{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Seasonality in time series data\n",
    "\n",
    "Consider the problem of modeling time series data with multiple seasonal components with different periodicities.  Let us take the time series $y_t$ and decompose it explicitly to have a level component and two seasonal components.\n",
    "\n",
    "$$\n",
    "y_t = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t\n",
    "$$\n",
    "\n",
    "where $\\mu_t$ represents the trend or level, $\\gamma^{(1)}_t$ represents a seasonal component with a relatively short period, and $\\gamma^{(2)}_t$ represents another seasonal component of longer period. We will have a fixed intercept term for our level and consider both $\\gamma^{(2)}_t$ and $\\gamma^{(2)}_t$ to be stochastic so that the seasonal patterns can vary over time.\n",
    "\n",
    "In this notebook, we will generate synthetic data conforming to this model and showcase modeling of the seasonal terms in a few different ways under the unobserved components modeling framework."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Synthetic data creation\n",
    "\n",
    "We will create data with multiple seasonal patterns by following equations (3.7) and (3.8) in Durbin and Koopman (2012).  We will simulate 300 periods and two seasonal terms parametrized in the frequency domain having periods 10 and 100, respectively, and 3 and 2 number of harmonics, respectively.  Further, the variances of their stochastic parts are 4 and 9, respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First we'll simulate the synthetic data\n",
    "def simulate_seasonal_term(periodicity, total_cycles, noise_std=1.,\n",
    "                           harmonics=None):\n",
    "    duration = periodicity * total_cycles\n",
    "    assert duration == int(duration)\n",
    "    duration = int(duration)\n",
    "    harmonics = harmonics if harmonics else int(np.floor(periodicity / 2))\n",
    "\n",
    "    lambda_p = 2 * np.pi / float(periodicity)\n",
    "\n",
    "    gamma_jt = noise_std * np.random.randn((harmonics))\n",
    "    gamma_star_jt = noise_std * np.random.randn((harmonics))\n",
    "\n",
    "    total_timesteps = 100 * duration # Pad for burn in\n",
    "    series = np.zeros(total_timesteps) \n",
    "    for t in range(total_timesteps):\n",
    "        gamma_jtp1 = np.zeros_like(gamma_jt)\n",
    "        gamma_star_jtp1 = np.zeros_like(gamma_star_jt)\n",
    "        for j in range(1, harmonics + 1):\n",
    "            cos_j = np.cos(lambda_p * j)\n",
    "            sin_j = np.sin(lambda_p * j)\n",
    "            gamma_jtp1[j - 1] = (gamma_jt[j - 1] * cos_j\n",
    "                                 + gamma_star_jt[j - 1] * sin_j\n",
    "                                 + noise_std * np.random.randn())\n",
    "            gamma_star_jtp1[j - 1] = (- gamma_jt[j - 1] * sin_j\n",
    "                                      + gamma_star_jt[j - 1] * cos_j\n",
    "                                      + noise_std * np.random.randn())\n",
    "        series[t] = np.sum(gamma_jtp1)\n",
    "        gamma_jt = gamma_jtp1\n",
    "        gamma_star_jt = gamma_star_jtp1\n",
    "    wanted_series = series[-duration:] # Discard burn in\n",
    "\n",
    "    return wanted_series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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EYE/rnejRYbLG5jSkfGK4DpFMF4mHdKIhnanMFERPYS3tBzQPMSjycGc+v23b2yA0wUR2+Gp1e8OjYFqEAxpPjz/NbR23cfc2NQ3nQjJbGoe5TLFkmboImzvI2NNqLH3UFa7Fn7VnOJY8xuv63lT6ThFDwEk+m8sIe0/r7Qi9wLnFM6va3AzwieE6xHymSHMsBMC3zn0LhCQ1o6pf+lrURuazLjE4Suj1A6oKY6xw8Ep3d1NASknBtNG0IifmTnDnljv5f992E3dtbeU9dw8Sd8qFk5liKfHsIi53AfD89PNXvN8bHW7y+HxGbZT0mr7Xlr6Lh8uhpFzRKnkMAHvb1ft0evGFK9fZawj+stvXIfKmVQpN/Gj0RzSwjZTRBlDyGGacUFLYsYK64l1E5ABJeegq9Hjjw7AkUsKiHMKSFvs69xEO6DzwG/cAcPTiIqBWYN3aFlv2v036IAsyzBOjz9AuXs7LtrZe8f5vVBSceQinlp6ht6GXG9u2o4oeKYWSipZNKm8u8+R6E93YxVaGUkeuRrevOnyP4TpEwbAJBzWWikscmT3CQHRf6Tt3G8/kCo8BoEPbR147x3x+/sp2eBPAVUAzxikEgr2de5d97xI5lJcncdEQDhO1d/DYyAF+9R+eXf/ObiIoj8Hk1OIhXtn7SqLBsi0cD3lyP9liKdwHKidhZbcykj26KddL8onhOkTBqX55duJZLGnxG3f9NK/a1c5dW1tpiqqyyNkVOQaA3vBeEJLnp/yQRb3hJjmnCifZ2bKTxlDjsu/dUBKoajIvYqEAenEbS9YY6WJ201bCrAcKpoUWGado53l598vRNMErd7YDMOsJ663M/USCGmZ2GzlriQ9/62H+7LubqzjAJ4brEG7N9ZPjTxILxHjlwJ184X0v54HfuKekgGY9VUku+uO7kXaAg1N+nqHeUMRgczF/gn0d+1Z9H63hMcTDOnahB5BokYnSJDgfa0fesNFjFwDY16nG5S/erby5V+1sL3kMC1ljmVenPIZtADx18SBPrdimdaPDJ4brEK7H8NTEU9zVdRdBLVj6rkwMq0NJLdEYVm6Ag5PPcWYqdWU7vcFRMCy08CRFO8ftnbev+j4WrEUMAfIZtYKMHrlYWiXXx9pRMC302AW6Y320R5Wn0NUU4fSf/DS/9urty94Pt6ADIKhraFY7Ua2ZtDjFwiZbldgnhusQBdPC1mcZTY1yT889y75zFdCsswR02PPgN0aDWNltnJo/xZs+/n1G57JXrtMbHEXLRo+pUmDXMvUioGuEnNnOK0NJ/S0x5peiSDOOHrnIgu8x1A25ooUeHeaWtuU5H3csvJ6cuyCli0hAp1XfhaGPbrp9THxiuA6RN2wy2nEAfqrnp5Z9p2nC2aVKxaljKx58K7sNiY0WGfb3gK4jCoaNHh2mKdhGb0PFbURKY9GxwmPY0REHBFa+Fy0yzsImU0LriancGFogU9GLA5aVqK4ihqBOXAwggzMsFTKlnRE3A3xiuA5RMC0WOUFXvIvBxsFV37vhpPaGMEG9PMSDbSqUhNTQY+eZy/iWab1QMBUx7Gi8hWpblccdJdS+QgHt6GwAwMr3oIWnmEln1rezmwjDmWMA3LFltRcHK6r2KhCDLPYghESEpkhtouVkfGK4DpE3LeatU9zReUdFJdTgEEN3U2TZ8cG2OMgQVq4PPXa+VNLqY+2YzSXRQvPsbLqpqowbtmiLLw8lDbTGCGgCO9+DEDbnl4bWta+bCWO5E0grwo2tOyt+7w0lda4ghnBAI5/eAoAeGd9U4SSfGK5DFOQseblQMZYNZY9hJTE0hAN0JMKY2W3o0TEmU34Cul44u6DKGW9o3lNVJhbS0QS0xJYTQ1DXlDeXVyGo4dTp9evoJsNk4QR2bisBXa/4/cpQqxfhoM7sYgxpRdAiE5sqAe0Tw3UGKSVW6DxQOckJqvwRVhMDwNa2GFZuECEszi2dWr+ObjKcT51ESsHulhurysRCOq3xMJq22svb0dGAMFvBjjCZ9z2GemA+P8+SdRG9uK2qzLKqvRWE3d4QYnqpiJXvRg9PbCqPwV8S4zqDYUm06AVCIsbO5srusYuupuiqY4NtcQ6OKct0IucroHphJHMKu9hBcyRRVaa9IVx145c37elC1wTP5vuZ186tVzc3FZ6dVLPIg8buqjLeUJK+grDdVQTsQjfB5oPMZTdP6NUnhusMBVOV33VFdqNrld3jVF4trd3TXNljkGYj0mxgFl8B1QNSSsayp7BzO0prU1XCH/7sHopmZWL4+Tv7+Pk7+3jdZwZJyh9h2VbV8fVxeTgwcQCdCFG5ukDDhbthUiX0OMRg5bsJaUVGFkdYvi39xoUfSrrOMJtZRAtP0R+rHst2N+Nxt5P04p4d7Qy0xmnUtpLBX4K7HpjITJC1FrHy/YQD1ZV5e0O4pGyqoSXUjxQG45nxendz0+GZyWdoEjcQCQSrylSrIIPlHgPAhdTmWYK7Xns+f0YIMS2EOOo51iqE+IEQ4ozzu8Xz3e8KIc4KIU4JId7sOX6ns0/0WSHEx0WtUdukeGH2BYSQbGuoTgyux9BdIZR052ALj/+319Ed3YmpT1CwNo97vF44OqseeyvXV9MCvRx0hgcAOL94fs392syYzc1yYekCcfuGVcucV0LrikoxKHsMmtGFlBoXs5sn9Fovj+GzwFtWHPsw8IiUchfwiPM3QoibgfuAPc7//J0Qwh25TwDvB3Y5Pyvb3PR4cfYwUmpsS1Qvi3yFs0jYlqZwVZm++E4QNieTfgXMWnE0eRSNAHahe83E0BNXYQ+fGNaG40k1ATRkbb0kMTz8wVfzg99+9arj7hL2TZEYutnJTGHzjEldiEFK+Tgwt+LwO4DPOZ8/B7zTc/x+KWVBSnketTj6XUKIbqBRSvmUVOvcft7zPz4cnJg7gl3ooinSUFXmL9+9l8d+57U1wxo7m1T1zHOTm3O9+Xri6OxRWgKD6CJIQF/bK9UUasY24wwtbB7rtN6YTRc4kVTlw6LYc0my3tmZoK1htRHV1RRBCGiKBgnLPhbt0XXp77WI9cwxbJFSTgA4vzud472A9w6POcd6nc8rj6+CEOL9QoiDQoiDMzMzde/4tQrLtji7eAIrN1DzYY8Edba2x2u2ta2pH2lFODqzuZYTrjdsaXMieYKWwHZCayQFUMs928UOhhaUdbqZlmGoB2bTBfb/ycN86+SzDCQGMMzQZYWSKiGoa2xJREhEgzSIXookyRqbY32xq5F8rpQ3kDWOrz4o5SellPullPs7Ojrq2rlrGecXz5O3sli52knOy0E8HMDK9zK06M9lWAsupi6SNtI0iMGaFUmXi0hQxy50cmHpPF85OMqO3/tOaaVcH5eGOwnt/NIZbmq7SW1qtYbw3i29jWxvj9Ooq2qkzeLJrScxTDnhIZzf087xMaDfI9cHjDvH+yoc9+HgxdkXAZTHsEYlFA5q2PleRtJnMWwDKaW/qN5LwPE5FcuOy61rzi9A2WNYKi7y0HG1BeXfPbo5lFE9kDcs0LJooTl2Nt1A3rResscA8L9/+Q7+58/dViKGswtn69XVaxrrSQzfBN7rfH4v8A3P8fuEEGEhxDZUkvkZJ9yUEkLc7VQj/Yrnf3wAL868SFRPIIttRNboMUSDOla+B1ManJw9y9v/9gle8dEfcmx8sU693Rw4OXeSgAgQsrvX7MVB2WMAiMTV5jBfPDDs7+p2mcgWLfTIBACy0LtmjyEc0AkFNJoC3SCDPjH8JBBCfBl4CrhBCDEmhHgf8FHgXiHEGeBe52+klMeAB4DjwEPAB6SU7lP/m8CnUAnpIeC79ejfRsGR2SP0xXYD2po9hmhIxy50AfDQmcMcvbgEwEhyc8RQ64UTcyfY3rwd09br4jGEAzp2UYVHk0WViiuaNjMpP5x0OcgZFlrkIgB2ocfZ7bAehB1AM7ZsmlBSXWY+Syl/scpXb6gi/xHgIxWOHwRuqUefNhqyRpazC2d5Zft9QO0Zm5eDSEDHLrSjoTO8NASodZeS/lLcl43/8a1jHF46xhsHX8PEnF2nHIOGNJoJaWEWzDFALecwncrT3xpbc/sbHbmihR4ZxzYakWbc2e2wPrkfaXRwYenC2jt5HcCf+Xyd4FjyGLa06QztAlizFaTWiAnQGupjPFuuz573ieGy8Q8HXiRjLjDYsKu03epaocZVY0u0n5Q1TlBXNRnTS77HcDnIGSZaZBw730uqYKpxqYPHEA5oWIU2JjITGNbGX0zPJ4brBC/OqMRza0AtnFcPjwGgNTTAVL68NIbvMVwepJSlkMWZsSYKplWnclU1Lp2RAXJMsLVNlR1P+6Gky8JiPosWmsHK95SMnLqE+IIaRqEVW9p85sBz/Oo/PMM3Dl9cc7vXKnxiuE5wZPYIg42DaFJNbFurdRoJqaFv0vtZMqdAFOltjvq7ul0msk7IQkpBeqnTsUzrkWNQbbSG+jBEkp4WHV0TTKfya257I0JKyY9Oz/ClAyPkihajmSGEkITtfmbT6lmuS44hoGMW2gD4zsmjPHpqhj/85jHUXNyNB3911esAQzNpDk0d4e6e/RTyFkJQCjG8VIR0DSGgQVNzCCOxGToSncz7G9FfFjIFEy08jiy2kZMBCka+brFsQFXBAFponvaGqB9KqoJj40u89zPPAGqG8nhGLXTXGtjGxKIi08bI2tVcOKghi4oYUtYk0M181mA4mb3kZNLrEb7HcB3gnX//XeYK0+xuvom8aRMJ6DVXhbwcCCGIBnUiUlUmRWJztMVDJNM+MVwO0gUTPXIRK99DKm+SN6065RjUK5nQFTHIwDSdiYgfSqqC01PlXQgXcwaThXNIM0ZrpJNxZ15OU7T66qqXi3BAR1px4oE4WXuSwTZVCHBodH7NbV+L8InhOkBWjAAwMd1BwbDqErIAZZ3qdhsgCEaStMRDvsdwmZhKz6OFFqDYSypvksqbNEbXbpm6uZ+oUHMZDG2GzkTYJ4YqGJpJlz6n8gazxXOIYi8N4WBpx7X6EIMGCLrj/RSYZl9/M7GQzuGRhTW3fS3CJ4brAO2tU0gpePpkuG7ld6AmuRlmgBCtiGBSeQyZ4oaNm9YTJ+bUGlNN+laW8gYL2WJdFJAbSpJ2FGnGycspOhJhfx5DFZybybCtPY4mYDGfY8kaRbf6aAiXSbopVr9x6Yr1YuozNEaD7O1r5vCoTww+rhLy2jB2oZO5lCBv1CdkASpumjMsQnYnMjBDSzxE0bTJFP1ZtpfC0KJarrw7soPpVAFbQnN09Zr+Pylc0l/MGtjFNjJyis5EmGSmgGlV3v1tM2NoJs2OjgYawgHGM8PYmESsAeIeYmiM1MtjgI5ILzIwRzQk2NoeY3xxYxYF+MRwjUNKiRUcxc73spgzSOXNZdbQWhAN6uSLFprVgaFN0+JYVv5chsq4uJDjQ195gafPJbmQOo1tNNLX1FFaAbUelqmmCUIBjWSmiF1sY8mcoCMRRkqY88N8y2DZkguzWXZ0xElEgkzk1azkuBhc7jHUI5TkhG+bg90IYUNgnpZYiPkN6mH7VUnXICYX8wR0QXtDmJGlCUQgBcV+MkWL2XSBlvjaH3RQ7nHetLCL7VjBLOGQsn6SmaI/y3YF8obFO//3j5lJFRACLhpD2PkeurvL26fWQwEBRAIac5kittFOyjxEQ1QpnrlMkc7E6u1aNyvG5rMULZsdHQ0kIgHmjHNoMkyD3kU8rLzqgCaIhepTrgoQcXYPKDJNb7wH05Ys5c26jf21At9juMbww5NTvP4vH+O+Tz6Nadk872yk0xlWE9uG57I0x9YesgDlMeSKFlZeleEVtSnA9xgq4bFTM6U4/0Iuw1xxDCvfQ5dn+9TmehFDUC95DACmNgvAnF8xtgwX51XVUV9rlEQkwJI9TNjuIxYMlkJJTdHgmiv4oOwxaJZaxyorp2lx3sON+L74xHCN4S++d5qgrnF2Os0/PzfGkZmjzlaeihgWskYp5LNWRII6ecMml1PbcaftScCf/VwJ33phnPaGEC/b2sJ49jwSG7vQw5bG8s5f9SLscFBjLlPALqotWnNSEbY/LsvhVmp1JiI0RHRyYhTd7CcW0kuhpHpZ8m5eL5+LI+0gKWuS1qxKV8kAACAASURBVAY13hsxxOcTwzWGmXSBn76lixu7Enzt0EVOzh/HLmxhsLW5JNNSJwUUCWrkDYtspgmBYK6otr/YiBbQWmDZkkdOTvGWW7robIyQNNTaUhF7gIQnsVm/UJLOXLrsMSyaahlpv5R4OVwPrrMxjB5KIkUBUewlEtKJhxQxJOrmxSlVOZdV47JgTNDqeww+rgRsWzKXKdLeEOaGrgTji1nOLZ3EyvXR31KO+dczlLSYM7BsnUSgk6nsGEFd+JbpCsxliuQNm91bEnQ0hEnLYYLEientJDyzapvr6MllihbYURLBZmbzak0ef/Lhckyn1GzzRDiAEVDrfVm5XqJBfVkoqR5wPYakQ9izhTFa4+o93Ijvi08M1xCW8gaWLWmNh+hqjDCdnSRjLmHn++hvXb9YNkBrqJfhpWFaYiHmMn7NvBfuOkWdiTBt8RBWcIwo/TSEg6XlFsIBrS5r8kDZOgXobehnLD1KUzTor2O1AtOpAp2NYYQQZBlG2kHyuXaiQb1E2PUjBjUmSSfEN5OboCmqxtv3GHysK9xFv9oaQnQ2RrCDasazle9dViVUr6qkqKdaoyPSy0hqhJZ4kLnMxl9W+CeBG7LoSIRpbQighSexcj00hAOlUFI9q1K8BDOQGGB4aZi2eMgnhhWYSRVKVVoL9jnsfA9LOZtYyOsx1Kfw0vUY5jJFpNGGKQ1S5iyhgObnGHysL5LOpu/tDWG6GiNokYsIAtiFrmXEUK9QUsQzg7o71kfGyNAYL/gewwp4k5yWPoXQTBYXO2kIB0pJznqFkWD5yrnbmgaZyk7RHFfWqo8yplMFOhrCWLZFsngOK9+LlIpYG5xy1bp5DI4Xl/TkfkbTo7Q6cxk2GtadGIQQF4QQR4QQh4UQB51jrUKIHwghzji/WzzyvyuEOCuEOCWEePN69+9aghvWaWsI0dUURo+OEjB7CGpBEuFAqR67bslnj8fQ1zCgjkXnmM/6HoMXXo9h0b4AQCHTTdwZE10TdZn17MINJTWEA2xt6gcgFltk3vfklmHGCSWdXzyPIQtYuT5AecKux1CPWc/gDSWViWFkaYSWeGhDethXymN4nZTydinlfufvDwOPSCl3AY84fyOEuBm4D9gDvAX4OyFEfQK31wFcj6EtHqY1HkCPjpJL9dMYUbXYrvVTt3JVj2U62KiIQQvNlvrhQ2EmVSARCRAJ6kwXziHtAHaxnYZwACEEDeEAjesQSrpzsIUBZ1xC0fkNmeR8qcgbFos5g46GMMeSxwCw84oYYiGdzkSE+17Wz+tu7KzL+YRQM9IBoloLYT3MaGrUCfFtvPflaoWS3gF8zvn8OeCdnuP3SykLUsrzwFngrqvQv6sC98VviQVZsC4gNAMjM7gskSZE/awgb47h7sFdBEQAS59hKW9i+OvylDCTKtCRUPMVRtJnsAvdQDnBubUtxvaO+q3JnzPUWlV3bWulL6GUnQwkmc8Wse2Nt/zCS4G3VPVY8hhhPVqa9xENKi/uoz93G7u3JOp2Tjf0Gg+H6E/0M7I0QnMsuCE97CtBDBL4vhDiOSHE+51jW6SUEwDOb5fWe4FRz/+OOceWQQjxfiHEQSHEwZmZmXXs+pVFMl2kJRYkoGscTb4AgJUbpMkJHTVFgzRFg2ja2mdyglouAOCm7kZaY1F6E73kcWY/b8CE2kvFdCpPZyKMlJIzC6eg2APAe+4eBOD+99/Dh958Q93Od2RsEVDE0BJuIR6MY4gZLFuSypt1O8/1jFlPPu5Y8hjbEjfgqrPX3NCxLud0945OhAOKGFIjxEMBchtw0ckrQQyvkFLeAfw08AEhxKtryFbSeKtMJCnlJ6WU+6WU+zs61uchuBpIZgq0NSjL9ND0IexiC9Js4pdfrsIJbQ0h2hvCtZr4iWA61ue771RW6UBigCVLTabyK2DKcKtfLqYvkiqm+C+vfh1H/vBN7HKs0WhIJ1iH/Z5dvNZRbLf1NSGEoK+hj4w9DUDW8IkBKCnjUABOzZ1i35ZbuGOgmc//+7vWbT0pN8/QGA0ykBhgLDVGOAAFc+MRw7ovoielHHd+TwshHkSFhqaEEN1SygkhRDcw7YiPAf2ef+8Dxte7j9cKZtNF2uIhpJQcmj7EDc23ces9gyXF/aE330gqXz+39d/c0Us8HOBnblW7hQ02DvLMxLOA9Nfl8WDaCSWdnDsJwD29ty2b8Vxv/MHP3MwH791dqk7qT/RzeOoUwIa0Tl8KCqYKdc4ZIxSsArd33srv/cdXrOs5Qw7539LbyEDjAHkrj62nyBsbL+y6rh6DECIuhEi4n4E3AUeBbwLvdcTeC3zD+fxN4D4hRFgIsQ3YBTyznn28lrCUM2iKBhlLjTGbm+W+217NH73jltIiYNva49zW13yJVi4f4YDOz+7tKYWmBhoHKNh5RCDFkh+yAJQ1mC1atMZDnJg7gS50drXsWtdzBnRtWUlyf6KfheIkYJfyD5sdeec+jGbUvhh72ves+zlH57MA7OtvoT+h7NcCUxRMa8Mtvb3eHsMW4EFHsQWAL0kpHxJCPAs8IIR4HzACvBtASnlMCPEAcBwwgQ9IKTfNm5A3LKIhneennwdgX+e+K3r+wYSKmWuhWTIFnxigbJmGAxqH506xrWkbkcCVXfq6L9GHKQ1EIFVSiJsd7rgMp0+RCCZKino9YVhK+d8x2EIoooypnJzClgOYtiSo1yf3dy1gXYlBSnkO2FvheBJ4Q5X/+QjwkfXs17UKd9vOQ9OHSIQS7GjecUXPP+ApWc0UfWKAsmUaCeqcmDzBXV1XvkjOrUzSgklyxY0XtngpcMdlaOkkN7fdjCbqGPyYvwDBGDRULnXd2hbDlhECWoCCcR4YoGDatfNMtg1anfpYSME/vQfe+N+hZ32MR3/m8zUEd9vOQ9OHuL3j9toPe34RFkarf/+TQkq6F8YJakFEMEm6mscgJfzrX9X33NcwCk78uCDnmM5Oc3PbzVe8D/0NyhoWoTk/lOSgYNogTM4vnuHm9ssYEynhiY/B9IlLy33+nfDt31711f94xx4+eO9uhBDomk6frRGZfUj1p9a4/OjP4aMDYF5ivsPiRfj6f4T8Um25F+6Hc4/Cj/+6ttwa4BPDWlHH2GLBtHnr6O9zbvEcd2y5o7bww38In3nLpc8/9EP4P68BI1dbbvjH6J++l/5IG3q4Rihp/gI88kdw6Iu12wOYOgbp6UvLFbNQSF9a7irADVlMFVUs+/aO22v/w/RJWBi5dMM/+l/wpfsuLZeepmv4AJrQ0ULJ6sSQHFLjPD9cuz2zAF/+RRi9jNTd1z8Ah790ablC6tLKrM4omBZaeBJTmuw58QP1XNbC5BH1zjzzydpyySGYPw9jz6766lfu2cr/8wYnv5SaZCC7xKQokCBL3qziyRUz8OhHoJiC2TO1z/1PvwyH/xHOPVZb7sS31O91nPvrE8NakJqCP+uDcz+qLSclfOqN8PwXaooVTJvFotqxbV/7qgjcckyfhKUxWLyE5X72EZg4DFPHL9GesqQGRIRAOEmmUEUBuS/g9LHa7UkJn/tZ+P7v15YD+PpvwJcvQ0me/Bf46n+4PDK+FBGCIqRv/mdYHKsq4pYiZka/SFgLcmPrjbXbfOA98LVfv/S5T30HTn9XPUO1cODvCX71fXSGWtGCc+SrVSUN/VCN86UU3+QRde5P3wt2DSs3vwSHvwhf/03Izddu85/fBx/th6NfvcS5j8JXfw2+86HacgDnH1dEl1uo3D3DRo+o5cj3XDgAR/65dntu3y4+X1tu6Ifqd3oKliaqy734AANGkZFggBvFheoewwv3lz/X8lbmL8D4IfU5eba6XCap7s2l5NYInxgqITUF3/3wpZXLxGEopuH0Q7XlMjPKAnnxn6qKGJZNyM5xPGAQkJI9xUuUpboK+uJzteWSaoN0Jl+8rPYGTROCSVL5KuWqJWK4hEuemoTsLIw+XVsOYOQAjDylFHUtHPmK+rmURX7mB/A/t8Lc+dpyowfg+c/XVKZ5w6aVJS5kTrEnmyJYcaqNg2JWWYUjT9VWKrYNM6r09ZLW4YQatwEbtNAc2Wq5H3d8D/8jGPnq7U17DIQT36wh5xnfp/++upyUcOZ76vPDf1RdDlTo48gD6n4vXqwuZxnw7Q+q96vK/SmYFu2xkzRZFr2mVb6f1fp49Gvq89Sx2iGdoR+C5pQiu4q6Es49Rr8eJ6tp7AyeKXmWqzD+PESaQAvATI135sIT5c+13q3Z04CEtp2KGNapGsonhko49iAc+ASc+X5tOdc1HLmE8nOZffSZqmRTMG36xQyHIyH2FIpELvy4entGHlLO9I6xg7XPPecSw5FLyCklOpBZBGEwX6gyo3zBCVXMnatNnK4Cmr8AmdnqcplZSE+CbdZ+EaH8wow8VVvuwr+CmVfjWAszam4AL35FKesKKJgWO7QRjodD7M0X4YUvV2/PfWmRtZXu/HkwHBI892jtPjrj1p+aVsnnajXzk0chlFDW/fATlWVAeY6BiEquDte4j1NH1e+GLTBc41l0Sbp1u3o20jVWIph4ARqdhQxqtXn0a5A8A0IrW8croDyGMfYUiojOPbU9gaVxWByBra8C21D3qhouHoSb3q7OPXG4utzcEANtyntsD52vTgyzZ2HLLUqR11L4c+dVaGj7a2vLue/fzjcqozQ1WV12DfCJoRLcB+L0pYjhtCP/goolVoNLDFZBWakVUDAs+rVxjobD7CtaSrlVgzd8VOuFsMyy1XwpYphXcoPzypKbM6rMK3Q9BmmXFWsleB/uWuQ15XlJq9wbQFl5JSK+BDG4L/7xr9eWc63M1HhVRVUwbdqjJzCFYG/RrG0suO2Fm2p7kVNOGK5lG5yvMc7paUWanTczkF1ABLIsFlKr5SxTEfHN71B/1xrr6ePQeTN03aae26p9PKqu48a3KbkqxFk61/5/r35frDLWxYxS9rf/krKgaz3fpx+Chi7Y8YaqxJA1cqRCKfaYEva8SxlAVcJOJUt933ucPlbxsnMLyrvvuV0p8qkq4VKzCAsjDDjzWSLhyeqhpOQZ1VbnTcu9tZWYOwfN/dB1q9IrVrUcn0MMO16vfrs6qM7wiaES3BfmzPervxCgFJUWBGnVVn7JISWnBaoqgrxpE4+cwxCCfS031Fa6rnLuvt15aas8lIsjykKKNKuHvJqclKrNcBODOaV4UmaVUMj8BWhSZa01LZvpExBtUVZQNWUBZSXesKU2McyeVvdZD9W2dEEpKz2s7k2tpOTsadhyqxqXoUcqihQMGy2qrOK9W9+o+ljNfZ8+rvp309sVYdeSQ8De+1SeKDtX5Tqc8NAd76XfWQojWagwLnNDykPa+ko1NpdDDN23Kblqz/fUMdiyR5VDFpZKhsNquaPKut77S+o+VkjaltqTNvTcAYOvqE6ItqW8qB2vh+2vUYq1Qh5mpnABW8DN0S7odQo1qln40w5h73yDeg9TVYwe17tu26nemWrG3sIISJvuzlvRgKVgoXLyOTsH2SS074KOG9WzWC3MN39eeV0dNykDstr9XhiGRLcaG1D3Zx3gE8NKFLPK8mvdDpnp2jH85Bm48a3qxbhQw31PnoXWbcqlHKtcDVIwLMyYemBv73+VshSrWUCusrvp7WBkqsfSk+fU7xt/prZcekqFNna/iU7LQpc6GbtKUnR+GHa8VineWgno6ePKKt2yp7qyAKUwGrpg172XULoOCe15F8yeUkm4SkhNqXHb9+/U32d+UP3cMyeVUul7WVXLtGBaLEXn6bU12re+St2rajmO6ZPQtgv6Xwb5BWUFVsLsGWgegD5nFfpqlqlbMHDrz9Mn1ZSjZKGCUnPzSO27lcVZjRgySWURd94E3XudZ2KosuzMKei8UclBdaU7eQRad0C8zXm+qxgBrrHVvVc9E/MXKpPSxGEVDtvxemjZ6vR7dXhqxlDPw+3tt0CzmphZtQJu5iTE2iHeDqFY9VzWrOPZt+2EYLQc7lsJ554F23fTJaJMBauUq7oebvtuiKk9HKjk8YF6Vlq2Ka8BqoeI5ofV9Tb2wi98EW54W2W5NcInhpWYPq4sm1d/SFl/1SotcvPqge3dr6ygWknEuXPqYet7mbIkK1juecNmLrrAgCVo7XImrVRzE+cvqDjxzjeqv6slll3FtOedl5BzCOPGn0FD0GFHKIgKxJBfgtycY9nsvnSVRdsOzzVXsUwXRlR7/S9X97RapcXMSWWRugq/WlJ7ylGKe96pXqCzlT0BMrPKmuu4QcWexw+puSErL7loMRwpcmuwTfURqns28xegbTv03qn+rhbmK2ZUOGXLLU6fqxBDfhEQEGujr13FsxeNCgrDVWDhBicUcaaytZtzPJOGTkXaUD2cVEyrPnbcpN6D8SrEkJooK7OmvhrK+ZQKTTX2QKgBkGBWyFG55xm8R+VBoOK1pKwjDBgG7d13KmVfRU6d+6QiQ4BgvLrCT55VRl7LNgjVknPItHUHfXoD40FROcfgWvNtO8vXYlToY3ZOjXXrdtU/qH7uhWFoGQQhlGHY2F1Zbo3wiWEl3EHvexnsepNKYFYKwbhVFc0DKmF08bmKigUplYJu3a7aLKYrVlDkDIMLEYNbSCilC9UrLVKTyp3svEkpy2oWotufgXsuIbdQvpa2nQyYNqZWIYnoysXaVDiiVgmskVMKoG+/CkVUIzkzp17sSynd3IJy7/tfrryV4Scry7mlp63blRdy/vHKVSiu1d+yDba9WhkDFYoIZrPDzAc0bm3Yqq5ZD1e/j0YWwo1KmQaiqiKlmlwwqsJnsfbleRYvzLySE4JEz500WTYpsxIxOAo2EFHEgCyHT6rJtW5XnyuV6lqmKgYIxiAQUsq8mgVr5MtKL5yorpyLGYg0KoUWipePrWrPUYiRJodAUO+MB7a0WeQcd+QLiohrtSelIqUOZ1n0Wp5A8qwyJgIhJVfNs5gbUiQXa6U/2MxYIEChUCFEtDACCNVmibwqtOkaZq3bPNdSYV6PWVTj5XpI6wifGFbCZfRQg0rmpScrv7juSxZqUMQgrcrKyjLUCx5tLocOKoRWhpcukNFhj9akBl4PV88zGDn1AAXCKnZZS1EJXVmSl5ID9TJ072VnMYUMzGKtJEQ3PhqMKSWZGq9c4y4dazAYVWRY5ZpL1xKIqBBMpLl6hZeRcxRVWIV/qsp5+jj4CjWelQjWa2W37VSfl1aXUI6mlJe1t6EfNF2NY75KiM/IqmvRAyoMU43YzbySE0KFVaoRg3tvANp3MWAYFKwKZZ6me81RZTCAKhWuJReKA6KKAvIQCKhqp0pyrmxJLl5bLhh15CorfMBDXtGqCv/84nmKIq+IIZSobWUXltSPG5aqFUpKni0/C8Fo9aq7pXHlJQlBX7iVlK6RzlUgzmJGPYd6oHYflxxybh6oTSCpcUAquXWGTwwr4T4MwWiZmSvEON0B/vKhaWZjzppGlRKd7ksWjCkrLdxYMXRwYl659LcG25UCat9V28p2X8Ytt9SonvBYc7Viz4ZHYXTvZXd+EaFZjKxUlF6F0eksQ1DJMvUqoNYdyvqraj07CkPTFHFWi2UbWQg619x/l5Kr5Ml5Sc5d66ZSrsargCJN6nMFj28sd4KYbXODu0hbpKn6LF8jX1Z+0ZbKHqR7bleubUf1nIV3/MJN9JkmOSoofK8nEHZ2LKsUy/bKCaFkK804974DoBR0tdi495pDDdWJwUtyYZcYqngMekgp0yrEcHBS5TH25wvq3HpA/U/F9lwDzmkrGKvuMWSTyouD2iGnYqZEboMx9YzNZi5UPrd7b9zflfrokkA44SHNCnLuGETrt8JyNfjEsBIlxRJTLzdUViyO8vvyoVm+diINiMrVJd6XTAiVAMuuTpyeWTpKs2XTH3LOmeiuHq/1PnCN3SrZWilp61WmW25R3k+lpK3pUZJdtzJgqgqY08kVyeoSgURgi0sMFcJJXqWraapSploowvQoloau6hU6XrlEtwp1VFK8zrj8t6+fohBoVMcqeTXecQlGVbVKhfbGi2e5tVAkHHYUS7hRWaAr4XpJrvKLNF0eMYQbFdFcavwijfSZJnmxgGGvmPzoJeISMVToo+nxpsBR5JcgEFCKvFqIaKUnYBVVyKNSm6XzOveyGikFosvlVpDNc1PPEbWi9JnmcvKqFZpyz12LGIxs2WKvFXLyjN9gg/LQkvkKIbll1+zmGCq06R4LRGvnIlYS9jrCJ4aVMHIqHh8IlYmhosJXg5knxHOjS4rFc9XlHjq1yHPDcyo+v6I9KSVDqRfZly+guy9DrLVye26b7gMUbVVKsqKF6FGmjWo7SjIVyKb0wEWgsZdBpzRyaOFCxWshEIVEj0rUpSqUT658gKPN1ZdVMLJlRXC5chHHYqoU0jGyGFqEB567yMEpu4bcCsKuoMgzRoZZa5zbCgWE+2JHGisrfMtQeQpXkbsKvxLMvOdamlRJcaWwheGRCyfoN0ykkEymJ5fnTdxnVg9enscQ9Ch8Vy49o67B7Z97b+AleAJVFL573lpWsZN/sWzJ0KIsH3MgpeTg1EG2FFrVHPSSRe5Y+LYNP/xIeeb5ymcxGCsf+8sb4Yd/Uj53MbtcziqqfMvXfl0txbLsWhxiSPSgSclcsUK1mJfYg7XyKp4+BsIq/OvKeSsJV5LcOsInhpXwsnzJY6hkcaqXJ0eI50cWkNHWip6AK/eNY/P83CeeUop8hdxYaoyF4hT35HJoIc+5s9WUpMdKi7U6faxAIqbH+nLL5Wr0kWAM4u10WBa6rTG8tGJBNtPjMWiaupZKs5orEkO1uHx+uZyRrZwsXhmmgaqeQB61yc0TY84koYqhpBUvWaRpldzByYNIJC/PrVDklRS+N2QIikAqWe1OH72eAKBkzeJyo8HMLSOaPseTGz39LbXkh+v9eYnGzR0UUsoLeeH+sgW/0hMINSir3TLhb++EZz+9XK7k1TSUrfuhH5YrmaRc7sl5Qz+5heXLgpg55oo6v/fgEc4sOAq/mFZe8cl/WXFvojxwcJQ3/s0zSIRqb/ok/NXNjE4cZCY3Q3e+cfn9DsVUe1NH4PE/h6/92opr8co5Sjc1AY//L/XZttT8gZUWvpmDF+9XS7GU+lgmkHC4iW7TYt6chhcfgAd+ZdW1LGuvosewwkgJxRVJXXgCPn47vPBPq+XWGT4xrEQxU77xekBZfhUVkOMxyBAzqQLFUEvNUJKrrPLBplXtPTWhJmzdnc+jhz2eQDFVtuKWtXn5SrJMIB5ikHJ5SMlNUutBZY0LnWYjzFh6dHV7UH55qoTFykrS00e3f/nFspIpvYwrPIHcgrqXy6ylHAumzl8/fAbpxlhz80pRffpNJeUnjRxpW61189j5rBMiWlh9j5xreePfHOCRE1NOUnm5J/D0xNPoMsDtBU8fvaGkhdEySawKvzQppWkW4cAnly+R7FXkYTe/saRk/v6V5bCSkfe0lyhNchubPa7GzC1H9lqmQjh9TKk8zIO/rhbNqzQuYSepXFhS1+7mtFwDwEsgrhfwnQ/Bo3+6Su7I2CIjaUedFNPw/f8P/vHdnvudZ2je4ksHRvhPX3XOU8zA85+D+39p+X0MxvjWC+NINPIiAsUMuYsvwtJFDpz9LgA9OU/IB8rK1IWbH/PmnNzflYyPVZ6FmxOooMiXkWGMftNgwZpVZHT8G+VZy6bHyCx5DFk1qfNLv1A2yAznOdWDnmtJlysk3WVTfI/hKsKrTGF5eMMTO5XOg7SjR23cPi8bylZ7arKcGDWXE8NQJrSKQJ6eeJqE3sJWw0SPeEJJUJ2USkrXkcvOqbkU3/5g5WvxEsPQI/CXN5T3VPAmOTUNM9xMR1FjIrsibrpSYXjDYmceLs9Q9eYYoEwMUsL9v1xe635ley7J5RfU0t5feKfn3DkOTRT42MOnOTbvLDecW1DVSaMHSon/TCZF1g4x2BbjxGQKO+KM3/hh+PPt5RJb5yUbScH7PncQO+yEkixDbYIy8QJPTzxNj+wiLPGQlyeU9Nm3qSWVvdfslQOldI88oBbrA3UPvOPnlZs/rxRa6XnzKJZII52WhWZrjOWcYoi0k7fxhpzASSqnyqS9NF6W895vN/nsXo+bB1qVfHaIQUp1z90SV0fuzLzJ2//2Cf7gITUGFDPqnLOny/NXjBxTOYEQMJ139gcrpsteWkmR5zD0CAfOz7GlMUzaDpFOLfDUMWUkfG/4OVojrXQUxPJrcUNJrtHhXtMqhR9Xx1bmN1YaPcEKFr77P95QbjBKv2GyID3vacoTxiqRqyd38J3fUct+uJV63iiFe24jW/bAql3LOsInhvwinPpu+W/voENZqc2chj/tKVX2ZDIqNvumvVuJhXQmjKhSkoU0fHwfHHKW2HYGMyfDtMSCHFsIqofDyMPZRzCmjvL0xNMMBm9EAIFQBU/g2U/D43/h6WOVcNfJf4GDn15hfa0IOWWSaoanbZTLJL2hDcCOtdNjSJL5CcyP7ysvbrfywYy1qrJIy4Qv/wI8+fHKctEW5RkYOeUFuJVHxopkqNcTWLyolL3r9hs5bF318fOHFstyLjE51nMqlSJPiP/wym1KRG9Qyid5VuUA3AouI4eNRtHZxHAs5ySfF0fhxDeZPf4gZxfO0me5VSoeC9/MK4tzcaycfF9Jct5KJ3dTJduunItw5VxCcNfCMvLL5DSg0QwxWvAYILA85ASOwl/yKPyJspz3foecHIObZyjJrSSQBtVnI6fadYnBkfvBGfX/GencI7dNq1Cq6LONHPNFnffcPUgWp13XW4HyvCBHzrIlv3TXIBkZwciliOOQkDnOnVvuJGQXMbSw8pCgbGW7no1LOCutbDeU5E26u2TtlSsRgyf3UyLY3DKi6TdNciJPyu2LlzjddgIRVHlw1pO7TJb76FX2biLdPfcqYtiEHoMQ4i1CiFNCiLNCiA+v+wkPf1ntjqctAQAAIABJREFUBeBaz0aOHGH+7f95ionFnEMMc6om3TZKG5xkM2lMqdHT2shtfU1cyEaUkkpNqoF2lwZwHjgRjPDzd/ZxZM61dufgwd/g2R/+Pqliih2amoATcKtfvInvI/8MB/9B/b2y+sXrWbhlte4KjN6QRSCsar6zyXKNu+uqeitBAD3ezqBpYGMxvjQCQ4+W2wPPuZ1QUjapEuBuKGJlktNLXrl5RQ6W6XkZV8otlL2vUrgkx5KpXO2vn8p42lstlyPMa2/oJKgLFmRceSAugXjujaFFaAgHuWFLgqNJgcwvluSemlUGwGCx3emjJ8cAysKVVjnctSou7/EEcguOkpxeXgHmbc+VA48n5xkXTaeoRWk2AowabsLY9dA8IScoewyrPIE8INSz4MoVU2XlXJJbEX5xk8XZpErI5heUAeRc88W05M17tpAVrsLPeBS+UpK2My5v39tDJBLDwkmwuqTkCf3MFXUaIwFetq2FLBHsQoaozDIe0JnT8uzruIOQLGBqnmt25ye47blbxVcKEUlruSeeTVZOUnvvhdtH217uYYdipRDfaLx5xbV4CMTNHRjZ8jtbSQ7KxOBeS8nQWzEu6wgh12k975cCIYQOnAbuBcaAZ4FflFJWnWK7f/9+efDgJZaeroDJP/1TCidOKqt0cUxNNIq2wOSLFEzJoWIfjdEgNwfG1SA19iqrs7EHWrdTnBlCz0yR2vIylnIGYnGMfjENXbeoGGI4odaFyUzDzGlOBnbT3d7C1MRFdosx6LkdOX6Y4XCUpC7oFv30ZE6pMtBoq7J8xg+r+QLz59XDM/hTqvPDT6pp8U39iiiGf6wmvbjWaedNKsxz8aAiA3fW58WDql9Cd2ZPd6kJPTMn1UvlLEYmZ04yl0txLgy7iwZN0TZov0FZsvPDqh9CU0p2cUwt5jd+SCn43v2KeKaddYiCsfLfPXth3Elc9u1Xfb/4nOpfvEMpwrHn1NoyiyNKkXXeCLF25PCTTMoWFiN9LGSL3KWfRkt0Ke8rt6DKdlt3UBw7TM6UNAzezomJJQbNCySCUt3ThZHyNSfPYqZnORG4ic5EGCt5nm5tHtF5E0wd41wkxpKusaXQRLd5Uc2d0EOl8SyNM6j7UUgpb7LrFpUryS+W/55yllnpvk0p8NFn1PyFRLez4u6z0L5TWaTFrJrv0tij5GKtpUlX1sgBzughsgGLfbk8IrFFTQycOqLupbvMxdQxRdSxNvV8R5rUPJb58yoh7D5H8xeUcuq4SXk+Qqjv0tNqWY2+/aq/6WlF+t17y4nn3jvUOccPcVr20dC6hXQ6zW7jlJq5Pz+svCp3/C48wTjtdA3ewOmpFLsKxwgktqjnOjevnt/mAbj4PItWkPHQIAOtMezxF4iEghRFhKyZ5EIowE2te8iOnaNNz6IPOHtwz55RhNXUX15WZesr1HOeHHJmzAfVPZ4750wsdLzHHmdXvvHD5ffPHb8tnhn+7btUXm34KWjdCo19YJtkxw5wLBxihwWtxYKaTNfUp0JF0WY1RlAeT1D9cnQJ0ycU2bj7N08dU0ao+8wGwmqi6MKI+tn6ypIeC990I12/93s/sf4DEEI8J6XcX+m7a81juAs4K6U8J6UsAvcD71jXM7rJXddikDaWsxnLUs4gZ2nqJXNrxx3WlraFhYYmBIlIAAN9eTvubyfGGgwESESC2GK53IKwaQo1IaQTi3X3edacOKxtLC8jLMk57QihJsR5++ha9lIu34BcCypLfWVZoly+UbnQg8SksoLyQpQTcNJW5yv1MVj2YEApAmmX48orr8W7sqSR81yLpz1Q1+Im8Jz7JKSNJQUtsSCRoI6Jrq7XNpe3LW1shBqXcJCCrSGtSvfGxkYjEtRpjoUw0dU5jDwSWMSiMdS4uo+iwrW4113pmt3Q0So5d/zccbbK1+ImRqVVbg+QQidkg4XEFEJZ76Dut3d/cE1f3p4rt2Kc0XQ1frb7vVze39K1OH21PAlbz7XYCCIBnUCgyrVIW71RQkcXglgogCU1ZIVrltKiaENDOIgmBBaaug/SYkHXCNkQ0iLowkZWumbpmfRoFsvX4l63+z9WOV+IVSznBEvX7MoZy+VWjZ9G2DGuS3fHvU+2tWJcnGsp5R89798qObt8LW4fVjwP64n/n70zD5OrqvP+59y19t6XdDpJZ18gIRKWsAUhIouI4ojLKKCguKEzoL6D24zLoKAz4+j4iisOODriOCr4iqiI7MieBMhG9nSS3rfaq27Vff8491bdqq6uatPdkcR8nydPV+qeutu59/f97Uc7IkeZPGYD3lSYbuD08kFCiOuA6wDmzj288vACy/7Xm2HHZlhzGbz+3+Ebp/JUop3vaR+jIWAwdPDbvF+9G3HqG+Cp5yDihxvv5OAPria/51FS772NtrDBt269hW8Z/w6nvgmedjqo3nir7LX0209w10mf5vzL1/KFW/+T25N/B+ecwYannuHTHUG+tOZ97H46w9q9H4VrPgVzT5cayy1zYf2H4A+fl/t72zVSu/m35XDpZ+CUd8vv/30lzF0hG8YlBuG0N8MlX4Zb5sGqS+ESJyXvR1dI7U/3w77thWvhPy+VL+g1ToD0j1/EfuhW3tk1nzeNJfnk6Ch86gfw+3+ULq1POeM2/VRmYrz6XHjQWc/gg5+SFs2vb4SP/geE2+QqZN8+B847D/7otA256BLZfPD218I7b5ANAfM5+HwjnPNueMSJqZz0Wrj0q3BzOz/JXsDaq/+ZF1/uZ9GTb2PRsnmIvs0wMgiNdfCROxm8ZRXbE7NY/fk72bTxILv+5++4MvAk6uLT4KUXoakBPnwn+buuYtfmZ3jujC9y1vmLueNzH+Nm/XaGX/UWel56ns/MnsXNZ9zAvl88yNrknfDpH0jNbc+jMuh89lXw6JPyHN9+rbx/d70D3vc5qVkP74GvnQTnnw8PONd8/nq5vsE318Kbr4MT3ySF+ucbYd018Ph/SGGx/Ex4653w+SY48x3wms8CMPL1ddwXT/OtjgQ/OjjAqoYOeP+dMpMp0gl/68zL3R+CHQ/AkpPh2Y3SavzknXIN550PwEedcU9+G37zf+Dc98JDzrVcd5O8xt99Cm76trQ2dv5RJgJceCn81pnny66QfabuuJSbMu/nM9e/n/sf3czNmy+E9dfL5AGQz+J5n4Rb53GP8QbO/ORX+X9/3EHHH1/PnBMWow5sg/49sGAVXHUnmVsW8GhsObOv/L80dkR49suXckbdEHu0dm6qS/D6aJrZb/g6Q9/7G+Y3JGm40bmW+z8Lj39DPjsP3SK/u+YG2SvrjzfDZ+6QWYbuM7v+Q/AHp63K694I9V3wo7+Baz8ju+P2bZHz5B235vVwzkfl+3bZ5+DkK8G2yX+ugb+dt4CLUgk+2zsIS06Vc/GFVlj7NrjAeX+/eabsh5TLwMtboaUFPnQn3H6xJLZ3Odfyiw/I9SoWnQzPOo0vP/oVmVr74v/CP9w5oVybLrzSLIZK6yaO83XZtv0d27ZPsW37lJaWlqkd0S348vjHhzIai1pD3HDBEgZyAanNu/3Rx7oL/tWkbeLTFRoCBsN2uHQ/AP1byTnadjAkt2shmR2U69vK/cEAmm2zOBFEWGX+QzMitRLvAuLeVdNKMqcait1CoSzG4PHDBprkGDcWMdYt9zduXDMCaMsq7NM1qQEN7R4XpC5kOnl7Ag1snzjG4MY0QJr75f52RZWCyNuLfnBnMYCPwZwGPx31fkbsEFZ8qFjrMbIPchZaTsYOAJqDBqMEUTJjxXoLJwicTsZI2AZdTUF8ukJCkX50MbSbx/3y92sDnWi5FHkU6UaCYkzA2/5keLcn/lIWO/C2uxjZN37+FEXOdayvuI+R/aWN7Bwovghzncy4bk0jN+aJHZQEn510VTdNN+MEg60yX7ZbDOdtfRLtGT8vlcaNdhfON2mbzGsKYPhC5G1RjH2AdD8612w7yQMBQyWGj3w6Ni7GIJxYxPL2CCFTI4EP1UrwkjJMWlG4MDHG7oN9+EmT92Zi6UFpFXrreUa7KWmx4b3v3q4CYwcrpLU6991bpzN6YPz8CUFa+Gi0DLqVfPG4+bx8b7zn6Aa+3Wse3uvJUgtMPA6K7+oRCDzDK48YuoE5nv93AhOsqjFFbLwLvnNeMcXSEeh2NsFAWmVeU5CmkMEooZLthc9WkiQGPl3Fp6sk3fYLA9uL5t7Adqx0gpwtME35UhhhGczM9W7m94EApydTDOzYjihvVyCEFKjeRnoTEkOj41d1ONTtde/NtwYPMQwUhbUrrLwPXFAK/K5smr26497p31IazHb3V7g3DqcPvDxesLjHcgPEqiFfCm+PJhe++uI4PVAiTJOYdNT7aQgYjBCEaB9kogwrDVKIJodQ80ViiPh1xuwgArsYJHYyZaxUnCQmLWETIQR5J1isje7hcb+fJekMVk8fWj5FVniyX9ygsruSFqJsXsqyjUqIYe/4egeQKavuOEWTwrS8kR2gBeqY77hc9usaSnJAWlnl8+IGlb0B1mhvaf0LFIPK3ur16CE5TiilefVQzMoBR0hKYeoLBAmaGiGfThwftnfcSPFacs45Bg2NhC2DyoXA6ugBsG3UXIokBiGfhl9XHWJI8pweI5zLsyaVJj18AJ/IYnvvoXuOsd6imycxND6w6z7nLnkpevXgc4FAhCTaCrUEWcWkxVLYrzrHHe0eXzPi/sabUmslpZI2YfDZk1Ib7R2fvTSDeKURw9PAYiHEfCGEAbwNqLJ47hSQz8rGbrEe+VLF+yE5jJ2JE7dlHnx9QGfEdl6e4T3FBluxXhRLVtj6dPkwZP1O9kr0UHFd2+QIuXScFAamITWWunCIOD6eTB/ioK7xumgKq387ojxDB2SgyiUkRSsTQGUpta6VEO5wAn8VhG6gST5cqRHZ3A6kVjLOEpDXsiwT5aCmkgUpZMrHBZ1r7t8q921GJOlkU8WCOZAPuqIXF4WJzJbB9UpZFv6GIjHUzSlJ21N0vxMT0Bm1Q+hjewDYYzkElYmj59PkFJl1U+f3zN9YNwSdpnoj+8BKkbIN/IbzMjuFZvnYXp7zmZyVTHFg9zZJDM7+gGLdQeF+t8vgd3nthqJKwesSSKhNCqDylFGQ1oW7v4YuR6CNnz8jWEcLcVosi52aX1qyBcFSlpUEUpCrzrlHD5Vms0GxhcXogSJ5x3qLWWqFVNAyAvHVO8eV59hUJ+9J0NRIYJIflcSQN5zanjIyDJgqcXySFDJReaxsHJLDKORJ2QY+TUEIQVb1o+YSPGVanJbMogPZUWkx2HqZNg5SgLrNE7OJCtq4SyCO1Rxqlec3Ll3V2bfrUQi1ylhbBcUso/jpyObo0VRiTkFexffULcJLjxXJKzVaoY4hKBWY5HBR5mQT4wlkBvGKIgbbti