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@parthi2929
Created September 13, 2018 18:02
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Illustrating sampling distributions..
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"toc": true
},
"source": [
"<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
"<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Sampling-Distribution-of-Sample-Proportions\" data-toc-modified-id=\"Sampling-Distribution-of-Sample-Proportions-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Sampling Distribution of Sample Proportions</a></span><ul class=\"toc-item\"><li><span><a href=\"#Gumballs\" data-toc-modified-id=\"Gumballs-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Gumballs</a></span><ul class=\"toc-item\"><li><span><a href=\"#Setup\" data-toc-modified-id=\"Setup-1.1.1\"><span class=\"toc-item-num\">1.1.1&nbsp;&nbsp;</span>Setup</a></span></li><li><span><a href=\"#Statistical-Outcomes:\" data-toc-modified-id=\"Statistical-Outcomes:-1.1.2\"><span class=\"toc-item-num\">1.1.2&nbsp;&nbsp;</span>Statistical Outcomes:</a></span></li><li><span><a href=\"#Notations-and-Conditions\" data-toc-modified-id=\"Notations-and-Conditions-1.1.3\"><span class=\"toc-item-num\">1.1.3&nbsp;&nbsp;</span>Notations and Conditions</a></span></li><li><span><a href=\"#Visual-Summary\" data-toc-modified-id=\"Visual-Summary-1.1.4\"><span class=\"toc-item-num\">1.1.4&nbsp;&nbsp;</span>Visual Summary</a></span></li></ul></li><li><span><a href=\"#Examples\" data-toc-modified-id=\"Examples-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Examples</a></span></li></ul></li><li><span><a href=\"#Sampling-Distribution-of-Sample-Means\" data-toc-modified-id=\"Sampling-Distribution-of-Sample-Means-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Sampling Distribution of Sample Means</a></span><ul class=\"toc-item\"><li><span><a href=\"#Temperature\" data-toc-modified-id=\"Temperature-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Temperature</a></span><ul class=\"toc-item\"><li><span><a href=\"#Setup\" data-toc-modified-id=\"Setup-2.1.1\"><span class=\"toc-item-num\">2.1.1&nbsp;&nbsp;</span>Setup</a></span></li><li><span><a href=\"#Statistical-Outcomes:\" data-toc-modified-id=\"Statistical-Outcomes:-2.1.2\"><span class=\"toc-item-num\">2.1.2&nbsp;&nbsp;</span>Statistical Outcomes:</a></span></li><li><span><a href=\"#Notations-and-Conditions\" data-toc-modified-id=\"Notations-and-Conditions-2.1.3\"><span class=\"toc-item-num\">2.1.3&nbsp;&nbsp;</span>Notations and Conditions</a></span></li><li><span><a href=\"#Visual-Summary\" data-toc-modified-id=\"Visual-Summary-2.1.4\"><span class=\"toc-item-num\">2.1.4&nbsp;&nbsp;</span>Visual Summary</a></span></li></ul></li><li><span><a href=\"#Examples\" data-toc-modified-id=\"Examples-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Examples</a></span></li></ul></li><li><span><a href=\"#Summary\" data-toc-modified-id=\"Summary-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Summary</a></span></li><li><span><a href=\"#Wish-to-do\" data-toc-modified-id=\"Wish-to-do-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Wish to do</a></span></li></ul></div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sampling Distribution of Sample Proportions \n",
"\n",
"This typically applies to case where the variable under study is categorical. For eg, a _population_ of gumballs, where 60% of them are yellow balls. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Gumballs\n",
"\n",
"### Setup\n",
"\n",
"**Bernoulli:**\n",
"\n",
"Let Y be the random variable of picking up a gumball out of say 10000 balls which is our population $T$. 60% of those balls are yellow and rest other colors. \n",
"\n",
"Our population would thus look like this (1 indicating yellow, 0 indicating other colors): \n",
"$[1,0,0,0,1,1,0,1,0,1,1,0,0,0,1, \\cdots ,1]$\n",
"\n",
"$\n",
"Y = \n",
"\\begin{cases}\n",
"1 \\ \\ \\text{if ball picked up is yellow} \\\\\n",
"0 \\ \\ \\text{if not}\n",
"\\end{cases}\n",
"$\n",
"\n",
"Then, the mean and variance of $Y$ van be calculated as below [Proof here](https://www.statlect.com/probability-distributions/Bernoulli-distribution) \n",
"\n",
"$\n",
"\\mu_y = p \\ \\ \\ \\ \\sigma_y^2 = pq\n",
"$ \n",
"where, $p$ is probability of picking up yellow ball, and $q$, other balls. \n",
"\n",
"Suppose, again by some Godly means, we know, $p = 0.6$ then \n",
"\n",
"$\n",
"\\mu_y = p = 0.6 \\ \\ \\ \\ \\sigma_y^2 = pq = (0.6)(0.4) = 0.24 \n",
"$\n",
"\n",
"$$\n",
"\\color {blue}{ \\mu = \\mu_y = p = 0.6 \\\\ \\sigma^2 = \\sigma_y^2 = pq = 0.24 \\\\ \\sigma = \\sigma_y = \\sqrt{0.24} = 0.4898 } \\tag{1}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [
{
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bee743160>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"\n",
"from random import shuffle \n",
"import matplotlib.pyplot as plt\n",
"from SDSPSM import get_metrics, drawBarGraph\n",
"\n",
"T = 10000 # total size of population\n",
"p = 0.6 # 60% has yellow balls\n",
"\n",
"y_freq = int(p*T) \n",
"y_pops = [1]*y_freq \n",
"o_freq = int((1-p)*T)\n",
"o_pops = [0]*o_freq\n",
"population = y_pops + o_pops\n",
"population_freq = [o_freq, y_freq]\n",
"shuffle(population) \n",
"\n",
"# population metrics\n",
"mu, var, sigma = get_metrics(population)\n",
"\n",
"#visualize\n",
"backgroundColour = '#F5F5FF'\n",
"fig, (ax1) = plt.subplots(1,1, figsize=(5,3), facecolor=backgroundColour)\n",
"drawBarGraph(population_freq, ax1, [T, mu, var, sigma], 'Population Distribution','Gumballs', 'Counts',xmin=0)\n",
"\n",
"\n",
"ax1.set_facecolor(backgroundColour)\n",
"# fig.patch.set_facecolor(backgroundColour)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A rough visualization of distribution, density (so total height of bars equal 1), and probability mass function of our current population"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bee076828>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1,ax2,ax3) = plt.subplots(1,3,figsize=(15,4))\n",
"\n",
"def mini_plot_SDSP(raw_list, norm_off=False, width=0.1): \n",
"\n",
" ax1.hist(raw_list) \n",
" ax1.set_title('Distribution')\n",
" \n",
" _, bins,_ = ax2.hist(raw_list, density=True) \n",
" ax2.set_title('Density')\n",
" \n",
" # probability mass\n",
" dummy_dict = {i:raw_list.count(i) for i in raw_list}\n",
" total = sum(list(dummy_dict.values()))\n",
" pmf = {key: round(val/total,4) for key, val in dummy_dict.items()}\n",
" ax3.bar(list(pmf.keys()), list(pmf.values()), width=width)\n",
" ax3.set_title('PMF')\n",
" \n",
" # normal approx overlay if needed\n",
" if norm_off == False: # so user wants normal curve overlay\n",
" mu, var, sigma = get_metrics(raw_list)\n",
" import numpy as np\n",
" X = np.linspace(min(bins),max(bins),10*len(bins))\n",
" from math import sqrt, pi\n",
" Cp = 1/(sigma*sqrt(2*pi))\n",
" Ep = -1/2*((X-mu)/sigma)**2\n",
" G = Cp*np.exp(Ep) \n",
" metrics_text = '$\\mu_x:{}$ \\n$\\sigma_x:{}$'.format(mu, sigma)\n",
" ax2.text(0.97, 0.98,metrics_text,ha='right', va='top',transform = ax2.transAxes,fontsize=10,color='red') \n",
" ax2.plot(X, G, color='red') \n",
"\n",
"\n",
"mini_plot_SDSP(population, norm_off=True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Statistical Outcomes: \n",
"\n",
">Let us randomly sample from the population. One trial/experiment is sampling about, say $n=10$ samples. Likewise, we sample for many experiments, say $N=2000$. \n",
"\n",
"_Steps:_\n",
"* 1.Take a random sample of $n=10$ balls from the population. Example sample output: $\\widehat{Y_1} = [1,0,0,1,0, \\cdots ,0]$ denoting our 1st sample of size $n=10$. **^** just indicates, its a statistical outcome\n",
"* 2.Take the mean of it and note down for kth experiment. $\\overline{\\widehat{Y_k}} = \\dfrac {1}{n} \\sum\\limits_{i=1}^n Y_{ki} = \\dfrac {1}{10} \\sum\\limits_{i=1}^{10} Y_{ki}$. Example sample output: $\\overline{\\widehat{Y_1}} = 0.7$\n",
"* 3.Do step 1 and 2 for $N=2000$ times. That is, $N=2000$ experiments $\\implies$ $2000$ mean values $\\overline{\\widehat{Y_k}}$, for $k = 0,1,2,3.... N$ Note by now $\\overline{\\widehat{Y_k}}$ itself looks like a random variable taking on different values of mean but with repetitions, which should give us an intuition, the highest repetition will be the one equal to population mean. \n",
"Example total output:\n",
"\n",
"|$\\widehat{Y_k}$|$\\overline{\\widehat{Y_k}}$|\n",
"|---|---|\n",
"|1|0.6|\n",
"|2|0.9|\n",
"|3|0.6|\n",
"|4|0.4|\n",
"|5|0.1|\n",
"|...|...|\n",
"|2000|0.3|\n",
"\n",
"* 4.Take the frequency count of the samples and prepare a concise frequency chart., with each row of mean value against its frequency. If the list is small you might already note, highest frequency happens around population mean.\n",
"Example total output: \n",
"\n",
"|$\\overline{\\widehat{Y_j}}$|&nbsp; $n(\\overline{\\widehat{Y_j}})$|\n",
"|----|----|\n",
"|0.1| 8|\n",
"|0.2| 23|\n",
"|0.3| 65|\n",
"|...|...|\n",
"|0.9| 20|\n",
"|1| 5|\n",
"\n",
"* 5.Calculate probability for each row of above table, by simply taking the frequency divided by total outcomes.Note denomitor sums up to 2000 because, statistically we get 1 outcome per experiment (which is a mean), so total no of occurances after 2000 experiments would be 2000 outcomes (2000 means). \n",
"$\n",
"p\\Big(\\overline{\\widehat{Y_j}}\\Big) = \\dfrac {n\\Big(\\overline{\\widehat{Y_j}}\\Big)}{\\sum n\\Big(\\overline{\\widehat{Y_j}}\\Big)} = \\dfrac {n\\Big(\\overline{\\widehat{Y_j}}\\Big)}{2000} \n",
"$ \n",
"\n",
"|$\\overline{\\widehat{Y_j}}$|&nbsp; $n(\\overline{\\widehat{Y_j}})$|&nbsp; $p(\\overline{\\widehat{Y_j}})$|\n",
"|---|---|---|\n",
"|0.1| 8|0.0001|\n",
"|0.2| 23|0.002|\n",
"|0.3| 65|0.034|\n",
"|...|...|\n",
"|0.9| 20|0.002|\n",
"|1| 5|0.0002| \n",
"\n",
">From above table, one could draw the **probability mass function** which is a **discrete probability distribution** where one could find for any $k$, the probability $p(X=k)$ discretly\n",
"\n",
"* 6.Calculate mean, variance and SD as below.Suppose there are total M rows in the table. We would find that, \n",
"$\n",
"\\mu(\\overline{\\widehat{Y}}) = \\overline{\\overline{\\widehat{Y}}} = \\sum\\limits_{j=1}^M \\overline{\\widehat{Y_j}}p(\\overline{\\widehat{Y_j}}) \\approx \\color {blue}{0.6}\\\\ \\\\\n",
"\\sigma(\\overline{\\widehat{Y}})^2 = \\sum\\limits_{j=1}^M \\Big(\\overline{\\widehat{Y_j}} - \\mu(\\overline{\\widehat{Y}})\\Big)p(\\overline{\\widehat{Y_j}}) \\approx \\color {blue}{0.0226}\\\\ \\\\\n",
"\\therefore \\ \\ \\sigma(\\overline{\\widehat{Y}}) \\approx \\sqrt{0.0226} = \\color {blue}{0.1505} \\tag {2}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Its much simpler programmatically.. "
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.6048 0.024 0.1549\n"
]
}
],
"source": [
"from random import choices \n",
"\n",
"N = 2000\n",
"n = 10\n",
"\n",
"Y_hat = []\n",
"Y_mean_list = []\n",
"for each_experiment in range(N): \n",
" Y_hat = choices(population, k=n) \n",
" Y_mean = sum(Y_hat)/len(Y_hat)\n",
" Y_mean_list.append(Y_mean)\n",
" \n",
"mu, var, sigma = get_metrics(Y_mean_list)\n",
"print(mu, var, sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A quick visualization of our resultant statistical outcome ```Y_mean_list```"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bee657358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, (ax1,ax2,ax3) = plt.subplots(1,3,figsize=(15,4))\n",
"\n",
"mini_plot_SDSP(Y_mean_list)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Notations and Conditions\n",
"\n",
"You could already see the resultant sampling distribution shaping up as normal. A visual summary is provided below where, normal distribution approximation is also applied. \n",
"\n",
"Back to variables, the complicated statistical notation are typically indicated by simpler notations as follows. We used former because we did not want to lose details for sake of simplicity.Now that we have the insight, we could swap with these simpler conventional notations. \n",
"\n",
"$$\n",
"\\color {blue}{\n",
"\\text{Random Variable} \\ \\ \\widehat{p} = \\overline{\\widehat{Y}} \\\\ \\\\\n",
"\\mu_\\widehat{p} = \\mu(\\overline{\\widehat{Y}}) \\\\ \\\\\n",
"\\sigma_\\widehat{p} = \\sigma(\\overline{\\widehat{Y}})\n",
"}\n",
"$$\n",
"\n",
"Comparing equations set $1$ and $2$, \n",
"\n",
"$$\n",
"\\color {blue} {\n",
"\\mu_\\widehat{p} \\approx 0.6 = \\mu = p \\\\ \\\\\n",
"\\sigma_\\widehat{p} \\approx 0.1505 \\approx \\dfrac{0.4898}{\\sqrt{10}} = \\dfrac {\\sigma}{\\sqrt{n}} = \\sqrt{\\dfrac {pq}{n}} \\tag {3}\n",
"}\n",
"$$\n",
"\n",
">$\\widehat{p}$ is called the sample proportion. The resultant sampling distribution could be satisfactorily approximated by normal density function when sample size is sufficiently large. \n",
"\n",
"**Conditions:**\n",
">How much is sufficiently large? General thumb rule is $np \\geq 10$ and $nq \\geq 10$ assures a normal distribtuion for sampling distribution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Visual Summary"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bee288128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"from SDSPSM import plot_SDSP\n",
"\n",
"# PLOT THE RESULTS\n",
"from SDSPSM import plot_SDSP, get_normal_curve_label\n",
"backgroundColour = '#F5F5FF'\n",
"fig, axarr = plt.subplots(2,3, figsize=(15,10), facecolor=backgroundColour)\n",
"\n",
"pop_axarr = [axarr[0,0],axarr[0,1], axarr[0,2]]\n",
