{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Основы анализа данных в Python\n",
    "\n",
    "*Тамбовцева Алла, НИУ ВШЭ*\n",
    "\n",
    "## Множественная линейная регрессия. Эффекты взаимодействия. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Загрузка библиотек"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Загрузим библиотеки `pandas`, `seaborn` и импортируем функцию `ols()` для линейной модели из `statsmodels`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Загрузка и подготовка данных"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Как и в прошлый раз, загрузим данные по ссылке и переименуем столбцы, содержащие точки в названии (у формул внутри `ols()` есть одна особенность – они воспринимают точки как специальный символ, поэтому точки потом будут нам мешать):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"https://vincentarelbundock.github.io/Rdatasets/csv/carData/Salaries.csv\")\n",
    "df.rename(columns = {\"yrs.since.phd\" : \"phd\", \"yrs.service\" : \"service\"},  inplace = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Множественная регрессия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим модель, на которой мы остановились на прошлом занятии. Модель, которая объясняет, каким образом заработная плата зависит от опыта работы и пола сотрудника университета:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.120\n",
      "Model:                            OLS   Adj. R-squared:                  0.115\n",
      "Method:                 Least Squares   F-statistic:                     26.82\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           1.20e-11\n",
      "Time:                        19:30:24   Log-Likelihood:                -4633.9\n",
      "No. Observations:                 397   AIC:                             9274.\n",
      "Df Residuals:                     394   BIC:                             9286.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept    9.236e+04   4740.188     19.484      0.000     8.3e+04    1.02e+05\n",
      "sex[T.Male]  9071.8000   4861.644      1.866      0.063    -486.208    1.86e+04\n",
      "service       747.6121    111.396      6.711      0.000     528.607     966.617\n",
      "==============================================================================\n",
      "Omnibus:                       24.056   Durbin-Watson:                   1.863\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               26.987\n",
      "Skew:                           0.584   Prob(JB):                     1.38e-06\n",
      "Kurtosis:                       3.515   Cond. No.                         100.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model = ols(\"salary ~ service + sex\", df).fit()\n",
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вспомним, что мы можем сказать об этой модели. Вот ее уравнение:\n",
    "\n",
    "$$\n",
    "\\widehat{salary}_i =  92360 +  747.61 \\times service_i + 9071.8 \\times Male_i.\n",
    "$$\n",
    "\n",
    "Проинтерпретируем коэффициенты (судя по p-value, они все значимы, правда, коэффициент при `sex` только на 10%-ном уровне значимости): \n",
    "\n",
    "* Среднее значение заработной платы за 9 месяцев для сотрудников без опыта работы (`service = 0`) женского пола (`Male = 0`) равно 92360 долларов.\n",
    "\n",
    "* При прочих равных условиях, у сотрудников, чей стаж на 1 год больше, заработная плата, в среднем, выше на 747.61 долларов. То есть, если мы сравним двух коллег одного и того же пола (смысл «при прочих равных» для данного случая), в среднем, заработная плата того, кто работает на год больше, будет выше на 747.61 долларов.\n",
    "\n",
