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probability_inf_fs2023.ipynb
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"<a href=\"https://colab.research.google.com/gist/jteichma/a9c2621e0a27faf1b8a885c039120778/probability_inf_fs2020.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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"source": [
"<div style=\"text-align: right\">Peter Norvig, 12 Feb 2016 and some small additions by Josef Teichmann, Feb-May 2023</div>"
],
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"source": [
"# A Concrete Introduction to Probability (using Python)\n",
"\n",
"This notebook covers the basics of probability theory, with Python 3 implementations. (You should have some background in [probability](http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html) and [Python](https://www.python.org/about/gettingstarted/).)\n",
"\n",
"\n",
"In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n",
"\n",
">*Probability ... is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n",
"\n",
"![Laplace](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG/180px-AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG)\n",
"<center><a href=\"https://en.wikipedia.org/wiki/Pierre-Simon_Laplace\">Pierre-Simon Laplace</a><br>1814</center>\n",
"\n",
"\n",
"Laplace really nailed it, way back then! If you want to untangle a probability problem, all you have to do is be methodical about defining exactly what the cases are, and then careful in counting the number of favorable and total cases. We'll start being methodical by defining some vocabulary:\n",
"\n",
"\n",
"- **[Experiment](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n",
" An occurrence with an uncertain outcome that we can observe.\n",
" <br>*For example, rolling a die.*\n",
"- **[Outcome](https://en.wikipedia.org/wiki/Outcome_(probability%29):**\n",
" The result of an experiment; one particular state of the world. What Laplace calls a \"case.\"\n",
" <br>*For example:* `4`.\n",
"- **[Sample Space](https://en.wikipedia.org/wiki/Sample_space):**\n",
" The set of all possible outcomes for the experiment.\n",
" <br>*For example,* `{1, 2, 3, 4, 5, 6}`.\n",
"- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n",
" A subset of possible outcomes that together have some property we are interested in.\n",
" <br>*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`.\n",
"- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n",
" As Laplace said, the probability of an event with respect to a sample space is the number of favorable cases (outcomes from the sample space that are in the event) divided by the total number of cases in the sample space. (This assumes that all outcomes in the sample space are equally likely.) Since it is a ratio, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n",
"<br>*For example, the probability of an even die roll is 3/6 = 1/2.*\n",
"\n",
"This notebook will develop all these concepts; I also have a [second part](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers paradoxes in Probability Theory."
]
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"source": [
"## Code for `P`\n",
"\n",
"`P` is the traditional name for the Probability function:"
]
},
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"source": [
"from fractions import Fraction\n",
"\n",
"def P(event, space):\n",
" \"The probability of an event, given a sample space of equiprobable outcomes.(Gleichverteilung)\"\n",
" return Fraction(len(event & space),\n",
" len(space))"
],
"execution_count": null,
"outputs": []
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"source": [
"Read this as implementing Laplace's quote directly: *\"Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.\"*\n",
"\n",
"\n",
"## Warm-up Problem: Die Roll"
]
},
{
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"source": [
"What's the probability of rolling an even number with a single six-sided fair die?\n",
"\n",
"We can define the sample space `D` and the event `even`, and compute the probability:"
]
},
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"source": [
"D = {1, 2, 3, 4, 5, 6}\n",
"even = { 2, 4, 6}\n",
"\n",
"P(even, D)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Fraction(1, 2)"
]
},
"metadata": {},
"execution_count": 5
}
]
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"source": [
"It is good to confirm what we already knew.\n",
"\n",
"You may ask: Why does the definition of `P` use `len(event & space)` rather than `len(event)`? Because I don't want to count outcomes that were specified in `event` but aren't actually in the sample space. Consider:"
]
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"cell_type": "code",
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"source": [
"even = {2, 4, 6, 8, 10, 12}\n",
"\n",
"P(even, D)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Fraction(1, 2)"
]
},
"metadata": {},
"execution_count": 6
}
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{
"cell_type": "code",
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},
"id": "a7dh8YZ5LC_q",
"outputId": "8952ed44-1a9e-4800-b237-114520e4ef0a"
},
"source": [
"import numpy as np\n",
"\n",
"np.exp(-1)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0.36787944117144233"
]
},
"metadata": {},
"execution_count": 7
}
]
},
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"source": [
"Here, `len(event)` and `len(space)` are both 6, so if just divided, then `P` would be 1, which is not right.\n",
"The favorable cases are the *intersection* of the event and the space, which in Python is `(event & space)`.\n",
"Also note that I use `Fraction` rather than regular division because I want exact answers like 1/3, not 0.3333333333333333."
]
},
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"source": [
"\n",
"\n",
"## Urn Problems\n",
"\n",
"Around 1700, <a href=\"https://en.wikipedia.org/wiki/Jacob_Bernoulli\">Jacob Bernoulli</a> wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=probability%20ball%20urn). (You'd think the urns would be empty by now.)\n",
"\n",
"For example, here is a three-part problem [adapted](http://mathforum.org/library/drmath/view/69151.html) from mathforum.org:\n",
"\n",
"> An urn contains 23 balls: 8 white, 6 blue, and 9 red. We select six balls at random (each possible selection is equally likely). What is the probability of each of these possible outcomes:\n",
"\n",
"> 1. all balls are red\n",
"2. 3 are blue, 2 are white, and 1 is red\n",
"3. exactly 4 balls are white\n",
"\n",
"So, an outcome is a set of 6 balls, and the sample space is the set of all possible 6 ball combinations. We'll solve each of the 3 parts using our `P` function, and also using basic arithmetic; that is, *counting*. Counting is a bit tricky because:\n",
"- We have multiple balls of the same color.\n",
"- An outcome is a *set* of balls, where order doesn't matter, not a *sequence*, where order matters.\n",
"\n",
"To account for the first issue, I'll have 8 different white balls labelled `'W1'` through `'W8'`, rather than having eight balls all labelled `'W'`. That makes it clear that selecting `'W1'` is different from selecting `'W2'`.\n",
"\n",
"The second issue is handled automatically by the `P` function, but if I want to do calculations by hand, I will sometimes first count the number of *permutations* of balls, then get the number of *combinations* by dividing the number of permutations by *c*!, where *c* is the number of balls in a combination. For example, if I want to choose 2 white balls from the 8 available, there are 8 ways to choose a first white ball and 7 ways to choose a second, and therefore 8 &times; 7 = 56 permutations of two white balls. But there are only 56 / 2 = 28 combinations, because `(W1, W2)` is the same combination as `(W2, W1)`.\n",
"\n",
"We'll start by defining the contents of the urn:"
]
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"outputId": "1b433932-ce7a-4a8b-9f47-2b2b5280715d"
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"source": [
"def cross(A, B):\n",
" \"The set of ways of concatenating one item from collection A with one from B.\"\n",
" return {a + b\n",
" for a in A for b in B}\n",
"\n",
"urn = cross('W', '12345678') | cross('B', '123456') | cross('R', '123456789')\n",
"#urn = cross('W', '12') | cross('B', '12')\n",
"urn"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'B1',\n",
" 'B2',\n",
" 'B3',\n",
" 'B4',\n",
" 'B5',\n",
" 'B6',\n",
" 'R1',\n",
" 'R2',\n",
" 'R3',\n",
" 'R4',\n",
" 'R5',\n",
" 'R6',\n",
" 'R7',\n",
" 'R8',\n",
" 'R9',\n",
" 'W1',\n",
" 'W2',\n",
" 'W3',\n",
" 'W4',\n",
" 'W5',\n",
" 'W6',\n",
" 'W7',\n",
" 'W8'}"
]
},
"metadata": {},
"execution_count": 8
}
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
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"base_uri": "https://localhost:8080/"
},
"id": "nz_mXNgjRGgc",
"outputId": "71ec9149-6a68-4e16-d44c-565fdefebe61"
},
"source": [
"len(urn)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"23"
]
},
"metadata": {},
"execution_count": 9
}
]
},
{
"cell_type": "markdown",
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"source": [
"Now we can define the sample space, `U6`, as the set of all 6-ball combinations. We use `itertools.combinations` to generate the combinations, and then join each combination into a string:"
]
},
{
"cell_type": "code",
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"outputId": "e6d141ca-148e-4062-c326-68323f7729ff"
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"source": [
"import itertools\n",
"\n",
"def combos(items, n):\n",
" \"All combinations of n items; each combo as a concatenated str.\"\n",
" return {' '.join(combo)\n",
" for combo in itertools.combinations(items, n)}\n",
"\n",
"U6 = combos(urn, 6)\n",
"\n",
"len(U6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"100947"
]
},
"metadata": {},
"execution_count": 10
}
]
},
{
"cell_type": "markdown",
"source": [
"Let us check what the function combos actually does:"
],
"metadata": {
"id": "zxFAO4MLm956"
}
},
{
"cell_type": "code",
"source": [
"combos({'1','2','3'},2)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "KUtJRnOdm8TM",
"outputId": "f3c0fa2b-601f-49e7-9028-d41d390bf2b0"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"{'1 2', '1 3', '3 2'}"
]
},
"metadata": {},
"execution_count": 11
}
]
},
{
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"button": false,
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"id": "9eizDTGHRGgc"
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"source": [
"I don't want to print all 100,947 members of the sample space; let's just peek at a random sample of them:"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
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"outputId": "5ffacf49-135e-49ea-85dd-63b409ac1895"
},
"source": [
"import random\n",
"\n",
"random.sample(U6, 10)"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"<ipython-input-12-c351e0ff2955>:3: DeprecationWarning: Sampling from a set deprecated\n",
"since Python 3.9 and will be removed in a subsequent version.\n",
" random.sample(U6, 10)\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"['R2 R7 B1 B5 R3 W2',\n",
" 'B1 R9 B2 W8 R6 W7',\n",
" 'R7 B4 B1 B5 W5 B2',\n",
" 'R2 B3 W1 B2 R3 R5',\n",
" 'R7 R1 W1 B2 R6 R4',\n",
" 'R2 B1 B5 R3 W8 R4',\n",
" 'R2 B4 B6 W3 R3 W8',\n",
" 'B1 R9 W3 W5 B2 W7',\n",
" 'R2 B4 B6 B5 W4 W2',\n",
" 'R7 R1 B3 W3 R5 W2']"
]
},
"metadata": {},
"execution_count": 12
}
]
},
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"cell_type": "markdown",
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"source": [
"Is 100,947 really the right number of ways of choosing 6 out of 23 items, or \"23 choose 6\", as mathematicians [call it](https://en.wikipedia.org/wiki/Combination)? Well, we can choose any of 23 for the first item, any of 22 for the second, and so on down to 18 for the sixth. But we don't care about the ordering of the six items, so we divide the product by 6! (the number of permutations of 6 things) giving us:\n",
"\n",
"$$23 ~\\mbox{choose}~ 6 = \\frac{23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18}{6!} = 100947$$\n",
"\n",
"Note that $23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18 = 23! \\;/\\; 17!$, so, generalizing, we can write:\n",
"\n",
"$$n ~\\mbox{choose}~ c = \\frac{n!}{(n - c)! \\cdot c!}$$\n",
"\n",
"And we can translate that to code and verify that 23 choose 6 is 100,947:"
]
},
{
"cell_type": "code",
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"button": false,
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"run_control": {
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"id": "T0sV4VEQRGgd"
},
"source": [
"from math import factorial\n",
"\n",
"def choose(n, c):\n",
" \"Number of ways to choose c items from a list of n items.\"\n",
" return factorial(n) // (factorial(n - c) * factorial(c))"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
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"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "k25WsJNQRGge",
"outputId": "06e71ca7-8e47-4a6f-ad1d-ec289af97fb1"
},
"source": [
"choose(23, 6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"100947"
]
},
"metadata": {},
"execution_count": 14
}
]
},
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"cell_type": "markdown",
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"source": [
"Now we're ready to answer the 4 problems:\n",
"\n",
"### Urn Problem 1: what's the probability of selecting 6 red balls?"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
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"run_control": {
"read_only": false
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"id": "rTmn1rhNRGge",
"outputId": "0a4eebaf-3904-4198-e4ec-d1f6d446a66a"
},
"source": [
"red6 = {s for s in U6 if s.count('R') == 6}\n",
"\n",
"P(red6, U6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Fraction(4, 4807)"
]
},
"metadata": {},
"execution_count": 15
}
]
},
{
"cell_type": "markdown",
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"button": false,
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"source": [
"Let's investigate a bit more. How many ways of getting 6 red balls are there?"
]
},
{
"cell_type": "code",
"metadata": {
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"id": "scRl4umBRGge",
"outputId": "c32d5490-a10b-4e9c-f52b-faac2724b274"
},
"source": [
"len(red6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"84"
]
},
"metadata": {},
"execution_count": 16
}
]
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"source": [
"Why are there 84 ways? Because there are 9 red balls in the urn, and we are asking how many ways we can choose 6 of them:"
]
},
{
"cell_type": "code",
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"outputId": "134ca8b1-118d-4474-d9e9-7ae4621fd702"
},
"source": [
"choose(9, 6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"84"
]
},
"metadata": {},
"execution_count": 17
}
]
},
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},
"source": [
