From 56777fe0a4f05f4bda2d796b3a5d18d85731c5f3 Mon Sep 17 00:00:00 2001 From: "Jacob.Fritsche" Date: Sat, 25 Jan 2025 13:47:22 +0000 Subject: [PATCH] =?UTF-8?q?Verteilungsstatistiken=20f=C3=BCr=20das=202.=20?= =?UTF-8?q?Tutorium?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- Tutorium 2.ipynb | 482 +++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 482 insertions(+) create mode 100644 Tutorium 2.ipynb diff --git a/Tutorium 2.ipynb b/Tutorium 2.ipynb new file mode 100644 index 0000000..f88d34a --- /dev/null +++ b/Tutorium 2.ipynb @@ -0,0 +1,482 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "id": "9b437a81-b193-48ae-91bf-48edcfb12e18", + "metadata": {}, + "outputs": [], + "source": [ + "#pip install numpy matplotlib scipy" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "a4ea5fe4-eaa9-4cc4-8677-385a68577332", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import scipy.stats as stats" + ] + }, + { + "cell_type": "markdown", + "id": "df08071e-cd3c-49dd-8623-baf38082eab0", + "metadata": {}, + "source": [ + "Generate a normal distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "id": "280f78b3-4338-49ec-8929-732d429762db", + "metadata": {}, + "outputs": [], + "source": [ + "# Generate 1000 random numbers from a normal distribution\n", + "mu, sigma = 3, 6 # mean and standard deviation\n", + "data = np.random.normal(mu, sigma, 1000)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f0ec0a0-ff5f-4fb1-93ae-509cf3d3b066", + "metadata": {}, + "outputs": [], + "source": [ + "# Create a histogram of the data\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "title = \"Histogram with random numbers from: mu = %.2f, std = %.2f\" % (mu, sigma)\n", + "plt.title(title)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "0df9c2e5-ae6d-48c0-93a4-12a6e70240c2", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Show the approximation with the normal distribution\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "xmin, xmax = plt.xlim()\n", + "x = np.linspace(xmin, xmax, 100)\n", + "p = stats.norm.pdf(x, mu, sigma)\n", + "plt.plot(x, p, 'k', linewidth=2)\n", + "title = \"Fit results: mu = %.2f, std = %.2f\" % (mu, sigma)\n", + "plt.title(title)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "817835f6-baf8-4b03-8136-426c81b7b4fa", + "metadata": {}, + "outputs": [], + "source": [ + "#Show the second normal distribution\n", + "mu2, sigma2 = 1, 1\n", + "p2 = stats.norm.pdf(x, mu2, sigma2)\n", + "plt2.plot(x, p2, 'r', linewidth=2)\n", + "title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu, sigma, mu2, sigma2)\n", + "plt2.title(title)\n", + "plt2.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f3c0c504-e041-4d85-8da0-3ef766f8e87a", + "metadata": {}, + "source": [ + "Generate a second normal distribution" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "f7118230-fc88-4a71-b813-2daa0c63c97c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generate 1000 random numbers from the first normal distribution\n", + "mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n", + "data = np.random.normal(mu1, sigma1, 1000)\n", + "\n", + "# Create a histogram of the data\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "\n", + "# Add a graph of the first normal distribution used to generate the data\n", + "xmin, xmax = -1, 5\n", + "x = np.linspace(xmin, xmax, 100)\n", + "p1 = stats.norm.pdf(x, mu1, sigma1)\n", + "plt.plot(x, p1, 'k', linewidth=2)\n", + "\n", + "# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n", + "mu2, sigma2 = 1, 0.4\n", + "p2 = stats.norm.pdf(x, mu2, sigma2)\n", + "plt.plot(x, p2, 'r', linewidth=2)\n", + "\n", + "# Add vertical lines at x = 1 and x = 3 with labels\n", + "plt.axvline(x=1, color='b', linestyle='--', label='mu theoretical distribution')\n", + "plt.axvline(x=3, color='m', linestyle='--', label='mu in sample')\n", + "\n", + "title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n", + "plt.title(title)\n", + "plt.xlim(xmin, xmax)\n", + "plt.legend()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "8b4766b1-6fb5-487b-b552-790f43f83707", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generate 1000 random numbers from the first normal distribution\n", + "mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n", + "data = np.random.normal(mu1, sigma1, 1000)\n", + "\n", + "# Create a histogram of the data\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "\n", + "# Add a graph of the first normal distribution used to generate the data\n", + "xmin, xmax = -1, 5\n", + "x = np.linspace(xmin, xmax, 100)\n", + "p1 = stats.norm.pdf(x, mu1, sigma1)\n", + "plt.plot(x, p1, 'k', linewidth=2)\n", + "\n", + "# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n", + "mu2, sigma2 = 1, 0.4\n", + "p2 = stats.norm.pdf(x, mu2, sigma2)\n", + "plt.plot(x, p2, 'r', linewidth=2)\n", + "\n", + "# Add vertical lines at x = 1 and x = 3 with labels\n", + "plt.axvline(x=1, color='b', linestyle='--', label='mu theoretical distribution')\n", + "plt.axvline(x=3, color='m', linestyle='--', label='mu in sample')\n", + "\n", + "# Calculate the 95% quantile for the second normal distribution\n", + "quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n", + "\n", + "# Plot the hatched area under the red curve for the 95% quantile and above\n", + "x_fill = np.linspace(quantile_95, xmax, 100)\n", + "p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n", + "plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n", + "\n", + "title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n", + "plt.title(title)\n", + "plt.xlim(xmin, xmax)\n", + "plt.legend()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "id": "665a50fe-8404-4db3-b412-aec36d81016e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T-statistic: 98.77295966495895, P-value: 0.0\n", + "The means of the two theoretical distributions are statistically different (reject H0).\n" + ] + } + ], + "source": [ + "# Define the parameters for the two normal distributions\n", + "mu1, sigma1 = 3, 0.5 # mean and standard deviation for the first normal distribution\n", + "mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n", + "\n", + "# Perform a t-test to compare the means of the two theoretical distributions\n", + "# Since we don't have samples, we use the means and standard deviations directly\n", + "# Calculate the t-statistic and p-value manually\n", + "n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n", + "se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n", + "t_statistic = (mu1 - mu2) / se # t-statistic\n", + "df = n1 + n2 - 2 # degrees of freedom\n", + "p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n", + "\n", + "# Print the t-test result\n", + "print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n", + "\n", + "# Interpret the result\n", + "alpha = 0.05\n", + "if p_value < alpha:\n", + " print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n", + "else:\n", + " print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")" + ] + }, + { + "cell_type": "markdown", + "id": "63072dac-c7e6-4237-b5cc-b9832a2c7707", + "metadata": {}, + "source": [ + "Now with narrowed mu" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "aa9ea3d5-3559-4fd7-a2c7-f041486c090e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generate 1000 random numbers from the first normal distribution\n", + "mu1, sigma1 = 1.8, 0.5 # mean and standard deviation for the first normal distribution\n", + "data = np.random.normal(mu1, sigma1, 1000)\n", + "\n", + "# Create a histogram of the data\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "\n", + "# Add a graph of the first normal distribution used to generate the data\n", + "xmin, xmax = -1, 5\n", + "x = np.linspace(xmin, xmax, 100)\n", + "p1 = stats.norm.pdf(x, mu1, sigma1)\n", + "plt.plot(x, p1, 'k', linewidth=2)\n", + "\n", + "# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n", + "mu2, sigma2 = 1, 0.4\n", + "p2 = stats.norm.pdf(x, mu2, sigma2)\n", + "plt.plot(x, p2, 'r', linewidth=2)\n", + "\n", + "# Add vertical lines at x = 1 and x = 3 with labels\n", + "plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n", + "plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n", + "\n", + "# Calculate the 95% quantile for the second normal distribution\n", + "quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n", + "\n", + "# Plot the hatched area under the red curve for the 95% quantile and above\n", + "x_fill = np.linspace(quantile_95, xmax, 100)\n", + "p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n", + "plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n", + "\n", + "title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n", + "plt.title(title)\n", + "plt.xlim(xmin, xmax)\n", + "plt.legend()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "id": "0db5895c-28ab-4617-ad67-7ad8311d0341", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T-statistic: 39.50918386598358, P-value: 8.942863909656787e-253\n", + "The means of the two theoretical distributions are statistically different (reject H0).\n" + ] + } + ], + "source": [ + "# Define the parameters for the two normal distributions\n", + "mu1, sigma1 = 1.8, 0.5 # mean and standard deviation for the first normal distribution\n", + "mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n", + "\n", + "# Perform a t-test to compare the means of the two theoretical distributions\n", + "# Since we don't have samples, we use the means and standard deviations directly\n", + "# Calculate the t-statistic and p-value manually\n", + "n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n", + "se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n", + "t_statistic = (mu1 - mu2) / se # t-statistic\n", + "df = n1 + n2 - 2 # degrees of freedom\n", + "p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n", + "\n", + "# Print the t-test result\n", + "print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n", + "\n", + "# Interpret the result\n", + "alpha = 0.05\n", + "if p_value < alpha:\n", + " print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n", + "else:\n", + " print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "id": "ab987426-9a37-4c22-b561-d2870b856071", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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wYcP47LPPmDx5svoNuCKv7YIFCyo0Q+v+++9X38NQ8H76v//7P4tm9J49e7J48WIuX75Ms2bNyn3/xYmPj+fhhx8mPDycV155pcz9O3XqVO73mb+/f5ViK0t5X4uy/j6Kez+WxcPDA4A1a9bQqVOnCrXcxsbGcujQIV577TWL1/v2228nIiKi1Pe+wWDgkUce4caNG3z55ZflOl95X6927dqVur2s5zElJaXU43NycnjhhRd4+umniYiIqPR5TPvUu6SlR48exTYfVZfivrWfPXuWI0eOlJi5xsfHA8Y+vl9//ZVhw4YRFBTE4MGDGT16dI0nMOHh4UyZMoXPPvuMRYsW0a9fP+6++27+7//+z+LNUVHm/YpQkBwFBwcXu748H0TVzcHBodZnPpTE0dHRYmyDSVZWlrq9MNO312HDhnHPPffQvn17XFxcmDRpUoXObW9vz4cffsiLL76In58fvXr14s4772TMmDHl+hC5ePGi+mFprnXr1hWKozy6du1aLfdjej4r+pyXRqPR8MILL7Bhwwa2bNmiflOuzGtbXrX9PktPT+fOO+8kNTWVHTt2lNoFZ+Lp6Vnv3mdl/X1U5jXr378/I0eO5J133uHzzz9nwIABjBgxgocffrjMD9OLFy8CFNt62bp161Knz0+ePJnff/+d//73v+X+8lVdr1dVn8fPP/+chISEMmc8Vef7uU4lLTWtuCfFYDBw++23l/iNxNTy4+vry6FDh9iwYQPr169n/fr1/PDDD4wZM4aFCxcClDjIU6/XVynuTz/9lMcee4zffvuNP/74g2effZaZM2eye/fucveXFlZSF1dJ68276Up7nNXZdabX68s9h9/Ly6v8U+YqISAggM2bN6MoisXjNzV7ltVy0Lx5c7p06cKiRYsqnLSAsc/4rrvuYuXKlWzYsIG33nqLmTNn8tdff9GlS5cK319NSUxMJCcnp8z9HB0dS026Tc3IxU1Nj42NxcvLq1LdKKZkwXysVEBAQInngbJf29JU5X1WkpL+n+Tk5HDfffdx5MgRNmzYQPv27csVY05OTrnHjvn4+FR797i5gIAALl++XGR94deirL+PyrxmGo2GZcuWsXv3blavXs2GDRv417/+xaeffsru3bvLlQBW1DvvvMPcuXOZNWsWjz76aLmPM41/KYu7u3upyYD581g4kY6NjbVonS0sOTmZGTNm8Mwzz5CSkqK2yqSlpaEoClFRUTg5OeHr61ut7+d6MXuoONU1I6V58+akpaUxaNCgYn/MvynZ2dlx1113MXfuXM6fP8/48eP573//y7lz5wDUZvvCM0RMWXhVHk+HDh1488032bZtG9u3b+fy5cvMmzevgo+2enh6ehY7C6Y8j7MiYmJiCAgIKNfPzp07q/XchXXu3JmMjIwiszH++ecfdXtZMjMzyz3gsTjNmzfnxRdf5I8//uDYsWPk5OTw6aefqttL+hsKDQ3l7NmzRdafPn260rGU5L777ivX61XW4PWgoCB8fHyKLZC2Z8+eStcyMs3MMG9Z7dy5MwcOHCgym+qff/7BycmpRrusS1Pc+ywnJ6fYf/wGg4ExY8awadMmfv75Z/r371/u8+zcubPc7zPT7J2a0rlzZ86cOVOkW6Lw+6x9+/bY2NgU+fvIycnh0KFDVap11atXL95//3327dvHokWLOH78OL/88gtQ+nsMqND7zFRn7Pnnn+fVV1+tUIzlfb3KKlhnep4KP49Xrlzh0qVLpT6PSUlJpKWlqQU3TT//+9//yMjIIDw8XJ0FVp3v53rb0mIqYHPjxg21L7IyRo8ezfTp09mwYUOR8S43btzAxcUFGxsbrl+/TpMmTdRtWq1WHTVuavJq3rw5ANu2bePuu+8GjM21ppaY8j4ecykpKTg5OVn0f3fo0AGtVmvR1JaQkEBCQgIhISEljnupLs2bN2f79u3k5OSorRtr1qwhJiamyv3x5qw1piU5OVkdEGhqDbjnnnt44YUXmDt3Ll999RVg/FY8b948goKC6NOnDwB5eXmkpqYWGXeyZ88ejh49ysMPP1zheDIyMtBqtWrfLxhfA1dXV4u/AWdn52KTyeHDhzN79mz27NmjfnMyDfysbtU1pgWM46sWLlxITEyM+i1w06ZNnDlzhhdeeEHdLzc3l/Pnz+Pu7q5+o0tMTMTd3d2iVSA3N5dZs2ZhZ2dnMfB01KhRLFu2jOXLl6uD3RMSEli6dCl33XVXtQyMrYzmzZuzbds2i3XffPNNsS0tkydPZsmSJcyfP99i6nZ5WGtMS3H/s0aNGsUnn3zCN998ow46z87O5ocffqBnz57q34G7uzuDBg3ip59+4q233lLH4f3444+kpaVx//33VziepKQkPDw8LBIT04ep6X1mirPw+ywgIIDOnTuzcOFCi3EtGzdu5MSJE0UG4i5ZsoRnn32WRx55hM8++6zCsVbXmJZ27drRpk0bvvnmG8aPH6++X77++ms0Go3F5I/C/xd9fX2LndL9xRdfsGvXLhYvXmwx8La87+ey1NukxdR3/uyzzzJkyBB0Op1FVdLyevnll1m1ahV33nknjz32GF27diU9PZ2jR4+ybNkyoqKi8Pb25oknniAxMZHbbruNpk2bcvHiRb788ks6d+6sToMdPHgwISEhPP7447z88svodDq+//57fHx8iI6OLjWO5s2b4+Hhwbx583B1dcXZ2ZmePXty+PBhJk2axP3330+rVq3Iy8vjxx9/RKfTMXLkSPX4ik55roonnniCZcuWMXToUEaPHs358+f56aef1KTN3OrVq9VR5bm5uRw5ckQdjX/33XeriV9xqntMS3ljWbFiBePGjbMYed+0aVOef/55Pv74Y3Jzc+nevTsrV65k+/btLFq0SH2zp6WlERwczAMPPEC7du1wdnbm6NGj/PDDD7i7u/PWW29ZxDRgwAC2bt1aarfAmTNnGDhwIKNHjyYiIgIbGxtWrFjB1atXLf7mu3btytdff82MGTNo0aIFvr6+3Hbbbbzyyiv8+OOPDB06lOeee06d8hwaGsqRI0csznXx4kW1jIDpW5HpOQoNDS2zCbu6xrQAvP766yxdupRbb72V5557jrS0ND7++GM6dOjAuHHj1P0uX75M27ZtLWYkrVq1ihkzZjBq1CjCw8NJTEzk559/5tixY3zwwQcWH76jRo2iV69ejBs3jhMnTqgVcfV6fZG++scee6xCU56r4oknnuDpp59m5MiR3H777Rw+fJgNGzYUmRI7e/Zs5s6dS+/evXFycuKnn36y2H7vvfeWWKUUqn9My48//sjFixfVmlHbtm1T/4YeffRR9QO8uP9ZPXv25P7772fq1KnEx8fTokULFi5cSFRUFP/5z38szvP+++/Tp08f+vfvz1NPPcWlS5f49NNPGTx4cJGxhhqNhv79+5dafn/hwoXMnTuXe++9l+bNm5Oamsq3336Lm5sbw4cPB4zdmhERESxZsoRWrVrh5eVF+/btad++PTNnzuSOO+6gb9++/Otf/yIxMZEvv/ySdu3aWVxaYM+ePYwZM4YmTZowcODAIl8e+vTpU+aXv+p8vT7++GPuvvtuBg8ezIMPPsixY8f46quveOKJJyxKPBT+v+jk5MSIESOK3N/KlSvZs2dPkW3lfT+Xqdxl6GpQWRVxIyMji1SLzcvLUyZPnqz4+PgoGo2mzMqdpVXHTE1NVaZOnaq0aNFCsbOzU7y9vZU+ffoon3zyiZKTk6MoiqIsW7ZMGTx4sOLr66vY2dkpISEhyvjx45XY2FiL+9q/f7/Ss2dPdZ/PPvus2MqjhSviKoqi/Pbbb0pERIRiY2OjPt4LFy4o//rXv5TmzZsrDg4OipeXl3Lrrbcqf/75p8Wx06ZNUwBl8+bNpT4PiqIogEVlV0UpeI7NK1EqiqJs3ry5SLVQRVGUTz/9VAkKClLs7e2Vm2++Wdm3b1+xj2ns2LEKUOxPbVf/LW8sptercHx6vV754IMPlNDQUMXOzk5p166d8tNPP1nsk52drTz33HNKx44dFTc3N8XW1lYJDQ1VHn/8cYvX36Rr166Kv79/qXEnJCQoEydOVNq0aaM4Ozsr7u7uSs+ePZVff/3VYr+4uDjljjvuUFxdXRXA4rU4cuSI0r9/f8XBwUEJCgpS3nvvPeU///lPkb9L0+td3E9Fqu1Wl2PHjimDBw9WnJycFA8PD+WRRx5R4uLiLPYx/e2aVzjet2+fctdddylBQUGKnZ2d4uLiovTt27fIc2aSmJioPP7440qTJk0UJycnpX///sX+Pxo5cqTi6OioJCUllRp3Rd9Pxf0P1Ov1yquvvqp4e3srTk5OypAhQ5Rz584poaGhFo+1tL/rwq9vbejfv3+JsZj/fyrpf1ZmZqby0ksvKf7+/oq9vb3SvXt35ffffy/2XNu3b1f69OmjODg4KD4+PsrEiROVlJQUi31SU1MVQHnwwQdLjfvAgQPKQw89pISEhCj29vaKr6+vcueddyr79u2z2G/nzp1K165dFTs7uyLVcf/3v/8pbdu2Vezt7ZWIiAhl+fLlRSriml7ruvJ/UVEUZcWKFUrnzp0Ve3t7pWnTpsqbb76pfvYVjrus+