    "* При прочих равных условиях, средняя заработная плата мужчин выше средней заработной платы женщин на 9071.8 долларов. То есть, если мы сравним двух коллег с одинаковым стажем, но разного пола, в среднем, зарплата коллеги мужского пола будет выше на 9071.8 долларов (смысл коэффициента при `sex[T.Male]` с учетом уточнения «при прочих равных»). \n",
    "\n",
    "Предсказательная сила у модели невысокая, $R^2$ равен 0.12. То есть, модель объясняет лишь 12% изменчивости заработной платы (то, что заработная плата отличается у разных людей, только на 12% можно объяснить различиями в опыте работы и полом человека). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В прошлый раз мы также попытались (по крайней мере, графически) сравнить «влияние» стажа на заработную плату у мужчин и женщин и пришли к выводу, что, в среднем, заработная плата женщин ниже, однако именно у женщин увеличение стажа сопровождается более значительным ростом заработной платы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jsk193IS/YjcwFGftEq4KouY5S9e63ja9cyMiUqcUWEtDKUwPWYrGc2yjYZuSY3sTLPmfzVJw3aUb+PR9u4ins7RGwyQynt65ERGpE0oFEWkwap6ztBXb2HvTFZv1okpEpA5oxVqkwZRqnqMc26VD79yIiNQnBdYiDUY5tnOnnHQREVkISgURaTCqjjI3qvssIiILRSvWUre0ylicqqPMjeo+i4jIQlFgLXVJlS9mphzb8iknXUREFopSQaQuqfKFVMq63jYSGW/KmHLSRUSkGhRYLzEP7x7kqm3bueSWh7hq2/a6zTNVdzmpFOWki4jIQlFgvYQ00iYurTJKpajus4iILBTlWC8hjbSJS93lpJKUky4iIgtBK9ZLSCOlV2iVUURERBqNAuslpFHTK1ytJyAiIiJSBgXWS0gjbeJqpHxwEREREVBgvaRctqmPK1+7hqOjKZ47PMrR0RRXvnZNXaZXqNyeiIiINBoF1kvIw7sHufepA6zobOZVKztZ0dnMvU8dqMtV4EbKBxcREREBBdZLSiOtAjdqPriIiIgsXQqsl5BGWgVupHxwEREREVBgvaQ00iqwyu2JiIhIo1GDmCWk0ZquqKmHiIiINBIF1kvIZZv6uAk/13pgKM7a3jauu3RDQwWvD+8e5I5H+tk/FGddA85fREREFi8F1ktMI68Cj9e2joZtSm3rm6BhH5OIiIgsHlXLsTazr5rZoJk9mzf2DTP7RfCxz8x+EYyvN7NE3m1/l3fO68xsp5ntNbPbzcyC8WVm9qCZPR987g3GLThur5ntMLPXVusxysKqdFWTh3cPctW27Vxyy0NctW17XZYdFBERkcZRzc2LXwMuzx9wzr3fOXeec+484FvAt/NufmH8NufcR/LGvwRcC5wdfIxf85PAD51zZwM/DL4HeGfesdcG5y8Jiz1QrGRVE3V2FBERkUqrWmDtnHsEOFHstmDV+X3A12e6hpmtArqcc4875xxwN/Ce4OZ3A3cFX99VMH63820HeoLrLGpLIVCsZFWTRqrpLSIiIo2hVuX23gQccc49nzd2lpk9bWb/ZmZvCsbWAAN5xwwEYwCnO+cOAQSf+/LO2V/inCnM7Foze9LMnjx69OipPaIaa6RAcb4r65Wsbd1INb1F6sliet4UEam0WgXWVzF1tfoQcIZz7nzgj4H/a2ZdgBU5181y7bLPcc5tc85tdc5tXbFiRRnTrl+NEiieysp6JWtbr+tt49hYiv6jY+w+PEL/0TGOjaXqsqa3SD1ZTM+bIiKVtuBVQcwsAvwm8LrxMedcCkgFX//czF4ANuKvNq/NO30tcDD4+oiZrXLOHQpSPcYjswFgXYlzFq11vW0MjiZpa5r8ldZj85f8lXWAtqYI8XSWOx7pLytArlRVkzdsWMbP9p0gZBAySHs5jo6l+e0Ll005TuX9REREpFy1WLF+G7DbOTeR4mFmK8wsHHy9AX/jYX+Q4jFqZhcFedkfBL4TnHYfcHXw9dUF4x8MqoNcBAyPp4wsZo3SArxeVtYf7z9BX2cTTeEQOQdN4RB9nU083j+5LWAp5K2LiIhI5VSz3N7XgceBXzGzATO7JrjpA0zftHgpsMPMngHuBT7inBuPcP4AuBPYC7wAPBCM3wy83cyeB94efA9wP9AfHP9l4P+r9GOrR43SArxe2qrvH4pzWnszG1Z0sGllFxtWdHBae/OUAL+R8tZFRESk9qqWCuKcu6rE+IeKjH0Lv/xeseOfBM4pMn4ceGuRcQd8dI7TXRQWuvnLfNIkFqKtejnzKid1Zv9QnJ7W6JTz6jFvXUREROpDrTYvSoObb5pEtVfWy51XOakz9bK6LiIiIo1BLc1lXk5lE2I1V9bLnddlm/q4KTh+YCjO2iIr2wuxui4iIiKLhwJrmZd6TZOYy7xmC/Av29THlQMnufPRF4mlPdqbwnz4krPKelGgaiIiIiJLj1JBZF7qNU2ikvN6ePcg9z51gBWdzbxqZScrOpu596kDs6a7qJqIiIjI0qTAWublVMr7zbfzYrXnVWi+VUFUTURERGRpUiqIzEs5Ocrj8tMiOpsjHB1L0d0anbKae1NwzdnMlmIxl3nNZr7pLvWaJiMiIiLVpcBa5q2cTYjjaRHRsNHTGmXv4BjZnKO9KYI12Zw2PRZeq1RQXqnNkfPtZtkoXTBnohxxERGRuVMqSAOoZupEtRWmRXjOETI4NpaaOKbc1dyFTrGYb1pJo3TBLEU54iIiBZIjkEnUehbSABRY17lGD3IKW5g3hf0/ubSXmxgrdzV3oduhz7fmdqN0wSxFOeIiInlix2FsEJyr9UykASgVpM6dSr3oelCYFrGis5mBoQSRsOGcm1Nt6FqkWMw3rWShu2BWknLERUTwA+mxI5Aaq/VMpIFoxbrOLfQqbaUVpkWEQ0ZvW5T1y9rmvJpbLMViJJFhKJaqeZpMI6frFKrXUooiIgsm58HwgIJqmTOtWNe5Rt8IV6xKx6d+9dXzXgXOv1ZHcwQHZHJuXhVGKqXcTZWNQh0nRWRJy6Zh9CB42VrPRBqQAus6txiCnEqmReRf66pt20l7uZqnyVQ6Xef2H+yZ1u3x+rdtnHJMNat2VLJkoYhIQ0nHYfSQ8qll3hRY1zkFOaXVSy5wJedx+w/2cNtDewkZREL+uxO3PbQXYCK4XogV8kbOERcRmZfkMMSOKaiWU6LAugEoyCmuXtJkKjmPOx99MQiq/e0PIYNsLsedj744EVg3+oZWESnDngfhsdvg5EvQcyZcfANsfHutZ7V4xY5DYqjWs5BFQJsXpS7MZ/NfvdSLruQ8YmmPkE0dC5k/Pq7RN7SKyCz2PAgPfAJGj0BLr//5gU/441JZzsHIIQXVUjEKrKXm5luru17qRVdyHu1NYXIF70LmnD8+TlU7RBa5x26DUBM0tYGZ/znU5I9L5XhZGN4P6VitZyKLiFJBpOZOJbWhXtJkKjWPD19yFrc9tJdsLkfI/KA65/zxcYthQ6uIzODkS/5Kdb5oK5x8uTbzWYwySX+TYs6b/ViROdCKtdScUhsmXf+2jdzwllfSGg2Tzfk/hxve8sopVUHqZaVeRKqk58zp7bMzCeg5ozbzWWySIzByQEG1VIVWrKXm6mUTYr24/m0bp5XXK1QvK/UiUgUX3+DnVKfxV6ozCcil/XE5NdqkKFWmFWupuXrZhHgqFlPnRRGpsY1vh3feCp2nQ/Kk//mdt6oqyKnQJkVZIFqxlppr9Frdi63zoojUgY1vVyBdKTkPRg5CNlXrmcgSoMBa6kIlUxuq2ZWwGNWVnruF/h0tJrmcI57xiKWy9LY10RTRG48iJXlZP5/ay9R6JrJEKLCWRWUhVo8Lg8LnB0dZ2dUy5ZiluvmyHFrhnzvnHLG0RzyVJZb2cEFnuN62phrPTKSOZVP+SrU2KcoC0lKHLCr5q8dm/udo2Ljjkf6KXL9Yze3RZJbjsalvMS7lzZezqfbvaLFwzhFLZRkcSfLS8TiDI0nGUtmJoFpEZpCOw/CAgmpZcFqxloYyWwrB/qE4Pa3RKedUcvW4WNpHb1uUE7EMbU0R1ZUuQ7V/R43MOUci4zGWyhJPeeQURIvMXXIYYsf8DYsiC0yBdQNQPqqvnBSCapfuKxYULu9oJuvl6OtsacjNlwtN5RWncs6RzOT8YDqdxStsvSki5VM5PakxBdZ1binnoxa+oDgZT8+6SbDaXQlLBYVnn97F16+9qCL3sdAW+oWbOkf6EmlPwbRIpTgHY0cgNVbrmcgSp8C6zi2VihOFwd0bNizj3qcOTHlBse94nLU9M28SrHbpvsUWFNbihVujl1c8FckgzSOWUjAtUjEqpyd1RIF1nVsK+ajFgru/ffgFetuidLf6gfT4BreBoQRuKEHOQciguzXCppXdU65Xza6Eiy0ovOORftJZj+NjWdJejqZwiM6WCDc/8FxVV7GXUufIZF7OdDaXq/V0ZCna8yA8dhucfMlvl37xDYunRnY2DaMH/bJ6InWgrMDazMLOOW2trYGlkI9abFU+m8sxmsyyonPyuKYQJPMW+XIOhuJZVnYtbMmxcoLCRsmL33NkhJFklhBG2Iys5xgcTXF4JEVLNI6XcxwbS/GJe5/h1itfU5ePod6Mb0CMpTyleUjt7XnQb48eaoKWXhg94n/PIujkmI7D6CFtUpS6Uu6K9V4zuxf43865fy/nBDP7KvBrwKBz7pxg7DPA7wNHg8P+wjl3f3DbnwPXAB5wvXPue8H45cBtQBi40zl3czB+FnAPsAx4Cvgd51zazJqBu4HXAceB9zvn9pX5OBfcbAHYYks9KKbYqnxzOEQqO3V1byw9fbXPgB/uPjptfKHl/x47myMcHUvR3RqteV78bH9fGc//DykUMgDMJqtTuRyEzXA5OBnPcPMDzymwLsE5RzztEUurmofUmcdu84PqpmAxpqkN0sF4IwfWqvwhdarcOtZbgD3AnWa23cyuNbOuWc75GnB5kfEvOOfOCz7Gg+pXAx8ANgfn/C8zC5tZGPhb4J3Aq4GrgmMBbgmudTYwhB+UE3wecs69EvhCcFxdKlYT+dP37eLh3YMTx1y2qY+brthMX2cLw4kMfZ0t3HTF5kUV4KzrbSORmfqGSHdblHDIiKezQdCSpdjCnwNGk7O/Bfjw7kGu2radS255iKu2bZ/yMz5Vhb/HF4/FOBnPkPVcTes0l/P31RQJgYOcczjclIAwFDLMjFDICBm8eHzxpB9VQi7nGMurM31kJMlYMqugWurLyZcg2jp1LNoKJ1+uzXwqIXYcxo4qqJa6VFZg7Zwbdc592Tl3MfBnwH8DDpnZXWb2yhLnPAKcKHMe7wbucc6lnHMvAnuBC4OPvc65fudcGn+F+t1mZsBbgHuD8+8C3pN3rbuCr+8F3hocX3fKbZRx2aY+vn7tRfz4xrfw9WsvWpCgupqBaKHrLt1AxnNTguhoOMxHL3vFlBcUwaIqZpMfMLnaOtNjmS3APBWFv0fPOUIGx8YmN9LUIi++nL+vs/s6Wd7ZRCRkeDlHZJaf5VKXyzlGkxmOjCR56cRk0xYF01K3es6ETGLqWCYBPWfUZj6nwjkYOaRyelLXygqsg9XjK8zsn/DTMv4a2AD8C3D/HO/zY2a2w8y+ama9wdgaYH/eMQPBWKnx04CTzrlswfiUawW3DwfH1539Q3Fao+EpY/WwMbHagWihUqvy179t45QXFB3NfuaSc5MfAO1N4RmuXv1Of4W/x6aw/88q7U2mriQyHu1N4QV7sVJsXjD97+u6SzcQDYdZ2d3Cr5zeycruFqJhI2xTV7FzDjYsb6/qfOuVl3OMJDMcHvaD6aOjKWLqgCiN4uIbIJf285Gd8z/n0v54I/GyMLwf0rFaz0RkRuXmWD8P/Aj4nHPusbzxe83s0jnc35eAz+K/g/9Z/AD99/BTZQs5igf+bobjmeW2KczsWuBagDPOWPhX7/W6MbEWJf7K2RC4pqeV0cOjU36ZFozPpNqVVQp/jys6mxkYShAJ28RGtuFEBgMyObdgedfl/H0Vq3Ly7tes5u+3v8RoMkvWyxEJhehti3Lj5ZuqMs9SarkBNOvliKU9YqksyYz2beer9fOmzNHGtwO3BlVBXvZXqhutKkgm4W9SVFUdaQCzBtZBnvPXnHM3FbvdOXd9uXfmnDuSd90vA/8afDsArMs7dC1wMPi62PgxoMfMIsGqdP7x49caMLMI0E2JlBTn3DZgG8DWrVsXfPmpXjcmnkogWs1gyDlHOORXrzDzF18852ZdOaz2C5jC32M4ZPS2RTmtvYnhRIa1vW00hUOkvdyCvlgp9++r2IuaLWt7alpSsBb1tTNejlgqSyztkVIwXVKtnzdlHja+vbEC6XyJkxA/rnxqaRizBtbOOc/M3gwUDaznwsxWOecOBd/+BvBs8PV9wP81s88Dq4GzgZ/hL0ieHVQAOYC/wfG3nXPOzH4EXImfd3018J28a10NPB7c/pCrk/dsiwWdN12xeV4BTDUD2PkGotUOhsbSHmt6Wjg2lp6oubyyo5lYeuYgqNovYIqt+n7qV1895TFfcstDC16P/FRqbte6znSp+tqVfiGSynrEU341j3RWq2EidcM5GBuE1GitZyIyJ+Wmgkpe2jAAACAASURBVDxmZn8DfAOYSHByzj1V6gQz+zpwGbDczAbwNzxeZmbn4adm7AOuC66zy8y+Cfw7kAU+Ol4328w+BnwPv9zeV51zu4K7uBG4x8z+Enga+Eow/hXg781sL/5K9QfKfIxVVTLovGLznFthVzuAve7SDfzpvc9wYChBNuenAnS2RPjUr756xvOqnUIyHvBvWNExMRZPZ+nrbJnhrIVp6jJbIFqrtJ9aB8jzVay+9vFYmqw3csrXTmb8FI942iPjKZgWqTte1k/9UCdFaUDlBtYXB5/zV60dfmWOopxzVxUZ/kqRsfHj/wr4qyLj91Nkg6Rzrh+/akjheBJ4b6n7qZVKBp2VDmCLtRNPZTzSXo6cg5zLlfXWeLVzma+7dAOfuPcZDpxM4OX8tJCO5tkDfqh9gFmvaT/1qmh97Zwj7c39zaf8GtOJtKeGLSL1TPnU0uDKCqydc2+u9kQWu0oGnZW8VrHV7y/+aC+e54hGQhO5zPFMjv/6zztZt6y9ZPrJQqzKGoDzgyWckfFy3PzAc/zX7zw7MSeg7roeLrZW6NXWFAmRSPuNVsb/BnFB3e0y5HKOeMYjHqxMqxyeSI2V01Y9OQIx1aeWxlbuijVm9qv4DVwm3ncvtaFRpqtk0FnJaxVb/c54DgNCNrlamHU5Bk4maY6GS6afVHtV9o5H+ulqjbKy268CMprMMDCUYN+JOK9c0cHgaJJP3PsMBnTVuOthqRx4BdK+Yu+SPN5/YuL75e1NRMPGSGIyx7qrPcr60zpKXtPLuYnOh4mMtyTK4blg826dluoX8ZXTVj1+wv8QaXDl1rH+O+D9wMfxFw3fC5xZxXktOsWaoMw36KzktYrVOobp9QnH3z2fqRZ0tbtEFs716GiKkPkB1ficxlJZRpPZqtWsLsdC1wGvlfk2EZreqXKM2x7ay77jYxM/r+OxNBnPFdTXDk/7G896OYYTGQ4NJ3jpeIxjo6mJfxeLkZdz7DkyyreeGuAz9+3i4psfYmAoMfuJIrWU31bdzP8cavLHwW9NrqBaFomyc6ydc1vMbIdz7r+b2V8D367mxBabSqYCVPJaxVa/m8JGxnPkcpNvwzugOTx1VaxY+kk1V2UL55r2chiTDVnADzwKg6qFbrpTizrgC+1UNtAW/nxGk1lCBiOJLMs7WibGm8Ihetqapv2Np7M54umlURYvnc2x+/AIOw8Ms3NgmF0HR6ZVwXli3wnWLatt7XuRGZ18yV+pzhdthaGXYPQwpMZqMy+RKig3sB5fEomb2WrgOHBWdaa0eFUy6KzUtYqlb3S3RhlLZkgFmxdDBmGDZR1NU85d6GY20+pFm5HNOZZ3NE8cEw4ZuKkvABZinrf/YA93PvoisSCfd3l7dMqLlXroqFlJp/LioXCPQNrLEbKpnSpbo2GGExke+EO//9R4MD0wFF/UZfFiqSy7DvqB9I6BYXYfHpnYyJmvr7OZc9d0c+nGFbx+Q102lhWZ1HOmn/7RlPc8nI5D50oF1bLolBtY/6uZ9QCfA57CX8C8s2qzkgVTqvPe3dtfwqWyE9U3oiG/5Fktq1oUzvWs5e0cHUtN6XDY0RzBYEHnefsP9nDbQ3sJGURCkMrC0bEMRoLTg3zweuioWUmlNtA+PzjKVdu2z7hxtPCdh/HmOfnvPCQyHqt7WjkZTzOWWrw1pofiaXYODLMjWJF+4egYxYqWnLGsjXPXdHPu2m62rOlmZbe/1WVtb1vZGzpFaubiG/yc6jT+SnU6Dl4Czvt4rWcmUnHlVgX5bPDlt8zsX4EW59xw9aYl+ard2rlw9fuqbdvpbo2yqnuyVXg8nSUaMnrbm2ta1aJwruM/m/zGLLCw1TfufPTFIKj2A5ymsCPt5TgWS9PX1bIoS+sVSyE6HksxmsxOyy0vTA8pfOehsyXC0bE0Xa0RvFyOeNojnc3xG+et4UQsXYNHVx3OOQ6PJKcE0vuL5EeHDF7Z18G5a7rZsraHc9d00dPWVOSKIg0iv6360EvQcTqc/3FY/8Zaz0yk4mYMrM3sN2e4Deec8qyrrBatnUutRg4nMnz3j+bWzKbaSqXEFI5V88VJLO2Rv2gYDhlRB5kcEy3NF1tpvWIpRCdiGXrborOmhxS+83Dmae38xnlr+OmLJzg4nGBlVysfuGAdF25YVqNHVxk553jpeJwdA8MTOdJHx6Y3vIiGjVet6goC6W42r+6a8oJFpOGUKq131ptg9GBj1qj2MrD7X2HL+2o9E6lzsz17//oMtzm0gbHqarERrlZdAgtVKhiu9ouT9iY/sAzlp3ab0dUS5sc3luyh1NCKpRCdjKen5LtD6dzyi15xGlvW9RBLZSe6H773gnULMfWqyXo5nh8cmwiknz0wzEgyO+249qYwm9f4KR1b1naz8fROpXPI4lGqtF7mJlh5TuPVqHYOXvghPHY7jByA9hXwCrX2kNJmDKydc7+7UBOR4qrdzbCYeugSWMlguNovTj58yVl84QfPk/U8HEETG+DDb17c+3uLpRDN9IJsvJV4LOWRbcQVqwLJjMdzh/IqdhwaIZmZ/rh626JBbnQPW9Z2c9bydn+TrchilF9aD/yc6lTWH/+NbbWd21wd3gmPfh4O7/C/t7A/psBaZqAGMXWuFqvH9dAlsJLBcLVfnGxZ20NXa4SRxOTqZFdrhC1re2Y9t9r58wup8AVZPJ0l7Tk+cME6Xjoea/hW4qPJDM8emKzYsefIKNkij2lVd8tEWse5a7pZ29uqBi6ydOSX1nM5P4Ui3AQjh2o7r7kYHoDH/wb2Pjg5tv5SeMdfwurX1G5e0hDKCqyDBjFtwJvxq4FcCfysivOSQK1Wj2vdJbDcYLicwLTaL07ueKSf5R3NnLGsfWKsnBcBtcifr6bLNvXx353jS//mvyA7vauF929dx7lruxsyqD42lprcaHhgmBePxqY1TgI4a3m7X7EjCKZXdDYXOUpkiRgvrRdphlwWcJBNQteqWs9sdskRePJO2PGNYO7AilfBG/8Q1m6FrtW1nZ80BDWIqXP1sHp8qmZrXz3fYLjcwLTaL07muyK+WBrJjJc6HEtlOWtFBzf/1rm1ntKcOec4cDIxEUjvGBjm0HBy2nHhkLHx9A62BKXvzlndTVfB715kSXvDx+H+PwYvDZEWP6jOZeD8q2s9s9K8NOz8R3jiTkiN+GMdp8MbPgYbL4eXHod/uhbGjkDvWZObMUWKKDewHv8fZrxBzAnUIGbB1Hr1+FQUBr/7jo/xs30nWNHRxPKO5lMKhssNTCv94qTwhUJnc4RExpvzingt8ufLVc47AcmMx2gySzydbbgVaS/nePFYjB0Dw+w4cJJnD4wULe3XEgnxqtVdE4H0q1Z10RoN12DGIg0gm4a+TfCmP4On7/LTP7pW+UF1PZbWcw5e+AE89kV/YyJAtB22/i685ir/hcG+n8Ajt0AoOnUzJrcquJaiyg2s/6VIg5gvV21WsmgUBr8jCb999Wgyy4rOlhmD4SsHTk50M2xvCvPhS86acsxcAtNKvTgptko+nMhMbFicy4p4vVRfKTTTOwEXveK0htyAmM7m2HNkNAikh9l1YHhaa3CAzpYI56z2Uzq2rO3m7L4OImFV7BCZVSYBo4f8Unrr31ifgXS+Q8/AT/7n1I2J5/wmXHAttOWV+nz6Lj+ojraAmb8pM42/GVOBtRRRbmC9G/Ccc98ys1cDrwX+uXrTksWiWPtqnCOe9th9eISmcIjlHU1Fc6fvfeoAKzqbOSMIVu996gBb1vZMBMi1CEyLrZID82qeUw/VV4opfIwt0TBeLsttP3yeM05rjO6R8XRha/DRot0bl3c0BU1Y/ED6zNPaCGmjocjcJEcgdrQxSukN7w82Jv5gcuys/wAXXw+966cfP3IQmrunjkVb4eTLVZ2mNK5yA+tPOef+0cwuAd4O/DXwJeD1VZuZLArretvYd3yMkUSWtJfDy7mJls0Zz5HNeew/keBXVnZOOa+cNI9TDUxv/8GeaSvi179t44znVLJ5TqlVeWDWtuDVtH8oTldLhKyXI+f8/ONo2Dg0PL1LYL04GU+z88AIOw+cZMfAMHsHi7cGX9vb6q9GB6kdK7taVLFD5FTET/gf9S45DE98BXaW2JhYStdqiB33V6zHZRLQc0Z15ysNq9zAevw9018F/s459x0z+0x1piSLyRs2LONn+04QMr9Vc6Yg2HHOzysaTUzNby0nzaOcdJFSbv/BHm57aG/Qitxf6b7tob0AMwbXlVwlf3j3IH+//SXS2RyGI53NceeP+2mOhulqjS54pZCsl2MslaWvo5n9QzHGUh4ZL0c0HKKjOcyanvbZL7JAJlqDB81YXj4xPf0nZPCKFR1BDeluzlnTzbJ2tQYXqQjnYGwQUqO1nsnMvDTs+KZf7WN8rp0r4aKP+hsTbZZUr/Ov9nOsM/gpIZk45NL+BkaRIsoNrA+Y2R3A24BbzKwZUOKhzOrxfn+j