3geuC3wBbgp7ZtV1kmbApwF+4AmRECkBhCsVKkkKZxQ8Bgt91eHOd2W83EEeWCJdjCmOKkq4Va5UuQiZHPSNPY7xBIU8hkR76DuyJhGq0ci2Mh/OlBhBuwKhH4jcW87JblxZcbxgv8wnUtk2PcVEWvJum+MCCzmkDuv1zjdFoUz7Ms8kLQrWvFh73ScfOWszqWk0vujnMFi2v9uK6uekfgl6e/QmkFcl2nU/MhX9qcM05aDKHCTw7YDkFl4uh2mpzjsoj4dAYJF/fd7GSHpEYRTusMd15EQM7dY6bAEoJ1ySTZxAhaPo3lJQbXEkgMyrnyNzrXUmYxuGNdSyAy2xEsqdrjsItuIK/F4K+nTYwwx7LY5X6fHK5sMYDUXJscBcAV5CWuJOdaxg7K69D8zvNQ7nIKFceBzKbKJgrXbPilsA2aGjHbXxh3wHKWx8yWutmChkYcH0rCEc5h5x1z3DZZxURTpWjKqQG2GDCiClYnpaKRio/hI1OmjXsshqDjXq4kTL0CX9ElKWfi45WUcldSsLW4P+92wFJ8dGVS5IVgk1ovlU43XXecxeC4iNxrdo9dbjGAVFpdYiiM++t0JWHb9r22bS+xbXuhbds3z9iBWpZTcH+4i5Y4D0HSNphV50dXFfrNOWQUOWm/2OtowJkYSi4lLQZN3sJ6v84uzdlPoLlgDuYzCceykONaQgYPKF087Pfx2mienBJAs+KolQS+u64ryKCVJ3e8RBDMOa34uXw5RO/+us4ZP67Sg1k/l4SvjXlZmQ2xT9OKAkMre8ncVciCLcUK2XLBAkVSUg05diKtKughr/o5MjvDEZKuj7o+oLPXbisMO2A7BJUcQsEuuCzCPo1N9sKS65LXHEN4XIEAmWAnWTTuCwaIWAonJTPY6RhGPo2leoS4oha1a3+Dk5s+XvgB0rpwM0siHaWCpXycm53jWpuuQNLLxgGdWYse3Xl2M65WXMFiyCaKzRNdQV7ifnEEfnrUafkcKJJXJZeTSwwhV0jKaxbOsUOmSgITJS5jHwetCLaHQNx9BgyVhO1DT5YRg1NfY6nFY+e0AL8Mh/Dn8yzNyFTPWGwMv0ijuQIUPMK0Twp7ze8hhjJt3B1nhig01Su3GBSlmKoLUvHJJitaDHnNz0JHgduiOft3W86UWzVurUU1S8Br/bj35q/ZYjiiMAJS2ILMroCC2ZjEJOBYAg1BHwO6nJx9tiO0MnG0XJK0KGo29QGdrXTJ7f56R0g6xGAbJRbD7yMKAnjn2BB5PYieS6DmKmjPC88vfg63T+x+Wfza4udqxOBaCVBi/YwLXgpBrHlVocvqbsPnkFLZOID558q/Rqi0YlMre4DdRYp8dcVCn3K/PMDctcXPdZ3OtUiBkddcYjB4OLeqMOygazE441wCURRB1mwsEHuRGOIolkwecOclHArxtDqfR/1+lsXCpIQfOxPH8FggBbj55v6GYqDQSjr9bjyJfl5LLjxLCoVKCoCruQPUOcTgFiGWF64BnZbFqJYnLZCkaecn3p+7cE+mgmAxi1YXvgiFdhHlBKLq0iWVz0rBaYaL4wDFEcrSEvAXUq977HpELlPwlStOVX/QlBZDAa6QdCxK7/1OGQb3BgNcFE8gDPn+pRJR/GTQfF5i8LScMELyOjOJ0t5nUPycGnEW+fEQiNf96Y515yHYUkYMpS0sTrCk8rLbvW+JCsSuB6VrLZ+tbgm4RJxLFxWqgsX+V2oxHFG4i824FoOjHSQw8WlSYNQHDPqFFDwHPS4LNZeWQUkH9QGDFyxH8CSHC9qznS3VTP1mhv11+1mXSDIvnwYjhJlPoOaSZLxBToD5Hg3f1cYrBp89C3eUCdNxGsaiC5wTdmL8hWyVsgeuaQn1+TxmTmW3bhaFX7nAn79O/h3aVey9U0mzmXeWc1798gUpcb94jr3g1cXPIVeTlALDdo4d8Wn0KXIuDqkqTzX28oWmBr68+xf8OhggrRmFXUR8OodMh/gLQjKO6lp8RpHYb6sLYglYGW91mrfF8JEZTwzuqnSK5sxLBS0bipacUBxh6rEsvGPdOYOixZCooHE2y0JFt9L2gKYVK7q98+JaNN79ZSu4Ar0EYkYcIVlBUYAiiZiRcS0blILFoBGzi7/rtd1KduccnXn2G6rsLebCnRdXAfBYDNuD/SQVhSvGYqRM6SLKJGP4SaP7KghT91yNYFGQV9LGS8Z5LAvv+6d7iCfUWuLW9N4fYQRpz1v483m63VqOSvNnBIr1E2GXDIcAu3KAHKRyIRRPvOS4xTDzmIAYUraB6bh+GgM6+2hnv6axq3EnF3V28MbuX/L5BoWftg3wdI9shFUf0NnstE94fOcgIzmjIMi9QeoHen6MraZ4/8goP82vBzOEL5/EziYL2TQFuCmPIB/ivFVsm1AuyN/7AFz4xWK3TtdiKBfkb74dLvuGrFAGj2ApPXbrWVcCELCb2KtplS0LKFbRzj29LMYwwTgoHVeupblz4V4zFEnOuRYhBHUBm681L+ZNnbPobt7M74MB/mf4BW5qbeb7kfsKq3zV+XUeDawH4NmoQ6DZuJP9YhbmJaf1sDEyzBXRGK/KxUkLP/lUDL9IV7B+HIE/tFvOg2vJld3DAsnZeSkUvIsLeceeck3xc5mQLBEEC6R15rbf7tY0jwDy7G/Was/+2ij06ClPS/ZFCmQjLblA0aopv2YnIUFaFoGC0E2h43MSK4Kmxg67SHJ9dn3JtaiOUA4aGpvtrsK4u7Y5wjJRahnats0Lvr0sS2c4MZMh5ZPEYOaT+EQWw2sxlGvcrj+/XBsfN87vcceVXXMhpViTAfe85YkdFPej+oIIYLZl0ac7mYHuvGgTCPxQqfusZJvXkjM9ltxxV9IRwinXwKX/XnQpOa6klDAxtaIm+aVQI5fM6WBr8w7aLZtO4WODqbHLF+Oa317DJT+/hEO5R3je6qL3tE/w0cS7GMhohQCrW+/w6IFHuWf3T8iOruHSsR/w7/4PYRsh/CRRcqnxminAR7fBDZul2es5x3GCd/YaOONDHmFawZUE8sU++cqiT7aSyQsyOP9PIyjaAvbrqid2EBi/v79/AS7+SlmMoWycqxUHW6QAsvOS5MqPKwSseZe0RPSyc3RcEbtHd5Of9e98L5xGSXdi7ngfD+87wGMN53P7oV5MTN77+/fyq52/IuLXuFu7hGdfdy9/81td9vdPjaLa2RIX39Njd2DnDT40PMqz/rPIqH7IxPGRRRjlxLBG/k2PFjVOqwJpzvG4xQrXUkGTrJ8jWzaAZ14qELaqk9Abi715dK2yAFI1WHKR/JzPUUiTrGTVLLmweN8LAr/COIeUUI3i/pwEDPddCZoaz+UXMaAq3B0K8mJ4lJd1ndGYzGZSjGJW0gv5+YVdP9mnl16zc+xNA5sYEX1cEY0hgIxfEkOjiDr78zxjDV3FynnTEfiVhKlqlI2rInTduTBCRUujwvxpfml5zclaDOtOlXIlYvda9q7FUGlce9FNWoz9xB03mYcMZxB/3cQQmSWrh41SYZpTfAjHpNzP/xAN/5FZytnEdn6Ufz6U5V/U+dy//wDv7zuFm067iQZfA38Y+Dq+2T/iwbY3cogmBrNyDVolK4PPm4ef4sYHb2RJwxJyfZdho1AfMMAMESIl0+/KNU6QsYW62RUE/gS+RvfBKTxwFfYJMojqpulCZU1ECBr0DvpVSKfHKGkj7EX9XHmckhhDhXF/txE+8LinKdtA5eO+/mtw9a/GX4sWYCQ1wgfu/wCoceZl/o5Dez+CX5Pukny0n1NTad4u3srJrSfzyUc/yaj5/xhNZ9kl5gICSwsU9pcWJrqqcN+e+9gVf5bUwGtYZ/0Xz9VfSFYNoOeS+EijmmUvo78Bzr0JrrqnmIJYyf+r+6BtpbQcvIJFNYptJly86164aX9VAQSw5XU/4w/iIkRen9hiAFltG5kNC84rjYOUz8tix7XYu7lMyy4nEIdoel8s7M8us4ZDpsbTQYvLZnfw6ZYmXpq1iTd1zuKCnnv5Xl0EYUgXX0BXGaRoDffhuJzcGJFDcrdtvA1DhDjb7YvnbySLRiPOF+VFYW7sxwhPPC9CFONdRtDjPquQ8dO+sngc934UiLh4H9XZJwEw17KI60ly4CE5zz5dKx2KlmEliyHQWFybxAx7iP24xXBk4QoqJ7fZrai8b/d9bEv9iszw6TQmr8LOtBC3fSRHegFQlCDvWP4O7rzoTi7tvA4ttJWvb/kwWt0zPKCm2WHFyOaSPBTJ8s/Pfpx5kXncdsFtLG6VZnl9QEcxQ/hFhiCp0rzsaufoLuNYbVwtAgH5YpS5acrR6u/EFrA/O1ZZk/SiEGNIVT5uQ5f01RZSAQcnPK48v1IhqRg+vvrcV+lL9LFMfISRoQXkbairk4LFdjJBAkYD33rNt7h80eV0cw995u30RWUANK34C9dsqT72R/dz859upiu0jOzQmUQzEPFr5NQAAZHCJzJoZoVrOe8TUosuZCVVcCUBvP8RuOruUuun0jWrmrS+vJ1MYdw+16xew1s+898Ydgv7db2yxQCyMeGNm2Uqth5w2mBnxs/L3DNgycXw2i94XEmp8dfiNm4TivMM2OSTwyTtIjH8fNcPsTrvZkE2y08PHGLZnov4St8AawnytcZ67hj8B7723NdI55MFKwM8LifnWoQe4PGDj/PYgcdYGbqc7TmZWebTnSpj4RJD2TW7xOD67Cfyy7tWUmpMXvNEFoObxRc9WPrMlsUi/IvkuPmZLLaS55CmViZsl2igGFSulL0ERfISinzGJpq/GcJxYgD5Umq+QjVkXvOTyCb4yjNfod1cSLrnDezqj9MWMUngQ0kOFsYBqIrKG+f/LYm97yOTs/B3/Iwft/ZxeR2c1wr3tI7wqpZT+MGFP6DZ31xYK+D5fSNoTgpikxhDVJv0gsXQV0PYlxFDJWFVGBucUDN10RGUQeo9Vqyyxlm+v6xj8k5kqbjjwKkFqDauNMaQ1BLcs+MerlhyBZ2B5XQPy+Bne0OQtK0jHO1LMQLoqs7nzvwcKwNvxwo8x88OfgahxkjiK9ybMSPPtb+9Fhubv1v1j+A0Qoz4dPJ6gCAp/GTQfVXMd3cuEkMTWl3yWjwkV+2aC/uroEl6YNLG/moWgxcl81w2TtXhb38iBX81V5Jmwjt+Btc9VCA5Oz4oizc1hScPPcm3Nv0H2bFV3JBYQTS1AFLtXBRP8C/pIN851Eu7bzHff+H7XH735QRCPfyx7WoABuy6kmtOGVk++cgnmV83n5PrX8fHs+/jR9Z6oq2nk1H8NExEDG6wPzlcXctecrH827NJjrNSUqEpv9ddZxU/6975K92f0S7Tyue7WXy6Xnn+vFair16S+USu3JPeLv8Gm+W2iZJJZgjHicGFESpxq3zvhe/Rl+jjTV3XAwp90TRzGgLEbRM9Jc1Er+unPmCQT82lZfSzxHfewFv2LebzA6O8ZzTFGw7O5j/O+7+EHEF32eoOTE3hA69eiOaXsYNmMVpc1nOi8wP5gFQTzuUB21okUs2VBMx9ywb/AAAgAElEQVSPyLTWfbmE07tnElZNfPzLU3HcRK6kwjjXldSPhcJe+z6EELz7xHfTEChaTB31fpk/7xC2ahSD1Kc3XEGy+28ZsnYR6PomjxgGPcl+flAX5qH2J4hlY3zngu+wpmMpiiPDI36dvB6UFgMZTH8VYvCSXLV58RJILXIFjyZZeWxQbeWAppEvCPwq86wHJrYsysdlJ3A5gXQ7zVrlIbkh0hgINcOnH/s08yLzUAbeytfqPslbMv9UqEcQiUFWJ23eOf9z3HnxneTtPFb71/iXsMEVHf9bTF2ND3JQU3lC/T4JK8G/nftv1PuD9FPPp6xr8QUCZBUfjVQoHgNY8UY4/zOw7uNOUkC8cryrZakUvJd/u7gtWYHYvdliJcRQtj+nE+sCp+5nl65PLMiXvk7+dYP9E72nK98M1z8LC9dTaF1faX8zhOPE4MIMFaqMR02446U7uHTBpaybe2phyJzGAAl8mBmXGIqT1BiU/tNd/QnsbBuBVAOXR0e5fniQzngTQaOYQqmrClu/cBEfWb8YIyC1pWbGKrssXBRcSX3VHw7NJ83PgsCvIYQKrqTK42ZFGvFbKvvybmX2JAR5enRyLqJ4f21BBZAYYK/iZ3/2QS5fdDntwXba64q/m1UnicElbG9MoM6vYUVX0R7/e8Dmn1osLqiz+bfGBgzb5LsXfJcVTStoCBqsXSDrDoKGhjBDhEjiFxn0qvPitX4mQ5r9tYW4uz+Y8P7U67NIK4L+VOWsstJjBzw+7xrjJkq9rXCOIjlECoM/Df03PfEevnDWFwgaAXpHZUqu2zhSSQ4WijxXt67mrkvvIpA+nX2537HVuBFt0b/wvrZWvqfEuKKjnRQxvn3Bt1nUsIiQWawLCZoaluqjSYxVvmZVg3Ufc6rwvddcIcHh8m9Jl1KhEnoCJeXa38N1Dxa3JSsT+981fZsbUzcicgHHYqiQRgwyK/Bd9zqWQLC6JdC8qLjAT6WYxQziODG4cLJ+MhgMBh/DxubvT/57lrVH0BxVsrPBTxwfqtO/3vZMUnPIIGxqpLJ5ZkV8xHHcTHYOSzFRFFFyODe47QtKV5IpsuiBeiaEawnk0qXZDeUQQl6LlQQEJbnY4645WKzMNSo/cI1BnbqsyX6tbI3diufoaT/hbb9R6bguvCm5Vcb9sC6CDVy78loALlherHzuqPeRsH0IZGGV6i/m50f80rI42NdGfNeNXNMb5GODw/xq/0HOir6TE5qL1eWXrJQBwcF4GowgESFdVWKCe1NyjplYbeEM0m3hLXwrh2bKFN5sXBaVTRBLajTluXZnnPRlX6TiOMARQH2l51txXEA+N5lo9XlxnnslOcQ+VefpoXu4fNHlrG5dTcjU5MqHQDAkz0lNjxDHVyzy9DfRkbuKpdZn8ScuJBdfzA5D52sNEeZnc6yPfIlXtcp4wbL24nUFDY2cFqBOOLUE3nqNSueYdVb689Y4lMO9H8mhykJ3zmkyduENPlcQ4qn6RTwi1mDk29ltaEXlSCkTsbqv6KIyAnKce77VrqVCmuxM4jgxuHAE7y69kTHtT1y28DLagm2oimB+s3x4pMui+PKnfcWW30IIFrbKfbRGfDLI6WBEmfgB9oWKL6Ba3znhuJKHO1JlHBQf9lBbaSXuROOgmCVRhjq/QSjjZ6/u7MesIoC8+3MLqyrBS1aRyscFnIpbgyzwu7BOl/9UOkKyxcPcpuIL4rqSANK2huIRvK4lF01ZYOssiYa5eixKl2WRMEoF9BWndPKuM7u49uz5qD7P/Q61MSG81xJsqTLO80K7zQcrwdUQ3eMKUXFYm1/eh/1OIWZVsvEWVgWqHLu8sKra/gBh5/hVo4VA4YOrPwhA0FQZS0lfezhSfFYG7EghSA1SyNuZdnKDryV16Ap+2B3nV/sPcuvBLC3+4rOzoiPC+cukklEf0EtbbVe7jyX3u9q8TFAYWA7vs13h3ixtC7OwJYRfzJauJIBQjSUBJvtMeBWTagrXNOI4MbhwBO9d4RC2yHLViqsKmxa2yG2qIsgoxUlKBUqF2iKHGJpDBjmtOG5Qa2ci+D3EUOhrUwlebbzaOChaF9WELhTJRtEmFH4BQ8WXDdGraSSFKLaVqLY/KLZ2qDjOS0g1rsUI8kjAT1SFEyLrSzZdt04Ww3XU+0k4Fbd9dkOh4AqkYHExp7E4DiBtlr6Mpqby2ctOYF5TEM3nud/hieevlAyr3G/vuGpCAIoCo4oQaA+2I2ynyE3RqxP2pAW+V/g11tzfgKqwKRznrLbX0R6U9yjoufd1kaJlO1RGDAFDJZ62JGEDVt6gy7IYsUOFrgMuvn3lGn5y3VoWt4ZKrPSqJDdZYVpe3TzhOC8hjRf4H1m/mF9+6CzqtNmMqCrDilKdkKB4vxW9hvXjfXaOE8ORhRkiJQT3hSwaxWoW1BcrcN99VhcAqzrryKrygcvZAstfOvGLHWJoDJYSw5A+scape9weJcGucnhdCjUFvvMgVdPavePCHePz6h34dBUjI89xn6aRCnXyiZ+/wLae6PjBk7VqvC9tNaELoAf5ZShIwFJZEj61ZNMnLl7Gtn++iIhPK1gMvTQUXBYArWEfYZ8UVkvbIoVAZxIforw+wXtYv5cYqpBXybVUGTdZDRZKLYYJUO8P0GgJWeQWaJrQsijZH9TQsr3ac21i+Fk4RF7YvGb2mwqbXNcdQFNdiJwtz2vQjhQaSYKMF4wksmRyeRqDBnFbzt+wHcJvlIolXVVYu6BJul8dIWmpvgndn95zlAebpMVQlRiq709T5TKxzaZ87vfo2p83z9Xmb7LnOI04TgwujBC/CgWIqXnm65eUbDp9QRO7v3QJy9ojskAKGCNYoplC0WJoCpnYnpdxxKimcXqFaQ3tuTCulsB3LYba2jhQVbv36QpKRmp++3SNf31ilP9+ah8/eXrf+MHmJK9Fr+3CcjEo4JGAn3ljbQSMUn+7EAJTUwkYGkmHGHrshhLNFGB2vXyx5jQWXYGDor6EQMphBCZrMXivucq1TNZtIA8u/1ZxRQQMlcasJi2GalZA+bEnIfDlAarsU/eTBf4nHKIp3kxXXVdh00mdRQu4OeQr3m/qSu53wFDpGZNB6tawWZi/YcLj5q8Ezr3JmFWuo/xaqgnoEsuimstwcvPX6pMW9W5dr00M7j7DVY7rPUen51Yyk+Md3/sTG/ePVP/dFHCcGBzk9SB3RiI0p0PMMk8Yt90NFruWwKgdHCdYFrc6qachE1svCgxRLeBn/hmxg8K4GgLf1T5qEoNz7CqCz6epkJFCYq+u859PSEKwxy24SqlmWk2b8zS5q2Ux/FpNYwlB3eiiCQWGqgjZ9A7pSiqskeHAJYZ6v0HccSUNUD9unBemlxgmEYgFqpOcohQzVGoKjNoWg09Xqcvqcq2Mam4fKM6FWVd678eNq+5HB9m/KK8F+EMwQJ+m0TC8vKRY7axFRaEZMNWCwB+wIyX3O+jJNmqN+EgWLIbqxKA4Vp7lq0WGHi17svNXbV68iQVVxjWareh52GVMghgKCkBtqxmQ7mQheOHAKI/tGKysnE0TjhODg0fsKHsMnc6RpQSMiQO2tjNJowTHPcBzmwL821tO4vJXzS5xU1TTTMeVwk8GtSwGd7nEWuMKazJPfFxFEeSUCE1Wjr2GSTYnGaE/lh4/uFr2x0SYQJj2jaXY1hPlt6bC8nSGeGZuiQAqh+ulkBZD6bgrz5C1GKd0NRQEVb8dwdQmnpdA2JP5NVk3TQ3rpyAIJi0wJnYbmJpCOOtjSFWJV8tSg6JgqfV8lSzCVHnsqTffzzU/fomfhkN0ZrPkYotL3oOVs4tCWK67IO/3kB0uiR00BIoE1Ro2C67AYUJViaGpQfrizbpaWrZnXqq6aSZpMXizi6rMX8AwaM8KaTHUcvu48zJZi8HJnNzaI9/vB7b2YVfU0KaO48Tg4J5kN425HPnRZeMESwmcSRqzAxUF/ptO7qQxaCA8lkDV/Xkf2moPsBe1BJDbwbOWxZCZRNofYKkB5llZ9hpFrak/Ok3EMIFm+uZvPcFF37iHTT6T18YT9NoNmFUERr0iUyR77YZx8/Lqpa3s/OIlnDSnvhBj6M3VVbUYAsEqwVwvvALIrHH9riCYhhiDT1cJZqUg34LBaTffzyd+volcvoKgKBBSraB3sPh3gjqGgViGRw8c4hmfyWWxOEPUlxC2piq0RUy5aJ+ukUQSwCCl93tZe9Ei87qSRuxQVUUq5KTAmpFaQneShWB/jouvcBITz5+pKbRkNHbrGnagme89sovr7nwGK5cfP9iNG07aYpDP15ZDkhh6x9K8dHBscuf8Z2LGiEEI8VkhxAEhxAbn3yWebZ8QQuwQQmwTQlzo+X6NEOIFZ9vXhZispDx82LbNQGKUhxL7uDCWoCffOC4rwouQKvP+RwkWWnNXguZYDHlEVQF0WKjmpoFiznNNAnF8lDWIwa/C3KzFPkcAhE2NgUoWg5saW810L0d5nreDfUMJtPCLALzGIYZq8xJxctsHqStxUxROTRFycXlHg+3N11W35CZLchME7Svv888U0FWIwdQUzKwct9nK0xdN899P7efJXYMT769mLMI/btzjOwfYP5QoGSbCm7GF4OJYYly2EcCDHzuPTf/0WvxGqSvJSyDLZxWJtzVsFuZFupKqKWYuuda6lkl2IfW+SxP1HytHFWL36SrNWdng8PcHLP7511v43eZeHnl5YPzgjFNnMVlLznkmNx+KsqRNfv5TpfmeBsy0xfBV27ZXO//uBRBCrADeBpwAXAR8Uwh3ZWxuA64DFjv/Lprh8+NHT+5j7de+RtrOccH817PbnlVVkOcdc+7F/PyS1LxyCH89vxTr+aDxxaoCDZAag1sqXw1d5xRbBleD26yrFjEsOE/+dRfbmQD7zYVE7AYGFRuUNPOaA5UtBpAN4z7wRO1zrIH5zUG08EsszmTosixiBKoSsV/IdgQJJUhjoLIfXVXk4vIA/dRXF0CuJnk4VlC1fbq9/athUq4kFd3NFqOoje4rE+Il+6tFDIVxUlBtPjjGld9/iqtvf4pUNle8jMgmlmZydOblUp7lLj6/oRL26SWupJhWj1fPa4sUF7lqjfiKFgPVLYbCvFRLVfVeS635q1Z5PxGqHNvUFOozPmwheHosiqEpNAR0/ve57vGD005mnzcVvRJU53k2Q+TyNtt7opy9qIUHP/Zqrj17fvXfHib+Eq6kNwA/sW07bdv2bmAHcJoQYhYQsW37CVs6zu4E3jjTJ/Pgtn70yAbq9Xbmnvtl8ihVXRbdTWdxdeYf+HbuUtrrJq50DZoan7Cu45n8Yny1LIaPbYO3/7j2yV79K/h0X+1xV9wB7/lDbcti6UXwqV7Z/6YKhB7gT3XvBUDRB5jXFCSaskqERQELXl29hsHFm74Lb/4BAD94bDf/ePeLZKyigNP0OGpgD4Lz2HjqlwGqEux3Gz7Kj63zGAguG1dl7kXOSQoYsGtYDO7Lesq7a18LQPOS2mOMoNQ2axnCrvCrkrPu0xVy+SB1uRwHKJL0/uEKxKBPkhjKLIvP/eol/LrKroE43390Nxkrj9CGUQP7eE3KJqE3AGLC2I9fV2XTQiChlVqlXpIoyUqyq8cYJm91uVp2DcthAou1Kqq8Vz5dJZKW2/fmYkR8Oq8/qYPfbe4teb6BQguemsTgqeA+OJIkmc2xtD1EV3OQmXKqVCmLnRZcL4S4CngG+Kht28PAbOBPnjHdzndZ53P59+MghLgOaVkwd26VgqtJoKU+jWrvoD7/etJZ6Z+tJjACpsZDedl/vaN+Ym0jYGgkHcFZ02KYLISYXBzCX19s21sL1XrnOPDpCorVCiooxiDzGuWD3x9NM6fxMEv0V72l8PGXzx9gY/couwfi3PbONYRMjRE2IoTN7qHT2XPqa4ENVTX8keB8Pmm9lzX11QXBDnM5/61exSMDK7mwKjGE4B/2FFfEq4b/s7t6OwwX4XbZiLAWllwoO4NWEUCmLrX1Tsuix5DxlVl1PvYNJccPNv58V1Iub/PM3mHee84C7nvxEFt7osTTFlpkEwBnpzQSWgBNEYV1z8sRMFSSGIzZfgzf+Hdldr2fAyNJWsO+oiupVrpqgbxqEIPiiLamRdXHTTNMTcGXDaPYNodyAwRNleWzImSsPP2xdCFDDpDN/npeLF3dsBJalsm/J76JvqhM8W2LTOJ5mwKmRAxCiPuBSpGTTyHdQl8AbOfvvwLXAJUkm13l+/Ff2vZ3gO8AnHLKKVMKy++IP44QNt3dy0g4bXOrCSDXf60ISjp8jh8nH+5kNjeuYOdog6mr2NlmUAWK2UdXk3w5+2NTIAYPDo6mmN8c5PGdg3z0pxv49pWnkNI3kc/Wk4i1FSyTapZcwJmX9hovjGH4+W7ub0gTry6AoGbspXjwSWaTXfIVyE2CGOavq+neMzWFmO1nTtbiifwouipY2BIaFw8APBbIJCuuA40MxNLk8jazG/xE/DpjySzxjIUeeYFcspNAboRRX1PVe+g3VP6UX0EGneawOW77Lz54Js/vHyHi1+ihkRSmtOSqWdjtK+Wa2x2rJx4DskL/9V+HZZNw0V761eIyv9UQaCo2N5wAPl3ll9armaUdZDR3kJCh0epce3+0jBg6T4EbX6p93Nbl8MlDYATof7EHkCnxM4kpEYNt26+ZzDghxHeB/+f8txuY49ncCRx0vu+s8P2M4mD2aXLpFqIjjewZkC9VNQ0/4Dy09QGjqhnnTXmtFAw9muDXVUaSGnVaGwNmH/OaihbDVJGx8gzE0rzj9LnsG0zwxK5B4pk4tn8b1shppLM28bRreU1MsAFHQNXSpAKmyq5+qXXVJIbpxmSJZhLw6Sr350/mdXW7Gcu9hN8QzGn08/vNveMHtyyFU98Li2q8rooCp78fll3KwRFpeXTU+Yj4dMZSWbrH+lD93aT7LuS2+rW0NkQwoxO/Az5N5ce59fw4t57XhMbHfVojPi48oZ20leMXubN5yX8qCU+zvYqIzIL33F/9OlysuXpy47xrblfD37/IBLpqAaamsMWexzn1K9nSv5M2U6XFIYY+p6DvsOBYj27SR0sFop1OzGRWkjfyeTnwovP5HuBtQghTCDEfGWR+yrbtQ0BUCLHWyUa6Crh7ps4PYCwzxpi9DSsqtQU3N7+axuIGnOv81YPArsUAlGoJRyF8ukIqkyOidqIYvYUGdtNBDL1jKWxbukFaIiaDsQwP7HsEoVhEcrLD5lA845zHxPOSc/K52+uqvzBBQ2M0KQPV9VUsvlc6TE0hhUk6cjY2OQL+KJ0NAQZiGeLpMqtE1eF1/1K7/QjAxbfC/HPocVpnt9fJliLRlMWTPY8DYMWWsjM/i16lrXoxmpMJBtU1XENVQNHYGpfPVcT3ClWkjEDNmIVr1baac0mLXnyGbMsCE9T+/JlwicFtDjlTmEkfx5ed1NNNwHnADQC2bb8E/BTYDNwHfMi23d7PfAD4HjIgvRP4zQyeH490PwIij5GWWTz9Y64mWUUzdQR+LWLwWgydDUemVe5MwaerpKwcIWU2ijlAXUBBiOkhhkOOAJpV56clZJLJ5fnt7j9g5/x0+CVhD8blcaoVuI05wr6mxeAh/Zk2x2cSmiJQBPiETGnV/UPMddx6FQPQfyYOeuYl4pOupGf7HyOfjVCvzSORyZHK5qrOCVDIJKt2r4WQBGLbMhV6opjF0QD3fjSbc0HkUY1BmkIGQkDf2PQQQ0NAR5/hezRj1Gzb9pVVtt0M3Fzh+2eAE2fqnMrxwL4HIBdmdmAp28bi9EVdAVSlh44zIbWIwbvAyJyGo9xi0FQpBOwOhMjREz9AY8CYFg3I7d3fUe9zLIM8z/Q9gRVbSkdjkI37owzEMlWDnEChS2dTsLqw9xJDUwX3xtECIQQ+XcXnhPhUo7+QDNEzmipZx+Bw0DMq12VuCOhE/BrRVJotw89gxU5gTthHPGORtvJV4z4A6azMxKnl+vAbKrG0RX3w6LXioGjV1mvSK55Te9BVhcaAUZAvU8FgLHNEFJqjl5qniEwuw6MHHiUXXc7cRpnC6GrA1VxJMcdMr+WGOFY0U5D3I5nJoeekd3Dn6E5awua0WAwHR1yXhZ/mkIni6yZujWLFljHLWaVtMJauGQ9QnRTVmvPiELahKYSP8tiPqSmIXBjF9mHr/YUg53QIoIOjKWbV+RBCEPbpZPRdpPIJcvGltIRNEunJWQxuZl6td8B1OdX7j16yhqLFEFE7wBZklEMA0/a+DMTSR0Sh+aslhqd6niJhJUhHVzDHcfUccAJuoSoC4+S5MoD49tOqp8l6A87V8uqPBpi6QsrKI7KtYAt2jOyYtgf90GiSsE8jZGo0hQy00DZAYMUXM8upEzk0miqJ2VTCl9+8io9esIQTOqprykGHsFtC5ozlgB8pmJpK2sqj5VqxlL6C8J2OeekZTRWIOeLT0EJbUdCw4otp9VgMVYsEPWiuIcyKSR3HhsWQy+vksw0kOADIQHt/dArBZwcDxy2GmcXu0d2E9DC5+ELmNMoXYO+g9M02TFA5C9DVHGTPLa8rrA88EQLT3QbjLwifppKx8iQzKrrdxK6RXbSEps9i6HAEUHPIRAttxZdbALkgs+olMfSMpWis4SLqqPfz4fWLawp7N/ZTS1AdDfDpCmkrj7BaSYteWXFsatNIDPL+h306anAbDepSyJu0hE1S2TyxlFU9g8iDSumqpddSzPY7muES5VgySz7dyljOIYawOS2W3EA0fZwYZhJXrriSb5z1S7B12iM+NEWQzOYI+zSMGubxZFCtXcbRBvelHYpn8NNRtBhi6Sl3dxxLZgtaYl4ZQ/UfIBuVVcSuYLJtufb0dMAl7KPdvQeOxZDNk0s3k2aQlJUqzMtUMRTPFDJfLGUI1deLL3sCioAm5/tDo8lJC/Ja97tgMdSI3b3S4cYnB+MZ8plWRq0DWHmLlrDJQCxNvlKTw0kilc0RTVsznqoKf8XE8OMn9/E3tz0NSC3FXeWraZrSwFxX0jtOn1pl9isBfkcLGopnCCud7BnbQ1NII2PlC+v7Hi7SVq5API8ffBSAsaHFAAVXBlDTYpgs3BjDMUEMukLKypFNNQE2e8f2SmKYYvaLbdsl87I7/gwAmbGlBA2t8GwPJ7I1kzBc1EpBdS2PakWjRwN0VWaLDcUz5NJt5GyLfWP7aAoaZHM2sczhvy+DTtr2kbB2/2qJYa6nYrfOrxP2yQdyuvKDDU1h4z++ls+/4YglWc0YvBZDvT4HK2+hGLICdKpui7SVLwTsHjnwCEq+jnx6FqoiSoT3tBG2o5kezRlJLtxssWRcdvv0WnJTQTZnk7eLbpEto0+RzzTSPxwhYKol8Z5axOC2167l4nMTPuqOcleSu6rgUDxDPiWTNbYPby+8QxX7i00SMUcJC5k62XyW6/9wPY8ffHzqJ10Bx46/w4NsNkt3dzep1MTBnibgu5fJicsPd/OFc+vJ5Orw6wpbtmw5Qmd6ZODz+ejs7ETXD08bcx9qK2/TZMyBLKQ4APjoj6YLS5oeDtyUx2w+yxMHn6CeVzGKQCDJ1dAUMlZ+2gi7GGM4NiyGwViGXLoFBY1tw9toCXdNA1k7LUg0lXQuzUvDz2DFTiadytES9pXU6NQihp9/8EySmdrC0HUlHe0WA0hCHYxJV5KCwvbh7XToUkFMZSqsyzBJuKTi0xWe7X2Wh7of4vLFl0/LOZfjmCSG7u5uwuEwXV1dVTWVtniavmiaJW1h9gzEiaUtGgMGndPQ/+eVAtu2GRwcpLu7m/nzD69FrzfzpM0/DyWhMGztA5ZMWTtNZXP4NIUNfRuIZWOc37SWvRQbFIZMjSErM43E4MQYjoCfdqZhaopT+6HSZM5h+/B2VoUvI5a2SGSsqisRVkPa6QJq6gpP9zxNOpfGislGbtKVVLQYaqdta5M6j0K66jFADK7FgK3RHpjDyyMvs7DZsRisw7cYisSgcv/e+/Frfs7sqNGA7zBxTLqSUqkUTU1NNc3XxqDJsvYIihAozlhVPbpTGMshhKCpqamq9VQL3hqCiBlgXmQeBxI7gWlyJekKD3c/jKZofPHiv+Hej5zD96+W3WHd1OHpIob5zUFCpsaKWTVaHR8FMHWVoYT0O3f4F/Dy0Mu0TEPKaoEYNIVHuh/Bp/rIJxcAstWLN7FiugS539nn0Z6VBFKRctu4zAsv5OXhlwvK1WSsp4mQcubF0GRx7tmzz8Z/OOtJTALHJDFAbZ9mOdwCKe1w+rO/wjHVfH0vMQQMlWWNy9g5ug2g0HfocJHO5jA1lUe6H2FN2xqCepAVHREWt0nBHZxmYpjTGODFz13IotZjgBgcNxtAZ3Ahfck+/D6pAEyFGArdbDVJ2Ke2n4qpSsIptxgmG3yuhWKB27FhMWScpTyXNCzlQOwAtpA1UlOJMbi/3R19gf5kP+vnrp/6yU6AY08KHiaKxHBsWQzTgVJi0FjeuJyeRA9hf5poamrEkLLyWGKAnaM7WTd7fKtptzp5uoLPxxK8rVu6InLdgZHcXqDYIuRw4LaxGMsdoDvWzbmd5xYyxJpDZlmMYXrmJeLXEKJ2S5OjAV7X68rmEwA4kNwOFLX+w4FLDI/1/pagHuT8uedP4Syr4zgxOHBdSdo0uJJGRkb45je/WXXMnj17+PGPa6/atmfPHk488S+b2eR90E+f38iyRulv9od6GEsevgCycnlyeZteawMA53SeM26Mq53OdDfJoxHeeVlSL2s/epO7AUhMwWXhBp+3R2U697rOdXzrnWu4/V2n8OlLl5e4kqbLYnjTyZ3c/q5TqTtGYgwuTm6XqyPui8uElqm4ktLZPIgMT/T8kQu7LpwxNxIcJ4YCXItBnQaLYTqJ4ZWAiJPKe/Lceha3hVneuBwALXBwShaD68vuTj9HZ6iTrkjXuDEhn44Qx4bvebrhFahkPvkAACAASURBVECzwi00+Zo4kNgFQGIK+fLuvGwZ+RNLGpYwKzSLpe1hzl/WRtinl/QSmy5iqPPrnLd04qVMjya4HWU1RdAcqGd+3Xx2RyUxpKcSfLZyaMGXSeYSXDz/4mk514lwTGYlefG5X73E5oNjNcfl8jYpK0fA0CouJefFio4I//T6EybcftNNN7Fz505Wr17NBRdcAMBvfvMbhBB8+tOf5q1vfSs33XQTW7ZsYfXq1Vx99dVcfvnlXHnllcTjcn3Xb3zjG5x55sxkHPy56Kj388NrT+PULrlSWb2vnnmReQzm9k7JZZHK5kBk6E5t4m3L3lIxFtIUNGgNm9NC2McavA3s5jUFWNKwhD3RHcDZheZ1h4NUNgdKgh1jL3LtyvGL2BiagqEq6KqYli4Bxxpcwl7UGkIIwcrmlTy0/xHg0qoWQzSV5b/+tI9rz55f8b6ms3nU0DaCeog1rWtm6vSB4xZDAaoiCOi1SWEyuOWWW1i4cCEbNmxg7dq1bNiwgY0bN3L//ffz8Y9/nEOHDnHLLbdwzjnnsGHDBm644QZaW1v5/e9/z3PPPcddd93FRz7ykWk4k+nDOYtbSmINJ7WcRErZxVg6c9j7TFt51OAOcnaWczvPrTjmw+cv4s5rTj/sYxzLcOejLSL9/ksbl7J3bBeQK6x6dzhIW3m00MvkybGus/ISowFTnTZr4ViDazGc0CHXC1/VvIrRzDBCH64afP7Rk/u49b6tPLS9v+L2ZMZCC23ljFlnoKsze++PeYuhmmZ/JPDoo4/y9re/HVVVaWtr49xzz+Xpp58mEintAprNZrn++uvZsGEDqqqyffv2v9AZTw4ntZzEPTvvYSTTM+GYAyNJIj6tUFVeDimAtmIqAU5pO6XimKaQSdMxUIw2E3AtBncN7iUNS8jkMyjGAMkpupK00BYiej0rm1dWHBM0NCLHiaEi3EWjVs6W7/jKFnkPVf9+ktnKwWfbtvn5c90APLdvmAtWtI0bcyi1E0Uf49w51dcDnw4c88Twl8Zkm8x99atfpa2tjY0bN5LP5/H5qq9E9pfG6la5GHuMHROOueK2xzlncQu3vnlVxe2JTBYttIUlkTUzrgEdy/ASA4A/1Dul4HMyk0ELbufUtlejKpW7pwZN9ZhILZ0JvNwbA+DE2dJiWNywGFM1yfj2TWgxbDkUZXtvDCHgub3DFcfsScieVWfPPnsGzroUx11JM4BwOEw0GgVg3bp13HXXXeRyOfr7+3n44Yc57bTTSsYAjI6OMmvWLBRF4Yc//CG53OG/2EcCC+sWogs/GW13RfIbjKU5OJri0R0DE+5j+/A2FD3KqsYzZvJUj1m4S3h2NUtiWFC/AEMx0P2HiE9ADPm8zTceeJl9gxMv/7k7uhmhJTirY3yWmIuLT5zFhSeM12qPo+hKWuGsDaIrOiuaVqAFuiesfN7YPQLAa5a3sbF7hGxuvGVxIPMcIj2HZn/zDJ15EVMiBiHEFUKIl4QQeSHEKWXbPiGE2CGE2CaEuNDz/RpnLegdQoivCyfiKIQwhRB3Od8/KYTomsq5/SXR1NTEWWedxYknnsgTTzzBqlWrOOmkkzj//PP58pe/THt7O6tWrULTNE466SS++tWv8sEPfpA77riDtWvXsn37doLB6ouO/6WhKirt5lKEb0/FQOeOPqk1HRhJ0j3BGsRP9z2CbQte1XycGA4HbjLAectkEz1d0VnUsAhhHpjQlbStN8q//G47677yxwkzl7aOPYltK1XbLdxwwRLeddbhtVg51nHnNadx2ztOLqn3WNm8EsV3gES6cuHhnsE4hqpw6apZpLJ5tvVES7YPpYYYzu3EyBwZ1/hUXUkvAm8Cvu39UgixAngbcALQAdwvhFhi23YOuA24DvgTcC9wEfAb4Fpg2LbtRUKItwG3Am+d4vn9xVCeivqVr3yl5P+6rvOHP/yh5LtNmzYVPn/pS18CoKurixdffHGGznJqmBtcwb7kRnqiIyxoKtViXnaIAeDJXUN0rhnff2rD4BPkk3NoDjTO+Lkei7j4xHY2f/7CEgG0rHEZW/t/Szw9ATF4BM5/P7Wfa88eL9x3JZ4ml5hPc7Bu+k/6rwDzmoLMaypV7Na0reHOzXdyKL0VWD3uN3sHEsxp9BcKCUcSWbK5PLc/upurzuji/r33AzYB66QjcAVTtBhs295i2/a2CpveAPzEtu20bdu7gR3AaUKIWUDEtu0nbOl/uBN4o+c3dziffwasF1Pt5XAcM4ol9ScihM3zvZvGbdvRFyNkatT5dZ7aPTRue1+ij/3x7Vix5SX5+McxeQghxjWoW9a4jLwSZzRb2YW3tSeKrgpm1/t5YufguO3d0W6Gs/uxYssw1OOe5unCae2nga1wKLOx4vY9g3G6moKFgs5Y2uLeFw7xpd9s5V9/t43f7fkdPtoIiiOzvstMzfxsYL/n/93Od7Odz+Xfl/zGtm0LGEV2xx4HIcR1QohnhBDP9PdXTu06jpnHsoYTsW3B833Pj9v2cl+URa0hTu1q5Mnd4wXQw90PA2DFlk963eDjqI0VTSsAGM5VTgrY1jPGwpYQZy1q4uk9Q+NWFHPnRUmuOOrXxH4lIWSEMKwFDObHK1G2bbN3MMG8pmChqjyetgpZZy/1HeDp3qepy51akjI+k6j5Rgoh7hdCvFjh3xuq/azCd3aV76v9ZvyXtv0d27ZPsW37lJaWluoXcBwzhrZQHflUBy8NPTdu286+OAtbQqxd0MiewQS9Y7K526HRJIOxNA/uf5A6vZV8uu24xTCNWNG4AoFOlJcrbt/WE2Vpe5jT5zcxmsyyrTeKbdu8545neGBrLw93P0xImYVpHw8sTzdC+RXE2cdAstSa64+mSWZzdDUHCk0jExkLyyHtvemHyNt5/JlT8R2hd6VmjMG27dccxn67gTme/3cCB53vOyt87/1NtxBCA+qA8T6I43jFIOzTySUWsjv2BEkrWdK7JZrK0hDQOW2+jB88uXuIy07q4IwvPYBQY9QvfYxX1b+ebkRJBe9xTA26qlMnFhFVxxPDWCrLwdEUS9vDhXl5du8wcxsD3L+ll/u37qNxxVPMUV/DoSOkmf41oUGsZIh7uHfHwxw6sIKPv3YpiiLY42SIzStxJeUwtRxgE9Uf4+TWkxnc0YIvdGTelZk6yj3A25xMo/nAYuAp27YPAVEhxFonfnAVcLfnN1c7n98MPGBPdaX545hRRHw6VnwhOTvLDb/8JX/aJV1Gtm2TzMo1g1fMihAyNZ72xBm0uuexbItlIdk22DwuhKYVLfoyctoBYplYyfeDMVml3h7x0RaRdTLD8UwhUK0Fd5DNZ2lgdSHl8jimD/VaF0o+xK+2/5HbHtzJnkHZ/sa1pmfV+fDrKoqQFkM8Y6EGdoE+wBsXXU46m3/luJKqQQhxuRCiGzgD+LUQ4rcAtm2/BPwU2AzcB3zIyUgC+ADwPWRAeicyIwng+0CTEGIHcCNw01TO7ThmHmGfRi7RhUDlgb2Pce8Lh4DimsF+Q0VTFeY2Bjg0mnR+ZaPXPcOiyApCigwvHbcYphcd5goQNk8depYv3ruF0YSsxHX79Ph1FUNTMDWFaNoi5hCDGt5CSA/hzy867t6bAfh1HSO7lD2J54E8fc6aGW66d8BQEUIQNDRnFb4ceuOj5K0gJ9atI2Xljg5isG37F7Ztd9q2bdq23Wbb9oWebTfbtr3Qtu2ltm3/xvP9M7Ztn+hsu961CmzbTtm2fYVt24ts2z7Ntu1dUzm3vzSuueYaWltbS1pmDw0NccEFF7B48WIuuOAChoeLFY7PP/8873nPewC4++67WbVqFatXr+aUU07h0UcfBSCTybBu3Tos6/DbHUwnAoZKyAgSyC9CC22lZ1RqPknPEoQADUGd4USWfN5G8XWj+nqZa7yaVLa4UthxTB/mBFdg5zV+/fJDfOfhXTz0skzQcIur3HkJ+3SiKcvpq5RHC23jzI4zyVjH3XszAb+uoqSWkcqPovgOFIjBrYZ2FysKmCqJdI5D8f1ooa1kh0/nwLBFKps/Yokax2d/hvCud72L++67r+S7W265hfXr1/Pyyy+zfv16brnllsK2L37xi3z4wx8GYP369WzcuJENGzZw++23FwjDMAzWr1/PXXfddeQupAqEEHQ2+BkdXITq66U7KsNF3kXLARoCBsPxDLGMhV7/LHZeIzW8krSVw9SU49kv04yIGSSX6GLjoFxPYShWKoCKxKARTWWJpS3U4A4ULcrJTeeSto6cy+KvCaauYsWWI1DQwi/R57iQCpac0848aGrEMhYvRu8FFLIja4mmLFLOaodHAsd+r6Tf3AQ9L0zvPttXwsW3VB2ybt069uzZU/Ld3XffzYMPPgjA1Vdfzatf/WpuvfVWotEomzZt4qSTZPFKKBQq/CYej5cIzje+8Y184hOf4B3veMf0XMsUMacxwPYdS9Fafs2h7HPAZeM0oMagwVAiw0A8hh7ZgBVdyYipko7kj2umM4CAoWLFF9Mb+g1CGyusP+yuzOYSdtgnXRbxtIVe/wy2FaBdX0Pa2nt8XmYAfl0lk/YRYSlW+KVxriQ34yhoaIylx9ijPIg1ugrbipDIWEdPjOE4/jz09v7/9s49uqrqzuOf330/8sYEAgmIghDA8ooIM5bW6qjFGRR5NIwjdgli1emaLrUDlmmXdnXscqzV2qozzsAqVSsgDsVxfABVassSERRUiEpQHAKJQAIhr/vMnj/OuTc35N4bILk394b9Weuue9hnn8ve2eec3/799t7f/RWlpaUAlJaWcvToUQB27tzZbZe2DRs2MHbsWK6//npWrVoVTZ8wYQLvvfde+grdA+WFHjoCxYT9xfiduwiGO6I3enQfX4+DpvYgWw7+EbH6CJ6cSmsgZHgMumfa57gdVsKtYwCw5X5MY5thGE4P8eU4bTT7Qhxra8SWs5fgqUkcORnCH9IGOxW47Bbag2HcgclYnceoOfkJYLSL02bBYu454nVaqQ2/ThgfXr+xfWezL0QgnL5Q0sD3GHro2WcCdXV1nL4eY86cOcyZM4e3336bH//4x2zZsgUAq9WKw+GgubmZ3Nz+39C+vMgNCKGmKThL3mBP/edYw8a6xMgLqMhjRyl47cuNdAQKyZextPgiPSD9AuprvA4bHf4huNVwwvm7aGy9Cegey8512Wg43saOY39ELGGCJy+jvqkdXzB9g5znE267lVCHItw8EVX4IjW+TcAcfIFwl13x7I4WGthMYcdl5DgvpoFOry9doST9VKaRwYMHU1dnzNypq6ujpMTYytDtduPz+eJeM3PmTA4cOMDx452LYvx+f8bIcpcXGhpIoVOTUUrYsH9DdFC5c/DZgcX1f9Q07yZ4Yjql+R5a/GGzZ6pfQH2Nx3zJ2Nsux+o+zOHWAwDd2iXHaeeUL8Duk28Qbi+DQCmt0XbRr4a+JvJ3P9ZkJdg0mROWd2n0NRpeRIwhPmp9BUWIAv9sCjx2HFZLdKqxHnwegMyePZvVqw05qNWrV3PDDcbi8YqKCmpqOiUMampqolLW77//PoFAgEGDjF54Q0MDxcXF2O2ZoYVfXmQYhksGlRNuGcObh1+m2W9MTY3cxAVuO86STTgkl8CJ6ZTmu2n1RwbT9C3Y10QMw4mjE1AdVuo7/gx0nxSQ67LRYtnH8cBBgicvozjXGY1la4Pd95TkGRtOtfhDBBq/DoR5avdTtAU6DcOBkweo69iKpeWvCPoH4XHY8DitNLRGDIP2GLKahQsXMmPGDD799FPKyspYuXIly5cvZ/PmzYwePZrNmzezfLmxVGPs2LE0NTVF92d46aWXmDBhApMmTeLuu+9m7dq10QHot956i1mzZvVbvU6nvMiNRaDywkICjVfQEjrJX+qN2ckR93h7wwZs3hqKQ38Hyklpvov2YJi2gA5ZpIKhBcYK9Dafk1DzeNocOwiEA3HGGKyE81/DYynG3jaNHKfN9BjCeoFbCigr7FQY9jCEwInLefGzF6kP7sFltxIMB1nxlxXYxUvg+FW0BULkOK14HTYaW42Baj3GkOW88MILcdNPl9qOcNttt7F27VqWLFnCsmXLWLZsWdx8v//976OS3JmAx2Fj5XcvY8LQfNbtPESJvYL/qX0aW95N7Gmw8MqhvTy3fzXB5nG0tE0DfJQWGGGwYy1+SvMzIyQ2kBhW4MZps+APdRBsqsSe/yF/2L8Rf9DYSS/ipR0O/Rmru5ZyWcyXThdep43WgDFfXntyfc/wok7DcFFxDh/VXcvYCxv4rOkJ3LmjufnVX1PdWM2Vhffxss9NszWEx2nD67RGZzCdrqabKnTrZwh33nknTmfyvY0DgQA33ngjY8aMSVOpzowrx5RQnOvE67Ax1fUDCh3DcA9by892/jOr963m6uHX4Du8kNpGHy67hUKPA4DaE20UmMeavsNiES4qNqc8t19CqHUkj7//OI3+47jsxrqR+tZ6tp34LeG24dBSSY7Thtdho6k9SHswnHCfbs25c0GOIxoyGpLvgg4X/zL1l+SHZqIsLTQHmnlk5iNMKDC27mxsDeB1WPE4bNHFo4Vpel60YcgQXC4Xt9xyS9I8DoeDRYsWpalEZ4/HYSMU8rBw2GO0fbmYJ6/8L7b//XZ++c1f4LQaRi/XZY8qSPqCHRR59AsoFYwqMQzD8CIv/vo5BDuCvHHiRziK3uH1g69z+6bbUSqMr24uX50K4HVa8TqtfGW+gHJdOpjQ14iIOYvP0KsCcEg+Oa3zmGj5Ka/NfY3rRl4XfT7AeKa8TmtUabUwTc+LNgyaPsPjsNIeCBMIQbhtNNOHXobX7kVEoj2dPJeNHGfnuIL2GFLDKNNjuLg4h45ACcsn/gYbXlTRBn74px/SFmpj6dif0REYTH2TD6/Dhsdh4yszZJGnPYaUEJnFN8QMobYHw/hOm5XkjQkX5ThtXcJH+WkyDLpboOkzPA4rbYEw7YEwFgG7tXPF9oRhedSf8mG3Wrrc+EVebRhSwcUl3uj3lmrwynAq7f/KnroanviH0YwbNI6PaluAdwiGlRFKctoImz3TPLc2DKkgMosvom7bHjSely6GIdZjcFrxxqxxKHDrUJImy3A7rLQFQtEeUKyUxx3fuBgwtpbMiQlTFGrDkBIqRxRxUbGX6SONac7tQaNdPJbBTCqZhMPq6DKO4HXauryAdCgpNYwenIPVYmiMgaGT1B7susBtUE7nM+F12PCYhiLHacORpkkBuvU1fYbXYaP+lK/bjQ5w2YVFXDW2hMoLi8iJ6RGlK2Z6vjEk38Wb934zKtTWFjBDFjHtEtsOXmfnCwh0KClVzJ9azuTywuiGPBHDEDtte3J5QfTYabNEDXZBGp8V7TGkiLOV3f75z3/OqFGjGDNmDG+88UY0XSnFt771LU6dOsWhQ4e48sorqaioYPz48fzqV7+K5rvvvvt4880301O5BLjNMQZfggVSK797GXd+8+IurnK6Zlmcr7gcnS8gXzDcZWvIAo+diFOX47R2GfvRHkNqcNgsjBuaFzXQrYEQgVBHl1CSiPDYdwxBzaEF7ujzog3DAOBsZLf37dvHmjVr2Lt3L6+//jp33XUX4bCxGOnVV19l4sSJ5OXlYbPZePTRR6murmb79u08+eST7Nu3D4Dvf//7XWS8+4PIGMPpPdPT6eIx6FBSSom8cHzBcDc9f4/Dxi3TRwDQGgh3GeTUYwypJdIuEQ0kt6Prq3jO5DL2/OQaJpYXRMfk0tmJGvDdgod3PMwnjZ/06W+OLRrLsmnxF6BFOBvZ7Y0bN1JVVYXT6WTkyJGMGjWKHTt2MGPGDJ5//nmWLl0KGIqsEXXW3NxcKioqOHz4MOPGjWPEiBE0NDRQX1/PkCFD+rS+Z4rHYSyQMlzjxH0Op82C1SKEOxRF2mNIKXarBZtFEhrsH82qoNkXYt7UMr40t5oUgVzngH819CsRw3AiYhjiKABEZiB5nJ0qxemit1t7zheRvSLSISKVMekXiki7iOw2P/8ec26qiHwkIjUi8oS59zPm/tBrzfR3ReTC3pQtE0kku3348GHKy8uj+crKyjh8+DAA27ZtY+rUqd1+6+DBg3zwwQdcfvnl0bQpU6awbdu2VFYhKZ5oKCkc90aPYGxfaMVpsyT1LDR9g9thNWa/nBZKAkMe47HvTGLK8MJozzTHYYtKQGtSg81qwWG10Ghuu5pMGqbTY0ifF9fbbsHHwE3Af8Q5d0ApNSlO+tPAUmA78CpwHca+z4uBE0qpUSJSBTwMfKeX5euxZ58JRATzYonM6GlsbOwmr93S0sLcuXN5/PHHycvLi6aXlJRw5MiR1BY2CR6HsRDnlC/Yo9ub67LjjVNvTd/jtlujoaRk+19EYtk6jJQeXHZLVAMpWQcpIopYkMZ26e2ez9VKqU/PNL+IlAJ5Sql3zL2efwfcaJ6+AVhtHq8HrhIZWHs+JpLdLisr49ChQ9F8tbW1DB06FACbzUZHR0f0XDAYZO7cudx8883cdNNNXX7f5/PhdrtTXY2EuM2eTWNLoEdxPK/Tqgee04TbHPvx9+DJRV5AeuA5Pbgd1qicdrJ26Rx8zpJQUg+MFJEPRORPIvJ1M20YUBuTp9ZMi5w7BKCUCgFNwKB4PywiS0Vkp4jsPHbsWGpKnwISyW7Pnj2bNWvW4Pf7+eKLL9i/fz/Tpk0DYMyYMXz++eeA4VksXryYiooK7rnnnm6//9lnn3XbCS6dRF4sDa2BpDc6GAt8IiqgmtTitltjpkUmfuQjkwL0VNX04HHYONHWs2GIPFeF3gwKJYnIFiDeaOYKpdTGBJfVAcOVUg0iMhX4g4iMB+J5AJF4QrJzXROVegZ4BqCysjIj4xELFy5k69atHD9+nLKyMh588EGWL1/OggULWLlyJcOHD+fFF18EYPz48SxYsIBx48Zhs9l48sknsVqNm+H6669n69atjBo1im3btvHss89y6aWXMmmSEaV76KGHmDVrFsFgkJqaGiorKxOWKdVEbmD/adPv4vHogolYBpZDmLG4HVZa/CFCHSqpJ+eJhpK0x5AOXHYrtSfajOMkoaQxQ3KZdekQpl8Ut5+cEnq8A5RSV5/tjyql/IDfPN4lIgeASzA8hLKYrGVAJCheC5QDtSJiA/KBxrP9vzOFs5XdXrFiBStWrOiWvmTJEhYtWsSSJUu44oor4o5HALzyyivMmzcPm63/HurY6Y496caX5Gq57XThtls5ER3kTNwu3mgoSXsM6cBttxAMG8+zJ+kYg42nbu4+ASWVpCSUJCLFImI1jy8CRgOfK6XqgGYRmW6OHywCIl7Hy8Ct5vE84E2V6C14HlFaWsrtt9/OqVOnkuYLhULce++9aSpVfGJv7sF6n4WMwW23Jp0WGSFi2PP0GENaiO1IZZox7tUdICJzgF8DxcD/ishupdS1wEzgpyISAsLA95RSkd7/ncBvATfGbKTXzPSVwLMiUoPhKVT1pmwDiQULFvSYZ/78+WkoSXJiZ1bEbkqi6V/cDiuNZiw72awkh83CqJIcxgzJS5hH03dEwnoiUJKbfC+WdNMrw6CU2gBsiJP+EvBSgmt2At1GSJVSPqD/326acyZWNbW8UBuGTMFttxIIGTPbevIGttzzjXQUSUNnR+qCHCd2a2aJUGRWaTRZjUd7DBlJV+XOzOqZns94TI8hE7e31YZB02fEvoDSKfilSU7suMIgrU2VMUSel8hubpmENgyaPiPWYxhgaxOzGu0xZCau2P2fMwxtGFJETk5OVvxmX3K6Do8mM4j1GPSMo8yjOAONtTYMmj4jIrw2I40LcTQ9E/EY7FbRnlwG0dRurC3JxLDrgO8+1D/0EP7qvpXddlaMZciPfnTG+R955BHWrVuH3+9nzpw5PPjggyxbtowRI0Zw1113AfDAAw+Qm5vLvffeGzd/trBjxVVaUiHDiIQsYufNa/qfpnZjCnEmihZqjyHFbNq0if3797Njxw52797Nrl27ePvtt6mqqmLt2rXRfOvWrWP+/PkJ82cLJbmuHgX0NOklMvaTbHWtJv2MH5oPwOiS3B5ypp8B34U4m559Kti0aRObNm1i8uTJgCGZvX//fhYvXszRo0c5cuQIx44do7CwkOHDh/PEE0/EzT9z5sz+rIYmi4mMMei9LzKL733jYv5m3GAuGawNw3mHUor777+fO+64o9u5efPmsX79eurr66mqquoxv0ZzLkQMg1eHkjIKq0Uy0iiADiWlnGuvvZZVq1bR0tICGLu1RXZuq6qqYs2aNaxfv5558+b1mF+j6Q06lKQ5U3QXIsVcc801VFdXM2PGDMCYcvrcc89RUlLC+PHjaW5uZtiwYdEtP5Pl12jOhWCHoUU5KEcvbtOcGZLtAqaVlZVq586dXdKqq6upqKjopxJlJvpvcv4SCnfwi02fcfvXR+oFbpooIrJLKRV3AxftMWg0Axyb1cLyb4/t72Josgg9xqDRaDSaLgxYw5DtIbK+RP8tNBrN2TAgDYPL5aKhoUG/EDGMQkNDAy5X5gl1aTSazGRAjjGUlZVRW1vLsWPH+rsoGYHL5aKsrKznjBqNRsMANQx2u52RI0f2dzE0Go0mK+lVKElEHhGRT0TkQxHZICIFMefuF5EaEflURK6NSZ8qIh+Z554QU+5RRJwistZMf1dELuxN2TQajUZzbvR2jGEzMEEp9TXgM+B+ABEZB1QB44HrgKdEJLLs8mlgKTDa/Fxnpi8GTiilRgGPAQ/3smwajUajOQd6ZRiUUpuUUiHzn9uBSCD7BmCNUsqvlPoCqAGmiUgpkKeUekcZI8O/A26MuWa1ebweuEq0eLxGo9Gknb4cY7gNiOhID8MwFBFqzbSgeXx6euSaQwBKqZCINAGDgOOn/0cishTD6wBoEZFPz7HMF8T7/SxF1yUz0XXJTHRdYESiEz0aBhHZAgyJc2qFUmqjmWcFEAKej1wW/xZ9tQAABCZJREFUJ79Kkp7smu6JSj0DPJOk2GeEiOxMtCQ829B1yUx0XTITXZfk9GgYlFJXJzsvIrcCfwtcpToXDtQC5THZyoAjZnpZnPTYa2pFxAbkA41nUAeNRqPR9CG9nZV0HbAMmK2Uaos59TJQZc40GokxyLxDKVUHNIvIdHP8YBGwMeaaW83jecCbSq9Q02g0mrTT2zGG3wBOYLM5TrxdKfU9pdReEVkH7MMIMd2tlAqb19wJ/BZwA6+ZH4CVwLMiUoPhKVT1smxnQq/DURmErktmouuSmei6JCHrZbc1Go1G07cMSK0kjUaj0Zw72jBoNBqNpgvnrWEQketMuY4aEVne3+U5W0TkoCktsltEdpppRSKyWUT2m9+F/V3OeIjIKhE5KiIfx6QlLHsieZVMIEFdHhCRw2bb7BaRWTHnMrIuIlIuIm+JSLWI7BWRfzLTs65dktQlG9vFJSI7RGSPWZcHzfTUtotS6rz7AFbgAHAR4AD2AOP6u1xnWYeDwAWnpf0bsNw8Xg483N/lTFD2mcAU4OOeyg6MM9vHCYw0283a33XooS4PAPfFyZuxdQFKgSnmcS6GxM24bGyXJHXJxnYRIMc8tgPvAtNT3S7nq8cwDahRSn2ulAoAazAkObKdWFmR1XTKjWQUSqm36b5GJVHZ48qrpKWgZ0CCuiQiY+uilKpTSr1vHjcD1RhqBFnXLknqkohMrotSSrWY/7SbH0WK2+V8NQxR+Q2TWGmObEEBm0RklykRAjBYGWtFML9L+q10Z0+ismdrW/2jqTq8KsbNz4q6mMrGkzF6p1ndLqfVBbKwXUTEKiK7gaPAZqVUytvlfDUMZyy/kcH8tVJqCvBt4G4RmdnfBUoR2dhWTwMXA5OAOuBRMz3j6yIiOcBLwA+UUqeSZY2Tlul1ycp2UUqFlVKTMJQiponIhCTZ+6Qu56thSCTZkTUopY6Y30eBDRju4lemgi3m99H+K+FZk6jsWddWSqmvzIe5A/hPOl35jK6LiNgxXqTPK6X+20zOynaJV5dsbZcISqmTwFaMrQpS2i7nq2F4DxgtIiNFxIGxyvrlfi7TGSMiXhHJjRwD1wAf01VW5FY65UaygURljyuv0g/lO2MiD6zJHIy2gQyuiylRsxKoVkr9MuZU1rVLorpkabsUi7kBmoi4gauBT0h1u/T3qHt/fYBZGLMVDmAoxfZ7mc6i7BdhzDzYA+yNlB9DpvyPwH7zu6i/y5qg/C9guPIRGfbFycoOrDDb6VPg2/1d/jOoy7PAR8CH5oNamul1Aa7ACDl8COw2P7OysV2S1CUb2+VrwAdmmT8GfmKmp7RdtCSGRqPRaLpwvoaSNBqNRpMAbRg0Go1G0wVtGDQajUbTBW0YNBqNRtMFbRg0Go1G0wVtGDQajUbTBW0YNBqNRtOF/we6UPlnXPJ1qQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "duration = 100 * 3\n",
    "periodicities = [10, 100]\n",
    "num_harmonics = [3, 2]\n",
    "std = np.array([2, 3])\n",
    "np.random.seed(8678309)\n",
    "\n",
    "terms = []\n",
    "for ix, _ in enumerate(periodicities):\n",
    "    s = simulate_seasonal_term(\n",
    "        periodicities[ix],\n",
    "        duration / periodicities[ix],\n",
    "        harmonics=num_harmonics[ix],\n",
    "        noise_std=std[ix])\n",
    "    terms.append(s)\n",
    "terms.append(np.ones_like(terms[0]) * 10.)\n",
    "series = pd.Series(np.sum(terms, axis=0))\n",
    "df = pd.DataFrame(data={'total': series,\n",
    "                        '10(3)': terms[0],\n",
    "                        '100(2)': terms[1],\n",
    "                        'level':terms[2]})\n",
    "h1, = plt.plot(df['total'])\n",
    "h2, = plt.plot(df['10(3)'])\n",
    "h3, = plt.plot(df['100(2)'])\n",
    "h4, = plt.plot(df['level'])\n",
    "plt.legend(['total','10(3)','100(2)', 'level'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unobserved components (frequency domain modeling)\n",
    "\n",
    "The next method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using trigonometric functions with primary periodicities of 10 and 100, respectively, and number of harmonics 3 and 2, respectively.  Note that this is the correct, generating model. The process for the time series can be written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n",
    "\\mu_{t+1} & = \\mu_t \\\\\n",
    "\\gamma^{(1)}_{t} &= \\sum_{j=1}^2 \\gamma^{(1)}_{j, t} \\\\\n",
    "\\gamma^{(2)}_{t} &= \\sum_{j=1}^3 \\gamma^{(2)}_{j, t}\\\\\n",
    "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1)}_{j,t}, ~j = 1, 2, 3\\\\\n",
    "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, 3\\\\\n",
    "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n",
    "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "$$\n",
    "\n",
    "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_1)$, and  $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$, where $\\sigma_1 = 2.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                Unobserved Components Results                                 \n",
      "==============================================================================================\n",
      "Dep. Variable:                                      y   No. Observations:                  300\n",
      "Model:                                fixed intercept   Log Likelihood               -1145.631\n",
      "                    + stochastic freq_seasonal(10(3))   AIC                           2295.261\n",
      "                   + stochastic freq_seasonal(100(2))   BIC                           2302.594\n",
      "Date:                                Mon, 24 Feb 2020   HQIC                          2298.200\n",
      "Time:                                        22:49:06                                         \n",
      "Sample:                                             0                                         \n",
      "                                                - 300                                         \n",
      "Covariance Type:                                  opg                                         \n",
      "===============================================================================================\n",
      "                                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------------\n",
      "sigma2.freq_seasonal_10(3)      4.5942      0.565      8.126      0.000       3.486       5.702\n",
      "sigma2.freq_seasonal_100(2)     9.7904      2.483      3.942      0.000       4.923      14.658\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                       34.17   Jarque-Bera (JB):                 0.08\n",
      "Prob(Q):                              0.73   Prob(JB):                         0.96\n",
      "Heteroskedasticity (H):               1.17   Skew:                             0.01\n",
      "Prob(H) (two-sided):                  0.45   Kurtosis:                         3.08\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "fixed intercept estimated as 4.053\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.tsa.UnobservedComponents(series.values, \n",
    "                                    level='fixed intercept', \n",
    "                                    freq_seasonal=[{'period': 10,\n",
    "                                                    'harmonics': 3},\n",
    "                                                   {'period': 100,\n",
    "                                                    'harmonics': 2}])\n",
    "res_f = model.fit(disp=False)\n",
    "print(res_f.summary())\n",
    "# The first state variable holds our estimate of the intercept\n",
    "print(\"fixed intercept estimated as {0:.3f}\".format(res_f.smoother_results.smoothed_state[0,-1:][0]))\n",
    "\n",
    "res_f.plot_components()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.80901699,  0.58778525,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        , -0.58778525,  0.80901699,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.30901699,  0.95105652,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        , -0.95105652,  0.30901699,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        -0.30901699,  0.95105652,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        -0.95105652, -0.30901699,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.99802673,  0.06279052,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        , -0.06279052,  0.99802673,  0.        ,\n",
       "         0.        ],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        ,  0.9921147 ,\n",
       "         0.12533323],\n",
       "       [ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "         0.        ,  0.        ,  0.        ,  0.        , -0.12533323,\n",
       "         0.9921147 ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.ssm.transition[:, :, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Observe that the fitted variances are pretty close to the true variances of 4 and 9.  Further, the individual seasonal components look pretty close to the true seasonal components.  The smoothed level term is kind of close to the true level of 10.  Finally, our diagnostics look solid; the test statistics are small enough to fail to reject our three tests."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unobserved components (mixed time and frequency domain modeling)\n",
    "\n",
    "The second method is an unobserved components model, where the trend is modeled as a fixed intercept and the seasonal components are modeled using 10 constants summing to 0 and trigonometric functions with a primary periodicities of 100 with 2 harmonics total.  Note that this is not the generating model, as it presupposes that there are more state errors for the shorter seasonal component than in reality. The process for the time series can be written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\mu_t + \\gamma^{(1)}_t + \\gamma^{(2)}_t + \\epsilon_t\\\\\n",
    "\\mu_{t+1} & = \\mu_t \\\\\n",
    "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^9 \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n",
    "\\gamma^{(2)}_{j, t+1} &= \\gamma^{(2)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\sin(\\lambda_j) + \\omega^{(2)}_{j,t}, ~j = 1, 2\\\\\n",
    "\\gamma^{*, (2)}_{j, t+1} &= -\\gamma^{(2)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (2)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (2)}_{j, t}, ~j = 1, 2\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$, and  $\\omega^{(2)}_{j,t}$ are i.i.d. $N(0, \\sigma^2_2)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                Unobserved Components Results                                 \n",
      "==============================================================================================\n",
      "Dep. Variable:                                      y   No. Observations:                  300\n",
      "Model:                                fixed intercept   Log Likelihood               -1238.113\n",
      "                            + stochastic seasonal(10)   AIC                           2480.226\n",
      "                   + stochastic freq_seasonal(100(2))   BIC                           2487.538\n",
      "Date:                                Mon, 24 Feb 2020   HQIC                          2483.157\n",
      "Time:                                        22:49:06                                         \n",
      "Sample:                                             0                                         \n",
      "                                                - 300                                         \n",
      "Covariance Type:                                  opg                                         \n",
      "===============================================================================================\n",
      "                                  coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------------------\n",
      "sigma2.seasonal                55.2934      7.114      7.773      0.000      41.351      69.236\n",
      "sigma2.freq_seasonal_100(2)    28.6897      4.008      7.159      0.000      20.835      36.544\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                      165.59   Jarque-Bera (JB):                 1.20\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.55\n",
      "Heteroskedasticity (H):               1.27   Skew:                            -0.14\n",
      "Prob(H) (two-sided):                  0.24   Kurtosis:                         2.87\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "fixed intercept estimated as 4.468\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.tsa.UnobservedComponents(series, \n",