"So the probabilty of 6 red balls is then just 9 choose 6 divided by the size of the sample space:"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "ntjjiBGMRGgg",
"outputId": "c6128b5f-c09a-4521-b081-360e0ea720b4"
},
"source": [
"P(red6, U6) == Fraction(choose(9, 6),\n",
" len(U6))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {},
"execution_count": 18
}
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"id": "LD6NifLERGgh"
},
"source": [
"### Urn Problem 2: what is the probability of 3 blue, 2 white, and 1 red?"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "M-S871AURGgh",
"outputId": "834da39e-3e72-470e-ed53-c119f5b790b2"
},
"source": [
"b3w2r1 = {s for s in U6 if\n",
" s.count('B') == 3 and s.count('W') == 2 and s.count('R') == 1}\n",
"\n",
"P(b3w2r1, U6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Fraction(240, 4807)"
]
},
"metadata": {},
"execution_count": 19
}
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"id": "RoK0qxhrRGgh"
},
"source": [
"We can get the same answer by counting how many ways we can choose 3 out of 6 blues, 2 out of 8 whites, and 1 out of 9 reds, and dividing by the number of possible selections:"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "aaem8ZNnRGgh",
"outputId": "e1135adf-fbca-4c86-d3b9-625552b2f19f"
},
"source": [
"P(b3w2r1, U6) == Fraction(choose(6, 3) * choose(8, 2) * choose(9, 1),\n",
" len(U6))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {},
"execution_count": 20
}
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"id": "z0zLgIexRGgi"
},
"source": [
"Here we don't need to divide by any factorials, because `choose` has already accounted for that.\n",
"\n",
"We can get the same answer by figuring: \"there are 6 ways to pick the first blue, 5 ways to pick the second blue, and 4 ways to pick the third; then 8 ways to pick the first white and 7 to pick the second; then 9 ways to pick a red. But the order `'B1, B2, B3'` should count as the same as `'B2, B3, B1'` and all the other orderings; so divide by 3! to account for the permutations of blues, by 2! to account for the permutations of whites, and by 100947 to get a probability:"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "042LFEgvRGgi",
"outputId": "b6032c0c-ca77-4454-a530-86b53581e63d"
},
"source": [
" P(b3w2r1, U6) == Fraction((6 * 5 * 4) * (8 * 7) * 9,\n",
" factorial(3) * factorial(2) * len(U6))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {},
"execution_count": 21
}
]
},
{
"cell_type": "markdown",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"id": "sgqetM0IRGgi"
},
"source": [
"### Urn Problem 3: What is the probability of exactly 4 white balls?\n",
"\n",
"We can interpret this as choosing 4 out of the 8 white balls, and 2 out of the 15 non-white balls. Then we can solve it the same three ways:"
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "oXCYD25iRGgi",
"outputId": "36f2b079-1c4b-4f4e-fd1d-462a14b2fb61"
},
"source": [
"w4 = {s for s in U6 if\n",
" s.count('W') == 4}\n",
"\n",
"P(w4, U6)"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"Fraction(350, 4807)"
]
},
"metadata": {},
"execution_count": 22
}
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "xONolzMURGgi",
"outputId": "f25a16d2-a912-4ae7-c743-1526a33cd17f"
},
"source": [
"P(w4, U6) == Fraction(choose(8, 4) * choose(15, 2),\n",
" len(U6))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {},
"execution_count": 23
}
]
},
{
"cell_type": "code",
"metadata": {
"button": false,
"new_sheet": false,
"run_control": {
"read_only": false
},
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "UKSAaI7XRGgi",
"outputId": "481c0412-7378-4b77-ac19-fad8d4db8937"
},
"source": [
"P(w4, U6) == Fraction((8 * 7 * 6 * 5) * (15 * 14),\n",
" factorial(4) * factorial(2) * len(U6))"
],
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"True"
]
},
"metadata": {},
"execution_count": 24
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "MUUhMP2_RGgi"
},
"source": [
"# Simple Random Walk\n",
"\n",
"We demonstrate in the sequel trajecorial and distributional properties of simple random walks. First we generate one trajectory of a simple random walk with $N$ steps."
]
},
{
"cell_type": "code",
"metadata": {
"id": "OqT17lKURGgj"
},
"source": [
"import numpy\n",
"import pylab\n",
"\n",
"def RandomWalk(N=100, d=2):\n",
" return numpy.cumsum(2*numpy.random.binomial(1,0.5,(N,d))-1)"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 430
},
"id": "dfAr2ANYRGgj",
"outputId": "477711be-e9d3-4a7c-8aec-ccae386ae554"
},
"source": [
"Y=numpy.random.binomial(1,0.5,200)\n",
"pylab.plot(numpy.cumsum(2*Y-1))\n",
"pylab.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 430
},
"id": "ItGULzO7RGgj",
"outputId": "db201872-02dc-47dc-9f30-69b89fec89db"
},
"source": [
"def PlotRandomWalkXT(N=100,W=5):\n",
" \"\"\"\n",
" Plot X(t) for one-dimensional random walk W times\n",
" \"\"\"\n",
" for i in range(W):\n",
" X = RandomWalk(N,1)\n",
" pylab.plot(X)\n",
"\n",
" pylab.show()\n",
"\n",
"PlotRandomWalkXT(10000,5)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "p-w4v1rfRGgk"
},
"source": [
"Notice the impressive roughess of the trajectories.\n",
"\n",
"Next we generate $W$ endpoints of a simple random walk with $N$ steps and draw a histogram of its distribution."
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 430
},
"id": "wdSbA3XuRGgk",
"outputId": "57ce19c1-6e64-4733-8e7f-7957653ba35e"
},
"source": [
"def Endpoints(W=10000, N=1000):\n",
" return numpy.sum(2*numpy.random.binomial(1,0.5,(W,N))-1,axis=0)\n",
"\n",
"def HistogramRandomWalk(W=10000, N=100):\n",
" sigma = numpy.sqrt(W)\n",
" X = Endpoints(W, N)\n",
" pylab.hist(X)\n",
" pylab.show()\n",
"HistogramRandomWalk(W=10000, N=10000)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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3335bhYVcKQEAABp4BGb27NkKhUK67bbblJKS4tzeeustZ8yLL76oO+64Q8OGDdOAAQPk8/n07rvvOvtjY2O1dOlSxcbGyu/366c//alGjRqlp59+2hnTuXNnFRYWqqioSL1799bzzz+v1157TZmZmedhyQAAwHbn9D0wzRnfAwOcOb4HBqfC98DgQrsg3wMDAADQFAgYAABgHQIGAABYh4ABAADWIWAAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdQgYAABgHQIGAABYh4ABAADWIWAAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdQgYAABgHQIGAABYh4ABAADWIWAAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdQgYAABgHQIGAABYh4ABAADWIWAAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdRocMOvWrdOdd96p1NRUxcTEaPHixRH7H3roIcXExETchgwZEjFm//79GjFihDwejxISEjRmzBgdPHgwYszmzZt16623qnXr1kpLS9PMmTMbvjoAABCVGhwwhw4dUu/evfXyyy+fcsyQIUO0d+9e5/bmm29G7B8xYoTKyspUVFSkpUuXat26dXrsscec/eFwWIMHD1anTp1UUlKiZ599Vk8++aReffXVhk4XAABEoZYNfcDQoUM1dOjQ045xu93y+Xwn3ff5559r+fLl+uSTT3T99ddLkmbNmqXbb79dzz33nFJTUzV//nzV1NTo9ddfl8vlUo8ePVRaWqoXXnghInQAAMDFqVHOgVmzZo2SkpLUtWtXjRs3Tt9++62zLxAIKCEhwYkXScrIyFCLFi20ceNGZ8yAAQPkcrmcMZmZmSovL9d333130tesrq5WOByOuAEAgOh03gNmyJAh+u///m8VFxfrP//zP7V27VoNHTpUtbW1kqRgMKikpKSIx7Rs2VKJiYkKBoPOmOTk5Igx9ffrx/xQQUGBvF6vc0tLSzvfSwMAAM1Egz9C+jHDhw93/r1Xr1665pprdOWVV2rNmjUaNGjQ+X45R35+vvLy8pz74XCYiAEAIEo1+mXUV1xxhdq1a6cvv/xSkuTz+bRv376IMceOHdP+/fud82Z8Pp8qKysjxtTfP9W5NW63Wx6PJ+IGAACiU6MHzO7du/Xtt98qJSVFkuT3+1VVVaWSkhJnzKpVq1RXV6d+/fo5Y9atW6ejR486Y4qKitS1a1ddeumljT1lAADQzDU4YA4ePKjS0lKVlpZKknbs2KHS0lJVVFTo4MGDmjRpkjZs2KCdO3equLhYd999t7p06aLMzExJUvfu3TVkyBCNHTtWH3/8sdavX6/c3FwNHz5cqampkqQHH3xQLpdLY8aMUVlZmd566y299NJLER8RAQCAi1eDA+bTTz/Vtddeq2uvvVaSlJeXp2uvvVbTp09XbGysNm/erLvuuktXX321xowZo759++oPf/iD3G638xzz589Xt27dNGjQIN1+++265ZZbIr7jxev1auXKldqxY4f69u2riRMnavr06VxCDQAAJEkxxhjT1JNoDOFwWF6vV6FQiPNhgB9x+dTCpp4CmqmdM7Kaegq4yJzpz29+FxIAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALBOy6aeABBtLp9a2NRTAICo1+AjMOvWrdOdd96p1NRUxcTEaPHixRH7jTGaPn26UlJSFBcXp4yMDH3xxRcRY/bv368RI0bI4/EoISFBY8aM0cGDByPGbN68Wbfeeqtat26ttLQ0zZw5s+GrAwAAUanBAXPo0CH17t1bL7/88kn3z5w5U7/+9a81Z84cbdy4UZdccokyMzN15MgRZ8yIESNUVlamoqIiLV26VOvWrdNjjz3m7A+Hwxo8eLA6deqkkpISPfvss3ryySf16quvnsUSAQBAtIkxxpizfnBMjBYtWqR77rlH0vdHX1JTUzVx4kT9/Oc/lySFQiElJydr3rx5Gj58uD7//HOlp6frk08+0fXXXy9JWr58uW6//Xbt3r1bqampmj17tn7xi18oGAzK5XJJkqZOnarFixdr+/btZzS3cDgsr9erUCgkj8dztksEGoyPkBBNds7Iauop4CJzpj+/z+tJvDt27FAwGFRGRoazzev1ql+/fgoEApKkQCCghIQEJ14kKSMjQy1atNDGjRudMQMGDHDiRZIyMzNVXl6u77777qSvXV1drXA4HHEDAADR6bwGTDAYlCQlJydHbE9OTnb2BYNBJSUlRexv2bKlEhMTI8ac7DmOf40fKigokNfrdW5paWnnviAAANAsRc1VSPn5+crLy3Puh8NhIgYAzpGNH4nysdfF4bwegfH5fJKkysrKiO2VlZXOPp/Pp3379kXsP3bsmPbv3x8x5mTPcfxr/JDb7ZbH44m4AQCA6HReA6Zz587y+XwqLi52toXDYW3cuFF+v1+S5Pf7VVVVpZKSEmfMqlWrVFdXp379+jlj1q1bp6NHjzpjioqK1LVrV1166aXnc8oAAMBCDQ6YgwcPqrS0VKWlpZK+P3G3tLRUFRUViomJ0fjx4/Xv//7veu+997RlyxaNGjVKqampzpVK3bt315AhQzR27Fh9/PHHWr9+vXJzczV8+HClpqZKkh588EG5XC6NGTNGZWVleuutt/TSSy9FfEQEAAAuXg0+B+bTTz/VwIEDnfv1UTF69GjNmzdPkydP1qFDh/TYY4+pqqpKt9xyi5YvX67WrVs7j5k/f75yc3M1aNAgtWjRQsOGDdOvf/1rZ7/X69XKlSuVk5Ojvn37ql27dpo+fXrEd8UAAICL1zl9D0xzxvfAoKnYeNIjEE04idduTfI9MAAAABcCAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALDOeQ+YJ598UjExMRG3bt26OfuPHDminJwcXXbZZWrTpo2GDRumysrKiOeoqKhQVlaW4uPjlZSUpEmTJunYsWPne6oAAMBSLRvjSXv06KEPPvjgby/S8m8vM2HCBBUWFuqdd96R1+tVbm6u7r33Xq1fv16SVFtbq6ysLPl8Pn300Ufau3evRo0apVatWumXv/xlY0wXAABYplECpmXLlvL5fCdsD4VC+q//+i8tWLBAf/d3fydJmjt3rrp3764NGzaof//+WrlypbZt26YPPvhAycnJ6tOnj5555hlNmTJFTz75pFwuV2NMGQAAWKRRzoH54osvlJqaqiuuuEIjRoxQRUWFJKmkpERHjx5VRkaGM7Zbt27q2LGjAoGAJCkQCKhXr15KTk52xmRmZiocDqusrKwxpgsAACxz3o/A9OvXT/PmzVPXrl21d+9ePfXUU7r11lu1detWBYNBuVwuJSQkRDwmOTlZwWBQkhQMBiPipX5//b5Tqa6uVnV1tXM/HA6fpxUBAIDm5rwHzNChQ51/v+aaa9SvXz916tRJb7/9tuLi4s73yzkKCgr01FNPNdrzAwCA5qPRL6NOSEjQ1VdfrS+//FI+n081NTWqqqqKGFNZWemcM+Pz+U64Kqn+/snOq6mXn5+vUCjk3Hbt2nV+FwIAAJqNRg+YgwcP6quvvlJKSor69u2rVq1aqbi42NlfXl6uiooK+f1+SZLf79eWLVu0b98+Z0xRUZE8Ho/S09NP+Tput1sejyfiBgAAotN5/wjp5z//ue6880516tRJe/bs0RNPPKHY2Fg98MAD8nq9GjNmjPLy8pSYmCiPx6PHH39cfr9f/fv3lyQNHjxY6enpGjlypGbOnKlgMKhp06YpJydHbrf7fE8XAABY6LwHzO7du/XAAw/o22+/Vfv27XXLLbdow4YNat++vSTpxRdfVIsWLTRs2DBVV1crMzNTr7zyivP42NhYLV26VOPGjZPf79cll1yi0aNH6+mnnz7fUwUAAJaKMcaYpp5EYwiHw/J6vQqFQnychAvq8qmFTT0F4KK2c0ZWU08B5+BMf37zu5AAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdQgYAABgHQIGAABYh4ABAADWIWAAAIB1CBgAAGAdAgYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIeAAQAA1iFgAACAdVo29QSA07l8amFTTwEA0AxxBAYAAFiHgAEAANYhYAAAgHUIGAAAYB0CBgAAWIerkAAAUcXGqxd3zshq6ilYhyMwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArEPAAAAA6xAwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOu0bOoJ4MK4fGphU08BAIDzhiMwAADAOs36CMzLL7+sZ599VsFgUL1799asWbN04403NvW0AAA4r2w8Sr5zRlaTvn6zPQLz1ltvKS8vT0888YT+7//+T71791ZmZqb27dvX1FMDAABNrNkGzAsvvKCxY8fq4YcfVnp6uubMmaP4+Hi9/vrrTT01AADQxJrlR0g1NTUqKSlRfn6+s61FixbKyMhQIBA46WOqq6tVXV3t3A+FQpKkcDjcuJO1RF31X5t6CgCAKNJYP1/rn9cYc9pxzTJg/vKXv6i2tlbJyckR25OTk7V9+/aTPqagoEBPPfXUCdvT0tIaZY4AAFzMvL9q3Oc/cOCAvF7vKfc3y4A5G/n5+crLy3Pu19XVaf/+/brssssUExPT6K8fDoeVlpamXbt2yePxNPrrNTXWG91Yb/S6mNYqsV4bGWN04MABpaamnnZcswyYdu3aKTY2VpWVlRHbKysr5fP5TvoYt9stt9sdsS0hIaGxpnhKHo/H2jfN2WC90Y31Rq+Laa0S67XN6Y681GuWJ/G6XC717dtXxcXFzra6ujoVFxfL7/c34cwAAEBz0CyPwEhSXl6eRo8ereuvv1433nijfvWrX+nQoUN6+OGHm3pqAACgiTXbgLn//vv1zTffaPr06QoGg+rTp4+WL19+wom9zYXb7dYTTzxxwsdY0Yr1RjfWG70uprVKrDeaxZgfu04JAACgmWmW58AAAACcDgEDAACsQ8AAAADrEDAAAMA6BMw5qK6uVp8+fRQTE6PS0tKIfZs3b9att96q1q1bKy0tTTNnzjzh8e+88466deum1q1bq1evXnr//fcv0Mwb5q677lLHjh3VunVrpaSkaOTIkdqzZ0/EmGhZ786dOzVmzBh17txZcXFxuvLKK/XEE0+opqYmYly0rPc//uM/dNNNNyk+Pv6UX/xYUVGhrKwsxcfHKykpSZMmTdKxY8cixqxZs0bXXXed3G63unTponnz5jX+5M+Tl19+WZdffrlat26tfv366eOPP27qKZ2VdevW6c4771RqaqpiYmK0ePHiiP3GGE2fPl0pKSmKi4tTRkaGvvjii4gx+/fv14gRI+TxeJSQkKAxY8bo4MGDF3AVZ6agoEA33HCD2rZtq6SkJN1zzz0qLy+PGHPkyBHl5OTosssuU5s2bTRs2LATvhz1TN7bzcHs2bN1zTXXOF9O5/f7tWzZMmd/NK21QQzO2r/8y7+YoUOHGklm06ZNzvZQKGSSk5PNiBEjzNatW82bb75p4uLizG9/+1tnzPr1601sbKyZOXOm2bZtm5k2bZpp1aqV2bJlSxOs5PReeOEFEwgEzM6dO8369euN3+83fr/f2R9N6122bJl56KGHzIoVK8xXX31llixZYpKSkszEiROdMdG03unTp5sXXnjB5OXlGa/Xe8L+Y8eOmZ49e5qMjAyzadMm8/7775t27dqZ/Px8Z8yf/vQnEx8fb/Ly8sy2bdvMrFmzTGxsrFm+fPkFXMnZWbhwoXG5XOb11183ZWVlZuzYsSYhIcFUVlY29dQa7P333ze/+MUvzLvvvmskmUWLFkXsnzFjhvF6vWbx4sXms88+M3fddZfp3LmzOXz4sDNmyJAhpnfv3mbDhg3mD3/4g+nSpYt54IEHLvBKflxmZqaZO3eu2bp1qyktLTW333676dixozl48KAzJjs726SlpZni4mLz6aefmv79+5ubbrrJ2X8m7+3m4r333jOFhYXmj3/8oykvLzf/+q//alq1amW2bt1qjImutTYEAXOW3n//fdOtWzdTVlZ2QsC88sor5tJLLzXV1dXOtilTppiuXbs69//pn/7JZGVlRTxnv379zM9+9rNGn/u5WrJkiYmJiTE1NTXGmOhf78yZM03nzp2d+9G43rlz5540YN5//33TokULEwwGnW2zZ882Ho/HWf/kyZNNjx49Ih53//33m8zMzEad8/lw4403mpycHOd+bW2tSU1NNQUFBU04q3P3w4Cpq6szPp/PPPvss862qqoq43a7zZtvvmmMMWbbtm1Gkvnkk0+cMcuWLTMxMTHmz3/+8wWb+9nYt2+fkWTWrl1rjPl+ba1atTLvvPOOM+bzzz83kkwgEDDGnNl7uzm79NJLzWuvvXZRrPVU+AjpLFRWVmrs2LH6n//5H8XHx5+wPxAIaMCAAXK5XM62zMxMlZeX67vvvnPGZGRkRDwuMzNTgUCgcSd/jvbv36/58+frpptuUqtWrSRF93olKRQKKTEx0bkf7es9XiAQUK9evSK+QDIzM1PhcFhlZWXOGBvXWlNTo5KSkoi5t2jRQhkZGc1+7g21Y8cOBYPBiLV6vV7169fPWWsgEFBCQoKuv/56Z0xGRoZatGihjRs3XvA5N0QoFJIk5+9pSUmJjh49GrHebt26qWPHjhHr/bH3dnNUW1urhQsX6tChQ/L7/VG91h9DwDSQMUYPPfSQsrOzI/6iHy8YDJ7wjcH194PB4GnH1O9vbqZMmaJLLrlEl112mSoqKrRkyRJnXzSut96XX36pWbNm6Wc/+5mzLZrX+0PnstZwOKzDhw9fmImehb/85S+qra2Nij+nH1O/ntOtNRgMKikpKWJ/y5YtlZiY2Kz/e9TV1Wn8+PG6+eab1bNnT0nfr8Xlcp1wXtcP1/tj7+3mZMuWLWrTpo3cbreys7O1aNEipaenR+VazxQB8/9NnTpVMTExp71t375ds2bN0oEDB5Sfn9/UUz4nZ7reepMmTdKmTZu0cuVKxcbGatSoUTIWfYlzQ9crSX/+8581ZMgQ/eM//qPGjh3bRDNvuLNZK2CrnJwcbd26VQsXLmzqqTSqrl27qrS0VBs3btS4ceM0evRobdu2ramn1aSa7e9CutAmTpyohx566LRjrrjiCq1atUqBQOCE3zNx/fXXa8SIEXrjjTfk8/lOOAO8/r7P53P+ebIx9fsb25mut167du3Url07XX311erevbvS0tK0YcMG+f3+qFzvnj17NHDgQN1000169dVXI8Y19/U2dK2n4/P5Trgq50zX6vF4FBcXd4azvvDatWun2NjYJn1fXij166msrFRKSoqzvbKyUn369HHG7Nu3L+Jxx44d0/79+5vtf4/c3FwtXbpU69atU4cOHZztPp9PNTU1qqqqijgycfyf7Zm8t5sTl8ulLl26SJL69u2rTz75RC+99JLuv//+qFvrGWvqk3Bs8/XXX5stW7Y4txUrVhhJ5ne/+53ZtWuXMeZvJ3nWn+RqjDH5+fknnOR5xx13RDy33+9vtid5Hu/rr782kszq1auNMdG33t27d5urrrrKDB8+3Bw7duyE/dG2XmN+/CTe46/K+e1vf2s8Ho85cuSIMeb7k3h79uwZ8bgHHnjAmpN4c3Nznfu1tbXmJz/5SdSexPvcc88520Kh0ElP4v3000+dMStWrGiWJ/HW1dWZnJwck5qaav74xz+esL/+xNbf/e53zrbt27ef9MTW0723m7OBAwea0aNHXxRrPRUC5hzt2LHjhKuQqqqqTHJyshk5cqTZunWrWbhwoYmPjz/hMtuWLVua5557znz++efmiSeeaJaX2W7YsMHMmjXLbNq0yezcudMUFxebm266yVx55ZXOGz+a1rt7927TpUsXM2jQILN7926zd+9e51Yvmtb79ddfm02bNpmnnnrKtGnTxmzatMls2rTJHDhwwBjzt8svBw8ebEpLS83y5ctN+/btT3oZ9aRJk8znn39uXn75Zasuo3a73WbevHlm27Zt5rHHHjMJCQkRV2vY4sCBA86fnyTzwgsvmE2bNpmvv/7aGPP9ZdQJCQlmyZIlZvPmzebuu+8+6WXU1157rdm4caP58MMPzVVXXdUsL6MeN26c8Xq9Zs2aNRF/R//61786Y7Kzs03Hjh3NqlWrzKeffnrC1z+cyXu7uZg6dapZu3at2bFjh9m8ebOZOnWqiYmJMStXrjTGRNdaG4KAOUcnCxhjjPnss8/MLbfcYtxut/nJT35iZsyYccJj3377bXP11Vcbl8tlevToYQoLCy/QrM/c5s2bzcCBA01iYqJxu93m8ssvN9nZ2Wb37t0R46JlvXPnzjWSTno7XrSsd/To0Sdda/3RNWOM2blzpxk6dKiJi4sz7dq1MxMnTjRHjx6NeJ7Vq1ebPn36GJfLZa644gozd+7cC7uQczBr1izTsWNH43K5zI033mg2bNjQ1FM6K6tXrz7pn+Xo0aONMd8ftfi3f/s3k5ycbNxutxk0aJApLy+PeI5vv/3WPPDAA6ZNmzbG4/GYhx9+2InZ5uRUf0ePf98dPnzY/PM//7O59NJLTXx8vPmHf/iHiP8RMebM3tvNwSOPPGI6depkXC6Xad++vRk0aJATL8ZE11obIsYYi87EBAAAEFchAQAACxEwAADAOgQMAACwDgEDAACsQ8AAAADrEDAAAMA6BAwAALAOAQMAAKxDwAAAAOsQMAAAwDoEDAAAsA4BAwAArPP/AGG58Uq6K6PXAAAAAElFTkSuQmCC\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true,
"id": "YjQhBn0lRGgk"
},
"source": [
"The fit to the bell shaped curve is actually quite good!\n",
"\n",
"Next we analyse some of many unexpected properties of random walks or random sequences. First we visualize two slightly different random walks: one random as sampled, the other one slightly modified which makes it unlikely in some respect. Which one is it?"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 430
