Skip to content

Instantly share code, notes, and snippets.

@Olshansk
Last active February 20, 2023 02:53
Show Gist options
  • Select an option

  • Save Olshansk/262eae3c7ceee79fbef5b97491768b6d to your computer and use it in GitHub Desktop.

Select an option

Save Olshansk/262eae3c7ceee79fbef5b97491768b6d to your computer and use it in GitHub Desktop.
A python notebook covering the most basic probability distributions (https://olshansky.substack.com/p/probability-distributions-101)
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm\n",
"\n",
"# Define the parameters of the normal distribution\n",
"mu = 0\n",
"sigma = 1\n",
"\n",
"# Generate the x-values for the plots\n",
"x = np.linspace(-5, 5, 1000)\n",
"\n",
"# Compute the PDF and CDF of the normal distribution\n",
"pdf = norm.pdf(x, mu, sigma)\n",
"cdf = norm.cdf(x, mu, sigma)\n",
"\n",
"# Plot the PDF and CDF\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, pdf, label='PDF')\n",
"ax.plot(x, cdf, label='CDF')\n",
"ax.legend()\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('Probability density')\n",
"ax.set_title('Normal distribution')\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import norm\n",
"\n",
"# Define the parameters of the normal distribution\n",
"mu = 0\n",
"sigma = 1\n",
"\n",
"# Generate the x-values for the plot\n",
"x = np.linspace(-5, 5, 1000)\n",
"\n",
"# Compute the PDF of the normal distribution\n",
"pdf = norm.pdf(x, mu, sigma)\n",
"\n",
"# Shade the area between -2 and -1\n",
"lower_bound = 1\n",
"upper_bound = 3\n",
"mask = (x >= lower_bound) & (x <= upper_bound)\n",
"# plt.fill_between(x[mask], pdf[mask], alpha=0.3)\n",
"\n",
"# Add vertical bars and y-axis labels\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, pdf, label='PDF')\n",
"ax.axhline(y=0, color='black', lw=1)\n",
"ax.axvline(x=lower_bound, color='red', linestyle='--', lw=1)\n",
"ax.axvline(x=upper_bound, color='red', linestyle='--', lw=1)\n",
"ax.text(lower_bound, -0.03, lower_bound, ha='center', va='top')\n",
"ax.text(upper_bound, -0.03, upper_bound, ha='center', va='top')\n",
"ax.text(2, 0.3, \"PDF [1,2]\", ha='center', va='top', color='red')\n",
"\n",
"x_shade = np.linspace(lower_bound, upper_bound, 100)\n",
"ax.fill_between(x_shade, 0, 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-(x_shade - mu)**2 / (2 * sigma**2)), alpha=0.3, color='blue')\n",
"\n",
"x_shade2 = np.linspace(-5, -2, 100)\n",
"ax.axvline(x=-2, color='red', linestyle='--', lw=1)\n",
"ax.text(-3.5, 0.3, \"CDF: (-∞, -2]\", ha='center', va='top', color='red')\n",
"ax.fill_between(x_shade2, 0, 1 / (sigma * np.sqrt(2 * np.pi)) * np.exp(-(x_shade2 - mu)**2 / (2 * sigma**2)), alpha=0.3, color='blue')\n",
"\n",
"ax.legend()\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('Probability density')\n",
"ax.set_title('Normal Probability Distribution Function ($\\mu$=0, $\\sigma$=1)')\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import scipy.special\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Generate some data for the random variable\n",
"rv_data = np.random.normal(size=1000)\n",
"\n",
"# Define the PDF and CDF for the continuous variable\n",
"def pdf(x):\n",
" return np.exp(-x**2/2)/np.sqrt(2*np.pi)\n",
"\n",
"def cdf(x):\n",
" return (1 + scipy.special.erf(x/np.sqrt(2))) / 2\n",
"\n",
"# Create the plot\n",
"fig, ax = plt.subplots()\n",
"x = np.linspace(-3, 3, 100)\n",
"ax.plot(x, cdf(x), color='blue', lw=2, label='Continuous RV')\n",
"ax.hist(rv_data, bins=20, density=True, cumulative=True, color='red', alpha=0.5, label='Discrete RV')\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('CDF')\n",
"ax.set_title('CDF of Discrete vs Continuous Random Variable (gaussian w/ $\\mu$=0, $\\sigma$=1)')\n",
"ax.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import scipy.stats as stats\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the parameters of the binomial distribution\n",
"n = 10 # number of trials\n",
"p = 1/6 # probability of success\n",
"\n",
"# Create a binomial distribution object\n",
"binom_dist = stats.binom(n, p)\n",
"\n",
"# Generate x values to plot the PMF\n",
"x = range(n + 1)\n",
"\n",
"# Compute the PMF of the binomial distribution for each x value\n",
"pmf = binom_dist.pmf(x)\n",
"\n",
"# Plot the PMF of the binomial distribution\n",
"plt.stem(x, pmf, use_line_collection=True)\n",
"\n",
"plt.xticks(x)\n",
"\n",
"\n",
"# Set plot labels and title\n",
"plt.xlabel('Number of successes (k)')\n",
"plt.ylabel('Probability')\n",
"plt.title('Binomial distribution PMF (n=10, p=1/6)')\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import scipy.stats as stats\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the parameters of the negative binomial distribution\n",
"n = 2 # number of successes\n",
"p = 1/6 # probability of success\n",
"\n",
"# Create a negative binomial distribution object\n",
"nbinom_dist = stats.nbinom(n, p)\n",
"\n",
"# Generate x values to plot the PMF\n",
"x = range(20)\n",
"\n",
"# Compute the PMF of the negative binomial distribution for each x value\n",
"pmf = nbinom_dist.pmf(x)\n",
"\n",
"# Plot the PMF of the negative binomial distribution\n",
"plt.stem(x, pmf, use_line_collection=True)\n",
"\n",
"# Set plot labels and title\n",
"plt.xlabel('Number of failures (r)')\n",
"plt.ylabel('Probability')\n",
"plt.title('Negative Binomial distribution PMF (n=2, p=1/6)')\n",
"\n",
"plt.xticks(x)\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from matplotlib import cm\n",
"\n",
"# Set the mean and standard deviation\n",
"mu, sigma = 0, 10\n",
"\n",
"# Create the x-axis data\n",
"x = np.linspace(mu - 4*sigma, mu + 4*sigma, 1000)\n",
"\n",
"# Calculate the y-axis data using the PDF\n",
"y = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x - mu)**2 / (2 * sigma**2))\n",
"\n",
"# Create the plot\n",
"fig, ax = plt.subplots()\n",
"ax.plot(x, y, color='blue')\n",
"\n",
"# Shade each sigma a different color\n",
"colors = cm.get_cmap('hsv', 5)\n",
"for i in range(1, 5):\n",
" x_fill = np.linspace(mu - i*sigma, mu + i*sigma, 1000)\n",
" y_fill = 1/(sigma * np.sqrt(2 * np.pi)) * np.exp(-(x_fill - mu)**2 / (2 * sigma**2))\n",
" ax.fill_between(x_fill, y_fill, alpha=0.3, color=colors(i-1))\n",
"\n",
"# Add vertical lines and text for each standard deviation\n",
"per = [34.1, 13.6, 2.1, 0.1]\n",
"heights = [0.02, 0.003, 0.00, 0.001]\n",
"for i in range(1, 4):\n",
" left = -i * sigma\n",
" right = i * sigma\n",
" ax.axvline(left, linestyle='--', color='gray', alpha=0.5)\n",
" ax.axvline(right, linestyle='--', color='gray', alpha=0.5)\n",
" ax.text(left+0.1, 0.035, f'{i}$\\sigma$', rotation=90, va='bottom', color='black')\n",
" ax.text(right+0.1, 0.035, f'{i}$\\sigma$', rotation=90, va='bottom', color='black')\n",
" p = f'{per[i-1]}%'\n",
" h = heights[i-1]\n",
" ax.text(left+2, h, p, rotation=0, va='bottom', color='black')\n",
" ax.text(right-8, h, p, rotation=0, va='bottom', color='black')\n",
"ax.text(0, 0.035, f'$\\mu$', rotation=90, va='bottom', color='black')\n",
"ax.axvline(0, linestyle='--', color='gray', alpha=0.5)\n",
"\n",
"# Set plot labels and title\n",
"plt.xlabel('x (value)')\n",
"plt.ylabel('y (probability)')\n",
"plt.title(f'Gaussian (Normal) Distribution ($\\mu$=0, $\\sigma$=10)')\n",
"\n",
"# Show the plot\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Define the parameters of the geometric distribution\n",
"p = 0.2\n",
"n = 10\n",
"\n",
"# Create an array of x values\n",
"x = np.arange(1, n+1)\n",
"\n",
"# Calculate the probability mass function\n",
"pmf = (1-p)**(x-1) * p\n",
"\n",
"# Calculate the cumulative distribution function\n",
"cdf = 1 - (1-p)**x\n",
"\n",
"# Plot the probability mass function as a line chart\n",
"lns1 = plt.plot(x, pmf, marker='o', label='PMF (left)')\n",
"plt.tick_params(axis='y', color='blue')\n",
"\n",
"# Add labels and a title\n",
"plt.xlabel('Number of trials until first success (k)')\n",
"plt.ylabel('Probability', color='blue')\n",
"plt.yticks(color='blue')\n",
"plt.title('Geometric Distribution (p=0.2, n=10)')\n",
"\n",
"# Plot the cumulative distribution function to the right of the line chart\n",
