt1nMohXkRe56l801gTgS0hUHOPbODntcmxsjtPWP19rS1xTg8IWQ1e/mymqu3L8Llrn0xkRBCCHG6kECzgQKHzdNDukb1W3hiiNGG2nf6DZt3iTdhCrbHud9CoJTTZCFQFYqCY8J9eCtrkSolRVhnPQchDFXX63HmWKwZvoVI7oOf4SnZHfTce7PiSLRo38veEg/vbAu+X7q/nu0HkBijvZdyRykbdv8chl4LIYQQpwYJNBsocCFQiKWN/BcCxWgZzVBWnJ92pY2qExOH49aH9aZp/QpMP8yP2OOMrUZiSOqnNVQvzu2voKreKuclWg080M9XxP25dcUUOKqe589gMDC05wV6++et31a76EgIIYQ43Uig2UCBpY3SQ7rGW+4faJ5YcV7z/Ew4qbTR6RxoAp7MgTgvukZvW//9OsqR/TVcUX/ajkGTQdE+d2/xNtyHvw567i09YuhUOa2h0Bna1pQDMkZgMVkBOFpwkD0528LUcyGEEKJ5k0Czgeqa0VQ9DtSKnBNXo0S1A07KaCZWzWi6PS6KyrS5igoKSXGpDej1qcF59S142mk1RhWnA9ub0yO2a5Ahpj3mjlf7nr1rFqqzsMp5FmNgEfd3tpWxu9hd5Tx/UdYY+nU9V2//vOWbhndYCCGEOAVIoNkQZSUYKheqqGYzamrrWi/RVpxrQ6dKVBqKUdsRZ0dhzTU0C0qPo1ZeFx+TjMkYPOt5WrFYcdz+GKpJe6/GvTuwzJsVsceZO/4BxVb5HbpLce58J+h5l3W0cXYr7XtzeWHqmqJa7z205xj99fYD6wIqCAghhBCnKwk0GyAgm9m6A4RQ11Itqzps7vKq7C7xBZpdg9XQDChtdJouBArC26ELzmtu1duWLz/CuHlNRJ6lGK1Yuk/W2+6c7/AUbKh6nqLw18G+rOb8fXZ+Puqo8d6pCa3JaJsFgIrKim3fhanXQgghRPMlgWYDhGt+5r4SN67KNSVtog3Emat+LYGljU7v+Zknc114Ne4+g/W29a2nobgwIs8ypQzCmOob5nZs/zuqt2pJokGpFsZ1itLbj60qqrWI+9l+pY5+yV6M3Vl7LU4hhBDiVCaBZgME1tCs+4pzpXLrycAV59UsBCo5A0obVcdgwHHrw3jjk7RmUT62d2ZErOSRpdsdYNSCSLV8P659Hwc97/GB8Vgq/wStPe5i3p6aA8eubXqTmtAGAIfLzq87l4Sv00IIIUQzJIFmAwTU0Ax5j3P/Gpqh7XEOkOc3dJ50hmU0AdSEZBy3PqS3TetXkLo6MjvtGKwtsHSZqLdde/8dUGT/hI5xJu7oFVjE3e6uPvhVFCVgruaKrQvxemsujySEEEKcyiTQbADDobplNFWvG7XikO/66NBraOb71dBMOQMDTQBP1hCcF/9Ob7f5fi6GfdkReZap7SUY4ntqDdWNY+vfgtbWvC8rjmSr9sfoQKmH17eU1njffl2GEWXR9nPPLznGlv1rw9txIYQQohmRQLO+Ksow5GvD2arRhNqyba2XqBWHQfUAoFhbopi04dls/xXnQUobebweCkqO6+3TdfvJUDivvgVPxwwADB43tjeeBEf45zoqihFrjz+Con0f3uKtuA99UeW8RKuBh/rF6e0X1pdwuMxT7X0tZitn9Rilt5du+lIKuAshhDhtSaBZT4bDvrmW3rR2YAqeifTnDbLiXFVVdvgVaw82R7O4LB9vZYAaG5WAxWytd79PeWYL9rseR7XaADAcOYD1g1cj8ihDbDrmjr/X285d/8Jrz61y3s09YuhZ+Q+EMrfK1LU1lzsa2vNCTAbtez50fA97pYC7EEKI05QEmvXkPz9TDXkhkG+oXancevK43UuhU8toxZgU2kTLivPaqGntcdzwR71tXrwA07JvI/Isc/rvUSqnOOCpwLn971UykCaDwowhvnJHH++qYGUN5Y5io+Lpn+Fb2b5k04LwdloIIYRoJiTQrKeAjGbIpY2qLgQ6eX6moihVrpNAsyr38IvJzzxLb1vfexHlcNUFOw2lGCxYe9yjtz15K/Ecq7pa/Lw2Ni7taNPbD66sudzRsMyxKGjfdfahDeTkR2Z7TSGEEKIpSaBZT4ErzkPLaAYUa48OfcW5f6B5Jmw9GRJF4cBvbsSbpmUbFYcd22tTwWEP+6OMiZmY2v5Wbzt2vI7qKqly3vTBCdgqa/avy3PxQXZ5tfdMiW9Fr46D9PbSTV+Fr8NCCCFEMyGBZj0FrjhPr/V8VfVUbj9Zeb2e0fTNz+yWWHsNTclo+nitNuyTp6Kate0gjQf3YJ39ckSeZekyEcXaQmu4CnFmv1XlnI5xJqb09i0MenJtMYWO6ssXndvnN/rrjXtWUFh6vNpzhRBCiFNRyIHmO++8Q1ZWFq1ateK8885j+fLlIV23a9cu2rVrR9u2ta/KPmU47CjHjwCgKgZtMVAt1IqjULnDjGJJQjFrAYn/ivPqSxv5B5pn7orzYLwduuC44W69bV7yFaalX4f9OYopBku3wO0p3cdXVjnv3qxY2sVoac3jdi8z1xdXe892LTrTKU0roeRVvSzf8k2Yey2EEEI0rZACzXnz5vHQQw9x//33s3jxYs466yyuueYaDhw4UON1TqeTm2++mXPOOScsnW0uDDkHUCrn36mt2kJlRq0m/ltPntgRCALnaAYbOldVlQLJaNbIfd4luM6+QG9b33sJw8E9YX+OKfVsjC3P09vObS9XGUKPNhl4clC83v7HljK2F7qozvDevqzm2h0/Ue6ouQ6nEEIIcSoJKdB87bXXuO6665gwYQLdu3fnueeeo1WrVsyaNavG65544gkyMzO5/PLLw9LZ5iJwj/NQV5xXXQhU4VbZX6qVLTIo0Dm+aqBZ7ijF4dLmHVpMVmJscVXOOeMpCo6b7sPbWvtcFaejcr5m+OtrWrvdBeZEAFRnftAh9Cs7RXFOK+0fH24VHl5ZVG2tzK5t+9AqScuIO90OVm37Pux9FkIIIZpKrYGm0+lk3bp1jBo1KuD4qFGjWLmy6tDhCd988w3ffPMNzz77bMN72cwE7HEe4taTql9poxOB5q5iNyfCj/RYI1ZjzSvOk+JaBl2VLgBbNPb/m4pq0WqMGg7vw/qvF8K+H7piScDaY4re1obQVwSeoyg8OzQRQ+VX9cNhB/P3BV+kpCgK5/plNVdsXYjL7Qxrn4UQQoimUmuV8by8PDweD6mpgaudU1NTOXbsWNBrcnJy+OMf/8js2bOJiws9A5edHZntBMP9rE47NnFisPywwUpBCPdqkb/Dd02BAWdFNotzjYAWGLUxOYP2aXfuJv21VYlu1M/oVHDy55F84bV0/OJdAMw/f0dOfAuODx4d5qe2JDF6ENHlawAo3/Qix9IeQTXG6GfYgCtbmflfjrbA68/LjtOxwk5MkD9xUd4UYqzxlDmKKbOX8M3yeXRvPTDMfW7e5Pf69CDf4+lBvsfTQ2N9jxkZGTX+vPbtbCqdnElTVbXa7Nptt93GzTffzODBg0O9PVB7Z8MlOzu7Qc+KLinQX7ccMIQW6TXfS1VVyg/7dpTp0P0cFEsS88qKAW2OX/+2CWRkJFS59mD5Fv11+9adG+0zOhUE/R4zMnAVH8O8WCuC3u67/5Iy6By83bLC+mw1/QEqVt6O6izA6C2mnedbbD0eCDjnhQ5eFs87Sq7dyzGngf+WtOSps6p+xwDneS5lwaoPAdh+bDVjz70aoyHkP56ntIb+eRTNg3yPpwf5Hk8Pzel7rHXoPCUlBaPRWCV7efz48SpZzhMWL17Ms88+S0pKCikpKUyZMoWysjJSUlJ49913w9LxJqOqKMdz9KY3tXXtlziOg6dyvqApVp/jl11U+4pzWQhUd44b/4inU3cAFI8H29+nohTmhfUZijkeS3ffanfP0R9w5/4ccE6i1cB0v8DyzS2lbMwPvjBoQMYIoq1a9r+w9DjrdoVW1UEIIYRozmoNNC0WC/369WPRokUBxxctWsSQIUOCXrN8+XKWLFmi//fII48QFRXFkiVLuOKKK8LS8aailBSiOLXtBdXoGIipfWrAyXucn8gE7yisW7H2ZCnWHhqLFfuUJ1HjtCDPUJSP7e9PgLv61d/1YUo9G2OrkXrbuf0VVFdgOaPfdY5ieJo2acKjwv3LC4PuGGQ12xiWebHe/mnDfDxeT1j7K4QQQjS2kFadT548mTlz5vD++++zfft2HnzwQXJycpg4cSIA06ZN47LLLtPP79WrV8B/rVu3xmAw0KtXLxITEyPyRhqLkuuXzWyRFtI1arl/oKmtUveqKjuL6xpoSkYzVGpKK+x3Po6qaL/ixuxNWP79RtifY+12F4olSXumswDH9lcDVpgrisILZydirvyTtirXyewdwXcMGtJzNFFWbZ5nQUkuG3b/HPQ8IYQQ4lQRUqB51VVX8cwzz/Dcc88xfPhwVqxYwccff0yHDtrq6ZycHPbsCX/dwubI4DdsroYYaAZkNKO1LRMPlXkod2sBSYrVQPKJvQv9uNxOSsoLtesUAwmxKfXt9hnJkzkQ5zW36G3LwnmYln0b1mco5jgsPf7oe+axJbhzAksUdUs080e/HYOeWFNEbkXVbKXVHMU5vS7S25LVFEIIcaoLeWegW265hY0bN3Ls2DF++uknhg0bpv/sjTfeYOPGjdVee/3113Po0KGG9bSZCJifWY9AU4kJssd5YjXzM0t9C4gSYlPOmMUh4eT6zbW4B43Q29Z3X8CwL7wr8UwthmJqM1ZvO3e8jrciJ+Cc+/vGkR6n/WOi0Kny+JrgOwYN7TkGmyUagLzio2zaU30JMSGEEKK5k73O66iuGU1VVfEG1NDUhs53hLAQKGDYPFaGzetFUbDf8lBgMfe/PYpSlB/Wx1i63oYS1UZreMpxbHkOVfVlI6NMCs8NTdTbH+0sZ2mOo8p9bJZozu51od7+ccN8vN7q90sXQgghmjMJNOtIyTuqvw4po+kqBHfltoLGKBRrC+CkFedBdgQCyC+W+ZlhERVNxd1/RY3S5j8a8o9he+VxcIWvMLpiisLa689QOSfUW7QZ1765AeeMaWfjso42vX3f8kIcnqoLg87ueSFWcxQAx4uOsGnvqrD1UwghhGhMEmjWkf9ioFAymifPzzyx4nynX6DZNZSMZrwEmg2htumI/c6/oFZ+/sadm7C+91JYdw4yJvTEnH6d3nbteR9PSeAw/TNDEok1VVYdKHLz3PrAvdIBoqwxDO05Rm//uOEzvKpkNYUQQpx6JNCsC1UNGDoPJaPpLT+ovzbEtNdf7yquW6CZJBnNBvP0HYrzd7frbfOSrzB/M7eGK+rO3PFaDPE9tIbqwbF5JqrHt/1k2xgjjw+M19t/21AStLbmOZkXYTFp2c/cwsNs2bc2rP0UQgghGoMEmnVRUoTi1IIGNSoGomNrvcRb7lsEpUS1BaDCrXKwTJu/Z1CgY2x1xdp9i4Fk6Dw8XGN/j2uYb2W35d9vYNwYvqFpxWDE2usBMGpBolp+AOeuWQHn3NIzhqEttdqabhWmLC3A7Q3MrEZbYxna8wK9/eN6yWoKIYQ49UigWQdVspnVbMHpT63wBZqGaC3Q3FPiy2Z2jDViMVa9j9frDVh1LsXaw0RRcNx0H54uvbSm6sX2+jSUI/truTB0hug2WDJ8mVP3wfm4j6/w/VxRePXcRKyVFa3W5bl4bXNplfuck3kxFpMVgKMFB9i6/5ew9VEIIYRoDBJo1oFSnxqa5Yd911cGmgHzM6tZCFRcXoDHq50XY4vTF4eIMLBYsd/9V7zJWvCulJcR9dIjUBq85FB9mFpfjLHF2XrbseUFvHbfPxwyEsw82M83hP7Mr8XsLAocQo+xxXFWj9F6+/tf/icr0IUQQpxSJNCsg7rOz1S9HtSKI77rK8vf+M/P7FzdinPZESii1MQU7Pc8jWrRMoaGoweJeuUvYVuJrigK1p736lUGcJfg2DwD1a8A+5TesfRJNgNg98Ddy6puT3lu799gNVfO1Sw6zLpdy8LSPyGEEKIxSKBZB3XNaKqOY6BqQaViSUYxaYW4Q1kIVCALgSLO2zED+20P623j9vVY/zkzbCvRFXM81syHOPHHzFu0GdfeD/Sfmw0Kfz83kRMzJ5YfdfLu9sDtKWNscQzL9BWD/2HdJ7g94d2zXQghhIgUCTTroO4rzv0WAlUOm0NgoNlFMppNyjP4fBy/v0Nvm3/+Dsu8WTVcUTfGxN6YO9+ot117/40n3zfXsm+KhT/28S0qe2JNEQdL3QH3OCfzImJs2haWRWV5rN6+KGz9E0IIISJJAs06CMxotqr1fNUv0DRESaDZXLnG/h7XyMv0tmX+bEyLvwrb/c0df4chqV9lS9V2DXIW6D9/oG+8vjtUiUvl7mWFqH5ZVas5ivOyfP37acN8HK6KsPVPCCGEiBQJNENVnxqaFVUzmkVOL8cqtAUdViO0izEGvVYCzUakKDhuvBt31hD9kPXd5zFuXhOm21eWPDInAqA6C7Bvfg61slyRzaTw6rBETtQe+OGwg1nbywLuMbj7SBJiUgAos5ewfPM3YembEEIIEUkSaIaqtAjFUVlD0xYNMXG1XhKQ0YzWFgLt9stmdoozYTQEL5EkNTQbmdGE/a4n8HToAoDi8WB79QkMB3eH5fYGazK2zAegMpz0FvyCa9/H+s+HtrIyOdM3hP6X1cXs8qtOYDKaGdXvSr29bPNXlNmr7iokhBBCNCcSaIaoPjU0vUGGzkMZNq9wlFHh1DJaZqOF2KiEevVZ1FFUNPZ7Z+BN0laKKxVl2F54ECXvWC0XhsaYPABzx9/pbdfu9/Hkr9Pbjw2Ip2ei9jtR7la5c0lgIfd+XYaRmqj9g8XhsrN44xdh6ZcQQggRKRJohqjOK869TlT7iQBFQaksbeRfQzOU+ZlJcan6/ugi8tTkVOz3zUC1aXVLDfm5RD3/ZygtCsv9zZ3GY0joVdnyYt/8jF5f02ZSeHNEEpVbobMq18nLG32F3A0GAxf0H6e3V239nqKyvLD0SwghhIgECTRDZMj1y2imhhBoVuQA2hw8xZaKYtS2HKzrHucybN74vB26Yr/7r6hG7fsxHN5H1IsPgaPhC3AUgxFr70dRLEnaAVcRjk1PoXq1+p19Uyw81D+wkPv6PF9tz54dBtKuRWcA3F4Xi9Z92uA+CSGEEJEigWaI6prRDLbHOciK81OFJ3MQjtsfRa3MJht3bcX26hPgdtdyZe0M1hSsmY+AUllfs3gbzux/6D+/p08sg1O1Qu5uFe5cXIDdrQ2hK4rCmIHX6Of+snMJxwoPIYQQQjRHEmiGyJB3VH8d0q5AFb6tJ0/sca6qKjtDCDQLJNBsFtxDRuK84W69bdq4Cus7MyAM20Aak/pg6XKL71mHvsB1ZKH2HIPCm8OTia4cQ99S6OapX33bY3Zu3YsubTIB7Xfq69UfNbg/QgghRCRIoBmigIxmSu01NL3lB/XXJwLNPIeXYqeWmYo1KbSKCv7xS0az+XBdcCXOy8frbfPP32H56PWw7B5kan8lxpYj9LZz+6t4SnYB0CXBxJODfEPof99UypIjDr198aA/6HN3sw9tZMfB9Q3ujxBCCBFuEmiG4uQamiHM0fSW+zKaJ4bO/RcCdY43VbvIJ1+2n2xWnFdOxDXyUr1t+XYu5s8/qOGK0CiKgrXHvSjRHbQDXieOjdNRXVrZokk9YhjVRtuLXQVuX5xPvl3bKz0tuQMDM87T7/XV6o/weBs+rC+EEEKEkwSaoSgrRrFrC0FUWxTExNdyAagV/jU0KwPNEBYCuT0uisu0XWMURSExtkW9uy3CRFFwjL8H9yBf9tH6v39i/vq/Db+1KQpbn7+AMRoA1X4Ex+YZqF4PiqLw2vAkkq3aH9PD5V7uWurbNWh0/3FYzTYAjhcdka0phRBCNDsSaIYgYMV5CDU0VY8d1XFcayhGFJs21L47lPmZpcdR0QKJhOgUTMbg54lGZjBiv/1R3L0G6IesH72G6YfPGn7rmPZYe96ntz35a3HuegeA1tFGXh+eqP/s6wN23tqq1ViNjYrn/L6X6z/74ddPKHf4yiEJIYQQTU0CzRDUfcW537C5LQ3FoAWLodTQDFgIFC/D5s2KxYr9nqfwdOujH7K99xKmpV83+NamludiTr9Wb7sPfILrsLbN5MXto7izV4z+s8dXF+klj4b2HENSXCoAFc4yKXckhBCiWZFAMwR13eM8cNi8jf667jU0U+vUT9EIrFFU3DcDT6cevkPvzMS0suHD1uZON2JMPUdvO7e/iqdwEwBTByWQlayVPHJ64eYf8yl1eTEZzVw86A/6Nau2fc+xwsMIIYQQzYEEmiFoUA3N6HbaMVVld7FHP15tDc1iv4VAsZLRbJaiYqj400zfvuiqF+tb0zH+sqxBt1UUA9aef8YQ20k7oLqxb/wr3oqjWI0K/zo/mdjKkke7ij38eYW2W1HPDgPplKYFvl7Vyzdr/t2gfgghhBDhIoFmCAzH/Wto1l7aSA3Y41zLaB4u81Dh0eZeJlsNJFmrKW1UKkPnp4TYeOx/fh5vm44AKB4PttemYly/okG3VUxRWPtMBXPl/vauIhwbp6K6K+iSYOL5sxP1cz/aWc5/dpWjKApjB1+HghaE7ji4nuyDGxrUDyGEECIcJNAMQZ0zmkFWnO8KyGYaq73WP6MpNTSbNzU+iYoHXsDbUvvHhOJ2YXvlLxh/Xd6g+xqiWmHr8zgoWtbbW7oHx5bnUFUvf+gaze+7ROnn3r+8kB2FLlqndGRAhm9V/FerP8LtkXJHQgghmpYEmrU5uYZmPbefDGXrSa/Xe9Iczdqzp6JpqUktqHjoJbyprYHKYPPVxzGuWdKg+xoTM7H08O1K5Dm+HNeuWQA8f3ai/o+VUrfKjT9o8zUvGOArd5RbdJjlmxu+SEkIIYRoCAk0a1NWgmIvB0C12iA2ocbTVVcpuLS5cxjMKDZtQc/OYpd+TtcEc9Bri8ry9KLbsbYEbJaooOeJ5kVNaUXFw3/zZTY9bmyvT8W4+scG3dfc+kJM7a/S2679c3EdnE+c2cC7I1OwVSbGtxe5mbK0kBhbPKP6+c7/cf1nFJTkNqgPQgghRENIoFmLKtnMWmpo+g+bK1FtUBTtIw5l6DyvxDcXNCVespmnEj3YbKUt/lI8HmyvP4lp5Q8Nuq+l6ySMLc7W284db+LO/Zk+yWZeOidJP/7J3gpe31LGkJ4XkJas7TTk8jj5YuVsvcC7EEII0dgk0KxFXednqn41NE/MzwTYFUINzbwi37Mk0Dz1qMkttWCzdXsAFK8X6xvTMS1fWO97KooRa+aDGOJPlFPy4tg8A0/RNq7tGs2kHoH1NVccc3PZ2TcFLAzasn9tvZ8vhBBCNIQEmrWo+/zMg75rK+dnur0qe0sC9zkPJq/Yl9FMlkDzlKTN2fybbzW66sX6j6cxLfq83vdUjDZsWVNRorR5oHgd2Dc8gbf8ME+flcCgVG0qhkeFiT/mY4pJZ1D38/XrF6z8EIerot7PF0IIIepLAs1aKH6ljUJbce63K1Blsfb9pR7claOXraMNxJqDf+z+Q+ct4mt/lmie1MQUKh7+G552Wj1MRVWxvfsC5i/n1PueiiURW9+/gjleO+Aqwr7+L1g8xbw3MoUWNu136liFl4mL8jm/39XE2LRzi8vz+UF2DBJCCNEEJNCsRZ13BQrIaGrz9ULZehIgr1iGzk8XanwSFQ+9hKdTd/2Y9eN/YPnPW1DPOZOG6HbYsqaCwaI9o+IQ9g1TaWNz8c/zkjFUTh9ecczJ9PVuLh7s2zFoxZZvOZK3r75vRwghhKgXCTRrUZc5mqqqBs1ohlLayON1B6wQlqHz00BcIhUPvoi7Rz/9kGXBR1j/9QJ4PdVfVwNjQi+svR6AyjmY3uKtODY9xYg0A08MjNfP+8fWMta5+tIprad2nupl/s/v4VW99X47QgghRF1JoFmTutbQdBWBu0x7bYxCsSQDJ+1xXk2gWVh6XA8C4qOTsJisDei4aDaiYrDf/yzu/sP0Q+afvsD6+l/B7arhwuqZWp6LJeN2ve3JW41jy/NMyYziso42/fifVhTRpuu1GA3a79zB47tYs/3H+r0PIYQQoh4k0KxJeSlKhRY4qhYbxNVcQ9N70taTinJiX+q6LQSSYfPTjMWKfco0XOdcqB8yr/4R24sPQ+XvV12Z21+BOf06ve059hOuHa/zxrmJ9EnWFge5VbhzlZk+3cbq53279j8UlubV840IIYQQdSOBZg3qXEPTf0eg6Hb6653+Gc0ECTTPSEYTjlsfwjnGV1DdtHkNUU//EaXgeL1uae50I6Z2l+lt9+EFmA+8z0ejk2kZpf3RLnCoPH9oKElxWjbe4bLz6fJ/Sm1NIYQQjUICzRoouX7zM1NDWAgUsMe5Nj/T7lY5WKrNxzMokB5XXaDpvxBIVpyflgwGnNdPwXHlRP2Qcf9Oov46GcPBPXW+naIoWDLuwNhqpH7Mte8/tMz7hDmjU7BW7guwtVjhV+vVnJjXuevwZtbs+LEh70QIIYQIiQSaNfDPaKoptWcZg+1xvqfEzYncUfsYI1Zj8KzocQk0zwyKguuKCdgnPYBq0P74GfKOEvXU/2Hc+ms9bmfA2vN+jC2G6Mdcu/5JX+f3/H2Yb+egz3Pb4E0+X29/vfrfFJbWL5MqhBBChEoCzRooef5D57UHmoEZTS3Q3BnCinOQofMzjXvEb7DfNwPVpu1nr5SXYXv+AUwrvq/zvRSDCWvmIxgS++jHnNtf4YropfwpK04/9mbe+Zht2u+W023n02WzZAhdCCFEREmgWQNDvq/ckJpcc/Cnql68AdtPVq2hWd38TLfHRVGZtkBDQSEpNrXefRanDk+fs6h45BW8iSkAKG4Xtjf+ivnzD+pca1MxWrFlTcUQl1F5RMW59SUeaLOS33bQVqJ7MPOR/Ur0IfQjMoQuhBAisiTQrIH/Ig1vUosaz1UdeeB1aA1THIpZyyRl+wWaGdUEmvkluXpmKSEmBbPJ0pBui1OIt2MGFX95Td+yEsA69x2sbz0FTked7qWYYrD1expDbJfKIyqurS/yVo9f6ZeirUQ/onZgA+fq18gQuhBCiEiSQLMG/oGmWlugWeGfzWyrv94ZQqAZsBAoQYbNzzRqizTKH/t7QGF388/fETXjHpTCupUiUsxx2Po/gyG284m7w/YX+V+/jXSM1VYHLVUvoAgtay5D6EIIISJJAs3qeL0oRb6/5GsLNL3+W09WBpqqqrKjyFeUu7pi7bLiXBATh/3Pz+E6/1L9kHHXVqKm3YFhX3adbqWY47H1ewYlJr3yiBfbzhdYMGgzKVYDHsx8o45D9RtCX7ntuzC9ESGEEMJHAs1qKMUFKB6tLJEaEw+Wmnfq8Z+fqURppY3yHF4KnVqmKNqk0CbGGPTagIVAcZLRPGOZzDhuug/H9VNQlcoV6fm5RE2fgnHN4jrdSrEkENV/RkCwmbjnBb4avIkoo8JROvCL6htC/2b1f8gpOBCmNyKEEEJoJNCsRl3mZwKoFf4ZTW0hkP/8zC7xJgzVFHyXFedCpyi4LhyH/f5nUaNjtENOO1GvPo7lf/+s0x7piiWxMtjsUHnES9sDL7JgwBoMCqxgDLlqawDcXhcf//Q6Tnfd5oUKIYQQNZFAsxp1mZ8JJ2U0K4u1h7IQCE4ONGXoXICnz2DK//I63la++b6W+bOxvfgQlBaFfB8t2HzWL9hU6XbsdT7vsxQvJr7h97hUbaFQbuFhvl71UTjfhhBCiDOcBJrVqNNCINWDWnFEbxsqi7WHUtrI6XZQXJ6vXacYSIqrPagVZwa1TUfKH38Dd+/B+jHTxtVEP3E7hr07Qr6PYkkiqv9zGOK66sf6Ff2Lud2/oYBUFuObF7p6xyI2710dnjcghBDijCeBZjUMBX41NJNqrmup2o+BqgWViiUJxRQNBGY0u1VX2sgvm5kYm4rRUH3mU5yBYuOx3z8D56U36IcMx3OImv5/mJZ8FfJtFEsCtv7PYkjopR872/4xH3f5jC0MIFvtrR//dPksCkvrttpdCCGECEYCzWoEztFMqfHcgK0nK+dnQuCuQNWvOJf5maIWBiPOq2+h4o/TUaMq5226nNjeeRbruy+EXG9Tr7OZNEA/Nsz9OXM7/YdFXE6xmgiA3VnO3MVv4qnDfFAhhBAiGAk0q1GnoXO/QNNQueLc5VXZU1z70LkEmiJUngHnUj71TTxt0/Vj5kWfE/XXu1CO7A/pHorRhi1rKsYWZ+vHzvZ+x9yOH7KIcXhV7X8J+47t4KcN88PafyGEEGceCTSrERho1jx07q3wz2hq8zP3lbhxV9bAbhNtINYc/KPOK5FAU4ROTWtPxeOv4xoyUj9m3L+L6Cduw7Ts25DuoRgtWHs/irGV7x4DWMm7HeaxXvGVPFq07jN2Hd4cvs4LIYQ440igWQ1Dof8czTpkNCsDzeyAhUDmaq/NK5Ji7aKObNE47nwc+/h7UE3a75bisGP7x9NY354Bjopab6EYTFh7/QlTu8v0Y92Vbcxsu5xcTkz/UHn/h9dki0ohhBD1JoFmMI4KlPIyAFSjCTU2ocbT/UsbBVtxHmppoxYSaIpQKQru0VdQ8fjreNPa64fNS78meuodGA7sDuEWRiwZd2LuMkk/1tF4iD+22Y0DbUGb113Gywv+hsvtDP97EEIIcdqTQDOIwGHzFDBU/zGpXheq/USwqKBEaQWws0NYCGR3VlBq12oiGg0mEmJqXnQkxMm8HTMon/oWrrMv0I8ZDu8jaurtmL/+GLzeGq9XFAVLx2uw9noQFO33tIOpgOtaHsdbuUWlu/wAM776p+yHLoQQos4k0AzC4B9oJtZS2qgiB9D+MlesqShGbavKUIq15/vNz0yKS8VQQ0ArRLWionHc/ij2SQ+iVm6VqrhdWD96Hdtzf0LJP1brLUxpI7H1/SsYtUxmhq2EMYkl+s+deSt46vvQyykJIYQQIIFmUEq+b35mbdtPBlsIBKEVaz8eMD9TFgKJBlAU3CPGUj7tH3g6ZuiHTVt+IfrRmzGt+L7WWxiT+2Mb8DyKJRmAQXFl9I7xzfcsPzCXJ5esl8ymEEKIkEmgGYRSWM/SRpWBZqHDS65dy3JajdA+xhj02sAV5zI/UzSc2qYjFY+/jvO316Mq2tC3Ul6K7Y2/Yn1zOpSV1Hi9Ma4ztkF/Q4lJR1HgoqRiWppd2s8UDwU73+HxFQcl2BRCCBESCTSDqEsNTW+QQNO/UHuXOBNGgxL02rxiX0ZTFgKJsDGZcV5zKxWPvIy3he/3yvzzd0Q/chPGX5fXeLnB1pKogS9ibDEUswGuSi3EZtD+4RSrFHN429v839LjuL0SbAohhKiZBJpBGOpSQ9N/V6DKYu3ZIQybQ+D2kzJ0LsLN2y2L8un/xHXuxfoxQ2EeUX97RMtulhZVe61iisba5y+YO1xDosnL5SlFgBZYtlH2cWznB9zwfR7l7poXGwkhhDizSaAZhFIQ+hxNtSJIRrPIpR8LtbSRBJoiIqJicNz6EBVT/oo3IUk/rGc31yyu9lJFMWLpOglLz/voFO1lZGKp/rMeyjoKDn7BuG/zKHRIsCmEECK4kAPNd955h6ysLFq1asV5553H8uXVD78tWbKEa6+9lu7du9O6dWvOOeccZs+eHZYON4ZQh85Vjx3VUXmuYkCxacOUoRRrL3eUUu7Q/uI2Gc3ERScFPU+IcPAMGk750+8GlkEqKiDq1cexvjYNpTCv2mvNrS/E1n8GZyWb6Rdbrh8/S1lE6bGl/GZBLkfKZV90IYQQVYUUaM6bN4+HHnqI+++/n8WLF3PWWWdxzTXXcODAgaDnr1q1iszMTN577z1+/vlnJk2axD333MN///vfsHY+IryegL90aww0K3yF2hVbGopBy16GUqzdP5uZHNcKgyLJZRFhsQk47niMinuexpvo+702r1pE9MMTMC2aX23dTWNib6IHv8LFHVrRyebQj4/kU2wlK7nwy1yy/TL5QgghBIQYaL722mtcd911TJgwge7du/Pcc8/RqlUrZs2aFfT8+++/n8cee4yhQ4eSnp7OpEmTuPTSS5k/f35YOx8JSnEhSuVftmpMPFTWJQwmYEegymFzj1dlV0ntxdoDFgIlyEIg0Xg8/c+h/Ol/BczdVMpLsb37IlFPTal2VyFDVCuiB77I1ZkDSa1cia4CI9W59Hb9yJgvcllyxBH0WiGEEGemWgNNp9PJunXrGDVqVMDxUaNGsXLlypAfVFJSQmJiYp072NjqMj/TW37Qd13l1pMHyjw4KkcRW0YZSLQG/4gD5mfGyfxM0chi4rS5m39+Hm/LNvph487NRD1xK5aP3wKHvcplitFCfJ8/c92Qq4gxav8gc6oKg7yfc5vt31z9zVE+yC5rtLchhBCieat+pUqlvLw8PB4PqamBq69TU1M5dqz2HUcAvv76a3766Se++eabGs/Lzs4O6X7hUN2zErZvpHPl6zJrNLtq6FNi/rbKHaHheKmZ8uxslhcYABsAbc2uap+z++B2/bXbrjTqez+dyOfWQNYElImPkrb0S1r+/A0GrwfF48Hy5UeoS7/l0JjfUdS9Pygnl+jqywXdPHy57UvcqkKh20SaYw0fttjFH3++jdV7E7iro4tqKntVId/j6UG+x9ODfI+nh8b6HjMyMmr8ea2B5gnKSX/RqKpa5VgwK1as4NZbb+XZZ59l4MCBNZ5bW2fDJTs7u9pnmfZv1l9Hte1QY58q1hZzYkZbWnp/jMkZfLe5FNDKxmSlxZGR0SHotV9uLNRfZ/UYSLsWnYOeJ6pX0/co6qhXJhWX/A7buy9i3LEBAGtRHp3nvoE7cyCOG+5GbdPxpIsyiE5tw0eL3wEgx2nGXJLPgrRpPJR3E0+bhvHG8CSiTTUPnMj3eHqQ7/H0IN/j6aE5fY+1Dp2npKRgNBqrZC+PHz9eJct5sp9//plrrrmGhx9+mEmTJjWsp42kbjU0/RYDRVUt1l5dDU2X26nvc66g0DKxbdDzhGhMatt0Kh7+G/ZJD6DGxuvHTZvXEv3YzVg+eh0qAofFe3UezmVnT9DbBxwWFuVbeCv1dc4qfocrvzosK9KFEOIMVmugabFY6NevH4sWLQo4vmjRIoYMGVLtdcuWLeOaa67hgQce4K677mp4TxtJqHM0VXcZuAq1hsGMYtOC0uwQVpwfKzykb+GXFNcSi6n6BUdCNCqDAfeI31D27Ac4R1+BWlkNQfF4sHz9MdEP3oBp8QLw+oLHwd1HcdGg3+vtXXYrX+QlMD52EdPNU7n5y1/4+agsEhJCiDNRSKvOJ0+ezJw5c3j//ffZvn07Dz74IDk5OUycOBGAadOmcdlll+nnL1myhGuuuYaJEyfyu9/9jqNHj3L06FGOHz9e3SOajVBraAbuCNQapfIv5IBi7fHBa2geLfAtImqV1K7efRUiYmLjcY6/h4on/4Gne1/9sKGoANs/ZxL1+G0YN63Rj5/b+zeMyLpUb28tt/FtQRw9zQf5MHkaXyz9gLc3F8ke6UIIcYYJaY7mVVddRX5+Ps899xxHjx6lZ8+efPzxx3TooM0/zMnJYc+ePfr5c+bMoby8nFdffZVXX31VP96+fXs2btwY5rcQXoZQi7X773EepQWLpS4vh8u1WZtmA3SMMwa99lihBJri1ODt0JWKh/+GaeUPWP79hv7nw3hgF1HP/Ql3n7Nw/uEOvO06c0H/cTic5azc9j0A60qjsSoq5yeW8kjSf1m5bx2PHr+LvwzrQZQpxFVCQgghTmkhLwa65ZZbuOWWW4L+7I033qjSPvnYqcI/o+mtYY6mN2DrSa08jH+h9k5xJkzVLLkNzGi2r3dfhWgUioJ76Gjc/c/BvOA/WBb8G8WplT4ybVyFcdMa3CN+g/PKm/jNkBuwOytYv1vbOWxlSQxGRWV4QhlDbNlkuh7ixW+v54Zzr6RjNRl/IYQQpw/ZjsafvRylcrGDajJDXEK1pwYMnVcWaw/cerL6GF6GzsUpyRqF68qbKJ/5Aa4Rv0GtrDqhqF7MP31B9J+vw/bxP7iy3zX0aD9Av2x5cSw/FMahqhBrcHCPbRZblj7K97uC7ywmhBDi9CGBpp+A+ZmJKUFqB/oEDp1XBpp+K84zqtkRqNxeSklFIaDtcS7F2sWpRk1qgWPSA1Q8+Q7u3oP144rLiWXBv4l/4EauL4mnW+ve+s9Wl0TzVVEaJ6ZojrBtIHPPFP679GOcnuDbXgohhDj1SaDpJ+T5maqK13+f88qM5s4QMppHC3xZnJaJbTAY5CsQpyZvhy7Y//wcFX+aiadjN/24UlFG7CfvMemLZfSy+v4htaFYZX5Fbz3YjDPY+Y1zFsX7/s6+Y3sbufdCCCEag0Q5fkKdn4mrGNyl2mtjFIolGQittNFR/4VAiTI/U5z6PH3OomLaW1T831S8rX0bFFiKC7n5m1VkFfgqMWw9nsuX6miOeNP0Y1nmbOI2/h+//PI+qteNEEKI04cEmn78a2jWWNrIfyFQVBsURcGrquwqDiHQ9MtoyvxMcdpQFDyDz6f8qVnYJz2IN0XLZBpVGL/+MANyfIXeNx3cxDrzENZHX4FL1SozWBU33QvnsOvHOynK3dAkb0EIIUT4SaDpp141NCuHzQ+Ueih3a2OCyVYDKbbgpY1kIZA4rRlNuEeMpfzZ2ThuuBtvUguMKly/9TiDj5Tqp63fs4JdRcXs7zKDrS7f1patOYBp4wPsX/ssqrOgKd6BEEKIMJJA00/9amhqpY025fuGBzOTgmczvaqXowW+a6W0kThtmS24xlxF+cwPsY+/B5JT+cO2PIYeLtFP2XFkMz8vfhMl/lo+M1xPmde3Q1ZK0SLyl06ifN9nqKpsYSmEEKcqCTT91KeGphKtZSU3+c1Dy0wOXh+wqDQPp1urPxhtjSU2qvrySUKcFixW3KOvoHzmhzgn3MvVx82M2Vuk//igt5Sl697msr2H2JrwF76xD9J/ZqMcddcb5