},
"id": "FxZDlGoSRGgk",
"outputId": "995ffcd9-bdce-4ecb-f2da-16403838e6f0"
},
"source": [
"Xrand = numpy.array([1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1,\n",
" 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1,\n",
" 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,\n",
" 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
" 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,\n",
" 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0,\n",
" 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
" 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,\n",
" 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0])\n",
"Xhumanrand = numpy.array([1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1,\n",
" 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1,\n",
" 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1,\n",
" 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0,\n",
" 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0,\n",
" 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0,\n",
" 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
" 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1,\n",
" 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0])\n",
"pylab.plot(numpy.cumsum(2*Xrand-1))\n",
"pylab.plot(numpy.cumsum(2*Xhumanrand-1))\n",
"pylab.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "UoUq22y1RGgk"
},
"source": [
"The phenomenon can be understood when one looks at distributions of longest runs."
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 447
},
"id": "bfhSvtr8RGgk",
"outputId": "1a4f1731-dfc2-405a-a2dc-e4b309e06b05"
},
"source": [
"def longestrun(walk):\n",
" y = 1\n",
" for i in range(2,4*int(numpy.log(len(walk))//1)):\n",
" for n in range(len(walk)-i):\n",
" if abs(walk[n+i]-walk[n])==i:\n",
" y = i\n",
" break\n",
" return y\n",
"\n",
"def longestrunhistogram(W,N):\n",
" z = []\n",
" for i in range(W):\n",
" helper = numpy.random.binomial(1,0.5,N)\n",
" walk = numpy.cumsum(2*helper-1)\n",
" z = z+[longestrun(walk)]\n",
" pylab.hist(numpy.array(z),bins=3*(max(z)-min(z)))\n",
" pylab.show()\n",
" print(numpy.mean(z))\n",
"longestrunhistogram(400,200)"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"8.0275\n"
]
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "KBQ5PmcqRGgk"
},
"source": [
"# Probability distributions\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "QAsEignARGgl"
},
"source": [
"# for inline plots in jupyter\n",
"#%matplotlib inline\n",
"# import matplotlib\n",
"import numpy as numpy\n",
"import matplotlib.pyplot as plt\n",
"# for latex equations\n",
"from IPython.display import Math, Latex\n",
"# for displaying images\n",
"from IPython.core.display import Image"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "6f8i31MBRGgl"
},
"source": [
"# import seaborn\n",
"import seaborn as sns\n",
"# settings for seaborn plotting style\n",
"sns.set(color_codes=True)\n",
"# settings for seaborn plot sizes\n",
"sns.set(rc={'figure.figsize':(5,5)})"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "GE52d70GRGgm"
},
"source": [
"# import distributions\n",
"from scipy.stats import uniform, norm, gamma, expon, poisson, binom"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "Qdi2q67dRGgm"
},
"source": [
"# random numbers from uniform distribution\n",
"def distribution(name):\n",
" if name == 'uniform':\n",
" n = 10000\n",
" start = 10\n",
" width = 20\n",
" data = uniform.rvs(size=n, loc = start, scale=width)\n",
" xlabel = 'Uniform Distribution'\n",
" if name == 'normal':\n",
" data = norm.rvs(size=10000,loc=0,scale=1)\n",
" xlabel = 'Normal Distribution'\n",
" if name == 'gamma':\n",
" data = gamma.rvs(a=5, size=10000)\n",
" xlabel = 'Gamma Distribution'\n",
" if name == 'exponential':\n",
" data = expon.rvs(scale=1,loc=0,size=1000)\n",
" xlabel = 'Exponential Distribution'\n",
" if name == 'poisson':\n",
" data = poisson.rvs(mu=3, size=10000)\n",
" xlabel = 'Poisson Distribution'\n",
" if name == 'binomial':\n",
" data = binom.rvs(n=10,p=0.8,size=10000)\n",
" xlabel = 'Binomial Distribution'\n",
" return data, xlabel"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 682
},
"id": "2Nbg2gEPRGgm",
"outputId": "ca368c83-9a00-4e74-8c48-612d3381d7f2"
},
"source": [
"data, xlabel = distribution('binomial')\n",
"ax = sns.distplot(data,\n",
" bins=100,\n",
" kde=False,\n",
" color='skyblue',\n",
" hist_kws={\"linewidth\": 1,'alpha':1})\n",
"ax.set(xlabel=xlabel, ylabel='Frequency')"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"<ipython-input-13-80f4df8dde81>:2: UserWarning: \n",
"\n",
"`distplot` is a deprecated function and will be removed in seaborn v0.14.0.\n",
"\n",
"Please adapt your code to use either `displot` (a figure-level function with\n",
"similar flexibility) or `histplot` (an axes-level function for histograms).\n",
"\n",
"For a guide to updating your code to use the new functions, please see\n",
"https://gist.github.com/mwaskom/de44147ed2974457ad6372750bbe5751\n",
"\n",
" ax = sns.distplot(data,\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[Text(0.5, 0, 'Binomial Distribution'), Text(0, 0.5, 'Frequency')]"
]
},
"metadata": {},
"execution_count": 13
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 500x500 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "Wa0am_qrRGgm"
},
"source": [
"# A simple example for conditional laws\n",
"\n",
"Assume that we have a coin flipping experiment with a coin, chosen from a pool of coins, whose success probability is $p$. Let us consider $1$ as success and $0$ a fail. The law which determines $p$ has a density $\\pi_0(p)$. Let us then flip the coin $k$ times with result $x_1,\\ldots,x_k$. What is the probability law for $p$ given $x_1,\\ldots,x_k$.\n",
"\n",
"This a typical question for conditional distribution. We consider the random variables $X_1,\\ldots,X_k$ which are Bernoulli distributed with success parameter $p$. Then\n",
"$$\n",
"P(X_1=x_1,\\ldots,X_k=x_k|p) = p^{(x_1+\\ldots+x_k)}(1-p)^{(k-(x_1+\\ldots+x_k))}\n",
"$$\n",
"holds true. Bayes' theorem says\n",
"$$\n",
"P(p|x_1,\\ldots,x_k)=\\frac{p^{(x_1+\\ldots+x_k)}(1-p)^{(k-(x_1+\\ldots+x_k))}\\pi_0(p)}{\\int_0^1p^{(x_1+\\ldots+x_k)}(1-p)^{(k-(x_1+\\ldots+x_k))}\\pi_0(p)dp} \\, .\n",
"$$"
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "0c_qXsWdRGgm",
"outputId": "e8a8884d-61c8-4bcd-98db-2b0bcd05dafa"
},
"source": [
"import numpy\n",
"\n",
"p0 = numpy.random.uniform(0,1,1)\n",
"def pi0(p):\n",
" return 1\n",
"\n",
"k=100\n",
"x = numpy.random.binomial(1,p0,k)\n",
"y = numpy.cumsum(x)\n",
"print(p0)\n",
"print(x)\n",
"print(y)"
],
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"[0.60597885]\n",
"[0 1 1 1 1 1 0 1 1 1 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1\n",
" 0 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1\n",
" 0 0 1 0 0 1 0 1 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 1 0]\n",
"[ 0 1 2 3 4 5 5 6 7 8 8 9 10 10 10 11 11 11 11 11 11 12 12 12\n",
" 13 13 14 15 16 17 17 17 18 18 19 19 20 20 21 21 21 21 22 23 23 23 23 24\n",
" 24 25 26 27 27 28 28 28 29 30 30 30 31 32 33 34 35 36 37 38 39 40 41 41\n",
" 42 43 43 43 44 44 44 45 45 46 47 48 49 50 51 52 52 53 54 54 55 55 56 56\n",
" 56 57 58 58]\n"
]
}
]
},
{
"cell_type": "code",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "VQ5hnzg0RGgm",
"outputId": "9d5f8dad-98bc-47f5-a6df-b50fccef36ab"
},
"source": [
"import matplotlib.pyplot as plt\n",
"\n",
"p = numpy.linspace(0,1,1000)\n",
"l = p**0*pi0(p)\n",
"l = l/numpy.sum(l)*1000\n",
"plt.plot(p,l)\n",
"plt.scatter(numpy.array([p0]),numpy.array([0]))\n",
"plt.show()\n",
"print('Prior mean', numpy.mean(l*p))\n",
"\n",
"for i in range(k):\n",
" p = numpy.linspace(0,1,1000)\n",
" l = p**y[i]*(1-p)**(i+1-y[i])*pi0(p)\n",
" l = l/numpy.sum(l)*1000\n",
" plt.plot(p,l)\n",
" plt.scatter(numpy.array([p0]),numpy.array([0]))\n",
" plt.show()\n",
" print(numpy.mean(l*p))"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Prior mean 0.5\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.3329996663329996\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5999995991987984\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6666661099979592\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7142849985689244\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7499991232469324\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6666666666629184\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6999999999940963\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.727272727263965\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7499999999875754\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6923076923127894\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7142857142925512\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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Ex8cjKysLAPDkk09i5syZePXVV3HHHXdg3bp1OHz4MN5++23HfydERGRjbRWZkxKDILVdv+q9wtSh4ZDJgHOVTahqbEdksO90U3kiu1pGKisrsWTJEiQlJeHWW2/FoUOHsG3bNsyZMwcAUFxcjPLyctv106dPx9q1a/H2228jLS0Nn376KTZu3IgxY8Y49rsgIiIbk1nCl13jRRb6wNoiPRkUqMLoGEsX/wF21bg9u+Ly3//+92t+fvfu3Vedu/vuu3H33XfbVRQREfXf94U1qGxsR2iA0jazxBdlDAtHXrkB2YU1WOCjocxTcG8aIiIvsynX0kJ9+5gYqPx899c8x414Dt/9KSUi8kJGkxlbT1rWcvKltUV6MmVoGOQyoKi6GfqGNtHl0DUwjBAReZHvi2pR29yBQQFKZAwLF12OUCH+SqTGhQAAsgu53og7YxghIvIim7u6aG4bEwM/BX/Fs6vGM/AnlYjIS7CL5mrW1iEufubeGEaIiLwEu2iuNrlr3EhJbSsu1beKLod6wTBCROQl2EVztSC1H1LiLOuNHL5YJ7ga6g1/WomIvAC7aHo3KTEMAHD4Qq3gSqg3DCNERF6AXTS9mzzEEkYOXWDLiLtiGCEi8gLWLpp5qeyiudKkIYMAAPl6AwxtnYKroZ7wJ5aIyMNd3kVzxzh20VwpWqvB4LAASBJwlONG3BLDCBGRh2MXzfVZW0cOs6vGLTGMEBF5OHbRXN8P40Y4iNUd8aeWiMiDmcwStp/iLJrrmdzVMnK8tB4dRrPgauhKDCNERB4sp6QO1U0dCNb42ZY+p6sNjwzCoAAl2jrNOHWpQXQ5dAWGESIiD7b9dAUA4OakKCjZRdMrmUyGibb1RjhuxN3wJ5eIyIPtOGUJI3NSogVX4v6mDLV01XDciPthGCEi8lAFlU0orG6GUiHDrKRI0eW4vUldg1gPX6yDJEmCq6HLMYwQEXmoHV1dNNOGhSNYoxRcjfsbExcCtZ8ctc0dKKxuFl0OXYZhhIjIQ+04bZlFM5ddNH2i8pNjXEIIAOBYcb3YYqgbhhEiIg9U1diOYyX1AIDZDCN9Nn6wZdzIsWIOYnUnDCNERB5oZ14FJAkYlxCC2BB/0eV4jPG6UABATleQI/fAMEJE5IGs40XmJLNVxB7pg0MBAPn6RrR0GMUWQzYMI0REHqalw4h9BdUAgDmpDCP2iA3xR4xWA5NZQm4pFz9zFwwjREQeZu/ZarQbzdCF+SMpOlh0OR5nfFfryDF21bgNhhEiIg/zQxdNDGQymeBqPI8tjHAQq9tgGCEi8iBGkxm78rnq6kD8MKOmnoufuQmGESIiD3LkYh3qWjoRGqC07URL9hkTFwKFXIbKxnaUN7SJLofAMEJE5FGsXTS3JEXBjxvj9Yu/SoHkWMtYGy5+5h74k0xE5CEkSbLt0ssumoEZr+PiZ+6EYYSIyEOcrWhCcW0LVH5yzBjFjfEGgjNq3AvDCBGRh7DuRXPD8HAEqv0EV+PZrINYc8sa0GE0C66GGEaIiDyEbUpvSozgSjzfkPAAhAYo0WE0I6/cILocn8cwQkTkASoMbTjetWLo7OQowdV4PplMhrSEUADAidJ6obUQwwgRkUewtoqk60IRpdUIrsY7pCWEAIAt5JE4DCNERB7AGkbmci8ahxnb1TLCPWrEsyuMZGVlYfLkyQgODkZUVBQWLVqEM2fOXPOeNWvWQCaTdTs0GqZ6IqK+amo3Ivt8DQBgLqf0Osy4rpaRc5XcwVc0u8LInj17sHTpUhw4cAA7duxAZ2cn5s6di+bm5mvep9VqUV5ebjsuXrw4oKKJiHzJnjNV6DCZMTQiEMMjg0SX4zWitRpEa9UwS8CpSxzEKpJdc8O2bt3a7eM1a9YgKioKR44cwYwZM3q9TyaTISaGo7+JiPrDOqV3Tko0N8ZzsLHxoagwVOBEaQMmDwkTXY7PGtCYkYYGSz9bWNi1/wKbmpqQmJgInU6HhQsX4tSpU9e8vr29HQaDodtBROSLOk1m7MqvBMBVV53B2lWTyxk1QvU7jJjNZjz11FO44YYbMGbMmF6vS0pKwnvvvYcvvvgCH374IcxmM6ZPn47S0tJe78nKykJISIjt0Ol0/S2TiMijHSqqhaHNiPBAFSYM5sZ4jmYNIyfKOIhVpH6HkaVLl+LkyZNYt27dNa/LyMjAkiVLkJ6ejpkzZ+Lzzz9HZGQk/va3v/V6T2ZmJhoaGmxHSUlJf8skIvJo1r1obhkdBYWcXTSONjbeEkYKq5phaOsUXI3v6lcYWbZsGTZt2oRvvvkGCQkJdt2rVCoxfvx4FBQU9HqNWq2GVqvtdhAR+RpJki5bdZVdNM4QHqRGfKg/AOAkW0eEsSuMSJKEZcuWYcOGDdi1axeGDh1q9wuaTCbk5uYiNjbW7nuJiHzJ6XIDyupboVHKcdNIboznLGk667gRhhFR7AojS5cuxYcffoi1a9ciODgYer0eer0era2ttmuWLFmCzMxM28cvvvgitm/fjsLCQhw9ehT3338/Ll68iEceecRx3wURkReytorcOCIS/iqF4Gq819j4UADACYYRYeya2rtq1SoAwKxZs7qdf//99/Hzn/8cAFBcXAy5/IeMU1dXh0cffRR6vR6DBg3CxIkTsX//fqSkpAysciIiL2dbdZVdNE71wyDWerGF+DC7wogkSde9Zvfu3d0+fu211/Daa6/ZVRQRka8rq2/FqUsGyGTALdwYz6nGdA1iLaltRV1zBwYFqgRX5Hu4Nw0RkRv6uqtVZOLgQYgIUguuxruF+CsxNCIQAKf4isIwQkTkhjiLxrWsU3y5+JkYDCNERG6mobUTBwq7NsZL5VYarmAbN8JBrEIwjBARuZndZyphNEsYERVk6z4g5xqXEAqAYUQUhhEiIjfDLhrXS43TQiYD9IY2VDe1iy7H5zCMEBG5kQ6jGXvOVAFgGHGlQLUfhoZbWqFOXeLmrK7GMEJE5EYOFNagsd2IyGA10ru6Dsg1UrsGsZ66xK4aV2MYISJyI9YumtnJUZBzYzyXSo2z7IN2qowtI67GMEJE5Ca4MZ5YtjDClhGXYxghInITuWUN0BvaEKBSYPrwCNHl+JzUOEs3zYWaFhjaOgVX41sYRoiI3IS1VWTGyEholNwYz9XCAlWIC9EAAPI4iNWlGEaIiNwEu2jEsw5iPckw4lIMI0REbqCktgX5+kYo5DLcMpob44nCcSNiMIwQEbmB7V2tIpMSB3HXWIGs40ZOs2XEpRhGiIjcwI7TegDsohFtTLylZeRcZRPaOk2Cq/EdDCNERILVt3Tg0IU6AMDcFG6MJ1KMVoOwQBVMZgln9I2iy/EZDCNERILtyq+EySwhKToYg8MDRJfj02QymW3cyEmOG3EZhhEiIsGss2jmprKLxh1Yx41wjxrXYRghIhKordOEPWe5MZ47+WFZeLaMuArDCBGRQNnna9DSYUKMVoOxXWtckFhjuv4e8vSN6DSZBVfjGxhGiIgEsk7pnZ0SBZmMG+O5g8SwAASp/dBhNON8VZPocnwCwwgRkSBms4Sv86yrrnIWjbuQy2VIieUOvq7EMEJEJEhOaT2qGtsRpPbDtGFhosuhy6RwRo1LMYwQEQlinUUzMykSaj9ujOdOflgWni0jrsAwQkQkiG1KL2fRuB3rINbTlwwwmyXB1Xg/hhEiIgGKqptRUNkEP7kMs5K4MZ67GREVBJVCjqZ2I0rrWkWX4/UYRoiIBLDuRTN1WBhC/JWCq6ErKRVyjIgKAgCcLmdXjbMxjBARCWDtopmTzC4ad5XcNaMmj2HE6RhGiIhcrKapHUcuWjbGm83xIm7LOqOGYcT5GEaIiFxsZ34lzBKQEqtFwiBujOeukmODAbCbxhUYRoiIXMzWRcNWEbdmXfistK4VhrZOwdV4N4YRIiIXau0w4dtz3BjPE4QGqBAbogEA5Jc3Cq7GuzGMEBG50L6CarR1mhEf6m9bWIvcFwexugbDCBGRC1mn9M5JiebGeB4ghWHEJRhGiIhcxGSWsDOvEgC7aDwFW0Zcg2GEiMhFjhXXoaa5A1qNH6YM5cZ4nsA6oyZf3wijySy4Gu9lVxjJysrC5MmTERwcjKioKCxatAhnzpy57n3r16/H6NGjodFoMHbsWGzZsqXfBRMReartXbNobh4dBaWC/xf0BInhgfBXKtBuNONCTbPocryWXf8a9uzZg6VLl+LAgQPYsWMHOjs7MXfuXDQ39/4XtH//ftxzzz14+OGHcezYMSxatAiLFi3CyZMnB1w8EZGnkCQJ209ZxovMTYkRXA31lUIuQ1KMdb0RzqhxFpkkSf3ejrCqqgpRUVHYs2cPZsyY0eM1ixcvRnNzMzZt2mQ7N23aNKSnp2P16tV9eh2DwYCQkBA0NDRAq+XocyLyPOcqGjHntb1QKeQ4+vwcBKn9RJdEfZT5eS7+dbAYT8wajv++bbTocjxKX9+/B9RO2NDQAAAIC+u97zM7OxuzZ8/udm7evHnIzs7u9Z729nYYDIZuBxGRJ7N20dwwIpxBxMNwWXjn63cYMZvNeOqpp3DDDTdgzJgxvV6n1+sRHd191Hh0dDT0en2v92RlZSEkJMR26HS6/pZJROQWrF00c9hF43FSugaxMow4T7/DyNKlS3Hy5EmsW7fOkfUAADIzM9HQ0GA7SkpKHP4aRESuom9ow/HSBshkwOyUKNHlkJ2SYiwtIxWGdtQ2dwiuxjv1K4wsW7YMmzZtwjfffIOEhIRrXhsTE4OKiopu5yoqKhAT0/v/DtRqNbRabbeDiMhT7ciz/A4crwtFVLBGcDVkryC1HxLDLRsasnXEOewKI5IkYdmyZdiwYQN27dqFoUOHXveejIwM7Ny5s9u5HTt2ICMjw75KiYg8lG0WTSq7aDxVcgzHjTiTXWFk6dKl+PDDD7F27VoEBwdDr9dDr9ejtbXVds2SJUuQmZlp+/jJJ5/E1q1b8eqrryI/Px8vvPACDh8+jGXLljnuuyAiclMNrZ3IPl8DAJjLVVc9lnUQ6+lLDCPOYFcYWbVqFRoaGjBr1izExsbajo8//th2TXFxMcrLy20fT58+HWvXrsXbb7+NtLQ0fPrpp9i4ceM1B70SEXmL3WcqYTRLGBEVhGGRQaLLoX6yLgt/mi0jTmHX/LK+LEmye/fuq87dfffduPvuu+15KSIir2Cd0stWEc9mXRb+fFUTOoxmqPy4gq4j8WkSETlJu9GE3fncGM8bxIf6Q6vxQ6dJQkFlk+hyvA7DCBGRk2Sfr0FzhwlRwWqkJYSKLocGQCaTYTR38HUahhEiIiexdtHMSYmGXC4TXA0NVArDiNMwjBAROYHZLGGHdbwIp/R6BVsY0TOMOBrDCBGRE+SU1qOqsR3Baj9kDAsXXQ45gG1GzSVDnyZ0UN8xjBAROcH2U5ZWkVmjozjzwkuMjA6CQi5DXUsnKgztosvxKvwXQkTkBNtPd626ylk0XkOjVGBYRCAAjhtxNIYRIiIHK6hsQmFVM5QKGWYlRYouhxyIi585B8MIEZGDWQeuZgyPQLBGKbgaciRrGMnXNwquxLswjBARORi7aLyXdSVWdtM4FsMIEZEDVRracKy4HgBXXfVG1paRwqomtHWaBFfjPRhGiIgcaFtXF02aLhTRWo3gasjRooLVCAtUwSwB5yq4LLyjMIwQETnQtpOWLprbx3ChM28kk8nYVeMEDCNERA5S19yB7MIaAAwj3iw5hjNqHI1hhIjIQXbkVcBklpAcq0VieKDocshJRttm1DCMOArDCBGRg2xlF41P+KGbppHLwjsIwwgRkQM0tnVi37lqAMBtDCNebURUEPzkMjS0dqK8oU10OV6BYYSIyAF25Veiw2TGsMhAjIwKEl0OOZHaT4HhkZa/Y3bVOAbDCBGRA1zeRSOTyQRXQ852eVcNDRzDCBHRALV2mLD7TBUA4PYxsYKrIVfgHjWOxTBCRDRAe85WorXThIRB/kiN04ouh1zAOqOGa404BsMIEdEAWbtobktlF42vsHbTXKhuRmsHl4UfKIYRIqIBaDeasDOvEgBw+1jOovEVUcEaRARZloU/W8FxIwPFMEJENAD7C2rQ2G5EtFaN8bpBosshFxodw64aR2EYISIagK9OlgMA5qXGQC5nF40vsXbV5OvZMjJQDCNERP1kNJmxo2uXXi505ns4o8ZxGEaIiPrpYFEt6lo6MShAiSlDwkSXQy52eTcNl4UfGIYRIqJ++qprFs3clBj4Kfjr1NeMiAqCUiFDY5sRl7gs/IDwXw8RUT+YzJItjNzGWTQ+SeUnty0Ln3eJXTUDwTBCRNQP3xfVoLqpHSH+Stw4IkJ0OSRIMhc/cwiGESKifth8wjKL5rbUGCjZReOzOKPGMfgviIjITkaT2bbq6o/SuBeNL2PLiGMwjBAR2elAYS1qmjswKECJjGHhosshgawzaopqmtHSYRRcjediGCEistPm3EsAgNvGxHIWjY+LDFYjIkgNSQLOVjSJLsdj8V8REZEdOk1m2yyaBePYRUM/jBthV03/MYwQEdlh//ka1Ld0IiJIhSlDudAZcdyII9gdRvbu3YsFCxYgLi4OMpkMGzduvOb1u3fvhkwmu+rQ6/X9rZmISJjNJ6xdNFzojCzYMjJwdv9Lam5uRlpaGlauXGnXfWfOnEF5ebntiIqKsveliYiE6jBeNotmXJzgashdWFtG8ssbuSx8P/nZe8Ptt9+O22+/3e4XioqKQmhoqN33ERG5i+8KqmFoMyIyWI3J3IuGugyL6FoWvt2I0rpW6MICRJfkcVzWxpieno7Y2FjMmTMH33333TWvbW9vh8Fg6HYQEYm2qWuhs/ljYqCQywRXQ+5C5SfHiCh21QyE08NIbGwsVq9ejc8++wyfffYZdDodZs2ahaNHj/Z6T1ZWFkJCQmyHTqdzdplERNfUbjRh+2lLF80d7KKhK3Al1oGxu5vGXklJSUhKSrJ9PH36dJw/fx6vvfYa/vnPf/Z4T2ZmJpYvX2772GAwMJAQkVDfnq1GY5sR0Vo1JiUOEl0OuZmUWC0+RxlbRvrJ6WGkJ1OmTMG+fft6/bxarYZarXZhRURE17apaxbN/LGxkLOLhq5gXYmVYaR/hMxLy8nJQWwsFwsiIs/Q0mHE9tMVADiLhnpm7aa5WNuC5nYuC28vu1tGmpqaUFBQYPu4qKgIOTk5CAsLw+DBg5GZmYmysjL84x//AAC8/vrrGDp0KFJTU9HW1oZ3330Xu3btwvbt2x33XRAROdGO0xVo6TBhcFgAJgwOFV0OuaHwIDWigtWobGzHmYpGTBjMrjx72B1GDh8+jJtvvtn2sXVsx4MPPog1a9agvLwcxcXFts93dHTg6aefRllZGQICAjBu3Dh8/fXX3b4GEZE7+3eOpYtmYbplsUeinoyO1aKysQp55QaGETvZHUZmzZp1zUVd1qxZ0+3jZ555Bs8884zdhRERuYO65g7sOVsFwBJGiHqTHBuMvWerkF/OGTX24lrGRETXsDm3HEazhNQ4rW0tCaKepHCPmn5jGCEiuobLu2iIrsU6oyZf3wizmcvC24NhhIioF6V1LTh4oRYyGbAgjWGErm1YZCBUCjma2o0oq28VXY5HYRghIurFl8cty79PHRqG2BB/wdWQu1Mq5BgZHQQAOM2uGrswjBAR9eKLnDIAwKL0eMGVkKfg4mf9wzBCRNSDfL0B+fpGqBRy3D6GizRS31gXP2MYsQ/DCBFRD6wDV2clRSIkQCm4GvIU1hk13DDPPgwjRERXMJslfGGbRcMuGuq70V1h5GJNC5q4LHyfMYwQEV3h8MU6lNW3Ikjth1uTo0SXQx4kLFCFaK1lo9czenbV9BXDCBHRFT47UgoAmD82BhqlQnA15GmSbYufsaumrxhGiIgu09phwuZcy5TeH09IEFwNeSLOqLEfwwgR0WW2ndKjqd0IXZg/Jg8JE10OeSDOqLEfwwgR0WU+O2rpovnxhATI5dyhl+xnnVFzhsvC9xnDCBFRl/KGVuwrqAbALhrqv6ERgVD5ydHcYUJJXYvocjwCwwgRUZfPj5ZBkoApQ8OgCwsQXQ55KD+FHKO6loVnV03fMIwQEQGQJMnWRfMTtorQACXHcEaNPRhGiIgA5JTUo7CqGf5KBeaP4/LvNDCjYzmjxh4MI0RE+GHg6m1jYhCk9hNcDXk624waLnzWJwwjROTz2jpNtr1oOHCVHMHaTVNS24rGtk7B1bg/hhEi8nk78yphaDMiLkSDjOHhosshLzAoUIUYrQaAZYovXRvDCBH5vE+PlAAA7poQDwXXFiEH4eJnfccwQkQ+7VJ9K/acrQIA/GSiTnA15E1se9SwZeS6GEaIyKd9crgEZgmYNiwMQyMCRZdDXiSZM2r6jGGEiHyWySxh/WHLLJp7pgwWXA15G2s3DZeFvz6GESLyWd+eq0JZfStC/JWYlxojuhzyMkPCA6H2k6Olw4SLtVwW/loYRojIZ6072DVwdXw8NEqF4GrI2/gp5EiKsbSO5LOr5poYRojIJ1U1tuPrvAoA7KIh5xkdwxk1fcEwQkQ+6bOjpTCaJYwfHGr73yuRo1kHsZ7mHjXXxDBCRD5HkiR8fMjSRfOzyZzOS85jDSP5XBb+mhhGiMjnfF9Ui6LqZgSqFPjRuDjR5ZAXsy4LX1rXCgOXhe8VwwgR+Zx1B4sBAHemxyOQm+KRE4UEKBEXYlkWPp9dNb1iGCEin1Ld1I4tuXoAwD1T2EVDzsfFz66PYYSIfMonh0vQYTIjLSEE4xJCRZdDPiAlrmsQ6yWGkd4wjBCRzzCZJXx0wNJF80DGELHFkM9IjQsBAOSWNQiuxH0xjBCRz9iVX4my+laEBijxo3GxosshHzEm3tIycraiEe1Gk+Bq3BPDCBH5jH8euAgAWDxJxxVXyWXiQ/0RGqCE0SzhrL5JdDluye4wsnfvXixYsABxcXGQyWTYuHHjde/ZvXs3JkyYALVajREjRmDNmjX9KJWIqP+Kqpux92wVZDLg/mmJosshHyKTyTA23tJVc/ISu2p6YncYaW5uRlpaGlauXNmn64uKinDHHXfg5ptvRk5ODp566ik88sgj2LZtm93FEhH114ddrSI3J0VBFxYguBryNRw3cm12T7C//fbbcfvtt/f5+tWrV2Po0KF49dVXAQDJycnYt28fXnvtNcybN8/elycisltrhwnrD1tWXH2ArSIkgHXcyCmGkR45fcxIdnY2Zs+e3e3cvHnzkJ2d3es97e3tMBgM3Q4iov769/EyGNqM0IX5Y+aoSNHlkA+ydtPk6RvRaTILrsb9OD2M6PV6REdHdzsXHR0Ng8GA1tbWHu/JyspCSEiI7dDpuDAREfWPJEn4YL+li+b+qYmQy2WCKyJfNDgsAMEaP3QYzThXwUGsV3LL2TSZmZloaGiwHSUlJaJLIiIPdaCwFqfLDdAo5fjpJP7HhsSQyWRI7Vr8jINYr+b0MBITE4OKiopu5yoqKqDVauHv79/jPWq1GlqttttBRNQff99XBAD4ycQEDApUCa6GfJm1q4bjRq7m9DCSkZGBnTt3dju3Y8cOZGRkOPulicjHFVU3Y2e+5T9DD90wVHA15OvGxHNGTW/sDiNNTU3IyclBTk4OAMvU3ZycHBQXW5ZYzszMxJIlS2zXP/744ygsLMQzzzyD/Px8vPXWW/jkk0/w61//2jHfARFRL97/rgiSBNw6OgrDI4NEl0M+zjq993S5ASazJLga92J3GDl8+DDGjx+P8ePHAwCWL1+O8ePH4/nnnwcAlJeX24IJAAwdOhSbN2/Gjh07kJaWhldffRXvvvsup/USkVPVt3Rg/eFSAMDDN7JVhMQbFhGIQJUCbZ1mFFZxEOvl7F5nZNasWZCk3hNdT6urzpo1C8eOHbP3pYiI+u1fB0vQ2mlCcqwWGcPDRZdDBLlchpQ4LQ5dqMPJSw0YGR0suiS34ZazaYiIBqLTZMYH+y8AsLSKyGSczkvuwbYSaynXz7ocwwgReZ0tueXQG9oQGazGgjTuzkvug3vU9IxhhIi8iiRJeOfbQgDAkmmJUPtxd15yH9YZNacvGWDmIFYbhhEi8ir7CqpxssyyyNl93IeG3MzwyEBolHI0tRtxoaZZdDlug2GEiLzKW9+cBwD8bPJghHGRM3Izfgo5kmOtK7Fy3IgVwwgReY2jxXXILqyBn1yGR2cME10OUY/GdA1iPcnFz2wYRojIa1hbRRaNj0d8aM/bTRCJNjbBEkaOl9SLLcSNMIwQkVc4o2/E13kVkMmAx2cOF10OUa/SdaEALMvCcyVWC4YRIvIKq/dYWkXmpcRgRBSXfif3NTwyCIEqBVo6TCio5EqsAMMIEXmBktoW/Pv4JQDAL29mqwi5N4Vcxq6aKzCMEJHHW7XnPExmCTeOiMC4hFDR5RBdV1pXV01Oab3QOtwFwwgRebTSuhasP1wCAPjVLSMEV0PUN+ldoZktIxYMI0Tk0VZ+U4BOk4Tpw8MxdRg3xCPPYG0Zydc3oq3TJLYYN8AwQkQeq6S2BesPlwIAfj1nlOBqiPouNkSDyGA1TGYJp7hPDcMIEXmuld8UwNg1VmTykDDR5RD1mUwmQ1pXV01OCcMIwwgReaSS2hZ8esTaKjJScDVE9kvXcUaNFcMIEXmkN3edg9Es4aaREZiYyFYR8jzWcSMnOKOGYYSIPE9RdTM+O1oGgGNFyHONiw8FAFyoaUF9S4fYYgRjGCEij/PnbWdgMku4ZXQUJgweJLocon4JCVBiaEQgAOB4qW+PG2EYISKPklNSj8255ZDJgGduSxJdDtGApHElVgAMI0TkQSRJwitf5QEA/mN8AkbHaAVXRDQwtpVYGUaIiDzDnrNVOFBYC5WfHMvncqwIeT5rN+PR4jqYfXgHX4YRIvIIZrOEV77KBwA8mJGI+FB/wRURDVxKnBYapRz1LZ0orG4WXY4wDCNE5BG+OF6GfH0jgjV++OUs7kFD3kGpkNs2dzx6sU5sMQIxjBCR22vtMOFPW88AAB6fORyDAlWCKyJynImJlq6aIwwjRETua9We8yhvaEN8qD8evnGo6HKIHGpi17iRwxdrBVciDsMIEbm10roW/G3PeQDAc3ckQ6NUCK6IyLEmdLWMnK9qRl2zby5+xjBCRG4t66t8tBvNmDo0DLePiRFdDpHDhQWqMCzSsvjZsRLf7KphGCEit/V9YQ02nyiHXAasWJAKmUwmuiQip7B21fjquBGGESJySyazhBe+PA0AuGfKYKTEcYEz8l7WQayHLzCMEBG5jbXfX0ReuQFajR+enstl38m7TRpiCSPHS+vRaTILrsb1GEaIyO1UGNpsU3n/a14SwjiVl7zcsIgghPgr0dZpRl65QXQ5LscwQkRu58UvT6Ox3Yg0XSjum5oouhwip5PLZZgwOBQAcMgHu2oYRojIrXyTX4nNueVQyGX4w11joJBz0Cr5hilDwwFYBm77GoYRInIbLR1G/G7jSQDAf94wBKlxIYIrInKdqcPCAAAHL9T63KZ5DCNE5Dbe2HkOZfWtiA/1x1OzuSsv+Zax8SEIUClQ39KJs5WNostxqX6FkZUrV2LIkCHQaDSYOnUqDh482Ou1a9asgUwm63ZoNJp+F0xE3ul4ST3e/bYIAPDiwlQEqv0EV0TkWkqF3DbF98B53+qqsTuMfPzxx1i+fDlWrFiBo0ePIi0tDfPmzUNlZWWv92i1WpSXl9uOixcvDqhoIvIubZ0mPL3+OExmCQvS4nBrcrTokoiEmDasa9xIkW/tU2N3GPnLX/6CRx99FA899BBSUlKwevVqBAQE4L333uv1HplMhpiYGNsRHc1fNET0g7/sOIuCyiZEBqvx4p2posshEmZa17iR74tqIUm+M27ErjDS0dGBI0eOYPbs2T98Abkcs2fPRnZ2dq/3NTU1ITExETqdDgsXLsSpU6eu+Trt7e0wGAzdDiLyTocv1OKdbwsBAFl3jcUgrilCPmxsfCg0SjlqmztwrrJJdDkuY1cYqa6uhslkuqplIzo6Gnq9vsd7kpKS8N577+GLL77Ahx9+CLPZjOnTp6O0tLTX18nKykJISIjt0Ol09pRJRB6itcOE/1p/HJIE/HhCAmansNWUfJvKT45JiZbWkQM+NMXX6bNpMjIysGTJEqSnp2PmzJn4/PPPERkZib/97W+93pOZmYmGhgbbUVJS4uwyiUiAl7ecxoWaFsRoNXh+QYrocojcwtShXV01hb4zbsSu4eoRERFQKBSoqKjodr6iogIxMX3b2lupVGL8+PEoKCjo9Rq1Wg21Wm1PaUTkYbaeLMeHB4oBAP939ziE+CsFV0TkHqYNDwd2AN8X1UCSJJ/YrdqulhGVSoWJEydi586dtnNmsxk7d+5ERkZGn76GyWRCbm4uYmNj7auUiLxGaV0Lnvn0BADg8ZnDcdPISMEVEbmPcQkh0CjlqG7ynXEjdnfTLF++HO+88w4++OAD5OXl4YknnkBzczMeeughAMCSJUuQmZlpu/7FF1/E9u3bUVhYiKNHj+L+++/HxYsX8cgjjzjuuyAij9FpMuP/+9cxGNqMSNeF4um5XNyM6HJqP4Vtafhvz1ULrsY17F5VaPHixaiqqsLzzz8PvV6P9PR0bN261Taotbi4GHL5Dxmnrq4Ojz76KPR6PQYNGoSJEydi//79SElh/zCRL3r967M4WlyPYI0f3rxnPJQKLgRNdKUZIyOw92wVvj1XhYdvHCq6HKeTSR4wkdlgMCAkJAQNDQ3QarWiyyGiftqVX4GHPzgMSQJW3jsBd4xjdy1RT87oGzHv9b3QKOU4vmIu1H4K0SX1S1/fv/lfEiJyiaLqZjy5LgeSBDwwLZFBhOgaRkUHISpYjbZOM45cqBNdjtMxjBCR0zW1G/HYPw6jsc2ISYmD8PsfsZuW6FpkMpltYPdeHxg3wjBCRE5lNkt4+pMcnKtsQrRWjbfunwCVH3/1EF3PjFERAIC9Z6sEV+J8/I1ARE71128KsO1UBVQKOVbdPxFRwdy1m6gvbhhhCSOnyw2oamwXXI1zMYwQkdNsPFaGv+w4CwB4cWEqJgweJLgiIs8REaRGapxl0Oe357y7dYRhhIicYv/5avzm0+MAgMdmDMPPpgwWXBGR55mVZBk3sjO/UnAlzsUwQkQOd7aiEb/45xF0miTcMTYWz942WnRJRB5pdrJlDa89Z6rQYTQLrsZ5GEaIyKH0DW146P1Dtpkzr/40DXK59++tQeQMaQmhiAhSo6ndiINF3rtxHsMIETlMVWM77n33AMrqWzEsIhDvLJkEjdIzF2sicgdyuQyzk6MAAF/nVVznas/FMEJEDlHf0oEH/v49CquaERuiwQf/OQWDAlWiyyLyeNaumh2nK+ABi6b3C8MIEQ2Yoa0TS947iHx9IyKD1Vj76DTowgJEl0XkFW4YEQG1nxxl9a3I1zeKLscpGEaIaEAMbZ146P1DOFHagLBAFdY+MhVDIwJFl0XkNfxVCtw00rLmyI7T3tlVwzBCRP1W09SOe985gCMX66DV+OEf/zkFI6ODRZdF5HXmpFi6ar46qRdciXMwjBBRv+gb2rD47QM4WWZAeKAK/3psGsbEh4gui8grzUuNgZ9chrxyAwoqva+rhmGEiOx2saYZd/9tPwoqmxAbosEnj2cgNY5BhMhZQgNUmDHKsgDav4+XC67G8RhGiMguRy7W4q639qOkthWJ4QFY/3gGhkcGiS6LyOstSIsFAGw6fsnrZtUwjBBRn32RU4Z73vketc0dGBOvxfpfZCBhEGfNELnCnJQYqP3kKKxuxqlLBtHlOBTDCBFdl9ks4Y2vz+HJdTnoMJoxJyUan/wiA1Fa7sBL5CpBaj/c2rUA2pcnLgmuxrEYRojomhpaOvHYP4/gta8tu+8+etNQrL5/IgJUfoIrI/I9C8bFAQC+zLkEk9l7umr424SIenWyrAFPfHQEJbWtUCnkeHFhKnffJRLo5tFRCPFX4lJDG749V4VZSVGiS3IItowQ0VUkScJH31/Ef6yyDFRNGOSPz56YziBCJJhGqcBd4+MBAB8fKhFcjeMwjBBRN5WGNjy05hCe23ASHUYzbh0dhc2/ugljEzh1l8gd/GyKDoBlNdaqxnbB1TgGwwgR2Ww6cQlzX9+L3WeqoPKT43d3JOOdJZMQEqAUXRoRdRkdo0W6LhRGs4TPjpaKLschGEaICGX1rXj0H4exbO0x1Ld0Yky8Fpt/dSMeuWkY5HKZ6PKI6Ar3dLWO/DP7Iowms+BqBo5hhMiHdZrM+Nue85j96h7sOF0BP7kMv7plBD5/4gbuMUPkxhamxyMsUIWy+lZsPeX5+9UwjBD5IEmSsCu/AvPf+BZZX+WjtdOEKUPCsOXJm/D03CSo/PirgcidaZQK3D8tEQDwzt5Cj1+RlVN7iXzM8ZJ6ZH2VhwOFtQCAQQFK/HZ+Mn4yMQEyGbtkiDzFkoxErN5zHsdLG3DoQh2mDA0TXVK/MYwQ+Yjc0gb89Ztz2HaqAgCg8pPjoRuG4JczR3CAKpEHighS48cTEvCvg8V4Y+dZfPTINNEl9RvDCJGXO1hUi79+U4C9Z6sAADIZcNf4eDw9Nwnxof6CqyOigfjlrOH49EgJviuowXcF1bhhRITokvqFYYTIC7V1mrD5RDn+eeAickrqAQAKuQwL0+LwxKzhHJxK5CV0YQG4b2oi1uy/gD9tO4ONw8M9sruVYYTIi1yobsa6QyX45HAJaps7AAAqhRw/mZSAx2cMx+Bw7rBL5G2W3jwCnxwuwfGSevz7+CUsTI8XXZLdGEaIPFxtcwc2nbiEDcfKcKy43nY+LkSD+6YlYvFkHSKC1OIKJCKnigxW4/GZw/GXHWfx0qbTmDkqEqEBKtFl2YVhhMgDlTe04uu8Suw4XYH9BdUwdu3eKZcBN46MxH1TB+PW0VHwU3CKLpEveHzmcHx5/BLOVTbh5c15+L+700SXZBeGESIP0GE043hpPb4rqMbXeRU4WWbo9vmx8SFYND4eC9JiERWsEVQlEYmi8pMj6z/G4iers7H+SCluTY7CbWNiRZfVZwwjRG6ordOEU5cMOFBYgwOFNTh8oQ6tnSbb52UyYMLgQZidHI25qdEYHhkksFoicgeThoThsRnD8PbeQvzX+hMYGR3sMb8bGEaIBGs3mnC+shm5ZfU4XtqAE6X1yC9vtHW9WIUHqjBtWDhmjorELclRHAfiBkxmCQeLalHZ2IaoYA2mDA2Dgnv5kEC/mZeEY8V1OHShDkv+fhCfPpGB2BD3n8Ivk/qxhuzKlSvxf//3f9Dr9UhLS8Obb76JKVOm9Hr9+vXr8fvf/x4XLlzAyJEj8cc//hHz58/v8+sZDAaEhISgoaEBWq3W3nKJhJMkCTXNHSita8XFmmacq2jC2YpGFFQ24UJNM8w9/CsMC1RhUuIgZAwPx/ThERgZFcRN69zI1pPl+J8vT6O8oc12LjZEgxULUjyqeZy8T3VTO+5enY2i6mYkhgfg/Z9PxjBBLSR9ff+2O4x8/PHHWLJkCVavXo2pU6fi9ddfx/r163HmzBlERUVddf3+/fsxY8YMZGVl4Uc/+hHWrl2LP/7xjzh69CjGjBnj0G+GSASTWUJNczuqGttR3dTR9Wc7yutbUVLXitK6FpTWtaKlw9Tr19Bq/JASp0VaQijSdKEYlxCC+FB/j1wvwBdsPVmOJz48iit/eVr/tlbdP4GBhIQqrWvBz94+gNK6VoT4K/HiwlTcmRbn8t8pTgsjU6dOxeTJk/HXv/4VAGA2m6HT6fCrX/0Kzz777FXXL168GM3Nzdi0aZPt3LRp05Ceno7Vq1c79Jsh6iuzWUK70Yy2ThPajCa0dpjQ1mlGm9FkOddpQkuHCY1tRhhaO2Fo64Sh1YjGtk4YLjtX29yBmuYO9OVfkUwGRAdroAvzx4ioYIyKDsLIrj8jg9UMHh7CZJZw4x93dWsRuZwMQEyIBvv++xZ22ZBQVY3tePQfh20LH04eMggP3zgMs5IioVEqXFJDX9+/7Roz0tHRgSNHjiAzM9N2Ti6XY/bs2cjOzu7xnuzsbCxfvrzbuXnz5mHjxo29vk57ezva29ttHxsMhl6vHYi/7ytCSW1Lr5+/PKdd+V5z5ZuPdMUVV3/+2vdfecVV9zvw9a689zofXrUb5PWfhX33X/361/7eTGYJJrMEo+1PM0xmCZ2my8+bf/i8qfs1bZ0mtBvNV1YxIDIZEB6oRkSQCpHBakQGqREdooFuUAASBvlDFxaAuFAN1H6u+QVAznOwqLbXIAJYfpzLG9pwsKgWGcPDXVcY0RUig9VY/3gG3vrmPFbuLsChC3U4dOEIVH5yjIoOQmJYIALVCgSoLFHg4RuHQhcmZmFEu8JIdXU1TCYToqOju52Pjo5Gfn5+j/fo9foer9fr9b2+TlZWFv7nf/7HntL6ZfOJSzh62SJR5JuUChk0fgqolQr4q+TQ+CmgUSrgr1JAq1FCq/GD1t/yZ7BGCa2/H7QaJYI1SoQFWsJHWKCK/wv2EZWNvQeR/lxH5ExKhRxPzh6Jn03R4b19Rfj38Usob2jDyTLDVUsE3Jke5xlhxFUyMzO7taYYDAbodDqHv86PJyZg+vDumwpd2VIuu8Ynr3zrufpe2XU+f537r9NsP5DXs/feq1/b3mdxnfuvc/3lF8hgCRB+cjn8FDIo5DL4yWVQyOXwk8suOye/7HMyKBWWjzVKuSVsKBVQ+8m5MBjZpa/ruHC9F3In0VoNMucn49nbR6O4tgV55QboG9rQ3GHpppYgIUYr7mfWrjASEREBhUKBioqKbucrKioQExPT4z0xMTF2XQ8AarUaarXzpy3eNzXR6a9BRN5lytAwxIZooG9ou7rLET+MGZkyNMzVpRFdl0wmQ2J4IBLDA0WX0o1d/yVUqVSYOHEidu7caTtnNpuxc+dOZGRk9HhPRkZGt+sBYMeOHb1eT0TkzhRyGVYsSAHQQ4tf158rFqSw247IDna3Ty9fvhzvvPMOPvjgA+Tl5eGJJ55Ac3MzHnroIQDAkiVLug1wffLJJ7F161a8+uqryM/PxwsvvIDDhw9j2bJljvsuiIhc6LYxsVh1/wTEhHRv1o4J0XBaL1E/2D1mZPHixaiqqsLzzz8PvV6P9PR0bN261TZItbi4GHL5Dxln+vTpWLt2LX73u9/ht7/9LUaOHImNGzf2eY0RIiJ3dNuYWMxJieEKrEQO0K8VWF2N64wQERF5nr6+f3MaAREREQnFMEJERERCMYwQERGRUAwjREREJBTDCBEREQnFMEJERERCMYwQERGRUAwjREREJBTDCBEREQll93LwIlgXiTUYDIIrISIior6yvm9fb7F3jwgjjY2NAACdTie4EiIiIrJXY2MjQkJCev28R+xNYzabcenSJQQHB0Mmc9wmVAaDATqdDiUlJdzzxon4nF2Hz9o1+Jxdg8/ZNZz5nCVJQmNjI+Li4rptonslj2gZkcvlSEhIcNrX12q1/EF3AT5n1+Gzdg0+Z9fgc3YNZz3na7WIWHEAKxEREQnFMEJERERC+XQYUavVWLFiBdRqtehSvBqfs+vwWbsGn7Nr8Dm7hjs8Z48YwEpERETey6dbRoiIiEg8hhEiIiISimGEiIiIhGIYISIiIqG8PoysXLkSQ4YMgUajwdSpU3Hw4MFrXr9+/XqMHj0aGo0GY8eOxZYtW1xUqWez5zm/8847uOmmmzBo0CAMGjQIs2fPvu7fC/3A3p9pq3Xr1kEmk2HRokXOLdBL2Puc6+vrsXTpUsTGxkKtVmPUqFH8/dEH9j7n119/HUlJSfD394dOp8Ovf/1rtLW1uahaz7R3714sWLAAcXFxkMlk2Lhx43Xv2b17NyZMmAC1Wo0RI0ZgzZo1zi1S8mLr1q2TVCqV9N5770mnTp2SHn30USk0NFSqqKjo8frvvvtOUigU0p/+9Cfp9OnT0u9+9ztJqVRKubm5Lq7cs9j7nO+9915p5cqV0rFjx6S8vDzp5z//uRQSEiKVlpa6uHLPY++ztioqKpLi4+Olm266SVq4cKFrivVg9j7n9vZ2adKkSdL8+fOlffv2SUVFRdLu3bulnJwcF1fuWex9zh999JGkVquljz76SCoqKpK2bdsmxcbGSr/+9a9dXLln2bJli/Tcc89Jn3/+uQRA2rBhwzWvLywslAICAqTly5dLp0+flt58801JoVBIW7dudVqNXh1GpkyZIi1dutT2sclkkuLi4qSsrKwer//pT38q3XHHHd3OTZ06VfrFL37h1Do9nb3P+UpGo1EKDg6WPvjgA2eV6DX686yNRqM0ffp06d1335UefPBBhpE+sPc5r1q1Sho2bJjU0dHhqhK9gr3PeenSpdItt9zS7dzy5culG264wal1epO+hJFnnnlGSk1N7XZu8eLF0rx585xWl9d203R0dODIkSOYPXu27ZxcLsfs2bORnZ3d4z3Z2dndrgeAefPm9Xo99e85X6mlpQWdnZ0ICwtzVpleob/P+sUXX0RUVBQefvhhV5Tp8frznP/9738jIyMDS5cuRXR0NMaMGYM//OEPMJlMrirb4/TnOU+fPh1HjhyxdeUUFhZiy5YtmD9/vktq9hUi3gs9YqO8/qiurobJZEJ0dHS389HR0cjPz+/xHr1e3+P1er3eaXV6uv485yv993//N+Li4q764afu+vOs9+3bh7///e/IyclxQYXeoT/PubCwELt27cJ9992HLVu2oKCgAL/85S/R2dmJFStWuKJsj9Of53zvvfeiuroaN954IyRJgtFoxOOPP47f/va3rijZZ/T2XmgwGNDa2gp/f3+Hv6bXtoyQZ3jllVewbt06bNiwARqNRnQ5XqWxsREPPPAA3nnnHURERIgux6uZzWZERUXh7bffxsSJE7F48WI899xzWL16tejSvMru3bvxhz/8AW+99RaOHj2Kzz//HJs3b8ZLL70kujQaIK9tGYmIiIBCoUBFRUW38xUVFYiJienxnpiYGLuup/49Z6s///nPeOWVV/D1119j3LhxzizTK9j7rM+fP48LFy5gwYIFtnNmsxkA4OfnhzNnzmD48OHOLdoD9ednOjY2FkqlEgqFwnYuOTkZer0eHR0dUKlUTq3ZE/XnOf/+97/HAw88gEceeQQAMHbsWDQ3N+Oxxx7Dc889B7mc/792hN7eC7VarVNaRQAvbhlRqVSYOHEidu7caTtnNpuxc+dOZGRk9HhPRkZGt+sBYMeOHb1eT/17zgDwpz/9CS+99BK2bt2KSZMmuaJUj2fvsx49ejRyc3ORk5NjO+68807cfPPNyMnJgU6nc2X5HqM/P9M33HADCgoKbGEPAM6ePYvY2FgGkV705zm3tLRcFTisAVDiNmsOI+S90GlDY93AunXrJLVaLa1Zs0Y6ffq09Nhjj0mhoaGSXq+XJEmSHnjgAenZZ5+1Xf/dd99Jfn5+0p///GcpLy9PWrFiBaf29oG9z/mVV16RVCqV9Omnn0rl5eW2o7GxUdS34DHsfdZX4myavrH3ORcXF0vBwcHSsmXLpDNnzkibNm2SoqKipP/93/8V9S14BHuf84oVK6Tg4GDpX//6l1RYWCht375dGj58uPTTn/5U1LfgERobG6Vjx45Jx44dkwBIf/nLX6Rjx45JFy9elCRJkp599lnpgQcesF1vndr7m9/8RsrLy5NWrlzJqb0D9eabb0qDBw+WVCqVNGXKFOnAgQO2z82cOVN68MEHu13/ySefSKNGjZJUKpWUmpoqbd682cUVeyZ7nnNiYqIE4KpjxYoVri/cA9n7M305hpG+s/c579+/X5o6daqkVqulYcOGSS+//LJkNBpdXLXnsec5d3Z2Si+88II0fPhwSaPRSDqdTvrlL38p1dXVub5wD/LNN9/0+DvX+mwffPBBaebMmVfdk56eLqlUKmnYsGHS+++/79QaZZLEti0iIiISx2vHjBAREZFnYBghIiIioRhGiIiISCiGESIiIhKKYYSIiIiEYhghIiIioRhGiIiISCiGESIiIhKKYYSIiIiEYhghIiIioRhGiIiISCiGESIiIhLq/weze2eytX2wHAAAAABJRU5ErkJggg==\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.7333333333422666\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6875000000000004\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6470588235294117\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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ivhVHzjmHaG4ZE/yzaC53w/ABAI7jyzP1MFvt0IYpRZdEAaTP64w4HA5YLJarvi8vLw9bt27t9NyWLVu67DEhIgpUriGavCHxiAuhIRqXEUlRSIzWwGx1cBdf8phHYSQ/Px+7du1CWVkZiouLkZ+fjx07duDee+8FACxcuBD5+fnu45988kls2rQJL774IkpKSvDLX/4S+/fvx+LFi/v3syAiEsw1RHNbCA7RAIAkSbi+Y6hmF9cbIQ95FEZqamqwcOFCZGVl4aabbsK+ffvw6aef4uabbwYAVFRUoKqqyn38tGnTsGrVKrz22mvIzs7GBx98gHXr1mHs2LH9+1kQEQl0rrENh88aoZCAW8aEziyay80YPgAA8PnX7Bshz3jUM/Lmm292+/4dO3Zc8dxdd92Fu+66y6OiiIgCyZajzhmCkzLjkBDke9F0Z/ow552RY1Um1DZZMCA6dK8FeYZ70xAR9dGW485G/VtCaG2RqxkQrcHoFOfCVntP8+4I9RzDCBFRHxhbrfii9AIAhNRCZ125YURH3wiHasgDDCNERH2w7UQ17A4ZWUnRyIiPFF2OcO6+kZO16ONuIxRCGEaIiPpg89GOIZoQbly9VG5GLNQqBWqaLCitaxFdDgUIhhEiol4yW+3Y2bH8+S2jQ2+hs6vRhikxcVAMAKDgdL3YYihgMIwQEfXS3tN1aG23I0Wvxdg07ijukjfE2TdSUMowQj3DMEJE1EuuIZqbRydBkiTB1fiPvKHOTfO+LK1n3wj1CMMIEVEv2B0yPnNP6eUQzaWy0/XQhilQ19yOkzXNosuhAMAwQkTUC0WVDahrbke0VoWpQ+JEl+NXNColJmU4rwn7RqgnGEaIiHrBNUQze2QiwpT8UXo511ANwwj1BL+DiIg8JMsyPu1YAp5DNFd33RBnGPniTD0cDvaNUPcYRoiIPHS6tgVl9a1QKxWYmTVAdDl+afxAPSLUSjS2WlFiaBJdDvk5hhEiIg9tL6kBAEwdEocojUf7jYaMMKUCkzM7+kY4xZeugWGEiMhDW0su9otQ11x9I18wjNA1MIwQEXnA2GbF/rIGAAwj15I35OJ6I3b2jVA3GEaIiDzw+cla2Bwyhg6I5MZ41zAmVYcojQomsw0lBpPocsiPMYwQEXlgW0e/yE2juDHetaiUCkzMiAUA7DtzQXA15M8YRoiIesjukLHjhHNjvBuzOETTE1MyO8JIx9AW0dUwjBAR9dChs4240OJcdXVSxy9Z6p5rRs1XZRe4Tw11iWGEiKiHth13DtHMGDGAq672UHZ6DNRKBWqbLCivbxVdDvkpfjcREfWQu1+Es2h6TBumxPiBegDOuyNEV8MwQkTUA1XGNhyrMkGSgJkjuOqqJyYPdg7VsImVusIwQkTUA9tLnI2rE9JjEB+lEVxNYJnS0Teyj3dGqAsMI0REPbCtY9VVTun13MSMWEgSUFbfipoms+hyyA8xjBARXYPZaseeU84lzTml13P68DCMTNYBAPad4RRfuhLDCBHRNRSU1qPNakeKXotRKdGiywlIF9cb4VANXYlhhIjoGly79N44MhGSJAmuJjC5mli/YhMrXQXDCBFRN2RZxtbjnNLbV64m1uMGE0xmq+BqyN8wjBARdeNkTTPONbZBo1Jg2tAE0eUErESdFhnxEZBl4ACXhqfLMIwQEXXDtdBZ3tB4hKuVgqsJbJcuDU90KYYRIqJu7OzYGG82h2j6zDVUwzsjdDmGESKiLjRbbNhf7vwrnquu9t3EDOeMmkNnG2G1OwRXQ/6EYYSIqAsFp+thtcvIjI9ARnyk6HIC3pCESMREhMFic+DYeZPocsiPMIwQEXVh59fOfhHeFekfCoWECekxAIAD5RyqoYsYRoiIrkKWZezo6BeZmcUw0l9yO4ZqCisYRugij8LIsmXLMHnyZERHRyMxMRHz58/HiRMnuj1n5cqVkCSp00Or1fapaCIibztT14KzDW1QKxW4bki86HKChqtvpJB3RugSHoWRnTt3YtGiRfjiiy+wZcsWWK1W3HLLLWhpaen2PJ1Oh6qqKvejvLy8T0UTEXnbzq+dd0WmDI5DhFoluJrgkT0wBgoJOG80o8rYJroc8hMefYdt2rSp09srV65EYmIiDhw4gBkzZnR5niRJSE5O7l2FREQCuMII+0X6V6RGhVEpOhw9b0JheSNuHx8uuiTyA33qGTEajQCAuLi4bo9rbm5GRkYG0tPTMW/ePBw9erQvL0tE5FVmqx1flDp36WW/SP9z9Y2wiZVceh1GHA4HnnrqKUyfPh1jx47t8risrCy89dZb+Pjjj/Huu+/C4XBg2rRpOHv2bJfnWCwWmEymTg8iIl/56swFmK0OpOi1GJ4YJbqcoOMOI2xipQ69DiOLFi3CkSNHsHr16m6Py8vLw8KFC5GTk4OZM2fio48+woABA/Dqq692ec6yZcug1+vdj/T09N6WSUTksUuHaLhLb/+bOMgZRo6dN8JstQuuhvxBr8LI4sWLsX79emzfvh0DBw706NywsDBMmDABp06d6vKY/Px8GI1G96OysrI3ZRIR9Qr7RbxrYGw4BkRrYLXLKD5nFF0O+QGPwogsy1i8eDHWrl2Lbdu2YfDgwR6/oN1uR3FxMVJSUro8RqPRQKfTdXoQEfnC2YZWnKpphlIhYdow7tLrDZIkIXcQ+0boIo/CyKJFi/Duu+9i1apViI6OhsFggMFgQFvbxelZCxcuRH5+vvvt5557Dps3b0ZpaSkKCwtx3333oby8HI888kj/fRZERP3EdVdk4qAY6MPDBFcTvCZmxABgGCEnj6b2vvLKKwCAWbNmdXr+7bffxoMPPggAqKiogEJxMeM0NDTg0UcfhcFgQGxsLHJzc7F3716MHj26b5UTEXmBa5deDtF4l6uJ9WBFA2RZZm9OiPMojMiyfM1jduzY0entl156CS+99JJHRRERidBuc2Dv6Y4pvSMSBVcT3Mak6qFWKlDX3I6KC63ciDDEcW8aIqIOhRUNaLbYEB+pxphU9qp5kzZMibFpzmvMoRpiGCEi6uDqF5kxYgAUCg4beNtENrFSB4YRIqIO7BfxrYt9I41iCyHhGEaIiADUmMw4VmWCJAE3DOeUXl/IGRQDADhR3YS2di5+FsoYRoiIAOw6WQcAGJemR3yURnA1oSFFH44knQZ2Bxc/C3UMI0RE4KqrouSkxwAAiirZNxLKGEaIKOTZHTI+P8kwIkJOurNvpKiyUWwhJBTDCBGFvMNnG9HYakW0VuX+S518w31nhE2sIY1hhIhCnmuI5obhCVAp+WPRl8YP1EMhAeeNZlSbzKLLIUH4XUdEIY/9IuJEalQYkRQNgFN8QxnDCBGFtIaWdhzq6FeYwTAixMUm1kahdZA4DCNEFNJ2n6qDQwaykqKRog8XXU5ImtCx3ghn1IQuhhEiCmnuIZos3hURxTWjpvisEXbHtTdkpeDDMEJEIUuWZfaL+IFhiVGIVCvR0m7HyZom0eWQAAwjRBSyjlc1obbJgvAwJSZlxoouJ2QpFRLGD4wBwCm+oYphhIhCluuuyLSh8dColIKrCW057r6RRqF1kBgMI0QUsnZ+XQOA/SL+gDNqQhvDCBGFpGaLDfvLnLM32C8i3oSOMPJ1dRNaLDaxxZDPMYwQUUjae6oONoeMzPgIZMRHii4n5CXqtEjVa+GQgcNnuYNvqGEYIaKQxFk0/mfCIGcT8UGuNxJyGEaIKOR0mtLLfhG/wU3zQhfDCBGFnNK6FpxtaINaqcB1Q+JFl0MdLp1RI8tc/CyUMIwQUcjZecJ5V2TK4DhEqFWCqyGXsal6KBUSaposqDJyB99QwjBCRCGH/SL+KVytxMhk5w6+nOIbWhhGiCikmK12fFFaD4D9Iv6I642EJoYRIgopX565AIvNgRS9FsMTo0SXQ5dhE2toYhghopDi6heZOWIAJEkSXA1dbkJHE2vxOSNsdofYYshnGEaIKKS4loCfwX4RvzQkIQrRWhXarHacqOYOvqGCYYSIQkblhVacrm2BUiFh+rAE0eXQVSgUErI7dvA9VMmVWEMFwwgRhYxdJ51DNBMHxUAfHia4GuqKq2/kEJtYQwbDCBGFDFe/yKysRMGVUHeyOaMm5DCMEFFIaLc5sPd0x5Re9ov4tex0PQDg65omNHMH35DAMEJEIeFAeQOaLTYkRKkxOkUnuhzqRmK0Fmkx4ZBloJg7+IYEhhEiCgmuVVdnDB8AhYJTev2d6+7IobONYgshn2AYIaKQwF16A8vFGTWNQusg32AYIaKgV20y43iVCZIEXM8pvQGBy8KHFo/CyLJlyzB58mRER0cjMTER8+fPx4kTJ6553po1azBy5EhotVqMGzcOGzdu7HXBRESe2tVxV2R8mh7xURrB1VBPjE3TQyEBVUYzqk3cwTfYeRRGdu7ciUWLFuGLL77Ali1bYLVaccstt6ClpaXLc/bu3Yt77rkHDz/8MA4ePIj58+dj/vz5OHLkSJ+LJyLqiYtDNJzSGygiNSqMSHLu4MuhmuAnybIs9/bk2tpaJCYmYufOnZgxY8ZVj1mwYAFaWlqwfv1693PXXXcdcnJysGLFih69jslkgl6vh9FohE7HLngi6jm7Q8bE57fA2GbFh49PQ25GrOiSqIee+fAwVu+rxBOzhuLH3xgpuhzqhZ7+/u5Tz4jR6JxyFRcX1+UxBQUFmDNnTqfn5s6di4KCgi7PsVgsMJlMnR5ERL1x6GwjjG1W6MPDkD1QL7oc8oBr8TPOqAl+vQ4jDocDTz31FKZPn46xY8d2eZzBYEBSUlKn55KSkmAwGLo8Z9myZdDr9e5Henp6b8skohC3o2PV1euHJ0ClZM9+IHHNqDlcaYTD0eub+BQAev2duWjRIhw5cgSrV6/uz3oAAPn5+TAaje5HZWVlv78GEYUGd78IV10NOCOSohAepkSTxYbSumbR5ZAX9SqMLF68GOvXr8f27dsxcODAbo9NTk5GdXV1p+eqq6uRnJzc5TkajQY6na7Tg4jIUxda2nG44xY/w0jgUSkVGJfmHFor4g6+Qc2jMCLLMhYvXoy1a9di27ZtGDx48DXPycvLw9atWzs9t2XLFuTl5XlWKRGRhz4/WQtZBkYmRyNJpxVdDvWCayXWosoGwZWQN6k8OXjRokVYtWoVPv74Y0RHR7v7PvR6PcLDwwEACxcuRFpaGpYtWwYAePLJJzFz5ky8+OKLuP3227F69Wrs378fr732Wj9/KkREnXHV1cCXkx4L4AwO8c5IUPPozsgrr7wCo9GIWbNmISUlxf1477333MdUVFSgqqrK/fa0adOwatUqvPbaa8jOzsYHH3yAdevWddv0SkTUVw6HjF1f1wEAZo3g+iKBynVn5HiVCWarXXA15C0e3RnpyZIkO3bsuOK5u+66C3fddZcnL0VE1CfHqkyoa7YgUq3k2iIBLC0mHAlRatQ1t+PoeRP/LYMU57kRUVByDdFMG5YAtYo/6gKVJEnufWq4Emvw4ncoEQWlnSc4pTdYuHfw5eJnQYthhIiCjslsxYEK5+wLhpHAlzMoBgB38A1mDCNEFHT2nqqD3SFjyIBIpMdFiC6H+mh8WgwAoLy+FQ0t7WKLIa9gGCGioMNVV4OLPiIMQxIiAXCoJlgxjBBRUJFlmf0iQcjVxMqhmuDEMEJEQeVUTTPOG83QqBS4bki86HKon2RzRk1QYxghoqCy/UQNAGDqkHhow5SCq6H+kn3JnZGerHlFgYVhhIiCyvYS5xDNbC4BH1RGpURDrVSgodWKygttosuhfsYwQkRBw2S2Yl/ZBQDA7JFJgquh/qRRKTEq1bmDexGbWIMOwwgRBY3dJ+tg65jSOyieU3qDTc7Ajh18KxrFFkL9jmGEiILG9hJnv8jsLG6MF4xci59xem/wYRghoqDgcMjY3jGl98aRDCPByLUs/JFzRljtDrHFUL9iGCGioHDkvBF1zRZEaVSYnBknuhzygsz4SOi0KlhsDpwwNIkuh/oRwwgRBQXXLJrruUtv0FIopE5TfCl48DuWiILCto71RW4cySm9wSyHi58FJYYRIgp4dc0WHO5oapzF5tWg5uob4Z2R4MIwQkQBb+eJWsgyMCZVhySdVnQ55EWuYZpTtc1oMlvFFkP9hmGEiAKea4hmNmfRBL0B0RqkxYRDloHic0bR5VA/YRghooBmszuw62tn8yqHaEKDa70RDtUED4YRIgpoB8ob0GS2IS5S7W5upOCW09E3wibW4MEwQkQBzbXQ2cwRA6BUSIKrIV/g9N7gwzBCRAHNtQT8LO7SGzLGpumgVEioNllgMJpFl0P9gGGEiALWucY2nKhugkJy3hmh0BChVmFEUjQA3h0JFgwjRBSwXHdFJg6KRUyEWnA15Es56R07+DKMBAWGESIKWK4wwo3xQg9XYg0uDCNEFJDMVjv2nK4DwPVFQpGribX4nBF2hyy2GOozhhEiCkgFpfUwWx1I1mkxMjladDnkY8MToxGhVqLZYsPp2mbR5VAfMYwQUUD67Fg1AGDO6ERIEqf0hhqlQsK4NPaNBAuGESIKOLIs47PjzjBy06gkwdWQKOwbCR4MI0QUcI6cM6HaZEGEWom8IfGiyyFBuPhZ8GAYIaKAs6XjrsiM4QOgDVMKroZEcd0ZKTE0wWy1iy2G+oRhhIgCztbjrn4RDtGEshS9FgOiNbA7ZBzhDr4BjWGEiALK+cY2HD1vgkICbuQS8CFNkiRkd2yax6GawMYwQkQBxXVXJDcjFvFRGsHVkGgTBsUAAA6d5Z2RQMYwQkQBZctx56qrcziLhoBL7ow0iC2E+sTjMLJr1y7ceeedSE1NhSRJWLduXbfH79ixA5IkXfEwGAy9rZmIQlST2YqCjlVX2S9CADBuoHOtkcoLbahvtgiuhnrL4zDS0tKC7OxsLF++3KPzTpw4gaqqKvcjMZHLNxORZz4/WQerXcbghEgMHRAluhzyA/rwMAwdEAkAOMyhmoCl8vSEW2+9FbfeeqvHL5SYmIiYmBiPzyMicnGvujqKf8zQRdnpMThd24KDlY3cNDFA+axnJCcnBykpKbj55puxZ8+ebo+1WCwwmUydHkQU2mx2B7adYL8IXWkCV2INeF4PIykpKVixYgU+/PBDfPjhh0hPT8esWbNQWFjY5TnLli2DXq93P9LT071dJhH5ucKKRjS2WhETEYbcjFjR5ZAfca3EeuhsI2SZO/gGIo+HaTyVlZWFrKws99vTpk3D6dOn8dJLL+Ef//jHVc/Jz8/HkiVL3G+bTCYGEqIQ59qLZnZWIlRKTgSki0Ym66BWKdDYakV5fSsyEyJFl0QeEvIdPWXKFJw6darL92s0Guh0uk4PIgptF3fp5RANdaZWKTAm1fl74tDZRrHFUK8ICSNFRUVISUkR8dJEFIBO1TSjtK4FaqUCM0Zw1VW6kmu9kYMVjULroN7xeJimubm5012NM2fOoKioCHFxcRg0aBDy8/Nx7tw5/P3vfwcA/PnPf8bgwYMxZswYmM1mvPHGG9i2bRs2b97cf58FEQW1T4861yXKGxqPKI3XR5cpAOVc0jdCgcfj7+r9+/fjxhtvdL/t6u144IEHsHLlSlRVVaGiosL9/vb2dvzv//4vzp07h4iICIwfPx6fffZZp49BRNQdVxj5xthkwZWQv3KFkaPnTWi3OaBWsa8okEhyALQem0wm6PV6GI1G9o8QhZhzjW2Y/sI2SBKw79k5SOB+NHQVsiwj57ktMLZZ8e/F0zG+Y9iGxOrp729GRyLya58ecd4VmZwRxyBCXZIk6eIUX643EnAYRojIr7mGaOZyiIauwTVUU1TJZeEDDcMIEfmtumYL9pVdAADMHcMpvdS9nHTnpnncwTfwMIwQkd/67Fg1HDIwLk2PgbERosshP+ea3nu6tgUms1VsMeQRhhEi8lubXEM0vCtCPRAfpUF6XDgAoJg7+AYUhhEi8ksmsxV7T9UD4JRe6jnX3ZEiNrEGFIYRIvJL20tq0G53YOiASAxLjBZdDgWIi02sjULrIM8wjBCRX+JCZ9Qbl4aRAFhGizowjBCR3zFb7dheUgsAmDuGYYR6bkyqHkqFhNomC6qMZtHlUA8xjBCR3/n8ZB3arHak6rUYl6YXXQ4FkHC1EiOTncN6XPwscDCMEJHf+eRIFQDnQmeSJAmuhgJNNvtGAg7DCBH5FYvNji3HqgEA3+AQDfVCDmfUBByGESLyK59/XYcmsw1JOg0mZ8aJLocCUM6gGABA8Tkj7A42sQYChhEi8isbip1DNLeNS4FCwSEa8tzQAVGIVCvR2m7HyZom0eVQDzCMEJHfMFsvDtHcMT5FcDUUqJQKCeM7hmoKyxuF1kI9wzBCRH5j19e1aLbYkKLXYkJ6rOhyKIDlZji/fg6Uc9O8QMAwQkR+Y/1hDtFQ/8jNdIWRC4IroZ5gGCEiv2C22vHZcQ7RUP+YOCgWkgSU1beitskiuhy6BoYRIvILO07UoLXdjrSYcPeS3kS9pQ8Pw4iOPY04VOP/GEaIyC+4hmhuH5/Chc6oX0zM4FBNoGAYISLhWttt2Hq8BgBw+zgO0VD/mMQm1oDBMEJEwm0vqUWb1Y70uHCMH8i9aKh/TOpoYj1yzgSz1S64GuoOwwgRCbf+8HkAwO3jUjlEQ/1mUFwEEqI0aLc7UHzOKLoc6gbDCBEJZTJbsbXEOUTDWTTUnyRJcg/V7C/jUI0/YxghIqE2FRvQbnNgeGIUxqTqRJdDQYaLnwUGhhEiEmpd0TkAwPwJaRyioX7nWvyssKIBssxN8/wVwwgRCWMwmlFQWg8A+GZ2quBqKBiNTdVDo1LgQks7SutaRJdDXWAYISJh/n3oHGTZOQUzPS5CdDkUhNQqBbI7Ns07wL4Rv8UwQkTCrDvonEUzf0Ka4EoomF3cp4ZhxF8xjBCRECerm3CsygSVQuJCZ+RVuYM6ZtRwJVa/xTBCREK4GldnZQ1AbKRacDUUzFwzak7XtqChpV1wNXQ1DCNE5HMOh8whGvKZ2Eg1hg6IBMChGn/FMEJEPnegogHnGtsQpVFhzqgk0eVQCJicGQcA+KqMQzX+iGGEiHxu3UHnEM3cMcnQhikFV0OhYOoQZxj58gzDiD9iGCEinzJb7fjPIdcQDdcWId+YMjgeAHDknBEtFpvgauhyDCNE5FNbjlXDZLYhRa/FtKEJosuhEJEWE46BseGwO2T2jfghj8PIrl27cOeddyI11bm75rp16655zo4dOzBx4kRoNBoMGzYMK1eu7EWpRBQM1hw4CwD4r9yBUCq4/Dv5zpTBHX0jHKrxOx6HkZaWFmRnZ2P58uU9Ov7MmTO4/fbbceONN6KoqAhPPfUUHnnkEXz66aceF0tEga3K2IbPT9YCcIYRIl+aOtjVN1IvuBK6nMrTE2699VbceuutPT5+xYoVGDx4MF588UUAwKhRo7B792689NJLmDt3rqcvT0QB7KNC5/LvUwbHISM+UnQ5FGKmdvSNHKo0wmy1s3naj3i9Z6SgoABz5szp9NzcuXNRUFDQ5TkWiwUmk6nTg4gCmyzLWLO/EgBwF++KkAAZ8RFIjNag3e5AUWWj6HLoEl4PIwaDAUlJndcRSEpKgslkQltb21XPWbZsGfR6vfuRnp7u7TKJyMv2lzegrL4VEWolbuPy7ySAJEmYOsR5d+TLUvaN+BO/nE2Tn58Po9HoflRWVoouiYj6yHVX5PZxKYjUeDxCTNQv3E2sZewb8Sde/4mQnJyM6urqTs9VV1dDp9MhPDz8qudoNBpoNBpvl0ZEPtLabsOGw1UAgLsm8U4nieNqYj1Q3oB2mwNqlV/+TR5yvP6vkJeXh61bt3Z6bsuWLcjLy/P2SxORn9hYbEBLux2Z8RGY3LGdO5EIwxOjEBephtnqQPE5o+hyqIPHYaS5uRlFRUUoKioC4Jy6W1RUhIqKCgDOIZaFCxe6j3/sscdQWlqKH//4xygpKcHLL7+M999/H08//XT/fAZE5PdWfVkOwHlXRJK4tgiJI0mSOxBzvRH/4XEY2b9/PyZMmIAJEyYAAJYsWYIJEybgF7/4BQCgqqrKHUwAYPDgwdiwYQO2bNmC7OxsvPjii3jjjTc4rZcoRByvMqGwohEqhYS7JnEWDYnnmuLL9Ub8h8c9I7NmzYIsy12+/2qrq86aNQsHDx709KWIKAis+tL5x8ktY5KQGK0VXA3RxSbW/WUNsNkdUCnZNyIa/wWIyGta223uHXq/OyVDcDVETqNSdNCHh6HZYsNh9o34BYYRIvKa/xw6jyaLDZnxEZg2NF50OUQAAKVCwnVDnHdHCk5zqMYfMIwQkdf8s2OI5p4pg6DgpnjkR6YPc+4YvedUneBKCGAYISIvKT5rxOGzRqiVCm6KR35n2lBnGNlf3gCz1S64GmIYISKvWPWVczrv3LHJiI/iIobkX4YOiESSToN2mwMHyhtElxPyGEaIqN+ZzFZ8XHQeAPDdKYMEV0N0JUmS3HdH9p7mUI1oDCNE1O/W7D+L1nY7hiVGuRsFifyNq6l6zyk2sYrGMEJE/crukPHO3jIAwIPTMrniKvktVxPr4bONMJmtgqsJbQwjRNSvtpfUoOJCK3RaFb49MU10OURdSo0Jx+CESDhk4MtSLg0vEsMIEfWrlR13Rf57yiBEqL2+MThRn+R1DNWwb0QshhEi6jcnq5uw+1QdFBJw/3VccZX833RXEyv7RoRiGCGifvN2x12Rm0cnIT0uQmwxRD3gujNyoroJNU1mwdWELoYRIuoXxlYrPio8CwB4aPpgwdUQ9UxcpBpj03QAgN0nOVQjCsMIEfWL1fsqYLY6MDI5GlMHczovBY6ZIwYAAHZ+XSu4ktDFMEJEfdZuc+DtPWUAgO9NH8zpvBRQZo5IBADs+roWdocsuJrQxDBCRH32cdE5GExmJOk0mDchVXQ5RB6ZMCgG0RoVGlqtOHLOKLqckMQwQkR94nDIeHVXKQDnXRGNSim4IiLPhCkV7gXQOFQjBsMIEfXJ1pIanKppRrRGhe9O5T40FJhmsG9EKIYRIuqTFTtPAwDuvS4D0dowwdUQ9c6MEc47IwcrGmBs5dLwvsYwQkS9tq/sAg6UN0CtVOB70zNFl0PUawNjIzAsMQoOGdjD1Vh9jmGEiHrt1Y67It/JTUOiTiu4GqK+cU/xPcGhGl9jGCGiXjlhaMJnx2sgScCjNwwRXQ5Rn1263ogsc4qvLzGMEFGv/N+2kwCAW8cmY8iAKMHVEPXdlMFx0IYpYDCZcaK6SXQ5IYVhhIg8dsLQhI3FVQCA/7lpuOBqiPqHNkyJvCHOvWq2ldQIria0MIwQkcf+b9tJyDJw27hkjEzWiS6HqN/cNCoJAPDZsWrBlYQWhhEi8gjvilAwu2mUc2n4g5WNqG2yCK4mdDCMEJFHXHdFbh3LuyIUfFL04RiXpocsA9s5VOMzDCNE1GNfV/OuCAW/OR1DNVuOc6jGVxhGiKjH/vDpCcgy8I0xyRiVwrsiFJzmjHYO1Xx+shZmq11wNaGBYYSIeuRA+QVsOVYNhQT8v7kjRJdD5DWjU3RI1Wthtjqw5xRXY/UFhhEiuiZZlvG7T04AAO7KTcewxGjBFRF5jyRJmDO6Y1YNh2p8gmGEiK5pW0kNviq7AI1KgaduZq8IBT9X38hnx2vgcHA1Vm9jGCGibtkdMn6/yXlX5MHpmUjRhwuuiMj7pg6JQ7RWhdomCw5UNIguJ+gxjBBRt9YePIcT1U3QaVV4YuYw0eUQ+YRGpcTNHXdHNhyuElxN8GMYIaIutVhs+MOnJQCAJ24cBn1EmOCKiHzntnEpAIBPjlRxqMbLGEaIqEsv7ziFapMFGfEReGh6puhyiHzq+uEJiNKoUG2y4GAlh2q8qVdhZPny5cjMzIRWq8XUqVPx1VdfdXnsypUrIUlSp4dWq+11wUTkGxX1rXj98zMAgGdvGwWNSim4IiLf0oYpMadjefgNhw2CqwluHoeR9957D0uWLMHSpUtRWFiI7OxszJ07FzU1XS+bq9PpUFVV5X6Ul5f3qWgi8r7fbjyOdpsD1w9LwM0d0xyJQg2HanzD4zDypz/9CY8++igeeughjB49GitWrEBERATeeuutLs+RJAnJycnuR1ISf7AR+bO9p+qw6agBSoWEn98xGpIkiS6JSIgZIwYgUq1EldGMg5WNossJWh6Fkfb2dhw4cABz5sy5+AEUCsyZMwcFBQVdntfc3IyMjAykp6dj3rx5OHr0aLevY7FYYDKZOj2IyDfabQ4s/bfze/S+qYOQlcwFzih0acOUuKljVo1rXybqfx6Fkbq6Otjt9ivubCQlJcFguPp4WlZWFt566y18/PHHePfdd+FwODBt2jScPXu2y9dZtmwZ9Hq9+5Genu5JmUTUB6/uPI2TNc1IiFLj6Zu57DvR7eOdQzXrD5+HnUM1XuH12TR5eXlYuHAhcnJyMHPmTHz00UcYMGAAXn311S7Pyc/Ph9FodD8qKyu9XSYRASitbcZft58CAPz8jtGIiVALrohIvFlZAxATEYZqkwV7T3OvGm/wKIwkJCRAqVSiurrzWv3V1dVITk7u0ccICwvDhAkTcOrUqS6P0Wg00Ol0nR5E5F2yLONn646g3ebADcMT8M3sVNElEfkFjUqJOzrujqwtPCe4muDkURhRq9XIzc3F1q1b3c85HA5s3boVeXl5PfoYdrsdxcXFSElJ8axSIvKqjwrPYe/pemhUCvx6/lg2rRJd4lsTBgIANh01oLXdJria4OPxMM2SJUvw+uuv45133sHx48fx+OOPo6WlBQ899BAAYOHChcjPz3cf/9xzz2Hz5s0oLS1FYWEh7rvvPpSXl+ORRx7pv8+CiPqkxmTG8xuOAQCenDMcGfGRgisi8i8TB8UgMz4Cre12fHqUa470N5WnJyxYsAC1tbX4xS9+AYPBgJycHGzatMnd1FpRUQGF4mLGaWhowKOPPgqDwYDY2Fjk5uZi7969GD16dP99FkTUa7Is45mPitHYasWYVB0evWGI6JKI/I4kSZg/IQ1//uwkPio8575TQv1DkmXZ71uDTSYT9Ho9jEYj+0eI+tn7+yrx4w8PQ61U4D8/vJ5TeYm6UFHfihl/2A6FBBTk34QkHVcTv5ae/v7m3jREIazyQiueW+8cnllyywgGEaJuDIqPwKSMWDhkZ48V9R+GEaIQZXfI+PEHh9FssSE3I5bDM0Q9cPck57pXq/dVcHn4fsQwQhSiXtlxCgWl9QgPU+LFu7KhVHD2DNG13JGdgmiNCuX1rdh7ul50OUGDYYQoBH1ZWo8/bfkaAPDcvDHITODsGaKeiFCr8K2JaQCAVV9x09f+wjBCFGLqmy34n9UH4ZCBb09Mw12TuN0CkSfumTIIALD5aDVqmsyCqwkODCNEIcThkPH/1hxCtcmCoQMi8fy8saJLIgo4o1J0mDAoBjaHjDX7u95njXqOYYQohPx560lsP1ELjUqB5fdORKTG46WGiAjAvVMzAADvflEOq90huJrAxzBCFCI2Flfh/7aeBAD85lvjMDKZa/YQ9dYd41OQEKVGldGMT45wRda+YhghCgFHzxvxv+8fAgA8cv1g/FcuV48k6gttmBL3Xee8O/Lm7jMIgPVD/RrDCFGQq2u24Pt/P4A2qx03DE/AM7eOFF0SUVC477oMqFUKHKpsRGFFg+hyAhrDCFEQa7HY8NDb+3CusQ2DEyLxt3smQqXktz1Rf0iI0mB+TioA590R6j3+VCIKUu02Bx579wCKzxkRF6nGmw9Mgj4iTHRZREHl4eudKxd/csSAUzXNgqsJXAwjREHI4ZDxkw8P4/OTdQgPU+KtBydjyIAo0WURBZ2s5GjcPDoJsgy8vP2U6HICFsMIUZCRZRnPrT+GtQfPQamQ8PJ9E5GTHiO6LKKg9T+zhwMA1hWdQ1ldi+BqAhPDCFEQcQWRlXvLAAC/+8543JiVKLYooiA3bqAeN2YNgEMGlvPuSK8wjBAFCVmW8fz643h7TxkA4IVvj+MUXiIf+eFNzrsjHx3k3ZHeYBghCgIOh4xf/ecY3trj7Ohf9u1x+O+O/TOIyPsmDorFrKwBsDtk/P7TEtHlBByGEaIA125z4Mn3itxDM7/51lj3Rl5E5DvP3DoSCgnYWGzAgXKuO+IJhhGiANZsseF7K/fhP4fOI0wp4S//nePeM4OIfGtksg535Tp3wf7NhmNcldUDDCNEAepsQyvuXlGA3afqEKFW4s0HJmNeTprosohC2pJbRiA8TInCikZsKK4SXU7AYBghCkBfltbjm3/bg2NVJsRHqvGvR6/DjBEDRJdFFPKSdFr8YKZzIbTn/nMMJrNVcEWBgWGEKIDIsox/FJTh3je+xIWWdoxN0+HfP7we2VxHhMhvPDZzKIYkRKKmyYI/bDohupyAwDBCFCAaW9vx+LuF+PnHR2FzyLgzOxVrfjANaTHhoksjoktow5T49bfGAgDe/bKczaw9wDBCFAD2lV3AbX/5HJuOGhCmlPDsbaPwf/+dg3C1UnRpRHQV04Ym4L9yB0KWgR99cAit7TbRJfk1hhEiP9babsNz/zmGu18twHmjGZnxEfjw8Wl4dMYQSJIkujwi6sbPbh+FZJ0WpbUt+NW/j4kux68xjBD5qc9P1uKWl3bhrT1nIMvAdyYOxPr/uQHjB8aILo2IeiAmQo2XFuRAkoD39ldiw2HOrumKSnQBRNRZRX0rfrvxODYdNQAA0mLC8ZtvjcUs7jFDFHDyhsbjiVlDsXz7aTzz4WGMSIrC8KRo0WX5HYYRIj9hbLPilR2n8dbuM2i3O6CQgIV5mfh/c7MQpeG3KlGgemrOCOwra8BXZy7ge+/sw7onpiM+SiO6LL8iyQGwRJzJZIJer4fRaIROpxNdDlG/MrZZ8dbuM3hrzxk0mZ1NbtcPS8DP7xiNrGT+BUUUDC60tGP+8j2ouNCKyZmx+MfDU6ENC/4G9J7+/mYYIRKkxmTGP74ox8q9Ze4QMiIpCj+aOxJzRiWyQZUoyJysbsK3X96LJosNNwxPwOsLJwV9IGEYIfJTBysasHJvGTYWV8Fqd377jUiKwpM3jcCtY5OhUDCEEAWrL0vr8eDb+9BmtWPGiAF47f7coA4kDCNEfqTaZMbHRefwUeE5lBia3M9PyojF964fjG+MYQghChVflNbjoY5AMmFQDF67fxIGRAdnDwnDCJFgNU1mbDtegw3FVdhzqg6Oju80tVKBO7NT8eC0TIwbqBdbJBEJ8WVpPb7/jwMwtlmRqtfitYWTMDYt+H4eMIwQ+ZjN7sDR8ybs+roWn5XU4FBlY6f352bE4lsT0nDH+BTERKjFFElEfqO0thmPvLMfpXUtCFNKePKm4Xhs5lColMGzBBjDCJGXtbXbcfS8EV+VXcCXpRdwoLwBzZbOSz6PH6jHnFFJmJeTioz4SEGVkrfYHTK+OnMBNU1mJEZrMWVwHJQcbiMPGFut+NEHh7D5WDUAYGyaDj+9bRSmDU0QXFn/8GoYWb58Of7whz/AYDAgOzsbf/3rXzFlypQuj1+zZg1+/vOfo6ysDMOHD8fvfvc73HbbbT1+PYYREkmWZVSbLCita8ax8yYcPW/CkXNGnK5tdg+9uOi0KkwZHI+bRiVi9shEJOm0Yoomr9t0pAq/+s8xVBnN7udS9FosvXM0vjE2RWBlFGhkWcbag+ew9N9H3TPrZo4YgEdvGILpw+IDemad18LIe++9h4ULF2LFihWYOnUq/vznP2PNmjU4ceIEEhOvXCFy7969mDFjBpYtW4Y77rgDq1atwu9+9zsUFhZi7Nix/frJEPWGLMtoaLXCYDSj2mSGwWTGuYY2nKlvwZnaFpTVt6C13X7VcxOiNMjNiMHUwfGYOiQOI5N1/Ms4BGw6UoXH3y3E5T88Xf/yr9w3kYGEPFbXbMH/bT2JVV9WwNbxl86wxCjMy07FreOSMSwx8NYd8loYmTp1KiZPnoy//e1vAACHw4H09HT88Ic/xDPPPHPF8QsWLEBLSwvWr1/vfu66665DTk4OVqxY0a+fDIUmWZZhsTnQ2m5Ha7sNZqu94//taGu3w2S