"plt.twinx()\n",
"lns2 = plt.plot(x, cdf, color='orange', marker='s', label='CDF (right)')\n",
"plt.ylabel('Cumulative Probability', color='orange')\n",
"plt.yticks(color='orange')\n",
"\n",
"leg = lns1 + lns2\n",
"labs = [l.get_label() for l in leg]\n",
"plt.legend(leg, labs, loc=0)\n",
"\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import poisson\n",
"\n",
"# Define the parameter lambda for the Poisson distribution\n",
"lam = 3\n",
"\n",
"# Generate a range of values for the x-axis\n",
"x = np.arange(0, 15)\n",
"\n",
"# Calculate the corresponding probabilities for each value of x\n",
"pmf = poisson.pmf(x, mu=lam)\n",
"\n",
"# Plot the PMF\n",
"plt.plot(x, pmf, 'bo', ms=8)\n",
"plt.vlines(x, 0, pmf, colors='b', lw=5, alpha=0.5)\n",
"plt.xlabel('Number of events (k)')\n",
"plt.ylabel('Probability')\n",
"plt.title('Poisson Distribution (lambda=3)')\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAnMAAAHHCAYAAADUA97wAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAA9hAAAPYQGoP6dpAACevUlEQVR4nOzdd3gU1dfA8e/2zab3HnrvvRcVQbGAIGAFVCxYsBdefyoiCogdG4oFOxZQUETAgiIgiBTpPaSQ3jZ127x/hCzEJJCEJJNyPs8zT9jZO3fObDbs2blNoyiKghBCCCGEaJC0agcghBBCCCGqT5I5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI5IYQQQogGTJI50SgdP34cjUbDhx9+qHYodSI3N5dp06YRFhaGRqPhvvvuUzukRue3335Do9Hw22+/VfnYWbNmodFoaj4oYPjw4QwfPrxW6v4vjUbDrFmz3I9LristLa1Ozt+8eXOmTp1aJ+cqz/PPP0/79u1xuVzufcOHD8disTBu3DisVqtqsZ2P9PR0PD09WbVqldqhiGqSZK6R+vDDD9FoNO7NbDbTtm1b7r77bpKTk93lSj6gSjaTyURoaCjDhw/nueeeIzU19Zx1n7k99thjdXmZNSY5OZmHHnqI9u3bY7FY8PT0pFevXsyZM4esrCx3ueHDh7uvVavV4uPjQ7t27bjxxhtZu3ZtuXU3b968wtersLCwRuJ/7rnn+PDDD5k+fToff/wxN954Y4VlzxbPJZdcUiPxNGRvvvmmal8Cpk6dWur34eXlRcuWLbn66qv55ptvSiUR52Pjxo3MmjWr1Hu7vqivseXk5DB//nweffRRtNrTH52PP/44M2bMYPny5SxYsKDGz+tyuXj++edp0aIFZrOZrl278vnnn1fq2LP9X52UlOQuFxgYyLRp03jiiSdqPH5RN/RqByBq1+zZs2nRogWFhYVs2LCBt956i1WrVrF7924sFou73IwZM+jTpw9Op5PU1FQ2btzIU089xUsvvcSXX37JhRdeWGHdZ+rcuXOtX1NN27p1K6NHjyY3N5cbbriBXr16AfD3338zb948fv/9d9asWeMuHxUVxdy5cwHIy8vj8OHDLFu2jE8++YSJEyfyySefYDAYSp2je/fuPPjgg2XObTQaa+QafvnlF/r3789TTz1VqfIVxRMREVEj8TRkb775JkFBQWXuAA0dOpSCgoIa+51VxGQysXjxYgAKCgqIjY1l5cqVXH311QwfPpzvvvsOHx8fd/kz35uVtXHjRp5++mmmTp2Kn59fpY8rKChAr6/dj42zxXbgwIFSiVRdev/993E4HFx77bWl9l988cVcfPHF/P3333zyySfMnj27Rs/7+OOPM2/ePG699Vb69OnDd999x3XXXYdGo+Gaa66pVB3l/V/939f2jjvu4LXXXuOXX34p9/97Uc8polH64IMPFEDZunVrqf0PPPCAAiifffaZoiiK8uuvvyqA8tVXX5WpY8eOHUpISIji5+enJCYmnrPu+uTYsWMKoHzwwQdnLZeZmalERkYqoaGhyr59+8o8n5SUpDzzzDPux8OGDVM6depUppzD4VDuvPNOBVAeeeSRUs81a9ZMueyyy6p3IZXUokWLSp+jLuJpyDp16qQMGzasRut86qmnlMr8dztlyhTF09Oz3Ofmzp2rAMrEiRPPO54FCxYogHLs2LFzlnU6nUpBQUG5z5VcV2pq6nnHVJ3Y6lLXrl2VG264ocLnFy9erADKli1bauyc8fHxisFgUO666y73PpfLpQwZMkSJiopSHA7HWY+v6v/VnTt3Vm688cbzilmoQ5pZm5iSb1zHjh07Z9lu3brxyiuvkJWVxeuvv14j5//jjz+YMGECMTExmEwmoqOjuf/++ykoKChVburUqXh5eZGQkMDYsWPx8vIiODiYhx56CKfTWapsVlYWU6dOxdfXFz8/P6ZMmVLpJppFixaRkJDASy+9RPv27cs8Hxoayv/+979z1qPT6Xjttdfo2LEjr7/+OtnZ2ZU6/7mkpKRwyy23EBoaitlsplu3bixZssT9fEkz+bFjx/jhhx/cTSjHjx8/7/MGBwczfPhwFEVx7z98+DCenp5MmjTJvW/48OF07tyZbdu2MXDgQDw8PGjRogVvv/12la8HTvd3fOGFF3jnnXdo1aoVJpOJPn36sHXr1jJ17t+/n6uvvpqAgADMZjO9e/dmxYoVpcqUNDf9+eefPPDAAwQHB+Pp6clVV11VqitB8+bN2bNnD+vXr3e/liX90crrM1fZ93NNeOyxxxg5ciRfffUVBw8edO8vr8/cwoUL6dSpExaLBX9/f3r37s1nn30GFPdze/jhhwFo0aJFmfeMRqPh7rvv5tNPP6VTp06YTCZWr17tfu7MPnMl0tLSmDhxIj4+PgQGBnLvvfeW6kJwtj6sZ9Z5rtjK6zN39OhRJkyYQEBAABaLhf79+/PDDz+UKlPyu/vyyy959tlniYqKwmw2c9FFF3H48OEKX/MSx44dY9euXYwYMaLCMm3atAFg6dKl56yvsr777jvsdjt33nmne59Go2H69OnEx8ezadOmStdltVrL/N/5XxdffDErV64s9TcvGgZJ5pqYI0eOAMV9JCrj6quvxsPDo9ymnOzsbNLS0kpt5/LVV1+Rn5/P9OnTWbhwIaNGjWLhwoVMnjy5TFmn08moUaMIDAzkhRdeYNiwYbz44ou888477jKKojBmzBg+/vhjbrjhBubMmUN8fDxTpkyp1PWtWLECDw8Prr766kqVPxudTse1115Lfn4+GzZsKPWc3W4v81rl5+eftb6CggKGDx/Oxx9/zPXXX8+CBQvw9fVl6tSpvPrqqwB06NCBjz/+mKCgILp3787HH3/Mxx9/THBw8FnrLi+etLQ0dxISEhLCW2+9xfr161m4cCFQ3Hdn6tSpeHt78+abb5aqLzMzk9GjR9OrVy+ef/55oqKimD59Ou+//36VrudMn332GQsWLOD2229nzpw5HD9+nHHjxmG3291l9uzZQ//+/dm3bx+PPfYYL774Ip6enowdO5bly5eXqfOee+5h586dPPXUU0yfPp2VK1dy9913u59/5ZVXiIqKon379u7X8vHHH6/wdazK+7km3HjjjSiKUmH/TIB3332XGTNm0LFjR1555RWefvppunfvzl9//QXAuHHj3E2FL7/8crnvmV9++YX777+fSZMm8eqrr9K8efOzxjVx4kQKCwuZO3cuo0eP5rXXXuO2226r8vVVJrYzJScnM3DgQH766SfuvPNOnn32WQoLC7nyyivL/f3PmzeP5cuX89BDDzFz5kw2b97M9ddff864Nm7cCEDPnj0rLFPyXv/666/Lfb68v7fytqKiIvcx27dvx9PTkw4dOpSqq2/fvu7nK+OCCy7Ax8cHi8XClVdeyaFDh8ot16tXL7KystizZ0+l6hX1iLo3BkVtKbm9vm7dOiU1NVWJi4tTvvjiCyUwMFDx8PBQ4uPjFUU5ezNriW7duin+/v5l6i5vO5f8/Pwy++bOnatoNBolNjbWvW/KlCkKoMyePbtU2R49eii9evVyP/72228VQHn++efd+xwOhzJkyJBKNbP6+/sr3bp1O2fcJSpqZi2xfPlyBVBeffVV975mzZqV+1o99dRTZz3XK6+8ogDKJ5984t5ns9mUAQMGKF5eXkpOTk6pc1SlmbWi39/cuXNLlb322msVi8WiHDx40N389e2335YqM2zYMAVQXnzxRfe+oqIipXv37kpISIhis9mqdD0lTeSBgYFKRkaGu+x3332nAMrKlSvd+y666CKlS5cuSmFhoXufy+VSBg4cqLRp08a9r+Q9O2LECMXlcrn333///YpOp1OysrLc+ypqZi35W/n111/d+yr7fq6JZlZFUZTt27crgHL//fe79w0bNqxUvGPGjDnre1RRzt6UCSharVbZs2dPuc+d+b4tua4rr7yyVLmSLgc7d+5UFOXs3R7+W+fZYmvWrJkyZcoU9+P77rtPAZQ//vjDvc9qtSotWrRQmjdvrjidTkVRTv/uOnTooBQVFbnLvvrqqwqg/Pvvv2XOdab//e9/CqBYrdZyn09PT1fMZrMSEhKiAMqmTZvKvc7KbGe+RpdddpnSsmXLMnXl5eUpgPLYY4+dNe6lS5cqU6dOVZYsWaIsX75c+d///qdYLBYlKChIOXHiRJnyGzduVABl6dKlZ61X1D8yAKKR+2+zQLNmzfj000+JjIysdB1eXl7lDrl/4403aNu2bZXi8fDwcP87Ly+PgoICBg4ciKIobN++nZiYmFLl77jjjlKPhwwZwscff+x+vGrVKvR6PdOnT3fv0+l03HPPPfzxxx/njCcnJwdvb+8qXcPZeHl5AZR5vfr168ecOXNK7WvZsuVZ61q1ahVhYWGlOlwbDAZmzJjBtddey/r167n88surFWd58cDppqISr7/+Or/99htXX301Bw8e5MYbb2TMmDFljtPr9dx+++3ux0ajkdtvv53p06ezbds2+vfvX+XrmTRpEv7+/u7HQ4YMAYqb1QAyMjL45ZdfmD17NlartdRrPmrUKJ566ikSEhJKvddvu+22UlOEDBkyhJdffpnY2Fi6du167hfuP6r6fj5fFb2/zuTn50d8fDxbt26lT58+1TrPsGHD6NixY6XL33XXXaUe33PPPbz55pusWrWqWq9rZa1atYq+ffsyePBg9z4vLy9uu+02Zs6cyd69e0sNyrrppptKDWA58z11tsFb6enp6PV69+v/Xx9++CGFhYWsWLGC0aNH8+WXX9K/f/9SZc52N/VMnTp1cv+7oKAAk8lUpozZbHY/fzYTJ05k4sSJ7sdjx45l1KhRDB06lGeffbZMV4iSv7e6mmpG1BxJ5hq5koRLr9cTGhpKu3btqjwaLDc3t9yEp2/fvvTu3btKdZ04cYInn3ySFStWkJmZWeq5//YzM5vNZZpX/P39Sx0XGxtLeHh4mf9k27VrV6l4fHx8anRuqNzcXIAyr1dQUNBZ+9uUJzY2ljZt2pT5fZU0ucTGxlY7zsrGExAQwGuvvcaECRMIDQ3ltddeK7dcREQEnp6epfaVJPrHjx+nf//+Vb6e/yZCJR80Jb//w4cPoygKTzzxRIVTKqSkpJRK5s5VZ1VV5f1cEyp6f53p0UcfZd26dfTt25fWrVszcuRIrrvuOgYNGlTp8/x35OO5/PdLQKtWrdBqtefdd/NcYmNj6devX5n9Z76nzkzSavr3D8VdPd5++2369+/PxRdfzIgRI/jqq6948cUXS31xqOrfPxR/WTiz2bVESX/EM79MVNbgwYPp168f69atK/OccqqvXG3NiShqjyRzjVx1Eq4z2e12Dh48WCNTjjidTi6++GIyMjJ49NFHad++PZ6eniQkJDB16tQyc2jpdLrzPue5tG/fnh07dmCz2Wpkyondu3cD0Lp16/Ouq7746aefgOIPvPj4+CpNZXE+Kvr9l3zglLxfHnroIUaNGlVu2f/+Hs5VZ1VU9f1cEyrz/urQoQMHDhzg+++/Z/Xq1XzzzTe8+eabPPnkkzz99NOVOk91koQz/TcZqCg5OFeH/JpW3d9/YGAgDocDq9VaJpH++eefOXToEE8++SRQfEd59erVbNy4sVQCfea8bmfj6+vrfv3Dw8P59ddfURSl1Gt48uRJoPpTCUVHR3PgwIEy+0uS2qCgoGrVK9QjAyDEWX399dcUFBRU+GFZFf/++y8HDx7kxRdf5NFHH2XMmDGMGDHivOY2a9asGSdPnnTfsShR3n9U5bniiisoKCjgm2++qXYMJZxOJ5999hkWi6VUs091NWvWjEOHDpVJCvbv3+9+vratXr2axYsX88gjjxAcHMyUKVNwOBxlyiUmJpKXl1dqX8mIy5LO8zV9PSXN1AaDgREjRpS7VacJvbJ3JWrj/XwuH3/8MRqNhosvvvis5UpGHH/wwQecOHGCyy67zD04AGr+zst/O9QfPnwYl8vl/t2X3AH77yjz8u4uVyW2Zs2alfu3XtN/IyUj3cubBeCtt94iODiYCRMmAMVNmUajkS+//LJUufDw8EptZ46G7d69O/n5+ezbt69UXSWDWbp3716t6zl69Gi5g0pKru+/Ay5E/SfJnKjQzp07ue+++/D39y/TJ6Y6Sr4Vn/ktWFGUckcyVtbo0aNxOBy89dZb7n1Op9M9AvNc7rjjDsLDw3nwwQdLTfdQIiUlpdy+Zf/ldDqZMWMG+/btY8aMGaUmda2u0aNHk5SUVOo/d4fDwcKFC/Hy8mLYsGHnfY6zycrKYtq0afTt25fnnnuOxYsX888///Dcc8+VKetwOFi0aJH7sc1mY9GiRQQHB7snYa7p6wkJCWH48OEsWrTIfafiTOWtXlIZnp6elZrapjbez2czb9481qxZw6RJk8o0a54pPT291GOj0UjHjh1RFMU9ErikSbymVll44403Sj0u+fu79NJLgeLuDEFBQfz++++lyv13VHRVYxs9ejRbtmwpNUVHXl4e77zzDs2bN69Sv7+zGTBgAFA8kfiZEhMTWbFiBdOmTXP3bfPz82PUqFF8/fXXpb64rF27tlLbmV+cx4wZg8FgKPU6lTTrRkZGMnDgQPf+kydPsn///lKjvcv7G1i1ahXbtm0rd7WXbdu24evrW6rfnmgYpJlVAMXzZRUWFuJ0OklPT+fPP/9kxYoV+Pr6snz5csLCws77HO3bt6dVq1Y89NBDJCQk4OPjwzfffHNe/VWuuOIKBg0axGOPPcbx48fp2LEjy5Ytq3R/JX9/f5YvX87o0aPp3r17qRUg/vnnHz7//HP3f+QlsrOz+eSTTwDIz893rwBx5MgRrrnmGp555plqX8+ZbrvtNhYtWsTUqVPZtm0bzZs35+uvv+bPP//klVdeOa+BGwkJCe5rOJOXlxdjx44F4N577yU9PZ1169ah0+m45JJLmDZtGnPmzGHMmDF069bNfVxERATz58/n+PHjtG3blqVLl7Jjxw7eeecd92oYtXE9b7zxBoMHD6ZLly7ceuuttGzZkuTkZDZt2kR8fDw7d+6scp29evXirbfeYs6cObRu3ZqQkJByZ8SvjfczFCe4Jb+bwsJCYmNjWbFiBbt27eKCCy4oNTVPeUaOHElYWBiDBg0iNDSUffv28frrr3PZZZe5X+OS9/jjjz/ONddcg8Fg4IorrijT77Gyjh07xpVXXskll1zCpk2b+OSTT7juuutKvUemTZvGvHnzmDZtGr179+b3338v9wtUVWJ77LHH+Pzzz7n00kuZMWMGAQEBLFmyhGPHjvHNN9/U2GoRLVu2pHPnzqxbt46bb77Zvf/dd99FUZQyA7UmTZrEypUr2bBhA0OHDgWq12cuKiqK++67jwULFmC32+nTpw/ffvstf/zxB59++mmpZuOZM2e6r73kjujAgQPp0aMHvXv3xtfXl3/++Yf333+f6Oho/u///q/M+dauXcsVV1whfeYaorofQCvqQmVn/i4Zsl+yGQwGJTg4WBk6dKjy7LPPKikpKdWuuzx79+5VRowYoXh5eSlBQUHKrbfequzcubPMkPyKpmgob4qH9PR05cYbb1R8fHwUX19f5cYbb3RP4XCuqUlKJCYmKvfff7/Stm1bxWw2KxaLRenVq5fy7LPPKtnZ2e5yJdNwlGxeXl5KmzZtlBtuuEFZs2ZNuXWfz4oLycnJyk033aQEBQUpRqNR6dKlS7nXVFNTkzRr1kxRlNPTgJw53YiiKEpOTo7SrFkzpVu3bu4pR0qma/n777+VAQMGKGazWWnWrJny+uuvV+t6SqaxWLBgQZnjKWdKlyNHjiiTJ09WwsLCFIPBoERGRiqXX3658vXXX7vLVPSeLW+6kaSkJOWyyy5TvL29FcA97Ud5ZSv7fq7K1CRn/j4sFovSvHlzZfz48crXX3/tnmrjTP+dmmTRokXK0KFDlcDAQMVkMimtWrVSHn744VLvY0VRlGeeeUaJjIxUtFptqalAgFIrDpzpv69/yXXt3btXufrqqxVvb2/F399fufvuu8usGpGfn6/ccsstiq+vr+Lt7a1MnDhRSUlJKfd3WlFs/52aRFGKf/9XX3214ufnp5jNZqVv377K999/X6pMRVMwVXalGEVRlJdeeknx8vJyT0fjcDiUyMjIMtOyKErx34mHh0eFr2NVOJ1O5bnnnlOaNWumGI1GpVOnTqWm9ylR8t45c0qXxx9/XOnevbvi6+urGAwGJSYmRpk+fbqSlJRU5vh9+/a5p7MSDY9GUWSqZyFE9Q0fPpy0tDR353whGqPs7GxatmzJ888/zy233KJ2ODXuvvvu4/fff2fbtm1yZ64Bkj5zQgghxDn4+vryyCOPsGDBgloZqaym9PR0Fi9ezJw5cySRa6DkzpwQ4rzInTkhhFCX3JkTQgghhGjA5M6cEEIIIUQDJnfmhBBCCCEaMEnmhBBCCCEaMJk0uBwOh4Pt27cTGhpaY5NOCiGEEKJ2uVwukpOT6dGjB3p900lxms6VVsH27dvp27ev2mEIIYQQohq2bNlCnz591A6jzkgyV47Q0FCg+M0QHh6ucjRCCCGEqIyTJ0/St29f9+d4UyHJXDlKmlbDw8OJiopSORohhBBCVEVT6yLVtK5WCCGEEKKRkWROCCGEEKIBk2ROCCGEEKIBkz5z58HpdGK329UOo0EwGo1Nrg+DEEIIURckmasGRVFISkoiKytL7VAaDK1WS4sWLTAajWqHIoQQQjQqksxVQ0kiFxISgsViQaPRqB1SveZyuUhMTOTkyZPExMTI6yWEEELUIFWTubRF72Bduxbb0aNozGY8evQg5MEHMbVscdbjclavJvXV17AnJGBs1oyQhx7Ea9gw9/OKopC2cCGZX32FK8eKR88ehD/1FMbmzc87ZqfT6U7kAgMDz7u+piI4OJjExEQcDgcGg0HtcIQQQgj+OprOO78f5d+EbFKsRSy6sRejOoWd9ZhNR9KZ88NeDiXnEu5n5u4LWjOhd3QdRVw+VTsx5W/div9119F86RfEvP8eisPOiWm34MrPr/iYf7aT8OBD+F09nhbLl+E14iLi7r6HwoMH3WXSFy8m4+NPCJ81i+ZfLkXrYeHEtFtxFRWdd8wlfeQsFst519WUlDSvOp1OlSMRQgghiuXbnXQI92H2mM6VKh+Xkc/NH25lQMtAVt07mJsHteCxZf+y/mBqLUd6dqremYtZ/G6pxxFz53Jo4CAK9+zBUsEyHBkff4TX4MEE3nILACH33kvexo1kfvoZ4U/PQlEUMj76iKA77sD7oouK650/j0ODBmNdtw7fyy6rkdilqbBq5PUSQghR31zQLoQL2oVUuvwnf8USHeDB/y7vCEDrEG+2Hs/gvQ3HGNY2uLbCPKd6NbzQZbUCoPX1rbBMwY6deA4cUGqf16DBFOzYAYA9Ph5nalqpMjpvbzy6dqVgx85y6ywqKiInJ8e9WU/FIYQQQoiGx2q1lvpcL6qBljmA7bFZDGodVGrf0LbBbI/NrJH6q6veJHOKy0Xyc3Px6NkTc9u2FZZzpKWhCyz9QuqCAnGkpRU/n1r8U/ef/my6oCAcaeXfBp07dy6+vr7urWPHjudzKUIIIYRQUceOHUt9rs+dO7dG6k3NLSLIy1RqX7CXCWuRg0K7et2I6k0ylzR7NkWHDhH50ot1fu6ZM2eSnZ3t3vbu3VvnMdSFqVOnotFo0Gg0GI1GWrduzezZs3E4HPz222/u57RaLb6+vvTo0YNHHnmEkydPlqpn1qxZ7rJnbuvWrVPpyoQQQojT9u7dW+pzfebMmWqHVKvqxdQkSbOfIfe39TT75GMMYWcfRaIPCsKZnlZqnzMtHX1Q8d06fXDxT2d6OoaQkDPKpGHq0KHcOk0mEybT6Uw7JyenWtdRGa6iItBo0Ko039oll1zCBx98QFFREatWreKuu+7CYDAwYEBxs/SBAwfw8fEhJyeHf/75h+eff5733nuP3377jS5durjr6dSpU5nkLSAgoE6vRQghRMPhdCkU2p0U2p0U2J14GvX4e9bOZ6G3tzc+Pj41Xm+wl4m03NJNtqm5RXib9JgNuho/X2WpmswpikLyM3OwrltHs4+WYIyKOucxHt27kbdpMwFTprj35W3ciEf37gAYoqLQBQeRt2kz5lPJmzM3l4Jdu/C79ppauY7Ksp88iSO9OPHUniNprS0mk4mwU+eePn06y5cvZ8WKFe5kLiQkBD8/P8LCwmjbti1jxoyhR48eTJ8+nQ0bNrjr0ev17nqEEEI0fE6XQr7NQb7NSV5R8c/i7fS+AruTvKLT+wrsTgptTgodTgpKHttd7oSt0F68v9DuwuZ0lTrfjAtb88DIdipdbfX0aObHb/tLd9nacCiNHs38VYqomKrJXNLs2eR8/wNRb7yO1tMTR2rxC6T19kZrNgOQ+Oij6ENCCXnwAQACbpxM7OTJpL//AV7Dh5HzwyoK9uwhbPbTQPGoyYDJk0l7+22MzZthiIwi9bXX0IeE4D1iRK1ch6IoKAUF5y4HuAoLsaemoquBbwwaD4/zHiXq4eFBenr6WZ+/4447uP/++0lJSSEkpPKjfoQQQtQeRVHItznJLXJgLbRjLXRgLXSQW+Qgt9BBTqHd/e88m+NUElaciOXZnBSc2lecoDkocrjOfdIaYtJrUersbBXLK3JwPD3P/TguI589idn4WYxE+nkwf/V+krMLeWlSdwBu6NeMjzbGMnfVPib0jmbTkTR++Pck708tfwaOuqJqMpf1+RcAnJg8pdT+8Oeew2/cVQDYE0+C5nTXPkvPHkS+sIDUV14l9eWXMTZvRvTrC0sNmgicNg2loICTTz6FKycHj149iX73HbSm0p0Wa4pSUMCBnr1qpe6zaffPNjTVnO9OURR+/vlnfvrpJ+65556zlm3fvj0Ax48fdydz//77L15eXu4yHTt2ZMuWLdWKRQghmiKH00V2gd29ZRXYySl5nG/HWuQ4laCdTspKkrWSfa5ayIh0Wg0Wow6LUYenUY/FpMNiKP7padTjYdThadThYdRjMeowG7R4GHSYDDo8Tm1mgw4PoxaTXoeH8Yx9Bh0mvRattn5MV7UrPptr393sfjznh30AjO8ZxYsTu5GSU0RC1umbNdEBFt6f2odnvt/LB38eJ8zXzLxxXVSdlgRUTuY67N93zjLNPv6ozD6fSy7B55JLKjxGo9EQPGMGwTNmnFd8jdH333+Pl5cXdrsdl8vFddddx6xZs9i6dWuFxyhK8f8WZ94FbNeuHStWrHA/NtVSoiyEEPVdkcNJZp6djDwbGXk2sgpsZOUXJ2U5BXb3v/+bsOUWOWrk/DqtBi+THm+z3v3T22zAy6THy6zH26TH01SceJX8tBj1eBp1WNyPTydqJr22ycwNOqBVIMfnVTz/7IsTu5V7zKp7h9RmWFVWLwZANHQaDw/a/bOtUmUdaenYU5LRenlhiok57/NW1QUXXMBbb72F0WgkIiICvf7cb4F9+4qT7uZnLIdWMhpWCCEaE0VRsBY5yMi1kZFvO/0zr+LtfJMyb5MeHw8DfhYDvh6nNx+PUwmZO0HT42UyFP88laR5mw2YDU0n+RLlk2SuBmg0mko3d+pDtDhzssHpRGMyodHV7egXT0/PKiVhBQUFvPPOOwwdOpTgYHVvIwshRHUV2p2kWotIsRaRai0iNffUT/dWSKq1iLRcW5mO+pWh02rwtxgJ8DTgZzHi62HA74zEzM9SnJwV/9t4OmEz69Hr6s0sYaKBkmSujmlMJjRGI4rNhisvr0YGQtSklJQUCgsLsVqtbNu2jeeff560tDSWLVumdmhCCFGGzeEixVpIUnYhJ7NP/0w5lZyVJG3WwqrdPbMYdQR4Gk9vllM/vc749xmbj9lQb/qBiaZHkrk6ptFo0Hl740hPx2m11rtkrl27dmg0Gry8vGjZsiUjR47kgQcekGlIhBB1rtDuPJ2k5RSUStZKfv53zq+zMem1BHubCPE2EVyyeZlP/9vbRJCXkSAvk6pzhglRVZLMqUDr7Q3p6bisVhRFqbO+Dh9++GGFzw0fPtw90OFcZs2axaxZs2omKCFEk1Vod5KQVUB8ZgHxmfmnfhb/Oy6joNKJmlGnJczXTJivmXBfM2E+ZkJ9Sidpwd4mvE166VsmGiVJ5lSgtVjQaLUoDgdKQSEaS9UHMgghRH3ncikk5RRyPC2P4+n5ZyRs+cRlFpBqPXey5mHQFSdoZyZrvh6E+5x+HOBplCRNNGmSzKlAo9Wi9fLCmZODM9eKVpI5IUQD5XIpnMwpJDYtj2PpecSm53MsLY/YU/8+10S0nkYd0QEWovw9iPIv+Vn870g/D/wsBknUhDgHSeZUovX2xpmTg8tqBVlVQQhRz1kL7RxJzeNwSi6HU3I5kprL8bQ8YjPysZ0lYdNrNcQEWGgWaCEmwHJGwlb8U5I1Ic6fJHMq0Xl5YQdcBQW47Ha0BoPaIQkhmjhFUUjPs7kTtpKk7VByLkk5hRUeZ9BpiA6w0DzQs3gLOv3vCD+zTL0hRC2TZE4lGoMBrYdHcTJntaINCFA7JCFEE5JX5OBAspX9J63sT8ph/0krB1OsZOXbKzwm2NtE62AvWocUby2CPGkR5Em4ryRsQqhJkjkVab29i5O53FyQZE4IUQtcLoX4zAL2nsxxJ237k3KIzcinvAHsGg1E+XuUStpah3jTOtgLX4u0IAhRH0kypyKdtzeOlBScubkoLhcarXyzFUJUn9OlcDQ1l13x2fybULztP5lDns1ZbvlgbxMdwn3oEOZNuzBv2oZ60yrYCw+jzLEmREMiyZyKNGYzGr0exeEoXg3C21vtkIQQDYTTpXAsLZd/E7LZFZ/N7oRs9iTmkF9O4mbUaWkT6kX7MB86hHvTIdyHdmHeBHmZVIhcCFHTJJlTkUajKR7VmpmJy2qVZE4IUaEUayH/xGax/UQm2+Oy2JOQXe4dN4tRR6cIH7pE+tElyodOEb60CPLEIH3ahGi0JJlTmc7HB2dmJk6rFX0drgYhhKi/7E4X+09a+edEpnuLyygoU85s0NIpwpcukcVb1yhfWgZ7oZM1QoVoUiSZU5nW0xO0WhS7HaWwEI1H7U4gnJSUxLPPPssPP/xAQkICISEhdO/enfvuu4+LLrqI5s2bExsbC4DZbCY0NJS+fftyxx13cOGFF7rrOX78OC1atChT//XXX88nn3xSq9cgRGNjLbTzd2wmW45lsC02k13xWRTaS8/dptFA2xBvejbzo0eMP92i/GgV7CmjSIUQksypTaPVoitZDSInB20tJnPHjx9n0KBB+Pn5sWDBArp06YLdbuenn37irrvuYv/+/QDMnj2bW2+9FZvNxvHjx/nkk08YMWIEzzzzDI8//nipOtetW0enTp3cjz1qORkVojHILrCz9VgGfx1L569jGexOyMb1n5Gl3mY9PWL86RnjR88Yf7rH+OFjltGkQoiyJJmrB7Q+PsWrQeTkQGhorZ3nzjvvRKPRsGXLFjw9Pd37O3XqxM033+x+7O3tTVhYGAAxMTEMHTqU8PBwnnzySa6++mratWvnLhsYGOguK4QoX1a+jc1HTyVvRzPYl5RTZlqQmAALfVsE0Ke5Pz1j/GkV7IVWmkuFEJUgyVwNUBSFAnv5Q/8rdbzRTKFDAUcBdms+WpOxUsd5GHSV7mOXkZHB6tWrefbZZ0slciX8/PzOevy9997LM888w3fffccjjzxSqXMK0VTZHC62xWay4XAqGw6lsSshu0zy1iLIk/4tA+jXIpC+LQKI8JO72kKI6pFkrgYU2J10fPKnGqotrtIl984ehcVYuV/h4cOHURSF9u3bVyuqgIAAQkJCOH78eKn9AwcORHvG/Hh//PEHPXr0qNY5hGioFEXhUEoufxxKY8OhVDYfzSjzBa9VsCf9WwbSr2Ug/VsEEOJjVilaIURjI8lcE6GUN9V7Ner4753ApUuX0qFDB/fj6Ojo8z6PEA1BbpGDDYdS+XlfCr8fSiU5p6jU80FeRga1DmJw6yCGtAkmzFeSNyFE7ZBkrgZ4GHTsnT3qvOpw2ewUHT4EgLltWzT6c/9qPAyVn6W9TZs2aDQa9yCHqkpPTyc1NbXMCNbo6Ghat25drTqFaGhi0/P4ZX8Kv+xPYfPRdOzO01+STHotfVsEuJO39mHe0udNCFEnJJmrARqNptLNnRUy6jF4WXAVFmIoKkBv8a+Z4E4JCAhg1KhRvPHGG8yYMaNMv7msrKyz9pt79dVX0Wq1jB07tkbjEqI+czhd/B2byS/7U/h5XzJHUvNKPd8s0MKF7UO4oF0IfVsEYK7CFywhhKgpkszVI1ofH1yFhcWjWv1rNpkDeOONNxg0aBB9+/Zl9uzZdO3aFYfDwdq1a3nrrbfYt28fAFarlaSkJOx2O8eOHeOTTz5h8eLFzJ07V+7CiUbP5nDx55E0Vv+bxNp9yWTk2dzP6bUaejf356L2oVzYIYSWQZ4y0bcQQnWSzNUjOh8fHCkpOHNzUZxONLqa/ZbfsmVL/vnnH5599lkefPBBTp48SXBwML169eKtt95yl3vyySd58sknMRqNhIWF0b9/f37++WcuuOCCGo1HiPqiwOZk/cFUftqTxLp9yVgLHe7n/CwGLmwXwoUdQhjSJhhfD5nrTQhRv0gyV49oTCY0RiOKzYYrLw+dj0+NnyM8PJzXX3+d119/vdzn/ztatSLNmzevkUEVQqilwOZk3b5kftx9kl/3p5YafRrsbWJUp1Au7RxOvxYBssqCEKJek2SuHtFoNOi8vXGkp+PMyamVZE6IpszudLHhcBordiTy054k8s9YqD7Sz4NLOodxaecwesb4y+AFIUSDIclcPaP18YH0dFxWa7lTgQghqsblUvjnRCbf7Ujkh39PluoDFx3gwRVdI7i0czidI33k700I0SBJMlfPaC0WNDoditNZ3NTq5aV2SEI0SEdTc/l6Wzzf7UgkIavAvT/Iy8jlXSO4snsEPaL9JIETQjR4kszVMxqNBq23D86sTFw5OZLMCVEFuUUOVu06yZd/x/F3bKZ7v5dJz6hOYYzpHsHAVoHSB04I0ahIMldNtdn5X+fjjTMrE2dODvrw8EZx50AGS4jaoigKW45l8NW2eFb9e9LdD06rgeHtQhjfM4qLOoTIHHBCiEZLkrkqMhiKpyXIz8/Hw6N2FsbWenmh0WpRHA5c+QXoPC21cp66ZLMV91PS1fB0K6LpSsst4su/4/hyaxzH0/Pd+1sGezKhVzTjekYSKuufCiGaAFWTufytW0l/730K9+zBkZpK1OsL8R4xosLyiY/NJPvbb8vsN7ZuRavvvwcgdeHrpL3xRunnW7Sg1Y+raiRmnU6Hn58fKSkpAFgsllq5c2bzsOCy5uBIT8OgC6nx+uuSy+UiNTUVi8WCvhLLlAlREUVR+Ds2k082x7Lq35Pu5bQ8jTou7xrBxD5R9IzxbxR3s4UQorJU/WR1FRRgat8O3/HjSLhnxjnLhz7+f4Q8+ID7seJ0cmzMWHxGXVKqnKlNa2Lef//0jhpOIMLCwgDcCV1tcBUW4szIgIwMDHl55z6gntNqtcTExMiHrKiW3CIHy7cn8MmmWA4kW937u0X7cX2/GC7vGn7+S+oJIUQDper/fl5Dh+I1dCgACZUor/P2Bm9v92PrunU4c3LwG3fVfwrq0QcH12CkpWk0GsLDwwkJCcFut9fKOVxFRRx//H8oBQWEv/Iy5nbtauU8dcVoNKLVSqdzUTWHU6x8uPE4y/9JIO9UXzizQcuYbpHc0L8ZXaJ8VY5QCCHU16C/ymZ9/Q2eAwZgiIwstd8WG8uhIUPRmEx4dO9OyAP3Y4iIqLCeoqIiioqK3I+tVmuFZc+k0+lqrw+Y2Yxv+3bkrPqRojVr8OvWrXbOI0Q9oygKfx5O570NR/n1QKp7f8sgT27o34zxPaPwtciSWkIIUaLBJnP25BRy//iDyBcWlNrv0a0rEXOfw9iiBY6UVNLeeIPjN9xAyxUr0Xl5llvX3Llzefrpp+si7CrxHjmKnFU/Yv1pDSEPPSRNlKJRK3I4WbEjkfc2HGN/UvEXKo0GRnQIZerA5gxsFSh/A0IIUY4Gm8xlf/stOm9vvC+6qNT+kmZbANq1w6NbVw5feBHW1T/id/XV5dY1c+ZMHnjgdF+8hIQEOnbsWCtxV4XX0CFozGbs8fEU7t2LR6dOaockRI3LzLPxyeZYlmyKJS23+A65h0HHxN5R3DSoBc2Dyv8SJoQQoliDTOYURSFr2Tf4jrkSjdF41rI6Hx+MzZtjiz1RYRmTyYTJZHI/zsnJqbFYz4fWYsFr6FCsa9Zg/WmNJHOiUUnOKeTd34/y2ZYT7rnhwnzMTB3UnGv7xEhTqhBCVFKDTObyt2zFHnsC3/Hjz1nWlZeHLS4O3yuvrIPIap73qJFY16wh56fVBN9/nzQziQYvLiOft9cf4au/47E5XQB0DPfh9mEtGd0lHIOsziCEEFWi7tQkeXnYTpy+Y2aLj6dw3z50vr4YIiJIefElHCnJRMyfX+q4rG++xtytK+a2bcvUmTz/ebwuGI4hIhJHSgppry9Eo9Xic/lltX05tcJr2HA0RiP22BMUHTzY4Ee1iqbrULKVt347wnc7E3G6iueH69Pcn7suaM2wtsHyRUUIIapJ1WSuYPceTkyZ4n6cMq84afMdO5aIeXNxpKZiTzxZ6hin1Yp1zVpC/29muXU6kpNIfPAhnFlZ6AICsPTqSfOlX6APCKi9C6lFOi9PPIcMIffnn7H+9JMkc6LBOZBk5ZV1B/lxd5J739C2wdw1vBX9WgaqGJkQQjQOGkUWzSwjPj6e6Oho4uLiiIqKUjscslesIPGRRzG2akWrH75XOxwhKuVoai6vrDvEyl2JlPwvc0mnMO68oBVdo/xUjU0I0TjVt8/vutIg+8w1NV4XXAAGA7YjRyg6fBhT69ZqhyREheIy8nn150Ms+yeeU62pXNo5jPtGtKVdmPfZDxZCCFFlksw1ADpvb7wGDiR3/XpyVv9E8N2SzIn6Jym7kIW/HGLp1jgcp7K4i9qHcP/FbekcKSs1CCFEbZFkroHwvuSS4mRu1SqC7rpTOouLesNaaGfR+qMs3nCUQnvx6NQhbYJ44OK29IjxVzk6IYRo/CSZayC8R1xE0lNGbEePUnTgAOb27dUOSTRxdqeLL7ac4JV1h0jPswHQu5k/D49qJwMbhBCiDkky10DovL3xGjYU69p15PywSpI5oRpFUVizN5n5P+7naFoeULxu6qOXtmdkx1C5ayyEEHVMkrkGxGf06OJkbtUqgh+4Xz40RZ37Nz6bZ77fy5bjGQAEehq5b0QbrukbI5P9CiGESiSZa0C8hg9HY7FgT0igcOdOPLp3Vzsk0URk5NlY8NN+vtgah6KASa/l1iEtuX1YS7zNsuyWEEKoSZK5BkTr4YH3hReS8/33ZK9aJcmcqHUOp4tP/zrBi2sOkFPoAGBs9wgevbQ94b4eKkcnhBACQNpFGhif0aMBsP64GsXpVDka0Zj9dTSdyxdu4KkVe8gpdNAx3Iev7hjAK9f0kEROCCHqEbkz18B4DR6E1scHR2oq+Vv/xrN/P7VDEo1MirWQOd/vY8XORAD8LAYeHNmO6/rGoNNKP00hhKhvJJlrYDRGI94jLyb762/IWbVKkjlRY1wuhc+3nmDej/uxFjrQaOC6vjE8NLId/p5GtcMTQghRAWlmbYB8S5paf/oJxW5XORrRGBxMtjJx0SYeX74ba6GDrlG+rLx7MM9e1UUSOSGEqOfkzlwDZOnXD11QEM60NPI2bcJr6FC1QxINVKHdyRu/Hubt9UewOxUsRh0Pj2rH5AHNpUlVCCEaCLkz1wBpdDp8Ro0CIOeHH1SORjRUfx1N59JX/2DhL4exOxVGdAhh7QPDuGlQC0nkhBCiAZE7cw2Uz2Wjyfz0U6zrfsZVWIjWbFY7JNFAFNicPP/Tfj7ceBxFgRBvE09f2YlLOofJRNRCCNEASTLXQHl0744+PBzHyZPkrv8dn1Ej1Q5JNADbYjN46KtdHDu1DNek3tE8fnkHfGTiXyFEE/bRpuMsWn+U1NwiOoT78PSVnege7Vdh+fc2HOPTzbEkZBUQ4Gnk0s7hPHJJO8wGXd0FfQZpZm2gNFotvpcVD4TI+X6lytGI+q7Q7uS5Vfu4+u1NHEvLI8zHzIc39WH+1V0lkRNCNGkrdyYy5/t93DuiDT/cM5iO4d5Mfu8v0nKLyi3/3Y4E5q/ez70j2rDugWHMH9+V73clsuCnA3Uc+WmSzDVgPldcCYD1t/U4s7LUDUbUWzvjsrjstT945/ejKApc3SuKn+4fyvB2IWqHJoQQqlu84RjX9I1mYu9o2oR68+zYLngYdXz5d1y55bfFZtK7mT9jukcSHWBhaNtgruwWwc64rLoN/AySzDVg5nZtMbVvD3Y7OatXqx2OqGecLoXXfznEuLc2ciQ1j2BvE4sn9+aFCd3w9ZC7cUKIxstqtZKTk+PeiorKv8tmc7jYnZDNoNZB7n1arYZBrYP4Jzar3GN6NfPn34RsdpxK3k6k5/PrgRQuaK/eF2TpM9fA+V55JSn795P93Qr8r7lG7XBEPZGYVcB9S3ew5VgGAJd3DWfO2M74WWTOOCFE49exY8dSj5966ilmzZpVplxmvg2nSyHIy1Rqf7CXiSOpeeXWPaZ7JBl5Nia8vRFFAYdL4fp+Mdx1Qesai7+qJJlr4Hwuu4yUF16gYPt2bCdOYIyJUTskobJV/55k5rJ/yS6w42nUMXtMZ8b1jJSRqkKIJmPv3r1ERka6H5tMprOUrppNR9J549cjPDOmM91j/Diels/slXt47edDzLioTY2dpyokmWvgDKEhePbvT97GjWSvWEnw3XepHZJQSb7NweyVe/lia3E/j25Rvrx6TQ+aB3mqHJkQQtQtb29vfHx8zlnO32JEp9WUGeyQmltEsFf5CeBLaw8wrmck1/QtvnnSPsyHAruDmcv+5e4LWqNVYZ5O6TPXCPiOKR4Ikb1iBYqiqByNUMO+kzlcvnADX2yNQ6OBuy5oxdfTB0oiJ4QQZ2HUa+kc6cvGw2nufS6XwsbD6fRs5lfuMQV2J/9t6NCe2qHWJ7DcmWsEvEeMQOPhgf3ECQp27MDSo4faIYk69OXfcTzx7W6KHC7CfMy8PKk7A1oFqh2WEEI0CNMGt+DBr3bSJcqP7tG+vLfhOPk2BxN6RQPwwNIdhPqaefSS9gBc1D6U9zYco1OELz2i/TiensdLaw9yUYdQ1VbPkWSuEdB6euJ98QhyVqwke8UKSeaaiAKbkye/281X2+IBGN4umJcndsffUwY5CCFEZV3RLYKMPBsvrz1IqrWIDhE+LLm5L8Hexc2sCVkFpfoc33NhazQaeHHNAZKyCwn0NHJRh1AeGtVOrUtAo0i7XBnx8fFER0cTFxdHVFSU2uFUSu6GP4mbNg2dry9t/vgdjVE+0BuzY2l5TP9kG/uTrGg18MDFbblzuDp9NYQQor5oiJ/fNUH6zDUSngP6ow8OxpmdTe7vv6sdjqhFq/49yRULN7A/yUqQl5FPpvXj7gvbSCInhBBNlCRzjYRGp8Pn8ssByP5uhcrRiNrgdCnMX72fOz/9h9wiB32bB/DDjCEMbBV07oOFEEI0WpLMNSIlo1pzf/sNZ3a2ytGImpRTaGfakq289dsRAG4b2pLPbu1HqI9Z5ciEEEKoTZK5RsTcvj2mtm1R7HZyfvxR7XBEDTmcksvY1//k1wOpmPRaXr2mO/83ugN6nfz5CiGEkGSu0fEdOxaArOXL1Q1E1Ihf9idz1Rt/cjQtjwhfM99MH8iY7pHnPlAIIUSTIclcI+N75RWg11O4cxdFhw6pHY6oJkVRePO3w9yy5G+sp/rHrbhnMJ0jfdUOTQghRD2jajKXv3UrcXdM59CQoexr3wHrunVnLZ/31xb2te9QZnOkppYql/Hppxy+8CL2d+3GsYmTKNi1qzYvo17RBwXhNXwYAFnL5O5cQ2RzuHjk6108v/oAigI39I/hk2n9yiwELYQQQoDKyZyroABT+3aEPvlElY5r+eMq2vzxu3vTBZ6e7T5n1SpS5s0n6K67aLHsG8zt2nFi2q040tNrOvx6y2/cOODU8l52u8rRiKrILrAz9YMtfLUtHq0GnhnTiTlju2DUy010IYQQ5VN1BQivoUPxGjoUgIQqHKcPDERXwQK66R8uwW/CBPzGFyc0YU/PInf9erK+WUbQbbeeb8gNgteQIeiCgnCmpZH7++94X3SR2iGJSojLyOemD7dyOCUXT6OO16/ryQXtQ9QOSwghRD3XIL/uHxt7FQeHDOHEzTeT/88/7v2KzUbhnj14Dhzg3qfRavEcMICCHTsqrK+oqIicnBz3ZrVaazP8WqcxGNzTlGR9s0zlaERlbD+Rydg3/uRwSi5hPma+umOgJHJCCCEqpUElc/rgYMJmzSLytdeIevU19GHhxE6eQsGePQA4MrPA6SzV7AqgCwrEkZZWYb1z587F19fXvXXs2LE2L6NOlDS15q5fX6ZPoahfVu8+yTXvbCY9z0anCB++vWsQHSPKv/MshBBC/FeDSuZMLVvgf80kPDp3wtKzBxHPPYule3cyliw5r3pnzpxJdna2e9u7d28NRaweU6tWeHTrBk4n2StWqh2OqMDHm2OZ/uk/FDlcXNg+hC9vH0CYr0wELIQQovIaVDJXHnPXrthjTwCg9/cDnQ7nfwY7ONPS0QdVvOSRyWTCx8fHvXl7e9dmyHXG91S/waxly1AUReVoxJkUReHVdYd44tvdKApc1y+Gdyf3xtOkajdWIYQQDVCDT+aK9u9DHxIMgMZoxNypE3mbNrufV1wu8jZvxqN7d5UiVI/P6NFozGZsR45QuHOn2uGIU1wuhadW7OHldQcBmHFRG54d2xmdVqNyZEIIIRoiVW8DuPLysJ044X5si4+ncN8+dL6+GCIiSHnxJRwpyUTMnw9AxpIlGKKiMLVujauoiKyvvyZv81/EvLfYXUfg1CkkPjYTc+fOeHTtQsaSj3AVFOA37qo6vz616by88Bk1iuzvviPrm2VNMqGtb2wOFw98uYPvd51Eo4FZV3RiysDmaoclhBCiAVM1mSvYvYcTU6a4H6fMK07afMeOJWLeXBypqdgTT7qfV+x2kuc/jyM5Ga3ZjKldO2Lefx/P/v3cZXxGj8aRkUnqwtdwpqZh6tCBmHffOWsza2PmO34c2d99R86qVYT+30y0Hh5qh9Rk5RY5mP7JNv44lIZBp+HFid25sluE2mEJIYRo4DSKdKYqIz4+nujoaOLi4oiKilI7nPOiKApHRo7CHhdH+Ny5+F01Vu2QmqTsAjtT3t/CjrgsLEYdb9/Qi6Ftg9UOSwghGpXG9PldFQ2+z5w4O41Gg9/48QBkffmlytE0TZl5Nq57dzM74rLwsxj47Nb+ksgJIYSoMZLMNQG+464CvZ6C7dspPHhQ7XCalFRrEde8s5k9iTkEehr5/Nb+dI/2UzssIYQQjYgkc02AISQE7wsuACDry69UjqbpSMouZNI7mziQbCXE28TS2/vTIVwmAxZCCFGzJJlrIvwmTQIg+7vvcBUUqBxN4xefmc/ERZs4mppHhK+ZL28fQOuQxjF/oRBCiPpFkrkmwnPgAAxRUbisVnJ+XK12OI1aXEY+kxZt5kRGPtEBHiy9fQDNgzzVDksIIUQjJclcE6HRavGbMAGArKVLVY6m8UrMKuDadzeTkFVAiyBPvrx9ANEBFrXDEkII0YhJMteE+JUMhNi5k8IDB9QOp9FJyi7k2nc3E59ZQLNAC5/f2p9wX5nXTwghRO2SZK4J0QcH433RRYDcnatpKdZCrlu8mdj04qbVz2/tT5ivWe2whBBCNAGSzDUxfhOLm1qzV6zElZ+vcjSNQ1puEde/+xdHU/OI9PPgs2n9ifCTO3JCCCHqhiRzTYzngAEYoqNx5eaS8+OPaofT4GXm2bhh8V8cSsklzMfMZ7f2kz5yQggh6pQkc02MRqt1353LXCorQpyP3CIHUz/Ywv4kK8HeJj67tR/NAmXUqhBCiLolyVwT5DduHBgMFO7aReHevWqH0yAVOZzc/vHf7IzPxt9i4LNp/WgZ7KV2WEIIIZogSeaaIH1gIN4jigdCZH7+hcrRNDwOp4t7P9/Bn4fT8TTqWHJzX9qEyoTAQggh1CHJXBMVcP31AGSvXIkzK0vdYBoQRVF4fPluVu9JwqjT8u7k3nSN8lM7LCGEEE2YJHNNlEevXpjatUMpLCRr2XK1w2kw5v24n6V/x6HVwMLrejCwdZDaIQkhhGjiJJlrojQaDf7XXwdA5uefozidKkdU/7312xEW/X4UgHnjuzKqU5jKEQkhhBCSzDVpvpdfjtbHB3tcHLl//KF2OPXa8u3xzF+9H4DHR3dgYu9olSMSQgghikky14RpLZbika1A5qefqRxN/bXxSBqPfL0LgNuGtuTWoS1VjkgIIYQ4TZK5Js7/umtBoyHvjz+wHT+udjj1zoEkK7d/vA27U+GyruE8dkl7tUMSQgghSpFkrokzxsTgNXQoUNx3TpyWnFPITR9swVrooE9zf16c0A2tVqN2WEIIIUQpkswJ/G8onqYk65tluPLyVI6mfsgtcnDTB1tJzC6kZbAn707ujdmgUzssIYQQogxJ5gSegwZhaBaDKzeX7JUr1Q5HdXani7s+/Ye9J3MI8jLy4dS++FmMaoclhBBClEuSOYFGqyXgulPTlHz6KYqiqByRumav3Mv6g6mYDVrem9KHmECL2iEJIYQQFZJkTgDge9VVaDw8KDp0mPy/tqgdjmo+3nScjzfHotHAa9f0oFu0n9ohCSGEEGclyZwAQOfjg++YKwHIWLJE5WjU8efhNGat3AvAw6PaMVImBRZCCNEASDIn3AImTwEg99dfKTp2TOVo6taxtDzu/PQfnC6Fq3pEMn1YK7VDEkIIISpFkjnhZmrZAq/hwwHI/PhjdYOpQ9kFdm5ZspXsAjvdo/2YO64LGo1MQSKEEKJhkGROlBIwdSoAWcuW48zKUjWWuuBwurjn8+0cTc0j3NfMO5N7yRQkQgghGhRJ5kQpln59MXXogFJYSObSL9UOp9bN/XE/v58aufru5N6EeJvVDkkIIYSoEknmRCkajYaAKZMByPzkExSbTeWIas93OxJ4b0Nx38AXJ3Snc6SvyhEJIYQQVSfJnCjDd/Ro9MHBOFJTyfnxR7XDqRX7k3J47Jt/AbhzeCsu6xquckRCCCFE9UgyJ8rQGI34X1+8xFf6kiWNbhLh7AI7d3y8jQK7kyFtgnhwZDu1QxJCCCGqTdVkLn/rVuLumM6hIUPZ174D1nXrzlo+Z80aTtx8MwcHDORAr94cn3QNuX9sKFUmdeHr7GvfodR25NLRtXkZjZLfpIlozGaK9u4jf8tWtcOpMS6XwoNf7uB4ej6Rfh68ek0PdFoZuSqEEKLhUjWZcxUUYGrfjtAnn6hU+fy//8Zz4ECi31lEi2++xtKvH3F33knh3r2lypnatKbNH7+7t2affVob4Tdqen9/fMeOASDjww/VDaYGvfnbYdbtS8Go1/L2Db0I8JQ1V4UQQjRsejVP7jV0KF5DhwKQUInyYf/3f6UehzxwP9Zffsb666+YO3Y8/YROjz44uAYjbZoCJk8h64ulxZMIHz2GqWULtUM6L+sPpvLi2oMAzBnTmS5RMuBBCCFEw9eg+8wpLheuvHx0vn6l9ttiYzk0ZCiHR1xMwkMPY09MPGs9RUVF5OTkuDer1VqLUTccppYt8LrgAgAyPnhf5WjOT3xmPvd+sR1FgWv7xjCxT7TaIQkhhBA1okEncxnvv48rPx+fSy9x7/Po1pWIuc8Rvfhdwp56Cnt8PMdvuAFnbl6F9cydOxdfX1/31vHMu3xNXOCt0wDI/vY77MkpKkdTPXanixmfbycr3063KF9mXSm/XyGEEI1Hg03msld+T+obbxL18kvoAwPd+72GDsXnkkswt2uH15DBRL+zCFeOFevqiqfYmDlzJtnZ2e5t73/64DVllp498ejZE8VuJ+OjJWqHUy0vrjnIPyey8Dbref26npj0ssKDEEKIxqNBJnPZP/zAySeeIPLll/AcOPCsZXU+PhibN8cWe6LCMiaTCR8fH/fm7e1d0yE3aCV357K+WIozJ0flaKrmtwMpvL3+CADPj+9KdIBF5YiEEEKImtXgkrns73/g5P89TuSLL+B9alH4s3Hl5WGLi5MBEefBa9gwTG3a4MrLI/PzL9QOp9KScwp54MudAEwe0IxLu8jEwEIIIRofVUezuvLysJ04fcfMFh9P4b596Hx9MUREkPLiSzhSkomYPx8oblpNnDmT0P+biUfXrjhSUwHQmM3oTt1NS57/PF4XDMcQEYkjJYW01xei0WrxufyyOr++xkKj1RJ46zQSH3mUjI8+ImDKZLTm+r2GqdOlMOPz7WTk2egY7sP/je6gdkhCCCHqqY82HWfR+qOk5hbRIdyHp6/sRPdovwrLZxfYeeGnA6zek0R2vp1Ifw+evLwjF7QPqbugz6BqMlewew8npkxxP06ZV5y0+Y4dS8S8uThSU7EnnnQ/n/Xll+BwkDz7GZJnP+PeX1IewJGcROKDD+HMykIXEIClV0+aL/0CfUBAHV1V4+Rz6aWkvPIKjsSTZC9fjv+116od0lm99vMh/jqWgadRx+vX9cBskH5yQgghylq5M5E53+9jzlWd6RHtx/t/HmPye3/xy0PDCfIylSlvc7i48b2/CPQ08tb1PQn1MZOQVYCP2aBC9MU0SmNbq6kGxMfHEx0dTVxcHFFRUWqHU29kfPwJyc8+iyE6mlY/rkKjV/W7QIU2HUnnusWbURR49ZrujOkeqXZIQggh6kB1Pr/HvPEn3aJ8mT2mM1C8UtCAeT8zZWBz7hzeukz5TzbH8s7vR/n5wWEYdPWjt1r9iEI0CH5Xj0fn7489Lo6cn35SO5xyZefbuX/pDhQFJvWOlkROCCFEhWwOF7sTshnUOsi9T6vVMKh1EP/EZpV7zLp9yfSM8ePJ73bTe85aRr68njd+PYzTpd69MUnmRKVpPTzwv/EGANLfXUx9u6mrKAr/9+2/JOUU0jLIk6dkPjkhhGiSrFZrqcUAioqKyi2XmW/D6VLKNKcGe5lIzS3/mBMZ+azanYTTpfDB1L7cc2Eb3v3jKAt/OVTj11FZksyJKgm47jo0FgtF+/eT9/vvaodTyrc7Evhh10n0Wg0vT+qOxVg/m4GFEELUro4dO5ZaDGDu3Lk1VreiQJCnkbnjutIlypcrukVw9wWt+fSviqdAq23yaSeqROfnh/+kSWR88AGpb76J59ChaDQatcMiLiOfJ7/dA8C9F7Wh21lGIQkhhGjc9u7dS2Tk6W42JlPZgQwA/hYjOq2GtP/chUvNLSK4nMEPAMHeJgw6DTrt6c++ViFepFqLsDlcGPV1f59M7syJKgu8+SY0JhOFO3eRt3Gj2uHgdCk8+OVOrEUOejXzZ/rwVmqHJIQQQkXe3t6lFgOoKJkz6rV0jvRl4+E09z6XS2Hj4XR6NvMr95jezfw5npaP64w+csdS8wjxNqmSyIEkc6Ia9MHB+E2aCEDam2+p3nfund+PsuV48TQkL0/sjr6ejC4SQghR/00b3ILPt8bx9bZ4DqdYefzb3eTbHEzoFQ3AA0t3MH/1fnf5G/o3I7vAztMr93A0NZdf9ifz5m+HmTygmVqXIM2sonoCb5lG1hdLKdi2jfwtW/Hs11eVOHYnZPPS2gMAzLqyEzGBslyXEEKIyruiWwQZeTZeXnuQVGsRHSJ8WHJzX4K9i+/mJWQVlOpOFOHnwZKb+/LM93u55NU/CPMxc9OgFtwxTL1WIZlnrhwyz1zlJM2eTeZnn2Pp149mSz6s8/MX2p1cvnADh1NyuaRTGG/d0LNe9N8TQgihjqb6+S3tUaLaAqdNA4OB/L/+Iv/vv+v8/C+vPcjhlFyCvU08N66LJHJCCCGaJEnmRLUZIiLwu+oqoLjvXF3650Qm7/5xFIC5V3UhwNNYp+cXQggh6gtJ5sR5CbztNtDrydu4kYIdO+rknIV2Jw9/tROXAuN6RDKiY2idnFcIIYSojySZE+fFGBWJ75grAUh9q27uzr287iBHTg0Df+qKTnVyTiGEEKK+kmROnLeg228HnY689b9TsGtXrZ7rnxOZvPt7cfPqc1d1wddiqNXzCSGEEPWdJHPivBljYvC94goAUl99rdbOI82rQgghRFmSzIkaEXTXncV95/78k/ytW2vlHCXNq8HeJp68omOtnEMIIYRoaCSZEzXCGB2N39XjAUh59dUaXxXi3/hsd/Pq3Ku64GeR0atCCCEESDInalDQHXegMRop+HsbeX/W3JqtDqeLx5btwqUUz9QtzatCCCHEaZLMiRpjCAvD/9prAUh95ZUauzv3wZ/H2ZOYg6+HgScvl+ZVIYQQ4kySzIkaFXjbrWgsFgp37yb3l1/Ou764jHxeWnsQgMcv6+BeK08IIYQQxSSZEzVKHxhIwI03AsUjWxWXq9p1KYrC49/upsDupH/LACb0ajrr7AkhhBCVJcmcqHGBN9+E1tubooMHyfnxx2rXs2JnIr8fTMWo1/LcVbL2qhBCCFEeSeZEjdP5+hJ4800ApC18HcXhqHIdmXk2Zq/cC8CMC1vTMtirRmMUQgghGgtJ5kSt8L9xMjp/f2zHj5O1bFmVj39u1T7S82y0DfXitqGtaiFCIYQQonGQZE7UCp2XJ0F33A4U351z5edX+tgtxzL4als8Gg3MHdcFo17epkIIIURF5FNS1Bq/a6/FEBWFIzWVjCVLKnWM3eniiW93A3BNnxh6NQuozRCFEEKIOvHA0h3kFp3udrQ3MQe7s/qDBM8kyZyoNVqjkeD77gMgffF7ODIyznnMR5tiOZBsxc9i4JFR7Wo5QiGEEKJufLsjgUK70/144qJNnMwqrJG6q5TM5W3eXK3O7KLp8hl9KeZOnXDl5ZH25ltnLZuSU8jLp+aUe/SS9vh7ypJdQgghGof/TqNfk8teVimZO3HzLTizs92Pj02ahD05ucaCEY2PRqsl5KEHAcj84gtssbEVln1u1T5yixx0i/ZjUu/ougpRCCGEaNCq1sz6nyzSdugwis1Wk/GIRshzwAA8hwwBh4OUV14pt8zmo+l8uyMRjQaeGdMJrVbmlBNCCNG4HErOZd/JHPadzEEBjqSeflyyVYe+ZsMUonwhDz3IsQ0bsP64moKbb8ajSxf3c3aniye/Kx70cH2/GLpG+akUpRBCCFF7rl+8uVRz681LtgKgobgZVgMcnXtZleutWjKn0RRvFT0WogLmdu3wvfJKsr/7jpQFLxCz5EP3ig5LNh7nYHIuAZ5GHhopgx6EEEI0Pn88ckGt1V21ZE5RODH1JtDrAHAVFhI/fToYDKWKtazGJLGi8Qu+dwY5P/5I/pYt5P76K94XXkiK9fSgh8cuaY+fRQY9CCGEaHyi/C21VneVkrmgu+4q9dj7wovO6+T5W7eS/t77FO7ZgyM1lajXF+I9YsRZj8n7awvJ8+dhO3QYfXg4QXfcgd+4q0qVyfj0UzLeex9HWhqm9u0J+9/jeHTtel6xivNniIggYMoU0t99l+T58/EaPJgXfzpIns1Jtyhfru4VpXaIQgghRK06lpbH2r1JxGcWoAGiAyyM7BhGTGD1k70qJXPBd9917kJV4CoowNS+Hb7jx5Fwz4xzlrfFxxN3xx34T5pE5IIF5G3azMknnkAfHIzXkMEA5KxaRcq8+YTNmoVHt65kLPmIE9NupdWPq9AHBtZo/KLqAm+/nazly7HHnmDj4qV8GVc8KfCTV8igByGEEI3bG78e5uW1B3EpCoFeJhQFMvKKmL96Pw+Palft5SurPQDCkZmJPT4BNBoMkRHo/f2rXIfX0KF4DR0KQEIlymd98QXGqEhCH3sUAFOrVhT8s42MJUvcyVz6h0vwmzABv/HjAAh7eha569eT9c0ygm67tcoxipql8/Ik5P77SHz8f8zbmYPiH8CV3SLo1azq7x8hhBCiodh4JI0X1xzgngvbcPOgFvhairuoZeXbeH/DMeavPkC3KD/6taz6jacqJ3NFhw5x8umnKfhne6n9lj59CHvqKUwtW1Q5iMrK37EDy4ABpfZ5DhpM8ty5ACg2G4V79pRK2jRaLZ4DBlCwY0eF9RYVFVFUVOR+bLVaazZwUYrv2LEs/+5P/vVvjgknj13aXu2QhBBCiFr16V8nmNQnhvsvbltqv5/FyAMj25GaW8Qnf52oVjJXpXnmHKmpxN44GWdGJqGPPUr0okVEL3qbkIcfLn7uhhtwpKdXOYjKcqamoQ8MKrVPHxSIKzcXV2EhjswscDrR/ac5VRcUiCMtrcJ6586di6+vr3vr2LFjbYQvTilyweLWFwMw/sAvBCSfUDkiIYQQonbtjMtiXM/ICp+/qkcU209kVqvuKiVzGUuWYIiIoMXyZQRMnozXkMF4DRlC4E1TabHsGwxhYWR8WLkF1euTmTNnkp2d7d727t2rdkiN2nsbjpGQ7yJYKWTCwV9JnjuvRpc1EUIIIeqbtNwiovw9Knw+OsCDVGtRhc+fTZWSudyNGwm8dRpak6lsRWYzAbfcTO6fG6oVSGXogoNwpJe+w+ZIS0fr5YXWbEbv7wc6Hc7/3B10pqWjDyp9R+9MJpMJHx8f9+bt7V0b4QuK119989fDADwysi0eOsjfvJncX35ROTIhhBCi9hQ5XBh0Faddeq0Wu9NVrbqr1GfOHheP+SxNkB6dO2OPi69WIJVh6d6d3PW/l9qXt3EjHt27A6AxGjF36kTeps3uKU4Ul4u8zZvxv/76WotLVN6Cnw6QZ3PSPdqP8Rd0Ju2mm0hftIjk+c/jOWQIWqPMMyeEEKJxWro1DotRV+5zeUWOatdbpWTOlZeH1surwue1np648vOrVJ/txOn+Urb4eAr37UPn64shIoKUF1/CkZJMxPz5APhdcw0Zn35G8oIF+I0fT97mzeSsXk3022+76wicOoXEx2Zi7twZj65dyFjyEa6CgjJz0Ym6tzcxh6//KU72n7i8I1qthsBbbyV72TLsJ06Q8f4HBN1xu8pRCiGEEDUvwteDz7ecvY94hF/FzbBnU+XRrK68PJzlNLMCuHJzoQp9nwp27+HElCnuxynzipM237FjiZg3F0dqKvbEk+7njVFRRL/9Nsnz5pH50cfow8IIf+YZ97QkAD6jR+PIyCR14Ws4U9MwdehAzLvvnLWZVdSN+av3oyhwWddw91QkOi9PQh55hMSHHybt7bfxveJyDJEVdxAVQgghGqI/H7uw1urWKFXoeb6vQ8ezr8WqKKDR0GHvnpqITTXx8fFER0cTFxdHVJSsSlATNh5O47rFf6HXalj3wDCaB3m6n1MUhROTp5C/dSveF48gauFCFSMVQgjRUNXnz++Nh9N4csUelt85EG9z6WVQcwrtjH9zI89e1YW+LQKqXHeV7szFLPmwyicQwuVSmPvjfgCu7xdTKpED0Gg0hD35BEfHXoV17Tpyf//dPZm0EEII0Ri8/+cxrukTXSaRA/AxG7iuXwyL/zharWSuSqNZLb16UbBzJ6kvv0LK8wvI++MPPLp2xbNv31KbEGf6/t+T/JuQjadRxz0XtSm3jKlNGwImTwYgac6zuIqqNzxbCCGEqI/2nbQyvF1whc8PaRPM7oTsatVdpWQubdEiUl9+Ba3Fgj40lIyPPiZp9jPVOrFoGoocThb8VHxX7o5hrQjyKr+/JUDQXXehDwnBfuIE6e+9V1chCiGEELUuNbcIvfZsU5NoSM+zVavuKiVz2d99R9iTTxLz3mKi33id6LfeJGflShRX9eZFEY3fp5tPEJdRQIi3iVuGnH2pN52XJyGPPgJA+qJ3sMXX3jQ3QgghRF0K8zFzILni5UL3J+UQ4lPxDY+zqdpyXokn8Rp2ui+T58CBoNHgSEmp1slF45ZTaGfhL4cAuG9EWyzGc3fR9Bk9Gku/fihFRSQ/+1xthyiEEELUiQvaBfPSmoMU2p1lniu0O3l57SEuah9arbqrlMwpTiea/0xLotHrURzVn+hONF6L1h8hM99Oq2BPJvau3KiiksEQ6PXk/vorOWvX1nKUQgghRO27+8I2ZBXYuPCF33h7/RHW7ElizZ4k3vrtCBe+8BtZBTbuuqB1tequ2jxzikLizJmlZul32WwkPTULreX0RHcytYRIsRby3oZjADxySXv0Z1nC5L9MrVoReMstxStDPDMHzwED0J1lsmohhBCivgv2NvHN9IH879vdPL96PyXzwmmAoW2DeWZMZ4K9q9fMWqVkznfs2LL7rriiWicWjdubvx6h0O6ie7QfIztW/bZx0PQ7yFn9I/bYE6S+9HLx3TohhBCiAYvyt/DhTX3JzrdzPD0PBWgR6Imvpex0JVVRpWQuYq70YRLnlpBVwGd/FS9Z8vCodmjONtF0BbRmM+FPP82JqTeR+fnn+FxxOZYePWo6VCGEEKLO+VoMdLP41Vh9VeozJ0RlvP7LIWxOF/1bBjCwVWC16/Hs3x/fq64CRSHpySdRbNUbsi2EEEI0ZpLMiRp1PC2PL/8unlLkoZHVuyt3ppBHHkYXEEDRocOkv/9+TYQohBBCNCqSzIka9erPh3C6FIa3C6Z386ovSfJfen9/QmfOBCDtzbcoOnbsvOsUQgghGhNJ5kSNOZRs5dsdCQA8eHG7GqvX5/LL8Bw8GOXUyGlFUc59kBBCCNFESDInasxLaw+iKHBJpzC6RPnWWL0ajYawWU+h8fAgf8sWspYurbG6hRBCiIZOkjlRI3YnZPPj7iQ0GnhgZNsar98YFUXI/fcDkPL8AmzxCTV+DiGEEKIhkmRO1IiX1h4EYEy3CNqGetfKOfxvuB6P3r1w5edz8on/SXOrEEIIgSRzogbsis/il/0paDVw74iavytXQqPVEvHss2jMZvI3bSZr6Ze1di4hhBCioZBkTpy3134+DMDY7pG0CPKs1XMZmzUj5IGS5tbnpblVCCFEkyfJnDgvuxOyWbcvGY0G7rqwegsEV5X/DTfg0UuaW4UQQgiQZE6cp9d/Kb4rd0XXCFoFe9XJOYubW+dIc6sQQgiBJHPiPBxIsrJ6T/EI1rvr6K5cCWPz5oTcfx9wqrk1Lq5Ozy+EEELUF5LMiWpb+MshAEZ3Dq+1Eaxn43/jjVh698aVn0/iI4+iOBx1HoMQQgihNknmRLUcTrHyw78ngbq/K1dCo9USPm8eWi8vCrZvJ/3dd1WJQwghhFCTJHOiWl7/5TCKAiM7htIh3Ee1OIxRkYQ9+QQAqa+/QcGuXarFIoQQomH6aNNxBs37hbb/+5Exb/zJjrisSh23YmcizR/7gVs/+rt2AzwHSeZElR1NzWXFzkQAZlzURuVowOeKK/AZfSk4nSQ+/Aiu/Hy1QxJCCNFArNyZyJzv93HviDb8cM9gOoZ7M/m9v0jLLTrrcXEZ+Tz3wz76Ng+oo0grJsmcqLI3fzuCS4GL2ofQObLm1mCtLo1GQ9hTT6EPC8MWG0vy/OfVDkkIIUQDsXjDMa7pG83E3tG0CfXm2bFd8