{
 "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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ljoM8/N5qurVOpF/7xjXvhP8NzV+IyC+B+iIyCngTeP8UYzXG1FLTszbz8Zpv+PkFXTkrtYnb4dRp0VHCU2P60DqpPuNnLGVPQZFf+/mbFH4B7AVWAXcC/wJ+dUqRGmNqpWVb9/OHf61jVPeW3H5OJ7fDMUByQhzPje3PwaOlTJyZTWm5t8Z9/H36yKuq/1DVa1T1amc5uBOFGmMixv4jJUycuYxWSfX469W9qbjVbNzXvU0j/nxVLxZt3sejH66rcXu/2hREZAjwCNDB2UcAVVX7OmBMHef1KvfNWU7e4RLeGj+YpAR/+rWaULqsT1tWbDvIS1m59G6XdMJt/W1ofhG4D9+oqPZEkDGm0rNfbGTe+r387rIe9EpJdjsccxwPXtSNNTsP8ot/rjrhdv62KRxU1Y9UdY+q5lf8nH6YxphItmBjPn/7z3ou6d2GsYNqHDjZuCg2OopnbuhH44S4E27nb1L4XEQeE5HBItKv4uf0wzTGRKo9BUVMmpVNarMG/PHKM60dIQI0axjPczf2P+E2/t4+Gui8ZlRZp8CIU4jLGBPhyr3KPbOyOVxcyszbBtIw3t9LiXFbn3YnvsXn129SVW0uZmNMpb9/soGFm/bx12t607XVqY6ib8KRv08fxQNXAalV91HV3wYnLGNMuPp8/R6mfO7h2owUru6f4nY4JsD8rfO9CxzE9/RRcfDCMcaEs50HjnLfG8vp1iqR317W0+1wTBD4mxRSVPWCoEZijAlrJWVeJry+jLJyZeoN/agXa7Pl1kb+Pn00X0TODGokxpiw9uePvyZ76wH+fFUvOjVv6HY4Jkj8rSkMBW4SkVx8t48qejT3Clpkxpiw8fHqXbyYmctNZ6dyca/WbodjgsjfpHBhUKMwxoStLflH+NmbK+mdksSDF3VzOxwTZP4OiLcFSAYucX6SnXXGmFqsqLScu2cuIypKmHJ9P+JjrB2htvN3Os7JwEyghfMzQ0QmBTMwY4z7fvP+WtbsPMTj1/amXZMEt8MxIeDv7aNbgYGqegRARP4MLACeDlZgxhh3zc3ezqxFW7nr3M6MPKOl2+GYEPH36SPh2NFRy511xphaKGd3Ab98ezUDUpvw0/O6uB2OCSF/awrTga9EZK7z/nLgpeCEZIxxU2FJGeNnLqNBfDRPX9+XmGh/vzua2sDfsY8eF5F5+B5NFeBmVc0OZmDGmNBTVR6au5qNew8z49aBtGxUz+2QTIj5O/bRa6p6I7CsmnXGmFpi9uJtzM3ewX0/7MKQtGZuh2Nc4G+9sEfVNyISDZx4UG5jTETJ2V3Aw++t4Zz0ZkwakeZ2OMYlJ0wKIvKgiBQAvUTkkPNTAOzBN0ieMaaWeGf5Dsq9yt9/1IeoKHuOpK46YVJQ1T+qaiLwmKo2cn4SVbWpqj4YohiNMSGQ6cmnb7tkmjWMdzsU4yJ/ezRbAjCmFjtYWMqq7QesHcH43aZgjKnFFmzKx6swNN2SQl1XU5tCx1AFYoxxT5YnjwZx0TXO32tqv5pqCm8BiMinIYjFGOOSLE8eAzs1JdY6qtV5NfVTiBKRh4EuInL/dz9U1ceDE5YxJlR2HDjKprwj3DCog9uhmDBQ09eCMUARvuSRWM1PjUQkWkSyReQD530fEVkoIstFZImIDKiy7YMi4hGR9SJy/qkUyBhzcrI8eQAMtUZmQw01BVVdD/xZRFaq6keneI7JwDqgkfP+L8BvVPUjEbnIeT9MRLrjS0I9gDbAf0Wki6qWV3dQY0xgZHnyaNYwni4tbYpNc3JzND/ufLNfIiJ/E5GkmnYSkRTgYuCFKquVbxNEErDTWb4MmK2qxaqaC3iAARhjgkZVyfLkMTStKSLWYc34nxReAgqAa52fQ/hGTq3JE8ADgLfKunuBx0RkG/BXoKIPRFtgW5XttjvrjiEid1Qkp7179/oZvjGmOut3F5B3uMT6J5hK/iaFzqr6sKpucn5+A3Q60Q4iMhrYo6pLv/PReOA+VW0H3Ae8WLFLNYfR761QnaaqGaqa0bx5cz/DN8ZUJzPH155gScFU8DcpHBWRoRVvRGQIcLSGfYYAl4rIZmA2MEJEZgDjgLedbd7k21tE24F2VfZP4dtbS8aYIMjy5NGpeQPaJNd3OxQTJvxNCncBz4jIZuciPwW480Q7qOqDqpqiqqn4GpA/U9Wx+C705zqbjQBynOX3gDEiEu90mksHFp1MYYwx/isp8/JV7j576sgcw99JdlYAvUWkkfP+0Gmc83bgSRGJwfe46x3OMdeIyBxgLVAGTLAnj4wJnuXbDlBYUm63jswx/J2OEzj1ZKCq84B5znImx5mLQVUfBR49lXMYY05OpiePKIFBnZq6HYoJI9an3Zg6KsuTR6+UZJLqx7odigkjlhSMqYMKikpZvu2AtSeY7/ErKYjINSKS6Cz/SkTeFpF+wQ3NGBMsX23aR7lXrT3BfI+/NYVfq2qB81jq+cArwLPBC8sYE0yZnjzqxUbRr4MNlW2O5W9SqHgK6GLgWVV9F4gLTkjGmGDL8uQxoGNT4mOi3Q7FhBl/k8IOEXke3xAX/xKR+JPY1xgTRnYfKiJnz2GGptlTR+b7/L2wXwv8G7hAVQ8ATYCfBS0qY0zQVAyVbe0Jpjp+JQVVLQTeBY6ISHsgFvg6mIEZY4Ij05NHkwZxnNGqUc0bmzrHr85rIjIJeBjYzbcjnirQK0hxGWOCoGKo7MGdmxIVZUNlm+/zt0fzZKCrquYHMxhjTHBt3HuY3YeKrX+COS5/2xS2AQeDGYgxJvgqhsq2pGCOx9+awiZgnoh8CBRXrFTVx4MSlTEmKDI9+bRvkkC7Jgluh2LClL9JYavzE4f1TzAmIpWVe1m4KZ9LerdxOxQTxvwdOvs3AM5QF6qqh4MalTEm4FZsP8jh4jK7dWROyN+xj3qKSDawGlgjIktFpEdwQzPGBFKWJw8RGNzZOq2Z4/O3oXkacL+qdlDVDsBPgH8ELyxjTKBlevLo0aYRTRrYHWBzfP4mhQaq+nnFG2fSnAZBicgYE3CFJWVkb91vvZhNjfx++khEfg285rwfC+QGJyRjTKAtyt1Hablae4Kpkb81hVuA5sDbwFxn+eZgBWWMCawsTx5xMVGcldrE7VBMmPP36aP9wD1BjsUYEySZnnwyOjSmXqwNlW1O7IRJQUSeUNV7ReR9fGMdHUNVLw1aZMaYgMg7XMy6XYf42fld3Q7FRICaagoVbQh/DXYgxpjgmL/RN2SZtScYf5wwKajqUuf1i9CEY4wJtKycPBrVi6Fn2yS3QzERoKbbR6uo5rZRBVW1obONCWOqSqYnj7M7NyPahso2fqjp9tHokERhjAmKLfmF7DhwlLuGdXY7FBMharp9tCVUgRhjAi/TY0Nlm5NT0+2jAqq/fST4Bsaz+fyMCWNZnjzaJtcntakNlW38U1NNITFUgRhjAqvcq8zfmM/5PVoiYu0Jxj811RQaqeohEam2G6Sq7gtOWMaY07Vm50EOHi218Y7MSalpmIvXndelwBLndWmV9zUSkWgRyRaRD6qsmyQi60VkjYj8pcr6B0XE43x2/kmVxBhzjIr2hLM7W1Iw/qvp9tFo57XjaZxjMrAOaAQgIsOBy4BeqlosIi2c9d2BMUAPoA3wXxHpoqrlp3FuY+qsLE8e3Vol0jwx3u1QTATxd0A8RKSXiFwqIldW/PixTwpwMfBCldXjgT+pajGAqu5x1l8GzFbVYlXNBTzAAH/jM8Z8q6i0nMWb99tTR+ak+TUgnoi8BPQC1gBeZ7XiGzX1RJ4AHgCqNlh3Ac4RkUeBIuCnqroYaAssrLLddmfdd2O5A7gDoH379v6Eb0yds2TzfkrKvAxJt6RgTo6/8ykMUtXuJ3NgERkN7FHVpSIy7DvnbAwMAs4C5ohIJ3yPuX5XdYPwTcM3ExwZGRnH7W1tTF2W6ckjNloYYENlm5Pkb1JYICLdVXXtSRx7CHCpiFwE1AMaicgMfDWAt1VVgUUi4gWaOevbVdk/Bdh5EuczxjiyPHn0bd+YBvH+/hc3xsffNoVX8CWG9SKyUkRWicjKE+2gqg+qaoqqpuJrQP5MVccC7wAjAESkCxAH5AHvAWNEJF5EOgLpwKJTKpUxddj+IyWs3nnQ2hPMKfH3a8RLwI3AKr5tUzhVLwEvichqoAQY59Qa1ojIHGAtUAZMsCePjDl5Czblo4r1TzCnxN+ksFVV3zvVk6jqPGCes1yCb47n6rZ7FHj0VM9jjPG1JzSMj6F3ig2VbU6ev0nhaxF5HXgfKK5Yqao1PX1kzGnZeeAoh4vL6NLSRlzxV5Ynj0GdmhIT7fcT58ZU8jcp1MeXDM6rss6fR1JNAJSWezlQWMqBwhIS68XSKqme2yGFhNer3Dx9Mbl5R3h2bD9GntHS7ZDC3rZ9hWzJL+Tms1PdDsVEKL+SgqreHOxA6oqjJeXsKyxh/5ESDhSWsr+whAOFJex3lvcf8S1XXVdQVFa5f2K9GL58YDjJCXEuliI0/rN2N+t3F9CsYTx3zVjK1Bv6M6q7JYYTyaoYKtv6J5hTVNOAeL8Cph5v4DsRGQEkqOoH1X1em3m9SkFRGfsLS9hXcWE/UnGRdy7w1awrLjt+O31ifAzJDWJpnBBHckIcHZs1IDkhjsYJcTRuEIuI8Ot3VvNiZi4/Oa92T8Kuqkz5PIcOTRN45+4h3PzyYsbPWMqU6/txQc9WbocXtjI9ebRsFE/n5g3dDsVEqJpqCquA90WkCFgG7MXX5yAd6AP8F/hDUCMMI8Vl5fxz6Q5e+HITm/OP4D1O17noKCG5fizJCb4LfErjBM5sG0uTBnHORT628rVxgzgnCcQS68c94PmePF7O2sxtQzuRlBAb4BKGj3nr97J6xyH+clUvGjeI49VbBzDupUVMfH0ZT1/XlwvPbO12iGHH6wyVPaxrcxsq25yymgbEexd4V0TS8XVGaw0cAmYAd6jq0eCH6L6i0nLmLNnGs/M2sutgEX3aJXP3sDTngh5beVFv7HyrT6wXQ1SQ5sO9Z2Q6H63+hhezcrl/VJegnMNtqspTn+XQNrk+l/f1jXTSqF4sr94ygJumL2birGyeVGV0rzYuRxpe1n1ziH1HSqx/gjkt/rYp5AA5QY4l7BSVlvP6V1t57ouN7CkoJqNDY/5ydS+GpjVz7ZvYGa0bcX6PlkzPyuXWoR1Jql/7agvzN+aTvfUAv7u8J3Ex39aeEuvF8sotA7hl+mLumZVNuVe5rM/3hseqsyraE6x/gjkd1ge+GoUlZcxcuJXn/7eJvMPFDOzYhCfG9GFwp6ZhUS2/Z2Q6/16zm+lZudz7w9pXW3jq0xxaNornmv4p3/usYXwM028+i1teXsx9byzHq8oVfb+/XV2U6cknvUVDWjaqG0+nmeCwpFDF4eIyXluwhX98uamyGj5pRF8GdmrqdmjH6NEmiVHdW/JSZi63DO1Io3q1p7awKHcfX+Xu49eju1MvNrrabRo4ieHWl5dw/5wVeL1wVTUJpC4pLitnUW4+Y86ykYPN6bGkABwqKuXV+Zt5ITOXA4WlnNulOfeMTKN/h/AdYXLyyHRGr93Ny1mbuWdkutvhBMzTn+XQtEEc1w848cUtIS6Gl246i9tfXcJP31pBuSrXZrQ74T612bItBygq9Vp7gjltNT2S+jTVDF9dQVXvCXhEIXTwaCnTs3J5KTOXQ0VljOzWgkkj0+nTLtnt0GrUs20SPzyjBS9m5nLzkFQSa0FtYfm2A3yZk8fPL+hG/bjqawlV1Y+L5oVxGdz+6hIeeGslXq8ypoZkUltlefKIjhIGdgrfLzImMtRUU/BrHuZIc6CwhJcyc5metZmC4jLO696SSSPSOTPCxoqZPLILl0zJ5JX5m5k4IvJrC1M+yyE5IZYbB3fwe596sdH848cZ3DVjKb94exXlqtww0P/9a4tMTx592iXXii8Hxl01PZL6SqgCCYX8w8W8kJnLq/M3c6SknIvObMXE4el0b9PI7dBOyZkpSYzo1oIXMnO5aUhHGkbw2Plrdh7kv+v2cP+oLiddjnqx0Tx/Y3/Gz1jGQ3NX4/UqNw5ODU6gYejg0VJWbj9QK74YGPfVdPvoCVW9V0Tep/pZ0C4NWmQBtLegmH98uYnXFq8E/McAABc0SURBVGyhqKyc0b3aMHF4Gl1bRf4ga5NHpnPZM1m8Mn8zE4anuR3OKXvmcw+J8TGMO8Uxe+Jjonl2bD8mzFzGr99dQ7lXuWlIx8AGGaYWbsrHq1h7ggmImr6Svea8/jXYgQTD7kNFPP/FJl5ftIWSMi+X9WnLhOGdSWsR+cmgQu92yQzr2pwXvtzETWenRuRMWzm7C/ho9TdMGJZ2Wv0u4mOimXpDfya+voxH3l9LucKtQ2t/Ysjy5JEQFx0RbWEm/NV0+2ips/gVkIavtrBRVYuCHdjp2HXwKM/N28isxdso9yqX92nLxBFpdGzWwO3QgmLyyHSumDqfVxdsYfywzm6Hc9Ke+dxD/dhobgnABTwuJopnbujHPbOy+d0Ha/F6ldt/0CkAUYavTE8eAzs2OaajnzGnqqbbRzH4xja6BdiCb/rOFBGZDjykqqXBD9F/2/cX8uy8jby5ZDteVa7un8Ldw9Jo3zTB7dCCqm/7xvygS3P+8eUmxp3dgYS4yKkt5OYd4b0VO7ntnE40aRCYkV9jo6N46rq+3Dt7OY/+ax3lqtx1buQlS3/sPHCUTXuP1PgIrzH+qunq8RiQCHRU1QIAEWmE73bSX4HJwQ3PP1vzC5k6z8NbS7cjAtdmtGP8sM6kNK7dyaCqySPTuerZ+cxYuIU7fhA5F8Bn53mIjY7itnMCe5snNjqKJ8f0ISpK+NNHX1Pu1YhuczkeG9rCBFpNSWE00MWZQxkAVT0kIuOBr3E5KRSXefnpmyuYm72D6CjhhoHtufPczrRJru9mWK7o36ExQ9OaMe1/m7hxUKpfz/m7bdu+Qt5etoOxgzrQIjHwQzPEREfx92t7EyXw2L/XU+7VWtXRD3xJoVnDOLrazHQmQGpKClo1IVRZWS4ix+3UFiobdhdQsmIn4wancue5ner8mC+Tf5jONc8tYOZXW7jtnPC/j/7cFxsRgTvPDV6sMdFRPH5tH6JFePyTDZR7lXt/mB4WY1idLlUl05PP2Z2bBW1UXlP31JQU1orIj1X11aorRWQsvpqCq5o1jOfLnw8PyrfMSHRWahPO7tyU577YxA0DO4R1beGbg0W8uWQ7V/dvR+uk4NbsoqOEx67pTVSU8OSnOXhVuX9Ul4hPDBt2HybvcLE9imoCqqakMAF4W0RuAZbie/roLHxzNl8R5Nhq1DqpniWE75g8Mp0fTVvI64u2hvXjmM//byPlqtwdoqeloqOEv1zVi2gRnv7MQ7lX+dn5XSM6MWRWtCfY1JsmgGp6JHUHMNCZdrMHIMBHqvppKIIzJ29gp6YM6tSE577YyA0D2x93pFE37S0oZtairVzepy3tmoTuYYCoKOGPV55JVJQwdZ4vKf3igm4RmxiyPHl0bNaAtnWwDc0Ej18PNqvqZ6r6tKo+ZQkh/E0e2aXywhuOXsjcREmZlwnDQ/+UVFSU8OjlPRk7qD3Pf7GJRz9cRzXNZmGvtNzLwk35DEkLr2HdTeSz3i610ODOTRnQ0VdbKCotdzucY+w/UsKMBVsY3asNnVyaXD4qSvjdZT0ZN7gDL2Tm8tsP1kZcYli+7QCFJeXWnmACzpJCLXXvyHR2HyrmjcXb3A7lGNOzcjlSUu56nwER4ZFLe3DzkFSmZ23mN+9HVmLIzMlDBAZ3sqRgAityur6akzK4c1POSm3Ms/M2MmZAO+Jj3G9bOFRUyvT5m7mgR6uwGIxQRPi/0d2JFuGFzFzKvF5+e2nPiHi8M8uTR6+2SSQl2FDZJrCsplBLiQiTR3bhm0NFzAmT2sKr8zdTUFTGxBHh07NYRHjo4jO48wedmLFwKw+94xt6O5wVFJWSve2A9WI2QWFJoRYbktaU/h0aM3XeRorL3G1bOFJcxouZuYzo1oKebcNrMiMR4RcXduPuYZ2ZtWgrv5y7KqwTw6LcfZR71doTTFAEPSmISLSIZIvIB99Z/1MRURFpVmXdgyLiEZH1InJ+sGOr7Xy1hXR2OR3F3DTzqy3sLywNq1pCVSLCz87vyqQRacxevI0H/rmS8jBNDJmePOJjoujXobHboZhaKBRtCpOBdUDl9GYi0g4YBWytsq47MAZff4g2wH9FpIuqhtfjMxHmnPRm9G2fzLPzNnJtRjtXhlcuKi1n2v9yGZrWjH7tw/dCJiLcP6oLUeL0fPYqj13Tm+gwa2PI8uQxoGOTsOyDYiJfUK8QIpICXAy88J2P/g48wLGzuV0GzFbVYlXNBTzAgGDGVxdU1BZ2HDjKW0vdqS3MXrSVvMPFTArTWkJVIsJ9o7pw/6guvJ29g8mzsykt97odVqU9h4rYsPuwtSeYoAn218Yn8F38K/9XicilwA5VXfGdbdsCVVtEtzvrzGk6t0tzerdL5pnPPZSUhfYCV1xWznNfbGJAahMGdoqcjlb3jEzn5xd044OVu7h75jLX22QqZG30DW1h7QkmWIKWFERkNLCnyuxtiEgC8BDwf9XtUs26793UFZE7RGSJiCzZu3dvwOKtzUSEe53awtvLQltbeGvpdr45VMSkkeFfS/iu8cM688gl3flk7W5uf3UpR0vcTwyZOfkkJ8TSvXWjmjc25hQEs6YwBLhURDYDs4ER+OZ87giscNanAMtEpBW+mkG7KvunADu/e1BVnaaqGaqa0bx58yCGX7sM69qcXilJTPncE7LbIaXlXp6dt5He7ZIj9pvtTUM68qcrz+TLnL3c/PIiDheXuRaLqpLlyWOIDZVtgihoSUFVH1TVFFVNxdeA/JmqXqWqLVQ11Vm/Heinqt8A7wFjRCReRDoC6cCiYMVX14gI94xIZ/v+o8xdtiMk53wnewfb9x/lnhFpETvoHMCYAe35+7V9WLx5Pz9+8SsOHnVnFtqNe4/wzaEia08wQRU2/RRUdQ0wB1gLfAxMsCePAmvkGS3o2bYRUz73UBbk2kK5V5k6byPdWzdiRLcWQT1XKFzety3PXN+XVTsOcsMLC9l3pCTkMVRMvRmptS4TGUKSFFR1nqqOrmZ9qqrmVXn/qKp2VtWuqvpRKGKrSypqC1v3FfLO8u/dmQuoD1buJDfvCJMivJZQ1QU9WzPtxgw27D7MddMWsqegKKTnz/Tk0a5Jfdo3rTtzj5vQC5uaggmNUd1b0r11I6Z8lhO02oLXqzzzuYf0Fg05v0eroJzDLcO7tWD6TWexdV8hY55fyK6DR0Ny3rJyLws35lstwQSdJYU6RkS4Z2Q6m/MLeW9FcGoL/1n7DRt2H2biiLRa2SA6JK0Zr906gD0FxVzz3AK27SsM+jlX7jhIQXGZtSeYoLOkUAed170l3VolMsWZljKQVJWnP/PQsVkDRvdqE9Bjh5OM1CbMvG0gBUVlXPPcAjbuPRzU82Xl+O6ynt3ZkoIJLksKdVBUlK+X86a8I7wf4NrC5+v3sGbnIcYP6xx2w0MEWu92ycy+YxCl5V5+9PwCvv7mUNDOlenJo0ebRjRpEBe0cxgDlhTqrPN7tKJry0Se+iwnYLUFVeWpTz2kNK7PFX3rRmf0M1o34o07BxMdJYyZtpBV2w8G/ByFJWUs27rf2hNMSFhSqKOionxtC5v2HuGDlYGpLWR58lm+7QDjh3UmNrru/GmltWjInDsH0yAuhuv/sZClW/YF9PiLcvdRWq7WnmBCou78zzXfc2HPVnRp2ZCnA9S28NRnObRqVI+r+6cEILrI0qFpA+bcNZimDeO48cVFzN+YV/NOfsry5BEXHcVZqU0CdkxjjseSQh0WFSVMGpGOZ89h/rVq12kd66tN+SzK3ced53YKi6k/3dA2uT5z7hxM2+T63Dx9MfPW7wnIcTM9+fTv0Jj6cXXz39WEliWFOu6iM1uT1qIhT3+Wc1qzjU353EOzhnGMOat9AKOLPC0a1WP2HYPo3Lwht7+6hH+v+ea0jpd3uJh1uw4xNN1uHZnQsKRQx0VHCZNGpLFh92E+Wn1qF7Dsrfv5MieP28/pZN9mgaYN45l1+yB6tEni7pnLTqs/yPyN+QDWnmBCxpKCYXSvNnRu3oCnPj212sKUzzwkJ8QydlCHIEQXmZISYplx20D6d2jM5NnZzFmyreadqpGVk0divRjODLN5rU3tZUnBOLWFdNbvLjjp2x2rdxzk06/3cOuQjjSID8XsrpGjYXwMr9w8gKFpzXjgrZW8umDzSe2vqmR68ji7c9Na3+fDhA9LCgaAS3q3oVOzBpVzE/vrmc89JNaLYdyQ1OAFF8Hqx0XzwrgMfnhGS/7v3TVM+99Gv/fdkl/IjgNHrX+CCSlLCgbw1RYmjkjj628K+M/a3X7ts2F3AR+t/oabzk6lUb3YIEcYueJjonl2bD8u7tWaP/zra578bw6qNSfeTGeobGtPMKFkScFUurR3G1KbJvDUp/5dtKZ85iEhLppbhnQMQXSRLTY6iqfG9OWqfin8/b8b+PPH62v8N87y5NEmqR4dmzUIUZTGWFIwVcRERzFheBprdx3ikxpqC5v2HuaDlTu5cVAHGtt4PH6JjhIeu7oXNwxsz3NfbOQ376897q26cq8yf2M+Q9Ka1Zr5KExksKRgjnFF37a0b5LAkzXUFqbO20hcTBS3ndMphNFFvqgo4feX9+TWoR15ef5mfjl3VbW9ydfsPMjBo6XWP8GEnCUFc4yY6CgmDk9jzc5DfLqu+h652/YVMjd7B9cNaE/zxPgQRxj5RIRfXXwGk0akMXvxNn4yZ/n3JjyqaE+wobJNqFlSMN9zRb+2tGtSn6c+q7628OwXG4kW4c4fdHYhutpBRPjJeV352fldeWf5TibNyqak7NvEkOXJo1urREu6JuQsKZjviY2OYsKwNFZuP8i89XuP+WzXwaO8tWQ712Sk0CqpnksR1h4Thqfx69Hd+Wj1N9z52hKKSsspKi1n8eb99tSRcYUlBVOtK/ul0Da5Pk98p23h+S824VXlrnOtlhAotw7tyB+uOJN5G/Zyy8uL+d+GvZSUea1/gnGFJQVTrbgY35NIK7Yd4IsNvtrCnoIiZi3ayhV929KuSYLLEdYu1w9sz9+u6c3CTflMmpVNTJQwoKMNlW1Cz5KCOa6r+/tqCxVPIr34ZS6l5V7uHp7mdmi10pX9Unj6un6Ue5V+HRrbsCHGFfZXZ44rLiaK8cM686t3VvPeip28tnALl/RuY52pgujiXq3p1LwBDS0hGJdYTcGc0DUZKbROqsdP5qygsKSciVZLCLozWjey23PGNZYUzAnFx0Rz97DOlHmVC3u2Ir1lotshGWOCyOqopkbXntWOzfmF/HiwzZdgTG1nScHUKD4mml+P7u52GMaYELDbR8YYYypZUjDGGFMp6ElBRKJFJFtEPnDePyYiX4vIShGZKyLJVbZ9UEQ8IrJeRM4PdmzGGGOOFYqawmRgXZX3nwA9VbUXsAF4EEBEugNjgB7ABcBUEYkOQXzGGGMcQU0KIpICXAy8ULFOVf+jqmXO24VAirN8GTBbVYtVNRfwAAOCGZ8xxphjBbum8ATwAOA9zue3AB85y22BbVU+2+6sO4aI3CEiS0Rkyd69e7/7sTHGmNMQtKQgIqOBPaq69DifPwSUATMrVlWz2fcG81fVaaqaoaoZzZs3D1i8xhhjgttPYQhwqYhcBNQDGonIDFUdKyLjgNHASP12XObtQLsq+6cAO4MYnzHGmO+QE83DG7CTiAwDfqqqo0XkAuBx4FxV3Vtlmx7A6/jaEdoAnwLpqlp+guMWAOuDGfsJJAEHXThvMyDPhfOClTmU3CqzW+UFK3MopatqUnUfuNGjeQoQD3wiIgALVfUuVV0jInOAtfhuK004UUJwrFfVjOCGWz0Rmaaqd7hw3iVW5pCeu06V2a3yOue2MofuvNOO91lIkoKqzgPmOcvHHWZTVR8FHg1FTAHwvtsBuMDKXPvVtfKClfkY1qP5FKlqnftDsjLXfnWtvGBl/q5ITwrHrQLVYlbmusHKXDeEXZlD0tBsjDEmMkR6TcEYY0wAWVIwxhhTKeySgoi8JCJ7RGR1lXW9RWSBiKwSkfdFpJGzPk5EpjvrVzj9Iajy2TQR2eCMynqVC8XxSwDLfJ2zfqWIfCwizVwoTo1EpJ2IfC4i60RkjYhMdtY3EZFPRCTHeW1cZZ9qR9AVkf5OmT0i8pQ4zzmHm0CVWUQSRORD5296jYj8ya0y1SSQv+cqn79X9f9JuAnw37Y71zBVDasf4AdAP2B1lXWL8XV2A994Sb9zlicA053lFsBSIMp5/xvg985yFNDM7bIFs8z4Hi/eU1FO4C/AI26X7TjlbQ30c5YT8Y2W292J+RfO+l8Af3aWuwMr8PVv6QhsBKKdzxYBg/ENk/IRcKHb5QtmmYEEYLizTRzwZW0vc5XjXYmvg+vqUJbDxb9tV65hrv8jHucfNvU7F8hDfNso3g5Y6yw/A4ytst2nwABneRvQwO2yhKrMQCywF+jgXCCfA+5wu1x+lv1dYBS+3umtnXWt8XVOBN/w6g9W2f7f+BJBa+DrKuuvA553uzzBLHM1x3kSuN3t8gS7zEBDINO5iIZtUghwmV25hoXd7aPjWA1c6ixfw7djJK0ALhORGBHpCPQH2sm3E/f8TkSWicibItIytCGftpMqs6qWAuOBVfjGjOoOvBjakE+eiKQCfYGvgJaqugvAeW3hbHa8EXTbOsvfXR/WTrPMVY+TDFyC74tBWAtAmX8H/A0oDEG4AXE6ZXbzGhYpSeEWYIKILMVXJStx1r+E7x9xCb5huufjGyIjBt+Aelmq2g9YAPw11EGfppMqs4jE4ksKffGNHbUSZwKjcCUiDYF/Aveq6qETbVrNOj3B+rAVgDJXHCcGmAU8paqbAhtlYJ1umUWkD5CmqnODEmAQBOD37No1zI2xj06aqn4NnAcgIl3wTdyD+ibrua9iOxGZD+QA+fi+UVT8Eb0J3BrCkE/bKZS5j/P5Rmf9HHz3LsOSk8T+CcxU1bed1btFpLWq7hKR1vjaSOD4I+hu59tJmqquD0sBKnOFaUCOqj4R7LhPR4DKPBjoLyKb8V2zWojIPFUdFooynKwAldm1a1hE1BREpIXzGgX8Ct/98oonMRo4y6OAMlVdq74bcu8Dw5xDjMQ30F7EONkyAzuA7iJSMcnEKI6dBjVsOE8IvQisU9XHq3z0HjDOWR6H735sxfoxIhLv3DJLBxY51fACERnkHPPHVfYJK4Eqs3Os3+Mb2fPeUMR+qgL4e35WVduoaiowFNgQxgkhUGV27xrmdkNMNQ0zs4BdQCm+LHorvnmeNzg/f+LbBthUfA0464D/Ah2qHKcD8D98t1E+Bdq7XbYQlPkuZ/1KfH9QTd0u23HKOxRfFXklsNz5uQho6vyucpzXJlX2eQjfkxnrqfK0DZCBr/1lI74ReMXt8gWzzPi+Sarze644zm1uly/Yv+cqn6cSxg3NAf7bduUaZsNcGGOMqRQRt4+MMcaEhiUFY4wxlSwpGGOMqWRJwRhjTCVLCsYYYypZUjDmJIhPpohcWGXdtSLysZtxGRMo9kiqMSdJRHri62HaF9/IpcuBC9TpTX6Sx4pW1fIAh2jMKbOkYMwpEJG/AEeABs5rB+BMfMMwPKKq7zoDor3mbAMwUVXni28OjIfxdVjso6rdQxu9McdnScGYU+AMNbIM30CFHwBrVHWGM7rlIny1CAW8qlokIunALFXNcJLCh0BPVc11pwTGVC8iBsQzJtyo6hEReQM4DFwLXCIiP3U+rge0xzew2RRnlM9yoEuVQyyyhGDCkSUFY06d1/kR4CpVXV/1QxF5BNgN9Mb3UEdRlY+PhChGY06KPX1kzOn7NzDJGSETEenrrE8CdqmqF7gRX6O0MWHNkoIxp+93+KZDXelMKv87Z/1UYJyILMR368hqBybsWUOzMcaYSlZTMMYYU8mSgjHGmEqWFIwxxlSypGCMMaaSJQVjjDGVLCkYY4ypZEnBGGNMpf8HuS99O3/9hvEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  loc = initial_p >= ub\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  loc = initial_p >= ub\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  loc = initial_p >= ub\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>SES</th>\n",