MaOHVtsRVxFKd/7uSwaRSnHyC8hRLVLTU3Fy8uL2bNnq0X+RN3m5+fHmDFj+Pjjj60diiindevWceedd3L48OFK19sRdUe9HYgrRH23bds2goKCePLJJ60diiiH48ePk5mZWeFBk8K6Nm/ezIMPPigJSwMhLS1CCCGEqBekpUUIIYQQ9YIkLUIIIYSoFyRpEUIIIUS9IEmLEEIIIeqFelFczmAwcOXKFVxdXautfL8QQgghapaiKKSmphIYGIhWW/V2knqRtFy5cqXIxZyEEEIIUT/ExMRU+gK/5upF0mK6rkRMTAxubm5WjkY0dunpYLp0Tsw5PYdbGC/W2OdKH3TONXcFXCGEqG9SUlIIDg5WP8erql4kLaYuITc3N0lahNWZXYMPN1c9zhiv6+Lm5iZJixBCFKO6hnbIQFwhhBBC1Av1oqVFiLrExgbGjjUu2zpo8BvrB4DGRgaJCyFETaoXZfxTUlJwd3cnOTlZuoeEEEKIeqK6P7+lpUUIUacpikJeXh56vd7aoQghCtHpdNjY2NRaORJJWoSoIEWBjAzjsqOjgpJpAEDrpJU6QtUsJyeH2NhYMkxPuBCiznFyciIgIAA7O7saP5ckLUJUUEYGuLgYl5OvGjjgtx2Afmn9ZPZQNTIYDERGRqLT6QgMDMTOzk6SQiHqEEVRyMnJ4dq1a0RGRtKyZctqKSBXGklahBB1Uk5ODgaDgeDgYJycnKwdjhCiGI6Ojtja2nLx4kVycnJwcHCo0fPJlGchRJ1W09/chBBVU5vvUflvIIQQQoh6QZIWIYQQQtQLFU5atm3bxl133UVgYCAajYaVK1eWecyWLVu46aabsLe3p0WLFixYsKASoQohhCjLY489xogRI6wdRoUsWLAADw+Paru/LVu2oNFouHHjRoWOM/9Mi4qKQqPRcOjQoWqLyyQsLIzZs2cXe96aPld9V+GkJT09nU6dOjFnzpxy7R8ZGckdd9zBrbfeyqFDh3j++ed54okn2LBhQ4WDFUIIYVSTH6o1qbgP0QceeIAzZ85YJ6ASBAcHExsbS/v27cvct6Kvxd69e3nqqaeqGKGlkhK/mjiXNVV49tCwYcMYNmxYufefN28e4eHhfPrppwC0bduWHTt28PnnnzNkyJBij8nOziY7O1u9nZKSUtEwhagxOh2MGmkABWzswGeUT/4G68YlhDXl5ORUuk6Ho6Mjjo6O1RxR1eh0Ovz9/av1Pk3PkY+PT7Xeb2lq81y1ocbHtOzatYtBgwZZrBsyZAi7du0q8ZiZM2fi7u6u/gQHB9d0mEKUm8P2jSzd2ZSlm71xWv8r7Za2o93SdugcJGupDenpJf9kZZV/38zM8u1bUQMGDGDy5Mk8//zzeHp64ufnx7fffkt6ejrjxo3D1dWVFi1asH79evWY4r4lr1y5stS6NOHh4QB06dIFjUbDgAEDLLZ/8sknBAQE0KRJEyZOnEhubq66LTs7m5deeomgoCCcnZ3p2bMnW7ZssTj+f//7H+3atcPe3p6wsDD1i6dJWFgY7733HmPGjMHNzU39Nr9jxw769euHo6MjwcHBPPvss6TnP5EDBgzg4sWLvPDCC2g0GvXxFff4V69eTffu3XFwcMDb25t7771X3fbjjz/SrVs3XF1d8ff35+GHHyY+Pr7E56o4Z8+e5ZZbbsHBwYGIiAg2btxosb1w60lSUhKPPPIIPj4+ODo60rJlS3744Qeg5NfC1FX3/vvvExgYSOvWrdXnrnBrU2xsLMOGDcPR0ZFmzZqxbNkydVtx3V2HDh1Co9EQFRXFli1bGDduHMnJyerzOn369GLPFR0dzT333IOLiwtubm6MHj2aq1evqtunT59O586d+fHHHwkLC8Pd3Z0HH3yQ1NTUCj2/NaXGk5a4uDj8/Pws1vn5+ZGSkkJm4f8a+aZOnUpycrL6ExMTU9NhClE2RYGPP4ahQyE2FpKS4OGH4eWXIS/P2tE1Gi4uJf+MHGm5r69vyfsWbjAOCyt+v8pYuHAh3t7e7Nmzh8mTJzNhwgTuv/9++vTpw4EDBxg8eDCPPvpolSr97tmzB4A///yT2NhYli9frm7bvHkz58+fZ/PmzSxcuJAFCxZYjCWcNGkSu3bt4pdffuHIkSPcf//9DB06lLNnzwKwf/9+Ro8ezYMPPsjRo0eZPn06b731VpHxiJ988gmdOnXi4MGDvPXWW5w/f56hQ4cycuRIjhw5wpIlS9ixYweTJk0CYPny5TRt2pR3332X2NhYYmNji31sa9eu5d5772X48OEcPHiQTZs20aNHD3V7bm4u7733HocPH2blypVERUXx2GOPlfu5MxgM3HfffdjZ2fHPP/8wb948Xn311VKPeeuttzhx4gTr16/n5MmTfP3113h7ewOlvxabNm3i9OnTbNy4kTVr1pR6/yNHjuTw4cM88sgjPPjgg5w8ebJcj6dPnz7Mnj0bNzc39Xl96aWXin3c99xzD4mJiWzdupWNGzdy4cIFHnjgAYv9zp8/z8qVK1mzZg1r1qxh69atzJo1q1yx1DilCgBlxYoVpe7TsmVL5YMPPrBYt3btWgVQMjIyynWe5ORkBVCSk5MrG6oQVZOWpigPPqgoxtSl6M+gQYqSkGDtKBuUzMxM5cSJE0pmZqbF+pJeAlCU4cMt78PJqeR9+/e33Nfbu/j9Kqp///5K37591dt5eXmKs7Oz8uijj6rrYmNjFUDZtWuXoiiK8sMPPyju7u4W97NixQqltH/RkZGRCqAcPHjQYv3YsWOV0NBQJS8vT113//33Kw888ICiKIpy8eJFRafTKZcvX7Y4buDAgcrUqVMVRVGUhx9+WLn99tsttr/88stKRESEejs0NFQZMWKExT6PP/648tRTT1ms2759u6LVatXXMTQ0VPn8888t9in8+Hv37q088sgjJT72wvbu3asASmpqqqIoirJ582YFUJKSkordf8OGDYqNjY3Fc7B+/XqLz7TCz+9dd92ljBs3rtj7K+218PPzU7Kzsy3WF34OAOXpp5+22Kdnz57KhAkTSnw8Bw8eVAAlMjJSUZTi/4YKn+uPP/5QdDqdEh0drW4/fvy4Aih79uxRFEVRpk2bpjg5OSkpKSnqPi+//LLSs2fPYh+7opT8XlWU6v/8rvGKuP7+/hZNTwBXr17Fzc2tzvVhClGsyEgYMQKOHAEgHSdcMDZ3J2t9OWD4Ff6Efl1vRvfbEujUyYrBNnxpaSVv0xXqoSutx6BwPayoqEqHVETHjh3NYtLRpEkTOnTooK4ztT5XtEujvNq1a4fO7MkICAjg6NGjABw9ehS9Xk+rVq0sjsnOzqZJkyYAnDx5knvuucdi+80338zs2bPR6/XqfXfr1s1in8OHD3PkyBEWLVqkrlMURb0kQ9u2bcsV/6FDh3jyySdL3L5//36mT5/O4cOHSUpKwmAwXv8rOjqaiIiIMu//5MmTBAcHExgYqK7r3bt3qcdMmDCBkSNHqi1lI0aMoE+fPmWeq0OHDuUa61P4/L179672Qdamx20+5CIiIgIPDw9OnjxJ9+7dAWOXkqurq7pPQEBAjf2tVlSNJy29e/dm3bp1Fus2btxY5h+IEHXCpUvQowckJBhvu7jAtz/DQ/nbl/8PRuRfffjiRejTB3btArMPLVG9nJ2tv29ZbG1tLW5rNBqLdaaxHKYPW61Wi6IoFseYj0GpjvObzpWWloZOp2P//v0WiQ2ASwX7w5wLPWlpaWmMHz+eZ599tsi+ISEh5b7f0r7QpqenM2TIEIYMGcKiRYvw8fEhOjqaIUOGkJOTU/7gK2jYsGFcvHiRdevWsXHjRgYOHMjEiRP55JNPSj2u8HNUGaaKs+Z/I1X5+yhLaX8/1lbhMS1paWkcOnRIzQAjIyM5dOgQ0dHRgHE8ypgxY9T9n376aS5cuMArr7zCqVOnmDt3Lr/++isvvPBC9TwCIWrSp58WJCwtW8I//8BddxVs713om1ZGBsyYUXvxiQbBx8eH1NRUdcAqUOa3bNO3d71eX6FzdenSBb1eT3x8PC1atLD4Mc2Wadu2LX///bfFcX///TetWrUqkuiYu+mmmzhx4kSR+23RooUar52dXZkxd+zYkU2bNhW77dSpU1y/fp1Zs2bRr18/2rRpU+FWgLZt2xITE2Mxpmb37t1lHufj48PYsWP56aefmD17Nt988w1Q+dfCXOHz7969W22ZMs0AMo+38N9HeZ5X0+M2Hyd64sQJbty4Ua4WqrqgwknLvn376NKlC126dAFgypQpdOnShbfffhswPqmmBAaMo6rXrl3Lxo0b6dSpE59++infffddidOdhagz0tIgf3YA9vawfTuU9sb29TX+Xr7c2EIjRDn17NkTJycnXn/9dc6fP8/PP/9cZhFOX19fHB0d+f3337l69SrJycnlOlerVq145JFHGDNmDMuXLycyMpI9e/Ywc+ZM1q5dC8CLL77Ipk2beO+99zhz5gwLFy7kq6++KnZwp7lXX32VnTt3MmnSJA4dOsTZs2f57bff1IG4YOx62LZtG5cvXybB9IWgkGnTprF48WKmTZvGyZMnOXr0KB9++CFgbLGxs7Pjyy+/5MKFC6xatYr33nuvXI/dZNCgQbRq1YqxY8dy+PBhtm/fzhtvvFHqMW+//Ta//fYb586d4/jx46xZs0ZNKir7WphbunQp33//PWfOnGHatGns2bNHfd5atGhBcHAw06dP5+zZs6xdu7bY2VxpaWls2rSJhISEYgd5Dxo0iA4dOvDII49w4MAB9uzZw5gxY+jfv3+Rrr66qsJJy4ABA1AUpciP6Q22YMGCIlPnBgwYwMGDB8nOzub8+fMVGuUthNX89BOY/vk8/DAUmgVXxLhxxt96PcyfX7OxiQbFy8uLn376iXXr1tGhQwcWL16sTlktiY2NDV988QXz588nMDCwyBiU0vzwww+MGTOGF198kdatWzNixAj27t2rduHcdNNN/Prrr/zyyy+0b9+et99+m3fffbfM/90dO3Zk69atnDlzhn79+qlfaM3Hjrz77rtERUXRvHnzEmuIDBgwgKVLl7Jq1So6d+7Mbbfdps7Q8fHxYcGCBSxdupSIiAhmzZpVZhdNYVqtlhUrVpCZmUmPHj144okneP/990s9xs7OjqlTp9KxY0duueUWdDodv/zyC1C118LknXfe4ZdffqFjx47897//ZfHixWrrh62tLYsXL+bUqVN07NiRDz/8kBmFWnT79OnD008/zQMPPICPjw8fffRRkXNoNBp+++03PD09ueWWWxg0aBDNmjVjyZIlFY7XWjRK4Y7UOiglJQV3d3eSk5Nxc3OzdjiiMVAU6NABjh833j5wAPJbF9PTC6bCJl/Vc8BvOwD9zrZA1zbcOP3Z1xeio40tNKJSsrKyiIyMJDw8vMYvdy+EqLzS3qvV/fktF0wUojibNxckLDffrCYspQoIKCgUEh8Pv/5ac/EJIUQjJEmLEMX58suC5cmTLTbpdDB8uPHHxg68hnvhNdzLWMbfrO/e4j6EEEJUWY1PeRai3rl4EVatMi4HBsJ991lsdnCA/PGKgI6Oa82mN998M3TuDIcOwd69xtlGPXvWQtBCCNHwSUuLEIV9/TWYahI8/TQUqllQKo3GsmVGWluEEKLaSNIihLnMTPj2W+OyrS2UUpWzRA89BPmVRfn1V4iLq774hBCiEZOkRQhzixdDYqJxefRoKObS9Onpxuqpzs6QEq9nm/M2tjlvQ5+eX9jJ0RGeeMK4nJsL+QWohBBCVI0kLUKYKEqpA3DNZWQYfwAMGQYMGYVKXE+YUHBxm3nzoAbLiwshRGMhSYsQJv/8YxxAC9C9e9UG0IaGwt13G5djY+G336ocnhBCNHaStAhhsmZNwfLTT1f9/iZMKFgumG4khBCikiRpEcJk48aC5eHDq35//fsbx7eY7rvuF58W9UhUVBQajabMCyvWVxqNhpUrV1o7DFHHSNIiBEBSEuzbZ1xu377YAbgVZm8Pt9xiXL5yBU6dqvp9CpEvODiY2NhY2rdvb+1QhKg1krQIAcay/abaLLffXn33a35f5i05QlSRTqfD398fGxupESoaD0lahAD488+C5UGDSt1VqzX2/PTvDzobcO/vjnt/9+LfTeb3ZX4OUWn6dH3JP1n68u+bWb59K2rAgAFMnjyZ559/Hk9PT/z8/Pj2229JT09n3LhxuLq60qJFC9avX68es2DBAjw8PCzuZ+XKlWg0mhLPU7h7aMuWLWg0GjZt2kS3bt1wcnKiT58+nD59usT7yMnJYdKkSQQEBODg4EBoaCgzZ85Ut3/22Wd06NABZ2dngoODeeaZZ0hLSysS95o1a2jdujVOTk6MGjWKjIwMFi5cSFhYGJ6enjz77LPo9QXPZVhYGO+99x4PPfQQzs7OBAUFMWfOnFKf15iYGEaPHo2HhwdeXl7cc889REVFlXqMaHgkRRcCClpBbG0LunRK4OgIW7aYbunosqWUiyl26GC84nN8vPGg3NyKVdgVRWx32V7iNq/hXhaXVfjb9++i09Hzufd3t3jtdoftJjcht8h+A5QBFY5x4cKFvPLKK+zZs4clS5YwYcIEVqxYwb333svrr7/O559/zqOPPkp0dDROTk4Vvv/SvPHGG3z66af4+Pjw9NNP869//Yu///672H2/+OILVq1axa+//kpISAgxMTHExMSo27VaLV988QXh4eFcuHCBZ555hldeeYW5c+eq+2RkZPDFF1/wyy+/kJqayn333ce9996Lh4cH69at48KFC4wcOZKbb76ZBx54QD3u448/5vXXX+edd95hw4YNPPfcc7Rq1Yrbi2npzM3NZciQIfTu3Zvt27djY2PDjBkzGDp0KEeOHMHOzq4an0FRl0nSIkRUFJw7Z1zu3RtcXKrvvrVaGDjQWLQuNRX27DFen0g0aJ06deLNN98EYOrUqcyaNQtvb2+ezK+w/Pbbb/P1119z5MgRevXqVa3nfv/99+nfvz8Ar732GnfccQdZWVk4ODgU2Tc6OpqWLVvSt29fNBoNoaGhFtuff/55dTksLIwZM2bw9NNPWyQtubm5fP311zRv3hyAUaNG8eOPP3L16lVcXFyIiIjg1ltvZfPmzRZJy80338xrr70GQKtWrfj777/5/PPPi01alixZgsFg4LvvvlNbn3744Qc8PDzYsmULgwcPruSzJeobSVqE2LSpYLmMrqFKGTTImLSAsYtIkpYq6ZfWr+SNOsubN8eX8lwX6s7rFVV9yUPHjgWtPTqdjiZNmtChQwd1nZ+fHwDx8fHVds7izh0QEKCeJyQkpMi+jz32GLfffjutW7dm6NCh3HnnnRYJwJ9//snMmTM5deoUKSkp5OXlkZWVRUZGhtpC5OTkpCYspscWFhaGi1ny7+fnV+Sx9u7du8jt2bNnF/uYDh8+zLlz53B1dbVYn5WVxfnz50t7OkQDI0mLEOYDZMuRtKSnQ1iYcfn8cT1H2+0GjB96Omdd0QMKj2uZNq0KwYpin+Na3rcstoW6ADUajcU6U2uBIX/wt1arRSk0JT43t2hXVUXPXfg8hd10001ERkayfv16/vzzT0aPHs2gQYNYtmwZUVFR3HnnnUyYMIH3338fLy8vduzYweOPP05OTo6atJT1WE3rSoqhPNLS0ujatSuLFi0qss3Hx6fS9yvqH0laRONmMBS0tLi5GSvhlkNCQsFyceMgLISEQKtWcOYM7N5t7CYq9I1RNG4+Pj6kpqaSnp6Os7MzQK3VX3Fzc+OBBx7ggQceYNSoUQwdOpTExET279+PwWDg008/RZt/SYpff/212s67e/fuIrfbtm1b7L433XQTS5YswdfXFzc3t2qLQdQ/MntING6HDxdkILfeCjU1fdTUT5+XB1u31sw5RL3Vs2dPnJyceP311zl//jw///wzCxYsqPHzfvbZZyxevJhTp05x5swZli5dir+/Px4eHrRo0YLc3Fy+/PJLLly4wI8//si8efOq7dx///03H330EWfOnGHOnDksXbqU5557rth9H3nkEby9vbnnnnvYvn07kZGRbNmyhWeffZZLly5VW0yi7pOkRTRu5tOQq7M+S2HmXURSr0UU4uXlxU8//cS6devo0KEDixcvZvr06TV+XldXVz766CO6detG9+7diYqKYt26dWi1Wjp16sRnn33Ghx9+SPv27Vm0aJHFdOiqevHFF9m3bx9dunRhxowZfPbZZwwZMqTYfZ2cnNi2bRshISHcd999tG3blscff5ysrCxpeWlkNErhjtQ6KCUlBXd3d5KTk+UPVFSvwYMLkohTp6B16zIPSU8vmGCUfFXPAT/jFNx+af1KHheRnAxeXsbuqIgIOH68OqJv0LKysoiMjCQ8PLzYmS+i/goLC+P555+3mJ0k6q/S3qvV/fktLS2i8crKgu35NT+aNjWOO6kp7u7Qo4dx+cQJY1l/IYQQFSJJi2i8du40Ji5g7BoqpfpotZDquEIIUSUye0g0XhWc6myi1UK3bsZlnQ24dsufCVTWV4Dbb4cZM4zLf/4JY8aUP1YhGhApvy8qS5IW0XiZt3YMHFjuwxwdYe9e0y0dXfd2Ld+BvXqBs7NxUMyff4Ki1HzrjhBCNCDSPSQap+vXYf9+43LHjpBfobRG2dkZr7IIEBtrHNsiylQP5goI0ajV5ntUWlpE47R1q7GlA8rdNTR+9fgy95l/1/zSdxg0CNatMy5v2gTt2pXr3I2RqapqRkYGjo6OVo5GCFGSjIwMoGh15JogSYtonP75p2C5jKs6F5aXbcuvE6cD8NBn73H3FGN9l3Vz1pV9sKmlBYwXTxQl0ul0eHh4qNescXJyUsvSCyGsT1EUMjIyiI+Px8PDA52u+i6FURJJWkTjtG9fwXI5S/ebKIqGtHhv4w2DBpf4/KIt5Wkhbd/e2E2Uk2MZgyiWv78/UDMXFhRCVA8PDw/1vVrTJGkRjY/BUDCeJTDQ+FNb7Oygc2djK8vp05CSYrzmkSiWRqMhICAAX1/fSl9AUAhRc2xtbWulhcVEkhbR+Jw7Z6xQCwVzl2tTt24FXUP79xuveSRKpdPpavUfoxCibpLZQ6LxMe+WsVbSUlwsQgghSiVJi2h8qjCepVqYn1OSFiGEKDdJWkTjU1AZDrqWszBcdWrTBpycisYihBCiVJK0iMZFr4cDB4zLoaHg41Phu9BoFDyDr+AZfAW0CsnBySQHJ0N5Z+Pa2ECXLsblyEhjoTshhBBlkoG4onE5dQryCyFVtmvIxj6X++e8o94uV32Wwrp1g7//Ni7v3w+DB1cqFiGEaEykpUU0LubdMdYYhGtinjBJF5EQQpSLJC2icbH2zKHizi2DcYUQolwkaRGNi3mCUMlBuHnZtiydOI2lE6ehpDgwfOJwhk8cji67AnVEWrYsKConSYsQQpSLJC2i8cjJgUOHjMstW4KHR6XuRlE0JMUEkhQTCAYN7jHuuMe4l6+Mv4lWW5A0XboEcXGVikUIIRoTSVpE43H8OGRnG5etUZ+lMOkiEkKICpGkRTQedWU8S3ExSNIihBBlkqRFNB51ZeaQicwgEkKICpGkRTQeptYMrbaguJs1hYWBl5dxed8+UCoyKEYIIRofSVpE45CVBUePGpfbtgUXF+vGA6DRFLT4xMcbB+QKIYQokSQtonE4fBjy8ozLVewa0mgUXHwTcPFNAK1Cmm8aab5p5S/jb066iIQQotykjL9oHKrxys429rk8/N0b6u3V362u/J0VHox7331ViEwIIRo2aWkRjUNdmzlkIjOIhBCi3CRpEY2DqevFxgY6dbJuLOaCgsDf37gsg3GFEKJUkrSIhi8tDU6eNC536AAODlW6u7xsW1ZMmcqKKVNRUuwZPGUwg6cMrlgZfxPzwbhJSXDhQpViE0KIhkySFtHwHToEBoNxuRq6hhRFw7VzYVw7FwYGLU3ONaHJuSYVK+NvTrqIhBCiXCRpEQ3fgQMFy5W8SGKNMk9azGMVQghhQZIW0fAdO1awXJfGs5h07FiwbB6rEEIIC5K0iIbPVFQOoF0768VRkqZNwd3duGweqxBCCAuStIiGTVEKWi/CwsDV1arhFEujgfbtjcsxMZCcbN14hBCijpKkRTRsFy8aZw9BQWJQF5nHJl1EQghRLElaRMNmngB06FBtd+vgloqDWyoAWW5ZZLllVe0OzWOTLiIhhCiWlPEXDZt5AlBNSYutQw5jfnpJvb3ipxVVv1Pz2KSlRQghilWplpY5c+YQFhaGg4MDPXv2ZM+ePaXuP3v2bFq3bo2joyPBwcG88MILZGVV8ZupEOVhnrTUl+4haWkRQohiVThpWbJkCVOmTGHatGkcOHCATp06MWTIEOLj44vd/+eff+a1115j2rRpnDx5kv/85z8sWbKE119/vcrBC1EmU6uFjQ20bm3dWErj5QWBgcblo0elnL8QQhSjwknLZ599xpNPPsm4ceOIiIhg3rx5ODk58f333xe7/86dO7n55pt5+OGHCQsLY/DgwTz00ENlts4IUWW5uXDqlHG5dWuws6uWu83LtmX161NY/foUlBR7bnv9Nm57/bbKlfE3Z2ptSUqC2NiqByqEEA1MhZKWnJwc9u/fz6BBgwruQKtl0KBB7Nq1q9hj+vTpw/79+9Uk5cKFC6xbt47hw4eXeJ7s7GxSUlIsfoSosDNnjIkLVOsgXEXREHusNbHHWpNwLgm/Y374HfPj+vnr3Lhxo/J3LINxhRCiVBVKWhISEtDr9fj5+Vms9/PzIy4urthjHn74Yd5991369u2Lra0tzZs3Z8CAAaV2D82cORN3d3f1Jzg4uCJhCmFUA4NwAS7sKLio4frpa9XlVa+twt/fnzlz5qBUpntHBuMKIUSpanzK85YtW/jggw+YO3cuBw4cYPny5axdu5b33nuvxGOmTp1KcnKy+hMTE1PTYYqGqJoH4Rr0Bv5Z+A9bv9hS4j7Z2dlMmjSJCRMmkJOTU7ETyGBcIYQoVYWmPHt7e6PT6bh69arF+qtXr+Lv71/sMW+99RaPPvooTzzxBAAdOnQgPT2dp556ijfeeAOttmjeZG9vj729fUVCE6KoaqzRkpyczIb3NxCzLwZwUte3uq0N/GVcDu0Zyul/TgMwf/58Tp06xbJly/D29i7fSSIijNVxFUWSFiGEKEaFWlrs7Ozo2rUrmzZtUtcZDAY2bdpE7969iz0mIyOjSGKi0xkHLFaqCV2I8jJ98Ds7Q2hope/m9OnT9OzZMz9hwZhY5Ov5WA91+bYXb+O///2vmnBv3bqV7t27c+TIkfKdyNERWrQwLp84AXp9pWMWQoiGqMLdQ1OmTOHbb79l4cKFnDx5kgkTJpCens64ceMAGDNmDFOnTlX3v+uuu/j666/55ZdfiIyMZOPGjbz11lvcddddavIiRLVLS4PISONy+/ZQTIteeZw9e5ZevXpx+rSxBcXe1Z4hbw4pcf9HH32UrVu3qi2PUVFR9OnThwMHDpTvhKYWoawsOH++UjELIURDVeGKuA888ADXrl3j7bffJi4ujs6dO/P777+rg3Ojo6MtWlbefPNNNBoNb775JpcvX8bHx4e77rqL999/v/oehRCFHT9esFzJriFFURg/frw6I8gz1JMhbwzB0cMbG/tsdb88+zyL43r27MnevXsZMWIE+/fvJz09nccff5y9e/diY1PGW65DB1i+3Lh87Bi0alWp2IUQoiHSKPWgjyYlJQV3d3eSk5Nxc3OzdjiiPvjPfyB/HBWzZ8Nzz1X4LhYuXMhjjz0GQFhYGANmDcDOqfRaL/Pvmq8uZ2Zm0qtXL7V76NNPP2XKlCmln3TZMrj/fuPy9OkwbVqF4xZCiLqiuj+/5YKJomGq4nTnhIQEXnzxRfX23Llzy0xYCnN0dGT+/Plo8sfAvP3220RHR5d+kNRqEUKIEknSIhqmKk53fvnll7l+/Tpg7BIdNmxYpcLo1asXTz/9NADp6elMnjy59AOaNwfTzDmp1SKEEBYkaRENk+kD39fX+FMBW7ZsYcGCBQC4u7vz+eefW2zPy7Fh/buTWP/uJAxpdtzy7i3c8u4taHOKfzt98MEH6sDcVatWsXLlypJPbmNjnPoMcPYsZGZWKHYhhGjIJGkRDU98vPEHKtw1lJWVxfjx49Xbs2bNIiAgwGIfxaAlZl8HYvZ1QJOnI2hfEEH7gtAYNIXvDgAPDw9mz56t3p40aRKpqaklB2GK2WAouHaSEEIISVpEA2TerVLBrqFZs2Zx5swZAHr37s1TTz1VLSGNHj2aIUOMU6UvX77MW2+9VfLOUhlXCCGKJUmLaHgqOQj33LlzzJw5EwAbGxvmz59fbMXmytBoNMydOxcHBwcAvvzySw4ePFj8zjIYVwghiiVJi2h4KtnS8vnnn6vXC3rxxRfpUI0XWQRo1qwZ0/KnMBsMBj788MPidzSPWQbjCiGESpIW0fCYt060a1euQ27cuMHChQsBcHZ25rXXXquJyHjhhRfw8fEBYNmyZVy6dKnoTkFB4OFhXJaWFiGEUEnSIhoWg6GgdaJZM3BxKddh33//Penp6QCMHTsWD1PSUM3s7e3VKdB6vZ6vv/666E4aTUEX0eXLkJRUI7EIIUR9I0mLaFguXoT85KO8XUN6vZ4vv/xSvV1mLZUqevrpp9Vy/vPnzyezuGnN0kUkhBBFSNIiGpZKDMJdvXo1UVFRAAwZMoQ2bdqUur+tQw5PrRrPU6vGo/HIZPGqxSxetRi9Q/muyhwYGMjo0aMBuH79OosXLy66kwzGFUKIIiRpEQ3LiRMFy+Ucz/Lvf/9bXX6uEtcoqoxnn31WXf7iiy8ocgkw89jNH5MQQjRikrSIhuXkyYLltm3L3P3IkSNs2bIFgFatWqm1VGpaz5496dmzJwCHDx9m27ZtljuYx27+mIQQohGTpEU0LKYPeI0GWrcuc/cvvvhCXX722WfLVZclL8eGjbOeYuOspzCk2XHzrJu5edbNJZbxL0nh1hYLPj7QpIlxWZIWIYQAJGkRDYmiFJS9DwsDR8dSd09ISGDRokWA8RpDY8eOLd9pDFoid3YlcmdXNHk6QnaGELIzpMQy/iUZNWqUeomAlStXcvHiRcsdTK0tsbGQnFyh+xZCiIbIxtoBCFFtLl8G0zV9ytE19M0335CVlQXA448/jks5p0dX1fjVBdc2Cro1iNifYzEYDNz9wt30GtcLgPl3zTc+hh07jDuePAm9etVKfEIIUVdJS4toOCowniU3N5e5c+cCxhL7EydOrMnIStR2aFu0Nsa34ak/TpGblWu2Uca1CCGEOUlaRMNRgaRl9erVXL58GYC7776bZs2a1WRkJXL0cKTFLS0AyEnP4fy28wUbJWkRQggLkrSIhqMCSYt5bZQJEybUVETl0u6OgunN57aeK9ggSYsQQliQpEU0HOVMWlJTU1m7di0APj4+DBw4sKYjK5V3C2/cAtwAiD0eS0ZShnFDcDA4ORmXJWkRQghJWkQDYvpg9/MDT88Sd1u9erVaOn/UqFFqSX1r0Wg0NO/XHADFoHDh7wvGDVotmKrzRkZC/qBhIYRorGT2kGgYEhMhPt64XEbX0JIlS9TlBx98sMKnsrHPYdyv+dcnssvh119/BUBvX74y/sVp3q85B389CMCFHRcKNrRtCwcOGC8EefZsuS9NIIQQDZG0tIiGoZxdQzdu3GD9+vWA8RpAffv2rfCpNBrj9YdsHXLQaEHvoDded6hiZVoseIV64RlsbB2KOxFHTEyMcYOMaxFCCJUkLaJhKGfSsnLlSnJzjdOK77///nJVwK0tzfoVzGBaunSpcUGSFiGEUEn3kGgYypm0VLVrCECfa8P2OY8A0P+pxfT6pgsAeyfutSgcV1HN+zZn/8/71TinTJkiSYsQQpipO18zhaiKciQtCQkJbNy4EYDQ0FD1goUVZdBrOfNXH8781QdydDT7qxnN/mqGRl+F/iHAo6kHTcKN1xvas2cPkZGR0KIFmAYKS9IihGjkJGkRDYPpA93VFQIDi91l+fLl6PXGwbKjR49Go6laklETTLOIAOMAX1tbY+ICcPo06Cs/2FcIIeo7SVpE/ZeRAaaLDbZpYxwpW4xffvlFXa5s11BNa9a3YFyLGq+p5Sg7G6Kiaj8oIYSoIyRpEfXf6dPGKzxDiV1DcXFxbN26FYAWLVrQpUuX2oquQtz83fBp6QPAoUOHOHPmjIxrEUKIfJK0iPrv1KmC5RKSlmXLlmEwGABjK0td7Boyad63oItoyZIlkrQIIUQ+SVpE/VeOQbjmXUMPPPBATUdUJeZdRJK0CCFEAZnyLOq/MpKWmJgY/v77bwAiIiJo3759kX2qMlW5urn4uNCnTx927tzJ8ePHOa7Xo15SUZIWIUQjJkmLqP9MH+R2dtCsWZHNK1asUJero5XFxj6HR3980XjDNZPlPy4HqlbGv7AHH3yQnTt3ArB03TrahYRAdLTxsSpKiYONhRCiIZPuIVG/5eXBmTPG5ZYtC2qamFm3bp26fO+991b5lBoNOLqn4eiehkYL2e7ZZLtnV6mMf2Hmca5bt66gBSk5GeLiqu9EQghRj0jSIuq3Cxcgvyx/cV1D6enpbNmyBYDg4OBiu4bqoqZNm9KxY0cA9u7dS3poaMFG6SISQjRSkrSI+q2M8SybNm0iOzsbgOHDh1fLrCF9rg075j3EjnkPoWTY0XVeV7rO64o2t3rfTnfccYe6fDgnp2CD+WwpIYRoRCRpEfVbGUmLedeQeRJQFQa9lhPrBnBi3QDI0dFqXStarWtV5TL+hZnH+7t5UTlpaRFCNFKStIj6rZSkRVEU1q5dC4C9vT233XZbbUZWZT179sTT0xOARfv3F2yQpEUI0UhJ0iLqN9MHuEYDrVtbbDp27BiXLl0CYMCAATg7O9d2dFViY2PD0KFDAbiQmkqum5txgyQtQohGSpIWUX8pSsH4jrAwcHS02GxqZYHq6xqqbcOHD1eXL5mSlitXjLOIhBCikZE6LaL+unwZUlMBOOqVx1eFCsSt+nGVulxfk5ahQ4ei0WhQFIV96emEmzacOgU9e1ozNCGEqHXS0iLqL7NukrimHhabstOyuXrqKgCtW7emWTFF5+oDb29veuYnJzuTkgo2SBeREKIRkqRF1F9mU39jgz0tNsUciEExGK/8XF9bWUxM8VukKZK0CCEaIekeEvWXWdJSuKUlel+0ulzdSYuNXS4Pffu68YZLFqu+NXZD6e2qr4y/uTvuuIO33noLi+osp0/XyLmEEKIuk6RF1F8lJC0GvYFLB4yzhmwdbenbt2+1nlajVXD1u67eTvdLr9b7L6xz584EBAQQHRtLJuAIUmBOCNEoSfeQqL/yWxvSXO1Jd3NQV187e42slCwAgjoHYWdnZ5XwqotGo2H48OEogNq+cv58weULhBCikZCkRdRPqanG2UOU3jUU0i2k2k+tz9Wx+4eR7P5hJEqGLZ1/6EznHzpXexl/c6apz2r7Sl6e8bpLQgjRiEjSIuonszEdhZOWmP0x6nJI1+pPWgx6HUdWDObIisGQY0PbFW1pu6JttZfxNzdo0CBsbW2xGMkiXURCiEZGkhZRP5l9YF8N8lCXMxIzSDifAIB3c2+cvJxqO7Ia4ebmRr9+/SwH40rSIoRoZCRpEfVTCS0tMQfMWllqoGvImu644w6ZQSSEaNQkaRH1Uwkzhy4fvqwuN+3StDYjqnHDhg3jjPkKaWkRQjQykrSI+in/AzvPRkuCnytgvKqzKWmxdbTFt5Wv1cKrCW3atME9IADTMGPl1Cnj9ZeEEKKRkKRF1D96PZw9C0B8gBsGnfHPOCk6icwbmQAEtAtAa9Ow/rw1Gg2DBg1Su4g0SUlw7ZpVYxJCiNokxeVE/XPxImRnA5aDcM27hoI6BdV2VNVqfKGLP5rEeMVwChhsWnH6NPg2rBYlIYQoiSQtov4px3iWmkxabOxyGfXVdOMNlyzWfrUWqLky/uYCOwUWnfbcr1+Nn1cIIeoCSVpE/VNM0mLIMxB7LBYAR3dHPEM9izuyWmi0Cl4hsertlJCUGjtXYS7eLsQ0cYbrxksH5Bw5Qv2u9yuEEOXXsDr9ReNgPt05v3so/mw8uZnGsvaBnQLRaGqu0Ju1pXYKVJdv7N5txUiEEKJ2SdIi6h+LwnLuAFw5fEVdF9SxZsez6HN17Pv5Tvb9fCdKhi3tf25P+5/b12gZf3O2PUJJzV/W5g9IFkKIxkCSFlH/mJIWf38yXeyBQuNZOtds0mLQ6zjwy10c+OUuyLGhwy8d6PBLhxot428usGOQOq7FMzkZsrJq5bxCCGFtkrSI+iUpCeLjjctt2gCQm5XL1dNXAXDzd8PV19Va0dUKexd7ovKTNR2QIF1EQohGolJJy5w5cwgLC8PBwYGePXuyZ8+eUve/ceMGEydOJCAgAHt7e1q1asW6desqFbBo5MxL17duDUDciTgMeQag5ltZ6oqrIQUDjU+tXGm9QIQQohZVOGlZsmQJU6ZMYdq0aRw4cIBOnToxZMgQ4k3ffgvJycnh9ttvJyoqimXLlnH69Gm+/fZbgoIax4eLqGbmpevzW1osuoZqeDxLXZHSPkBdvrZjhxUjEUKI2lPhpOWzzz7jySefZNy4cURERDBv3jycnJz4/vvvi93/+++/JzExkZUrV3LzzTcTFhZG//796dSpU5WDF41QaUmLBgI7BhZzUMOT2SNUXVZOnUKRcv5CiEagQnVacnJy2L9/P1OnTlXXabVaBg0axK5du4o9ZtWqVfTu3ZuJEyfy22+/4ePjw8MPP8yrr76KTqcr9pjs7Gyy8yueAqSk1F4dDFHHmXcPtWlD1t9ZXL9wHYAm4U1wcHMockhJ1WXrs+thXhgwfusITk/nwoULNG/e3NphCSFEjapQS0tCQgJ6vR4/Pz+L9X5+fsTFxRV7zIULF1i2bBl6vZ5169bx1ltv8emnnzJjxowSzzNz5kzc3d3Vn+Dg4IqEKRoyU0uLgwOEhHDliNlU53peur8i8uxsSPbyAqANsOnPP60bkBBC1IIar4hrMBjw9fXlm2++QafT0bVrVy5fvszHH3/MtGnTij1m6tSpTJkyRb2dkpIiiYuA3Fw4d8643KoVaLVcOnxJ3VxbSYvONpcRn35gvOGUzYZPNwBgsDXUyvlNNK1bw65duAL716yB8Q2vRUkIIcxVKGnx9vZGp9Nx9epVi/VXr17F39+/2GMCAgKwtbW16Apq27YtcXFx5OTkYGdXtAi5vb099vb2FQlNNAaRkZCXZ1zOH89iKiqntdHiH1H832B10+oUfFteVG8ntkyslfMW5tajB+R3y8Zv24bBYECrlSoGQoiGq0L/4ezs7OjatSubNm1S1xkMBjZt2kTv3r2LPebmm2/m3LlzGAwF30LPnDlDQEBAsQmLECUqNAg3KiqKlDjjeCe/Nn7YOthaKTDr0EZEqMsBKSkcPnzYitEIIUTNq/DXsilTpvDtt9+ycOFCTp48yYQJE0hPT2fcuHEAjBkzxmKg7oQJE0hMTOS5557jzJkzrF27lg8++ICJEydW36MQjYN50tK6NX/99Zd6szanOutzdRxePpjDywejZNjSZnkb2ixvU2tl/FX5dWogf1yL2ZcJIYRoiCo8puWBBx7g2rVrvP3228TFxdG5c2d+//13dXBudHS0RRN1cHAwGzZs4IUXXqBjx44EBQXx3HPP8eqrr1bfoxCNQ6GWli2zZ6s3a3Oqs0Gv458FIwHoeNt2uizoAsDZ4WehNht78rvIAFoDX27ZwksvvVSLAQghRO2q1EDcSZMmMWnSpGK3bdmypci63r17s1tKjYuqMpvurLRsqf6t6ex0+LT0sVJQVuTri+LhgebGDdoA27dvR6/Xl1hKQAgh6jsZtSfqB0WBkyeNy8HBRCUkEBMTA4B/W390to3wg1qjQZPf2hIK5KWkcOjQIauGJIQQNUmSFlE/JCQYL5YI0Lq1RYtegFlJ+0bHbFxLK2Dr1q3Wi0UIIWqYJC2ifihUCdf8w7lRJy2FxrUU1z0rhBANhSQton4oNHPIfDyLbytf68RUF5glLW0pGNcihBANkSQton4wjWcB4jw9uXjRWNzNr41f4xzPYmKWtLQBbty4wZEjR6wXjxBC1KAaL+MvRLUwa2nZfu2aumyNriGdbS53vv+p8YZTNpveN9ZHqe0y/gA0bw42NpCXhyl92bJlC126dKn9WIQQooZJS4uoH0xJi6sr68xmyAS2r736LCZanUJghzMEdjiDxs5AfId44jvEo+iUWo8FW1to0QIwDsTVIoNxhRANlyQtou7LzDRedwiMg3C3bQOM16jyadUI67MUlt9F5Ihx6vO2/OsQCSFEQyPdQ6LOGr/aeNXioMjrvK0YWzG22SYQmZ/AeLXywsau9v+EDXlaTm64BYCIgdtptakZAOeGnEOxsUJrS9u2sHIlYBzXsj4piaNHj9KpU6faj0UIIWqQtLSIOi/g0g11+bSmYL01uoYA9Hk2/D3/If6e/xBk2dFtfje6ze+GNs9Kb6dCM4hApj4LIRomSVpEnedvlrQcTs1Wlxt1fRZzhWYQgYxrEUI0TNI9JOo8/0tJ6vLuK8kA6Gx1+LZuxPVZKOg+c8jI4d/569ppNWBQWPfnOp767Sm+uecb6wUohBDVTFpaRJ3nf8mYqOTpNBxOSAfAt5WvVcaz1EVZTnYkeTkB0EZr7D/LTs0mKTqptMOEEKLekaRF1Gkag4Lf5RsAXHZ3JC9/fUAH6RoyFxfsCYBXnoEm+euuHLtivYCEEKIGyFdVUad5xadil2MsS3/WpiDHttYg3LoqLsidtocvA8bBuDuA2GOxahdSaebfNb9mgxNCiGoiLS2iTvPPb2UBOJyeA4DWRtvox7MUZmppAWhvZ7ysQeyxWBTFClOwhRCihkhLi6jTAmJuqMumpMW3lS829tb709XZ5jH0rS+NN5xy2PqWcaaOVcr454tr6qEud/V0gqupZKVkkRSThFeIl9XiEkKI6iRJi6jTzKc7m64+ZO2pzlqdgZDux9TbV7pbf+yIedISYXYBydijsZK0CCEaDOkeEnVaXUxa6qIbXk5kOtoC0DwjR10fezzWWiEJIUS1k6RF1GmmpOWKTkMqoNFp8GvjZ9WYDHlaTm/qzelNvVGydIRvCid8UziaPE3ZB9cUjUZtbfFJysDNwdiIGntcxrUIIRoOSVpEneWckoVrShYAJ/TGD16fFj7YOthaMyz0eTZs/fdjbP33Y5BlR69/96LXv3tZr4x/PlPSolWgV7hx4nNmUiYpsSlWjEoIIaqPJC2iziq2a6iddA2VxHxcS3dvF3U59ph0EQkhGgZJWkSdZZ60nMz/LUlLyWLNpj23szcbjCvjWoQQDYQkLaLOCogpKEN/CkADfm2tO56lLjNvaWmRkYvOVK9FkhYhRAMhSYuos8wLy50CmoQ1wd7F3mrx1HXX/N3Q64yDgf2vJOPX2pjgpcWnkRqfas3QhBCiWkjSIuosU/dQCnAFmepcFoONlvgAdwD8riQTaNYqFXc8zlphCSFEtZGkRdRNmZk0uWpsHTANwvVv52+9eOoJUxeRXY6ejkEe6nrpIhJCNARSEVfUTWfPos0vL6IOwo2oGy0tOts8Br2Sf5FBpxx2vLIDsG4ZfxPzcS0dHGzQ6DQoekWSFiFEgyBJi6ibTp5UF08BHk09cPRwtF48ZrQ6A836HlBvx/SNsWI0lsyTlqC4VHxb+nL11FWSLyeTkZSBk6eT9YITQogqku4hUTedOqUunkS6hsorNthDXfa/fMNiinjcCRnXIoSo3yRpEXVToZaWulSfxaDXcmHHTVzYcRNKjo7gHcEE7whGo7diGf98V83GsQTEJOHfviDZky4iIUR9J0mLqJvyW1pygfPUraRFn2vDnx+N58+PxkOGHX0/6kvfj/qizbX+2ynLyY4kL2MXkP+lG/i38UejNSZTMoNICFHfWf+/rBCFGQwop08DcA5w9HPFxcel9GOEKi6/Mq5LajaeegNN8q9DdD3qOtlp2dYMTQghqkSSFlH3XLyIJst4ocS61jVUH8QFuavLATFJBeOBFIg7Ka0tQoj6S5IWUffIINwqiTO7BpH/JcvBuHLxRCFEfSZJi6h7TpxQF6WlpeLMpz0HxCThHyGDcYUQDYMkLaLOMRw7pi5fcLPHLcDNitHUP1fMWloCYm7g6O6IZ/66hHMJ5GbmWis0IYSoEklaRJ2TsW+funyjfQAajfWnEtcnKZ6OpOdfWDIw2nilbFMXm2JQuHrqqtViE0KIqpCKuKJuURRsz54F4ALg0SHIuvEUQ2eTR//nFhhvOOSw+7ndABhsrF/GHwCNhishnrQ8EYfn9XQc07IJaBfAyd+NtW9ij8fStEtTKwcphBAVJ0mLqFtiYrDPNk7LPU7dvLKz1sZA64G71NuRAyOtGE3xTEkLGMe1JLSXwbhCiPpPuodEnWI4elRdPmWnU8diiIqJDSl43gKjk3Bu4oybv3FsUPyZePJy8qwVmhBCVJokLaJOifvrL3U5NthTreZalxj0WqL3tid6b3uUHB2BewMJ3BtYJ8r4m5gPxi08rsWQZyD+TLxV4hJCiKqQpEXUKcl//60uJ9XBriEwlvH//b3J/P7eZMiwo/97/en/Xv86UcbfxLylJSA/aQlsH6iuizsmReaEEPVP3fkvKwRgc+YMAAYgq0+4dYOpx1I8HElzNc4gCoixbGkBqdcihKifJGkRdYZiMBBw4wYAFzUaXFr5Wjeg+kyjITa/i8gzMQPHtGxc/Vxx9nYGjOX89bl6a0YohBAVJkmLqDPOb96Mi6IAEO/jg1Ynf55VcaXQYFyNRqNWF9bn6Ek4n2Ct0IQQolLkU0HUGWdXrlSXlYgI6wXSQBROWsByCrl0EQkh6htJWkSdkbRjh7rs3b+/FSNpGK6EeKnLpnEtcvFEIUR9JkmLqBMURVEH4QKEDh9uxWgahthgD3XZ1NLiHuSOo4cjAHEn4jDo60gVXyGEKAepiCvqhMjISMIzMgDjzCHb9u2hjl4iR2eTx83jFxtvOOSwb7zxWkl1pox/vtT8GUQuqdkERicCqONaLvx9gdzMXK5HXrdylEIIUX6StIg6YduWLYzKX77h5YWXk5NV4ymN1sZAuzu2qLfP3nHWesGURqPhSogXrY7H4p6UiVNqFhmuDgS0NyYtIONahBD1i3QPiTrh2Lp1uOQvG9q2tWosDYn5YNyAmBvG3zKuRQhRT0nSIuqEJLNKuB59+lgxkrIZ9BquHG3FlaOtUHK0+B71xfeob50q429ieQ0iYxeRZ4gn9vmF5+JOxGEw1K1uLSGEKIkkLcLqLl26RJO4grLyNp06WTGasulzbVnzxouseeNFyLBn4BsDGfjGwDpVxt+kuGnPGq0G/whjddzs1GyOHz9uldiEEKKi6t5/WdHobNu2jXbmK6RGS7WJLebCiWBZr2Xr1q21GpMQQlSWJC3C6rZu3aomLYpWC23aWDWehiTVw5FUNweg4MKJYHnxxG3bttV6XEIIURmStAir2751K6aht0p4ODg6WjWehsbUReR+IxPnlCwAvMK8sHWyBYxJo5J/+QQhhKjLJGkRVnX16lUyT5/GOf+2tn17q8bTEMVazCAytrZodVp1XEt8fDxnzAr7CSFEXSVJi7Cq7du3W45nadeupF1FJRU3GBcspz7LuBYhRH1QqaRlzpw5hIWF4eDgQM+ePdmzZ0+5jvvll1/QaDSMGDGiMqcVDcT41ePVn2k/TLNIWr7L3q1uE9WjPEnLli1bajMkIYSolApXxF2yZAlTpkxh3rx59OzZk9mzZzNkyBBOnz6Nr69vicdFRUXx0ksv0a9fvyoFLBqW2KOxFkmLeVdGXaXV6en52P+MN+zyOPjYQQAUXd0cF2Jx4USzpMWnhQ82DjbkZeWxZcsWFEVBo6l7tWaEEMKkwi0tn332GU8++STjxo0jIiKCefPm4eTkxPfff1/iMXq9nkceeYR33nmHZs2aVSlg0XBkJGWQFJOkJi0GrYa4IHerxlQeOls9ne77g073/YHGKZdT953i1H2nMNjWzSJt6W4OpLgbZxCZt7RobbQERBhbW2JjY2VcixCizqtQ0pKTk8P+/fsZNGhQwR1otQwaNIhdu3aVeNy7776Lr68vjz/+eLnOk52dTUpKisWPaHhij8WiAXXm0DV/N/Ls5HJYNcHUguWWXDCDCCCgQ0EX0ebNm2s9LiGEqIgKJS0JCQno9Xr8/Pws1vv5+RFnVtHU3I4dO/jPf/7Dt99+W+7zzJw5E3d3d/UnODi4ImGKeuLK0SuEAaZLI16pB11DYCzjH382lPizoSg5WrzOeuF11qtOlvE3uVJCkbnADgX1WmRcixCirqvR2UOpqak8+uijfPvtt3h7e5f7uKlTp5KcnKz+xMTE1GCUwlquHL1S78azgLGM/8oXX2fli69Dhj1DXhzCkBeH1Mky/iYljWvxbu6Nq6srgDquRQgh6qoKtcV7e3uj0+m4evWqxfqrV6/i7+9fZP/z588TFRXFXXfdpa4zXZzNxsaG06dP07x58yLH2dvbY29vX5HQRD2Tfj2d5MvJdDBbZ94aIKqXeUIYdDFRXdbqtNxyyy2sXbuWq1evcvLkSSLkMgpCiDqqQl8N7ezs6Nq1K5s2bVLXGQwGNm3aRO/evYvs36ZNG44ePcqhQ4fUn7vvvptbb72VQ4cOSbdPIxZ7LBYA80sjXgr3Kn5nUWWXwwqe26aR1y22DRgwQF2WcS1CiLqswqMep0yZwtixY+nWrRs9evRg9uzZpKenM27cOADGjBlDUFAQM2fOxMHBgfaFKpx6eHgAFFkvGpcrR68ABUlLrq2Oq0EeVounoctwsSfB1wXv+DSaXkxEY1BQtMYxOLfeequ635YtW5g4caK1whRCiFJVOGl54IEHuHbtGm+//TZxcXF07tyZ33//XR2cGx0djVZbd/v2Rd1w5egVHIGWptuhnhh08ndTky6FNcE7Pg2HzFyaXE0lIcANgM6dO+Ph4cGNGzfYsmULBoNB3sNCiDqpUvNLJ02axKRJk4rdVtYMhAULFlTmlKIBSUtIIyU2he6ALn9dTFgTa4bUKFwKb0LnPRcBCI68riYtOp2OW265hVWrVpGQkMDx48fp0KFDaXclhBBWIV+nRK2LPWocz9LZbN2lcElaapr5mKGmUSWPa5Gpz0KIukoqeYlaV3g8C9SvQbhanZ6bHlxtvGGXx9EHjwJ1t4y/ySWz1qzCg3HNx7Vs3ryZyZMn11pcQghRXpK0iFp35VjRpOVyPeoe0tnq6fbwGvX2sYePWTGa8kvwdyPL0RaHzNwiSUvHjh3x8vIiMTGRrVu3yrgWIUSdJP+VRK2Kjo4mNS4VDdApf/bKdR8XMlykLk9NU7QaLocaW7S849NwTMtWt2m1Wvr37w9AYmIiR44csUqMQghRGklaRK0y1QEJA1wNxu6U+tQ1BKAYNCRGB5AYHYCSp8Et2g23aDeom9dLtHDJvF5LVKLFNhnXIoSo6yRpEbXKlLSYdw3FhJf/Eg91QV6OLcsmTWfZpOmQ5sAdk+7gjkl3oMvRlXmstcU0MxvXElX6uBYhhKhrJGkRtcr0Db6LtuDigvWtpaU+K20wbrt27dRrhG3duhW9Xl+rsQkhRFkkaRG1JjIykosXjXVCepiNYblUjwbh1neXw7ww5OeLTSMtu4fMx7UkJydz+PDh2g5PCCFKJUmLqDXmXQ4d9MYBIFmOtiT4u1krpEYnx8GWawHuAARGJ6LVWw7EMe8i+uuvv2o1NiGEKItMeRa15s8//wTADQhKzwHgcqiXeg0cUTsuhXnhdyUZuxw9vleSGb96vLotSZOkLn+x+AvOtj4LwPy75td6nEIIUZi0tIhaYTAY1KTlJruCAavms1lE7TCvPlx4XItHUw+cvJwAiD0eiz5XxrUIIeoOSVpErTh69CjXrl0DoF9AQXeQlO+vfebPeXChpEWj0RDUKQiAvOw8rp66WquxCSFEaaR7SNSKjRs3qsvdHG3V5fqYtGh1ejre+4fxhl0eJ+89CdT9Mv4mMRYtLYlFtjft3JSzm43dQpcOXSKwQ2CtxSaEEKWRpEXUClPXEEBEZh4ABg1qhdb6RGerp9e4/6m3D407ZL1gKiHJ25l0F3uc07KL1GoBCOocpC5fPnwZHq3N6IQQomTSPSRqXFZWFtu2bQMgJDCQkNhkAK4FuJNt1uoiaolGo9bG8UjMwCU502Kzk6cTnqGeACScSyDbrNy/EEJYkyQtosbt2rWLzEzjB+MjPXpgl2Mc3FlfB+EqBg2pV5uQerUJSp4G56vOOF91rhdl/E1KKzIHxi4iAMWgcPnI5VqLSwghSiNJi6hx5uNZhgcVdD3Ux/EsYCzjv/jJD1j85AeQ5sDdT97N3U/eXS/K+JtcKmNci2kwLsDlQ5K0CCHqBklaRI0zT1q6aAv+5Opr0tIQWAzGLWZcS0D7ALQ2xtdKkhYhRF0hSYuoUYmJiezfvx+ADh064HzunLotRpIWq4kN9kCfX9SvuO4hWwdb/Nr4AZASl0JkZGStxieEEMWRpEXUqL/++gtFMU4Fvv322yH/ejbpznYkeTtbM7RGLc/OhrimHgAEXLqBrpgicuZdROazv4QQwlokaRE1yvzDbnj37nDlCpDfNaSR8v3WZOqes8kzEBCTVGS7aTAuWHbxCSGEtUjSImqU6cPOzs6OPi4u6noZz2J9ZQ3G9W7hjZ2zHQCbNm3CYKhH06OEEA2SJC2ixly4cIELFy4A0KdPHxxPnVK3SdJifeZjikIuJBTZrtVp1Wq4iYmJHDx4sNZiE0KI4khFXFFjzLuGBg0aBHv3qrcvNve2RkjVQqszEDF8i/GGnZ4zw88A9aeMv0m02WsQeu5asfs07dyUqN1RgLHVrGvXrrURmhBCFEtaWkSNMR8Hcfvtt8OePQBk29sQG+JprbCqTGebR9+nF9P36cVonHLY//R+9j+9H4Nt/eo+SXdz4Jq/KwAh5xPQ5hWN37ykvwzGFUJYmyQtokbo9Xr++usvADw8POgaEgJRUYDxG75BJ396dUFkS18A7HL0BEYXHdfiFuCGi69xLNKOHTvUysZCCGEN8skhasTBgwdJTDR+CN52223oDhxQt0W19LFWWNVCUSAz2YXMZBcUA9gn22OfbA/1q3cIgItmr0XY2aJdRBqNRp1FlJ2dzfbt22stNiGEKEySFlEj/vjjD3V50KBBatcQQFQrX2uEVG3ysu348dFP+fHRTyHFkfsevY/7Hr0PXXb9KeNvEmn2WhSXtIBlvRbz11UIIWqbDMQVNWLdunXq8tChQ2HSJPV2fW9paUhimjXBoNWgNSilJi0arQbFoPD9r9+T2j+12P3m3zW/JkMVQghpaRHV7/r16+zatQuAtm3bEh4WVtDS0qQJCX6u1gtOWMhxsOVy/qDowIuJ2GbnFdnHwc0B3/wWmaSYJFKvFp+0CCFETZOkRVS7P/74Qy1ENnz4cLh4ERLy64B07y6VcOsYU3edzqAQcr5ovRaA4G7B6nL0/uhaiUsIIQqTpEVUu7Vr16rLw4cPtxjPQo8eVohIlOZiC/PBuPHF7hPSNURdjt4nSYsQwjokaRHVSq/X8/vvvwPg6upK3759LZOW7t2tFJkoSWQrs6TlTPHjWpo0a4KTlxMAV45cIa+YbiQhhKhpkrSIarV3716uX78OGAvK2dnZWVTClaSl7rkS4kWOnXHmU0mDcTUaDcFdjV1E+hw9V45eqbX4hBDCRJIWUa3Mu4buuOMO0Oth/37jitBQ8POzUmTVR6sz0Oq2nbS6bSfY6blw2wUu3Hah3pXxNzHYaIluZizp7xuXgnNKVrH7hXSTLiIhhHXJlGdRrcynOg8bNgxOnoT0dOOKBtLKorPNY8DzC9Xb/zz/jxWjqR5RrXxoceoqYLwO0YmbgovsE9QpCK2NFkOegZh9MSiKgkYGVQshapG0tIhqExsby4H8yrc33XQTAQEBMgi3nohqaVZkroRxLXZOdgS0CwAgNT6VG5du1EZoQgihkqRFVJv169ery8OHDzcuNMBBuIoCuVl25GbZoRhAl6VDl6Wrl2X8TcwL/oWXMIMIUMe1AMTsi6nRmIQQojBJWkS1KTLVGQoG4Wo00LWrFaKqfnnZdvww+kt+GP0lpDgyevRoRo8eXS/L+JtcC3Aj3cUegNCz14yZWTFkXIsQwpokaRHVIicnh40bNwLQpEkTevToAVlZcOSIcYe2bcFVKuHWWRqN2trifiMTz4T0YndzD3LH1d/4OsaeiCUnI6fWQhRCCElaRLX4+++/SU01lncfOnQoOp0ODh2CvPx6HjKepc6Lall2kTmNRqO2tih6hUuHLtVKbEIIAZK0iGpSZKozyCDcesZiXEsJg3HBsjqujGsRQtQmSVpEtTBNddZqtQwePNi4UorK1SvmM4hCSygyBxDQIQBdfjG66P3RKIZ6PAJZCFGvSNIiqiwyMpKTJ08C0KtXL5o0aWLcYGppsbODjh2tFJ0orxQvJxK8jONVQs8moNEbit3Pxs6GoE5BAGQmZXI98nqtxSiEaNykuJyosjVr1qjLuc1yGb96PI5p2cw+cwaAyDB3Zm2YbK3wRAVcCAvEO/E0jlk5+F9OJjbEs9j9QrqGEL3XOHvo4t6LeDf3rs0whRCNlLS0iCpbsWKFuhzS3TjeIfRcQfeCebdDQ6DRGgjvs5/wPvtRbPRE94kmuk80irb+d5OcDwtQl0vrIjK9zgBRu6JqMiQhhFBJS4uokmvXrrF161YAWrRogVeYFwDNThXMPjEf4NkQ2Njlcftr36i3/37tbytGU73Ohweqy81OXWX3wFbF7ufi44JPCx+unbvG9cjrpMSl1FaIQohGTJIWUW7jV48vsu7UH6cwGIxjH5w7OqvXoml1PFbd51yEf+0EKKrsfHgAuRodtoqelkfjSt03vE841/Jb1CJ3RcKTtRGhEKIxk+4hUSWRuyLV5fA+4QDocvU0P2n8wEv0dibBT4rK1RfZ9nYcc2kLQOCVJFyTMkrcN6x3mLosXURCiNogSYuotJz0HC4fvgyAs7czPi2M3UCh565hl6MH4Gy7AGMJ/wYkN8uOb+6ezzd3z0e54chDdz/EQ3c/ZLz+UAOwx6OLutzyeMmtLR5BHniGGgfqXj11lcuXL9d4bEKIxk2SFlFpF/dexJBn7BoK7x2ORpvfNXSsoGvoTPuAYo8Vddce94KkpdWxK6XuG947XF02H5AthBA1QZIWUWnmXUPmXQWStNRvB9w7os//11DmuBazpGX58uU1GpcQQkjSIiolNyuXmP3GEu4O7g74tzUOttXqDTQ/dRWAZE9H4gPdrRajqJw0G2dOurcAoGlMIs4pWSXu6xXmhVuAGwBbt27l2rWSp0kLIURVSdIiKuXSgUvo88ethPUMQ6sz/imFnE/AITMXyG9laWDjWRqL/T7t1eWWZjPBCtNoNGpri8FgYNWqVTUemxCi8ZKkRVRKcbOGoFDXULtARP2037uDumz+mhbH/PX/3//+V2MxCSGEJC2iwvS5ei7uvQiAnbMdgR0KkpOW5klLBxnPUl8daNIeA8ZWspZlJC0+LX1w9nYG4M8//+TGjRs1HZ4QopGSpEVU2OUjl8nNMHYBhfYIRWdrnOqr0RtoecL4AZfi7khcUw9rhVijNFoDwd2OEtztKIqNnsvdLnO52+UGUcbfJNXOhdPuzQBoGnUdp7TsEvc17yLKzc1l7dq1tRKjEKLxkYq4osIid5p1DZnNHmkalYhjfjJztp1/gx3PYmOXx7C3v1Jvb3t7mxWjqTkHfSNom3werQItTsRxpEdoifuG9w7n2OpjALz51Ztscyv+OZl/1/waiVUI0ThIS4uoEIPewMV/jF1DNvY2NO3SVN1mXtNDpjrXfwf8zAbjltFF5NfWD0d3RwBiDsSQm5Vbo7EJIRonSVpEhcQdjyMrfwpscNdgbOwLGuss67PIINz67qBPO3W51dHSkxatTktoL2NLjD5HT8yBmBqNTQjROFUqaZkzZw5hYWE4ODjQs2dP9uzZU+K+3377Lf369cPT0xNPT08GDRpU6v6ibju37Zy6bN41pDEotDhhLESW5mpPbIhnrcdWW3Kz7Pj+/i/4/v4vUG44cv/993P//fc3mDL+Jjfs3TjrFgZAyIUEHDJySt2/WZ9m6vL5bedrMjQhRCNV4aRlyZIlTJkyhWnTpnHgwAE6derEkCFDiI+PL3b/LVu28NBDD7F582Z27dpFcHAwgwcPluuU1EN5OXlc+PsCADYONoT2LBjjEHgxEZdU42DNs+0CULQNczyLSV62PXnZ9gDYZNtgk90wh4cd8I0AQKso6kUwSxLYIRAHdwcAovdGk13K4F0hhKiMCictn332GU8++STjxo0jIiKCefPm4eTkxPfff1/s/osWLeKZZ56hc+fOtGnThu+++w6DwcCmTZuqHLyoXdF7o8lJN37bDu8djq2DrbqtlVkBsrPtZDxLQ3HAt2BcS1n1WrQ2WlrcYqykq8/VqwmuEEJUlwolLTk5Oezfv59BgwYV3IFWy6BBg9i1a1e57iMjI4Pc3Fy8vLxK3Cc7O5uUlBSLH2F9ZzafUZdb3trSYltLud5Qg3TAt2BcS1nXIQLLv4uzm8/WSExCiMarQklLQkICer0ePz8/i/V+fn7ExZX9Dw3g1VdfJTAw0CLxKWzmzJm4u7urP8HBwRUJU9SAa9euqdcacvJysigoh6Kopd4znO24FFZyQirql0QHTy64GN9/oeeuYVfGrCDv5t54BHsAEHcijpQ4+cIhhKg+tTp7aNasWfzyyy+sWLECBweHEvebOnUqycnJ6k9MjMxEsLZffvkFRW8sntZyQEv1WkMAATE3cEs2zig6F+GPopNJaQ3JAT9ja4uNwUDzk1dL3Vej0dDq1lbq7bNbpLVFCFF9KvTp4u3tjU6n4+pVy39cV69exd/fv9RjP/nkE2bNmsUff/xBx44dS93X3t4eNzc3ix9hXT/++KO6XLhrSOqzNGx/2/dUl81f65K06N+C/CsAcHbzWRSl4VQKFkJYV4WmPNjZ2dG1a1c2bdrEiBEjANRBtZMmTSrxuI8++oj333+fDRs20K1btyoFLGrfqVOn2Lt3LwBNmjXBK9Sy+6f9voKWsFMdg2o1NmvQaBQC2p823tAauNo+P4lvgBOmUuO92JQ3CHgHgHZ7L/Hboz1KPcbFx4XADoFcOXKFlNgU4k/H49fG2KU8fvX4Ms8pVXOFECWp8DzNKVOmMHbsWLp160aPHj2YPXs26enpjBs3DoAxY8YQFBTEzJkzAfjwww95++23+fnnnwkLC1PHvri4uODi4lKND0XUlNJaWWyz82hzxDh9PcnLiZhmTWo1Nmuwsc/lrg8+U2//9cFfVoym5qTGe5F61RuaJnDsWivaJ50hNCoBz2tpJPmU/t5teWtLrhwxtsqc3XxWTVqEEKIqKjz44IEHHuCTTz7h7bffpnPnzhw6dIjff/9dHZwbHR1NbGzBTJKvv/6anJwcRo0aRUBAgPrzySefVN+jEDXGYDDw008/AaDRatQprSZtD1/GLkcPwNHuIQ32ekONTVqCJ6lXvXH1S8DVN5EdQQUtpB32RZd5fHjvcHR2xmJ757efR5+rr7FYhRCNR6UqYk2aNKnE7qAtW7ZY3I6KiqrMKUQdsX37dqKjjR9STbs0xcnTyWJ7h70X1eWj3Uu+oJ6oP3IyHchKdsY9KB5X30QAtgd25+ljPwPQYW8024ZFlHofdk52hPcO59zWc2SnZRO9L9qigrIQQlSGTPMQpfrvf/+rLrccYNk1hKLQYa8xocmx03GyU8MfzwLGMv7//b9P+O//fYJyw5F7/+9e7v2/extMGf/cTHtcfBPVhAXglGczrjoYu/7aHL6CbXZemfcjNVuEENVNkhZRoszMTJYuXQqAq6srYb3CLLYHX7iOZ2IGYByAm2vfMEvZFycrxZWsFFcAHFIccEgpeQp/fWPrmI2Ld5LlSo2GHYHGLiK73DzaHi77MhxBnYJw9DRe+Tl6X7R6oU0hhKgsSVpEiVauXElqaioAo0aNsriiM0BHi66hkFqNTdQcO8fik4vtQd3VZfNuwZJodVpa9je2thjyDJzfIRdRFEJUjSQtokRff/21ujxmzJgi201dQwBHu0nS0tDt9etEltYOgA57YqAc9VfMu4hOrj8pNVuEEFUiSYso1pEjR9i+fTsAbdu2pX///hbb3RIzCD97DYDo8CZlToEV9V+WjT17fDsB4JmUTvCF62Ue0yS8iTrdOfFiInHHy3e5DyGEKI4kLaJYc+bMUZcnTZqEptBUZvNpr9I11HjsaFow9bljObqIANrdUXDRxeNrj1d7TEKIxkOSFlFEUlKSWpvF1dWVRx99tMg+5knLEZnq3GjsCDCr17Kn7HotAOF9wnH0MA7IjdwVSfr19BqJTQjR8EnSIopYsGABGRnGWUFjx47F1dXVYrtNTh4RBy8BkOLuwMWWPrUeozVpNAo+LaLwaREFWgPXW1zneovrDbKMf2FXnX045dYMgPBz13DLnz1WGp2tjrZD2gKgGBRO/n6yRmMUQjRckrQICwaDwaJraOLEiUX2aX00Fvv8Oh3HuoWgaBvBp7UZG/tc7v1sJvd+NhONWzZ/fPYHf3z2B3r7xlH11byLqDzVcQHaDm2LJv/v5OTvJ6VCrhCiUiRpERY2bNjA+fPGqamDBg2iTZs2RfYxn+4qXUONj+XU5/IlLc5NnNWKuJnJmUTujKyR2IQQDZskLcJC4QG4RSiK+u06z0bLic6NowquKHDcqyXX7dwBaHvoMjY5ZVfHBRmQK4SoOklahOr8+fOsW7cOgJCQEO68884i+wReTMI7Pg2AM+0DyHayq9UY64K8bFt+fuJ9fn7ifZQUB+564i7ueuIudNkNo4x/WRSNlr/zq+M6ZOfS+mhsGUcY+bfzxyvUC4Crp65y7dy1GotRCNEwSdIiVF9//bVa/GvChAnodEU/hLvsLmjWb6xdQ4qiIS3em7R4bzBocIl3wSXeBRpR3TTzLqLOu8rX1aPRaKS1RQhRJZK0CAAyMjL4z3/+A4C9vT2PP/540Z0UhV5/GS98Z9DAoULXIhKNxy7/LmTojNdb6ro9slwXUARoMaAFds7G1rnz287L9YiEEBUiSYsA4Mcff+TGjRsAPPjgg/j4FJ3G3PzkVXzjUgDjBRKlCm7jlWnryJ/BfQBwzsym057yFZqzdbCl9aDWAOhz9ZzcINOfhRDlJ0mLIDc3l1mzZqm3ix2AC/TZdFpd3n1bqxqPS9Rta8NvU5d7bzpT7uMihkWoNW2OrjpKblZudYcmhGigJGkR/Pe//yUqKgqAoUOH0q1bt6I7ZWTQdccFALIcbTnYO6z2AhR10n7f9lx2NF5XKOLgJdzLWenWPdCdZn2NBeqykrM4sf5EjcUohGhYJGlp5HJzc3n//ffV22+//XbxO65ciWOm8Rvx/j7h5DjY1kZ4og5TNFrWhRsvpKlVFHpuPVfuY2964Ca1teXI8iPklXNMjBCicZOkpZH76aefiIw0zv64/fbb6d27d/E7LlyoLu4a2Li7hjQaBc/gK3gGXwGtQnJwMsnByY2ijH9h5l1EvTadAaV8U6i8QrxodrOxtSUzOVNaW4QQ5WJj7QCE9eTl5Vm0skybNq34HS9fhj//BCDB15VzEQG1EV6dZWOfy/1z3lFvr5uzzorRWFeMayAHvSLokniCoJgkQs4nEN2ifNeiuumBm7iQ3+V4ePlhIoZFYGMv/5KEECWTlpZGbNGiRWrJ/oEDB3LzzTcXv+NPP4HBAMCu21o2umsNidL9FjxYXe79V/kH5HqFehHeJ7+0/41MuZCiEKJMkrQ0Unl5ecyYMUO9XWIri6JYdA3JrCFhLifDgV/yHiJTYw9A963n0VXgYohdH+yqLh9afkjGtgghSiVJSyO1ePFizp0zDpy89dZb6devX/E77t0LJ43fgM9G+JPg71ZbIdZZedm2LJ04jaUTp6GkODB84nCGTxzeaMr4m+RkOJAY1ZRMJzu2BPUCwDU1q9xXfgbwCvMiLH8mWmZSptRtEUKUSpKWRkiv15evlQUsB+BKKwtgLOOfFBNIUkwgGDS4x7jjHuPeqMr4mxIWG/tsvMIus7b5AHVb701nK3Rf5q0th5cfJitLquQKIYonSUsjtGjRIs6cMY496N+/P/379y9+x+xsWLzYuOzoyP782hqicSucsGh1Bv7x60y8vfFiiO33ReOSnFnu+2sS3oSw/EtCZCRmMG/evJoIWwjRAEjS0sikpKTw6quvqrdLbWVZtQqSkozL995LViO8orOwVFzCAmDQ6lifX7PFxmCg55by12wBuOnBm9Tld955h/j4+OoLWgjRYEjS0si89957xMXFAXDPPfdw6623Fr+josAnnxTcfuyxmg9O1GklJSwmq8MHqsu3/nYMbZ6h8F2UyLuZN63yux9v3LjB66+/Xj1BCyEaFElaGpGTJ08ye/ZswHgl588//7zknf/6C/bsMS537AiDBtV8gKLOKithAYh0D2GHv3F8ik9CKj22Vay1pcfYHtg6GSst/+c//+Gff/6peuBCiAZFKjk1Eoqi8Oyzz5KXZ5xS+tprrxEeHq5uH796vMX+L7yxhjb5y98O8WHfmqdrK1RRx5QnYTH5od399I3bD8DQpYf4Z0D56/o4eTrR7eFu7PpuFwATJ07kn3/+QadrXLOyhBAlk5aWRmL58uX8mV/VNiwszGJcS2HNTl2lzdErAFwNcGN/n/AS922MNBoFF98EXHwTQKuQ5ptGmm9agyzjX5GEBeCQTwT7m7QDIODyDTrvjqzQ+drd0Y727dsDsH//fr7//vvKBS6EaJAkaWkEMjIyeOGFF9Tbn3/+OY6OjiXuP3TZQXV5w8jOKDr5MzFnY5/Lw9+9wcPfvYHGLYvV361m9Xer0duXv6hafVDRhMXkh/aj1OVhvx4q9/WIALQ6LV999ZV6e+rUqSQmJpb7eCFEwyafRo3ABx98QExMDABDhw7lnnvuKXHfoMjrdNpjLA6W6O3M7ltb1kqMom7JybSvVMICsMv/Jk54tAAg9EICEQcvVejc/fv356GHHgLg+vXrvPnmmxU6XgjRcEnS0sCdO3eOjz/+GABbW1v+/e9/o9GU3I8x9H+H1OU/7u2E3lbGEzQ2+jwdN6IDK5WwAKDR8EM7s9aWpYcqHMPHH3+Ms7MzAPPmzePAgQMVvg8hRMMjSUsDlpuby//93/+Rk5MDwIsvvkirViVXtfW5kky3/Kvupro5sGNwmxL3bczysm1ZMWUqK6ZMRUmxZ/CUwQyeMrjBlPHPTnVBZ59TuYQl3+amvbjgEgxAq+OxND8RV6Hjg4KCePvttwHjIPIxY8aQmVn+gnVCiIZJkpYGbPr06eq00ebNm/PGG2+Uuv+Q5YfRGozjDzbd3YFce5lcVhxF0XDtXBjXzoWBQUuTc01ocq5Jgynjr9Xp8QyJrXTCAqBotCxsd596uzKtLc8//zwdO3YE4Pjx47z44ouVjkcI0TBI0tJA/fXXX8ycORMAGxsbFi9ejIuLS4n7e1xPp/dfxtL+mU62bBkeUStxirrH3jUdrbbyCYvJ76H9ueLoC0CH/dE0vZBQoePt7OxYvHixOmj866+/ZsWKFVWOSwhRf0nS0gAlJCTwf//3fyj5szY++OADunfvXuoxI/67B5v8CqZbhrcj08W+xuMUdZNGUz1NRnlaG/4bca96e9R//qnQTCKAiIgI/v3vf6u3H3/8cXVQuRCi8ZGkpYFRFIVx48YRGxsLwO233152s/qff9J7s/HKvOnOdvx5T4eaDlM0EqvCB3HFydja0vboZXptrtgVoAGeeOIJRo0yDuxNSkrikUceQa9vWNPLhRDlI4MWGpivvvqKNWvWAODj48PChQvRakvJTTMz4emCarfLH+tJmnvJNVyEqIhsG3tmdXuaL7a9C8Co/+zmaLcQ0t0cyn0fGo2Gb775hj179hAdHc327duZMWNG6Rf7zFe40nNx5t81v9yxCCGsS1paGpD9+/fz8ssvq7cXLFhAQEBA6Qe9/z6cPw/A2Qh//r5dZgyJ6vV3YDc2NO0HgGtqFqO+313h+/D09GTx4sVqSf93332XLVu2VGeYQoh6QJKWBuLChQvccccdZGdnA/DCCy8wfPjw0g86fhw+/BCAPBstP03sV+7rxDR2Dm6pOLilApDllkWWW5aVI6rbPu36BCk2xrorff46Q+vDlyt8H3369GH69OkAGAwG7r33Xo4dO1adYQoh6jhJWhqA+Ph4hgwZwtWrVwHjP3fTzKESGQzw1FOQfwHF30d2Ji7Ys6ZDbRBsHXIY89NLjPnpJTQemaz4aQUrflqB3kHGWZTkuqMnX3Yaq95+eO4ObHLyKnw/U6dOZciQIQDcuHGDoUOHEh0dXW1xCiHqNkla6rm0tDSGDx/OuXPnAONsi9WrV2NvX8bsn2+/hZ07jcutWrH+/s41G6ho9Fa0GMwBL+NUev/YZIb/erCMI4rS6XQsW7aMbt26AXD58mWGDh3K9evXqzVWIUTdJElLPZaTk8PIkSPZv38/AE2bNuX333/Hy8ur9ANjY8H8Ks/z5pFnJ2OyRc3SG2x4JfBdcrAFYMj/DhN4seIXQ3RxcWHt2rW0bGm8LtbJkye58847ycjIqNZ4hRB1j3xS1VMGg4F//etf/PHHHwB4eHjw+++/ExwcXGRf8xkUttl5THljDc2SkwHYObAVC9N+qZ2gG4i8bFvWvzMZgDtfm8PAWTcDsHXa1gZ3pefqYtBrSYwKIl5rzw8tRzH+7GJs9AbGv/8nH31yt8VsovLM+AHo+nJXLr16icykTHbv3k3bAW0Z/PpgtHJVciEaLHl310M5OTmMHTuWRYsWAeDg4MDq1atp165dqcdpDAqPzd5CszPxgPEqzsvG9arxeBsaRdEQe6w1scdag0GL3zE//I75NZgy/tXNlLDkZdvjFXaJBZ1HcsY9DAD/uBuM/2AjutyKJ3tu/m4MmzYMW0djy0303mj+/PBP8rIrPlZGCFE/SNJSz5gGH/70008AaLVaFi9eTN++fcs89u5Fe+n2t/GCiFmOtsx5a2iF6mUIUVGFExY7pyxydHa8cMubJNgbB363PhHLo19tq3C1XADvZt4MeWMIWhvjv7Ko3VGseWMNmTfk4opCNETSPVSHFW4mT7uWxvp31pMUnQSAzk7H0l+WMmLEiDLvq/em0wzPv2idQavh25cGcim8SXWHLISquITFJM7Zlym3vME3m17HwZBD781nuRrkzvrRN1X4PIEdAxn61lA2ztpIbmYu8WfiWfnKSoZNG4ZHkEc1PiIhhLVJS0s9kXAhgZUvr1QTFgc3B+6ccSf33ntvGUdCq6NX+L8529Xbvz7Rm2PdQ2osViFKS1hMjjdpxVu9XlBvj/hpH922n6/U+Zp2acrds+7GuYmxFkxqXCq/vfIbcSfjKvcAhBB1kiQtdZyiKJzbeo7VU1eTkWicHeEW4MY9H92DXxu/su/g0CGenrlRvRji5jvasfnO9jUZsmjkypOwmPwVcjNfdByj3h77+ZZKFZ4DaBLehHs+vgevUOPsuezUbNa+uZaTG06qFw8VQtRv0j1kJeWZIZGZnMmOr3cQuTNSXefb2pchbw7BMf/6QKXdT8d/onj8079wzjIOTDzaNZhfn+hdxciFKFlFEhaThW1HEpJ6hRGRf2KXp+fZaev5+Zm+/D244peUcPF24e5Zd7Nx1kYuH76MPlfP9jnbidodxS2TblFbYoQQ9ZO0tNRRUbujWDZpmUXC0qJ/C+6ccaeasJRIUbh9xWEmfPAHDvkJy4XWvnz38kAMMh20WtjYZ2Njb7xkQp59Hnn2MmOlMgkLABoNM7tNYFtAdwBsDAbGfLWNkT/sRqM3VDgOO2c7hk0bRtuhbdV1MftjWDppKWe3nJVWFyHqMY1SD97BKSkpuLu7k5ycjJubm7XDqRYltZBkJGWwZ+Eezvx1Rl1n72pPvwn9aNa3WZn3q8vV8/C8HfTdeFpdt6dfc/77bH9y7aVhTZQu9WoT9v50N05eN7Cxzy33cZVOWMzoDHqeP/g9D59dra471COU71+8jez8ac0VFb0vmm1fbVO7VgHCeofR58k+uHi7AHKVZyFqUnV/fsunWB2RnZbN4eWHObb6mEWdiZAeIdwy8RacPJ3KvA/Pa2mMm72Z1kdj1XWrH+rKmgdvAo1cCFHUjOpIWAD0Wh2fdn2SSLemvHrgG2wUPZ33XOSlV1bx3asDudrUo8L3GdIthFFfjmLnNzs5t9V4qYuoXVHE7Iuh7bC2dBnVpVKxCiGsQ1paakB5K3oC5GTkcGz1MY6sPEJOeo663tbJlj5P9qHVba3QlJFw2OTkcfvKIwxbegj7/IQn11bHguf6s++WFpV7EKJRqmhLS3UlLIX1jDvIrB0f4ZaXDkCeTsumu9uz9oGbyHayq9R9Xvj7Atvnbic7NVtdZ+NgwytTXuGll17C07PkC4aW5z0tLTZCFCUtLQ3Ejcs3OPXHKc5sOkNWSsE/eq2NlrZD29Ll/i7lal3psPcio7/dhW9cirou2cORr18fTGR5ZheJCsvLsWHjrKcBGDLlGwZ8ZqwqvOO1HRjsKj4Go76qqYQF4B//Lowb/DGfb51BSPoVbPQGhqw4Qs8t51n+WA/+GdCiwq2HzW5uRmCHQGOL5ppj6HP05GXl8cEHHzBnzhwee+wxnnjiCdq3l9l1QtRVkrTUorzsPC7svMDpP04TezzWYptGq6HVba246cGbcPV1Lf2OFIXWR65w+8ojdNgfo67WazVsHR7B6oe7keFSxlWeRaUpBi0x+zoAoMnTEbQvyLhsaDxdcDWZsJhEuTXloWH/ZuyJZYw9tRx7Qy4eSen86/PN9Ft3kj/u78SxrsEVGlzu4OZAz8d60uHuDhxcepCTG05iyDOQnJzMv//9b/7973/Ts2dPnnjiCR544AFcXct4LwohapUkLWZqogk4IymDmP0xRO+L5tKhS+RmWDa5a220NLu5GTc9cBMeZfTZO6dk0WfTafptOIXflWSLbafbB/DLUzdzJayMKzwLUUW1kbCYZNnYM7/jI6xpNpAXDnzPrVd2A9DydBwtZ8SR6OXC30Nas+P21tzIH1hbHk5eTtw8/mY63tuRA0sOcG7LOfT51z/6559/+Oeff5gweQJBnYII6RpCcNdgXHzKf/9CiJohSUs1u3r