2orG149HWDmOrFY1tVjS2tqO22YJqkwXtNke3r6FUSBgYG46RydEYm6rH2DQ9xqTqkMg7HyHH7pBx/e+2dbojcikJQLJei90/mc1gSr1ypq4Fb+85gw8PnEXLJX8Ipei1mJgRi4mDYjEsMQqZ8RFIiwn36x6Tnv7+9miN6fb2dhw4cAD5+fnu5xQKBebMmYOCgoKrnlNQUIAlS5Z0em7u3LlYt25dl69jsVhgsVjcb5tMJk/K7LE3d59B5YXWq77v0ox2eVq7NL7Jl7338mgnd/O+S997xXk9fI3uarvi3G5rk7t5X+/Ou/L1uvk8ZMDmkGFzOGCzX/yv1SHDZnf9vwN2h+z8f7sDNocMs9WONqv9KtfWc/GRaiTptEjWa5Gi12JwQiQGJ0QiMyES6bERUKv89xuefOerMxe6DCKA88u+ymjGV2cuIG9ovO8Ko6AxOCESz80bix/NzcLG4ipsOmLA7lN1qDKaseFwVacN95QKCbERYYiJUCM2IgzR2jColQqoVQqEKRVQqyQoFRKkjvt2rhEfV0y+dAjo4esHIz0uwlefZicehZG6ujrY7XYkJSV1ej4pKQklJSVXPcdgMFz1eIPB0OXrLFu2DL/61a88Ka1XNhw+j8KKRq+/DvmOWqVAhFqJ8DAlwjv+q9OGIabjmzUmIgwx4c639eFqxEepkazTIlGngUYVvAsPUf+paeo6iPTmOKKuRGvDsGDyICyYPAit7TYcqjTiQPkFHD5rRHl9K8rqW2CxOVDX3I665vY+v968nNTACCO+kp+f3+luislkQnp6er+/zndyB3bqWL68R6jTm5e9U+r6Xe4EerX3X37TttP7umlS6u41uq37itfvurYrX/OS1+j2Y3Z93rWOvfSdKoUElUJCmFIBpUJCmFKCSqGASul8TqWQoLrsOa1KCa1agQi1CuFhSt4WJ69LjO7Z0FxPjyPqiQi1CnlD4zvdbXM4ZNQ2W1Df3I7G1nY0tFrRbLGi3S7DanPAaneg3ea8i+y+edxxG1m++L/uu9YiG+49CiMJCQlQKpWorq7u9Hx1dTWSk5Ovek5ycrJHxwOARqOBRuP91ejunZrh9dcgouAyZXAcUvRaGIzmK4ZJgYs9I1MGx/m6NAoxCoWEJJ02KGbteTQIrlarkZubi61bt7qfczgc2Lp1K/Ly8q56Tl5eXqfjAWDLli1dHk9E5M+UCglL7xwN4Cp3BTv+u/TO0bxLR+QBjzvylixZgtdffx3vvPMOjh8/jscffxwtLS146KGHAAALFy7s1OD65JNPYtOmTXjxxRdRUlKCX/7yl9i/fz8WL17cf58FEZEPfWNsCl65byKS9Z3/Ik3Wazmtl6gXPO4ZWbBgAWpra/GLX/wCBoMBOTk52LRpk7tJtaKiAgrFxYwzbdo0rFq1Cj/72c/w05/+FMOHD8e6det6vMYIEZE/+sbYFNw8OpkrsBL1Ay4HT0RERF7R09/fXDiBiIiIhGIYISIiIqEYRoiIiEgohhEiIiISimGEiIiIhGIYISIiIqEYRoiIiEgohhEiIiISimGEiIiIhPJ4OXgRXIvEmkwmwZUQERFRT7l+b19rsfeACCNNTU0AgPT0dMGVEBERkaeampqg1+u7fH9A7E3jcDhw/vx5REdHQ5L6bxMqk8mE9PR0VFZWcs8bL+J19h1ea9/gdfYNXmff8OZ1lmUZTU1NSE1N7bSJ7uUC4s6IQqHAwIEDvfbxdTodv9B9gNfZd3itfYPX2Td4nX3DW9e5uzsiLmxgJSIiIqEYRoiIiEiokA4jGo0GS5cuhUajEV1KUON19h1ea9/gdfYNXmff8IfrHBANrERERBS8QvrOCBEREYnHMEJERERCMYwQERGRUAwjREREJFTQh5Hly5cjMzMTWq0WU6dOxVdffdXt8WvWrMHIkSOh1Woxbtw4bNy40UeVBjZPrvPrr7+OG264AbGxsYiNjcWcOXOu+e9CF3n6Ne2yevVqSJKE+fPne7fAIOHpdW5sbMSiRYuQkpICjUaDESNG8OdHD3h6nf/85z8jKysL4eHhSE9Px9NPPw2z2eyjagPTrl27cOeddyI1NRWSJGHdunXXPGfHjh2YOHEiNBoNhg0bhpUrV3q3SDmIrV69Wlar1fJbb70lHz16VH700UflmJgYubq6+qrH79mzR1YqlfLvf/97+dixY/LPfvYzOSwsTC4uLvZx5YHF0+v83e9+V16+fLl88OBB+fjx4/KDDz4o6/V6+ezZsz6uPPB4eq1dzpw5I6elpck33HCDPG/ePN8UG8A8vc4Wi0WeNGmSfNttt8m7d++Wz5w5I+/YsUMuKiryceWBxdPr/M9//lPWaDTyP//5T/nMmTPyp59+KqekpMhPP/20jysPLBs3bpSfffZZ+aOPPpIByGvXru32+NLSUjkiIkJesmSJfOzYMfmvf/2rrFQq5U2bNnmtxqAOI1OmTJEXLVrkfttut8upqanysmXLrnr83XffLd9+++2dnps6dar8gx/8wKt1BjpPr/PlbDabHB0dLb/zzjveKjFo9OZa22w2edq0afIbb7whP/DAAwwjPeDpdX7llVfkIUOGyO3t7b4qMSh4ep0XLVokz549u9NzS5YskadPn+7VOoNJT8LIj3/8Y3nMmDGdnluwYIE8d+5cr9UVtMM07e3tOHDgAObMmeN+TqFQYM6cOSgoKLjqOQUFBZ2OB4C5c+d2eTz17jpfrrW1FVarFXFxcd4qMyj09lo/99xzSExMxMMPP+yLMgNeb67zv//9b+Tl5WHRokVISkrC2LFj8dvf/hZ2u91XZQec3lznadOm4cCBA+6hnNLSUmzcuBG33XabT2oOFSJ+FwbERnm9UVdXB7vdjqSkpE7PJyUloaSk5KrnGAyGqx5vMBi8Vmeg6811vtxPfvITpKamXvHFT5315lrv3r0bb775JoqKinxQYXDozXUuLS3Ftm3bcO+992Ljxo04deoUnnjiCVitVixdutQXZQec3lzn7373u6irq8P1118PWZZhs9nw2GOP4ac//akvSg4ZXf0uNJlMaGtrQ3h4eL+/ZtDeGaHA8MILL2D16tVYu3YttFqt6HKCSlNTE+6//368/vrrSEhIEF1OUHM4HEhMTMRrr72G3NxcLFiwAM8++yxWrFghurSgsmPHDvz2t7/Fyy+/jMLCQnz00UfYsGEDnn/+edGlUR8F7Z2RhIQEKJVKVFdXd3q+uroaycnJVz0nOTnZo+Opd9fZ5Y9//CNeeOEFfPbZZxg/frw3ywwKnl7r06dPo6ysDHfeeaf7OYfDAQBQqVQ4ceIEhg4d6t2iA1BvvqZTUlIQFhYGpVLpfm7UqFEwGAxob2+HWq32as2BqDfX+ec//znuv/9+PPLIIwCAcePGoaWlBd///vfx7LPPQqHg39f9oavfhTqdzit3RYAgvjOiVquRm5uLrVu3up9zOBzYunUr8vLyrnpOXl5ep+MBYMuWLV0eT727zgDw+9//Hs8//zw2bdqESZMm+aLUgOfptR45ciSKi4tRVFTkfnzzm9/EjTfeiKKiIqSnp/uy/IDRm6/p6dOn49SpU+6wBwBff/01UlJSGES60Jvr3NraekXgcAVAmdus9Rshvwu91hrrB1avXi1rNBp55cqV8rFjx+Tvf//7ckxMjGwwGGRZluX7779ffuaZZ9zH79mzR1apVPIf//hH+fjx4/LSpUs5tbcHPL3OL7zwgqxWq+UPPvhArqqqcj+amppEfQoBw9NrfTnOpukZT69zRUWFHB0dLS9evFg+ceKEvH79ejkxMVH+9a9/LepTCAieXuelS5fK0dHR8r/+9S+5tLRU3rx5szx06FD57rvvFvUpBISmpib54MGD8sGDB2UA8p/+9Cf54MGDcnl5uSzLsvzMM8/I999/v/t419TeH/3oR/Lx48fl5cuXc2pvX/31r3+VBw0aJKvVannKlCnyF1984X7fzJkz5QceeKDT8e+//748YsQIWa1Wy2PGjJE3bNjg44oDkyfXOSMjQwZwxWPp0qW+LzwAefo1fSmGkZ7z9Drv3btXnjp1qqzRaOQhQ4bIv/nNb2SbzebjqgOPJ9fZarXKv/zlL+WhQ4fKWq1WTk9Pl5944gm5oaHB94UHkO3bt1/1Z67r2j7wwAPyzJkzrzgnJydHVqvV8pAhQ+S3337bqzVKssx7W0RERCRO0PaMEBERUWBgGCEiIiKhGEaIiIhIKIYRIiIiEophhIiIiIRiGCEiIiKhGEaIiIhIKIYRIiIiEophhIiIiIRiGCEiIiKhGEaIiIhIKIYRIiIiEur/A9QWIcF0abnTAAAAAElFTkSuQmCC\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6666666666666666\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6315789473684211\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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utsfESa1Wu5YPOx9ERF3ZeaIOre02pOg0GJUSfO8VqhAFpmU5lvhu56oa8lNuhZGCggLs2LEDp0+fxqFDh1BQUIBt27bh1ltvBQAsWbIEBQUFruPvv/9+bNy4EU8//TSOHTuGxx57DPv27cOyZcs8+1sQUdBy3rl2zshESJIkuBoxZjqX+B5nGCH/5FYD6/nz57FkyRJUV1dDp9Nh7Nix+PzzzzFnzhwAQGVlJRSKi/lm6tSpePvtt/HII4/gd7/7HYYOHYp169Zh9OjRnv0tiCgo2eyya8OvOSODr1/EaWa2o2/kQGUDGlssiA7nEl/yL33eZ8QbuM8IEXVlf0U9fvxSIaI0ISj6wxyEKoP3DhfXP7sdx2ua8cLN47AgJ0V0OUQAvLDPCBGRaJsOO0ZFZg1PCOogAnReVUPkb4L7by8R+bUvjjrCyOwRwbeK5ruuHeoII7tP1vEuvuR3GEaIyC9VXmjBqVoTlAoJ0ztGBYLZxMGxUCkVOGdoQ3mdSXQ5RG5hGCEiv/Rl6XkAwIT0GOjCQgVXI16YSom89BgAwK5TFwRXQ+QehhEi8ktbjznCyKzhCYIr8R3XDHXsN7LrRJ3gSojcwzBCRH6n1WJDYZnjX//XMYy4TM0cAADYfaoONm4NT36EYYSI/M7uU3WwWO0YGB2GoQmRosvxGWMG6hClCYGxzYqSs9wanvwHwwgR+R3nFM11w+ODdtfVroQoFcjPcIyO7DzJqRryHwwjRORXZFnGto57sLBf5HKuvhGGEfIjDCNE5FeO1zTjbGMr1CEK5GfEiS7H5zhvmrfvdANaLTbB1RD1DMMIEfkV55Le/MwBCFMpBVfjezLiIpCk1cBis2NfRb3ocoh6hGGEiPwKl/RemSRJrtER9o2Qv2AYISK/YWhpx/6KBgDAddkMI925ZmjHEt+T3PyM/APDCBH5ja9O1sJml5GVEIm02HDR5fisaZmOkZGScwY0mCyCqyG6OoYRIvIbnKLpmQStBkMTIiHLwNflHB0h38cwQkR+wW6XseO4Y0nvTN4Y76qmdOw3sqeMTazk+xhGiMgvHNUbUddsQbhKiQmDY0WX4/MuhhGOjJDvYxghIr+w47hjZUh+xgCoQvjWdTWTMxyB7Zi+iX0j5PP4N5qI/IJzimY6p2h6JC5SjayO+/bsPc2pGvJtDCNE5PNMZqtrAy+GkZ6b0jE6wqka8nUMI0Tk8/aUXUC7TUZqTBgGD+CS3p5iEyv5C4YRIvJ5l07R8C69PTdpiLNvxIjGFvaNkO9iGCEin/fVCUfz6vShnKJxR0KUBpnxEZBlYG85R0fIdzGMEJFPq6pvQVmdCUqFhKlZA0SX43c4VUP+gGGEiHzajhOOKZrxg6Kh1YQKrsb/OMMId2IlX8YwQkQ+zdUvwimaXnHuN3Kk2ghDS7vgaoi6xjBCRD6r3WZ33Xn2Wi7p7ZWEKA0ynH0j3G+EfBTDCBH5rG+rGtFktiI6PBRjBupEl+O3uDU8+TqGESLyWc4pmmuy4qBUcElvb03uWOLLvhHyVQwjROSztjuX9HKKpk+cIyOHzxlhaGXfCPkehhEi8kkNJgsOnmkEwObVvkrUapAR5+gb2ce+EfJBDCNE5JN2nqyDLAPDEiORpNOILsfvTRzsmKphEyv5IoYRIvJJXNLrWRM7+kb2nW4QXAnR5RhGiMjnyLKMXScd/SJc0usZEwfHAAAOnmlEW7tNcDVEnTGMEJHPKa8z4ZyhDSqlApM6pheobwbFhiMhSo12m4xvqxpFl0PUCcMIEfkc56hIXnoMwlRKwdUEBkmSXH0j37BvhHyMW2Fk5cqVmDhxIqKiopCQkIBFixahtLT0iuesWbMGkiR1emg0bEYjou7t6th1dRpvjOdRzqmavewbIR/jVhjZvn07li5dij179mDz5s1ob2/H9ddfD5PJdMXztFotqqurXY+Kioo+FU1Egctml7H7lGNkZFpWnOBqAouzibWoogE2uyy4GqKLQtw5eOPGjZ2+XrNmDRISErB//35Mnz692/MkSUJSUlLvKiSioFJy1gBjmxVRmhBuAe9hw5O0iFKHoMlsxdFqI0bz+pKP6FPPiMFgAADExl65way5uRnp6elIS0vDwoULcfjw4SsebzabYTQaOz2IKDjs6hgVmZIxACFKtrV5klIhYXy6Y6qGfSPkS3r9N91ut+OBBx7AtGnTMHr06G6Py87OxmuvvYaPP/4Yb775Jux2O6ZOnYozZ850e87KlSuh0+lcj7S0tN6WSUR+xtm8eg2naPqFs2+E+42QL+l1GFm6dClKSkqwdu3aKx6Xn5+PJUuWIDc3FzNmzMCHH36I+Ph4vPzyy92eU1BQAIPB4HpUVVX1tkwi8iNt7TZ80/EhyX6R/nHpTqyyzL4R8g1u9Yw4LVu2DOvXr8eOHTuQmprq1rmhoaEYN24cTp482e0xarUaarW6N6URkR/bX9EAi9WORK0amfERossJSDlp0VApFahtMqOyvgXpA3idSTy3RkZkWcayZcvw0UcfYevWrRgyZIjbL2iz2XDo0CEkJye7fS4RBbadJy+uopEkSXA1gUkTqsSYVEfj6t5y9o2Qb3ArjCxduhRvvvkm3n77bURFRUGv10Ov16O1tdV1zJIlS1BQUOD6+vHHH8emTZtQVlaGoqIi3HbbbaioqMBdd93lud+CiALCbvaLeAU3PyNf41YYeemll2AwGDBz5kwkJye7Hu+++67rmMrKSlRXV7u+bmhowN13340RI0Zg/vz5MBqN2L17N0aOHOm534KI/J6hpR0HzzpW6LFfpH+xiZV8jVs9Iz1pdtq2bVunr5999lk8++yzbhVFRMGnsKwOsgxkJUQiUctdmvvThHTHyEhZnQm1TWbER7FHj8TiIn4i8gmuLeAzuQV8f9OFhyI7MQoAsI9TNeQDGEaIyCfsOskt4L1p4hDn5mecqiHxGEaISLhzja0oqzNBIQFTODLiFWxiJV/CMEJEwjlHRcamRkOrCRVcTXCY0BFGjlQb0WKxCq6Ggh3DCBEJxy3gvS9Fp0GSVgObXca3VQbR5VCQYxghIqFkWcauUx3NqwwjXiNJEvI6bppXVMm+ERKLYYSIhDpxvhm1TWZoQhUYnx4tupyg4gwj+ysYRkgshhEiEmrnCccUzcTBsVCHKAVXE1wuDSN2O2+aR+IwjBCRULtPsV9ElJEpWmhCFTC0tqOsrll0ORTEGEaISJh2mx17yhxLS9kv4n2hSgVyUqMBcKqGxGIYISJhDp5pRLPZiujwUIxM1oouJyg5p2p4nxoSiWGEiIS5uAV8HBQKSXA1wcnVN8IVNSQQwwgRCbOzY3+RqVncdVWU8YMcYaSs1oR6k0VwNRSsGEaISIgWixUHOv41zuZVcWIiVMiMjwAA1/8fRN7GMEJEQuwtr0e7TUZqTBgGxYaLLieoufpG2MRKgjCMEJEQrrv0ZsZBktgvIhI3PyPRGEaISAhX8+pQTtGIlpfuuGnet1WNaLfZBVdDwYhhhIi87kKzGUeqjQCAqZlsXhUtIy4C0eGhMFvtOHLOKLocCkIMI0Tkdbs7bow3PCkKcZFqwdWQQiG5VtWwb4REYBghIq/jFvC+x3UHX4YREoBhhIi8zrm/CPtFfMfFFTX1kGXeNI+8i2GEiLyq8kILqupbEaKQMGlwrOhyqENOajRCFBJqjGacbWwVXQ4FGYYRIvKqXR1TNOMHxSBCHSK4GnIKUykxKsVxfyAu8SVvYxghIq/iFvC+azz7RkgQhhEi8hq7Xcbuk2xe9VW8aR6JwjBCRF5zVG9EQ0s7IlRK5KRFiy6HvsMZRo5WN8FktgquhoIJwwgReY1zC/jJGQMQquTbj69J1oVhYHQYbHYZ31Y1ii6HggjfDYjIa1xbwHOKxmeN531qSACGESLyCrPVhr3l9QDYL+LL8gZFA+BOrORdDCNE5BUHKhvR2m5DXKQKwxIjRZdD3ZjQsfdLUWUD7HZufkbewTBCRF7hXEUzLSsOkiQJroa6MzwpCmGhSjS1WXGytll0ORQkGEaIyCt2XhJGyHeFKBXI7VjpxL4R8haGESLqd8a2dnx7xgCAYcQfTBjccZ+a0wwj5B0MI0TU774uq4fNLmNIXAQGRoeJLoeuwrUTKzc/Iy9hGCGifrfLNUXDLeD9wfg0RxgprzPhQrNZcDUUDNwKIytXrsTEiRMRFRWFhIQELFq0CKWlpVc97/3338fw4cOh0WgwZswYbNiwodcFE5H/2cUt4P2KLjwUQxMcK56KKhvFFkNBwa0wsn37dixduhR79uzB5s2b0d7ejuuvvx4mk6nbc3bv3o2bb74Zd955Jw4cOIBFixZh0aJFKCkp6XPxROT7aoxtOHG+GZIETMngyIi/yOPmZ+RFkizLvV5IXltbi4SEBGzfvh3Tp0/v8pjFixfDZDJh/fr1ruemTJmC3NxcrF69ukevYzQaodPpYDAYoNVqe1suEQnw0YEzePDdbzE2VYdPll0juhzqoff2VeGhDw5i0uBYvHdPvuhyyE/19PO7Tz0jBoOjOz42NrbbYwoLCzF79uxOz82dOxeFhYV9eWki8hM7T3ALeH80oWNk5NszjbBY7YKroUDX6zBit9vxwAMPYNq0aRg9enS3x+n1eiQmJnZ6LjExEXq9vttzzGYzjEZjpwcR+R9Zli82r2YyjPiTIXERiAkPhdlqx+FzBtHlUIDrdRhZunQpSkpKsHbtWk/WA8DRKKvT6VyPtLQ0j78GEfW/U7Um6I1tUIUoXHtXkH+QJIl9I+Q1vQojy5Ytw/r16/Hll18iNTX1iscmJSWhpqam03M1NTVISkrq9pyCggIYDAbXo6qqqjdlEpFgu085RkUmDo6BJlQpuBpyF/cbIW9xK4zIsoxly5bho48+wtatWzFkyJCrnpOfn48tW7Z0em7z5s3Iz+++IUqtVkOr1XZ6EJH/2XmCW8D7s7xBF0dG+rDWgeiq3AojS5cuxZtvvom3334bUVFR0Ov10Ov1aG1tdR2zZMkSFBQUuL6+//77sXHjRjz99NM4duwYHnvsMezbtw/Lli3z3G9BRD7HarOjsKyjeZX9In5pbGo0QhQSaoxmnG1svfoJRL3kVhh56aWXYDAYMHPmTCQnJ7se7777ruuYyspKVFdXu76eOnUq3n77bfz9739HTk4OPvjgA6xbt+6KTa9E5P9KzhnR1GaFVhOC0QN1osuhXghTKTEqxTEyzb4R6k8h7hzck2G6bdu2XfbcjTfeiBtvvNGdlyIiP+dcRTM1Mw5KhSS4GuqtvPRYfHvGgP0VDViYO1B0ORSgeG8aIuoXF/tFuOuqP+OKGvIGhhEi8rhWi8314cXmVf82Pj0aAHC02giT2Sq2GApYDCNE5HH7KuphsdmRotNgSFyE6HKoD5J1YRgYHQa7DHxb1Si6HApQDCNE5HE7nf0iWXGQJPaL+LvxnKqhfsYwQkQe52xevYZTNAEhb1A0AGA/Nz+jfsIwQkQe1WCy4PA5x/2kprJ5NSDkpTtuhlpU0QC7nZufkecxjBCRRxWWXYAsA8MSI5EQpRFdDnnAiOQohIUqYWyz4mRts+hyKAAxjBCRRzn7RbiKJnCEKBXITYsGwL4R6h8MI0TkUewXCUzcb4T6E8MIEXlMVX0LKi60QKmQMDmD/SKBxBlGihhGqB8wjBCRx+w+5RgVyU2LRqTarbtNkI8b17GipqzOhHqTRWwxFHAYRojIY3ae7LhLL6doAk50uApZCZEAOFVDnscwQkQeYbfL7BcJcHmD2DdC/YNhhIg84ki1EfUmCyLVIa4hfQoseYPZN0L9g2GEiDxi+/FaAEB+5gCEKvnWEoicTazfnmmExWoXXA0FEr5jEJFHfHXCEUamD+UUTaDKiItAdHgozFY7jlQbRZdDAYRhhIj6zGS2uvoIrh0aL7ga6i+SJLFvhPoFwwgR9dnX5RfQbpORFhuG9AHhosuhfnTxDr71giuhQMIwQkR9tuO4YxXNtUPjIUmS4GqoP126E6ss86Z55BkMI0TUZ+wXCR45qdEIUUioMZpxtrFVdDkUIBhGiKhPzja24lStCQoJyM9kGAl0YSolRqVoAbBvhDyHYYSI+mRnx6hIblo0dGGhgqshbxjP+9SQhzGMEFGf7DhxsV+EgoOrb6SSYYQ8g2GEiHrNdskW8NOHcYomWDjDyNHqJpjMVsHVUCBgGCGiXis5a0BjSzui1CHISY0WXQ55SbIuDCk6DWx2Gd9WNYouhwIAwwgR9dqOji3gp2YNQAi3gA8q49O5+Rl5Dt89iKjXvmK/SNBi3wh5EsMIEfVKU1s7ijo+iKYzjASdCemxABwraux2bn5GfcMwQkS9sqesHla7jPQB4RjELeCDzvDkKISFKmFss+JUbbPocsjPMYwQUa84d129lruuBqVQpQI5aToA7BuhvmMYIaJecfaLcIomeDn7RvYxjFAfMYwQkduq6ltQXmeCUiEhP3OA6HJIkDzuxEoewjBCRG7bVnoeAJA3KAZRGm4BH6zGpTnCSFmdCfUmi+BqyJ8xjBCR27aVOvpFZmRziiaYxUSokBkfAYB9I9Q3DCNE5Ja2dht2n7oAAJjJMBL0nEt8952uF1wJ+TOGESJyyzen69HabkNClBojk7WiyyHBJg5xhJG9DCPUB26HkR07dmDBggVISUmBJElYt27dFY/ftm0bJEm67KHX63tbMxEJ5JyimZkdD0mSBFdDok0a7Agjh84Y0GqxCa6G/JXbYcRkMiEnJwerVq1y67zS0lJUV1e7HgkJCe6+NBH5gC87mldnZvPvMAFpsWFI1Kphtcs4UMW+EeqdEHdPmDdvHubNm+f2CyUkJCA6Otrt84jId1TVt6Cs1rGkd1oWNzsjQJIkTBwci/UHq/FNeQOmZvLPBbnPaz0jubm5SE5Oxpw5c7Br164rHms2m2E0Gjs9iEi8S5f06sK4pJccJnX0jXzDvhHqpX4PI8nJyVi9ejX+/e9/49///jfS0tIwc+ZMFBUVdXvOypUrodPpXI+0tLT+LpOIeoBLeqkrEzv6RooqG2C12QVXQ/7I7Wkad2VnZyM7O9v19dSpU3Hq1Ck8++yz+Ne//tXlOQUFBVi+fLnra6PRyEBCJNilS3qvY78IXSI7MQpaTQiMbVYcPmdETlq06JLIzwhZ2jtp0iScPHmy2++r1WpotdpODyISa2+5Y0lvolaNEclRosshH6JQSJgwmFM11HtCwkhxcTGSk5NFvDQR9ZJrimYYl/TS5SYyjFAfuD1N09zc3GlUo7y8HMXFxYiNjcWgQYNQUFCAs2fP4o033gAAPPfccxgyZAhGjRqFtrY2vPrqq9i6dSs2bdrkud+CiPrdtuNc0kvdmzSk4w6+pxsgyzIDK7nF7TCyb98+XHfdda6vnb0dd9xxB9asWYPq6mpUVla6vm+xWPCb3/wGZ8+eRXh4OMaOHYsvvvii088gIt/GJb10NWMGRkMdosAFkwWnak3ISogUXRL5EbfDyMyZMyHLcrffX7NmTaevH3roITz00ENuF0ZEvoNLeulqVCEK5KZF4+vyenxzup5hhNzCe9MQ0VV9ySW91AOu/UbK2TdC7mEYIaIrarXYsOtkHQDgeyPYL0Ldczax8qZ55C6GESK6op0n62C22jEwOgzZiVzSS90bnx4DhQScaWhFtaFVdDnkRxhGiOiKth6rAQDMHpHAFRJ0RZHqEIxK0QFw7EtD1FMMI0TULbtdxpajjubVWSMSBVdD/oD7jVBvMIwQUbdKzhlwvsmMCJUSUzJiRZdDfsC538g35Q2CKyF/wjBCRN36omNU5Nqh8VCHKAVXQ/7AuS18aU0TGlssgqshf8EwQkTdcvaLcBUN9VRcpBoZ8REAHLuxEvUEwwgRdUlvaEPJWSMkCbhuOMMI9dzkIQMAAHvKLgiuhPwFwwgRdWlLx6hIblo04iLVgqshf+LsL9pTzjBCPcMwQkRd2trRLzKbq2jITVMyHCMjh88ZYWhtF1wN+QOGESK6TKvFhp0du67O4hQNuSlRq0FGXARkmVvDU88wjBDRZXZdsuvq8CTuukrum5LJvhHqOYYRIrrMlktW0XDXVeoN51QN+0aoJxhGiKgTu13G5iOOfpHvsV+EemlKxx18D58zwtDCvhG6MoYRIurkQFUD6prNiNKEIL/jX7dE7krQapAR7+gb4V186WoYRoiok88PO6ZoZg1PgCqEbxHUe66pGvaN0FXwnYaIXGRZxueH9QCAuaOSBFdD/i6fYYR6iGGEiFxKa5pQcaEFqhAFZgyLF10O+bnJHZufHalm3whdGcMIEbl8XuKYopk+NA4R6hDB1ZC/S4jSILOjb+RrrqqhK2AYISIX5xTN9ZyiIQ+52DfCJlbqHsMIEQEAqupbcKTaCIXELeDJc9jESj3BMEJEAC6OikwcHIvYCJXgaihQOMPIUb0RjS0WwdWQr2IYISIAwKaOJb1cRUOeFB+lRlZCZEffCKdqqGsMI0SEumYzvqlwfFBcP4pTNORZziW+hac4VUNdYxghInxxpAayDIweqEVqTLjocijATMuKAwDXnaCJvothhIgubnQ2klM05Hn5GQOgkICT55uhN7SJLod8EMMIUZAztLS7/sX6/dEMI+R5uvBQjEmNBgDs4ugIdYFhhCjIbTqiR7tNRnZiFIYmRokuhwLUNVmOvhGGEeoKwwhRkPv0UDUA4IaxyYIroUB2ad+ILMuCqyFfwzBCFMQMLe3YecLxL9X5YxhGqP+MHxQDdYgC55vMOHm+WXQ55GMYRoiC2OdH9LDaZQxPikJWQqTociiAaUKVmDTEceM8rqqh72IYIQpinx50TNH8gFM05AXOqRr2jdB3MYwQBakGk8X1ocApGvKGazrCyJ6yerTb7IKrIV/CMEIUpDZ1TNGMSNYiI55TNNT/RiZrER0eimazFQfPNIouh3yI22Fkx44dWLBgAVJSUiBJEtatW3fVc7Zt24bx48dDrVYjKysLa9as6UWpRORJ6zlFQ16mUEiYltmxquYEt4ani9wOIyaTCTk5OVi1alWPji8vL8cNN9yA6667DsXFxXjggQdw11134fPPP3e7WCLyjHqTBbs77hPCKRryJvaNUFdC3D1h3rx5mDdvXo+PX716NYYMGYKnn34aADBixAjs3LkTzz77LObOnevuyxORB2ws0cNmlzEqRYshcRGiy6Eg4uwbKapsQFNbO6I0oYIrIl/Q7z0jhYWFmD17dqfn5s6di8LCwv5+aSLqxrriswCABTkpgiuhYDNoQDgGDwiH1S67RueI+j2M6PV6JCZ2viV5YmIijEYjWltbuzzHbDbDaDR2ehCRZ5xpaMHe8npIEvBDhhESYMaweADAttJawZWQr/DJ1TQrV66ETqdzPdLS0kSXRBQwPvn2HABg8pBYpESHCa6GgtHM7AQAwI7jtdwangB4IYwkJSWhpqam03M1NTXQarUIC+v6jbCgoAAGg8H1qKqq6u8yiYKCLMtYd8AxRfMf4wYKroaC1ZSMAVCFKHC2sZVbwxMAL4SR/Px8bNmypdNzmzdvRn5+frfnqNVqaLXaTg8i6ruj1U04XtMMlVKB74/mKhoSI0ylxOSOreG3H+dUDfUijDQ3N6O4uBjFxcUAHEt3i4uLUVlZCcAxqrFkyRLX8ffccw/Kysrw0EMP4dixY3jxxRfx3nvv4cEHH/TMb0BEPeZsXJ01PAG6MK5iIHHYN0KXcjuM7Nu3D+PGjcO4ceMAAMuXL8e4cePw6KOPAgCqq6tdwQQAhgwZgk8//RSbN29GTk4Onn76abz66qtc1kvkZTa7jE+KHf0iizhFQ4I5+0b2ltejxWIVXA2J5vY+IzNnzrxiw1FXu6vOnDkTBw4ccPeliMiDvi67AL2xDVpNCK4bHi+6HApymfERGBgdhrONrSg8dQHfG5F49ZMoYPnkahoi8jznFM38MclQhygFV0PBTpIkzMx2hGL2jRDDCFEQaGu34bNDegCcoiHf4Zyq2VbKJb7BjmGEKAhsLNGjyWzFwOgwTBocK7ocIgBAfuYAhColVNa34PSFFtHlkEAMI0RB4P39jr16bpyQCoVCElwNkUOkOgQTO8LxttLzgqshkRhGiAJcVX0Ldp28AEkCfpKXKrocok6cfSNbjzGMBDOGEaIA98H+MwCAaZlxSI0JF1wNUWfOVTR7yi6gqa1dcDUkCsMIUQCz22VXGLlxAkdFyPdkxkciIy4C7TYZX52oE10OCcIwQhTAdp+6gLONrYjShGDuqCTR5RB16XsjHKtqvjhSc5UjKVAxjBAFsPf2ORpXF+amQBPKvUXIN83umKrZWnoeVptdcDUkAsMIUYAytLRj42HH3iI3TUgTXA1R9/LSYxAdHorGlnbsr2gQXQ4JwDBCFKA++fYsLFY7hidFYcxAnehyiLoVolRgVscGaF8c5VRNMGIYIQpAsizjra8dN6y8cUIaJIl7i5Bvmz3SMVWz+UgNd2MNQgwjRAGoqLIBx/RNUIco8OPx3P6dfN/0YfFQKRU4faEFp2pNosshL2MYIQpAb+5xjIosyElBdLhKcDVEVxepDsGUzAEAOFUTjBhGiAJMvcmCTw9WAwBum5IuuBqinpvdscR3M5f4Bh2GEaIA8/6+KlhsdoweqEVOKhtXyX/M6egb2V/RAL2hTXA15E0MI0QBxG6X8fZexxTNbZPT2bhKfiVZF4bxg6IBAJ93LEun4MAwQhRAvjpZh4oLLYjShOCHuSmiyyFy2/wxyQCADYeqBVdC3sQwQhRA3txTAQD48fhUhKtCBFdD5L7vj3bctmDv6XrUNpkFV0PewjBCFCAqLphcqxBumzJIcDVEvZMaE46cVB1kmVM1wYRhhChA/HPXacgyMGNYPLISokSXQ9Rr8zqmaj4r4VRNsGAYIQoAxrZ2vN9xU7w7rxkiuBqivpk/2hFG9pTV40Izp2qCAcMIUQB4d28VTBYbhiVG4tqhcaLLIeqTQQPCMXqgFja7zD1HggTDCJGfs9rsWLP7NADgF9OGcDkvBYR5HaMjn3JVTVBgGCHyc5uO1OBsYytiI1RYNI73oaHA4Fziu/vUBdRxqibgMYwQ+bl/7CwHANw6eRA0oUrB1RB5xpC4CIxN1cFml123N6DAxTBC5Mf2ltdjf0UDVEoFbud9aCjALMx1jPStKz4ruBLqbwwjRH5s1ZcnAQA/mZCKBK1GcDVEnrUgJxkKCThQ2YjTdSbR5VA/Yhgh8lMlZw3YfrwWCgn41fQM0eUQeVxClAbXDI0HAHxcfE5wNdSfGEaI/NRL204BABbkpCB9QITgaoj6x6KOeyytKz4LWZYFV0P9hWGEyA+dqm3Gho7dKe+dmSm4GqL+M3dUEsJClSivM+HgGYPocqifMIwQ+aGXt5+CLAOzRyRgeJJWdDlE/SZCHYI5IxMBAB8dYCNroGIYIfIzVfUtrjfl+67LElwNUf/7j479c9YfPAerzS64GuoPDCNEfuaFrSfQbpMxLWsAxg+KEV0OUb+7Zmgc4iJVqGu2YFtprehyqB8wjBD5kbLaZvy7yDEq8pvrswVXQ+QdoUoFfjQ+FQCw9psqwdVQf2AYIfIjz285AZtdxqzhCRwVoaBy04Q0AMCXpedRY2wTXA15Wq/CyKpVqzB48GBoNBpMnjwZe/fu7fbYNWvWQJKkTg+NhpszEbmrVN+ET7517LWwfM4wwdUQeVdWQiQmDo6BzS7jg/1nRJdDHuZ2GHn33XexfPlyrFixAkVFRcjJycHcuXNx/vz5bs/RarWorq52PSoqKvpUNFEwenbzccgyMG90EkYP1Ikuh8jrFk8cBAB4b18V7HbuORJI3A4jzzzzDO6++278/Oc/x8iRI7F69WqEh4fjtdde6/YcSZKQlJTkeiQmJvapaKJgc/BMIzYe1kOSgAc5KkJBav6YJESpQ1BxoQV7yi+ILoc8yK0wYrFYsH//fsyePfviD1AoMHv2bBQWFnZ7XnNzM9LT05GWloaFCxfi8OHDV3wds9kMo9HY6UEUrGRZxn+vPwoAWJQ7EMMSowRXRCRGuCoEP+zYkXXtXjayBhK3wkhdXR1sNttlIxuJiYnQ6/VdnpOdnY3XXnsNH3/8Md58803Y7XZMnToVZ850P+e3cuVK6HQ61yMtLc2dMokCyueHa7D3dD3UIQr8di5X0FBwu3mSY6rms5JqnG9iI2ug6PfVNPn5+ViyZAlyc3MxY8YMfPjhh4iPj8fLL7/c7TkFBQUwGAyuR1UVEzAFJ4vVjpWfOUZFfjk9AynRYYIrIhJr9EAdxg2KRrtNxjtf87MhULgVRuLi4qBUKlFTU9Pp+ZqaGiQlJfXoZ4SGhmLcuHE4efJkt8eo1WpotdpOD6Jg9EbhaVRcaEF8lBr3zOA9aIgA4GdTBwMA3vq6AhYrd2QNBG6FEZVKhby8PGzZssX1nN1ux5YtW5Cfn9+jn2Gz2XDo0CEkJye7VylRkGkwWfA/W04AAP7r+mGIUIcIrojIN8wbnYz4KDXON5mx8XDXLQLkX9yeplm+fDleeeUVvP766zh69CjuvfdemEwm/PznPwcALFmyBAUFBa7jH3/8cWzatAllZWUoKirCbbfdhoqKCtx1112e+y2IAtBfN5XC2GbF8KQo/CSPfVNETqoQBW6d7OgdeX33abHFkEe4/U+txYsXo7a2Fo8++ij0ej1yc3OxceNGV1NrZWUlFIqLGaehoQF333039Ho9YmJikJeXh927d2PkyJGe+y2IAkxRZQPe2VsJAHjsh6OgVEiCKyLyLbdMHoRVX57E/ooGlJw1cO8dPyfJsuzzO8cYjUbodDoYDAb2j1DAs9rsWPC/u3C02ogfj0/F0zfliC6JyCc9sPYA1hWfw8LcFDz/03Giy6Eu9PTzm/emIfIxrxdW4Gi1EbqwUPxu/nDR5RD5rLuuzQAArD9Yjar6FsHVUF8wjBD5kGpDK57ZVAoAeHjecAyIVAuuiMh3jR6ow/Rh8bDZZfx9R5nocqgPGEaIfIQsy/jDusMwWWwYPygaiyewaZXoau7tWPL+3r4q1DaZBVdDvcUwQuQjPjpwFl8crUGoUsLKH42Fgk2rRFc1JSMWuWnRMFvtWLO7XHQ51EsMI0Q+QG9ow2OfOO7Z9MDsYchO4v1niHpCkiTcO9MxOvJGYQWMbe2CK6LeYBghEkyWZRR8eBDGNityUnX41fQM0SUR+ZU5IxKRlRCJpjYrXtvJ0RF/xDBCJNhbX1fiy9JaqEIU+NuNOQhR8q8lkTsUCgkPzh4GAHj1q3LUmyyCKyJ38V2PSKCj1UY8vv4IAOChudkYmsjpGaLemDc6CaNStGg2W7F6+ynR5ZCbGEaIBGmxWPHrdw7AYrXjuux43HnNENElEfkthULCf83NBuDYIr7G2Ca4InIHwwiRIH/85AhOnm9GQpQaf7sxB5LE1TNEfTFzWDwmpMfAbLW7bjJJ/oFhhEiAd/ZW4t19VZAk4Lmf5nJzMyIPkCQJv+0YHVn7TRVO1DQJroh6imGEyMv2V9Tj0Y9LAAD/dX02pmbGCa6IKHBMzhiAOSMTYbPLeHz9EfjB7dcIDCNEXlVjbMM9bxah3SZj/pgk3NexPwIRec7v54+ASqnAVyfqsPXYedHlUA8wjBB5iclsxd1v7ENtkxnZiVH460/YJ0LUHwbHReAXHQ3hT6w/ArPVJrgiuhqGESIvsNrsWPZ2EQ6eMSA2QoW/L8lDhDpEdFlEAWvZrCzER6lx+kILXvySS319HcMIUT+TZRl/+LgEX5bWQhOqwKt3TED6gAjRZREFtEh1CFYsGAkAeHHbSRxnM6tPYxgh6keyLONvm0rxzl7HypnnfzoO4wfFiC6LKCjcMCYZs0ckoN0m4+F/H4TdzmZWX8UwQtSP/mfLSazqGCJ+fOFozB2VJLgiouAhSRKeWDQakeoQFFU24rVdvG+Nr2IYIeonL207hWe/OA4AeOSGEbh9SrrgioiCT7IuDA/PGw4A+MvGUhytNgquiLrCMELkYbIs45lNpXhq4zEAwG/nZuOua3knXiJRbp08CLNHJMBis+M/3zmAtnaurvE1DCNEHmS3y1jxyWH8z9aTAID/un4Yll6XJbgqouAmSRKe+vFYxEWqceJ8s+vmlOQ7GEaIPKSt3Yb/XHsAbxRWQJKAJxaOwrJZQ0WXRUQABkSq8fRNOZAk4O2vK/HeN1WiS6JLMIwQecB5YxsWv1yI9QerEaKQ8NziXNyeP1h0WUR0iRnD4vHg7GEAgEfWlaC4qlFsQeTCMELUR99WNWLhql349owB0eGheOPOSViYO1B0WUTUhWXXZeH6kYmw2Oz45Rv7cKahRXRJBIYRol6TZRmvflWGn6zejWpDGzLjI7Duvmm88R2RD1MoJDx9Uw6GJUbifJMZS17bi3qTRXRZQY9hhKgX6k0W3PX6Pvz3p0fRbpMxb3QSPrxvGgbHcWdVIl8XpQnF67+YhBSdBmW1JvxizTdoNltFlxXUGEaI3CDLMv7v23OY88x2bDl2HqoQBZ5YNBov3joeurBQ0eURUQ8l68Lwxp2ToAsLRXFVI5b842sY29pFlxW0GEaIeqja0Iq739iHX79zABdMFgxLjMS6+6bh9inpvPsukR/KSojCvzoCSVFlI25/9Ws0tnDKRgSGEaKrMJmteGbzccz623Z8cfQ8QpUSHpw9DOt/fS1GpmhFl0dEfTA2NRpv3z0ZsREqfHvGgP94cTfK60yiywo6kizLPn/nIKPRCJ1OB4PBAK2Wb/7kHRarHR8WncEzm4/jfJMZADAhPQZ//tEYDEuMElwdEXnSiZom/Oyf3+BsYyuiw0Px4i3jMTWLzeh91dPPb4YRou9oa7fh/X1VWL29DGcbWwEAabFhKJg3AvNGJ3FKhihAnW9qw91v7Me3VY2QJODX12XhP783FCFKTiL0FsMIkZvONLTgnb2VePebKtQ1O+aN46PU+NX0DNyenw51iFJwhUTU39rabXj04xK8t+8MAGD8oGg8+eOxHA3tJYYRoh5oa7dhW+l5vL/vDLaWnofzb0OKToN7Zmbipglp0IQyhBAFm4+Lz+L3H5Wg2WxFqFLCL6dn4N6ZWYhUh4guza8wjBB1o9Viw66Tdfj0UDU2H6nptL/AtKwBuG1yOmaPTEQoh2aJgtrZxlas+LgEXxw9DwCIjVDhvpmZuG1KOv+R0kMMI0Qd7HYZpTVN2HG8FjtO1OKb8gZYbHbX91N0GvwgJwU/nZiGjPhIgZWSv7HZZewtr8f5pjYkRGkwaUgslAr2FAUSWZbx+eEa/GXjMZR1rLKJi1Th5kmDcMvkQUjWhQmu0Lf1axhZtWoV/vrXv0Kv1yMnJwcvvPACJk2a1O3x77//Pv7whz/g9OnTGDp0KJ566inMnz+/x6/HMEI9Jcsy9MY2HKtuwoHKBhyoakRxZSOavrO7YopOg+tHJWFBTjLGpcVAwQ8QctPGkmr88f+OoNrQ5nouWafBigUj8f3RyQIro/5gtdnxYdFZPL/lhKuxXamQcE1WHG4Yk4zrRyUiOlwluErf029h5N1338WSJUuwevVqTJ48Gc899xzef/99lJaWIiEh4bLjd+/ejenTp2PlypX4wQ9+gLfffhtPPfUUioqKMHr0aI/+MhQcZFlGY0s7zjS04kxDC842tuJUbTOO1zTjeE0Tmtou39Y5LFSJyRmxmD40HtOHxSMzPoKrYqjXNpZU4943i/DdN0/nn6iXbhvPQBKgrDY7Nh+pweuFp7GnrN71vFIhYcxAHfIzByA/YwDGDNQhJoLhpN/CyOTJkzFx4kT87//+LwDAbrcjLS0Nv/71r/Hwww9fdvzixYthMpmwfv1613NTpkxBbm4uVq9e7dFfhvyLLMswW+0wma1osdhgslhhMlthMtvQ1GZFvcmMCyYLLjRbUG+y4ILJjAvNFpxtbEWLxdbtz1UqJGTERWBsajTGDYrG+EExGJYYyeV55BE2u4xrntraaUTkUhKAJJ0GO//fLE7ZBLiy2mZsOFSN9QercUzfdNn3k7QajEiOwpC4SKTGhCE1Jgwp0WGIjVAhJlyFMFXg95309PPbrbZgi8WC/fv3o6CgwPWcQqHA7NmzUVhY2OU5hYWFWL58eafn5s6di3Xr1nX7OmazGWaz2fW10Wh0p8we+8fOclTVX3776Evzmdzp+Uv++5LvdH6+6+PR3fF9+JmXHu/8z87H9uT3uPrx6EmNMmCTZbTb7LDaZFhsdlhtdrTbHM+12+yw2mW0W+1ot8swt9tgsthgs/e+ZSk+So3UmDAMjA7D4AERGJYUhWGJkRgSF8FluNRv9pbXdxtEAMdfl2pDG/aW1yM/c4D3CiOvy4iPxLJZQ7Fs1lCca2xF4akL2H3qAvZV1KPiQgv0xjbojW34srS2y/PVIQrERqgQrlJCE+p8KKAJcfy3UiFBIQEKSYLikv+WpEuel+CxUd47rxmCtNhwj/wsd7kVRurq6mCz2ZCYmNjp+cTERBw7dqzLc/R6fZfH6/X6bl9n5cqV+OMf/+hOab3y6cFzKKps7PfXoasLC1UiQq1EuCoEEeoQRKqViI1QYUCkGgMiVIjteAyIUCMlWoOU6DB2s5MQ55u6DyK9OY4CQ0p0GH6cl4of56UCAJra2lGqb8JRfRPO1LegqqEFZxpaca6xDY0tFljtjpHhKwVbb/thbop/hBFvKSgo6DSaYjQakZaW5vHX+XFeKqZmXtzu99Jw2SlnXvINqeunIV3yne+G1G7P6SbN9uTn9qaOzq/Rk9+pm+O7OUapUCBEKUGldPxvqFLR6b9DO/43RKGAOlSBSHUIwlWOAMLhbPIXCVEajx5HgSlKE4oJg2MxYXDsZd+TZRnNZisaW9pRb7KgxWJDm9UGc7sNbe12tLXb0NZug012HGuXZdhlOP7Xfsl/y47Vgp6SpBX3Z9atMBIXFwelUomamppOz9fU1CApKanLc5KSktw6HgDUajXUarU7pfXKrZPT+/01iCiwTBoSi2SdBnpD22UNrMDFnpFJQy7/ECICHP+4i9KEIkoTKmwkwte41dGnUqmQl5eHLVu2uJ6z2+3YsmUL8vPzuzwnPz+/0/EAsHnz5m6PJyLyZUqFhBULRgL4zgjqJV+vWDCSo31EbnB7ecHy5cvxyiuv4PXXX8fRo0dx7733wmQy4ec//zkAYMmSJZ0aXO+//35s3LgRTz/9NI4dO4bHHnsM+/btw7Jlyzz3WxARedH3RyfjpdvGI0nXeVg7Safhsl6iXnC7Z2Tx4sWora3Fo48+Cr1ej9zcXGzcuNHVpFpZWQmF4mLGmTp1Kt5++2088sgj+N3vfoehQ4di3bp1Pd5jhIjIF31/dDLmjEziDqxEHsDt4ImIiKhf9PTzm7tAERERkVAMI0RERCQUwwgREREJxTBCREREQjGMEBERkVAMI0RERCQUwwgREREJxTBCREREQjGMEBERkVBubwcvgnOTWKPRKLgSIiIi6inn5/bVNnv3izDS1NQEAEhLSxNcCREREbmrqakJOp2u2+/7xb1p7HY7zp07h6ioKEiS525CZTQakZaWhqqqKt7zph/xOnsPr7V38Dp7B6+zd/TndZZlGU1NTUhJSel0E93v8ouREYVCgdTU1H77+Vqtln/QvYDX2Xt4rb2D19k7eJ29o7+u85VGRJzYwEpERERCMYwQERGRUEEdRtRqNVasWAG1Wi26lIDG6+w9vNbewevsHbzO3uEL19kvGliJiIgocAX1yAgRERGJxzBCREREQjGMEBERkVAMI0RERCRUwIeRVatWYfDgwdBoNJg8eTL27t17xePff/99DB8+HBqNBmPGjMGGDRu8VKl/c+c6v/LKK7j22msRExODmJgYzJ49+6r/v9BF7v6Zdlq7di0kScKiRYv6t8AA4e51bmxsxNKlS5GcnAy1Wo1hw4bx/aMH3L3Ozz33HLKzsxEWFoa0tDQ8+OCDaGtr81K1/mnHjh1YsGABUlJSIEkS1q1bd9Vztm3bhvHjx0OtViMrKwtr1qzp3yLlALZ27VpZpVLJr732mnz48GH57rvvlqOjo+Wampouj9+1a5esVCrlv/zlL/KRI0fkRx55RA4NDZUPHTrk5cr9i7vX+ZZbbpFXrVolHzhwQD569Kj8s5/9TNbpdPKZM2e8XLn/cfdaO5WXl8sDBw6Ur732WnnhwoXeKdaPuXudzWazPGHCBHn+/Pnyzp075fLycnnbtm1ycXGxlyv3L+5e57feektWq9XyW2+9JZeXl8uff/65nJycLD/44INerty/bNiwQf79738vf/jhhzIA+aOPPrri8WVlZXJ4eLi8fPly+ciRI/ILL7wgK5VKeePGjf1WY0CHkUmTJslLly51fW2z2eSUlBR55cqVXR5/0003yTfccEOn5yZPniz/6le/6tc6/Z271/m7rFarHBUVJb/++uv9VWLA6M21tlqt8tSpU+VXX31VvuOOOxhGesDd6/zSSy/JGRkZssVi8VaJAcHd67x06VJ51qxZnZ5bvny5PG3atH6tM5D0JIw89NBD8qhRozo9t3jxYnnu3Ln9VlfATtNYLBbs378fs2fPdj2nUCgwe/ZsFBYWdnlOYWFhp+MBYO7cud0eT727zt/V0tKC9vZ2xMbG9leZAaG31/rxxx9HQkIC7rzzTm+U6fd6c50/+eQT5OfnY+nSpUhMTMTo0aPx5z//GTabzVtl+53eXOepU6di//79rqmcsrIybNiwAfPnz/dKzcFCxGehX9worzfq6upgs9mQmJjY6fnExEQcO3asy3P0en2Xx+v1+n6r09/15jp/1//7f/8PKSkpl/3hp856c6137tyJf/zjHyguLvZChYGhN9e5rKwMW7duxa233ooNGzbg5MmTuO+++9De3o4VK1Z4o2y/05vrfMstt6Curg7XXHMNZFmG1WrFPffcg9/97nfeKDlodPdZaDQa0drairCwMI+/ZsCOjJB/ePLJJ7F27Vp89NFH0Gg0ossJKE1NTbj99tvxyiuvIC4uTnQ5Ac1utyMhIQF///vfkZeXh8WLF+P3v/89Vq9eLbq0gLJt2zb8+c9/xosvvoiioiJ8+OGH+PTTT/HEE0+ILo36KGBHRuLi4qBUKlFTU9Pp+ZqaGiQlJXV5TlJSklvHU++us9Pf/vY3PPnkk/jiiy8wduzY/iwzILh7rU+dOoXTp09jwYIFrufsdjsAICQkBKWlpcjMzOzfov1Qb/5MJycnIzQ0FEql0vXciBEjoNfrYbFYoFKp+rVmf9Sb6/yHP/wBt99+O+666y4AwJgxY2AymfDLX/4Sv//976FQ8N/XntDdZ6FWq+2XUREggEdGVCoV8vLysGXLFtdzdrsdW7ZsQX5+fpfn5OfndzoeADZv3tzt8dS76wwAf/nLX/DEE09g48aNmDBhgjdK9XvuXuvhw4fj0KFDKC4udj1++MMf4rrrrkNxcTHS0tK8Wb7f6M2f6WnTpuHkyZOusAcAx48fR3JyMoNIN3pznVtaWi4LHM4AKPM2ax4j5LOw31pjfcDatWtltVotr1mzRj5y5Ij8y1/+Uo6Ojpb1er0sy7J8++23yw8//LDr+F27dskhISHy3/72N/no0aPyihUruLS3B9y9zk8++aSsUqnkDz74QK6urnY9mpqaRP0KfsPda/1dXE3TM+5e58rKSjkqKkpetmyZXFpaKq9fv15OSEiQ//u//1vUr+AX3L3OK1askKOiouR33nlHLisrkzdt2iRnZmbKN910k6hfwS80NTXJBw4ckA8cOCADkJ955hn5wIEDckVFhSzLsvzwww/Lt99+u+t459Le3/72t/LRo0flVatWcWlvX73wwgvyoEGDZJVKJU+aNEnes2eP63szZsyQ77jjjk7Hv/fee/KwYcNklUoljxo1Sv7000+9XLF/cuc6p6enywAue6xYscL7hfshd/9MX4phpOfcvc67d++WJ0+eLKvVajkjI0P+05/+JFutVi9X7X/cuc7t7e3yY489JmdmZsoajUZOS0uT77vvPrmhocH7hfuRL7/8ssv3XOe1veOOO+QZM2Zcdk5ubq6sUqnkjIwM+Z///Ge/1ijJMse2iIiISJyA7RkhIiIi/8AwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQDCNEREQk1P8Hn10iN034HesAAAAASUVORK5CYII=\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.6\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5714285714285713\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5454545454545455\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5217391304347826\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5416666666666666\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.52\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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G9p+pQ2s7W8MT+QuGESJyKnSEkSGB3XW1K0P6RSFJp0abxYZ9p9kanshfMIwQEQDgQoMZZTUNAOBcWxFsZDKZs739Tt7iS+Q3GEaICACwp9w+KjIqSYvYKKXgarzHsW5kx3GuGyHyFwwjRATgqvUiQ4JzVMRhSsfIyDFDA+qa2gRXQ0QAwwgRdSg8ZZ+2CNbFqw5x0SoMi48GAOzluhEiv8AwQkQ4V9+CM5eaoZDLMGFQrOhyvC6nY/THMTVFRGIxjBCR8y6ajBQdNOpwwdV4n2OBLsMIkX9gGCEi7HZM0QT5ehGHSan20Z9jhgZc5roRIuEYRohCnCRJQd9f5Nv6RquQlqABYO86S0RiMYwQhbgzl5pRbWyFUiFH9sA+osvxmcmD7aMjnKohEo9hhCjE7epo/jVuYAzU4QrB1fjOlXUjvKOGSDSGEaIQV9gxMpAzODSmaBwmdYSRspoGXGo0C66GKLQxjBCFMEmSnM9oyQmRxasOsVFKjEjsWDfCfiNEQjGMEIWwM5eacaHBDGWYHBkpOtHl+Bxv8SXyDwwjRCFs32n7m3BWSmitF3FwhBHH3UREJAbDCFEI23e6DgAwMTX4u652xtFv5ERtIy5y3QiRMAwjRCFs3xn7iECohpE+V60b4VQNkTgMI0Qh6nx9C6out0Ahl2FcCPUX+TbHVM0+LmIlEoZhhChE7T9jf/MdnaxFtCpMcDXiOEaF9p+pE1wJUehiGCEKUY6RgIkh8JTeaxk/yD4qdMxggrGlXXA1RKGJYYQoRDnDSIiuF3GI16gxqG8kJAkoruToCJEIDCNEIehyUxtO1DYCACaE+MgIcOUa7Oe6ESIhGEaIQpBjvcjwhGj0iVIKrkY8Zxg5wzBCJIJbYeTVV19FRkYGtFottFotcnJy8Pnnn1/znDVr1mDEiBFQq9UYM2YMNmzY0KuCiaj3OEXjakLHdfi6yojWdqvgaohCj1thJCUlBUuXLkVRUREOHDiAW2+9FbNnz8bhw4c7PX737t2499578dBDD+HgwYOYM2cO5syZg0OHDnmkeCLqmSthJLSeR9OVQX0jERetRJvVhtJzRtHlEIUct8LIrFmzMHPmTAwbNgzDhw/HH/7wB0RHR2PPnj2dHv/SSy/hjjvuwOOPP46RI0fi2Wefxbhx4/D3v//dI8UTkfsaWttx+Lz9DTfU76RxkMlknKohEqjHa0asVitWr16NpqYm5OTkdHpMYWEhpk2b5rJv+vTpKCws7OnLElEvFVfWwyYBA2IjkahTiy7Hb4znIlYiYdzudFRaWoqcnBy0trYiOjoaa9euxahRozo91mAwICEhwWVfQkICDAbDNV/DbDbDbL7ynAiTyeRumUTUBcfD8bhexJVjlOhARR1sNglyuUxwRUShw+2RkbS0NJSUlGDv3r145JFHMG/ePBw5csSjRRUUFECn0zk3vV7v0c9PFMr2Ox6OxykaFyOTNIhSKtDQakFZTYPocohCitthRKlUYujQocjOzkZBQQEyMzPx0ksvdXpsYmIiampqXPbV1NQgMTHxmq+Rn58Po9Ho3Kqqqtwtk4g60W614Ztz9QCA7EGh+zyazoQp5M5n9BzguhEin+p1nxGbzeYypXK1nJwcbN261WXfli1bulxj4qBSqZy3Dzs2Iuq9o9UmtLbbEBMZjsFxUaLL8TvjB9pHi/bxOTVEPuXWmpH8/HzMmDEDAwYMQENDA1atWoXt27dj06ZNAIC8vDz0798fBQUFAIBHH30UU6dOxQsvvIA777wTq1evxoEDB/D66697/ishousqrrC/yY7Vx0Am45qIb5uQah8Z2X/6MiRJ4jUi8hG3wkhtbS3y8vJQXV0NnU6HjIwMbNq0CbfddhsAoLKyEnL5lcGW3NxcrFq1Cr/5zW/w5JNPYtiwYVi3bh3S09M9+1UQUbcUV9YDAMYO4BRNZ8bq+yBMLoPB1IqzdS3Qx0aKLokoJLgVRt56661r/v327du/s++ee+7BPffc41ZRROQdjgfBjWMY6VSEUoH0/jqUVNVj/5nLDCNEPsJn0xCFiNoG+2/7MhmQqdeJLsdvTehY2Luf60aIfIZhhChEFFfUAwDSEjTQqMPFFuPHsjsWsR6sZBgh8hWGEaIQ4Xhz5XqRaxs3MAYAUFbTAFNru9hiiEIEwwhRiLiyXiRGbCF+Ll6jhj42ApIEfF1VL7ocopDAMEIUAtosNnxz1v5wPEdjL+padsfoUVEFp2qIfIFhhCgEHDOYYLaw2Vl3ZQ9kGCHyJYYRohDAZmfucayrKamsh80mCa6GKPgxjBCFAEezM/YX6Z4RiRpEKhVoMFtworZRdDlEQY9hhCgEOBevcr1It4Qp5MjSxwDgVA2RLzCMEAW5q5udZaSw2Vl3cd0Ike8wjBAFOTY76xnHlBabnxF5H8MIUZBjs7OeGdvRj6X8YhMuN7WJLYYoyDGMEAU5NjvrmZhIJYbGRwO4cjcSEXkHwwhREGOzs95xND8r5lQNkVcxjBAFsaPVbHbWG47n1HARK5F3MYwQBTHHb/RsdtYzjjtqvj5bj3arTXA1RMGLYYQoiB1ks7NeGRwXDV1EOFrbbThabRJdDlHQYhghCmJsdtY7crnMufCXi1iJvIdhhChIOZqdyWVAZkc3UXKfY1SpqGOUiYg8j2GEKEg5mp0NT9AgWhUmtpgA5lg3wpERIu9hGCEKUgc5ReMRmfoYyGXAufoWGIytosshCkoMI0RB6uo7aajnolRhGJmkBcB+I0TewjBCFITY7MyznOtGOFVD5BUMI0RBiM3OPMvR/IwjI0TewTBCFITY7MyzHCMjh8+ZYLZYBVdDFHwYRoiCUDGbnXnUgNhI9I1Sos1qw6FzbH5G5GkMI0RByHEbKteLeIZMJsPYjmB3kFM1RB7HMEIUZGpNrThXz2ZnnsZ1I0TewzBCFGQcUzRsduZZjikvRzM5IvIchhGiIMNmZ96RkaKDQi6DwdSK8/UtosshCioMI0RBxvlwPC5e9ahIZRhGJmkAcKqGyNPcCiMFBQWYMGECNBoN4uPjMWfOHJSVlV3znJUrV0Imk7lsarW6V0UTUedcmp11PG2WPIdTNUTe4VYY+eqrr7Bw4ULs2bMHW7ZsQXt7O26//XY0NTVd8zytVovq6mrnVlFR0auiiahzVzc7S2WzM49zhhGOjBB5lFur2zZu3Ojy8cqVKxEfH4+ioiLcdNNNXZ4nk8mQmJjYswqJqNvY7My7nM3PzhvR2m6FOlwhuCKi4NCrNSNGo304ODY29prHNTY2YuDAgdDr9Zg9ezYOHz58zePNZjNMJpPLRkTXx2Zn3qWPjUBctBLtVgmHzxtFl0MUNHocRmw2Gx577DFMmTIF6enpXR6XlpaGt99+G5988gneffdd2Gw25Obm4uzZs12eU1BQAJ1O59z0en1PyyQKKWx25l1XNz/juhEiz+lxGFm4cCEOHTqE1atXX/O4nJwc5OXlISsrC1OnTsXHH3+Mfv364bXXXuvynPz8fBiNRudWVVXV0zKJQgabnfkG140QeV6POiItWrQI69evx44dO5CSkuLWueHh4Rg7dixOnjzZ5TEqlQoqlaonpRGFLMebI5udeZfjLqXiyjpIksS1OUQe4NbIiCRJWLRoEdauXYtt27YhNTXV7Re0Wq0oLS1FUlKS2+cSUdec60U4ReNVGSkxCJPLUGMy47yxVXQ5REHBrTCycOFCvPvuu1i1ahU0Gg0MBgMMBgNaWq50I8zLy0N+fr7z42eeeQabN29GeXk5iouLcf/996OiogLz58/33FdBRFc6r3LxqldFKBUYmaQFcGWNDhH1jlth5NVXX4XRaMTNN9+MpKQk5/b+++87j6msrER1dbXz47q6OixYsAAjR47EzJkzYTKZsHv3bowaNcpzXwVRiGOzM9+6eqqGiHrPrYllSZKue8z27dtdPl62bBmWLVvmVlFE5B5Hs7M+bHbmE+MG9sE7hRXOqTEi6h0+m4YoCDibnQ3owwWVPuCYCjvS0fyMiHqHYYQoCDh+Qx/LW3p9IqVPBOKiVWi3Sjh0js3PiHqLYYQoCLDZmW/JZDKuGyHyIIYRogDHZmdiOIJfEe+oIeo1hhGiAMdmZ2Jc6cRa363F/UTUNYYRogDHZmdiZKToECaX4UKDGWfrWq5/AhF1iWGEKMA514uw2ZlPqcMVGJXc0fyM60aIeoVhhCiAtVls+OYcm52J4giAB9lvhKhXGEaIAtiRahPa2OxMmLG8o4bIIxhGiALYQTY7E+pK8zMTm58R9QLDCFEAcy5e5RSNECl9ItBPo4LFJjmfDURE7mMYIQpgXLwqFpufEXkGwwhRgLq62VkGm50J4+w3wuZnRD3GMEIUoNjszD9kD2TzM6LeYhghClBsduYf0vvrEK6Q4WIjm58R9RTDCFGA4noR/2BvfqYDwHUjRD3FMEIUgNjszL84F7Fy3QhRjzCMEAUgNjvzL1c/NI+I3McwQhSAHL+Bs9mZf3Cs2zlabUJLG5ufEbmLYYQoADnWJnCKxj8k69RI0Dqan9WLLoco4DCMEAWgg87Oq1y86g/szc84VUPUUwwjRAHm6mZnmWx25jeuhBEuYiVyF8MIUYBxvNmlJWoRxWZnfmPcwBgA9ocXsvkZkXsYRogCDB+O559GJzuan7Wh6jKbnxG5g2GEKMBcfScN+Q91uAKj2fyMqEcYRogCCJud+TeuGyHqGYYRogDCZmf+zbFuhGGEyD0MI0QBhM3O/JtjZORodQOa2yyCqyEKHAwjRAHE8Rt3Np/U65eSYyKQqFXDapPwzVmj6HKIAgbDCFEAuTIyEiO2EOoSp2qI3McwQhQgqo0tOG9shUIuQ2ZKjOhyqAvORawV9WILIQogboWRgoICTJgwARqNBvHx8ZgzZw7Kysque96aNWswYsQIqNVqjBkzBhs2bOhxwUShyvHmNjJJw2ZnfsxxyzWbnxF1n1th5KuvvsLChQuxZ88ebNmyBe3t7bj99tvR1NTU5Tm7d+/Gvffei4ceeggHDx7EnDlzMGfOHBw6dKjXxROFkqIKx8PxuF7En6X310KpkONSUxsqLzeLLocoIMikXkT3CxcuID4+Hl999RVuuummTo+ZO3cumpqasH79eue+yZMnIysrCytWrOjW65hMJuh0OhiNRmi12p6WSxTQ5izfhZKqerz04yzMzuovuhy6hv96ZRcOVtZj2dxM/NfYFNHlEAnT3ffvXq0ZMRrtq8VjY2O7PKawsBDTpk1z2Td9+nQUFhZ2eY7ZbIbJZHLZiEJZa7sVh887mp1xZMTfcd0IkXt6HEZsNhsee+wxTJkyBenp6V0eZzAYkJCQ4LIvISEBBoOhy3MKCgqg0+mcm16v72mZREHh0Dkj2q0S+mlUSOkTIbocug52YiVyT4/DyMKFC3Ho0CGsXr3ak/UAAPLz82E0Gp1bVVWVx1+DKJA41otks9lZQHDc3nvMwOZnRN3RoyX5ixYtwvr167Fjxw6kpFx7PjQxMRE1NTUu+2pqapCYmNjlOSqVCiqVqielEQUl5+LVjjc58m9Juggk6dSoNrbi6yojcob0FV0SkV9za2REkiQsWrQIa9euxbZt25Camnrdc3JycrB161aXfVu2bEFOTo57lRKFKEmSUFxZD4CdVwMJp2qIus+tMLJw4UK8++67WLVqFTQaDQwGAwwGA1paWpzH5OXlIT8/3/nxo48+io0bN+KFF17AsWPH8PTTT+PAgQNYtGiR574KoiBWdbkFFxvNCFfInI+oJ//n6JJ7kGGE6LrcCiOvvvoqjEYjbr75ZiQlJTm3999/33lMZWUlqqurnR/n5uZi1apVeP3115GZmYkPP/wQ69atu+aiVyK6wvGbdXp/HdThCsHVUHeNG+gYGaln8zOi63BrzUh3/kFt3779O/vuuece3HPPPe68FBF1uHrxKgWO0cn25meXm9pw5lIzUuOiRJdE5Lf4bBoiP3dl8SrDSCBRhSmQ3t/e5MnxgEMi6hzDCJEfazJbcMxgb/rHxauBh4tYibqHYYTIj31dVQ+bBPSPiUCCVi26HHLT1etGiKhrDCNEfszxGzWnaAKTY2SkzGBCo5nNz4i6wjBC5MeuLF6NEVsI9UiiTo1knRo2Cfimql50OUR+i2GEyE/ZbFeanXFkJHCNHch1I0TXwzBC5KfKLzbB2NIOdbgcI5O6fvQ2+bcri1jrxRZC5McYRoj8lON20MyUGIQr+E81UI27qhMrm58RdY4/4Yj8FBevBofRyToow+Soa27H6YtNossh8ksMI0R+ip1Xg4MyTI4x/e3PFOJUDVHnGEaI/FBdUxtO1DYC4MhIMHBM1XARK1HnGEaI/JBjVGRofDRio5SCq6Heci5iZVt4ok4xjBD5of1nLgMAJgziqEgwcIxuHa9pYPMzok4wjBD5IUcYGT8wVnAl5AkJWjX6x0TAJtlb/BORK4YRIj/T2m5F6TkjAGBiKsNIsBjrWDfCqRqi72AYIfIzX1fVo90qIUGrQkqfCNHlkIfwCb5EXWMYIfIzzimaQbGQyWSCqyFPcawbOVhVz+ZnRN/CMELkZ/afsf/mPIG39AaVUUlaqMLkqG9uRzmbnxG5YBgh8iNWm+RcUzCB60WCikvzM64bIXLBMELkR8oMDWgwWxCtCsOIRD4cL9g4pmqKGEaIXDCMEPkRx3qRcQP7QCHnepFgM2GQfbRrX8f/ZyKyYxgh8iPOZmdcLxKUHE3syi804UKDWXA1RP6DYYTIT0iS5HInDQWfmEglRiRqAAAHODpC5MQwQuQnzta1oMZkRrhChix9jOhyyEscjez2nmYYIXJgGCHyE45RkfT+OkQoFYKrIW9xhJF9DCNETgwjRH7C2V+EUzRBbWLH/9+jBhOMLe2CqyHyDwwjRH7igPPheFy8GszitWqkxkVBkoCiCo6OEAEMI0R+oa6pDSdqGwFw8WoocIyOcN0IkR3DCJEfONDRBGtofDRio5SCqyFv47oRIlcMI0R+YG/5JQBX+lBQcHOEkdKzRrS0WQVXQySe22Fkx44dmDVrFpKTkyGTybBu3bprHr99+3bIZLLvbAaDoac1EwUdx3D95MF9BVdCvpDSJwLJOjUsNgkHK9kansjtMNLU1ITMzEwsX77crfPKyspQXV3t3OLj4919aaKgZGxpx+HzRgAMI6FCJpOx3wjRVcLcPWHGjBmYMWOG2y8UHx+PmJgYt88jCnYHzlyGTQJS46KQoFWLLod8ZEJqLNaVnOe6ESL4cM1IVlYWkpKScNttt2HXrl2+elkiv3dlioZ30YSSSR0jI8WVdWiz2ARXQySW18NIUlISVqxYgY8++ggfffQR9Ho9br75ZhQXF3d5jtlshslkctmIgtWejsWrk1I5RRNKhvSz3zlltthQeq5edDlEQrk9TeOutLQ0pKWlOT/Ozc3FqVOnsGzZMvzrX//q9JyCggL8/ve/93ZpRMI1tLbj0Dn7epFJHBkJKTKZDBMHxWLjYQP2nr6M7IH8/0+hS8itvRMnTsTJkye7/Pv8/HwYjUbnVlVV5cPqiHznwJk62CRgUN9IJOkiRJdDPsZ+I0R2Xh8Z6UxJSQmSkpK6/HuVSgWVSuXDiojE4BRNaHOEkaIzdbDaJCjkMsEVEYnhdhhpbGx0GdU4ffo0SkpKEBsbiwEDBiA/Px/nzp3DP//5TwDAiy++iNTUVIwePRqtra148803sW3bNmzevNlzXwVRgNrjWLw6hEP0oWhkkhYadRgaWi04fN6IjJQY0SURCeF2GDlw4ABuueUW58eLFy8GAMybNw8rV65EdXU1KisrnX/f1taGX/3qVzh37hwiIyORkZGBL774wuVzEIUil/UiHBkJSQq5DJNS++KLozUoPHWJYYRClkySJEl0EddjMpmg0+lgNBqh1WpFl0PkEV+W1eLBf+zHgNhI7HiC4TxUvbXzNJ5dfwRTh/fDO/89UXQ5RB7V3fdvPpuGSJC95ewvQkDuEPuo2P4zl9FuZb8RCk0MI0SCOBavsgV8aEtL0CA2SonmNiu+OVsvuhwiIRhGiARoNFtQ6uwvwjASyuRymXN0bPfJS4KrIRKDYYRIgKIK+62c+tgI9I9hf5FQlzMkDgCw+xTDCIUmhhEiAXafugiAd9GQnWPdSFFlHVrbrYKrIfI9hhEiARzD8TcMjRNcCfmDwXFRiNeo0GaxobiyTnQ5RD7HMELkY3VNbTh03r5eJHcoR0bI/pwax+hIIadqKAQxjBD5WGH5JUgSMDwhGvEatehyyE/kct0IhTCGESIf23nSvl5kCqdo6Co5HSMjX1fVo8lsEVwNkW8xjBD52O6OMML1InQ1fWwkUvpEwGKTsP8Mn+JLoYVhhMiHqi4348ylZijkMucTW4kccgZz3QiFJoYRIh9y3NKbpY+BRh0uuBryN44Fzbs6vk+IQgXDCJEP7eq4pZfrRagzju+LQ+dMuNRoFlwNke8wjBD5iM0mYZdj8eoQ3tJL3xWvUWNkkv3Jpo6FzkShgGGEyEfKahpwqakNEeEKjB3QR3Q55KduGmYfHfnPCYYRCh0MI0Q+4hgVmTQ4Fsow/tOjzt04rB8A4D8nLkCSJMHVEPkGfyIS+ciVKRquF6GujR/UB6owOWpMZpyobRRdDpFPMIwQ+UCbxYa9p+29I7h4la5FHa7ApI5bfHccvyC4GiLfYBgh8oGiijo0t1kRF63EiESN6HLIz3HdCIUahhEiH9h+vBYAcNOwfpDLZYKrIX/nWDey9/QltLZbBVdD5H0MI0Q+8FWZfbh9alo/wZVQILA/RFGF1nYbiirqRJdD5HUMI0ReVmNqxTFDA2QyPo+GukcmkzlHR3ac4LoRCn4MI0Re9lXHIsSM/jr0jVYJroYCxU3DO9aNHOe6EQp+DCNEXuYII1PT4gVXQoHEcdfVkWoTLjSwNTwFN4YRIi+yWG3Y2XFHxNThXC9C3RcXrcLoZHtr+P9wqoaCHMMIkRd9fdYIY0s7dBHhyEzRiS6HAszNHQuetx2rFVwJkXcxjBB5kWOK5oZhcQhT8J8buefWEfapvR3HL8BitQmuhsh7+NORyIuc60U4RUM9kKXvgz6R4TC1WniLLwU1hhEiL7nc1IZvztYDYBihnlHIZc7vnW1lnKqh4MUwQuQl28tqIUnAyCQtErRq0eVQgLqlY6rmS64boSDGMELkJVuP2t88po3kLb3Uc1OH94NcBhyvacTZumbR5RB5hdthZMeOHZg1axaSk5Mhk8mwbt26656zfft2jBs3DiqVCkOHDsXKlSt7UCpR4Giz2JzrRb43MkFwNRTIYiKVyB7YBwDwZRlv8aXg5HYYaWpqQmZmJpYvX96t40+fPo0777wTt9xyC0pKSvDYY49h/vz52LRpk9vFEgWKvacvodFsQT+NChn9eUsv9Q6naijYhbl7wowZMzBjxoxuH79ixQqkpqbihRdeAACMHDkSO3fuxLJlyzB9+nR3X54oIDimaL43Ip5P6aVeu3VEPJ7fWIbdpy6itd0KdbhCdElEHuX1NSOFhYWYNm2ay77p06ejsLCwy3PMZjNMJpPLRhQoJEnCF0drAHCKhjwjLUGDZJ0are02FJ66JLocIo/zehgxGAxISHD9gZyQkACTyYSWlpZOzykoKIBOp3Nuer3e22USeYx9oWELVGFyPqWXPEImk+HWjoXQWzqCLlEw8cu7afLz82E0Gp1bVVWV6JKIus0xKnLD0DhEKDmcTp5x26hEAMCWIzWw2STB1RB5lttrRtyVmJiImhrXJF9TUwOtVouIiIhOz1GpVFCp+Kh1CkycoiFvyBncFxp1GC40mHGwqt55hw1RMPD6yEhOTg62bt3qsm/Lli3Iycnx9ksT+dzFRjNKquoBAN9jfxHyIGWY3Pmsms2HDYKrIfIst8NIY2MjSkpKUFJSAsB+625JSQkqKysB2KdY8vLynMc//PDDKC8vxxNPPIFjx47hlVdewQcffIBf/vKXnvkKiPzItqP2rqtj+uvYdZU87vaOqZpNhw2QJE7VUPBwO4wcOHAAY8eOxdixYwEAixcvxtixY/G73/0OAFBdXe0MJgCQmpqKzz77DFu2bEFmZiZeeOEFvPnmm7ytl4LS54eqAQDTR3OKhjxvalo/KMPkOHOpGSdqG0WXQ+Qxbq8Zufnmm6+ZyDvrrnrzzTfj4MGD7r4UUUAxtrRj58mLAIA70pMEV0PBKFoVhhuGxmHbsVpsPmzA8ASN6JKIPMIv76YhCkTbjtWg3SphWHw0hsZHiy6HgpRj1G3TYd7iS8GDYYTIQzaU2hcVzhjDURHynmkjEyCXAaXnjDhf33mvJqJAwzBC5AFNZgt2dDwYb0Z6ouBqKJj1jVZh/MBYALyrhoIHwwiRB3xZVguzxYZBfSMxIpHz+ORdt3dM1Ww4xDBCwYFhhMgDPu+YorkjPQkyGR+MR941s2MqcP+ZyzAYWwVXQ9R7DCNEvdTabsWXZfan9M4cwyka8r7kmAhMGNQHkgR8VlotuhyiXmMYIeqlr45fQHObFf1jIjCmv050ORQi7spIBgCs/+a84EqIeo9hhKiX1n9j/830jvRETtGQz8wYkwi5DDhYWY+qy82iyyHqFYYRol5oMluw5Yh9vcjdmcmCq6FQEq9RY1JqXwCcqqHAxzBC1AtbjtSgtd1+F01GCqdoyLdmZXKqhoIDwwhRL3xScg4AMDurP6doyOfuSE+EQi7DoXMmnL7YJLocoh5jGCHqoUuNZuw4YX8Wzd1ZnKIh34uNUmLK0DgAwPqvOTpCgYthhKiHNhwywGqTMKa/DkP68Vk0JMasDHvPkU++Pn/Nh5gS+TOGEaIe+tQ5RcNRERJnenoiVGFynKxtROk5o+hyiHqEYYSoB87WNWP/mTrIZFf6PRCJoFWHY/poe7O9j4rOCq6GqGcYRoh64ONi+6jI5NS+SNSpBVdDoe4H2SkAgE+/Po82i01wNUTuYxghcpPNJmFNURUA4J7xKYKrIQJuGBqHeI0Kdc3t2HasVnQ5RG5jGCFy097Tl1F1uQXRqjDMSE8SXQ4RFHIZ/mtsfwDAx8WcqqHAwzBC5CbHqMiszCREKBWCqyGy+/44+yjdl2W1uNzUJrgaIvcwjBC5oaG1HZ+X2tu//zBbL7gaoivSEjVI769Fu1VyNuMjChQMI0Ru+OybarS0WzG4XxTGDYgRXQ6Ri3s6AvK/91Wy5wgFFIYRIjes6bh18p5sPdu/k9+ZM7Y/1OFyHK9pRFFFnehyiLqNYYSom44ZTCiqqINCLsP3x/UXXQ7Rd+giwjGro+/Nqn2Vgqsh6j6GEaJuendPBQDg9lEJSNCytwj5p3snDQBgn1I0NrcLroaoexhGiLqh0WzB2o5GZw9MHii4GqKujdXHYESiBmaLDR/xNl8KEAwjRN2w9uA5NLXZF67mDOkruhyiLslkMtzXMTqyigtZKUAwjBBdhyRJeLfQPkXzwOSBXLhKfm/22P6ICFfgZG0j9pRfFl0O0XUxjBBdx/4zdSiraUBEuMLZWIrIn2nV4fivjkXW/9h1WnA1RNfHMEJ0He8UngEAzM5Khi4iXGwxRN3031MGAQC2HK1B5aVmscUQXQfDCNE1VF1uxuel1QCAvJxBYoshcsPQeA2mDu8HSQJW7j4juhyia2IYIbqGt3edhk0CbhwWh1HJWtHlELnlv29IBQB8cKAKDa28zZf8V4/CyPLlyzFo0CCo1WpMmjQJ+/bt6/LYlStXQiaTuWxqNXs0kP8zNrfj/f32h+ItuHGw4GqI3HfTsDgMjY9Go9mCDw7wNl/yX26Hkffffx+LFy/GkiVLUFxcjMzMTEyfPh21tbVdnqPValFdXe3cKioqelU0kS+s2leJ5jYrRiRqcOOwONHlELlNJpPhwY61I//YdRoWq01sQURdcDuM/PWvf8WCBQvw4IMPYtSoUVixYgUiIyPx9ttvd3mOTCZDYmKic0tISOhV0UTe1maxYeVu+10I828czNt5KWB9f2wK+kYpcbauBZ9+fV50OUSdciuMtLW1oaioCNOmTbvyCeRyTJs2DYWFhV2e19jYiIEDB0Kv12P27Nk4fPjwNV/HbDbDZDK5bES+tK7kHGpMZiRoVbg7M1l0OUQ9FqFUONeOvLL9FGw2NkEj/+NWGLl48SKsVut3RjYSEhJgMBg6PSctLQ1vv/02PvnkE7z77ruw2WzIzc3F2bNdz18WFBRAp9M5N71e706ZRL1isdqw/MuTAICHbkiFMozrvCmw5eUMhFYdhpO1jdh0uPOf1UQief2nbE5ODvLy8pCVlYWpU6fi448/Rr9+/fDaa691eU5+fj6MRqNzq6qq8naZRE7rSs6j4lIz+kYpcT+fQ0NBQKMOx09zBwEA/v7lSbaIJ7/jVhiJi4uDQqFATU2Ny/6amhokJiZ263OEh4dj7NixOHnyZJfHqFQqaLVal43IFyxWG17edgIAsOCmwYhUhgmuiMgzHpySikilAofPm7C97ILocohcuBVGlEolsrOzsXXrVuc+m82GrVu3Iicnp1ufw2q1orS0FElJSe5VSuQDn3SMisRGKfl0XgoqfaKUzgfoLfviOEdHyK+4PU2zePFivPHGG3jnnXdw9OhRPPLII2hqasKDDz4IAMjLy0N+fr7z+GeeeQabN29GeXk5iouLcf/996OiogLz58/33FdB5AEWqw1/71grsuDGwYhScVSEgsvPpw5BlFKBb84a8fkhrh0h/+H2T9u5c+fiwoUL+N3vfgeDwYCsrCxs3LjRuai1srIScvmVjFNXV4cFCxbAYDCgT58+yM7Oxu7duzFq1CjPfRVEHrB6fxVOX2xCn8hw5OVwVISCT1y0CvNvHIyXtp7AXzaV4fZRCQhTcIE2iSeTAmCszmQyQafTwWg0cv0IeUWj2YKb//wlLja2YcmsUXhwSqrokoi8oqG1HVP/vB2Xm9qw9Ptj8OOJA0SXREGsu+/fjMREAF7fUY6LjW0Y1DcS903iqAgFL406HAtvGQoAePGLE2httwquiIhhhAg1pla8saMcAPDEHSPYV4SC3n2TBqB/TAQMV33vE4nEn7oU8v66+Tha2q0YNyAGM9K7d4s6USBThyvwxB1pAIDl20/iXH2L4Ioo1DGMUEgrrqzD+wfsTfWeunMkn0FDIePuzGRMTI1Fa7sNf/zsqOhyKMQxjFDIslhteGrtIQDAD7NTkD0wVnBFRL4jk8nw9KzRkMuAz0qrsevkRdElUQhjGKGQ9U5hBY5Wm6CLCEf+jBGiyyHyuVHJWucjD57+9DDaLDbBFVGoYhihkGQwtuKvm8sAAL+eMQJ9o1WCKyISY/FtwxEbpcSJ2kZn0z8iX2MYoZAjSRKeWluKpjb7otW54/lUaApdMZFK/P7u0QCAV748icPnjYIrolDEMEIhZ03RWWw9VgulQo6C72dALueiVQptd2Uk4Y7RibDYJDy+5hu0WzldQ77FMEIh5WxdM575f0cAAItvH460RI3giojEk8lkeHZOOmIiw3Gk2oRXvjwluiQKMQwjFDIsVht+9cHXaDRbkD2wDxbcOFh0SUR+o59G5ZyueWnrcew7fVlwRRRKGEYoZLy09QT2nr6MKKUCL9yTCQWnZ4hc3J2ZjP8a2x82Cfg//z6Iy01tokuiEMEwQiFhx/ELzjsF/vj9MRgUFyW4IiL/I5PJ8NycdAzuFwWDqRW/+qAENpvfP0uVggDDCAW9qsvNeOz9EkgS8JNJAzA7q7/okoj8VpQqDMt/Mg7KMDm+LLvA233JJxhGKKg1mi2Y/84BXG5qQ3p/LX531yjRJRH5vZFJWjw7275+5K9bjmP9N+cFV0TBjmGEgpbVJuHRfx9EWU0D4jUqvJE3HupwheiyiALC3AkD8NANqQCAX33wNUqq6sUWREGNYYSCkqOx2dZjtVCFyfF63ngk6SJEl0UUUJ6cORK3joiH2WLD/HcO4MzFJtElUZBiGKGgI0kSln5+DKv3V0EuA16cm4UsfYzosogCjkIuw9/uHYsRiRpcbDTjvjf34mxds+iyKAgxjFBQkSQJy7Ycx2s7ygEAS7+fgRljkgRXRRS4olVh+NdDkzA4Lgrn6ltw35t7YTC2ii6LggzDCAUNSZLw7Pqj+Ns2++r/39w5Ej+awOfOEPVWP40K7y2YBH1sBCouNePHrxei6jJHSMhzGEYoKFisNvz6o1K8ves0AODpWaMwnx1WiTwmSReBVfMno39MBM5casb3X93Nh+qRxzCMUMCrb27DT/+xH+8fsK8R+fMPM/DTKamiyyIKOvrYSHz8i1yMSNTgQoMZc1/bgx3HL4gui4IAwwgFtBM1DZi9fBd2nryIiHAFXr0/G/eM59QMkbckaNV4/+c5mJgai0azBfP+sQ9/33aCnVqpVxhGKCBJkoRVeytx9993oeJSM/rHROCjR3IxfXSi6NKIgp4uIhz//O+J+PEEPSQJ+Mvm41jwzwO41GgWXRoFKJkkSX4fZ00mE3Q6HYxGI7RarehySLALDWbkf1yKL47WAACmDO2Lv/14LPpGqwRXRhR63t9fid9+chhtFhv6Rinx7Jx0zOQdbNShu+/fDCMUMCxWG97bW4m/bC5DQ6sFSoUcj09Pw0M3pELOJ/ASCXP4vBG/+uBrHDM0AABmpCfiyZkjoY+NFFwZicYwQkFDkiR8dfwCnt9YhiPVJgDA6GQt/vzDTIxK5vcDkT8wW6x4eetJvPrVKVhtEpRhcsy/IRWP3DwEGnW46PJIEIYRCniSJGHHiYt46YvjKK6sBwBo1WF4/I4R+MnEAVBwNITI7xw5b8Kz64+gsPwSAPu/2Z/mDsKDU1LRJ0opuDryNYYRClim1nasLT6HdwrPoPyC/VkY6nA5Hpg8EA9PHcK1IUR+TpIkbDlSgz9tPIZTHf+GI8IVuDszGT+eqEeWPgYyGX+ZCAUMIxRQWtut2HasFp+WnMe2slq0WWwA7K2o507Q4+dTByNeoxZcJZErq03CvtOXUdvQiniNGhNTYzlidxWrTcKmwwYs//IkDp83OfePSNRgVmYypo9OxND4aIEVkrd5NYwsX74cf/7zn2EwGJCZmYmXX34ZEydO7PL4NWvW4Le//S3OnDmDYcOG4U9/+hNmzpzZ7ddjGAk+FqsNx2sasfvURXx1/AL2nb4Mc0cAAYCh8dF4YPJA/CA7BdGqMIGVEnVu46Fq/P7/HUH1Vc9pSdKpsWTWKNyRzrtJriZJEvafqcPqfZX4rLTa5d/6kH5RmDo8HpMGx2JSaixiIjmVE0y8Fkbef/995OXlYcWKFZg0aRJefPFFrFmzBmVlZYiPj//O8bt378ZNN92EgoIC3HXXXVi1ahX+9Kc/obi4GOnp6R79Ysg/NZktKL/QhFMXGnHUYEJJZT1KzxnR3GZ1Oa5/TATuykzC3ZnJGJWk5TAu+a2Nh6rxyLvF+PYPT8d37Kv3j2Mg6YKxuR2flVZj02EDdp+6iHar61UcnhCN0ck6jEzSYGSSFmmJGvSLVvHnQYDyWhiZNGkSJkyYgL///e8AAJvNBr1ej//5n//Br3/96+8cP3fuXDQ1NWH9+vXOfZMnT0ZWVhZWrFjh0S+GfKfdakNDqwWmlnaYWttharGgrrkNNaZWGIytMJhaUWNqxdm6FpffHK8WpVRg3MA+mDq8H24a3g/D4qP5A4f8ntUm4YY/bevy+1oGIFGnxs7/vZVTNtdham3HjuMXsKf8EvaUX8bJ2sZOj4sIVyClTwRS+kRAHxuJBK0asVFK9IlUom+0ErFRSsREhCNKFQZVmJw/R/xId9+/3Rr/bmtrQ1FREfLz85375HI5pk2bhsLCwk7PKSwsxOLFi132TZ8+HevWrevydcxmM8zmK538TCZTl8f2xpv/KcfZuhaXfY5sJrns6/jvVXuvjnBSJ/sce12Ou8bnud7rdfbHq3NkZzVc6zjXz3elVotNQpvFZt+sNpc/m9utaLPa0Nxm/c6oxvXERSsxpF80hsZHIzMlBlkDYjCkXzR/WFPA2Xf6cpdBBLD/06o2tmLf6cvIGdLXd4UFIK06HHdlJOOujGQA9oaGJVX1OFZtwlGDCceqG3D6UhNa2q04UduIE12ElavJZUCkMgwRSgUilQpEhCugDlcgXCGDQi5DmFyOMIUMYR1/VihkCJfLoJDLIZNdGd2y/1kGR66x/1d21d/hyt91HHfl3MD8ufbQDanCesO4FUYuXrwIq9WKhIQEl/0JCQk4duxYp+cYDIZOjzcYDF2+TkFBAX7/+9+7U1qPfFZajYMdt4xSz0QpFdBGhEOrDocuIhwJOjUStSokaNVI1KmRpIvAkH5RnAemoFHb0HUQ6clxdEU/jQq3jUrAbaOuvGeYLVZU17eiqq4ZVZdbcLauGRcazLjc1IZLTW2oa27D5cY2NJgtAACbBDSaLWjs+Ji67+6s5MAII76Sn5/vMppiMpmg13v+4Wc/zE7BlCFxAK4kXOBKur16p+y7uyDDVX8vcz3OZV8nKbmzz9NZDdd7PdfPKeu6hs6O6+T1FHI5lGEdm0IOVZjrx8owOSKVCugiwhGtCkOYgo83otDS3bu6ePeXZ6jCFBgUF4VBcVHXPM5itaGl3YqWNiua2qxobrOgpWMU12yxwWqzod0qwWqT0G61wWqTYLFJsFht9v/aJJdRaeefpSsjx5Lzv677IEkuo9PSd1YTBYYErbjvWbfCSFxcHBQKBWpqalz219TUIDGx8weUJSYmunU8AKhUKqhU3u8lcd+kgV5/DSIKLhNTY5GkU8NgbO30LcexZmRiaqyvSwtpYQo5NAo5u70GKLd+rVUqlcjOzsbWrVud+2w2G7Zu3YqcnJxOz8nJyXE5HgC2bNnS5fFERP5MIZdhyaxRAFxHHK/+eMmsUVwPReQGt8fYFy9ejDfeeAPvvPMOjh49ikceeQRNTU148MEHAQB5eXkuC1wfffRRbNy4ES+88AKOHTuGp59+GgcOHMCiRYs891UQEfnQHelJePX+cUjUuQ5rJ+rUvK2XqAfcXjMyd+5cXLhwAb/73e9gMBiQlZWFjRs3OhepVlZWQi6/knFyc3OxatUq/OY3v8GTTz6JYcOGYd26dd3uMUJE5I/uSE/CbaMS2YGVyAPYDp6IiIi8orvv37wVgoiIiIRiGCEiIiKhGEaIiIhIKIYRIiIiEophhIiIiIRiGCEiIiKhGEaIiIhIKIYRIiIiEophhIiIiIRyux28CI4msSaTSXAlRERE1F2O9+3rNXsPiDDS0NAAANDr9YIrISIiInc1NDRAp9N1+fcB8Wwam82G8+fPQ6PRQCbz3EOoTCYT9Ho9qqqq+MwbL+J19h1ea9/gdfYNXmff8OZ1liQJDQ0NSE5OdnmI7rcFxMiIXC5HSkqK1z6/VqvlN7oP8Dr7Dq+1b/A6+wavs2946zpfa0TEgQtYiYiISCiGESIiIhIqpMOISqXCkiVLoFKpRJcS1HidfYfX2jd4nX2D19k3/OE6B8QCViIiIgpeIT0yQkREROIxjBAREZFQDCNEREQkFMMIERERCRX0YWT58uUYNGgQ1Go1Jk2ahH379l3z+DVr1mDEiBFQq9UYM2YMNmzY4KNKA5s71/mNN97AjTfeiD59+qBPnz6YNm3adf+/0BXufk87rF69GjKZDHPmzPFugUHC3etcX1+PhQsXIikpCSqVCsOHD+fPj25w9zq/+OKLSEtLQ0REBPR6PX75y1+itbXVR9UGph07dmDWrFlITk6GTCbDunXrrnvO9u3bMW7cOKhUKgwdOhQrV670bpFSEFu9erWkVCqlt99+Wzp8+LC0YMECKSYmRqqpqen0+F27dkkKhUJ6/vnnpSNHjki/+c1vpPDwcKm0tNTHlQcWd6/zT37yE2n58uXSwYMHpaNHj0o//elPJZ1OJ509e9bHlQced6+1w+nTp6X+/ftLN954ozR79mzfFBvA3L3OZrNZGj9+vDRz5kxp586d0unTp6Xt27dLJSUlPq48sLh7nd977z1JpVJJ7733nnT69Glp06ZNUlJSkvTLX/7Sx5UHlg0bNkhPPfWU9PHHH0sApLVr117z+PLycikyMlJavHixdOTIEenll1+WFAqFtHHjRq/VGNRhZOLEidLChQudH1utVik5OVkqKCjo9Pgf/ehH0p133umyb9KkSdLPf/5zr9YZ6Ny9zt9msVgkjUYjvfPOO94qMWj05FpbLBYpNzdXevPNN6V58+YxjHSDu9f51VdflQYPHiy1tbX5qsSg4O51XrhwoXTrrbe67Fu8eLE0ZcoUr9YZTLoTRp544glp9OjRLvvmzp0rTZ8+3Wt1Be00TVtbG4qKijBt2jTnPrlcjmnTpqGwsLDTcwoLC12OB4Dp06d3eTz17Dp/W3NzM9rb2xEbG+utMoNCT6/1M888g/j4eDz00EO+KDPg9eQ6f/rpp8jJycHChQuRkJCA9PR0/PGPf4TVavVV2QGnJ9c5NzcXRUVFzqmc8vJybNiwATNnzvRJzaFCxHthQDworycuXrwIq9WKhIQEl/0JCQk4duxYp+cYDIZOjzcYDF6rM9D15Dp/2//+7/8iOTn5O9/85Kon13rnzp146623UFJS4oMKg0NPrnN5eTm2bduG++67Dxs2bMDJkyfxi1/8Au3t7ViyZIkvyg44PbnOP/nJT3Dx4kXccMMNkCQJFosFDz/8MJ588klflBwyunovNJlMaGlpQUREhMdfM2hHRigwLF26FKtXr8batWuhVqtFlxNUGhoa8MADD+CNN95AXFyc6HKCms1mQ3x8PF5//XVkZ2dj7ty5eOqpp7BixQrRpQWV7du3449//CNeeeUVFBcX4+OPP8Znn32GZ599VnRp1EtBOzISFxcHhUKBmpoal/01NTVITEzs9JzExES3jqeeXWeHv/zlL1i6dCm++OILZGRkeLPMoODutT516hTOnDmDWbNmOffZbDYAQFhYGMrKyjBkyBDvFh2AevI9nZSUhPDwcCgUCue+kSNHwmAwoK2tDUql0qs1B6KeXOff/va3eOCBBzB//nwAwJgxY9DU1ISf/exneOqppyCX8/drT+jqvVCr1XplVAQI4pERpVKJ7OxsbN261bnPZrNh69atyMnJ6fScnJwcl+MBYMuWLV0eTz27zgDw/PPP49lnn8XGjRsxfvx4X5Qa8Ny91iNGjEBpaSlKSkqc2913341bbrkFJSUl0Ov1viw/YPTke3rKlCk4efKkM+wBwPHjx5GUlMQg0oWeXOfm5ubvBA5HAJT4mDWPEfJe6LWlsX5g9erVkkqlklauXCkdOXJE+tnPfibFxMRIBoNBkiRJeuCBB6Rf//rXzuN37dolhYWFSX/5y1+ko0ePSkuWLOGtvd3g7nVeunSppFQqpQ8//FCqrq52bg0NDaK+hIDh7rX+Nt5N0z3uXufKykpJo9FIixYtksrKyqT169dL8fHx0nPPPSfqSwgI7l7nJUuWSBqNRvr3v/8tlZeXS5s3b5aGDBki/ehHPxL1JQSEhoYG6eDBg9LBgwclANJf//pX6eDBg1JFRYUkSZL061//WnrggQecxztu7X388celo0ePSsuXL+etvb318ssvSwMGDJCUSqU0ceJEac+ePc6/mzp1qjRv3jyX4z/44ANp+PDhklKplEaPHi199tlnPq44MLlznQcOHCgB+M62ZMkS3xcegNz9nr4aw0j3uXudd+/eLU2aNElSqVTS4MGDpT/84Q+SxWLxcdWBx53r3N7eLj399NPSkCFDJLVaLen1eukXv/iFVFdX5/vCA8iXX37Z6c9cx7WdN2+eNHXq1O+ck5WVJSmVSmnw4MHSP/7xD6/WKJMkjm0RERGROEG7ZoSIiIgCA8MIERERCcUwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQDCNEREQkFMMIERERCcUwQkREREIxjBAREZFQ/x+Or05sudV9AwAAAABJRU5ErkJggg==\n"
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"0.5\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": 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