       "      <th>Holt's</th>\n",
       "      <th>Exponential</th>\n",
       "      <th>Additive</th>\n",
       "      <th>Multiplicative</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\alpha$</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.974306</td>\n",
       "      <td>0.977634</td>\n",
       "      <td>0.978825</td>\n",
       "      <td>0.974909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\beta$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.980000</td>\n",
       "      <td>0.981647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$l_0$</th>\n",
       "      <td>263.918414</td>\n",
       "      <td>258.882637</td>\n",
       "      <td>260.341678</td>\n",
       "      <td>257.354986</td>\n",
       "      <td>258.951988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$b_0$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>5.010784</td>\n",
       "      <td>1.013780</td>\n",
       "      <td>6.644341</td>\n",
       "      <td>1.038144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SSE</th>\n",
       "      <td>6761.350218</td>\n",
       "      <td>6004.138200</td>\n",
       "      <td>6104.194747</td>\n",
       "      <td>6036.555016</td>\n",
       "      <td>6081.995045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  SES       Holt's  Exponential     Additive  Multiplicative\n",
       "$\\alpha$     1.000000     0.974306     0.977634     0.978825        0.974909\n",
       "$\\beta$           NaN     0.000000     0.000000     0.000000        0.000000\n",
       "$\\phi$            NaN          NaN          NaN     0.980000        0.981647\n",
       "$l_0$      263.918414   258.882637   260.341678   257.354986      258.951988\n",
       "$b_0$             NaN     5.010784     1.013780     6.644341        1.038144\n",
       "SSE       6761.350218  6004.138200  6104.194747  6036.555016     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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  loc = initial_p >= ub\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "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": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:725: RuntimeWarning: invalid value encountered in less_equal\n",
      "  loc = initial_p <= lb\n",
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:731: RuntimeWarning: invalid value encountered in greater_equal\n",
      "  loc = initial_p >= ub\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/statsmodels/tsa/holtwinters.py:743: ConvergenceWarning: Optimization failed to converge. Check mle_retvals.\n",
      "  warn(\"Optimization failed to converge. Check mle_retvals.\",\n"
     ]
    },
    {
     "data": {
      "image/png": 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dTJs2jYiICAoKCirNHzFihDnR2rZtG0888USl18OHDweM2ymdPn2axMRE+vfvz8yZMwkJCWHcuHEUFBRUu52YmBhGjx7N4MGDGT9+PGlpaaZDOIa5c+cyevRolixZwpo1awgNDWXAgAGMGjWq2v1ct26duQYmMTGRK664gkGDBjFo0CBzvCLC7NmzCQ4OZsKECZw6dcq8/tdff02/fv0YOXIk//3vf2s8ngsWLODyyy8nNDSUWbNmmWsDY2JiGDBgAFFRUbz77rvm5QsKCrj99tsJDw/ntttuq3J8y+3du5chQ4YQERFBeHg4hw8fBmDlypXm6Q8++CClpaUAPPzww0RGRhISEsKLL75oLue5554jODiY8PBwnn76aaDmc2DGjBnMmTOH4cOH07NnT3PtX25uLmPHjmXQoEGEhYXx2WefVRvzpEmTiG5DX1KaprUy0dFEL76XwMlJ2L0gBE5OInrxvW0n+RKRRnsAW4C+pufzgdcA3wrznwBW1VbO4MGD5WL79u2rPGH06KqPd9815uXlVT9/+XJjfmZm1XlWsLOzkwEDBpgf3bt3lz/84Q8iInLDDTfIihUrRETkn//8p9x0000iIvLiiy/Ka6+9Zgp5tPz666/Vlr18+XK59957RUQkIiJCCgoKZMSIESIicvXVV8vGjRtFRCQgIEAyMzPl+PHjYm9vL7/99puIiNx6663y0UcfVdlOUVGRREVFyalTp0REZNWqVebtjB49Wh5++GFzDKGhoZKSkiIiImfPnq0S47Fjx2TQoEHm13l5eVJQUCAiIocOHZLy923dunVy9dVXS0lJiZw8eVI8PDxkzZo1UlBQIP7+/nLo0CEpKyuTW2+9VSZMmFDt8cjKyjI/nz59unz++eciIhIWFiabN28WEZGnn35aQkJCRETkjTfeMO/Xnj17xN7evtpjPXv2bFm5cqWIiFy4cEHy8/Nl3759csMNN0hRUZGIiDz88MPy4YcfVoqjpKRERo8eLXv27JGsrCzp06ePlJWVVTpWNZ0D99xzj9xyyy1SWloqe/fulV69eomISHFxseTk5IiISGZmpvTq1ctcppubmznmlJQUCQ0NrfY4VflcaJqmNTMrx3QW17kI839/uM5FVo7pbOvQGgywS2rIaRr7qsZHgWjTFY3HgHuBt5VSEYAAicCDDbKlzZtrnufqanm+l5fl+TVwcXEhNjbW/HrFihXmfkTbt2831+DcddddPPvss5dU9ogRI3jllVc4fvw4gYGBODs7IyLk5uYSExPDkCFVKwqDgoKIiIgAYPDgwSQmJlZZ5uDBgyQkJHDNNdcAUFpaiq+vr3n+bbfdVimGGTNmMHXqVKZMmVKlrLS0NCrWRhYXFzN79mxiY2Oxt7fn0KFDAPz000/ccccd2Nvb4+fnx1VXXQXAgQMHCAoKonfv3gBMnz6dpUuXVns8Nm3axKuvvkp+fj5nzpwhJCSEUaNGkZ2dzejRowHjOH/11Vfmbc6ZMweA8PBwwsPDqy03KiqKRYsWkZKSwpQpU+jduzcbN24kJiaGyy+/HDBqz7p06QLAJ598wtKlSykpKSEtLY19+/YRHByMs7MzDzzwABMmTDD3U7N0DkyaNAk7OzuCg4PJyMgAjH+C5s6dy08//YSdnR0nT54kIyMDHx+fSjF36dKl0frsaZqmNbZ5EVnkO1Welu9kTJ9mm5CaVKMmXiISC0ReNPmuxtxmc1Xb1Zw7duzgwQeNHHTBggVMnDiRs2fP8sUXXxAVFQUYydTy5csJCgqq0rEfoF27dubn9vb21TaviQghISFs37692jjc3NzMz99//3127NjBl19+SUREBLGxsXTu3Nk838XFpdK4UYsXL6Zr167s2bOHsrIynJ2da93/mqaPHz+ejIwMIiMjeeedd3jkkUfYtWsX3bt3Z/78+RQWFiIiFo9rdfPWr1/PSy+9BMCyZcu48847GTp0KF9++SXjx49n2bJliAj33HMPL7/8cqV1jx8/zuuvv86vv/5Kx44dmTFjBoWFhTg4OLBz5042btzIqlWreOedd/jhhx8sxlPxvRJTs2l0dDSZmZnExMTg6OhIYGBgteNyFRYW4uLiUuN+a5qmNWcnPC5temuj79XYSIYPH86qVasA4wd15MiRVZZxd3fn/PnzAAwdOpTY2FhiY2OZOHEiYNTGLFmyxJx4RUVF8dZbb5n7d1mr4nb69u1LZmamOfEqLi5m79691a539OhRhg4dyoIFC/Dy8iI5ObnS/D59+lSqVcvJycHX1xc7Ozs++ugjc7+oUaNGsWrVKkpLS0lLS2PTpk0A9OvXj+PHj3P06FEAPv74Y3NZ33zzDbGxsSxbtsycfHh5eZGbm2vuE+Xp6YmHhwc///wzQKV+T6NGjTK/TkhIIC4uDoDJkyebj3NkZCTHjh2jZ8+ezJkzh4kTJxIXF8fYsWNZu3atuS/amTNnSEpK4ty5c7i5ueHh4UFGRoa5di03N5ecnByuv/563nrrLXMtqDXnQEU5OTl06dIFR0dHNm3aRFJSUrXLHTp0qMarNzVN05q7Ho6dL2l6a9NibxnU3L399tvcd999vPbaa3h7e7N8+fIqy8yYMYOHHnoIFxcXtm/fXqUWY8SIEWzYsIHISKPSMCoqimPHjl1y4nXxdtauXcucOXPIycmhpKSExx9/nJCQkCrrPfPMMxw+fBgRYezYsQwYMKDSfDc3N3r16sWRI0e47LLLeOSRR7j55ptZs2YNV155pbn2bPLkyfzwww+EhYXRp08fc9Ogs7MzS5cuZcKECXh5eTFy5EgSEhKqxOHp6cnMmTMJCwsjMDDQ3AQIsHz5cu677z5cXV0ZP368efrDDz/MvffeS3h4OBEREdU2zQKsXr2alStX4ujoiI+PDy+88AKdOnVi4cKFjBs3jrKyMhwdHXn33XcZNmwYAwcOJCQkhJ49ezJixAgAzp8/z0033WSuhVu8eDFg3TlQ0bRp07jxxhuJjIwkIiKCfv36Vbvcpk2bmDBhgsWyNE3TmqtFE5dw37q7KVJl5mmuyolFE5fYMKqmo8qbOZqzyMhIuXgMpv3799O/f38bRaSVW79+PTExMSxcuNDWobQZo0aN4rPPPqNjx6pD4OnPhaZpLcF1/9ePr8sOAuDv6ssr177GtLDW08NLKRUjIhd3tQJ0U6NWT5MnTyYwMNDWYbQZmZmZPPnkk9UmXZqmaS3Fq7PWcKuH0Xrz5eA3WlXSVRudeGn19sADD9g6hDbD29ubSZMm2ToMTdO0egnrGsac/jMASE89ZNtgmphOvDRN0zRNazKnj+9lzc39aZdsDN6ddvq4jSNqWjrx0jRN0zStyWzZvoqp4QfI7WhcgJV2NrmWNVoXfVWjpmmapmlNJvb4duzKYOgVt7MjNZOeg6+2dUhNSidemqZpmqY1mdjsA/QrdsC1SzeGPPqKrcNpcm2mqTE6PprAtwKxe8mOwLcCiY6v/804Lx49fsWKFcyePdviOvPnz+f11183L1/drV+ys7Pp3LmzeUTz7du3o5QiJSUFMAba7NSpE2VlZVx//fVkZ2db3GZN22kIaWlp5lvkWGvGjBnmQVAr2rx58yWXZa0xY8Zw8ZAkLUn5uZaZmWm+KbmmaVpL9JvdKSLKjNuwfb31Qz5aP9+2ATWxNpF4RcdHM+uLWSTlJCEISTlJzPpiVoMkX/VRU0Lk6emJj48P+/fvB2Dbtm0MHDiQbdu2AfDLL78wdOhQ7Ozs2LBhA56ennXajiUlJSVWLffmm28yc+bMSypbqztvb298fX3ZunWrrUPRNE27ZFl5p0l2LSbCbxAAKz5/iQVb2tY4kK0m8RqzYkyVx3u/vgfAn77/E/nF+ZWWzy/O57GvHgPgdP7pKuvWV1JSEmPHjiU8PJyxY8dy4sSJSvPXrl3Lrl27mDZtGhEREVXuqzhixAhzorVt2zaeeOKJSq/LR68PDAzk9OnTJCYm0r9/f2bOnElISAjjxo2joKCg2u3ExMQwevRoBg8ezPjx40lLM64sGTNmDHPnzmX06NEsWbKENWvWEBoayoABAxg1alS1+7lu3TpzDUxiYiJXXHEFgwYNYtCgQeZ4RYTZs2cTHBzMhAkTzLfiAfj666/p168fI0eONN9QujqBgYHMnTuXqKgoIiMj2b17N+PHj6dXr168//77QNUas9mzZ7NixQqL79PevXsZMmQIERERhIeHc/jwYQBWrlxpnv7ggw+ab3/08MMPExkZSUhICC+++KK5nOeee47g4GDCw8N5+umngZrPgRkzZjBnzhyGDx9Oz549zbV/ubm5jB07lkGDBhEWFsZnn31WbcyTJk2qdHskTdO0lqKTa2eOzTnGPY/+EwBfZ2/SnUvB9B3bFrSaxMuSlHMp1U7PKsiqV7kFBQVERESYHy+88IJ53uzZs7n77ruJi4tj2rRpzJkzp9K6t9xyC5GRkURHRxMbG1vldkHDhw83Jy7Hjh3j1ltvNTeVbdu2zXy7mooOHz7MH/7wB/bu3Yunpyfr1q2rsh0HBwceffRR1q5dS0xMDPfddx/z5s0zl5Gdnc2PP/7IU089xYIFC/jmm2/Ys2cPn3/+eZXtHT9+nI4dO5pv+NylSxe+++47du/ezerVq837vH79eg4ePEh8fDwffPCBeb8KCwuZOXMmX3zxBVu2bCE9Pd3i8e7evTvbt2/niiuuMDdX/vLLL5WO+6V6//33eeyxx4iNjWXXrl34+/uzf/9+Vq9ezdatW4mNjcXe3t6c6CxatIhdu3YRFxfHjz/+SFxcHGfOnGH9+vXs3buXuLg4nn/+ecDyOZCWlsbPP//M//73P5577jnAuIXS+vXr2b17N5s2beKpp56iujtLREZGsmXLljrvs6Zpmq0oIKhjEF3cjKZGH3c/cttB7sm2M6REq+lcv3nG5hrn9fDoQVJO1RsOB3gEAODl6mVx/Zq4uLiYb4gMRpNeeXK0fft2cw3OXXfdxbPPPntJZY8YMYJXXnmF48ePExgYiLOzMyJCbm4uMTEx1d57MCgoiIiICAAGDx5c6QbW5Q4ePEhCQgLXXHMNAKWlpfj6+prn33bbbZVimDFjBlOnTmXKlClVykpLS8Pb29v8uri4mNmzZ5uTlUOHjEHxfvrpJ+644w7s7e3x8/PjqquuAuDAgQMEBQXRu3dvAKZPn87SpUtrPCblNw8PCwsjNzcXd3d33N3dcXZ2rrWfW02ioqJYtGgRKSkpTJkyhd69e7Nx40ZiYmLM94QsKCigSxfjS+KTTz5h6dKllJSUkJaWxr59+wgODsbZ2ZkHHniACRMmmGvdLJ0DkyZNws7OjuDgYDIyMgCjZnDu3Ln89NNP2NnZcfLkSTIyMvDx8akUc5cuXRqtz56maVpj+mDueJzi93HPF8mgFL6dekAepCUm0LvHZbYOr0m0iRqvRWMX4eroWmmaq6Mri8YuarIYlFIW5+/YscNcc/b555/Tu3dvzp49yxdffEFUVBRgJFPLly8nKCioSsd+wFzzBGBvb19tPy0RISQkhNjYWGJjY4mPj+fbb781zy+/sTUYtUELFy4kOTmZiIgIsrIq1xC6uLhQWFhofr148WK6du3Knj172LVrF0VFRbXuf03Tx48fT0RERKVR8cv3z87OrtK+2tnZUVJSgoODA2Vlv990tWJs5davX28+zrt27eLOO+/k888/x8XFhfHjx/PDDz8gItxzzz3mY3Tw4EHmz5/P8ePHef3119m4cSNxcXFMmDCBwsJCHBwc2LlzJzfffDOffvppjZ3fK+5rxfjLa7Wio6PJzMwkJiaG2NhYunbtWu0+FBYWVqkh1TRNawmWlG5jbY9cMH0f+voYyVbayQO2DKtJtYnEa1rYNJbeuJQAjwAUigCPAJbeuLRR7w01fPhwVq1aBRg/qCNHjqyyjLu7O+fPnwdg6NCh5h/68pqdqKgolixZYk68oqKieOutt8z9u6xVcTt9+/YlMzOT7du3A0Yt1d69e6td7+jRowwdOpQFCxbg5eVFcnLlQe769OlTqVYtJycHX19f7Ozs+Oijj8z9okaNGsWqVasoLS0lLS2NTZs2AdCvXz+OHz/O0aNHAfj444/NZX3zzTfExsaybNkyq/czIB7R8nQAACAASURBVCCAffv2ceHCBXJycti4cWOVZSZPnmw+zpGRkRw7doyePXsyZ84cJk6cSFxcHGPHjmXt2rXmvmhnzpwhKSmJc+fO4ebmhoeHBxkZGXz11VeA0TcrJyeH66+/nrfeestcC2rNOVBRTk4OXbp0wdHRkU2bNpGUVLWWFuDQoUOEhoZafVw0TdOag4KifA645BHhEmSeNnLYVFL6LWX46Ok2jKxptZqmxtpMC5vWpDfhfPvtt7nvvvt47bXX8Pb2Zvny5VWWmTFjBg899BAuLi5s3769Si3GiBEj2LBhA5GRxg3Oo6KiOHbs2CUnXhdvZ+3atcyZM4ecnBxKSkp4/PHHCQkJqbLeM888w+HDhxERxo4dy4ABAyrNd3Nzo1evXhw5coTLLruMRx55hJtvvpk1a9Zw5ZVXmmvPJk+ezA8//EBYWBh9+vRh9OjRgNGnaenSpUyYMAEvLy9GjhxJQkLCJe1bRd27d2fq1KmEh4fTu3dvBg4cWOs6q1evZuXKlTg6OuLj48MLL7xAp06dWLhwIePGjaOsrAxHR0feffddhg0bxsCBAwkJCaFnz57mfnbnz5/npptuorCwEBFh8eLFgHXnQEXTpk3jxhtvJDIykoiICPr161ftcps2bWLChAmXeHQ0TdNsK2H/ZkrtYKDfYPM0l05d6XZb27oyXlXXebe5iYyMlIvHYNq/fz/9+/e3UURaufXr1xMTE8PChW3rcmBbGjVqFJ999hkdO3asMk9/LjRNa66WfjiHBxP/xtFhH9Nz/O3m6X/96CH6dQjippv+aMPoGpZSKkZEIqub1yaaGrXGM3nyZAIDA20dRpuRmZnJk08+WW3SpWlaMxIdDYGBYGdn/NVDwHDSqZCOZe0IGjK+0vR3Ev7F+u/fsVFUTU8nXlq9VewArzUub29vJk2aZOswNE2zJDoaZs2CpCQQMf7OmtXmk6+X7lhK2p9zUBf94+hb5kJa2TkbRdX0WnTi1RKaSTWtqejPg6Y1E/PmQX7lQbvJzzemt2WJibRTVbuW+9p5kGafX80KrVOLTbycnZ3JysrSPzaahpF0ZWVl4ezsbOtQNE07cYLoMAh8HOxeNP5GhxnT26ojaXu59s9BxLz0UJV5vu28SHcuaTOj17fYqxr9/f1JSUkhMzPT1qFoWrPg7OyMv7+/rcPQtDYvenQnZg3PIt/JeJ3kCbNuBDp3oumurW9edu36nG8ug1d69qkyz9fdl7P8RsmpdBx8u9kguqbVYhMvR0dHgoKCal9Q0zRN05rQvKsh/6Lxq/OdjOltNfGKPbIFx1IIjryuyrw/3v4Oz6dlYN/Zu5o1W58Wm3hpmqZpWnN0ouTMJU1vC37L2kvIGYVTn6rD3Th3D4LubacipcX28dI0TdO05qiHR49Lmt7aiQi/SRoDizqDvX2V+amnj/PQG1eyc9NKG0TX9HTipWmapmkNqDncH7g5yS/OJ9QrmBEjbq92fill/CN3M7Fb1jRxZLahmxo1TdM0rQGV355u9pezyb6QTfcO3Xn56peb9LZ1zYmbkxs/PBFb4/yuHbsDkH4utalCsqlGTbyUUp7AMiAUEOA+4CCwGggEEoGpInK2MePQNE3TtKY0LWwaZWVl3P3p3Xx/9/f06Vz1ar62Qo4dQ504AcOHg5NTlflO9k54XbAnrfC0DaJreo3d1LgE+FpE+gEDgP3Ac8BGEekNbDS91jRN07RWpb93f6bkB6LW/dfWodjU9OgpTFx6JRQU1LiMT4kL6aU5TRiV7TRa4qWU6gCMAv4JICJFIpIN3AR8aFrsQ0Df/0TTNK2FiY6OJjAwEDs7OwIDA4lu47fDqU6kXyTr/lNC720HbB2KTe0sPIpTO1fw8KhxmQDlSemFmhOz1sRiU6NSyhm4AbgC8AMKgATgSxHZW0vZPYFMYLlSagAQAzwGdBWRNAARSVNKdalh27OAWQA9erTNK0E0TdOao+joaGbNmkW+6bY4SUlJzJo1C4Bp09pmP6YadeuGpJ5E2ToOGzl/4TxHnHKZ4dTP4nL/e2yHcUPxNqDGvVRKzQe2AlHADuAfwCdACfCKUuo7pVS4hbIdgEHA30VkIJDHJTQrishSEYkUkUhv77YxqJqmaVpLMG/ePHPSVS4/P595bf1ehNXodVUCT3v9ZuswbGbPiZ0ARHSNsLygnx/4+DRBRLZnKb38VUQGi8hTIvIfEfleRP4nIm+KyI0YA/BW7SX3uxQgRUR2mF6vxUjEMpRSvgCmv6caYD80TdO0JnKihnsO1jS9LbO3d+Ak52wdhs3E7vkGgIj+Yywu9/22ldzwUl+yD8c3QVS2VWPiJSJfXjxNKWVn6ruFiJwSkV0W1k8HkpVSfU2TxgL7gM+Be0zT7gE+q2PsmqZpmg3U1P1Ddwupyq+dFyc72kNxsa1DsYnewVcws/tN+I2/1eJyWenH+JJDnIzb2kSR2U6tDapKqf8opToopdwwEqeDSqlnrCz/USBaKRUHRAB/AV4BrlFKHQauMb3WNE3TWohFixbRrl27StNcXV1ZtKhtDhBqSbfgoaT29QNHR1uHYhPjg29k6X2fojp1sricj58x3EZaxpGmCMumrOnJFiwi5zCuPtwA9ADusqZwEYk19dMKF5FJInJWRLJEZKyI9Db9bbs3r9I0TWuBpk2bxtSpU82vu3fvztKlS3XH+mr4tfcj9XwqImLrUJpcSVkJqe/9Ffn221qX9e0RAkDa6cRGjsr2rEm8HJVSjhiJ12ciUowxGKqmaZrWRjk7O5uff/vttzrpqsFo91BmJXlR/NX/bB1Kk9t3ai/dMp9jzZev1rqsb+dAANLPt/7R661JvP6BMcK8G/CTUioA2nBPQU3TNI34+Hhzc2NaWpqNo2m+bug3kSUfpOB0sPU3oV0sdt8PAIT1jKp1Wfd27vQ/1w7HnNzGDsvmar1lkIi8DbxdYVKSUurKxgtJ0zRNa85EhISEBEaNGsV3331Hamrrr6WoM09PLri1Q1JP4Fz70q3Kbwd/xKUY+gy62qrl9/05HdzdGzkq26s18VJKtQNuxri3YsXlFzRSTJqmaVozlpSURG5uLuPGjeO7777TNV4WJOYkEfTMBZan/8IMWwfTxGIz4wjPAPsBA61bwdOzcQNqJqxpavwM4zY/JRiDoJY/NE3TtDYoISEBgKioKNzc3HSNlwVd3boCkJqfYeNImpaIEFtykoF57tChg1XrvLzifib/KQha+YUItdZ4Af4icm2jR6Jpmqa1CPHxxiCXoaGh+Pn56cTLAhdHFzpKO1K9LI033vqUSinv3PJPetpbf+eZ9PQj/EAiZGWBl1fjBWdj1iRe25RSYSLS+oeT1TRN02qVkJBAjx498PDwwNfXVzc11sKvy2Wc7N/b1mE0KQc7B6aFT7+kdXw8unHuAuQnH8O1FSde1jQ1jgRilFIHlVJxSql404ComqZpWhsUHx9PaGgogK7xsoKfuzGWV1sS8/Mn7H5gAhw+bPU6vl5BAKSf2NdYYTUL1iRe1wG9gXHAjcANpr+apmlaG1NcXMyBAwcICwvjD1/+gZSAFNLS0trkAKHWmuEQyf3/TbykJKSle2nrX5juvAGUsnodH5/LAEhLO9RYYTULtSZeIpIEeGIkWzcCnqZpmqZpWhtz6NAhiouLCQ0N5b1d7/Gzy8/k5eVx/vx5W4fWbN3pcw2zvjoFKSm2DqXJxOYdJSLTHnr2tHqdwKCBjEhW2OcXNmJktmfNvRofA6KBLqbHSqXUo40dmKZpmtb8lF/RGBYWxt0D7qazQ2dAD6JqSVFXL457woWTbaPOIis/i2T7XAbadQM7axrWDP38I/j5g1KGPflmI0Zne9YckfuBoSLygoi8AAwDZjZuWJqmaVpzFB8fj729PQ5dHCgsKeRsyVlQ6H5eFmy4kEDPx2Hvyd9sHUqTiE0z9jPCO+zSV76EpsmWyprESwGlFV6XmqZpmqZpbUxCQgJ9+vThjZ1v8MneTyijDNrrGi9L/Lr0AiD19HEbR9I0YhO3AxARfNUlr3v1wj48PndQQ4fUrFgznMRyYIdSar3p9STgn40XkqZpmtZcxcfHM3jwYH5J+YX2Tu0Z2HUgWxy26BovC/zc/QBI9XGzcSRN4/4RjxLZaxTegaMved3svCwOnU5uhKiaD2s6178J3AucAc4C94rIW40dmKZpmta85OXlcezYMS4LvYz9p/fznNNYfnR/FLciPXq9JV3duqJQnBzUx9ahNAlPZ09G1yHpAvB17Eiaw4VWPXp9jYmXUqqD6W8nIBFYCXyEcZPsTk0SnaZpmtZs7N27FwDHQEcAhr37GWrqVD2Iai0c7R3p2r5rmxjLq6C4gP97+nIOzJxcp/V9nb1Jay9w5kwDR9Z8WKrx+o/pbwywq8Kj/LWmaZrWhpRf0ZjjnoNCcXkqDHysHUUjinSNVy3+WngF059f3aprcgASTiXwgvsu9hXX7Xzw8ejGKTcoOdl6mxtr7OMlIjeY/gY1XTiapmlac5WQkICLiwt/HPtHrj/tTIcLfyXXvyvYQdo2XeNlyd1uwyF+DZw9C51ab6PRbyd2ABAROKxO60f6D2Hqr19TkHsW94YMrBmpMfFSSlm8rEBEdjd8OJqmaVpzFR8fT0hICL4dfPHNaA/u7vh7dOdw9jFSU7NsHV6zltHFlaPdYXhqaqtOvGIPbKZDIQRdXrc+XhNvepaJNz3bwFE1L5auanzDwjwBLv06UU3TNK3FSkhI4IoJV/DGtje487H78Y2IwP9fN7I3xN08er27e2utp6if90t2MP9+KEo5gaPpPpetUWzab0Skg4qIqFc5IoJqpWN61djHS0SutPDQSZemaVobcvr0adLT03Ho7cDT3z1NVkEW9O6N/zk4a5+nB1GthV9XYyyv9JT9No6k8YgIR+Q0A12CIDCwTmWknk/F8wUn/vmXWxo2uGbEUlPjFEsrish/Gz4cTdM0rTkq71if65GLe4kb/e9+Cl75K8NS4Ia8ID51OEpqaip9+/a1caTNk1+3fgCc7OJCdxvH0liUUqT+KYuC4oJLulVQRZ1dOpNjX0x6yoEGjq75sNTUeKOFeQLoxEvTNK2NiI+PByCxNJEh4of9N9/C8hXcdLYLo5MG8WnxUT2khAXdvIybRaf29rFxJI1IBIcLxbi71L25uZ1DOzoVO5BW1HqHk7B0VeO9TRmIpmma1nwlJCTQsUtH9mXtY+KpPtCjB/j6QkAAblmndVNjLcyj17fi2wa9/+1f2L/keZZMj4Y776xzOT5lbqSXnWvAyJoXSwOoTjf9fbK6R9OFqGma1vSio6MJDAzEzs6OwMBAoqOjbR2STcXHxxN4eSBKKYbFnoZhxnABWY/eT8fR23Ac7qhrvCzwcvXi4yMRTHjhI1uH0mg+3buOn3oAQfUbhcrX3oM0h4JWO+aZpUbY8ptKudfw0DRNa5Wio6OZNWsWSUlJiAhJSUnMmjWrzSZfIkJCQgLDA4eTM+MA1/ySCUOHAtBx+kyKVBluvvq2QZbYKTtutx9A0NHW2YQmIvx2/hAD04F6XrV5c5fRTCwMgIKChgmumbHU1PgP09+Xmi4cTdM025s3bx75+fmVpuXn5zNv3jymTZtmo6hs58SJE5w/f57Q0FBcc4tg1JUwciQAdgWFdHP2prBTEWkHdY2XJbu72XG23UnGlpXVufN5c5Wem84p8ogo6Qz1HFLk4Uf/3UBRNU+WOtcDoJQKAh4FAisuLyITrVg3ETgPlAIlIhKplJoPzAQyTYvNFZENlxq4pmlaYzlx4oTxpCNQgvEtVnF6G1N+ReNqWU2nsk5M/eGH32d+9x3d96eS5NlR13jVYlH73RwYV8be06ehSxdbh9OgYtNjARjYMaRBysstysXFwQV7O/sGKa85sSbl/hTjJtl/wxhUtfxhrStFJEJEIitMW2yaFqGTLk3TmpsePXoYTx4zPS6e3sbEx8dDB9h8ajOnzl1UqxUQgP85KGx3QSdetfBz9yPVHWiFxymvKJdAu06ET36w3mWt3vJ33F9259B/3m6AyJofaxKvQhF5W0Q2iciP5Y9Gj0zTNM1GFi1ahKOHo/HCVM/v6urKokWLbBeUDSUkJNB5QGcAhs14Hl555feZAQHcdACuy/I3j16vVc+vezDZLpDv7mzrUBrcLSG3cvzPWXhMqfvVjOW6dA4AIO3EvnqX1RxZk3gtUUq9qJSKUkoNKn9YWb4A3yqlYpRSsypMn62UilNK/Usp1fHSw9Y0TWs806ZNI3hcsPFiOXTr1o2lS5e2yf5dYNR4uQe742zXjvCjudC9whCgnp7cltSe55ICAT2khCXdAsMBSO1Yay+flufECUhKapArEX27GGOepZ9NrndZzZE1iVcYRp+sV/i9mfF1K8sfISKDgOuAPyilRgF/B3oBEUAaNTRbKqVmKaV2KaV2ZWZmVreIpmlao8lwyjB6p6bCqlWr2mzSVVxczIEDByjuUsxge3+cSjEPJQGAUkhAD+wLs8EBPaSEBeaxvE7stXEkDevchXP0XBbGJzf3a5DEy6e9MchsWm7rPJesSbwmAz1FZPSl3qtRRFJNf08B64EhIpIhIqUiUgZ8AAypYd2lIhIpIpHe3t7W7Y2maVoDuHDhApnbMvHJ8YH74Zejv9g6JJs5fPgwRUVF+Lj7cE1mB/Dygp49Ky3z65/vp89VO6GnrvGy5HK/y9n6344MfP9TW4fSoOIy4jhufw5X/6AGuVrTo50HzqV2pF3IaoDomh9rjtAewPNSC1ZKuSml3MufA+OABKWUb4XFJgMJl1q2pmlaY9qzZw+lx0u5t/+94AP7UltnXxNrlF/RuOyaZbz47QVj/C6lKi3jf/3txpMOusbLEg9nD4bbBeB+8rStQ2lQv6XtBmBg98sbpDylFC86juVqr2rrZZq16PhoAt8KBF8G17SMNQ3NXYEDSqlfgQvlE60YTqIrsF4ZH1AH4D8i8rVS6iOlVARG/69EoP6XQGiapjWg7375DnrAdSOv4+V1L5N4JtHWIdlMfHw8dvZ29OvbF2bONG4VdJGuuWCPHY6d7HSNVy0+CVV4nTqIVc1GLUTskZ/xygO/kKgGK/O5P3/bYGU1lej4aGZ9MYv84nyLy1mTeL1YlwBE5BgwoJrpd9WlPE3TtKby+ZHP4T7w7+YPAidzT9o6JJtJSEig/fT2TFx7E98+Xv2Pof3mH/HLKaPU21knXrWYF3CUSLnQuhKvkzEMTAc1JaLByswtyiUzL5OgjvW7/VBTmrdxXq1JF1hIvJRSSgw1Dh1RvkwdY9Q0TWuWDuQdwLm9M0EbttEp356s4tbZ18Qa8fHxlE4txb0IY/wpP7+qCwUE4L8RTnZQpO3TTY2W+Dl0JNUxCYqLwdHR1uE0iFGXXU3vDiUQHt5gZT637Daikzdw9q69EBzcYOU2phM51g2wbKmP1yal1KNKqUr1ykopJ6XUVUqpD4F76hGjpmlas3P+/HnOeZwjoqgrTJ/OLftLKUxtnfeMq01eXh5H04+S1y6PYdtT4Oqrq18wIIA5O+DalC66xqsWft36ktqrC5SV2TqUBrN4yj945KF/gqtrg5Xp4+ZDtjMUnkxqsDIbWw+HTlYtZynxuhbjYuqPlVKpSql9SqljwGHgDozR51fUN1BN07Tm5KutX4EHXHPeuKboH/8Dp6/yuXDhQi1rtj779u2DbsbzYTtTKw8jUZGvL7cfdOTWtM66c30t/HqEkmqXizg52TqUBnH+wnlKV34EBw40aLm+3qaxvFIattzG9OjWUtqV1L5cjYmXiBSKyHsiMgIIAMYCg0QkQERmikhsg0WraZrWTHy2+zMArj/0ey1XEJCSkmKjiGwnISEB/MFB2TP4QE7NiZedHXlB3Tjvep7cglw9er0Ffm5dyS/O51zyEVuH0iBe+PZP+MTdTdknqxu0XN9ufQFIS285x+k3l2wE8M+xvJxVA26ISLGIpIlIdgPEpmma1mwVxBbQ68uuDP75MEycSHQYJDwL8UfjbR1ak4uPj8cp04lnPSbgWowxlEQNNrzyAFOuOgid9ZASlszwv4GkxeD+xTe2DqVB/HZ8G73Ogt2AhutYD+DbpRcA6Wdbxo3pD2cd5uNQmLMDkhfDYAsfgfqPdKZpmtaK7N65mwfa9caxRODee2ln50SRK8SfaHuJV0JCAmFOYSw6GgBubhASUuOy/pGm6/Q89CCqlnTu3pceufbYpaXbOpR6ExFisw8wMA0YUGUQg3rp2bEnfyu4kvDgKxu03Mby8s8v42TvyFM77WtdVidemqZpJoknE0nqnYSKDIDp02H8eHzWfQ/AwfSDNo6u6e05uIfAiEDkiSdg7VpwqHkEIv/TRQDYddCJlyW5pQW8PN6NHaf32DqUekvKSSJHCojIcYaAgAYt28PZg9mv/ECvGU82aLmNITE7kY/iPmLm5Q/h8+6HtR4LnXhpmqaZrN6yGkaCXBEKH30ELi707toHgKSzLefqqoZw+vRpTnmdYl33dRzpUALXXmtxeZ+YA9iVgbsevd4ihWLukHNsKmr5ifxvab8BMNCjX5W7GTSEg5kH2H8ipsHLbWiJ2YkEqk482+4qmDYNEhOJgRoDrzXxUkoNU0r9qpTKVUoVKaVKlVLnGjZsTdM02/vuwHcA3NFjuPlmv94rPsGhBFLz2lYtTnnH+g52bly2ZiNkW+7i6xjYC59caO+pR6+3xM3JDY8SB04Wn7F1KPXW37s/C4bNJfSNjxql/DveGc0zzw9pkBtvN6YxEsDBhdn4/2utVctbU+P1DsbwEYcBF+AB4G91jlDTNK2Zis+OxzPbgYDLR8OWLQDYJSbxwG4oTi6ycXRNqzzxGlbmh3r4YSioZSyzgADe/gpGH/bQNV616ObhT+rQ/rYOo976efXjz+MX4do3tFHK93HsRJpLGTTjq2S3JW/jwh+fws7eAV55xap1rL2q8QhgLyKlIrIcaBm93TRN06xUVlZGpnMmQ862BycnuNx0w9+gIP6+AVy3Nt8v/8YQkxAD3jAis51xf0ZfX8srdO/OzfvhyvMddI1XLfy6XkaqixUDPjVzP234O9kv/rHW2tC68nXtSpo70EwT+fTcdMauuJLnzq2H554Df3+r1rMm8cpXSjkBsUqpV5VSTwBu9QlW0zStufn1wK8IwrUpdsZ4VS4uxozAQAA88nLIy8uzXYBNbOfJnaAgavepmsfvqsjZmZRe3mR2L9Q1XrXwc+xE2qljkFPLgE/NWFZ+FqN/fYQPNr7aaLc+8vX055QblJ5MbpTy6+uNra9RVFrEIyd94emnrV7PmsTrLsAemA3kAd2Bm+sUpaZpWjN1Yu8JOrwKf/jxLIwZ8/uMoCAWjIZf/wSJSYm2Cq9JiQgndp7gplOjGbr7lMXxuyr6+I17mXt1BidPt92bilvjHffbOPz8Kdi719ah1FlsujGG+kC7bsZQI43AxzuIUjs4nXK4Ucqvj9P5p/l7zD+43SGC3gve/f0fNSvUmniJSJKIFIjIORF5SUSeNDU9apqmtRo7d+7kKnsHnEqkcuIVGIiHU0fEHuKOxdksvqaUnJxM7qlcHrAPp8MFrKvxArr3GghAnn2eHr3eAvful+FYhnHT8RaqPPEa4Deo0bZx3cBbWV80Bfd+DXfz7YayePti8ovzmfdgNEyefEnr1ph4KaU+Mf2NV0rFXfyoZ8yapjUDJWUlSDO/YqipLC9Yzr6bfGDVqsqJhqsr7Z9/DYCE5AQbRde04uLiIBJybxgOWVm/93erhX+yqelMDylh0UGXfP5wPRxLbrk/pbHJv9LtHHiHDmm0bfTyD2fSonW4DhnRaNuoCxFh+7bV3Nz+coK9gy95fUs1Xo+Z/t4A3FjNQ9O0Fq7bm90Yt3KcrcOwuay8LLK8s+jYsxvcdluVZoMBQcao3IdPNb8mj8bwU/xPcAOku6RDp05W9+HxP2SMxu6uB1G16Kyz8N4QOJC539ah1NlvJ3cx8JR9g49YX1FRaRFf71nH4f0/N9o26kIdPszG/0viX/v71mn9GochFpE009+2NWqgprUROYU5nMo7xffHvrd1KDa3docx/s49WW5w8iR061Zpfq8PPwXgRHbLuG9cfW09sRV8YOz7X0J+fxg/3qr1/ALDIFYPolobvw7G+ZWa03JvvP7vOz6hbGoJ+DReU2NpWSnXfXoLi44FMvfD4422nUuRW5TLhWcfpbOzC+4LX61TGZaaGs8rpc5V8zivB1DVtJZvywljnKrnRjxn40hsb0PcBlQZ3LXyBzhctVbLM7+Up7aCpJTaILqmdzDvII4ldgR//D1kZlq9nlNgL775CCJidY2XJT7tfQBIvdq6ixaao0G+g4j0H2LxNlL15eLogkepI2nFZxttG5fqb9FzCAr+lvR5j4GPT53KqDHxEhF3EelQzcNdRDrUOWpN05qFTcc30c6+HS+OedHWodjc7szddMsAN9Wu2o7kKjCI178D9z0t9/J/a5WUlHDG9Qx9cz2xF6zuWA9AQADjjkJ4noOu8bLAyd4Jb1dvTjrUMihtMxQdH43v676o+YqABR2Jjo9u1O350J50cht1G9bKy8/hzUP/ZuRpV3wef77O5VidqiqlugDO5a9FpG3UuWtaK3Vn2J1069CNTcc3MaTbEDq7drZ1SDZTlFrEnclOqGHDwNm56gJBQeQ7QklO6//a23tgL+ItXJHiBp0V9Opl/cqenuzq7cZZzzLO6Rovi3o4eVOwP65F9ZiOjo9m1hezyC/OBwUnJJtZX8wCYFrYtEbZpq9jR9Jczhqj17u7N8o2rPV+7Aecdi7l+fELoV27Opdjzb0aJyqlDgPHgR+BROCrOm9R07Rm4cCmA7z62Ktc/5/rCb4mmOjoxv3Ptbm6cOECZSvP8MYPxZWHkagoKIhHr4Odd10gpwUPemmNQ/sPwaswd4e9MX7XJd78eMWrd7JsoL7Y2wAAIABJREFUXJGu8arFr/nT+fcff4EWNCjvvI3zjKSrgvzifOZtnNdo2/R17Up6e2w+en1BcQGvbXudq4KuYvjNT9SrLGsGUP0/YBhwSESCgLHA1nptVdM0m/rrv/7K/X+5n4zDGQCcKjrFrFmz2mTytWP3DvqVlBgJRk2JV48edHTuQkF7OJZ0rEnja2rx8fE4Fiv8OnWr+XhY4O/Vk1LHUlJOtdyO401BlV/A0YJqBk/UUONb0/SG8PyYF1jT8znj6lob+u7F6WTkZfDnUX+ud1nWJF7FIpIF2Cml7ERkExBR7y1rWhNYvH0x/97zb1uH0ews+noRFyZfgFygFPCA/Px85s1rvP9cm6unf3yanx+ElLg4GFHDeEFOTjjdcj8oiD0W27QBNrF1p9bRcYI3dj//DM88c8nr+x85BUDq+ZaTUNjC/1ySmXgHFKe0nObr7g7VJz89apjeEIIHX8vAx14GL69G20at9u5l4qufsf/07YwOGF3v4qxJvLKVUu2Bn4BopdQSoOXf3VNr9USEJ799kns+vcfWoTQ75zufh2SMT/I5wMOYfuJEy/kRaCj7c/fTLq8d3YODLY5XFdI9BIC9yS33Ni/WONThEO0uq3v/Ff80o+lMHPL16PUWpLqU8EVfyEhuOWN5/fGnMlRZ5WmuRbCoEUekOZmTwrIvXiLz4O7G28j/s3fe4VFVWx9+90x6r6SRRhJ67x2CCOpVULFjAf0ABRXUC6JYrgV794oIKIrG60UUEUEShCRAQiKdUEJNTyAhjfRkZvb3xyQIXAiTZM7MJOZ9nvMMOXPO2os2s85ea/1WY0hJ9dNPgrMzXV/+FNHE1PuVMCTwmgxUAk8Bm4BTtKpywHb+rpwo0ssC3F8RbmZPLItzlefAF33VJkAp4Kb/ZVBQkJm8Mg95ZXmUW5fzeJ4asW1bo9f2+1n/7XKyoO1OTDtx9gQaRw33n66F++5rlo3Ajnolb492La9G8Q/oCkDumdYjyjt7cwnfroWgEhASgktg2XqYGl+k2Jqp51KZsfdfHPmqeZpZLaVu/S/07LqVxQuHG23XrdGuRiGEGlgnpRwP6IBvjLJqO+2YgORT8QAs+OYkmOf/rEWyLUMfYKiz1WjR6h+ntODg4MDixYvN65yJ2XpiKwB3plZe40oIdfDng02wo5vumte2Vtb+uRaAm1LLYXjzdr2Cwgawfz4sKNYHXp07dzami20Gfx/9A2Hu9U2Q6zAj+/L2ERwewNSUbKamXPZmsHIPbH4u/gDklWYptsZV0Wr57vPHODUU+twyw2hmG93xklJqgUohhKvRVmynHROxZ98GAE4tnElJdYmZvbEcEjITcLB2oI9X/aiPM+Bn5ceyZcuYOlWZlnBL5dd9v2Klgd7nrPQdfI1gHxLBU0ngcNRwQdHWRuzJWIQGBp+qaJp+10VYh4bR5yyE1baLqDbGBfV6jeWIg14NjU7DXWvu4tZ7r/CmgwMo+MDWIDZ7piJfsTWuhkZI3hhnQz/nzvyj22Sj2TUk1VgNpAghvhRCfNJwGM2DdtpRiPdPhbNig5rbzi9j/5m2XRDdFN65/h32z9pPTmYOXbt2BReY/NpkbrjtBnO7ZnLcCtyYtxnUA4dcWb/rYkJDSXeD0vJTpnHODOQX5OObKbDRcs1A9Kr4+PDjQAfS+rSnGhvD28GbYGtvxA7LFwlYdWAVJ4tO8s8EoEMHCArSdwEHB8OyZaDgA5u7nTs2OhV5tcqlM6+ITsd/D/2Xk5VZvHDjm0ap7WrAkMBrA/Ai+uL6PfXHbkOMCyHShRApQoj9Qojd9ec8hBCbhRAn6l/dm+t8O+00htrHj9H+wwDISGsPvBpQq9SoS9WcPXtWv8PlDUuzl3Io/5C5XTM5NUlneTsZbK6//toXh4by+E2QOLIAKaXyzpkBrz1evP+7l34Xo2fP5hlRqVj1VCTRw0X7jlcjqFVq0g+N57HPks3tSqPUaGp4Jf4VBqkCuWVLNnz5JWRkgE4H6emKBl0AQgh8pSN5mLhRY/Zs3l89j54denJr11uNatqQwMtNSvnNxQfQlGApUkrZV0o5sP7nhcAWKWUEsKX+53baMSoHzx7k0S4nYO5cADJO7DKzR5ZBzKkYZm+YzebtmwG45ZZbcKh1AJTV4rFEss9nczAjkX2+HWD8+GvfEBCAo20HSl2gsLBQeQfNQEpKCue7dIGnnmrRDL6OLoEI1/bA65r4++t1vCw4kP9y35dklmby2upziJtugptvNrkPmyd8y4d3f2W6P6f9+2HZMn6tnMzKyStRCUNCJcMxxNqVevGntWDNyfxVpP8NYNxQsp12gK1HN/LFni9wCumCbxlkFrZt0UtDWXt0Ld8d/I59yftwdnamZ8+ehHqEApBRmmFm70zL8qTl7Lu1gPVPP3Z1/a6LUatRD7oOjQMcTzuuvIMm5oP4D8iblEf+pAnw+uststXxxBl0djqyz7aLqDbGYs8j3HVzFVjwNISDZw8y0qMvE3Qh8OGHZvGh88jJeN5+f5OnKDQLKZFznwRPTzq++C4D/Qde+54mctXASwhxrxBiPRAqhPj1oiMOMPRxTwIxQog9QoiZ9ed8pJR5APWvHVrgfzvtXJHkmK8ILFfjF9yD4DIVGRXtT94AsemxjAoexc6EnQwdOhS1Wk2noE6oq9VklPy9Aq/NRzcjCiFycKTB93Tx1Xfo7W+DqetNRzchnGBYx5bLr3Qs1e9M5BX/vXZRm0qug4Y/OmHR6vVLb15KzKOJiEOHwUwdqjtSY3jrq4eVHRsUFQUhIaBWs/7sdiL/z4o8q2pFlmpsxysReB9IrX9tOJ4GDK3CHSGl7A/cCMwRQow21DEhxEwhxG4hxO6CgrbbRdSOMiTXpTOkxgtUKpYcCuazk+0t7XlleRwrPMYw32GkpKQwfPhwAEJDQ5El8m+VapRSklJ8gKlZMGS/4UHUkN93AnAk54hSrpmN/QX76ZQN4++7D86ebZGtjj4RAOiqWmanrRPgHkyxPVRlpV37YhNTXlvOiYJU+PRT7Gt1ptltugpbU37luayV1MZtUWaBqCiYORMyMpBS8tpoyKg+i9e6GEWWu2rgJaXMkFLGAeOB7VLKeCAP6AgY9Dcgpcytf80H1gKDgbNCCD+A+tcr9ohKKZdJKQdKKQd6e3sb/jtq529PwelDpDnVMcRXv0Xc360bnY+dM7NX5icuPQ4A91J3pJSMqE+vhYSEoPtBx2fjPjOjd6bldPFpykUlI7PArl8/g+8bFDiQNf8F29y2peV1rvIcBboChueqkIGB4OPTInsjI66j8G0ITK2mvLzcSF62Pfy76ztH8wZ1NbMn/8unyZ/SbUkP0l56EjZsMKsvfvWaZ2dzFUrxL1oElXotv+hw2B0Az22TWL/wsiLLGVLjtQ2wE0IEoC+Gnw58fa2bhBCOQgjnhl8DE4BDwK/8VTf2ELCu6W63087VyYpbR0gxDBmoLx9M/+hffP7pQ397La8qTRU9vHuQfzAfIQRD6uUCQkNDoQRKz1hunYmxScjSt/APylXB4MEG3+cZ1oMpR0GdagYxRwVJztZ31t2Wp0Y0U7/rYmxDI/CoghDaJSUaw99dLzyaW25Zf0al1aW8m/AON6SrCe01Cu6806z++PmEAZBXoNDOYGYmUb0geB7cOBXUOrDR6M8rgSGBl5BSVgK3A59KKW8Duhtwnw+wQwhxAPgT2CCl3AS8BVwvhDgBXF//czvtGI3+CadJ+8aNkeOmAZCiO8PsLU9x7Nwx8zpmZh7u9zCHZh9iZ8JOevXqhYuLC1RXExIQAN7wZtKbf5vgdJDjIJZ+DZ4uYdfW77qY0FASAiG7rG3Na3Szc8Mp1YoJGXXN1++6mMBAXvmHKyd6t4uoNkaIWwjDCERER5vblUv4MOlDimtKeDVGA59+atY0I4Cfc716vUI1g1FjPJh5C2S6AQK0Kph9s/68EhgUeAkhhgFT0Wt6wTVGDQFIKU9LKfvUHz2klIvrzxdKKa+TUkbUv5pYFa2dNs/DD8PHHyPq2+GDy/T/zP/OkhJanRYpJVqtlqSkJH19l04H7u70ePFF8ISfzv3EyaK2O4fwYo4n/MmMdLAaY3hhPQAhIcy7AZI7ta1uvSARxLgfNDjW0WzF+kuwseH78T4kdm8PvBqjs2dnEv/rxIhoyxmUXVhZyAcJ73H7Ueh/62PQp4+5XbqgXp9XoUzN4KLxUGlz6blKG/15JTAk8JoHPAeslVIeFkJ0AmKVcaeddlqGTurocWAmS7tXEhUVRUhICA+N1OvOxEavNrN35uP7lO8J/DCQLbu2UFZWpq/v2rABqquxjo7GSesE8LfobDxfc573jn7GdG8VHR59tGk3+/pia+VBnkMdOl3bqPPSSR2xe2LZBRx/9lno398odoPcgqAVDsrW6rS8HPsyeWUm8rtBy8tCSMhKoE5qeEWMg9deM7c7APg5+5F//WZmLvxREfuZmivv/1ztfEu5ZuAlpYyXUk6SUr5d//NpKeWTinjTTjst5Fj8zxwpOMLeP/cwc+ZMMjIyyKoBl2pIOpxAVFSUuV00C7HpsVRpqji5T7+jNXzYMHjjDX37dF0doe56La+/Q2djcnYyO+x3kTQgHOsmFNYDIATWwb2pcoGzLez8sxSOFhzloQMPkdcTvJ99FuztjWI3JKMYN5fWt+MVnxHPq9teZUfmDpOsd0v/VOYEXT512nxM6jKJ3Gfy6PmfLeChTKqtqaiECu/h41H17KWI/SDXwKucV2b49zUDLyFErBBi6+WHIt60004LSf7hPQB++2IDlfVdKoVAYCnUOutYtGiRGb0zH7HpsYwJHsPOxJ34+PgQmpkJSUmwYAFYWREWEIaoE38LEdUdmTtABzf7NU8YMdzJH2zhaJrlpIdaQnKOvrD+wQpn3Ov/zxiDwFo7SpwgJ691NSKMCx3HgUcPcEf3O0yyXomd4Ih9hUWo16flHIInnsC9uMrcrvwPn298hX9/dC9UG19ba3Gvp7DWXnrOwdqBxdcpM/zbkFTjP4H59ceLwH4MnNXYTjsmRUqSiw7iorUmL+XSNMF7/4Hnf4ZMhbpULJn0knTSS9KJDIkkMTGR4cOHI3x94ZFHYPhwGDmS66xtoBRyy1rX7kRz2HI4mj75cH9J875chuzTT0FoKyKqSdlJWNeoWJleBrHGqyLp6BGCfR2U5LWeusGiKn1qqbdPb6MORW4Mfztvcl2A4mKTrHc1ss9n0215X97d+2/9DEYLY13KGlYd+QFycoxue6rnWLpVOmIlrBAIgl2DWXbLMqb2UmYOpSGpxj0XHQlSyqcBI7S9tNOOkTl6lGSPKgY7hBMcFHzJW3UlEFgDQUHKbB1bMg36Xb2ce3H69Gl9fVe3brBiBXh5QUICPaRELpd8MuoT8zqrMFqdln3n9jE8C9xvbd60sgkdR5G0HNRZxtsdMic7s3fimyVRSYzT0VjPQ53vpGIxuJxqHRp62eezCf4omC/3fmnSdf37jybHxwHp3pQRyMbnjd+eRafTcmeX2/QPZBaGn7MfeU4ool6v7d2LdC81j/R/BN3LOtLnpSsWdIFhqUaPiw4vIcREwFcxj9ppp5nILVuITIM7+93PwoWXzl6/3Qeuu8GKF157wUzemY/u3t15auhTFKbqJ33dnpsLR+vTZP7+4OBAcG0t1EBGRttONWadzwKNhoFZEDhlSrNsBPYYxJAc0Bxp/fMay2rKOJx/mL5ZkhpHRwhv+bigBtQhnRCAff4VNbItjhe2vkCdto7rOl0HWu21bzASAS4dqairoKy2zGRrXk5acRorjv2HR1KsCVlsmULKvu5BnHECXa7xd7xS0pM5X3OeUUGjjG77ShiSatyDPrW4B9gJPAM8oqRT7bTTHMSOHbx/PISZE5+nrEz/IeZe/xTpGOaKZqiGwRMMF8tsKwwOGMwHEz8gaWcSvaytCfnwQ/2IDNDr84SH41VSAkGwIHEBFbUV5nVYQULcQkj+yJYe2a6oHR2bZUOEhvJdbzhevNfI3pketUrN4wGP8/ARqO7b16h6TXUd/ZnygDP7wyxfvX5f3j5WHVjF3CFzCSmogy5dIDHRJGv3cQzjzrIgqqPNpw7/2vezUOkki4YtAD8/s/nRGH4dOqFRQ1GOkVPX6emkTBkJwKhgCwm8pJShUspO9a8RUsoJQLIJfGunnSZxbtlHaDZHo9Pp+PzzzxkzZgy7dum1u56/4W4AMg+b5sPUUjhXeY49uXvQ6rQkJCTwppsbws4O5s7966LwcJxyc8EVtp3f1qY7G2sLCuheUUVpt57NNxIayqJxsNct3Wh+mQsHawd8TjowqQAcIpuoaXYNrN092Rhex4FAy5aUkFLyTMwzeDp48vyo5zn+2GOUpqURNGIEISEhindCX9/1Jla/n0mHA+aphSuvLWdjxX4ekwPoOO8ls/hgCH6+4dho4Fx+unENx8fzwH5J0S07FOtivBxDdrwAvYqqEGKcEGIF0LbUA9tpEzwW8yS9o28lOjqatLQ0Zs+eTVBQEGq1Gm3meQAyTrX+XYqm8EvqLwxcPpCU3BTyd+/mhsJCmDEDLp5/OmoUql69cJUuAG26s3H8mil4DYCahx669sVXw8MDG+nMCfta4zlmJn4/8TuxGbsZ0akT1k88YXT7Hew6gIVLSpwoOsHO7J38a8y/+O2n3xiYmMgInY4s9Kn3mTNnKht82dqClxdSgRSaITjZOHFi7ilefuEPsLG59g1m4vZuU6i+O4WuC94xruG4OPD0xL3vMOPabQRDaryGCCE+BjLQz1ncDljeRM92/t58+y3Jh6Lp3aEXS5YswdfXl1tvvRVra2uCg4M5WViNrQYyzrWeDitjEJsei6+TLxUZFTxZV6fv1PrnPy+9aN48+Okngt1DgLar5ZVfkc/2/O0U20LvCROab0gIbFwDKbWvQ6PRGM9BEyOl5KFfHuJP6z8J6NcPOnQw+hphBTX0sHAR1c6enTn++HFm2gzl/YULKauq4uKBUJWVlYrK0FTVVeE5o5h3tdsUW+NqFJ06hHbiBJzTcnCzczP5+k1BrVIjevYEIzchnNqzmZsesmLf2QNGtdsYVw28hBCL6+cpvgGkAP2AAinlN1JK8/a9ttPOZeSt/oosVRkRDp3ZsGEDM2bMwKb+6S08PJyDmVkEnRfk/Q3kEhqQUhKbFsvYkLHs3LmTCqD6wQch8MpigRG+EaBru+r1O7N2AnB9kUOLu1s7qT1QuUCOmXYpjEFaSRoFlQWMOFLG/XV1iqwRJFwpsuAdr+zz2UgpCcQF69vu4NPsKydzlJShsbe2p04NuTWFiq1xNWZ+fhMjgv9AWvBOVwNanZbpSybw4/sPG89oRgbxVjn87nIWWytb49m9Bo3teM0EzgKfA99JKQsB8yu8tdPO5dTWkpypr91KS0hDpVIxc+bMC2+HhYVx6vRp9m3rzqpDEeby0uQcLzxOXnkekSGRJCQk8GVYGA5fffW/F5aUQEgIU0vOQxFUaSxPPNEYJJ7cio0G7sG/xRpNAzJL0VlBysmDRvLO9CRlJwGwIBv6linTUdfZrROuNVCUnqaI/ZZQUl1C36V9eX7L8/Dkk5CZyTteXle8VmkZGn/hTI6TaUdQ7d2wgp+cs5joNxLRqZNJ124OapWan87GkbD9e+MZdXRk+x2D8bR1p5tXN+PZvQaNBV6+wGJgEnBSCPEtYC+EuOaA7HbaMSl//kmydy1WqNn01SYmTZpEx44dL7wdHh5OcXExVuHdELZ2ZnTUtDTod431GABxcYy4mjaPqysUFhKu0cC/4Zmez5jOSROy40g0A/JADB3ZYlt3eUaS8z7UnLTMnRxDSMpOwhYbRhWA3ZgxiqzxfMTDHP0MNCdPKWK/Jbyx/Q2Kqoq4K9cNVq1CLlrEySukWx0cHFi8WBkF8wYCwvuTO6CzomtcgkbDS+ufxr1GxVNzfzDdui3EV+VCnnUNVBnp4dDLi+1OhYwKHWMywVxoJPCSUmqllL9LKR8EwoF1QCKQI4QwYsjZTjstZOtWphyF6c53U3i2kNmzZ1/ydlhYGABfPTKOB+6zo1pj/JETlsjU3lPZ/MBmPD77nrUlJdwUGnrlC+slJXzrdz3SLVC12hh0zK3hplTwa6Zw6sUE9RmCfxlUHT5iBM/MQ1J2Ep3OO2GlA++bb1ZmkfqdIvVVUnjmIq04jY+TP+bB8Cn0m/sWDBnCEk9Pjhw5wiOPPEJwcDBCCIKDg1m2bBlTpyonpgng7+xv0qkRO5e9xAa/MuYH3oObh7/J1m0pfraenHECzpwxir28NSs5VXzKZPpdDRjU1SilrJZSrpFSTgEigGhl3WqnnaYxsPcNHFqTRufOnRk3btwl74XXi0IeTD/Idwe/I6u0dc2Oay5ONk6M9xuB4/IVbAK639HI7LmICFwLCqAbzEqYhUbXeovGr8Yna+oYlgADjKDKbd2tM6+NhoNnk4zgmXmIvj+aOTG2VKlUqPv0UWSNbB97+s2yI97ZOF+UxuK5Lc+hFmoWD38RbriBtNdeY/5zz3HjjTeyfPly0tPT0el0pKenKx50Adyo7srdB7Rw6JDiawF86ZuLt8qZJx5eapL1jIWfoy95zoAxagYzMiic8zAjrToxNmRsy+01AYPlJBqQUp6XUn6jhDPttNMc8p6awZJ5t7Bz904ee+wxVKpL/1l3qq9fcDqqL4TO2B9nahdNzqmiU7wc+zK5yz/A/vx5PnFwoHv37le/ISIC6+xsVA5wuOpwm5vZWFV5noqKcva5ueF9sZRGM7EJ68wbo+CQyvJSaIbibu+Ox+lSTvn4gJUyFSSOPoHs96tmt815Rew3h+KqYuIz4vnnsGcICO2N5ttvue+ll7Czs2PFihUmTTk1cJ/fBN5amQVpCtbCRUVBSAioVHzxTCzxHV/AydZZufUUINQrHPs6jDM2KD6envmw/eaf6e/Xv+X2mkCTA6922rEoNBo2nNjAnKQ52Haw5aEr6DPZ29sTEBBAdbZekT0jbZ+pvTQ5m05u4tVtr1K1fAn7HRzQjRyJWq2++g1jxiBmzMBP6FvK21pn4wO/PUz3+6r5c/x4o9gTLi7Y19iyz9F0o2WMybrUdTwf/Tz3VVXy+7x5iq3jZueGNdbobGssRr3e3d6d46NW8+zrcZCVxbvvvktSUhKfffYZ/v5mSrv5+1NlBbU5CnVPRkUR9eF0gm/LQPWSJOzWTPZ+9sJfEyxaCW/esZQDr5+DZo77uoT4eGq83KBXr5bbaiLtgVc7rZsXXyTpw2egCqbeMPXCiKDLCQsL43heOSodZBa0fS2v2PRYAu19CTlby4uVlQwfMaLxGyZMgM8/x9stBGhbIqpSSrZnbKfmTA2DBhtvZJSdlQeFVq1zvFJUShQr968ECb1691ZsHSEEgWWC0Rai5XWy6CR1ZaU4PzQTx2OnOXT6NC+//DJ33nkn99xzj9n8StKk4fACbM1TZrJG1Iq5zJxYR6YbSAEZbjBzYh1RK+Ze+2ZLwtoaPD2NMtqqJGELrrPPs2L/FTq9FcagwEsIMVwIcZ8Q4sGGQ2nH2mnHILZuJcGzGnJgzuw5V70sPDyclLRMOherqC0tMqGDpkcndcSlxxHZeQKxX37Fb8BwQ+qaNBp6eugL8NuSiGpGaQb5lfnckgWDjRh4BeucsLGvo7a2dSnYpxWnsf74evqfcWAb0EthKQE/nRMlFhB41WhqmPDtBO59oz+kplL35ZdMffJJPDw8WLJkiVlSjA34uuq7sHNLlKk/XdS3kMrLpLoqbfTnWxOH8w9z/eud2fP5iy0zlJ1Ngi6DGpWOMPcw4zjXBAxRrv8WeA8YCQyqPwYq7Fc7BhAVFUVISAgqlcokM8UsjtJSyg7s4phrLQEE0L//1fP0YWFh5J05w6HY7rx5pPV08TSHQ/mHKKwqJDJwNNt370alUjFkyJBr3+jvz5xTmZADNirLF1Q0lMSjMQD4ZNHov5Gm0qtIi9YBMjPSjWbTFDwd8zRqoeaxrTpChcA/Qlltu/7WIXQphjNm7pb99M9PSStJY9bq0/DMM/xr+3YOHjzI8uXL8bqKfpep8HPSD6bOcVUm+Mt0bdp5S0Ui+UN7glPb1rXMUEAA29+YhbXKmiEdDfhsNDKG7HgNBEZIKWdLKZ+oP55U2rF2GicqKoqZM2eSkZGBlNI0M8Usjfh49vhJpAruGdl4mqBBUqK4d28IDjaFd2bjVNFJHDUqxv7raxITE+nduzfOzgYU0QYF0bGqCpbDnR3vVN5RE5G4dx2OtVBpF2TYn4OBPGY3gfI34FyKaTrRjMGmk5v4JfUXXhj9Av2P5XHCw0PxnZ43gx8h6meoSE1VdJ3GOFd5jte3vc6N59y53rkPyZMm8dZbbzF9+nRuueUWs/nVgK2VLV4OXuQObqQBpgUEWXs26byl4uvkC8CZqoKWGRKCbaUHGeA/AAdrByN41jQMCbwOoRdTbceCWLRoEZWVlZecU3qmmMWxdSsDc1R4fe/CwnsXNnppg6TE2+P9GTfwMFpd6yyKNoTbclwofkNH0D+mkpSUZFiaESAiAo8ifRo2TcnuKhNzc5oNr2wBh1HGFQn16tUPtYTzB0w3462lBLsGM63vNOaF3ot/TQ1FnZUX7XToplcErz1pvtrKV+Nfpay2jHefiabqhx94cMYMOnbsyEcffWQ2ny7H39mf3HJluokXT/oYK3np172DsGHxpI8VWU8pPOw9sJYq8rQlLbJTNe9xdufsYnTQaCN51jQMCby8gCNCiGghxK8Nh9KOtdM4V5sdpuRMMUvj3IABvKKRPHzro3i5NJ4qaNjxOn3mNLHpsZwptyxdIaPy5ptY+/hxaMAAysvLmxR42efnoxoIDyY+iJRtY0LYuN+P0zcZ+g0dalS7ul5hzLoZ9mRuN6pdJenm3Y2Vk1dSHr0FADFsmOJrJnlU0mGuiu3/c9LvAAAgAElEQVTCPDVeGp2GnUdjmNF7Oj1CBvHskiUcP36cr7/+GhcXF7P4dCUer+vHPSuSQIGawam9pvLC2JfwsPdAIAh2DWbZbV8xtZfyGmXGRCVU+Agn8qyqoaameUays6lb+hlv2N7ElO5G6I5sBoYEXv8CbkU/LPv9i452zMjVZocpPVPMkvj3qVO8d51kwG0Drnmtm5sbnp6euB+p1/L6M0Zp98zCgT++o1/EVvbMvYsdu3YBMOJaHY0NhIcjdDq8rCCrLovCqtZVeHslskoy+XVgAF8JGDRokFFtu3XrwbKBcKLK8rtks89n89AvD13QZzuVn896wOfGGxVf294ngAJ3HftlseJrXQmr1OMkvZDO+zGCrVu38umnn/Lkk08SGRlpFn+uxgy7Edy7Jd9oquyXkJbGy15TKJx/Dt3LOtLnpbe6oKuBYfad8a5RQ0Ez043x8bjUwD8n/IvBAcZrtmkK1wy8pJTxVzpM4Vw7V2fx4sVYW1tfcs4UM8UshbrDh4n++hMYCWeEYR9UYWFhnM/Tp2czMlpPeqgpbI1eyn4/8HngURITE/Hz8yPY0Jq2YcNg8WKcVXpJjrbQ2fjNwVXc2WkzPzpZ09vIsgmubr5Y1anY5m75qjzzN89n9eHV1GhqiIqK4oa332YScM/06YrXhXZ00Xfs1VSYfpf5WG4KxdPuRu3ojHbefKZPn07nzp158803Te7Ltajy9eS4J2hzjN/ZeGzJq8Te3p+6SsvQUmsJq59J4t0NdXDRPN4mERfHju5OFIT5GdexJnDVTwwhxI761zIhxPmLjjIhhOXIEP9NmTp1Kj179rzws5+fn0lmilkKWfPm8ZiD/gl6SIBhXSnh4eEcPq2vYco4e1wx38xJbD93wp2C6OjflcTERIYPH2548XREBDz/PM5u+kCtLYioJqZuxqncgb5d+2Jra2t0+3Z1DpzTtazeRGni0uP44dAPLByxkMQNCRyfPh2nEr3P2dnZijfleNp7YqOBgRrTyrjopI77ll7Pdf0PIb/8knlvvUV2djarVq3CwcH0BdXX4hvNHro8AWczjxrd9pd5G7nhXg0aG2UmFJgUtbpFOl6abXHcMKWKf21/zYhONY3GhmSPrH91llK6XHQ4SyktJzH+N6W2tpYTJ04wcKBe2ePzzz//2wRdADYJCfwWYoWN2oa+vn0NuicsLIzUjDyG5qlxLGr9T36Xo62pZlvmdiI7TyQvL4+0tDTD67sayMtjuL3+SbC1i6jqpI6dGQmMOV5l9DRjAx3r7HGy4OfQOm0dT/z+BCFuISwYsYDsJ57glbo6HrjoGqWbcoQQ+FTbUO4sqagwneBs1A+L2Ks+yzP24/hNCFauXMnChQsNk1YxA/7+XQDIzTPyQ2FhIbEO+QxVBWFvbW9c22bgmz+X0X2RG3Xrfm76zRUV7Ougo0KtZVSwaQdjX4zl75G3c0USExMpLy9nzhy9aOiJEyfM7JHpOLFlCx2rqkjt7kJf377YWhm2kxEeHo5OpyN2W2eeSG1jzw5paewb4E9pTSmRIZEkJuoVsA2u72pg8mSe2nsUToKnbetqNb+c1FNJlNhoUWVKxQKvruXW+OkklectM/haunsph/IP8eHED7H/cS3PlpQQBbx12XVKN+VElgcw5Czk5eQouk4DlXWVPJe1koHVHlw/70tmzJhBnz59ePnll02yfnPwD+gKQK6rcb+WS7duZK8fjA0dZ1S75qJaaDlqU0p+cmzTb3Z0ZPs7+u/MUUFtOPASQqiFEPuEEL/V//wvIUSOEGJ//XGT0j60RaKjo7GysuL222/Hy8vrbxV4Jb35JhKo7OBocJoR/upszBwwQF/P1JZ47z2sSsu4I/QfjA0ZS2JiIra2tvTr169pdiIi8D1fBt/BcJcm7pZZGInx+vRZrpEV6y9mvmYiu5bDmd27FbHfUu7ueTcfTPiAybkuMG0aCdbWPAxc3q+qdFPOQptbeGEHnEtJUXQdAKTkg8T3yak6y/uz1jLnn/MpKipi1apV2NhYrjCwf716fU5P4+oMbt/5X3QqiBx2r1HtmgtfZ70Adl5hetNvlpLtmdvp5N6JAJcA4zrWBEyx4zUXuDxp/aGUsm/9sdEEPrQ5YmJiGDZsGC4uLkRERHD8eNusWbqc8vJy1PHxlNnacvKf6bw34T2D723Q8lrUu5peHj+0GbkEzpyBL7+k7w3T+PHB3/Bz9iMxMZFBgwY1/YsmIgLHoiJsgdOnTyvirqm4K0XHhu9UnK52oEuXLoqs4dCjBwDF+yxv8LqUkg6OHXhq6DzEq6+iCQ3lXltb6i6rjzFFU45D165I4PwhE4jNrlrF0bXLuS38FnJ25rBmzRpeffVVozdXGBsfRx9UQnWh89RYbBvXCVuVDUNDzbfDY0z8nPWlEHnnm757KocMZkdqjFl3u8CwkUFvG3LuKvd2BP4BrGi6a+1cjfz8fPbu3cvEiRMBiIiI+NvseEVFRTFboyH9s89ApcJGbXhg0aFDBxwdHTl77iyH8g9RXHFOQU9NyEcfodHUkjVHX7lTXV3Nnj17ml7fBRARgZASp0i4N7l1PyG7xO3EO9+J3gMHoVarFVmjsIsXN02F/Se3KWK/uezM2snwr4aTXpIOQiDXreOx0FDO1tby5ptvEhwcjBCC4OBgkzTl/B5SivUiOIjCtZWnTsHjjxO1vxPvj/iAOXPmMGzYMObPn6/sukZArVLzefEIJr2+2qh2F9/4Pntm7cXOys6ods1Fw3ilvMr8pt2Ymwu7drPD4XGeG/mcAp4ZjiE7Xtdf4Zyh4i8fAQsA3WXnHxdCHBRCfCWEcL/SjUKImUKI3UKI3QXN1etoo2zevBmAm/v25cWFgynskEJOTs7/KNm3NaSULFmyhNC+ffkh5BSzN8xu0v1CCMLCwvBJ1be1ZyRFK+GmaSkvhyVL2HP/dQStG8Ovx35l9+7d1NXVNb2+C/SdjUAHraBQW0hlXev8N1VUVcTL/xzEbJsKxdKMAB169+L3CDhVajlaXlqdlsd/f5yskky83voEKiv5dt06VkRHs3jxYp599lnS09PR6XSkp6ebpCnHN7QrWms4UKmspMTJZ6Zx0gPkN98w+7EnqK6u5ptvvlEs8DY2MzV9GLSviQFFY8TFYf32u/RwDDGeTTPj4+TDOE0gXjSxMzU+HgF0GXcXXbyU2QE3lMbkJB4TQqQAXeqDpIYjDTh4LcNCiJuBfCnlnsve+hwIA/oCeVxFjFVKuUxKOVBKOdDb29vQ38/fgujoaDw9PemVlcWe7F1kVuxDACfNOJLDFCQmJtLx4EG+CA1lXeovzeq6Cw8PJz9H/9TdJrS8nJxg0yZiJ+vTKEM7Dr1QWD+sOXVs3bvDqlXUqvXPQ1mlxtcUMgWJWYm8emoFux21ihXWA4T56Qui//BzVGyNprJi7wr25u3lvf0dcHr3Y87+9htPPPEEo0aN4qmnnjKLT4EugQBUZRtfKuEChYX8034HI6ZLPo/ewKZNm3jnnXeIUHgIuDHJ8nMg2bEEjPQQHffT+8xLfoUinem6SZXGRm3DltcyuX1dE8tr4uJYPsKO1Tbmzw41tuP1PXAL8Gv9a8MxQEp5vwG2RwCThBDpwA/AOCHEd1LKs1JKrZRSBywHzCMd20qRUhITE8P111+PatMmIgrhtDv4Q5uv81qyZAkzrKzovC+Jo+dSm1RY30BYWBiHTuh3UNuMltfw4cRWHKKHdw86OHYgMTGRiIgImvXA4uQEDzyAi2u9llcrlZRI3PwVaqmCXOMr1l+Mg7UD6ho1Z6osYwRVYWUhz299njE1ftz93X50n33GvUuXotPp+Prrr82289MgohqSq1zgtfWFhWwKB5FUweOPPk737t2ZPbtpu+Lm5g27Xdx8H5BnnPFKv5zbwRd9NTjauxrFXqsmPp7FowU/pv5kbk8a1fEqlVKmSynvBbKBOvTNME5CiGu2wEgpn5NSdpRShgD3AFullPcLIS6Wi70N/RDudgzk4MGDnD17lhvHjWNx+UY+GQoVNhDo3LYlJfLz81mzejXjrazYM7EXEtmswCs8PJyi8xpuOm2F77kqBTw1IUuXwqxZ1FaWsSNzB5EhkUgpLwinNpsjR7hR6wy0TvV6qdWyJXUj3QrUeLt5G67c30w6VNvirXAKzVA+2PkBpVUlfPplHuK55/i0pobY2Fg+/PBDOnXqZDa/vB29sdLCeZtqRexHRUUxNX4VNVZw9pT+ATUtLY3//Oc/iqynFP5ugZxzhJrs9JYby84m1q2EEdZhBkvutBamr5zM+HkeYOiAeq2WzCnjybCtMnthPRhWXP84cBbYDGyoP35rwZrvCCFShBAHgUjAPHvfrZToaH1d0k1OTvweXHfhfGCgY5sOvL788ku6ajQ4VVeT3F2vwdWcOVsNkhI/JIZwd2orVnGurYU33oCjR9l17iCVdZVEhkZy8uRJCgoKmlff1cBbb/H0tn2wH/wd/I3ns4mIjnqFP71q8D7lyKBBgwxX7m8mvUsd6VVS1/yhvUbkxd6Ps/FXZ3qNv4+jU6eycOFC/vGPf/DII4+Y1S+VUHH7aW9GZetAgW7iRYsWcaZjLWiA+k3aqqoqRYVhlSAgUN8lm2enabGtwj9+5aAvjI24Upl260ar03JCFIOhnddqNdvv1pdetIrAC5gHdJFS9pBS9qo/mtSXK6WMk1LeXP/rBxpsSCknSSnNM7K+lRITE0PPnj2xr6vgzwC4I2IyAC5+Nm028NJqtSxdupRH62s1PLr159aut+Juf8W+jEZpkJQ4MGQI8rbbjOqnSfn+e8jKgueeo5t3N7697dtLhFNbtOMVEYFnaRn2v0CYCDOSw6bj1Ibv6FFszfY/ShRNMzbwRHkkX6+D8iNHFF/rauikjsq6Suy8/ZiwZh91X3zBg9Om4ejoyIoVKxQPPg1hVvEgHjgCFQqIqLpnZODZCVRZ6HMz9SgtDGts/EP1X625/s4ttrUtdycAkUPvabEtS8PPM4QzTiBzDZTeOH6c7adjcbF1obeP+WVFDAm8soBSpR1p59pUVFSwfft2Jk6cSOKIYOrU8NDA/yPZYS7B9oPabI3Xxo0byczMJLJXL+jdm0evf461d69tlq2OHTtibW3NgpDTBJebb1ZXi9Dp4O23oW9fuOEGPOw9uL/3/bjbu5OYmIirqyvdunVrvv36ALcTcPjkYeP4bCoSEpizOo2bV9qi0errApUeAm3bVV9gX2hGEdVvN75FtzcCyChOh9BQ3nj/fXbv3s0XX3yBr6+v2fy6GNEplBI7KNy71+i2n3B25uAqsLksF6O0MKyx8a8XB809l9ZiWyU3jiPULZRBHS1zRFJL8OvQiVorKM4zcMdr0iRy4n9jROAI1Crzd7g21tX4tBDiaeA0ECeEeK7hXP35dkxMfHw8tbW13DB+PHHpsaiFmjHBYxg8/yNsRo4jPz+f8xY6uqQlLFmyBH9/f8L/+1/qdv+JVqdtti21Wk2nTp04X1hK1vksKsuLjeipidi4EVJTYcECarS1LNm1hJx6McHExESGDRuGStUCbeT6wKtsMszcO9MYHpuEyrpK3lv3AQcEfHpe37laUFCg+BDo451U9HoMDh/ertgajVGacYwF21/E/0wFgbV27Nq1i9dee43777+fKVOmmMWnK7GsSxae/4RMKyOn+KXkTnt79lcLqgv/Om0KYVhjE+Yexprt/gz/cE2LbU3vN51TT55qktZha8HXpV69vsCAwCsvD44dY73/M/xyzy8Ke2YYjX06O9cfmejru2wuOtfyfdB2mkx0dDR2dnaMPnyY7m+uYE6f/8PZ1pnYw7+RrdVvK7e1dOOpU6fYtGkTs2bNwsrKirXH1+H2thvHC5u/uxcWFkZAfWdjZnKMsVw1Hd27w4IFcMcdJOckM2fjHHbn7qakpITDhw+3rL4LLgReARWCYm1xiwJdU/JR0kfMd/yZvh3g4mZ8pYdAe3XuwiEfOFFmhrRWeTn/enE0BXY6/n3nSmpcXHnggQfw9fXl008/Nb0/jRDcsRs6KzhabORU49GjrOiUz9LxrlhZWZlUGNbYONo4MqWmE/5ZJS2yI7/+GoYORRQVGccxC6O7d3ceLA7G1t2Azu1t9eLGY8daTBDaWFfjK40dpnSyHT0xMTGMGTMGm82bmZrtwceTlwKwft27fFm5DjfR9gKvpUuXYmVlxbyaGhg+nOTMRDQ6DaFuoc22GR4eTmamPnue2Rq1vDp10qcara2JTYtFIBgdPJqkpCSklC2r7wJwcYH4ePLUnuiEjrxyyy/DLKgo4K34xYhU9K1Al6FkrU/f8P4AbOlo4sHrGg2Hpt3Ep6H5zOxwIwPGTeW5557j2LFjrFy5Ejc3N9P6cw26BejT30W7thjVrvz1Vz4YBrGe55k5c6ZJhWGVICHMhh11p1pkY03Sl3QasZs00TarhHr79Oabj9IJf2vZtS+Oi+P18Tbck/6exYyJM6Srcb0Q4tfLjm+FEHOFEG1jBkErIDMzk9TUVP4xdiwFybEU3/TXpPkIn25UWUOQc9vS8qqqquKrr77itttuwyUpCSorScrbRX+//lirrZttNywsjMz8WgAy8o4Zy13T8OGHsHPnhR9j02Pp59fvQn2XSqUyjlL76NG4u+pFLzNKLF/L67XfF1JZV8kLCfZXfF/JWp8QjxCQkHXexGKzycmsrNiBq9qRxdO+ZevWrXz88cc8/vjjXH+95XWydfHVq4U7HDBuSvbY6T/JdoXyEzrGjx9vVNvmYH7gUV7u3IJ5jVISV7SXAkdBx/r/w20RKSV12rprXxgXx/q+9uSW51lEkwkYVlx/GihHL3a6HDiP/pmyc/3P7ZiABhmJyc7OfDCgFj+3FVRr9Jo4ESEDAAgNcWlTO16rV6+mqKiIx//v/yAhgbpxY9ibt7dZ+l0XExYWRmUZTDtkTXi+Af9xLYX0dJg/H9bqGwuq6qrYmb2TyJBIQF/f1adPH5ycnFq+1u7dTC3ST/qydC2vk0Un+fzQ1zyyF9YXq//nw1XpWh8btQ1OVWoCcxRUZb8SI0bw3qfHSX58P1Z1VkybNo3OnTvz9tsGjdI1OUFu+uC3RBp3F+aP/9M/hIo0QWRkpFFtm4MAWy9yHbRQVtY8A8ePE9uhkpEOXVr0gGrp+LzuysL7faCu8c/wihWfs9e53CJkJBowJPDqJ6W8T0q5vv64HxgspZwD9FfYv3bqiYmJISAggMCUFOLCVAzwH3Bh6GlEd/0/KNc2IikRFRVFSEgI06ZNw8rKitr4eKip4eCQUKo11S0OvMLDw0EH7+0OIPJ4Kwq8Pv4YhIAnnwTg4NmD1GnriAyJRKPRkJSU1PL6rgZiYngs/gDW2yDYUVkB0paSlnuY4FLJ2N1OpKnVZhkCPeiMC8PyaqDCBKNZ/vMfyld/R25ZLiI8nHCPcJ588klyc3P59ttvcXBo4gw7E+Hj6MNduxwYlmZcEdXNpzdjW2nLkM5DLC692hz8O3Yj19tW373cDM5sXstRb4jsdpORPbMsXIQdeXXFcPYKtQUXkeSnRSO1jApuXYGX98VK9fW/9qr/sVYRr9q5BI1Gwx9//MHEiRMpv/l6dvlDZKfrLrwf6NsZWw3oXHWtPvCKiopi5syZZGTo01sajYY977yDTqXCc/h1vDj6RUYGjWzRGiEhIQgh+GPgAIpnPmgMt5WnuBiWL4d774WO+vErQzoOoXBBIdd1uo6UlBQqKipaXt/VQEQEDnXQbSu4Vln2uJHIjcc4/rHkk4Iq1q5da5Yh0NMKhvLcDpBpLZcBaJT4eJg2jcXRi+j2WTfyK/L5+eefWbVqFc8//7yiA8Fbilql5tb0UMZnaqHKSFMjHn4Y7d691Byqscj0anPwD+/PeWoot2+e7EG8q74wf+wAy+loVQI/e2/ynIDGtLzWrGHb1q9QCRXDA4302WgEDAm8ngF2CCFihRBxwHZgvhDCEfhGSefa0bNr1y5KSkqYOHEiCV0d0aJjbMjYC++rhIqsvquYEPAgRUVFFBYWXt2YhbNo0SIqLxsQu1ujYYWTEyGBvXg18lUCXAJatIatrS1BQUE8H7SPvhkLW2TLZCxbpt9NeeaZS06727tjZ2VnHOHUi6kXmg22g52pO69xsXmQUvLj4R/Z98lHbJPw+DffmC3VZF3fCVqekqLcIlLCzJkc7+XP+yF53Nr1VmS5ZNasWfTv358XXnhBubWNRGmgN6fc0Yv/tpTaWvjpJ/69rytspM0EXgENWl7NHCgeEnkbjw54lP7+A4zplsXh6+zHGScan2v58st03H6QB3o/gIutiZtfGuGagZeUciMQgV7BvkHFfoOUskJK+ZHSDrajr+8SQjDR3Z3YXT9irbL+n+jde8oDuEXqax1a867XlbrP1gCPlpWxM2snZTXNrHu4jLCwMHRnq8g5n4OmrBV0/tjbwz33QJ8+gF6z6qaom4hLjwP09V3+/v7GKyKvD7xSJ8NLR18yjk0j8+uxX7lrzV0M9spj/wsvmLWLLblTGW4LIfNAsnKLHD2KPH6cuVMcsLOy463r3mLGjBmUlZWxatUqbGwso1W+MZYOPkv3qVDRnAHul7N9O7qy8/xuZYWjoyNDhrQNodCJviNJXg5BazY3/ebiYoZYBfP5zZ9jpWrFI9EMwM8jmDxnrr7jlZ8PR44wo/v9fH3r16Z07Zo0JqA6rv71duAfQBh6Meub6s+1YyJiYmIYNGgQrosX83//TiTq9igcrC+t49iyezVRhxZj08olJS4PHPyADkBAeADDvxrOJ8mfGGWd8PBwOqQVo5VacnZvNYpNRXnySbho4G9CZgK/n/z9QoNFQkICI0aMMF7XjrMz0teXkPOCc5pzFtOG3YBGp2HWmlmozsGMoTOY++qrZvWnQ1AYpXZwtCZfuUV++YX1XWBT7RFeGfsKm9ZsYv369bzxxhv06NFDuXWNiK9bELUukHvuXMuNrV/PuOmCRR4JjB07tlUEnobg7RPK4FIn7PIKmnxv6aplHOrjh8zOVsAzy2Jiz8nMKQhB5+115Qu2baPcBmpGW06KsYHGdrzG1L/ecoXjZoX9aqee4uJikpOTmTRmDOzYQcSY27izx53/c92pXTH8tzaZENfWHXgtXrz4EtX1Z4B04P6n7gZgaMehRlknLCyMM2f1QUtG2n6j2FQEKWHTJtBeKmIamx6LlcqKkUEjycnJISMjw3hpxnrE7t2k2HhTJ+ooqW6ZoKOxmfvNXM5qz/L9VhVLpj9i9jbxXiH6+W+xIU2fH2owAwcSc2d/+vn242afm5k7dy5jxoxh3rx5yq1pZII9gsEG8tf90DJDUnJ+0zp2BELxmbI2k2YE/dzNr0c4klTc9LT1xv0/0ms27FMr+ABgIfyj6yQWr0hDdcf/fh8CEBfH5yNscNs6weI+vxoTUH25/nX6FY6HTefi35stW7ag0+mY4uzMAS8t3/VTU1X3v4WpEcH6BtPwTm6tWstr8ODB6HQ63NzcEEJwg7U1pd2749DdFYFgUIBxhh6Hh4dTUP9/MSPPxDIATWHzZrjxRvjxxwunarW1rE1dyyD/QTjZOLGzXtfL2IEXAQH4Oenr6TJKLUfLK25nHEuOLqFvtpo7Snyw6tfP3C7RN7QvAKfOtUz4slEmTODfr+1h1//tYsbDMwD4+uuvWzYeysR09ukMQNmWFo5uqasj7q7BaIWE022nvgv0NbtPDDrHf1VNHLqu1RJbloKrzoY+Pn2Ucc6CkFJSVFV0xe9DAFJS2NbLlSDXINzsLKvb1RABVVshxH1CiOeFEC81HKZwrh19mtHFxYXOJ0/y3WBbHjn2zhWvi+iu7/Rr7ZISDV8khw8fRldQQI+6OnzvvZfknGS6eXczWoFkWFgYVaXw/E4beuVa8Eic994Df3+4/a/s/otbXyT1XCoLR+obAxITE7Gzs6Nv377GXXv3bmY1KPxbiJbX6dOnmTJtCi7VViz9XYv66WfAAlJM/i7+qLQQvjdOmQUOHmTt++8REhKClZUV8fHx3HPPPYSEhCiznkL0CNSnRAsqWiAQCmBjwx/DfFDr1Php/Fo2FN4C8dc5kKtr4tzd/fuJ9a9ltHNPixgErTQHzx7E8x1PNt595QcvXexWEvzqGB002sSeXRtDHpXWAZMBDVBx0dGOwkgpiY6O5rpx41Bt3Upcd0eGdhyKvfX/qnP7B/XAvg