"titles = ['Population Distribution','Population Discrete\\nDensity Function','Population Probability Mass\\nFunction (PMF)']\n",
"plot_SDSP(population, pop_axarr, titles, index_list=['A','B','C'], norm_off=True)\n",
"\n",
"stat_axarr = [axarr[1,0],axarr[1,1], axarr[1,2]]\n",
"titles = ['Statistical Distribution','\\nStatistical Discrete Density Function','Statistical Probability Mass\\nFunction (PMF)']\n",
"plot_SDSP(Y_mean_list, stat_axarr, titles, index_list=['D','E','F'])\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Note that, normal approximation is best fit not for our discrete probability mass function F, but for Discrete Density Function E. This is because, probability density function has area equal to 1 (total probability is 1), so our discrete function \"bars\"'s heights should total to 1 as well. This is not possible on our last derived discrete function F, but intermediate density function E. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Examples\n",
"\n",
"**Example 1**\n",
"\n",
"The safety officers of a mining company take a Simple Random Survey of $500$ employees and finds that $15\\%$, percent of the sampled employees wear contact lenses. The safety officers may take several more samples like this. Suppose it is really $12\\%$, percent of the approximately $34,000$ employees in the company who wear contact lenses. \n",
"\n",
"What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses? [Ref: Khan Academy](https://www.khanacademy.org/math/statistics-probability/sampling-distributions-library/sample-proportions/e/sampling-distribution-sample-proportion-mean-standard-deviation) \n",
"\n",
"<u>Ans</u> \n",
"\n",
"The problem at hand is what proportion wears contact lenses. Our random variable indicates they wear contact lenses or not, thus a Bernoulli one. Its a categorical problem. Thus we deal as sample proportions. Since in any Bernoulli distribution, $\\mu = p$, we proceed as follows. \n",
"\n",
"Given **True** population parameters: $p = \\mu = 0.12$ \n",
"\n",
"One Sample result: n=500, $\\widehat{p_1} = 0.15$. \n",
"\n",
">Note officer may take more like this. So eventually with many experiments of 500 samples, one should arrive at normal distribution (normal assured because $np = 500*0.12 = 60 > 10$)\n",
"\n",
"So resultant normal sampling distribution will have below parameters. \n",
"\n",
"$$\n",
"\\mu_\\widehat{p} = \\mu = 0.12 \\\\\n",
"\\sigma_\\widehat{p} = \\sqrt{\\dfrac{pq}{n}} = \\sqrt{\\dfrac{0.12(1-0.12)}{500}}\n",
"$$\n",
"\n",
"<br><div style=\"background-color:'#E3F2FD; padding: 10px 10px 10px 10px;\">Typically problems extend further to also calculate probability. But once we know the sampling distribution parameters mean and variance, it is easy to calculate probability of any case next naturally, as we have standard methods to derive probability from normal distributions. Only take care they meet the condition of sample proportion (np > 10 and nq > 10) or sample means (n>30). Since finding probability from normal distribution is currently not yet covered, we skip that part. What one should be careful is to <b>detect</b> if the question has a sample distribution associated and tackle it accordingly. The same applies to Sample means we see next as well. \n",
"</div><br>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Sampling Distribution of Sample Means \n",
"\n",
"This typically applies to case where the variable under study is continuous. For eg, a temperature distribution over a range of values. \n",
"\n",
"## Temperature"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Setup\n",
"\n",
"**Random:**\n",
"\n",
"Let Y be the random variable indicating temperature over a distribution of certain values.\n",
"\n",
"If limiting values are say, 0 deg C to 40 deg C, our population would thus look like this:\n",
"$[23,13,35,50,10,2,5,0,33, \\cdots ,21]$\n",
"\n",
"Unlike Sample proportions,we do not know or designate any proportion of temperatures in this example, but we know the mean and variance by simply calculating all values in the distribution. These would be our population parameters. \n",
"\n",
"Population mean $\\mu = \\mu_y$ \n",
"Population variance $\\sigma^2 = \\sigma_y^2$ \n",
"\n",
"Since it is a random distribution, there is no theoretical calculation of these values, so we create such a population distribution programmatically, and calculate their parameters. "
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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fDz/cTpL92//mm4O1fv0arVixweoyly5dUoMGNTVu3Gd6773hCg+vrA8+GOe4Dfr/tmzZrKFDh+j333fo7Nmz6e77/fe/FBAQqHbtWurJJ3vpsceecPj6b2bL8SplvC9sOV4dse6RI0foo49G6a+/TmT5s8SZPdflypXPUl5mzIx/WwQG+mjYsHfVs+czGd6f0X4CgNyCM7QAYKMdO7bJMAzVqFHL6jKjRr0jX9+Cd/yX3VN569dvqLVrV2nfvj8lSXv37tGaNSv10EMPS5KuXbum7du3qnnzB9M9rnnzB/XrrxsdVseuXTtUoUJFSzMrSTt3bpenp6fCwsLTLevM5/Hy5ctKS0tT0aLeksxt/4IF8xURUVc9enRXcLCv6tWrrokTx8m46W/FffvGqWPHroqMbGZXvbb444/datUqUqGhYVq8eLUWLVqpkiX9FBFRR59//pXKli2nuLgn1aRJs0yb2ew8hm/dF1Lmx6sjGIah6dM/V1TU41luZm15rm+WG18TbkhNTdXs2d8oISFBdes+YHW5jPYTAOQWXBQKAGy0fftWFStWTKVLW7+QTs+evTOdwliqVICjS7ujAQNeVkLCZdWqFS53d3elpKRo0KAhiot7VpJ07txZpaamyte3ZLrH+fqW1KpVyx1Wx65dO1StWs10t+3cuV2hoeG655570t3uzOdx0KDnVbVqddWtW1+Sue0/dOhvffbZBD333Ivq3/8V7dq1Qy+91FeS1Lv3c5o27TMdPPiXpkxxzuesbxg48Hk9+GBrjR798f+/pZIef/xJzZ8/R1FR0dq4cb3mzv1WlStX1U8/zZckTZkyQ5UrV7ktKzuP4Vv3hZT58eoIK1Ys0+HDhxQT83SWH5vZc32r3PiasHv372rWrL6uXLmiggUL6ptv5mV4LNyQ0X4CgNyChhYAbLRjx7bbGrJb+fj4yMfHJ5sqss2cOd/q66+/1LRpXyssrJJ27dqhQYOeV5kyZRUT09Oy3K2fqTQMw6Gfs9y1a4c6dOiS7rYdO7apatXqty3rrOfx5Zf7a+PG9Vq+fL3c3d3T3WfP9qelpalmzQjLtOTq1Wvo4MEDmjx5vJo1a6mhQwfr55/XydPT07EbcpOzZ89q/fo1+uGHpelu9/LystT/wAMNlZCQZlNedh3D1vaFrcerGV988Zlq1aqtatVuP/buxJbn+la58TXh/vtDtGnTDl26dFHz589VXFyMFi9erUqVKt+27J3GDADkBkw5BgAb7dy57Y7TjaXcOb1wyJCBev75l9StW5QqV66ixx57Qn379rdcZKdYseJyd3fXqVMn0z3uzJnTt521tFdaWpr27Nmt6tXT/0Fg+/YtGTa0zngeBw16UbNnz9KiRSvTTQs1s/1+fv4KDU0/XTokJExHjx7Rr79u0tmzZ1W7dmUVLuyhwoU9tG7dGk2ePEGFC3vo6tWrWarfmu3btyo1NVVVqqT/DPK2bVtUs2btLOdlxzFsbV9ImR+vZp0+fVoLFvygp57qleXH2vNc58bXBE9PT5UvX8Hyx5gqVapr3LgPb1vuTvsJAHILztACgA0SEhL0118HbmvIbpUbpxf+91/SbWdW8uVzV1ra9TN2np6eqlGjllauXKbOnbtZllm5ctltZ1TttX//PiUlJcnfv5Tltt27f9eBA/szbGgd/Ty+9NLzmjPnGy1ZslohIaHp7jOz/fXqNdCBA/vS3fbXX/sVFBSsdu06qmbNiHT39e79lMqXr6iBAwc77KxtamqqJOnKlf8stx08+JeWL1+qWbPmZTnP2cfwnfaFlPnxataMGdOUP39+de0aleXH2vNc58bXhFulpaXd9geWzPYTAOQWNLQAYIOdO7crLS0t04bWkdMLExISdPDgX5Kuv+E8duyIdu7cIR8fH8vneG1ZpnXrdhoz5j2VKVNWYWGVtHPndo0b94EefbSHZV19+/bX008/oYiIOqpXr4GmTJmo+PgTevrp3g7Zll27dkiSJk0ap+eee1H//HNYL7/8giRleKbSkc/jiy/+n2bNmqFvvpmvokW9dfLk9TOxBQsWtFygypbtnzhxnCZNGqft2/+03Na374tq1uwBjRw5Ql26dNfOndv16acfa+jQd1S0aFEVLVo0XS1eXl7y8fHJcGqnvWrXrqsCBQpoyJBBevXVN3T06BENHNhPXbtG6cEHW2U5z97n3pZj0ZZ9Ycvxeuu+sGXd0o2LQU1R165RKlSoUJa30Z7n2pnPpy3L3Ppcvf76K2rVqo0CA0vr8uXL+u67r7Vu3WrNnfu/76K1ZT8BQG7B1/YAgA3Gjx+rESPe1PHjFxz+/Z3WrF27Wq1bN73t9ujoGE2e/IXNy1y+fFnDh7+un36apzNnTsvPz19du0bp1Vff0L333mt5zOTJE/ThhyN18mS8wsMr6/33P1TDho0lSTNmfKHevZ/Snj2HFBxcJsvb8tprL2vnzu269957tXz5UlWocL/efPNt9e79lOrVa6A5c37KcqatvLwy3l+DB7+pIUOGWn6+0/ZL0ogRQ/XOO8OUmJj+1+aSJQv15puDdeDAPpUuHaRnnnlOffr0zfA4adUq8rav7TH73F6vYZFefbW/Dh36W6VKBSgmpqcGDHhFHh7Z93drW45FW/aFLcfrrfvClnVL0po1q/Tww820Zs2vioioY9d2Ztdz7ajxf+tzFRf3pNauXaVTp06qcOEiqly5ql54YaBatnzI8nhbxwwA5AY0tACATL399puaP3+Ofvllp11v3Nu3f0jVq9d02Hfa3k3MPrcAAORlXBQKAJCppUsXacyYcXY3XL//vlOVK1d1cFV3B7PPLQAAeRlnaAEATnXq1CmVK+en337brfDwSjldDgAAuIvQ0AIAAAAAXBJTjgEAAAAALomGFgAAAADgkmhoAQAAAAAuiYYWAAAAAOCSaGgBAAAAAC6JhhYAAAAA4JKy9Vvcw8LKqGDBQnJ3d5eHh4fWr9+i8+fPq0eP7jpy5LCCgspoxozv5O3tnZ1lAQAAAABcULafoV28eJV++WWH1q/fIkkaM+Y9RUY2165dBxQZ2VxjxryX3SUBAAAAAFxQjk85XrjwB0VHx0iSoqNjtGDB/ByuCAAAAADgCtwSEw0ju1YWHl5WRYt6y83NTT17PqPY2DiVKlVUJ05ctCwTEOCt48cv3PbYqVMna+rUyZKkqKhoRUc/kV1lAwAAAACykbd3cZuWy9aGNj7+hPz9S+n06dNq166lxoz5RI880t6mhhYAAAAAgJtl65Rjf/9SkiRfX1+1b99JW7Zslq9vScXHx0uS4uPjVaKEb3aWBAAAAABwUdl2lePExESlpaWpUKFCSkxM1IoVP+uVV97Qww+318yZ0/XSS69o5szpatOmQ3aVBABwYSGzg3Qs6ajdjw8sUFr7uh1xYEUAACC7ZVtDe/r0KUVFdZIkpaam6JFHHtODD7ZSrVq19cQTj+jLLz9XYGCQvvpqdnaVBABwYceSjuqbpvPsfnzUqk4OrAYAAOSEbGtoy5Ytp19/3Xnb7cWKFdOiRSuyqwwAAAAAwF0ix7+2BwAAAAAAe2TbGVoAAADAGj4XD8AeNLQAAADIcXwuHoA9mHIMAAAAAHBJNLQAAAAAAJdEQwsAAAAAcEk0tAAAAAAAl0RDCwAAAABwSTS0AAAAAACXREMLAAAAAHBJfA8tgBwVMjtIx5KOmsoILFBa+7odcVBFcBaz+9oV93Ne3GbkDbx2A8gtaGgB5KhjSUf1TdN5pjKiVnVyUDVwJrP72hX3c17cZuQNvHYDyC2YcgwAAAAAcEmcoQUAAA7DNGsAQHaioQUAAA7DNGsAQHZiyjEAAAAAwCXR0AIAAAAAXBJTjgEAAAAb8BlxIPehoQUAAABswGfEgdyHKccAAAAAAJfEGVonMDsdRWJKCgAAAABkhobWCcxOR5GYkgIAAAAAmcn2KcepqamqX7+GunRpK0k6fPiQmjSpq6pVK6pHj+66du1adpcEAAAAAHBB2X6Gdvz4sQoJCdPly/9Kkl5//WU999yL6tYtSv369db06Z+rV68+2V0WAAAAADgcH0d0rmxtaI8fP6YlSxZq0KAh+uSTD2QYhtasWalp076WJEVHx2jEiKE0tAAAAADuCnwc0bmydcrxoEEvaMSIkcqX7/pqz507pyJFisrD43pfHRAQqBMnjmdnSQAAAAAAF5VtZ2gXL16gEiV8VaNGLa1du1qSZBjGbcu5ubll+PipUydr6tTJkqSoqGhFRz/htFrNCvcMl1uS+YwLF846piAgF2O85B1m9/Wt+9nRedGruunM1dP2B0oqkd9XM5vOTrcOR9boCvLiNudFznjtdoVjJ7fX6IzXMZjHex37eHsXt2m5bGtoN23aoIULf9TSpYt05coVXb78rwYNekGXLl1USkqKPDw8dPz4Mfn7l8rw8bGxcYqNjcuuck3Zc22PjALmM2zdiYArY7zkHWb39a372dF5ay6vdsiUMGfW6Ary4jbnRc547XaFYye31+iM1zGYx3sd58q2KcfDh7+rAweOae/ew5o+/Rs1adJM06bNVOPGTTVv3hxJ0syZ09W2bYfsKgkAAAAA4MJy/Hto33rrfcXERGn48NdUrVoNxcT0zOmSAJuZvWodV6wDAAAA7JcjDW3jxpFq3DhSklS2bDmtXbs5J8oATDN71TquWAcAAADYL1uvcgwAAAAAgKPQ0AIAAAAAXBINLQAAAADAJdHQAgAAAABcEg0tAAAAAMAl5fjX9sA2fD0McHdhTAMAAJhHQ+si+HoY4O7CmAYAADCPKccAAAAAAJfEGVoAAPIwpr8DAFwZDS0AAHkY098BAK6MKccAAAAAAJfEGVoAAAAALouPTuRtNLQAAAAAXBYfncjbmHIMAAAAAHBJnKEFAAC5ltmphBLTCQHgbkZDCwAAci2zUwklphMCwN2MKccAAAAAAJfEGVoAAAAAcCFc2fl/7G5o//vvP23atEEVKlRUUFCwI2sCAAAAAFjBlZ3/x+Ypx3FxT2ry5AmSpGvXrqlx4zpq3/5BVa8eoqVLFzutQAAAAAAAMmJzQ7t8+VLVrl1PkrRw4Y9KSLisv/8+qcGDh+qdd4Y6qz4AAAAAADJkc0N78eIF+fr6SpKWLVuiDh26yNfXV926RenPP/c4rUAAAAAAADJic0NbsqSf/vhjt1JTU7V8+VI1bdpCkpSQkKB77rnHaQUCAAAAAJARmxvaHj1iFRPTXbVrV5a7u7uaNm0uSdqy5Vfdf39opo+/cuWKGjeuo7p1qykiopLefvtNSdLhw4fUpEldVa1aUT16dNe1a9fs3BQAAAAAQF5ic0P76qtv6NNPp+qpp+K0fPl6eXp6SpLc3T3Uv//LmT4+f/78WrRopX79dac2bdqhZcuWaPPmX/T66y/ruede1K5dB1S0qLemT//c/q0BAAAAAOQZNje069evVdu2HdS374sKCAi03B4VFa2iRb0zfbybm5sKFiwoSUpOTlZycrLc3Ny0Zs1KderUVZIUHR2jn36an9VtAAAAAADkQTY3tK1bN9X58+dvu/3SpUtq3bqpTRmpqamqV6+6ypTxVbNmLVW2bHkVKVJUHh7Xvw43ICBQJ04ct7UkAAAAAEAe5mHrgoZhyM3N7bbbz58/Jy8vL5sy3N3d9csvO3Tx4kU9+mgn7du397ZlMlqHJE2dOllTp06WdP2scHT0E7aWnu3CPcPllmQ+48KFsw7LvDUPjsF+Mc8Z48UVOPrYiV7VTWeunrY7r0R+X81sOtv+gmzg6G3ObXnOyMyOYzu3PY/ZsV/yIke/RjBe7H+8M2vMq+MlL+6X3L7NjuDtXdym5TJtaLt1ay/peqPZs+fjyp8/v+W+1NRU7dmzW3XrPpCl4ooWLapGjSK1efMvunTpolJSUuTh4aHjx4/J379Uho+JjY1TbGxcltaTU/Zc2yOjgPmMm3ei2cxb8+AY7BfznDFeXIGjj501l1frm6bz7M6LWtXJ6c+ho7c5t+U5IzM7ju3c9jxmx37Jixz9GsF4sf/xzqwxr46XvLhfcvs2Z6dMpxz7+BSTj08xGYYhb29vy88+PsUUEBConj176/PPv8p0RWfOnNHFixclSf/9959WrVqu0NAwNW5oFaoRAAAgAElEQVTcVPPmzZEkzZw5XW3bdjC5SQAAAACAvCDTM7STJk2TJAUHl9Hzz79k8/TiW508Ga+4uBilpqYqLS1NXbo8otat2yo0NFwxMVEaPvw1VatWQzExPe3KB5A9QmYH6VjSUbsfH1igtPZ1O+LAigAAAJBX2fwZ2sGD3zS1oipVqmrTpu233V62bDmtXbvZVDaA7HMs6ajpaWsAAACAI9jc0J4/f17Dhg3R6tUrdObMaaWlpaW7/+TJfx1eHAAAAAAA1tjc0D77bE/t3LldsbFx8vMrZfVqxAAAAAAAZAebG9rVq1fop5+WqXbtus6sBwAAAAAAm2R6leMbSpTwlZdXQWfWAgAAAACAzWw+Q/vmmyP09ttvaPLk6SpYkMYWAAAAuNvx7QbI7WxuaN9//20dOXJYZcr4KigoWB4e96S7f/PmXQ4vDgAAAEDO4dsNkNvZ3NB26tTVmXUAAAAAAJAl2fY9tAAAAAAAOJLNF4UCAAAAACA3sfkMbcmShe743bMnT/7rkIIAAAAAALCFzQ3tmDHj0v2ckpKsnTu3a/78uRo0aIjDCwMAAAAA4E5sbmgffzwmw9urV6+pVatWqE+fvg4rCpC4TDzsx7EDAACQN9jc0FrTuHFTDRr0giNqAdLhMvGwF8cOAABA3mD6olBz5nyjYsWKO6IWAAAAAABsZvMZ2tq1q6S7KJRhGDp9+pQuXDivsWM/dUpxAAAAAABYY3ND26lT13Q/58uXT8WLl1CjRpEKCQl1eGEAAAAAANyJzQ3t4MFvOrMOAAAAAACyJMsXhVq9eqX+/HOP3NzcFBZWSY0bRzqhLACOwhV/ASA9XhfzBrP7WWJfA67A5ob2xInjiorqpO3bt8rfv5QkKT7+hGrWjNA338yz3AYgd+GKvwCQHq+LeYPZ/SyxrwFXYPNVjl96qZ/c3d31++9/af/+o9q//6h27Togd3d3vfRSP2fWCAAAAADAbWw+Q7ty5TItXrxaZcqUtdxWtmw5jR79sdq0ae6U4gAAAAAAsMb099C6uZmOAAAAAAAgy2zuRiMjm2vgwH46dux/H64/evSIBg16XpGRnKEFAAAAAGQvm6ccjx79sR55pIMqVSonf/9ScnNz04kTx1W5clWNHv1xpo8/duyoevXqoVOnTipfvnx66qk4/d//Pa/z58+rR4/uOnLksIKCymjGjO/k7e1taqOQOa78BwBA7sWVmAHANjY3tIGBpbVx4zatWLFM+/f/KcMwFBoarmbNWtj0eHd3D73zzhjVqFFTly9fVsOGtdSsWUt99dUXioxsrpdeekWjR7+nMWPe09tvv2/3BsE2XPkPAIDciysxA4BtMp1yvHTpYoWFldGlS5ckSc2bt1SfPn317LP9VKtWbYWFldHy5T9nuiJ/f3/VqFFTklSoUCGFhITpxInjWrjwB0VHx0iSoqNjtGDBfDPbAwAAAADIIzI9Qztp0ji98MJAFSlS5Lb7ihQpov79X9aECWPVosWDNq/0n38Oa+fO7apdu65Onz4lf39/Sdeb3jNnTmf4mKlTJ2vq1MmSpKioaEVHP2Hz+rJbuGe43JLMZ1y4cNZhmY7OyyjT0Ry9zdGruunM1YyPL1uVyO+rmU1np1uHI2t0htx27GTHsch+MZ/nDLl9mzkW7X88+8Xxctvz6Ir7xRVqdLS8uM031pGba8yr+8Usb+/iNi2XaUO7e/cuvffeB1bvb9KkmUaOHGFzYQkJCXrssS4aOfIjFS5c2ObHxcbGKTY2zublc9Kea3tkFDCfcfNONJvp6LyMMh3N0du85vJqh0yzduZ+cYbcduxkx7HIfjGf5wy5fZs5Fu1/PPvF8XLb8+iK+8UVanS0vLjNN9aRm2vMq/slu2Q65fjs2TPKl8/6Ym5ubjp//pxNK0tOTtZjj3VR9+7R6tChsyTJ17ek4uPjJUnx8fEqUcLXpiwAAAAAQN6WaUMbEBCo3bt3Wb1/9+5dKlUqINMVGYahPn16KiQkTP369bfc/vDD7TVz5nRJ0syZ09WmTQdb6gYAAAAA5HGZTjl+6KE2euut1/XQQw/rvvvuS3dfUlKS3n77DT30UJtMV7Rp0wbNmjVDlSpVUb161SVJQ4e+owEDXtETTzyiL7/8XIGBQfrqq9mZJAEAAACAc/C1Wa4l04Z20KAhmj9/jqpWrajevfsqJCRUkvTnn3s1adI4GYahgQMHZ7qiBx5oqMREI8P7Fi1akcWyAQAAAMDx+Nos15JpQ+vr66uVKzfq+ef7aOjQwTKM602pm5ubWrR4SB99NEElS5Z0eqEAAAAAANws04ZWkoKCgjVv3iJduHBBf//9lwzDUPnyFeXt7e3s+gAAAAAAyJBNDe0N3t7eqlWrtrNqAQAAAADAZple5RgAAAAAgNyIhhYAAAAA4JJoaAEAAAAALomGFgAAAADgkmhoAQAAAAAuiYYWAAAAAOCSaGgBAAAAAC4pS99DC8C5QmYH6VjSUbsfH1igtPZ1O+LAigDkJmZfIyReJwAAdxcaWiAXOZZ0VN80nWf346NWdXJgNQByG7OvERKvEwCAuwtTjgEAAAAALokztACQCaaCAwAA5E40tACQCaaCAwAA5E5MOQYAAAAAuCQaWgAAAACAS2LKMQAAAJADuEYDYB4NLQAAAJADuEYDYB5TjgEAAAAALokztHAYps0Adw+z41liTAMAAOejoYXDMG0GuHuYHc8SYxoAADhftk057t07VsHBvoqIqGy57fz582rbtqWqVq2otm1b6sKFC9lVDgAAAADAxWVbQ/v4409q/vwl6W4bM+Y9RUY2165dBxQZ2VxjxryXXeUAAAAAAFxctjW0DRs2lo+PT7rbFi78QdHRMZKk6OgYLVgwP7vKAQAAAAC4uBy9yvHp06fk7+8vSfL399eZM6dzshwAAAAAgAtxmYtCTZ06WVOnTpYkRUVFKzr6iRyuyLpwz3C5JZnPuHDhrMMyHZ3njMzcnueMTGfnOSMzt+U5I5P9kjf3S17YZmdk5vY8Z2RmNKYdLbc9j664X/JCja64zc6Q255H9otjeHsXt2m5HG1ofX1LKj4+Xv7+/oqPj1eJEr5Wl42NjVNsbFw2Vme/Pdf2yChgPuPmnWg209F5zsjM7XnOyHR2njMyc1ueMzLZL3lzv+SFbXZGZm7Pc0ZmRmPa0XLb8+iK+yUv1OiK2+wMue15ZL9krxydcvzww+01c+Z0SdLMmdPVpk2HnCwHAAAAAOBCsq2hjYl5VE2b1teBA/tUsWKgpk//XAMGvKKVK5epatWKWrlymQYMeCW7ygEAAAAAuLhsm3I8ffqsDG9ftGhFdpUAAAAAALiL5OiUYwAAAAAA7EVDCwAAAABwSTS0AAAAAACXREMLAAAAAHBJNLQAAAAAAJdEQwsAAAAAcEk0tAAAAAAAl0RDCwAAAABwSTS0AAAAAACXREMLAAAAAHBJNLQAAAAAAJfkkdMFAAAAuLKQ2UE6lnTUVEZggdLa1+2IgyoCgLyDhhYAAMCEY0lH9U3TeaYyolZ1clA1AJC3MOUYAAAAAOCSaGgBAAAAAC6JhhYAAAAA4JJoaAEAAAAALomGFgAAAADgkmhoAQAAAAAuiYYWAAAAAOCSaGgBAAAAAC6JhhYAAAAA4JJoaAEAAAAALilXNLQ//7xE1auHqEqVCho9+r2cLgcAAAAA4AJyvKFNTU1V//7/p3nzFmvr1j2aPXuW9u7dk9NlAQAAAAByuRxvaLds2axy5SqobNly8vT0VNeuUVqw4IecLgsAAAAAkMvleEN74sRxBQaWtvwcEBCo+PjjOVgRAAAAAMAVuCUmGkZOFvD997O1fPlSTZgwRZL09dcztHXrZo0Z80m65aZOnaypUydLkq5c+U/33ntfttfqSGfPnlHx4iXyTJ4zMvNijWxz7szMizXmxW12RmZuz3NGZl6sMS9uszMyc3ueMzLzYo1sc+7MzIkaixUrrh9+WJJpjocji7JHQECgjh07avn5+PFj8vMrddtysbFxio2Ny87SnKphwwitX78lz+Q5IzMv1sg2587MvFhjXtxmZ2Tm9jxnZObFGvPiNjsjM7fnOSMzL9bINufOzNxcY45POa5Vq7YOHjygw4cP6dq1a5oz5xu1adM+p8sCAAAAAORyOX6G1sPDQ2PGjFOHDg8pNTVVPXrEKjy8Uk6XBQAAAADI5dyHDBk6NKeLqFChovr06atnn31eDRo0zulysk2NGrXyVJ4zMvNijWxz7szMizXmxW12RmZuz3NGZl6sMS9uszMyc3ueMzLzYo1sc+7MzK015vhFoQAAAAAAsEeOf4YWAAAAAAB70NBms969YxUc7KuIiMoOyTt27Khat26qmjXDFBFRSePHjzWVd+XKFTVuXEd161ZTREQlvf32mw6pMzU1VfXr11CXLm0dkhcWVka1a1dRvXrV1bBhhOm8ixcvKjq6q2rUCFXNmmH69ddNpvL279+nevWqW/75+RXWuHEfmcr85JMPFRFRSRERlRUT86iuXLliKm/8+LGKiKisiIhKdteW0fF8/vx5tW3bUlWrVlTbti114cIFU3nffz9bERGVVLBgPm3blvUr4WWUOXjwQNWoEao6daoqKqqTLl68aCpv+PDXVadOVdWrV13t2j2o+PgTpvJu+Oij0fLyctPZs2dtzrOWOWLEUFWoEGA5JpcsWWS6xk8//UTVq4coIqKShgwZZLrGHj26W+oLCyujevWqm8rbuXOHIiPrWV4ntmzZbCpv166datq0vmrXrqKuXdvp33//tTnP2mu1mfFiLdPeMWMtz8x4sZZp75jJ7HdeVseMtTwz4+VONdozZqzlmRkv1jLtHTPW8uwdM9beixw+fEhNmtRV1aoV1aNHd127ds3mbbaWOXHiOFWpUiHLr7XW8p56Kvr/7+PK6t07VsnJyaYz+/Tpqbp1q6lOnaqKju6qhIQEU3k3DBjQV76+BU3XFxf3pMLDy1qOx507d5jONAxDQ4cOUbVq96tmzTBNmPCxqbyWLRtZ6itfvpS6d+9ousZVq1bogQdqql696mrRoqEOHvzLVN7q1Sv1wAM1FRFRWb16xSglJcXmGqXb32ubGS8Z5dk7Vu6UaWa8pJOYaBj8y75/S5euMdav32qEhVVySN5ff50w1q/faiQmGsbJk/8aFSpUNLZs+cPuvISENOPUqctGYqJhXLx4zYiIqGOsWrXJdJ3vvjvG6NbtUaNVqzYO2e6goGDjn3/OOGy/PPZYD2P8+M+MxETDuHDhqnH8+AWHZf/7b4rh61vS2Lv3sN0ZBw4cM4KDyxhnzyYZiYmG0blzN2PixGl2523e/LsRFlbJOHMm0bh0KdmIjGxu7Ny5P8s5GR3PL7ww0Bg27F0jMdEwhg1713jxxUGm8rZu3WNs3/6n0ahRE2Pdut8cUuMPPyw1Ll1KNhITDePFFweZrjE+/pLl/6NGjTV69nzGVF5iomHs23fEaN78QaN06aAsH+sZZQ4e/KYxYsQou46XjPIWLVppREY2N86fv2IkJhrGoUOnTGfe/K9v3/7Ga68NM5XXrFlL4/vvFxmJiYYxd+5Co1GjJqbyataMMJYsWW0kJhrGhAmfGy+//JrNedZeq82MF2uZ9o4Za3lmxou1THvHzJ1+59kzZqzlmRkv1jLtHTO2/J7P6nixlmnvmLGWZ++YsfZepHPnbsYXX8wyEhMNo2fPZ4yPPppg8zZby9ywYZuxZ8+hLL+vsJY3d+5CIyEhzUhISDO6do1ySI03j5fnnnvR8pphb15iomGsW/ebERX1uOHl5WW6vujoGOOrr2bbNV6sZX766VTj0UefMC5fTs3SeLHlfWyHDp2NyZOnm66xQoWKxtate4zERMP48MPxRnR0jN15K1ZsMAICAo0dO/YZiYmG8corrxsTJkzJ0nN563ttM+Mlozx7x8qdMs2Ml5v/cYY2mzVs2Fg+Pj4Oy/P391eNGjUlSYUKFVJISJhOnDhud56bm5sKFrz+17rk5GQlJyfLzc3NVI3Hjx/TkiUL9eSTT5vKcZZ///1XGzasVUxMT0mSp6enihYt6rD8VatWqFy58goKCjaVk5KSov/++08pKSlKSkqSv//t39dsq3379qpOnXoqUKCAPDw81KhRE/3447ws52R0PC9c+IOio2MkSdHRMVqwYL6pvNDQMN1/f0iWa7tTZosWD8rD4/pF3uvUqafjx4+ZyitcuLDl/4mJiVkaM9ZeE15++UW9/fZIu8afo19nMsqbMuVTDRjwivLnzy9J8vX1dViNhmHo+++/U7duj5rKc3Nz0+XL188I/fvvpQy/4zwreQcO7FPDhtcvXNi8eUv98MNcm/OsvVabGS/WMu0dM9byzIwXa5n2jpk7/c6zZ8w4+nfonTLtHTOZ1WjPeLGWae+YsZZn75ix9l5kzZqV6tSpq6Tr4+Wnn2wfL9Yyq1evoeDgMjbnZJbXqtXDcnNzk5ubmyIi6mRpvFjLvDFeDMPQlSv/2XyMW8tLTU3VkCED9fbbI7OyyU55j2gtc8qUT/Xqq28oX77rrYqt4yWzGi9fvqw1a1aqXTvbz9Bay7x5vFy6dMnm92UZ5bm7uyt//vyqWPF+SVKzZi01f77tv2Nufa9tGIap8ZLRe3d7x8qdMs2Ml5vR0N5F/vnnsHbu3K7ateuayklNTVW9etVVpoyvmjVraTpv0KAXNGLESMuLkiO4ubmpffsH1aBBLU2dOtlU1qFDf6t48RJ65pmnVL9+DT377NNKTEx0UKXSnDnfZOmNRkZKlQrQ88+/pNDQIJUv76/ChYuoRYsH7c4LD6+sDRvW6ty5c0pKStLSpYt0/PhRUzXecPr0Kfn7+0u6/ibnzJnTDsl1li+/nKoHH2xtOmfo0CG6//7S+vbbmXrtteGmshYu/FH+/gGqWrWa6bpuNmnSONWpU1W9e8dmaWprRg4c2K+NG9epSZO6euihJtq69TcHVSlt2LBOvr4lVaFCRVM5I0d+pCFDBur++0tr8OCXNHz4u6bywsMra+HCHyVdn9Z77Jh9Y+bm12pHjRdHvf5nlmdmvNyaaXbM3JzniDFza32OGC83ZzpizGS0X8yOl5szHTFmbs4zM2ZufS9Stmx5FSlS1PLHlYCAwCz/8cHR72/ulJecnKxZs2aoZctWDsl85pmnVLasn/bv/1N9+vQ1lTdx4jg9/HB7y2uPI+obNmyI6tSpqkGDXtTVq1dNZx46dFBz536rhg0j1LFja/311wHTNUrSjz/OU2Rk83R/VLM3c/z4Kerc+WFVrBiob76ZoQEDXrE7LyKijpKTky0fE5k3b06Wxsut77XPnTtnarw44737nTLtHS830NDeJRISEvTYY100cuRHWR6kt3J3d9cvv+zQ/v3HtHXrZv3xx267sxYvXqASJXwdfpnvFSs2aOPGbZo3b7EmTRqv9evX2p2VmpqiHTu2qVevPtq0absKFPDSmDHvOaTOa9euadGiH9WpUzdTORcuXNCCBT/ojz8O6a+/TigpKVGzZn1ld15oaJj6939Z7dq1VMeOrVSlSjW5u+f411Jnu5EjR8jDw0NRUdGms4YOHaH9+4+qe/doTZo0zu6cpKQkjRw5Qq+/bq4pvtXTT/fR7t0H9csvO+Tn569XXx1gKi8lJUUXL17Q6tW/aMSIUXriiUdkOOii+bNnzzL9RyDp+lnk99//UPv3H9X773+oPn16msr79NOpmjRpvBo0qKWEhMvy9PTMcoYjX6udlWktz8x4ySjTzJi5Oc/Dw8P0mLm1PkeMl1szzY4Za/vFzHi5NdPsmLk1z8yYufW9yL59e29bJqtnBx35/iazvBdeeFYNGjRWgwaNHJI5adI0HTx4QiEhYZoz51u789avX6t582ZnqSnOrL5hw97V9u1/at2633Thwnl98MH7pjOvXr2q/Pnv1fr1W/TUU73Up0+sqbwb7B0vGWWOG/ehvv9+kQ4cOKbHH39Kr7zS3+68PXv+0PTp3+jll19U48Z1VKhQIUszmpmM3mtn9Npi63hxxnv3zDLtHS830NDeBZKTk/XYY13UvXu0OnTo7LDcokWLqlGjSC1btsTujE2bNmjhwh8VFlZGMTFRWrNmpWJjHzdd241pHb6+vmrfvlOWLvZyq1KlAhUQEGj5C16nTl21Y8c20zVK0s8/L1a1ajVVsmRJUzmrVi1XmTJlVaJECd1zzz1q376zfv11o6nMmJie2rhxm37+ea28vX1Mnw27wde3pOLj4yVJ8fHxKlEia1NRs8tXX03X4sULNHXqTNNTpm7WvftjWZomdKu//z6ow4cPqV69agoLK6Pjx4+pQYOaOnnypKm6SpYsKXd3d+XLl09PPdXL1JiRrv+1t337zpZpQvny5bP7IhE3S0lJ0Q8/fK+uXbubzpo5c7rlNbFz527autXcNoeEhOqnn37Whg1b1a3boypbtnyWHp/Ra7XZ8eLo139reWbGS2Y1ZnXM3JpndsxkVJ/Z8ZJRppkxY+05NDNeMso0M2YyyjM7ZqT/vRfZvPkXXbp00XKhnOPHj9n90RtHvL+5U9477wzT2bNn9P77HzgsU7reBHXp0j1LH3e4NW/t2lU6ePAvValSQWFhZZSUlKQqVSqYqs/f319ubm7Knz+/nnjiKbt/v9ycGRAQqI4du0iS2rfvpN27d5nKk66ftdy6dbNatWpjV303Z/7882L9/vtOy3vHrl272/W+7OYa69atr2XL1mnt2s1q0KCxze/LMnqvPWjQC3aPF2e8d79TpiPGCw2tizMMQ3369FRISJj69bP9L0PWnDlzxnIFy//++0+rVi1XSEio3XnDh7+rAweOae/ew5o+/Rs1adJMU6faf2ZRuv55q8uXL1v+v2LFzwoPt/+q0X5+fgoMLK39+/dJklavXqHQ0HBTNd7gqDNNpUsH6bffflFSUpIMw9Dq1SsUEhJmKvP06etTG48ePaIff/zeIXVK0sMPt9fMmdMlXX9z1KZNB4fkOtLPPy/Rhx++r++++1EFChQwnXfzVKiFC380NWYqV66if/45rb17D2vv3sMKCAjUhg3b5OfnZ6rGG02TdH3KVaVK5q603q5dR61Zs1LS9enH165dU/HixU1lStLKlddfcwICAk1n+fuX0rp1ayRdv3pk+fLm/mhzY8ykpaXp/fffVs+evW1+rLXXajPjxdGv/9byzIwXa5n2jpmM8syMGWv1mRkv1jLtHTN32s/2jhdrmfaOGWt59o6ZjN6LhIaGqXHjppo3b46k6+OlbVvbx4uj399Yy/viiylavnypvvhiVpana2aUef/9IZar5xqGoUWLftL999tWd0Z5NWrU0qFDJy3jpUCBAvr9d9uuzmttm2+MF8Mw9NNP87P0nsxaZtu2HbV69fXxsm7dGlWocL+pPEmaN2+2WrVqq3vvvdfm+qxlhoaG6d9/L+nAgf2SpJUrl9n8vsxajTfGy9WrV/XBB+/bPF4yeq89bdpMu8eLM967W8s0M15ulvfmGOawmJhHtW7dap07d1YVKwbqtdeGWS5GZI9NmzZo1qwZqlSpiuWS/UOHvqNWrR62K+/kyXjFxcUoNTVVaWlp6tLlEbVu7Ziv2nGU06dPKSqqk6Tr04UfeeQxPfigfXPubxg9+hPFxkbr2rVrKlu2nCZOnGa6zqSkJK1cuUwffzzJdFbt2nXVsWNXNWhQU+7uHqpWrYZiY+NMZUZHd9H58+fk4XGPPvhgvLy9vbOckdHxPGDAK3riiUf05ZefKzAwSF99NdtUnre3jwYM6KuzZ8+oc+c2qlq1un78campzNGj39XVq1fVrl1LSdcvdPPxxxPtzlu6dJH279+nfPnyKSgo2OYsa3lmXhOsZa5du1q7du2Qm5ubgoPLZOm4zCivR49Y9e4dq4iIyvL09NTkydOzdObO2nbb+5nzjPLGjftMAwc+r5SUFN17770aN872z9tnlJeQkKDJk8dLktq376wePZ6yOc/aa7WZ8WIt89q1q3aNGWt5Awf2s3u8WMv88svP7Rozjv6dZy1v9uxZdo8Xa5n2jpk7bbO948Vapr1jxlrewYMH7Boz1t6LhIaGKyYmSsOHv6Zq1Wpk6bXSWuaECR/rww9H6tSpk6pbt6oeeuhhTZgwxe68woU9FBQUrKZN60uSOnTorFdffcPuGlu1aqOWLRvp33//lWEYqlKlmsaO/dTUNtvLWl7r1s109uwZGYahqlWrZ+l3oLXM+vUbKjY2WuPGfaiCBQtq/PjM98md8qTr1zTp39/2z7lmljlu3Gd67LEuypcvn7y9vfXpp1NN5Q0ePFBLlixQWlqann66jyIjm2W51pu99db7do+XjNg7Vu6kX7/edo+Xm7klJjroQ08AAAAAAGQjphwDAAAAAFwSDS0AAAAAwCXR0AIAAAAAXBINLQAAAADAJdHQAgAAAABcEg0tAAAAAMAl0dACAPIMLy+3O/6Li3syp0t0mitXrsjLy02LFy/I6VIAAHAYj5wuAACA7HLwYLzl/0uWLND//V+vdLfdd999OVGWKWlpaTIMQ+7u7tm2zuTkZN1zzz3Ztj4AAKzhDC0AIM/w8/Oz/CtSpGgGtxWRJB058o8ef7ybSpUqqtKli6lbt/Y6fPiQJef1119Rw4YRmjbtM4WEBMnXt6D69n1GKSkpGjfuI1WoEKCgoOJ67bWXZRiG5XFly/pp5MgRiomJUokSXipfvpQmTPg4XY3nz59Xnz49FRxcQn5+hdW6dTPt3LnDcv+UKRMVFFRcCxb8oFq1wlW0qKcOHz6kX37ZqDZtWqh06WLy9y+iBx9srK1bf7M8LiysjCSpa9d28vJyU40aoem25WY31nHr9k6dOlnh4WXl7Z1fKSkpSktL08iRIxQeXlbFit2nOnWqau7c78zsIgAAsoSGFgCAm1y+fFmtWkWqaFFv/fzzOi1btl5FihRVu3YtdfXqVSSZy0kAAAVwSURBVMtyBw7s06pVyzV//hJ9+eW3+vrrL9WlS1vt27dXCxeu0IcfTtDYsaO1dOmidPkffjhS1arV1MaN2zVw4GC9+uoALVlyfZnU1FR17NhK58+f07x5i7V+/VbVrBmhNm2a6cyZM+lq/OijUZow4XNt2fKH/Pz8lZCQoB49YrV8+QatWvWLQkLC1Lnzw7p06ZIkad26683tlCkzdPBgvJYtW5+l52X//j+1YMEP+vrr77Vp0w65u7tr8OCB+u67r/Xxx5O0dese9es3QHFxMVq5crldzz0AAFnFlGMAAG4ya9YMFSjgpXHjJltu+/TTzxUY6KPly5eqTZv2N90+VV5eXgoLC1dkZHPt2LFNc+cukIeHh0JCQvXJJx9ozZpVatWqjeUxDRo0Vv/+gyRJFSver82bf9Enn3ygVq0e1rJlS/X3339p+fL18vT0lCSNGDFSixb9qNmzZ+nZZ/tJkq5du6aPP56k8PBKltwWLR5Mtx1jx36qefNma+XKZerUqauKFy8hSSpatKj8/Pyy/LykpKRoypQZ8vHxkSRdvHhREyd+ohUrNqhWrdqSpDJlymrz5k367LMJatasRZbXAQBAVtHQAgBwk+3bt2r//j/l61sw3e1JSUn6+++Dlp/LlCknLy8vy8++viUVEhImDw+PdLedOXM6XU7duvVv+3nkyBGSpB07turSpUsKDPRJt8yVK1fSrfu+++5L18xKUnx8vN5663WtX79GZ86cVmpqqpKSknT06JGsbL5VZcqUtTSzkvTHH78rOTlZrVs3TbdccnKy7r8/1CHrBAAgMzS0AADcJC0tTbVr19XkydNvu69Ysf99rvTWiyK5ublleFtaWlqW1h0QEKiFC1fcdl/hwkUs/y9QoMBt98fGPqakpCSNGvWxSpcOUv78+dWiRUNdu3btjuvMly9fus/5Steb0lsVKOCV7ucb2zV//hKVLJn+jO+Ns8sAADgbDS0AADepXr2mlixZIF/fkipUqJDD8zdv/uW2n0NCwizrfv/9t5U/f34FBpa2OdMwDG3atEGTJ0/XQw+1liQdP34s3dlhDw8Pubm5KTU1Nd1jixcvoVOnTqa7bdeuHcpMpUpV5OHhoWPHjuqBBxraXCsAAI7ERaEAALhJdHSMChYspO7dO2rD/2vv7kHajKIwjj8hmTNkSmoLBmzFxYRMSRexS7CUCgWhlYIpDgmihKA2HVwsfqAGIkJr/aBgQOngFDCgBESShsg71LFSjYlDDdQhi3Xt2lhKrVLKK//ffDnce7aHey73Y07l8pFyuR0NDUV1fFy5dv18fkezswkdHHzR4uJbra9/0MBATJIUDD6U1+tTV9djZbNbqlTKKhYLGh0dkWHs/ramxWJRU9Ndra2ltL//WYaxq1DoWd03RDabTQ0Nt7W9nVW1WlWtVpMktbU90MnJVyWTMyqVDrW8/E6ZTPqP53A4HOrri2p4OKrV1ZRKpUPt7X3SwsIbray8v2aXAAC4HAItAAA/sdvtymbzcrluqbv7iXy+FkUiL3R+/r1u7PeqYrGXMoyiAgGvJidfa2xsWh0djyRJVqtV6fSW/P77CodD8njuqafnqcrlo1/Gei9aWkrp9PSbAgGvenufKxzul9PpqlszNZXU5mZGzc131N7ulyS1tnqUSMxpfn5Ofr9HhUJesVj8UmcZH5/W4OArJRIT8vla1NkZ1MZGWo2N7it0BgCAv2c5O7vwcAYAAPwTbrdT8fiIIpH+/70VAABuBG5oAQAAAACmRKAFAAAAAJgSI8cAAAAAAFPihhYAAAAAYEoEWgAAAACAKRFoAQAAAACmRKAFAAAAAJgSgRYAAAAAYEoEWgAAAACAKf0ARMHRfDDsNb8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23beef6e438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"from math import floor\n",
"import matplotlib.pyplot as plt\n",
"from random import random, seed, shuffle\n",
"from SDSPSM import get_metrics, drawBarGraph, getPopulationStatistics\n",
"\n",
"seed(0)\n",
"\n",
"popMin = 1 # Min population\n",
"popMax = 40 # Max population\n",
"freqMax = 50 # freq of any set of population (for eg, no of occurances of temperatures at 25 deg C)\n",
"\n",
"def createRandomPopulation(N):\n",
" \"\"\"\n",
" Create a random distribution for N values\n",
" \"\"\"\n",
" population = []\n",
" population_freq = []\n",
" for i in range(0,N):\n",
" temp_freq = (floor(random() * freqMax)) # random frequency for each population\n",
" temp_list = [i]*temp_freq\n",
" population += temp_list\n",
" population_freq.append(temp_freq)\n",
" shuffle(population)\n",
" return population, population_freq\n",
"\n",
"population, population_freq = createRandomPopulation(popMax - popMin + 1)\n",
"\n",
"#mu, var, sigma = get_metrics(population) # just to cross check..\n",
"#print(mu, var, sigma) \n",
"\n",
"N, mu, var, sigma = getPopulationStatistics(population_freq, popMin)\n",
"\n",
"#visualize\n",
"backgroundColour = '#F5F5FF'\n",
"fig, (ax1) = plt.subplots(1,1, figsize=(16,3))\n",
"drawBarGraph(population_freq, ax1, [N, mu, var, sigma], 'Population Distribution','Temperature', 'Counts')\n",
"ax1.set_facecolor(backgroundColour)\n",
"fig.patch.set_facecolor(backgroundColour)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the above graph, we have temperature ranging from 1 deg C to 40 deg C, and each temperature with random frequency. For eg, 4 deg C happens about 10 times indicated by height of bar at Temperature=4 and Counts = 10. \n",
"\n",
"Summarizing, our population parameters: \n",
"\n",
"$$\n",
"\\color {blue}{ \\mu = \\mu_y = 20.64 \\\\ \\sigma^2 = \\sigma_y^2 = 128.17 \\\\ \\sigma = \\sigma_y = \\sqrt{128.17} = 11.32 } \\tag{4}\n",
"$$\n",
"\n",
"Let us visualize the density and PMF as usual.. "
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bedfd2320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"def mini_plot_SDSM(raw_list, bins, width=0.5): \n",
"\n",
" ax1.hist(raw_list, bins) \n",
" ax1.set_title('Distribution')\n",
" \n",
" n, bins,_ = ax2.hist(raw_list, bins, density=True) \n",
" ax2.set_title('Density')\n",
"\n",
" # probability mass\n",
" dummy_dict = {i:raw_list.count(i) for i in raw_list}\n",
" total = sum(list(dummy_dict.values()))\n",
" pmf = {key: round(val/total,4) for key, val in dummy_dict.items()}\n",
" ax3.bar(list(pmf.keys()), list(pmf.values()), width=width)\n",
" ax3.set_title('PMF')\n",
"\n",
"fig, (ax1,ax2,ax3) = plt.subplots(1,3,figsize=(15,4))\n",
"mini_plot_SDSM(population, popMax, width=1)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Statistical Outcomes: \n",
"\n",
">Let us randomly sample from the population. One trial/experiment is sampling about, say $n=10$ samples. Likewise, we sample for many experiments, say $N=2000$. \n",
"\n",
">This step is same as we did in Sample proportions case\n",
"\n",
"_Steps:_\n",
"* 1.Take a random sample of $n=10$ values from the population. Example sample output: $\\widehat{Y_1} = [33,20,40,1,22, \\cdots ,37]$ denoting our 1st sample of size $n=10$. **^** just indicates, its a statistical outcome\n",