    "                                    level='fixed intercept', \n",
    "                                    seasonal=10,\n",
    "                                    freq_seasonal=[{'period': 100,\n",
    "                                                    'harmonics': 2}])\n",
    "res_tf = model.fit(disp=False)\n",
    "print(res_tf.summary())\n",
    "# The first state variable holds our estimate of the intercept\n",
    "print(\"fixed intercept estimated as {0:.3f}\".format(res_tf.smoother_results.smoothed_state[0,-1:][0]))\n",
    "\n",
    "res_tf.plot_components()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plotted components look good.  However, the estimated variance of the second seasonal term is inflated from reality.  Additionally, we reject the Ljung-Box statistic, indicating we may have remaining autocorrelation after accounting for our components."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unobserved components (lazy frequency domain modeling)\n",
    "\n",
    "The third method is an unobserved components model with a fixed intercept and one seasonal component, which is modeled using trigonometric functions with primary periodicity 100 and 50 harmonics. Note that this is not the generating model, as it presupposes that there are more harmonics then in reality.  Because the variances are tied together, we are not able to drive the estimated covariance of the non-existent harmonics to 0.  What is lazy about this model specification is that we have not bothered to specify the two different seasonal components and instead chosen to model them using a single component with enough harmonics to cover both.  We will not be able to capture any differences in variances between the two true components.  The process for the time series can be written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & = \\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n",
    "\\mu_{t+1} &= \\mu_t\\\\\n",
    "\\gamma^{(1)}_{t} &= \\sum_{j=1}^{50}\\gamma^{(1)}_{j, t}\\\\\n",
    "\\gamma^{(1)}_{j, t+1} &= \\gamma^{(1)}_{j, t}\\cos(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\sin(\\lambda_j) + \\omega^{(1}_{j,t}, ~j = 1, 2, \\dots, 50\\\\\n",
    "\\gamma^{*, (1)}_{j, t+1} &= -\\gamma^{(1)}_{j, t}\\sin(\\lambda_j) + \\gamma^{*, (1)}_{j, t}\\cos(\\lambda_j) + \\omega^{*, (1)}_{j, t}, ~j = 1, 2, \\dots, 50\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                                 Unobserved Components Results                                 \n",
      "===============================================================================================\n",
      "Dep. Variable:                                       y   No. Observations:                  300\n",
      "Model:                                 fixed intercept   Log Likelihood               -1101.455\n",
      "                   + stochastic freq_seasonal(100(50))   AIC                           2204.910\n",
      "Date:                                 Mon, 24 Feb 2020   BIC                           2208.204\n",
      "Time:                                         22:49:06   HQIC                          2206.243\n",
      "Sample:                                              0                                         \n",
      "                                                 - 300                                         \n",
      "Covariance Type:                                   opg                                         \n",
      "================================================================================================\n",
      "                                   coef    std err          z      P>|z|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------------------\n",
      "sigma2.freq_seasonal_100(50)     0.7591      0.082      9.233      0.000       0.598       0.920\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                      883.25   Jarque-Bera (JB):                 0.72\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.70\n",
      "Heteroskedasticity (H):               1.00   Skew:                            -0.01\n",
      "Prob(H) (two-sided):                  0.99   Kurtosis:                         2.71\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "fixed intercept estimated as 4.426\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.tsa.UnobservedComponents(series, \n",
    "                                    level='fixed intercept', \n",
    "                                    freq_seasonal=[{'period': 100}])\n",
    "res_lf = model.fit(disp=False)\n",
    "print(res_lf.summary())\n",
    "# The first state variable holds our estimate of the intercept\n",
    "print(\"fixed intercept estimated as {0:.3f}\".format(res_lf.smoother_results.smoothed_state[0,-1:][0]))\n",
    "\n",
    "res_lf.plot_components()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that one of our diagnostic tests would be rejected at the .05 level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unobserved components (lazy time domain seasonal modeling)\n",
    "\n",
    "The fourth method is an unobserved components model with a fixed intercept and a single seasonal component modeled using a time-domain seasonal model of 100 constants. The process for the time series can be written as:\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "y_t & =\\mu_t + \\gamma^{(1)}_t + \\epsilon_t\\\\\n",
    "\\mu_{t+1} &= \\mu_{t} \\\\\n",
    "\\gamma^{(1)}_{t + 1} &= - \\sum_{j=1}^{99} \\gamma^{(1)}_{t + 1 - j} + \\omega^{(1)}_t\\\\\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "where $\\epsilon_t$ is white noise, $\\omega^{(1)}_{t}$ are i.i.d. $N(0, \\sigma^2_1)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            Unobserved Components Results                             \n",
      "======================================================================================\n",
      "Dep. Variable:                              y   No. Observations:                  300\n",
      "Model:                        fixed intercept   Log Likelihood               -1564.378\n",
      "                   + stochastic seasonal(100)   AIC                           3130.756\n",
      "Date:                        Mon, 24 Feb 2020   BIC                           3134.054\n",
      "Time:                                22:49:06   HQIC                          3132.091\n",
      "Sample:                                     0                                         \n",
      "                                        - 300                                         \n",
      "Covariance Type:                          opg                                         \n",
      "===================================================================================\n",
      "                      coef    std err          z      P>|z|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "sigma2.seasonal  3.558e+05   2.96e+04     12.012      0.000    2.98e+05    4.14e+05\n",
      "===================================================================================\n",
      "Ljung-Box (Q):                     2223.75   Jarque-Bera (JB):                25.29\n",
      "Prob(Q):                              0.00   Prob(JB):                         0.00\n",
      "Heteroskedasticity (H):               0.49   Skew:                             0.85\n",
      "Prob(H) (two-sided):                  0.00   Kurtosis:                         3.37\n",
      "===================================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Covariance matrix calculated using the outer product of gradients (complex-step).\n",
      "fixed intercept estimated as 4.690\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.tsa.UnobservedComponents(series,\n",
    "                                    level='fixed intercept',\n",
    "                                    seasonal=100)\n",
    "res_lt = model.fit(disp=False)\n",
    "print(res_lt.summary())\n",
    "# The first state variable holds our estimate of the intercept\n",
    "print(\"fixed intercept estimated as {0:.3f}\".format(res_lt.smoother_results.smoothed_state[0,-1:][0]))\n",
    "\n",
    "res_lt.plot_components()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The seasonal component itself looks good--it is the primary signal.  The estimated variance of the seasonal term is very high ($>10^5$), leading to a lot of uncertainty in our one-step-ahead predictions and slow responsiveness to new data, as evidenced by large errors in one-step ahead predictions and observations. Finally, all three of our diagnostic tests were rejected. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison of filtered estimates\n",
    "\n",
    "The plots below show that explicitly modeling the individual components results in the filtered state being close to the true state within roughly half a period.  The lazy models took longer (almost a full period) to do the same on the combined true state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assign better names for our seasonal terms\n",
    "true_seasonal_10_3 = terms[0]\n",
    "true_seasonal_100_2 = terms[1]\n",
    "true_sum = true_seasonal_10_3 + true_seasonal_100_2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_s = np.s_[:50]  # After this they basically agree\n",
    "fig1 = plt.figure()\n",
    "ax1 = fig1.add_subplot(111)\n",
    "idx = np.asarray(series.index)\n",
    "h1, = ax1.plot(idx[time_s], res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n",
    "h2, = ax1.plot(idx[time_s], res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n",
    "h3, = ax1.plot(idx[time_s], true_seasonal_10_3[time_s], label='True Seasonal 10(3)')\n",
    "plt.legend([h1, h2, h3], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n",
    "plt.title('Seasonal 10(3) component')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UpTCRUvLxoY/Zfm07TokDaBIawntWv4LPi4iuswrknLmu85dS7gXuZFn2r5QyzfDyEOD2sGMIISoDpaWUBw2l/e+BR05+XVRERkYyevRoxowZgxCC9u3bs3btWgAuXLjA9evXqVevHtWrV+fEiRPo9XpCQkLw9/fPPIZer8/s1fPTTz/Rtu39U63Wq1ePyMjIzOSfmppKYGDgY8VbunRpatSowS+//AJof4AnT54EoE2bNqxfvx4g8xoeJi4u7r7keuLECdzdtdJKt27d7qu6yviwiYmJwdXVFdDaQTJcuXKFmjVr8s4779C3b19OnTpF+/bt2bx5MwkJCcTHx7Np0ybatWv30JhiY2OpXLkyqampuboGRTGXr45/xcaLG7GO7UbTm/Cx5Sqo2wP6LIICusfElA2+I7i/BF9DCHFcCPGfECLjv9QVCDXaJtSwLFtCiFFCiAAhREB2DZ+FQWJiYmZXzy5dutCtWzemT58OwJtvvkl6ejpeXl4MGjSI1atXY2NjQ5s2bahRowZeXl6MHz+eJk2aZB7P3t6ewMBAmjZtyq5du5g2bdp957O2tubXX39lwoQJNGrUCB8fH/z8/B47/rVr1/Ldd9/RqFEjPDw8+P333wH48ssvWbJkCb6+vsTExNy3T0YVizEpJXPnzqVevXr4+Pgwffr0zIS+aNEiAgIC8Pb2pmHDhixduhSADz/8kEmTJtGmTRvS09Mzj7VhwwY8PT3x8fHh3LlzDBs2jCZNmjB8+HCaN29OixYteO2112jcuPFDr+3jjz+mRYsWdO3alfr16z/2e6QoBemPy3/w7elvEbEtaHanCgsslyCqtoDnVoFFwTXL5mkOX0Nd/p8Zdf5Gyz8CmgH9pZRSCGEDOEgpowx1/JsBD6Ae8JmUsothv3bAh1LKPo86d7NmzWTWyVyCgoJo0KBBruNXHp+DgwNxcXHmDsOs1N+bYmonIk7wyj8jSI93xze6O9+mz0Ln7A6v/AV2ziY5hxDiqJSyWdbl+f5YEUK8jNYQ3Dmj4VZKmQwkG54fFUJcBuqilfSNq4bcgJv5jUFRFKWouRl3k3d2vQOpTlQJ78Zy27noSpWDlzaaLPE/TL6qfYQQPdAaePtKKROMllcQQlgYntcE6gBXpJS3gFghREuhtSYOA37PTwzKk1HSS/2KYkrxqfGM2TmG2ORkEoIH86vjCiwEMHQTlK7yRGLIS1fPdUBHoLwQIhSYjta7xwbYbugZktGlsz0wSwiRBqQDo6WUGY3Fb/C/rp5/Y4KePoqiKEVFuj6diXsncin6MvHXX+EXt+M43LyklfjL135iceQ6+Usph2Sz+Lsctt0IbMxhXQDgmd06RVGU4u7L41+yJ3QPKeHP8EYFO5rc/Al8R0LtLk80DjW8g6IoyhOy+dJmVp1ZhS62DXVFS96LXwjlakMB9eV/GJX8FUVRnoDTkaeZdXAWdmn1SYvow09VfkUXFw79l4N1qScej0r++SSEYOjQoZmv09LSqFChAr179wZgy5YtzJ492yTnymlwNVMPK50bS5cu5fvvv3/0hgZ6vZ533nkHT09PvLy88PX15erVqwUY4eOrXr06t2/fNncYSjESlRjFuD3jsJRORFwZyNpWYThe3AQdJoBrU7PEVGwGdjMXe3t7zpw5Q2JiInZ2dmzfvj3zrlWAvn370rdv3wKNwRzDSo8ePTpP22/YsIGbN29y6tQpdDodoaGhmcNMKEpxlqZP48O9HxKVeJeYy6/zQYtK+Jz8QEv67d43W1yq5G8CPXv2ZOvWrQCsW7eOIUP+1zZuPHzzM888k1laXrZsGS+++CJArodVzo28DCvdr18/+vTpQ40aNVi8eDELFiygcePGtGzZkjt3tM5ZOQ2LbDwhSseOHZkwYQLNmzenbt267Nu374G4bt26ReXKldHptD85Nzc3nJ21vsz//vsvrVq1okmTJgwcODCzW+msWbPw9fXF09OTUaNGZY7vs2jRIho2bIi3tzeDBw8G4M6dO/Tr1w9vb29atmzJqVOnMuMcMWIEHTt2pGbNmixatCgzpn79+tG0aVM8PDxYvnx5rt5fRcmrRccW4R/mT2r4szRxacgb0QsgPQWeXV6gd/A+kpSySDyaNm0qszp79uz/Xvw1QcqVvUz7+GvCA+fMyt7eXp48eVIOGDBAJiYmykaNGsndu3fLp59+Wkop5apVq+Rbb70lpZQyLCxM1qpVS+7du1fWqVNHRkVFSSmlfOqpp+SFCxeklFIeOnRIdurUSUopZZ8+feSaNWuklFIuXrxY2tvb5xhDVk5OTjIsLEzOmzdPDh8+XEopZVBQkKxatapMTEyUq1atkrVq1ZL37t2TERERsnTp0vKbb76RUkr57rvvyi+++EJKKeXt27czj/nRRx/JRYsWSSmlnD59uvz888+llFJ26NBBvvfee1JKKbdu3So7d+78QDwhISHS3d1dNmrUSL733nvy2LFjUkopIyMjZbt27WRcXJyUUsrZs2fLmTNnSill5vsjpZQvvfSS3LJli5RSysqVK8ukpCQppZR3796VUko5ZswYOWPGDCmllDt37pSNGjXKjLNVq1YyKSlJRkZGyrJly8qUlJT7jp+QkCA9PDwyr9Xd3V1GRkY+cA33/b0pSi5su7pNeq72lK2Xvym9pm+Td3Z/JeX00lL6r3hiMQABMpucqqp9TMDb25vg4GDWrVtHr169ctzOxcWFWbNmZY5kWbZsWZMPq5xB5mJY6U6dOuHo6IijoyNlypShTx9tlA0vL6/MknNuh0XOGHraeEhlY25ubpw/f55du3axa9cuOnfuzC+//EJiYiJnz56lTZs2AKSkpNCqVSsAdu/ezdy5c0lISODOnTt4eHjQp08fvL29efHFF+nXrx/9+vXLvM6M9+qpp54iKioqc0yip59+GhsbG2xsbKhYsSLh4eG4ubmxaNEiNm3aBEBISAgXL17MnIxGUfLrcvRlph6YSnnLulwN6sbaXhY4/zcLaneFZiPMHV4xSv49TdOo+rj69u3L+PHj2bNnD1FRUTlud/r0acqVK8fNm9qoFgUxrHJuhpWG+4dC1ul0ma91Oh1padpgrbkdFjljXwsLi8x9s9umZ8+e9OzZExcXFzZv3ky3bt3o2rUr69atu2/bpKQk3nzzTQICAqhatSozZszIHPp669at7N27ly1btvDxxx8TGBiY7XVmvHdZh3xOS0tjz5497Nixg4MHD1KqVCk6duz40KG1FSUvYlNieXf3u1gKW4LPDuC1puVpc2w02JeHZ5cW2EideaHq/E1kxIgRTJs2DS8vrxy38ff35++//+b48ePMmzePq1evmnRYZcj9sNK5ZaphkY8dO3bfB96pU6dwd3enZcuWHDhwgEuXLgGQkJDAhQsXMhNx+fLliYuLyxzmOmMY7E6dOjF37tzMbyTG17lnzx7Kly9P6dKlc4wnJiYGZ2dnSpUqxblz5zh06NBjX5uiGJNSMmX/FK7HhpB04wXqla3CpOSFcO8WDFyjfQAUAir5m4ibmxtjx47NcX1ycjIjR45k5cqVVKlShfnz5zNixAiklI81rLKxxxlWOrdMNSxyREQEffr0wdPTE29vbywtLRkzZgwVKlRg9erVDBkyJLOx9ty5czg5OTFy5Ei8vLzo168fvr6+gDZz2UsvvZTZgD1u3DicnJyYMWNG5rDREydOZM2aNQ+Np0ePHqSlpeHt7c3UqVNp2bLlY1+bohhbf349u0J2USltAAn33Pmx/gEsLv0LPT6Dqr7mDi9TnoZ0Nic1pLNiburvTXmUK9FXeP7P53Gx8iDw+EBWtovjqSOjwWugdjOXGap7chrSWZX8FUVRTCA1PZWJ+yZirbPl/JlevFjfkk6Bk6FCfeizsFDU8xtTyV9RFMUEvj75NUF3gkgNH0A1B2dmJs9FpKXAoB/AuvDd0KiSv6IoSj4dDT/Kd6e/o6y+HTFR9fmlxlYsbx2FfkugfB1zh5ctlfwVRVHyITYllsn7JuNo4cK1C11Y1TSYcmdXQ6sx0PAZc4eXI5X8FUVR8mG2/2zC4sMIu9yfNxoIWp+dBdVaQZcZ5g7toXKd/IUQK4UQEUKIM0bLygohtgshLhp+OhutmySEuCSEOC+E6G60vKkQ4rRh3SLxOHcxKYqiFAL/BP/DlstbIKYLHg7V+SD6E4S1Azy3CiyszB3eQ+Wl5L8a6JFl2URgp5SyDrDT8BohRENgMOBh2OfrjDl9gW+AUWjz+tbJ5phFRlRUFD4+Pvj4+FCpUiVcXV0zX6ekpOTqGL/99lvmQG4Abdu2zfFuX0VRCo/w+HBmHZyFbXoNUm93Ym3FtejuXoHnVkLpyuYO75HyMo3jXiFE9SyLn0Gb1xdgDbAHbUL3Z4D1Uspk4KoQ4hLQXAgRDJSWUh4EEEJ8D/SjiM7jW65cucxEPWPGDBwcHBg/fvx922QMopQxmmVWv/32GzqdLl83UCmK8mSl6dOYsG8CCSnJRF8dwBafMzie/gM6T4ca7cwdXq7kt87fRUp5C8Dws6JhuSsQYrRdqGGZq+F51uXZEkKMEkIECCECIiMj8xnqk3Pp0iU8PT0ZPXo0TZo0ISQkBCcnp8z169ev57XXXmPfvn389ddfjBs3Dh8fn8wB0davX0/z5s2pV68efn5+ZroKRVFysuzUMo6GHyX2xjNMrG+NV+DnUK8XtHnX3KHlWkEN7JZdPb58yPJsSSmXA8tBu8P3YSec4z+Hc3fOPWyTPKtftj4Tmud+JE1jZ8+eZdWqVSxdujTHgc7atWtHr169eO655zJHpwTt24K/vz9btmxh1qxZbNu27bFiUBTF9A7fOsyyk8vQxfnS1NaHUWEfQhk36PcN5PANvzDKb6ThQojKAIafEYbloUBVo+3cgJuG5W7ZLC92atWqlTkeTV49anhkRVHMIyoxion7JmIjK5Ec1oeVjssQCVHw/Pdg5/ToAxQi+S35bwFeBmYbfv5utPwnIcQCoApaw66/lDJdCBErhGgJHAaGAV/lMwaAxy6hFxTjKQp1Ot19Qw4/aujg3AyPrCjKk6WXej7a/xF3k2K4d/VNNtXai33wPuj7FVRuZO7w8iwvXT3XAQeBekKIUCHEq2hJv6sQ4iLQ1fAaKWUg8DNwFtgGvCWlTDcc6g1gBXAJuEwRbezNC51Oh7OzMxcvXkSv12dOIALg6OhIbGysGaNTFCU3Vgeu5sDNA6SE92Fsubs0Cl4JTV6GJsPMHdpjyUtvnyE5rOqcw/afAp9mszwA8MzteYuLOXPm0KNHD6pVq0bDhg0zZ+saMmQIr7/+OvPnz2fz5s1mjlJRlOyciDjBV8e+wj61CVXi3Xg7ZRq4+UKvz80d2mNTQzorSi6pv7eSKSY5hoF/DCQ2KZ24s8M45DwPe5EMo/4rEv35cxrSufhM46goilIAPj38KREJEcRfHcUW5x+xT7wFw7cWicT/MEWnX5KiKMoTtvP6Tv6++jdWsd2YahFAg3h/6DUXqrUwd2j5VuRL/lLKx5rkXFHyoqhUjyqmE5Mcw8cHP6a0zh2vm9YMs9qoNfA2G2Hu0EyiSJf8bW1tiYqKUv+YSoGSUhIVFYWtra25Q1GeoDn+c7ibHI315RYssllR5Bt4syrSJX83NzdCQ0MpSkM/KEWTra0tbm5uj95QKRb2hu7ljyt/UDquEz+IH7GyKw3P/wCWNuYOzWSKdPK3srKiRo0a5g5DUZRi5F7KPWb6zaSMhRvTw45TxSoKMajoN/BmVaSrfRRFUUxt3pF53E6KosvVUnS1OIWumDTwZqWSv6IoisGBGwfYdGkTdWPrMiN9BymNhhabBt6sVPJXFEUB4lLimHFwBmV1FVkWuYeYco2x7jPf3GEVmCJd568oimIqC44uICI+grk3krCwsKfMy+uKVQNvVqrkryhKiXck7Ai/XPiFrrE2PJVyGzHoh2LXwJuVSv6KopRoSWlJzDw4kwrSjllRFwjymULpum3NHVaBU9U+iqKUaEtPLuXavWssDYvguH03Wj9TdKZizA+V/BVFKbGCooJYHbiarnGSWkkOWL39dYkZLkZV+yiKUiKl6dOY7jcde72O6VGh3Gw/h3Llyps7rCcm38lfCFFPCHHC6Fln0oEAACAASURBVHFPCPGuEGKGEOKG0fJeRvtMEkJcEkKcF0J0z28MiqIoefX92e8JuhPE1IhbnC/zNE2ees7cIT1R+a72kVKeB3wAhBAWwA1gE/AK8IWUcp7x9kKIhsBgwANtft8dQoi6RtM8KoqiFKhr966x5PgSWsZLGifaYf+6SaYSL1JMXe3TGbgspbz2kG2eAdZLKZOllFfR5vJtbuI4FEVRsiWlZObBmejS0/k06iYxXebjUKasucN64kyd/AcD64xejxFCnBJCrBRCOBuWuQIhRtuEGpY9QAgxSggRIIQIUCN3KopiChsvbuRI2BHG344krOzT1G3zrLlDMguTJX8hhDXQF/jFsOgboBZaldAtIOM+6eya0rMdkF9KuVxK2UxK2axChQqmClVRlBIqLD6MeUfm45Eo6RhvS/2XF5k7JLMxZVfPnsAxKWU4QMZPACHEt8CfhpehQFWj/dyAmyaMQ1EU5QF6qeej/R+RmprA57dvkdprFdYOzo/esZgyZbXPEIyqfIQQxvdGPwucMTzfAgwWQtgIIWoAdQB/E8ahKIrygJ+CfsI/zJ+Jt28TX6E3br59zR2SWZmk5C+EKAV0BV43WjxXCOGDVqUTnLFOShkohPgZOAukAW+pnj6KohSky9GX+SJgPu0SkqiXWJVaY742d0hmZ5LkL6VMAMplWTb0Idt/CnxqinMriqI8TGp6KpN2j6NUWgovR1iRNPAnrGztzR2W2ak7fBVFKdaW+s8l6N5VxkYms7XGApo3rGnukAoFNbaPoijF1smQfaw4v56n45P4If5Dlj3T0dwhFRqq5K8oSrGUkHiHyTvfxiU9jcu3htOzc2cqlbE1d1iFhkr+iqIUP/p0FmzsTwhp1InuQpRzG0a0qWHuqAoVVe2jKEqxc3jHBDakR9FZ1GNzZA9+eNUDa0tV1jWm3g1FUYqVpGt+zLy+FTes2XZ5GD09K9GujhohICuV/BVFKT6S7rFs2+uEWFniwusgrZnSu6G5oyqUVPJXFKXYOP/HG6y2kbRzbMaeIFfe6lgbVyc7c4dVKKnkryhKsZB+Yh2z7hzB0cKWU5cHULOCPaM6qD79OVHJX1GUou/OFTb8N4VTtjZ4OYwkNErwST9PbCwtzB1ZoaWSv6IoRVt6KmEbX+HL0nY0cWrEvwFu9G/sSutaJWc+3sehkr+iKEWa3PUpn6aGorew5l74IEpZWzH56QbmDqvQU8lfUZSiK+QIO44vY499Kdq5DOP4FR2TetanvIONuSMr9NRNXoqiFFn3AlbwWfmy1Cldm93+9WnmXprnm1V99I6KKvkrilI0ydQkZobv4Y6Fjgopw4hN1PPps17odNnNFKtkpZK/oihF0toDM/nXzpohZbvyz3FrXmtXk3qVHM0dVpFhkuQvhAgWQpwWQpwQQgQYlpUVQmwXQlw0/HQ22n6SEOKSEOK8EKK7KWJQFKXkOBFxgvnXttIpKY1dF3rh6mTHO51rmzusIsWUJf9OUkofKWUzw+uJwE4pZR1gp+E1QoiGwGDAA+gBfC2EUJ1xFUXJlTtJdxj/3/u4pKXxskULzkcmM+sZD0pZqybMvCjIap9ngDWG52uAfkbL10spk6WUV4FLQPMCjENRlGIiXZ/OpH2TuJsYxYLwCL4Na0yLGmXp3MDF3KEVOaZK/hL4VwhxVAgxyrDMRUp5C8Dws6JhuSsQYrRvqGHZA4QQo4QQAUKIgMjISBOFqihKUbX81HL8bvoxSVeJ6sKZf+Jq8k7nOuYOq0gyVfJvI6VsAvQE3hJCtH/Ittk1xcvsNpRSLpdSNpNSNqtQQQ3Jqigl2YEbB/jm5Df0rd6D/lePsiWtBY2rlaV1rXLmDq1IMknyl1LeNPyMADahVeOECyEqAxh+Rhg2DwWMO+K6ATdNEYeiKMVTWHwYE/dNpLZzbaY4NESXnsK6BF/e7lwHIVTXzseR7+QvhLAXQjhmPAe6AWeALcDLhs1eBn43PN8CDBZC2AghagB1AP/8xqEoSvGUqk/lg/8+ICU9hQUdFmATuIUbwgVZpQkd66oagcdliuZxF2CT4dPXEvhJSrlNCHEE+FkI8SpwHRgIIKUMFEL8DJwF0oC3pJTpJohDUZRi6KvjX3Ei8gSft/+c6hb26K/+x6bU3ox5SpX68yPfyV9KeQVolM3yKKBzDvt8Cnya33MrilK87Q3dy6ozqxhYdyA9avRAf/hbdDKdM85deFP18MkX1TFWUZRCKSw+jI/2f0Rd57p86PshAHf913Fb70bvrl3UMA75pIZ3UBSl0EnTpzFh7wSS05OZ12Eetpa26O+GUC7qKAdsO9DTs7K5QyzyVPJXFKXQWXJiCccijjGt1TRqlKkBwIXdPwDg1u5FLFSpP99U8lcUpVA5cOMAK06vYECdAfSu2RsAKSW6wN84p6vNU61bmTnC4kElf0VRCo2IhAgm759MbafaTGg+IXP5oQB/6qZfJKlePywtVNoyBfUuKopSKKTr05m4byKJaYnM7zAfO0u7zHVhB34CwKPbcDNFV/yo5K8oSqGwKnAVR8KOMKn5JGo61cxcfi8plfp3d3PdwRsrZzVLl6mo5K8oitmdjjzNkuNL6F69O/1q97tv3aEj/jQQ1xAN+5opuuJJJX9FUcwqPjWeCfsmUL5Ueaa2nPrAXbv3jv0GgGvL580RXrGlbvJSFMWsPjv8GTfibrCy+0rK2JS5b11sUip17+zmhn0DXMu6mynC4kmV/BVFMZttwdv4/fLvvOb1Gk1dmj6w/uCx43iLy+gbqCofU1PJX1EUs7gVd4tZfrPwLu/N6Eajs90m+qihyqfVoCcZWomgkr+iKE9cRrfOdJnO7HazsdJZPbBNfHIatW7vIsy2NrrytcwQZfGmkn8xtfS/y0zedJp0fbaTpCmKWa04vYJjEceY0nIKVUtn333zwIkzNOYCqfX7POHoSgbV4FtMrfe/TnBUAlY6wYy+HiYf9zziXhJrDgZTxcmOwb7V1FgrSq4dCz/GNye/oWeNnpnDN2TnTsBv6ISkiqryKRAq+RdDMQmpBEcl4Opkx5qD16jsZMfoDqb52nw3PoWl/11mzcFgklL1APwSEMrsAV7Ur1TaJOdQiq87SXf44L8PcHVwZVrLaTkWShJS0nCP2EGkrTsVXBo84ShLBlNM41hVCLFbCBEkhAgUQow1LJ8hhLghhDhhePQy2meSEOKSEOK8EKJ7fmNQ7nfmZgwAnz7rSZ9GVZj99zk2HQ/N1zFjk1JZuOMC7ebu5od9ZxlX/RonW+3lH6891IrazWuLfmfu30EkpapJ2ZTs6aWeSfsmEZ0czfyO83GwdshxW79T52nOWZLqPP0EIyxZTFHyTwPel1IeM8zle1QIsd2w7gsp5TzjjYUQDYHBgAdQBdghhKirpnI0nVOhWvJv5OZEq1rluB2bzAe/nKK8gw3t6mQ/5+mF8Fi2nw0nLV2iE6DTCXRCoBNwLzGZY4f34pNynF8dz1HX4iy6kBS4aU0ZfTrzZTpYQ8QhJ44F1MbNow3V2gwCF48nedlKIfftqW/xu+nHtFbTqF+2/kO3DT/yGxaqyqdAmWIax1vALcPzWCFEEOD6kF2eAdZLKZOBq0KIS0Bz4GB+Y1E0Z27EULWsHc721gAsG9aU55ceZPQPR9nweis8XbUbadLS9ewICmeN3zUuXbmEh+4alUUUlcQdKnKXSuIOLuIuVcRtSotEsALKeELNUVDrKXBvrZ0w7AzcPAbnD1Ll6hHcTi4i+cy3WI89gijjZqZ3QSlM/G/58/XJr+lVoxfP1XnuodsmpqRTLWwHUTZVKFflgRliFRMxaZ2/EKI60Bg4DLQBxgghhgEBaN8O7qJ9MBwy2i2Uh39YKHl06kY0Xq7/u1OytK0Vq19pTv+vD/DK6iOsHFyfS6f2c/PMfmqmnGOhxRVcbKMyt5cIcKiIdKiM3tED6VgF3FtCzY7gmM28qVV9oaovFVu8TlJqOgt/+5fRZ18mbO2bVH7jdyiASbYjYpOwtbKgtO2DXQSVwuV24m0+3Psh1RyrMb3V9Ed2Pjhw5hLtOU1E7REF8rejaEyW/IUQDsBG4F0p5T0hxDfAx4A0/JwPjACy+21m2x9RCDEKGAVQrVo1U4VarN2NTyHkTiIvNL//VvhKZWxZM6I5a775Pxp+/xxeQnvLE0pXw7ZGJ3BtClV8wKkawsEFLKwQ5L1RyNbKgrEDe/DDwuEMj1hG5MG1VGj9kmkuziAuOY3ei/bjVMqKP99uh7Xlo6NM10uuRMZRx8XRpLEoD5euT2fC3gnEp8azvNtySlmVeuQ+t/w3Yy3SqaTG8ilQJunnL4SwQkv8a6WUvwFIKcOllOlSSj3wLVrVDmglfeOOvW7AzeyOK6VcLqVsJqVsVqFC9nXVyv1O39Dq+73dyjywro6LIx+4BRFn48LN3j/Ah1cp9cFpdM99B63e1KpxyriBRf5K0xY6Qbfh0zhFHay3TyIlJiJfx8tq8a5LRMQmcyE8jqX/Xc7VPjP/CKTbwr1cvR1v0liUh1t6ain+Yf5MbjGZus51H7l9Umo6rrf+JdqqIpZuzZ5AhCWXKXr7COA7IEhKucBoufEMy88CZwzPtwCDhRA2QogaQB3AP79xKJqM5O9Z5cHkjz6dMpFHKePVgyrN+kKpsgUWR5WyDsR0XYCdPp6L379lsuMG345n5f6rDPKpwDNe5Vm86xKXIuIeus/OoHC+P3gNKWH72TCTxaI8nN8NP5adXEbfWn15ts6zudrnQOBV2nCSuJq9QKfuQS1Ipnh32wBDgaeydOucK4Q4LYQ4BXQCxgFIKQOBn4GzwDbgLdXTx3ROh8bgXq4UZUplU3oPOw3J98C9zROJpV2b9vxX6WU8ov7l7J4NJjnmJ1uDsLaQfBL1LgtuvsTLVjuYuvEY+hzuZI6MTebDX09Rv5IjdV0c2BFk2m8hSvbC4sOYsG8CtZxq8VGLj3K9X4j/79iIVCq1HFiA0SlgguQvpdwvpRRSSm8ppY/h8ZeUcqiU0suwvK+hV1DGPp9KKWtJKetJKf/ObwzK/5y+EXNfY+99rvlpP59Q8gdoM/xTrujcKbdnInfv3M7XsfZeiGRHUDjzPUOwigzEwrYMH7GC2bde5dDmr0F/fxlCSsmHv54kLjmNRUMa092jEgHBd7gbn5KvOJSHS01PZfx/40lJT2FBxwW5qucHOBkSTaWQv4mzLIulu5qkvaCp71XFSFRcMjeiE7Ot7wfg2gFwrg5lnlznqlJ2pZB9F1Ne3uXUqneQ8vHGGkpN1zPrz7O4l7Wja9QPUK42vHUY+cIvSGtHWp+aTNqS1nDuLzCc44dD19h9PpLJvRpQ18WRzg1c0EvYc0GV/gvSgqMLOBl5kpltZlKjTI1c7ZOarmf1z7/Qw+IIVs2Ggs6igKNUVPIvRjLq+71cnR5cqddrJf8nWOrPUMunPYHVh9Ihdivbt/7yWMf48dA1LkXEsbBJBLrw09D2PdBZIOp2Q77+H2PTxxJ1Lw7WD4HlHQjf+RVLtvrTqV4FhrXSej55u5ahgqONqvopQP8G/8uPQT/yYoMX6VG9R673W/HfBV6L+YokOxdsOn1YgBEqGVTyL0ZOG+7s9XDNZoydyHOQeMcsyR/A68XZhFlWod6RKWw8fDFP+96JT+GL7RdoV7scPsEroEw18P5fN8AaFRyp+9QwWsd+RmDTT9Dr03HZN4X9lm+w1GoB4tyfkJaMTifoXL8i/52PJCVNb+pLLPGCY4KZ5jcN7/LevN/0/dzvdzue27u/wUN3Ddvec8Am52EfFNNRyb8YOXUjhprl7bO/8enaAe1nxl25T5iwtsdhwBLcRTg3/viEqZvP5DoBz//3PPEp6XzWOBoRegTajn2gO+qo9jWpU8mJV0835COXpfRM/oxb9V7GJuwYbHgJ5teDf6fSuV554pLT8L96pyAus8RKTEvk/f/ex0pnxbwO87DKZXdhKSWzf/mPdy02kOzeERr2e+Q+immo5F+MnLkRg9fD6vtLu2p1/mbi0OAp9F7P85bVnxw4fJAXvj1ERGzSQ/c5e/Me6/yvM7SlO25nloBDJfB58KYxKwsdn/X3Ijw2iXX+12nesj3VhiyAcWfhpY3aNx6/RbQXJ7Cx1LEjKLygLrNE+r/D/8fFuxf5rN1nVHao/OgdDH4JCKX7zcWUEmnY9F2g7uh9glTyLyYiYpO4FZOUfU8fKQ31/a3N/s+l6/4pFtb2bHD7lcCbMfRetJ+j1+4+sF1EbBLbzoQx6bdTlLGzYnyDGLi6F1q/DVa22R67cTVn3u1clxY1yjKpl2EYYAtLqN0FBq4G+4rYnPqRtrXLsyMo/LEbn5X7/Xz+ZzZf2szrjV6nrWvbXO8XGZvMP1t/5VmLA+jajoVyarauJ0mN519MnMm8szebxt6oyxAXbrb6/vs4VITOU6nw13h2dItkyMGqDF5+kAk96mNloePY9bscu36XkDuJAFhb6Ph8oDcO/uPAriw0e+Whhx/bpQ5ju9R5cIWFFfi8AH5f0bvT++w8l8j58Fg1B0E++d3w4/8O/x/tXNsx2jv7eXhz8smWE0yUK0gtUw2r9uMLKEIlJyr5FxOnQmMQAjyqZJPMMuv7C0HyB2g2Ak6sxfXwJ2wZ6cc7m67wydYgAFxK29CkmjPDWlanibszHlVKY3v7DGz+B56aAtb2j3/eJsPgwEK6puwAPNkZFKGSfz5cvHuR9/57j9pOtfm8w+dY5KF75s6gcCqdXUUdq1B4egNY2RVgpEp2VPIvJs7ciKFWBQfsbbL5lV47APYVoHw2JWJz0FlA7y9geSecDs5l1fA5BATfwdXZDlcnuwdHfdw3H2xKg+/I/J23XC2o3g6HwHU0cl3E9rPhvNWpdv6OWULdTrzNWzvfwt7SnsWdF2NvlfsP5ai4ZBZt2sMGq9/Q1+2Jrl7uu4QqpqPq/IuJU6ExeD/szt5CUN9/nyqNwfc1OPItFmEnaVGzHG7OpR5M/JHn4ewWaD4S7LKp0sqrJsPg7lVernKDk6HRRMYm5/+YJUxiWiJv73yb6ORovur8FZXsK+V63+S0dEb/EMCbSSuwthDoes4pwEiVh1HJvxgIv5dERGxy9j197l6DmBBwz31D3BPz1BQoVR7+HPfA0AwApKfCf3O0KoGWb5rmnA36gG0Znkr4Gylh9zl1w1de6KWeyfsmExgVyJx2c2hYrmGu95VSMmXTGbxC19Fd54+u4wRwdn/kfkrBUMm/GMiYtjHbnj6Z4/mYp3//Q9k5Qff/02YBO7pKuwv51inwWwxrB8Kc6nBmI/i+CvblTXNOKzvwHkyZ4L+pXzqV7arLZ54sPLqQHdd38IHvB3Sq1ilP+67Yd5XI438wxWot1O8Nbd4toCiV3FB1/sXA6Rsx6AQ0zLaxdz/YOUPF3JfQniiv5+D49/DvNNj1qXYXMkC5OuA9CGp2gHomnsS7yTCE/zLernSc8RdtSUpNx9ZKjSXzKBvObWBV4CoG1xvMSw3yNkHP7nMR/LrtXzbbLEG4eEL/5WrIZjNTyb8YOB0aTZ2KjpSyzq6x1w+qtS68/2hCwNNfwKZRUL6eluyrtyvYwecqeYJrUzrE/UViqi9+l2/zVP1spqdUMv128Tc+OfwJHdw6MKH5hEdOxWjsQngs09ft4WfbBdiUckQMWZ+/XluKSajkX8RJKTl9I4aO9So+uPLeLbhzBZq9+uQDy4vytWHkrid7zibDcPhjLC2tr7IjyF0l/4fYdHETM/xm0Na1LfM7zsdSl/u0cSc+hdGr/Vikm4+LiEEM+euJjiqr5KyQFgeV3LoVk8TtuJQc6vsN/furF5L+/YWJ5wCwsmdMGT92qrt9c7T50mam+02ndZXWLOy0EBsLm1zvm5Km540fAng7fjE+8hzi2W+0uaKVQsFsyV8I0UMIcV4IcUkIMdFccRR1mcM4Z9fT59oBsHYEF68nHFURYOMInv1pmbCbuHvRnAiJNndEhc6Wy1uYdmAaLSu3zHPi1+u1iXQah6zhWd1e6DgZPPsXYLRKXpkl+QshLIAlQE+gITBECFFIWyQLt9OhMVjoBA0rZ9fY6wfVWmrj2ygPavIylumJDLQ9wuy/z6nSv5E/Lv/BlP1TaFG5BYueWoStZfbjKeVk7j/nsTy9jglWG7RvWR3UGP2FjblK/s2BS1LKK1LKFGA98IyZYinSTt2Ioa6L44O9VeJva2P4F8YunoWFWzOo0IAxTn4cvnqHjcdumDuiQuHPK38y5cAUmldq/liJ//uDwUTv/5Z5VsugZkd4ZknhusFQAcyX/F2BEKPXoYZlSi4kpKTx+4kbvLLKn/0XI/Gpms2drxn9+6sXwpu7CgshoOnLlI8+xbNV7vJ/fwWV+Pl9f73wK5P3TaaZSzO+6vwVdpZ5G3Nn25kwLvy5kNlWK9DX7qL17FHj9hRK5kr+2RUDHvjOLYQYJYQIEEIEREZGPoGwCq+0dD27z0fw7vrjNPtkB2PXn+B8WCyj2tfiw+71/rdhXARc3gXHfwBLO6jsY76giwLvQWBpx7SK+4lJTGXOtnOmPX7SPdg+Db5uDbFhpj22ia0JXMPMgzNp49qGxZ0Xa4lfSu0aoi7D9cMQEZTj/gHBdziy4TM+sVpFep0e6Ab/lOPw24r5masyOBSoavTaDbiZdSMp5XJgOUCzZs1KbIXsqdBoRn4fQPi9ZErbWvKMjyv9fKrgW70suqt7YN/3EH4GwgMh4fb/dvQeDJbWZou7SChVFnyG4Hx8Le+0GMoXB0MY0NQN3+pl83XYtNQU7vmtxMFvDtbJ2o1r6cd/wqL9e6aI2qSklCw9uZSvT35NV/euzNE7Y/VdD63qMD4S0u8f/yixbAMsGr+AdePB2hDdwKWIOPasns5Ui+9JqfM01oNWq7+9Qk6Yo5FLCGEJXAA6AzeAI8ALUsrAnPZp1qyZDAgIeEIRFh5Hr91l+Ep/ypSyYmrvhnSsVwEbS0P9/qWd8OMAsLSFig3AxQNcPA0/PbTEpjza7YuwuBkp7SbS6UgL7G0s2PpOO6ws8vbF+GRINAt3XKBcuB8jE1ZQTxeCv74eH6cOZarVD9QtnYbT+0cLVf23lJJ5AfP4/uz3PFPrGWbUfxnLxb5QyYvUCg0JSbbnTLQ1RyItuJ5sj7sIo7/FPnx0V0hDx2nbZlxw6c3dGxcYnfYjCbV7U2rI6gem2VTMRwhxVErZLOtys5T8pZRpQogxwD+ABbDyYYm/pDp0JYoRq4/gUtqWta+1oIqTUd1p9HXY+KqW9F/boe6YzI/ydaBON6yPrWTm0y/x2tpTfLf/KqM75H5mKb1eMufnnYyOXUJ7jhJtVwU/jwVYevZjRXl7fvs2guaxi0gOOYZNtcLR1z1dn87Hhz5m48WNvNjgRT70/RDdv1PRCwves5jEX8cEKel6nEpZ8VT9igxq6EL1cvYER8VzJvg0lYI343N3G42vTQMgumZfnIasUr3Ligiz/ZaklH8Bf5nr/IXd3guRjPohADfnUvz0WgsqljaqO01Ngp+HaSNhDvpRJX5TaPkm/NCPLml76dqwHgt3XOBpr8pULVsqV7v/ExjGyOgvaW19ATrNxKnFaFob1Xc36fkKyRu+4dL2b/F41fzJPyktiakHprIteBujvEcxxmcMSQlxyMOr2ZXWlGN37RjWyoUuDV1o5u6MpdG3oIZVSoNXZaAb6NORV/cib1/EqdkIlfiLEHWHbyG0Myic19YEUL2cPetHtbw/8QNsmwA3j8OzS9W8p6ZSsyNU9IBDXzOjT0N0QjBjS2Cu+v7r9