40blpOnDhhcTU5hqDValm1ahUTJ07E398f4uIAkJGRJOckt1i/62LCwsJAA3MOd6DvyXKj2TUqBw7od7yefPKS4OKG8Bt4cfSLTOoyCdDXdw0ePNj4NS4ZGdz752kC10OIfYhxbTeDwsJCbrzxRmSBJPPEdQwpc4EZM8ztFqCXShh53JmRmTVQYvy0Ru4DD/B14nwyhv218xgVFaXo8G8lGBw6mP9bL+iT1sKvkMRENp+MQZWlYsJ1E8yeajY2/l6dyO3WtO7t7C1rOekJkb0mKeSVZeHr5AtA3vkrB/GHC45QXFNiUfpdDRgSeHWUUt4tpXxHSvl+w6G4ZxexZ88eQkJCWt2HTEs5duwYmZmZTLzhBkr3JrLXoeSCSvnlqFRqepQ7YCO0lJWVkZ/f+nL8W7ZsITs7m+nTpzecACcnGDSIDfdt4OlhTxttLScnJ3x8fFjetwsnFlrGl/f/8P77+t//rFkAF4LpyNBIXo3UF5NXVVWxd+9e46cZASIicKmBYXtAV9Q8MUdjUVVVxeTJkzlte5ofl3+Ka8xmeOwx/VxJC+HW7N7ccwgwtpbX+fO4pxzkj3Cg5q/TSg//VgIPBw/6nnShe075/9QtGsy5c+hGjeSuNDfqdta1iTFBl+Mf3INce02T7okb3AGAyD6TlXDJ4vB29EYtBWdkGWgu+7NavJjt7z0BYFGK9Q0YEnglCiF6Ke7JNcjIyGDmzJl/q+CrYUzQhAkT2KwmhiYAACAASURBVF58AJ28VL/rcv58aAczrvsQaJ0zG1euXImHhweTJtU/sS1YAKtXI2xsGBwwmJ4dehp1vbCwMP4ddIBbDlug/lFtLezaBY88Am5uSCm5f+39vBR7aZZ/9+7daDQaZQKvekkJdy/YcsS4g42bgk6n48EHHyTheAK6KTo2Oe/X/9k89ZTZfLoSqrAwKq1Bnj5tXMObNnHYDyodgMtKyJQc/q0Upzo5c7iDbFx/qTE2bkSlk4TWDoRU2mbgZetNbmkOsgm7p7cMfYhf7/mV3j69FfTMclAJFT5qF72I6uXq9T/8wNgTdXww4QNC3ELM4V6jGBJ4jQT2CCGOCSEOCiFShBAHlXbsEuofalvjE15LiImJISIigtB33mF/9NfYqm0b7eoT/frRcZQ+um9tdV4lJSWsXbuW++67D1tbW/3JkBC48UbWpa5jXeo6o68ZHh6OyKsisyitSR9wJsHGBg4dgtdfByAqJYrvU77HVm17yWUNwqnDhg0zvg8ODmj9/NhxI3xyyjgyHs1h/vz5rFmzhh5ze+Bk68SCEQugf3/w8TGbT1dic0Q2bgvh/CEjfzyuW8fa8PpU2mWBl5LDv5Vi1fhyRk92uDCBocmsX09SH09WnjhAr1698PX1Na6DFsB8++s49W4NJBuoC5eaiuu3q7nFbwwq0XqaLVqKn62XXsvr4iC+oAAOHaL74H/w1LCnLDINbcjf0I3oBVQn8JeUxC1KOnU5qotKmlrjE15zqKmpIS4ujimjR8MXX/BCcW+ynsq6MJ/xSiTs+okZ/7kBb091qwu8fvjhB2pqapg2bZr+xPbtsGIF1NbyVsJbvL/T+NntsLAwPHMrqJK1FOxPMLr9ZlNVpT/UanByIr0knTkb5zAicMSFgvoGEhIS6NKlC15eV9GyaSGqbt0IqNfyMgeffPIJH3zwAbc/dTuHNYdZWDcU78cXND9NpSD+PmHUqSHV2ojzP7VaiI5mcz8XyOOS6lqlh38rhZuVJ+W2zZzXWFuLLnoTkyZVsMMlsU11M15Mh5Ae+JeBMHBXMGfNSt74diY5RZbTfWwK5vWZxcOuY8HR8a+T27aR7wi/9bCmotYyy9ENUa7PuNJhCuca0KmA+rrh1viE1xx27NhBZWUld7m66rWcbroJb8fG1Z612VnEak/SN9y91QVeK1eupFevXvTvXz93/auv4NlnqRU69uXtM2phfQPh4eGUNUhKnN5rdPvNZulSCA6GggK0Oi0PrH0AKSXf3vbtJd1KUkoSExOVSTPWI2Ji2G/jTaWq8oJYq6n4+eefmTdvHrfeditZ3bLo6BzAvH/vhsJCfVBqYXT17wrANmNqeanVcOwYD0x8GqvdVjg5OZl0+LcS+Nh3wNpJR83q1U2/eft2UhzKKVBXozuha7OBV76LmtdHw5EcwzQG/zjyG4uug0L71tdU1RLunzifOz6LhYu7WuPj+b27DbfsX0BaicKzU5tJq9mTtPJsvU94zSEmJgZra2t6ZmWxeYAbd51+mzPlZxq9J6Lb/7N33vFRVen/f5+ZTHrvjbRJCAKhN+lFijSxLUhZBRXruvoVXRX3Z0Fcu7i2FVRQiYKCSpcEDIh0RGqkhTRCSCM9mbQ5vz8mgQAJmSTTEub9et3XJHfuPefjSJLnnvM8n2cQAO4BqjaV45WYmMi+ffuYPXu2blm4sBB+/hnGjOFw9lEqairoH2z4wEutVpNb2y0o9byFeHlVVcGiRdC5M/j4cOD8AfZl7OPj8R8T7hF+xaWnT58mLy/PqIEXSiVBTrrqqvRCA/TX05Ndu3YxY8YM+vfvz6dffoqfsx8LGIFD9kV45hmT6WgO3WpNVE9mGPjfkpcXN6kGUv1HNbGxsSZt/m0Mgt06UGEH2Wt/aPriqxkxgvhFuqRpVbqKIUMsL3HaEJQoa/j3SNh7UQ8T1YoKtlWcxEtrb/A8WEunuKKYw5mHqNHU8/Ly9WXHsDA87D3o7NPZfOKuQ5sJvNQRrm32Ca8lbN68mSEDB6LasoWNQwNZd3o9HvbXf5L2j+yJcwVUu9Zw5swZtFrzVqLpy7Jly7Cxsbn8//a//9WV5D/zDHvO7QEw2opXxUX4+Bc7+mRYyJPiqlWQlgbz5gHQP7g/Jx47wcxuM6+5tC6/a9CgQcbTc/w4/zih2+5IKUgx3jzo7BHCwsJQKBQMGTIEV1dX1q5di7+7P+vu/ol7P94JAwbA4MFG1dFSuoXqAq9Oa77WrVK3Filh6lT2r3yPletXYm9v3y4SydXeagDSL5xs/s0KBVuqT2FXZMegboNwqr/F1I4IrGuUXXr9h20A9u4lIaSGYR49b6j8LoDlR5bTY3FPsp+sV5n+4ovsCIXBIYMt9vO4riohhFIIscVUYhrDoRpm3TL6hgm6Lly4wOHDh7lt0CDo04cEvzIGdhiInY3dde8TNjZEltlx0bGc8vJyzjfWPNSCqK6u5ptvvmHChAn4+vrqVrveew8mT4ZevTiWfYwA5wCCXVuYiHsdPD09cXNwY/xZN8KS8gw+frORUmeY2qkTpbcMY/2p9QCEe4Q3mCC6c+dOPDw8iI6ONqqs2w9dYGgshNuHN31xC4mNjWXu3LmkpqYipUSr1VJUVMTbP71N0sUk+PFHxNlkXaWrBSbLgq68ffABewak1+gSfFvLn3/C998z7cwbxJbEMnLkSBwdHZu+z8IZHTWaF5dDyNlm/sydPEnFow/xW/I2KhIr2u02I4C9jT2eNi6c79+0MWzKwV9JdYcRPaeYQJllUefldaEut620lKyiTE7lnbJIG4k6rht4SSlrgDIhhJuJ9DRIRA7EZBixB5qFERcXB8CQu+7i4poVHNGkMjx0uF73Dqnwp0OtH2hbyPP65ZdfuHDhwmXvrsxMnY3BSy8B8L+J/+Pww4eNUpkihCAyMpJnuwey5/VHDT5+s9m7Fw4ehKef5uktzzD5u8n8ldP4ttWuXbu4+eabjdsyRq3GrUIw7DQUZBqv8nP+/PmUlZVdcU4jNbyb/C6Pb3pct9L18su6gNxCEUIwOFnN4DQM4+X188+c8RKcrc6h/Gg5kyaZtKbJaHRXd8frDPhm5DZvZfCnn7D9dDHvuj0He9pXm6CGCPQM5bxj00UkiRP6Yae0Y8RNE0ygyrIIcAkAILO4tgjhhRfYOUnXLskSjVPr0Oc3tgY4KoT4Qgjx37rD2MLq85dCwRaHa93a2ytxcXH4+PjQPSyM7SnbkUhGhDdsnHo1/315L6+/uB9oG15eS5cuxcfHh/Hjx+tOdOoE+/bp7ALQ/TFrqqigNajVajaEneKRP14x2hx6078/bN/OugEefPbHZzx989Pc5NPwE29+fj6JiYnGze8CsLenyt+fqnBYd2yd0aZpsFp5MGjttbw+8nUICdEF4xaYVF+fSnUHUtyBlJTWD7ZmDZvHROi+PgMTJrSPP6weHh781knBPn8tFDWjLc66dYhevdh/KA0P4XG5EKedEmjjSWZaIjSRMjI+ajwFzxVYbD6TMbnkXq+prbreto0ptt048vARegf0NqOy66NP4LUB+DfwG/BHvcNkKF2VfO70OVrZNnKWWoNWqyUuLo6pgwej8PGBbQn0D+pP30A9m0P7+REUFYW9vb3Fr3jl5uaybt06Zs6ciUqlgl9/1VWs1a5u7UjdwayfZnG+2HhbppGRkagyy0m9cFI3tzkRgqxe0dy/6RF6+PfgtZGvNXhZbGwsnTrpKug+/PBDo5sKK6Ki2DACYtONN8811cquwABwOuNEz//9DL//brS5DcnWmHQGzwFtUiubZScnw5EjxHWxx77cnm4dutGhQwfDiDQzQgjWTobZd4aBm56bKTk5sHs3L0xyZN1f6xg1ahRKCw/CW8sqzWR2/uvU9betf/sNJk3CPiPLIv2qjM2lrUZtke5zOnoUxfARxPjFoFKqzCvuOuhjJ/EV8B2XA65va8+ZDDcJ5fblnCs6Z8ppzcKhQ4fIyclhuocH1NRw+5C57HlgT5P5XXX8dWQrN73iTfe+nhYfeH377bdUVVXpthkLCuDOO+HRy1t+W85u4duj3xqsMXZDqNVqfPMl+ZRTfMyMlhL/+Afy2WeYs3YOxZXFxN4R2+D/87pcqLqWUFlZWUbv6GBz8814FQlyqgyQt9QICxcuxMbG5vKJEYCADzs/Bq++Ctu3G21uQxLoFsJ5Z8gODmzdQPn5VA0dxK8yGc1xDZMnWe4Wa0uwr3IgvyZf/xs2biTPXvKG2EmuXW67KDJoCpfgCJQSuE6ubtIv3zHAfz17KloZ6LdR7G3s+TL6WSYPfRC2bKHIVjLXdy+HLuhnw2Eumgy8hBDDgdPAx8AnwCkhhN7tvmsT9P8UQqyv/d5TCBEvhDhd+9pk8pa91D3ZJGbqUVrbxqnL7+qZmUllaDBVnTo2634vrT2nFPkE+CksPvBaunQpvXv3JiYm5nIl43OXDUL3Zuyli08XnG2djaZBrVZTUmspkZZkpsArMxMWL0aUljEjZgYf3vpho9sGDeVCGb2jwxtv8JedL8Wi2GirzjNmzMDHxwd7e3sQ4GLnwmSfycw+cUFnjvjII0aZ19CovdVIBewNaWVOaq9eqLb/zqvBr8HvMHHiRMMItBDcpSsuNfnwg56WEuXl/DoyHImEpPaf3wWw36mAhydCXtqJRq9JOLWZvcHg7tnKQL8NM3vam8Qs+Az27mWX2pYl59eRW2Yew2d90Wer8V1gjJRymJRyKDAWeL8Zc/wTqJ8h/BywVUoZBWyt/f662Kl0+V37D8Y1Y9q2yebNm+kdE4P9jh2sm3ITHm95cjz7uN73+3TqjasGtK7VJCUlUWOBDt+gW9k7dOjQ5dWu99+H226Dnj0BnTnovox9RrGRqE9kZCR5dSaqGfp/zgblo4/QVlXCU08xPWY6D/R6oNFLG+vcYOyODgEOAUiFbNJLrqWcO3eOzMxMXnvtNaRWUrSyiDW3fwTffgsPPACenkaZ19DcFKTLyTtxbFfLBykrg3zdatC+zfvwtfWlb189Uw3aCF523hQ6a2H3bv1uePhh4h+6BZsaG8LtwomIiDCuQAsgw7GGz/pA6rlGfi8VFZFACv7SiWgv41Y2WzKnc0+x6+hGGD2aHfeNQCmU122tZwnoE3ippJSXDFeklKcAvTZPhRDBwATg83qnbwPqtiq/ApqsgbV1cMJVA8eS9ukzbZulpKSEnTt3MrdzZygpYVuULRJJlFeU3mMIe3uiilXkO5RTWVlpsS2Wli1bhq2tLffcc8/l1a7aSkaA0xdPk6/JN4pxan0CAgIQRXas/sGOAelm8PIqKaHys08YMs+TZSXXz2OSUuLs3PDqn1E7Opw/z1OHdFV6KfkpRpkiPj4eAL8+fuxI3aE7+cEHuqo3C2uGfT16hPcAIHjJ200mRTfKqlXg68u87+aw9q+1TJgwwbiVq2YgwDmQfAcoTNGjAKisDKnVEp8UD8kw5pYxxhdoAQR20K16n89tuOm6/O03EsIkw3373ZD5XXW88stzzPxiApw/zw7vMnoF9DLqLokh0Oen+UBtRePw2mMJ+ifXLwKeBer/BvKTUmYC1L76NjWIytmZ2Yegw/lqPadtmyQkJFBVVUXnu+6CDz4gQZ5lcMhgbJW2zRonSutBuoNuO8oStxsrKyuJjY3ltttuw9PTU5dIPGXKpdUugLyyPLr4dDH6k4tCoSCyQySdzzvimWQG37OlS/l3zwJ2OV3E0+H6qzpvvvkmxcXFV+ZCYYKODp6e3Ha0kEc+gSBlkFGmiI+Px9/fn8+SPmPWT7OoqqnSVTL+4x+69klthO6h3Rm6WUG/c/LKxr3N4eefyQ715t1TSylzK2t324wA4wLG8eknYHM6pemLn3uOgu7RUCWpPll9Q2wzAgR66B6mzg/u3uD7pyszyXSB4T1vN6UsiyMgV0OmM2gencve5B0MKTNO31pDok/g9QhwHHgC3bZhIvBQUzcJISYC2VLKFlVACiHmCiEOCCEOFJSVMTZOQbeMgJYM1WaIi4vD0dGRvpMmkX3/NI7n/cWIMP1sJOozWhXNqEzd9qwlBl7r168nNzf3snfX0qVwVd+2mzvczLFHj5mkBYZarWZqjBO/fPhPo891Ndu6u/H2YMHcXnOZHN14AvWXX37J888/z/Tp01m6dCmhoaGm69lnb4/KzZfB2ZCZ3sJg4jpotVq2bNnC4LGD2Zm+kzk95+gqkp54QrcF3YZwsnUiKj2QqIu0zMurvFzXFHtyFwBsUm3aZaDRuUNnRDaozmVc/0IpYd06PMI6cW/pfXAARo4caRKN5sbPyQ+BIENR1uD7FYMGMDl6MiM7jjOxMgsiNhb/n7egUcFRXwgqgqFfbgUjV3q3Fn0Cr4ellO9JKe+QUt4upXwfXTDWFIOAyUKIFGAFMFIIsRzIEkIEANS+Zjd0s5RysZSyj5Syj4+PD09HR7PKBmq0lpmzZAg2b97MnQMGYLdyJdv/2gTA8LDhzR5nzru/suSbApydnS3Sy2vp0qUEBgYypn9/qNOnurx7XVlTabRcooaIjIzkmPo8r+5+w2RzAuSX5/P3P14k0jOS98a+1+h1a9eu5cEHH2TMmDEsXbqUmTNnkpKSYtKefdqICE52h1VHVxl87CNHjpCTk4NHXw8kkolhY3SBeHXbXOG+2NGHP/1pWeC1ZQuUlREXKVBoFIyIHoGLi4vBNZobTz9PVvSF3WF2uv6kjXH8OKSkICdOJD4+nr59+uLhcWOYaauUKoLtfSk72kDRT0UFMa6RrJm2plmpKO2O+fMJuKj79+NcCWc/gMlHKsGYxUYGQJ/A694Gzt3X1E1SyuellMFSyjBgGvCrlHImsLbemPcCa/QR6tLLhXXd1nE0u31WNiYnJ3P69GnmeHrCvfcSI/x5edjLLTOBq92KioiKsLgVrwsXLrBp0yZmzZqF8qOPdM2g069svvzOrnfo9FEnk9mHqNVqXC9qSUk9DFlZJpkTKdn4+n1cKM4k9o5YnGwb7jn3+++/M3XqVHr37s3q1auxtW3etrOhsOvalR9vhvWZ6w0+dl0lb6ZLJgHOAfSMPwZTp+o8itog+/tk8cBkWhZ4rVmDdHVhU/EhtKe17c5Goo4A/wC2TYC3pva+4qHrGtato0ZAWPECdtfsbperf9cj9cxE3v7PgWvOy40byQpyh8OHzaDKgkhLI6BY9+WF2rQuUXvekmk08BJC3COEWAeECyHW1jsSgNY4Tb4BjBZCnAZG137fJLNyKkDAX9mJrZjactm8eTMAfXJyICqKTr3H8tLwl1pkAleYehLnl1UEdCm1uMBr+fLl1NTUcP+dd+q2kSZNgnrGkEkXk1jw2wJGq0cbpT9jQ0RGRuJZCBcUZVSeMFFl486dzHhtLWc8XqJvUMMVa8eOHWPSpEmEhISwYcOGRhPrTYFq5EgcihTkVDS4QN0q4uPj6dylM38V/MX4yFsR776ry/cb0fxtdkvA18Gfv9ygevjw5t/8r3+R/eVH2FSq2pVb/dUE+gZCGZwvaSKvct06DozsRFppBrJU3nCBlwgM0j0MXrUqeOK31fj/s5KV8piZlFkIISH0uADrvoWpd8Pi3pfPWzLXW/Hahc5K4kTta93xNNCsTWUp5TYp5cTar/OklKOklFG1rxf1GSPKMxIh4eCxtmGk2Fzi4uLoGByM09695E8YyeYzmymranhvvync3Pywq6jBxlFDcnIyVddbyjchUkqWLl3KzTffTNSmTbpKxv/3/654/9GNj6JSqPhg3Acm06VWqykpACkg3QReXqkFqez69AXw8iLk/v9r+JrUVMaOHYujo+OlFlJm5Z57SLP1oUhRbNBhy8vL2bFjB2NGj+Hk4yd5V3sLnDgBzzxjsc2wm6KDawfKnSApyK/5N0dF4Xfn3+mU0InO1Z0JDzdeY3JzIoTAvlyF+7lEWLGi8Quff54tf9P9NXXIdODmm282kULLYLlHOvfcIa9Zid929lcA+oRYtm2C0Vm4kI1dVDw4CXKc4IWRENtbBcYsNjIAjQZeUsrU2oDpZinl9nrHQSmlyZMvPLv1JrQAjqdcu+za1qmqqmLr1q081qULQqMhvq8X42LHcSy7hU8z7u5EFSrJty+jpqaGZEM07DUABw4cIDExkYemTtWtdl1Vybjy+ErikuJYOHIhgS6mMwQMDQ2lqFj3o9CoZ46BqNHWMOvbu5jYYQfFj94Pjo7XXJObm8vYsWMpKyvjl19+IdRCqvr8HPyotqmmQGO4Ztm///47FRUVjB49GqVCidsHn+mqGO++22BzmBq1jxqAk/Grm3fjd9/Bjz9yMf8iO3bsaLfbjHU41DhRYF8JR6+TPjJpEvG257C7aMfwfsOxs9Ovg0d74axjBStioPJc6uWT2dkk2GUSjBsRHu3fz+x6xHaDuZMFF2rTIPOcdN/HdjOvrqa43lbj77WvxUKIonpHsRCiGZ1NDYPPzTfTKReSSlKbvriNsXfvXoqKirjFzQ0cHUlwysHF1oVeAS1vAhtZ4066fSlgOZWNS5cuxcHBgbuCgnTVW/VWuwD2Z+ynT2AfHu37aCMjGAcbGxsCbELZtcSWQanG9fJ6e9fb7Mg5wAdbbHB57NrVrpKSEiZMmEBqaipr167VufpbAjU1/N8enZ2fIb284uPjUalULMpZxCc7F+me7OfOvZSn2BbpEqyrSHR6+0X9CwSkhJdeonTJx4R9HEZ1THW7tJGoj4fSkzRXGs/H+eEHSg7tY1f6Lir+qrgh2gRdTaCPLrC6kHY5xUYmJLAtDEYEDryh/bsA5m+dT5msvOJcmaxk/tY2mlwvpRxc++oipXStd7hIKY3XPK8RggYMYOYhGJ9k8qmNTlxcHAqFgoD//Q9SUth2bgdDQodgo2j5H58ouwDOOVSCjWUEXhqNhu+++4477rgDp7vu0vUfq7faBfDu2HfZft92lArTN7+NCo3CsUCFXb7xnilqtDW8u/tdJtCRmSP+CX5XbkVVVVVx1113ceDAAVauXMmQIUOMpqXZKJWMyXTm8zfAq9rLYMPGx8fTc2RP4lPiqVIKSEyEefMMNr45GNllJCNXQPcL8prCkUY5cQJOn2b7mGiKa4pxkS4MGNC+t5FGMILYjxWQ2sDDdEUFzJlDxf8+ZrTTaEi8MdoEXU1gR9026/nel1vHJUa6kuMEI3rdYS5ZFkNaYSOdPBo5byno06tRLYSwq/16uBDiCSGEu/GlXYnK3p7CDHeCzxvHwNGcbN68mf79++Ph4UGmfTUnck+0yL+rPqMDBvHi6QDcPVwtIvD6+eefKSgo4OG6p/h6LWAOXTjE0SzddoOj6tqtN1MQGRnJoJgaVr461Whz7M3YS25ZLjPvfAXx9jtXvKfVapk9ezabN29m8eLFTJ5sedtMqqAwemh0+WeGIDs7m0OHDuE7SOehPCFstC6vy0yVm4YizDcMhzRHvMvQv7Lx558B2BRUDtUwsdtElErTP4CYEnWAmpwyLdqG/j1t3w4lJXhNvBvX/a741/jTtavxPf0sjUCvMADOV16uZwvo3J/PJ33O2I7jzaTKcghxaziJvrHzloI+dhKrgRohRCTwBRAOfGtUVY3wc7++fCUKyStrTVGlZZGXl8f+/ft5wcsL7r6b35K2Ai3z76rPoBf+x6ux54kKi7YIL69ly5bRNTiYQQ8/fMUWY1VNFff+fC+TV0ymWms+3ya1Wk1pFw2f7P3EaHPkleYQ5RDEuLArt0yklMybN4/Y2FgWLlzI/fffbzQNrUHZqRM/DoPvjhjmx3/rVt2/9RzPHKKdw4jsNBASEgwytrnJ6unJzg7oH3itWQN9+rA29VdIgSkTmuyk1uax97Fn0Sg4GOOv22qtz7p14ODAzmhH4n+N55Zbbrkht9WCXIIIU3pTs6u2nVhuLp6bf+P+jlNNmgdrqSwctfCah3VHlSMLR7XR5Pp6aGuT6W8HFkkpnwLMYiEfEOnH0VFHWXnsOlUwbYwtW7YgpWRIZiacOMFd3e7hwIMH6Onfs+mbmyCvLI/gTsFmX/E6d+4ccXFxfBARgSgshNsvt7j4YO8HHMk6wntj3mvV1mprqbOUOHdqv24b1AhMyvXi1L8ycN+w9Yrzb7/9Nu+//z5PPPEEzz//vFHmNgTOPXvyQzfYmfmrQcaLj4/H3dedP/P/ZEK+N5SWgqXktLWSUzcX8tpQ9Au8ysshP5/UycNIK0tDcVbB2LFjja7R3Lj5uHFwCKy5d8yVFay1bvWZ4wYz+NtR5EXl3ZDbjAA+Tj4krw3n7h90OV7aTRtZ+srtZBzZaWZllsGMmBksnrSYULdQBIJQt1AWT1rMjBjjm0q3Bn0CryohxD3ozE7r3BObby5lAGZlluBcAYdP69nRvg0QFxdHBzc3XI8cgfHjUSqU9A7s3fo8p6IiOi30p9TtT9LS0tBoNIYR3AK+/vprXKVk2J9/XlHJmFqQykvbXmJy9GSmdDLvE75arcalAM7ZlqM9dbLpG5qJplpDzfcrwN4exl/eIli2bBn/+te/mDZtGu+//75FP9Wrhg9HUaIgqyq31WNJKYmLi2PQyEFM73oPd/ySCuPGgbfl91nTBw+lJ3vdFTB9etMXOzjAiROoHvsH3one9HPvh5ubm/FFmpmuobqtw6ScpCvfSEuDCxfYMqzWx+8sN2Ri/SUCAy89DB7b+RNzpsAWBzP0lbVQZsTMIOXJFLQvaUl5MsXigy7QL/CaDdwMLJRSJgshwoHlxpXVME4x3YjOg+Ppf5pjeoMjpWTz5s38o3NnRFUVmaP689iGxziZa4A//C4uROZoKVQVIaXk7NmGO9wbmzrvrvdDQ1EWF1/aZpRS8vimxxEIPrz1Q7MHHBEREZQWQqUNZCUdMfj4nx9YjL/jp+RMGgW1LWDWr1/PAw88wC233MJXX32FQqHPj6MZ6d2bfKU3Fw3g5XXixAkyMjKYPGIy91hyMgAAIABJREFUS93vY9AfOWCC1kemwt/Bn3wXLZoIPcr9tVoQAk1BDbnf5zJ1tPHyDC0JdQc1ohyct/x4pZdXaCjk5REfqEFVpeImj5sIDLxxt9X+r2MyD0Xr0kUS0nTdHIaH3xj9KtsrTf6ml1ImSimfkFJ+V/t9spTStE3tavEeMIDoXEgqs+yKBX1JTEzU/fFRKsHNjQTfEj458AmlVaWtH1wIoqpdSbcrATBbnteuXbs4e+YMd5aXX7HapZVaevr35PVRr1tEIqSDgwNKpS7hP/2c4d2g1+1bjmepFp87ZwG6z+Vvf/sbPXv25McffzRbK6DmEmjrQ6VdJRXVFa0aJz4+HoDQvqHI2OXg7AwWWFDQUkLcQ8Ae0r/83/UvLC6GoCCqY7/hnZ/fARvavY1EHZ6enogiyLargKQrV72koyPxaQnUnK5hzOgxZlJoGaQ6VfO7bwWcOME214uEK7wIdbcMbz8rLeN6Pl7f174eFUIcufowncTLBA8aRFQeXFCWtNjV3ZKo61HnO3QoPPwwCWk7cLd3p7tfd4OMH6Xy57x9JajMZymxdOlSHJycUBw+DB99dOm8UqHk1RGv8kT/J8yiqyE6OnQh6R0V/VIMm+RfXFHMtosHmXBGQednnkGhUDBkyBBcXV3ZsGFDm2qCPOdwCnaVkFGY0apx4uPjCe4TzLi14/huUjh88kmDZrJtlSg/XePiqpefgutt8//yC1y4wD7XYj4t/pSA4QFERkaaSKV5EUJgW2VPtpO47OWVnQ0DBpD4y9dcKLmA9oz2hs3vqiPQ2Z/zLqD9fiXbw2BEyFBzS7LSSq634vXP2teJwKQGDpPj4OrKwJMKFmzzQWC5uTD6snnzZjp16oTHwoXwxhskpCQwNHSowXysotx12xweEe5mCbxKS0v5ecUKpt51F87+/hCkswJ54/c32HR6k8n1NEVUeBRnqhQGtzOIS4qjUtSwMcmGv9LTkVKi1WopKiq6tPLTVphYFM7u10FR3PJt0aqqKrZt20bAMF2NzqiRD8CsWYaSaBFM6jKJcZ9BRD4N+1TVsWYNeHmx1iYFtHBHjxvLm6l7YneWfu98+TPasAH27iXatzMzNDOwOWPDsGHDzCvSzAT1GkaBAxy8fzz5DjCix+1N32TFormegWpm7Zd3ANW1LYQuHaaRdy0H3KIoyPbBQeVgLgkGoby8nO3btzP15puhspL0wnSS8pNa7d9Vn0HdJrAkpRtdfSPMEnitXr2ax0pL+TAhAUp0W54Hzh9g/q/zWX9qfRN3m57IyEjG9q/g09k9DDru+tPrUVQoOJl0pcNyeXk58+dbtsPy1SijOhIFpLSiDdWePXsoKSmhyK+IvqpQ/I5ZRksrQ9JN3Y3iTLCvpvHKxqoqXaAxaRI/HV0D5+HuiW23VVJLCPIPIgUuB17r10NwMDa9+pC4OZGBPQaatTm8JRDoGQaAu4MHWfOymHKTNfBq6+jz2OoKxAkhdgghHhNCtKDzq+FIGjSIpbYX+DOz7SbYx8bGEhYWhkajYfzy5WR1705qYSpBLkGt9u+qT4cZj/LA0sNERMSYJcfrhyVLeFqhwKF3b3B2plpbzUPrH8LXyZfXR71ucj1NoVaroTN8d+g7g44755Dgto1a0F77Xlpj7VIsFPuYrjw+BVbuW9ziMeLj4xFOglNlp5jw6zldj8J2hqOjI8kDHUgIo/HA67ffoKCA/AmjOF12GrtzdgwaNMiUMs2OTQcb/jmujPNjB+rc6uPiqJx4K4+ueYw/M/684bcZASL3nGJIuoKq6Ch8O/bE+Yc15pZkpZXok1z/ipSyC/AYEAhsF0JsMbqyRugUHEzJ8Iu8kfCauSS0itjYWObOnUt2djaeQO+qKr44c4bUHamkP5VusPyuOhJzEnFUO3D+/HlKSw2QtK8nycnJ9Pr9d1y1WkRtJePH+z7mYOZBFo1dhJu95ZXLq9VqvAsg9+TexvvHNZfqaoZ8vJ45pxvOXwoJMX9hQXPw6NuP+Ag4mrO/xWPEx8cTMTYCiWTCXzXtqpqxPjlDqljWg8YDr+BgeOop4sMlUkiGBAzBpg33qGwJTt5OnOxSw1+PTYdt26CkhD3DI/n08KfgeYPbSADExjLw/94n4UstL42AePvzul6msbHmVmalFTQnUSMbuADkAb7GkdM0AzQahuVBYlrbXPGaP38+ZWW6woAxgBJYU13NC/NfQAhhWFsFrZa5L/Vif/EqAM6cOWO4sZtg5Wef8RRQNm4c9OhBZnEmLya8yLjIcfyty99MpqM5qNVq7Ashw74SDGS/Effzu+y2y8GlATd6R0dHFi60bIflq1H17YuiREkaLetpmZ+fz759+7izy538dDyGXo5q6NvXwCotA6caZ+L8HOCppxq+IDoa3nuPoMoIWAJ/H/V30wq0ACL9dIUEx1KP6nIrJ08m3iMfIQWuea706dPHzArNzPz5xKrLCP4/+KELTL8TYtVl0MZSFKxciT69Gh8RQmwDtgLewINSym7GFtYYnn37Ep0LZzXnkFe3mWgD1N9amgDkAPvdIO2ONDaf2WzYyRQKoopVnFPpfJdMleel1WqpXLwYd8DxP/8BwM/Zj0VjF/Hx+I/N7tnVGO7u7lBhT5E9FJxNNMiY8w69xfNjFJTVJgj7+PgghCA0NJTFixczo62t9vj6UqH0JEfZMi+vhIQEtFotd/Toz5RVx1DMmHmla3k7wsvGi2z7CghooNFHaqpuq7Gmhk0bNqG8oGTCrRNML9LMdA7uDEDFK09Dfj6sWUN8WgKqHBWjBo+64VYArybWNZW5k+BCbeFzrhPMnaQ7b6Xtos+KVyjwpJSyi5TyJSmlYf4itZCgwYPpmAdloorMksymb7AwOnToAOg++HHAJkCGAW4Q4GL4TkxRNn5csK0AW9N5eW3fvp1X8vPZMn8+9OiBVmpRCAX397qfCA89DCXNiJNTEG4ayEpr/T/z1LwkjqouMsm+G1+uWIG3tzfnzp1Dq9WSkpLS9oKuWkKFBxV2GrSygaS1JoiPj8chwoEt+eso8Hdvt9uMAAFOAUhnLZp33rn2zS+/hBEjOHV2P/9L+x+9R/XGs17j+BsFdbAaNJDhrIV9+yjQFLD//H4q/6q05ncB88cqKbuqyLrMVnfeSttFnxyv56SUh0whRh/c/f3xztM9IRvE4d3E1JkjSmAy8C6gjFTirHCmq29Xg88X5RYOgHdHb5OteC378ktc3NwYNH8+pZWl9PysJz8c/8Ekc7eWXi79SHxbSXRy693Z1x9ZDcDw/n9n7dq1zJgxo80YpV6PKWcLCb8IOUU5zb43Pj6egDEBvHI+FsXpMxAVZQSFlkGoeyhSBaX/75lLVb2XWLMGBg5k+ZmN5KnzuGXUjZnLFBgYCLkgBfDmm5w+ux9HHCEJa+AFpDnXNOu8lbaBhfcoaZiAQme+WeFEv6B+5pbSLLRaLdu2bSMoKIgOISHsEYLC0FA8enowJnoMCmH4/x1RAbpgLjjK0+iBV2xsLF2Dg/n38uXcWlHBjz/+yMvbXuZI1hECXdpGy4+oyCg21dRQbYAWJesyfiXKM4o9xbZUVlZy3333tV6gBTBF9uDYx1CcVdis+5KTk0lKSqIssJShoUNxdWrfKzzTOk1j8tvgWc6VCfbJyXD4MEyZwupDqyEXZk1uXz5m+uLp6Ynt17b8t9bWr2/n0Yz6cxQhIkRXZXyDE+LWsEN9Y+ettA3aZOC1vUd/fixwwcnWydxSmsWPP/5IYmIi77z1Fqlz5qDds4dth7aRW51rUP+u+nS6eRKbCibS37mbUQOvumrNuzIyiAQSNRoemP8A7+1+jwd7PcigkLZRJq9Wq3lgMiwY1LqVqSpNGX+k72NSx0ksW7aM7t2706OHYf3BzIWqc2ccgMw//mjWffHx8eAOF7RZTFh1RGcf0I7pHNGZzFJ0Vs/1A6+1awHQTBzHCc0J3HLciI6ONotGcyOEICAggH9PmAAnTlBdXU3CrwmMGT3GYnNBTcnCUQtxVF1ZEe2ocmThqLZVlGPlStpk4KUdOJCfnbNY+sdSc0vRG61Wy4IFC4iOjuZuR0d4+WU4dQopJY/0eYQxauP0I7MfOpJx768jomtfsrOzKSxs3iqFvtRVa94PrAeOCNCM1kA5vHGLWVp7tojIyEgIgV/P/tqqcVTbfiPj3/n8PTmYAwcOMHv2bAMpND/2vboz/D74/nDzfv7i4+Nx66OzEZkgOoKdnRHUWQ5efl4cGw6/hgMpKZff2LIFunQhvvosWoWW4R2G39BBhm0PWz6K2skZHyWh74VS5FVk3WasZUbMDBZPWkyoWygCQahbKIsnLWZGTPvNjbwRaLRkRAhRjC4V6Zq3ACmldDWaqia4yd+foB6S/7dlPrN7t40/aGvXruXIkSN8/dVXKN98E8LCYNo0wm1s+GTCJ0ade3fyDnJd0wFdZaMxSrTT0tLoCHQAFgKEA8Gg/VGL5xttZ0tJrVbjXQiaxF06S4mIFhYDfP89tk6urDiZho2NDdOnTzesUDMSNHAIh46DU4H+xRo1NTVs3bqVnnd5k5NdSMc75xpRoWXg4uhC+RDYpBKMrL/i9eOPcO4c23/7GArggVsfMJ9IC8DZx5nT7qf5+vDXnC8/DyUwatQoc8uyGGbEzLAGWu2M67UMcpFSujZwuJgz6ALo5OjI/bmQUZ6Jpvo6DWgtBCklCxYsQK1WMz0oCPbsgWeeQSqVHL5wmBqtcRMlP58/jq/OLQGMZykREhJC3a/KrQBngSUQUti2DEJ9fX2xL1GS7qK9cpWiGWgrNIxQfMO398Sw9LvvmDhxIj4+PoYVakaUYWHYlNiQ6KD/VuHBgwfJz89ncXI4h5fZw+3tv+2JQiiwrbBlldob3qi36qtSQXg4hb8X4vKlC2OGG2e1u60Q7BIMwLJDy7DV2NIrpBdeXl5mVmXFivHQe6tRCOErhAipO4wpqikChwwhurYS5nSe6XsQNpeNGzdy8OBBXnjhBZRvvQV+fjB7NskFyfT4rAdLDi4x6vxRwptsVQXYGS/wWrhwIX8ArwFnak3pHfMdeX2h5bUGuh5CCBwUHmQ5gya5ZZ/V/jWfsK1DNUn+vmRlZbWbpPpLKBQI4U62Qn8T1bi4OJQC1AcPopw8BVxcjCjQcnDRupClKLm8rfr00/DWW1RVV7F+w3rGjR3XLipdW0O4l67yOr0onapTVYwZfWMHolbaP/oYqE4WQpwGkoHtQAo6+ymz4RMejlee7uuTeZZtKVG32hUaGsqs6dMhJkbnOuzgQEJyAgDDQocZVUOUSxgA/p39jebl1a9fP/YBb3Z3hifAd4Bv2zQIBbxcwumaBRdTT7To/vW7v0aphT8Tq/Dx8WH8+PEGVmh+wqUr1aoyva+Pj4/Hc5YX417ogGzMyb0d4q3yRtqVI+fNA40GPvsMkpNZsG4BF6ZdYOC4geaWaHaiAy4XFsgz0tomyEq7Rx9b4AXAAGCLlLKnEGIEcI9xZV0fIQSO5Y5AGafyTN/8uTnEx8ezd+9ePvvsM1T29lDPTHFb6jb8nPzo5N3JqBqiAjoDv+EX5WG0Fa+NS5bQDyi9P4QqUc2RHUews2mbydNDfUfw6Fv78Z+Z26L710Vp6a+JYcOaOB599FFUKpWBFZqf0VkKXAuhsCgfN1eP615bUlLCzl07cRjmgHNwBKJf27KBaQ2BzoGcFSeR/3kX0b07lJbClCn8tHseKGH6pPaT+9dSIgIjdKkJKrDLuPEahVu58dBnq7FKSpkHKIQQCillAmD2uvhKNx/++EDJc4OfM7eURpFS8uqrrxIcHMy9gwdDXBzUtjmSUpKQnMDwMONXNEWG65LpPX2URgu8qr/+mu884PjFRB7u/XCbDbpAl2D/LVDQAh+h9MJ0DuccxbdG3a68u65msstQtnwDOfsPNnntb7/9hsqzmmJFMRO8b6wVnjnhcxj/H1BIYNEicHGhZugQ/qr6C58iH3x9zNb21mIICgrSVeS8DMN6D8Pe3t7ckqxYMSr6BF4FQghn4DcgVgjxAVBtXFlNs3/cOO4pFkit5fZr3LZtGzt37uS5557D7u23YcoUuHgRgKT8JDKKMxgeNtzoOhwHDuMv1VPc6XMb+fn55OXlGXT8Y8eO0TUri+/66vJ2but0m0HHNzVqtZoX7oUX1dnNvrfsv+9wl10vTq8/TY8ePejevbsRFJofp1pPsvx9+5q8Nj4+ns7Rul8140X7dapviIjQCFLqfkUdPAi33srmU9uosa1hRIhxvPvaGjt37rz09b59+4iNjTWjGitWjI8+gddtQDnwFPALkARMauomIYS9EGKfEOKwEOK4EOKV2vMvCyEyhBCHao8WJcB49u7NqZBq7vvhPottlv3qq68SEBDA/aNHw/Ll8OCDUFutE+QSxKYZm7gt2gRBSmQknV54j9DeAwDD92z8YflyhgCbezsR4xtj8f0YmyIyMhI84VDGQdA2ox+hRkP0O8v4bG8Ix3873m5XuwCUvTsT+QR8n/pTk9fGx8dT3UlB71xbAkZMNoE6y8HB24HEybCjrhxp2jQWb10MwKNjHzWfMAshNjaWp59++tL3BQUFzJ071xp8WWnX6NOrsVRKWSOlrJZSfiWl/G/t1mNTVAAjpZTd0W1NjhNCDKh9730pZY/aY2NLhEf7+zPcB5afXE5WaVZLhjAqO3bsYNu2bTz77LPYf/SR7uS8eZfed1A5MC5ynFEaYzfE9gOr2HjhW8CwlY1SSs588w2OwIrer/PF5C8MNra5CA4OxqcQbE/uvdJxvAnKf1lHsqKI1QoFKpWqTRYW6EtU3yGku0JGafp1rzt//jw5x4/z4J/VPOU+Dm4wo9BA/0CqesGuUBt45hm4/XayD2TjdtCNob2Hmlue2akzXq5PWVkZ8+fPN5MiK1aMjz5VjXcIIU4LIQqFEEVCiGIhRJN15FJHXWdYVe1hsKWp8LAwnq/NfbbEZtkLFizA19eXubffDp9/DrNmQYcOAPyZ+ScPrH2Aogr9y/Fby743/8mnGd8hHIRBA68//viD6PPn0QpB4C130Deor8HGNhdKpRLnSkdS3WiWl9fmTR8R8SS8cCaBiRMn4u3tbTSN5sZGZYtNmQ27vZTXvW7Lli1MBR7bDzPu+Y9pxFkQvi6+iGrBN70j4a23KC8v59DPh5gVMuuGdquvIy0trVnnrVhpD+iz1fgWMFlK6dZcA1UhhFIIcQjIBuKllHtr33pcCHFECPGlEOL6JVGNENSlCz51gZeFWUrs3r2b+Ph4nnnmGRzT03Xbi//6FwCaag0zf5rJxtMbqaqpMpmmKBfdXkdgTKBBA68VK1bwjo0NL33+d1am/2Kwcc2Ni60351yh5mySfjeUl7M+dxcu1TbkHstv19uMddhrXcmRBde9Ji4uDhllS9aQXtC5s4mUWQ5CCOw0dmRX6TYJlm9aTrlbORMmTDCzMssgJKRhS8jGzlux0h7QJ/DKklL+1ZLBa7coewDBQD8hRFfgU0CNbvsxE3i3oXuFEHOFEAeEEAdycnKuFa5QQIUd9lWWt+K1YMECvLy8ePjhh2HwYN2qSW0T3Be2vkBiTiJLb1uKl6Pp3JmjfHV/9LyjPA2W46XValm5ciWDx4/m3czv+T3td4OMawl0cO/MLWehOEW/f1va7CzWd1IQkueOj5cPt956q5EVmp9QrTNKVSlUN1xrI6Ukfms8i6fBv57qamJ1loMbbhSLYgAW7V0Ec2DQUKtlAuiMlx0dr2oC7ejIwoXWJtBW2i/6BF4HhBArhRD31G473iGEuKM5k0gpC4BtwDgpZVZtQKYFlgANmvpIKRdLKftIKfs01m6l0NOLjrmCwgrjNH5uCQcOHGDTpk08/fTTOKekQFUVKHXbMVvPbuX9Pe/zWN/HGBs51qS61OG9EBLcvXWWEoYoSNi1axch585xq1su5dXlbb6asT5jw8bzSSzYnUzV6/o/bHLIsq3kxJ58Zs6c2S69u65mZIkvfzsFJYmJDb5/9OhRCm2zqVRWMqHjRBOrsxz8bf2p0FSg1Wo5WX0S/3J/XBxvDOf+ppgxYwaLFy8mNDQUIQShoaFt1njZihV90SfwcgXKgDHoqhknAU3+FhVC+Agh3Gu/dgBuAU4IIepnk98OHGuu6Do0wcHsWyxZMvbjlg5hcBYsWICHhwePzZkDo0bB/fcDuqf/Jzc/SUevjrw1+i2T67KP7ESHQrCzr6KkpISsrNYXJKxYsYJpSiUHSw/iZudmdAd+U6JWq/kvkB4T0/TFGg3r/vwOgaDmRM0Nsc0IML7DBJasg9zduxt8Pz4ujr93BBspGKO+cdvA3OdzH/JzyfKNy6lxrWFUqLUBdH1mzJhBSkoKWq2WlJQUa9Blpd3TpHO9lHJ2C8cOAL4SQijRBXjfSynXCyG+EUL0QJdonwI81MLxSb3rLtz27SMlPx9/f/+WDmMwDh06xNq1a3nllVdwXbUKsrPhgQcAXa7HxukbKdAU4KhybGIkI9CzJyfOf8kelQNx3MPp06db9ZlVV1fzww8/sNvZkVdu0jCx40RUyvazytMhrAOLnoTzHomsbOrijRv5x72L2NE3iMJOPnTr1s0UEs2Oe9++SCD/4AHCGvgxTl29mt09YbB9R9zs3Uwv0ELoUFtU8/7a9yEIHr/1cTMrsmLFijnRp6oxWAjxkxAiWwiRJYRYLYQIbuo+KeURKWVPKWU3KWVXKeWrtednSSljas9PllJmtlR8SNeuVATAbT/cZhHNsl977TVcXV154pFH4K23YOBAGDKEMxfPIKWkg1sHYvz0WEExBp6eOMyaTWhtu5bW5nlt27YNsrOxlcWE2/oypdMUA4i0HDqqO4ItpGUmNprDdImVK/FQubMj4dwNs9oFIKP9cHgR1hXuuOY9jUaD74l9HPODif1mmkGd5VDlXgUz4ZDzIexK7RjQcUDTN1mxYqXdos9W41JgLRAIBAHras+ZnciQEJ4E9l3cx7HsFu9YGoRjx46xevVqnnjiCdw3bYK0NHj+eTKKz9NvST+ejX/WrPoAdm5Zyr82zcHGxabVlY0rVqxggr09wUWw/9afuPOmOw2k0jKws7PDt0SJe/qx61tKlJayIXENzwx3QNjaMH36jdN7r0toVypsIKviWof/3Tt28ECBlj2/9eLeAQ+bQZ3lcPzYcYgEtoNqtcpqDmrFyg2OPoGXj5Ryaa2BarWUchnQcLa7iQmNjGRerZXridwTZtWycOFCnJ2defLJJ2HdOujWDTl+PHPWzqGipoIHez9oVn0AF7/4iFW521ttKVFRUcHq1asZHtOVsogO0KtXu/Qkcq1xJtWd6wdeGzfySbcKloReYOKE9u3ddTX2KntU5Uo2dLg2UTz5iy/wB7rd/zTejjfOZ3I1sbGxvPtSbeG2A5ScLbE6s1uxcoOjT+CVK4SYWevJpRRCzAQM2+yvhdja2ZGPLT6lCrN6eZ04cYKVK1fy+OOP4+XlBStXwi+/8MmBT4lLiuPdMe/S0auj2fTVEeXbCQDPSM9WBV5xcXEUFBRQ8uxsvObksOlsnKEkWhTudv6kuoE8e7bRa0p/+JatEVB6Qsuc2XNMqM4ycKpxIa/m4jXnl506To/7nDk8oMmshHbN/PnzKS8s130zWvdidWa3YuXGRp/Aaw7wN+ACOt+tu2rPWQR57u5E5kizBl4LFy7EwcGB/3vqKSguBoWCE6pCnol/hlsjb+Wh3i2uHzAoEaE9UGjBxVdnKaFtTh/CeqxYsQJPDw9yvHLQVGvo4d/DwEotgy6+fZl+BIpOHm/0mq1PTKTCBtyz3Bk3bpwJ1VkGHbQuOCtLdFvrteTm5rKj9BiHw0oo1JabUZ35sTqzW7Fi5Wr06dWYVpsE7yOl9JVSTpFS6mduZALKg4IYlibxd/Qzy/xnzpzh22+/5ZFHHsHn6FFdW6D9+7lYfpFo72i+mPyFxWzD2UZGE1oIWvtSNBoNGRkZzR6jrKyMNWvWsKhrV9b9/AYD/PqYrN+kqZl80+08vx6qExsvRPghcxto4N4R994Q3l1XM0LexBN/QsnevZfOHf3gAzpHgb3CnmFh7cdipCVccmD/AHivgfNWrFi54Wg08BJCPFv7+qEQ4r9XH6aT2ASRkTz5Kyzt/rpZpn/99dextbVl3rx58Prr4OgI3boxsMNADs49aFlBiVpNr0zwEDoXkZZsN27YsIHS0lK6OFbxh6eGKV3bV1J9fSIjI3lBwB+9uzd8wZtvcvbA73AG5txrMYvAJmV0l7/x/O9QsH//pXMeXy2jMApGq2/B3sbejOrMzyVn9nygtjWr1ZndipUbm+uteNW1CToA/NHAYRFo7rkHf+DMVR3uTUFycjJff/01c+fOxT81FX79lT1P3sW/d75GVU2Vxax0XSIyklWPbuPTv30HtCzwWrFiBQF+fuyqPArAbe3MRqI+noGerHwRPrA7eu2bJSXw8sv8Y2kpPc/2vGG8u64moHt3kpwgP/EQADInB1lxjgx3mBQ92czqzI/Vmd2KFStX02jgJaVcV/tlmZTyq/oHOid7iyAyKgocYUr8FL4+/LVJ537jjTdQKpU8++yz8J//UOrjziy7DXxz5BvKqizmI7qMnR0MG0Zg587Y29s328urqKiIDRs28M+RIxlzpJT3Pe6hk3cnI4k1P0FeQQitoPB8IlRWXvnm+vVoKzR8nJPD7Pta6jHc9il1KSPyGdhRocuDy/74Y4ocIETrw/io8WZWZxlYndmtWLFSH32S65/X85xZiIiI4MtyyNZkcjSrgZUJI5GWlsbSpUu5//77CaqqgrVrmfeomqSCZL6a8pXFOnUfWfc5g97qSGDf5ltKrFmzhoqKCqZ6e9MxD568w/Stj0yJEALvMhW++SnXWkqsXMmABxXsGiu45557zCHPIogJ0RkCp9jqHjRqvvkGr1TYOnMnQa5B5pSuqHnHAAAfEklEQVRmxYoVKxbJ9XK8bhVCfAgEXZXftQxowsrbdDg6OjJAaUNogdKklY1vvvkmAM899xyEhbFh3Xv8T/zBvIHzLDqh2GHtJvZUJOEe5d7swGvFihWEhoaSOTSCtfMmURNoQflrRsJd60qqG1cGXkVFnNuxkf2BWm4K63xDeXddjYeDB4oqBavCPECjIbfoIms83VBHRppbmhUrVqxYJNdb8TqPLr9Lw5W5XWuBscaXpj85bm5EZWtNFnhlZGTw+eefc9999xHSoQNVNVU8cuo9YnxjWDBigUk0tJSwkG4oteDga0NSUhI1NTV63ZeXl0dcXBxTp05lEbt5yH+/5eWwGQEfp0DS3KCy/rZsWhqrejsD8MjIR8ykzHJwqnYitzqXKqWSAeEVvPJ4Gacvmr+FlxUrVqxYIo02yZZSHgYOCyG+lVJWmVBTsynz96dbdh7x+WepqqkyWrPm2NhY5s+fT2qqzk3jpptugqeeQqXRsPalNdgoVdjZ2BllbkOhiuxI+G7QepVQVVVFamoqERERTd73448/Ul1dzd9GDGH4Hx8zvdsMFEKfneq2zeCQMYyNPULBxT/xrTvZtStvdrVFWajgwSnm70hgbgKkG1rFOc689x7lHcpxUbmg9lCbW5YVK1asWCT6/OUME0KsEkIkCiHO1h1GV9YMpFrN8DS4O2QCJZUlRpkjNjaWuXPnXgq6AD6cP5/0rz+Gmhp6BPSkq29Xo8xtUCIjiboI+eQD+lc2rlixgo4dO5K9ZwUl1aXcFjzKmCothjt73s30HVB5qvZz0mhISz7FBYcLdHPojq2trXkFWgC3OA/nlZ3Q8fnnUEXCrZG3olQozS3LihUrViwSfZtkf4our2sE8DXwjTFFNRe7nj3xPgMvu96Lh4OHUeaYP38+ZVdZVtxlV06Xh6t5b1IbyvFRqxmWAt2kTrM+gVdmZiYJCQlMmzaNNRlbca5WMDLmxrAKCI8IZ7YLrOtXaxfxww84do/BczvMGzPPvOIshDExdzL9KOwNhipHuKPrHeaWZMWKFSsWiz6Bl4OUcisgpJSpUsqXgZHGldU8XCdOpC9wHNBUa4wyx9UtPlwF7LxdF43eMdQyWgLphacn//rmLCvm/4Gzs7NegdeqVauQUjJt4kT+FFncStQNY4xZblPO70/DSnlMd+L776mqgPCyXkwfNt284iyEw4lHWBkAi2IALRQeLDS3JCtWrFixWBrN8aqHRgihAE4LIR4HMuByuosloFbr8kkeOvoQkxST+OK2Lww+R0hIyBXbjL0HQkIoxCS4EeYeZvD5jEp4OAKIjIrUy8trxYoVdOvWjZtyc9mzRFK08Q3ja7QQglyDEFoQ5xMhK4uaXzbxXGQNU++dZm5pFkFsbCwLv1xI5UMgtgIb4Km/nsJJ6WT1q7JixYqVBtBnxetJwBF4AugNzALuNaao5uLh4cEqW1uCsko4kXfCKHMsXLgQG5vaONUPEkaC+oTg2Qc+Msp8xuTCz8sJftkVm742Ta54paamsmvXLqZNmwZbtyJsbXEbNsZESs2PUqHEQ2NHYGUOLFrEIZ8avp4GTr2dzC3NIpg/fz6V2TpzWVkO/KHr5zl//nzzCrNixYoVC0WfJtn7pZQlUspzUsrZUso7pJR7TCGuOfg5ONAps4qTucaxlJgxYwYBAQHY2dmBO9gU2zDv1k+YOXOmUeYzJt77j5OtLcbW14aUlBSqqhovWv3+++8BmDp1KiOid/PBkvt1/ShvILyFO6nuIN98k9hoARLu7nG3uWVZBGlpaVBXz9ILEPXOW7FixYqVa2gy8BJCdBRCLBFCxAkhfq07TCGuORT7+dH9QjV55XnkluUafPz09HTS09NZ+NJLyH6zKJ/+Ow///WGDz2MKbNRRRORDjV0JNTU1JCcnN3rtihUr6NevH1WuVWw7vwtlp84mVGoZ+LkEk+oGx/r354uOkpucb8LHycfcsiyCkJAQkLXfBHLp65CQEHNJsmLFihWLRp+txh+Ag8CLwDP1DouiJiKCmNp4yxirXhs2bAAHUFYfQPPdN9jkXjT4HCZDrSYqD/Kl7r+hsTyvU6dOcfDgQV014+ZFAPz/9u48Pqr63v/460MSkIQ1LMqaIAZZrIoCbpWqaAVZXKgUS629va22VdF7a2/tpfchVelP7aZ1qY11u14K1IuihFsrIrhURfZFATGGHdnFSIAQ8vn9MScYbRIScmbOZPJ+Ph7nMZPvzHzncz4MmU/OOd/vd1RO4znNWGF0v29z1xyYUbiUTzvDtwbqovoKkyZNIjMzE2YC/xtry8zMZNKkSZHGJSKSrGpTeJW5+x/d/V13X1SxxT2yOmrWty/9P4Ybsy+nY1b41/7PmjWL7CHZ/Fv5c3xwTi8YOjT090iYnj3J2w2byncA1U8pMW3aNMyMMWPGMOP95zljWxO6tzv6ZKupJm1TOt9dDns7xUbMphfWZkxK4zBu3Djy8/PJ2ZmDvWfk5OSQn5+vC+tFRKpRm8Jrppn92Mw6mVl2xRb3yOqo7bnnMr8Yrim/kLx2eaH2XVJSwuw5s/HTShm8Dk69+iZoyMvldO7MkM3N+Bf607pd6yoLL3dnypQpnH/++aS1TuOdjG1cUZYH6Y2r6Jg8eTL/8Z//wYVdYFEh8DDcefOdTJ48OerQksa4ceNYt24d5eXlrFu3TkWXiEgNalN4XUfs1OJbfL5e48J4BnUsup53HlcBbzc5xIe7Pwy177lz53Kw20H2ZHzGTQuA0aND7T/hmjRh+OJiHrpjPif3PLnKwmvFihWsWrWKsWPHUrr+I65fBKN7XxlBsNGaMGEC+5vuZ94PYN5JwA7YX7Jfo/ZEROSY1Fh4BfN33e7uPb60Jd35puOPP56srCz+tPWPjPjLiFD7LigoIO2cNDpba64YdB107hxq/5HIyODQ4UPk9sqt8hqvqVOnkpaWxujRo+k+fzWPFkDfrze+IxkbNmyAivlArwSyKrWLiIjUUY2Fl7uXAzcmKJZ6MTOeTU/nomWbKdxTyKHD4azr7e7M/NtMWhzfgh9+7SdkPPFUKP1Grfy56WT/MpNNPTexceNGDhz4fMZ/d2fq1KkMGTKErDZZLFj3Ft6lM/TrF2HE0ejevXtseYIKByq1i4iI1FFtTjXONrPbzKxbMl/jBUC7dpy2tZSy8jKKPql+ioS6WL58OZvXbya/1U+5fdC/h9JnMmiyeQvdd5VR1mwf7k5hYeGRxxYsWEBRURFjx47lpQ9fYlDa47z52jMN+7q2Y3Rk1N4GoBA4rFF7IiJy7GpTeH2P2FGv10nia7wAynJyOGNHbCKhsKaUmFEwA5rBVU88QcY3rwmlz6TQsycn7YbdVYxsnDp1KhkZGVx55ZXMWDODds3bcU6PwVFFGqkjo/bm5MD/oFF7IiJSL7WZuf7L13cl5TVeABl9+nByMJfX6p3hLB309LKnSb/N2LT7IxgR7rVjkaqYUqJsB9jnc3mVl5czbdo0hg0bRlbLLApWTGfkRxmk7z8YccDRqRi15+WuUXsiIlIvtZm5PtPMfmFm+cHPeWZ21ArEzI4zs3fNbJmZvWdmvwzas81stpmtDW7b1n83YtqceSZtD8DEsssY3mt4vfvbvn07RR2KOHF/JjnFTeCqq0KIMknk5pK3Gw5wiOzc7CNHvN588022bNnC2LFjeWPDG3zi+7l8DZCltQlFRETqqzanGp8ESoFzg583AXfX4nUHgYvc/TTgdGComZ0N3A7Mcfc8YE7wcyg6nXceDwKnlZ1K3w71X9rm98//HjrCT5Y0xYZcDO3b1z/IZNGsGYNbnsI9XEzP7j2PFF5Tp06lefPmjBw5kpmrX6D5Ifj6yZdFHKyIiEhqqE3h1dPd7wMOAbj7fo4shVs9j6lYPjcj2By4HHg6aH8auKKuQVen60kncVvTprzse5m5Zma9+3tmzTNkHDCufWMPjBkTQoTJpc+rK/jZHbPp16Mfa9eupaysjGeffZaRI0fSokULftXySuY9BZlDGvAs/SIiIkmkNoVXqZk1J1j+1sx6EjuadVRmlmZmS4HtwGx3nw8c7+5bAYLbKtf3MbPrzWyhmS3csWNHbd6OtLQ0euXmsnj7q4yaOord+499PcXNn2xmc8vN9C49heav/aPhT5pajc2fbib7pGy2bNnCiy++yM6dOxk7diwAzee9yaDNwIUXRhukiIhIiqhN4TUReAnoZmaTiZ0e/FltOnf3w+5+OtAVGGRmp9Q2MHfPd/cB7j6gQ4cOtX0Zv96/n5vfiZ02q8/Ixg+WfACPwq1n3wrnngtt2hxzX0lrxgyGTjyJ1zNeBeDuu++mVatWDBs2jPxF+dzZZhl+w/WpdYpVREQkQrUZ1fgycBXwXWAKMMDd59blTdz9E2AeMBTYZmadAILb7XULuWal3boxcHs5AGt2HXvhVVBQwMDd6Xx79juwdWtY4SWXsjLythxgU/F6AJYsWcLhw4eZPn06Dy94mFeytmGP/iniIEVERFJHbUY1znH3Xe4+y90L3H2nmc2pxes6mFmb4H5z4GJgNfAisfUfCW5fOPbw/1l679702APplnbMR7ymrZzGY7sf46bcTjR96ilo3jzMEJNHz57k7YLt7Dly1d6+ffv4/k+/z/Jty7ki59Jo4xMREUkx1RZewXQQ2UB7M2tbadb6XKA2ixV2Auaa2XJgAbFrvAqAe4BLzGwtcEnwc2ha9u9PRjl087bHfMTrnnn3UNyimMt3FcOll6bmaUY4MpdXeTrQ+vPmAzmxdXEuH3cnVFpKSEREROonvYbHbgBuJVZkLeLzkYyfAg8frWN3Xw70r6J9FzCkzpHW0gnnnQfAxMJTOX/8b+v8+oVbFrJ011Jy34XWez6Bb34z7BCTR6tWtN8V3G8HfBLc7w09t0HPvLPguOMiCk5ERCT1VHvEy90fcPcewG3ufmKlWetPc/eHEhhjneT068d4M0qanUiPtj3q/PqHFzxM2uE0bt/QBpo1g1Gj4hBl8thdnMmo6cC2oMEgowS+uxIYErf6WEREpFGq6YgXAO7+oJmdC+RWfr67/3cc4zpmTZs2ZWZODhtLd3Jo/oNc3e9qTmhxQq1eu6tkF1NWTKF8STkn9egDw3pDq1Zxjjhazf6QzyvXXw8lJbEGh9EzmvKL0lL4lQovERGRMNXm4vpngN8AXwUGBtuAOMdVL2d260Z50RLGvzSeRVsW1fp1jjO0zVB8vtP03nvhiSfiGGVyGDduHBMenEDHsztiZnTN68ovBw+OLRE0aFDU4YmIiKSUox7xIlZk9XV3j3cwYbn2wAG+unI97YfEppQYTu3WbWyf2Z42C9vQr7Q155x9dpyjTBIFBSx5dSKtr+7Cutf30eHXHZje51R+fuON0LRp1NGJiIiklNpMoLoSqN25uiTRJC+PdvshO6N1raeUeHvj2xSsKeBvswp44+BB0sePj3OUSaJtW/I+PkTRZxt56cOX2HdoHwNPGwZXhLaSk4iIiARqc8SrPfC+mb1LpaWC3D1przpvcfrp8Je/0ONw7aeUuGPeHSzbsozeu3fRtpzGs0xOMJdXmR/m/vn30zq9BV97azN0OwQZGVFHJyIiklJqU3hNjHcQYet4zjkAdP0kjfmZRy+8Vu9czeyPZnPB4QsYU74dz8zEhtfu9GSDd/zx5JUcBxzg9fWv863iXDLuvw2+dW3UkYmIiKSc2oxqfC0RgYQpt39/dgE3v9uKyXOWHfX5jyx4hKZpTdk9aztjMzKwESNiF5c3BmbktcoltqgAXPHOXrjoEmhSm7PQIiIiUhfVFl5mVgxUdUG9Ae7uSTvPQlZWFj9o25YeHXswpGnNBVTxwWKeWvoUI3JH8MmC52gLMGZMQuJMFh1HX8cM+4A1vbIZ+qvfwnc0jYSIiEg8VFt4uXvLRAYSto39+rF+z8f8bPbPGJY3jAtyL6jyeR/s+oDWx7Umb08eDwAb77+fbpddltBYo2a3387lAA8/DKVo4lQREZE4SdnzSWedcAJnLHuP373zO1756JVqn3dm5zMpuqWIlS+vpFOPHnQdPz51F8Wuyb59sHgx5ObCiSdGHY2IiEhKStnC63x3Hty9lx7Nu7B65+oqn7Pts22UHi7l0MFD7Ht5Ng927IgVFyc40iQwdy60aAHf+Q4sWQJmR3+NiIiI1FnKFl6Zp54KQPdDraqdUuJHs37EgPwBvPrqq3y7tJSvr1jROCcN7d49dltYCG3aRBuLiIhICkvZwqv9WWcB0HUnrN21lsPlh7/w+Ia9G3hhzQuM6DWCl158kSuBJldcAccdF0G0EasovP71X6GsLNpYREREUljKFl65AwfyKZCzcT+ZGZls37f9C48/uvBRAG448wY+fe45soG0a65JfKDJoPJEqem1mdpNREREjkXKfsu2zc5mWVoao+cfYOK0XVil65YOlB3gscWPMerkUezdsJcLd+7kYPPmNLvkkggjjtj06bHrvERERCRuUrbwAri7Tx8sO5u/fuli8ZlrZrKzZCc3DbyJgqkFdAPKvvENmjVrFk2gyeCqq6KOQEREJOWl7KlGgPRTTmHRpk38eNaPuffNe4+0f6PvN3jtu69xUY+LKCgo4A8DBpD19NMRRioiIiKNQUoXXgPbteNbRUUsXj+fvxf+/Ui7mTE4ZzC7du3i/bffZvjw4ZpCQUREROIupU819mnRgmHurClpzj8OxKaUuPn/bqZt87bceeGd/P2FF1gPFO/YEW2gIiIi0iik9BGvdsGUEl22HWZL8RYKdxeSvzifPfv3ALDlySdpDXQeNSrCKEVERKSxSOnCq9ugQZQA3dbvA+Cns39K6eFSbhx0I4cOHSJ3/nyKmzWjidYmFBERkQRI6cLrhM6dKTLjpLV76NuhL8+vfp6LT7yY3u1789YrrzCsrIydX/ua5q4SERGRhEjpwsvM+LhlS77y0afcdeFdANw08CYAih55hBbACePHRxihiIiINCYpXXgBPDl4MCM7d+bkdidzy1m3MKLXCAD+tGoV9/ftS/NLL404QhEREWksUr7w6tS7Nx8WFdGnfR/uH3o/aU3SWLt2Le8UFpL2wx/qNKOIiIgkTMoXXqdnZ/PAwYNsf/nlI21LH3iA7wPDG/MSQSIiIpJwKV945XTvzg3A3jlzjrSd8Ne/Mik9nRPz8qILTERERBqduBVeZtbNzOaa2Soze8/MbgnaJ5rZZjNbGmyXxSsGgK5nn81B4MDKlQB8unkzA3bsYO2pp0JaWjzfWkREROQL4nmBUxnwE3dfbGYtgUVmNjt47Pfu/ps4vvcR3XJzWQs0KSoCYPWvf80goMX3vpeItxcRERE5Im6Fl7tvBbYG94vNbBXQJV7vV520tDS2ZmXR4+OPAUh/7jm2mNHvBz9IdCgiIiLSyCXkGi8zywX6A/ODppvMbLmZPWFmbat5zfVmttDMFu6o51qKezp25NDBg5SXlVG6dStLe/UivWnTevUpIiIiUldxL7zMrAUwHbjV3T8F/gj0BE4ndkTst1W9zt3z3X2Auw/o0KFDvWKYN3w4Z2Zk8O7ChZxTVsbeX/yiXv2JiIiIHIu4Fl5mlkGs6Jrs7s8BuPs2dz/s7uXAY8CgeMYAcFJeHsXFxTzz5z/TpEkTLr0srtfzi4iIiFQpbtd4mZkBjwOr3P13ldo7Bdd/AVwJrIxXDBV6d+jAP4BzH3+cLr16kZ2dHe+3FBEREfkn8TzidR5wLXDRl6aOuM/MVpjZcuBC4N/iGAMAK9ev59zg/itbtjB58uR4v6WIiIjIP4nnqMY3Aaviof+L13tWZfLkyfzXXXfx78HPcz/7jPnXXw/AuHHjEhmKiIiINHIpP3P9hAkTKCkp4WpgWNBWUlLChAkTogxLREREGqGUXyF6w4YNAPxvNe0iIiIiiZLyR7y6d+9ep3YRERGReEn5wmvSpElkZmZ+oS0zM5NJkyZFFJGIiIg0VilfeI0bN478/HxycnIwM3JycsjPz9eF9SIiIpJw5u5Rx3BUAwYM8IULF0YdhoiIiMhRmdkidx9Q1WMpf8RLREREJFmo8BIRERFJEBVeIiIiIgmiwktEREQkQVR4iYiIiCSICi8RERGRBFHhJSIiIpIgKrxEREREEkSFl4iIiEiCqPASERERSZAGsWSQmRUDa0LoqjWwNwX7aQ/sDKGfZNsv5Scx/Sg/NVN+aqb81Ez5qVmq5ifP3VtX+Yi7J/0GLAypn/wU7Uf5UX6UH+VH+UnOfpQf5ecLW2M71TgzRfsJS7Ltl/KTmH7Ckmz7pfwkpp+wJNt+KT+J6ScsybZf1fbTUE41LvRqVvkW5edolJ+aKT81U35qpvzUTPmpWWPMT0M54pUfdQBJTvmpmfJTM+WnZspPzZSfmik/NWt0+WkQR7xEREREUkFDOeIlIiIi0uBFUniZWTczm2tmq8zsPTO7JWjPNrPZZrY2uG1b6TU/N7MPzWyNmV1aqX1e0LY02DpGsU9hCjk/Tc0s38w+MLPVZjY6in0KU1j5MbOWlT43S81sp5ndH9V+hSXkz881ZrbCzJab2Utm1j6KfQpTyPn5ZpCb98zsvij2J2x1zY+ZtQue/5mZPfSlvs4MPj8fmtkfzMyi2KcwhZyfSWa20cw+i2Jf4iGs/JhZppnNCr633jOze6Lap9CFMWzyGIZZdgLOCO63BD4A+gL3AbcH7bcD9wb3+wLLgGZAD6AQSAsemwcMiGI/Gkh+fgncHdxvArSPev+SKT9f6ncRMDjq/UuW/ADpwPaKz0zw+olR718S5acdsAHoEDzvaWBI1PsXQX6ygK8CPwQe+lJf7wLnAAb8DRgW9f4lWX7ODvr7LOr9Srb8AJnAhcH9psAbqfD5cY9oOgl33+rui4P7xcAqoAtwObFfXgS3VwT3LwemuvtBdy8CPgQGJTbqxAk5P98D/l/QV7m7hzFRXaTi8fkxszygI7H/3A1aiPmxYMsKjlS0ArYkbEfiJMT8nAh84O47gue9AjT4I8p1zY+773P3N4EDlfsxs05AK3d/22Pfnv/N5zltsMLKT/DYO+6+NSGBJ0hY+XH3EnefG9wvBRYDXROyE3EW+TVeZpYL9AfmA8dXfAiD24rThl2AjZVetiloq/BkcKrov1LhUHZl9cmPmbUJfr7LzBab2bNmdnxCAk+QkD4/ANcA04IviJRRn/y4+yHgR8AKYgVXX+DxhASeIPX8/HwI9DazXDNLJ/ZF0i0xkSdGLfNTnS7EclWhqv93DVo985PywspP8F02EpgTfpSJF2nhZWYtgOnAre7+aU1PraKt4gtynLt/BTg/2K4NN8rohJCfdGJ/IfzD3c8A3gZ+E3qgEQnp81NhLDAlrNiSQX3zY2YZxAqv/kBnYDnw89ADjUh98+Pue4jlZxqxI6XrgLKw44xKHfJTbRdVtKXMHzYh5CelhZWf4I+aKcAf3P2jsOKLUmSFV/BLfTow2d2fC5q3BYenKw5Tbw/aN/HFvyS7EpzycPfNwW0x8BdS5BRkSPnZBZQAzwftzwJnxDn0hAjr8xM89zQg3d0XxT3wBAkpP6cDuHthcCTwr8C5CQg/7kL8/TPT3c9y93OIrSe7NhHxx1sd81OdTXzx1NAX/t81ZCHlJ2WFnJ98YK27N/iBTxWiGtVoxE5ZrHL331V66EXguuD+dcALldrHmlkzM+sB5AHvmlm6BaOsgn/oEcDKROxDPIWVn+DLciZwQfC8IcD7cQ4/7sLKT6XXXUMKHe0KMT+bgb5m1iF43iXErtdo0ML8/FgwijoYofVj4M/x34P4Oob8VCk4nVRsZmcHfX7naK9pCMLKT6oKMz9mdjexRatvDTvOSNX36vxj2YiNYHBipy6WBttlxEYJzSH2V+McILvSayYQG020hmBkA7HREIuCft4DHqCK0WoNbQsrP0F7DvB60NccoHvU+5dM+Qke+wjoHfV+JWN+iI00WhX0NRNoF/X+JVl+phD7Y+Z9YGzU+xZhftYBu4HPiB3p6hu0DyD2x3Ah8BDBpN0NeQs5P/cFP5cHtxOj3r9kyQ+xI6Qe/P6p6Of7Ue9fGJtmrhcRERFJkMhHNYqIiIg0Fiq8RERERBJEhZeIiIhIgqjwEhEREUkQFV4iIiIiCaLCS0RSisW8aWbDKrWNMbOXooxLRATQdBIiknrM7BRiKzX0B9KIzQE01N0Lj6GvNHc/HHKIItJIqfASkZRkZvcB+4hNtLyP2GTCXyG2hulEd38hWMT3meA5ADe5+1tmdgFwB7AVON3d+yY2ehFJVSq8RCQlmVkWsBgoBQqA99z9f8ysDbElf/oTmxm73N0PmFkeMMXdBwSF1yzgFHcvimYPRCQVpUcdgIhIPLj7PjObRmwZkjHASDO7LXj4OKA7sUWbHzKz04HDQK9KXbyroktEwqbCS0RSWXmwGTDa3ddUftDMJgLbgNOIDTY6UOnhfQmKUUQaEY1qFJHG4O/AzWZmAGbWP2hvDWx193LgWmIX4ouIxI0KLxFpDO4CMoDlZrYy+BngEeA6M3uH2GlGHeUSkbjSxfUiIiIiCaIjXiIiIiIJosJLREREJEFUeImIiIgkiAovERERkQRR4SUiIiKSICq8RERERBJEhZeIiIhIgqjwEhEREUmQ/w9n1yTPwxaBsQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "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": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Additive</th>\n",
       "      <th>Multiplicative</th>\n",
       "      <th>Additive Dam</th>\n",
       "      <th>Multiplica Dam</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>$\\alpha$</th>\n",
       "      <td>4.546459e-01</td>\n",
       "      <td>3.659223e-01</td>\n",
       "      <td>7.771267e-15</td>\n",
       "      <td>0.000189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\beta$</th>\n",
       "      <td>7.794133e-09</td>\n",
       "      <td>7.316443e-19</td>\n",
       "      <td>5.975782e-20</td>\n",
       "      <td>0.000189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\phi$</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>9.446193e-01</td>\n",
       "      <td>0.913789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$\\gamma$</th>\n",
       "      <td>5.243837e-01</td>\n",
       "      <td>1.060914e-12</td>\n",
       "      <td>4.955475e-14</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$l_0$</th>\n",
       "      <td>1.421754e+01</td>\n",
       "      <td>1.454811e+01</td>\n",
       "      <td>1.417767e+01</td>\n",
       "      <td>14.534881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>$b_0$</th>\n",
       "      <td>1.307698e-01</td>\n",
       "      <td>1.661090e-01</td>\n",
       "      <td>2.399716e-01</td>\n",
       "      <td>0.484079</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SSE</th>\n",
       "      <td>5.001687e+01</td>\n",
       "      <td>4.307029e+01</td>\n",
       "      <td>3.530344e+01</td>\n",
       "      <td>39.666447</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              Additive  Multiplicative  Additive Dam  Multiplica Dam\n",
       "$\\alpha$  4.546459e-01    3.659223e-01  7.771267e-15        0.000189\n",
       "$\\beta$   7.794133e-09    7.316443e-19  5.975782e-20        0.000189\n",
       "$\\phi$             NaN             NaN  9.446193e-01        0.913789\n",
       "$\\gamma$  5.243837e-01    1.060914e-12  4.955475e-14        0.000000\n",
       "$l_0$     1.421754e+01    1.454811e+01  1.417767e+01       14.534881\n",
       "$b_0$     1.307698e-01    1.661090e-01  2.399716e-01        0.484079\n",
       "SSE       5.001687e+01    4.307029e+01  3.530344e+01       39.666447"
      ]
     },
     "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": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\hat{y}_t$</th>\n",
       "      <th>$b_t$</th>\n",
       "      <th>$l_t$</th>\n",
       "      <th>$s_t$</th>\n",
       "      <th>$y_t$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2005-01-01</th>\n",
       "      <td>41.721301</td>\n",
       "      <td>-34.969418</td>\n",
       "      <td>49.317727</td>\n",
       "      <td>-7.593396</td>\n",
       "      <td>41.7275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-04-01</th>\n",
       "      <td>24.190405</td>\n",
       "      <td>-35.452731</td>\n",
       "      <td>49.932372</td>\n",
       "      <td>-25.834541</td>\n",
       "      <td>24.0418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-07-01</th>\n",
       "      <td>31.460402</td>\n",
       "      <td>-36.532791</td>\n",
       "      <td>51.126130</td>\n",
       "      <td>-19.182969</td>\n",
       "      <td>32.3281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-10-01</th>\n",
       "      <td>36.634633</td>\n",
       "      <td>-37.397668</td>\n",
       "      <td>52.210116</td>\n",
       "      <td>-15.209764</td>\n",
       "      <td>37.3287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-01</th>\n",
       "      <td>45.097596</td>\n",
       "      <td>-38.467294</td>\n",
       "      <td>53.476795</td>\n",
       "      <td>-7.837304</td>\n",
       "      <td>46.2132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-04-01</th>\n",
       "      <td>27.191816</td>\n",
       "      <td>-40.276313</td>\n",
       "      <td>55.513851</td>\n",
       "      <td>-27.017281</td>\n",
       "      <td>29.3463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-07-01</th>\n",
       "      <td>36.544210</td>\n",
       "      <td>-40.625014</td>\n",
       "      <td>56.224439</td>\n",
       "      <td>-19.713825</td>\n",
       "      <td>36.4829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-10-01</th>\n",
       "      <td>41.449390</td>\n",
       "      <td>-42.041777</td>\n",
       "      <td>57.766084</td>\n",
       "      <td>-15.523320</td>\n",
       "      <td>42.9777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01</th>\n",
       "      <td>50.934403</td>\n",
       "      <td>-41.543765</td>\n",
       "      <td>57.536686</td>\n",
       "      <td>-7.588718</td>\n",
       "      <td>48.9015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-04-01</th>\n",
       "      <td>31.418131</td>\n",
       "      <td>-42.197821</td>\n",
       "      <td>58.150971</td>\n",
       "      <td>-26.874297</td>\n",
       "      <td>31.1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-07-01</th>\n",
       "      <td>38.718290</td>\n",
       "      <td>-42.303417</td>\n",
       "      <td>58.362916</td>\n",
       "      <td>-20.191886</td>\n",
       "      <td>37.7179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-10-01</th>\n",
       "      <td>44.140504</td>\n",
       "      <td>-41.085655</td>\n",
       "      <td>57.181734</td>\n",
       "      <td>-14.982807</td>\n",
       "      <td>40.4202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-01-01</th>\n",
       "      <td>49.315669</td>\n",
       "      <td>-42.961440</td>\n",
       "      <td>58.852914</td>\n",
       "      <td>-8.619795</td>\n",
       "      <td>51.2069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-04-01</th>\n",
       "      <td>32.306929</td>\n",
       "      <td>-43.186468</td>\n",
       "      <td>59.366898</td>\n",
       "      <td>-27.309123</td>\n",
       "      <td>31.8872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-07-01</th>\n",
       "      <td>39.207416</td>\n",
       "      <td>-44.826955</td>\n",
       "      <td>61.095541</td>\n",
       "      <td>-20.925483</td>\n",
       "      <td>40.9783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-10-01</th>\n",
       "      <td>44.551342</td>\n",
       "      <td>-44.899323</td>\n",
       "      <td>61.462001</td>\n",
       "      <td>-17.319727</td>\n",
       "      <td>43.7725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td>54.357955</td>\n",
       "      <td>-46.192151</td>\n",
       "      <td>62.816712</td>\n",
       "      <td>-7.881574</td>\n",
       "      <td>55.5586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-04-01</th>\n",
       "      <td>35.153811</td>\n",
       "      <td>-45.980030</td>\n",
       "      <td>62.831978</td>\n",
       "      <td>-28.447763</td>\n",
       "      <td>33.8509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-07-01</th>\n",
       "      <td>43.066343</td>\n",
       "      <td>-46.227986</td>\n",
       "      <td>63.082485</td>\n",
       "      <td>-20.550579</td>\n",
       "      <td>42.0764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-10-01</th>\n",
       "      <td>45.871156</td>\n",
       "      <td>-46.852335</td>\n",
       "      <td>63.748644</td>\n",
       "      <td>-17.997619</td>\n",
       "      <td>45.6423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-01</th>\n",
       "      <td>57.166477</td>\n",
       "      <td>-48.770316</td>\n",
       "      <td>65.777461</td>\n",
       "      <td>-7.372023</td>\n",
       "      <td>59.7668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-04-01</th>\n",
       "      <td>36.761409</td>\n",
       "      <td>-48.308126</td>\n",
       "      <td>65.649780</td>\n",
       "      <td>-29.816638</td>\n",
       "      <td>35.1919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-07-01</th>\n",
       "      <td>44.932417</td>\n",
       "      <td>-48.798443</td>\n",
       "      <td>66.119177</td>\n",
       "      <td>-21.517279</td>\n",
       "      <td>44.3197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-10-01</th>\n",
       "      <td>48.399507</td>\n",