"* 2.Take the mean of it and note down for kth experiment. $\\overline{\\widehat{Y_k}} = \\dfrac {1}{n} \\sum\\limits_{i=1}^n Y_{ki} = \\dfrac {1}{10} \\sum\\limits_{i=1}^{10} Y_{ki}$. Example sample output: $\\overline{\\widehat{Y_1}} = 11.34$\n",
"* 3.Do step 1 and 2 for $N=2000$ times. That is, $N=2000$ experiments $\\implies$ $2000$ mean values $\\overline{\\widehat{Y_k}}$, for $k = 0,1,2,3.... N$ \n",
"Example total output:\n",
"\n",
"|$\\widehat{Y_k}$|$\\overline{\\widehat{Y_k}}$|\n",
"|---|---|\n",
"|1|33.2|\n",
"|2|22.1|\n",
"|3|20.4|\n",
"|4|40.2|\n",
"|5|11.3|\n",
"|...|...|\n",
"|2000|23|"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"* 4.Take the frequency count of the samples and prepare a concise frequency chart., with each row of mean value against its frequency. \n",
"Example total output: \n",
"\n",
"|$\\overline{\\widehat{Y_j}}$|&nbsp; $n(\\overline{\\widehat{Y_j}})$|\n",
"|----|----|\n",
"|1| 8|\n",
"|2| 23|\n",
"|3| 65|\n",
"|...|...|\n",
"|39| 20|\n",
"|40| 5|\n",
"\n",
"* 5.Calculate probability for each row of above table, by simply taking the frequency divided by total outcomes.Note denomitor sums up to 2000 because, statistically we get 1 outcome per experiment (which is a mean), so total no of occurances after 2000 experiments would be 2000 outcomes (2000 means). \n",
"$\n",
"p\\Big(\\overline{\\widehat{Y_j}}\\Big) = \\dfrac {n\\Big(\\overline{\\widehat{Y_j}}\\Big)}{\\sum n\\Big(\\overline{\\widehat{Y_j}}\\Big)} = \\dfrac {n\\Big(\\overline{\\widehat{Y_j}}\\Big)}{2000} \n",
"$ \n",
"\n",
"|$\\overline{\\widehat{Y_j}}$|&nbsp; $n(\\overline{\\widehat{Y_j}})$|&nbsp; $p(\\overline{\\widehat{Y_j}})$|\n",
"|---|---|---|\n",
"|1| 8|0.0001|\n",
"|2| 23|0.002|\n",
"|3| 65|0.034|\n",
"|...|...|\n",
"|39| 20|0.002|\n",
"|40| 5|0.0002| "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
">From above table, one could draw the **probability mass function** which is a **discrete probability distribution** where one could find for any $k$, the probability $p(X=k)$ discretly\n",
"\n",
"* 6.Calculate mean, variance and SD as below.Suppose there are total M rows in the table. We would find that, \n",
"$\n",
"\\mu(\\overline{\\widehat{Y}}) = \\overline{\\overline{\\widehat{Y}}} = \\sum\\limits_{j=1}^M \\overline{\\widehat{Y_j}}p(\\overline{\\widehat{Y_j}}) \\approx \\color {blue}{19.69}\\\\ \\\\\n",
"\\sigma(\\overline{\\widehat{Y}})^2 = \\sum\\limits_{j=1}^M \\Big(\\overline{\\widehat{Y_j}} - \\mu(\\overline{\\widehat{Y}})\\Big)p(\\overline{\\widehat{Y_j}}) \\approx \\color {blue}{12.4631}\\\\ \\\\\n",
"\\therefore \\ \\ \\sigma(\\overline{\\widehat{Y}}) \\approx \\sqrt{12.4631} = \\color {blue}{3.5303} \\tag {5}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As usual, its much simpler programmatically"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"19.6139 13.0506 3.6126\n"
]
}
],
"source": [
"from random import choices \n",
"\n",
"N = 2000 # No of experiments\n",
"n = 10 # Sample size\n",
"\n",
"Y_hat = []\n",
"Y_mean_list = []\n",
"for each_experiment in range(N): \n",
" Y_hat = choices(population, k=n) \n",
" Y_mean = sum(Y_hat)/len(Y_hat)\n",
"# print(Y_mean)\n",
" Y_mean_list.append(Y_mean)\n",
" \n",
"mu, var, sigma = get_metrics(Y_mean_list)\n",
"print(mu, var, sigma)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A quick visualization of our resultant statistical outcome ```Y_mean_list```"
]
},
{
"cell_type": "code",
"execution_count": 79,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bee4b36d8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import matplotlib.pyplot as plt \n",
"\n",
"fig, (ax1,ax2,ax3) = plt.subplots(1,3,figsize=(15,4))\n",
"\n",
"mini_plot_SDSM(Y_mean_list,popMax )\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Notations and Conditions\n",
"\n",
"You could already see the resultant sampling distribution shaping up as normal. A visual summary is provided below where, normal distribution approximation is also applied. \n",
"\n",
"Back to variables, the complicated statistical notation are typically indicated by simpler notations as follows. We used former because we did not want to lose details for sake of simplicity.Now that we have the insight, we could swap with these simpler conventional notations. \n",
"\n",
">Note this is slightly different notation compared to Sample proportions case\n",
"\n",
"$$\n",
"\\color {blue}{\n",
"\\mu_\\overline{Y} = \\mu(\\overline{\\widehat{Y}}) \\\\ \\\\\n",
"\\sigma_\\overline{Y} = \\sigma(\\overline{\\widehat{Y}})\n",
"}\n",
"$$\n",
"\n",
"Comparing equations set $4$ and $5$, \n",
"\n",
"$$\n",
"\\color {blue} {\n",
"\\mu_\\overline{Y} \\approx 20.6 = \\mu \\\\ \\\\\n",
"\\sigma_\\overline{Y} \\approx 3.5303 \\approx \\dfrac{11.32}{\\sqrt{10}} = \\dfrac {\\sigma}{\\sqrt{n}} \\tag {3}\n",
"}\n",
"$$\n",
"\n",
">$\\overline{Y}$ is called the sample means. The resultant sampling distribution could be satisfactorily approximated by normal density function when sample size is sufficiently large. \n",
"\n",
"**Conditions:** \n",
">How much is sufficiently large? General thumb rule is $n > 30$. However, if population distribution is already normal, even if n is small, resultant sampling distribution would be normal. \n",
"\n",
"### Visual Summary"
]
},
{
"cell_type": "code",
"execution_count": 80,
"metadata": {},
"outputs": [
{
"data": {
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Awly5x7p1a08FBAwx7bFes2a1JCksbKROn86Ut7eH3n13tqZMufSq1Sv3WHfo4KMOHXyUkZEhSZoz53/6739HydvbQ+7ujdhjDQAAgHKFHBgAYIHYYw0AAACYYwUGAAAAAACweAQwAAAAAACAxSOAAQAAAAAALB4BDAAAAAAAYPEIYAAAAAAAAIt3T76FJDZ55TXP9XUdcAd7AhTten9HgbsZ8zMsHfMz7kU3+nvP/Iyyxtx872AFBgAAAAAAsHgEMAAAAAAAgMW75QBGSspx9er1gFq39pSvb3O9//4cSdLp06fVp8/DatGisfr0eVh//PFHqXUWAAAAAADcm245gFGxokGvvz5LP/64T99+u03z5r2vffv2atas6erW7UHt2nVI3bo9qFmzppdmfwEAAAAAwD3olgMYTk5OatWqtSSpRo0aatrUU2lpqVqzZpVCQsIkSSEhYYqLI6EKAAAAAAAomVJ5C8mxY0n65Zef1LZte2VknJCTk5OkS0GOkycziqwTETFPERHzJEmnTp0sjW6UKTLfAoBlYn4GAMvE/AzgZpU4ieeFCxcUHBygN998RzVr1ix2vREjRis+PkHx8Qmyt69b0m4AAAAAAIC7WIkCGLm5uQoODlBQUIj69x8kSXJwcFR6erokKT09XXXrOpS8lwAAAAAA4J52ywGMgoIC/ec/I9W0qafGjh1vOt67dz9FR0dKkqKjI+Xv37/kvQQAAAAAAPe0W86BsXXrD1q8eIGaN/dWhw4+kqRJk17XM8+8oOHDhygq6lO5uLhq4cLlpdZZAAAAAABwb7rlAEanTn7Kyioo8tyXX2685Q4BAAAAAABcrVTeQgIAloBs5gBgeZibAcAylcf5ucRvIQEAAAAAALjdCGAAAAAAAACLRwADAAAAAABYPAIYAAAAQDGsX79OPj5N5e3toZkzpxc6n5OTo9DQIHl7e6hr1/Y6dixJkpSZmalevR6Qg0N1jR8/xqxOz57d5OPTVB06+KhDBx9lZGTciaEAQLlEEk8AAADgBvLz8zV+/JOKjd0gZ2cXdenSVv7+/eTp6WUqExn5qWxta2v37sNavnyJwsMnKCpqqaytrRUePlV79/6qvXt/LdR2RES0Wrf2vZPDAYByiRUYAAAAwA0kJOyQu7uHGjZ0V+XKlRUYOFRxcavMysTFrVJISJgkaeDAQG3atFEFBQWysbFRp05+qlLFuiy6DgB3DQIYAGCBWKYMAJYlLS1VLi71TZ+dnV2Unp56zTIGg0E1a9ZSZmbmDdt+4ol/qUMHH02fPlUFBQVFlomImCc/P1/5+fnq1KmTJRgJAJRfBDAAwMJcXqa8YsVaJf4/9u48Lqp6/+P4a1gEBBQREQYQt1RUXHGpMM3MXcpcccOsrFveuprZYt5s00pb9Hfrtmlh7lJaam4t5pYLVO57LmymggqabMP8/uA6ObErMiO+n4+HD5lzvt9zPufL+Jnj53zPmbh9LFmygP3791m1uXqa8pgxY5k06VkAyzTlKVOmF7jt2bPnsXXrb2zd+hu+vr43/FhERCqKggoLBoPh761K0Mba7Nnz2LFjN+vWbWTz5o3Mn/9Fge1GjRrNpk2xbNoUi49PjRLHLSJSkaiAISJiZzRNWUTE/gQEBJKQEG95nZiYgJ+f0aqN0fhXm5ycHNLSLuDt7V3kdo3GAAA8PT0ZOHAIcXHbyzhyEZGKQwUMERE7o2nKIiL2p3XrNhw9epjjx4+RlZVFTMxCevWKsGrTq1cE8+ZFA7B0aQwdO3YucgZGTk4OZ8+eBSA7O5vVq1fQuHHTG3cQIiI3OX0LiYiInbmR05SNxgDS09MZMqQf8+d/wdChI/K1GzVqNKNGjQYgPFxPxRcRgbxi8dtv/4f77uuGyWRixIhRNG7chFdf/TetWoXRq1cEUVEP8fDDwwkNrU+1at5ERy+09A8JqU16ehpZWVksX76Mb75ZS61awdx3Xzeys7PJzTXRqVMXHnzwERsepYiIfVMBQ0TEzpRmmnJAQOB1TVMuqIAhIiIF6969J92797RaNmnSK5afXV1dmTt3SRFdZzAAACAASURBVIF99+8/XuDyzZvjyiw+EZGKTreQiIjYGU1TFhERERHJTzMwRETsjKYpi4iIiIjkpwKGiIgd0jRlERERERFruoVEREREREREROyeChgiIiIiIiIiYvdUwBARERERERERu6cChoiIiIiIiIjYPRUwRERERERERMTuqYAhIiIiIiIiInZPBQwRERERERERsXtOtg5AYPnJZbYO4ZahsRaRklK+KF8abxEpKeWL8qOxFnujGRgiIiIiIiIiYvdUwBARERERERERu6cChoiIiIiIiIjYPRUwRERERERERMTu6SGeIiIiIiIi10APuRQpXypgiBUlYRER+6PcLCIiIqJbSERERERERETkJqAChoiIiIiIiIjYPRUwRERERERERMTuqYAhIiIiIiIiInZPD/EUkeuihwuKiNgf5WYREamIVMAQERERERERKQcqMF8f3UIiIiIiIiIiInZPBQwRERERERERsXsqYIiIiIiIlNDatatp0aIhoaH1mT79jXzrMzMzGTFiEKGh9enYsR0nThwHICUlhR497sbX14Nx48ZY9fn11zjatAklNLQ+48c/idlsLo9DERG56aiAISIiIiJSAiaTiXHjnmDp0lXExe1jyZIF7N+/z6pNdPQsvLyqsXv3EcaMGcukSc8C4OrqyqRJrzJlyvR8233qqX/wn/98zK5dhzly5DBr164ul+MREbnZ6CGef6OHqpQ9jalI6a1du5oJE57CZDIRFfUw48c/Z7U+MzOTRx4Zwa+/xuHtXZ05cxYRHFyblJQUhg3rT1zcDoYNG8k77/zH0ufXX+MYPXokGRmX6datJ9OmzcBgMJT3oV0z5ZKypfEUKb3Y2O3UrVufOnXqAtC//2BWrPiakJDGljYrVnzNxImTAejbtz9PPz0Gs9mMu7s7d9wRztGjR6y2mZycTHp6Gu3a3Q7AkCEjWLFiGd269SifgyoDyidlS+MpUjjNwBARsTO6wiciYp+SkhIJDAyyvA4ICCQ5ObHQNk5OTlSpUpWUlJRCt5mcnIjRGGi1zaSkxHztZs/+mPDwMMLDwzh79sz1HoqIyE1JBQwRETtz9RW+SpUqWa7wXW3Fiq8ZOjQKyLvCt37991ZX+FxcXK3aX32Fz2AwWK7wiYhIyRX0bIr8M9lK0qa024RRo0azaVMsmzbF4uNTo/hgRUQqIBUwRETsjC2v8IGu8omIFCYgIJCEhHjL68TEBPz8jFZtjMa/2uTk5JCWdgFvb+9Ct2k0BpKUlGC1TX9/Y6HtRURuZSpgiIjYGVte4QNd5RMRKUzr1m04evQwx48fIysri5iYhfTqFWHVplevCObNiwZg6dIYOnbsXGR+9vf3x8PDk+3bt2I2m5k/fw69et13Q49DRORmpYd4iojYmdJc4QsICNQVPhGRcuLk5MTbb/+H++7rhslkYsSIUTRu3IRXX/03rVqF0atXBFFRD/Hww8MJDa1PtWreREcvtPQPCalNenoaWVlZLF++jG++WUtISGNmzPiv5SHLXbv2uKke4CkiUp5UwBARsTNXX+EzGgOIiVnIZ5/Nt2pz5Qpfu3a3l/oKX5s27Zg/fw6PPfbPG30oIiIVTvfuPenevafVskmTXrH87Orqyty5Swrsu3//8QKXt2oVRmzsnjKLUUSkolIBQ0TEzugKn4iIiIhIfipgiIjYIV3hExERERGxdl0P8XzssVEEB/sSFtbUsiw1NZXeve+lWbPb6N37Xs6dO3fdQYqIiIiIiIjIre26ChjDho1k2bLVVsvefvsNOnW6h127DtOp0z28/fYb1xWgiIiIiIiIiMh1FTDCw+/K99T7lSu/ZujQKACGDo1ixYpl17MLEREREREREZGyfwbG6dN/4O/vD+Q99f7MmdMFtps9+2Nmz/4YgLNnz5R1GCIiIiIiIiJSgVzXDIzrMWrUaDZtimXTplh8fGrYKgwRERERERERuQmUeQHD17cmycnJACQnJ1Ojhm9Z70JEREREREREbjFlXsDo2TOCefOiAZg3L5peve4r612IiIiIiIiIyC3mugoYUVGR3H337Rw+fJDbbgskOnoWTz/9HD/8sI5mzW7jhx/W8fTTz5VVrCIiIiIiIiJyi7quh3hGRy8ocPm3335/PZsVEREREREREbFis4d4ioiIiIiIiIiUlAoYIiIiIiIiImL3VMAQEREREREREbunAoaIiIiIiIiI2D0VMERERERERETE7qmAISIiIiIiIiJ2TwUMEREREREREbF7KmCIiIiIiIiIiN1TAUNERERERERE7J4KGCIiIiIiIiJi91TAEBERERERERG7pwKGiIiIiIiIiNg9FTBERERERERExO6pgCEiIiIiIiIids/J1gGIiNgD58t/ct/0l3E05QCw8p/PcbF6DRtHJSJya2ny4xqa/rS2wHU5Ts5crlKVs0G1cegVRG791uUcXZ61a1czYcJTmEwmoqIeZvz456zWZ2Zm8sgjI/j11zi8vaszZ84igoNrAzBt2lTmzJmFo6Mj06bN5N57uwEQElIbDw9PHB0dcXJyYtOm2PI+LBGREjPk5hK4bxfGQ/uonnACl0sXcczOJtvVDWfjfHIbtCGnfQTmwIZlvm/NwBARAYJ3/WIpXgDU+XW7DaPJO0Fu0aIhoaH1mT79jXzrMzMzGTFiEKGh9enYsR0nThy3rJs2bSqhofVp0aIh69atsSwPCalNmzahtG/fgvDwsPI4DBGRa3bZ3dPyJ6OyBw4mE56pZ6mzMxbXKQNxXjaj3GMymUyMG/cES5euIi5uH0uWLGD//n1WbaKjZ+HlVY3du48wZsxYJk16FoD9+/cRE7OQ2Ni9LFu2mrFjH8dkMln6rVr1I1u3/qbihYjYterxJ+j+/lvcEfMFtXfF4Zl6FsfsbHJcXKh0+RKOR+Jw/vZD3P7dk0rvPw45WWW6f83AEBEB6v66DYBDbcNpsH0TdX6LZU/nHjaJ5coJ8vLl6wgICKRDhzb06hVBSEhjS5urT5CXLFnIpEnPMmfOIqsT5OTkJHr37sLOnYdwdHQE8k6QfXx8bHJcIiKl8c0zk61eG3JzqZ5wgparluGdnIDzNzMxNQ0v15kYsbHbqVu3PnXq1AWgf//BrFjxtVV+XrHiayZOzIu9b9/+PP30GMxmMytWfE3//oNxcXGhdu061K1bn9jY7bRrd3u5xS8icj2MB/dyx+I5OJpyyHSrzIE7OpHQuJll1rIhN5cIc30c49bg9ONcnOLWkJWVAU6VyiwGzcAQkVtetaQEqp1KIsvVjZ339uZiteq4XUzD7/ABm8Rz9QlypUqVLCfIV1ux4muGDo0C8k6Q16//vsgTZBGRm53ZwYGzteqwafCDlmWOv35XrjEkJSUSGBhkeR0QEEhycmKhbZycnKhSpSopKSkkJ+fvm5SU19dgMBAR0ZU772zN7NkfF7jv2bM/Jjw8jPDwMM6ePVPWhyYiUiSPlDO0+2o+jqYcLtSoyZrHnuZAh3usbrk2OziQW6cZ2f2f4fKbP5HTskuZx6EChojc8ur8b/bFySYtyHV25nizvKt5V2ZllDdbniCDTpJFxL5druqF2aNa3ouMP8t132azOd8yg8Hw91YFtimq7/ffb2bLll9YunQVH330Pps2bcjXdtSo0WzaFMumTbH4+OgZTSJSvkJ/WEWlzAxynJzYNOhBLlf1KrqDhxdZ//wI3DzLNA4VMETkluaQnU3w7l8BON689f/+DsOMAeOhfXDhbLnHZMsTZNBJsojYN7e0CxgungPA7FenXPcdEBBIQkK85XViYgJ+fkarNkbjX21ycnJIS7uAt7e31fIrff398/pe+dvX15eIiL6aOScidsXlYjqB+3YBcDK0FRdLc36Y7xz2+qiAISK3tKD9u6iUcZl0bx9SauWdCF/yrs6ZWnVwyM3F6eel5R6TTpBFRPIz5OZSPf44dy78DABzlerk3PlAucbQunUbjh49zPHjx8jKyiImZiG9ekVYtenVK4J586IBWLo0ho4dO2MwGOjVK4KYmIVkZmZy/Pgxjh49TFhYWy5dukR6ejoAly5d4vvv19K4cdNyPS4RkaL4HjuCw/8ukiWEhNo0Fj3EU0RuaXV+yftP/PHm1t/KcaJ5a3xP/o7TxiXkdH+kXGO6+gTZaAwgJmYhn30236rNlRPkdu1uz3eC/OCDQ3jyyXEkJydZnSDn5ubi6elpOUF+7rl/l+txiYiURsS0yZafDWYzlS7/iYM5lywXV3La30f2A09D5SrlGpOTkxNvv/0f7ruvGyaTiREjRtG4cRNeffXftGoVRq9eEURFPcTDDw8nNLQ+1ap5Ex29EIDGjZvQr99AWrdujJOTE++88z6Ojo6cPv0Hgwf3BcBkymHgwCF07dq9XI9LRKQoVc+csvx8zi/AhpGogCFiM8tPLrN1CLc899QUfI8fxYzB8tyLK042aUHLVctwSj6Kw5G4cn3KvU6QRWxL+dk+uF1KL3C5U3YW5svpGNLOYvYp/xPp7t170r17T6tlkya9YvnZ1dWVuXOXFNh3woSJTJgw0WpZnTp12bZtZ9kHKiJSRlz+/Ot5Q1lulW0YiQoYInILq/PrdgyYOR1clz+reVuty3F1JbFRU4L3/IrTxhiyyrGAATpBFhFZNPltq9cO2dlUOXua27Zvou6vP+CwdxNZj83A1KqrjSIUkfKk4rIt5X/Gmq3oGRgicmvKzaXOzh1A/ttHrjjeIm+54/aVkHGp3EITEZH8cp2dOe8fwI77BpHTqiuGnCwqzZoAlwueqSEiImUjs7K75edKl8v325/+TjMwROSW5Hf0IJXTLgDQ9pvFtP1mcaFtDZmXcNzxLaYOA8orPBERKULOXYNw+mUthsvpOO5aj6ldH1uHJCJSYV2o4Wf5udqpRJKrVLVZLJqBISK3pLq/lO4bOJw2Fny7hoiIlD9z9b+efWE4m2DDSEREKr7TdeqT+7+vQw3cv9umsWgGhojcclwuXcR4cC8AmwdGcapew0Lb9nIKwfXVvjgeicOQfBSzf73yClNERAphOPfXE/Gp5Ga7QEREbgGZHp4khDSj1r6d1Nr9K/vv7MxFnxol62w2w/+KH2VBMzBE5JYTvDMOx1wTWS6uJDVoTI6LS6F/cus0I/d/RQvNwhARsQ9O276x/JxbJ9SGkYiI3Bp2d+5BdiUXnHKyCV/0OW7/uxW7UJcuUOn9x8v8OUUqYIjILafur3m3jyQ2akquU/ET0UxhPQBw2rIUTDk3NDYRESmca3oaTb9fhdPmrwAw1WtJbr1WNo5KRKTiu+hTg219IzE5OlL1zCm6fvg2jTb9gEfKWUsbQ24uhhN7cV76Lm7PdsIpbk2Zx6FbSETkllI9/gRVz+RNPY5v3LxEfXLa9MR5+X8wpJ3FcdePmFreeyNDFBERIGLaZKvXjjnZVMrMsLzODWxI1uPvl+nUZBERKVxiSCjro/5B22UL8Uw9S/PvVtL8u5WYHB3JqeSCc8ZlHMx5X7lqNhjIadenzG/zUwFDRG4pdX7dBkCWiyt/1GtQoj7mwIbk+tfHIfkIjhuXqIAhIlIO3C5ZTzs2OThy2cOT8zWNeHeIwnRHX3CqZKPoRERuTWdr1WHVmGcJ3LsT46F9VE88iculizhlZpLlVhnngBByG7Yl5/a+mP3rlvn+VcAQkVtKbMRAYiMGlrpfxutlPwVORESs7b27G3vv7lZsuz617i+HaEREpCBmBwfiQ1sSH9oy37obnZ/1DAwRERERERERsXsqYIiIiIiIiIiI3VMBQ0RERERERETsngoYIiIiIiIiImL3VMAQEREREREREbunAoaIiIiIiIiI2D0VMERERERERETE7qmAISIiIiIiIiJ2TwUMEREREREREbF7KmCIiIiIiIiIiN1TAUNERERERERE7J4KGCIiIiIiIiJi91TAEBERERERERG7pwKGiIiIiIiIiNg9FTBERERERERExO7dsALG2rWradGiIaGh9Zk+/Y0btRsRkQqpuByamZnJiBGDCA2tT8eO7Thx4rhl3bRpUwkNrU+LFg1Zt25NibcpIiLFU34WEbGdG1LAMJlMjBv3BEuXriIubh9Llixg//59N2JXIiIVTklyaHT0LLy8qrF79xHGjBnLpEnPArB//z5iYhYSG7uXZctWM3bs45hMJuVlEZEyoPwsImJbN6SAERu7nbp161OnTl0qVapE//6DWbHi6xuxKxGRCqckOXTFiq8ZOjQKgL59+7N+/feYzWZWrPia/v0H4+LiQu3adahbtz6xsduVl0VEyoDys4iIbTndiI0mJSUSGBhkeR0QEEhs7DarNrNnf8zs2R8DcOjQAcLDw0q9n7Nnz+DjU+P6gi1Diqd49haT4imareJ5k9cKXG6LeAqLBYqO5+TJ49e8z5Lk0KvbODk5UaVKVVJSUkhOTqRNm/ZWfZOSEgGK3eYVys83nuIpmuIpmr3lZij/mIqKBSpmfi6L3Px39vTeViyFs6d4FEvBbB3L1TnRnmKBksdT0tx8QwoYZrM53zKDwWD1etSo0YwaNfq69hMeHsamTbHXtY2ypHiKZ28xKZ6iKZ6i3ah4SpJDoeA2hfXNzc0twTbzKD/feIqnaIqnaPYWD9hfTBUxP5dFbv47e/q9KZbC2VM8iqVgiqVwZR3PDbmFJCAgkISEeMvrxMQE/PyMN2JXIiIVTklyqNH4V5ucnBzS0i7g7e1ttfxKX39/o/KyiEgZUH4WEbGtG1LAaN26DUePHub48WNkZWURE7OQXr0ibsSuREQqnJLk0F69Ipg3LxqApUtj6NixMwaDgV69IoiJWUhmZibHjx/j6NHDhIW1VV4WESkDys8iIrblOHHi5MllvVEHBwfq1buNhx4axocf/h+RkcO4//5+Zb0bAFq2bH1DtnutFE/x7C0mxVM0xVO0GxFPYTn01Vf/zcWL6TRo0JCmTZuxaNE8XnrpBXbt+o2ZMz+kWrVq1Kjhy7lzqTzxxMMsXjyf6dP/j9tua1CuefmKW+F3dT0UT9EUT9HsLR6wv5iUn0vGnn5viqVw9hSPYimYYilcWcZjuHSpgBvyRERERERERETsyA25hUREREREREREpCypgCEiIiIiIiIidu+mLWCsXbuaFi0aEhpan+nT37B1OISE1KZNm1Dat29RJt/LXVqPPTaK4GBfwsKaWpalpqbSu/e9NGt2G71738u5c+dsGs/rr0+mfv0A2rdvQfv2LVi9+ttyiychIZ4ePe6mVasQwsKa8P77MwDbjVFh8dhqjDIyMrjrrra0a9ecsLAmvPbaSwAcP36Mjh3b0azZbYwYMYisrCybxjN69EgaN65jGZ+dO38rl3iuMJlM3H57S/r16w3Ybnzsmb3lZlB+Lkk8ys/Fx6P8XHQ8ys83F3vL1bbM0/aUo+0pP9tTblZeLn0stszJNzof35TPwDCZTDRv3oDly9cREBBIhw5t+PzzBYSENLZZTCEhtdm4MRYfHx+b7H/Tpg24u3vwyCMjiI3dA8DEiROoVs2b8eOfY/r0Nzh//hyvvfamzeJ5/fXJuLt78K9/jS+XGK6WnJzMqVPJtGzZivT0dMLDW7Nw4TLmzv3cJmNUWDxffbXYJmNkNpu5dOkSHh4eZGdn06VLONOmzeD//u8dIiIeYMCAwTz55GOEhjbnkUf+YbN4Pv30Q3r06E3fvv1veAwFmTnzHX75JZb09DS+/HIFw4cPtMn42Ct7zM2g/FySeJSfi49H+bnoeJSfbx72mKttmaftKUfbU362p9ysvFz6WGyZk290Pr4pZ2DExm6nbt361KlTl0qVKtG//2BWrPja1mHZVHj4XXh7e1stW7nya4YOjQJg6NAoVqxYZtN4bMnf35+WLVsB4OnpScOGISQlJdpsjAqLx1YMBgMeHh4AZGdnk52djcFg4KeffrAkvqFDo1i+vHzGp7B4bCkxMYHVq1cycuTDQN4Hhq3Gx14pNxdM+bloys9FU34unvJz6ShXW7OnHG1P+dmecrPyculjsZXyyMc3ZQEjKSmRwMAgy+uAgECSk233Joa8N09ERFfuvLM1s2d/bNNYrjh9+g/8/f2BvH/4Z86ctnFE8NFH/6Ft22Y89tiocp0yfbUTJ46zc+evtGnTzi7G6Op4wHZjZDKZaN++BbVr+9K5873UqVOPqlW9cHJyAvL+nZXnh8Xf47kyPi+/PJG2bZsxYcJYMjMzyy2eCRP+xeuvv4WDQ17aTElJsen42CN7zM2g/FxSys9FxwPKz4XFo/x8c7HHXG1vedoe8s/VbJ2f7Sk3Ky8XH4stc3J55OObsoBhLuCuF1tX/7//fjNbtvzC0qWr+Oij99m0aYNN47FHDz/8D/bsOcrWrb/h5+fP888/Xe4xXLx4kSFD+vHWW+9RpUqVct9/cfHYcowcHR3ZuvU3Dh1KIC5uOwcP7s/Xpjz/nf09nr179/Dyy1P59dcDbNy4g3PnUnnnnfKZcr9q1Qpq1PC1+g5re8xDtmavY6L8XDzl5+LjUX4uPB7l55uLPY6P8nThbJ2f7Sk3Ky+XLBZb5eTyysc3ZQEjICCQhIR4y+vExAT8/Iw2jAj8/fP27+vrS0REX2Jjt9s0nrxYapKcnAzk3TtWo4avTeOpWbMmjo6OODg48OCDj5T7GGVnZzNkSD8GDRrKffc9ANh2jAqKx9ZjBODl5UWHDp3Yvn0rFy6cJycnB8j7d3blfW6LeNatW42/vz8GgwEXFxeGD3+w3Mbn5583s3LlN4SE1CYqajA//fQDEyb8yy7Gx57YY24G5eeSsHXuUX4uGeXn/JSfS88ec7W95Wl7ytG2zD32lJuVl0sei61ycnnl45uygNG6dRuOHj3M8ePHyMrKIiZmIb16RdgsnkuXLpGenm75+fvv19K4cdNiet14PXtGMG9eNADz5kXTq9d9No3nSrID+OabpTRpUn5jZDab+cc/HqJhwxCefHKcZbmtxqiweGw1RmfOnOH8+fMAXL58mR9//I5GjUK46667Wbo0Bsgbn969y2d8CoqnYcNGlvExm80sX76s3P6dvfLKVA4fTmD//uNERy+kY8fOfPbZPJuNj72yt9wMys8lpfxcfDzKz4XHo/x8c7G3XG2PedqecrStco895Wbl5dLFYqucXF75+Kb8FhKA1au/5dln/4XJZGLEiFFMmDDRZrEcO/Y7gwf3BcBkymHgwCHlHk9UVCQbN64nJeUsvr41efHFl+nd+36GDx9IQsJJAgNrMXfuknJ7MFBB8WzYsJ5du37DYDAQHFybmTM/stxDd6Nt2bKJe+/tQJMmoZZ7siZPnkKbNu1sMkaFxbNkyQKbjNHu3bsYPToKk8lEbm4u/foN5Pnn/82xY78TFTWYc+dSad68JbNmzcXFxcVm8fTo0ZmzZ89gNptp1qwFM2d+aHlwUXnZsGE9M2ZM58svV9hsfOyZPeVmUH4uaTzKz8XHo/xcdDzKzzcXe8rVts7T9pSj7Sk/21NuVl4ufSy2zsk3Mh/ftAUMEREREREREbl13JS3kIiIiIiIiIjIrUUFDBERERERERGxeypgiIiIiIiIiIjdUwFDREREREREROyeChgiIiIiIiIiYvdUwBARERERERERu6cChoiIiIiIiIjYPRUwRERERERERMTuqYAhIiIiIiIiInZPBQwRERERERERsXsqYIiIiIiIiIiI3VMBQ0RERERERETsngoYIiIiIiIi12Dhwnn06dP1mvqGhTVhw4b117X/11+fzKhRw65rGyUVElKbH3747pr6du/eic8//7TAdfHxJ/H19cBkMuVrez3jKxWTChgiIiIiIlIhbdmyic6d78DfvyqBgd7cc8+dxMXtAOCLLz6nS5fwEm/rxInjuLsbyMnJsSwbPHgoy5evLbbv6NEjefnlF62Wxcbu5a67OpV4/6W1YcN6PDwc8PX1oGZNT1q0aMicOZ/dsP1dq6CgWpw+fRFHR8d86/4+vu7uBo4ePXJN+9mwYT3u7gYiIx+wWr5r107c3Q10797pmrYr5cvJ1gGIiIiIiIiUtbS0NPr378177/2Xfv0GkpWVxebNG6lUycXWoZUbf38jhw8nYDabWbHia4YO7U+bNu0ICWls1S4nJwcnp4r/X0Mfnxps3bqFlJQUqlevDsC8edHcdlsDG0cmJaUZGCIiIiIiUuEcOXIIgIEDI3F0dMTNzY0uXboSGtqMAwf289RTj7Ft28/4+npgNHoBsHr1Sm6/vSV+flVo0CCI11+fbNle1653AWA0euHr68G2bT9bzeIwm81MmDCW4GBf/P2r0rZtM/bu3cPs2R+zaNE83n33LXx9Pejfvw9gfUuGyWRi2rQpNG1aj5o1PbnzztYkJMQDMH78UzRoEISfXxXuvLM1mzdvLPVYGAwG+vS5n2rVqnHgwD7LbJLo6Fk0bFiLnj07A7By5TeEhTXBaPSie/dOHDiw32o7cXE7aN26MQEB1Xj00QfJyMgA4Ny5c/Tr15vg4BoEBFSjX7/eJCYmWPX9/fej3HVXW/z9qzJw4H2kpqYCBc9sueLq8b0y/u3bN8fX14OYmEWEhTXl22+XW9pnZ2dTq5YPO3f+VuA4VKpUiT597icmZiGQN+5ffbWYQYOGWrUrasxjY7cTHh6Gn18VateuybPPjgMgIyODUaOGERRUHaPRiw4d2vDHH38U9WuRa6AChoiIiIiIVDj16zfA0dGRRx6JYs2aVZw7d86yrlGjEGbM+JB27W7n9OmLJCWdB6ByZXc++WQOSUnn+fLLlXzyyX9ZvnwZAGvXbgAgKek8p09fpF2726329913a9m8eQM7dx4iKek8c+Yswtu7OqNGjWbQoKGMHTuB06cvEhOznL+bOfMdFi9ewFdffcupU2n897+zcXOrDEDr1m34+effSEhIZeDAIQwbNsBSOCip3NxcvvlmKefPn6dJk1DL8o0bf+KXX/bzoCGa9AAAIABJREFU9ddrOHz4ECNHRvLmm+9x4sQZunbtyYABfcjKyrK0X7RoHl9/vYbdu49y5Mgh3nzzNcv2hw9/kP37T3DgwEnc3NwYN26MVQzz58/hv/+dzZEjSTg5OTF+/JOlOoYr4791605On75I//6DGDJkBAsXzrW0WbPmW2rW9Kd58xaFbmfIkBHMnz8HgHXr1hAS0gR/f6NVm6LG/JlnnuLxx5/i1Kk09uw5Sr9+A4G8mRxpaRc4eDCe+PgUZs78EDc3t1IdoxRPBQwREREREalwqlSpwrp1mzAYDIwZ8wjBwTUYMCCiyKvid93ViaZNQ3FwcCA0tBkDBkSyceNPJdqfs7MzFy+mc+jQAcxmM40aheDv71+ivtHRn/LSS6/RoEFDDAYDzZo1t9ziEBk5jOrVq+Pk5MRTTz1NVlYmhw4dLNF2k5OTMBq9qFXLhylTXubTT7+gQYOGlvUTJ07G3d0dNzc3vvxyEd279+Kee+7F2dmZf/1rPJcvX2br1i2W9o89NobAwCC8vb155pmJLFmyAIDq1atz//39qFy5Mp6enjzzzEQ2bbIet8jI4TRp0hR3d3cmTXqVr75abHlw57WKjBzGmjXfkpaWBsCCBV8QGTm8yD7t29/BuXOpHDp0kAUL5jBkyIgCt1vYmDs7O/P770c4e/YsHh4etG3bHgAnJ2dSU1M4evQIjo6OtGzZmipVqlzX8Ul+KmCIiIiIiEiF1KhRCB9//DmHDyewY8cekpOTmDDhX4W237FjGz163E1wcA38/asya9aHpKScLdG+OnXqzKOPjmHs2CeoU6cmY8aMtvzHujgJCfHUqVOvwHUzZrxNq1Yh+PtXxWj04sKFCyWOyd/fSFLSeRISUtm69TcGDBhstT4wMMjyc3JyEkFBwZbXDg4OBAYGkZSUWGD7WrWCSU5OAuDPP//kn/98lEaNgvHzq0K3bndx/vx5qwLF3/tmZ2dz9mzJjqOo42vf/k6WLfuS8+fPs3btKgYPHlpsv8jI4Xz00X/46acfiYjom299UWP+wQezOHz4EK1aNaJDhzasWrUCgCFDhtOlSzdGjhxMvXpGJk6cQHZ29nUdn+SnAoaIiIiIiFR4DRs2YtiwkezbtwfIey7E3z344BB69ozg4MF4kpMv8NBDj2E2mwtt/3ePP/4kmzfHsWPHXo4cOcR7700rUd/AwCCOHTuab/nmzRt55503mTNnMYmJ50hKOk/VqlUtMV2vq+Py9zcSH3/C8tpsNpOQEI/RGGBZduW5HJD39adXbr2YOfNtDh8+yPr12zh1Ko01azZYtlFYX2dnZ3x8fK77GIYOjWLhwrksXbqEtm1vt4q3MJGRw/n44w/o1q0nlStXtlpX3JjXr38b0dELOH78NOPGPcvQof25dOkSzs7OvPDCS8TF7eOHH7awevUKy60qUnZUwBARERERkQrn4MEDzJjxtuVhkgkJ8SxZssAy5d/XtyaJiQlWz3hIT0+nWjVvXF1diY3dzuLF8y3rfHxq4ODgwLFjvxe4v7i4HezYsY3s7Gzc3d1xcXG1fDWor2/NQvsBREU9zCuvTOLIkcOYzWZ2795FSkoK6enpODk54eNTg5ycHKZOfaXEszpK64EHBrJ69Up+/PF7srOzmTHjbVxcXGjf/g5Lm48+ep/ExARSU1OZPn0K/foNAvLGzdXVDS8vL1JTU5k69eV821+4cC779+/jzz//5LXX/s399/cv8KtTi1LQOPbpcz87d/7C++/PKPB2kILUrl2HNWt+YvLk1/OtK27MFyyYy5kzZ3BwcKBq1byHvzo6OvLTTz+yZ89uTCYTnp5VcHJyxsGhdMcnxVMBQ0REREREKhxPT09iY7fRsWM7atRwp1On9jRu3JSpU98G8m75CAlpQt26ftSqlTcT4L33PuC11/5NzZqeTJ36iuUBjQCVK1dmwoSJdOlyJ0ajF9u3b7XaX1paGk888QgBAdUICQnG27s6Tz01HoCoqIc4cGAfRqMXgwbdny/WJ58cR79+A4mI6IqfXxUef/whMjIuc++93ejatQctWjSgUaNgXFxcrW7FKEsNGjRk1qy5jB//T2rV8mHVquUsWbKcSpUqWdoMHDiEiIiuNG1al9q16/Lssy8CMGbMv8jIuEytWj7cfXd77r23e77tR0YO59FHR1K3rh8ZGRlMnz6z1DFOnDiZ0aOjMBq9+PLLxQC4ublx3339OHHiGPfd90CJt3XHHeH5Ht4JFDvm69atJiysCb6+HkyY8BTR0QtxdXXljz9OMWxYf/z8qtCqVQgdOnQkMnJYqY9Rima4dKmM5h+JiIiIiIiIlLOpU1/h8OFDzJ49t/jGclNzsnUAIiIiIiIiItciNTWV6OhZfPrpF7YORcqBbiERERERERGRm85nn31Cw4ZBdO3ag/Dwu2wdjpQD3UIiIiIiIiIiInZPMzBERERERERExO6pgCFlYuHCefTp0/Wa+oaFNWHDhvXXtf/XX5/MqFHX95RfX1+PIr/eqjSmTZvC448/DMCJE8dxdzeQk5NTJtuOjz+Jr68HJpOpTLYnIqWnnHdruf/+HsydG23rMMrM9bx/RaRiePLJx3jjjVdvyLb3799HeHjYDdl2QSIjH2Dt2tXltj+xLRUwbhFbtmyic+c78PevSmCgN/fccydxcTsA+OKLz+nSJbzE2yroP+SDBw9l+fK1xfYdPXokL7/8otWy2Ni93HVXpxLvv7Q2bFiPh4cDvr4e+Pp6cNttgQwfPtBy/FecPn2ROnXqFrut224LLHafzzzzAh988Ol1xX1FSEhtfvjhO8vroKBanD59sdTfmy1yK1HOK5ucV5ZKO+4F9ff0dLQcV+PGdXj00Qc5fPhQGUZZsGXLVjFsWJQljus5jtGjR+LlVclyHL6+HsTELCqrUPO5nveviNwYISG1qV7dzSoPJCcn3bD9FZS3Zs78kOeem3RD9vfqq5MsXx8L1sdbu3ZNHn30QS5evAhA9+6dcHc3sGvXTqttDBp0P+7uBkvB//XXJ1O1qrPVmL3zzlsAPP30c7z88sQbcixif1TAuAWkpaXRv39vHnvsnyQkpHL4cCLPP/8SlSq52Dq0cuPvb+T06Yv88Uc669dvpUGDRtx7bwd+/PH7Mt9XWc20EJFro5xXvjkPwGw2k5ube0O2fbV27W7n9OmLJCdfYMWK73BzcyM8vDV79+654fsuS2PHTuD06YuWP/37D7J1SCJSzpYsWW6VB/z9jbYOqUwkJyezYcOP9Olzv9XyK8e7ZcsvxMXt4M03X7Osu+22BsyfP8fyOiUlhe3bt+LjU8NqG/36DbIas3HjJgAQFtaW9PQ0fvkl9gYemdgLFTBuAUeO5F2dGjgwEkdHR9zc3OjSpSuhoc04cGA/Tz31GNu2/YyvrwdGoxcAq1ev5PbbW+LnV4UGDYJ4/fXJlu117Zr3hF+j0QtfXw+2bfvZqrJrNpuZMGEswcG++PtXpW3bZuzdu4fZsz9m0aJ5vPvuW/j6etC/fx/AeoaByWRi2rQpNG1aj5o1PbnzztYkJMQDMH78UzRoEISfXxXuvLM1mzdvLPVYGAwGAgICmTTpFUaOfJhJk561rHN3N3D06JH/Hf+3tG7dmJo1PalfP4D33pvOpUuX6Nu3B8nJSVbV8tdfn8zQof0ZNWoYfn5VmDv38wKnd8+ZM5t69YzUrevPjBlvW5b//Qrt1bM8HnpoOPHxJxkwoI+l0vz3q2nJyUkMGBBBYKA3oaH1+eyzTyzbev31yQwfPpCHHx5BzZqehIU1UXKXCk857y/Xk/OuWLHia9q3b4GfXxWaNq1nmabbvXsnJk+eyD333ImPT2WOHfudCxcu8I9/PETduv7Urx/Ayy+/iMlkKnTcMzMzef758TRsWIvatWvy5JOPcfny5WKPy9HRkbp16/Heex8QHt6RKVP++n1t376Vzp3vwGj0ol275la363Tv3olXXpnEPffcSc2anvTp05WzZ88CkJGRwahRwwgKqo7R6EWHDm34448/LP0+//zTAo8jLm4HtWvXtCpeL1v2Je3btyjlb8v6dwLWnw9XPhtmzHib4GBf6tb1Z86czyxtL1++zHPPPU2jRsH4+1elS5dwLl++XOz7F2Dr1i106NAGf/+qdOjQhq1bt5RozESkbBU00/fqz4zizusSEuKJjHyA4OAaBAVVZ9y4MYXm37+ff3722SeEhtYnMNCbAQMirGaEuLsb+PTTD2nW7DYCAqoxduwTmAv5HogfflhH8+atcHV1LXC90RhA16492Lfvr8LzoEFD+fLLRZbbo5csWUBERF8qVapU4rHr0KETq1evLHF7uXmpgHELqF+/AY6OjjzySBRr1qzi3LlzlnWNGoUwY8aHlqtaSUnnAahc2Z1PPplDUtJ5vvxyJZ988l+WL18GwNq1GwBISjrP6dMXadfudqv9fffdWjZv3sDOnYdISjrPnDmL8PauzqhRoxk0aKjlylNMzPJ8sc6c+Q6LFy/gq6++5dSpNP7739m4uVUGoHXrNvz8828kJKQycOAQhg0bQEZGxjWPS0TEA/z22y9cunQp37rHH3+ImTM/4o8/0tmxYw8dO3bG3d2dpUtXWa5sXl0tX7Hia/r27U9S0nkGDRpa4P5++ulHdu06zDffrOWdd96wui2kMLNmfUFQUC1L1fpKpflqI0dGEhAQyJEjScydG8PkyS9YXWVdufIb+vcfTFLSeXr2jGDcuDElHSKRm5JyXsFKm/MAYmO388gjI3j99WkkJZ1n7doNBAfXtvRbsOAL/u//PuaPP9KpVSuY0aOjcHJyYvfuI2zZ8ivff7+Wzz//tNBxf/HFZzly5BA///wbu3cfISkpkalTXyn1cV0p7iQlJdKvXy8mTHiRhIRUpkyZztCh/Thz5oyl/eLF8/nww884fvw02dlZzJiRV6yZNy+atLQLHDwYT3x8CjNnfoibm5vVvgo6jtat21C9enW+/36dpd3ChXOJjBxequMoiT/+OEVa2gWOHEnkgw9mMW7cE5b39wsvjOe33+L44YctJCSk8tprb+Hg4FDs+zc1NZV+/Xrxj388SXx8Cv/85zj69etFSkpKsWMmIuWvsPM6k8lEv369CQoKZt++4xw+nEj//oMLzb9XW7/+B1566XnmzFnM0aPJ1KoVTFTUYKs2q1atYMOGHWzdupOvvlrMunVrCoxv797dNGjQsND4ExLiWbv2W5o3b2lZ5u9vpFGjxnz3Xd6tbfPnz2HIkBGlGpeGDUPYvXtn8Q3lpqcCxi2gSpUqrFu3CYPBwJgxjxAcXIMBAyIsV5YKctddnWjaNBQHBwdCQ5sxYEAkGzf+VKL9OTs7c/FiOocOHcBsNtOoUQj+/v4l6hsd/SkvvfQaDRo0xGAw0KxZc6pXrw5AZOQwqlevjpOTE0899TRZWZkcOnSwRNstiL+/EbPZzIUL+RO5s7MzBw7sIy0tjWrVqtGyZasit9Wu3e306XM/Dg4O+U54r3jhhZdwd3enadNQhg17kCVLFlxz7FckJMSzZcsmXn31TVxdXWnevAVRUQ+zYMEXlja33x5O9+49cXR0JDJyuJK7VHjKeQW7lpwXHT2L4cNHcc899+Lg4IDRGEDDho0s/YYNG0njxk1wcnIiNTWVtWtX8dZb7+Hu7o6vry9jxowlJmZhgfGYzWY+//wT3nzzXby9vfH09OSZZ14otH1Rx3XuXCoACxbMpWvXnnTv3hMHBwfuuedeWrYMY82aby3thw9/kNtua4CbmxsPPDCQXbt+A8DJyZnU1BSOHj2Co6MjLVu2pkqVKiWKYciQKBYunAvkFQS++24NAwcOKbT9jBnTMRq9MBq9qFXLp8TH6uzszPPP/xtnZ2e6d++Ju7sHhw8fJDc3lzlzZvPWWzMwGgNwdHSkffs7cHEp/rap1atXUq/ebQwZMhwnJycGDoykQYNGfPvtXwW3wsZMRK7d4MH3W/LAoEH3F9/hfwo7r4uN3c6pU0lMmTINd3d3XF1dueOOkj2vZ9GieQwfPoqWLVvh4uLCyy9PZdu2nzlx4rilzdNPP4eXlxdBQbW46667C80DFy6cx8PDs9Dj7dIlnPDwjjzzzAtW64cMGcH8+XM4dOggFy6cz1dsBfjqq8WWMTMavaxmiXh6enL+fP7PN6l4VMC4RTRqFMLHH3/O4cMJ7Nixh+TkJCZM+Feh7Xfs2EaPHncTHFwDf/+qzJr1ISkpJZsy2qlTZx59dAxjxz5BnTo1GTNmNGlpaSXqm5AQT5069QpcN2PG27RqFYK/f1WMRi8uXLhQ4pgKkpSUiMFgoGpVr3zr5s//kjVrviUkJJhu3TqybdvPRW4rICCo2P0FBv7Vplat4DJ5WFNycpLlxP/qbSclJVpe16zpZ/m5cuXKZGRk6DkdUuEp5+V3LTkvISGeunULjg+s81p8/Amys7OpV8/fcnL55JOPcubM6QL7njlzhj///JPw8NaW9vff352zZ88U2L4wycmJVKvmbYlh6dIlVie4P/+8iVOnki3tr86Jbm6VuXQp70FyQ4YMp0uXbowcOZh69YxMnDiB7OzsEsUQGTmMVauWc/HiRb76ajF33NGhyCLWU0+NJynpPElJ5zl5suS/U2/vvILWFZUrV+bixYucPXuWjIyMIn9XhUlOTqJWrWCrZXmfUQV/jlw9ZiJy7RYuXGbJA4sWLStxv8LO6xIS4gkKCrbKESX19zzg4eGBt3f1Qs8ni8oDXl7VuHgxPd/yK8d74MAJ3nvvg3wX/O677wF++ukHPvzw/wqdwfbAAwMtY5aUdN7quSHp6el4eeX/fJOKRwWMW1DDho0YNmyk5d4zg8GQr82DDw6hZ88IDh6MJzn5Ag899JjlXreC2v/d448/yebNcezYsZcjRw7x3nvTStQ3MDCIY8eO5lu+efNG3nnnTebMWUxi4jmSks5TtWrVQu+/K4nly5fSokUr3N3d861r3boNixd/zfHjp+nd+36GDx9YZPwlGZMr97VD3lehXkm67u7u/Pnnn5Z1f/xxqsTb9vc3kpqaSnr6Xx8U8fEnMRoDio1H5FahnJfnWnJeYGAQv/+eP74rrj6+gIAgXFxcOHnyrOXk8tSpNGJj9+ZrC+Dj44ObmxuxsXst7ZOTL3D6dOn+c/zNN0u5884OlhgiI4dbneCeOXOJ8eOfK3Y7zs7OvPDCS8TF7eOHH7awevUKq4fKFXTMVxiNAbRtezvffLOUBQu+uObbRypXrlzk50FhfHx8cHV1LfB3Vdx70N/fyMmTJ6yW5X1G6XNEpLy5u7tz+fJfOcBkMpW4qBsYGER8/MkCL1KVNg9cunSJ1NSUazqfbNq02TV9O1TlypXp2rUHn3zy32vKoQcP7ic0tHmp+8nNRwWMW8DBgweYMeNtEhMTgLz/SC9ZsoC2bdsD4Otbk8TEBLKysix90tPTqVbNG1dXV2Jjt7N48XzLOh+fGjg4OHDs2O8F7i8ubgc7dmwjOzsbd3d3XFxcLV/56etbs9B+AFFRD/PKK5M4cuQwZrOZ3bt3kZKSQnp6Ok5OTvj41CAnJ4epU18p8RXOq5nNZpKSEpky5WU+//xTJk+ekq9NVlYWCxfO48KFCzg7O1OlShWr+FNTU7hw4UKp9/3GG6/y559/sm/fXr744jP69ct76nyzZi1Yu/ZbUlNTOXXqFO+//55VP1/fmhw/XvCYBQYG0b79Hbz00vNkZGSwe/cuoqNnFfocDpFbgXLeX64350VFPcTcuZ/x44/fk5ubS1JSIgcPHihwX/7+/txzT1eee+5p0tLSyM3N5fffj1puxfn7uDs4ODBy5CM8++xYTp/Om6WRlJRY6H3VVzOZTBw/foynn/4nGzeu5/nnXwLyZkJ8++1y1q1bg8lkIiMjgw0b1lveC0X56acf2bNnNyaTCU/PKjg5OePgkP/rqgt6/0De9Od3332LvXt3ExHRt9j9FaRZsxYsXjwfk8nE2rWr2bSpZLcxOTg4MGLEKJ57bhzJyUmYTCa2bfuZzMzMYt+/3br15MiRQyxaNJ+cnBxiYhZx4MA+evTofU3HICLXrn79BmRkZLB69Uqys7N5883XyMzMLFHfsLC2+Pn5M2nSc1y6dImMjAx+/nkzUHjeumLgwCHMnfsZO3f+RmZmJi+99AJt2rSzeuZRSXXufC87d/5yTc9sevnlKaxZ89M17XfTpp/o2rVHqfvJzUcFjFuAp6cnsbHb6NixHTVquNOpU3saN27K1Kl534TRqVNnQkKaULeun+Ve3Pfe+4DXXvs3NWt6MnXqK/TrN9CyvcqVKzNhwkS6dLkTo9GL7du3Wu0vLS2NJ554hICAaoSEBOPtXd3yXdBRUQ9x4MC+Qu/3e/LJcfTrN5CIiK74+VXh8ccfIiPjMvfe242uXXvQokUDGjUKxsXF1WrqcnGu/uaQDh3asHfvblavXk+XLl0LbL9gwRc0blwbP78qfPrph8yalXdvc8OGjRgwIJKmTevmu/euOB06dCQ0tD69et3DU0+Nt+w7MnI4oaHNady4NhERXS2FjSvGj3+eN998DaPRy+qbAa74/PMFnDhxnPr1jURG9uXFF1/mnnvuLXFcIhWNcl7Z5bywsLZ8+OFnPPvsWPz9q9KtW8d8V+uv9sknc8jOzqJ168YEBFRj6ND+lts3Chr31157k7p163P33e3x86tC795dOHy48Od8XHmKvp9fFbp370RaWhobNuygadNQIK+ou3jx10yfPoXg4Bo0bBjEe+9NK9FXvP7xxymGDeuPn18VWrUKoUOHjkRGDsvXrqDjAIiI6Et8/An69Olb4CyXkpg2bQarVi3HaPRi0aJ59O5d8vvip0yZTpMmoXTo0IbAQG8mTXqW3NzcYt+/1atXJyZmBTNnvk1QUHXeffctYmJW4ONT8mdziEjZqFq1Ku+++wGPP/4w9esHULmyOwEBgcV3JO/bmWJilvP770do1KgWDRoE8uWXi4DC89YVd999D5MmvcrQof2oV8+fY8eOEh1duucRXVGzZk06duzMihVfl7qvv7+xxM/tuFpc3A4qV3YnLKxtqfvKzcdw6dJ1zEcVEREREQCaNq3HzJkf0blzF1uHIiJiM/v372P06Cg2bNheotswr9eQIf0YMeIhunfvecP3JbanAoaIiIjIdVq27EsmTXqWnTsP4eCgCa4iIiI3QukfUysiIiIiFt27d2L//n18+ukXKl6IiIjcQJqBISIiIiIiIiJ2T5cJRERERERERMTu2cUtJLVq+VCrVm1bhyEiUmZOnjzOyZNnbR3GdVN+FpGKpiLkZ+VmEaloSpqb7aSAUZtNm2JtHYaISJkJDw+zdQhlQvlZRCqaipCflZtFpKIpaW7WLSQiIiIiIiIiYvdUwBARERERERERu6cChoiIiIiIiIjYPRUwRERERERERMTuqYAhIiIiIiIiInZPBQwRERERERERsXsqYIiIiIhI0bKzAXCa+Q7OLz5rWVzpsVE4v/bSDd2niIjIFSpgiIiIiFRAlQZE4BZQjUpD+1/Xdgz79uKwYxsAOSNG4RizEDIycIyehSEhnuwXbkwBw3HhPMjKuiHbFhGRm5MKGCIiIiIVUM6YsWR9Muf6NnLxIk7zosm9IzzvtZcXpm49cf738zi/8yaZn80Hh2s7nXTp1B5DYgKQVyRx6dfbar2pVwTOb7yar58hIR6X7p1wbd0Y13bNcfz6q2vav4iI3HxUwBARERGpIAzxJzHEnwQgt+PdmD08C23rsGVTsdtznjGdnP6DrJaZho3E6YMZZH0cDTVqXFugZjOGU8mYAwLzYtmzi9wmodZtvL3BZMKwd491V0cnst58j4y4fWQsX4fzM0/Bn39eWxwiInJTUQFDREREpCK4eBHHedGYg2qVqLnZ3QPHxQsKb3D+PA7frcHcsvVVncw4TZsC1X3AZCqwm2tY0wL/GBLiLW0Mvx/FXKeu5XWBBQwgZ/AwnKdMtl7o74+5eYu8n319wasahpSzxR6viIjc/FTAEBERkVuOw6YNVBoQgWv9ACq7G3D84nNbh3TdnGdMxzRoaInbm5u3wGH7Vjh3rsD1jutWk9u8pdUyp+lToUpVsv7vI5w++k+B/TJi9xT4xxwYZGnz94KFw2+/FFjAMIc0zouxkBkWDr/EQk621bZFRKTicrJ1ACKFWX5yWaHr+tS6vxwjERGRq1WI/HzxIubGTckeMoJKj4ywdTTX78wZHH6Nwzxxcqm6mfrcj/Pbb5D92pv51jmuXompQ0fLa4cfv8fpqyVkfL8ZXFxwfnEChuQkzP7GUofrsGcXhv8VJQy//oLD5g2YGzQssK25QSMcfvqB3B7Wz8ggJYVKj4wg64NZYDCUOgaRiqKonPx3N02OFimEZmCIiIjILSe3e0+yX56CqW//a34IpT1xWhaD6fbwUvfL7dARx2UxYDbnW+ewZxfmoGAg78GZlZ58lMwvFkPlyuDoSE7UwzjN+uia4jXs2QWXLuHashFOn32MuVYwjgvmFtjWHFQLhz27rRdmZuIS2Zfsp58nt/0d1xSDiIjcfDQDQ0REROQm57h6Jdn/eNJqmUuvLjjs2ZlXKLgtkKy5S8htd7t1RwcHzDV8cfglltzWbaxW/T97dx4eVXm3cfx7ZiYhLLLEgGRhSQyyhjUBxEgAQQLBIBIVRUmNSl14peLWVmNbsa5gbbVVaUVjQWmJAhJWRVGibMMiKFEBWcxSIWETAklm5rx/RCIxAUK2k0nuz3Xlauac55y5H9oeht88i3HgB2jeHAAzpB2ntu8qdd71wCOVzmv7egenPt8CjRsDUHSOtuZFzTEOHjjjgInv5F/hiRmG++ZbK51BRES8j/d/5SAiIiLSwNk2rsPsdFmpYwVLPuTkvoOczM3n1M7MssWLn5idOhevM/FLhw9hNm1W/WFPnAC7vaR4cV7NmmEcyit5aVv7GfZ3/4OSEiLsAAAgAElEQVR98UL8BvbGb2BvjF+O0BARkXpJIzBERERE6hCfPz2Gz3N/PmebU8s+xjN4SPGLoiI4dAizeYtKvZ/ZvHnxaItfatEC42Q+ZSeXVFHTppxyflXx9vn5mC1blrz0DIrm5HFPdacSEREvoAKGiIiISB1SdO9vcE245ZxtSm2VmpuLYZpw0UWVe8OLmkM525CarS+BY8cqd89qZPx4DE/HUKtjiIhIHaAChoiIiEgtsC98F8eb/8K2eSMcO4bZvgOuW2/DNe2R4ikVpwUEYAYEVPzGTZoU/2dhITiKP9o1aXruXTnyT5wxrqKgABo3KdPGc1lnjOysn9/mPPesTmfmM3KyMa8eVWvvLSIidZfWwBAREZGG5/hxjC+2YnyxFTwejMz9xa+/31/97+V245t4E40mJmB8twvXuOtx3XkP2Gz4/vFRfO9Kqtr9W7TAbNQIjh4tOXTym/24r4zB06Urnh49KXj7XfJPmCU/ZzKOHcVsc0nZ2CNHY9u6ueT1mdef6+fUJ+txRw3Ac8aaHAX/fKvC15fJt+NL3MNGVO3PSERE6gUVMERERKTBsW120nhQHxoP6oNx8iS+T/6BxoP64DP98Wp/L5+HpuJInUfRA7/l1OYMiv76CkXPv8ipjV/iHjgIx9tvYWTsqNJ7mKFhpdaxMO0OCp99kVObdnBq8Qf4PDQV8vPLv/jAD5hhl5Y57B4Zh22L88KC5Ofje/stFP71VU5t/QbXpCQKn/8r7pvOPSXmbIx9ezG7dCvZDUVERBo2FTBERESkwfEMHlLuN/+Fs96s1vexbVyPY9Y/cI0ZS9ETT5dM8QDAxwfXxMSSdlXhHh6LbdvWnw8EBmL26l38e5s20LIVRjnrXADYdnyJe+jwsifatsXTuy/Gt99UOIf94w/xXB5d8t6eiF5w9AgYlZt+Yp83h6LfVX9RSUREvNN5Cxh33ZVEhw5tiIzsUebciy/OoGlTg9zc4r8QTdPkwQfvIyIinP79e7Jly+Yy14iIiIg0FI5XXipeYLNxE3z+/McyP/ZVK4sbmlXb68N9zbXYNqwt95xtsxNcRZgh7cqezMnB7BAKZ+zycaaiR5JxvP1WhXMYGTvwdPv5M6Nt+xeYvfpU+PpS8vMx8vLwDBxUuetFRKTeOe8inrfc8it+/esp3HnnpFLHMzO/56OPPqDdGatgr1ixjF27drJt2042blzPb35zN598UrVvFERERES81ekChWP+O+dsV2pXkUrwRA/G8fJfihfkbNTo5xN5efjeOYnCf7xe7igIx7w5FD386Nlv3Lo17hGx2Jwb8ET2P3+QFi2wOTcAYGzZjG2zk8IX/3Gh3QHAPv8dih79Y6WuFRGR+um8IzCiowfj7+9f5vgjj9zPk08+h3HGX4ZLlizi5psnYRgG/fsP5OjRI+Tk5FRvYhERERFvcOoURu5B3NGDz7topWdYOVM4LpDrgd9i/+8ZhZKCAhrdNI6iB35X/iiGU6cwsrPwxAw95309V1yJp3PXimW44WaM/+XgFxWB7+O/pWDO/NIFlQvgHn8jtGhRqWtFRKR+qtQaGEuWvE9gYDA9e/YqdTw7O4uQM4YnBgWFkJOT9cvLRURERKqsSVOjzv4AJdNCzrb2RHXzRA0APz84eBBME9/Jv8ITMwz3zbeW296+IJWi3/+hYje/6KKKtWvRgoJFyzm1cTsFi1dinrETyQVr1qzy19aQlSuX07t3ZyIiwpkx45ky5wsKCpg06UYiIsKJiRnAvn17AcjLy2PUqKG0adOMadOmlLqmsLCQKVMm06vXZfTp04WFC9+tja6IiHilCy5g5Ofn89xzfyY5+Yky58xy5m8aZ1m0afbsWURHRxIdHUlu7sELjSEi0iCd78NzevqnDBrUl+bNHSxYkFpy/IsvtjJ06OVERnanf/+epKb+pzZji9SIC9mWs7Z/AGjcGE+PntgydmBf9F65fbB9ng5ud7X9mbivnwAXXYRt7WfY3/0P9sUL8RvYG7+BvTG+3F667bgEaNWq2t67vnO73Uybdi8LFixj06YdzJ//Dhm/2D0mJeV1WrZsxfbtu5gy5X6Skx8BwM/Pj+Tk6Tz11Iwy933uuT/TunUbvvjiWzZt2kF0dEyt9EdExBuddw2MX/ruu93s3buHgQOLR19kZWVyxRV9+eSTDQQHh5CZ+X1J2+zsTNq2DSr3PklJk0lKmgxAdHRkZbKLiDQopz88L178AcHBIVx5ZRRxcfF07dqtpE27du157bU3+etfS39IbtKkCf/851uEh3ciJyebK67ox/DhI2l5loX7RKR6FP75eRqNj6PRzeNxDx2Op0dP8HgwcrKwbdkERUWc+mZ/9b6pnx+eQdGcPO45bzupOKdzA2Fh4YSGhgGQkDCBtLRFpZ7BaWmLePSndTvGjUvggQemYJomTZs2ZdCgaHbv3lXmvm+9NZstW74GwGazERAQUPOdERHxUhdcwOjRI4J9+w6UvO7atSNr1jgJCAggLi6eV199meuvn8DGjetp3rwFgYGB1RpYRKShqsiH5w4dOgLFH4LP1OmMYdyBgUG0bt2G3NyDKmBIg2XbsA6/oZfX2P1Pj8LwDL+ago8+x/HCs9g/T8e2ZjW0aIF5SSDuocNxX3dDjWWQ6vXLqdLBwSE4nevP2sbhcNC8eQvy8vLOWpQ4cuQIAE88kcyaNasJC7uUmTNf5pJLLqmhXoiIeLfzFjASE29izZrV5OXl0qlTCI899icSE28vt+3IkaNZsWIpERHhNG7chNdee6PaA4uINFQV+fBcEU7nBoqKCgkLu7Tc87Nnz2L27FkAmuIn9ZZt4/qfp3rUME+/KArnpp6/odRpFZsqXfHp1AAul4usrEwuv/wKnn32Bf72txf4/e8f5PXX/12mrZ7NIiIVKGCkpJx726+MjL0lvxuGwV/+8vcqhxIRkbIuZJ2hs8nJyeGOO25l1qyUMqM0TtMUP6n33G7w8bE6hXiZX06VzsoqO1U6KKi4TXBwCC6Xi2PHjpa7m99pF198MU2aNCE+fhwA1113PW+99Xq5bfVsFhGp5C4kIiJS+yry4flcjh07xvjxcTz++JP07z+wJiKKeAXb2s9wDyhnW1GRc+jXL4rdu3eyd+8eCgsLSU2dR1xcfKk2cXHxzJ2bAsCCBanExAw7Z6HZMAxGj76GTz9dDcDHH6+iS5duZ20vItLQXfAaGCIiYo0zPzwHBQWTmjqPN954u0LXFhYWMmHCOG6+eRLXXXd9DScVqdts27/Adff/WR1DvIzD4WDmzJcZO3YkbrebSZOS6NatO9OnP07fvpHExcWTmHg7d9xxKxER4bRq5U9KyryS67t27ciPPx6jsLCQxYsX8v77K+natRvTpz/LHXfcysMP/4aAgNaagi0icg4qYIiIeImKfHjetGkjEyaM48iRwyxbtpg///kPOJ1f8e67/+Wzzz7l0KE85sx5E4DXXnuTXr16W9spkTrC8fzT2N9/D9vOb6BRIzxRAyn809OY3XtYHU3qkNjY0cTGji51LDn5iZLf/fz8mDNnfrnXnjnt+kzt23dg5cpPqy2jiEh9pgKGiIgXOd+H5379oti5M7PMdTfddAs33XRLjecTsYLNuQGfPz6KbftWjNzcUudObt+FecaCtcbOb/F06lzmHvY1q3HdeQ+eflFgmvg8+Th+Y4ZzctMOOMcaBiIiIlJ7tAaGiIiIeC3jqy9pFDsET5eunFq2mlNLP8K8pC3uyP4UvD4H2+fp2JYvKWlvW7Maz+AhZe5T8P4K3JNuw+zeA7NHBIX/+jfkHsS+7rOSNn79utGkqVHuj8+f/1gLvRUREWnYVMAQERERr+X70FTcV4+iaMbfMLt1xxMzFNctv8I4fAj3uATMNpfg+M/Pa8UYRUXg63v+G//4I4bHg9myVcmhgnkLATj13lLyd+eQvysbs0kTCv7xOkXTHqn2vomIiEhpmkIillq8f2Gt3vOa9tdW+/uJiNQ3NfFsPt99K/V8zs3Flv4JBYtWlDpsNm0KhlG8lsXVsRjPPQkuFxw9inlxQIVu7fvwVDw9e+MZcHnJMePAD5iGgeeKK6FZM4zduzDy8/EMiobGjS88v4hIHXWhfw/oM7bUFhUwRERExCvZtmzCcLvxRPQqfXyzE0/fqJLXnkFXYkv/FOPAD7hHxJ73vj6PTMP2eToFH6aD3f7zfbd/gRkaBs2aFb/ethWzSRPMS8OrqUciIiJyLipgiFeqqW8HRUSkamr1+ex2A2CcOon50yFj9y7sH66g4J0FPzcbMxb7f9/BvKwztGpVzo1+5vPw/ThS53Fq2cfFxYoz2L7cVqpYYtu2FU+3HmDTjFwREZHaoL9xRURExCt5ogZgNmmCz6MPY3ydge2DFTQaH4c7YQKeq2NLtbNtXIfZqNE57+fz4FQc/327eCHQzl3KnDe+3IanR8+S17ZtWzF/MfpDREREao4KGCIiIuKdLr6Ygn/Px7ZtC34De+E79S5cN91K4d//WbqdYWD26InnyiFnvZXP/ffimPMGBW++U7xw5//+V/xz/HhxA48H244vMc8oYBh7duNp36EGOiYiIiLl0RQSERER8Vqe2NGcih193naFTzwDF1981vM+s/4BgF/cVaWOF/3+DxQ9+keM73ZjnDhRagSGp3sEPi88i6dXXzwjR1WyByIiIlJRKmCIiIhI/XeO4gVA/gnznOfN8E5l2hT++79VjiUiIiIVpykkIiIiIiIiIlLnqYAhIiIiIiIiInWeChgiIiIiIiIiUuepgCEiIiIiIiIidZ4KGCIiIiIiIiJS52kXEhEREaka06TxD3k0352JvaCQglbNOXZpO4qaN7U6mYiIiNQjKmCIiIhIpThOnCT87WWELviI5nuySp3z2GwcjOrGzptHkzV8ANg06FNERESqRgUMERERuWDtl6yhz1P/wu/QMQ5EdmPXhJEc6RKKq4kffrlHuHjrN3RYuoboqc+RFxHOxiencPSyDlbHFhERES+mAoaIiIhUmK2wiMg/vELowo/J7XUZa155lEM9LyvTLmdIJF/93wTap62h93NvMCLhQTb98S72XHeVBalFRESkPlABQ0RERCrEcTyfK+95ijYbv+LLe25gx903YDrsZ21v2u3sGzuE/13Zh4EP/oX+j75M08wf+PL/bgLDqMXkIiIiUh+ogCEiIiLn5ThxksF3PcnFX3zL2ufvZ/+YwRW+tsC/BZ/OSibyD6/Q/ZX5YMKXU2+uwbQiIvXb4v0L6+S9RGqaChgiIiJybh4PAx/6Cxdv+Ya1M6eRGXvFBd/CdNjZOP0eTJtB91fnkx/Umu+uH1EDYUVERKS+UgFDREREzinib28T/PFGNj12Z6WKFyVsNjb94S6a/C+Pfk+8xo8dAjnYv0f1BRUREZF6TXuaiYiIyFmFrPicbq+9y+6E4ey6eVSV72c67Kx94QF+7BDIFVOfw+/AoWpIKSIiIg2BChgiIiJSLr8Dh4j8wyvk9ezE5uTJ1bbwZtFFTfnspd9iP1VA/0dfBtOslvuKiIhI/aYChoiIiJRlmvR/7GXsBYWse2YqHl+far39j6HBbH34NgLTtxD+9rJqvbdITVq5cjm9e3cmIiKcGTOeKXO+oKCASZNuJCIinJiYAezbtxeAvLw8Ro0aSps2zZg2bUq5977++ngiIzWtSkTkbFTAEBERkTLC5n9A4JotfPFgIsdDg2vkPXZPGEn24H70ej4FY893NfIeItXJ7XYzbdq9LFiwjE2bdjB//jtkZOwo1SYl5XVatmzF9u27mDLlfpKTHwHAz8+P5OTpPPXUjHLvvWjRezRt2qzG+yAi4s3OW8C4664kOnRoU6oa/PvfP0SfPl3o378nEyaM48iRIyXnnn/+aSIiwunduzMffLCiZlKLiIhIjWl06Ci9Zr7FD/17sOum2Jp7I8PA+cTdmHYbvg9Nrbn3EakmTucGwsLCCQ0Nw9fXl4SECaSlLSrVJi1tERMnJgIwblwCq1evwjRNmjZtyqBB0TRq5FfmvsePH+ell17gkUceq5V+iIh4q/MWMG655VcsXLi81LFhw0awceOXbNiwjfDwy5gx42kAMjJ2kJo6D6fzKxYuXM7999+D2+2umeQiIiJSIyJenIsj/1Txuhe2mh2sefKSi/lqygTsy9KwL3m/Rt9LpKqys7MICWlX8jo4OIScnKyztnE4HDRv3oK8vLxz3veJJ5K5774HaNKkyVnbzJ49i+joSKKjI8nNPViFXoiIeK/zfiqJjh6Mv79/qWPDh1+Nw1G8A2v//gPJysoEiivOCQkTaNSoER07hhIWFo7TuaEGYouIiEhNsG3aSFjqh3x76xiOhbc7/wXV4Ntb4vB07Y7Pg/fByZO18p4ilWGWs+CsUWZx24q0+dkXX2zlu+92ER8/7pzvnZQ0mfR0J+npTgICWlcor4hIfeOo6g3eems248ffCEBOThZRUQNLzgUHh5CdnVXudbNnz2L27FkAqiJLnbd4/8Kznrum/bW1mEREpAaZJj4P/4ZTF7fkq3tuqL239XFQOPMl/EYPw/Hqy7juf6jC1+r5LLUpODiEzMzvS15nZWXStm1QqTZBQcVtgoNDcLlcHDt2tMyXgWfasGEtW7ZsomvXjrhcLg4ePEBs7BCWL19dU90QEfFaVRoX+txzf8bhcDBhwkSgolXpYqoii4iI1C225Uuwr/ucr6bciKvZ2Yey1wRPzFDcV4/CZ+bTcMbaWiJ1Sb9+UezevZO9e/dQWFhIauo84uLiS7WJi4tn7twUABYsSCUmZtg5R2Dceefd7N6dTUbGXj78MJ3w8MtUvBAROYtKj8CYMyeFZcvSWLJkVclD+XTF+bSsrEwCA4POdgsRERGpKzwefP/4KJ5Lw/nuuqssiVD4p6fxG9QHnxeepeiJpy3JIHIuDoeDmTNfZuzYkbjdbiZNSqJbt+5Mn/44fftGEhcXT2Li7dxxx61ERITTqpU/KSnzSq7v2rUjP/54jMLCQhYvXsj776+ka9duFvZIRMS7VKqAsXLlcv7yl2dZvvyTUosNxcXFc9ttN3PffdPIyclm9+6dREb2r7awIiIiUjPs8+dh+3IbBW++g+lT5RmmlWL27IX7hptx/OOvFN19HwQGWpJD5FxiY0cTGzu61LHk5CdKfvfz82POnPnlXpuRsfec9+7QoSNO55dVzigiUl+ddwpJYuJNDB16OTt3fkOnTiGkpLzOAw9M4ccff+Saa0YwcGBv7rvvLgC6devO+PE30K9fN669NpYXXvg7dru9xjshIiIiVeB24/PUH/FE9MI9vvbWvihP0WN/gsJCfP46w9IcIiIiUvec9yuWlJR3yhxLTLz9rO0ffvhRHn740aqlEhERkVpjX/gutl07KZibWuPbpp6PGXZp8SiM11+l6MHfQUCApXlERESk7rD2U4qIiFyQlSuX07t3ZyIiwpkx45ky59PTP2XQoL40b+5gwYLUUufmzEmhZ89O9OzZiTlzUmorstR1ponP80/huawz7vNs41hbih78HZw8ic/fX7Q6iohIvbJ4/8IyPyLeRAUMEREv4Xa7mTbtXhYsWMamTTuYP/8dMjJ2lGrTrl17XnvtTW644eZSxw8dOsTTT/+J1avX88knG3j66T9x+PDh2owvdZRtxTJs27+gaNpvLR99cZrZpSvusdfhePUl7UgiIiIiJerGJxURETkvp3MDYWHhhIaG4evrS0LCBNLSFpVq06FDRyIiemL7xT9EP/xwBcOGjcDf359WrVoxbNgIPvhgeW3GlzrKZ+bTeNq1x/3Tluh1RdGDv8c4dgzHm/+yOoqIiIjUESpgiIh4iezsLEJC2pW8Dg4OIScnq9LXZmeXf+3s2bOIjo4kOjqS3NyDVQstdZqxZRP2z9Nx3fsb8PGxOk4pZp++uK+MwfHay+ByWR1HRERE6gAVMEREvIRpmmWOGYZR7dcmJU0mPd1JerqTgIDWFxZSvIrPP/6G2awZrklJVkcpl+ueqdj278P+i5FGIiIi0jCpgCEi4iWCg0PIzPy+5HVWViZt2wZV+trAwIpdK/XUDz9gT52H65ZfQYsWVqcplzsuHk+Hjji0mKeIiIigAoaIiNfo1y+K3bt3snfvHgoLC0lNnUdcXHyFrh0+fCSrVq3k8OHDHD58mFWrVjJ8+MgaTix1mWP2axiFhbh+PcXqKGdnt+O6+z7sn6djbNlkdRoRERGxmAoYIiJewuFwMHPmy4wdO5K+fbsyfvwNdOvWnenTH2fJkvcB2LRpI506hbBgwXzuu+/XREZ2B8Df359HHklm8OAoBg+O4re/fRx/f38ruyNWKizE55+v4L56FOZlna1Oc06uSUmYzZrh8/e/Wh1FRERELOawOoCIiFRcbOxoYmNHlzqWnPxEye/9+kWxc2dmudcmJiaRmFg31zqQ2mV/978YP/yPonumWh3l/Fq0wHXrbTj+9So8NQPatLE6kYiIiFhEBQxpUBbvX3jWc9e0v7YWk4iIWMfx+qt4wjvhuWqE1VFKnOv5HH/7Xfi88hKOt9/C9ZsHazGViIiI1CWaQiIiItKAGBk7sK/9DNev7gSbd3wMMLt2w335FTjemAXl7KgjIiIiDYN3fHIRERGRauFIeR3TxwfXxESro1wQ122Tse3aiW3NJ1ZHEREREYuogCEiItJQFBTgeDsF95ixXreWhHtcAmaLFjje+KfVUURERMQiKmCIiIg0EPbFCzHy8oqnj3ibJk1w3XQr9oWpkJdndRoRERGxgAoYIiIiDYTjjX/iad8Bz7DhVkepFNdtkzEKC3G882+ro4iIiIgFVMAQERFpAIw932FfvQpX4u1es3jnL5k9InBHDcDx5r+0mKeIiEgD5J2fYEREROSCON5+C9MwcN96m9VRqsR9y6+wZXyF8cVWq6OIiIhILXNYHUBERERqmGlinzcHT8wwzOAQq9NUieu6G/B5aCqOt9+iqHcfq+OIiNSqxfsXWh2hXBeS65r219ZgEqnvNAJDRESknrNtWIftu924brrV6ihV5++Pe/Q1OP4zF4qKrE4jIiIitUgFDBERkXrO/s6/MRs3xj32OqujVAv3zZMwcg9i+3CF1VFERESkFqmAISIiUp8VFuJ49z+4x1wLF11kdZpq4R4RixkQgOPtt6yOIiIiIrVIBQwREZF6zL5yGcahQ7gm3GJ1lOrj64vr+puxL3kfn6PHrU4jIiIitUQFDBERkXrM/s6/MVu3wTP8aqujVCvXxEkYBQW0W/G51VGkAVm5cjm9e3cmIiKcGTOeKXO+oKCASZNuJCIinJiYAezbtxeAvLw8Ro0aSps2zZg2bUpJ+/z8fK67Lo4+fboQGdmd5OTf1lZXRES8kgoYIiIi9dXhw9iXLsZ1/U3gqF8bj5m9++Lp3IX2S9ZYHUUaCLfbzbRp97JgwTI2bdrB/PnvkJGxo1SblJTXadmyFdu372LKlPtJTn4EAD8/P5KTp/PUUzPK3Hfq1AfZsuVrPv98C+vWfcaKFctqpT8iIt5IBQwREZF6yr5gPkZhIe6b6tH0kdMMA1fCBNps/Aq/A4esTiMNgNO5gbCwcEJDw/D19SUhYQJpaYtKtUlLW8TEiYkAjBuXwOrVqzBNk6ZNmzJoUDSNGvmVat+kSRNiYoYC4OvrS69efcnOzqydDomIeCEVMEREROopx3/m4uncBU+fflZHqRHu8TdimKamkUityM7OIiSkXcnr4OAQcnKyztrG4XDQvHkL8vLyKnT/I0eOsGzZYoYMuarc87NnzyI6OpLo6Ehycw9WshciIt6tfo0nlTpp8f6FVkcQEWlwjJxsbJ+toejRP4JhlDlfH57NZucuHO7SkfZL09l56xir40g9Z5pmmWNGmf9vVaRNWS6Xi1/96ibuvvs+QkPDym2TlDSZpKTJAERHR54/sIhIPaQRGCIiIvWQfUEqhmniHne91VFq1P7R0QRs/YYmWQesjiL1XHBwCJmZ35e8zsrKpG3boFJtgoJ+buNyuTh27Cj+/v7nvfeUKZMJD+/ElCm/qd7QIiL1jAoYIiIi9ZD9vf/i6R6B2aWr1VFq1PejogFov+wzi5NIfdevXxS7d+9k7949FBYWkpo6j7i4+FJt4uLimTs3BYAFC1KJiRl23hEYf/rTYxw7dpTnnnuxxrKLiNQX5y1g3HVXEh06tCEyskfJsUOHDjFmzAh69uzEmDEjOHz4MFA8tO7BB+8jIiKc/v17smXL5ppLLiIiIuUysjKxr/0M1/gbrI5S406EXEJez8totyzd6ihSzzkcDmbOfJmxY0fSt29Xxo+/gW7dujN9+uMsWfI+AImJt3PoUB4REeG89NILPPHEz1utdu3akd/9bhpz5rxJp04hZGTsICsrk+ee+zNff72DQYP6MnBgb958819WdVFEpM477xoYt9zyK3796ynceeekkmMzZz7DkCFX8eCDv2XGjGeYOfMZnnzyWVasWMauXTvZtm0nGzeu5ze/uZtPPllfox2QuqE+zKUWEakv7AtSAfhgYCuON4Dn8/5RV9Dn2TdotieL46HBVseReiw2djSxsaNLHUtOfqLkdz8/P+bMmV/utRkZe8s9fuJE2XUzRESkfOcdgREdPbjM3L0lS37eImrixETS0haWHL/55kkYhkH//gM5evQIOTk5NRBbREREzsb+7n/w9OzdYP4x//2oKzANQ9NIRERE6rlKrYFx4MAPBAYGAhAYGMjBg8ULZ/1ye6mgoLLbS52mraBERESqn7F/H/YN63BdV/+nj5x28pKLOdivK+2XahqJiIhIfVat26hWbHupYtoKSkREpPqdnj7iHn8DsN3aMLXo+9gr6PfkP7lo9/f8eGm7818gIlKHaXq2SPkqNQKjTZtLSqaG5OTk0Lp1G6Ds9lLZ2WW3lxIREZGaY3/vv7j79MMMu9TqKLUqc8RAAEI+WGdxEhEREZg+HRkAACAASURBVKkplSpgjB798xZRc+emEBc3FijeOurtt9/CNE02bFhH8+YtSqaaiIiISM0y9u3F7tyAuwFNHzntVBt/cnt3pt1KFTBERETqq/MWMBITb2Lo0MvZufMbOnUKISXldR544Ld89NEH9OzZiY8++oAHHvgtACNHjiY0NIyIiHDuvfdOXnzxHzXeARERESlmX/QeAO5rx1ucxBqZV19Oq4zvaJr5g9VRREREpAacdw2MlJR3yj2+dOmqMscMw+Avf/l71VOJiIjIBbMvXoAnoleDmz5yWuaIgfR+7k1CPljHN7eNtTqOiIiIVLNKTSERERGROuaHH7Ct/QxX/Dirk1jmRMglHO4aRsjKtVZHERERkRqgAoaIiEg9YF+yCMM0ccdfZ3UUS31/9UACtn6D34FDVkcRERGRaqYChoiISD3gWPQenrBLMbv3sDqKpbQbiYiISP2lAoaIiIi3O3IE2+pVxaMvDMPqNJb68dJ2HL00hJAPVcAQERGpb867iKeIiIjUbfblSzBcLtwNeP2LM2UOH0jXf73HqdxcCAiwOo6ISIUt3r/Q6ggidZpGYIiIiHg5+/vv4WkbiCdqgNVR6oTMqy/H5vZgX7LI6igiIiJSjVTAEBHxIitXLqd3785ERIQzY8YzZc4XFBQwadKNRESEExMzgH379gJQVFTEnXcmEhUVQd++XXn++adrObnUmPx87B8sx33NtWDTX+sAR7qGcjy4DY5F71kdRURERKqRPumIiHgJt9vNtGn3smDBMjZt2sH8+e+QkbGjVJuUlNdp2bIV27fvYsqU+0lOfgSA996bT2FhARs3bic9fROzZ79WUtwQ72ZftRIjP7/B7z5SimEUj8L46AM4etTqNCIiIlJNVMAQEfESTucGwsLCCQ0Nw9fXl4SECaSllR4in5a2iIkTEwEYNy6B1atXYZomhmFw4sQJXC4XJ0+exNfXl4suam5FN6Sa2Re9h9mqFZ4rY6yOUqdkDR+AUVSE/YPlVkcRERGRaqIChoiIl8jOziIkpF3J6+DgEHJyss7axuFw0Lx5C/Ly8hg3LoGmTZty6aWBdOnSnqlTH8Tf37/c95k9exbR0ZFER0eSm3uw5jokVVdUhH3ZYtyjrgEfH6vT1Cl5vS7DDGiNfcn7VkcRERGRaqIChoiIlzBNs8wxo8yWmeW3cTo3YLPZ2bUrm6++2sPf/jaTPXu+K/d9kpImk57uJD3dSUBA6+qILjXE9ulqjCNHcI/V9JFfMu123KPGYF+5FIqKrI4jIiIi1UDbqIr8RNtWSV0XHBxCZub3Ja+zsjJp2zaoVJugoOI2wcEhuFwujh07ir+/P//979uMGBGLj48Pbdq0YeDAK9i82UloaFhtd0OqkX3p+5iNG+MeNsLqKDWqss9nd1w8jn+/ge2zNXiGDKvmVCIiIlLbNAJDRMRL9OsXxe7dO9m7dw+FhYWkps4jLi6+VJu4uHjmzk0BYMGCVGJihmEYBiEh7fnkk48wTZMTJ06wceM6LrusixXdkOpimtiXvI976HBo0sTqNHWSe9gITD8/7GnaTlVEpK5YvH+hvjiUStMIDCnlXA+Ta9pfW4tJROSXHA4HM2e+zNixI3G73UyalES3bt2ZPv1x+vaNJC4unsTE27njjluJiAinVSt/UlLmAfDrX9/LXXfdRlRUD0zT5JZbbiMioqfFPZKKKu/Z3OKbvcR+v5+i3yZbkMhLNG2KZ+hw7Evfp+j5F6HMlCsRERHxJipgiIh4kdjY0cTGji51LDn5iZLf/fz8mDNnfpnrmjVrVu5x8V7BH20EwB07xuIkdZtrzFgaLUvD+HI7pop2IiIiXk1TSERERLxQ0McbyOt5GbRta3WUOs096hpMw8C+VLuRiIiIeDsVMERERLyM34FDXLx9F1lDI62OUvddcgmeqAFaB0NERKQeUAFDRETEywStdgKQPay/xUm8gztuLPbNTozsLKujSD2wcuVyevfuTEREODNmPFPmfEFBAZMm3UhERDgxMQPYt28vAHl5eYwaNZQ2bZoxbdqUUtds2bKJqKgIIiLCefDB+8rdNltERFTAEBER8TpBH2/keHAbjnZqb3UUr+D+abce+9LFFicRb+d2u5k27V4WLFjGpk07mD//HTIydpRqk5LyOi1btmL79l1MmXI/ycmPAMVrFCUnT+epp2aUue/UqXfz8suz2LZtJ7t27WTlyuW10h8REW+jAoaIiIgXsZ8s4JK128geFqVdNSrI7NIVz6XhmkYiVeZ0biAsLJzQ0DB8fX1JSJhA2i/+d5WWtoiJExMBGDcugdWrV2GaJk2bNmXQoGgaNfIr1T4nJ4cffzzGgAGXYxgGN988ibQ0bTEpIlIe7UIiIiLiRS5Z+wWOgkKyh0RZHcV7GAbu0fE4XnsZfvwRLrrI6kTipbKzswgJaVfyOjg4BKdz/VnbOBwOmjdvQV5eHgEBAeXeMycni6CgkFL3zC5nutPs2bOYPXsWALm5B6vcF6k+5W11Led35p/bNe2vtTCJeBONwBAREfEiwR9tpLBZEw5GdrM6ildxjxmLUViI/cMVVkcRL1be2hRGmZFQFWlzofeEpKTJpKc7SU93EhDQ+vxhRUTqIRUwREREvIXHQ9Dqjfzvyr54fH2sTuNVPAMHYfr7Y1+i7VSl8oKDQ8jM/L7kdVZWJm3bBpVqExT0cxuXy8WxY0fx9/c/6z2DgkLIzs4sdc/AwKCzthcRachUwBAREfESF2/biV/eUbK1feqFczhwx47BvmIJuFxWpxEv1a9fFLt372Tv3j0UFhaSmjqPuJ8WiT0tLi6euXNTAFiwIJWYmGHnHIERGBhIs2YXsWHDOkzT5O233yIubmyN9kNExFtpDQwREREvEbR6Ix67jZwr+1odxSu54+JxvP0WtrWf4bkyxuo44oUcDgczZ77M2LEjcbvdTJqURLdu3Zk+/XH69o0kLi6exMTbueOOW4mICKdVK39SUuaVXN+1a0d+/PEYhYWFLF68kPffX0nXrt34619fYfLkX3Hq1EmuvnoUI0eOsrCXIiJ1lwoYIiIiXiLoo40c7NeNwpZahLIy3MNHYjZqhD1tkQoYUmmxsaOJjR1d6lhy8hMlv/v5+TFnzvxyr83I2Fvu8b59I3E6v6y2jCIi9ZWmkIiIiHiBppk/0HLnfrKHaveRSmvWDE/MMOxL34dyFk4UERGRuk0jMKTCtEWUiIh1gj7eCFCmgKFn84Vxx8XjO/VujG++xuzS1eo4IiIicgE0AkNERMQLBH20kaOXhnC8Q6DVUbyae9QYAO1GIiIi4oWqVMB46aW/EBnZncjIHiQm3sSpU6fYu3cPMTED6NmzE5Mm3UhhYWF1ZRUREWmQfI6doI3zK00fqQZmcAie3n2Lp5GIiIiIV6l0ASM7O4tXXvkba9Y4cTq/xONxM3/+PJKTH2HKlPvZtm0nLVu2IiXl9erMKyIi0uC0XbMZm8tN1rD+VkepF1xx8djWr4WDB62OIiIiIhegSiMwXC4XJ0+exOVykZ+fT9u2gXzyyUeMG5cAwMSJiSxerLm5IiIiVRG82smpVs051LOT1VHqBffoeAzTxL58idVRRERE5AJUuoARFBTM1KkP0qVLey69NJDmzVvQp08/WrRoicNRvDZocHAI2dlZ5V4/e/YsoqMjiY6OJDdX34CIiIiUq6iIwE83kTMkEtNutzpNvWD26o0nOETTSERERLxMpQsYhw8fJi1tEV99tYddu7LJzz/BypXLyrQzDKPc65OSJpOe7iQ93UlAQOvKxhAREanXbJ+n43vsBFla/6L6GAbu0ddgX7USTp2yOo2IiIhUUKULGB9//CEdO4bSunVrfHx8iI+/jvXrP+fo0SO4XC4AsrIyCQwMqrawIiIiDY19yfu4fX34YVAvq6PUK+7R8RgnTmD75GOro4iIiEgFVbqA0a5dezZuXEd+fj6mabJ69Sq6dOnG4MFDWbAgFYC5c1MYM2ZstYUVERFpUEwT+7LF/DAgAlfTxlanqVc8g4dgNm2qaSQiIiJepNIFjKioAVx7bQJXXNGXqKgIPB4PSUmTmT79WV566QUiIsI5dCiPxMTbqzOviIhIg2F8nYHtu91kD9P0kWrn54d7+EjsSxeDaVqdRkRERCrAUZWLH3vsTzz22J9KHQsNDePTTzdUKZSIiIhQ/I9rIHtIpMVJ6if36Hgci97D2LoFs09fq+OISB22eL92VqxJi/cv5Jr211odQ7xAlbZRFRERkZpjX7YYT68+nGwbYHWUesk9cjSmYeDQNBIRERGvoAKGiIhIXXTwILZ1n+MefY3VSeqv1q3xDBxUMtJFRERE6jYVMEREROog+4qlGKaJKy7e6ij1mnt0PLatmzGyMq2OIiIiIuehAoaIiEgdZF+2GE9gEGZvrc1Qk06PcNEoDBERkbqvSot4isi5F3U612JElb1ORBqAggLsH67AdcPNYBhWp/FaFXnOmp274Lk0HPvSxbjuvLvC14mIiEjt0wgMERGROsb26WqM48dxa/pIzTOM4mkkq1fB8eNWpxEREZFzUAFDRESkjrEvW4zZuDGemGFWR2kQ3KOvwSgsxL5qpdVRRERE5Bw0hURERKQuMU3sSxfjHjYCGje2Ok2D4Ln8CsxWrYr/3MdeZ3UcEZEG6VzT986kqXwNm0ZgiIiI1CHGl9uxfb9f26fWJh8f3FePxr48Ddxuq9OIiIjIWaiAISIiUofYl74PgDt2jMVJGhb36GswcnOxbVhndRQRERE5C00haYAqOjxLRERqz+ln8/CFb0HPTnxYuA72WxyqAXGPiMV0OIq3U71zoNVxREREpBwagSEiIlJH+B08zMXbdpI9JMrqKA1PixZ4rhxSMgJGRERE6h4VMEREvMjKlcvp3bszERHhzJjxTJnzBQUFTJp0IxER4cTEDGDfvr0l57Zv38bQoZcTGdmdqKgITp06VYvJpSICP9kEQPbQSIuTNEzu0ddg+zqDZvtyrI4idVhVnsPPP/80ERHh9O7dmQ8+WFFy/KWX/kJkZHciI3uQmHiTns8iImehAoaIiJdwu91Mm3YvCxYsY9OmHcyf/w4ZGTtKtUlJeZ2WLVuxffsupky5n+TkRwBwuVzcfvst/PWvr+J0fsXy5avx8fGxohtyDsEfb+BEYGuOdO5odZQG6fTCqUEfb7Q4idRVVXkOZ2TsIDV1Hk7nVyxcuJz7778Ht9tNdnYWr7zyN9asceJ0fonH42b+/HlWdE9EpM5TAUNExEs4nRsICwsnNDQMX19fEhImkJa2qFSbtLRFTJyYCMC4cQmsXr0K0zT58MOV9OjRk549ewFw8cUXY7fba70Pcnb2UwVc8vkXxaMvDMPqOA2S2TEUT/cIFTDkrKryHE5LW0RCwgQaNWpEx46hhIWF43RuAIqLzCdPnsTlcpGfn09gYFCt901ExBtoEU8RES+RnZ1FSEi7ktfBwSE4nevP2sbhcNC8eQvy8vLYtetbDMMgPn4kubkHSUiYwLRpD9dqfjm3Nuu24zhVSPZQrX9hJffoa2j9wjP4HD1OUYtmVseROqYqz+GcnCyiogaWujY7O4sBAy5n6tQH6dKlPY0bN2bYsKsZPvzqMu89e/YsZs+eBUBu7sGa6F6DcKGL2V/T/toaSiKVVd5/h/rvqeFQAUOkBmnHF6lOpmmWOWaU+aa+/DYul4u1a9P59NONNGnShLi4q+jTpx9Dh15Vpr0+JFsjaPVGipr4caB/D6ujNAhnez7792vBCLeHwDWb2T9mcC2nkrquKs/hs117+PBh0tIW8dVXe2jZsiW33HI977wzh5tuuqVU26SkySQlTQYgOlrr5IhIw6QpJCIiXiI4OITMzO9LXmdlZdK2belhxkFBP7dxuVwcO3YUf39/goNDiI6OISAggCZNmjBy5Gi2bt1c7vskJU0mPd1JerqTgIDWNdch+ZlpEvSxk/9F98Hjq7VJrHQoIpyTAS0J/kjTSKSsqjyHzzx++trAwCA+/vhDOnYMpXXr1vj4+BAffx3r139eOx0SEfEyKmCIiHiJfv2i2L17J3v37qGwsJDU1HnExcWXahMXF8/cuSkALFiQSkzMMAzDYPjwkXz55Tby8/NxuVysWfMJXbt2s6IbUg5j62aaHDik3UfqApuNnJhI2q7ZjK2wyOo0UsdU5TkcFxdPauo8CgoK2Lt3D7t37yQysj/t2rVn48Z15OfnY5omq1evonPnrlZ0T0SkztMUEhERL+FwOJg582XGjh2J2+1m0qQkunXrzvTpj9O3byRxcfEkJt7OHXfcSkREOK1a+ZOSUrySfatWrfi//5vG4MFRgMHIkaOJjY2ztkNSwrF0MaZhkDO4n9VRBMgaFkXYux8SsCmDA5f3tDqO1CFVeQ5369ad8eNvoF+/bjgcDl544e/Y7XaiogZw7bUJXHFFX+x2B7169SmZKiIiIqUZJ06UMyGvlkVHR5Ke7rQ6RoOhdRnqPi1E5P3qy3OtvvSjrvO7oh95tnw+mvu01VEEsJ8s4NrLJ/HdDSPY8vs7Sp3T89n71YfnWn3og1Uqu4inPj/XbXo2e7+KPtc0hURERMRCRlYmtq2byR6i3UfqCnfjRvxweU+CPtoI1n/PIyIiIj9RAUNERMRC9mVpANo+tY7JHhpFs6wDtNi53+ooIiIi8hOtgVFPaZibiEjdU96zeXDqLJq1b8uxS0MsSCRnkz2keEHVoI83cvSyDhanEREREdAIDBEREcs4jufTZt12soYPAMOwOo6c4VQbf/IiwrWdqkgDt3j/Qn0xKFKHqIAhIiJikcBPN2MvcpF11QCro0g5sof2x3/7TvwOHrY6ioiIiKAChoiIiGWCV63n1MUtyOt1mdVRpBxZw6IwTJPATzZZHUVERERQAUNERMQStsIigj7ZRNbQKEy73eo4Uo6jl3XgRFBrgj/eYHUUERERQQUMERERS7TZ8CU+J05q+khdZhhkD43iks+/wH6qwOo0IiIiDZ4KGCIiIhYI/nA9RU38+OHynlZHkXPIGhqF41QhbdZuszqKiIhIg1elAsaRI0eYODGBPn260LdvV9avX8uhQ4cYM2YEPXt2YsyYERw+rIWvRERESvF4CP5oA/+7sg+eRr5Wp5FzOBjVnaKmjQn+WLuRiIiIWK1KBYyHHprKiBGxbNnyNevWfUHnzl2ZOfMZhgy5im3bdjJkyFXMnPlMdWUVERGpF/y376LxwcOaPuIFPL4+5FzZh6DVTvB4rI4jIiLSoFW6gHHs2DE+++xTEhNvB8DX15eWLVuyZMkiJk5MBGDixETS0rRvsoiIyJmCV63HY7eRPbif1VGkArKHRtH44GH8v9xldRQREZEGrdIFjD17viMgoDW//vVtXH55H+655w5OnDjBgQM/EBgYCEBgYCAHDx4o9/rZs2cRHR1JdHQkubkHKxtDRETE64SsWs+BqB4UtWhmdRSpgJzB/fDYbQSv0m4kIiIiVqp0AcPtdrF162buvPNu1q7dQpMmTS9oukhS0mTS052kpzsJCGhd2RgiIiJe5aLvMmn+XRZZwzV9xFsUtryIA/0jCFm5FkzT6jgiIiINVqULGEFBIQQHhxAVVfwBbNy4BLZu3UybNpeQk5MDQE5ODq1bt6mepCIiIvXA6W/xs4b1tziJXIjMEQNpvjcbI2OH1VFEREQarEoXMNq2bUtISDu+/fYbAFavXkWXLt0YPTqeuXNTAJg7N4W4uLHVk1RERKQeCF61nkPdL+VkYIDVUeQCZA0fgGkY2Be9a3UUERGRBstRlYtnzHiJpKSJFBYWEhoaxquvvoHH4+HWW2/grbdeJySkPXPmzK+urPILi/drgVQRkbrmXM9mvwOHCPjiW7bfd3MtJpLqcKp1K3L7duHiRe/h+t3jVscRERFpkKpUwOjVqzfp6c4yx5cuXVWV24qIiNRLJdNHrtL0EW+UOXwgrZ99A+O73Zhhl1odR0REpMGp9BQSERERuTAhK9dyLDSYo53aWx1FKiFzxEAA7IvesziJiIhIw1SlERgiIiJSMY0OHaXNxi/JuOM6MAyr40gl5Ae3wd2nH/ZF7+K6/yGr44iIyE9+OX3zmvbXWpREappGYIiIiNSC4FUbsLk9ZI4cZHUUqQL32PHYN67HyMq0OoqIiEiDowKGiIhILQhZuZYf27flSJeOVkeRKnCPvQ4A+/sLLE4iIiLS8KiAISIiUsN8jh7nknXbyLz6ck0f8XLmZZ3xdO2u7VRFREQsoAKGiIhIDQv+eAM2l7u4gCFez33teGyfrYEDB6yOIiIi0qCogCEiIlLDQlas5URgaw71CLc6ilQDV/x1GB4P9iWLrI4iFli5cjm9e3cmIiKcGTOeKXO+oKCASZNuJCIinJiYAezbt7fk3PPPP01ERDi9e3fmgw9WlBw/cuQIEycm0KdPF/r27cr69WtroysiIl5HBQwREZEa5PPjCdp+tpXMkZo+Ul+YET3xhF2KQ9upNjhut5tp0+5lwYJlbNq0g/nz3yEjY0epNikpr9OyZSu2b9/FlCn3k5z8CAAZGTtITZ2H0/kVCxcu5/7778HtdgPw0ENTGTEili1bvmbdui/o3LlrrfdNRMQbqIAhIiJSg4JWO7EXufhe00fqD8PAHX8dttWr4PBhq9NILXI6NxAWFk5oaBi+vr4kJEwgLa30SJy0tEVMnJgIwLhxCaxevQrTNElLW0RCwgQaNWpEx46hhIWF43Ru4NixY3z22ackJt4OgK+vLy1btqz1vomIeAMVMERERGpQyIq15F9yMXm9LrM6ilQj97gEjKIi7GmaRtKQZGdnERLSruR1cHAIOTlZZ23jcDho3rwFeXl55OSUvTY7O4s9e74jIKA1v/71bVx+eR/uuecOTpw4Uea9Z8+eRXR0JNHRkeTmHqyhHoqI1G0qYIiIiNQQx4mTtE3fQubVA8Gmv3LrE0+/KDwdQ3G8+x+ro0gtMk2zzDGjzNSw8tuc7Vq328XWrZu58867Wbt2C02aNGXmzLJrayQlTSY93Ul6upOAgNaV7oOIiDfTpykREZEaEvjJJhwFhXx/9SCro0h1Mwzc42/E9tEHkJtrdRqpJcHBIWRmfl/yOisrk7Ztg0q1CQr6uY3L5eLYsaP4+/uXOn762sDAIIKCQggODiEqagBQPO1k69bNtdAbERHvowKGiIhIDWm/NJ2TrVuR16ez1VGkBrjG34jhdmN/X4t5NhT9+kWxe/dO9u7dQ2FhIamp84iLiy/VJi4unrlzUwBYsCCVmJhhGIZBXFw8qanzKCgoYO/ePezevZPIyP60bduWkJB2fPvtNwCsXr2KLl261XrfRES8gcPqACIiIvWRz48nCPx0E7tuGoVpt1sdR2qA2bMXnss645g/D3fSZKvjSC1wOBzMnPkyY8eOxO12M2lSEt26dWf69Mfp2zeSuLh4EhNv5447biUiIpxWrfxJSZkHQLdu3Rk//gb69euGw+HghRf+jv2nZ8OMGS+RlDSRwsJCQkPDePXVN6zspohInaUChoiISA0I/nA99iIX++OirY4iNeWnaSSOZ6ZDTg4EBlqdSGpBbOxoYmNHlzqWnPxEye9+fn7MmTO/3GsffvhRHn740TLHe/XqTXq6s3qDiojUQypgiNRBi/cvPOu5a9pfW4tJRKSy2i9Zw/F2l3AoopPVUaQa/fL53HxQAKNMk6/feJwuv/+nRalEREQaBq2BISIiUs0a5R3hknXb2D86GsrsUCD1ybHwdhy5rAPtlqVbHUVERKTeUwFDRMSLrFy5nN69OxMREc6MGWW32SsoKGDSpBuJiAgnJmYA+/btLXX+++/306ZNM158cUYtJW6Y2i3/HJvbw/7RV1odRWrB/tHRtN78NcYZO0yIiIhI9VMBQ0TES7jdbqZNu5cFC5axadMO5s9/h4yMHaXapKS8TsuWrdi+fRdTptxPcvIjpc4/8sj9XH31qNqM3SC1X7qGo+HtOHpZB6ujSC3YP+oKAOzv/tfiJCIiIvWbChgiIl7C6dxAWFg4oaFh+Pr6kpAwgbS0RaXapKUtYuLERADGjUtg9epVmKYJwOLFC+nYMYyuXbvXevaGpEn2QVpv/pp9cRp90VCcaB/IoR7h2FPnWR1FRESkXlMBQ0TES2RnZxES0q7kdXBwCDk5WWdt43A4aN68BXl5eZw4cYIXXniW3//+D7WauSE6vRbC/tHafaQh2T/qCuybnRi7d1kdRUREpN5SAUNExEucHklxJqPMApHlt3nyyT8wZcr9NGvW7LzvM3v2LKKjI4mOjiQ392Bl4zZYHZakk9ezEyfaa0vNhmT/qOKClf2/b1ucREREpP5SAUNExEsEB4eQecYigVlZmbRtG1SqTVDQz21cLhfHjh3F398fp3M9jz32MF27duTvf3+RGTOe4tVXXy73fZKSJpOe7iQ93UlAQOua61A9ZHz7Da0yviv5x6w0HCcDA3APHoLjnX9DOcVGERERqToVMERE/r+9O4+OokzbOPzr7sqCICRRlpCIEINIIAxbBBQIoigaDGBQNiEaFmVAQWRARRTFBRUcFR0VJU5YFCWKSBAEF1TGhYmCIORTRAJmUXZZs3R3fX+gGQNJgGzV6b6vczwnXanqut9T9GPz8NZbNUSHDjFs376NzMwdFBQUkJq6mLi4+GL7xMXFs2hRCgBLl6YSG9sTm83GmjWfk5GRSUZGJmPHTmDSpPu4/fZxVgzDqxlL3sC02XT7iI9yDhqGfftP2P/7tdVRREREvJIaGCIiNYRhGMye/Tx9+15D+/YtSUi4iaioVsyY8QArVrwHQGLiCPbv30d0dCRz5jzNww+f+qhVqSKmieP1+ezu1Jq8BiFWpxELuPoPwAwMxPHGAqujiIiIeCXD6gAiInLmeve+jt69ryu2bdq0h4t+DgwMZOHCJWW+x9Sp06sims+zf7EOe+YOMm+7o6At+wAAIABJREFU0+ooYpW6dXH16YeRupjCJ/4J/v5WJxIREfEqamCIiIhUAmNRCmbt2mT16mx1FLGQc/AwjNTFOFavxNWnr9VxRHzK8l3vWh1BPERZfxaub9KvGpNIZdMtJCIiIhV17BiOd97C1W8Aztq1rE4jFnJfdTVm/Qa6jURERKQKqIEhIiJSQY60ZdgOH8Y5NNHqKGI1w8B542Ac7y+HAwesTiMiIuJVKtzAcLlcdOnSjoSEPgBkZu4gNrYTbdo0Z/jwgRQUFFQ4pIiIiCczFqXgvqAJ7m6xVkcRD+AcMgxbQQGOpWWvRyMiIiJnp8INjBdeeJYWLVoWvZ42bQrjxt3Fpk3bCAoKJiVlXkVPISIi4rFsuTnYP16Da/AwsGtio4DZtj3ullEYfzzSWERERCpHhb5pZWdnsWrVCm65ZSQApmny6acf07//AACGDk1k+XItpiMiIt7L8cZCbG43ziHDrY4insJmw3nzrTi++gLb/2VYnUZERMRrVKiBMXnyBB599Ensf/yL0759+6hXLwjDOPFwk7CwcHJysks8Njl5Ll27dqRr147s3bunIjFERESsYZoYr8/H1akLZvOLrU4jHsQ5ZDimYWDMT7Y6ioiIiNcodwNj5co06tdvQLt2HYq2maZ5yn42m63E45OSRrNuXTrr1qVz/vn1yxtDRETEMvb09dgztuDS4p1ysgYNcMXFn7iNROuBiYiIVAqjvAd++eV/WLHiPT744H3y8vI4fPgQkydP4PffD+J0OjEMg+zsLEJDG1dmXhEREY9hJM/FrF0b542DrY4iHsg5fATGsndwrEzD1fcGq+OIiAiwfFfxJQ6ub9LPoiRSHuWegfHww4+zbVsWGRmZpKQsJja2J6+9toju3a9g6dJUABYtSqFPn76VFlZERMRjHDqEI3UxrgGDoG5dq9OIB3L3ugZ34zCMf79qdRQRERGvUOnLpc+Y8QRz5jxNdHQk+/fvIzFxRGWfQkRExHLGkjewHTuGM2m01VHEUzkcuIbdiv3DD7Bl/WJ1GhERkRqvUhoY3bv34O230wBo1iyCzz5bz+bNP7Fw4RICAgIq4xQiIiIexUiei7t1G9wdYqyOIh7MOexWbG43joX/tjqKiIhIjacH1ouIiJwl24ZvsW/8Fueto6CUxapFAMxmEbh6XHniaSRut9VxREREajQ1MERERM6S8e9XMAMDcQ662eooUgM4bxmJfWcm9o/WWB1FKsHq1ato27YF0dGRzJo185Tf5+fnM3z4QKKjI4mN7cTOnZlFv3vqqceJjo6kbdsWrFnzQbHjXC4XXbq0IyGhT1UPQUSkxlIDQ0RE5GwcOYLx5iJcN9wEQUFWp5EawBXfH/P8+hiv/MvqKFJBLpeLiRPHsnTpSr75ZitLlrxBRsbWYvukpMwjKCiYzZt/Yty4u5g2bQoAGRlbSU1dTHr6Ft59dxV33fV3XC5X0XEvvPAsLVq0rNbxiIjUNGpgiIiInAXH229iO3z4xO0jImciIADnraNwrEzDtmun1WmkAtLT1xMREUmzZhH4+/szYMAg0tKWFdsnLW0ZQ4cmAtC//wDWrv0I0zRJS1vGgAGDCAgIoGnTZkRERJKevh6A7OwsVq1awS23jKz2MYmI1CRqYIiIiJwp08TvpedxR7XG3eVyq9NIDeIccRsAxqsvWZxEKiInJ5vw8AuKXoeFhZObm13qPoZhULduPfbt20du7qnH5uScOHby5Ak8+uiT2O36ai4iUhbD6gAiIiI1hf2Lddg3bST/+blavFPOinlBE1xx8Rgpr1J434MQGGh1JCkH0zRP2WY7pRaUvE9px65cmUb9+g1o164Dn322ttRzJyfPJTl5LgB79+45q9zeZvmud62OICIWUQPDw6lAi4h4DuOlOZjBwSy/rC4u1Wc5S87RYzGWv4vjnSW4hgyzOo6UQ1hYOFlZvxS9zs7OolGjxsX2adz4xD5hYeE4nU4OHfqdkJCQou1/PTY0tDErVrzHihXv8cEH75OXl8fhw4dISrqZ5OSFxd43KWk0SUmjAejatWMVjlJExHNpnpqIiMgZsGVn4Vj2Ds7EkbhqBVgdR2og9xVX4r64BcbcF6yOIuXUoUMM27dvIzNzBwUFBaSmLiYuLr7YPnFx8SxalALA0qWpxMb2xGazERcXT2rqYvLz88nM3MH27dvo2PFSHn74cbZtyyIjI5OUlMXExvY8pXkhIiInaAaGiI8oazbP9U36VWMSkZrJeOVFME2co/8ObLQ6jtRENhvOUX/H/x/jsX+bjrv9iX9FV32uOQzDYPbs5+nb9xpcLhfDhycRFdWKGTMeoH37jsTFxZOYOIKRI4cRHR1JcHAIKSmLAYiKakVCwk106BCFYRg8/fQLOBwOi0ckIlKzqIEhIiJyOnl5GK/NxRUXj3lhU9ilBoaUj3NoIn7T78N4cQ4Fr6RYHUfKoXfv6+jd+7pi26ZNe7jo58DAQBYuXFLisZMnT2Xy5Kmlvnf37j3o3r1HpeQUEfFGuoVERETkNBxLFmPbuxfn7XdYHUVqunr1cA67FceSN7Dl5lidRkREpEbRDAyRGkZTjUWqmWni9+JzuFu2wh17hdVpxIOdaX12jrsLY+6/MP71HIUzZlZHNBEREa+gGRgiIiJlsK/9GPt3GygcN0GPTpVKYTaLwNUvAWPeS3D4sNVxREREagzNwBARESmD3z+fxGzYCNdgPfZSKo9z/CSMd5ZgpMyD+KZWxxER8VllzZ4riWY8W0szMEREREph+24jjo9WUzh2AgTo0alSedwdL8XVtTvG8//EVui0Oo6IiEiNoAaGiIhIKfyeeQrz3HNxjrjN6ijihZzjJ2H/ZRcXrP7S6igiIiI1ghoYIiIiJbDtzMTx9ps4k26DoCCr44gXcvWOw93iEi6Z9y6YptVxREREPJ4aGCIiIiUwnpsNdjvOseOtjiLeym6n8M67Cc74mUb/2Wh1GhEREY+nBoaIiMhJbLk5GK+9gmvwMMywcKvjiBdzDRnO0dDzafXCm5qFISIichpqYIiIiJzEePpJcDopnDzV6iji7fz9yRiVwPkbf6DBV5utTiMiIuLR1MAQERH5q9xcjOSXT8y+aBZhdRrxATsSruRYw/M0C0NEROQ0DKsDyNk/e1ikNPqzJFJxfs88BYWFfHDzpRzRZ0oqSZn12d+P/xvZn/aPvkr9/25hz6Wtqy+YiAfT9xoROZlmYIiIiPzp118x5r2Ea+BQjlwYanUa8SHbb+zF8frBtH5+sWZhiIiIlEINDBERkT/4zXoc8vO19oVUO3eAPxmjE2jw3y00/OI7q+OIiIh4JDUwRERqkNWrV9G2bQuioyOZNWvmKb/Pz89n+PCBREdHEhvbiZ07MwH46KM1XH55B2Jiorn88g6sXftxNSf3fLbMHRivvogrcQRm84utjiM+aPtNV3MkrAF/m70A3G6r44iIiHgcNTBERGoIl8vFxIljWbp0Jd98s5UlS94gI2NrsX1SUuYRFBTM5s0/MW7cXUybNgWA8847n9TU5fz3v5uZOzeFkSOHWTEEj+b38DRwOCi870Gro4iPcvv78f0dgwnO+JkLVn1hdRwRERGPowaGiEgNkZ6+noiISJo1i8Df358BAwaRlras2D5pacsYOjQRgP79B7B27UeYpknbtu0IDW0MQFRUK/Lz88jPz6/2MXgq26bvcLz1Os6xEzAbh1kdR3zYrj7dOHjxhUQ/+zq2QqfVcURERDyKGhgiIjVETk424eEXFL0OCwsnNze71H0Mw6Bu3Xrs27ev2D7vvvs2bdq0IyAgoMTzJCfPpWvXjnTt2pG9e/dU8ig8k/+D90JQEIUTp1gdRXyc6XCwacJQzt2VS0Tqh1bHERER8ShqYIiI1BBmCU8msNlsJ+9V5j5bt25h2rQpzJnzcqnnSUoazbp16axbl87559cvd96awv7xhzhWr6Tw7hNNDBGr5fboyO4OUbR+/g04eNDqOCIiIh7DKO+BWVm/MGrUcH777Vfsdju33jqasWPHs3//foYPH8iuXZk0adKUBQveIjg4uDIzi4j4pLCwcLKyfil6nZ2dRaNGjYvt07jxiX3CwsJxOp0cOvQ7ISEhRfsPHtyfV16ZT0TERdWa3WMVFuI/eTzuZhE4x9xhdRqRE2w2Nt6bRK8b/4Fz5gwKZ862OpGIiPxh+a53K3T89U36VVIS31TuGRgOh8Fjj83m228z+OSTr5g79wUyMrYye/ZMevS4kk2bttGjx5XMnn3qKvkiInL2OnSIYfv2bWRm7qCgoIDU1MXExcUX2ycuLp5Fi1IAWLo0ldjYnthsNg4ePMgNN8Tx0EOP06XL5VbE90jGKy9iz9hK4cynITDQ6jgiRQ60uoifE67EePE5bD/+YHUcERERj1DuGRihoaGEhoYCcO6559KiRUtycrJZsWIZK1euBWDo0ESuvbYHjzzyRKWErckq2qkTETEMg9mzn6dv32twuVwMH55EVFQrZsx4gPbtOxIXF09i4ghGjhxGdHQkwcEhpKQsBuDll5/n559/YubMGcycOQOA995bTYMGDawckrX27IEZ95F7eVs+i3aD6rR4mM3jhxKxej3+90wk/50VVscRERGxXLkbGH+1c2cm3323gZiYTuze/VtRYyM0NJQ9e3aXeExy8lySk+cC+MwicSIiFdW793X07n1dsW3Tpj1c9HNgYCALFy455bgpU+5nypT7qzxfTeL38P04juWx4d4kOGUtERHr5Z8fROE9D+B/3yTsK9NwX9vH6kgiIiKWqvAinkeOHGHIkASefPIZ6tate8bH+doicSIi4jnsX3+J8dorbBt6HYcvuuD0B4hYxDnmDtwto/C/aywcOWJ1HBEREUtVaAZGYWEhQ4YkMHDgUPr2vQGABg0akpubS2hoKLm5udSv78PTk0VqiNPd4uRNiw35vfssfu89V2ybabNBQG3MWnUwQ0JxN2mFu2VnXG2vBMPfoqRSZQoK8B87CjMsnO/vGGx1GpEyLf/1fc6//2auHHofv0wewsZ7kop+5021+WQl1eqyHEveXoVpilu9ehWTJ4/H5XKRmDiSSZPuKfb7/Px8Ro0azoYN3xASch7z57/JhRc2BeCppx5n/vx5OBwOnnrqOXr1uqbUhfFFRDzV2dToyq7P5W5gmKbJmDEjaNGiJXfeObFo+3XXnVhAbtKke1i0KIW4uL6VElREpLKZdc//34vCPGwHf8N+4Fcc2zfAJwsx6wRT2P8unD2G6BYDL2I8/QT2jC3kvZ2Gs3ah1XFETmtv+5b8NPAami9Ywc7rYznQyreeIlSsVlvM5XIxceJYli9fQ1hYON26xRAXF0/LllFF+6SkzCMoKJjNm39iyZLFTJs2hfnz3yQjYyupqYtJT99Cbm4OffpcxXff/Vi0MH67du05fPgwXbt2oGfPXsXeU0TEU1V3jS53A+PLL//DG28soFWraDp3bgvA9OmPcffd9zBs2E3Mnz+P8PAmJd6LLSLiCY4/83XxDW4XtpyfcGxZh/HRAux7f8F/wQPYt6VTMOppNTG8gO2H/8PviUdwDhiEu3ecFu6UGmPTxGGEfbyemGn/Ys1bT2IaDqsjVZtTarWF0tPXExERSbNmEQAMGDCItLRlxZoNaWnLmDp1OgD9+w/g7rvHYZomaWnLGDBgEAEBATRt2oyIiEjS09fTqVOXEhfGVwNDRGqC6q7R5W5gXHZZV44eNUv83fvvf1TuQCIilrE7MMNb4AxvgbPHEPxfuwdjfRrGV+/hDrsYZ9wYqxNKRTid+I9Jgtq1KXjyGavTiJyVwrq1+eb+UXQd/yQtX05l69iBVkfySTk52YSH/2/dnLCwcNLTvy51H8MwqFu3Hvv27SM3N5uYmM7Fjs3JyS527F8XxhcRkVNVylNIRES8TkAtCkY+hf3XHdh3bcHv/Zdwxg6GOkFWJ5NyMmbPxPH1l+S/9jo0bGh1HJGzln11FzKv706rF9/i1+7toYnViXyPaZ76j3e2U2bnlbzP6Y493cL4nv4Ev9OtpyUiUhkq/BQSERGvZfhT2OfErAvb8SM4NqyxOJCUl/3bdPweewjnjYNx3aSFO6Xm+vb+0eTVD6bTlGfh2DGr4/icsLBwsrJ+KXqdnZ1Fo0aNi+3TuPH/9nE6nRw69DshISHFtv95bGjoiWNLWhj/ZHqCn4iIGhgiImVyte6OaT9xr7njB8+5D1vOwrFj+I+4GbNhIwr++YLVaUQqpLBubb5+7E7q7sjGb9oUq+P4nA4dYti+fRuZmTsoKCggNXUxcXHxxfaJizuxoD3A0qWpxMb2xGazERcXT2rqYvLz88nM3MH27dvo2PHSUhfGFxGRU+kWEhGRsgTWxqx/AbbfMrHt3mV1GikH/7vvwP7jD+SlfQjBwVbHEamw3V3a8EPi9bR46Xnc3Xrg6pdgdaQqVWtC2etBOC+No3DIA9WSxTAMZs9+nr59r8HlcjF8eBJRUa2YMeMB2rfvSFxcPImJIxg5chjR0ZEEB4eQkrIYgKioViQk3ESHDlEYhsHTT7+Aw+Hgiy/Wlbgwfu/e11XLmEREKqKsGp33jwWYYRdX6vnUwKgkuu9PxHuZtU+se2E7+rvFSeRsOVKSMeYns+W2AXx/0WE9dUS8xqaJw4jcuhv/MUnktW6DGdnc6khVxnZob9m/P364mpKc0Lv3dac0F6ZNe7jo58DAwFKfwjd58lQmT55abFtZC+OLiHi6Mmu0y1np51MDQ0TkdEpYeE08n23jBvwnjuXXzm3Ycscgq+OIVCq3vx8FC94i8LJ2BAwdQN7ar6BWLatjVYljydutjiAiIqWo7hqtNTBERE7DduzEzAtTTyCpOfbvJ+DmAZgh5/HV7ImYDofViUQqnXlBE/JfXYj9+03433Gbmq0iIuL11MAQESlL3lFse06sGm820DMLa4SCAgKG3IAtO4uChUvID6lndSKRKuO+5loKpj2M8cYCjFkzrY4jIiJSpXQLiYicVllrvFzfpF81Jql+ju8/w+Z2AeBqUfZCcuIBTBP/caNxfP4p+fMW4u7UReteiNcqqs2DW9N5Q3cunH4f/w06QNY1l3l9bRbraN03kYo5k8+Qanjp1MAQESmNswC/tBcBMGudi6v91RYHktMxnnoMY1EKBVOn4xo01Oo4ItXDZmP9I2Opnb2bTlOe5XjD80ATxkRExAvpFhIRkZIU5OE/bzL2XVsAKIwbA+fUtTiUlMV49SX8H7of58ChOO+tnkcqingKd4A/6+ZM4XjDELrd/gi2zZusjiQiIlLp1MAQEfmT240t6weMD+YReH9vjK+XA+Ds0g/ntaMtDidlcby+AL8Jf8fVO46Cl5LBZrM6kki1yz8viLXJD+EKDCAw/mpsP22zOpKIiEil8slbSHz5fn4R+Z9aE/6ypoWzAI4fwWa6izaZdUIovOEunD2GWJDON5WnPjuWpuJ/2y24u19B/sIl4O9fVfFEPN6xsAasTZ7OtYkPEdDnKvJXfoLZLMLqWBVSrFaXIn/cv3BHdqiGNCIiYiWfbGCIiADYDu0FwLTZwP8czHr1cZ/XGHeTKNwtL8PVticY+suwJ3Msmo//mCTcMZ3If2sZ1KpldSQRyx2OCCdv2WoCr7+KgF7dyE/7EPOSllbHKrc/a3WZnIVVH0RERCynBsZZ0KrLImfHE2c7FfYbT2G/8ZacWyqX8fIL+E8chyu2J+/OHolz/4ew3+pUIp7BbNuOvFWfEnh9LwKv6U7estWYbdsBnlmbT6ZaLSLiuays0VoDQ0REaha3G7+Hp+E/cRzOPn3Jf2cFztqaeSFyMrNVa/JWf4YZWIvA3rHYV6+yOpKIiEiFaAbGSTTLQkTEMy3f9S6O4/l0uvdZLvjgS35OuIr0B2/G3K2/lImUxoxsTv7HXxCQ0IeAhDgKZz0H14ZZHUssou+5IjXD2XxWPWXmXHVRA0NEKkRfhqS6nJO9m8vHP0nw1p/ZMOUWfkyM19NGREpxcm02XptC53/8k7CJ4+jw9dVsuHcE7gCt8SMiIjWLbiERERGPF7bmK665YSJ1duby+Qv38uMtfdW8EDkLztq1+M+cKWSM6E/km6u5avA91MnMsTqWiIjIWVEDQ0REPJbjWB7tZ8yl651PcKRJKKvfmU3uFTFWxxKpkUyHg02ThvP5v+7jnJw9XD1gEk2XfgymaXU0ERGRM6IGhoiIeKQGX26id98JNH99JT/cEs9Hix7j6AWNrI4lUuPlXBHD6nee5sAlzeh03xy63fYItXLP4FGlIiIiFvPaNTB0X76IZ6sJj/GTqnG6+hy45wDRzywk4p2POXxhKB8teJS9HaOqKZ2IbzjWuD6fzJ9B89dX0ubpBVx7/Z1sGTuQFUMLcfv7lXiMarOIiFjNaxsYIiJSs9jzC7h4fhpRLy3BXugkY2R/towdiCswwOpoIt7JbmfbzXHkxHag/SOv0vbJfxOxZA0b/5FIbo+OWmdGREQ8To1uYGiWhYiIZzqb+uw4ns9Fb63mknlLqbXnANk9Y9j4j1s40rRxFSYUkT8dvaARn798P6GffkPbmcl0//tj7GvTnO/HDuTXbu3VyBAREY9RoxsYIiJSc/kfOETE2x9xccp71Np7kN8ubc2Xsyay59LWVkcT8Um5sR34rUsbmi5bS9RLS4i97RH2tWnOD7f0JeuqTlbHExERUQNDRESqkWkSsnkbkW+sosn763AUFPJr5zZ8+fQk9sS0sjqdiM9z+/vx8429yOzbg6bL1tLylbe5bOIsjtcPxjF6C65bRmI2DrM6poiI/MHT7kqo6vWS1MAQEZEqd+6ObJq8v44mKz6n7o5sCs8JZMcNV/LT4N78fvGFVscTkZP82cjYcUNPGn2+gcjXV9L40emYjz2Eu1sPnAOH4OqbAMHBVkcVEREfogaGiIhUOntBIfXTt9LoPxto9PkGgrbtwrTZ2B3Tih8Tr2dnXDecdc6xOqaInIbpcJDboyO5PToS74zGsXghxluvEzB2FOb4Mbgv64qr17W4rr4Ws1VrrZchIiJVSg0MERGpPE4n/oNvoP8nqzGO5+PyM9jTIYoNCVex69rLyWsQYnVCESknM+IinPc9iPPeB7Bt3IDxzls4Vq/Ef9oUmDYFd+Mw3Jd1w935MtyduuCO/hv4lfxIVhERkfJQA0NEPE5Z9/JV9X11UkGGAYEnbg/Jvbwtey5tjbN2LatTiUglKFabzwNGdYZRnan12z6u2WrD8dEH2L/4HCN1MQBmrVq4W0VjRrXG/cd/ZlQrzEahmqkhIiLlYq+qN169ehVt27YgOjqSWbNmVtVpRER8yulqa35+PsOHDyQ6OpLY2E7s3JlZ9Lunnnqc6OhI2rZtwZo1H1RZxoIFb/Ht/aPIvSJGzQsRH3C84Xm4EpMomP8meduyOP7DLvLnv4kz6TaoXQfHyjT875lIYPzV1IoMo1b92gS2b0lAv2vxGz8GY/YTOBYvwv7RGmybvoPcXCgstHpYpaqKOqzvzSIiZ6ZKZmC4XC4mThzL8uVrCAsLp1u3GOLi4mnZMqoqTiciPqS6V1r2pBkfZ1JbU1LmERQUzObNP7FkyWKmTZvC/PlvkpGxldTUxaSnbyE3N4c+fa7iu+9+xOFwWDgiEfEWp9TmGH+IiQViAQjYd5B6P/1C3Z9+oXb27j/+20bt//6HgIOHS3zP/Hp1yA+ui7POORTUOQdnnVoU1jmHwjrn0CysHc4Rt2GGhVfxyIqrijoM6HuziMgZqpIGRnr6eiIiImnWLAKAAQMGkZa2TIVYRKQCzqS2pqUtY+rU6QD07z+Au+8eh2mapKUtY8CAQQQEBNC0aTMiIiJJT19Pp05drBiKiPiY/POC2H1eELs7RZ/yO+PocWrt3k/Avt8J3P87Aft//9/PBw5jHDmG39FjBO48iN+R4/gdPYZxZCXOvglQzQ2MqqjDgL43i4icoSppYOTkZBMefkHR67CwcNLTvy62T3LyXJKT5wLw44//R9euHasiCgB79+7h/PPrV9n7eyJfHDP45rg15qr1BI+U67hduzIrNwhnVlv/uo9hGNStW499+/aRm5tNTEznYsfm5GSXeB7V56qlMfsGXxwzVNW4bUBtqFMb6vxl89iR5Xq3itTnqqrDp3tPqN7aXBpf+XPtK+MEjdUbWT3Oqv7uXCUNDNM0T9lmO2mxpqSk0SQlja6K05+ia9eOrFuXXi3n8hS+OGbwzXFrzL7jTGorlLzPmR17gupz1dKYfYMvjhm8f9xVUYfdbvcZvGf11ubSePv1/ZOvjBM0Vm/k7eOskkU8w8LCycr6peh1dnYWjRo1ropTiYj4jDOprY0b/28fp9PJoUO/ExISUmz7n8eGhqoui4icjaqow/reLCJy5qqkgdGhQwzbt28jM3MHBQUFpKYuJi4uvipOJSLiM86ktsbFxbNoUQoAS5emEhvbE5vNRlxcPKmpi8nPzyczcwfbt2+jY8dLrRiGiEiNVRV1WN+bRUTOnGPq1OnTK/tN7XY7F13UnBEjbuall+YwePDN9OuXUNmnOSvt2nWw9PxW8MUxg2+OW2P2DaXV1hkzHuDIkcNcfHELWrduw5tvLuLBB+9j06aNPPfcSwQHB1O/fgMOHNjP2LEjeeut15k1aw7Nm19s9ZAA37yWGrNv8MUxg3ePuyrqsCd+by6LN1/fv/KVcYLG6o28eZy2o0dLuCFPRERERERERMSDVMktJCIiIiIiIiIilUkNDBERERERERHxeF7XwLj99iQuvLABHTu2Ltq2f/9++vTpRZs2zenTpxcHDhywMGHlK2nMjz46ncjIMDp3bkvnzm1Ztep9CxNWvqysX7j22ito374lHTu24oUXngW8+1qXNmZvvtZ5eXl0734pnTr9jY4dW/HIIw8CkJm5g9jYTrRp05zhwwdSUFBgcVI5HV+szaD6rPrsvdda9dm7+VKDVB+uAAAEQ0lEQVTN9pU67Uu12Zdqsi/WYq9bA2Pdus+oXbsOo0YNJz39ewCmTp1McHAIkybdw6xZMzl48ACPPPKExUkrT0ljfvTR6dSuXYcJEyZZnK5q5Obm8uuvubRr157Dhw/TtWsHFi9+l4UL/+2117q0Mb/zzltee61N0+To0aPUqVOHwsJCrrqqK0899Sxz5jxNfPwN3HjjIO6883aio//GqFFjrI4rZfDF2gyqz6rPqs+qzzWTL9VsX6nTvlSbfakm+2It9roZGF27dickJKTYthUrljF0aCIAQ4cmkpb2rhXRqkxJY/Z2oaGhtGvXHoBzzz2XFi1akpOT7dXXurQxezObzUadOnUAKCwspLCwEJvNxqeffkz//gOAE9d5+XLvuc7eyhdrM6g+qz57L9Vn7+ZLNdtX6rQv1WZfqsm+WIu9roFRkt27fyM0NBQ48Qd6z57dFieqHi+//DyXXtqG229P8orpYKXZuTOT777bQExMJ5+51n8dM3j3tXa5XHTu3JamTRvQs2cvmjW7iHr1gjAMA4CwsHCv/Z+St/OVz2tJvPkz+1eqz959rVWffYuvfIb/5M2fXV+qzb5Qk32tFvtEA8MXjRw5hu+/385XX22kUaNQ7r33bqsjVYkjR44wZEgCTz75DHXr1rU6TrU4eczefq0dDgdffbWRH3/M4ptv1vPDDxmn7GOz2SxIJlI+3v6Z/ZPqs+ozqD5LzeTNn11fqs2+UpN9rRb7RAOjQYOG5ObmAifuiapfv4HFiapew4YNcTgc2O12br11FOnp662OVOkKCwsZMiSBgQOH0rfvDYD3X+uSxuwL1xogKCiIbt16sH79V/z++0GcTicA2dlZhIY2tjidlIe3f15L4wufWdVn1WdQffY23v4Z/itv/ez6Um32xZrsK7XYJxoY110Xz6JFKQAsWpRCXFxfixNVvT8LEcB77y2lVavWZexd85imyZgxI2jRoiV33jmxaLs3X+vSxuzN13rPnj0cPHgQgOPHj/PJJx9yySUt6d79CpYuTQVOXOc+fbznOvsSb/68lsWbP7Og+qz6rPrsrbz5M3wyb/zs+lJt9qWa7Iu12OueQpKYOJjPP1/Lvn17adCgIfff/xB9+vRj2LCbyMraRXh4ExYuXOJVi/WUNObPPlvLpk0bsdlsXHhhU5577uWi+9u8wRdfrKNXr260ahWN3X6iDzd9+mPExHTy2mtd2piXLHnDa6/15s2bGD06EZfLhdvtJiHhJu699wF27PiZxMRBHDiwn7/9rR3z5i0kICDA6rhSBl+szaD6rPqs+qz6XDP5Us32lTrtS7XZl2qyL9Zir2tgiIiIiIiIiIj38YlbSERERERERESkZlMDQ0REREREREQ8nhoYIiIiIiIiIuLx1MAQEREREREREY+nBoaIiIiIiIiIeDw1MERERERERETE46mBISIiIiIiIiIe7/8BGT6wJEo28d4AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x23bedf00c88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"from SDSPSM import plot_SDSM\n",
"\n",
"# PLOT THE RESULTS\n",
"from SDSPSM import plot_SDSP, get_normal_curve_label\n",
"backgroundColour = '#F5F5FF'\n",
"fig, axarr = plt.subplots(2,3, figsize=(15,10), facecolor=backgroundColour)\n",
"\n",
"pop_axarr = [axarr[0,0],axarr[0,1], axarr[0,2]]\n",
"titles = ['Population Distribution','Population Discrete\\nDensity Function','Population Probability Mass\\nFunction (PMF)']\n",
"plot_SDSM(population, popMax, pop_axarr, titles, index_list=['A','B','C'], norm_off=True)\n",
"\n",
"stat_axarr = [axarr[1,0],axarr[1,1], axarr[1,2]]\n",
"titles = ['Statistical Distribution','\\nStatistical Discrete Density Function','Statistical Probability Mass\\nFunction (PMF)']\n",
"plot_SDSM(Y_mean_list, popMax, stat_axarr, titles, index_list=['D','E','F'])\n",
"\n",
"plt.tight_layout()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Again recall that, normal approximation is best fit not for our discrete probability mass function F, but for Discrete Density Function E. This is because, probability density function has area equal to 1 (total probability is 1), so our discrete function \"bars\"'s heights should total to 1 as well. This is not possible on our last derived discrete function F, but intermediate density function E. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Examples\n",
"\n",
"**Example 1:** \n",
"\n",
"A machine automatically dispenses a beverage of a desired size. When set to **small**, the machine dispenses varying amounts of liquid with a mean of $275mL$, space, m, L and standard deviation of $10mL$. Suppose that we take random samples of 5 of these drinks and calculate the mean amount of liquid $\\bar{x}$ in each sample. We can assume that individual drinks are independent. \n",
"\n",
"Calculate the mean and standard deviation of the sampling distribution of $\\bar{x}$ \n",
"\n",
"<u>Ans:</u>\n",
"The problem at hand is about varying amounts of liquid - this is a _continuous random distribution_.Thus we deal as sample means. \n",
"\n",
"**True** population parameters: $\\mu = 275\\ mL \\ \\ \\ \\sigma=10\\ mL$\n",
"Sample Size = 5\n",
"\n",
"$\\therefore$\n",
"$$\n",
"\\mu_{\\overline{Y}} \\approx \\mu = 275 \\ mL\\\\\n",
"\\sigma_{\\overline{Y}} \\approx \\dfrac {\\sigma}{\\sqrt{n}} = \\dfrac {10}{\\sqrt{5}} = 4.47 \\ mL\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Summary"
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![image.png](attachment:image.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Wish to do\n",
"\n",
"1. Theoretical Derivation for both Sample proportions and Sample means. [blocking point](https://math.stackexchange.com/questions/2878417/how-sample-mean-equals-population-mean/2879037?noredirect=1#comment5944891_2879037)\n",
"2. Visualization for Conditions for Sample proportions and Sample means. [blocking point](https://math.stackexchange.com/questions/2881045/why-sampling-distribution-not-skewed-when-np-10-and-nq-10?noredirect=1#comment5948209_2881045)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:Anaconda3]",
"language": "python",
"name": "conda-env-Anaconda3-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
},
"toc": {
"base_numbering": 1,
"nav_menu": {
"height": "225px",
"width": "290px"
},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": true,
"toc_position": {
"height": "calc(100% - 180px)",
"left": "10px",
"top": "150px",
"width": "165px"
},
"toc_section_display": true,
"toc_window_display": true
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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