1Khf3XuTqqatcOniJhHMJxe7n0dSDNre3oeVtLUudwuxxPZ02hy/TYV80nXZHYZtn2f2Q6O3M/8b1Yl/fZjLYVtS42kxYzF128eelW16nd+wBXtz/HeFplwDwSkzjrsX7ueOXAxztGsLRHiGc6BzEdf/y9Z27+rrSf3J/eo3rxdktZzm98TTXI68DkJeVx8V/LnLxn4vGc4V60fSmpvi39cenpY/UfBHCCiqVtMyZM4ePP/6YuLg4OnXqxJdffkmPHj1K3H/p0qW89dZbREVF0bJlSz788EOGDx9e6aDrgpycHM6fP8+ZM2c4deoU+/fvZ8+ePVy8eLHEY+xd7QntEUqb29vg19avyABbjUHBKz6VplGJtD56hbaHLhEYc6PY+zrVMZBtQ9tyqGcYeltddT40IYplrYTF3K6AmxjWfRFdz59iXPqP3Hp9JzoMaBWFTvsu0mmf8f0X7+vGqS6BnOoUREx4E675u6GU0o1k72JP+zvb0+6OdiScT+DUH6eI3BVJVnLBY0y8mEjixUSOrDgCgHMTZ3xa+uDdwhvPpp4cb3ac5s2b4+AgFyEVoqZUOGlZsmQJU6ZMYd68efTs2ZPZs2czZMgQTp8+ja+vb5H9d+7cyUMPPcTMmTO58847+fnnnxkxYgQHDhyokwPeFEVBn6MnKyWLrNQsMhIzSL+eTvr1dDISMwiZHkLylWRS41NRDGVPvPJu7k1w12BCuoXg09IHGwXckzLwPHUVz+vpeF5LJ+BSEoEXkwiMScIhs+QZG6luDuwa2IrtQ9oSH+henQ9biFLVhYQFIDXei9R4b/a20HHK9xX80q9x94U/GXFhI/6ZBa2avvEp+G5I4ZYNpwDIsbXhSlNPYsM8iA3xJNHbhSRvZ5KaOJPcxJm8/MRfo9Hg08IHnxY+9H26L9fOXyNmfwwx+2KIPxsPZm950/+FqN1RALSf1R6NRkNYWBgtW7akadOmBAUFqT+BgYF4e3vj5eWFs7NzmbMChRBFVXjKc8+ePenevTtfffUVAAaDgeDgYCZPnsxrr71WZP8HHniA9PR01qxZo67r1asXnTt3Zt68eeU6p2nK1I4lS3B2dESv12PQ69Gb/eTl5aHPyyMvL4+cnBzy8vLIzc0lLzeXrKwssrOyyMrKIic7m+ysLDLS08lITyc9LY2M9HQy09O5fO0Seek5KHkGNBjLBeswZnY2Zsu2gF2hH0fA1UaLj5cT3u6OeLnY08TBFrdcPc5p2TilZeOcmo1LSibacj7jeq2GqFa+nOwUxMnOQUS28pVWlTogN8uOH0Z/CcCT/32eh8eMAODXX39F76C3YmRVV9yU5zqVsFz1xtUvAVffRIttWoOetknn6RF3iJ5xh+mccBJbpfxVilNcHEl3dSDDxY4MVzsyXO3JdLYj296GHAdbcuxtSDMoXLueRmJ8Gtfj00iITSYjR08OoAfy8n/0+T+GQj9K/o8BsLW1xd3DA3cPD5ycnXFycsLZxQVnFxecnJxwcHTE3t5e/XFwcMDWzg47OztsbGywtbXl/9u7v5Cotj0O4F9nbLJy0kzT1MbyaEpxNdIUjRBSEhHJF5GImuzlImMoFpQRmQ8xvXQxSsII7Dwk1osGUZ1k8A+Bln8QtK6R3TjjJWfMupozR2dsZt8HT55jaudMbtsu+35gg7Pce/mdpYy/2bP22qtWrYLa2xtqtRpqtRre3t5QqVRQq9VQqVRzNi8vr7/cPn/EPPP496+/tJg2ubH4W97GbTbE7N+vzCXPTqcTXV1dKCsrm2lTqVTIyMhAW1vbvMe0tbWhtLR0VltmZiYaGhoW/DkOhwMOxx9rKYyNTU86jcjPx7JepeWTGxi2TW8LWPg7wMgmX7zdsgEW3Qb8GhmIVztC4Fj3pzUpplzTGylqahIApi8xd044YMf0WiLO35xwucX+/UxNOOD+ZIdtRA2VN+B2e2F8KAiuTyqsDx7C5LgLk+PftjrtYkyMavHbBz+sDRiBJI3jo/XLDKvQhp1oC9wJBB7GGtcEdo0+xz8+/huRtl/xk82MiMn/Qo0F3jHYJrDONoHvNktlagp49256I1rBPr8iyrUknEdFy8jICFwuF4KDZ6//ERwcjP7+/nmPsVgs8+5vsSx8y3ij0YiKioo57Vs8CSuizwXPny5jpuXqBgDg538CP+P3M4bHlEsjr3/N2/rhP985xjz+t/CUsTl6ly4GEXno/fv38PNb/LSGZXn1UFlZ2ayzM6Ojo4iIiIDZbJblSf+oPn78iC1btmBwcFCIlYWXM46lfDiW8uA4yodjKZ+xsTHodDoEBMizHIdHRUtgYCDUajWsVuusdqvVipCQkHmPCQkJ8Wh/ADOf437Jz8+Pf0AyWL9+PcdRJhxL+XAs5cFxlA/HUj4q1d9fBPKr/Xiys0ajQUJCAkwm00yb2+2GyWRCSkrKvMekpKTM2h8AGhsbF9yfiIiIaD4efzxUWloKvV6PxMREJCUlobKyEna7HQUFBQCAo0ePIiwsDEajEQBQXFyMtLQ0XL58GdnZ2airq0NnZydu3Lgh7zMhIiKiFc3joiU/Px/v3r3D+fPnYbFYsGvXLjx69Ghmsq3ZbJ51Gig1NRW1tbU4d+4czp49i+joaDQ0NHi0Rsvq1atRXl4+70dG9PdxHOXDsZQPx1IeHEf5cCzlI/dYerxOCxEREZES5JkZQ0RERLTEWLQQERGREFi0EBERkRBYtBAREZEQWLQQERGREIQrWi5evIjU1FSsXbsW/v7+SscRSlVVFbZu3QofHx8kJyfj2bNnSkcSTmtrK3JychAaGgovL6+v3viTFmY0GrFnzx5otVps2rQJubm5ePnypdKxhHT9+nXExcXNrN6akpKChw8fKh1LeJcuXYKXlxdKSkqUjiKcCxcuzLmDeGxsrCx9C1e0OJ1O5OXlobCwUOkoQrlz5w5KS0tRXl6O7u5uxMfHIzMzE8PDw0pHE4rdbkd8fDyqqqqUjiK0lpYWGAwGtLe3o7GxEVNTUzhw4ADsdrvS0YQTHh6OS5cuoaurC52dndi/fz8OHjyI58+fKx1NWB0dHaiurkZcXJzSUYS1c+dODA0NzWxPnjyRp2NJUDU1NZKfn5/SMYSRlJQkGQyGmccul0sKDQ2VjEajgqnEBkCqr69XOsaKMDw8LAGQWlpalI6yImzYsEG6efOm0jGEND4+LkVHR0uNjY1SWlqaVFxcrHQk4ZSXl0vx8fFL0rdwZ1rIc06nE11dXcjIyJhpU6lUyMjIQFtbm4LJiKaNjY0BgGx3gv1RuVwu1NXVwW638/5u38hgMCA7O3vW6yV57tWrVwgNDUVkZCQOHz4Ms9ksS78eL+NP4hkZGYHL5Zq51cJnwcHB6O/vVygV0TS3242SkhLs3bvXo9t70B96e3uRkpKCyclJ+Pr6or6+Hjt27FA6lnDq6urQ3d2Njo4OpaMILTk5Gbdu3UJMTAyGhoZQUVGBffv2oa+vD1qtdlF9L4szLWfOnJkzaefLjf9ciVYmg8GAvr4+1NXVKR1FWDExMejp6cHTp09RWFgIvV6PFy9eKB1LKIODgyguLsbt27fh4+OjdByhZWVlIS8vD3FxccjMzMSDBw8wOjqKu3fvLrrvZXGm5eTJkzh27NhX94mMjPw+YVagwMBAqNVqWK3WWe1WqxUhISEKpSICioqKcP/+fbS2tiI8PFzpOMLSaDSIiooCACQkJKCjowNXrlxBdXW1wsnE0dXVheHhYezevXumzeVyobW1FdeuXYPD4YBarVYwobj8/f2xfft2DAwMLLqvZVG0BAUFISgoSOkYK5ZGo0FCQgJMJhNyc3MBTJ+SN5lMKCoqUjYc/ZAkScKJEydQX1+P5uZmbNu2TelIK4rb7YbD4VA6hlDS09PR29s7q62goACxsbE4ffo0C5ZFsNlseP36NY4cObLovpZF0eIJs9mMDx8+wGw2w+VyoaenBwAQFRUFX19fZcMtY6WlpdDr9UhMTERSUhIqKytht9tRUFCgdDSh2Gy2We8W3rx5g56eHgQEBECn0ymYTCwGgwG1tbW4d+8etFotLBYLAMDPzw9r1qxROJ1YysrKkJWVBZ1Oh/HxcdTW1qK5uRm//PKL0tGEotVq58ypWrduHTZu3Mi5Vh46deoUcnJyEBERgbdv36K8vBxqtRqHDh1afOdLck3SEtLr9RKAOVtTU5PS0Za9q1evSjqdTtJoNFJSUpLU3t6udCThNDU1zfv3p9frlY4mlPnGEIBUU1OjdDThHD9+XIqIiJA0Go0UFBQkpaenS48fP1Y61orAS56/TX5+vrR582ZJo9FIYWFhUn5+vjQwMCBL316SJEmLL32IiIiIltayuHqIiIiI6K+waCEiIiIhsGghIiIiIbBoISIiIiGwaCEiIiIhsGghIiIiIbBoISIiIiGwaCEiIiIhsGghIiIiIbBoISIiIiGwaCEiIiIh/B8wj2H0UTxHxgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generate 1000 random numbers from the first normal distribution\n", + "mu1, sigma1 = 1.03, 0.5 # mean and standard deviation for the first normal distribution\n", + "data = np.random.normal(mu1, sigma1, 1000)\n", + "\n", + "# Create a histogram of the data\n", + "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n", + "\n", + "# Add a graph of the first normal distribution used to generate the data\n", + "xmin, xmax = -1, 5\n", + "x = np.linspace(xmin, xmax, 100)\n", + "p1 = stats.norm.pdf(x, mu1, sigma1)\n", + "plt.plot(x, p1, 'k', linewidth=2)\n", + "\n", + "# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n", + "mu2, sigma2 = 1, 0.4\n", + "p2 = stats.norm.pdf(x, mu2, sigma2)\n", + "plt.plot(x, p2, 'r', linewidth=2)\n", + "\n", + "# Add vertical lines at x = 1 and x = 3 with labels\n", + "plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n", + "plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n", + "\n", + "# Calculate the 95% quantile for the second normal distribution\n", + "quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n", + "\n", + "# Plot the hatched area under the red curve for the 95% quantile and above\n", + "x_fill = np.linspace(quantile_95, xmax, 100)\n", + "p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n", + "plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n", + "\n", + "title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n", + "plt.title(title)\n", + "plt.xlim(xmin, xmax)\n", + "plt.legend()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "id": "9c019dea-d687-4dc1-b48f-fe629e54172e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "T-statistic: 1.4815943949743855, P-value: 0.13860593668122914\n", + "The means of the two theoretical distributions are not statistically different (fail to reject H0).\n" + ] + } + ], + "source": [ + "# Define the parameters for the two normal distributions\n", + "mu1, sigma1 = 1.03, 0.5 # mean and standard deviation for the first normal distribution\n", + "mu2, sigma2 = 1, 0.4 # mean and standard deviation for the second normal distribution\n", + "\n", + "# Perform a t-test to compare the means of the two theoretical distributions\n", + "# Since we don't have samples, we use the means and standard deviations directly\n", + "# Calculate the t-statistic and p-value manually\n", + "n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n", + "se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n", + "t_statistic = (mu1 - mu2) / se # t-statistic\n", + "df = n1 + n2 - 2 # degrees of freedom\n", + "p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n", + "\n", + "# Print the t-test result\n", + "print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n", + "\n", + "# Interpret the result\n", + "alpha = 0.05\n", + "if p_value < alpha:\n", + " print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n", + "else:\n", + " print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}