ZKt//xNJ4uT6NqPh7bvPtDQ2aJhTY7btaRKyFYSEhML5hpy6UbcDYb9PYxtwdsY13Qcbzd+m8uR8XyzeA6l9HEkNBrB7vEdmdK7IS1rlrsv8T9AZ4Go1Qldi1Eq8RcxKvkXMtvO3GL0j0epX9mR9aNaUt4hy12Vx3+Eo6uh7Tiob+LRLksyIaDlGxB+Bte7RxjXpS47z0Ww7cyje+jsCArn6ZifSLF0RNci59nGyrV5GWfu8d9f6x47zIU7LjBl8+nH3v/AjQMM+nMQobGhfPXUV4zwHMHvJ27Qd/E+eiX+QZxTPZ4fMAgLXeFpl1AKhkr+hcjRa3d566fjeLmW4cfXWuBUKktviVsnYev7UKMDdJpiniCLM6+B2nSXB5cwvE11PKqUZvKm04TfS8pxFyklv/+7k54WR7Bs+TrY5jCbGlCndT/u6ZywPL2B2KTUPId3KyaRJbsv8eOh6xwJvpOnffVSz7KTy3hjxxtULFWR9b3X07JSOz7adJqx60/Qv3wo9QnGoe0bhapBWik4KvkXIpuP38DaQseaEc0pbZult0TCHdgwFEqVg+dWqq/YBcHKVpta8uI/WN29zJeDG5OYms77P59Er8+++mfP+Ui63FlLqoUdulaPmG3MworkBv1pLwP4ac+pPIe3Yt9V9BLK2VszJw/DUdxLucc7u95h8YnF9KzRkx97/ohLKVcGLTvI2sPXeb1DTWZV9gObMuD9fJ7jUoomlfwLCSklO4PCaVunPI5ZE79eD5teh3s34fnvTTerlfKgZq+ChQ0c+obaFR2Y1tuD/Zdus2L/lQc2lVKy4d+99LU4iM73VbAv98jDV2jzMjYijfBD64hJyH3p/058Cj8dvs4zPlV4r1tdAq7dZff5R09BeTbqLIP/HMyBGweY1HwSs9vNppRVKTYfv8HJ0Bi+GNSISW2d0QVtgcYvqc4DJYhK/oXEubBYbsYk0aVBNuPyH10FF/+FHp9p49EoBcehAngPhJPrIOEOQ/6/vfuOj6pKHz/+eWYy6YU0SAglhBZqEhAMSFFRQAXLqqwKIrtqFMGK/uxf/eJaVtdFsaKgwBcB2+oqRZo0pVcpCRhCJyEkGSAJmUlm5vz+uANEDC0hGZg579drXjNz5t4751Ce3Dz33Od0bUy/iTn54QAAGi9JREFUdg14a842NrsrqB639PcCeuVPAZMf5isePrfjx6dgi2zF9a7FVf5AOZ2Jv+6krMLJ8N7NGXRZYxKjg3nzp20nfyPZvRxWfmLckYuR5pm0ZRKDZw3G7rTzWf/PuKvNXYgILpdi3JIc2saHc3NqgnENyeUwlsvUfIYO/heJBe61ZK86dVGWowdg3ktGnr/LfR7omQ9KfwgqjsHaiYgIb/ylI1Eh/jwyfT3Hyh2Acdb/xdxl3O63FNLuhrC4czu2CIGdB3OZaTvzf1lO0TnUEiq2VTBx2S76tWtAywZhWMwmnujbmqy8Ymau3wlznofPr4PZT8G+1RSUFTB8/nD+teZf9EroxbcDvyWtftqJ4y3IyifnUCkP9E5CXA5Y8zm0uEbPHPMxOvhfJBZk5ZPSKOKP0zqVgplPgqsCBozRF+LqSoN2xtTPVZ+Ao5zIEH/GDEplZ0Epr8zYCsDynELS877ALGDueZ4LkXcchELo71rMuMU7zrr5Fyv3cNTm4KErW5xoG9AhngGxBbSbcRMsfx86DYWAcJYs+ye3/nAr6w6u48X0F3nnqneoF/jHwn/jFu8goV4QN3SIh8wfoSQPumac3xi0S54O/heBghI7G/Ye/vNSgpk/wLaZcOWz+qysrqWPgOJcWPImOOx0bxFDRq8kpq3ay0+bc5k0dxV3+i3E1WEQ1GtyfscOb4gkXcmQoGVMXp5zxtlEtgon45fupGfLGFKOV291OjD98jZjS0cR6jrKgk4fYLv+TV5vnsoI23ZiAuoxfcB0BrUe9Ke1dtfuLmLNbiv39WxmzN9f9SlEJhpn/ppP0cH/IrAwKx+loE/lfH/ZYZj1FMR1gG4jPdc5X9XiGmjVH5a8BWPTYM1njLq6GR0SInj8y42k7p+KPw78eo2q3vFT7iS6Io80tY27Pl3B/sNV3/j19dp9FJTYT571F+00Ujw/v4Ik38DTcR/z1I69DPxuIFPLdjHkyFGmRqTTvF7VJwvjFudQL9jCX7s0hrxNsGeZkU40mavcXvNeOvhfBH7OyqdBeADtGlZajWv+S0ZFxRvf09M6PcFkgjunw93fQ3gCzHgc/w+78FnHTKI4wlC/ebja3mwsPl8dbQaAJYQxyVnkH7Vz64fL2JZX/IdNKpwuxi3eQacm9UhPijLKeUy/Cw5tQ93yKb92v4+DseOoiJqK0xHChL4TeDqyMwHrJoHzzzOJsvNLmJd5kKHpTQn29zPO+v2CIHVw9cagXdJ0VPGwcoeLJdsPcWNqwslf0Xf9YszA6DYSGqadcf8LraS8hJwjOew4vOPE8+6ju3EqJxaTBYvZgp/4YTFbsJgshFpCqRdQj8jAyD88B5oDsTlt2J12bA7j2e60YxITrSNbkxydTLh/FUtPXkxEoPlVRv4/ewEsfJXYhU+yJCAYs8MGvZ+s/rH9Q6DtTTTImsnX973C0MmbuP3jZUwY1uVEOekfNx5gn7WMlwe2M/5tbPwS8rey9frX+PfBuazcsJKE0ARa8ADZ25rT6qZUuPwBmDrIyOWfsmbu+KU5+JtNDO2eCEf2wW9fQYfbdPVXH6WDv4et3FlIabmTPsnulE+FDX581MgjX/XcBf0uh8vBlsItZBZmYrVbOWI/gtVm5bD9MFablcKyQvLLTs4d9zf5kxiRSJvoNvib/KlwVVDhqsDhclDhqqDcWU7+sXy2WbdhtVmxn1L3/WwahzWmbXRb2ka3JTkqmejAaCICIgj3DyfIL+hP+WqPEYGW10CLPrB9DuYlb0GDtsaF4ZpIuQM2TiU5fzbfDh/EPZ+tYsj4lbx/Vyf6JNfnw0U7SI4L4+rk+pTbjrL4l1f5oUlzFmV+TL2AejzT9RkGtRrEjkNlXPfuUj5enMMz/a4xcvirPv1D8M8vtvGfdfu5/bJGxARbYMoIEBP0rGbaSrvk6eDvYQsy8wnwM3FFC/eNW0v/BYXZMOQ/F+SGm71H97I8dznLDyxnZe5KiitOphYqn7XHBMXQMrIlzSKakRSRRPN6zUkITcDPdO7/RI5VHDN+kNitlDvLCTAHEGgOJMAv4MRru9NOVlEWWwu3srVwK5sObWLOrjl/OpafyY9w/3DC/cNJikiiQ2wH2kW3o11MO8/9xiACrfsbjwshsSc06QZz/4fGI/ryzfDu/G3iah74vzXcnJZAdn4xTwz05x8rX+Gn7P9SHGYi1j+IjOS/MazdMML8wwBIjrNwS2oC45fmYDbBY53+jmXB/xg5/bgOAEz8dRcVLhf390yCNRMgZ5Exgyyq2YUZi3bJ8chiLtXhjYu5KKXo9dZCWtYP47NhXYwl8j7uAe1vg7+Mq9YxXcrF+vz1zN01lyX7lrCvZB8A8SHxdGvYjW7x3Uitn0p0YDSWi2TBDavNSvbhbKw2K0fLjxoPu/F82H6Y7dbt7D66+8T2ieGJtI9pT/uY9qTWT6VVZCsspotjLOetcAd8dIWx1vLgrykpr2DYF9/xm3UZQfV+w+VXQJA5kD4lxQwMbsrlQ2ZhruLi7JGyCkb/uJVv1+2jXZSLH+z3YU4ZBDe+R4ndQbfXF9CjRQwf9Y8w/o0lXgGDv9HTh33ARbWYi2bIzi9hb1HZyUVD5r0ElhDo99p5HcelXGw8tJE5u+Ywb9c88svyCTAH0C2+G0PbDaVbfDeahje9eNIop4gMjKRLXJczbnPEfoQthVvYUrCFTQWbWJm7khk5MwAINAfSLqYdKbEppMSmkFo/lajASySPHd2cY32eZ/nSV1ny42CW2HIpMBcQGGOidb00hrR/nGty1hCc/S488OVpZ+VEBFl4e1AKt3ZK4PnvN/OlvRu3rf+S4m7P813WMYptDjJ6NIHv7zSWV7zxPR34fZwO/h60IMvIr1+dXB92L4Pf50Cfl86pRgxAka2ISVsmMSNnBvnH8vE3+dOzUU/6Jfajd6PeBFvObSGSS0FEQATdG3ane8PuJ9rySvPYkL+BjYc2svHQRiZvnYzDZdyB26JeC7rGdaVrfFcua3AZEQGnr7ZZ15wuJ1nWLFblrmJl7kpW562mvEEsYYW/cUXj3vROuo6eCT2NPh/NhWkZRsXR+JSzHrt7ixhmP9qTr2aW4L9hIRM/eJWp5hu5vFkUaXsnw77V8JfxEN6wDkaqXcxqlPYRkbeAgUA5sAP4m1LqsIgkApnANvemK5RSD7r36QxMBIIwVvJ6VJ1DJ6qT9lFK8cZPWTSPCWVQl8Zn36GODfp4OSV2B7Me6QET+sKRvfDwOvA/c9A+Yj/CpC2TmJI5BbvTTq9Gveif2J/ejXoT6h9aR72/+NgcNjKLMll7cC2rclexPn89NqcNQUiOSiatfhr1g+sTHRRNVGAU0UHRRAdGExkYiVIKh8thPJTjxEXtEEsIEf4RVaZazpXdaWfXkV2szlvNqrxVrDm4huJy49pLs4hm9EzoSe+IVqR9PRxLk8uN6z3Hz8p/fMxYw2Hk6vPOz5eN68uR/D10L32LL28Op8vcWyH5erh9kj7r9yG1lfaZBzzrXpP3n8CzwNPuz3YopVKr2OcjIANYgRH8+wOza9iPKjlciszcYsYtzsHhUtx1+XneiVmLrKXlrNldxMirWsC2WbBvFQx454yB/1jFMaZkTmHilokUlxfTP7E/w1OHkxSRVIc9v3gF+gWSVj+NtPpp3NfhPiqcFUaKKM84u/4u+zvKHOe/ipYgRAREEBkYSWRAJFGBUYT6hxJoDiTQL9C4mO0XSKA5EKdykleaR25pLrmlueSV5lFkO1l7v3FYY/o27UvXuK50ietCbHDsyS+6Nh9mPQnrJkHnYcbC8usmGzdhVePCbFCP4QR9PYyVt9iIXfcGBEXCDbpMiGaoUfBXSs2t9HYFcNuZtheReCBcKbXc/X4ycDO1FPwtZhOf3N2Z4VPW8tx3m3Aqxd3pTWvjq87b4u2HcCm4unU0zBgK0S2MAmFVsDvtTM+azoRNE7DarVzZ6EpGpo2kdVTrOu71pcVittCpQSc6NejE8JThgPEDtNBWSJGtiMIy4/mw/bCxvcmCn8nvxH0MZjFTWlGK1W7FarNSZCvCarOy88hOSipKTtzDYHP+sTxDsF8w8SHxxIXG0Ta6LXHBcSSEJdCpficahp4h3XLZvUZJjzkvQPOr4edXwBIEvZ6q3h9A8gAIiyd2/iNGobo7p59zSlHzfhcy5/934MtK75uJyHrgKPCCUmopkADsq7TNPndblUQkA+O3BJo0qd5Ze6DFzMd3d2bEF+t48fvNOJ0uhl3h+elt8zMPEhMaQMeCWXAoy6jTf8qdvE6Xk5k7Z/L++vfJLc0lPT6dh9MepmNsRw/1+tIXbAkm2BJM47ALlwZUSp24iU1ECLOEVe/iuskEN74PH3WHqX+F/K1GXafQ2LPvWxWzBS77Oyx8FVKHQOvrqncczSudNfiLyHygqnq1zyul/uve5nnAAXzh/iwXaKKUKnTn+L8XkXZAVf8jTpvvV0p9AnwCRs7/bH09nQA/Mx8O7szIqet4+cetOFyK+3p6LlVS4XSxePshBraNxLT4EUjoDG1uPPG5UopfD/zKmLVj2G7dTpuoNoy+YjTp8eke67N2eiJipH38As++8dlENoW+r8CMxyE4BrqNqNnx0ocbvz10Hlbzvmle5azBXyl1xnJ/InIPMADoc/zCrVLKDtjdr9eKyA6gFcaZfqNKuzcCDlSv6+fH38/EB4M78ci09fxjZiYupcjo5ZlKmWt2WSm2ORhqngdH98MtH5/Iw24p3MKYNWNYmWfcuv9mrzfpl9gPk+gyTD6j89/AuguaXgEBYTU7VkAYdD/HhWY0n1KjtI+I9Me4wNtbKXWsUnssUKSUcopIEtASyFFKFYlIsYikAyuBocB7NenD+bCYTYy9M43Hv9zAa7Oy2FN0jK7NokmKCSExJoTQgNqf+aqUYvLyXUSby2j9+yfQvA8060VxeTFj1o7h6+1fExkQeeLW/YvlRiytDonAtaM93QvNy9U02r0PBADz3DnO41M6ewGjRcQBOIEHlVLHpzwM5+RUz9nU0sXe07GYTbzz11SC/c1MWbGHKSv2nPgsJjSApJgQkuPDGHx5U1rH1fCsqwrjluQwe3Me37b8Bdl7GK55mUV7F/HKilcoKCvgnrb38GDKgz49ZVPTtNrn0+Udysqd7C4qZeehUnYWlrKroJSdBaVs3n+UsgonV7WOJaNXc9KToi7I3bELt+Xz94mruauNhX/sGYo1uR9v1G/A7J2zaRnZktHdR9M+pv0FGJmmaZpBl3eoQpC/meS4cJLj/lgozFpazpQVu5m4bBd3frqClEYRPNC7Of3axWE2Ve+HQM6hEh6Ztp42ceG8HDKFmUF+/LP8d0p2/8aI1BHc2/5eneLRNK3O+PSZ/9nYKpx8s3Yf45fmsKvwGInRwbx/VyfaJ5xfqYCjtgpu+eBXrMcq+PKGUt5bMYqFIcF0jO3I6O6jT7vqkqZpWk2d7szf+6eQlJdWe9dAi5kh6U1ZMOpKPhrciQqnYvD4lWzef+Scj+FyKR6fvoHdhccY3q+U+ze+yC/BwTyZ9iiT+0/WgV/TNI/w7uCvFEy5zbhh5tD2ah/GbBKu6xDP9Ix0QvzNDJmwkq0Hjp7Tvv+et50F2/bRvesSxma+SJSjnOlpT3FPx/tqVC9G0zStJrw7569c0KofLH0bPkw37na88hkIialiWwW5G4xaKjmLwFEOrgpwOcDpAJeDxmYLP/R8mYFLmzB4/AqmZaT/6XrBycMpvl6zjw+XLya+zbesP3KAu4+W8mhcbwJShtbuuDVN087CN3L+pQWw6HVY87mxOlavJ6HrA2AJhDIrbPrGKKaVt8lY0LpFHwisZ9RON1vA5Gc89q+FPcsp6vG/XL+qAxVOF9My0mnV4OSUUKdLMWtTLh8s+p2c8hkExM4jNjiKV48J3fJ+h5FrILT+BfpT0TRNO7PT5fx9I/gfd2gbzH3RqJtfrwk06gJZM8FhM2qldxpqrKIVVK/q/R12+PY+yPwB62WP0W9DD1zAtPvTaRIdzHfr9jNuSQ67Du8nMvEbKizZXNPkWl4ObUvEzFEw8F19m72maXVKB//KchbB3BfAugc63m5U02xYVfXpKjgdMOMxWP9/HGl/D9dmDcCF4GcykXfURrOm2ygJ+wqTKJ67/DlujOuOfNAFYpNh2CyjeJemaVod0fP8K0u6Eh78xcjzn+/NW2Y/Ywm8oEgilo1lQcvDXL97MA2iTbRNmc/qgvmkRKXweo/XaRzeGL57EOwlRq1+Hfg1TbtI+GbwP666d+2KGJUXg6MIm/8y77Qo5DlLKdmFVh5Kupn7EwfiV5wPO3+FjdOMeuz1ky9s3zVN02rAt4N/TfV4nB9sB3hp32zibA4mHSokJWcsMPbkNlFJ0HOUx7qoaZpWFR38a2Di5om8vf8nLo9uzzvN7yS0qnrujboY9dQ1TdMuIjr4V4NLuXh7zdtM3jqZfon9eK3Ha/ib/T3dLU3TtHOmg/95qnBW8MKvLzBr5yzuSr6Lp7s+rRda0TTtkqOD/3korSjliUVPsOzAMh7t9Cj3tr/3gpR61jRNq2s6+J+jgrICRi4YSVZRFqO7j+aWlrd4ukuapmnVVqN8hYi8LCL7RWSD+3F9pc+eFZFsEdkmIv0qtXcWkU3uz8bKJXDqnG3NZvDMwew4vIN3r3pXB35N0y55FyJZPUYplep+zAIQkbbAHUA7oD/woYgcL2H5EZCBsa5vS/fnF61lB5Zx9+y7KXeVM/G6ifRu3NvTXdI0Taux2rpSeRMwXSllV0rtBLKBriISD4QrpZYro67EZODmWupDjX29/Wsemv8QDUMbMu2GabSLbufpLmmapl0QFyL4jxSR30TkMxGJdLclAHsrbbPP3Zbgfn1qe5VEJENE1ojImkOHDl2Arp6b41M5Ry8fTbeG3Zh83WTiQuLq7Ps1TdNq21mDv4jMF5HNVTxuwkjhNAdSgVzg7eO7VXEodYb2KimlPlFKXaaUuiw2Nvasg7kQyhxlPLHoCSZumcgdre/gvavfI8QSUiffrWmaVlfOOttHKXXNuRxIRD4FZrjf7gMaV/q4EXDA3d6oivaLQnF5MSMXjGR9/nqe7vI0g9sM1lM5NU3zSjWd7RNf6e0twGb36x+AO0QkQESaYVzYXaWUygWKRSTdPctnKPDfmvThQimyFXHvnHv5reA33ur9FkPaDtGBX9M0r1XTef5vikgqRupmF/AAgFJqi4h8BWwFHMAIpZTTvc9wYCIQBMx2PzzqYOlBMuZlsL9kP2OvGkvPRj093SVN07Ra5ZuLuVSyt3gv98+9n8P2w7x39Xt0ietywb9D0zTNU/RiLlXYcXgHGXMzsLvsjO87nvYx7T3dJU3TtDrhsxXJthZuZdhPw3Dh4vN+n+vAr2maT/HJM/9sazYZ8zII9gtmfN/xNAlv4ukuaZqm1SmfC/57i/eSMS8Di8nChL4TjHV2NU3TfIxPBf/8Y/ncP/d+yl3lfN7vcx34NU3zWT4T/K02KxlzM7DarIzvO56WkS093SVN0zSP8YngX1JewvD5w9lbvJePr/2YDrEdPN0lTdM0j/L64G9z2Hj454fZVrSNd656R8/j1zRNw8uDf4WrglGLR7H24Fre6PmGrsWvaZrm5tXB30/8SAxPpHd6b65Puv7sO2iapvkIrw7+IsJTXZ7ydDc0TdMuOj57h6+maZov08Ff0zTNB+ngr2ma5oN08Nc0TfNBOvhrmqb5IB38NU3TfJAO/pqmaT5IB39N0zQfdMms4Ssih4Dd1dw9Bii4gN25VOhx+xY9bt9yruNuqpSKPbXxkgn+NSEia6pawNjb6XH7Fj1u31LTceu0j6Zpmg/SwV/TNM0H+Urw/8TTHfAQPW7fosftW2o0bp/I+Wuapml/5Ctn/pqmaVolOvhrmqb5IK8O/iLSX0S2iUi2iDzj6f7UJhH5TETyRWRzpbYoEZknIr+7nyM92cfaICKNRWShiGSKyBYRedTd7tVjF5FAEVklIhvd4/5fd7tXjxtARMwisl5EZrjfe/2YAURkl4hsEpENIrLG3VbtsXtt8BcRM/ABcB3QFrhTRNp6tle1aiLQ/5S2Z4AFSqmWwAL3e2/jAEYppdoA6cAI99+zt4/dDlytlEoBUoH+IpKO948b4FEgs9J7XxjzcVcppVIrze+v9ti9NvgDXYFspVSOUqocmA7c5OE+1Rql1BKg6JTmm4BJ7teTgJvrtFN1QCmVq5Ra535djBEUEvDysStDifutxf1QePm4RaQRcAMwvlKzV4/5LKo9dm8O/gnA3krv97nbfEkDpVQuGEESqO/h/tQqEUkE0oCV+MDY3emPDUA+ME8p5Qvjfgf4f4CrUpu3j/k4BcwVkbUikuFuq/bYvXkBd6miTc9r9VIiEgp8CzymlDoqUtVfv3dRSjmBVBGpB3wnIu093afaJCIDgHyl1FoRudLT/fGAK5RSB0SkPjBPRLJqcjBvPvPfBzSu9L4RcMBDffGUgyISD+B+zvdwf2qFiFgwAv8XSqn/uJt9YuwASqnDwCKMaz7ePO4rgBtFZBdGGvdqEZmCd4/5BKXUAfdzPvAdRmq72mP35uC/GmgpIs1ExB+4A/jBw32qaz8A97hf3wP814N9qRVinOJPADKVUv+u9JFXj11EYt1n/IhIEHANkIUXj1sp9axSqpFSKhHj//PPSqkhePGYjxOREBEJO/4a6AtspgZj9+o7fEXkeowcoRn4TCn1qoe7VGtEZBpwJUaZ14PAS8D3wFdAE2APcLtS6tSLwpc0EekBLAU2cTIP/BxG3t9rxy4iHTEu8JkxTuK+UkqNFpFovHjcx7nTPk8qpQb4wphFJAnjbB+MdP1UpdSrNRm7Vwd/TdM0rWrenPbRNE3TTkMHf03TNB+kg7+maZoP0sFf0zTNB+ngr2ma5oN08Nc0TfNBOvhrmqb5oP8PUEsF/FtAxSsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_s = np.s_[:50]  # After this they basically agree\n",
    "fig2 = plt.figure()\n",
    "ax2 = fig2.add_subplot(111)\n",
    "h21, = ax2.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s], label='Double Freq. Seas')\n",
    "h22, = ax2.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s], label='Mixed Domain Seas')\n",
    "h23, = ax2.plot(idx[time_s], true_seasonal_100_2[time_s], label='True Seasonal 100(2)')\n",
    "plt.legend([h21, h22, h23], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth'], loc=2)\n",
    "plt.title('Seasonal 100(2) component')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_s = np.s_[:100]\n",
    "\n",
    "fig3 = plt.figure()\n",
    "ax3 = fig3.add_subplot(111)\n",
    "h31, = ax3.plot(idx[time_s], res_f.freq_seasonal[1].filtered[time_s] + res_f.freq_seasonal[0].filtered[time_s], label='Double Freq. Seas')\n",
    "h32, = ax3.plot(idx[time_s], res_tf.freq_seasonal[0].filtered[time_s] + res_tf.seasonal.filtered[time_s], label='Mixed Domain Seas')\n",
    "h33, = ax3.plot(idx[time_s], true_sum[time_s], label='True Seasonal 100(2)')\n",
    "h34, = ax3.plot(idx[time_s], res_lf.freq_seasonal[0].filtered[time_s], label='Lazy Freq. Seas')\n",
    "h35, = ax3.plot(idx[time_s], res_lt.seasonal.filtered[time_s], label='Lazy Time Seas')\n",
    "\n",
    "plt.legend([h31, h32, h33, h34, h35], ['Double Freq. Seasonal','Mixed Domain Seasonal','Truth', 'Lazy Freq. Seas', 'Lazy Time Seas'], loc=1)\n",
    "plt.title('Seasonal components combined')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Conclusions\n",
    "\n",
    "In this notebook, we simulated a time series with two seasonal components of different periods.  We modeled them using structural time series models with (a) two frequency domain components of correct periods and numbers of harmonics, (b) time domain seasonal component for the shorter term and a frequency domain term with correct period and number of harmonics, (c) a single frequency domain term with the longer period and full number of harmonics, and (d) a single time domain term with the longer period.  We saw a variety of diagnostic results, with only the correct generating model, (a), failing to reject any of the tests.  Thus, more flexible seasonal modeling allowing for multiple components with specifiable harmonics can be a useful tool for time series modeling.  Finally, we can represent seasonal components with fewer total states in this way, allowing for the user to attempt to make the bias-variance trade-off themselves instead of being forced to choose \"lazy\" models, which use a large number of states and incur additional variance as a result."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.2rc2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