DDq+PLvigfWOV0K9y3dwf0XtyE6wFKH0ZZPkjlRJQlZBXy7vXiiXrX6ypVH5+tLxLy5AGQtXYr1l19VjkgIIYRarFYrOTk57q2oqPy7bDaHi90J2QxqHeTep9VqGNQ6iH9isyqs/9WfDxHoaWRSn5iaDr1aJJkTVbL4j6M4XAoDWwXSI8Zf7XBK8ezfn4CpUwE4+b//4UhLUzcgIYQQqujYsSO+vr7ube7cueWWy8y34XQpBHmZSu0P9jKRWkEz69bjGXy5NY5547vWeNzVpVc7ANFwZOTZ+GJL8W3n6cNbqRxN+YLvv4+8jRspOniQxEcfI/rdd9Bo5TuLEEI0JXv37iUyMtL92GQynaV05eUWObh/6Q7mju9CgKexRuqsCZLMiUpbsvE4BXYnnSJ8GHzGLen6RGsyEfniCxybMJG8P/8kffF7BN12q9phCSGEqEPe3t74+Jx7pgV/ixGdVlNmsENqbhHBXmUTwNj0POIzC5i25PToVdepJSVb/d8qfnlwGM0Ca3eN8vJIMicqJd/mYMmm40DxXTmNRqNuQGdhatOGsCf+x8nH/0fqq69i6d0LS8+eaoclhBCinjHqtXSO9GXj4TRGdQoDwOVS2Hg4nckDm5Up3yrYi5/uG1pq3wtrDpBX5OCpKzoR7utRJ3H/V71I5jI+/ZSM997HkZaGqX17wv73OB5dy2+Ljr1xMvlbt5bZ7zlsKDGLFgGQ+NhMsr/9tvTzgwcTs1gmla2uL7bEkZVvp1mghUs7h6sdzjn5jhtH3ua/yFm5koQHH6LFsm/Q+9evPn5CCCHUN21wCx78aiddovzoHu3LexuOk29zMKFXNAAPLN1BqK+ZRy9pj9mgo11Y6RWPfMwGgDL765LqyVzOqlWkzJtP2KxZeHTrSsaSjzgx7VZa/bgKfWBgmfJRC19Dsdvdj51ZWRwdexU+oy4pVc5zyBAinnvW/VhjrD9t2w2NzeFi8R9HAbhtaEt02vp7V65EyXQlhbt2YYuN5eTj/yPqjdfr9R1FIYQQde+KbhFk5Nl4ee1BUq1FdIjwYcnNfQn2Lm5mTcgqqPefHaonc+kfLsFvwgT8xo8DIOzpWeSuX0/WN8vK7euk8/Mr9Thn1Sq0ZjM+l4wqtV9jNKIPDq61uJuSFTsTScwuJMjLxPieUWqHU2k6L08iX3mZ45OuIfeXX8j8+GMCJk9WOywhhBD1zJSBzZkysHm5zy29fcBZj31xYrdaiKhqVB3mp9hsFO7Zg+fA0y+URqvFc8AACnbsqFQdWV9/g8/o0WgtpSfty9+yhYMDB3Hkkks5OWsWjszMmgy9yXC5FBatPwLALYNbYDboVI6oaswdOhDy2KMAJC94gYJ/d6sckRBCCFGzVE3mHJlZ4HSi+09zqi4osFJzhBXs2kXRoUP4Tbi61H7PIYOJmD+PmA8+IOShB8nf+jdxt92O4nSWW09RUVGpyQWtVmu1r6mx+Xl/CodScvE26bm+f/2YHLGq/K+9Fu+RI8FuJ+G++3BmZakdkhBCCFFjGvQEXFlff4OpbdsygyV8L7sM7wsvxNyuLd4jRhD99lsU/vsv+Vu2lFvP3LlzS00u2LFjx7oIv0F4+9Rduev7N3N38mxoNBoN4XOewRAdjT0hgYSHH6kwsRdCCCEaGlWTOb2/H+h0ONPTS+13pqWjDzr7PGau/HxyVq3C7+rx5zyPMToanb8/ttgT5T4/c+ZMsrOz3dvevXsrfQ2N2fYTmWyLzcSg03DzoOZqh3NedD4+RC18DY3ZTN4ff5D2xhtqhySEEELUCFWTOY3RiLlTJ/I2bXbvU1wu8jZvxqN797Mem7P6JxSbDZ8rrjjneexJSTizstCHlD8gwmQy4ePj4968vdUbXlyfvLfhGABXdoskxMescjTnz9y+PeGznwYg7c23ZP1WIYQQjYLqzayBU6eQ9dVXZC3/lqIjR0ia9TSuggL8xl0FQOKjj5Ly4ktljsv65hu8R1xUZu4wV14eyc8voGDHDmzxCeRt2kT8nXdhjInBc/DgOrmmxiA+M58fdycBxQMfGgvfK6/E//rrgeL3li02VuWIhBBCiPOj+tQkPqNH48jIJHXhazhT0zB16EDMu++4m1ntiSdBUzrnLDp6jIJt2wh6b3HZCnU6ig4cIO7bb3FarRiCg/EcNIjge2eglbnmKm3JxuM4XQoDWwXSMeLcS6I0JKGPPkLh3r0UbN9O/N330HzpF2VGQwshhBANhUZRTi0qJtzi4+OJjo4mLi6OqKiGM69aTcktcjDguZ+xFjl4f2pvLmwfqnZINc6enMKx8eNxpqXhc9llRLywoN5PCimEEOLsmurnt+rNrKL++XJrHNYiBy2DPRneNkTtcGqFITSEqJdfAp2OnB9+IOP9D9QOSQghhKgWSeZEKU6Xwvt/Fg98uGVwC7QNYOmu6rL06UPoo8UTCqe88ALW335TNyAhhBCiGiSZE6Ws2ZNEfGYBfhYD43o0/lvU/jfegN+ECaAoJD74EEWHDqkdkhBCCFElksyJUhafmo7khn7N8DA2rKW7qkOj0RD2xP+w9OmDKy+PuDvvkqXfhBBCNCiSzAm3MycJnjygmdrh1BmN0Ujka69iiIrCHhdHwox7UWw2tcMSQgghKkWSOeHW2CYJrgq9vz/Rb72J1mIhf+tWkuY8iwz0FkII0RBIMicASM4pZPWpSYJvHtxc3WBUYmrThogXXwCNhqwvvyTz40/UDkkIIYQ4J0nmBACf/nUCh0uhT3N/OkX4qh2OarwvuICQhx4EIHnuXKw//6xyREIIIcTZSTInsDlcfPbXCQAmD2iubjD1QMDNN+M3cSIoCgkPPkTBzp1qhySEEEJUSJI5wY+7T5KWW0SIt4lRncLUDkd1Go2GsCefwHPYUJTCQuKm34ntxAm1wxJCCCHKJcmc4KNNxYvNX9cvBqNe3hIAGr2eqJdewtyxI86MDOJuvU2mLBFCCFEvySd3E7c7IZttsZnotRqu6xujdjj1itbTk+hFb2OIiMAWG0v8nXfhKixUOywhhBCiFEnmmrglG48DcGmX8CY3HUll6IODiX5nEVofHwq2byfxkUdRnE61wxJCCCHcJJlrwjLzbHy3MxGAKU1okuCqMrVuTdTrC9EYDFjXrCFp9jMyB50QQoh6Q5K5Jmzp33HYHC46RfjQq5m/2uHUa559+xKxYEHxHHRLl5L6yqtqhySEEEIAksw1WU6XwsenBj5MGdAcjUajckT1n88lowh7ehYA6YsWkf7Bh6rGI4QQQoAkc03WL/tTSMgqwM9i4MruEWqH02D4T5xI8AMPAJAyfz5Z3yxTOSIhhBBNnSRzTdRHm44DMKl3NGaDTt1gGpjAW6cRcPPNAJx84gms69apHJEQQoimTJK5JuhEej5/HEoD4Pp+MvChqjQaDSEPP4Tv+HHgcpFw/wPkbdqkdlhCCCGaKEnmmqDPtxavZjCkTRAxgRaVo2mYNBoN4U8/jffFI1DsduKm30neli1qhyWEEKIJkmSuibE5XHz1dxyATBJ8njR6PREvvojnkCHFy37dMZ38f/5ROywhhBBNjCRzTczavcmk5doI9jYxomOo2uE0eFqjkaiFr+E5cABKfj5xt95Gwa5daoclhBCiCZFkron5fEtxE+vE3lEYdPLrrwlas5moN97A0rcvrrw8TtwyjYI9e9QOSwghRBMhn+ZNyPG0PDYcTkOjgWv6SBNrTdJ6eBD91pt49OqFy2rlxM23ULh/v9phCSGEaAIkmWtCSgY+DG0TTHSADHyoaVpPT6IXLcKjWzdc2dmcmHqT3KETQghR6ySZayJsDhdf/x0PwHX95K5cbdF5eRK9+F3MXbvizMoqTuh27lQ7LCGEEI2YJHNNxJq9SaTn2Qj1MXFR+xC1w2nUdN7exLz/Hh49exY3ud50M/l//612WEIIIRopSeaaiM/+Km5indQ7Gr0MfKh1Oi8vYt59B0u/frjy8zlx620ysbAQQohaIZ/qTcCxtDw2HklHo4FJMrdcnSnuQ/d28Tx0BQXE3X4HuevXqx2WEEKIRkaSuSbgi1PTkQxvG0ykn4fK0TQtxdOWvI7XhRei2GzE3X0POatXqx2WEEKIRkSSuUbO7nTxzT/FAx+ulbtyqtAajUS9+grel1wCdjsJ9z9A5uefqx2WEEKIRkKSuUbu1/0ppOXaCPIycYEMfFCNxmAg8sUX8Js0CRSFpKdnk/rGGyiKonZoQgghGrh6kcxlfPophy+8iP1du3Fs4qSzLoeUtWw5+9p3KLXt79qtVBlFUUh97TUODhnC/m7dib3pJmzHj9fyVdRPX20rvis3vmekrPigMo1OR9ispwi6804A0ha+TvIzc1BcLpUjE0II0ZCp/umes2oVKfPmE3TXXbRY9g3mdu04Me1WHOnpFR6j9fKizR+/u7fWv/xc6vn0xYvJ+PgTwmfNovmXS9F6WDgx7VZcRUW1fTn1Soq1kF/2pwAwoXeUytEIAI1GQ/CMewj93/9AoyHzs89IfOghFJtN7dCEEEI0UKonc+kfLsFvwgT8xo/D1Lo1YU/PQms2k/XNsooP0mjQBwef3oKC3E8pikLGRx8RdMcdeF90EeZ27YiYPw9HSgrWdevq4Irqj2+3J+B0KfSI8aN1iLfa4YgzBNxwPREvLACDgZxVPxJ3x3ScublqhyWEEKIBUjWZU2w2CvfswXPgAPc+jVaL54ABFOzYUeFxrvx8Dl14IYeGX0DcnXdRdOiQ+zl7fDzO1LRSdeq8vfHo2pWCHU1nJn5FUfjy1IoPE3tHqxyNKI/vZZcR/dZbaCwW8jZuJPa667GfPKl2WEIIIRoYVZM5R2YWOJ3oAgNL7dcFBeJISyv3GGOL5oQ/O4foN94g4vn54HJx/NrrsCclFdeZWnxc2TqDcKSllltnUVEROTk57s1qtZ7nlalvR1wWh1NyMRu0XN41XO1wRAW8Bg+i2ZIl6IKDKDp4kOMTJ8l6rkIIIapE9WbWqrL06IHf2LGYO3TAs29foha+hi4ggMylS6td59y5c/H19XVvHTt2rMGI1VFyV25053C8zQaVoxFn49GlMy2++AJTm9Y4UlOJveFGrL/8qnZYQgghGghVkzm9vx/odDj/M9jBmZZeqh/c2WgMBswdOmCPLZ4YVx9cfFzZOtPQBwWXW8fMmTPJzs52b3v37q3ildQvBTYnK3cmAjBBmlgbBENkJM0++wzPgQNRCgqIv/tuMj76WO2whBBCNACqJnMaoxFzp07kbdrs3qe4XORt3oxH9+6VqkNxOik6eBB9cHGiZoiKQhccVKpOZ24uBbt24dG9W7l1mEwmfHx83Ju3d8MeLPDj7pPkFjmICbDQr0WA2uGIStJ5exO96G38JkwAl4vk554j6Zk5KA6H2qEJIYSox/RqBxA4dQqJj83E3LkzHl27kLHkI1wFBfiNuwqAxEcfRR8SSsiDDwCQ+sYbeHTrjrFZDM6cHDLeex97YiJ+E64Giqd+CJg8mbS338bYvBmGyChSX3sNfUgI3iNGqHaddemrU02sV/eKQqvVqByNqAqNwUDY7KcxNosh5YUXyfz0U4qOHiHypZfQ+/urHZ4QQoh6SPVkzmf0aBwZmaQufA1nahqmDh2IefcddzOrPfEkaE7fQHTl5HDyySdwpqah9fXF3KkjzT//DFPr1u4ygdOmoRQUcPLJp3Dl5ODRqyfR776D1mSq8+urayfS89l0NB2NBsb3krnlGiKNRkPgtGkYYmJIfGwm+Zs2c3zCRKLeeANzu7ZqhyeEEKKe0SiynlAZ8fHxREdHExcXR1RUw0qIXlpzgNd+OcyQNkF8fEs/tcMR56nwwEHi77oLe3w8GouFiHlz8Rk5Uu2whBCiXmrIn9/no8GNZhUVc7kUlm1PAIqbWEXDZ27XluZffYmlf3+U/HwSZtxL6muvyRJgQggh3CSZa0T+js0kPrMAL5OeUZ3C1A5H1BC9vz8xi98lYMpkANLefIv4u+7GmZOjcmRCCCHqA0nmGpHl24sHPlzaOQyzQadyNKImafR6QmfOJHzuXDRGI7m//sqxceNlgmEhhBCSzDUWhXYn3+8qXgrqqp6RKkcjaovfVWNp9tlnGKKisMfHE3vtdWR+sRTp+iqEEE2XJHONxC/7U7AWOgj3NdO/ReC5DxANlkfnTrT45mu8LrwQxWYjadYsEh99FFd+vtqhCSGEUIEkc43Esn+KBz6M6R4pc8s1ATpfX6LeeJ2Qhx8CnY6cFSs5NnEiRUeOqB2aEEKIOqb6PHPi/GXk2fjtQAoA46SJtcnQaDQE3nILHl27kvDAg9gOH+HY+KsJnTkTv4kT0GgkqRdCiMr4aNNxFq0/SmpuER3CfXj6yk50j/Yrt+znW06w7J94DiRZAegS5cvDo9pXWL4uyJ25RuD7XYk4XAqdInxoG9qwlyITVWfp04cWy5cVr+taWEjSU0+RMGMGjsxMtUMTQoh6b+XOROZ8v497R7Thh3sG0zHcm8nv/UVablG55TcfTefKbhF8flt/lt05iHBfD2587y+SsgvrOPLTJJlrBEqaWK/qIXflmip9UBDRi98l5JFHwGDAunYdx8ZeRd7mzec+WAghmrDFG45xTd9oJvaOpk2oN8+O7YKHUceXf8eVW/7Va3pw44DmdIrwpXWIF/PHd0VR4M/DaXUc+WmSzDVwR1Nz2RGXhVYDV3aPUDscoSKNVkvgzTfR/IvPMbZogSM5mRM33UzKiy+h2O1qhyeEEPWOzeFid0I2g1oHufdptRoGtQ7in9isStVRYHdid7rwsxhqKcpzk2Sugfv21IoPQ9oEE+JtVjkaUR94dCoe7eo3YQIoCunvvsvxa6+TwRFCiCbDarWSk5Pj3oqKym8yzcy34XQpBHmVXrs92MtEagXNrP8178d9hPqYSyWEdU2SuQZMURSW7yhO5mTggziT1mIh/JnZRL72KlpfXwp37+bYVeNIf+89FKdT7fCEEKJWdezYEV9fX/c2d+7cWjnPm78dZuXOkyy6sZeqk/XLaNYG7O/YTOIyCvA06hjZUZbvEmX5jByJR7dunHziCfJ+/4OUBS9gXbuO8LnPYWrRQu3whBCiVuzdu5fIyNM3OUwmU7nl/C1GdFpNmcEOqblFBHuVf0yJd34/wlu/HeHTaf3oEO5z/kGfB7kz14AtP9XEeknncDyMsnyXKJ8hNJToRYsIf3YOWk9PCnbs4NjYq8hYsgTF5VI7PCGEqHHe3t74+Pi4t4qSOaNeS+dIXzaeMXjB5VLYeDidns38Kqz/7fVHWPjzYZbc3JeuURWXqyuSzDVQdqeLH/8tXr5rbA8Z+CDOTqPR4Dd+PC1XriiewqSoiOS584idPJmiY8fUDk8IIVQzbXALPt8ax9fb4jmcYuXxb3eTb3MwoVc0AA8s3cH81fvd5d/67QgvrTnI81d3JcrfgxRrISnWQvKKHGpdgjSzNlQbDqeRmW8nyMvIgJayfJeoHENEBNHvLSZr6ZckP/88BX9v49iYsQRNv4PAW25BYzSqHaIQQtSpK7pFkJFn4+W1B0m1FtEhwoclN/cl2Lv4bl5CVkGpSdg/2RyLzeli+qf/lKrn3ovacP/Fbes09hIaRVboLiM+Pp7o6Gji4uKIiopSO5xyPfDlDpb9k8DkAc2YPaaz2uGIBsgWH0/SrKfJ27ABAGPrVoTPno2lZ0+VIxNCiOppCJ/ftUGaWRugQruTNXuSgeJvFEJUhzEqiuh33yFiwQJ0AQHYDh8h9rrrOTlrFs6cHLXDE0IIUUmSzDVAvx1IJbfIQYSvmV4x/mqHIxowjUaD7xWX02rVD/hePR6ArC+WcuSyy8hZtQq5cS+EEPWfJHMN0MqdiQBc3i0CrVYWUxfnT+fnR8ScOcR8tARjixY4U9NIeOBBTkyZSuGBg2qHJ4QQ4iwkmWtgcosc/Lz/VBNrV2liFTXLs29fWnz3LUEz7kFjNpO/ZQvHxo0jac6zOLOz1Q5PCCFEOSSZa2B+3pdMod1FiyBPOkeqO0mhaJy0RiPBd95Jqx++x3vkSHA6yfzkE45ccimZX30lc9MJIUQ9I8lcA7NiR3ET6xVdw0sNlRaiphkiI4l67VViPngfY6tWODMzSXriSY5PnET+P/+cuwIhhBB1QpK5BiQr38bvh1IBGcUq6o7ngAG0/HY5IY89itbLi8Ldu4m97nri75mB7fhxtcMTQogmT5K5BuSnPUnYnQrtw7xpE+qtdjiiCdEYDAROnUqr1T/iN2ECaLVY167lyOVXkPTMHBwZGWqHKIQQTZYkcw3IilOjWOWunFCLPiiI8Gdm0/K7b/EaNgwcDjI//ZQjF48kbdE7uAoL1Q5RCCGaHEnmGogUayGbjqQDMopVqM/Upg3Ri94m5sMPMXfsiCsvj9SXXy4eJLH0SxS7Xe0QhRCiyZBkroH48d8kXAp0i/YjJtCidjhCAODZvx/Nv/6KiAXPo48Ix5GURNJTT3Fk9GVkLf8WxaHewtNCCNFUSDLXQPzw70mgeBSrEPWJRqvF94oraPXjj4T+3/+hCwrCHhfHyZkzOXrFlWT/8INMZyKEELVIkrkGIMVayNbjxR3ML+0iyZyon7QmEwGTb6T1mp8IefghdH5+2I4dI/HBhzg2Ziw5a9ZIUieEELVAkrkG4Kc9ySinmlgj/TzUDkeIs9JaLATecgut1q0laMY9aL29KTp0iIQZ93L0yivJXrFCml+FEKIGSTLXAPx4qol1dOcwlSMRovJ0Xl4E33knrdetJXD6HWi9vLAdPkLiI48WD5T4Yikum03tMIUQosGrF8lcxqefcvjCi9jftRvHJk6iYNeuCstmfvklx6+/gQN9+3Ggbz9ib7qpTPnEx2ayr32HUtuJabfW9mXUivTcIjYfLR7FemlnaWIVDY/O15eQe++l9a+/EHzffej8/bHHx5M0axZHRlxM+gcf4srPVztMIYRosFRP5nJWrSJl3nyC7rqLFsu+wdyuHSem3YojPb3c8vlbtuJz2WiaLfmQ5l98jiEsnBO3TMOenFyqnOeQIbT543f3FvniC3VxOTVuzd5kXAp0jvSRUayiQdN5exN0x+20/uVnQv9vJvrQUBwpKaTMn8/hCy8i5dVXcaSmqh2mEEI0OKonc+kfLsFvwgT8xo/D1Lo1YU/PQms2k/XNsnLLR76wgIDrrsPcoQOmli0Jn/MMuFzkbdpUqpzGaEQfHOzedL6+dXE5NW7VqSZWuSsnGguthwcBkyfTau0awp6ZjSEmBmdWFulvvc3hCy8iceb/UXjggNphCiFEg6FqMqfYbBTu2YPnwAHufRqtFs8BAyjYsaNSdbgKClEcjjLJWv6WLRwcOIgjl1zKyVmzcGRmVlhHUVEROTk57s1qtVbrempaZp6NjUdKmlilv5xoXLRGI/4TJtDqx1VEvvoqHj16oNjtZC9fzrExY4m96SZy16+XEbBCCHEOqiZzjswscDrRBQaW2q8LCsSRllapOlJefAF9SAieAwe693kOGUzE/HnEfPABIQ89SP7Wv4m77XYUp7PcOubOnYuvr69769ixY7WvqSat3ZeM01W8FmvLYC+1wxGiVmh0OnxGjaT555/R/IvP8b70EtBqyd+0mbjb7+Do5VeQ8cmnOOvJlywhhKhvVG9mPR9p77xLzqofiXp9IVqTyb3f97LL8L7wQszt2uI9YgTRb79F4b//kr9lS7n1zJw5k+zsbPe2d+/eurqEs3KPYpW55UQT4dG9O1Evv0yrNWsImDoVracntqNHSZ4zh0PDhnPyqVkU7t+vdphCCFGvqJrM6f39QKfD+Z/BDs60dPRBQWc9Nv2990l/911iFi/G3K7dWcsao6PR+ftjiz1R7vMmkwkfHx/35u3tXaXrqA3ZBXY2HC6+Ozm6izSxiqbFGBVJ6GOP0nr9b4Q+/jjGVq1Q8vPJWrqUY2Ov4vi115G9cqVMbSKEEKiczGmMRsydOpG3abN7n+Jykbd5Mx7du1d4XPrixaS99RYx776DR5fO5zyPPSkJZ1YW+pDgmgi7Tvy8Lxm7U6FNiBetQ9RPLoVQg87Li4Abb6Dl9yuJWbKkuAlWr6dg+3YSH36Ew8OGk/LCCxQdPaZ2qEIIoRq92gEETp1C4mMzMXfujEfXLmQs+QhXQQF+464CIPHRR9GHhBLy4AMApL37LmmvLSTihRcwREa6pzLQWixoPT1x5eWR+sab+Iy8GF1QMPa4E6QseAFjTAyegwerdp1VterfJECW7xICQKPR4NmvL579+mJPSSH7m2/IXPoljqQk0he/R/ri9/Do0QO/8ePwvuRSdF6eaocshBB1RvVkzmf0aBwZmaQufA1nahqmDh2IefcddzOrPfEkaE7fQMz6/AsUu52Ee+8tVU/QXXcRfM/doNNRdOAAcd9+i9NqxRAcjOegQQTfOwOt0Vin11Zd1kI7vx8qTlKliVWI0gwhIQRNn07grbeSu349WV99Te7vv1OwfTsF27eT9Oxz+Iwahd/4cXj07o1Go1E7ZCGEqFUaRVEUtYOob+Lj44mOjiYuLo6oqKg6P/93OxK494sdtAzy5OcHh8mHkRDnYE9JIWfFCrK+WYbt2OkmV0NMDL5jx+B72WUYmzVTMUIhRF1Q+/NbLQ16NGtjtWZP8WoWl3QOk0ROiEowhIQQOG0aLVf9QLPPPsNvwtVoLRbsJ06Q9tpCjoy6hGMTJ5Hx0UeyyoQQotFRvZlVlFZod/LbgRQARnWSJlYhqkKj0WDp2QNLzx6EzpxJzpo15Hz/A3kbN1K4axeFu3aRPG8+nv374XPZ5XiPvBhdPRi9LoQQ50OSuXpm05F08mxOwnzMdIlsmEuQCVEfaC0W/MaOxW/sWBxpaeT8uJqc77+nYOdO8jZuIm/jJpKefhrPoUPwGTkSr+HD0fn4qB22EEJUmSRz9cyavcWjWC/uGIpWK02sQtQEfVAQATfeQMCNN2CLiyPnhx/IXvk9tiNHyF33M7nrfgaDAc/+/fEeeTHeF12EPiBA7bCFEKJSJJmrR5wuhbV7i/vLjewUqnI0QjROxuhogu64g8Dbb6fowAFyfvoJ65q12I4cIe+PP8j74w+SnpqFpU8fvC++GO+LR2AIlb9HIUT9JclcPbIjLpO0XBveZj39WgSe+wAhRLVpNBrM7dtjbt+ekHvvpejIEaxr15KzZg1Fe/eR/9df5P/1F8lz5mDu3Bmv4cPxGj4cc8cOaLQydkwIUX9IMlePrDl1V+7C9iEY9fJhIURdMrVqhalVK4LuuANbfDzWNWuxrllDwY4dFO7eTeHu3aS9/jr64GC8hg/Da/hwPPv3R+spExQLIdQlyVw9oSiKe0qSiztKk44QajJGRRF4800E3nwTjtRUcn//ndzffiP3z404UlPJ+uprsr76Go3BgKVfP7yGDcNz0ECMLVrIdEJCiDonyVw9cSQ1l2NpeRh1Woa1bThryArR2OmDg/EbPx6/8eNx2Wzkb9lK7vr15P76K/b4ePI2bCBvw4bisuHheA4cgOfAgXgOGCCDKIQQdUKSuXrip1N35Qa2DsTbbFA5GiFEebRGI16DB+E1eBDK/83EdvRo8R27DRso+HsbjpMnyf5mGdnfLAPA1LEDXoMG4TlwIB49e6I1mVS+AiFEYyTJXD1R0l9uZEeZKFiIhkCj0bj72QXecguuggLy/95G3saN5P35J0UHD1K0dx9Fe/eR/u5iNEYjHt27Y+nTB0ufPnh074bWbFb7MoQQjYAkc/VAck4hO+Oy0GhgRMcQtcMRQlSD1sMDryGD8RoyGABHaip5mzaR9+dGcjf+iTM1jfwtW8jfsgUAjcGAuWtXLH16Fyd4PXqgtVjUvAQhRAMlyVw9UDK3XI9oP0K85Zu6EI2BPjgY3yuvxPfKK1EUBduxY+Rv2Ur+1uLNkZJCwbZtFGzbRvrbi0Cvx6NzZzx69sSjezc8unfHECJf7oQQ5ybJXD1Q0sR6sTSxCtEoaTQaTC1bYmrZEv9rJqEoCvYTJ9yJXd7WrTgST1KwYwcFO3a4jzNERODRvTsePXrg0b075vbt0BikT60QojRJ5lSWU2hn05E0QFZ9EKKp0Gg0GJs1w9isGX5XXw2ALT6B/K1b3Qld0aFD2BMTsScmkrNqVfFxZjPmzp2wdO+OuXMXzJ07YYiMlOlQhGjiJJlT2W8HUrE7FVoFe9Iq2EvtcIQQKjFGRWKMisTvqrEAOHPzKPx3FwU7dpC/YweFO3bizM6m4O9tFPy9zX2cztcXc6dOmDt3xtypEx6dO6GPiJAET4gmRJI5lf28T5pYhRBl6bw88RwwAM8BAwBO9bs77r5zV7hnD4UHD+LMzi4eQbtx4+lj/fzcyZ25Y0fM7dpiiImRZciEaKQkmVORw+nitwOpAIzoIB2dhRAVK+531wJTyxb4jbsKAJfNRtHBQ8XLje3ZQ8Ge3RQdPIQzK6vUZMYAGg8PTG3bYG7bDlO7dpjbtcXUrh06Hx+1LkkIUUMkmVPRPyeyyC6w42cx0CPGX+1whBANjNZoxKNzcdNqCVdREUUHDxYnd7t3U7T/AEWHDqEUFFC4cxeFO3eVqkMfEe5O8EytW2Nq3QpjixYyB54QDYgkcyr6eX9xE+sF7ULQaaV/ixDi/GlNJjy6dMGjSxdKviIqTie22FiKDhyg8MABig4cpPDAfhyJJ3EkniQ38SS5v/12uhKNBkNkJMZWLTG1bFWc4LVsialVK7mTJ0Q9JMmcin7ZlwLABe2liVUIUXs0Op17ahSfSy9173fm5BTfxTtwoPgO3pEj2I4cwZmdjT0+vnjt2fW/l6pLFxxUnOC1aomxeXOMzZphiInBGBUl06YIoRJJ5lRyIj2fQym56LQahrUJVjscIUQTpPPxwdK7N5bevd37FEXBmZFRnNgdPUrRkaPYjhym6MhRHMnJxStZpKaR/9df/6lMhyEionjKlZgYjM1PJXkxzTBGRaIxGuv46oRoOiSZU8kvp5pYezfzx9ci32aFEPWDRqNBHxiIPjAQz759Sz3nzM09neAdPYIt9gS22FhsJ06gFBRgj4vDHhdH3n8r1WoxRERgiI4qbr6NjMRwxqYPDkaj09XZNQrR2Egyp5Kf9xc3sV4ko1iFEA2EzssLj65d8ejatdR+RVFwpKRiPxFbnNyVJHlnJnqnmm3LZTBgiAgvk+QZIiMxhIUVJ3vShCtEhSSZU0FukYO/jmYAcGF7WfVBCNGwaTQaDKEhGEJDsPTpU+q5UoleQgL2hATsCYmnfiZgP3kS7HbssSewx54o/wRabfHdwrAwDGGh6EP/8zMsDH1oKFppyhVNlCRzKthwKA2b00WzQAutgj3VDkcIIWrN2RI9AMXhwJGSgj0hoTjZi084neglJGBPSQG7HUdqKo7UVAr//bfCc+kCAtCHhWIIDUMfEoI+KAh9cFDxz6AgdEHB6IOD0JpMtXnJQtQ5SeZUUNJf7sL2IbLkjhCiSdPo9cX96SIiyk/2XC6cGRnYk5JxJCdhT0rCkZSMPbn0T6WoCGdGRvHgjb37znpOrbc3+uBgd5KnDw5CFxSEPujUvsAAdP7+6AICJPETDYIkc3XM5VL49dSqDxdJE6sQQpyVRqt1J12cMTnymRRFwZmVhSM5+VSyl4QjNQ1HWsmWivPUY8Vmw2W1YrNasR09eu7zWyzo/f1PJXf+6P1PJ3o6fz/0AQHo/E//W+vtLcumiTonyVwd252YTaq1CE+jjr4tAtQORwghGjyNRoPe3x+9vz/m9u0rLKcoCi6rtTjBSy1O8hypqTjdj4s3Z0YGjqwssNtR8vOx5+djT0ioXDA6HTpfX3Q+Puh8fdH6+qDz8S3e5+uD1scHna8fOl+f02V8Tj0nq26IapJk7v/bu/e4qOq8D+CfmYG5ADMgIDdBkHxAvMTFVgRL2FIxi0dqU1IzerzUbnbxVtqr3ZC1DUtbzR5bs1JK3XTNzE28hAqomOXKJRQfVLzkBQUUmOEyA8z5Pn+MnBxhUBQZBr/v12tezPmd7znz/Z2f8zpfz2062Z7rDwp+5L96Qm7H/3tjjLHOIpFITAWURgNFYGCbsUQEoabGdOq2shJN1yphrLzxfaWp6Kv87b1QWwsYjeLp3nbnp1BAptGYCkBnF8icnCC9/pKpr793dIJU7XTDPDVkTo6m92o1JHI5X75zH+JirpPtvf5Ikkf5kSSMMdZlSSQSyNRqyNRqwN//tpYRGhpMhV1VNYzVVRC0WhirtTBWV8OorTZNV1XDqNWaXtVVEKpN7yEIIIMBTeXlQHn5nSdubw+ZoyOkarWpCGx+7+Dw28vRARKV6vq0I6QqFaSO1+ddb5c4/DbNzwDs+riY60RXtHoUXqwGYPo9VsYYY92HVC6H1NMT9p7tux6aBAFCbS2M1VoI2uvFXlU1hNoa09FBnemvUHvD+5oaGGt0EGpqxWkAQGMjjFVVMFZVdVi/JEqlWOSZCr0bCkGlEhKlAlKlClKVEhKF0vRXqYJUqTD9NWtXQtr8cnaBzImf6NARukQxd239elz7YjWaKiqg6NcPXn9+u8VDKW+k3bkT5R8tR+PFi5D7+8Nj7hw4xcSI84kIFR9/jMpNmyBodVBFhMM7ORnygIBO6I1lmdePyoX6uaCnmu+QYowxZrrJQzwKiF53tA4SBAh1dRB0uuuF3g1Fn05nmldXB6qvh1Brei/U14vtQn0d6KZ2CIJp3Xo9jHo9jJWVHdhrwHXqFHi+8UaHrvNOffXjWXyafRrlNQaEeGuQ8t8DEObnYjE+/ZdSfJhRjAuV9ejj5oj5j/ez6u+sW72Y027fjrJF78NrwQKoQh/EtS+/wq/TpuOBHdth5+bWIr4uNw8X58yFx+xZcIqNRfW2bTj/yqvos/kbKIOCAABXP/8c19aug8+iVNj7+qL8o+X4ddp0BKZvs+pt5ldrG6Cyl+ExKw44Y4yx7kcilULmZLqWriMQEchgMBV2tXUQ6mpNhWBz8VdXD6G2FmTQQ6jXQzDoQfV6CPp6kN4AQa83xRsMpr96PUivh3D9RXo9pEpVh+R6t74vuIR3tx3Hu08NRLifC1bnnMHzX/yEvXNj4e7UsmY4cu4aXtuQhzfjgvFYiAe25l/Ci2v/g22vPoJgL7UVegBIiIis8snXnRmfCNXAgfB65y8ATP+7OBX7e/R47jm4vzi9RfyFWbNAdfXw+3Tlb+tITISyXwi8UxaAiHBy+HC4vfA/cJs6BQBg1OlwctjD8E59D85PPHHLnC5cuAA/Pz+cP38evr6+HdRTE32jEQ1GARol/zQNY4yx+xcRdfjNGney/x67Igehvs7469iBAEyPEItatAdJ0QF4ObZvi/gZ/8xFfYMRq1/47bmICSty0N9Hg/eeGtQxHWknq95OSQ0N0B87BsfoKLFNIpXCMSoK9fn5rS5Tn19gFg8ATsMeFuMbL1yAsbzCLEamVkP14IOozy9odZ0GgwFarVZ86XS6u+tYG5T2Mi7kGGOM3ffu5V23Op3ObL9uMBhajWtoEnD0YjWG9XUX26RSCYb1dUfuuapWl8k7V2kWDwDDg3oi91zHnoZuD6sWc02VVYDRCNlNp1Nl7m5oqqhofZmKCsjc3C3GN5Wb/rZcpzuaKlq/Qyg1NRXOzs7iq3///nfSHcYYY4x1Af379zfbr6emprYaV1nXAKNALU6n9nRSoLym9QKwvMYAdyf5TfFyVFiI7wxWv2auK3jrrbcwe/ZscfrixYtc0DHGGGM2qqioCL16/XYziaKb/yybVYs5ux4ugEwG49WrZu3Giqumn25pbRl3dxivVliMt+tp+mu8ehX2Hh43xFRAERLS6joVCoXZQGu12nb3hTHGGGNdg1qthkajuWVcDwc5ZFJJi6Nq5TUG9Gzl5gfAdNSuoqbhpviGVm+W6CxWPc0qkcuhHDAAtT8eEttIEFB76BBUYWGtLqMKCzWLB4DagwfFeHtfX8h6upvFGGtqUP/LL1CFhXZ4HxhjjDFmm+R2Ugzs5YyDp347SCQIhIOnriLC36XVZcL9e5jFA8CBk+WI8O9xL1Ntk9V/T8rthSRUbdqEqi3fwVBSgssLUiDU18Pl6acAAJfmzUPZh38X410nP4+aAwdwdfUaGE6fRvnH/4v6Y8fQY9JEAKYLKl2ffx4VK1dCt3cv9MUncGnefNh5eEA9YoRV+sgYY4yxrmnaw33w9eHz+ObIBZwq0+Ht746irqEJ4wb7AQBmb8zH+zv/T4yfMiwA2SfK8dm+0zhVVoOlGSdQeLEaSVEBVupBF7hmTjNmDJquVaL84+UwlptOhfb+bJV42rTxUikg+a3mdIgIR68li1G+7COUL10KeYA//P73Y/EZcwDgNm0aqL4epe8kQ9BqoRocAb/PVln1GXOMMcYY63riQ31wrbYBSzNOoFxnQIiPBl9OGSI+3P9iVb3ZnbeD/V3x0bPh+PCHYizeVYwAdwesmvyQ1Z4xB3SB58x1RffyOXOMMcYYuzfu1/231U+zMsYYY4yxO8fFHGOMMcaYDeNijjHGGGPMhnExxxhjjDFmw7iYY4wxxhizYVzMMcYYY4zZMKs/Z64rEgQBAFBaWmrlTBhjjDF2u5r328378fsFF3OtuHLlCgBgyJAhVs6EMcYYY+115coV9O7d29ppdBp+aHArmpqakJeXB09PT0ilHXcmWqfToX///igqKoJabb0nRd/veBy6Bh6HroHHoWvgcegYgiDgypUrCA8Ph53d/XO8iou5TqTVauHs7Izq6mpoNBprp3Pf4nHoGngcugYeh66Bx4HdDb4BgjHGGGPMhnExxxhjjDFmw7iY60QKhQLJyclQKBTWTuW+xuPQNfA4dA08Dl0DjwO7G3zNHGOMMcaYDeMjc4wxxhhjNoyLOcYYY4wxG8bFHGOMMcaYDeNijjHGGGPMhnEx18FWrFiBgIAAKJVKREZG4ueff24zftOmTejXrx+USiUGDRqE7du3d1Km3Vt7xiEtLQ0SicTspVQqOzHb7mffvn2Ij4+Hj48PJBIJvvvuu1suk5WVhYiICCgUCvTt2xdpaWn3PM/7QXvHIisrq8X3QSKR4PLly52TcDeUmpqK3/3ud1Cr1fDw8EBCQgKKi4tvuRzvH9jt4mKuA23cuBGzZ89GcnIycnNzERoairi4OJSVlbUaf/DgQUyYMAFTp05FXl4eEhISkJCQgKNHj3Zy5t1Le8cBADQaDUpLS8XXuXPnOjHj7qe2thahoaFYsWLFbcWfOXMGTzzxBH7/+98jPz8fM2fOxLRp07Br1657nGn3196xaFZcXGz2nfDw8LhHGXZ/2dnZmDFjBg4dOoSMjAw0NjZi1KhRqK2ttbgM7x9YuxDrMEOGDKEZM2aI00ajkXx8fCg1NbXV+PHjx9MTTzxh1hYZGUkvvfTSPc2zu2vvOKxZs4acnZ07Kbv7DwDasmVLmzFvvvkmDRgwwKwtMTGR4uLi7mFm95/bGYvMzEwCQJWVlZ2S0/2orKyMAFB2drbFGN4/sPbgI3MdpKGhAUeOHMGIESPENqlUihEjRuDHH39sdZkff/zRLB4A4uLiLMazW7uTcQCAmpoa+Pv7w8/PD2PHjsWxY8c6I112HX8Xup6wsDB4e3tj5MiRyMnJsXY63Up1dTUAwNXV1WIMfydYe3Ax10EqKipgNBrh6elp1u7p6WnxWpPLly+3K57d2p2MQ3BwMFavXo2tW7di3bp1EAQB0dHRuHDhQmekzGD5u6DValFfX2+lrO5P3t7eWLlyJTZv3ozNmzfDz88PsbGxyM3NtXZq3YIgCJg5cyaGDRuGgQMHWozj/QNrDztrJ8CYtUVFRSEqKkqcjo6ORkhICD799FMsXLjQipkx1vmCg4MRHBwsTkdHR6OkpARLly7F2rVrrZhZ9zBjxgwcPXoUBw4csHYqrBvhI3MdxN3dHTKZDFeuXDFrv3LlCry8vFpdxsvLq13x7NbuZBxuZm9vj/DwcJw6depepMhaYem7oNFooFKprJQVazZkyBD+PnSAV155Bdu2bUNmZiZ8fX3bjOX9A2sPLuY6iFwux+DBg7Fnzx6xTRAE7Nmzx+yoz42ioqLM4gEgIyPDYjy7tTsZh5sZjUYUFhbC29v7XqXJbsLfha4tPz+fvw93gYjwyiuvYMuWLdi7dy/69Olzy2X4O8Haxdp3YHQnGzZsIIVCQWlpaVRUVEQvvvgiubi40OXLl4mIaPLkyTR//nwxPicnh+zs7GjJkiV0/PhxSk5OJnt7eyosLLRWF7qF9o5DSkoK7dq1i0pKSujIkSP07LPPklKppGPHjlmrCzZPp9NRXl4e5eXlEQD6+9//Tnl5eXTu3DkiIpo/fz5NnjxZjD99+jQ5ODjQG2+8QcePH6cVK1aQTCajnTt3WqsL3UZ7x2Lp0qX03Xff0cmTJ6mwsJBef/11kkqltHv3bmt1web96U9/ImdnZ8rKyqLS0lLxVVdXJ8bw/oHdDS7mOtjHH39MvXv3JrlcTkOGDKFDhw6J82JiYigpKcks/l//+hcFBQWRXC6nAQMGUHp6eidn3D21Zxxmzpwpxnp6etKYMWMoNzfXCll3H82Pt7j51bzdk5KSKCYmpsUyYWFhJJfLKTAwkNasWdPpeXdH7R2L999/nx544AFSKpXk6upKsbGxtHfvXusk3020tv0BmP0b5/0DuxsSIqLOPhrIGGOMMcY6Bl8zxxhjjDFmw7iYY4wxxhizYVzMMcYYY4zZMC7mGGOMMcZsGBdzjDHGGGM2jIs5xhhjjDEbxsUcY4wxxpgN42KOMcYYY8yGcTHHWDf2xRdfYNSoUW3GnD17FhKJBPn5+Z2T1A0CAgKwbNmyTv9cdveGDh2KzZs3WzsNxhi4mGOs29Lr9fjLX/6C5ORkse2FF15AQkKCWZyfnx9KS0sxcODATs6wYyxYsABhYWHWTsOm3ck2/POf/4z58+dDEIR7kxRj7LZxMcdYN/XNN99Ao9Fg2LBhbcbJZDJ4eXnBzs6ukzJj3cHjjz8OnU6HHTt2WDsVxu57XMwx1sWVl5fDy8sL7733nth28OBByOVy7Nmzx+JyGzZsQHx8vDi9YMECfPnll9i6dSskEgkkEgmysrJanGbNysqCRCLBrl27EB4eDpVKhUcffRRlZWXYsWMHQkJCoNFoMHHiRNTV1YnrFwQBqamp6NOnD1QqFUJDQ/HNN9/csn86nQ4TJkyAo6MjevXqhRUrVpjNr6qqwrRp09CzZ09oNBo8+uijKCgoAACkpaUhJSUFBQUFYp/S0tIwd+5cPPnkk+I6li1bBolEgp07d4ptffv2xeeffy5Of/755wgJCYFSqUS/fv3wySefmOVx/vx5jB8/Hi4uLnB1dcXYsWNx9uxZcX7zUc8lS5bA29sbbm5umDFjBhobG9vs/9atWxEREQGlUonAwECkpKSgqakJADBx4kQkJiaaxTc2NsLd3R1fffUVgFtv9+bx3LNnDx566CE4ODggOjoaxcXFbW5DIsKCBQvQu3dvKBQK+Pj44LXXXhPXK5PJMGbMGGzYsKHN/jHGOgExxrq89PR0sre3p8OHD5NWq6XAwECaNWtWm8s4OzvThg0bxGmdTkfjx4+n0aNHU2lpKZWWlpLBYKAzZ84QAMrLyyMioszMTAJAQ4cOpQMHDlBubi717duXYmJiaNSoUZSbm0v79u0jNzc3WrRokbj+d999l/r160c7d+6kkpISWrNmDSkUCsrKyrKYo7+/P6nVakpNTaXi4mJavnw5yWQy+uGHH8SYESNGUHx8PB0+fJhOnDhBc+bMITc3N7p69SrV1dXRnDlzaMCAAWKf6urq6N///jc5OztTU1MTERElJCSQu7s7zZs3j4iILly4QADo5MmTRES0bt068vb2ps2bN9Pp06dp8+bN5OrqSmlpaURE1NDQQCEhITRlyhT65ZdfqKioiCZOnEjBwcFkMBiIiCgpKYk0Gg398Y9/pOPHj9P3339PDg4OtGrVKov937dvH2k0GkpLS6OSkhL64YcfKCAggBYsWEBERNu2bSOVSkU6nU5c5vvvvyeVSkVarfa2tnvzeEZGRlJWVhYdO3aMHnnkEYqOjiYisrgNN23aRBqNhrZv307nzp2jn376qUVf/vGPf5C/v7/F/jHGOgcXc4zZiJdffpmCgoJo4sSJNGjQINLr9RZjKysrCQDt27fPrD0pKYnGjh1r1mapmNu9e7cYk5qaSgCopKREbHvppZcoLi6OiIj0ej05ODjQwYMHzdY9depUmjBhgsU8/f39afTo0WZtiYmJ9PjjjxMR0f79+0mj0bTo6wMPPECffvopERElJydTaGhoi/5LpVI6fPgwCYJArq6ulJqaSpGRkURkKt569epltr5//vOfZutYuHAhRUVFERHR2rVrKTg4mARBEOcbDAZSqVS0a9cuIjJtW39/f7GAJCIaN24cJSYmWuz/Y489Ru+9955Z29q1a8nb25uIiBobG8nd3Z2++uorcf6ECRPEdd7Odm9tPNPT0wkA1dfXW9yGH374IQUFBVFDQ4PF/Ldu3UpSqZSMRqPFGMbYvccXyTBmI5YsWYKBAwdi06ZNOHLkCBQKhcXY+vp6AIBSqbzjz3vwwQfF956ennBwcEBgYKBZ288//wwAOHXqFOrq6jBy5EizdTQ0NCA8PLzNz4mKimox3XyHa0FBAWpqauDm5mYWU19fj5KSEovrdHFxQWhoKLKysiCXyyGXy/Hiiy8iOTkZNTU1yM7ORkxMDACgtrYWJSUlmDp1KqZPny6uo6mpCc7OzmIep06dglqtNvscvV5vlseAAQMgk8nEaW9vbxQWFlrMs6CgADk5Ofjb3/4mthmNRuj1etTV1cHBwQHjx4/H+vXrMXnyZNTW1mLr1q3iqc32bPcbx9Pb2xsAUFZWht69e7ea27hx47Bs2TIEBgZi9OjRGDNmDOLj482urVSpVBAEAQaDASqVymI/GWP3FhdzjNmIkpISXLp0CYIg4OzZsxg0aJDFWDc3N0gkElRWVt7x59nb24vvJRKJ2XRzW/OdjDU1NQCA9PR09OrVyyyuraLzVmpqauDt7Y2srKwW81xcXNpcNjY2FllZWVAoFIiJiYGrqytCQkJw4MABZGdnY86cOWa5f/bZZ4iMjDRbR3NhVlNTg8GDB2P9+vUtPqdnz57i+7a2kaX+paSk4Omnn24xr7kQnzRpEmJiYlBWVoaMjAyoVCqMHj3aLPfb2e43jyeANnPz8/NDcXExdu/ejYyMDLz88stYvHgxsrOzxXVdu3YNjo6OXMgxZmVczDFmAxoaGvDcc88hMTERwcHBmDZtGgoLC+Hh4dFqvFwuR//+/VFUVGT2nDm5XA6j0djh+fXv3x8KhQK//vqreMTrdh06dKjFdEhICAAgIiICly9fhp2dHQICAlpd3lKfYmJisHr1atjZ2YnFT2xsLL7++mucOHECsbGxAExHGH18fHD69GlMmjSp1c+IiIjAxo0b4eHhAY1G067+tSUiIgLFxcXo27evxZjo6Gj4+flh48aN2LFjB8aNGycWU3ez3W9kaRuqVCrEx8cjPj4eM2bMQL9+/VBYWIiIiAgAwNGjR2955JUxdu9xMceYDXj77bdRXV2N5cuXw8nJCdu3b8eUKVOwbds2i8vExcXhwIEDmDlzptgWEBCAXbt2obi4GG5ubuJpxLulVqsxd+5czJo1C4Ig4OGHH0Z1dTVycnKg0WiQlJRkcdmcnBx88MEHSEhIQEZGBjZt2oT09HQAwIgRIxAVFYWEhAR88MEHCAoKwqVLl5Ceno6nnnoKDz30EAICAnDmzBnk5+fD19cXarUaCoUCw4cPh06nw7Zt27Bo0SIApmLumWeegbe3N4KCgsQcUlJS8Nprr8HZ2RmjR4+GwWDAf/7zH1RWVmL27NmYNGkSFi9ejLFjx+Kvf/0rfH19ce7cOXz77bd488034evre0fb7Z133sGTTz6J3r1745lnnoFUKkVBQQGOHj2Kd999V4ybOHEiVq5ciRMnTiAzM7NDtvuNWtuGX3/9NYxGIyIjI+Hg4IB169ZBpVLB399fXG7//v23fCg1Y6wTWPuiPcZY2zIzM8nOzo72798vtp05c4Y0Gg198sknFpc7duwYqVQqqqqqEtvKyspo5MiR5OTkRAAoMzPT4g0QlZWV4nJr1qwhZ2dns/XffNG8IAi0bNkyCg4OJnt7e+rZsyfFxcVRdna2xRz9/f0pJSWFxo0bRw4ODuTl5UUfffSRWYxWq6VXX32VfHx8yN7envz8/GjSpEn066+/EpHpJoA//OEP5OLiQgBozZo14rKhoaHk5eUlTl+9epUkEgk9++yzLXJZv349hYWFkVwupx49etDw4cPp22+/FeeXlpbS888/T+7u7qRQKCgwMJCmT59O1dXVRNT6zSWvv/46xcTEWOw/EdHOnTspOjqaVCoVaTQaGjJkSIu7RouKiggA+fv7m92EQXTr7d7aeObl5REAOnPmjMVtuGXLFoqMjCSNRkOOjo40dOhQs5soLly4QPb29nT+/Pk2+8cYu/ckRETWKyUZY/fSuHHjEBERgbfeesvaqbBuZt68eaisrMSqVausnQpj9z1+aDBj3djixYvh5ORk7TRYN+Th4YGFCxdaOw3GGAA+MscYY4wxZsP4yBxjjDHGmA3jYo4xxhhjzIZxMccYY4wxZsO4mGOMMcYYs2FczDHGGGOM2TAu5hhjjDHGbBgXc4wxxhhjNoyLOcYYY4wxG8bFHGOMMcaYDft/kLCSNDqUsPcAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.stats import expon\n",
"\n",
"# Set the parameter λ of the exponential distribution\n",
"λ = 0.5 # mu = 2\n",
"\n",
"# Generate a sample of 1000 values from the exponential distribution\n",
"x = np.linspace(expon.ppf(0.01, scale=λ), expon.ppf(0.99, scale=λ), 1000)\n",
"\n",
"# Calculate the PDF and CDF of the exponential distribution\n",
"pdf = expon.pdf(x, scale=λ)\n",
"cdf = expon.cdf(x, scale=λ)\n",
"\n",
"# Plot the PDF and CDF of the exponential distribution\n",
"fig, ax1 = plt.subplots()\n",
"\n",
"# Plot the PDF on the left y-axis\n",
"color = 'tab:red'\n",
"ax1.set_xlabel('x (time between events)')\n",
"ax1.set_ylabel('PDF', color=color)\n",
"lns1 = ax1.plot(x, pdf, color=color, label='PDF')\n",
"ax1.tick_params(axis='y', labelcolor=color)\n",
"\n",
"# Add a second y-axis on the right side\n",
"ax2 = ax1.twinx()\n",
"\n",
"# Plot the CDF on the right y-axis\n",
"color = 'tab:blue'\n",
"ax2.set_ylabel('CDF', color=color)\n",
"lns2 = ax2.plot(x, cdf, color=color, label='CDF')\n",
"ax2.tick_params(axis='y', labelcolor=color)\n",
"\n",
"# Set the plot title\n",
"plt.title('PDF and CDF of Exponential Distribution (λ=0.5)')\n",
"\n",
"# Show the legend\n",
"leg = lns1 + lns2\n",
"labs = [l.get_label() for l in leg]\n",
"plt.legend(leg, labs, loc=0)\n",
"\n",
"# Show the plot\n",
"plt.show()\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.9"
},
"orig_nbformat": 4,
"vscode": {
"interpreter": {
"hash": "b0fa6594d8f4cbf19f97940f81e996739fb7646882a419484c72d19e05852a7e"
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment