{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorial \n", "\n", "Let us consider chapter 7 of the excellent treatise on the subject of Exponential Smoothing By Hyndman and Athanasopoulos [1].\n", "We will work through all the examples in the chapter as they unfold.\n", "\n", "[1] [Hyndman, Rob J., and George Athanasopoulos. Forecasting: principles and practice. OTexts, 2014.](https://www.otexts.org/fpp/7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exponential smoothing\n", "\n", "First we load some data. We have included the R data in the notebook for expedience." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.020317Z", "start_time": "2017-12-07T12:39:14.263100Z" } }, "outputs": [], "source": [ "import os\n", "import numpy as np\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "from statsmodels.tsa.api import ExponentialSmoothing, SimpleExpSmoothing, Holt\n", "\n", "data = [446.6565, 454.4733, 455.663 , 423.6322, 456.2713, 440.5881, 425.3325, 485.1494, 506.0482, 526.792 , 514.2689, 494.211 ]\n", "index= pd.date_range(start='1996', end='2008', freq='A')\n", "oildata = pd.Series(data, index)\n", "\n", "data = [17.5534, 21.86 , 23.8866, 26.9293, 26.8885, 28.8314, 30.0751, 30.9535, 30.1857, 31.5797, 32.5776, 33.4774, 39.0216, 41.3864, 41.5966]\n", "index= pd.date_range(start='1990', end='2005', freq='A')\n", "air = pd.Series(data, index)\n", "\n", "data = [263.9177, 268.3072, 260.6626, 266.6394, 277.5158, 283.834 , 290.309 , 292.4742, 300.8307, 309.2867, 318.3311, 329.3724, 338.884 , 339.2441, 328.6006, 314.2554, 314.4597, 321.4138, 329.7893, 346.3852, 352.2979, 348.3705, 417.5629, 417.1236, 417.7495, 412.2339, 411.9468, 394.6971, 401.4993, 408.2705, 414.2428]\n", "index= pd.date_range(start='1970', end='2001', freq='A')\n", "livestock2 = pd.Series(data, index)\n", "\n", "data = [407.9979 , 403.4608, 413.8249, 428.105 , 445.3387, 452.9942, 455.7402]\n", "index= pd.date_range(start='2001', end='2008', freq='A')\n", "livestock3 = pd.Series(data, index)\n", "\n", "data = [41.7275, 24.0418, 32.3281, 37.3287, 46.2132, 29.3463, 36.4829, 42.9777, 48.9015, 31.1802, 37.7179, 40.4202, 51.2069, 31.8872, 40.9783, 43.7725, 55.5586, 33.8509, 42.0764, 45.6423, 59.7668, 35.1919, 44.3197, 47.9137]\n", "index= pd.date_range(start='2005', end='2010-Q4', freq='QS-OCT')\n", "aust = pd.Series(data, index)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple Exponential Smoothing\n", "Lets use Simple Exponential Smoothing to forecast the below oil data." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.189907Z", "start_time": "2017-12-07T12:39:15.022229Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\n" ] } ], "source": [ "ax=oildata.plot()\n", "ax.set_xlabel(\"Year\")\n", "ax.set_ylabel(\"Oil (millions of tonnes)\")\n", "plt.show()\n", "print(\"Figure 7.1: Oil production in Saudi Arabia from 1996 to 2007.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we run three variants of simple exponential smoothing:\n", "1. In ```fit1``` we do not use the auto optimization but instead choose to explicitly provide the model with the $\\alpha=0.2$ parameter\n", "2. In ```fit2``` as above we choose an $\\alpha=0.6$\n", "3. In ```fit3``` we allow statsmodels to automatically find an optimized $\\alpha$ value for us. This is the recommended approach." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:15.785068Z", "start_time": "2017-12-07T12:39:15.191930Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit1 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.2,optimized=False)\n", "fcast1 = fit1.forecast(3).rename(r'$\\alpha=0.2$')\n", "fit2 = SimpleExpSmoothing(oildata).fit(smoothing_level=0.6,optimized=False)\n", "fcast2 = fit2.forecast(3).rename(r'$\\alpha=0.6$')\n", "fit3 = SimpleExpSmoothing(oildata).fit()\n", "fcast3 = fit3.forecast(3).rename(r'$\\alpha=%s$'%fit3.model.params['smoothing_level'])\n", "\n", "ax = oildata.plot(marker='o', color='black', figsize=(12,8))\n", "fcast1.plot(marker='o', ax=ax, color='blue', legend=True)\n", "fit1.fittedvalues.plot(marker='o', ax=ax, color='blue')\n", "fcast2.plot(marker='o', ax=ax, color='red', legend=True)\n", "\n", "fit2.fittedvalues.plot(marker='o', ax=ax, color='red')\n", "fcast3.plot(marker='o', ax=ax, color='green', legend=True)\n", "fit3.fittedvalues.plot(marker='o', ax=ax, color='green')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Holt's Method\n", "\n", "Lets take a look at another example.\n", "This time we use air pollution data and the Holt's Method.\n", "We will fit three examples again.\n", "1. In ```fit1``` we again choose not to use the optimizer and provide explicit values for $\\alpha=0.8$ and $\\beta=0.2$\n", "2. In ```fit2``` we do the same as in ```fit1``` but choose to use an exponential model rather than a Holt's additive model.\n", "3. In ```fit3``` we used a damped versions of the Holt's additive model but allow the dampening parameter $\\phi$ to be optimized while fixing the values for $\\alpha=0.8$ and $\\beta=0.2$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.114361Z", "start_time": "2017-12-07T12:39:15.786542Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fit1 = Holt(air).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n", "fcast1 = fit1.forecast(5).rename(\"Holt's linear trend\")\n", "fit2 = Holt(air, exponential=True).fit(smoothing_level=0.8, smoothing_slope=0.2, optimized=False)\n", "fcast2 = fit2.forecast(5).rename(\"Exponential trend\")\n", "fit3 = Holt(air, damped=True).fit(smoothing_level=0.8, smoothing_slope=0.2)\n", "fcast3 = fit3.forecast(5).rename(\"Additive damped trend\")\n", "\n", "ax = air.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n", "fit1.fittedvalues.plot(ax=ax, color='blue')\n", "fcast1.plot(ax=ax, color='blue', marker=\"o\", legend=True)\n", "fit2.fittedvalues.plot(ax=ax, color='red')\n", "fcast2.plot(ax=ax, color='red', marker=\"o\", legend=True)\n", "fit3.fittedvalues.plot(ax=ax, color='green')\n", "fcast3.plot(ax=ax, color='green', marker=\"o\", legend=True)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Seasonally adjusted data\n", "Lets look at some seasonally adjusted livestock data. We fit five Holt's models.\n", "The below table allows us to compare results when we use exponential versus additive and damped versus non-damped.\n", " \n", "Note: ```fit4``` does not allow the parameter $\\phi$ to be optimized by providing a fixed value of $\\phi=0.98$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:16.605618Z", "start_time": "2017-12-07T12:39:16.116424Z" } }, "outputs": [ { "data": { "text/html": [ "
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SESHolt'sExponentialAdditiveMultiplicative
$\\alpha$1.0000000.9743060.9776330.9788470.974911
$\\beta$NaN0.0000000.0000000.0000000.000000
$\\phi$NaNNaNNaN0.9800000.981646
$l_0$263.917700258.882647260.341533257.357648258.951944
$b_0$NaN5.0107751.0137806.6445381.038144
SSE6761.3502186004.1382006104.1947466036.5550046081.995045
\n", "
" ], "text/plain": [ " SES Holt's Exponential Additive Multiplicative\n", "$\\alpha$ 1.000000 0.974306 0.977633 0.978847 0.974911\n", "$\\beta$ NaN 0.000000 0.000000 0.000000 0.000000\n", "$\\phi$ NaN NaN NaN 0.980000 0.981646\n", "$l_0$ 263.917700 258.882647 260.341533 257.357648 258.951944\n", "$b_0$ NaN 5.010775 1.013780 6.644538 1.038144\n", "SSE 6761.350218 6004.138200 6104.194746 6036.555004 6081.995045" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit1 = SimpleExpSmoothing(livestock2).fit()\n", "fit2 = Holt(livestock2).fit()\n", "fit3 = Holt(livestock2,exponential=True).fit()\n", "fit4 = Holt(livestock2,damped=True).fit(damping_slope=0.98)\n", "fit5 = Holt(livestock2,exponential=True,damped=True).fit()\n", "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'initial_level', 'initial_slope']\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$l_0$\",\"$b_0$\",\"SSE\"] ,columns=['SES', \"Holt's\",\"Exponential\", \"Additive\", \"Multiplicative\"])\n", "results[\"SES\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Holt's\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Exponential\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Additive\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "results[\"Multiplicative\"] = [fit5.params[p] for p in params] + [fit5.sse]\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Plots of Seasonally Adjusted Data\n", "The following plots allow us to evaluate the level and slope/trend components of the above table's fits." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:17.105928Z", "start_time": "2017-12-07T12:39:16.607306Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.\n" ] } ], "source": [ "for fit in [fit2,fit4]:\n", " pd.DataFrame(np.c_[fit.level,fit.slope]).rename(\n", " columns={0:'level',1:'slope'}).plot(subplots=True)\n", "plt.show()\n", "print('Figure 7.4: Level and slope components for Holt’s linear trend method and the additive damped trend method.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Comparison\n", "Here we plot a comparison Simple Exponential Smoothing and Holt's Methods for various additive, exponential and damped combinations. All of the models parameters will be optimized by statsmodels." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:18.038995Z", "start_time": "2017-12-07T12:39:17.108323Z" } }, "outputs": [ { "data": { "image/png": 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5+dGuXTsAfH19qVOnDtWqVaNLly5PXIbPMAzee+89ChcuzK+//grA22+/jZubG5UrV2bMmDGx55YsWZLhw4dTp04d3Nzc2Lt3Ly1btqRMmTLMnDkztpaGDRvSsWNHKlWqRL9+/YiOjk6wtvi+CxEREckkzmH1RP8KfAV8RoZNpRm07MQZjNXHbsvH4ERcd+XKlbz88suUK1eOAgUKsHfvXsBq/Th27BgHDx5kzpw5bN++HYDw8HD++9//8tNPP7FlyxYuXLjw2Jh169bF3d2diRMnsm/fPsqUKRP7WvPmzdm5cye3b98GYMmSJXTt2pUrV64wYcIE1q9fz969e3Fzc2Py5MmJ+ARQrVq12BYVLy8v/P39OXDgAJs2beLAgQOx5xUrVowdO3bQoEGD2HC/c+dORo8eHXvOrl27+Pzzzzl48CB///03y5cvj7e2xHwXIiIikoEdBGoDJ4CfgX72LSelMnWYtpdFixbRrVs3ALp168aiRYsA2Lx5M927dydLliwUKVKEpk2bAnD06FFKlSpF2bJlMQyDnj17Jul6WbNm5eWXX+ann34iMjKSNWvW0L59e3bu3Mnhw4epV68erq6uzJ8/n6CgoESN+eA280uXLqVatWpUrVqVv/7666FWE3d3dwCcnZ2pVasWuXPnplChQuTIkYMbN24AULNmTUqXLk2WLFno3r07W7dujbe2lH4XIiIiko75AvWAKGAL0Mq+5dhCpl5neqodrnn16lV+//13Dh06hGEYREVFYRgGn332GWC1UcQlvuOJ1bVrV2bMmEGBAgWoUaMGuXPnxjRNmjdvHhvmk+LPP/+kWbNmBAQEMGnSJHbv3k3+/Pnp3bs34eHhsedlz54dAAcHh9jf7z2PjIyM87MZhhFvbfv27UvxdyEiIiLp0FysWejKwBqgqH3LSYqbN+N/TTPTNrZs2TJ69epFUFAQgYGBnD59mlKlSrF161YaNmzI4sWLiYqK4vz582zcuBGAChUqEBAQwN9//w0Qb/jNnTs3ISEhcb7WuHFj9u7dy5w5c+jatSsAtWvXZtu2bZw8eRKA0NBQjh8/nmD9pmni7e3N+fPnefnll7l58ya5cuUib968XLx4MbaPOil27dpFQEAA0dHRLFmyhPr168dbW2K/CxEREckgooHhwH+Bl7BmpDNQkF61CipViv91hWkbW7RoER07dnzoWKdOnVi4cCEdO3akbNmyODs78/bbb9OoUSMAcuTIwezZs2nTpg3169enRIkScY7drVs3Jk6cSNWqVWPD5j1ZsmShbdu2/Prrr7FLyRUqVIhvv/2W7t274+LiQu3ateNdqm/IkCGxS+Pt3r2bjRs38tRTT/Hiiy9StWpVKleuTN++falXr16Sv5M6deowbNgwqlSpQqlSpejYsWO8tSX2uxAREZEMIBzoAXwMeAA/AXnsWlGinT0LnTpBhw5QoED85xkP9sZmNG5ubqa/v/9Dx44cOULFihXtVJE8ys/Pj0mTJvHzzz/bu5Rk078pERGRZLiKtfTdVuBTrOXvMkAnZ3Q0zJwJw4ZBRAR4esL//gdPPWXsMU3T7dHzM3XPtIiIiIjYwUmgNXAKa/3oVxM+Pb04dAg8PGDHDnjpJStUP7CAWpzU5iGpqnHjxhl6VlpERESSaDvW0nfXsHY0zABBOiwMRoyAqlXh+HH47jvw9X1ykAbNTIuIiIiIrSwFegHFgV+AF+xbTmL8/ju89RacPAm9esHnn0PBgol/v2amRURERCRlTKy+6K5ADWAH6T5IX70KffpAs2ZgmrBuHcyfn7QgDQrTIiIiIpISEcBbwDCgG7AOeNquFSXINGHBAqhQwfr54Ydw8KDVI50cavMQERERkeS5idUT/RvWWtLjSddTtf/8A/36WbPQtWrB7Nng4pKyMdPxx824DMPgtddei30eGRlJoUKFYtd/ToiTkxMAgYGBLFy4MPa4v78/AwcOTPC9gYGBVKlSJdHnx2fq1KmEhobGPm/dunXs1uApUbJkSZydnXF2dqZSpUqMHDmSO3fupHhcW/D09GTSpEn2LkNERCTjOAM0ANZj7W7oRbpNlhER8NlnUKUK7NwJ06bBtm0pD9KQbj9yxpYrVy4OHTpEWFgYAOvWreP5559P0hiPhmk3Nze8vb0T/f6knv+gR8P0L7/8Qr58+ZI11qM2btzIwYMH2bVrF//88w8eHh42GVdERETS0D6gFhAI/Aq8YddqErR7N9SoAUOHQvPmcPgwDBgAWbLYZnyF6VTSqlUr1qxZA1i7Inbv3j32tUdnQatUqUJgYOBD7x82bBhbtmzB1dWVKVOm4OfnFzuz7enpyWuvvUbTpk0pW7Ysc+bMeez6D55/69Yt+vTpg7OzMy4uLvz4448AvP3227i5uVG5cmXGjBkDgLe3N+fOnaNJkyY0adIEsGaUr1y5wtChQ/nyyy8f+hyff/45ABMnTqRGjRq4uLjEjpUQJycnZs6cycqVK7l27Rq3bt2iWbNmVKtWDWdnZ1atWgVYf1RUqFCBN998kypVqtCjRw/Wr19PvXr1KFu2LLt27XridxJfbV5eXpQvX56XXnqJY8eOPbFmERERwVqlowGQBWtDlub2LSc+N2/Cu+9a7RyXLsGPP8LKlVDUxluZZ+6e6cFYfznZkisw9cmndevWjXHjxtG2bVsOHDhA37592bJlS6Iv88knnzy0c6Cfn99Drx84cICdO3dy+/ZtqlatSps2beIda/z48eTNm5eDBw8CcP36dcAKkwUKFCAqKopmzZpx4MABBg4cyOTJk9m4cSMFH7mdtVu3bgwePJj+/fsDsHTpUtauXYuvry8nTpxg165dmKaJu7s7mzdvpmHDhgl+xjx58lCqVClOnDhB9erVWbFiBXny5OHKlSvUrl0bd3d3AE6ePMkPP/zA7NmzqVGjBgsXLmTr1q2sXr2ajz76iJUrV8b7nRw6dCjO2nLlysXixYv5888/iYyMpFq1alSvXj2R/3VERET+pb4CBmDloZ+AIvYtJy6mCcuXw8CBcP489O8PXl6QN2/qXC9zh2k7cnFxITAwkEWLFtG6dWubj9++fXty5sxJzpw5adKkCbt27cLV1TXOc9evX8/ixYtjn+fPnx+wwvDs2bOJjIzk/PnzHD58GJcEmoeqVq3KpUuXOHfuHJcvXyZ//vwUL14cb29vfH19qVq1KmDNhJ84ceKJYRrg3nb2pmkyfPhwNm/ejIODA2fPnuXixYsAlCpVCmdnZwAqV65Ms2bNMAwDZ2fnh2b04/pOtm7dGmdtISEhdOzYEUdHR4DY4C4iIiJxiAaGApOANsBiwMmuFcUpKMhq4fj5Z3jxRStU16qVutfM3GE6ETPIqcnd3Z0PPvgAPz8/rl69Gns8a9asREdHxz4PDw9P8tiGYST4/EGmaT72ekBAAJMmTWL37t3kz5+f3r17J6qOzp07s2zZMi5cuEC3bt1ix//www956623kvQZQkJCCAwMpFy5cvj4+HD58mX27NlDtmzZKFmyZGw92bNnj32Pg4ND7HMHBwciIyNjX4vrO4mvtqlTpyb4nYmIiEiMMOA14EfgHax8lc4SZEQEfPEF3OvmnDQJBg2CrGlQp3qmU1Hfvn0ZPXp07KzqPSVLlmTv3r0A7N27l4CAgMfemzt3bkJCQuIde9WqVYSHh3P16lX8/PyoUaNGvOe2aNGC6dOnxz6/fv06N2/eJFeuXOTNm5eLFy/y66+/Jura3bp1Y/HixSxbtozOnTsD0LJlS+bNm8etW7cAOHv2LJcuXYq3HrBmiPv370+HDh3Inz8/wcHBPPPMM2TLlo2NGzcSFBSU4PvjEtd3El9tDRs2ZMWKFYSFhRESEsJPP/2U5OuJiIhkepeBpsByYDIwjXQXpP/4w7rBcMgQaNrUusHw/fdtG6R3nN4R72vp7OvIXIoWLcqgQYMeO96pUye+++47XF1dqVGjBuXKlXvsHBcXF7JmzcqLL75I7969Y9sU7qlZsyZt2rTh1KlTjBo1iiJFijx2E+M9I0eO5J133qFKlSpkyZKFMWPG8Morr1C1alUqV65M6dKlqVevXuz5Hh4etGrViueee46NGzc+NFblypUJCQnh+eef57nnngOssH7kyBHq1KkDWDcXLliwgGeeeeaxWpo0aYJpmkRHR9OxY0dGjRoFQI8ePWjXrh1ubm64urpSoUKFBL7ZuMX1nRQpUiTO2qpVq0bXrl1xdXWlRIkSNGjQIMnXExERydSOAa2B81iz0h3tW86jgoNh+HD46isoUsS6wbBjR7Dl/3jedmobYzeNZd0/6+I9x7jXs5oRubm5mf7+/g8dO3LkCBUrVrRTRWnD09MTJycnPvjgA3uXkm6k5nfyb/g3JSIi8pDNQAcgG9aNhjXtW86DTBOWLbPaOC5etHqkx4+HPHlsd42tp7bi6efJhoANFHIsxJC6Q/i/+v+3xzRNt0fPVZuHiIiIiNy3EGu5u2eBnaSrIB0QAG3awKuvwnPPWS0eX3xhuyC9OWgzzb5rRoNvGnDw0kEmNZ9EwKAAhtQbEu971OaRAXl6etq7hHRH34mIiEgKmVi7GI4CGmP1See3Z0H3RUTAlCng6WlttjJlijUjbau+6E2Bmxi7aSwbAzfybK5n+bzF5/Rz64djNscnvldhWkREROTf7i7wFvAt1sodc4Gn7FeOj48PI0aM4NSpUzz7bAeyZfua06fz06EDeHtDsWK2uY5foB+efp5sCtpEYafCTGk5BY/qHokK0fdkyjAd11JwIsmRke8pEBERSZQbQCfgd8ATGA3YMUb5+Pjg4eFBaGg2YAYXLryFYZzjvfcOMHlyoxSPb5qmFaI3ebI5aDPPOT3H1JZT8ajuQc5sOZM8Xqbrmc6RIwdXr15VCJIUM02Tq1evkiNHDnuXIiIikjqCgHrAFqxZ6THYLUibpsnJkyd5992BhIZ2wFpOxAOYimlWZPny11M8/oZ/NtDo20Y0/a4pJ66ewPtlb/4e+DeDag9KVpCGTDgzXbRoUc6cOcPly5ftXYpkAjly5KBo0aL2LkNERMT2/IG2QDjwG9Ak7Uu4fv06v//+O+vWrcPX15eAgGzAUqAZ1t2PLwP7ADh16nayrmGaJhsCNuDp58m209t4PvfzTGs1jTervUmOrCmfMMt0YTpbtmyUKlXK3mWIiIiIpF+rgP8AzwAbARuuAPtgv3Px4sXx8vKiR48eAERERLBr1y58fX3x9fVl165dREdH4+RUiCJFppM1ayeiokIwzbeAOVh3RVqKFy+epDpM02T9P+vx3OTJ9tPbeT7380xvNZ03qr1hkxB9T6YL0yIiIiKSgC+A9wA3rDWkn7Xd0Pf7nUMBCAoK4s0332TdunXcuHGD33//nZCQEBwcHKhZsyYjR44kT54ufPllZY4fN3jtNahdewNDhiwgNPR+kHZ0dMTLyytRNZimie/fvozdNJYdZ3ZQNE9Rvmz9JX2r9iV71uy2+7AxFKZFRERE/g2igP8B3li7GS4AEr9oRaKMGDEiNkjfEx4ezvz58ylZsiTdu3enRYsWNG3alNDQ/AwebG3AUr48/P47NGkC0Im8ecPjnd2Oj2ma/Pb3b4zdNJadZ3ZSLE8xvmrzFX1c+6RKiL4n0+2AKCIiIiKPuI3V1rEaa1Z6IpDF9pdxcHCIcxEIwzCIiorCMAwiI2HGDBg5EiIjrZ8ffADZk5l3TdNk7cm1jN00lj/O/kHxvMUZXn84vV172zREG4YR5w6ImpkWERERycwuYN1o+CcwHXgndS5z584dcuXKxa1btx57rXjx4hiGwR9/QL9+sG8ftGoF06dD6dLJu55pmvx68lc8/TzZfW43JfKWYHbb2bzu+jpPZUm7RbJTfWk8wzCyGIbxp2EYP8c8/9YwjADDMPbFPFxjjhuGYXgbhnHSMIwDhmFUS+3aRERERDK1v4BawBGsmw5TKUgHBARQr149bt26RdZHtiV0dHRk+PCJvP021KkDly9brR1r1iQvSJumyZrja6g5tyZtFrbhcuhl5rSbw/F3j/Pf6v9N0yANaTMzPQjrP+GDu6YPMU1z2SPntQLKxjxqAV/F/BQRERGRpFqPtRlLLqx1pFNpmnL16tW8/rq1BrIF0oAAACAASURBVPTKlSu5detWbL9zsWLFad3ah1Gj6nH1KgweDGPHQu7cSb+OaZr8fPxnxm0eh/85f0rlK8XcdnPp9WIvsmXJZuNPlXipOjNtGEZRoA3WppRP0h74zrTsBPIZhvFcatYnIiIikil9gzVNWRxrueZUCNIREREMGTKE9u3bU6ZMGfbu3Uv79u3p0aMHgYGBHD4cTZkygcycWY9SpcDfHyZPTnqQNk2T1cdW4zbHDffF7lwLu8Y893kcG3CMN6q9YdcgDanf5jEV+D8g+pHjXjGtHFMMw7jXGf48cPqBc87EHHuIYRgehmH4G4bhr41ZRERERB5gAqOAvlibsGzFCtQ2dubMGZo0acKkSZPo378/27Zti93nIzTUuqnQxQX+/BNmzoTt28HVNWnXME2TVUdXUX12ddovbk9weDDftP+Go+8cpU/VPnYP0fekWpg2DKMtcMk0zT2PvPQhUAGoARQAht57SxzDPHY7qGmas03TdDNN061QoUK2LFlEREQk47oD9AQmAG8Ca4C8tr+Mr68vVatWZf/+/SxatIgZM2aQPWYpjtWroVIl8PKCbt3g2DF46y1wSELijDajWXFkBdVmV6PDkg6E3A3h2/bfcnTAUXq79k43Ifqe1JyZrge4G4YRCCwGmhqGscA0zfMxrRx3sP4nRM2Y888AxR54f1HgXCrWJyIiIpI5XAWaAwsBL2A2YOPMGRUVxZgxY3j55ZcpXLgw/v7+dOvWDYCAAGjXDtq3Bycn2LQJvvsOnnkm8eNHm9EsP7KcarOq8crSV7h99zbzO8znyDtHeN31dbI6pM9F6FKtKtM0P8SahcYwjMbAB6Zp9jQM4znTNM8bhmEAHYBDMW9ZDQwwDGMx1o2HwaZpnk+t+kREREQyhZNAayAIWAR0s/0lLl68SI8ePdiwYQO9e/dmxowZODo6cucOTJxozURnzQqTJsHAgZAtCUH+3kz0uM3jOHDxAOWeLsf3Hb+nW5Vu6TZAP8geFfoYhlEIq61jH9Av5vgvWP8UTgKhQB871CYiIiKScWzHWsIhGtgA1Lf9JTZv3ky3bt24fv068+bNo08fK6L5+sKAAXDiBHTpYt1cWLRo4seNNqP58fCPjNs8jkOXDlH+6fIs6LiAblW6kcUhFXaUSSVpEqZN0/QD/GJ+bxrPOSaptvqhiIiISCbzA/AaVpPsL1iLC6eQj4/PA8vaFaNOnTosW7aMMmXKsHbtWlxcXDhzBv73P/jhByhbFn77DVq0SPw1os1olh1exrhN4/jr8l9UKFiBha8s5NXKr2aoEH1P+p87FxEREZH7TOAzYBjWHWorgYIpH9bHxwcPDw9CQ0MBOHXqFKdOnaJWrVr4+vqSM2ceJk0CT0+IioLx42HIkMRvAx4VHcUPh39g/ObxHL58mIoFK7Ko0yK6VOqSIUP0PQrTIiIiIhlFBNb/x5+D1Rv9DZDDNkOPGDEiNkg/6Pz58+zbl4f+/eGvv6BtW/D2hpiV8J4oKjqKpX8tZfzm8Ry5coRKhSqxuNNiOlfqnKFD9D0K0yIiIiIZwU3gVeA3YDgwHpuuy3bq1Kk4jj7DqVPjadQISpSAVavA3T1x40VFR7HkryWM3zyeo1eOUrlQZZZ0XkLnSp1xMFJ7q5O0ozAtIiIikt6dxtpT+jDWvtJv2P4SxYsXJygoKOaZA/A21qLVjgwfDiNGgKPjk8eJjI5k8aHFTNg8gWNXj1HlmSr80OUHXqn4SqYK0fdkvk8kIiIikpnsxVo0OAj4lVQJ0gBDhgyJ+a0msAuYjoPDn3z22Vq8vJ4cpCOjI/l+//dUmlGJ11a8xlNZnmJZl2Xs77c/081GP0gz0yIiIiLp1RqgK9ae0VsB59S71JYtRzGMuZjmG8A5ChYcwJQpdejZs0eC74uMjmThwYWM3zyek9dO8uKzL/Ljqz/SoUKHDB+gr2N11axJ4ByFaREREZH0aAYwEHAFfgKKpM5loqJg2LAAliwZi4NDXt5/H0aPLkLu3NMTfF9kdCQLDizAa4sXJ6+dxLWwKyu6rsC9vHuGDdEmVifNGuBnrGW8o4CnE3iPwrSIiIhIehIFDAGmAO2wtgh3Sp1L7dgBAwaY7N1biqee2sa2ba64ueVK8D0RUREsOLCACVsm8M/1f6hauCoru67Evbw71gbXGUsY1mYoP2OF6Htd465Yqw+2wWp8iS80K0yLiIiIpBehQE9gBfAuVqBOhdXjLl2CYcPgm28gX75QoC9z57bDza1evO+JiIrgu/3f4bXFi4AbAVR7rhqruq2iXbl2GS5En8YKzmuwNo4MAxyBl7AWSmkNJHYzR4VpERERkfTgIuAO7AamAoNsf4moKJg5E0aOhFu3YODAOyxa5EKdOs/G2xsdERXB/P3z8driReCNQKo/Vx3vVt60Kdsmw4ToKGAn9wP0gZjjpbDu52wLNCJ5S3YrTIuIiIjY22GsfoKLWLPS7W1/ie3b4Z13YN8+aNYMpk2Dr78ewZUrAfz669LHgvHdqLvM32eF6KDgIGoUqcH0VtNpXbZ1hgjRN7BuHvwJWAtcxZrkrw9MxPq6KwAp/SQK0yIiIiL29DvwCta06Caghm2Hv3gRhg6F+fOhaFFYuhQ6d4Zjx47yxRdf8MYbb1C9evXY8+9G3eXbfd/itcWLU8GnqPl8Tb5s8yWtXmiV7kP0Sazw/BOwBYjE2mm9TcyjBZDPxtdUmBYRERGxl/nAm0B5rP6DErYbOjISvvoKRo2C0FCrR3rECHByAtM0GTx4MLly5cLLywuAO5F3+GbfN3y89WNOBZ+i1vO1mNV2Fi3LtEy3IToSa8WNewH6WMzxKsAHWPdv1iJV2s5jKUyLiIiIpDUTGIO1JfhLwA/YdMp061arpePAAWje3GrpKF/+/us///wzv/32G1OmTCFvgbx8tfsrPt76MadvnqZ20drpOkTfwGrb+Bn4BWst6GxAY+AdrP7nUmlYj8K0iIiISFq6A/TFWvKuLzATKw3awIULVkvHd99BsWKwbBm88go8mInv3LnDe++9R/nK5XGo5cAL017gzM0z1C1Wl7nuc2leunm6C9HxtW+4Y4XnFkAeO9WmMC0iIiKSVq4CHbESoRfwISm/Aw6IiLBmn8eOhfBwGD7ceuSKY8nozyZ/xt9P/03BDgUZ5DuIesXq8U37b2hWqlm6CdFRWO0bq7FmoI/GHE/L9o3EUpgWERERSQsnse6CC8Sale5um2E3bIB334UjR6BVK5g6FcqVe/y88MhwJv4+kTFXx0BrqFC4Ap6NPGlaqmm6CNG3AF/uB+ir3G/f6E/at28klsK0iIiISGrbjrXcXTTWLiH1Uz5kUBC8/z78+COULg2rV0Pbtg+3dACERYQxe89sPt32Kedvnce4bvB9x+/pUbeH3UP0OazWjdVYX8sdID/W3xzuQEvs176RWArTIiIiIqlpKdALKIZ1x1zZlA0XFgYTJ8Inn1jPJ0ywQnWOR3YcCYsIY9aeWXy67VMu3LqAaz5Xzn97nuE9htOzXs+UFZFMJnAIWIUVoHfHHC+NNfvsDtTDZi3kaUJhWkRERCQ1mMCnWH3R9YCVWHfNJXc405p9HjwYAgOhSxeYNAmKF3/4vNCIUGb5z+Kz7Z9x4dYFmpRsgk9HH4Z0GcLzEc/z4YcfJr+IZIjAahG/F6ADY47Xwmobbw9Uwiat43ahMC0iIiJiaxFYU61zgW7ANyRvr+oYx47BoEHw229QubLVJ9206cPn3L57m5n+M5m4fSIXb1+kaammLOm8hIYlGjJ37lz27t3LokWLyBXXXYk2Foy1fN0qrMn4YKyP/xIwHKv/+blUryJtKEyLiIiI2FIw8CrW3XTDsdaSdkjeUCEhMH68dVOho6P1s39/yPZAH8Ttu7f5yv8rJm6fyKXbl2hWqhk/NPqBBiUaAHDjxg0+/PBDGjRoQNeuXVP22RJwDmvmeSXWpo4RQCGszR3dgeZA6sf4tKcwLSIiImIrp7DunjsKfI21jnQymCb4+MD//R+cPw99+8LHH8Mzz9w/5/bd23y5+0smbp/I5dDLNC/dnDGNxlCveL2HxvL09OTatWt4e3vb/IbDo1jheSXwR8yxMsAgrPaNOqSP5etSk8K0iIiIiC3swepfCAV+xeppSIY//7SWutu2DWrUgBUroFat+6/funuLGbtmMGnHJK6EXqFFmRaMaTSGusXqPjbW4cOHmT59Oh4eHri6uiavoAdEA7u4H6Dvbd9dA5gAdCBj9z8nh8K0iIiISEr9hNUbXRBYD1RO+hBXr8KoUTBrFjz9NMydC336gENMi0jInRBm7J7BpO2TuBp2lZZlWjKm0RjqFKsT53imaTJw4EBy587N+PHjk/nBrOXqNmKF51XABawA2QQYiNXCUTTZo2d8CtMiIiIiKTENGAxUwwrVhZP29shImD3bCtLBwTBggLWTYb581ushd0KYvms6n+/4nKthV2n1QitGNxpN7aK1Exx35cqVbNiwgWnTplGwYNKWEQnGmlxfiXUDYQjgBLTCmn1uDeRL2sfMtAzTNO1dQ7K5ubmZ/v7+9i5DRERE/o2igP8B3lgNwj4k+Q47Pz8YOBAOHoQmTeCLL8DZ2Xrt5p2bsSH6Wtg1WpdtzZhGY6j5fM0njhsWFkalSpVwcnLizz//JGvWJ8+fXsSaeV6BtYFKBPBMzEfrADQlRQuSZHiGYewxTdPt0eOamRYRERFJqtvAf7CWrxgMTCJJd9oFBcEHH8CyZVCihPXzlVes3Qtv3rmJ9x/eTN4xmevh12lbri2jG46mxvM1Ej3+559/TmBgIBs2bEgwSAdiheflwDaspbHv3UDYEWst6Mx+A2FKKUyLiIiIJMV5rBsN92G1eAxI/FtDQ+HTT+Gzz6zgPG6cFapz5oTg8GC8//Bmys4pXA+/Trty7RjdaDRuRR6bDE3Q6dOn+eijj+jcuTNNH1mM2gQOcz9A/xlz/EVgDNYydlX4d91AmFIK0yIiIiKJdRBr6btrWLPSbRL3NtOEpUthyBA4fRq6dbMCdbFicCP8BhM3WSH6RvgN3Mu7M7rhaKoXqZ6k0nx8fBgxYgRBQUEA1K9fH7BW4PDHCs8rgOMx59fFmlDviLWdtySPwrSIiIhIYvgCnYHcWPtjV03c2/bts3Yv3LwZXF2t9aMbNLBCtKffVKbunErwnWA6VOjAqIajqPZctSSX5uPjg4eHB6GhodaBLFkYunYta15+mcPly3OW+ytwvIfVB51ZdiC0N4VpERERkSeZA7yNteTdGhK1FtyVKzByJMyZAwUKWEvevfEG3Lx7nTEbp/LFH18QfCeYjhU6MrrRaFwLJ38d6BEjRhAaGQlt2ljN1+7u3ClYkPVhYbQHPsbqTMmf7CtIfBSmRUREROITjbUl+KfAy8BSrJnpBERGwldfwejR1nbg774LY8aAmeMaYzdbIfrmnZu8UvEVRjcczYuFX0x2eff2hwn66CNo2xby5IEbN+Cnn2DFCkxfX1bcupXs8eXJFKZFRERE4hIG9AKWAf2wbjZ8QnLasMFq6fjrL3jpJZg6FZ4rfY3Pd0zG+w9vQu6G0KliJ0Y3Go3Lsy7JKusm1uT4j1hBOhQwWrTAXLIEfvwRfv8dIiIAKFGiRLKuIYmnMC0iIiLyqEtYjcV/YN2l9z8SXOIiIADef9/a+rtUKetn/eZXmbJzMtNWTyPkbghdKnVhVMNROD/rnORyrmPd7/gjVuv2Haye595A8+BgeleowM1r13hw/xBHR0e8vLySfC1JGgd7FyAiIiKSrhwFamMtffcD8D7xBumQEBgxAipWhN9+Ay8v2Ox/hV25h1PKuyQfb/2YVmVbcfDtgyztsjRJQfoyVqv2y1ibp/QG9gP9ga3AGWC6afJ9376E3rzJhAkTKFGiBIZhUKJECWbPnk2PHj2S+y1IIj1xZtowDDegAVAE6394HALWm6Z5LZVrExEREUlbflhrxT0V83utuE+LjobvvoMPP4QLF6BnTxgy+ioLgyZSYeZ0QiNCebXyq4xqOIrKz1RO9OXPYS1ftwzYjNWy/QJWnu8EuPFwrv/m229Zvnw5n332GUOGDGH48OFJ/MCSUvGGacMwegMDgQBgD3AMaxfJ+sBQwzAOAaNM0zyVBnWKiIiIpK7vgDex0usaoFTcp23fbvVF+/tDrVowb+F1/CI/oe4PMwiNCKVrla6MajiKSoUqJeqyZ7DC8zJgO9bGKpWAEVgB2oW4J8b//vtvBg4cSJMmTXj//feT9FHFdhKamc4F1DNNMyyuFw3DcAXKAgrTIiIiknGZwNiYRxOsxuQ41pA7fRqGDoVFi6BIEZgxN5h/nvei844ZhEWE0a1KN0Y1HEXFQhWfeMnTWOH5B2BHzLEXgXFYAfpJI0RGRtKzZ0+yZs3K/PnzcXBQ5669xBumTdOckdAbTdPcZ/tyRERERNLQHazZ6AVYTcmzsFo8HhAaau1W+Nln1k6G7w29RVTdjxhy6AvCz4bTvUp3RjYcSYWCFRK81CnuB+idMcdcAS+gC9YMZWJ5eXmxc+dOFi9eTLFixZLwTrG1xPRMfwZMwOqXXov1h9Ng0zQXpHJtIiIiIqnrB6wgPQFrPekH+ilM05qFHjoUzpyB9p3CKOT+OTNPf8SdfXf4j/N/GNlgJOULlo93+CDuB+g/Yo5VBT7CCtAvJKPknTt3Mn78eHr27EnXrl2TMYLYkvHgEipxnmAY+0zTdDUMoyPQAWsXyo2maSZ/hXEbcXNzM/39/e1dhoiIiGRUJrCLx2403L3b6ovesQOcXSOo0GMmP935P+5G3aWnS09GNBhBuafLxTlkIPcD9K6YY9WwwnNnkheg7wkJCaFq1apERkayf/9+8ubNm4LRJCkMw9hjmqbbo8cTs850tpifrYFFpmleM4wEFloUERERySgMHgrS585ZK3R89x0UeiaKlwYvZUuBNzgcej9El3368YaMAO4H6N0xx6oDn2AF6DI2Knfw4MEEBATg5+enIJ1OJCZM/2QYxlGsNo/+hmEUAsJTtywRERGRtBMWBpMnw8cfQ0SESfUu6zlYvjsbs92gl0svhjcYzgsFHp5TPoUVnpdwP0C7Ye083hkobeMaly9fzrx58xg+fDgNGjSw8eiSXE9s8wAwDCM/cNM0zSjDMByBPKZpXkj16p5AbR4iIiKSEqYJy5bBkCEQFASl6+znTO1uROU7wesvvs7wBsMpU+D+vPJZrBnoJdxfhaM68CpWG0c8q+ml2Llz53B2dqZ06dJs376dbNmyPflNYlMpafMAa4WWkoZhPHj+dzapTERERMROFiyAXr3g6VJnyNqnL6dKbYwJ0Wsond+aW77I/QC9FavN+kVSdhNhUkRHR9O7d2/Cw8NZsGCBgnQ688RFCQ3D+B5rV/r6QI2Yx2OpXEREJLPx8fGhZMmSODg4ULJkSXx8fOxdkthYjhdXk+WVN7jxehn6dCzJ8QHHmes+l9z5SzMLaIq1BfQA4BrWUtRHsXYa/5DUD9IA06ZNY926dUyePJny5eNfOUTsIzErfLthbd7S3zTNd2MeA1O7MBER+feyRYhN6Rg+Pj54eHgQFBSEaZoEBQXh4eGhQJ3JNC5TB4++2Tk56BiftJvN7/lL0QJ4DuiHtb33SOBQzGMUkJZx9uDBgwwdOpR27drh4eGRhleWxErM0ng/AANN0zyfNiUlnnqmRUQyn3shNjQ0NPaYo6Mjs2fPpkePHqk2xp07d7hx4wbBwcHcuHGDdu3acenSpcfOK1GiBIGBgUn7UJJuBQMrsVo41gGRWCtvdI15OBP3Vt5pITw8nJo1a3Lx4kUOHjzIM888Y6dKBOLvmU5MmN6ItUHPLqx9ggAwTdPd1kUmlcK0iEjmU7JkSYKCguJ8LX/+/OTKlYtcuXLh5OQU+/ujz2fNmkVwcPBj73dycqJt27bcuHHjsUd4eOIWqjIMg+jo6BR9Rkk/lmH1PZfEuomwK9amKulhEeD333+fyZMns2bNGlq3bm3vcv71UnIDoqftyxEREYnbqVOn4n3tP//5D7dv337ocenSpceO3blzJ87337p1iz179pAvXz7y5ctHsWLFYn/Pmzdv7O/58uXjjTfe4OLFi4+NkS1bNrZt20a9evVs9pnFftpg7UxYg/QRoO9Zv349kydPpn///grS6Vxil8Z7FuvfGcAu0zQf//9edqCZaRGRzCe+memktFeUKFEizlCelDHiahV56qmnyJkzJ8HBwXTs2JGPP/5YN4SJzV29ehUXFxfy5MnDnj17cHR0tHdJQvwz04lZzeNVrBaPLlj/B+QPwzA6275EERER8PLyInv27A8dc3R0xMvLK9FjfPTRR48FkKSO0aNHD2bPnk2JEiUwDIMSJUowb948zp49y/jx41m3bh2VK1emf//+cc5gS+rKrCutmKbJW2+9xeXLl/Hx8VGQzghM00zwAewHnnngeSFg/5PelxaP6tWrmyIikvn06dPHBEzDMMwSJUqYCxYsSPIYCxYsMEuUKJGiMRJy8eJF85133jGzZs1qOjk5mWPHjjVv3bpl02tI3BYsWGA6OjqaWEs+m4Dp6Oho8//Gaenev9d7n6dr1672LkkeAfibceTRxNyAeNA0TecHnjvEhGnnBN6WJtTmISKSOX3wwQfMmDGD27dv4+CQmFVc7ef48eMMHz6cH3/8kcKFCzNu3Dj69OlD1qyJ3RdNksoWrUCxBg+GfftsU1gyXbx4kWPHjz90Y6uDgwPly5Xj2WeftWNl8iBj06bktXkAaw3D+M0wjN6GYfQG1gC/2LpAERGRe44fP84LL7yQ7oM0QLly5Vi2bBnbtm2jdOnSeHh44OLiwk8//cSTJqwkeeK7STWhm1fTs4CAgMdWiImOjiYgIMBOFUlSPPHPZtM0hxiG0Qmoh3Wj62zTNFekemUiIvKvdeLECSpWrGjvMpKkbt26bN26lZUrVzJs2DDc3d1p1KgRzZo14+uvv+bUqVMUL14cLy+vRK+X/SAfHx9GjBiR4nEyMtM0WbRoEYZhxPmHSvHixZM+6NSpNqgsZeo6OBDXn13G3btE+/mldTkSHyPu9V4S9f+gTNP8EfjRlvWIiIjEJSoqir///pv27dvbu5QkMwyDjh070rZtW+bOncvQoUPZtGlT7Ov3dlEEkhSEH11ZJLnjZGQHDhxgwIABbNmyhVKlSnH+/PmH1gZP6g2m6cXdu3fJkSMHYWFhj72WrD8OJM3F2zNtGMZW0zTrG4YRAg/9wWQApmmaedKiwISoZ1pEJPP5559/KFOmDHPnzuWNN96wdzkpUrx4cU6fPv3YccMwyJcvHzly5CB79uxkz579od8ffb5q1Spu37792Dj/ht0Yr1+/zujRo/nyyy/Jnz8/n3zyCX379mXRokUZfqY+IiKCrl27smLFCp566inu3r0b+1pSd/2U1JfkTVtM06wf8zN3ahYmIiLyoBMnTgBQtmxZO1eScmfOnInzuGma9OjRgzt37sQ+wsPDY3+/ffs2165de+h5XDJqj3BiREdH88033zBs2DCuXbvG22+/zbhx4yhQoABgzchn5KAZGRnJa6+9xooVK/D29qZAgQIZ/o+Df6t4w7RhGAUSeqNpmtdsX46IiPzbZaYwXbx48XhXnZg2bVqix4lv9YrM2gawa9cuBgwYwO7du6lXrx7Tp0/H1dXV3mXZTFRUFH379mXJkiVMnDiRd999F/j3tOxkNgndJr0H8I/5+ehDvRUiIpIqTpw4gZOTE4ULF7Z3KSnm5eWV4s1jbDlOenf58mXefPNNatWqxenTp/n+++/ZsmVLpgrS0dHRvPXWW3z//fdMmDCBDz74wN4lSQrFG6ZN0yxlmmbpmJ+PPkqnZZEiIvLvcfz4ccqWLYsRz53zGUlcuygmpw/20XEAunfvnmFnMh/dvfD7779n+vTplCtXjvnz5/PBBx9w7NgxevbsmSn+HdxjmiYDBgzg66+/ZuTIkYwYMcLeJYkNJHQDYrWE3mia5t5UqSgJdAOiiEjm88ILL1C9enWWLFli71LSJdM0ady4MYcPH+bEiRPky5fP3iUlyaMrkwCxS9299NJLeHt7p9myiGm53KBpmvzvf/9j6tSpDBkyhE8//TRT/aHwb5DkGxCBzxN4zQSaprgqERGRB0RERBAYGEi3bt3sXUq6ZRgGX3zxBdWrV8fT05Op6WCd5KQYMWLEQ0EarKBZsGBBfH190yxgpuVyg6ZpMnz4cKZOncqgQYMUpDOZJ24nnp5pZlpEJHM5fvw45cuXZ/78+fTq1cve5aRrb7/9NnPmzOHAgQNUqlTJ3uUkmoODQ5wbrhiG8dgugKnJpluSP4Gnpydjx46lX79+fPnllwrSGVR8M9Px9kwbhtE05ucrcT1Ss1gREfl3On78OJA5VvJIbePHjydPnjwMGjQow2xbfuHCBXLkyBHna2m9Mkl8ywoGBQVx/vx5m13n448/ZuzYsfTt25cZM2YoSGdC/9/encdHVd3/H399wh5kFxWQTETwV6GiKIJLVaqsimALVCW4sMVKFSh+RSUWcUnF3aIoBhWjxAUVFRW1IBWxChgqCi4kbAkUFCq7Yc/5/ZELBpLAJJmZO5m8n4/HfWTm3Jk77zkZxw83555zpNk8LvJ+Xl7M1jPMuUREpBKKpWnxwu3YY4/lnnvuYfbs2bzzzjt+xzmiA8uAt2nThr1791KtWrVD9vsxM8mRivfExEQGDhzI0qVLy/Uajz76KGPGjGHAgAGkpaURF3eksksqqiPN5nGX93NgMdugyEUUEZHK4sAFdY0aNfI7SoXw5z//md/+9reMGjXqkKW1o8mGDRvo27cv/fv3p1WrVixZsoQpU6aUe4aT8ippusFHHnmEoUOHMm3aNE477TS6d+/OrFmzSn32/8knn+SWW26hX79+TJkyhSpVqoQyvkQT59wRN6A+MBx4FJhwF6Qp0wAAIABJREFUYDva8yKxnXXWWU5ERGJH586dXYcOHfyOUaHMmTPHAe6+++7zO0oR06ZNc8cee6yrXr26e+CBB9y+ffv8jnSIqVOnukAg4MzMBQIBN3Xq1IP7fv75Z5eamupOOOEEB7i2bdu69PR0t3v37qMeNy0tzQGud+/ebs+ePeF8CxJBQKYrph496gWIZvY5MB9YAhy8MsA5lx6G2r5UdAGiiEhsCQQCXHDBBUydOtXvKBVKv379mDlzJsuWLePEE0/0Ow7/+9//uOmmm3jttddo37496enpFeoiycJ2797Nyy+/zCOPPMK3335L06ZNufnmm7nhhhto0KBBkcenp6czcOBAevTowfTp06lRo4YPqSUcSn0BYiE1nXOjnHNTnHPpB7YwZBQRkUps165drFmzRuOly+Dhhx8mPz+f0aNH+x2Ft956izZt2jB9+nRSU1P54osvKmwhDVCjRg0GDhzIkiVL+PDDD2ndujV33HEHzZs3Z8SIEaxatergIjRmxvXXX0/r1q158803VUhXEsEU0y+Z2VAza2JmDQ9sYU8mIiKVyooVK3DOccopp/gdpcIJBALcdtttvPLKK8ybN8+XDJs2bWLAgAH88Y9/pFmzZmRmZjJmzBiqVj3SkhYVh5nRrVs3Zs2axeLFi+nTpw9PPfUULVq04Lrrrjtkmr2VK1fy5ptv+phWIimYYnoP8BDwBbDI2zS2QkREQkrT4pXP6NGjad68OTfffDP79++P6Gu/9957tGnThtdee427776bBQsW0LZt24hmiKTTTz+d9PR0Vq9eTd26dYv0986dO7VUeCUSTDE9CmjpnEt0zp3kbS3CHUxERCoXTYtXPgdmovj666959tlnw/Y6B4Y0xMXF0bx5cy688EIuv/xyGjduzMKFCxk7dmyRqe9iVbNmzdi+fXux+0qax1piTzDF9LdA3lEfJSIiUg7Z2dk0btyYevXq+R2lwurbty8XXXQRKSkpbN68OeTHP7AEd05ODs451q5dy7x587jiiivIzMykXbt2IX/NaFfSfNWRXoRG/BNMMb0fWGxmz5jZhANbsC9gZlXM7Csze8+7f5KZLTCzbDN7zcyqe+01vPvLvf2JZXlDIiJSMWVnZ2u8dDmZGRMmTGDz5s3cddddIT9+SkoKeXlFz6999dVXVK9ePeSvVxGUNF91pBehEf8EU0y/DaQCn/PrmOlFpXiNEcD3he4/ADzmnGsFbAYGe+2Dgc3OuZbAY97jRESkksjKytIQjxBo27Ytf/7zn3nqqafKvYLf4UoaulCZhzQkJSWRlpbm+yI04p+jFtOFp8Mr7dR4ZnYicBnwrHffgIuBN7yHpANXeLd7e/fx9l9iWsBeRKRS2LFjB+vXr1cxHSL33HMP9erVY8SIEaVeua84O3bsYNiwYSUeq7IPaUhKSmL16tXk5+ezevVqFdKVTInFtJm9a2aXm1mRqwjMrIWZ3WNmR1tW/HFgNL8u9tII2OKc2+fdXws08243A9YAePu3eo8XEZEYt3z5ckAXH4ZKo0aNuPfee5kzZw7Tp08v17E+/fRTTj/9dCZNmkT37t2pVavWIfs1pEEquyOdmR4KXAD8YGZfmtlMM5tjZquAZ4BFzrnnS3qymfUENjjnCg8JKe5MswtiX+HjJptZppllbty48QjxRUSkojgwk4fGTIdOcnIybdu25ZZbbmHnzp2lfv7OnTv561//SqdOnQCYO3cuH3zwAZMnT9aQBpFCSpxJ3Tn3IwVnlUd7FwM2AXYCWc65YGb3OB/oZWaXAjWBuhScqa5vZlW9s88nAuu8x68FmgNrzawqUA/YVEyuNCANCpYTDyKHiIhEuQNzTLds2dLnJLGjatWqTJgwgU6dOvHQQw8xduzYoJ87f/58rrvuOrKyshg2bBgPPPAAxxxzDFAwpEHFs8ivgrkAEefcaufcF865xUEW0jjn7nDOneicSwSuAuY455KAfwF9vYddB7zj3Z7h3cfbP8eFYqCXiIhEvezsbJo2bUrt2rX9jhJTLrroIv70pz8xfvz4oC4S3LVrF7fddhvnn38+u3btYvbs2UycOPFgIS0iRQVVTIfYbcAoM1tOwZjo57z254BGXvso4HYfsomIiA80LV74PPTQQwDceuutR3zcokWLOOuss3jwwQcZNGgQS5Ys4ZJLLolERJEKLSLFtHPuE+dcT+/2SudcB+dcS+dcP+fcbq99l3e/pbd/ZSSyiYiI/7Kzs3XxYZgkJCRw++23M23aNObOnVtk/549exg7diwdO3Zky5YtzJw5k8mTJ1O3bl0f0opUPH6cmRYRETloy5YtbNy4UcV0GN16660EAgGGDx/Ovn37DrZ/8803dOzYkXvvvZekpCSWLl1Kjx49fEwqUvGUeAHiAWbWCrgfaE3BhYQAOOdahDGXiIhUEgdm8lAxHT61atXikUceoW/fvhx//PFs3ryZunXrsn37dho3bszbb79N7969/Y4pUiEFc2Z6CvA0sA/4PfAi8FI4Q4mISOWhafEiY9euXcTFxbFp0yacc2zduhUzY9y4cSqkRcohmGK6lnPuY8CccznOuXEUrGIoIiJSbllZWZgZLVroD57hlJKSQn5+/iFt+/fvZ/z48T4lEokNRx3mAewyszgg28xuAv4LHBfeWCIiUllkZ2eTkJBAzZo1j/5gKbOSpsYLZso8ESlZMGemRwLxwHDgLOAafp0PWkREpFw0k0dkJCQklKpdRIJz1GLaOfelc26Hc26tc26gc+6Pzrn5kQgnIiKxzTmnOaYjJDU1lfj4+EPa4uPjSU1N9SmRSGwocZiHmT3unBtpZu8CRVYidM71CmsyERGJef/73//YsmWLzkxHwIElwFNSUsjNzSUhIYHU1FQtDS5STkcaM31gxo6HIxFEREQqH02LF1lJSUkqnkVCrMRi2jm3yPt5cLkkM2sANHfOfROBbCIiEuNUTItIRXfUMdNm9omZ1TWzhsDXwBQzezT80UREJNZlZ2dTpUoVTjrpJL+jiIiUSTCzedRzzm0D/ghMcc6dBXQObywREakMsrKyOOmkk6hWrZrfUUREyiSYYrqqmTUB/gS8F+Y8IiJSiWhaPBGp6IIppu8BPgKWO+e+NLMWQHZ4Y4mISKzTtHgiEguOugKic+514PVC91eamdYeFRGRclm/fj2//PKLzkyLSIUWzHLiAJhZa+Aq4GpgK9A+XKFERCT2aSYPEYkFRyymzSxAQfF8NbAPCADtnXOrwx9NRERimYppEYkFJY6ZNrPPgZlANaCvN4vHdhXSIiISCtnZ2VSvXp2EhAS/o4iIlNmRLkDcCNQBjgcae21FlhUXEREpi6ysLE4++WSqVKnidxQRkTIrsZh2zvUGTgP+A9xtZquABmbWIVLhREQkdmlaPBGJBUecGs85t9U597xzrgvQERgLPG5mayKSTkREYlJ+fj4rVqxQMS0iFV4w80wD4Jzb4Jx7wjl3HvC7MGYSEZEYt3btWnbt2qU5pkWkwgu6mC7MOZcT6iAiIlJ5ZGVlAZrJQ0QqvjIV0yIiIuWhafFEJFaomBYRkYjLzs4mPj6epk2b+h1FRKRcjroCopk1BoYCiYUf75wbFL5YIiISy7Kzs2nZsiVxcTqnIyIVWzDLib8DzANmA/vDG0dERCqDrKwsTjvtNL9jiIiUWzDFdLxz7rawJxERkUph3759rFy5kj/+8Y9+RxERKbdg/r72npldGvYkIiJSKeTk5LBv3z5NiyciMSGYYnoEBQX1TjPbZmbbzWxbuIOJiEhs0rR4IhJLjjrMwzlXJxJBRESkctC0eCISS0osps3sN865H8zszOL2O+f+E75YIiISq7Kzs6lTpw7HHXec31FERMrtSGemRwHJwCPF7HPAxWFJJCIiMS07O5tTTjkFM/M7iohIuZVYTDvnkr2fv49cHBERiXVZWVl07NjR7xgiIiGh2fJFRCRi9uzZQ05OjsZLi0jMUDEtIiIRs3LlSvLz81VMi0jMUDEtIiIRc2AmD80xLSKxIpgVEDGzPwK/o+DCw8+cc2+FNZWIiMQkzTEtIrHmqGemzewp4M/AEmApcIOZTQx3MBERiT3Z2dk0bNiQhg0b+h1FRCQkgjkzfRHwW+ecAzCzdAoKaxERkVI5MC2eiEisCGbM9DIgodD95sA34YkjIiKxLDs7W0M8RCSmBHNmuhHwvZkt9O6fDXxhZjMAnHO9whVORERiR15eHmvWrFExLSIxJZhiemzYU4iISMxbsWIFoIsPRSS2HLWYds7NNbMA0Mo5N9vMagFVnXPbwx9PRERihabFE5FYFMxsHkOBN4BnvKYTgbfDGUpERGKPpsUTkVgUzAWIfwHOB7YBOOeygePCGUpERGJPdnY2xx9/PHXq1PE7iohIyARTTO92zu05cMfMqlKweIuIiEjQNJOHiMSiYIrpuWY2BqhlZl2A14F3wxtLRERijeaYFpFYFEwxfTuwkYKFWm4AZgJ3hjOUiIjElm3btvHjjz/qzLSIxJxgZvPIN7OpwKfOuWURyCQiIjFm+fLlgC4+FJHYE8xsHr2AxcCH3v0zDizYIiIiEgxNiycisSqYYR53AR2ALQDOucVAYhgziYhIjDlQTJ988sk+JxERCa1giul9zrmtYU8iIiIxKysrixNPPJH4+Hi/o4iIhFQwy4kvNbP+QBUzawUMBz4PbywREYklmhZPRGJVMGembwbaALuBVyhYvGVkOEOJiEhs0bR4IhKrgpnNIw9I8TYREZFS2bRpEz///LPOTItITDpqMW1mpwD/R8FFhwcf75y7OHyxREQkVhy4+FDFtIjEomDGTL8OTAKeBfaHN46IiMQaFdMiEsuCKab3OeeeDnsSERGJSdnZ2cTFxdGiRQu/o4iIhFyJxbSZNfRuvmtmw4C3KLgIEQDn3KYwZxMRkRiQlZVFIBCgRo0afkcREQm5I52ZXgQ4wLz7txba5wCdYhARkaPStHgiEstKLKadcydFMoiIiMQe5xzZ2dmce+65fkcREQmLo84zbWb9zKyOd/tOM5tuZu3CH01ERCq6jRs3sm3bNp2ZFpGYFcyiLX9zzm03s98B3YB0Cmb3EBEROaKsrCxAM3mISOwKppg+MB3eZcDTzrl3gOrhiyQiIrFC0+KJSKwLppj+r5k9A/wJmGlmNYJ8noiIVHLZ2dlUrVqVxMREv6OIiIRFMEXxn4CPgO7OuS1AQw6d2UNERKRY2dnZtGjRgqpVg1nWQESk4jnqt5tzLg+YXuj+emB9OEOJiEhsyMrK0hAPEYlpGq4hIiJh4Zxj+fLlKqZFJKapmBYRkbBYt24deXl5nHLKKX5HEREJGxXTIiISFprJQ0Qqg1IX02Y228w+MLOe4QgkIiKxQXNMi0hlUJbLq68FmgDnhDiLiIjEkOzsbGrUqEHz5s39jiIiEjbBLCd+VuH7zrl1QFPn3MSwpRIREV9kZGSQmJhIXFwciYmJZGRklPlY2dnZtGzZkrg4jSgUkdgVzDfcZDM77cAdM7sauDN8kURExA8ZGRkkJyeTk5ODc46cnBySk5PLXFBrWjwRqQyCKab7AulmdqqZDQWGAV3DG0tERCJtzJgx5OXlHdKWl5dHSkpKqY+1f/9+VqxYoWJaRGLeUYtp59xK4CrgTQoK667Oua1He56Z1TSzhWb2tZl9a2Z3e+0vmNkqM1vsbWd47WZmE8xsuZl9Y2Znlu+tiYhIsBYsWEBubm6x+3Jycti8eXOpjrdmzRr27NmjafFEJOaVWEyb2RKvqP0GeIOCZcQTgQVe29HsBi52zp0OnAF0N7MDFy3e6pw7w9sWe209gFbelgw8XaZ3JCIiQfvpp58YOHAg55xzzhHHNjdp0oQBAwbwySef4Jw76nE1LZ6IVBZHms2jXFPfuYJv2x3e3WredqRv4N7Ai97z5ptZfTNr4i1fLiIiIbR3716eeOIJ7r77bnbu3Mno0aM55ZRTGD58+CFDPeLj4xkzZgzr168nIyODjIwMWrZsyaBBg7j++utp0qRJscfXtHgiUlmUeBrCOZfjnMuhYBq8TYXubwJOCObgZlbFzBYDG4BZzrkF3q5U76z3Y2ZWw2trBqwp9PS1XpuIiITQrFmzaNu2Lbfccgvnn38+S5cu5YEHHmDw4MGkpaURCAQwMwKBAGlpaaSkpPDkk0+ybt06pk6dyoknnsiYMWNo3rw5vXv35t1332Xfvn2HvEZ2dja1a9cusdgWEYkVdrQ/15nZV8CZ3hljzCwOyHTOBT2m2czqA28BNwM/Az8C1YE0YIVz7h4zex+43zn3mfecj4HRzrlFhx0rmYJhICQkJJyVk5MTbAwRkUpt5cqV3HLLLbz99tu0bNmSxx9/nMsuu6xMx8rOzub555/nhRde4Mcff6RJkyZcf/31DB48mPnz5zNkyBB27dpFIBAgNTWVpKSkEL8bEZHIMrNFzrn2RdqDKKYXO+fOOKztG+dc21IGuAv4xTn3cKG2TsD/Oed6mtkzwCfOuVe8fcuATkca5tG+fXuXmZlZmhgiIpVOXl4e48eP58EHH6Rq1arceeed/PWvf6VGjRpHf/JR7N27l5kzZ/Lcc8/x/vvvk5+fT1xcHPn5+QcfEx8fT1pamgpqEanQSiqmg5kab6WZDTezat42AlgZxAs29s5IY2a1gM7AD2bWxGsz4ApgqfeUGcC13qwe5wBbNV5aRKTsnHNMmzaN3/zmN9x777306dOHZcuWcfvtt4ekkAaoVq0avXv3ZsaMGeTm5lK/fv1DCmko+/R6IiIVQTDF9J+B84D/eltHvGEWR9EE+Jc388eXFIyZfg/IMLMlwBLgWOA+7/EzKSjSlwOTKZjPWkREgnD4yoXjx4/n4osv5sorr6RRo0bMmzePjIwMmjUL36UozZo1Y+vW4mdOLWnaPRGRiu6owzyimYZ5iIj8unLh4Quu1K5dm0ceeYQhQ4ZQpUqViGRJTEykuGtZAoEAq1evjkgGEZFwKPMwDzM70czeMrMNZvaTmb1pZieGJ6aIiJRWSkpKkUIaoEGDBtxwww0RK6QBUlNTiY+PP6QtPj6e1NTUiGUQEYmkYIZ5TKFgPHNTCqaqe9drExGRKFDSEIr//ve/EU4CSUlJxU6vp4sPRSRWlXU2jyJtftAwDxERDa0QEYmE8szm8T8zG+AtwFLFzAZQMFe0iIhEgdGjRxdp09AKEZHICKaYHgT8iYKFVtYDfYGB4QwlIiLBW7BgAXFxcTRt2lRDK0REIqxqEI9p7pzrVbjBzM4HNM+RiIjPPv30U1588UXGjBmjM9EiIj4IZsz0fw5fOry4Nj9ozLSIVGZ79+6lXbt27Nixg++++67ILBoiIhI6JY2ZLvHMtJmdS8FiLY3NbFShXXWByM2zJCIixZowYQLffvst77zzjgppERGfHGmYR3XgGO8xdQq1b6Ng3LSIiPhk7dq13HXXXfTs2ZNevXod/QkiIhIWJRbTzrm5wFwze8E5lwNgZnHAMc65bZEKKCIiRY0aNYr9+/czYcIEv6OIiFRqwczmcb+Z1TWz2sB3wDIzuzXMuUQkCmVkZJCYmEhcXByJiYlkZGT4HalS+uc//8nrr79OSkoKJ510kt9xREQqtWCK6dbemegrgJlAAnBNWFOJSMiVtxDOyMggOTmZnJwcnHPk5OSQnJysgjrCdu/ezU033USrVq249Vad1xAR8VswU+NVM7NqFBTTTzrn9prZkacAEZGocqAQzsvLAyAnJ4ehQ4eyfv16OnfuzM6dO9m5cyd5eXkHbx++Pf744weff0BeXh4pKSmazziCHnroIbKzs/noo4+oUaOG33FERCq9YKbGGw7cBnwNXEbBmempzrkLwh/vyDQ1nkhwSlpuOhTMjPz8/LAcWw61atUqWrduzeWXX860adP8jiMiUqmUemq8A5xzE4DCV7jkmNnvQxlORMIrN7fkNZamT59OrVq1qFWrFvHx8QdvF95q1KjBSSedVGxB3rx583BGl0KGDx9O1apVeeyxx/yOIiIinqMW02Z2PPB3oKlzroeZtQbOBZ4LdzgRKb+8vDxq1KjBrl27iuwLBAL84Q9/COo4qamphwwVOaBx48bs3buXatWqhSSvFG/GjBm89957PPzwwzRr1szvOCIi4gnmAsQXgI+Apt79LGBkuAKJSOhs27aN7t27s2vXLqpXr37Ivvj4+FItP52UlERaWhqBQAAzIxAIcO2117Jo0SIGDhyooR5hlJeXx/Dhw2nTpg3Dhw/3O46IiBQSzAWIxzrnppnZHQDOuX1mtj/MuUSknP73v//Ro0cPFi9ezKuvvsq+fftISUkhNzeXhIQEUlNTS33hYFJSUpHn/OY3v2HMmDHUqVOHp556CjML5dsQCv4qkJOTw6effqq/AIiIRJlgiulfzKwR4ADM7Bxga1hTiUi5rFu3ji5durBy5UrefvttLrvsMoCwzLpxxx13sG3bNsaPH0+dOnV44IEHVFCH0LJly3jooYe49tprueAC36/7FhGRwwRTTN8CzABONrN/A43RcuIiUWvVqlV07tyZDRs28MEHH9CpU6ewv+bf//53tm3bxkMPPUTdunW58847w/6alYFzjr/85S/Ex8fz4IMP+h1HRESKEcxsHovM7CLg/wEGLHPO7Q17MhEptR9++IHOnTuTl5fHxx9/TIcOHSLyumbGE088wY4dO/jb3/5GnTp1GDFiREReO5ZNmzaNjz/+mIkTJ3L88cf7HUdERIoRzGweXwOvAa8551aEP5KIlMVXX31F165dqVKlCnPnzuW0006L6OvHxcXx3HPPsWPHDkaOHEmdOnUYNGhQRDPEkm3btvHXv/6Vs846ixtuuMHvOCIiUoJgZvPoBewDppnZl2b2f2aWEOZcIlIK//73v/n9739PfHw88+bNi3ghfUDVqlV5+eWX6datG0OHDtXCIuUwbtw4fvzxR5566imqVKnidxwRESnBUYtp51yOc+5B59xZQH+gLbAq7MlEJCizZs2ia9euHHfcccybN49WrVr5mqdGjRpMnz6d888/n6SkJN5//31f81RE33zzDRMmTCA5OTliQ3VERKRsgjkzjZklmtlo4FXgN8DosKYSkaC89dZb9OzZk5YtWzJv3jwSEqLjj0bx8fG8++67nH766fTp04d//etffkeqMPLz8xk2bBgNGjTg73//u99xRETkKI5aTJvZAmA6UAXo55zr4Jx7JOzJROSIpk6dSr9+/WjXrh2ffPJJ1F2gVq9ePT766CNatmxJr169WLBggd+RKoQXX3yRf//73zz44IM0bNjQ7zgiInIUwZyZvs45d6Zz7n7n3MqwJxKRo3r66ae55ppruPDCC5k1axYNGjTwO1KxGjVqxKxZszj++OPp0aMH33zzjd+RolJGRgaJiYnExcUxePBgWrVqxXXXXed3LBERCUKJxbSZDfBuXmpmow7fIpRPRDi02GrQoAHDhg2jZ8+ezJw5kzp16vgd74iaNGnC7NmzqV27Nl26dCErK8vvSFElIyOD5ORkcnJycM6Rn5/PmjVreOWVV/yOJiIiQTjSmena3s86xWzHhDmXiHgOL7a2bNlClSpV6NevHzVr1vQ7XlASExOZPXs2zjk6d+7MP/7xj4P/OEhMTCQjI8PviL5JSUkhLy/vkLZdu3aRkpLiUyIRESkNc86V/klmI51zj4chT6m0b9/eZWZm+h1DJKwSExPJyckp0h4IBFi9enXkA5XD119/zbnnnsuuXbso/N0THx9PWlpaWJY7j3ZxcXEU9z1sZuTn5/uQSEREimNmi5xz7Q9vD2o2j2JomIdIhOTm5paqPZqdfvrp1K1bt0jxmJeXVynPxDrnqFevXrH7omVmFhERObKyFtMW0hQiUqKSLi6sqMXWhg0bim2viP84KI+dO3cyYMCAg8N2CouPjyc1NdWnZCIiUhplLaZLPzZERErtrbfeYtOmTcTFHfqfakUutkr6R0BF/cdBWaxfv55OnTrx8ssvk5qaSnp6OoFAADMjEAhU2iEvIiIV0ZFm89huZtuK2bYDTSOYUaRSmjt3LldffTXnnHMOkydPjpliKzU1lfj4+EPaatWqVWH/cVBa//nPf+jQoQNLly5l+vTpjBkzhqSkJFavXk1+fj6rV6+usL9bEZHKqEwXIEYLXYAosWrx4sVcdNFFNGvWjHnz5tGoUSO/I4VURkYGKSkpB4d2tGrViu+++67IcIdY8+abb3LNNddw7LHHMmPGDM444wy/I4mISJBCfQGiiITJihUr6N69O3Xr1uWjjz6KuUIaOORMbHp6OllZWTz44IN+xwob5xz33nsvffv25YwzzuDLL79UIS0iEiNUTItEkR9//JGuXbuyd+9e/vnPf9K8eXO/I4XdgAED+NOf/sTYsWNZtGiR33FCbufOnfTv35+xY8dyzTXXMGfOnKhb+l1ERMpOxbRIlNi6dSs9evTgxx9/ZObMmZx66ql+R4oIM+Ppp5/m+OOPJykpqcgCJhXZunXruOiii3jttdcYP3486enpFWahHRERCY6KaZEosGvXLnr37n3worSOHTv6HSmiGjZsSHp6OsuWLWP06NF+xwmJzMxMzj77bL777jvefvttbrvtNsw0q6iISKxRMS3is/3799O/f3/mzp1Leno63bp18zuSLy655BJGjRrFxIkTmTlzpt9xymXatGlceOGFVKtWjc8//5xevXr5HUlERMJExbSIj5xz3Hjjjbz11ls8/vjj9O/f3+9IvkpNTeW0005j0KBBbNy40e84QcnIyCAxMZG4uDgCgQB9+vThyiuv5Mwzz2ThwoW0bdvW74giIhJGKqZFfDR27FgmT57MmDFjGDFihN9xfFezZk2mTp3K5s2bGTp0aJFlx6NNRkYGycnJ5OTk4JwjNzeX6dOnc8EFF/Dxxx9z3HHH+R1RRETCTMW0iE+eeOIJ7rvvPobjTE0vAAAcUElEQVQMGcJ9993nd5yo0bZtW+6//37eeecdnn/+eb/jHFFKSkqxF0zm5ORQo0YNHxKJiEikadEWER+88sor9O/fnyuuuILXX3+dqlWr+h0pquTn59OlSxcWLFjA4sWLadmypd+RihUXF1fs2XMzIz8/34dEIiISLlq0RSRKfPTRR1x77bVcdNFFvPLKKyqkixEXF0d6ejrVqlVjwIAB7Nu3z+9IRWzevJlatWoVuy8hISHCaURExC8qpkUiaOHChfTp04c2bdrwzjvvaM7hIzjxxBOZNGkSCxYs4O9//7vfcQ4xe/ZsTjvtNHbu3Em1atUO2RcfH09qaqpPyUREJNJUTIuEWeHZHs4991zi4+P58MMPqVevnt/Rot6VV17JgAEDuOeee1iwYIHfccjLy2P48OF06dKFOnXqsHDhQqZMmUIgEMDMCAQCpKWlkZSU5HdUERGJEI2ZFgmjA7M9FL5IrWbNmjz77LMquIK0detW2rZtS/Xq1fnqq6845phjfMnx5Zdfcs0117Bs2TJGjBjB/fffX+IwDxERiT0aMy3ig+Jme9i1axcpKSk+Jap46tWrx0svvcSKFSsYNWpUxF9/7969jBs3jnPPPZdffvmF2bNn8/jjj6uQFhERQMW0SFjl5uaWql2Kd+GFFzJ69GgmT57MjBkzIva6P/zwA+eddx533303/fv3Z8mSJVxyySURe30REYl+KqZFwuSTTz4pcZ9meyi9e+65hzPOOIPBgwfz448/hvW18vPzmTBhAu3atWPVqlW88cYbvPjii9SvXz+srysiIhWPimmRMHj99dfp1q0bTZo0KTIcQLM9lE316tXJyMhgx44dDB48OGyrI65Zs4auXbsyYsQILr74YpYuXUqfPn3C8loiIlLxqZgWCbEnnniCK6+8krPPPpslS5YwefJkzfYQIq1bt+ahhx5i5syZTJo0qdzHKzzTSiAQ4MYbb+S0005j/vz5pKWl8d5773HCCSeEILmIiMQqzeYhEiLOOVJSUrj//vvp3bs3r7zyii5SCwPnHD169GDOnDk0btyY9evXk5CQQGpqaqn+kVLcTCsArVq14oMPPuDkk08OdXQREanASprNQ0uviYTA3r17GTp0KOnp6SQnJzNx4kStbBgmZkbPnj356KOPWLduHQA5OTkMHTqUDRs20KNHD/bu3XvItmfPniJtI0aMKFJIA+zevVuFtIiIBE1npkXK6ZdffqFfv3588MEH3H333fztb3/DzPyOFdMSExPJyckJy7HNjPz8/LAcW0REKi6dmRYJg40bN3LZZZexaNEi0tLSGDp0qN+RKoUjTS348ssvU61aNapVq0b16tUP3j78fpcuXQ6e2S5MM62IiEhpqJgWKaOVK1fSvXt31qxZw1tvvUWvXr38jlRpJCQkFHtmOhAIcPXVVwd1jAcffLDImGnNtCIiIqWl2TxEyuCrr77ivPPO4+eff+bjjz9WIR1hqampxMfHH9JW2kI4KSmJtLQ0zbQiIiLlojHTIqU0e/Zs/vCHP9CwYUM+/PBDTj31VL8jVUoZGRmkpKSQm5tbptk8RERESqOkMdMqpkVK4eWXX+b666/nN7/5DR988AHNmjXzO5KIiIhEQEnFtIZ5iBxB4UU9GjZsSFJSEueddx6ffvqpCmkRERHRBYgiJTl8UY/NmzdTpUoVrr/+eurXr+9zOhEREYkGOjMtUoKUlJQii3rs37+fcePG+RNIREREoo6KaZESlDSX8ZHmOBYREZHKRcW0SDGWLl1KXFzx/3loUQ8RERE5QMW0yGFmzpzJeeedxzHHHEPNmjUP2adFPURERKQwFdMiHuccjz/+OJdffjktW7Zk6dKlPPvss1rUQ0REREqkeaZFgL1793LTTTeRlpbGH/7wB1566SVq167tdywRERGJEppnWqQEmzZtonv37qSlpXHHHXfwxhtvqJAWERGRoGieaanUsrKy6NmzJzk5OaSnp3Pttdf6HUlEREQqEBXTUmnNmTOHvn37UqVKFT7++GN+97vf+R1JREREKhgN85BK6ZlnnqFbt240bdqUhQsXqpAWERGRMlExLZXKvn37GDlyJH/+85/p0qULn3/+OSeddJLfsURERKSCUjEtlcbWrVvp1asX//jHPxg5ciQzZsygbt26fscSERGRCkxjpqVSWLVqFT179iQrK4tJkyZxww03+B1JREREYkDYzkybWU0zW2hmX5vZt2Z2t9d+kpktMLNsM3vNzKp77TW8+8u9/YnhyiaVQ0ZGBomJicTFxdGyZUtWrVrFRx99pEJaREREQiacwzx2Axc7504HzgC6m9k5wAPAY865VsBmYLD3+MHAZudcS+Ax73EiZZKRkUFycjI5OTk458jPz8c5x/r16/2OJiIiIjEkbMW0K7DDu1vN2xxwMfCG154OXOHd7u3dx9t/iZlZuPJJbBszZgx5eXmHtO3atYuUlBSfEomIiEgsCusFiGZWxcwWAxuAWcAKYItzbp/3kLVAM+92M2ANgLd/K9AonPkkNm3fvp3c3Nxi95XULiIiIlIWYS2mnXP7nXNnACcCHYBTi3uY97O4s9Du8AYzSzazTDPL3LhxY+jCSkxYtWoV5513Xon7ExISIphGREREYl1EpsZzzm0BPgHOAeqb2YFZRE4E1nm31wLNAbz99YBNxRwrzTnX3jnXvnHjxuGOLhXIvHnz6NChA2vXruW2224jPj7+kP3x8fGkpqb6lE5ERERiUThn82hsZvW927WAzsD3wL+Avt7DrgPe8W7P8O7j7Z/jnCtyZlqkOM899xyXXHIJDRs2ZMGCBYwfP560tDQCgQBmRiAQIC0tjaSkJL+jioiISAyxcNWrZtaWggsKq1BQtE9zzt1jZi2AV4GGwFfAAOfcbjOrCbwEtKPgjPRVzrmVR3qN9u3bu8zMzLDkl4ph//793HrrrTz22GN07dqVV199lQYNGvgdS0RERGKMmS1yzrU/vD1si7Y4576hoDA+vH0lBeOnD2/fBfQLVx6JPVu3buWqq67iww8/ZPjw4TzyyCNUrap1iERERCRyVHlIhbR8+XIuv/xyli9fzjPPPENycrLfkURERKQSUjEtFc6cOXPo27cvZsasWbPo1KmT35FERESkkorIbB4ioTJp0iS6detGkyZNWLhwoQppERER8ZWKaakQ9u3bx0033cSNN95I165d+eKLLzj55JP9jiUiIiKVnIppiXqbN2+mR48eTJw4kVtuuYUZM2ZQt25dv2OJiIiIqJiW6JORkUFiYiJxcXE0a9aMU089lblz5/L888/z8MMPU6VKFb8jioiIiAC6AFGiTEZGBsnJyeTl5QGwbl3BApljx45l4MCBfkYTERERKUJnpiUqOOfIyclh5MiRBwvpwtLT031IJSIiInJkOjMtvti2bRtffvklCxYsOLj99NNPJT4+Nzc3gulEREREgqMz0xJShcc7JyYmkpGRwb59+1i8eDHPPPMMgwYNok2bNtSvX5/OnTuTkpLCDz/8QNeuXXnyySc54YQTij1uQkJChN+JiIiIyNHpzLSEzOHjnXNycrj22msZOHAge/fuBaBRo0Z07NiRK6+8ko4dO3L22WfTsGHDg8eoX7/+IccAiI+PJzU1NbJvRkRERCQIKqYlZFJSUoqMd87Pz6d27dq88MILdOzYkRYtWmBmJR4jKSnp4LFyc3NJSEggNTX1YLuIiIhINDHnnN8Zyqx9+/YuMzPT7xgCbNy4keOOO67YfWZGfn5+hBOJiIiIhI6ZLXLOtT+8XWOmpVycc0ydOpVTTz21xMdovLOIiIjEKhXTUmY5OTlceumlXHPNNbRq1Yrx48cTHx9/yGM03llERERimYppKbX9+/czYcIE2rRpw7x585gwYQKfffYZt912G2lpaQQCAcyMQCBAWlqaxjuLiIhIzNKYaSmVb7/9liFDhjB//ny6d+/OpEmTCAQCfscSERERCSuNmZZy2b17N+PGjaNdu3ZkZ2czdepUZs6cqUJaREREKjVNjSdH9fnnnzNkyBC+//57kpKSeOyxx2jcuLHfsURERER8pzPTUqLt27dz880387vf/Y4dO3bw/vvvM3XqVBXSIiIiIh4V03JQ4aXAjzvuOBITE5k4cSI33XQT3377LZdeeqnfEUVERESiioZ5CFB0KfCNGzdiZowdO5Zx48b5G05EREQkSunMtAAwZsyYIkuBO+d44YUX/AkkIiIiUgGomBaWLVtGbm5usftKahcRERERFdOV2u7du7n77rtp27YtZlbsY7QUuIiIiEjJVExXUnPnzuX0009n3Lhx9OnThyeffFJLgYuIiIiUkorpSmbTpk0MHjyYTp06sWfPHj744ANefvllhg0bpqXARUREREpJy4lXEs45MjIyGDVqFJs2beL//u//GDt2bJGz0SIiIiJSVEnLiWtqvEpg+fLl3HjjjcyePZtzzjmH2bNn07ZtW79jiYiIiFR4GuYRw/bs2UNqaiq//e1vWbhwIU899RT//ve/VUiLiIiIhIiK6RhRePXCxMRE7rrrLs4880zuvPNOevXqxffff8+NN95IXJx+5SIiIiKhomEeMeDw1QtzcnK45557aNiwIe+++y49e/b0OaGIiIhIbNJpyhiQkpJSZPVCgNq1a6uQFhEREQkjFdMxoKRVCteuXRvhJCIiIiKVi4rpGNC4ceNi27V6oYiIiEh4qZiu4L744gs2b95cZDlwrV4oIiIiEn4qpiuwpUuXctlllxEIBHjyySe1eqGIiIhIhGk2jwpq5cqVdO3alfj4eGbNmkViYiLDhg3zO5aIiIhIpaJiugJav349Xbp0Yffu3cybN4/ExES/I4mIiIhUSiqmK5jNmzfTrVs3fvrpJ+bMmUPr1q39jiQiIiJSaamYrkB++eUXevbsybJly3j//ffp0KGD35FEREREKjUV0xXEnj176Nu3L/Pnz2fatGl07tzZ70giIiIilZ6K6Qpg//79XHfddXz44YdMnjyZPn36+B1JRERERNDUeFHPOcfNN9/Mq6++ygMPPMCQIUP8jiQiIiIiHhXTUW7s2LE8/fTT3HbbbYwePdrvOCIiIiJSiIrpKPbYY49x3333MXToUO6//36/44iIiIjIYSptMZ2RkUFiYiJxcXEkJiaSkZHhd6RDpKenM2rUKPr27cvTTz9dZLlwEREREfFfpbwAMSMjg+TkZPLy8gDIyckhOTkZICqW4H7nnXcYPHgwXbp0YerUqVSpUsXvSCIiIiJSDHPO+Z2hzNq3b+8yMzNL/bzExERycnKKtAcCAVavXh2CZGX3ySef0L17d8444wxmz57NMccc42seEREREQEzW+Sca394e6Ub5rF8+fJiC2mA3NzcCKcpUHjIycUXX0yjRo14//33VUiLiIiIRLlKUUw75/j444/p1asXp5xySomPO+aYY9izZ08Ek/065CQnJwfnHM45Nm/ezIcffhjRHCIiIiJSejFdTO/cuZNnn32Wtm3b0rlzZ+bPn8+dd97Jk08+SXx8/CGPrVq1Ktu3b+eCCy4o8cx1OIwZM+bg2O3CuVNSUiKWQURERETKJiYvQFy3bh1PPfUUkyZN4ueff+b0009nypQpXHXVVdSsWROA+vXrk5KSQm5uLgkJCaSmplKzZk0GDRpEu3bteOmll7jsssvCmnPZsmUlDi3xa8iJiIiIiASvQl+AaGYuEAiQmppKUlISCxcu5B//+AfTpk1j//799O7dmxEjRnDRRRcFPbXc8uXL6devH4sXL+b222/n3nvvpWrV0P6bY8eOHdx33308+uij7Nu3j+J+B9FwMaSIiIiIFCjpAsQKX0wDVK9enYSEBJYvX06dOnUYMmQIN910Ey1atCjTcXfu3MnIkSNJS0vjggsu4NVXX6Vp06blzuuc47XXXuOWW25h3bp1XH/99Zx99tnceuuthwz1iI+PJy0tLSqm6RMRERGRGJ/NY8+ePaxevZoJEybw3//+l0cffbTMhTRArVq1eOaZZ3jppZdYtGjRwWnqymPJkiX8/ve/5+qrr+aEE07g888/Z8qUKQwbNoy0tDQCgQBmRiAQUCEtIiIiUkHExJlp7zb5+fkhf43vvvuOfv368f333zNu3DhSUlJKtYjKli1buOuuu5g4cSL16tXj/vvvZ/DgwVqIRURERKQCiekz0wAJCQlhOW7r1q1ZuHAhAwYM4K677qJHjx5s2LDhqM/Lz89nypQpnHLKKTzxxBMkJyeTlZVFcnKyCmkRERGRGBETxXR8fDypqalhO37t2rVJT09n8uTJfPrpp7Rr147PPvusxMdnZmZy3nnnMWjQIFq2bElmZiZPPfUUjRo1CltGEREREYm8Cl9MR2qMsZkxZMgQ5s+fT3x8PJ06deKhhx5i6tSpB1cvbN68ORdffDEdOnRg9erVpKen89lnn3HmmWeGNZuIiIiI+KNCj5lu3769y8zMjPjrbt26lSFDhvDGG29QpUoV9u/ff8j+7t278+qrr1KvXr2IZxMRERGR0Iv5MdORVK9ePaZNm0aDBg2KFNIA33//vQppERERkUpAxXQZmRlbtmwpdp9WLxQRERGpHFRMl0NJM4iEa2YREREREYkuKqbLITU1lfj4+EPawj2ziIiIiIhEDxXT5ZCUlKTVC0VEREQqMc3mISIiIiJyFJrNQ0REREQkxFRMi4iIiIiUkYppEREREZEyUjEtIiIiIlJGKqZFRERERMpIxbSIiIiISBmpmBYRERERKSMV0yIiIiIiZaRiWkRERESkjMJWTJtZczP7l5l9b2bfmtkIr32cmf3XzBZ726WFnnOHmS03s2Vm1i1c2UREREREQqFqGI+9D7jFOfcfM6sDLDKzWd6+x5xzDxd+sJm1Bq4C2gBNgdlmdopzbn8YM4qIiIiIlFnYzkw759Y75/7j3d4OfA80O8JTegOvOud2O+dWAcuBDuHKJyIiIiJSXhEZM21miUA7YIHXdJOZfWNmz5tZA6+tGbCm0NPWcuTiW0RERETEV2Evps3sGOBNYKRzbhvwNHAycAawHnjkwEOLebor5njJZpZpZpkbN24MU2oRERERkaMLazFtZtUoKKQznHPTAZxzPznn9jvn8oHJ/DqUYy3QvNDTTwTWHX5M51yac669c65948aNwxlfREREROSIzLkiJ39Dc2AzA9KBTc65kYXamzjn1nu3/wp0dM5dZWZtgJcpKK6bAh8DrY50AaKZbQeWlTNqPWBrOY8RquNEyzGOBf4XBTli7XcTS/0aTb8b9WvojwHq13AcIxR9GqossXSMaPmshuo40XKMaOnXaPrdtHLO1SvS6pwLywb8joJhGt8Ai73tUuAlYInXPgNoUug5KcAKCgrkHkG8RmYIcqaF6P2W+zhRdIyo6NcY/N3ETL9G2e9G/Rqe3436NfTHKHefRtn7iZZjRMVnNcr6JGb6tSL8bsI2NZ5z7jOKHwc98wjPSQVSw5WpBO9G0XGi5RihEE3vJZqylFe0vJdo+t2EQrT0SbQcI1Si5f1EyzFCJVreT7QcIxSi6TstWo4RCtH0XsKWJWzDPCLBzDKdc+39zhFr1K/hoX4ND/VreKhfQ099Gh7q1/BQvwavoi8nnuZ3gBilfg0P9Wt4qF/DQ/0aeurT8FC/hof6NUgV+sy0iIiIiIifKvqZaRERERER30RdMe2tirjBzJYWajvdzL4wsyVm9q6Z1fXak8xscaEt38zO8Pad5T1+uZlN8Kbqq5RC2KefmNmyQvuO8+s9RYNS9ms1M0v32r83szsKPae716/Lzex2P95LNAlhv6722hebWaYf7yWalLJfq5vZFK/9azPrVOg5+m4tJIT9qu9Xj5k1N7N/ef9Nf2tmI7z2hmY2y8yyvZ8NvHbzPovLrWB15TMLHes67/HZZnadX+8pGoS4X/cX+qzO8Os9RY1QTDcSyg24EDgTWFqo7UvgIu/2IODeYp53GrCy0P2FwLkUzCjyAUFMtRerWwj79BOgvd/vJ1q20vQr0B941bsdD6wGEoEqFEwH2QKoDnwNtPb7vVX0fvXurwaO9fv9RMtWyn79CzDFu30csAiI8+7ruzU8/arv11/7rwlwpne7DpAFtAYeBG732m8HHvBuX+p9Fg04B1jgtTcEVno/G3i3G/j9/ip6v3r7dvj9fqJpi7oz0865T4FNhzX/P+BT7/YsoE8xT70aeAUKFoYB6jrnvnAFv/UXgSvCkzj6haJPpahS9qsDaptZVaAWsAfYRsEiRcudcyudc3uAV4He4c4ezULUr3KYUvZrawoWzsI5twHYArTXd2tRoejXCMSsUJxz651z//Fubwe+B5pR8N2Y7j0snV8/e72BF12B+UB977PaDZjlnNvknNtMwe+iewTfSlQJYb/KYaKumC7BUqCXd7sfhy47fsCV/Fr4NaNgefID1npt8qvS9ukBU7w/6/ytsv95twQl9esbwC/AeiAXeNg5t4mCz+WaQs/XZ7V4pe1XKCi0/2lmi8wsOZJhK5CS+vVroLeZVTWzk4CzvH36bg1Oafv1AH2/HsbMEoF2wALgeOetoOz9PDAUpqTvUX2/lqCc/QpQ08wyzWy+mVXqf1BDxSmmBwF/MbNFFPxpYk/hnWbWEchzzh0Ys1bcl5CmLTlUafsUIMk5dxpwgbddE6mwFUhJ/doB2A80BU4CbjGzFuizGqzS9ivA+c65M4Ee3nMvjHDmiqCkfn2egv9xZgKPA58D+9DnNVil7VfQ92sRZnYM8CYw0jl3pL84lfS51Oe1GCHoV4AEVzAHdX/gcTM7OcQxK5SwrYAYSs65H4CuAGZ2CnDZYQ+5ikPPoK4FTix0/0RgXTgzVjRl6FOcc//1fm43s5cpKGReDH/aiuMI/dof+NA5txfYYGb/puDPu2s49MyUPqvFKEO/rnTOrfOeu8HM3qLg8/ppkYNXYiX1q3NuH/DXA48zs8+BbGAz+m49qjL0q75fD2Nm1Sgo+DKcc9O95p/MrIlzbr033GCD176W4r9H1wKdDmv/JJy5o12I+pVC368rzewTCs5yr4jAW4hKFeLM9IGrms0sDrgTmFRoXxwFf0Z79UCb92eK7WZ2jvensmuBdyIaOsqVtk+9P0se692uBvSk4E+ZUsgR+jUXuNi7Oro2BRdz/EDBhUqtzOwkM6tOwT9idGX0YUrbr2ZW28zqeM+pTUFho8/rYUrqVzOL9/oNM+sC7HPOfafv1uCUtl/1/Xoo77P1HPC9c+7RQrtmAAdm5LiOXz97M4Brve+Bc4Ct3mf1I6CrmTXwZqjo6rVVSqHqV68/a3jHPBY4H/guIm8iWvl9BeThGwVnQ9cDeyn4V9FgYAQFV51mAePxFpvxHt8JmF/McdpT8GW0Aniy8HMq2xaKPgVqU3Dl+TfAt8A/gCp+v7eK0q/AMcDrXt99B9xa6DiXeo9fAaT4/b783kLRrxTMjvK1t32rfi11vyYCyyi4QGk2ECh0HH23hrhf9f1apE9/R8Fwgm+Axd52KdCIggs4s72fDb3HGzDR+0wuodCsKBQMuVnubQP9fm+x0K/Aed79r72fg/1+b35vWgFRRERERKSMKsQwDxERERGRaKRiWkRERESkjFRMi4iIiIiUkYppEREREZEyUjEtIiIiIlJGKqZFRERERMpIxbSIiIiISBmpmBYRERERKaP/D0FG1vPtdWXcAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.\n" ] } ], "source": [ "fit1 = SimpleExpSmoothing(livestock2).fit()\n", "fcast1 = fit1.forecast(9).rename(\"SES\")\n", "fit2 = Holt(livestock2).fit()\n", "fcast2 = fit2.forecast(9).rename(\"Holt's\")\n", "fit3 = Holt(livestock2, exponential=True).fit()\n", "fcast3 = fit3.forecast(9).rename(\"Exponential\")\n", "fit4 = Holt(livestock2, damped=True).fit(damping_slope=0.98)\n", "fcast4 = fit4.forecast(9).rename(\"Additive Damped\")\n", "fit5 = Holt(livestock2, exponential=True, damped=True).fit()\n", "fcast5 = fit5.forecast(9).rename(\"Multiplicative Damped\")\n", "\n", "ax = livestock2.plot(color=\"black\", marker=\"o\", figsize=(12,8))\n", "livestock3.plot(ax=ax, color=\"black\", marker=\"o\", legend=False)\n", "fcast1.plot(ax=ax, color='red', legend=True)\n", "fcast2.plot(ax=ax, color='green', legend=True)\n", "fcast3.plot(ax=ax, color='blue', legend=True)\n", "fcast4.plot(ax=ax, color='cyan', legend=True)\n", "fcast5.plot(ax=ax, color='magenta', legend=True)\n", "ax.set_ylabel('Livestock, sheep in Asia (millions)')\n", "plt.show()\n", "print('Figure 7.5: Forecasting livestock, sheep in Asia: comparing forecasting performance of non-seasonal methods.')" ] }, { "cell_type": "markdown", "metadata": { "ExecuteTime": { "end_time": "2017-10-05T09:40:15.958575Z", "start_time": "2017-10-05T09:40:15.615Z" } }, "source": [ "## Holt's Winters Seasonal\n", "Finally we are able to run full Holt's Winters Seasonal Exponential Smoothing including a trend component and a seasonal component.\n", "statsmodels allows for all the combinations including as shown in the examples below:\n", "1. ```fit1``` additive trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit2``` additive trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation..\n", "1. ```fit3``` additive damped trend, additive seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "1. ```fit4``` additive damped trend, multiplicative seasonal of period ```season_length=4``` and the use of a Box-Cox transformation.\n", "\n", "The plot shows the results and forecast for ```fit1``` and ```fit2```.\n", "The table allows us to compare the results and parameterizations." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.375871Z", "start_time": "2017-12-07T12:39:18.040674Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/holtwinters.py:725: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n", " ConvergenceWarning)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/holtwinters.py:725: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n", " ConvergenceWarning)\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/travis/build/statsmodels/statsmodels/statsmodels/tsa/holtwinters.py:725: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n", " ConvergenceWarning)\n" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\n" ] }, { "data": { "text/html": [ "
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AdditiveMultiplicativeAdditive DamMultiplica Dam
$\\alpha$4.546141e-013.662202e-019.082834e-090.000182
$\\beta$5.824107e-096.273474e-201.550290e-110.000182
$\\phi$NaNNaN9.431182e-010.913648
$\\gamma$5.244166e-019.043075e-141.290373e-060.000000
$l_0$1.421752e+011.454882e+011.415855e+0114.534854
$b_0$1.307774e-011.661481e-012.454178e-010.484784
SSE5.001652e+014.307295e+013.527230e+0139.711041
\n", "
" ], "text/plain": [ " Additive Multiplicative Additive Dam Multiplica Dam\n", "$\\alpha$ 4.546141e-01 3.662202e-01 9.082834e-09 0.000182\n", "$\\beta$ 5.824107e-09 6.273474e-20 1.550290e-11 0.000182\n", "$\\phi$ NaN NaN 9.431182e-01 0.913648\n", "$\\gamma$ 5.244166e-01 9.043075e-14 1.290373e-06 0.000000\n", "$l_0$ 1.421752e+01 1.454882e+01 1.415855e+01 14.534854\n", "$b_0$ 1.307774e-01 1.661481e-01 2.454178e-01 0.484784\n", "SSE 5.001652e+01 4.307295e+01 3.527230e+01 39.711041" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fit1 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add').fit(use_boxcox=True)\n", "fit2 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul').fit(use_boxcox=True)\n", "fit3 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='add', damped=True).fit(use_boxcox=True)\n", "fit4 = ExponentialSmoothing(aust, seasonal_periods=4, trend='add', seasonal='mul', damped=True).fit(use_boxcox=True)\n", "results=pd.DataFrame(index=[r\"$\\alpha$\",r\"$\\beta$\",r\"$\\phi$\",r\"$\\gamma$\",r\"$l_0$\",\"$b_0$\",\"SSE\"])\n", "params = ['smoothing_level', 'smoothing_slope', 'damping_slope', 'smoothing_seasonal', 'initial_level', 'initial_slope']\n", "results[\"Additive\"] = [fit1.params[p] for p in params] + [fit1.sse]\n", "results[\"Multiplicative\"] = [fit2.params[p] for p in params] + [fit2.sse]\n", "results[\"Additive Dam\"] = [fit3.params[p] for p in params] + [fit3.sse]\n", "results[\"Multiplica Dam\"] = [fit4.params[p] for p in params] + [fit4.sse]\n", "\n", "ax = aust.plot(figsize=(10,6), marker='o', color='black', title=\"Forecasts from Holt-Winters' multiplicative method\" )\n", "ax.set_ylabel(\"International visitor night in Australia (millions)\")\n", "ax.set_xlabel(\"Year\")\n", "fit1.fittedvalues.plot(ax=ax, style='--', color='red')\n", "fit2.fittedvalues.plot(ax=ax, style='--', color='green')\n", "\n", "fit1.forecast(8).rename('Holt-Winters (add-add-seasonal)').plot(ax=ax, style='--', marker='o', color='red', legend=True)\n", "fit2.forecast(8).rename('Holt-Winters (add-mul-seasonal)').plot(ax=ax, style='--', marker='o', color='green', legend=True)\n", "\n", "plt.show()\n", "print(\"Figure 7.6: Forecasting international visitor nights in Australia using Holt-Winters method with both additive and multiplicative seasonality.\")\n", "\n", "results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Internals\n", "It is possible to get at the internals of the Exponential Smoothing models. \n", "\n", "Here we show some tables that allow you to view side by side the original values $y_t$, the level $l_t$, the trend $b_t$, the season $s_t$ and the fitted values $\\hat{y}_t$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.399765Z", "start_time": "2017-12-07T12:39:28.377215Z" } }, "outputs": [ { "data": { "text/html": [ "
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$\\hat{y}_t$$b_t$$l_t$$s_t$$y_t$
2005-01-0141.721221-34.96940049.317697-7.59340841.7275
2005-04-0124.190248-35.45284349.932487-25.83470824.0418
2005-07-0131.460568-36.53279351.126161-19.18295932.3281
2005-10-0136.634784-37.39762252.210084-15.20968537.3287
2006-01-0145.097632-38.46724653.476749-7.83727746.2132
2006-04-0127.191721-40.27627655.513814-27.01737229.3463
2006-07-0136.544194-40.62503156.224457-19.71384836.4829
2006-10-0141.449477-42.04172657.766045-15.52329542.9777
2007-01-0150.934454-41.54381257.536734-7.58867148.9015
2007-04-0131.418231-42.19784858.151014-26.87428931.1802
2007-07-0138.718348-42.30349658.363010-20.19191637.7179
2007-10-0144.140665-41.08582157.181923-14.98278540.4202
2008-01-0149.315841-42.96148758.853001-8.61985751.2069
2008-04-0132.306999-43.18655359.367006-27.30918531.8872
2008-07-0139.207465-44.82698961.095601-20.92558840.9783
2008-10-0144.551262-44.89948061.462177-17.31991143.7725
2009-01-0154.358086-46.19223362.816830-7.88166555.5586
2009-04-0135.153854-45.98019562.832171-28.44788533.8509
2009-07-0143.066497-46.22814063.082678-20.55066542.0764
2009-10-0145.871207-46.85251763.748866-17.99780845.6423
2010-01-0157.166623-48.77038665.777575-7.37214759.7668
2010-04-0136.761380-48.30834165.650021-29.81682835.1919
2010-07-0144.932496-48.79866566.119447-21.51748944.3197
2010-10-0148.399587-49.26982266.667428-18.52228247.9137
2011-01-0161.337982NaNNaNNaNNaN
2011-04-0137.242908NaNNaNNaNNaN
2011-07-0146.842670NaNNaNNaNNaN
2011-10-0151.005290NaNNaNNaNNaN
2012-01-0164.470874NaNNaNNaNNaN
2012-04-0139.776989NaNNaNNaNNaN
2012-07-0149.635936NaNNaNNaNNaN
2012-10-0153.901538NaNNaNNaNNaN
\n", "
" ], "text/plain": [ " $\\hat{y}_t$ $b_t$ $l_t$ $s_t$ $y_t$\n", "2005-01-01 41.721221 -34.969400 49.317697 -7.593408 41.7275\n", "2005-04-01 24.190248 -35.452843 49.932487 -25.834708 24.0418\n", "2005-07-01 31.460568 -36.532793 51.126161 -19.182959 32.3281\n", "2005-10-01 36.634784 -37.397622 52.210084 -15.209685 37.3287\n", "2006-01-01 45.097632 -38.467246 53.476749 -7.837277 46.2132\n", "2006-04-01 27.191721 -40.276276 55.513814 -27.017372 29.3463\n", "2006-07-01 36.544194 -40.625031 56.224457 -19.713848 36.4829\n", "2006-10-01 41.449477 -42.041726 57.766045 -15.523295 42.9777\n", "2007-01-01 50.934454 -41.543812 57.536734 -7.588671 48.9015\n", "2007-04-01 31.418231 -42.197848 58.151014 -26.874289 31.1802\n", "2007-07-01 38.718348 -42.303496 58.363010 -20.191916 37.7179\n", "2007-10-01 44.140665 -41.085821 57.181923 -14.982785 40.4202\n", "2008-01-01 49.315841 -42.961487 58.853001 -8.619857 51.2069\n", "2008-04-01 32.306999 -43.186553 59.367006 -27.309185 31.8872\n", "2008-07-01 39.207465 -44.826989 61.095601 -20.925588 40.9783\n", "2008-10-01 44.551262 -44.899480 61.462177 -17.319911 43.7725\n", "2009-01-01 54.358086 -46.192233 62.816830 -7.881665 55.5586\n", "2009-04-01 35.153854 -45.980195 62.832171 -28.447885 33.8509\n", "2009-07-01 43.066497 -46.228140 63.082678 -20.550665 42.0764\n", "2009-10-01 45.871207 -46.852517 63.748866 -17.997808 45.6423\n", "2010-01-01 57.166623 -48.770386 65.777575 -7.372147 59.7668\n", "2010-04-01 36.761380 -48.308341 65.650021 -29.816828 35.1919\n", "2010-07-01 44.932496 -48.798665 66.119447 -21.517489 44.3197\n", "2010-10-01 48.399587 -49.269822 66.667428 -18.522282 47.9137\n", "2011-01-01 61.337982 NaN NaN NaN NaN\n", "2011-04-01 37.242908 NaN NaN NaN NaN\n", "2011-07-01 46.842670 NaN NaN NaN NaN\n", "2011-10-01 51.005290 NaN NaN NaN NaN\n", "2012-01-01 64.470874 NaN NaN NaN NaN\n", "2012-04-01 39.776989 NaN NaN NaN NaN\n", "2012-07-01 49.635936 NaN NaN NaN NaN\n", "2012-10-01 53.901538 NaN NaN NaN NaN" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(np.c_[aust, fit1.level, fit1.slope, fit1.season, fit1.fittedvalues],\n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit1.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:28.574783Z", "start_time": "2017-12-07T12:39:28.401234Z" } }, "outputs": [ { "data": { "text/html": [ "
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$\\hat{y}_t$$b_t$$l_t$$s_t$$y_t$
2005-01-0141.858321-36.53396551.2489310.81581641.7275
2005-04-0125.838073-35.86963550.7398760.49533124.0418
2005-07-0131.657988-37.28817152.0653470.61293032.3281
2005-10-0135.189322-39.17458654.1932510.66412737.3287
2006-01-0144.929298-40.31183355.7126980.81497446.2132
2006-04-0127.934180-42.09397957.7637980.49301129.3463
2006-07-0135.825130-43.10690959.1348130.61003536.4829
2006-10-0139.769843-45.65169061.9158890.66164942.9777
2007-01-0151.176261-45.12724961.8636120.81351448.9015
2007-04-0130.814974-46.41491763.1424900.49025531.1802
2007-07-0139.009470-46.39225763.3339480.60816837.7179
2007-10-0142.486262-46.17568163.1492660.66038740.4202
2008-01-0152.173235-46.76468563.7075060.81330851.2069
2008-04-0131.677038-47.84145764.8771500.48951231.8872
2008-07-0140.035343-49.24602666.4751740.60761840.9783
2008-10-0144.516461-49.58119967.0722360.65952643.7725
2009-01-0155.343093-50.60881268.1969970.81268955.5586
2009-04-0133.773328-51.52192469.2921090.48783633.8509
2009-07-0142.644144-52.03193169.9780780.60631742.0764
2009-10-0146.778696-52.31674770.3725030.65863745.6423
2010-01-0158.008481-54.10117572.2197440.81221259.7668
2010-04-0135.648733-54.50665972.9174040.48647735.1919
2010-07-0144.784147-55.17072173.6909730.60534344.3197
2010-10-0149.174718-55.39584174.0369860.65776947.9137
2011-01-0160.966729NaNNaNNaNNaN
2011-04-0136.993678NaNNaNNaNNaN
2011-07-0146.711883NaNNaNNaNNaN
2011-10-0151.482746NaNNaNNaNNaN
2012-01-0164.455796NaNNaNNaNNaN
2012-04-0139.017212NaNNaNNaNNaN
2012-07-0149.291377NaNNaNNaNNaN
2012-10-0154.320260NaNNaNNaNNaN
\n", "
" ], "text/plain": [ " $\\hat{y}_t$ $b_t$ $l_t$ $s_t$ $y_t$\n", "2005-01-01 41.858321 -36.533965 51.248931 0.815816 41.7275\n", "2005-04-01 25.838073 -35.869635 50.739876 0.495331 24.0418\n", "2005-07-01 31.657988 -37.288171 52.065347 0.612930 32.3281\n", "2005-10-01 35.189322 -39.174586 54.193251 0.664127 37.3287\n", "2006-01-01 44.929298 -40.311833 55.712698 0.814974 46.2132\n", "2006-04-01 27.934180 -42.093979 57.763798 0.493011 29.3463\n", "2006-07-01 35.825130 -43.106909 59.134813 0.610035 36.4829\n", "2006-10-01 39.769843 -45.651690 61.915889 0.661649 42.9777\n", "2007-01-01 51.176261 -45.127249 61.863612 0.813514 48.9015\n", "2007-04-01 30.814974 -46.414917 63.142490 0.490255 31.1802\n", "2007-07-01 39.009470 -46.392257 63.333948 0.608168 37.7179\n", "2007-10-01 42.486262 -46.175681 63.149266 0.660387 40.4202\n", "2008-01-01 52.173235 -46.764685 63.707506 0.813308 51.2069\n", "2008-04-01 31.677038 -47.841457 64.877150 0.489512 31.8872\n", "2008-07-01 40.035343 -49.246026 66.475174 0.607618 40.9783\n", "2008-10-01 44.516461 -49.581199 67.072236 0.659526 43.7725\n", "2009-01-01 55.343093 -50.608812 68.196997 0.812689 55.5586\n", "2009-04-01 33.773328 -51.521924 69.292109 0.487836 33.8509\n", "2009-07-01 42.644144 -52.031931 69.978078 0.606317 42.0764\n", "2009-10-01 46.778696 -52.316747 70.372503 0.658637 45.6423\n", "2010-01-01 58.008481 -54.101175 72.219744 0.812212 59.7668\n", "2010-04-01 35.648733 -54.506659 72.917404 0.486477 35.1919\n", "2010-07-01 44.784147 -55.170721 73.690973 0.605343 44.3197\n", "2010-10-01 49.174718 -55.395841 74.036986 0.657769 47.9137\n", "2011-01-01 60.966729 NaN NaN NaN NaN\n", "2011-04-01 36.993678 NaN NaN NaN NaN\n", "2011-07-01 46.711883 NaN NaN NaN NaN\n", "2011-10-01 51.482746 NaN NaN NaN NaN\n", "2012-01-01 64.455796 NaN NaN NaN NaN\n", "2012-04-01 39.017212 NaN NaN NaN NaN\n", "2012-07-01 49.291377 NaN NaN NaN NaN\n", "2012-10-01 54.320260 NaN NaN NaN NaN" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df = pd.DataFrame(np.c_[aust, fit2.level, fit2.slope, fit2.season, fit2.fittedvalues], \n", " columns=[r'$y_t$',r'$l_t$',r'$b_t$',r'$s_t$',r'$\\hat{y}_t$'],index=aust.index)\n", "df.append(fit2.forecast(8).rename(r'$\\hat{y}_t$').to_frame(), sort=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally lets look at the levels, slopes/trends and seasonal components of the models." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2017-12-07T12:39:29.636548Z", "start_time": "2017-12-07T12:39:28.576279Z" } }, "outputs": [ { "data": { "image/png": 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c6hyWY/rE8tCZ3ZjYN069xa1EfwVF2oCFmwu47cNVZBfv5fqJvfi/43oT4Nf+5q0UEfFWxXtr+Hh5Jm8t2s7m/HIigv35/bhkfndUEt2iQ9wdXrujAlnEi1XW1PHIzPW8smAryTEhTL92DMOSIt0dloiIHKaMnBJeX7idT3/Zxd6aOoYmRfDPc1M5dXC8hrO5kQpkES+1cmcRN3+wgs355Vw6uht3nNxXQyNERLxAbZ2DWWtzeX3hNhZv3U0HPx/OHJLAxaO7MTAh3N3hCSqQRbxOTZ2Df8/dxDPfbSIutANvXXkU43rHuDssERE5hIKyKt5bsoO3F+8gu7iSxMgg7jq5L+eP6EpEcIC7w5MGVCCLeJGNuaX88YMVrNlVwllDE7j3jAGEB/m7OywRETmIlTuLeP2nbXyxMpvqOgfjesXwwOSBHKuL7jyWCmQRL+BwWF5ZsJVHvllPxw5+PD91GCcNjHd3WCIicgBVtXV8tTqb1xduZ8XOIkICfLlgZFcuGd2NXnGh7g5PDkEFsoiH21ZQzh0frWLx1t0c368Tfz9rkOa/FBHxQNZaNueXM2PFLt5dsoOCsmp6xIRw3+n9OXt4IqGB+sTPW6hAFvEQdQ7L1oJy1maXsDarhHXZJazNLiG/tIqOHfx49JzBnDM8UXerExHxEBXVtazcWczyHXtYtn0Pv+zYw56KGoyBY1PiuHRMd8b1isFHwyi8jgpkETcoq6olI/u/RfDa7FLW55RQWeMAwN/X0CsulPG9Y+kXH8opg+LpEhHk5qhFRNovay2Ze/ayfMcelm/fw7Ide1iXXUqdwwLQMzaEE/p3Yni3SMb0jKFrVLCbI5bmUIEs0krySiv525fr+GVnEdsLK/avjwj2p1/nMC46qhv948PoFx9Gr7iOutGHiIibZeSU8OOGApY5C+L80ioAggN8GdI1gusm9GRYUiRDkyI0C0UbowJZpBVszC3lsld/Znd5NRNSYjlnWCL9u9QXw/HhgRo2ISLiQXaXV/PIzAze+3knAElRwYztGc3wbpEMTYqkb+dQ/HzVidGWqUAWaWGLthQy7Y2lBPj58sHVoxmUqEngRUQ8UZ3D8v7PO3nkmwzKKmuZNr4Hvx+XTFxYoLtDk1amAlmkBc1YsYvbPlxF16ggXrt8pMakiYh4qJU7i7hnxhpWZhZzVHIUD545kD6dNB1be6UCWaQFWGt57ofNPDJzPSOTo3jp4jTCgzW9j4iIpymqqOaRb9bz7pIdxHTswJMXDOGM1C4a+tbOuaRANsZEAP8BBgIWuAJYD7wPdAe2AedZa/e44nwinqy2zsE9n6XzzuIdnJ7ahcfOHUwHP193hyXyKwfI2ycCVwH5zs3+ZK39yj0RirQsh8Py4bKdPPx1BiWVtVw+JpmbTuhNmOYqFlzXg/wkMNNae44xJgAIBv4EzLHWPmyMuRO4E7jDRecT8UjlVbVc/85yvlufz7UTenLbpBTNfymeqrG8fSLwhLX2MfeGJtKy1uwq5u4Za/hlRxEjukfywOSB9IsPc3dY4kGaXSAbY8KA8cBlANbaaqDaGDMZmODc7HXge1QgSxuWV1rJla8tJT2rmL+eOZCpo7q5OySRRh0kb7szLJEWV7y3hn/OWs9bi7YTFRLAP89N5axhCRpOIf/DFT3IPaj/OO5VY0wqsAy4Eehkrc0GsNZmG2PiGtvZGDMNmAaQlJTkgnBEWt+mvFIufaV+GreXLknjuH6d3B2SyMEcKG8DXG+MuQRYCtyioXHSFtTWOfjkl108/HUGeyqquXhUN26elEJ4kIZTSONcMYmfHzAMeM5aOxQop344xWGx1r5orU2z1qbFxsa6IByR1rV4SyFnPbuQqloH7189SsWxeIMD5e3ngJ7AECAb+GdjOxtjphljlhpjlubn5ze2iYhHKKms4aV5Wzjm0e+5bfoqukUH89n147h/8kAVx3JQruhBzgQyrbWLna+nU59oc40x8c7e43ggzwXnEvEomsZNvFSjedtam7tvA2PMS8AXje1srX0ReBEgLS3NtnCsIkdse2E5ry7YxodLd1JeXcdRyVHcc3p/TujXSdeFyGFpdoFsrc0xxuw0xqRYa9cDxwFrnY9LgYedyxnNPZeIp7DW8vwPW/jHzAxGJkfx4sXDdZtR8RoHytv7OjWcm00B1rgvSpEjY61l8dbdvDJ/K7PX5eLnYzh9cBeuGJfMwATdoEmOjKtmsbgBeNt5JfQW4HLqh298YIy5EtgBnOuic4m4RVbRXhZsKuCnzYUs2FxAbkmVpnETb9ZY3n7KGDOE+mnftgFXuy88kcNTXevgi1VZvDx/K+lZJUQG+/OHCb24eHQ3OukOeNJELimQrbUrgLRG3jrOFccXcYfCsioWbdnNgs0FLNxUwLbCCgCiQwIY3TOaiSlxTBmaoI/rxCsdIG9f7I5YRJpid3k17yzezhs/bSevtIpecR3525RBTBmaQFCAOi2keXQnPRGnsqpalmwtZMGmQhZuLmRddgkAHTv4cVRyFBeP7s6YntGkdApVUSwi4gb5pVWs3FnEnIw8Pl6eSVWtg6N7x/DIOYMZ3ztWuVlcRgWytHtfrsrm5flbWJlZTJ3DEuDnQ1q3SG6d1IcxvWIYnBCOn68rJnwREZHDVV5Vy+pdxazcWcTKzCJW7ixmV9FeAAL8fDhraAJXjEumT6dQN0cqbZEKZGm3rLU88e1GnpqzkT6dOnL1+B6M7RXD8G6RBPrr4zkRkYYcDktpZS17Kqop2lvDnopqiivql0UVNRTvrcHHGCKC/YkI9ic8yJ+I4ID6ZVD9utBAf3wb6eWtqXOwPqfUWQjXF8Mb80pxOOdI6RoVxNCkCC4f253UrhEM6BJGcIBKGGk5+umSdqmypo5bP1zJF6uyOS8tkb+eOYgAP/USi4iszynlzUXb2LVnL3uche+eimqK99ZgDzKpX2igH9bWD1c7EGMgLPC/BXR4kD/lVbWkZ5VQVesAICokgNTEcE4e1JnUxAgGJ4YT3bGDq5spclAqkMWjVNbUkVtSSU5xJXsqqhndI4bwYNdO5p5fWsW0N5eyYmcRd57cl6vH99BtRkWk3VuVWcTTczcxa20uwQG+9IgNITI4gMTIICKDA5w9wwFEBPkTGeJPeFAAkcH/7SXe1zNcU+egeG+Ns1f5v73LRRU1FO2todjZA71vfYCvDxeP6kZq1wiGdI0gMTJIOVncTgWytAprLSWVteSWVJJdXElucf0yp6SSnOK95JRUkVNc31vRUFRIAHee1Jdzhie65OKLjJwSrnxtKbvLq3nuouGcNLBzs48pIuLNlmzdzdPfbWLehnzCAv248bjeXD62e5Pndvf39SGmYwdi1OsrXkwFsrSYwrIq5mTkMSs9l0VbChv92C06JIDO4YF0CQ9kWFIEncMC6Rxe//A1hsdnb+D2j1bxzpIdPDh5IIMSmz7Z+3cZedzw7i+EdPDlw2tGa+J4EWm3rLX8uLGAp+duYsm23cR0DOCOk/oydVQSoYG6BbOICmRxqe2F5cxem8us9FyWbt+Nw0J8eCBnDOlCcnQIncIDiQ8PpHNYIHFhHQ55g43RPaP5ePku/v71Os54Zj6/G5nEbSemHHHPxmsLtvLAF2vpFx/Gy5eOoHO4Jo8XkfbH4bB8uy6Xp7/bxKrMYjqHBXLv6f25YESS5g4WaUAFcju2MbeUbYUVdIkIpEt4EBHB/kc87stay+pdxfuL4vW5pQD07RzK9RN7MWlAZwZ0CWvyeDJjDGcPT+T4/p14YvYG3vhpG1+tzub2k/pyflrXQw67qK1z8MAXa3njp+2c0L8T/zp/CCEd9GMvIu1LncPyxaosnv1uM+tzS0mKCubvZw3irGEJuhOoSCNUKbRD1lpeX7iNv365jlrHfy9JDvL3rS+WI4LoEh5Uv4wIJCEiiPiIIOLDAwn096W61sHirYXMXpvL7LW5ZBdX4mNgRPco7j6tP5P6d6JrVLBLYw4P8ue+MwZw/oiu3DNjDXd9vJr3luzggckDSe0a0eg+JZU1XP/OL8zbkM/V43twx0l9NYm8iHitjbmlfL4yCx8fg7+vD34+Bj9fH/x9DX4+Pvj5mv3PG67LKqrkpR+3sLWgnF5xHXni/FROH9xF87uLHIQK5HamorqWuz5ezYwVWRzfL45rJ/Qir6SSXUV7yS6uJKtoL1lFe1mXXUpBWdX/7B/TMYCqGgelVbUE+vswvncst0xK4di+cUSFNO2CjiPRLz6MD64ezacrdvG3rzI489kFXDAiidtPTCGywfl37q7gitd+ZmtBOf84exDnj0hq8dhERFpKRk4JF7y4iKLfXMh8uAZ0CeO5i4Zx4oDO6igQOQwqkNuRrQXlXPPmMjbklXLbiSlce0zPgybKqto6coqdxXORs3gu3gsYju0bx7heMW4Zs2aMYcrQRI7v14l/fbuR1xZu4+s12dx2YgoXjEhixc49THtjGbUOyxtXjmRMz5hWj1FExFW25Jcx9T9LCPTz5cfbx5EQEUSNw0FtnaW2zu5/XlPnoNZhqa1zUFNnqXXULzv4+TRrqJtIe6QCuZ2YlZ7DLR+sxM/X8PrlIxnfJ/aQ+3Tw86VbdAjdokNaIcIjFxroz92n9ee8tK7cPWMNf/5kDW/+tJ0t+eV0iQjklctG0CO2o7vDFBFpsp27K7joP4ux1vLW70ftH77WwccXXU4h0nL069XG1Tks/5y1nme/38zgxHCevWgYiZGuHR/sbimdQ3l/2ig+W5nF375ax/BukTx70bBfDbkQEfE2uSWVXPSfxVRU1/HuVaPoFad/+EVaiwrkNqywrIob31vB/E0FXDgyiXtP70+gf9u8WtkYw+QhCZw2uAs+Bn2UKCJerbCsiov+s5jCsirevmoU/buEuTskkXZFBXIbtWJnEde9tYyC8moeOXsw543o6u6QWoWvLj4RES9XvLeGi19eQuaeCl6/fCRDDjBTj4i0HM3x0sZYa3ln8Q7Oe/4njDF8dM2YdlMci8jhM8ZEGGOmG2MyjDHrjDGjjTFRxpjZxpiNzmWku+Nsb8qrarns1SVszCvlhYvTOKpHtLtDEmmXVCC3IZU1ddw+fRV/+mQ1o3pG88UN45p1a2YRadOeBGZaa/sCqcA64E5gjrW2NzDH+VpaSWVNHb9/fSmrMov594XDOOYwLqYWkZahIRZtxM7dFVzz1jLSs0r4v+N6c+NxvTXcQEQaZYwJA8YDlwFYa6uBamPMZGCCc7PXge+BO1o/wvanutbBtW8tY9HWQp44bwgnDezs7pBE2jUVyF6sts7Bgs2FfPrLLmauycHf1/DypWkc16+Tu0MTEc/WA8gHXjXGpALLgBuBTtbabABrbbYxJs6NMbYbtXUObnr/F75bn8/fzxrEmUMT3B2SSLunAtnLWGtJzyrhk1928dnKLPJLqwgL9OPMoV249pheJEW3rSncRKRF+AHDgBustYuNMU9yBMMpjDHTgGkASUm6S2VzOByW2z9axVerc7j7tP5cOFJfTxFPoALZS+zcXcFnK7P45JddbMorw9+3/m52U4YmMCElrs1O3yYiLSITyLTWLna+nk59gZxrjIl39h7HA3mN7WytfRF4ESAtLc22RsBtkbWWez5bw8fLd3HLCX24clyyu0MSEScVyB6suKKGr9Zk88nyXSzZthuAkd2j+NuUQZwyqDMRwboRhogcOWttjjFmpzEmxVq7HjgOWOt8XAo87FzOcGOYbZq1lr9/ncFbi3ZwzTE9uf7YXu4OSUQaUIHsYay1zF6by8fLdzE3I4/qOgc9Y0O47cQUzkjtsv82oyIizXQD8LYxJgDYAlxO/cxGHxhjrgR2AOe6Mb42q7Syhsdnb+DVBdu4ZHQ37jgpRTc3EvEwLimQjTHbgFKgDqi11qYZY+4DrqL+QhCAP1lrv3LF+doqay33f76W1xZuI6ZjB6aO6saUoQkMTAhT8hQRl7LWrgDSGnnruNaOpb2oqK7l9YXbeWHeZooqapg6Kon7Th+g/C7igVzZgzzRWlvwm3VPWGsfc+E52ixrLQ9/ncFrC7dx5bhk7jq5L36+mqZaRMTbVdXW8c7iHTzz3WYKyqqYmBLLzSekaJ56EQ+mIRYe4onZG3hh3u9bHjEAACAASURBVBYuHtWNv5zaTz0KIiJerqbOwfRlmfx7zkayiisZ1SOK56cOI617lLtDE5FDcFWBbIFZxhgLvOC8whngemPMJcBS4BZr7R4Xna9NeXruRp6au4nz07py/xn6uE1ExJvVOSyfrdzFv77dyPbCCoYmRfDYuamM6RXj7tBE5DC5qkAea63Nck4qP9sYkwE8BzxIffH8IPBP4Irf7tje59N8ad4WHpu1gSlDE/jbWYPw0d3vRES8ksNh+SY9h8dnb2BjXhn948N45bI0JqbEqeNDxMu4pEC21mY5l3nGmE+AkdbaefveN8a8BHxxgH3b7Xyab/y0jYe+Wsepg+J59JzBujW0iIgXstby3fo8/jlrA+lZJfSK68izFw3jpAGd1ekh4qWaXSAbY0IAH2ttqfP5JOCBfZPNOzebAqxp7rnakveW7OCeGemc0L8T/7pgiC7IExHxQpl7Krj5/ZUs2babpKhgHj8vlclDEtThIeLlXNGD3An4xPnxkR/wjrV2pjHmTWPMEOqHWGwDrnbBudqEj5dnctcnq5mQEsvTvxuKv4pjERGv8/36PG56fwV1dZaHpgzkvLSuyucibUSzC2Rr7RYgtZH1Fzf32G3RF6uyuPXDlYzpGc3zU4fTwU+3iBYR8SYOh+WpuRt5cs5GUjqF8vzU4XSPCXF3WCLiQprmrRV9k57Dje+tIK1bFC9dkkagv4pjERFvsqe8mpveX8EPG/I5a1gCD505iKAA5XKRtkYFciv5LiOP699ZzuDEcF65fATBAfrSi4h4k5U7i7ju7eXkl1bxtymDuHBkV81OIdJGqUprBfM3FnD1W8tI6RzKa5ePpGMHfdlFRLyFtZZ3luzg/s/WEhvagenXjmZwYoS7wxKRFqRKrYUt3lLI79/4mR4xIbx5xVGEB/m7OyQRETlMe6vr+POnq/l4+S6O6RPLv84fQmRIgLvDEpEWpgK5BX2/Po8/vL2cxMhg3vr9UUqqIiJeZGtBOde+tYz1uaX88fg+3HBsL81rLNJOqEBuAXvKq3nwy7V8vHwXveM68vbvjyKmYwd3hyUiIofpm/Qcbv1gJb6+htcuH8kxfWLdHZKItCIVyC5kreWzlVk88PlaivfWcMOxvfjDxF6arUJExEvU1jl4dNZ6XvhhC6mJ4Txz0TASI4PdHZaItDIVyC6yq2gvd3+6hrkZeaR2jeDtswfRt3OYu8MSEZHDtKOwgtumr2Tx1t1MHZXE3af111z1Iu2UCuRmcjgsby7aziMzM3BYuPu0/lw2prtuMyoiHs0Ysw0oBeqAWmttmjHmPuAqIN+52Z+stV+5J8LWU1pZw9PfbeLV+dvw8zU8fl4qZw1LdHdYIuJGKpCbYUNuKXd+tIrlO4o4uncMf5syiK5R+ihORLzGRGttwW/WPWGtfcwt0bSyOodl+rKdPPrNBgrKqjh7WCK3n5RCp7BAd4cmIm6mArkJqmrrePa7zTz7/SZCOvjx+HmpTBmaoAnjRUS8xOIthTzwxVrSs0oY3i2Sly9NI7Wr5jYWkXoqkI/Qsu17uPOjVWzMK2PykC7cfVp/zVAhIt7IArOMMRZ4wVr7onP99caYS4ClwC3W2j1ui7AF7Nxdwd+/XsdXq3PoEh7IUxcO5fTB8ergEJFfUYF8mMqqanl0ZgZvLNpOfFggr142gol949wdlohIU4211mYZY+KA2caYDOA54EHqi+cHgX8CV/x2R2PMNGAaQFJSUutF3AxlVbU8+90m/jN/K77G8Mfj+zBtfA+CAnQRnoj8LxXIh1Bb5+CDpZk88W39GLVLR3fn1hNTdLtoEfFq1tos5zLPGPMJMNJaO2/f+8aYl4AvDrDvi8CLAGlpabYVwm0yh8Py0fJMHvlmPfmlVUwZmsDtJ6UQHx7k7tBExIOpyjsAay1z1uXx8MwMNuWVMbxbJC9ePJyhSZHuDk1EpFmMMSGAj7W21Pl8EvCAMSbeWpvt3GwKsMZtQbrAz9t288Dna1m9q5ghXSN44eLhDFMOF5HDoAK5Easyi3joy3Us3rqb5JgQnp86jBMHdNYYNRFpKzoBnzhzmh/wjrV2pjHmTWPMEOqHWGwDrnZfiE1XU+fgr1+s5fWfttM5LJB/nT+EM1K76DbRInLYVCA3sHN3BY98s57PV2YRHRLAA5MHcOHIJPx9fdwdmoiIy1hrtwCpjay/2A3huFRBWRXXvb2cJVt3c8XYZG49sQ/BAfpTJyJHRlkDKKqo5um5m3jjp+34+MD1E3tx9TE9CA30d3doIiJymFZlFnH1m8vYU1HNkxcMYfKQBHeHJCJeql0XyJU1dbzx0zaenruJ0qpazh2eyM0npNA5XJPEi4h4k4+WZXLXJ6uJ7diB6deMYWBCuLtDEhEv1i4LZIfD8tnKLB79Zj27ivYyISWWO0/uS9/OYe4OTUREjkBNnYO/fbWOVxdsY0zPaJ7+3TCiQgLcHZaIeLl2VyD/smMP98xIZ/WuYgZ0CeORcwYztleMu8MSEZEjVFhWxR/eWc6iLbu5clwyd53cFz9dMyIiLtBuCuQ95dU88k0G7/28k7jQDjx+XipnDknQVc0iIl5oza5irn5zGQVlVTxxfipThia6OyQRaUPafIHscFjeX7qTf8zMoLSylt+PS+bG4/voRh8iIl7q0192ccdHq4gOCeCjazXeWERcr01XiWt2FfOXT9ewYmcRI7tH8eCZA0npHOrusEREpAlq6xw8/HUG/5m/laOSo3jmomHEdOzg7rBEpA1qkwVycUUNj81az1uLtxMdEsDj56UyZWiCbvQhIuKldpdXc8O7y1mwqZDLxnTnz6f20xz1ItJiXFYgG2O2AaVAHVBrrU0zxkQB7wPdqb8r03nW2j2uOudvWWv5aPku/v7VOvZUVHPp6O788YQ+hAdpPmMREW+1cmcR1729nPyyKh47N5Vzhmu8sYi0LFf3IE+01hY0eH0nMMda+7Ax5k7n6ztcfE4A1mWXcM+MNfy8bQ9DkyJ4/YqRGpcmIuLF0rOKeWrORr5Jz6VzWCAfXj2a1K4R7g5LRNqBlh5iMRmY4Hz+OvA9Li6QSytreGL2Rl7/aRthgX784+xBnDu8q2anEBHxUg0L49BAP246vjeXj03Wp4Ei0mpcWSBbYJYxxgIvWGtfBDpZa7MBrLXZxpi43+5kjJkGTANISko6rBPV1jlYsm03s9Jz+WJVNoXlVVw4MonbT0whIlgTxIuIeCMVxiLiKVxZII+11mY5i+DZxpiMw9nJWUi/CJCWlmYPtF1FdS3zNuQzKz2XORl5FO+toYOfD0f3juGGY3vrYzcRETeoqXNgrW3WRdAqjEXE07isQLbWZjmXecaYT4CRQK4xJt7ZexwP5B3JMQvKqpizLpdZ6bn8uKmA6loH4UH+HNcvjkn9OzO+TwzBAW1yIg4REa+QkVPKsAdnM6BLOAO6hNG/SxgDuoSTHBOC7yGGuqkwFhFP5ZLq0hgTAvhYa0udzycBDwCfAZcCDzuXMw51rK0F5cxem8Os9FyW7diDtZAQEcRFRyUxqX9nRnSP1K1ERUQ8RJeIICb170x6djGvLthGdZ0DgOAAX/p2DmVgQn3hPKBLOL07daSDn68KYxHxeMbaA45qOPyDGNMD+MT50g94x1r7kDEmGvgASAJ2AOdaa3cf6DhhXVNs1EWPA9A/PoxJAzoxqX9n+sWHag5jEfF4xphl1to0d8fRmtLS0uzSpUsBqK51sCmvjPSsYtKzSkjPKmZtVgnl1XUA+PkYkqKD2ZJfTmigH1eOS1ZhLCJuc7Cc7ZIeZGvtFiC1kfWFwHGHexw/Hx/uPb0/x/frRNeoYFeEJiIijWiJuesD/Hzo7xxmca5zncNh2b67Yn/RvCGnlDNSu6gwFhGP5lEDeHvEhnD52GR3hyEi0l60+Nz1Pj6G5JgQkmNCOG1wl+YcSkSk1Wgwr4iI7DOZ+jnrcS7PdGMsIiJuowJZRKR92jd3/TLnfPTwm7nrgf+Zu15EpD3wqCEWIiLSapo0dz007QZPIiLeRD3IIiLtUMO566mfhWj/3PUAB5u73lr7orU2zVqbFhsb21ohi4i0GpdM8+YqxphSYH0Tdg0Hij10nxig4JBbNf88Td1PbaqnNjX9PE3dz5Pb1NSvQ29rbXgT9mtVjcxdP5v6ueuPAwobXKQXZa29/RDHakrebms5u6nnUpuavo/a1LxzeXKbWvPv0IFztrXWYx7A0ibu96IH73PEbWrKedQmtUltcm9szdmvtR9AD2Cl85EO/Nm5PhqYA2x0LqO8+XvSWj9japPapDa5rk2e8neorYxB/tyD92mKpp5HbWreuVrrPGpT887VGudpza9Dq7Mumru+Gdpazm7qudSmpu/TVGpT6+7TFB7xd8jThlgstW3sLlRqk3dQm7xDW2yTt2tr35O21h5Qm7yF2uRZPO0ivRfdHUALUJu8g9rkHdpim7xdW/uetLX2gNrkLdQmD+JRPcgiIiIiIu7maT3IIiIiIiJu1aIFsjGmqzHmO2PMOmNMujHmRuf6KGPMbGPMRucy0rneGGOeMsZsMsasMsYMa3CsOmPMCufjs5aMuxXblGSMmeU81lpjTHdvbpMxZmKD79EKY0ylMcYtt6p18ffpEecx1jm3MW2gTf8wxqxxPs53R3ua2Ka+xpifjDFVxphbf3Osk4wx653tvdMd7WkLXPxzprzt4W0yytve0h7l7NbWlKk0jmD6jHhgmPN5KLAB6A88AtzpXH8n8A/n81OArwEDjAIWNzhWWUvG6qY2fQ+c4HzeEQj29jY1OGYUsNvb2wSMARYAvs7HT8AEL2/TqdTPe+sHhABLgTAvaVMcMAJ4CLi1wXF8gc3UT18WQP30Zf3d0SZvf7g4xylve0GbGhxTedsz26Oc7Y62tvIXdgZwAvWTysc3+GKvdz5/AbiwwfYNt/OIROuqNjl/oOa7O35Xf58arJsGvO3utrjg+zQaWAYEAcHOxNTP3e1pZptuA/7SYP3LwHnubs/htKnBdvf9JtmOBr5p8Pou4C53t6ctPJS3lbe9rU2emreVs70rZ7faGGTnx1BDgcVAJ2ttNoBzGefcLAHY2WC3TOc6gEBjzFJjzCJ3ffzzW81sUx+gyBjzsTHmF2PMo8YY39aK/UBc8H3a5wLg3ZaM9XA1p03W2p+A74Bs5+Mba+261on8wJr5fVoJnGyMCTbGxAATga6tE/mBHWabDuRwfiblCClv76e83craWt5Wzv4fHp+zW+VGIcaYjsBHwE3W2pKDDAVq7I1902wkWWuzjDE9gLnGmNXW2s0tEO5hcUGb/ICjqf/h2gG8D1xG/X+GbuGi7xPGmHhgEPCNy4M8Qs1tkzGmF9APSHSum22MGW+tnef6aA9Pc9tkrZ1ljBkBLATyqf/4sbZFgj1MR9CmAx6ikXWaoqcZlLf/h/J2K2lreVs5u/FDNLLOo3J2i/cgG2P8qf8ivm2t/di5Otf5y7jvlzLPuT6TX/9XlAhkAVhr9y23UD8GbGhLx34gLmpTJvCLtXaLtbYW+BQYhpu46vvkdB7wibW2pmWjPjgXtWkKsMhaW2atLaN+fNio1oi/MS78fXrIWjvEWnsC9YlqY2vE35gjbNOBHOpnUo6A8rbytru0tbytnH1AHp+zW3oWC0P9f9brrLWPN3jrM+BS5/NLqR/Dsm/9JabeKKDYWpttjIk0xnRwHjMGGAusbcnYD8RVbQJ+BiKNMbHO7Y7F+9u0z4W4+WM6F7ZpB3CMMcbPmRSOAdzyUZ0Lf598jTHRzmMOBgYDs1qlEb/RhDYdyM9Ab2NMsjEmgPqPit02a4I3U97ev155u5W1tbytnH1Qnp+zW3KAMzCO+i7zVcAK5+MUIBqYQ/1/QHOAKOf2BniG+isbVwNpzvVjnK9XOpdXtmTcrdEm53snOI+zGngNCGgDbeoO7AJ83PU9cvHPni/1F06so/4P4eNtoE2BzrasBRYBQ7yoTZ2p73koAYqcz8Oc751C/RXVm4E/u/Pnz5sfLvw5U972njZ1R3nbk9ujnO2Gh+6kJyIiIiLSgO6kJyIiIiLSgApkEREREZEGVCCLiIiIiDSgAllEREREpAEVyCIiIiIiDahAFhERERFpQAWyiEg7Yox50BizyhizwhgzyxjTxbl+gjGm2Ll+hTHmHnfHKiLiLpoHWUSkHTHGhFlrS5zP/w/ob629xhgzAbjVWnuaWwMUEfEA6kEWEWlH9hXHTiHU3xVLREQa8HN3AA3FxMTY7t27uzsMEZEmWbZsWYG1NtbdcRyKMeYh4BKgGJjY4K3RxpiVQBb1vcnphzqW8raIeKuD5WyPGmKRlpZmly5d6u4wRESaxBizzFqb5gFxfAt0buStP1trZzTY7i4g0Fp7rzEmDHBYa8uMMacAT1prex/g+NOAaQBJSUnDt2/f7vpGiIi0sIPlbA2xEBFpY6y1x1trBzbymPGbTd8BznbuU2KtLXM+/wrwN8bEHOD4L1pr06y1abGxHt9hLiJyxJpVIOtqaBER72KMadgrfAaQ4Vzf2RhjnM9HUv/3obD1IxQRcb/mjkF+1Fp7N+y/Gvoe4Brnez/qamgREY/zsDEmBXAA2/lvzj4HuNYYUwvsBS6wnjQGT0SkFTWrQHb11dC5JZWs2FnE4IRwfHxMcw4lIq2gpqaGzMxMKisr3R1KqwoMDCQxMRF/f393h3LErLVnH2D908DTLXhe1ueWsmBTIUOTIhiWFNlSpxKRA1DOPvyc3exZLJp7NXTDiz0COvfizGcWENMxgIkpcRzXL45xvWPp2MGjJtsQEafMzExCQ0Pp3r07zk/n2zxrLYWFhWRmZpKcnOzucDxaZU0di7YUMmddHnMz8thVtBcAY2DqUd24/aQUQgO9758MEW+lnH34OfuQleehroa21v4Z+LPzaujrgXuB5UC3BldDfwo0ejW0tfZF4EWAocOG2/suGMKcdXl8k57Dh8sy8fc1jOoRzbF94zi2bxzdokMOu3Ei0rIqKyvbVaIFMMYQHR1Nfn6+u0PxSHmllXyfkc+363KZv6mAiuo6gvx9Gdc7hhuO7cWoHtG8/tM2Xlu4jdlrc3nwzIGc0L+Tu8MWaReUsw/fIQtka+3xh3msd4AvgXsbDr2w1n5ljHnWGBNjrS042AF8fQyThyQweUgCtXUOlm3fw9yMPOZk5HH/52u5//O19IrryHHOYnl4t0j8fDURh4g7tadEu097bPPBrNlVvD9Xr9xZBECX8EDOGpbAcf06MbpHNIH+vvu3v/f0AZyR2oW7Pl7NVW8s5ZRBnbnvjAHEhQa6qwki7UZ7zF9NaXOzxi4YY3pbazc6X/7qamgg11prm3o1tJ+vD0f1iOaoHtHcdUo/theWMzej/mO6VxZs5YV5WwgL9GNi3zhuOLY3veI6NqcpIiLSBBk5pZz27/kYA6mJEdw6qQ/H9u1Ev/jQg/5RGpoUyec3jOPFeVt4cs5G5m8s4E+n9OP8EV3b5R9wEfEszR3c22pXQ3eLDuHysclcPjaZsqpa5m/MZ866PGam5/D1mhxuPqEPvx+XrB5lEWHChAk89thjpKW5/Z4dbV6Qvy+PnDOYiSlxxIZ2OKJ9/X19+MPEXpw8sDN3fbyaOz9ezacrdvH3swaTHKPhdCLthSfm7GZVk9bas52Tzw+21p5urd3lXP+0tXaAtTbVWjvKWrvQNeHW69jBj5MGxvPouanMueUYJqbE8vDXGZz9/E9szC115alEROQgukUHc15a1yMujhvqEduRd68axd/PGkR6Vgkn/msez3y3iZo6hwsjFRE5fF7f3RoXGsjzU4fz7wuHsqOwnFOfms+z32+iVolVpF0oLy/n1FNPJTU1lYEDB/L+++//6v13332XQYMGMXDgQO6444796zt27Mgtt9zCsGHDOO644/ZfwLF582ZOOukkhg8fztFHH01GRkartqe98vExXDgyiTk3H8Px/eJ49Jv1nP7v+axwjmkWkbbBW3J2m5g/zRjD6aldGN0zmrs/XcMjM9czc00Oj56TSkrnUHeHJ9Iu3P95OmuzSg694RHo3yWMe08fcNBtZs6cSZcuXfjyyy8BKC4u5rnnngMgKyuLO+64g2XLlhEZGcmkSZP49NNPOfPMMykvL2fYsGH885//5IEHHuD+++/n6aefZtq0aTz//PP07t2bxYsXc9111zF37lyXtksOLC4skGcvGs6s9BzumZHOWc8u4LIxydwyqQ8hmvJTxGWUsw/O63uQG4rp2IHnpg7nmd8NI3PPXk7/93yenrtRH9OJtGGDBg3i22+/5Y477uDHH38kPDx8/3s///wzEyZMIDY2Fj8/Py666CLmzZsHgI+PD+effz4AU6dOZf78+ZSVlbFw4ULOPfdchgwZwtVXX012drZb2tXeTRrQmdk3j+eio7rxyoKtnP7v+WwrKHd3WCLSTN6Ss9vkv+OnDo5nVI8o7vksncdmbWBmeg6PnZtK385h7g5NpM06VK9BS+nTpw/Lli3jq6++4q677mLSpEn73zuSa4ONMTgcDiIiIlixYkVLhCpHKDTQnwfPHMgpg+L5wzvLOfPZBbwwdThH9Yh2d2giXk85++DaVA9yQ9EdO/DM74bx3EXDyCmu5PR/z+epOepNFmlrsrKyCA4OZurUqdx6660sX758/3tHHXUUP/zwAwUFBdTV1fHuu+9yzDHHAOBwOJg+fToA77zzDuPGjSMsLIzk5GQ+/PBDoD5Zr1y5svUbJb8yumc0n1w3huiQAKa+vJiPlmW6OyQRaSJvydlttkDe5+RB8cz64zGcNDCex2dv4MxnFrh8zI2IuM/q1asZOXIkQ4YM4aGHHuIvf/nL/vfi4+P5+9//zsSJE0lNTWXYsGFMnjwZgJCQENLT0xk+fDhz587lnnvuAeDtt9/m5ZdfJjU1lQEDBjBjxgy3tEt+rVt0CB9fO5aRyVHc8uFKHv0mA4ejWbOHiogbeEvONs2cntil0tLS7NKlS1vs+DPX5PCXT9dQVFHNFeOSuW5CTyKCA1rsfCJt3bp16+jXr5+7w2iSjh07UlZW1uT9G2u7MWaZtdZzJvJsBS2dt3+rps7BPTPSeXfJDk4Z1JnHzxvyq7v0iciBKWcffs5u8z3IDZ00sDOz/zieKUMTeOnHLRz9yHc8890mKqpr3R2aiIgcBn9fH/42ZSB/ObUfX6/J4fwXF5FXWunusESkjWlXBTJAZEgAj56byswbxzOqRzSPfrOe8Y98z5s/baO6VuOTRdqL5vREiHsZY/j90T14YepwNuSUMuWZhWTkaOicSFvW2jm73RXI+6R0DuWlS9L46Nox9IgN4e4Z6Rz/+A/MWLFL49pEjoAnDdNqLe2xzZ5o0oDOfHjNaGodDs5+diHfZeS5OyQRj9ce81dT2txuC+R9hneL5P1po3jt8hF07ODHje+t4NR/z+e7jLx2+UMkciQCAwMpLCxsV78r1loKCwsJDAx0dygCDEwIZ8YfxtE9JoQrX/+Z1xZsdXdIIh5LOfvwtauL9A7F4bB8sTqbf85az/bCCkYmR3HHSSkM7xbltphEPFlNTQ2ZmZlUVravMaCBgYEkJibi7+//q/W6SM99Kqpruem9Fcxam8slo7txz2n98fNt931AIr+inH34OVsFciNq6hy8//NOnpyzkfzSKo7v14nbTkzRbatF5KBUILuXw2H5x8wMXpi3hWP6xPL074YSGuh/6B1FpF3SLBZHyN/Xh6mjuvHDbRO47cQUFm8t5KQn53HH9FUUV9S4OzwREWmEj4/hrlP68fBZg1iwqYDJzyxgVnpOu/o4WURcQwXyQQQH+PGHib348faJXHV0D6Yvz+SEJ35g9tpcd4cmIiIHcMHIJN64ciQOh2Xam8uY/MwCvluv60pE5PCpQD4MEcEB/OmUfsz4w1iiO3bgqjeW8n/v/sLu8mp3hyYi0iTGmFuNMdYYE+N8bYwxTxljNhljVhljhrk7xuYY0zOGb28+hkfOHszu8mouf/Vnzn5uIQs2FahQFpFDUoF8BOqvlh7LzSf04es12Zzw+A98sSpLyVZEvIoxpitwArCjweqTgd7OxzTgOTeE5lJ+vj6cN6Irc2+ZwENTBpJdXMlF/1nMBS8uYsnW3e4OT0Q8mArkIxTg58P/HdebL244moTIIK5/5xeufWu57uQkIt7kCeB2oOF/95OBN2y9RUCEMSbeLdG5WICfDxcd1Y3vbp3Avaf3Z3N+Oee98BMXv7yYX3bscXd4IuKBVCA3UUrnUD6+dgx3ntyXuevzOOHxeXy8PFO9ySLi0YwxZwC7rLUrf/NWArCzwetM57o2I9Dfl8vHJvPj7RP58yn9SM8qYcqzC7nitZ9Zs6vY3eGJiAdRgdwMfr4+XHNMT76+8Wh6xXXk5g9WcuXrS8ku3uvu0ESkHTPGfGuMWdPIYzLwZ+CexnZrZF2j//EbY6YZY5YaY5bm5+e7MvRWERTgy1Xje/Dj7RO57cQUlm3fw2n/ns/Vby7VLatFBNA8yC5T57C88dM2Hpm5Hj8fw59P7cf5I7piTGN/c0SkLfL0eZCNMYOAOUCFc1UikAWMBO4HvrfWvuvcdj0wwVqbfbBjenPe3qeksoZX5m/l5R+3UlZdy83H9+EPE3vh46P8LdKWaR7kVuDrY7h8bDLf3DSegQnh3Pnxai5+eQk7d1ccemcRkVZgrV39/+zdd3ib1dn48e+RvPd2POPsvSeEBEIIe7eU3QbaUnYpbWkpfUvbt7xdtP21hbLKaguUUEJZgbBCSELixM7ew45HvPeQba3z+0OSoyS243hJj3J/rkuX5UfSo3Ms+ejWee7nPlrrFK11jtY6B1caxUytdQXwDvB1dzWL+UDjqYLjQBETFswDF4xl7Y8Wc+W0dP7w8QHufmULLR12XzdNCOEjEiAPsOzECF751jweu2Yy20oauPQva9lTJofs+Jh89AAAIABJREFUhBB+byVQABwCngPu9m1zhl5cRAj/7/rp/PSyCXy0p4JrnlzPkZpWXzdLCOEDEiAPApNJcfO84Xzw3YVEhQax7EWZSRZC+B/3THKN+7rWWt+jtR6ltZ6itTZ23kQfKaX41sKR/POb86hp6eDKJ9axen+Vr5slhBhiEiAPoqyECF6+fS7tNgffeGGTLCwihBAGsWB0Eu/cew4Z8RHc/tJmnlx9SKoUCXEGkQB5kI1Njeb5ZXM42tDG7S9txmKVnDYhhDCCrIQIVtx1NpdPTef3q/Zzz6tbaJW8ZCHOCBIgD4E5OQn85cYZ7Cht4J5XtmBzOH3dJCGEEL0QHmLmLzdM5yeXjufDXRVc+7cvKaqVvGQhAp0EyEPkoknD+N+rJ7N6fzU/WbFTDtUJIYRBKKW4Y9EoXr59LhVN7Vz5xHrWHDBe/WchRO9JgDyEbp43nO8uGcMb+aU8/tF+XzdHCCHEaVg4Jpl37z2HtNgwbntxE0+vOSyTHUIEKAmQh9gDF4zhxrlZPLn6MC9/ecTXzRFCCHEashMjWHH32VwyJY3ffLCPe1/bKueWCBGAgnzdgDONUor/vWoy1c1Wfv7ubpKiQrlsapqvmyWEEKKXIkKCeOLGGUxOj+V3q/ZxuKqFx6+bxuSMWF83TQgxQAZsBlkp9QOllFZKJbl/V0qpvyilDimldiilZg7UcxldkNnEEzfNYGZ2PN97fRsbDtf6uklCCCFOg1KKu84bxUu3zaW8sZ3L/7qOW/6eyxcHqiXtQogAMCABslIqC1gKFHttvgQY477cATw1EM8VKMKCzTz/jdlkJ0Zwxz/y2Fsuq+0JIYTRnDs2mS8eWsyPLxnPwapmvv7CJi7581pWbCnFapeKRUIY1UDNIP8JeAjw/tp8FfAP9+pMG4E4pZTkEniJiwjh5dvnEhkaxDdekNX2hBDCiGLDg7nz3FGsfeh8fv/VqTi15sHl21n0u9U8+8Vhmtttvm6iEOI09TtAVkpdCRzVWm8/4aYMoMTr91L3NuElIy782Gp7L8pqe0IIYVQhQSaum53FqgcW8eJtcxiRFMn/rdzH2b/+jF+v3Et5Y5uvmyiE6KVeBchKqU+UUru6uFwFPAL8rKuHdbHtpMQspdQdSqk8pVRedfWZWVdy3LBo/v6NOZTWy2p7QghhdEopFo9L4bU75vPuvedw3vgU/r6ukIW/Xc2Dy7dJSp0QBqD6czKBUmoK8CngyQ3IBMqAucAvgM+11q+577sfOE9rXd7d/mbPnq3z8vL63B6j+3BXBXe/ks+isck8dNF4xqZGEWSWSnxCGIVSKl9rPdvX7RhKZ/q43VsldRaeX1fI8rwSLFYHi8Ym88MLxzElUypfCOErPY3Z/QqQu3iiI8BsrXWNUuoy4F7gUmAe8Bet9dyeHi8DLfxrYxE//e8uAMKDzUzJjGV6VlznJS02DKW6mpwXQviaBMjiVBosVl7JLebF9YV02Jy8cddZjB8W4+tmCXFG6mnMHsw6yCtxBceHcM0w3zaIzxUwbpk/nHPHJpNfVM+2kga2ljTw0vojWB2us6FTokNdwXK2K2CemhlHVKiUsxZCCCOIiwjhnsWjuWZGBtf8bT23vbiZt+5ewLDYMF83TQjhZUBnkPtLZiK61mF3sLe8mW3FrqB5W0kDR2pdWS1KwZiUKGZkxfOthSMYkxrt49YKceaSGWRxOnaXNfK1pzeQnRjJ8u/MJzos2NdNEuKM4qsZZDFAQoPMnSkWHvWtVraXNnQGzCt3lrNyZzlP3zqLBaOTfNhaIYQQvTEpPZa/3TKL21/azD2vbuX5b8wmWM47EcIvyH+iQcVHhnDeuBQeuGAsL902l1XfW0R6XDjfeGETb+SVnHoHQgghfO7cscn83zWT+eJANT99a5eswieEn5AAOUCkx4Xzxl1nMX9kIj/8zw7++PEBGWiFEMIArp+TzX3nj+b1vBKeXH3I180RQiABckCJCQvmxdvm8NVZmfzl04N8/43tZ9RSpw0WKz98Yzsvri/0dVOEEOK0PLh0LNfOyODxjw7w1tZSXzdHiDOe5CAHmGCzid9/dSrZCRH88eMDVDS289Qts4gND+yTP7YU13Pfq1s52tAG+RAXEcw1MzJ93SwhhOgVpRS/+cpUyhvbeeg/O0iNCePsUXI+iRC+IjPIAUgpxf1LxvDHr01j85E6rnv6S0rrLad+oAFprfn72gK+9vQGlIL/3HkWZ41M5KH/7GDD4VpfN08Iv6WU+oFSSiulkty/n6eUalRKbXNfulohVQyikCATT986i5zESL7zz3wOVDb7uklCnLEkQA5g187M5OXb5lLe2M41f/uSXUcb+71PrTV2h3+kbTRYrHz7H3n86v29XDAhlffvX8jsnASvD5g8DlXJB4wQJ1JKZQFLgeITblqrtZ7uvvzSB00748WGu1LlwoLN3PbiZqqa2n3dJCHOSBIgB7izRyfx5l1nE2I28bVnNvDZvsrT3ke7zcHq/VU88tZO5v/6U6b8/CN+9J8dbC9p8NmJgPlF9Vz657WsOVDNz6+YyFO3zOxMI4kND+aFZXMICTKz7MXNVDd3+KSNQvixPwEPAXImrx/KjI/gxWVzqLdYuf3lzbR22H3dJCHOOBIgnwHGpkbz1t1nMzI5km+9nMc/Nxad8jF1rVbezC/lzn/mM/N/P3at9rT1KDOz47lsahrvbC/jqifXc/lf1/FKbhEtQzSAO52aZ9Yc5vpnNmA2K96862yWLRhx0vLbWQkRvLBsNrUtVr758mYsVvmAEQJAKXUlcFRrvb2Lm89SSm1XSn2glJo01G0Tx0zOiOXJm2ayt7yZe1/d0qcjd3aHkx2lDXyws5x2m2MQWilE4JKV9M4grR127nttK5/tq+KORSP58cXjMZmOBZaFNa18sqeSj/dUkldUh1NDakwoF0xI5YKJqZw1MpGwYDMATe023t56lFdyi9lX0UxkiJkrp2dw87xsJmfEDkr761utfP+N7Xy2r4pLJg/jN1+ZesqTDz/eU8kd/8zjggmpPH3LLMwm1eP9hegPf1lJTyn1CTCsi5seAX4CXKi1blRKHQFma61rlFIxgFNr3aKUuhT4s9Z6TDf7vwO4AyA7O3tWUdGpv3SLvnk1t5ifvLWTm+dl86urJ580GeDNYrWztbiBzUfqyDtSz5bieixWV2CcGR/OTy+bwEWThvW4DyHOJD2N2RIgn2HsDic/f3c3/9pYzGVT0vjG2Tl8tq+Kj/dUcLi6FYAJaTEsnZDCBRNTmZIR2+NgqrVma0kDr+YW896OMtptTqZmxnLj3GyunJZOZOjAFErJL6rj3le3Utti5aeXT+DW+cN7Pci/tL6Qn7+7h9sW5PDoFTIpJgaPvwTI3VFKTQE+BTxn7WYCZcBcrXXFCfc9gjt47mmfMm4Pvt9+uI+nPj/Mjy4ez13njercXtPSQd6RevKO1LH5SB27yppwODVKwYRhMczJiWd2TgLhwWZ+v2o/+yubOXtUIj+7YiLjh8X4sEdC+AcJkMVxtNY8+0UBv/5gHwBBJsX8kYlcMCGFJRNSyUqI6NN+G9ts/HfrUV7NLWZ/ZTNRoUFcNT2dm+ZlMym9b7PKTqfmmS8KePyj/WTGh/PkTTP7NEP9v+/t4fl1hfzs8oncfs6IPrVFiFPx9wD5RCfMIA8DKrXWWik1F/gPMFyf4kNCxu3B53RqHnh9G+9sL+OexaOoabayuaiOAvekRkiQielZcczJiWdOTgIzh8cTE3b80TW7w8mrm4r5w0cHaG63cfO84Ty4dCzxkSG+6JIQfkECZNGlTYV1VDa1s2hs8oDWSdZas6W4nldyi3l/RzkddicT0mLIiAsnNjyY2PBgYsKDjl0PCyY2wut6eDBhwSbqLTYeXL6Nz/dXc9mUNH79lSknDfq95XBq7n4ln4/2VPLMLbO4cFJXR5+F6B+DB8j3AncBdqANeFBr/eWp9iHj9tDosDv4+vObyC2sIzY8mNnD45kzIoE5OfFMzoglNMjcq/3Ut1r50ycH+NfGIqLDgnlw6VhunpdNkFlOSRJnHgmQhc80WKys2HKUj/dUUm+x0tRmo7HNRqu15xNGQswmlAKt4X+umMgt87L7nTfXZnVww3Mb2V/RxOt3nMW0rLh+7U+IExktQB4IMm4PnXabg6MNbYxIjDzu/JG+2FfRxC/f3cOXh2sZmxrFo1dMYsFoWZhEnFkkQBZ+x+5w0tRup7HN1hk0N7bZaGp3/2yz025z8NVZmQN60l91cwfXPrWeNquDt+5e0Od0EiG6IgGyMBKtNat2V/LYyj2U1LVx4cRUfnrZRLITh2ZctDuc1LZaCTIpEqNCh+Q5hfAmAbIQXg5VtXDt39aTEhPGm3eeTWxEYC/DLYaOBMjCiNptDp5fV8iTqw9hd2i+tXAE9ywe3eeTrNttDqqbO6hqbqeqqYMqr+vVLR2d22pbO/CEIOOHRbNgdBILRicyd0QiUQN0grcQPZEAWYgTbCyo5evPb2Lm8Dj+cfs8QoIk/070nwTIwsgqGtv53Yf7WLH1KMnRoYxOjsKhNU6nxqk1Ds2x606N1pxwu6bRYqOp/eS682aTIikqhJToMFKiQ0mJCSXZfb2p3caXh2rZdKQOq91JkEkxIzuOBaOTOGd0EtOy4giWHGkxCCRAFqILb287ynf/vY1rZ2Twh69Nk9qgot8kQBaBYEtxPU9+doimdhsmpTCbFCalMJkUZkXndZPi2G3u+0WHBbkC4OgwkmNCO68nRIacsg59u81BflE96w7VsP5QDTuPNqI1RIaYmT8y0T3DnMTY1CgZr8WA6GnMlmMY4ox11fQMSuosPP7RAVCwYFQSOUkRZCdEkhQVIgOwEOKMNDM7nueXzRny5w0LNncGweA6yXvD4VrWH65h/aFaPt1XBUBydCiLxiRz+zk5fS4hKsSpSIAszmj3LB5NTYuVlzccYcWWo53bI0PMZCdGkpMYQXZiBMMTjl1Piw2XFfmEEGKQxUWEcMmUNC6ZkgZAab2FLw/Vsu5QDat2V/DmllIumJDCPYtHMyM73setFYFGUiyEwFVjtLS+jaLaVopqLe5LK0V1Fkrr2rA6nJ33DTGbyEwIZ3J6LL+4cpIU2hedJMVCiKHR2Gbj5S+P8ML6QhosNhaOSeLexaOZNzLR100TBiIpFkKcQmiQmVHJUYxKjjrpNodTU97YRnGthaI6C0dqWymutfDh7goOV7fwyrfmERchQbIQQgyV2PBg7l8yhtvPGcErG4t4bm0B1z+7kbk5Cdx7/mgWjkmSNDnRLzKDLEQfrTlQzbf/kcfY1Che+eZ8KRcnZAZZCB9ptzn496ZinvmigPLGdqZlxnLv+WO4YEKKBMqiWz2N2VI3RYg+OndsMs/cOosDFS3c8nwujW02XzdJCCHOSGHBZpYtGMHnPzyPX187hTqLlW//I49L/ryW93aU4XD6z2SgMAYJkIXoh8XjUnjm1lnsr2jm6xIkCyGET4UGmblxbjarv38ef/zaNGwOJ/e+upWlf1rDm/mlEiiLXpMAWYh+Wjw+hadumcme8ia+/sImmtolSBZCCF8KMpu4dmYmH33vXJ68aSYhZhPff2M71/xtPbvLGn3dPGEAEiALMQCWTEjlqZtnsaeska8/v4lmCZKFEMLnzCbFZVPT+OC7C/nzDdMpa2jjyifW8+uVe2mzOnzdPOHHJEAWYoBcMDGVJ2+aya6jjXzjBQmShRDCXyiluGp6Bp88eC7XzcrkmS8KuPD/rWHNgWpfN034KQmQhRhAF04axhM3zWRHaSPLXtxMS4fd100SQgjhFhcRwm++MpV/3zGfYLOJb7ywiQf+vZWalg5fN034GQmQhRhgF08exhM3zWBbSQPLXtgkQbIQQviZ+SMTWXn/Qu5fMob3d5ZzwR/XsDyvBH8qfSt8SwJkIQbBxZPT+OuNM9ha0sDtL26mVYJkIYTwK2HBZh5cOpaV9y9kTEoUD/1nBzc9l0tBdYuvmyb8gATIQgySS6ek8ecbppNfXM9tL23GYpUgWQgh/M2Y1Ghev+Ms/u+aKewqa+TiP6/lic8OYrU7fd004UMDEiArpX6glNJKqST37+cppRqVUtvcl58NxPMIYTSXT03nT9dPJ+9IHbdLkCyEEH7JZFLcNC+bTx88l6UTUnn8owNc/te15BfV+bppwkeC+rsDpVQWsBQoPuGmtVrry/u7fyGM7spp6Wit+d7r27j9pc3cPG84ESFmIkKCiAgxExlqJjwkiMgQM+EhZkLMJlkaVQghfCAlJownb57JtXsr+Z//7uKrT29gWmYcI5MjGZkUycjkKEYkRTIiKZKwYLOvmysGUb8DZOBPwEPA2wOwLyEC0lXTM9Aavv/GdjYW9DwjYTYpdwBtJjIkiIhQM1dPz+Cb54yQwFkIIYbAkgmpzB+ZyDNrDpNfXM+Gw7Ws2HK083alID02vDNwHuEOnkcmR5IeG47JJGO10fUrQFZKXQkc1Vpv7+KD+yyl1HagDPiB1np3f55LCKO7ekYGi8YmU9PSgcXqwGK1Y+lwYLE5sHTYsVgdtNkctHquWx20Wu0cbWjjV+/vZWtJA7/7ylQiQwfie604Uymlfg58G/AUgP2J1nql+7aHgW8CDuB+rfUqnzRSCD8QGRrEgxeO6/zdYrVTWNNKQXWr+2cLBTWtvLnl6HHVikKDTMwaHs+3F47kvHHJMrFhUKf8pFVKfQIM6+KmR4CfABd2cdsWYLjWukUpdSnwX2BMN/u/A7gDIDs7u5fNFsKYEiJDSIgMOa3HaK155osCfvfhPg5VtvDMrbPISYocpBaKM8SftNaPe29QSk0EbgAmAenAJ0qpsVprWW5MCCAiJIhJ6bFMSo89brvWmuqWDgqrWymoaeVwVQvv7yzntpc2My41mjsWjeTK6ekEm6UugpGovtb8U0pNAT4FLO5Nmbhmi+dqrStOuO8RYLbWuqanfc6ePVvn5eX1qT1CBLq1B6u577WtOJ2aP98wg8XjU3zdJHECpVS+1nq2r9vRE/cMcksXAfLDAFrrX7t/XwX8XGu9oaf9ybgtxMlsDifvbi/jmTUF7K9sJj02jNvPGcGNc7PlKKAf6WnM7vPXGa31Tq11itY6R2udA5QCM7XWFUqpYcp9TEEpNdf9PLV9fS4hBCwck8y7955DZnwEt7+8mb98ehCnU4raiz65Vym1Qyn1glIq3r0tAyjxuk+pe9tJlFJ3KKXylFJ51dWyVK8QJwo2m7h2ZiYfPrCQF5fNITMhgl+9v5ezf/MZj6/aT3WzrNzn7wZrvv+rwC53DvJfgBu0LE8jRL9lJUTw5l1nc9W0dP748QG+8698mtttvm6W8DNKqU+UUru6uFwFPAWMAqYD5cAfPA/rYlddjtta62e11rO11rOTk5MHpQ9CBAKlFIvHp7D8O2ex4u6zOWtkIk9+fogFv/2MR97ayZGaVl83UXRjwOb53bPInutPAE8M1L6FEMeEh5j50/XTmZoZx2Mr93LVk+t59tbZjE6J8nXThJ/QWl/Qm/sppZ4D3nP/Wgpked3sSZsTQgyAmdnxPH3rLA5Xt/D3tQW8kVfKa5uKuWRyGt85dyRTM+N83UThRTLGhTAgpRS3nzOCV741j0aLjaufXM+q3RWnfqA44yml0rx+vQbY5b7+DnCDUipUKTUC14nVm4a6fUIEulHJUfz62qms+9FivnPuKL44WM2VT6znhmc3sHJnOTaHrODnDyRAFsLA5o9M5N37zmFUciTf+Wc+j6/aj0PykkXPfqeU2qmU2gEsBr4H4C7FuRzYA3wI3CMVLIQYPCkxYfzo4vF8+ePz+cml4ympa+PuV7aw4Def8cePD1De2ObrJp7R+lzFYjDI2dBC9E27zcGjb+/m9bwSzhuXzJ+vn0FsRPBJ97M7nJQ3tlNSb6G0ro3iOgsl9RZK6iwU17XR3G5jeGIEI5NcBe89he9HJUV1uT9xPCNUsRhoMm4LMTAcTs3qfVX8K7eINQeqMSnFkvEp3DJ/OOeMTpLFRwZBT2O2BMhCBAitNa9uKubn7+wmPS6cexePpqq5g9J6CyXuYLisoQ271wyz2aRIiw0jOyGCrPgIosKCKKp1FcIvrrMcd9/EyBD3qlHHB8/ZCRFS39NNAmQhxEAorrXw6qZilueVUNdqJScxgpvnDeerszKJP81a+qJ7EiALcQbJL6rnrn/lU+UuI5QUFUJmfARZCRFkJ4ST1Xk9gmGxYd0GtzaHk+I6CwXV7hWjqlspqHH9rG21dt4vxGxi6cRUrpudycIxyZjP4FkOCZCFEAOpw+7gg50V/GtjEXlF9YQEmbh8ahq3zB/OjKw4WaWvnyRAFuIM09xuo7yxnYy48EEpSt9osXHYHSzvKG3g3e1l1FtspMWG8dVZmVw3K4vsxIgBf15/JwGyEGKw7C1v4pXcIt7acpRWq4NJ6THcNC+bc8cmkxEXLsFyH0iALIQYVB12B5/urWJ5XglfHKjGqWH+yASun5PFxZPSCA8x+7qJQ0ICZCHEYGvpsPPW1qO8srGIfRXNAAyLCWNWTjyzsuOZnRPPhLQYSX3rBQmQhRBDpryxjTfzS1meV0pxnYXo0CCumJ7O12ZnMS0zNqBnOSRAFkIMFa01e8ub2XykjryievKP1FHW2A5AeLCZ6VlxzBoez6yceGZmxxMbLidan0gCZCHEkHM6NZuO1LF8cwkrd5XTbnMyLjWa62Zncs2MDBKjQn3dxAEnAbIQwpfKGtrIL6onv6ievKI69pY343BqlIKxKdHMHB7P7OHxjE2NJishnNjw4ICetDgVCZCFED7V1G7jve3lLM8rYVtJA8FmxSOXTmDZghG+btqAkgBZCOFPWjvsbCtpcAfM9Wwtqqe5w955e3RoEJkJEWTGe07gPnYid2b84JzD4k96GrMDu+dCCL8QExbMTfOyuWleNgcqm/n1yr384r09pMeFc+GkYb5unhBCBKTI0CAWjE5iwegkwFVr+VBVC4U1re4SoBZK6tsoqm1l3cEa2mzHrw2UEBlCVnw4mQkRXDgxlaumZ/iiGz4hAbIQYkiNTY3mbzfP4oZnN/Ddf2/jjTvPYnJGrK+bJYQQAc9sUowbFs24YdEn3aa1prbV2hk0e2rol9Zb2FbcwPs7ytlUWMejV0wiJCjwTwCUAFkIMeTCQ8w8943ZXP3Eer71ch7/vWcBw2LDfN0sIYQ4YymlSIoKJSkqlBnZ8cfd5nBqfr9qP0+vOcz+imb+dstMUqIDe8wO/K8AQgi/lBIdxvPL5tDcbuNb/9iMxWo/9YOEEEIMObNJ8eNLxvPXG2ewq6yRK/+6nm0lDb5u1qCSAFkI4TMT0mL4600z2FPWxAP/3obT6T8nDQshhDjeFdPSWXHXAoLMiq89s4HleSW+btKgkQBZCOFT549P5X8un8hHeyr57Yf7fN0cIYQQPZiYHsO7957DnJx4HvrPDh59exc2h9PXzRpwEiALIXxu2dk53Dp/OM98UcC/NxX7ujlCCCF6EB8Zwsu3zeXbC0fw8oYibv57LjUtHb5u1oCSAFkI4XNKKR69YiKLxibz0//u4stDNb5ukhBCiB4EmU08ctlE/t/109le0sCVf13HztJGXzdrwEiALITwC0FmE0/cNIMRSZHc+a98DlW1+LpJQgghTuHqGRm8edfZKKX46tNfsmJLqa+bNCAkQBZC+I2YsGBeWDaHkCAT33x5M3WtVl83SQghxClMzojlnXsXMCM7jgeXb+eX7+7BbvC8ZAmQhRB+JSshgmdunU15Yzt3/jOfDrvj1A/qhtY6IE8eEUIIf5MYFco/vzmP2xbk8ML6Qr7+wiZDT3LIQiFCCL8za3g8j183jftf28rDK3byh+umoZTq1WMb22ysP1TD5/urWHOgmvpWG/NHJXLBhBSWTEglIy58kFsvhBBnpmCziUevmMSk9Fh+8tZOzv3daiZnxDI+LZoJaTFMTIthdEoUYcFmXzf1lCRAFkL4pSunpXOkppU/fnyAkUmR3Hv+mC7v53Rq9pQ3seZANZ/vr2JLcQMOpyYmLIiFY5JJiQllzf5qfvb2bn729m7GD4vmggmpLJmQwrTMOEym3gXeQggheuerszIZPyyaV3KL2FPezGubimm3uY7mmU2KkUmRTEiLOS5wTokO7fVEyFCQAFkI4bfuO380hTWtPP7RAXKSIrl8ajoADRYraw/W8Pn+atYcqO4sLzQ5I4a7zh3FeeOSmZ4VR5DZnUV2BRyubuHTvZV8sreKp9Yc5onVh0iKCmXJ+BSWTEjhnDFJRIQE/pColPo58G2g2r3pJ1rrlUqpHGAvsN+9faPW+s4hb6AQIiBMzojl19dOBVxLVRfVtrK3vJl9FU3sLW8iv6ied7aXdd4/ITKE8cOimZQew6KxycwdkUBokO9mmpXW/rNy1ezZs3VeXp6vmyGE8CMddgc3P5fLzqON3LZgBJsKa9lW0oBTQ1xEMAvHJHPe2GQWjU0mOTq0V/tssFj5fH81n+ytZM3+apo77IQEmVgwKpEl7tnltNjTT8VQSuVrrWef9gOHkDtAbtFaP37C9hzgPa315NPZn4zbQoi+arTYOgPmzuC5ohmr3UlkiJlFY5M5f3wKi8enkBTVu/H9dPQ0ZkuALITwe7UtHVzzty8pqbcwNSOWc8elcN64ZKZlxmHuZ4qE1e5k85E6Ptlbyad7qyiuswCuZbAXj0tm8fgUZnjPRvdAAmQhhOifNquDLw/X8MneKj7bV0llUwdKwfSsOC6YkMr541MYPyx6QNIxJEAWQhhec7sNm0OTEBkyaM+hteZQVQuf7qti9b4q8orqcTg1seHBLBqbzOJxyZw7NpnEbmYyDBQgLwOagDzg+1rreneAvBs44L7tp1rrtafan4zbQojBorVmd1kTn+6t4tN9lexwL0SSERfO+e70uPkjE/t80p8yJWiAAAAgAElEQVQEyEII0Qeeihir91Wxer8r11kpmJoZ55pdHpfClIzYzhP9/CVAVkp9Agzr4qZHgI1ADaCB/wXStNa3K6VCgSitda1SahbwX2CS1rqpi/3fAdwBkJ2dPauoqGiQeiKEEMdUNbXz2b4qPtlbxbpD1bTbnIQHmzlnTBLjUqNJjQklJSaM1JgwUmNCSYoKJbiHo38SIAshRD85na6ZjNX7q1i9v4ptJQ1oDUlRIe7Z5RSunJ7hFwFyb/WUVqGU+hz4gda6x0FZxm0hhC+02xxsOFzLp/sqWXOgmrKGdhzO42NapSAxMpTUmNDOoDkl+lgAfcHEYd2O2YF/yrYQQgwAk0kxJTOWKZmx3L9kDHWtVr44UM3q/VV8tq+KFVuO+rqJvaKUStNal7t/vQbY5d6eDNRprR1KqZHAGKDAR80UQogehQWbWew+gQ9clTJqWzuoauqgsqmdSvfPquZj13eUNlLb2kFv5oYlQBZCiD5IiAzh6hkZXD0jA4dTs62kntm/9XWreuV3SqnpuFIsjgDfcW9fBPxSKWUHHMCdWus63zRRCCFOj9mkSIkOIyU6jMkZsd3ez+ZwUtPSQWVTBzN6GLMlQBZCiH4ymxSzhif4uhm9orW+tZvtbwJvDnFzhBBiSAWbTaTFhp+ylOep6xYJIYQQQghxBpEAWQghhBBCCC8SIAshhBBCCOHFr8q8KaWagf19eGgs0Oinj0nCVXN0sJ+nr4+TPrlIn/r+PH19nD/3qa9/hzFa6+7PDglAfRy3A23M7utzSZ/6/hjpU/+ey5/7NJSfQ92P2Vprv7kAeX183LN+/JjT7lNfnkf6JH2SPvm2bf15nJEv/vyaDNV7TPokfZI+DVyf/OVzKFBSLN7148f0RV+fR/rUv+caqueRPvXvuYbieYby73AmCrQxu6/PJX3q+2P6Svo0tI/pC7/4HPK3FIs8baBVqHpD+mQM0idjCMQ+GV2gvSaB1h+QPhmF9Mm/+NsM8rO+bsAgkD4Zg/TJGAKxT0YXaK9JoPUHpE9GIX3yI341gyyEEEIIIYSv+dsMshBCCCGEED4lAbIQQgghhBBeBjVAVkplKaVWK6X2KqV2K6W+696eoJT6WCl10P0z3r1dKaX+opQ6pJTaoZSa6bUvh1Jqm/vyzmC2ewj7lK2U+si9rz1KqRwj90kptdjrNdqmlGpXSl1t5D65b/udex973fdRAdCn3yqldrkv1/uiP33s03il1AalVIdS6gcn7OtipdR+d39/7Iv+BIIBfp/JuO3nfVIybhulPzJmD7W+1Jo7jfpyacBM9/Vo4AAwEfgd8GP39h8Dv3VfvxT4AFDAfCDXa18tg9lWH/Xpc2Cp+3oUEGH0PnntMwGoM3qfgLOB9YDZfdkAnGfwPl0GfAwEAZFAHhBjkD6lAHOAx4AfeO3HDBwGRgIhwHZgoi/6ZPTLAI9xMm4boE9e+5Rx2z/7I2O2L/o6xH/Yt4GluFZdSvP6Y+93X38GuNHr/t7384uBdqD65H5DrfN1+wf6dfLadgfwiq/7MgCv01lAPhAORLgHpgm+7k8/+/RD4Kde258Hvubr/vSmT173+/kJg+1ZwCqv3x8GHvZ1fwLhIuO2jNtG65O/jtsyZhtrzB6yHGT3YagZQC6QqrUuB3D/THHfLQMo8XpYqXsbQJhSKk8ptdFXh39O1M8+jQUalFIrlFJblVK/V0qZh6rt3RmA18njBuC1wWxrb/WnT1rrDcBqoNx9WaW13js0Le9eP1+n7cAlSqkIpVQSsBjIGpqWd6+XfepOb96T4jTJuN1Jxu0hFmjjtozZJ/H7MTtoKJ5EKRUFvAk8oLVu6iEVqKsbPHXosrXWZUqpkcBnSqmdWuvDg9DcXhmAPgUBC3G9uYqB14FluL4Z+sQAvU4opdKAKcCqAW/kaepvn5RSo4EJQKZ728dKqUVa6y8GvrW9098+aa0/UkrNAb4EqnEdfrQPSmN76TT61O0uutgmNSz7Qcbtk8i4PUQCbdyWMbvrXXSxza/G7EGfQVZKBeP6I76itV7h3lzp/mf0/FNWubeXcvy3okygDEBr7flZgCsHbMZgt707A9SnUmCr1rpAa20H/gvMxEcG6nVy+xrwltbaNrit7tkA9ekaYKPWukVr3YIrP2z+ULS/KwP4//SY1nq61noproHq4FC0vyun2afunOo9KU6DjNsybvtKoI3bMmZ3y+/H7MGuYqFwfbPeq7X+o9dN7wDfcF//Bq4cFs/2ryuX+UCj1rpcKRWvlAp17zMJWADsGcy2d2eg+gRsBuKVUsnu+52P8fvkcSM+Pkw3gH0qBs5VSgW5B4VzAZ8cqhvA/yezUirRvc+pwFTgoyHpxAn60KfubAbGKKVGKKVCcB0q9lnVBCOTcbtzu4zbQyzQxm0Zs3vk/2P2YCY4A+fgmjLfAWxzXy4FEoFPcX0D+hRIcN9fAU/iOrNxJzDbvf1s9+/b3T+/OZjtHoo+uW9b6t7PTuAlICQA+pQDHAVMvnqNBvi9Z8Z14sReXB+EfwyAPoW5+7IH2AhMN1CfhuGaeWgCGtzXY9y3XYrrjOrDwCO+fP8Z+TKA7zMZt43Tpxxk3Pbn/siY7YOLLDUthBBCCCGEF1lJTwghhBBCCC8SIAshhBBCCOFFAmQhhBBCCCG8SIAshBBCCCGEFwmQhRBCCCGE8CIBshBCCCGEEF4kQBZCCCGEEMKLBMhCCCGEEEJ4kQBZCCGEEEIIL0G+boC3pKQknZOT4+tmCCFEn+Tn59dorZN93Y6hJOO2EMKoehqz/SpAzsnJIS8vz9fNEEKIPlFKFfm6DUNNxm0hhFH1NGZLioUQQgghhBBeJEAWQgghhBDCiwTIQggh+kxrX7dACCEGnl/lIAshho7NZqO0tJT29nZfN6VX6lqtKAXxESG+bgphYWFkZmYSHBzs66b4XEuH3ddNGDB1rVZ+9d4eHr1iErERgfHaaq052tBGZnyEr5syYLTWNHfYiQkLjNeot4w2ZvuTvozZfhUg7ylvos3qIDzE7OumiG4szyvhkz2VPPv12b5uiuin0tJSoqOjycnJQSnl6+b0yKk1e8qaCDGbGDss2qdt0VpTW1tLaWkpI0aM8Glb/IHN4fR1EwbMyp3lrNh6lEumpLF0YqqvmzMgPt5TyXf+lc/q759HTlKkr5szIN7bUc4P3tjOxoeXEB/p+y/MA+GzfZU8ufow/75jPsHmrg/uG2nMBmhpt9HUbic9Ltyn7ejrmO1XKRYOp6a4zuLrZgyYg5XNPPdFga+bMaBeWFfIR3sqabM6fN0U0YPiWgsHKpt7vE97ezuJiYmGGGjbrQ6cWmN1ONE+PqavlCIxMVFmcdysARQg5xbWAVDW0ObjlgycNQeq0RoKalp83ZQB89m+KjrsTgprW33dlAHz1tYy8ovqqWjsflwx0pgNUNtqpaalA6fTmGO2XwXIAEcC6A3/x48P8NjKvTRabL5uyoA4UtPKvgpX0FVSHzhfZALRD97Yznf/ve2U9zPKQNtqdR3Gd2qNww+SXo3yd/OmlLpYKbVfKXVIKfXjLm7PVkqtVkptVUrtUEpd2pv92uyBESBrrdlYUAsEVoDsCfqPNgTGFzqtNbkB9jqdTp+MMvZorWntcE2k+cOX6L783fwuQC4KkAC5ud3GZ/uqgMAJJj/cXdF5vSSAZvoDTXO7jfzieopqW30+2zpQPAMtgM0xdH0677zzAqLGr1LKDDwJXAJMBG5USk084W4/BZZrrWcANwB/682+h/L1GEyFNa1UN3cAUNbDLJ6RVDd3cKjKNXMcKMFkaX1b5+tTHiBBf1GtharO915gvE4ddid2pyswHso0rIEcs/0qQDabFEdqAyPw+nhPJR3umZVASRv5cFcFWQmuXKJA6VMg2nC4FodTY7E6qA+Aoxdaa1qtdsKCXOcmBMqM5RCbCxzSWhdora3Av4GrTriPBmLc12OBst7s2B9mhwbCxgLXTGt6bFjABJOb3LPHJgXlAdInz4w4wNGA6VNt5/WyAAn6W71O3jXql2i/CpBDzCaKAyRAfmd7GcnRoUBgBJPljW1sK2nghjnZRIaYA6JPHluL63l/R7mvmzFg1h2q6bxe6sdHL1pbW7nsssuYNm0akydP5vXXXyc/P59zzz2XWbNmcdFFF1FeXk673cnyf73E9Zeex3UXnsPNN3wNi8XVrzfeeIPJkyczbdo0Fi1aBLjy9G677TamTJnCjBkzWL16NQAvvfQS1157LRdffDFjxozhoYce6mzLXXfdxezZs5k0aRKPPvro0P8xBl8GUOL1e6l7m7efA7copUqBlcB93e1MKXWHUipPKZVnczhx+DjHcCBsLKglJTqUs0YlBUyAnFtYS0SImelZcQETeOUW1BIfEczolKjAeZ0K6kiMDCEuItiv+9TbMRvg78/9nZsuP5/rLjyHr99ozDHbr6pYhAaZAiIHua7VyrqDNXxz4Qj+k1caEMHkql2u9IqLJw/j3e1lAZNiobXm4RU7qWhq57Kpab5uzoBYd7DGNQvW2E5pfRtTM+NO+ZhfvLubPWVNA9qOiekxPHrFpG5v//DDD0lPT+f9998HoLGxkUsuuYS3336b5ORkXn/9dR555BF+95enWHLJFfzkwXs5UNHM83/+Dc8//zz33Xcfv/zlL1m1ahUZGRk0NDQA8OSTTwKwc+dO9u3bx4UXXsiBAwcA2LZtG1u3biU0NJRx48Zx3333kZWVxWOPPUZCQgIOh4MlS5awY8cOpk6dOqB/Dx/rKgHvxKj2RuAlrfUflFJnAf9USk3WWp80Ray1fhZ4FiA0bYyuam4nLda3Z6r3h9aa3MJa5o1MJCMujMqmdmwOZ7fVBIwit6COWcPjSYoK7ZxNNrrcwjrm5CTQYXdSHiCpMLmFdcwdkUBRraXXffLnMfv5559n0YWXcePXb6PVauepxx8z5JjtV//9IUEmyhra6LAbu0LCB7vKsTs1V05LJyshIiCCyQ93VzA2NYpRyVFkJUQERNAPsKW4gX0VzTRYbDS2GT8dobTeQkFNK9fNzgLgaL3/zkZMmTKFTz75hB/96EesXbuWkpISdu3axdKlS5k+fTq/+tWvKC0txdJh58jBfVyw+Dy+snQBK5b/m927dwOwYMECli1bxnPPPYfD4Ro31q1bx6233grA+PHjGT58eOdgu2TJEmJjYwkLC2PixIkUFRUBsHz5cmbOnMmMGTPYvXs3e/bs8cFfZFCVAllev2dycgrFN4HlAFrrDUAYkNSbnfvzrFdvHKm1UNnUwfyRCaTHhePUUNlk7OCrrtXK/spm5o9MJN0d9Bt9pr+8sY3iOgvzRiaSHhdu+PcduMbsow1tzBuR4Pd96u2YbbU72btnN9dfsZSrzz+Lt/7zuiHHbL+bQbZrVxL+qOQoXzenz97ZVsbI5EgmpsWQnRDBtpIGXzepX2pbOthUWMe9i0cDkJ0QwdqD1WitDXNGbXdezS3uvF5ca2FKZqwPW9N/6w660isum5rGC+sLe51i0dOswWAZO3Ys+fn5rFy5kocffpilS5cyadIkNmzY0HkfrTX7Kpp55Ht38947bxOZNooVr/+LPfkbAXj66afJzc3l/fffZ/r06Wzbtq3HExNDQ0M7r5vNZux2O4WFhTz++ONs3ryZ+Ph4li1bFogl3DYDY5RSI4CjuE7Cu+mE+xQDS4CXlFITcAXI1b3Z+dGGdmYNH8DWDjFPBYF5IxI7A5TyxnZDL66xqdDTpwT2VTRjd2qqmzsYFhvm45b1nWcWfN6IBCwddmpbrbTbHIQFG3fthFx37vvcEYkU1LR2vm6n4q9jNkBdawf/8/27eWvFW6SOGMer//on+7cab8z2sxlk15vcyJUsKhrb2XSkjiunpaOUIjshgqMNbdgNfCLLx3sqcWq4eLIrBSE7IYJ2m5Pqlg4ft6x/Gi023ttRxsxsVwpCUZ1x33ceaw/VkBoTypiUKDLiwin14xnksrIyIiIiuOWWW/jBD35Abm4u1dXVnYOtzWZj246d2BxOLC0tpKWloZx2/vuf1zv3cfjwYebNm8cvf/lLkpKSKCkpYdGiRbzyyisAHDhwgOLiYsaNG9dtO5qamoiMjCQ2NpbKyko++OCDwe24D2it7cC9wCpgL65qFbuVUr9USl3pvtv3gW8rpbYDrwHLdC/LoPjzrFdvbCyoJSkqlFHJkZ2LGhi/T3WEBZuYmhlHhrtPRj+pbWNBHdFhQUxIi+l8nYyeZrGpsI7Y8GDGD4smPS6cpna7365O2Zsxe/fu3bR2OLC0tDA8KwOcDt5505hjdr9mkJVS1+E6sWMCMFdrned128O4Dtk5gPu11qtOtb+QIBMW4EiNcQ/fv7ejDK3hymnpgCuYdDg15Y3tZCUYczbig10VZCdEMCHNtYJZtrsfJXUWUqKNOxuxYmspHXYnP75kAl97ZgNFBj9B1OHUrD9Uw5LxqSilyIz37/SenTt38sMf/hCTyURwcDBPPfUUQUFB3H///TQ2NmK32/n2Xfdy/tXZPPqLXzBv3jzSMrLIGTMetBWAH/7whxw8eBCtNUuWLGHatGmMHz+eO++8kylTphAUFMRLL7103CzEiaZNm8aMGTOYNGkSI0eOZMGCBUP1JxhSWuuVuE6+8972M6/re4DT7rxZKUMHk676x3XMH5mAUor0ONeYZvRgMrfQlX8cEmTyCibbgHjfNqwfcgtrmZOTgNmkjvsiM8LAKwR6+mQyKdLcs/vlDW2MSfXtiqFd6c2Y/cADD7Dw8iy+//D/MH/+fNIzs8gZPR6n0zWhZqQxu78pFruAa4FnvDe662veAEwC0oFPlFJjtdY9JhcHmRRRoUGGnkF+d3sZkzNiGOlOEfEExcV1FkMGyI1tNr48XMNtC0Z0plN492nW8ARfNq/PtNa8tqmYqZmxzB2RQFJUqOErqOwua6TBYmPhGFfaaGZ8OBsO1/htKsxFF13ERRdddNL2L774ovN6SZ2F5nY7991zN/ffew81LR2UNbQxIc1VjWzFihUnPT4sLIyXXnrppO3Lli1j2bJlnb+/9957nde7uj/A559/3rvOnMGCzSZDB8jFdRYqmtqZNzIRgIiQIL+vJnAqjRYb+yqa+N4FYwFIcwf9Ru5TdXMHBdWtXO8+vyI9APpU2dTOkVoLN89z5Sd5z/T7Y4DcmzHbanewr6KZO++6i5/+8AEa26wU1VoYk+KKiYw0ZvcrxUJrvVdrvb+Lm64C/q217tBaFwKHcNXhPKXhiREU+fGsV0+O1LSyvbSRK6amd27LTjwWTBrR6n1V2ByaiycP69yWGe+uhVxr3IEpv6ieA5Ut3Dg3G/C874z7xQxgrTv/eMHoYwFyq9Vh6JMPW612IkLMnQG+p6rAUBaeFz0LDlKGLiHmWT3vrJHHvuynx4Ybuk+bjtShtStXFyAmLJjo0CBj98mTf+z+IuPJpTZyn3I7++R6ndICIG3Es6hTZIgrZfbYmG28E0QHKwe5NzU3gePraVZXV5OTGGnYQ93vbnedFH75tGMB8rCYMILNyrAB8ge7ykmNCWW6V6mwsGAzw2LCDL1C4Ku5xUSFBnWmwgxPiDD8DPK6gzVMSIvprL/tOcHIn/OQe2JzOLHanUSGHjvQFWxW7tuMN9gGqhCzydCrf+UW1JEUFXLcieH+Xk3gVHILagkJMjEt69i4nR4Xbui0EU9N50nprqNHoUFmkqJCDf86RYUGMdF9RCw1OhSTMvaseKvVjtmkOk+c9ATIRlxQ6JQBslLqE6XUri4uJ67CdNzDutjW5Sea1vpZrfVsrfXs5ORkhie68iaNeFLbuzvKmJMT33mYBFyrA2bGG7MsmsVqZ82Bai6aNAyT6fiXNNvApd4aLFbe21nOVdPTO4Ov7MQIypvaDVti0GK1k19U35leAcdm+v15sZCeeFZiigw9doa6zCD7n2CziQaL7biVs4zClX9cy7wRicelIWXEGXs1vY2FtczIijuuukNaXJg7B9mYPDWdvWtTZ8SFGfrL2SZ3nniQu09BZhOpMWGGnhVv7XAQGRLU+f8UZFIopQw5Zp8yQNZaX6C1ntzF5e0eHtabmptdykmMxO7UhnuD7Kto4kBlC1d4zR57GLUW8pr91bTbnMelV3gYtU8AK7YcxWp3ctO87M5twxMj0BpK6ow52OYW1mF1ODlndFcBcvd96mWRAp9o7XBgUopwrw95fxls/fnvNtQ8AYsRg6+SujbKGtuZP/L4cynS3NUEmtuNl57U1G5jT1lTZyqCh2tW3Fifqx71XjWdvRl5pr+2pYODVS2d6RUep+qTP489NoeTDrvjuEkNpRTBZoXN7tt29+XvNlgpFu8ANyilQt11N8cAm3rzwOHunF2jraj3zrYyzCbFpVNOXo0tOyHckLOtH+6uID4imLk5J5+Il50QQUVTO+02Y824aq15dVMx07LimJR+rOZxdoLrLOhig+YhrztYQ0iQibkjjr1WseHBRIUGdRsgh4WFUVtb67cD7on5x+A92PouQNZaU1tbS1iYcSu4DKSQINfrc9SAwddGT63gLgIvMGYuaN6ROpyak4L+jLhw6lqttFmNNWaDK6cajuVUe6S5c8X9dQzriXdNZ29psd3Pivv9mN151O/4+g/BZpNPJzX6Omb3t8zbNcBfgWTgfaXUNq31Re76msuBPYAduOdUFSw8ctzlWlyVLJL707who7Xm3R1lnD0qkaSok0uTDE+I7FypLTY82ActPH0ddgef7a3i0ilpnYd/vGUlhKO162xbIy3qsvlIPYeqWvjtV6Yct91Tus6o+e/rDtYwNyfhuEOqrlJv3ddCzszMpLS0lOrqXq0FMaScTk1ZYzux4UF01Bz/P1Pd7CoX1FrVfRmgwRYWFkZmZqbPnt+feGaQjTiTt7GgloTIkM4z7D0yvEq9jfXDagI9yS2oI8RsYmb28eXcOkuINbZ1VlkyityCOkKDTCct5JQeF0abzXUiclxEiI9a1ze5ha461VMy4o7bnhEXzkd7KnE69Umpjf48ZoMrfdFidRDUFHbcxEZdqxWr3Ym11neTCn0Zs/sVIGut3wLe6ua2x4DHTnefKdGhhAWbDBWobCtpoKSujfvOH9Pl7VledYNjM4yxUtuXh2pp7rB3mV4BxwLK4jqLoQLkV3OLiA4NOikVJikqhIgQs6Hedx6VTe3sr2zmmpknnwfrCpC77lNwcDAjRowY7Ob1ySd7Kvn2O3ks/85ZTDhhhuW517exsaCWLx9e4qPWCW9BZhNmkzFrIecW1DFvRMJJZRA7Z5ANOStex7Ss2JNWlztWN7jdeAFyYS0zs+MJDTq+T95l0YwYIHvqVHtLjwvHandS22rtPOHaw5/HbIAL/7SG1Jgw/vnNmcdtf3zVfp5ac5gDv7oEs8n/So52x69W0gPXrNfwhEiOGChQeWd7GSFmExdNOnUwaRQf7qogOjSIs0cndnm792IhRlHfamXlrgqunpFBRMjx3w09qx4a6TXy8Cwv7Z1/7JERF87R+ja/PSTXnU1HXLNgU7tY+jstLozK5g4cTmP1KVApXGffG61CQkmdhaMNbSfltQKkRIcZMuhv6bCz62gj80ac3KcMg64Q2NRuY09500m5unCsLJrRcqs9darn5pz8OnnP9BtJXauVA5UtXf4/pceF43BqqpqN9Tr5XYAM7pq0BslBdjg17+0o57xxyd2mT2QluOsGGyT4sjucfLSngvMnpJz0jd0jOTqU0CCToUqjvbml9KST87wZ6X3nbd2hGhIjQzpLBXnLjI+gucNOU5uxKgxsKqxj+gln4XukxRpzsA1kRjxZylP/uKsPdLNJMSzGeJUs8o7U4XDqLoPJ1JgwlMJwVR/yOms6dxV4GTOY3OzpUxevk1GXOvfkVM8d0dUXGWPWrPbLADknKZKiOgtOA8wQ5RbWUt3cwZXTT65e4REdFkxCZIhhAuRNR+qot9i4uJsZcTDejKvn5LwZ2XGdq7CdaHhiJCX1bYZ433lorVl7sIYFo5NOyleDY5UsjFSzutU9CzZnRNdL4mYYdNYokBmxQkJuYR3xEcEn5R97pMeFGW5WPLewjiCTYtbwk/93QoJMJBuwbrAnp3pGdtxJtyVFhhJsVgZ8nWoJMZuYnnVyn9INOr5tKnTliXd11C891phBv18GyMMTI7DanVQ0+f8b5N3tZUSEmFkyPrXH+xmpLNqHuyoICzZx7rieT5I0UoCcW1hHQXVr58p5XclOMM77zmNfRTM1LR2cM+bk9Ao4tliIkT5AthY3YHdq5nYxYwTHZiOMNmsUyNLjwilvNNaXS0/9466+WII76DfYeyy3oJapmbEnpZB5GPGLTHc51QAmkyItNtxwueI9HSGLjwgmLNh4y7dvOlLLjOy4Lo86G3Wm3y8D5JxEVyULfy/1ZrU7WbmzgqUTUwkP6ToVwcMowaTTqVm1u4JzxyZ3O8h6eIJ+I+S3vrapmOiwoOOWAT+Rp8SgkU7U8+QfL+w2QD51LWR/s+lIHSYFM7uYMQJXigUYbzYikGXEhWFzaGpaOnzdlF4prbdQWt92Uik0b+lx4VQ0thsm6LdY7ewobTypZJ23dIMtrNHaQ061R7rBFnVp6bCzq6zrnGpwHZ1Njw03VInBztrb3bxO0QZd6twvA+TOk9r8PFBZd6iaxjZb53LFPclOcJ0s5e8rBG4taaCyqaPb6hXeshMiaLU6qLf4dzH9ulYrH+ys4NoZGT1+kRluwFrIaw/VMDolqjNoPFFcRDARIWZDraa3qbCWSemxRId1ndMfExZEZIjZcINtIEv3qiZgBLkF7hq0PQaT4YYK+vOL6rE79Ul1db2lx7pyxY0wqQGuPnWXU+3h6ZNRePLEu8rV9TDasuD5R+px6pNrOnsz4nkKfhkgp8eFE2xWfl/J4p1tZcSGB7NwzKnrNWcnRGB3ar//VrhqdwXBZhOqaJ8AACAASURBVMX5p0gZAeNU53gzvxSrw8lN84b3eL/0uDCCTMowM8jtNge5BbVdVq/wOFUtZH9jtTvZWtzAnC4Wp/FQSpHmPqQv/IPR8iY3FtQSFxHMuB5qHKfHHquFbAS5BXWYTYrZPfzvpMeF025z+v2khkduYS1mkzqpprO39LhwKps7/H7yyWNTD3niHmmxxloWfGNhLcFmxYweXqc0gx29AD8NkM0mRVaCf1cUaLM6+GhPJZdMHnZSHcOuZBmgLJrWmg93VXD2qKReLWiSnej/AbLWmtc2FTNreDzjhvVc8D/IbCIjPpwiP+6Pt/yiejrszm7TKzwy4yMMEyDvPNpAh93Z4+wKeD5AjBGMnQmMduZ9bmEdc3MSus0/BuMF/bmFtUxOjyEqtPvUuPTOagIGeZ0K6piSEXvSymzejpUQM8ZMf25hHVN6yBMHV5+qmjuw+nDF0NOxqbCOqZlxPR6hTY8zXq64XwbI4MpD9ucZ5E/3VWKxOnqVXgHGmG3dU95EcZ2FS3qRXgGQFe//Qf/GgjoKalq5qYeT87xlJ0T4fWqPx9qDNQSbVZdlqrxlxodz1CApFpsK6wGYk9P9TAR4Dqsaa7ANZDFhQUSFBhlitrWsoY3iOssp/2+MFPS32xxsL2kMvD6VNvSYXgHeJcT8v09tVgc7ShtOOQGQHheG1q5FoPydxWpnZ2ljj+kV4DoiU9tqpd1mnKXO/TZA9tSk9ddcqXe3l5EcHdpjDpu3tFhX2og/B8irdlVgUnDBxFOnVwCEh5hJigr164Dy1U3FxIQFcdnUtF7d30i1kNcdqmZGdnyPsyvgCpCb2u00tvn/YdVNhbWMTokisYsl272lxYVR09JBh904g20gU0oZ5mSp3MLu6x978wT9RjgsvKW4HqvDecpg0kgB8pbiemwOzfweTtADr7KPBjiitLWXfTLU61TkqTrUu/eekY78+W2AnJMYicXqoNoPT5Boarexen81l01J6/WyiWaTIjM+wq8P33+wq4I5OQkknSI48ZadEO63QX9tSwcf7irn2pmZXZbT6crwhEia2u00WKyD3Lr+qW3pYNfRJhb2kH/skRHnLvXm52kWDqcmr6i+x/xjD89gW9nof+PDmcooZdE2Hq4jNjyY8adIuTJU0F/gqvzSU/4xQGJkCCFBJkMEKZ4+zTrF0STPynNGeJ02Fva2T8YJJnMLa1196iGnGrz6ZIDXycNvA2R/Lrm1alcFVruzx8VBuuLPtZAPVbVwsKql1+kVHv5cvu4/+aXYHJqbu1k5ryvZ/7+9M4+P5Kru/fe2WlJ3a6RubaPp1joznn08iz0ejMHG+wo2YAw27wWS8MIjLwQICcGEJUAgCTghibM7CQlJMMYrHsf2aMZ4w8tsnlXS7NLMSBq19l1qqZf7/qguqS1r6aW6+5Zc38+nP5J6qaqjqr517rnn/I7C110sr5/VomBz6R/HMi31prZNJ/xDDAdCCy7VwbTwvBmW9N8tmCXHcE9LL9uXz59/rOM1SSrPnuZe1vuKKJpD+UVHkxAzRwOUvS3x2VToyKXQYTeFg7wvTpv0XHFznKc+NlbOrTqkU2kypRtQ2kHWJLdUdFSeOdpBVbGTrbN0wZkPlaOt9Y1+AG5JwkHuGBxXrphAL867oq6YVfNUqs9kamKm6HnSee10N0UOO5uqFr4GdQdZ9YFpvlalM7GahahHpcepfI5hx+A453vH4pqEgTmkqQLBMIdaB+bVCo7FDDZNhMIcuhC/TZUmaICSiE2uPDseV67y41sgGOZw6wDb41j1q3BrK9NmiIrrKOsgV3qc5NiEcvmgvSMTvH6mhw9t9iFEfOkVOjUlLgbGgkrmgu5s8LOl2jOnnu5cVJe4iEj1lrfePNvLud4xPplA9BhiNbjVuu5iiW0vHU+KT0lBHs7cHOWVLPaf66PS45xKn5gPn4mWIN8tmEEhQdc/Xij/WKfSo35h0ZHWASZDkbhtMkM3vaNtg3Gp2eh43eqnwhxp1WyKe3JmgtUL/dqLpxYr355DeaG5Wp0r6yDn2W1UepzKKVk8d6yDcETGrV4RS42iUm9t/WMcax+MqznITFRV5/jpvgu4nbnctjG+4jwdV56d8sJ8JVcudM52j9IxGIgrvQJitZDVtUlKyb6WvrhvHs68HDyuXFMNtosdn1t9WbS9Lb0UOeys8xbF9X4zFBbtbelDCOKK4oGmJtA1HCCosG7w3mYthSxum0ygi74vWhwaT40FmCPSr197C6kO6fjcDlMUU+oo6yCDmooCO45cZNXSJQsWeMyGqlrIOxu09IpbNyThIEdTEloVcr56RibY1ejn7gSK82KpLVG7mPK1090AXBNHgxqdSsWbhbT0jNIzMskVcTrIoOWHquy4vNswQ+X9nuY+ti8vibu42gw27W3pZe2yItyuhbXrQbMporiE2N6WPtYuK6S4IC+u9/s8TvrHgoxNhtJ8ZMmTuE3qR8X3tfSxpqIQjys+m7wm63qYkoMshLhHCNEohIgIIbbFPF8nhBgXQhyOPv4pme3XlRbQ0qOO1NvFgXH2n+tPKr0Cph1k1aKt9Y1+1i4rpK6sIOHPVhQ6yMuxKWWTXpz3yfdUJ/X5mlK1tZB/dbqH2lLX1PUUD6p300sk/1jHZ4Jl1XcTy9wOhFA3171zKEBLz2jcqQigfjHoZCjCW+f74155AfUboATDydikp/csJps0ec6RCTWd/mRt6jBRq/NUI8gNwEeBV2d57ayUckv08blkNl5b6mI4EGJAkbaY/3P0IkBS6RUARY5cil25SjmTXcMBDpzvTyq9AsBmE1SVOJWJikciWnHe9uUlXLI08Sg/aFJv/qGAknmHwXCEPQu0l56NqmIXg+NBhgNqfJdmsu9cH2VL8liRwCRNW1ZV84b4biQ3x0ZFobqTlj3RZft4C79AKywSQt0I8tG2AQLBCFcuoH8ci0/xAteG9kHGJsNsT+A8TdckLB6bdPk6VWXRjrUPMh4Mx90LArRrb3QyzNC4mk7/TFJykKWUx6WUJ406mJnU6UoWijhfO45cZFOVO6lIq45qsmi7GjuRkoRzdWNRyaY3zvZyvncsIWm3mehKFqo4/bEcujDA6GR4wfbSM1FdyWJfSx9X1JUktDLj9TgYHA8yqmiERTWEELcKIU4KIc4IIe6f5fW/iln1OyWEGEh0H16PQ1kt5D3NfRTm21nviy//GKKFRUvULSzaO7XykojjpfZYsDeZ1STFU2GSsUl1WTS94DXenGqIOU+KjhEzSWcO8nIhxCEhxCtCiKuT2cC0FnL285Cbu0doaB9KOnqso5oWcn2jn+VlBayuWJL0NlRqz/zwvvMUu3K5JYl8ah2VtZBfO92NTcB7VyYeQQZo61NvYLo4ME5b/3hCAy2oHzVSCSFEDvD3wG3AeuA+IcT62PdIKX9PX/UD/hZ4MtH9qKyQsDeqfxxv/rGOyisVe5p7WVNRSEmcea0ABfl2pQtc9zb3srK8gPLC+BtWTaf3qHme9jb3siJBm7yKF4jua0n8PJmpqQvE4SALIV4QQjTM8rhrno91ADVSyq3Al4GHhRCzTtuFEJ8VQhwQQhzo7u5+22vVJS6EgHM92XdUnjnSgRDE3bJ4LmpKXLT1jxNSoIJ4YGySN8/2csuGZUnlVOtUF7u0VsZZToVp6RllZ4Ofj2+rTqo4T6e2RF0t5FdP97C52oPbGV9Bjo4ejVBRyWL/ucSjKxA72Kp5A1GM7cAZKWWzlHISeASYbwy/D/hZojup9DhpVzDHsGsoQHP36IKtmGfD51GzscZUDmgSNnndajZ1CUckB871J7RsD1p6z9LCfCXTEaZsSiDKD1BRmI9N0fQe3aZEVi7AXG3BIQ4HWUp5o5Ry4yyPp+f5zISUsjf6+1vAWWD1HO99SEq5TUq5rbz87VX5jtwcvEWOrEeQ+0Yn+cmb57hqZWnCOsEzqSlxEYpIJWaFLxzvIhSRCXfPm4kqxYf/8NIZcnNsfObq5Sltp6QgjyX5duW0kAfHghxtG4irvfRMypbkkW+3KVmot7dFW/qOV3pLZ1qCSz2bFKQSaI35uy363DsQQtQCy4EXE92Jz+1gMhShd1StVu36EnciBXo6vmjlvWpOv57XmqjjBZq+s4pO//GOIYYn4uumORNVW53rNiWSJw5gz7FRUeRQMgCQrE1lS/LJzRFKTmRmIy0pFkKI8uiSHkKIFcAqoDmZbdWWFnAuy47Kn/xPE0PjQb75wfULv3kBahTKb33myEV8bgebqtwpbUcFLeTWvjGePNTOJ99Tw9JCR0rbEkJQo6DU25vNPUQkvD8BeTcdXQtZxZvi/pY+Lq8rTnjpu6LIES2gUu8GoiCz/XPn8vjuBR6XUs5ZpTrXyp+quaB7mntZkm9nfYKTMNBsCgQj9CtSLK6zpzm5lRdQV2M3mUJKHZ+iUfFk8o91VD9PidpkswmWmUh9KFWZt48IIdqA9wLPCiHqoy9dAxwVQhwBHgc+J6XsS2YfdWWurOaCvnyyi6cOtfPb165k7bLEB9eZqOBMArx6qptXTnVz3/aalNIrAKpLtJtiNm36h5fPkiME//ealYZsr1ZBqbdXT/dQkJfD1prEWpzrVBW7lIsg941OcrprJOH8Y9CaCZUtybciyPHRBsTqHlYBF+d4770skF4x18qfyg7yFXXF2HMSv+WpatPeJHJAdbxuNSXE9rb0UVvqYpk78SCHngqjWqR/b3MvNSWupFafvW6HkuPbvpa+FGxyLp4Ui/mQUj4lpaySUuZLKSuklLdEn39CSrlBSrlZSnmZlPKZZPdRW1pA7+hkVuSpRidCfP2pBlaWF/D56y8xZJtetxO7TWTVmQwEw3zr6QbqSl381jUrUt5eoSOXkoK8rNnUPjDO42+18okrqpMaWGejptRFa/8Y4Yg6g+1rp3t478pScpO4yQNKdtPT84+TWVIFtQuoFGM/sEoIsVwIkYfmBO+Y+SYhxBqgGHgzmZ1MV96rc066hyc4252Y/nEslQo6yKFwJKlcXZ0pqTeFbIpEJPvPxd9NcyZet5OJUIQ+hdJ7IhHJvhRsqvRozqRKTr9uUzIRcYjapNB1Nx9Kd9KDmIKpLETzHqg/SfvAOD+4exP59uSLvmLJsWlL3dl0kB96tZlzvWN8966NKRWzxVJd4sqa8/XPr5wF4HPXGhM9Bk0LORiWyszeL/SOcaFvLGH941gqi7VuUypFjfa19JFnt3Fpkmk+VrOQ+JBShoDPA/XAceBRKWWjEOK7Qog7Y956H/CITPKO7HHl4szNUeqc7I22+E3WmfR61Ku8b+oYYmQilLLTr1LK1amuYQbGggkXfumo2Bb8dNdI1KZknX71cvp1m5KfyDjoHAooFXyaC/UdZF0LOcMO8sEL/fzkzXP82pW1bEti+Xc+sin1dr53lL976Qx3XOrlmtWJ57LORba0kDuHAjyyv5WPXV41NegbgS4xmO1UGJ1fndHyPK9O4ZzpUm/tCqVZ7D/Xx9ZqT9ITUK11qVoRFlWRUj4npVwtpVwppfx+9LlvSSl3xLzn21LKd2gkx4sQQrkWuXub+yjIy2FjAvrHsZQW5JFntym1LKxr0F6ZrJOioDOp25RKtBXUcvr1yVmyExkV03umJpxJTmS8HifBsKRnZMLIw0oLJnCQtZt6Jgv1JkMR7n/iKMuKHPzhrWsM3362nEkpJd/e0UiuTRhScBhLTYmT9izI1/3zK82EI5Lf/oAxKTA6U7niiuQh/+pUDz63I6FOczOZbhaihk0jEyEa2geTviGCtlQ8HgwzOK5WAdW7GdUKi/Y093LF8pKk8o9Bc/p1+TpV2NPcy/KyApYWJZdSpqKE2N6WXio9zilVpERRMdK/t7kPn9sxNfYmioptwfe29OF1O6ZqjxKlUsHzNBfKO8gF+XbKC/MzKvX2jy+f5VTnCN/78EYKHYnpzcZDTYmL/rEgQxnOq65v7OSlk9383k2rDcvV1cmGfF338AQ/3Xuej2ytnFIHMQqfx0lujlBCySIckbxxtof3rypLqaBSH6RVKdR763w/EQlXpOAg60UiKt1A3u3oeZMq0DMywemukaSjXToqRcXDKea1giYhtqxIHak3KSX7WlKzSY/0qxIVl1Kyt0XL1U123FYtgqyfp1RsMtOYrbyDDFBX6uJchiJ5pzuH+buXTvOhzT5uWFeRln3o0clMplmMToT47jONrF1WyK9fVWf49quzYNO//qqZYDjC71xnbPQY9FxxNZQsjrYNMBQIJSXvFkv5knyltJD3t/SRYxNcVlOc9Db0qJEqueIW2k29e3iCidCcKnEZY9+U/nFqaXIqSYgd7xhiOBBKqkFILF6POjad7R6lZ2Qy6VxdUC/S39wzSs/IRNK57wDFrlwcuTZlHOSWnlG6hydSmnCaSb/eFA5ybWlBRiLIkYjkq08cpSDfzh9/yNgUhFiqs7B8/+CLp7k4GOB7H96Y9FLjfGRavq5vdJL/2nOeOzf7WJ5C2sF8aFrI2W8W8qvTPQhBSgV6MH0DUUXJYl9LHxt9RRTk25Peht5uWpWIpcX0DdCvwDnZ09yLKy+HjZWpab17PU46hwMEFeiAquvqph4VV6exRqqFlDpehYp296Wgf6wjhNAmZwp8l8AYm4ocdgrycpSZyMyHKRzkulIXnUMTjE+mNyLxX3vOc/DCAN+8Yz1lSxLXloyXmgwXgJ3qHObfftXCx7dVGV5wqJNp+bp/e62Z8WDYMPm92agt1TS4s10A9trpHjb4iigpyEt5W5XFTiUiyIFgmMNtAykNtADlhfnYbebpzPRuQJcQU+EGuLe5j211JUlLI+pUehxIqYbTr+vq+lIsSvZ5HHQMBIgooCawt7mPpYX51KWYKudTKCq+t7mXsiX5KdWNgGaTCt8l0CZnZUvyWFmevE1aIa8652k+TOEg10SVLNLpfLUPjPPDnSe4elUZH71s1g6shlHkyMXjys2IMyml5Bu/aGCJw879t61L235ybILKDMnXDYxN8pM3znP7pV4uWVqYtv3UlLgYDoQYyGIHrZdOdLHvXB83r0+tHbhOVbFLCRWLo22DTIYiSTUIiSXHJqgocigTYbGI1Q3O7jnpHZngZOdwyukVoE4uaKq6urH43E4mwxF6RrOrJmBEXquOT5FIv55//J4VqdukUrMQo86TV6HVi/kwhYNcl2YlCykl33jqGBEJf/qRS1M++fFQmyEli6cOtbOvpY+v3rrWkAjkfNRkSL7u318/x8hEiN9NY/QYYiQGs1So1zMywVceP8LaZYV81oCGLqAV6vWOTjI2mV0tZL1BSKoOMkx30LJQA70AONvO5D6DUhEgxkHO8k39ZKemFZxqKgLE5IJmeSJzoW8M/1DAGJvcWqS/cyi7NrX1j9MxGDBmIuNx0jU8wWQou05/a98Y7QPjbDdgzK70OLI+gY4HUzjItSW6FnJ6HOQdRy7y0slu/uCWNUlLzCRKJrSQB8eC/Olzx9lS7eET26oX/kCKVGfA6R8KBPnx6y3csqHCkNbf86FLDGZSQUVHSslXHz/KUCDE39y71bCGLlNSb1mOIu9t6WN1xRKKDZi0ed1OZSIsFpBvz6G8MD+rDnIgGObBF89QWpDHpiSb0MTiU6Ty/s2zugatMRNLyP5EJlVN51hUkUXb05yaVnAsPo8aTv/UhNOAiYzX7aRnRI1C3vkwhYPsduVS7MpNi5JF3+gk33mmic3VnrSoO8xFTYmLtv7xtHaT+YtdJ+kbneR7H96IzZb+qLguX5fOtuD/+cY5hgMhfvf6VWnbh042tZB/uvcCvzzRxf23rmXNMuPSSPRmIdnMQz7TNcKBc32GRI9BU7LwD6qRS2mh4XNnN6r/Z88d53jHEA/csynl/GMAZ14Oxa7crDqT3cMT/MPLZ9jgKzIkkKM7/dk8T5GI5ImDbZQtyeOSpUtS3p4qTv/LJ7spduWyyhCb1Ejv2dPci9uZy5qK1O9HqhTyHrzQP+/rpnCQIX1KFn/yP00MjQf5wd2XkpMBJ1JnWjc4PRf90bYB/nvveT713rqUK7jjZVq+Lj02jUyE+NfXWrhh7dKM2OTIzaGiKD/jKRZnukb43rNNXLO63PBJ27QWcnbSRs50jXDfv+zBlWfn/1xtTNqIzx3tzJTlXEqLabLZLGRXo5+fvHmez7x/OdevNU6qM5s2RSKS33/sCMOBEH/1iS2GbFNvC57N/P1/fa2ZvS19/P7NawxJbZzS2M3iilJ9o59nj3XwiStqDAlM6TZl8zwd7xji6cMXuX7tUkNs8k2lYWXPpu7hCT77nwfmfY9pHOS6Uhfneoy9qb98sounDrXz29euTPty/UzSKYsWjki+/lQDZUvy+fLNqw3f/lykW+rtv/ecZ2AsyO/ekP7osU5tSUFGI8iToQhffOQQrjw7f/GxTYZH/suX5JOXY6MtCzd63TmWEn72W+8xTJ7PGx1ss51LWd/oz+r+VUJzJjPfAvziwDhfefwol1a6De+CqtuUDf7ttRZePdXNtz60ntUGRPAg+23Bj7UN8kD9SW7buIx7rzAmBbAg344ni5H+jsFxvvqEdv19+SZj7r3ZVoUJBMN84WeHcLty+cYdxhT6e7McFZdS8oePH2EoMH8tjmkc5NrSAjoGxw3LWRmdCPH1pxpYWV6QVqmwuUhnY42H957nWPsg37hjHUVp6AQ4F+m0aWwyxL+82sw1q8vZUu0xfPtzUVOaWS3kv9x9ksaLQ/z5Ry9Nuo3sfNiiaiOZTrGY6RyvMugmD2oIzz97tIP/+19vZW3/quHzOBkPhjOqABMKR/jSI4cJhSP87X1bybcbk7evU5mlCPLRtgF+WH+CWzcs45Pbawzddrai4qMTIb7wyCHKluTzZx81tjDe687ORCYckfzezw8zGYrwN/duIc9ujHvlytOc/myNb99/9jinu0b4y3s2U2qQ/O1UUCNLNv3kjXO8dLKbP7pt7bzvM5GD7CIijcudfKD+JO0D4/zg7k2GD6Tx4HU70qIb3D08wQ/rT3LVylLu3OwzdNsL4Xbm4namR77u4b0X6B2d5Is3ZHYyU1uiaXAHgukvJnjzbC8PvdrMfduruXmDMbJus1GVYQc5nc4xZL8w59CFfr786GEur02+I+BiozILUa8HXzzDvnN9fO8jG6lLQ/Mgn8fB8ESIoTTWWMxkZCLEF36mOZJ/frfxCks+d3bagn/3mSbO9Y7yo49vweMyVl2pMktR8X965Sx7mvv49p0bWFGeeu5xLL4sOf0vNHXyX3vO83/ev5xrVqfWyTUWR24OpQV5tGfBphP+If70+RNct6acTy+QwmgiB9k4JYuDF/r5yZvn+LUra9PWOGMh7Dk2KoudnDd4+f7PnjtOIBjmu3dtzIhc3Uxq0qBkEQiG+edXm7lqZSmX12b2fGWqqcvgWJAvP3qY5aUFfPOD6eviCJqD3J6hHOR0O8egtWPNt9uyEo1o7Rvjt/7zAEuL8nno1y7P+P5VJdOFRW+e7eXvXjzN3ZdV8ZGtVWnZx1QuaAZv6t96uoELfWP89SeMdyQhO23BnzvWwc8PtPL/rl3Je1emrogwk2xExQ9e6OdHu0/xwU1e7rnc+OsvG6kwXUMB/vCJo6z3FvEVg9OVINrUJcNjdiAY5os/O0yRw84D92xe0EcyjYM8pYWcYh5yJCL5oyePsazIYXiOWqIYrRu8p7mXJw+189lrVhhSEZwM6dBC/vn+VrqHJ/hCBnOPdaYnZulzKKWU/NEvjtE9PMFf37sFV17yrZfjodLjpGdkMu2dKTPhHMN0Z6ZMR1iGAkE+85P9TIQi/PuvX2HY8uNiIJMOct/oJF/6+SHqSgv47l0b0rafTDv9Tx1q48mD7fzu9asMkdaaDT2/NVNqAhcHxrn/iaNsrvbwpRvTUx/jdTsZCoQYmciM1vtQIMgXHznEsiIH309TH4VMO/16UejYZIgH79uSllX2bLQF//PnT3Cyc5gH7tkcV7fklBxkIcQDQogTQoijQoinhBCemNe+JoQ4I4Q4KYS4JZX9AJQU5FGYb085gry3pY8T/mG+fNNqCjOYnzsbRuoGT4YifPMXDVR6nHz+usw7kjpVJU5D5esmQmH+8eWzbK8r4co03STmo7Yk/VrITx5s59mjHfzeTavZVJX+/Gpd6i2dy99nuka49yHNOX7ks+lzjnW8bkdGK9dD4Qiff/gQzd2j/NP/vjytHR3NSGlBHnl2W9qX76WUfOWxI/SPBnnwvq0U5Kdvcql3CMxE2sj53lG+8VQDV9QVp7UhUibTk8IRyZd+fphwRPLgvVsMkd+bDd3pz1T7+W/9ooGLAwEevG8Lbmd6fAqfJ7NO/49fb+FXp3v45gfXp21sy3S76ZdOdPEfb5zj16+q47o1S+P6TKpX6G5go5RyE3AK+BqAEGI9cC+wAbgV+AchREpTECEEtWWulLWQHzvQSmG+nQ9uymx+7mzousFG5LT9+PUWTneN8J07N+DMy3xOtU5NiYvJcMQwUfPH32rDPxTISvQYNCmkQoc9bSkWF3rH+OMdjWyvK+FzH1iZln3MJN1Sb7pzDJpznAnn0evO3GArpeSPdzTy6qluvvfhjbzvkrKM7NdMCCGo9DjT7kz+++vn+OWJLr52+9q0Sz+WF+Zjt4m0R70mQxG+8LND5NgEf33vVuxpciQhs1Hxf3z5DPta+vjuXRunVubSQSYnMk8ebOMXhy/yxRtWpTX9b1qpJ/02NbQP8oOdJ7hpfYXhRaGxZDKnv3t4uivt/QsU5sWS0jdPSrlLSqlPafYAevLNXcAjUsoJKWULcAbYnsq+QFvuTsVRGQoEea6hgw9t8WXVidSpMUj1YTgQ5MFfnubGdUu5cb1xup/JYKTUWzAc4R9eOsvWGg/vuyTz0WOITsxKXWlJsQiFI3zp54cQAn70ic0Z0+FOZ7OQbDjHoA22XcMBqN38awAAIABJREFUQuH0t2P98evn+OneC/zfD6zg3jTeQMxOuvMmG9oH+fPnT3DjuqUZafKUYxMsczvSrkf7o92nONI2yA/u3jTl7KULb4bagh+60M9fvXCaOzf7+OhllWndl9eTGd3gcz2jfPMXDWxfXsLvXJfe4nH9Okj3isz4ZJgvPnKIkoI8fnD3prTWMWWq1bmUkq9EJd0S7Upr5NT0N4Hno79XAq0xr7VFn0uJ2mh+a7I3wWeOXCQQjPDxDLRdjgejHOT6xk7GJsP8vzR/SePBSAf5qYPttA+M84UbVmWl4FCntiS1idlc/P1LZzl4YYDvfXjjlNOaCZYW5pObIwx3kLPlHIMWQY5I6BxOb7OQ3U2dfO/ZJm7dsIyv3hJ/JOLdiFZ5n76mQb/7M+1G/sDHFi62MQqfO71R8V+d7uafXjnLJ99Tw22XetO2Hx1dTSCdjtdwIMgXHzmM1+3gex9Jf/F4RWE+NpFep1/Xq8+xCf76E1vSHtzIlG7wnzzbRHOPpi5SUmB8UWgsU01d0mzTf7xxjpdPdvP129cl3JV2QQdZCPGCEKJhlsddMe/5OhACfqo/NcumZk1KFUJ8VghxQAhxoLu7e95jqSstIBSRSedLPXqgjdUVS9hclZnOcgthlELC04fbqS5xsjWD+sBz4fM4sQloS9GmUDjC3710hk1Vbq41UF4mGWpKXbT1jxnaFvzghX4efPE0H97i464t6Y2ozMRm04rajEyxyKZzDJnJO2xoH+QLPzvEpZVu/uoTWzLSvt3M+DxOuoYnCKYhqv+tpxs43zvKX9+7heI038hjSWdUvGdkgi8/eoRVS5fwzTvSq2QTS7oLwP746Uba+jUljkzo8ttzbFQUpbfVeWyU35fmKD9kxunf2eDn4b0X+OzVKzKSNjYdFU+fTSf8Q/zZ8ye4fu1SPvXe2oQ/v6CDLKW8UUq5cZbH0wBCiE8DHwT+l5xum9QGxIZpq4CLc2z/ISnlNinltvLy+R2hWl3JIomCqZP+YY60DvDxbdVZjUbGUuTIxeNKTTe4e3iCN872cudmnxJ25ebY8HmcKTv9r57u5kLfGL/9gZVZt6u2xEUwLA0bnEYmQnzpkcMsK3Lw3Q9vNGSbiVJVbFwkLNvOMcTkUqYpEuYfDPCZn+yn2JXLv35qmxIpWqpT6XEipfEKCU8enFZ3yHThrs/jxD8YMHSyDJpqwB88doTB8SB/+8mtGb2+0un0P324nScPtfOFG1ZlVFI1nQVgr5/p4Z9fPct926szEuWHaac/XcWU/sEA9z95lI2VRfz+zZlR99Jz+tN1nvQOgEWOXH74seTSRVJVsbgV+Cpwp5Qy1iPaAdwrhMgXQiwHVgH7UtkXMCX+noyiwGMHWrHbBB/Zmtlo3UJousHJD07PHesgHJHcuVkdu4zQQn50fxtlS/KynlMNxmshf2eHFlH5qwxFVGajyuMyJMWie3gi684xpDeXcnQixGd+sp/RiTA//o0r0tLhcDGSjgKwlp5RvvGLBrbXlaRV3WEufB4noYik2+BUnn+PLgN/8451rF1WZOi2F8IbTYUxui14a98Y33iqgW21xXw+w+l/Po8zLZHJvtFJfu/nh1lRln69+pmkK9IfiUi+/OhhJoIR/uberYZ1AFyIHJuIOv3pmZz92XPHOdU5wl9+PD5Jt9lI9T/xd0AhsFsIcVgI8U8AUspG4FGgCdgJ/I6UMmXR1aWF+ThybQkrWUyGIjx5qJ0b11Uop1VanaJu8I4jF1m7rDDh3Jp0kqrT3zsywS9PdPKRrZVpkwJKBCO1kJ871sFjb7Xx29euZPvy7DSpAS2C3D2ceofAHUcu0jMywX/8xhVZlTordORSmG83PMUiHJF88ZFDHO8Y4m8/uTXjzouZ0dNejHJUJkJhfvdnB8mz2/jre7ekVd1hLtKxLKwVGx7npvUV/O8rE18GTpVKj5PRyTBDAeMkxEJhLUcXQVbOlc/toGMgQMTASL+Ukj98/AgDY0H+9r7L0q5XPxOv25GWxhoP/aqZN8728u0717PS4A6AC+HzpEee88UTnfzkzfP85vuW84EUUjRTVbG4REpZLaXcEn18Lua170spV0op10gpn59vO/EihKCutCBhR+XFE530jU7yiSvUKM6LpaYk+fzW1r4x3jrfz51bsi9ZF0t1iYuekQnGJpMbcH9x+CLBsOQeRYoplxU5yMuxcb4vNS3k/tFJvvbkMTZVudMmkh8vVSXGSCHtbOhg7bLCtEtsxYPX4zA8xeJPnzvOC8e7+M6dG+LWzrTQMFpj9wfPn6ShfYgfZijvcza8HmNXKkajraRLC/L5YZpVA+YiHZH+B188w8ELA3z/I5dmtABZx+dxMhmO0Ds6adg2/2vPeV443sX9t61lvS/zE+VKj9YW3MhI/9G2Af6i/iS3bVyWFfECbxpaaHcNB/jKY0dZu6ww5WZw2Q/PJYgmuZWYo/LogTYqivK5epV6eqU10fzWZGaGO45oad0fUkDTOZZpdY7EbZJS8tiBVjZXe1id5uYS8ZJjE1SVOLmQYgT58bfaGBwP8ucf3ZT1yHilJ3Wpt67hAAfO93PrxmVGHVZKeN3Gti79rz3n+bfXWviN99Xxa++tM2y77xZ0hQQjct1fPNHJj19v4dPvreXmDdm73ox2Jr/zTCMtvaP81ScyW2wYi9FO//5zfVNtv+/cnJ17k9Hn6YR/iO89e5zr1pTzG++rM2SbieJ1O5gMGef0j06E+OIjhykvzOfPPpqeDoALoef0GxXpj0QkX3nsKCMTIf72vsQk3WbDhA5yAef7xuL+h/oHA7x8sou7L6vKypLcQqQii/bMkYtcXltMdUnmZ+jzkYpNx9oHOeEf5uPbjO9nnwq1JalpIUsp+dm+C2yrLc5K9GEmerOQ9hQc5F2NnUgJt23MTKHKQvg8DsMKPl451c23dzRyw9qlfCODigKLDaPyJh+oP8UlS5fwtdvXGXBUyVMUTeUxIur1zJGLPHqgjc9fdwnvXZkdnXcwVmN3cDzIlx45THWJi++kse33QhhZkxBb7PXAPZmTFJyJ0U7/d59p4lyvJunmcWVncubzOJgMR+gZNSan/z/eOMcrp7r5xh3rDOneqp7HuAC1pS4mQxH8cXZqe+JgGxGJMtrHM0lWC/mkf5gT/uGszdDnozoFB/nRA63k2218SDG79CY1yS5v7Wnuo7lnlPsUaSxRUeTAbhMpSb3tbPCzoqyA1RWZzVubC5/bSe/oZMp51a19Y/zOTw+ypqKQB+/bmrEGLulGCHGrEOKkEOKMEOL+Od7zcSFEkxCiUQjxcKr79LpTL8K50DvG8Y4h7r2iOuWIkBH4DOgQKKXkBztPsLnKzRez1CVUp3yJpotuhOP1nR2NdA4F+Jt7t7IkjW2/F8JIp/9Po8VeP0qh2MsIjExZeu5YBz8/0Mpvf2BlVidnPrdxzUKOdwxNNQ4yKpffdA5yXbRgKh6pN325fvvykikFDNXwuh3k2ETCzuSOI+3k2AS3Z0hmJhGKXbksybcn7PQHgmGePnyR2y/1Zk3dYS5qSlyMTIToS3J56+F9Fyhy2LljkxrnK2dKCzm5m2L/6CRvNvdy68ZlWZfh09HF9FOVFXvqUDujkyH++dcupyCLN3kjEULkAH8P3AasB+4TQqyf8Z5VwNeA90kpNwBfSnW/Po+T9v7UFBLqG/0A3JLF1IpYfJ7Ui6UaLw7R1j/O/7qyNusrmzaD1AQGxibZceQin76qji1Z1uT3uHJx5NpStql/dJKf7r3A/76yhmuyrMdvVAQ5EAzz9aeOsbnKze/dlN1aGKPSe/SiULcr19AOgKZzkHUt5HiWu/ef6+dc75iy0WPQ9A0rPc6EVB+klOw4cpGrVpZSXqiWKgdoxZTVSUi91Tf6GQ6EuEex9AqIue6SiIr3jkxQ3+Dno5dVKREB06kqTr5ZyO7jnYQjUpn0CtAq1yH1wXZ3Uydbqz3KpS6lyHbgjJSyWUo5CTwC3DXjPb8F/L2Ush9AStmV6k6NUEjY2ehnvbdImfPh9aReWLSzwU+OTXDjuuzLWIIxusG/PN5FKCKVWNUUQgsApDqReSE6zqngQxRHnf5UbXrjbA/9Y0G+dNNqBWphjIn07z/Xz6nOEb5++zpDlcpM5yB73U7ycmxxRZB/vr+VJfl2br9UjcjDXCSqG3yodYDWvvGMd2BLhJqSxJuFPHqgleoSJ1cuz96Sz1zoDnIyhXpPHGxjMhzhk+9RI71CpzKFpeKdDX4qPU42VmY/n1rHa8Bg2zE4zrH2QW5ar/aYkQSVQGvM323R52JZDawWQrwuhNgT1blPiVSjXl1DAd5SqBAUtO9N3+gk45PJp/LsbPSzva4k7e184yWVsUCnvtGP1+1gkyKdajWbUnO86hs78bkdXKqASo8QItq+PUWbGjpZkm/nqiymVui4nbk4c3NSDmrUN/rJs9u4yeC+CaZzkHNsguo4FAWGA0GeO9bBhzZ7M65XmCg1pYlpIe84fJE8u41bNqgRfZiNmqi+c7xLq619Y7xxtpePXVatZAvfqmIXQiSuhawV57WyrbZYGVUOnapiF51DE0yEErvRDweCvHa6R6n0CpguzElFC/mFpk4AwwdaBZjtRM38ctrRmjpdC9wH/KsQYta1ciHEZ4UQB4QQB7q7u+fcqS/FJdRd0fOhSnoFpK7vfKZrmDNdI0o5/V63A/9Q8h0CxyZDvHq6m5vXVygzJqSa/z42GeJXp7u5eYM641yqDVDCEckLxzu5bu1S8u3ZX83UIv2ppSxJKdnd1Mk1q8oMT4kznYMMWh7yQs1Cnj3awXgwrIyW7nzUlLjoG51kOBBc8L2hcIT/OdrBDWuXUqhYnm4sNSUuJkKRuDtOPXGwDYC7L1czKu7IzWFZkSNhLeQ3m3tpUag4LxZdySLRiMSLJ7qYDEe4TaEbPGjnqKQgL6UI8q6mTpaXFbCyXM2ahRRoA2IHwyrg4izveVpKGZRStgAn0RzmdyClfEhKuU1Kua28fO7czMoUI8j1jX6WK1QICtOFRcnbpDn9NysU4PB5nIRT6BD46qluAsEItyg0Jvg8WjOkRAMAOq+c7GYiFFHqPKXq9B8410fv6KRSwTVfiilLjReHaB8YT4v8oykd5JqoFvJ80cmfH2hl1dIlbM1ysUA8JKIb/GZzLz0jE0rkec1HIkoWkYjksQNtvP+SsqyIysdLdYkr4RSLn+1rVao4LxbdQU40D3lng5/ywnwuqylOx2GlRCrdpoYDQfY093KTQlEwA9kPrBJCLBdC5AH3AjtmvOcXwHUAQogytJSL5lR2WhZVSEhmqXtwLMibZ3u5RaEIHkynjSSbs7uzwc+Wag9ed3aancyGPpFJNs2ivrGTYlcu2+uy1x10Jvp56hxMzunf2ehX0qau4QmC4UhSn69v7CTPbuNahZoe+dypSUHWN/qxCbhhrfE2mdJBristYGwyTPfI7Bf+6c5hDl0Y4OPbqpUaWOdiWjd44ejkjsMXKcy3c10aLgYjSUQL+c3mXtoHxpWP9teWuBIq0lO1OE+nqiTxZiHjk2FePtnNLRsqlEyF8bqTLzZ65VQ3wbBcjOkVSClDwOeBeuA48KiUslEI8V0hxJ3Rt9UDvUKIJuAl4CtSyt5U9muziWi3rMRvgL880UkoIpWKdgEsczsQIjlnsq1/jGPtg0qlV0BqagKToQgvHO/kxnUVWVfkiEWP9CdzniZDEV480aWeTR4HUian1COlpL7Rz/svKcuqBN9MvB4H3SMTTIaSdfr9XFFXYmhxno46Zz4BFlKyeOytNuw2wUcuU3O5fibxRlsDwTA7G/zcvGGZkg5XLJXFToSIz0F+9IAWZb1ZccekttRF93D8LbRVLc7TqSjMJ8cmEmoW8sqpLsaDYaXUK2Kp9DiSztHb3dRJaUGekpFxI5BSPielXC2lXCml/H70uW9JKXdEf5dSyi9LKddLKS+VUj5ixH59nuSWhesb/SwrcrC5Sq1VwNwcG0sL85O0Sb2caoiJiifx3dnT3MtwIKSgTdGahCRselNZm/TzlLiDrKciqDbh9LmdSAmdcfa2iKWlZ5RTnSNpO0+mdJCntJB73hlxDYYjPHmwjRvWLc2qqHciuJ25uJ25CzqTL5/sZngixF1b1E6vAMi35+Atcixo0+BYkOcb/Hx4a6XyTn9N9LqLx+lXuThPx55jw+t2JJRisbNBW3Z8z3J1lh1j8XqcDAdCceXzxxIMR3jpRBfXr126aBqDqEIy3fTGJkO8cqqbmxVdqUi2WKq+wc/aZYUsV0yXP5UOgfWNflx5Obx/VVkajix5UlFQUdUmbwr577uiqQiqSAvqpHKedkU10tO16mdKB7my2Dlnc40XT3TRMzKphG5hImhSb/NfIDuOtFO2JE8JeZZ4qC5ZWJ1jx9GLTIYipjhftSXxa3CrXJwXi6aFHN/ANBEK88vjXdy0Xq1lx1imlCwSjLDsb+ljKBDiRsVXMcxIpcdJ5/AEoQTyJvWir1sVi+DpJFNY1D08wf7zfcpFJXWS6RAYiUh2NXVy3ZqlygU49KLdRPPfwxHJrsZOrl1TrpxNelQ8mbSR+sZOtqUpFSEVvCmowtQ3+tngS59Gupp3uQXIzbFRVeycVcnisQOtlBfm84Esd71JlJoFnMnhQJBfHu/ijku9yjonM4mnWchjB1pZu6yQDT519HTnIhEtZJWL82KpKnbF7SC/caaX4YmQsukVkHw0YldTJ/l2G1crFjFaDOgKCV0JKCTUN3biceWyXdGVispoVDyRDoG7mzqREuXyj3W8SchtHWrtp3t4Qimlh1iSkRA7dKGfnpEJJScyrjw7Hlduwjad6xnlZOewkjZNq8IkNpHpGgpwqHUgrTaZw9OahZoSTckilq6hAC+d7Obuy6pM40TqVJe4aOsfm1OHcldjJxOhCHcq3BxkJjUlms5uIDi7zM4J/xBH2wZNU0zpceVR5LAvKPXWOzLBzoYOZYvzYqkqdtI5HIirQOL5hg4K8+1cdYm6KxjJRJB1Hc2rV5Upr5luRhKdtKha9BWL1+1gIhRJqPX8zkY/taUu1i5TM+Uqmah4fWMnuTlC2aLxZApE6xv9StuUTLMQvV27inU+zrwcil25CZ+n3ce1CaflIM9CXWkBLT1vl3p74mB7tC2keq2KF6KmxEUwLPHPkai+48hFqoqdXFajVsHKfNRMqSTMUUx5oI3cHMGHt5rH6a8tLVgwxeKJg20Ew1LZ4rxYKj1agcRCEYlQOMLupk6uX6eGwPxcVBRpCgOJNAs53jFM+8D4olSvUIHKBJeF9aIvVdMrINbpj89RGRwP8saZHm5VTLIulkQ7BEop2dng532XlFGkqCZ/ZYIttDWlh06uWqmuTckUvaY7FSFVtLbgiU/OaktdadVIN62DXFvqYjgQYmBMK8aRUvLYgVauqCtmRbk6ovLxMiWLNovz1TMywWtnerhzs0/ZwXU2qufRd54MRXjqUDs3ra9Qpt1qPNSUzp82YobivFh03emF0iz2tfTRPxZUrjnITKYUBhIYbHc3dSIEXL/WcpDTgTfBJdSdihZIxZKobvCLumSdwt+f6dWX+Gw64R/mQt+Yksv2Oj6Pg+GJEENxFu2aw6bEouJdQwEOXkhvKkKqJBrpHwoEefNsT9o10lNykIUQDwghTgghjgohntLbkgoh6oQQ40KIw9HHPxlzuNNMKVlE0yzeOt9Pc8+o8lq6czHdLOSdztdzxzoIRyR3mkC9Ipb5tJBfPNFJ3+ik6c5XbYmL9v7xOQuO9OI8M0SPIf5mIc83+HHm5vCB1WouO8aiRSPiH2xfON7J1moP5YVqFa8sFgrytbzJeG6AeoGUikVfsSSaNlLf0ElFUT5bFJOsiyXRqPjOBj9CQVWEWBJVfahv1GxSeTXJ63YyFAgxMhGf3KiK7dpnUplgVPylE10Ew+nXSE81grwb2Cil3AScAr4W89pZKeWW6ONzKe7nHdSVvV1R4NEDrRTk5XDHpeoWEM2Hz+OYU5ljx+GLrKkoZO0y9QvZYilbkoczN2dWmx490MayIgfXrDJXMWVtqYtQRM55E3l47wWKHHZuN8l16HVr1918EeRIRBOYv3ZNOc48dZ0WHV8CzUI6Bsc51j7ITevVvXksBuLtljVVIKVwpBWg2JWLI9cW10RsfDLMy6e6uGXDMiUl63QSbQte3+jnitoSpSeWiXY93NngZ1ttseI2RSP9CZynujSnIqSK15Og09/YSdmSfLZWp1ezPiUHWUq5K9qhCWAPkLHk36piF0JoDvLIRIj/OdrBBzf5KFCoQ0wi2HNsVHqc7+jU1tY/xoHz/aaLHgMIIaLydW+3qXMowMsnu/joZZWm05ytKdFWLmYr1OsdmaC+Ud3OebNhz7GxrMgxr4N88EI/XcMTylbfz8TrdtAep8LAC9HoisoRo8WAz+OIKx1hZ4OfvBwb161Re+IshIi7WOoVxSXrdPT8/XjO0/neUU74h5VVr9BJJBXmQu8YJ/xqKj3EMjWRiSONbHBczXbtM5meyCx8ngLBMC+f1ORG0z3hNDIH+TeB52P+Xi6EOCSEeEUIcbWB+wE0jUOf28n53lGeO9rB2GSYj19hvuK8WGZzJp850gHAnZvN5yDD7FrITxxsIyIxXXoFzN/F0UzFebFUFjvn7aanOy3XK1rVPROvx8lEKEL/2MJ5h7uaOllRVsAlS9WNriwG4smblFJS3+TnfZeUUqhogVQs8eoG1zf6lZas08mz2yhfkh9XVFxXRVDdmSwvzMduE3FFxc1ikzeBSP9LJ7oIRSQ3K26Tz61rIS/s9L9+pofRyXBGOgIu6CALIV4QQjTM8rgr5j1fB0LAT6NPdQA1UsqtwJeBh4UQs+YHCCE+K4Q4IIQ40N3dndDB15S4ONc7yqMHWllZXmD6FrGzOZNPH25na41H2erThdCdfj2apxVTtrG9rkS5blLxsKzIQZ7d9o6JjNmK82LRmoXMnoMspeT5Bj/vX1VmCqcFYgbbBW4gw4Ege5p7reYgGcAXXUKdr8NhU8cQrX3jplmpiEdNQJesu0lhybpY4pV6q2/sVFoVQSfHJqgocsSlkFDf6Ge9V32bKgrzscWp1FPf6GdpYT5bq9XNfYfEnP5djZ2a3OjK9BfxLviNlVLeKKXcOMvjaQAhxKeBDwL/S0a9ICnlhJSyN/r7W8BZYPUc239ISrlNSrmtvDyxZbW6MheNF4c4cL7fNFq681FT4qJvdHLqJnKqc5gT/mHuMmn0GKCmxMnYZJjeqF7ogfP9tPSMco8JpfgAbDZBdbHzHRrcZivOi6Wq2IV/aHYt5Ib2IdoHzOO0wPRgu9BN8ZVT3QTD0kqvyAC+OM5JfWOnkq1w58LncdI9MjGvhvibumSdSb4/8Tj9mipCv/KRVp3KOCL9XcMB3jKJTfYcGxVFjgU7BGqpCN0ZSUVIlXid/nBE8sLxTq5du5Q8e/onnKmqWNwKfBW4U0o5FvN8uRAiJ/r7CmAV0JzKvmajtrSAiVCEHJvgI5eZR0t3LmpmyKLtOHwRm4A7NpnYQS59u5LFY9FiSrMUsc3GbFrID++9gNuZa0q7qoqdRCT4Z3Fenm/oIMcmuMkkTgtMR5AXWire3dRJaUGe6VeezEA8Wsj1DX6uULAV7lz4ohrinXNo14OWnlSQl8P7LlFXsi4Wn9vJxcH58/d3Kd4RcCbeOJx+vcvhLRvNMc7Fo9Tzq9M9jAfDi8rpP3Cuj97RyYykV0DqOch/BxQCu2fIuV0DHBVCHAEeBz4npexLcV/voC7qfF2/dilLCx1Gbz7jxMqiSSnZceQi77ukTOmK2oWoLp6WrxtdBMWU8M60kenivErTFOfFMpfUm94I4MoVJRSbSKu6bEk+uTli3qXiYDjCSye6uH7tUtMVipqRhWTRWhRuhTsXeovcuZz+cESyu8nPdWvVlqyLxedxEgjOn79f3+hneVkBq0ySt+/zOOkcCszZpRamm06sMUl6nNe9sNNf3+in0GHnyhXqdj6NJR6nf1dTJ3k5Nq5dk5l6mFRVLC6RUlbPlHOTUj4hpdwgpdwspbxMSvmMMYf7djb43OTl2PjUe2vTsfmME6uFfLh1gAt9Y3zIxOkVMN2I4kLvGM8eWxzFlLWlLsYmw/SMaGkjj7+lFefdt9186RUAVZ5os5AZA+7prhGae0a5daO5ouI2m2CZ2zHvYLuvpY+hQMhKr8gQSws1OcG5bupTBVImiUrCtNzWXDa9db6fnpFJ00RaYWGbBsc0VYSbN1SYJqXR53YQDEt6RiZmfV1vOqFyl8OZVHqcXBwMzBnpD4Uj/PJ4JzdkKBXBCBZy+rUuh1oR75IMBdjM8Z+bg+oSFw3fuYWrTaalOxduVy5FDjsX+sbYceQieXabqQbX2XDm5bC0MJ/W/jEeO9DKikVQTFk7lTYyGi3Ou2DK4jydZW4HNvHObnrPH9NE8zO1nGUkC3Vm2t3USb7dpnS3tsVEjk2wrMgxZ1R/Z4OfTVXuKQkrM7BQVHxng588e+aiXUawkE0vntQ6AqouWRfLQjbpTSdUV3qIxet2MBmKTNX2zGTfOa3zqZlWZBZy+ps6hmjrH8+oTaZ2kAHTzI7ipaZUU+b4n6MdXLemXNl+8IlQU+Li9TO97D/Xzz2XL4ZiyqgWcu8Yb57t5VzvmCmL83Ty7LoW8ttTLJ5v6GBbbbEp05d87rmdMSklu5s6uXpVGa4886b6mI25iqX8gwEOt6rdCnc2HLk5lBbkzZo3qUe7rllVlrFolxEs5EzqHQE3K9wRcCYLdQjc2WAOpYdYFjpPuxq1AMAHFNcTj2Uhp3+qiDeDq36Ly7tcBNSUuHjjbC/dwxPctcX8hYeg2dQ+ME6OTXD3IiimrC5xTjWpeXifeYvzYqkqdr0tgnyuZ9QUovlz4Z0n7/B4xzDtA+NWekWGmUsHBvq1AAARC0lEQVQhYVeTOfRnZ2OuvEld/cVsNpUW5JFnt82qR6t3BLx5vdodAWfim6fdtJmUHmKZz+mXUrKr0c/Vq8pNFQBYqOvhrkY/22pLKMtgEa/lICtGdYmLcESyJN9umsYMC6HrSl67upylReaLRs4k356Dt8jBodYBUxfnxVI1o1nI8w2a02LWFB+f20EoMnve4e6mToSA69daDnImmatYameDn0uWLjFls5a58iZ3NmrqL2aRrNPROgTObtOrp6MdAU02JhQ57RTk5XBxlomMrvRgNpvmiyAfax/k4mDAdKlxuk2zrTLpXQ4z3bnRcpAVoza6fH/zhgrTO106es6uGTvnzUVNqYtXozq6nzRpcV4slcVO/EMBQmFN03Vno5YTqhdZmg3vPFGjF453cllNsanVYcyIz+N8R7FU/+gke1v6THcz1/F5tInlzLxJM6q/6MzV9bC+0Y/bqX5HwJkIIea1qchESg86xa5c8u22WVcv6hv9ppycTWulz24TZH6VyXKQFWPNMq3Q6+7LzK30EMttG7088LFNi2pJW5/IXFFXzCqTFufFUlXsJByRdAwGuDgwzpHWAdNFVWKZqzFFx+A4x9oHTXfzWAxUzhIheuF4J+GI5NYN5kxRqvQ4GZ0MMxQITT13pmuYs92jpipki0UrcH379yYYjvBCUyc3rqsg1wQdAWfinaVDYCisdTm8wYQ2CSG0orZZ0hHqGzvZXme+ydm00/9Om3Y1+VmXhS6H5roq3gVcXlvMr/7wOtMIy8eDMy+He7ZVLyq9Wb0Bilml3WaiR4rb+sfZqadXmPQGD3PLVb3Q1AmwqCZrZmG2ZeH6xk4qPU42VhZl67BSYjab9O+PmVQRYqn0OOgaDhAMT3cI3NusySKaNdJf6Xmn7OO+lj4GxoKmtcnncb4jbeRs9whnukZMaZMe6Z+ZYtE9PMGB8/3cnIUx23KQFUT1XvAW2lLPJ7ZVm744Tye2WcjOBj9rKgpZUW6+nFAdtzMXZ27OO6IRu5o6WVFWYMp8V7Mzc9IyOhHi1dPdptLUnYluU6zztbPRz2U1HipMWm/h82idNWM7BO5s7MCZm8M1q82jihCLz+2kZ2SSQDA89Vx9o598u820Ns2W/66nIph1cubzON7RbvqF49Euh1mwyXKQLSyS4JKlS/jBxzYtmjxxr1tT5jjcOsD+832mTq8ALRoxs8XsUCDInuZeK3qcJQoduRQ67FPLwq+c6mYyFDH5SoWeNqLZ1No3RkP7kKm/P94ZCgmRiGRXYyfXrik37XjnnZFyJaVkV1MnH1htLqWHWHweJ13DE2+L9Nc3drKpyj11XZqN2dJ76hv9VJc4WefNfCqj5SBbWFiQZ7dRUejgyYPtSAm3XWreG7yOz+18m1yVXlSZSR1Ni7cTq4W8s8FPaUEe2+rMVfQVS/lUW3PNpmwVExlJ5Yyo+OG2AbqGJ0xt01SkP3qejrYN0jEYML1NUmo64qD9PGJCPfFYNKd/Or1nOBDkjTO93LI+O10OLQfZwsIC0NIsxoNhlpcVsGYRFB563W9frtvd1ElpQZ7pOzmaGX1ZeCIU5sUTXdy0vsLUtQl6W/NYB3mdt4ja0oIsH1ny6Aow+kSmvsGP3Sa4zsSyo74ZNu2MKj3csM7ENs2Iik/riZs3AOBzO96W3vPyyW4mw5GspYxYDrKFhQUwnYd868bszNaNxutx0j0ywWQoQjAc4aUTXVy/dqmpHbJUEELcKoQ4KYQ4I4S4f5bXf10I0S2EOBx9/B+jj0GX23rjbC8jEyFTR7t0fNG25l3DAQ6c7zd1yghAQb4djyuXiwPjUx0Br7qkDLfTvF1dl7n1qLjmeNU3ajJ8Hpe5lB5imSllWd/oZ0V5AZcsNW9wY6bTX9+orTJdXpudoIblIFtYWADTShZmv8Hr+NzaEmTnUIB9LVoV/rs1/1gIkQP8PXAbsB64Twixfpa3/lxKuSX6+Fejj8PncdI/FuQXh9pZkm/nqkvMpT87G76o3NbuJq2YyMz5xzp6LuipzhHO9Y6ZOioJWlvwsiX5XBwY50zXMM0mluHTmSp6HRxnYGySPc193Lx+kdgUXWXSuxxmK6hhzux0CwsLw9E6AtrYVOXO9qEYQmw0YndTJ/l2G1evMmfFugFsB85IKZsBhBCPAHcBTZk8CF0L+dmjHdx+qZd8uzmLvmLxeRz4hwI8d6yD5WUFrK4wv0JKpccxJfkoxOKQRfR5HLQPjFPfqEs9mtuZdOVNR/p/ebyLcESafiIzHRUPTK0yZbp7XixWBNnCwgKAFeVL+Pz1qxZFegW8PRqxu6mTq1eV4cwzv0OWJJVAa8zfbdHnZnK3EOKoEOJxIYThrS/1SUsoIhdFegVoNoUjktfP9HLLhsWRnqSnwtQ3+rm8ppilheaUrIvF53bSMRigvtHPlmrPVNqFmfG5nXQMaDZVFOWzucqT7UNKiYJ8O26n5vTvavRTkJfDVSuz1xPCcpAtLCwWJXo04sUTXbQPjC+KKFgKzOa1yRl/PwPUSSk3AS8AP5lzY0J8VghxQAhxoLu7O+6D0CcteXYb165ZHNH8WEmtxZBeAdp3ZygQoqljaFFNZM73jnK0bXAR2eTgbPeIpie+fhm2RVBf4fM4aesfY3dTJ9euXZpVaUHLQbawsFiUFOTbKXLYeb6hAyHg+rXvage5DYiNCFcBF2PfIKXslVJORP/8F+DyuTYmpXxISrlNSrmtvDx+R7eiyIFNwDWryijIXxwZfnraiNftYFPlYklPmo6uLiZnMhjW5oRmT0XQ8XmcnOsdIxCMLJ7z5Hbw+tleekYms25Tyg6yEOJPoktyh4UQu4QQvujzQgjxYLRi+qgQ4rLUD9fCwsIifnweJ8Gw5LKaYsoL87N9ONlkP7BKCLFcCJEH3AvsiH2DECK2LeSdwHGjDyI3x8b3Pnwpv3/zGqM3nTV8Hic2oTmSiyGCB9NO/zpvETWli6Ozqx7pX12xxNRdQmPRV8nczlzes8K8euKx+DxOJkMRcnNE1leZjJjCPyCl/CaAEOILwLeAz6FVS6+KPt4D/GP0p4WFhUVG8LodnPAPv9vTK5BShoQQnwfqgRzgx1LKRiHEd4EDUsodwBeEEHcCIaAP+PV0HMsn31OTjs1mjSX5dn7ym9vZVGnu/M9YqksWl6INTDvI2Y5KGoke6b9h7VJycxZHQoA3atNVK8socmRXWjBlB1lKORTzZwHTeW13Af8ppZTAHiGERwjhlVJ2pLpPCwsLi3jQW8zeuO7d7SADSCmfA56b8dy3Yn7/GvC1TB/XYmCxqaNUFDn478+8h211i6epzgZfEZ+9ZgW/dmVttg/FMFZGI+Ef3Oxd4J3mQW/qosJExpAkMCHE94FPAYPAddGn56qathxkCwuLjPDRrZUUOuxcsnRxLKlaWGSK96/KnnpAOsjNsfFHt6/L9mEYysZKNy/9wbUsLzNv58aZvH9VGR+7vIo7NmXf6Y8rJi+EeEEI0TDL4y4AKeXXpZTVwE+Bz+sfm2VTM6umk66GtrCwsFiIbXUlfO22xXVTtLCwsNBZTM4xQNmSfP7ins1KdG6MK4Ispbwxzu09DDwL/DFxVE1Ht/0Q8BDAtm3b3uFAW1hYWFhYWFhYWGQSI1QsVsX8eSdwIvr7DuBTUTWLK4FBK//YwsLCwsLCwsJCdYzIQf5zIcQaIAKcR1OwAK0Y5HbgDDAG/IYB+7KwsLCwsLCwsLBIK0aoWNw9x/MS+J1Ut29hYWFhYWFhYWGRSYTmx6qBEGIYOJnER91oChoqfqYM6MnAfpL9nGWThmVT8vtJ9nMq25Ts/2GVlHJxtFOLkyTH7cU2Zie7L8um5D9j2ZTavlS2KZP3obnHbCmlMg80wfpkPveQwp9J2KZk9mPZZNlk2ZTdY0vlc2Z+qHxOMnWNWTZZNlk2GWeTKvehxdF6BZ5R+DPJkOx+LJtS21em9mPZlNq+MrGfTP4f3o0stjE72X1ZNiX/mWSxbMrsZ5JBifuQaikWB6SU27J9HEZi2WQOLJvMwWK0yewstnOy2OwByyazYNmkFqpFkB/K9gGkAcsmc2DZZA4Wo01mZ7Gdk8VmD1g2mQXLJoVQKoJsYWFhYWFhYWFhkW1UiyBbWFhYWFhYWFhYZJW0OshCiGohxEtCiONCiEYhxBejz5cIIXYLIU5HfxZHnxdCiAeFEGeEEEeFEJfFbCsshDgcfexI53Fn0KYaIcSu6LaahBB1ZrZJCHFdzDk6LIQICCE+bGaboq/9MLqN49H3iEVg0w+EEA3RxyeyYU+SNq0VQrwphJgQQvzBjG3dKoQ4GbX3/mzYsxgw+Dqzxm3FbRLWuG0We6wxO9MkI6WRgHyGF7gs+nshcApYD/wQuD/6/P3AD6K/3w48DwjgSmBvzLZG0nmsWbLpZeCm6O9LAJfZbYrZZgnQZ3abgKuA14Gc6ONN4FqT23QHsButUVABcAAoMolNS4ErgO8DfxCznRzgLLACyAOOAOuzYZPZHwaPcda4bQKbYrZpjdtq2mON2dmwNcP/2KeBm9BE5b0x/+yT0d//Gbgv5v2x71NioDXKpugF9Vq2j9/o8xTz3GeBn2bbFgPO03uBtwAn4IoOTOuybU+KNn0F+EbM8/8GfDzb9sRjU8z7vj1jsH0vUB/z99eAr2XbnsXwsMZta9w2m02qjtvWmG2uMTtjOcjRZaitwF6gQkrZARD9uTT6tkqgNeZjbdHnABxCiANCiD3ZWv6ZSYo2rQYGhBBPCiEOCSEeEELkZOrY58KA86RzL/CzdB5rvKRik5TyTeAloCP6qJdSHs/Mkc9NiufpCHCbEMIlhCgDrgOqM3PkcxOnTXMRzzVpkSDWuD2FNW5nmMU2bltj9jtQfsy2Z2InQoglwBPAl6SUQ/OkAs32gi6zUSOlvCiEWAG8KIQ4JqU8m4bDjQsDbLIDV6NdXBeAnwO/jjYzzAoGnSeEEF7gUqDe8INMkFRtEkJcAqwDqqLP7RZCXCOlfNX4o42PVG2SUu4SQlwBvAF0oy0/htJysHGSgE1zbmKW5yyJnhSwxu13YI3bGWKxjdvWmD37JmZ5TqkxO+0RZCFELto/8adSyiejT3dGv4z6l7Ir+nwbb58VVQEXAaSU+s9mtBywrek+9rkwyKY24JCUsllKGQJ+AVxGljDqPEX5OPCUlDKY3qOeH4Ns+giwR0o5IqUcQcsPuzITxz8bBn6fvi+l3CKlvAltoDqdieOfjQRtmouFrkmLBLDGbWvczhaLbdy2xuw5UX7MTreKhUCbWR+XUv4o5qUdwKejv38aLYdFf/5TQuNKYFBK2SGEKBZC5Ee3WQa8D2hK57HPhVE2AfuBYiFEefR912N+m3TuI8vLdAbadAH4gBDCHh0UPgBkZanOwO9TjhCiNLrNTcAmYFdGjJhBEjbNxX5glRBiuRAiD22pOGuqCWbGGrennrfG7Qyz2MZta8yeF/XH7HQmOAPvRwuZHwUORx+3A6XAL9FmQL8ESqLvF8Dfo1U2HgO2RZ+/Kvr3kejPz6TzuDNhU/S1m6LbOQb8B5C3CGyqA9oBW7bOkcHXXg5a4cRxtBvhjxaBTY6oLU3AHmCLiWxahhZ5GAIGor8XRV+7Ha2i+izw9Wxef2Z+GHidWeO2eWyqwxq3VbbHGrOz8LA66VlYWFhYWFhYWFjEYHXSs7CwsLCwsLCwsIjBcpAtLCwsLCwsLCwsYrAcZAsLCwsLCwsLC4sYLAfZwsLCwsLCwsLCIgbLQbawsLCwsLCwsLCIwXKQLSwsLCwsLCwsLGKwHGQLCwsLCwsLCwuLGCwH2cLCwsLCwsLCwiKG/w+2Ndn0A8QwXgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "states1 = pd.DataFrame(np.c_[fit1.level, fit1.slope, fit1.season], columns=['level','slope','seasonal'], index=aust.index)\n", "states2 = pd.DataFrame(np.c_[fit2.level, fit2.slope, fit2.season], columns=['level','slope','seasonal'], index=aust.index)\n", "fig, [[ax1, ax4],[ax2, ax5], [ax3, ax6]] = plt.subplots(3, 2, figsize=(12,8))\n", "states1[['level']].plot(ax=ax1)\n", "states1[['slope']].plot(ax=ax2)\n", "states1[['seasonal']].plot(ax=ax3)\n", "states2[['level']].plot(ax=ax4)\n", "states2[['slope']].plot(ax=ax5)\n", "states2[['seasonal']].plot(ax=ax6)\n", "plt.show()" ] } ], "metadata": { "anaconda-cloud": {}, "hide_input": false, "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": "3.7.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": false, "latex_user_defs": false, "report_style_numbering": false, "user_envs_cfg": false }, "toc": { "colors": { "hover_highlight": "#DAA520", "navigate_num": "#000000", "navigate_text": "#333333", "running_highlight": "#FF0000", "selected_highlight": "#FFD700", "sidebar_border": "#EEEEEE", "wrapper_background": "#FFFFFF" }, "moveMenuLeft": true, "nav_menu": { "height": "98px", "width": "252px" }, "navigate_menu": true, "number_sections": false, "sideBar": true, "threshold": 4, "toc_cell": false, "toc_section_display": "block", "toc_window_display": true, "widenNotebook": false } }, "nbformat": 4, "nbformat_minor": 1 }