       "      <td>-49.269581</td>\n",
       "      <td>66.667135</td>\n",
       "      <td>-18.522045</td>\n",
       "      <td>47.9137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-01-01</th>\n",
       "      <td>61.337759</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-01</th>\n",
       "      <td>37.242799</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-07-01</th>\n",
       "      <td>46.842530</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-10-01</th>\n",
       "      <td>51.005064</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>64.470463</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-04-01</th>\n",
       "      <td>39.776728</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-07-01</th>\n",
       "      <td>49.635627</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-01</th>\n",
       "      <td>53.901136</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            $\\hat{y}_t$      $b_t$      $l_t$      $s_t$    $y_t$\n",
       "2005-01-01    41.721301 -34.969418  49.317727  -7.593396  41.7275\n",
       "2005-04-01    24.190405 -35.452731  49.932372 -25.834541  24.0418\n",
       "2005-07-01    31.460402 -36.532791  51.126130 -19.182969  32.3281\n",
       "2005-10-01    36.634633 -37.397668  52.210116 -15.209764  37.3287\n",
       "2006-01-01    45.097596 -38.467294  53.476795  -7.837304  46.2132\n",
       "2006-04-01    27.191816 -40.276313  55.513851 -27.017281  29.3463\n",
       "2006-07-01    36.544210 -40.625014  56.224439 -19.713825  36.4829\n",
       "2006-10-01    41.449390 -42.041777  57.766084 -15.523320  42.9777\n",
       "2007-01-01    50.934403 -41.543765  57.536686  -7.588718  48.9015\n",
       "2007-04-01    31.418131 -42.197821  58.150971 -26.874297  31.1802\n",
       "2007-07-01    38.718290 -42.303417  58.362916 -20.191886  37.7179\n",
       "2007-10-01    44.140504 -41.085655  57.181734 -14.982807  40.4202\n",
       "2008-01-01    49.315669 -42.961440  58.852914  -8.619795  51.2069\n",
       "2008-04-01    32.306929 -43.186468  59.366898 -27.309123  31.8872\n",
       "2008-07-01    39.207416 -44.826955  61.095541 -20.925483  40.9783\n",
       "2008-10-01    44.551342 -44.899323  61.462001 -17.319727  43.7725\n",
       "2009-01-01    54.357955 -46.192151  62.816712  -7.881574  55.5586\n",
       "2009-04-01    35.153811 -45.980030  62.831978 -28.447763  33.8509\n",
       "2009-07-01    43.066343 -46.227986  63.082485 -20.550579  42.0764\n",
       "2009-10-01    45.871156 -46.852335  63.748644 -17.997619  45.6423\n",
       "2010-01-01    57.166477 -48.770316  65.777461  -7.372023  59.7668\n",
       "2010-04-01    36.761409 -48.308126  65.649780 -29.816638  35.1919\n",
       "2010-07-01    44.932417 -48.798443  66.119177 -21.517279  44.3197\n",
       "2010-10-01    48.399507 -49.269581  66.667135 -18.522045  47.9137\n",
       "2011-01-01    61.337759        NaN        NaN        NaN      NaN\n",
       "2011-04-01    37.242799        NaN        NaN        NaN      NaN\n",
       "2011-07-01    46.842530        NaN        NaN        NaN      NaN\n",
       "2011-10-01    51.005064        NaN        NaN        NaN      NaN\n",
       "2012-01-01    64.470463        NaN        NaN        NaN      NaN\n",
       "2012-04-01    39.776728        NaN        NaN        NaN      NaN\n",
       "2012-07-01    49.635627        NaN        NaN        NaN      NaN\n",
       "2012-10-01    53.901136        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": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>$\\hat{y}_t$</th>\n",
       "      <th>$b_t$</th>\n",
       "      <th>$l_t$</th>\n",
       "      <th>$s_t$</th>\n",
       "      <th>$y_t$</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2005-01-01</th>\n",
       "      <td>41.860019</td>\n",
       "      <td>-36.529901</td>\n",
       "      <td>51.244121</td>\n",
       "      <td>0.815914</td>\n",
       "      <td>41.7275</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-04-01</th>\n",
       "      <td>25.838329</td>\n",
       "      <td>-35.866598</td>\n",
       "      <td>50.735921</td>\n",
       "      <td>0.495384</td>\n",
       "      <td>24.0418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-07-01</th>\n",
       "      <td>31.659094</td>\n",
       "      <td>-37.283662</td>\n",
       "      <td>52.060074</td>\n",
       "      <td>0.613001</td>\n",
       "      <td>32.3281</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2005-10-01</th>\n",
       "      <td>35.189675</td>\n",
       "      <td>-39.168718</td>\n",
       "      <td>54.186389</td>\n",
       "      <td>0.664203</td>\n",
       "      <td>37.3287</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-01-01</th>\n",
       "      <td>44.928949</td>\n",
       "      <td>-40.305567</td>\n",
       "      <td>55.705171</td>\n",
       "      <td>0.815073</td>\n",
       "      <td>46.2132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-04-01</th>\n",
       "      <td>27.933400</td>\n",
       "      <td>-42.087113</td>\n",
       "      <td>57.755569</td>\n",
       "      <td>0.493065</td>\n",
       "      <td>29.3463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-07-01</th>\n",
       "      <td>35.824218</td>\n",
       "      <td>-43.100038</td>\n",
       "      <td>59.126477</td>\n",
       "      <td>0.610108</td>\n",
       "      <td>36.4829</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2006-10-01</th>\n",
       "      <td>39.768767</td>\n",
       "      <td>-45.643430</td>\n",
       "      <td>61.906160</td>\n",
       "      <td>0.661726</td>\n",
       "      <td>42.9777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-01-01</th>\n",
       "      <td>51.174397</td>\n",
       "      <td>-45.120736</td>\n",
       "      <td>61.855424</td>\n",
       "      <td>0.813614</td>\n",
       "      <td>48.9015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-04-01</th>\n",
       "      <td>30.814215</td>\n",
       "      <td>-46.408183</td>\n",
       "      <td>63.134340</td>\n",
       "      <td>0.490309</td>\n",
       "      <td>31.1802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-07-01</th>\n",
       "      <td>39.009005</td>\n",
       "      <td>-46.386264</td>\n",
       "      <td>63.326558</td>\n",
       "      <td>0.608240</td>\n",
       "      <td>37.7179</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2007-10-01</th>\n",
       "      <td>42.486130</td>\n",
       "      <td>-46.170456</td>\n",
       "      <td>63.142772</td>\n",
       "      <td>0.660464</td>\n",
       "      <td>40.4202</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-01-01</th>\n",
       "      <td>52.174114</td>\n",
       "      <td>-46.759046</td>\n",
       "      <td>63.700745</td>\n",
       "      <td>0.813407</td>\n",
       "      <td>51.2069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-04-01</th>\n",
       "      <td>31.677045</td>\n",
       "      <td>-47.835416</td>\n",
       "      <td>64.869947</td>\n",
       "      <td>0.489565</td>\n",
       "      <td>31.8872</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-07-01</th>\n",
       "      <td>40.035566</td>\n",
       "      <td>-49.239072</td>\n",
       "      <td>66.466994</td>\n",
       "      <td>0.607690</td>\n",
       "      <td>40.9783</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2008-10-01</th>\n",
       "      <td>44.516066</td>\n",
       "      <td>-49.574721</td>\n",
       "      <td>67.064385</td>\n",
       "      <td>0.659603</td>\n",
       "      <td>43.7725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-01-01</th>\n",
       "      <td>55.343283</td>\n",
       "      <td>-50.601802</td>\n",
       "      <td>68.188673</td>\n",
       "      <td>0.812789</td>\n",
       "      <td>55.5586</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-04-01</th>\n",
       "      <td>33.772845</td>\n",
       "      <td>-51.515006</td>\n",
       "      <td>69.283811</td>\n",
       "      <td>0.487890</td>\n",
       "      <td>33.8509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-07-01</th>\n",
       "      <td>42.644046</td>\n",
       "      <td>-52.025095</td>\n",
       "      <td>69.969874</td>\n",
       "      <td>0.606390</td>\n",
       "      <td>42.0764</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2009-10-01</th>\n",
       "      <td>46.778562</td>\n",
       "      <td>-52.310277</td>\n",
       "      <td>70.364685</td>\n",
       "      <td>0.658714</td>\n",
       "      <td>45.6423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-01-01</th>\n",
       "      <td>58.009042</td>\n",
       "      <td>-54.093333</td>\n",
       "      <td>72.210619</td>\n",
       "      <td>0.812312</td>\n",
       "      <td>59.7668</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-04-01</th>\n",
       "      <td>35.648092</td>\n",
       "      <td>-54.499545</td>\n",
       "      <td>72.908816</td>\n",
       "      <td>0.486531</td>\n",
       "      <td>35.1919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-07-01</th>\n",
       "      <td>44.784147</td>\n",
       "      <td>-55.163485</td>\n",
       "      <td>73.682353</td>\n",
       "      <td>0.605416</td>\n",
       "      <td>44.3197</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2010-10-01</th>\n",
       "      <td>49.174608</td>\n",
       "      <td>-55.389037</td>\n",
       "      <td>74.028798</td>\n",
       "      <td>0.657846</td>\n",
       "      <td>47.9137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-01-01</th>\n",
       "      <td>60.967374</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-04-01</th>\n",
       "      <td>36.993488</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-07-01</th>\n",
       "      <td>46.712003</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2011-10-01</th>\n",
       "      <td>51.482604</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-01-01</th>\n",
       "      <td>64.455898</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-04-01</th>\n",
       "      <td>39.016675</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-07-01</th>\n",
       "      <td>49.291081</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-01</th>\n",
       "      <td>54.319649</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            $\\hat{y}_t$      $b_t$      $l_t$     $s_t$    $y_t$\n",
       "2005-01-01    41.860019 -36.529901  51.244121  0.815914  41.7275\n",
       "2005-04-01    25.838329 -35.866598  50.735921  0.495384  24.0418\n",
       "2005-07-01    31.659094 -37.283662  52.060074  0.613001  32.3281\n",
       "2005-10-01    35.189675 -39.168718  54.186389  0.664203  37.3287\n",
       "2006-01-01    44.928949 -40.305567  55.705171  0.815073  46.2132\n",
       "2006-04-01    27.933400 -42.087113  57.755569  0.493065  29.3463\n",
       "2006-07-01    35.824218 -43.100038  59.126477  0.610108  36.4829\n",
       "2006-10-01    39.768767 -45.643430  61.906160  0.661726  42.9777\n",
       "2007-01-01    51.174397 -45.120736  61.855424  0.813614  48.9015\n",
       "2007-04-01    30.814215 -46.408183  63.134340  0.490309  31.1802\n",
       "2007-07-01    39.009005 -46.386264  63.326558  0.608240  37.7179\n",
       "2007-10-01    42.486130 -46.170456  63.142772  0.660464  40.4202\n",
       "2008-01-01    52.174114 -46.759046  63.700745  0.813407  51.2069\n",
       "2008-04-01    31.677045 -47.835416  64.869947  0.489565  31.8872\n",
       "2008-07-01    40.035566 -49.239072  66.466994  0.607690  40.9783\n",
       "2008-10-01    44.516066 -49.574721  67.064385  0.659603  43.7725\n",
       "2009-01-01    55.343283 -50.601802  68.188673  0.812789  55.5586\n",
       "2009-04-01    33.772845 -51.515006  69.283811  0.487890  33.8509\n",
       "2009-07-01    42.644046 -52.025095  69.969874  0.606390  42.0764\n",
       "2009-10-01    46.778562 -52.310277  70.364685  0.658714  45.6423\n",
       "2010-01-01    58.009042 -54.093333  72.210619  0.812312  59.7668\n",
       "2010-04-01    35.648092 -54.499545  72.908816  0.486531  35.1919\n",
       "2010-07-01    44.784147 -55.163485  73.682353  0.605416  44.3197\n",
       "2010-10-01    49.174608 -55.389037  74.028798  0.657846  47.9137\n",
       "2011-01-01    60.967374        NaN        NaN       NaN      NaN\n",
       "2011-04-01    36.993488        NaN        NaN       NaN      NaN\n",
       "2011-07-01    46.712003        NaN        NaN       NaN      NaN\n",
       "2011-10-01    51.482604        NaN        NaN       NaN      NaN\n",
       "2012-01-01    64.455898        NaN        NaN       NaN      NaN\n",
       "2012-04-01    39.016675        NaN        NaN       NaN      NaN\n",
       "2012-07-01    49.291081        NaN        NaN       NaN      NaN\n",
       "2012-10-01    54.319649        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": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:307: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  layout[ax.rowNum, ax.colNum] = ax.get_visible()\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The rowNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().rowspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n",
      "/usr/lib/python3/dist-packages/pandas/plotting/_matplotlib/tools.py:313: MatplotlibDeprecationWarning: \n",
      "The colNum attribute was deprecated in Matplotlib 3.2 and will be removed two minor releases later. Use ax.get_subplotspec().colspan.start instead.\n",
      "  if not layout[ax.rowNum + 1, ax.colNum]:\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 6 Axes>"
      ]
     },
     "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": "3.8.2"
  },
  "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
}