P88BU/hpqbovRBCiAaSQNNPqHM01XLf8PeJYu3+Gc3e1QSaOSfNz1RqKJ8kxGnFbME96nIqZn7AqJG3Mu6IF6Vy+fnxKBOvOTfR5/1HuXKnif8UXMdul2+1us2+G/svf6J8w1N4K3Ka6h0IIYSoBwk0T/B6UIry9aaamBL0NNXrwVvmH2hqq2wDAs2k2vc4b5ko8zPFGchkxn3eJfR78F2u73ABpsoSmqUWI6/1bcnBPSu4e/4s0pdE8dXhwdi9vj9L6vEllK24BefOWajusmoeIIQQojmRQLOSUlyI4tX+1lNj48FiDXqeWnEYVC2oVKwtUMyxlLi87CnR5pEZFeiRWHugKQuBxBnNYKT76PHcdMmjWBXtz4vTZODtrJb82D6OtAPbuGnhEixfW9ia65vLbFDduPZ/TNnPk3AdWoDqlfmbQgjRnEmgWcl/2LzG+Zlle/TXhph0ALb4ZTO7JZiwmYIPiR8rlD3OhfDXsVU3Luo3iYQYbQRBVRQ+65rMnB4puAzQOjeP8xdkY/taJb8wVr9OcRXi3P4KFatux31sCeqJKvBCCCGaFQk0K4Vc2qh0n/7aEJsOBC4Eqm5+ptvj5niRb35Zq6S29e2qEKeVxOgW3H7J47RP7aofW9M6lr8PbEuRRSsTlnDUQY/PjhO/2Imr3Fc6TC0/iGPTU9jX3I0n/xcJOIUQopmRQLNSyIFm2V7fNZUZzVAWAh0vOoy3skxLYmwLrOaoBvRWiNNLXHQiN1/8EAMyRujH9seaeGFEV3Z3SQdAAaL2eGk7r4zYX1yoTt/13pJs7Osewb7uYTxF2xq380IIIaolgWalUGtoekv3+q6J1QpNb8737QhUXaAp8zOFqJnJaOaKc27mkiE3YFC0/zWVeOy8nm7kp5sn4TzrfFSjEcUDMRs9tJxnJ3qTG9y+LKa3YB32tfdgX/cYnqKtTfVWhBBCVJJAs1IoczRVj0NbDASAAUN0B7yqyuaCuq04l/mZQgSnKApDe45h/Jg/EWWNAcDjdfPpnu/4oHcrCma8h/OKCXgTUzA4IG6tmxafOIja4QavL+D05K/BvvZeCTiFEKKJSaBZKZShc2/5fkD7y0yJbo1itLK3xENZZUYl1WagVXQ1W0/6LwSS0kZC1KhLm0zu+O3UgOz/xj0reH3pK+wbMYryF/5Dxd1/xZU1BEO5QvzPblI+c2Ld4wE1WMD5KJ7CzU3xVoQQ4owmgWalUIbOA4bNK+dnbgxhfibA0ZOKtQshapYc15LbLnmcgRnn6cfyio/yjy//yqqdP+EecC6O+5+l/IWPKP7teEo8ySQudpHymRPbbs9JGc612H+5n4o19+E+vhJV9TbFWxJCiDOOBJqVArefDB5oqn4LgQx1WAhU4SijqEwrBm80GGmRkNbA3gpxZrCYrFwx7GauHnEHFpMNALfXxecr3uc/P71GhaMMtUUahmtuxvzqf9h523RWJA7FtlTVAs5dgQGnt3gLjg1PYF8yEdeRhahed3WPFkIIEQampu5As2AvR6nQdhpRzWaIDb4HeeBCoHQgMNDMrGZ+5rFC397oLRLaYDTIxy5EXfTtfDZtUzrxnx9fI6dgPwCb965m/7FsrjjnZrq16wtGE2nDziVt2Lks253Lms++YuT6H+m/YQ9lvY3YOxu1HRUAr/sozq0v4Nr0OpaWF2PseR2KJa4p36IQQpyWJKPJSfMzE1tANXuQe8v8amieyGiGUENThs2FaLgWCWncdslfOKv7KP1YSXkhs797kc+Wz8LhqtCPn9U5lTvuuZHN9/2dS/rN5B8HLsb5RRTRm90oLl+GUzVW4Mj7hPIff4f7q/+D3Ssb9T0JIcTpTlJrhDY/U3WVoDoqzzOYUaLaUOjwcqBUq41pNmi7AgUjK86FCA+zycKlZ0+ga9s+fLb8X5TZiwFYs+Mndh7ezFXn3kqntB4AGBSFqztHc2nHQby7vSdD119L95ytjF/yE79NXoO3uxc1qvIflSYVh2knjr1PYF5txRJ9Nkrfa1Dbd672H55CCCFqJ4EmoOQd1V9XV9ooIJsZ3QHFYGRzgUM/1j3RjMUY/C8k/0AzTTKaQjRYzw4D6NCyK/N/fo8t+9YAUFh6nFlfP8PQnmO4YMDVWM3anE6rUeH2XrHc2C2ad7bG88DGTO6qcHDplrXcZfmGnu32oSb5/uy6Uh24+BHj2h+wfR6LKXUk3gGj8HbuCQYZBBJCiLqQQBMw5Pq2hlRTWwc9x39+phKjFWoPWAiUFPyjVFVVirULEQExtnj+cP7/sXHPCr5YMZsKpzbPesXWhWzZt5ZLhtxAr44D9fOjTQbu7hPHTd1jeHNLKX/fdDb/cw0lqsDOH48u4LqkJaS0KtbP9yQYKEsoB/cX2H74DNvsOJTOw/H0H4anZ38wWxr9PQshxKlG/nkOKLmH9dfe6gJN/xXnQRYCVTc/s7g8H7urHACbOZr46OQG9lYIcYKiKGR1Ppv/u+IpMtpm6ceLy/P5aNErfPj93ygszQu4Jt5i4IF+8Wy4Jo1H+sdhi45iRtRVZNlf4oL9T/DT0UzcLr//NZoU7F1NFJ5XQUn016hfPkLUvZdhe/VxTEu/huLCRnq3Qghx6pGMJmDIPaK/DiWjGWwhUJ9qAs2cfN9CoJZJbVFkvpcQYRcfncSNF9zHht0/89Xqj/S5m9sO/MruI1sY1e9Khva6EKPBt6FColULOO/KjOXd7WX8fVMpWys6cJ39PqKOOLgmahl3xnxDh2jfHG53ioGSFAMlHhXr/p+J+mIp0e+oqJ174s4agqfvELwdu8kQuxBCVJJAE1D8hs6DZTRVVa2S0XR7VbaGsOJ87/+3d+fBdZUHnve/zzl333S1L9Zm2bIt23gBY4ND2AxkoQkJaTrbTHdCmO63A3krNU06JG+qaFLVQ97Q6bc7k0D1hGKGDMkkhECahCaEEAcMxmBjY/AuL9r37e7rOc/7x7m6V9eSLdlGyKDnU3XqrPfeRxIWPz3r4NH88ZLype9CaRVFmYkQgvXLttJav44X3nyCPcdeAiCdTfG7PT9n7/EdfOzyz7F8ySVFr/PZNe5e6+fOVT5+djzOv7wToSvq5Cfx6/lJ/Do2Ok7xV74/8knfbuwiN++mLkgt1Ukt1dGiEveJY7j+cBjn0/8TM1CKcclmjHWbya65DPzB9/g7oSiKcvFQQTOdQpuwaiyk0JBlVdMekekxyEatE92DcFZyIpQlaQ04p9ajUe6aeenJjoEj+eOltW3vbtkVRZnG4/Rx69Y72LDsKp557TGGcsu/Dk308tgL/8SK+vV8dNNnqQzWFb3OZRPcscrLX67w8GxXkh8eiLB7OMO+dAv7xlq4b+JzfNLzOn9Z8iqrbB3515k+QWy9jdh6G/ZhE9fJMK49z2N/9XmkEJjNKzDWbMJYuwmjdS3YzryCmKIoygfNog+aYmTKQKDyKrBN/5aY0VP5Y83XjBDitIFAM/+PI5lO0DfaYX0OgqbqFe9SqRVFmU1T9Qq+8on7efXg87y0/99JZ61ZIo717Od47wE2r7qe69Z/Eo/LV/Q6mya4tdnNrc1u3hhK8aODUX7TmSRkenksej2PRa9ntb2b/+Tfwe3+XXiI5V+bqdTIVGpELrfh6DVxnTJwdh/Fceoo/PanSKcLY9UGjNWXYrRtxGxYpprZFUX5QFv0QVObpdkcQBZN1D7DiPMzNJt3DR3DzK2pXF3WgMfpm/E5RVHmh67ZuPqSm9m47EP8Yd+v2Ne+A4nElAa7Dr/A/hM7+fAlN7Ol7QYcNue012+ucrK5yklHJMv/OBzlp+1xQmnJoUwD3xr7PPeP3c4Nnv18qfR1NtveRifXtK4J0g066QYdshLnZOjsTWLbvwvb/l0ASF8AY9UGsqsvw2jbgKxtVPN2KorygaKC5pQR5+c0EGjq0pNnCJqnpjSbt9SoZnNFWSh+T5BPfejLbFl1A7/b/bP8v81EOsbv33yCnQef55r1t7BpxbXY9On/npv9Nv7b5iDfvjTAr04meORIjP2jGVLYeTa+iWfjmyjVonzKt5s7Sl9nKe2FF9sEqSadVJMOGYmzx8TVZeDoMdGiYWx7Xsa252UAzEAp5sp1GCvXY6zagLmkWdV4Koryvrbog6aYMuL8nKY2msNAoFMDh/PHzbnVShRFWTh15U186SP3crhrL8/v+TljkSEAoskQz77+OK8ceI7r1t/KhuVXFY1Qn+SxafznFV7+U6uHvSMZfnw4yq87EiQNGDd9PBq+jkfD19FkG+KLpbu5zb+HCqOr8Ab2wiAiDHD0Gbi6TJzdBloKtPA42u6XsO22BjJJXwCj9RKMFdZmNrWq+TsVRXlfWfRBc7apjaQ0MGOF/1Fo3iZGkwb9catJ3KnD8sD0b+Pp/TObq1e+yyVXFOV8CCFY3XQZKxvWs7d9B3/a/++E4+MAhGKj/Hrno7z8zrN8+JKPs2HZh2as4RRCcFmlg8sqy/juFpMnT8b5ybE4b+daOjqzVdw/fDP3D9/Mclsf/1flXj7u2U1JtrB4AzqF5nVpxz4icHamcXab2MLWeuwiGsa271Vs+14FQNrtmEvbMFrXYixfg7F8DQSC8/sNUxRFuQCLPmjOVqMpE4NgWoMIhKMU4QhyoC+Zv98WtGPTpvep6ho6hpTW/yxqyhpxO73vdtEVRbkAumbj8pXXsWHZh9h9dDsvv/MbYskIAGORQf595/9k+1u/Zuuaj7JpxbX5JS1PF3Rq3Nnm4842H/tH0zx+LM4TJ62+nADHs3Xc01/HPdzMGkcvd1Xv51rnXkoyHYU3EZCplGQq7UQ3gZZy4uzK4jqZwD5oImTusUwG/djb6Mfezr/UrKrLh05z2WrM+pYZBzUqiqIshMX920jKWWs0zVhhxPnk0pPvzGEg0Mn+QrP5UtVsrigXLbvNwdY1H+GyFdew6/ALvHLgP0imrdW8wvFxfrf7//DS289wxaobuaLtxmmj1KdaX+5g/ZUOvnN5Cc93J/nFiTgv9CTJSgDBwXQ9X+muB25muWOYu2ve5gbXmwRTxxDI/PuYzhSJVki0OgA79mgJzo4EriOj6LHiz9SG+tCG+rDvfAEAaXdgNq3AaFmF2dKG0bIKWVWnBhkpirIgFnfQjEUQCeu3tnS4kIHSaY8UDQTyWROuz2XEuZo/U1HeX5x2F9esu4Utq25gz7HtvHrwd0QTIQASqRjb9/+aVw78B+uXXckVbTdRXVp/xvdy2wSfXOrmk0vdjCYNnj6V4Bcn4uweLvzuOJ6u5Gtd24Bt1NtDfKX2MDd59lOT2o/ItaJYMmR8I2TWQnStC00rxx4pwdkZx/FOL3oyU/TZIpNGP34A/fiB/DXpDWA0r7Dm9Fy6ErN5BbKiRoVPRVHm3aIOmlpRs/nMv3TNGaY22j969qCZTMfpG+sAcvNnVqn5MxXl/cLlcHPV2o+zZdUNvHXiVXYceJbxyDAAGSPNnmMvsefYS7TUruaKthtZWb8B7Swjw8tder5p/WQ4y687Ejx9KlHUMtKTKeFbXVfwLa7AIzJ8ufYEnyp5m+XZfejpoaL3M81RUt5RUquBNQ50Ryv2WAn27jTOw93ow0OcTsTC2A7ugYN78tekL4DR1IrZ1IrZ2IrRtBxZUw8zDIJSFEU5X4s6aIqRc1/jvC9mcHjCmivPrsGG8ulBs3Ow0D+ztlz1z1SU9yO7zcHlK6/j0tarOdjxBjsO/AcDY4WBgSf7D3Gy/xClvkouX3kdG5dfhc9dctb3bAnY+K/r/PzXdX6OhzL8uiPJ06fiHBzP5p+JSzv/vW8V/71vFXA7H6sY4Qvlh9hkewd/7ADIKTWY0sBIncSwQXIpRJa70L2bsWUqcAwJ7O2D2E4eRcQi08oiomFsB9+Eg28W3s7hwmxchtmwDKNhmXVc3wJuz/l/IxVFWdQWddDUhmYZCGSmkYnCKFHN28SLJwsDga6sduKzT6/JmDp/ZrOaP1NR3td0TWddy5VcsvQKOoeOsevQCxzq2pP/Y3I8Oszv33yCP+z9FasaN7JpxbUsq1uDJs4+/+XyEjv3rLdzz3o/7aEMz3YmebYrUdS8DoLnRip5buQa4BrqnBnurDvJTb7DNGUPoMVPFb+pkcQIv40BpPzA5S70bZeg25uwRdw4uqLoHcfRO44h4tFpZRLpJPrxg+jHDzL1T2izsg6zocXalizFaGhBVi8BfVH/L0RRlDlY1L8lZp3aKN4DuZV9hKsGYXPzYu9Y/v4NS6avJAKn9c9UA4EU5QNBCGuasubqlUxER3njyIvsaf8TiZTVz9uUBoc693Cocw9BbwWXrriaDS1bKfVXzvrerSV2vrbOztfW+emPGzzXZYXOl/tTZMzCc30pO985tZLvsBLBJ7m6IsHnKo5xpeMQFcm3IXVas7mRxBjfi8Fe0kC8yoa2bDl6ya3oog7bqMDe3YfW2W5toTFmog33WYtb7H0lf03a7Jh1jZhLlmIuaaZEOBB+N7KqVjW/K4qSt6iD5tSm85lqNIsHAjWRNSV/mjK10bYl06c7KeqfKVT/TEX5IAr6yrlp019w7YZbOXDqDd5s/xNdQ8fz9ydiI/xx31P8cd9TNFWvYH3LVtY2b55TN5paj84dq7zcscpLJGPyp74Uv+9O8kJPkoFEIXVK4KURNy+NrAfW47F9nk9Uh7i1tJ31tiOUxA9MD54yixk+ghk+wmS9qairRWtbhV7yRXStDttwGr2nE637BFrXcbT+LoRpcjqRzaB3nUDvOgFAC8AvH7Lm+qxptEJobROyrhGzthGzpgEcM/9xrijKB9eiDppTm85lxUxB82ThWe9S9o6kmcjNjVfr0VhdOv3bV9Q/s6xJ9c9UlA8wh83Jpa0f5tLWDzM43sPe9pd568SrxFOFZunOwWN0Dh7j2dcfZ0X9eta3XElr/boZ11Y/nd+ucUuTm1ua3JhS8vZoht/3JPljb4rdw2mMwoxIxLOSn/cG+HnvZcBlBByCT1SHuSV4nHW2Y5QkDyPj3dM+Qyb7MZL9GIPbrQuaA61mOVrrCvTAVjT3UvTxNHpPB1rvKbTuk9Z+bHjGMotMBr37BHr3ieLPEQJZUYNZ02BttQ3ImnrMmkZkaYVaalNRPqAWb9A0DcToYOF0hhpNY2xf/lgLtPKHnsKUI9uWuBAzjFKfuuykajZXlMWjurSej23+PDdedjuHOt/krROvcqLvAGau+41hZjnc9SaHu97EYXOyon49a5ovZ8WS9Tjss4dOTQg2VDjYUOHg7zdAKG2yoz/F9r4U23uTnIwYRc+H05LHu/083r0R2EjALthWleLm0lNc5minKnMEosfBLJ4eCTONGTqEGTpEfoiSzYvmb0W/rBXt2pvR/MsRpg+9rxOttxOtt4Pk8UP4xofRJkZmLL+QEjHcb3VZeueNonvS4cSsqkNW12NW12NWL0FWL7H2QRVCFeX9bNEGTTE+ishav2Clv2TaqEozNYoZzf1FLnT00g28uKswU/K2M/TPPFXUP1MNBFKUxcam21nXcgXrWq4gmgjxzqnX2X9yJ70jhYE76WyKAx1vcKDjDey6g9b6daxuvIzW+nV4nGeeEH6qEofGnzW5+bMmNwAdkSwv96fYkdumNrMDhDOSp3sdPN27EliJU/8zNpULPlbWz1bPCZZyHGfsCDI5fXoksjHM8bcwx98qXNM9aP5laEta0FaupHfjGppWXYVIptD6OtH6u6wtdyyG+hFyehM8gEin0HtOQc+pafek3YFZWYesqrPCaG5vVtZac4Gq5nhFuagt3qA5dQ7NGZrNjdHClB9ayVrGsi72jkxY5wKurZvePzORitE/Zs27KYSgqVr1z1SUxcznLuHK1Tdx5eqbGA718/bJ1zjQ8QYjocLvn4yRzg8i0oRGY1UrKxs2sLJ+AxUltTO2nMyk2W+j2W/jL1d4kVJyPJxlR3+aHf0pXhucHjxTBrw6JHl1qAaoAT7EEo/O9ZUJtgU6Wes4RY1xAhE9Bpnw9A804pgT72BOvANAJRAf+ieEpwHN14LWtBRt9UY0320IZyUik0Yb6kUM9KANdKP1d6MN9KANdCGiM7x/jsik0fs6oK9jxvtmsAJZVYtZUYusrMWsqEFW1lj70kq1HKeiLLBF+y9QmzoQqGqmoFlo2tHLN7G9L5VfIG5ThYNS5/SmnM4p65vXlTXjcqi55xRFsVSW1LJt421s23gbg+M9HOzczcGOPQxNFKZQM6VJx+BROgaP8vyeX1Dmr2ZF/TqW162luWbVGddbP50QgtYSO60ldu5YZQXPjojBzsEUuwbTvDaY5ng4O+11vXGD/93p4H/TCrQigJVBnW3lIT7s62aVvYPK7CmryT0Tmv7B0kTGOjFinYU+n2DVfvqa0bxNaNVNaC1tCO9HEY4yK0hHw2iDvWiDPWiDPYjBXiuEDvUhYmcOoYDVVD8xgn7snenFERqytAJZUY1ZXo0sr8asqEaWVSPLqzDLq8Ct+tErynxavEHzLAOBpJnFGC/0z7SVX86L+6b0z6yfvdm8WfXPVBTlDKpL66kuref6DZ9ieKKPQ11vcrR7Hz3DJ5FT1jwfiwyy6/AL7Dr8Arqm01jVyvK6S1hWt4basqazrkg0lRCCpQEbSwM2vtBqBavhhMHu4TR7htO8MZRm70iGeFYWvU4CRyYMjkz4+BFtQBuagBUlOh8ujXCVv5s2ew81ZgcyfAxbdub+mRjxfL/PIjYvmqcRzduI8NSjrWhA23AjwlWLmJwiKRbJr+cuhvqsWtGRAet8bGjGEfH5r1uaiLEhGBtCZ3oQBZAeL2ZZFTK3mWWVyLLKomOc7rl8mxVFmcGiDZpFTeenDQQyQ4cha/XHFM5KpKeRF3sLA4dumGFaI4AONRBIUZRzVBms45pgHdesu4VoIsSxnv0c6X6LE30HSGcLf+AapsGpgSOcGjjCC3t/icvhobl6JUtr2lhas4rqsoZZJ4kv+ly3zscb3Xy80QpRWVNycDzDm8MZ9o6k2TuS5shEFrM4e2LKyfDp4cdY/T0BKh0mWyrh6kA/6109NGo9BDJdEOuA7PTJ4a0PjWGGD2OGDxdfFzaEuxbNU4/mqUO469FW1CE2rCvUggJks4ixIbThfmug0ciAFUJzezExipBy+udO/ah4DD0+c//QSdLjwyytQAYrrBrS0grM0krrOFhubSWlagJ7RZnBov1XMbXpXJ7WdG6M7c4f6+WXc3A8y1Cuf1OZU5tx2cmJ6Aj9o9bydKp/pqIo58PnLuHS1qu5tPVqMtk0nUPHON57gON9BxgcL56aKJmOc6R7H0e6rdYXt8NLU/UKGqtaaaxqpa68GbvNMefPtmmC9eUO1pc7uAOr1jOWMdk/agXPt0cz7B/N0B6eHj4BhtMav+2F3/YuAZYAW9AFLAvoXBGMsMXXz2pHH3X04sv2QKwTjPjMhZFZZLwbI96Ncfo93YXmrrWCqLvO2tfWIVo2WX1Bp04Wn0lbQXRkEDE6iDY6iJg8HhuyakQzmdM/YRoRj6LHo9DbccZnpBDIQOmU4FlmbcFyzKnnJWXgnFsXCEX5IFi0QVMMnXkwkDFaHDRf7C3UKly/xImuTe+cv/Pg8/kmr6U1bap/pqIoF8Ruc7C8bi3L69YCEIlPcLzPCp0n+w8RTRT3kUykY0XBU9ds1JU301jVSkPVcuorWgh4Suc8uAjAa9fYWuNka02hu1AsY3JwPJMPngfHMxwez5IwpqdPQ8KxkMGxkIefsAxYZpVNQLNf4/KSGJu9/bQ5B1gi+giafdiSPcjU6JkLZSQxo6cgemp6CBU6wlmFcFdbYdRVjeauQdRXI5ZvQThKEVNrfaVERCYQo0OI0SErfI6PIMaH0caGEWPDiPHh/AwlZyOkRITGIDQGne1nfVa63IXgGSjFLClD+oPIklJkoAwZyB37g1Yf0nP4mSnKxWZRBk2RzeTnepNCQ5ZX5++ZyWHrlxiAsKGXbuAPewrNPjOtBhRPRtnT/qf8+VVrPz4/BVcUZdHye4JsXH4VG5dfhZSSkfAAHQNHONl/mI6BI0STxcHTMLN0Dx+ne/g4HMy9hzvIkooW6itbWFKxlLry5jlPpzTJa9fYXOVkc1UhfBqm5I/vnCAaqOPgWJYD4xmOTGToiEyLgtbzEk6ETU6E3fycFnLrCgEQdAguKcmw2T/MWtcQzbZBqsUA/mw/WrLvzM3wANJAJvuRyf7iqZgmaXYriLqq0VxVCFclwlWFFqxCVC9DuLYgtNNqgaWESAhtfDgXQkfQcmFUTIzmNy08PufvoUgmEMleGOyd9VlpsyP9JVZtqT9oHfuDVhg9/dxXAh6fmndUuagsyqDpCBX+WpblxdNfGGN78sdacC0R08nrg4X1f6+vmz4Q6PWjL5LJpgGoLm3I10AoiqLMByEElSW1VJbUcvnK66zgGeqnc+gYXUPtdA21MxoenPa6SGKCI917OdK9N3+txFtObVkTdeVN1JY3UVvWdM41n7omaPZIWpd6+NTSwvVoxuTYRJbDE1at59GJDEdDWbqjBmfqOTmRluwYtrFjuBYobm0KOmB9IMlG7yht7mGabUPUiCEC5iCOVD9kZgl7ZgaZ6EUmejnjECJ7EM1VgXBWWE3xzgrrPFCBqKhHODcgbDMMDspmEaExxMRIbj+KNjGWPxahUURo3Do3po/4PxORzSDGR2D8DAOtTiOFhvQFwF+C9AVyW0luCxQ2bwDyx36wz72bhaKci0UZNJ3jhaXTztZsbiu/nD/2p5gciHlJmZ1qj170fCabZtehF/LnH1778XP6Ba0oinKhhBBUBuuoDNaxacW1AMSSYbqGjtM11E7vyEl6RzpIZ5PTXhuKjRKKjRaFT7fDS1XpEqpLG6gO1udHyZ9rlyCfXePSSgeXVhaHmHjW5Hgoy7FQlqMTWU6EsxwPWftY9syDdybS8NKIi5dGJvuBFmgClnqyXOofZ417lOWOEer1YcrFMD5jGEdm6Oy1oZMyE5iZCYgcP/MzuicXRMvQnOXWAKXJfXkZorYF4bhs5kAqJcSjiNAYWigXRMMTiPB48XF43GrWT03/mZ2NkCYiMgGRiXN6nXS6kN4AK+0OHKUVVgj1+Kwg6vEjvT7w+nPH1rn0+q2mfTUISjmLRflfh2PKEmmyqq5wbGYwxt7Kn+vll/Pi/kL/zBtmWA1o3/EdxFMRAILeCtYu3TwPJVYURTk3XleAtsZLaWu8FADTNBkO9dE7cpKekZP0jpxicLwHw5xeu5ZIx/JrtE/l9wSpLKmztmAdVSV1VJTU4nOXnFPZPDaNdeUO1pUXB1ApJQMJK4QeD2U5FclyMpzlZCRLR8SYNv3SVKaEEzEbJ2KV/JLKGZ9Z4kyy0T/BavcYLc5x6vVRKrVRSuQo7uwwemYMcea6zgIjjox3IeNdZ39ad1n9Qh2lVgh1BHPHuX1dENHUhnAEQXfPXEmRSuTC5wQiMo4IhxDRkBVCwxPWPpK7Fg0h4rHp7zEHIpVEpJJ4AAZ7Znu8iHS5rQDq8YHHZwVUjw/p8RbO3V7rvtuL9HiR7tw9t9da3UlV0HxgLfqgaVbUFI5Dh/KjIIWrGtz1/KG3sBzbtvri/pmmafLKwefy51vXfARdW5TfUkVRLnKapuVrJi9tvRqw+nEOT/TRP9ZF/2gn/WOd9I91kcokZnyPSHyCSHyCk/3F82E67S58jlLq+pqoCNRQHqimLFBNmb8Kj9M351YeIQS1Hp1aj86Ha4v/sJdSMpgwORnO0hk16Ihk6YxYx52RLH3x2QNib8pFb6qG31Iz430dgxZnmNXeECtcEzQ7x1mij1OhjRNkDI85hiM7hpBzbPo2kshEPzLRP/uzmh1hD1oh1F6CcJSAvQRhDyAcJYhACaI8gLA3IOwBsPsQQp/+PtkMIhrOhdEQTB5Hw4Xr0Yh1HAtb92Phs85HOhurz2kCxmZYvnQOpK6Dy4t0e6xwmj/2gctjhVS3J3fsQbo8VmB1uYuvudyqdvUitCh/Is6pNZpT5tA8fbT5iYhBV9TqzO63Czaf1vxzqGsP4xGrGd7t9HJZ6zXzWWxFUZR3la7ZqClrpKaskY3LrwKsQBeKjTE43s3geA+DEz0MjnczEhqYsfYTIJVJksr0M3pqeqBy2t2U+isp81dR5q8i6Kug1FdB0FdB0FuBwz63tcqFENR4dGo8OltnKoMh6Y0ZdEWzdEUNuqPWcU/MoDe3ZWbJUgY67alS2lOlZ3lKUqpFaXZMsMIdZqkzRL0jTK0+QYUeIsg4XhnCaYyjydlHq+eZGWRqGJkanv1ZAATYfFYQtftz+wDY/Qib37pW5ocqP8Jek7+GzTM9oEoJiRgiFqH78EGayoMQi1oBNBpBxCOImLURjyJiUetaPGqdzzJX6axfiWFALDzrKlBzIR3OfOicupdON7hze5e7aC9dbnC6kU5X7pqrcO50q2VML9Ci/O4V1WhOaTrPnhY0f9NZ6Btzda0Th174q1xKyY53ns2fb1l1w5x/YSqKolyshBAEfeUEfeWsbNiQv26YBhPRYYYm+hie6GM4ZG0joYEz1oACpDIJBsa6GBjrmvG+x+kn6CunxFtGiXfqvpyApxS/p2ROLUVOXdASsNESmPlZU0qGEia9MYOemEFfzKAvXrzvjxukZ63YE4ybfsaTfvadtfukJCASVOohqm0hWlxhGh1Rau1hqm1hyrUIQRHCJ0O4ZRhdpmf9Gk9/f7IRZDaCPPO3f8byY/MgbD6EzZcLpl7r2OZD9yRJljQhyr1gq0bYWhA2D+hehM2bC6pTRrWbJiTjiHjUCqPxqBVa41HrOGbtRSKGSMSsYJo7Jx5DJGNzmst0zl9dOoVIp+AcZgGYjbTZwemywqnTdVoQdSEdrsJ1x+TemXveWbjucFrXHZP3rT02+we668DiDJpTBgPJXNO5mRxCxjqti8JOp7aaf9ofyT/3kYbiZvNTA4fpG+0AwKbb2bLqhvkttKIoygLSNZ3yQA3lgZp8v0+w/uiOJSO8dWg37oCd0dAAI+EBxiPDjEWGZhyANFU8FSGeiuR/n55OIPC6AgS8QfyeUit8uoP43CX4PUH87iB+dwled+CsgVSbUiN62cxdOJFSMp4y6Y+bDCQMBuIGA3GTgbjBYMJgMGFa+7g547yhp5c8LD2Esx5OZGvZOcuYHrdIUaFbAbRCt7Y6e4xaR4QqW5QKPUpQRPCLKF4iuOT59cW0AmoMmY0hmT4zQQBIz1axqHus8GnzInRPIYBO7kvdiIrJ+1XWNd1t9UO1uXPHHqu7gBCQSUMing+jIhHLn5OcvB63AmwijkjGc9enHCcT1v4Ca1dnIrIZq0tCLDL7w+dBClEIoE4n2J1TQqkzF1IdYJ9yze4oPGO3znHkrrk8YPfPS1nPx+ILmrEItpT15590OK1VGihuNhfBS/jrVxP5juergjb+oqV4tOWOd/4jf3xp69X43IH5LrmiKMpFRwiBzx2gOtBIa2tr0b3JEDoeGWIsMsRYdJhQdITx6AgT0RFCsVEMc+a5NvPvgSSaDFnzhI52nvVZj9OH1x3A5wrgdZXgcwfwugJ4XX48Lj9elx+v04/XFcDl9ExbslMIQZlLp8yls4bpK8BN/brCGclwwmAoYTKcNBmaPE4YjCTN/DacNAilZw8/CemkO1tJ9xkGMp1OxyCoxSjVopTpUYJazDrXo5RpMSptcSptUUr1OCVaDL+I4xNR3JxT9efMjDjSiENq5IzTVM2J0K3wOSWEWudWjaHwuKbcDyL0GmuAle6y9prrtHMnZE1EKotI5fqNJhOIZByRSljhNZmwBlilcvemPpdKQCpZdI9Ucl7Ca9G3Qcrc5ybhXciyZkkZfPX/vfA3epcsuqCpTV3jvKI2X11tjBbmz3w5dQlvjlhV+XYN/sfVpbhshWrt/rEujve9A1i/mD60+iPvRdEVRVHeVyZDqM8doKFq+bT7pmkSSUzkplgaO20/Sjg2QSwZzq+6Npt4Kko8FWWYvjmVze3w4nb68Dh9eFzW3u304XZ48Ti9uCb3Ti9uhxeXw4PL4UHXdEocghKHxvI5DLhPG5LRlMlocnIzis7H0yZjSZOxlLWNp0wimbN/zQY6o2aAUTMAc5+WEx2DgJagRItRosUJaHGCmhVGA1qcgJbI74NanFLdOvZrCXwigVuc23RLZyUNyEaRuWmn3r04p4HutAKo5iwcB5yIUidok/ccoJdZAVV3WpP1565b1xwI4QCpQVaiZaUVZDMSLZ2FtIFIpRGZlBUSU0lE2tqTPu1aOpW7l8o/IzIp6/wc5lWdk4tsTtRFFzTFcOEXkKy0ms2lmcYY35e//u3jhXXK/5+NgaIpOCLxCX7z2v/Kn69pupyyQGFlIUVRFGVuNE3L9cksO+MzhpklmggRjo0Tjo8TSVgj3619iEhigmgiRDwZmXMgBatWcjKYnmXByxk5bC7cTg9OuweXw43L4cFpd1vHdg9OhxuX3Y3T4cZpd+O0u3Da3VTbXTQGXThsLhz26TWqU2VMyUQudI6nCmF0Ii2ZSJtMpExCaes8lDu2NnnWuUgNdMZNH+Pmua0INUnDxK8l8IsEPi055TiBP3fuE7n9lGOvSOHVkvi0JD5h7e3i7LXZ588EI4E0CrW381cnKazA6nAgXI5ceLVboTW3Cc0OmnfKscPqNjB5LHWEFAgpwLCKLwyJyFp7DBORMRFZA5ExIGPtRToL6SxaJgPpLCKdQaRTyEBw3r7a87HogqY2PJA/Nitrkdk4qSP/HxjWX2m9RiXHM1ZwvLLawVfXFv4xdgwe5Rd/+lHRGsNquUlFUZT5o2u2/OCgszFMg3gyQiwZJpoME0sU9rGUdd26b21nG8A0m3Q2met7Ojbrs2fjsDlzoXOmvbXZc3uf3UmpzYnD6cTudWDXHdhtTuw2h7XpDuy69TyajVhWJ5yBcC58hjMm4bRJOC2JZKwa00jaJDx1nzGZiKdJoBPNyBlH6ZtohEwvIbxMX2z+HL9+Mni1FB6RxKul8OX2XpHEo6XwihQeLYlHpHJBNYVHpHCLFB4tnX/OI9K4RTp3PYVj3gLsTCSYKTBTRWF23oKtBjhz2+mEBsKOcM2t+8V7ZREGzULTebbSTWLP/42MFyan/T+RKwGBzyZ4+MOl6JpASsnOQ8/z+z2/wJTWvzyB4CObPsOSiqWnf4SiKIryHtM13Roc5AnO6XnDzJJIxYglIyRyNZvxVJRkOk48FSWRipFIx6x9KkYyHc9v51JzejbpbIp0NgXvYmv0JIHAptux2ezYdYd1rDuw2+yU6XaqdHvumh2b247dZ90PhyJUVlRi0+0gbGTRyUobGWkjI3XSUiclbaRMnZSpkTRtJEyNhKGRMHRihk7M0IhnBTFDI5bViWQFCUMQz8qiSffT2EmbdsbxXXBoncpGFo9I49ImA6i1ebQUbpHGJYqvTz7nEpn8PdeUc5fI4NKKz5257b0NtbOQJsgUkeQ8/Ad1AeYcNB955BF+8IMfMDg4yKpVq3jggQfYunWm2cwsBw8e5Otf/zp79+6ltLSUL37xi/z93//9gi/PONl0nmzWiDh+A/HCtAr/K3IdPwzdDMB3ryih2W8jmU7w9KuPcKiz0IfT4/TzF9f8Lcvq1ry3hVcURVHeFbpmw+cuOedVjUxpks4krfCZSZBKx0lmEiTTcVLpRO5aglQmd5xJkEonrX3GqglNZ5JWwJxHEknGSJMx0iQ4xxHqs3dxncYG+HPbTDSho2s6mkNH03Q0oSM0HSFs1qAgoSPRkMKGxDo20TDRMXLHWWkdZ6W1GVIjkzvOSI2MKchIjbTUyJgaaVNgSA2JRgaNcTRG0ZDYMHFYn4fARM/ttdznivznF56x9sXnGgKJXRg4yOIUBnZhYBdZHMLEIbI4RRaXyFjPCCMXUK1rDpHFkQ+t2VxwzVob1rXJZybfyyGy2Jk8tq7bRRaXKPTzHEvrF1Ut4pzK8tRTT3Hvvffy/e9/nyuuuIJHHnmE22+/nV27dtHQ0DDt+XA4zKc+9Sm2bt3KH//4R9rb27nrrrvweDx89atffde/iHMhRvoZvNxOeIUdsgYSjbR08L3Qp3k+tpoltHNlaZTy8QQ/3z5Kz8gJQrFC80hD5TI+c+1dszbjKIqiKB88mtDyg4IuhClNMtkUqUwyt08VhdB0JkUmV+OZzhaOM9m0tRlpMrnzdDZFxkiTzWby9840uf5CMaWBaRgXVHNpy23nNGP1e1m3JZlTm7kpBRJBFo0MgiiiKMQWb5Nh1wm4ZrgvIL/HGuCs+/i7i6ixdU5B80c/+hGf//zn+au/+isAHnzwQV588UUeffRR7rvvvmnP//KXvySRSPDwww/jdrtZvXo1x44d46GHHuLuu+9euFpN0yTLIL+vKWFvn7foVjl/4PPiD9bJBOycmP7yK9pu5CObPotNLXGlKIqiXABNaLmBQu55eX/TNK3waWTI5vaZbG5vZDBy++xp28BgP8GyIMaUa4aZJWtYm2FmMEwjf90wsmRz+8nnTNOw7uW3i6h5+SKgiclEev7Lfp6Nrp9tZav33qyJKZ1O89Zbb02ribz++ut5/fXXZ3zNG2+8wZVXXonbXfgHtG3bNv7xH/+Rzs5OmpubZ3xde3v7ORT9PJgm/mvvYmL4Oc6lU4xdd7Bl2cdpKVvLqZOn5q98yjmb9/9mlPeE+jl+MKif4/uFDujYcBVCgGZtFfXvflWYlBJTmpjSQEoTwzSQ0sDInZvSxDSN/DPWZlr3TBMT6/7ks/nXSBMpDUwpkZjT7k/fS6sMSGT+3LovMa33yZ9LpJzyHOaUczP/HtZnS8iVwZSFY5m7N/ke71bf3tm4hRVg36t/j6fPn3u6WYPm6OgohmFQWVk8iqmyspKhoaEZXzM0NERdXd205yfvnSlozlbYd8XKlQz++zCE3sTUnNg1sGkCu6bhtNkJ+spz6/BWEvSWE/RVUFPWMG9/dSrnr729/b35b0aZV+rn+MGgfo4fDOrnOL+ssDol4E4GVNOcEkqZFnhNaeYCrMwF4qmhl/w5gKbpREdTF83Pcc5twKc3d0spz9oEPtPzM11fCJ9efS2trf9loYuhKIqiKMoiIoRACIHGmedQfTe0j148rQuzfqXl5eXouj6t9nJkZGRaLeekqqqqGZ8HzvgaRVEURVEU5YNl1qDpcDjYsGED27dvL7q+fft2tmzZMuNrNm/ezGuvvUZyylxO27dvp7a2lqampgsssqIoiqIoivJ+MKe627vuuouf/exn/OQnP+Ho0aN84xvfYGBggC996UsA3H///XziE5/IP//nf/7nuN1uvvKVr3Do0CGeeeYZ/uVf/oWvfOUrF0XTuaIoiqIoijL/5tRH87bbbmNsbIwHH3yQwcFB2traeOKJJ2hsbARgYGCAU6cKo7FLSkp4+umnueeee7juuusIBoPcdddd3H333fPzVSiKoiiKoigXnTkPBrrzzju58847Z7z38MMPT7u2Zs0annvuufMvmaIoiqIoivK+Nr/DnhRFURRFUZRFSwVNRVEURVEUZV6ooKkoiqIoiqLMCxU0FUVRFEVRlHmhgqaiKIqiKIoyL1TQVBRFURRFUeaFCpqKoiiKoijKvBATExNyoQuhKIqiKIqifPCoGk1FURRFURRlXqigqSiKoiiKoswLFTQVRVEURVGUeaGCpqIoiqIoijIvVNBUFEVRFEVR5oUKmoqiKIqiKMq8WHRB85FHHmHdunVUV1dzzTXXsHPnzoUuknIOXn31VT772c/S1tZGMBjkpz/96UIXSTkP//zP/8x1111HQ0MDy5Yt4zOf+QyHDh1a6GIp5+jHP/4xW7dupaGhgYaGBm688Uaef/75hS6WcgG+//3vEwwG+frXv77QRVHO0QMPPEAwGCzaVqxYsdDFWlxB86mnnuLee+/l7/7u73j55ZfZvHkzt99+O93d3QtdNGWOYrEYq1ev5rvf/S5ut3uhi6Ocp1deeYUvf/nLPP/88zzzzDPYbDY++clPMj4+vtBFU85BXV0d999/Py+99BLbt2/n6quv5gtf+AIHDhxY6KIp52H37t089thjrFmzZqGLopyn1tZWjh49mt8uhsq0RTVh+7Zt21izZg0/+MEP8tcuvfRSbr31Vu67774FLJlyPpYsWcL3vvc9vvCFLyx0UZQLFI1GaWxs5Kc//Skf+9jHFro4ygVobm7mvvvu40tf+tJCF0U5B6FQiGuuuYZ//dd/5Xvf+x6rV6/mwQcfXOhiKefggQce4JlnnuG1115b6KIUWTQ1mul0mrfeeovrr7++6Pr111/P66+/vkClUhQFrKBpmibBYHChi6KcJ8Mw+NWvfkUsFmPz5s0LXRzlHH3ta1/j1ltv5ZprrlnooigXoKOjg7a2NtatW8cdd9xBR0fHQhcJ20IX4L0yOjqKYRhUVlYWXa+srGRoaGiBSqUoCsC9997LJZdcogLK+9DBgwe56aabSCaTeL1eHn/8cdX0+j7z2GOPcfLkSf7t3/5toYuiXIBNmzbx0EMP0draysjICA8++CA33XQTu3btoqysbMHKtWiC5iQhRNG5lHLaNUVR3jvf+ta32LVrF7/73e/QdX2hi6Oco9bWVnbs2EEoFOKZZ57hb//2b/ntb3/L6tWrF7poyhy0t7fzne98h+eeew6Hw7HQxVEuwI033lh0vmnTJjZs2MDPfvYz7r777gUq1SIKmuXl5ei6Pq32cmRkZFotp6Io741vfvObPPXUU/zmN7+hubl5oYujnAeHw0FLSwsAGzduZO/evTz00EP88Ic/XOCSKXPxxhtvMDo6ypVXXpm/ZhgGO3fu5NFHH6Wvrw+n07mAJVTOl8/nY9WqVZw8eXJBy7Fo+mg6HA42bNjA9u3bi65v376dLVu2LFCpFGXx+sY3vsGTTz7JM888c1FMwaG8O0zTJJ1OL3QxlDm6+eab2blzJzt27MhvGzdu5NOf/jQ7duxQtZzvY8lkkvb2dqqrqxe0HIumRhPgrrvu4m/+5m+47LLL2LJlC48++igDAwNqdOT7SDQazf91ZpomPT09vP3225SWltLQ0LDApVPm6p577uEXv/gFjz/+OMFgkMHBQQC8Xi8+n2+BS6fM1T/8wz9w0003sWTJEqLRKE8++SSvvPIKTzzxxEIXTZmjyfkWp/J4PJSWlqruD+8z3/72t/noRz9KfX19vo9mPB7nc5/73IKWa1EFzdtuu42xsTEefPBBBgcHaWtr44knnqCxsXGhi6bM0b59+7jlllvy5w888AAPPPAAn/vc53j44YcXsGTKuXjkkUcAuPXWW4uuf+Mb3+Cb3/zmQhRJOQ+Dg4P89V//NUNDQwQCAdasWcOTTz7Jtm3bFrpoirLo9PX1ceeddzI6OkpFRQWbNm3ihRdeWPCMs6jm0VQURVEURVHeO4umj6aiKIqiKIry3lJBU1EURVEURZkXKmgqiqIoiqIo80IFTUVRFEVRFGVeqKCpKIqiKIqizAsVNBVFURRFUZR5oYKmoiiKoiiKMi9U0FQURVEURVHmxf8PSD8tBXiobrwAAAAASUVORK5CYII=\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 5, 100)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "\n", "df1 = [10, 5, 8, 15]\n", "df2 = [5, 10, 15, 8]\n", "\n", "for df in zip(df1, df2):\n", " f_pdf = sp.stats.f.pdf(x, dfn=df[0], dfd=df[0])\n", " ax.plot(x, f_pdf, lw=3, label=\"$df_1 = %.d, df_2 = %.d$\" % (df[0], df[1]))\n", "ax.legend(fontsize=15)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\chi^2$ and $F$ distribution are mostly used for statistical testing, we will elaborate the topic later." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Student's t Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **t-distribution** is used when data are approximately normally distributed, which means the data follow a bell shape but the population variance is unknown. We will come back to this topic in chapter of estimation.\n", "\n", "The PDF of t-distribution is derived from normal and $\\chi^2$ distribution\n", "$$\n", "f(t)=\\frac{\\Gamma\\left(\\frac{\\nu+1}{2}\\right)}{\\sqrt{\\nu \\pi} \\Gamma\\left(\\frac{\\nu}{2}\\right)}\\left(1+\\frac{t^{2}}{\\nu}\\right)^{-\\frac{\\nu+1}{2}}\n", "$$\n", "where $\\Gamma(\\cdot)$ is the Gamma function that\n", "$$\n", "\\Gamma(x) = (x-1)!\n", "$$\n", "\n", "So far we just need a visual memory about the comparison of t-distribution and normal distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If a sample has $n$ observations, the degree of freedom (d.o.f.) of t-distribution is $n-1$, the larger the d.o.f. the shape is closer to normal distribution." ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(-3, 3, 100)\n", "y_norm = sp.stats.norm.pdf(x, loc=0, scale=1)\n", "fig, ax = plt.subplots(figsize=(10, 6))\n", "ax.plot(x, y_norm, label=\"Normal Distribution\")\n", "for i in range(1, 11):\n", " y_t = sp.stats.t.pdf(x, df=i, loc=0, scale=1)\n", " ax.plot(\n", " x,\n", " y_t,\n", " color=\"tomato\",\n", " alpha=0.1 * i,\n", " label=\"t-Distribution with dof = {}\".format(i),\n", " )\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Gamma distribution is commonly used to model positive variables, such as variance. The common pdf form follows\n", "$$\n", "f(x)=\\frac{1}{\\beta^{\\alpha}\\Gamma(\\alpha)} x^{\\alpha-1} \\exp \\left[-\\frac{x}{\\beta}\\right] \\text { for } x>0 \\text { and } \\alpha, \\beta>0\n", "$$\n", "where $\\alpha$ is _shape_ parameter and $\\beta$ is _scale_ parameter. Also note that the probability shall be integrated to unity, this implies\n", "$$\n", "\\beta^{\\alpha} \\Gamma(\\alpha)=\\int_{0}^{\\infty} x^{\\alpha-1} \\exp \\left[-\\frac{x}{\\beta}\\right] d x\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In Bayesian statistics, another formulation of Gamma distribution is more common\n", "$$\n", "p(x)=\\frac{1}{\\left(\\frac{2 \\mu}{v}\\right)^{v / 2}} \\frac{1}{\\Gamma\\left(\\frac{v}{2}\\right)} x^{\\frac{v-2}{2}} \\exp \\left[-\\frac{x v}{2 \\mu}\\right] \\text { for } x>0 \\text { and } \\mu, v>0\n", "$$\n", "where \n", "$$\n", "v = 2\\alpha\\\\\n", "\\mu=\\alpha \\beta\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The two special form of Gamma distribution are Chi-Square distribution $(m=\\mu)$ and Exponential distribution $(v=2)$." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 10, 100)\n", "fig, ax = plt.subplots(figsize=(18, 6), nrows=1, ncols=2)\n", "for i in range(1, 11):\n", " y_gamma = sp.stats.gamma(a=i, scale=1).pdf(x=x)\n", " ax[0].plot(x, y_gamma, label=r\"$\\alpha={}, \\beta=1$\".format(i))\n", " y_gamma = sp.stats.gamma(a=1, scale=i).pdf(x=x)\n", " ax[1].plot(x, y_gamma, label=r\"$\\alpha=1,\\beta={}$\".format(i))\n", "ax[0].legend()\n", "ax[1].legend()\n", "plt.suptitle(\"Gamma Distribution\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate Normal Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a vector of random variables\n", "$$\n", "X=\\left(x_{1}, x_{2}, \\cdots, x_{N}\\right)^T\n", "$$\n", "that follows a multivariate normal distribution, the pdf is given by\n", "$$\n", "f(X)=(2 \\pi)^{-N / 2}|\\Sigma|^{-1 / 2} \\exp \\left(-\\frac{1}{2}(X-\\mu)^T \\Sigma^{-1}(X-\\mu)\\right) \\text { for } \\sigma>0\n", "$$\n", "where \n", "$$\n", "\\mu=\\left(\\mu_{1}, \\mu_{2}, \\cdots \\mu_{N}\\right)\n", "$$\n", "and $\\Sigma$ is an $N\\times N$ covariance matrix." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multivariate t Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a vector of random variables\n", "$$\n", "X=\\left(x_{1}, x_{2}, \\cdots, x_{N}\\right)^T\n", "$$\n", "that follows a multivariate t distribution, the pdf is given by\n", "$$\n", "f(X)=\\frac{v^{v / 2} \\Gamma\\left(\\frac{v+N}{2}\\right)}{\\pi^{N / 2} \\Gamma\\left(\\frac{v}{2}\\right)}|\\Sigma|^{-1 / 2}\\left[v+(X-\\mu)^{\\prime} \\Sigma^{-1}(X-\\mu)\\right]^{-(v+N) / 2} \\text { for } v>0\n", "$$\n", "where \n", "$$\n", "\\mu=\\left(\\mu_{1}, \\mu_{2}, \\cdots \\mu_{N}\\right)\n", "$$\n", "and $\\Sigma$ is an $N\\times N$ covariance matrix, $v$ is the degree of freedom." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
    " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.stats import multivariate_t\n", "\n", "x, y = np.mgrid[-10:10:0.01, -10:10:0.01]\n", "pos = np.dstack((x, y))\n", "rv = multivariate_t(loc=[1, -3], shape=[[5, 0.3], [2, 1.5]], df=2)\n", "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"}, figsize=(10, 7))\n", "ax.view_init(30, 0)\n", "ax.plot_surface(x, y, rv.pdf(pos))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Multinomial Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **multinomial distribution** differs from multivariate normal distribution, the former is the generalization of binomial distribution, i.e. multiple categories of 'success'. The PDF is " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{aligned}\n", "\\operatorname{Pr}\\left(X_{1}=x_{1}, \\ldots, X_{k}=x_{k}\\right)\n", "&= \\begin{cases}\\frac{n !}{x_{1} ! \\cdots x_{k} !} p_{1}^{x_{1}} \\times \\cdots \\times p_{k}^{x_{k}}, & \\text { when } \\sum_{i=1}^{k} x_{i}=n \\\\\n", "0 & \\text { otherwise }\\end{cases}\n", "\\end{aligned}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For instance, in a black bag, there are $10\\%$ of red candies, $40\\%$ of yellow candies and $50\\%$ of blue candies. The probability of catching exactly $2$ red, $3$ yellow and $4$ blue has a probability of \n", "$$\n", "\\frac{(2+3+4)!}{2!3!4!}\\times .1^2 \\times .4^3 \\times .5^4\\approx 5\\%\n", "$$" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The probability is 0.0504\n" ] } ], "source": [ "import math as mt\n", "\n", "prob = (\n", " mt.factorial(2 + 3 + 4)\n", " / (mt.factorial(2) * mt.factorial(3) * mt.factorial(4))\n", " * 0.1**2\n", " * 0.4**3\n", " * 0.5**4\n", ")\n", "print(\"The probability is {:.4f}\".format(prob))" ] }, { "cell_type": "markdown", "metadata": { "jp-MarkdownHeadingCollapsed": true, "tags": [] }, "source": [ "## Dirichlet Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Normal-Gamma Distribution " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a vector of random variables\n", "$$\n", "X=\\left(x_{1}, x_{2}, \\cdots, x_{N}\\right)^T\n", "$$\n", "and a scalar random variable $h$. The joint pdf for $X$ and $h$ follows a Normal-Gamma distribution if it takes the form\n", "$$\n", "f(X, h)=(2 \\pi)^{-N / 2}(h)^{N / 2}|\\Sigma|^{-1 / 2} \\exp \\left(-\\frac{h}{2}(X-\\mu)^{\\prime} \\Sigma^{-1}(X-\\mu)\\right) \\frac{1}{\\left(\\frac{2 m}{v}\\right)^{v / 2}} \\frac{1}{\\Gamma\\left(\\frac{v}{2}\\right)} h^{\\frac{v-2}{2}} \\exp \\left[-\\frac{h v}{2 m}\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The condition pdf of $X$ given $h$ follows a normal distribution, denoted as\n", "$$\n", "X \\mid h \\sim N\\left(\\mu, h^{-1} \\Sigma\\right)\n", "$$\n", "And the marginal pdf of $X$ follows a $t$-distribution\n", "$$\n", "X \\sim t\\left(\\mu, m^{-1} \\Sigma, v\\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The marginal pdf of $h$ follows a gamma distribution, denoted as\n", "$$\n", "h \\sim \\operatorname{Gamma}(m, v)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# What is Kernel? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A **Kernel** is the core part of a pdf function that cannot be factored out of any terms which do not depend on $X$, e.g.\n", "$$\n", "P(X)= Kg(X)\n", "$$\n", "where $g(X)$ is the kernal and $K$ is the constant that ensures integration equals to unity. That also implies\n", "$$\n", "\\int_{X} g(X) d X=\\frac{1}{K}\n", "$$" ] } ], "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": "3.9.12" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "471.323px", "left": "161px", "top": "180px", "width": "209.396px" }, "toc_section_display": true, "toc_window_display": true } }, "nbformat": 4, "nbformat_minor": 4 }