4mjSX7HOZ/gpayGDo7HMlNvKrQoyW7pI/rH5m/Ge2X8yCKr9P+OQQTaX485HX5wxsK5k+sYt393NUDxDOGREwiGcg9GURzKbY2V3K1D9SiFZL0cs5TGWzpLK+K+fX7O2m18M+D8fM8h4OY7Hcvzaud2zXK06nHO8fGKyNfiOgWEGR4u3Bt+0snMitWPz6i7am9UaXKTicp6fT52ZXjmnbhTbmNjUDq/7vWBjYpllMde/EbjRz7UeG/TTRVQVRGZQ7v867wMuB251zp00s1XAn1ZvWtKoCgPY5wdHWdnVwopO/220Zw8MT3QnbAmqK3hFNsFVsipIsc148YxHtOClYciYtqGtWHWMm67YXJEKI/3HYsFKvp+KYOav3qe9qcv6la4UkvFyxFMesXSWZGb6Br6n9w+zrC1KLD25Yt3eFObp/cP8TsVmUZqXc+wdHAvK3vkVO4YTmWnHtTWF2by6ayI/etPKLrUGF6k2L+PnHXvT/03WjUPPwKNfgCM7/e8tDOf8Flx4LbT2zv1645sxu1ZPdpQUKaGswNo5FyevbrVz7hDQQG2UGku9duObbV7FAtjRZJZoOMXyDj+wbo6ESGZzYOBwOAc5B2evmJpmUE6JvHKrghQLwEMGmRxE8iqn5Ry0N00OlKyOccVmvn7t3PKpy2UwrQnJqW7IdM6RyuaIpbLEg2B5JodGEvS2N7GsfTL32OE4PFKdHOtUxmP34cmKHf9+cIREkYC/p9VvDT4eSL9iRYdag4sspEwSRg/6lT/q0cn98PgX4YUfTo7NtDFRpAr0PmmdqddufOXMq1gA29sW5UQsQ1tThNZomN72KEdGUoTNT0OIhEL0tkW58fJN0+5zthJ55eY7FwvAT2uPcnQsQzaXI2R+UJ1zTGweLPV4KpmWcdZpbew5MkbG8yZW8R1+SsOpppp4OUc87QfSibRHbg679Vd1tXI8lppSrzmZybGyq3VOcyhlLJnl2YOT+dG/PFy8NfjKrpYpgfQ6tQYXqZ3UqJ8KUY+VP5LDfnOXnd+c3JjY92p/Y+Ka19V2brLkKLCuM/Xaja+ceRULYJd3NJP1cvR1tjAwFGf9aR1cdcEZPN5/4pRTKcrNdy4WgHe1NtEcCTOSzJasClLtBi7vOncVewafn/h/yuGno2w9o4ddh0bnvCHTyzli6SyxVJZkJoeb53+AH7hgHbc99DyJjEdLNEQykyObc3zggnXzut7xsdREbvTOA8P0l2gNvv60tomNhueu6aavq6XIUSKy4BJDfmWMelNyY+LHYON/nH1jokgVKLCuM/Xaja+ceZVaQT779K5pqRPXz3MehekoV752zaxBeqkA/C/fc25FVsTn6/H+E5ze1TxRirApHKI5EuKp/cOs7W2ddUMm+MH0WMrvfpgo0vBkPi7csIwbOJt7ntjP4ZEEK7ta+cAF67hww7JZz3XOcfBkkh0HhtkZBNIHTk5PIQkZbDy9c2I1+pw13XSrNXjZzIxIyNACvlTd2FF/RbieOAd7H/TrUZ/KxkSRKlBgXWdOJZirZm52OfOqdsOTYukod29/iRUdzUVXQMfNt6V5tR/P/qE4p7U3T+SfA7wwOIqXczO+M5DxcsTTXkWD6UIXblhWViCdc5OtwccD6eNFWoM3R0K8atVka/BXr+qitUmtwWcTDYeIhI1IKERTJERTOEQ0bOoGKdXnHIwehnSs1jOZ6tAv4NH/ObkxMRSGzVfChb8/v42JIhWmwLrOzDeYq3Zudjnzmm8AW67CdJSs5zgZzzCWzPLKvo4ZH/N8WppX+/EUe7GS8nK0RKYGnK3RMPtPxBiKpYmls0U7CC6UjJfjl4dH2XnAD6KfPTDCWCo77biO5gjnrPED6S1rezj79A6iCganMTOiYfMD6KDsYv73yimXOdvzoN9u++RL0HPm/ErD5Ty/8kd2elnLmim2MXHDm+ENH4feM2s3L5ECCqzrzHyDuTse6Sed9Tg+NplW0NkSqVhudrnzmk8AW67CdJRjYylCBp5zmNmc89HnssJfje06xV6sREL+7w381eBckDe9vKOFofj0leBqS6Q9dh0cngiknzs0SqpIYH9aR9NEbvSWtd2sX96u1uCBkBmRsNEUDhEJVqCb8gJpkYrZ8yA88AkINUFLL4we8b/n1vKD63orp5c46edQ7/zHvI2Jm+GSP4LV59d2biJFKLCuQ/MJTvccGWEkmSWEETYj6zmOx9JkvZGKz69We8ILV3jTXg4DmvKCk3Lz0ctZ4a/2uwDFXqy865yVfPvpgwwn0n5pwhIbB3/Wf4J7ntjPoZEEq+aQAz2b4XhmIojecWCY54+MFm0NvqbHbw1+bpDasbp7abcGLwyeC1ehRRbEY7f5QfV4reWmNkgH4+UE1uk4jB2uj3J6Xhp2fAOe/ErexsRVQcdEbUyU+qXAepHIBE1FQqHJZiO5nJvWbGS+KhlkzjcXvHCFNxzyX0Cs6JzcqFJuPno5VU4WokLLmzauYOtZy4insyTTObK5HGt62mbcOPiz/hPc9tDzREJGV0uE47EUtz30PDdw9pyD68GR5EQQvXNgmH3Hp78oMWDDivZgNbqHLWuXZmvw8eA5Gg5N5D5HQ8p5lgqoRPoG+Oe3FOQZR1vh5Muzn5s4CbFjc7/PSnMOnv8+bP/bvI2JHbD1Gtjyfm1MlLqnwHqRaIqEJuoVmwWlRh3z7kRXGPwOxVIVCTJPJUAvXOFdv6yN47E04ZDhnJvT5sL9Q3HCBv1HxyZSZ5Z3NE1Z7T6VCi0zvXgYbyNeqvPhbBsH73liP5GQTdSZHk8jueeJ/TOe55xj/4mEH0QHgfThkektiSMh41dW5lXsWN1NR8vSeKoImRGNhIiGbDJ4DgJpNaORqqhE+sa4njP98/O7A2YS0HPGzOfVS+WPQ7+ARz8PR3b534fCcM6VcIE2JkrjWBr/W9aJalbtOLuvk33Hx6aUbutqj7L+tI55zbMw+N13PMbanqkNQuZTBnAuq8DFfl7jHNDb3sy7zl01r5rYnc0Rnh8cIxwyf+U75zhwMsnZfZM/r/lWaCn28/vUd57lk6lNnHdmL6kiwXS+2dI8Do0k6CoIdFuioWmdEb2c44WjYxP1o3cODHOySGvwlmiIzau7g42G3Wxa2UlzdHFX7AiHjKaIHzBPVttQ8Cw1cKrpG/kuvsEPytP4K9WZBOTS/ngxuZyf+pGubTlXTu6Hx26H/ocmx7QxURqUAusFslBVO1Z2R065NFyx4DcaCnFkNEVX62QKwHxqOpe7Clzs5/Wn9z6DA7pboxNj9z51gJuu2DyttfpsL2BcfleWvM/5TVXmW6Fl/OfXEg3jOUckFCJNji//+EU+v7prxnN/1n+CW763m1gqi5dzDMXS3PK9GDf+x00TwXWpzoh9nS08M3ByouzdroMjxIuU4+tqifiNWNb2sGVNN6/sW7ytwcNBjnNT8BGNTOZBi9SFU0nfKLTx7cCtQVrJy/5Kdam0Ei/rtyfPLvym6AkTGxO/6VciAW1MlIZXtcDazL4K/Bow6Jw7Jxj7HPDr+K+nXwB+1zl30szWA88BvwxO3+6c+0hwzuuArwGtwP3ADc45Z2bLgG8A64F9wPucc0Pm76C6DXgXEAc+5Jx7qlqPs1zVztetZGm4YsHv6V3NDJxMzqumc36gO5LIkPVyrOicrN1cLEAv9vM6MJQAg1XdrRNjhT/Dcl/AjKU9etsiHI9lyDm/Yclp7VFieYHofH6myYzHvuMxOpsjZPKqZxRbUS5m24/7GUlkCIWMcNhwDkYSGbb9uH8isB7vjBhLZ3HOMZrySGY8Dg4n+aNvPDPtmn2dzWxZ2z2x2fCMZW2LaqNhOC9tY8rmwVBoYs+BSN2ab/pGKRvfPvtKdzblV/7IVacO/qy8NDxzj78xMT3mj3Wugjd8DM5+hzYmSkOr5or114C/Ae7OG3sQ+HPnXNbMbgH+HLgxuO0F59x5Ra7zJeBaYDt+YH058ADwSeCHzrmbzeyTwfc3Au8Ezg4+Xh+c//rKPrS5W4iOipUqdVcsBSISDrGxr4OetqY5Be6Fga6XyzE46q+QLO9oLhmgF/t5ZXO5aQFh4c+w3Bcwnc0RDg8niYZDEznpQ/EsZ/dNbaM92890PLd7LOU3a/FyjtM7W4quKK/sai15nfzHHTImStVZUE6w/1iM993xOB1NEVb3+tc5cHJ6fjTAmcv81uDjOdKnL4LW4FMapYx/reBZFoO5pm/km8+mx9QYjB0JNuIssPGNiY//jb9aDtqYKItO1QJr59wjwUp0/tj3877dDlw50zXMbBXQ5Zx7PPj+buA9+IH1u4HLgkPvAh7GD6zfDdzt/Pf0t5tZj5mtcs4dOsWHdEqq3R67kkqlQHzqVzfNOXAvDHTHuwzGUh7DiUzJAL1ocB8K+SUq8hyPpYilPC655SHW9bbx/OAoKwsCyWIvYMpJBSkll3Mksx6xlN/90CuoRze+opzIeLRES5fMm8n4PLycY3zd+9hYmmOk2Xdi8rGEzM+vP3dtF1vW9HDumm662xqzNfiUzYKh/I2DapQii9hc0jfyzWfTY/yE/1ELB5+Gn3yhYGPie+GCD2tjoiwqtcyx/j38VI5xZ5nZ08AI8F+dcz8G1gADeccMBGMAp48Hy865Q2Y2HpmtAfYXOWdaYG1m1+KvhnPGGfN8261M1W6PXUnVTis5rb2ZSCjDj298S8nziv28OlsiOJgYOx5LMTiaZkVH00Tax2gySzScmtImvNgLmLG0x5qeFo6NpSc2e67saJ6SCpLPyznGUlliqSypbG7GAPzCDcu4gbNnLJk3bnyj4sHhOL1tzbREjLGUw5WoFm74lV56WqP8yTs2snl1d0O1Bp9Sqm68PXdIwXMjWcjnzSWjnPSNQqU2Pf7wM9NXsV/5Fhg9BJni73JVVamNiRdfP/90F5E6VpPA2sz+C5AF/iEYOgSc4Zw7HuRU/7OZbWba+iQwe3+Sss9xzm0DtgFs3bq1qu+LVbs9dqVVM62knJX6yzb1ceXASe589EViaY/2pjAfvuQstqztmfgZxlIenc1hRpNZjsfSNIVDtEZDnIhlaGuaeRPn+Lw2rJisAhJPZ+nLy/3OejliaX9VOlEi4J5NqT+qrJfjn58+yN//9CUyXo50djJFppiulgjdrVGaI37qymgyy9b1p94QphrMjEhB1Y1okP+s4LnxLeTzpsyg2KbHXAaOvgC9r5hcxb7/T+DSG+GMBc6ILLYx8fTN8EZtTJTFbcEDazO7Gn9T41uDdA2ccykgFXz9czN7AdiIv9q8Nu/0tUCQmMWR8RSPIGVkMBgfANaVOKemqtnuu9IqVRpwviv1D+8e5N6nDrCis5kzgvPufeoAW9b28PVrLwLgdZ/9/rRuk2kvR0vE6OtsmfEFTKl5XfPG9ZyMp4mnvaI1pstRrIHLF364h18fXE06l/Nbgx8cIVmkNXjI/NSVnrYmkhk/oG9vDtPbNrUJTjn52tU2UfM5CJrzNxAqgBapsmKbHkcPT13Fjrb4GwV//pWFC6yzqcmOiRMbE1fDxR+HV77d3zgisogtaGBtZpfj50H/B+dcPG98BXDCOeeZ2Qb8jYf9zrkTZjZqZhcBPwU+CHwxOO0+4Grg5uDzd/LGP2Zm9+BvWhyudX51PSknYK5kacD5rtSXswmxVLdJs9BE8F3OvF4+EWNVdyvv37qODX0dnIjNXH5qtjrT9zyxH8NPHzk2liaR9khmc9z5kxenXSsaMlqbwrRG/Y9IGMZSHn9/zYUT93Wq+dqnyswmguepq9DauS9SM6U2PXYF6RU5D3JZiLTAyAL8F+hyeRsTg/vTxkRZgqpZbu/r+JsLl5vZAPDf8KuANAMPBita42X1LgVuMrMs4AEfcc6N77D4AybL7T0QfIAfUH/TzK4BXgbeG4zfj19qby9+ub3frdZjbDTlBsyVLg04n5X6cqqozLfbpHOOZCbH5jXd3Pxb507bfDiTUu3EP5RYTyhk7DwwzLMHh8mWuOZEa/A13Xz7qQOMJDNTqocUrkbPJV/7VIy36x4vVzdecWM8F1pE6kyxTY/hKHgZP6DOZf3jsknoWlXduRx8Gh79AgwWbkz8fWjtqe59i9SZalYFuarI8FdKHPst4FslbnsSOKfI+HHgrUXGHfDROU12ESusId3eHKa71c8jLhUwL0RpwNms623jxWNjjCYnO0l2tkQ4a/lkTvRcuk3mco54xiOeypLIeHMKpvPd88R+wgZhM0YS/rViaY//8d3dRY9viYRobQoTDhkru1q4/arJ3ML2pkhZq9GztTgvV37wHA2HiEZCRIIa0PNpEFPNTqIiUobCTY97HoT/90d++kekxQ+qcxk4/+rq3P/QS/D4F6H/R5Nj2pgoS5w6Ly5ihSvUh4eTJNIezZEwnS1+4FwsYF7X2zY9YG2NzKs9+ny9YcMyfrbvRFDTGdJejqNjaX77wskA87pLN/CnIDxkzgAAIABJREFU9z6Dl3M45/ByjqzneMOGZVy1bTsvn4ixuruVD1y4jteeuaysUnrFeDlH/9ExdhwY5rnDI2Rzrmhg3hINsXlVF73tTWzvP04q45HxcuRSjvbmCP/59VNb81ZjNXq802A0aNUejfil66Jhf7xSwXC1O4mKyBw5B6u2wJv+FJ6+y0//6FrlB9Xr31jZ+0oMwRNfhmfv1cZEkQIKrKukHlbzClM6miMhP0AdTU0E1sUqdBQLagdH01x1wcJVoXi8/wR9nU3TgvvH+09wfd5xDsD8PGCHI5HOctdj+2hvidDWFObwSJJbv7+HG95ydtkBazqb45eHR9lxwG8PvuvgSNEyfOMbDSNhf7Pk3/72+UTCIX7Wf4KfvzRE2sthOVe8Tk1gPqvRhVU3ohOl62Zeea5kMFztTqIiMgc5b7Kc3vo3Vj6QHpdNwY574MmvTt2YONExURsTRRRYV0G9rObtH4oTNug/OkbayxECcs5vbjLeMbBYhY7H+0+woqNpWhpGYVBb7bmf1t48pR61c25al8Wulgh9nS3knCPnHPuOx0glM8SD1eJoOERHc5h7nthfMoCNpbLsOjjCzgPD7BgYZvfhkYmNkfn6OptZ3d1C/7EYbU1hOprDpLKObM5xzRvPIhLkIt/zxH46miOs6JhayWOmOZQSDYdojkymbpxK2bpKBsP1kC4kIoCXhZEDfm51tZTamHjBh/2NieGm6t23SINRYF0Fcwlgqrmy3dEUZu/RGGHzy9E556c1hAyeOzw6URu68P72D8VZ3tHMis7SQW21lap/vaanlXg6Szzt8eKxMTpbImS9ybJ1Wc+Rc4A5QiEjm3MMxTJkc7GJY4bi6YkgeufAMC8cHaNYyvUZy9o4d0035671Nxuu7PZ/HuNVQUqlbxwaSdDVMvWfVks0xOGRRMnHGzJ/BXriI+x/VLJdd+ELraZwiOUdTfP6vTZSJ1GRRSub9oPq3CylQff9JEgPOQhdq+eWHnLgKfjJ/5y6MfHc98HWD2tjokgRCqyroNzVvGqvbE+sapr/4eX8ANQ5CIf8FI+7t7/ElrU9U+6vHoKm/DrTLZEQsbRH2svxnvPXcHjY7x62squV47HUlKoa42nUoYkVXb8leCyV5dbv/5KdA8PsH5oe4IYMXtnXMRFIn7umm9624qsws6VvrCoyr2Qmx8qu1snSdePBc/A5sgCVNzqbIzw/OEY4yL/O5hwHTiY5u2/uufON1ElUZEZ7HpzeqXCuXRBrITHktyefbe/Ivp/AI7dAKArN3RA77n/PjTMH10MvweO3Q//Dk2Mb3uLXo9bGRJGSFFhXQbmBabXzVEdT2Sltu8f7kTj8qhYuByfjGW5+4Lkp91froCmXc1y4YRmfeMdG/vdP9nFoOG9l+KzJgPYDF6ybVlXD4b+OyASr2OMr0Z7nuH/n4Ylzo2HjVau6/NJ3a7vZvLpryu/rVIzPK5n1aI2G/RbowEff/ArWn9ZWs+YpE5s3x/8fdgXjc9BonURFitrzoF8LOtQ02anwgU8At9ZvcJ3zYOwIpMt8p+npu/ygOhq8AxltgUwwXiywTgzBz74Mu/I3Jp4Dl/wRrDqvIg9BZDFTYF0F5Qam1c5TLWzb/eyBYRz+6qyZ+bWfc469R8e4atv2KekoN12xeV5B03xSW7ycI5X1SGZyJDOeH4g6xzlruvnr972m5HkXbljGx3Kv5GuP7+PwcAIzI2R+MF0YK4YMtp7ZG6R19PArKztnrXddjvEV6CdfHOL//PQlDg4nWNfbxge2rmX7i0N1FXSOpb0pL7SawiFWdjQX3ZhZjkbqJCpS1GO3Te1U2NTmN1x57Lb6DKwzST/HebbUj3wjB/2V6nzFmsZMbEz8CqSD1LmuNf7GRHVMFCmbAusqKHc1r9opF4UB/nisGQlNBpRezuE5GBxNTk1HuWLzrN0LC5VKbbly4CSP95+YCLavuWQ9F71iOYm0RyrrkS7S2ruUZMbjuUP+RsOdA8PsOjRCMlO8NXhbU5hI0OTkj9+2kYtecdqcHk+haF7qxngudDQoYff5H+whGjaWtTVxbCzFt54+yE1XbK6rwLPwhRZAPJ2lLy+XflyxF0hAzSvdiFTUyZf8lep80Va/4Uq9SQ5D7NjsqR+Fulb76R/RvH/n+U1jXA72fA+2/+3kxsTmzsmOidqYKDInNt/avovN1q1b3ZNPPrmg95kfiOavbFcyIBsPkAaG4hwfS5PIeBB0KRzvVtgUNn5lZdfEOePB1lwD66u2bZ/2QuHoaIITsQyre1ppjoQmHmO55e9Gkxn+//bePM6R8rz3/T5VWlq9z74Cw8CMsYFhx2wmxAYbL8ckJyQ2zk1IYgd/cm2DneMc7JObEx9nMwn32jiLL8RxwPcmxs4kjrmOgWAIwQv7GMbYjIdhGJiFmZ6e3ru1Vr33j7ekltTV3ZJaakndz/fz6VHrVVXprRp16VdPPc/veeHwtGPH3mPjoV0NN/R12PzoTX1g4LsvHuPYeKqQQgLM2Ya8mOKW3U++fIK7f3iAQyNTnLyyK1RMhu13rcewkVT6eQtbbiyZxQB9iWjDPqtKU6kpHNmM82Zdufs9Nv0jVhTMyExBzzr4jW83b17FGGMFdWq0tvWLc6yLm8Zceau9iCgpTIwEhYkf1MLEMHo3ln5WlOVO6HlTI9ZNpN55qrOlYeS398Xv7uULD79UyDvOX1P1JUo/BrWmoxwcnqK3I1Jo2OIbm8Pt+YaY62AMdERcjJndem5wIs2PD42y+/AoT+4f4uhYKvS9Tl3dVciPPntTH2t64iWvv/uc6Ra+s7Uhv/bYOp4/OMrrYyk29yf47bds5eo3rSs4cTy6Z4A/e2APUVdY0Rmbtbg0LKUn5/nsem2YK257pGWiu5V+3sJy/w8PJ0FgQ1+iMKa+1Urbc9ktNqc6gxWZ2ST4GTveChhjo8iV5lOHseVy4NbSpjHbroWf/DO88p/Ty532Nrj0Y9B/0qybUhRlflRYN5l65alW4jDy+P4h1vXGS5quZD2f8bTH+qJtVZqO4vvWEzud9UnnfNZ0xxmcKHXDyHiGeFkuc956zhjD4ZFkQUj/+PAoR0bChXQsaIJyyakrOTae5vhEmtdOTHHZ1lUzRHU59z59MIi+RnAEejpchiZT/MOTr3HSyk5WdcUYmsrwx995kVjEKRyvSotLy1N6xlNZDo+kiFTg9rLYjYQq+byFXij4/oyiS/WtVtqe7dcAtweuIK9Zt4tWcQXxcjBx1OZVL5R805h8YeJjnysqTDw7KEycvZ5FUZTKUWG9RKhEBIY1XRlLZjg0kqrIASST80nnbHFhKjszN/p9F8506XAdoStmhbYxhnTO58RkmlTOcM3nHwv1j+6IWPs5R6C3I0JH1MURYXgqzWP7Blnf21ESeb6F0rSSfFOVfB708YkUKzpjJcJwLJnDN8x7vCopLs23Vj88nCTn+3i+zfFe12Pt9WYT5K3SSKicsNz/iOPMuOmlvtXKkmD7Na0hpItJjcHk8erzqWcjl4Ln74Vnv6KFidUgApE4RBI2Rz2aaPaMlDZAhfUSoRIRGCqYXIfta7vp74yVpAdcsW01E+kc6cClI+/UMRcXb13JLWwrNE9Z29PB2Rt7+d6+E7w2NEXG80OFtAicsa6Ht2xfwzmb+zh9bTe//pWn6O2IIEVqbjyVw/dNISKeiLqkch7fePYg7zhrPR1Rl3hkZlOVk1d2zdjvtOfTEXFLlgs7XgdOTMxoq75l1Uzf5/LW6uW7GSbIW7UteJirTU9HBAPqW60ojaTafOr5Gr8UChP/CsYDu9F4j23usuNXtDCxHDfIQ4922Ec3phcdStWosF4iVOIwUh5ZjTi2Vfmf/9IOLj19NemsX0jteG2o+lv8U5kc4sBZm3sxhwwvHh1n9+GZXxCOQFcsQiLqkog5eL4hHnELRYYQ3mQln1biOlKwC4xFHI6Pp1nRNfsXRJhQzO97MeXH69KtK3nqwBCO2DlnPJ+B8Qw3XFSaG37nY/vpS0QL+cf5zoaDE2l6g4udsOjubBdDLx0bm2F/uJhCOywX+w/e/SZ2Hxrhy99/hcmMN2vXTkVRasTLWvGbS1e2/HyNXw7vgh98HgZ+apd3InD2++CiD0JH35ybXhY4TiCiE4GIjtsxRVkgKqyXCJV6Z/tmOp5qMOR8w7HxNEdGZm+3PRsjUxl+fHiMHx8eYfehUfYNhLcG37wiwY6g0PDL33+F/kQER6ZPYAYzo933DRfbtJKM5wdNVjyirkNfIlrSpfD4eIqpjDdnkWCYULzunI3s3HV4zuP1+P4h1nTHGE9NR6x7OiI8vn+Im4u2Xy6Q1/TEOTycLET5Z/u/CLsYGpxIM572ZtofsrjpIeW52I/uGWDnrsOs6YlzcnC8du46PKNrp6IoNVCLld5sjV+eujO8MPGyj0HfMi5MjMSsgC78aLReaQwqrJcIV52xluvLIoofvHwLl5y2itGpLGnP446HX6IzFmFV13SxXzLrce9TB0s6Gs7GsbFUwT9696FRXg2JajsCW9d0s2NzHzs29XHWpj5WFkWTH3jhWBCJnl4nlfXZ0JegOx4hHnXpiDpsXXMy63o7SsTwL5y7qUQMD06kOT6RYW1PbF4RGla0t2Nz/5wOGQeHp1jdHWdNkc+zMWZGSke5QO7piLK6x2My7TGazM7qvhF2MTQ8laUr5nJ0NFWSftLs9JBWTVtRlAXTzJbmvm+7KO7995kpHTB3mkd54xc/B6kRGDkwPbZ+B1z+8eVXmOi4gXiO24i0RqOVRUSF9RLA9w3f/ekxvvHsIVZ2xdjQZ/2i733mEOt6E4XCviOjSXrL0h/yDh3lGGN4bWiq4B+9+9AoA+Mzb1FGXeEN63qs7d3mPs7c2Ed3vPQ9nto/VPCQ7opFmEjnANvAJR0UQN7ytm2s7S1tVDKfGJ7KeKztiRWKMasVe/M5ZFTawCdMIEddly++f8ec2w+LpB8fTzOeyuE4gusIOd8wOJ4h643Puz+N5ODwFK5Mp7nEXIfV3TF1BVHam2a2NM+mrOvHy/85M6Xj4c8AYvOhw9I8YLrxSyRm3T6mTticarCFiZfdbCPVSz1HWGQ6nSMSt4+OO/96itIgVFg3iEbYqPm+ddXI5Hwynk/W88l5hpzv8zePvozAnH7RYXnLqazP+t4Enm/YNzDB7kMj7D48ynOvjYS2uk5EXc7c2FsQ0mes6yEenf0klveQzjtfpHM+rkBn1GEq41Xt3V0shq+47ZGGtoSvNL1mIX7k5eJ+x2ceBAEn+DIUAV9MVd0pG0F3zGXf8UlcEVwRcp7h8EiK09d0NXVeirIgmtHS3BgrhJPD9vewlI58B8TuNdNjWeyyeWF97q/BI/8LRsfA5M/VAm+6Dn7u1qVbmOhGikR0orSjpKK0ACqsG0A9bNQ83xTs7TKBK0fWm11cvT42fzT6/RedxG0P7uHYeArPM4hjbdQ83/COL4Rb37lBgWDUdfj1S7Zw3XkbcZ3ZIyBP7R/i3mesK8jm/k7GklkSUYeuuBXAsYiL6wgruzt4cIFdCRfaEn6+i59qBHO9/MijrpDM2ouofGdMsD7ezaRgVShM2+4ZZnhbK0pbsdgtzcO8qctTOmDaY7qYSIdt8AJw+FmbS50cnn69ay1c/gnY/vb6z7tZFOzuinKjXZUtSmujn9AGUG0+as6zEei8gE5nfXL+3BHK4vSKDb0JumIRRqYyTKQ9sp5P1HXojrts6rcRxYlUjj1Hx5jKeGRzQfmiZ9/7yGhpAwIBumIuq7vjRF3rwJHMenx/3yD/9YJNofOJug4/enWYv3p0HzFXWN0VZ3gqw4ETU2zuL40o1CuqXGlEOYxKL37qJZgrZfu6Xl4ZnCgrmIxy6uqZFn+VUK87J+PpHJv6OxicyBTmtb43XkjraQS1zn2xm+4obUz/KTNbmmeTtlFMvUlPwOSAzasuJp/SURx5DUtlyKUgsQL+7XdLCxNPvwYu/cjSKEwUseI51mmj0ZH40k9lUZYcKqwbQJiNWkfE4eDQJGOpLDnPkA1SObKemdcfupywFt1DE2kms9Mn7Jzvk8z6rO72+O2vPsP+45MzvJWLcSVf2yFkPdtR8dh4qiDSV3RGS6LfsYgT2OW5xIMo9H/fuZt4xCm5oIi6wrGxNL2J6duSlUaV6xlRLmchxXiNFG75i4X1fZEF+0XXswFN/u7A1jXTAn8qk2NtT2Nuw9Y691ZtuqO0KIvR0tz3rONHepY6ifNutPnTWayozKUg1gWIjWxHOmxTl+QQjL4GA8F5fqkUJjoORLvsPkc7tchQaXtUWDeATf0JBsZTNs8Zezt/KpNjdXcHgyEFgNVy79MHiThSyJXuiDiFIsByXjw682Se92UGyK9WbGEHhpxPIWqe831So2lOW93J2t4OElE3NB0k7IJiXU+cQyPJqqPKjY4oV9pVsdZ51Sq+F3KxUE49nTwWcnegFmqdu7qXKFXR6Jbm6XHbQXGuO5BbLgduDRxAXofeDXDF79rXdv09DO6D7GRZYeLH4LSr2zeaG4kViWnNkVaWFiqs68hkOsfgRJpfPHcTdzzyEjnPFFp753xT0gBlLsrTPN5/0UklLbuPjE7REXUZnsqQzPoksx7eHOFowQYB8inaArhBVGC+lJM8Bkjl/BmOH8WctKIzJI0hwrY13azoilclFOstkMqFbk88QjLrVZ2fXcm8Fho1rVf6Sa0XD7PNqV6CvxJqnXs991lZJtTa0nwumz7fs4I6PVHZtrZcHtIx8QGbf50JgiPxXrjot+HsX7YdAtsJERuNjnVaQa150soSRj/ddcQzBs83XLx1JdceXcc3nj1EMuuRiLr8ygWbS8TxbISleXzh4b384olN5Izhx4dHOTGRxTOZiucVi1gR7QUi2jPgGlPSi8D3DY6U9ifIP5cgwn18Yu73DOtUeHwiwwcuPpmbr95e8XyhvvZuYUJ3NJkt1OBVE4GtRLi1StR0ocWd5TQy37z8wqc75tZ04VPvfVYaTDM9pBfCXDZ9Wy633tRhBYiVcOgZ2zHx+B77vF07JubFdLzHRqbbNbquKFWiwroBPLV/iAd+eoyVXbFCxPqBnx7jDet75xXX9z59EEdsh8QTEzYincp6fOmx/aHLi9gIdJijR55Mzp+RX+0bQ9R1SMQcxlMeOd8WNOYzPKwbyHQBjVdBZPvx/UOs7YkxlsyVNDcp71RYCT3xCC8NTOAW+TkfHkmxbW31RXxhQhcgnclxfDxdVYvuSoRbq0RNK03faHaxX9iFz1gyW/jMVnPhs9gpK8oCaIaHdL2EfJhNX9rA9/4CVp5a29yGX4EffBEOPDY9dvrVcOlH26cw0Y0WRaY7VUwryxIV1g2gPAc6/wVf7CldzGgyywtBI5YXjoySm0Ulb+pPsGNzHy8cHmUilSWZtYI46joks7ML37CtbV/XQzrnM5rM0puQghNJxHHI+gbfN6SyHoYglURg+7q5Re3B4SlWdcULDVsgvFNhJRQKOvOTN2XjVRAmdHOez+vjabas6qqqRfeHr9zKJ3c+z+GRJJ5vcB2hOx7hunM2csNdT3BweIqxZJac55d0bFyMqGmYQP7se8+cM32jFYr9ZrvwibkO/Z2xqlJPFjtlRVkAi+0hXU8hP/IqZNMw9HLgIe1AYiUkT8A3b5q9W2IYU0Pw9F3wwr9M+1GvPycoTNxRy54uHiLTRYexLm3MoiiosG4I83lKDwStwXcH7cEPnAgXnvHAecN1YH1vgr/8wHkA3PC3T7C6J44wHQ3YO1BhLl+w3fFUjs0rOom5DhnPL4nAHhqeZHhq2kbNBD/vPGv9nNut5234iYw3096tO87gRLogYCuNrobN69h4mqjj1JSuIQAmEPlGyHo+X33iVfoSUfoTUTzfZ2Dcps2s7o7PGTWtV7R4VoH83jP52hx+4a2QtjJbhH80meX+j19Z9fYW2yJRqZHF9pCuq5AXmDxW9NyH5CDgWOu82bolFpNLwXP/CM/ebYsTAfo2w6Ufa+2OiW4EYt1WTEcTrTtPRWkSKqwbQHGHQ2MMWc8wmsoC8IG/fZKjY6kZ60Qc4Q3re1jdFWf34RE6oy6dcbdQ+Phrl5wSuv1KsKkl9nF1V4x41OV7t74VCO9emM76OEAi5pYUIc6X0vHhK7fyezuf5/BwshD97umI8AfvflNF8ywmzN7t+HiK8bTHwHiqqujqbOkBtfhr3/nYfnoTUdb3JQpjLx0bJ53z2RCM5SP2k2mP0WR21qjpbGL4+kMjPL5/qCqxXatAboVW5ZoXvUxZTA9pqK+Qnzw+ywt+aQfF8m6JYAsTf3Y/PPHXNhcbrBC/6EOtWZjoONbyL5qwhYeRJdrRUVHqhArrOuP5hitOX81XnzjA4ESaTM4vc+ywArsj6nDmxj52bLKtwd+4fro1eN4V5OhYkvUhriDvv+gk7njkJZJZr5DDLZSmfOS79glWMOZFk+tKiWAJEzVpzycRc0tEbaUpHQZAgo58Ep6GUglhYnh4KsvKrmjV4jEsPSAfqS8mTMyVR5T3HhsrCOg8Od+f0YFwVVeciJMtXMCEESaGBydS/PWjL7N5RaKqi4da87pboVW55kUvUxbDQ7qYegr5bAr79elBIWEu5GxX3C0R4NDTQWHiz+xzJwo7fgUu/BB09FY/j3qTLziMdoAbt23R1cFDUapC/2LqxD8/e4h/3nWI5w6OMJWZWQ3eFXM59+R+dmzqY8fmfk5f2z1ra/CLt66cs8jx4q0rufbYOv7p2UNMBYV3m1ckyPl+SeGgYJjI2K6OeZeOo6NpBsfTnPY/vkNXzOVtZ6zhcJnPdD7SXEwya99nrjSMOx/bT18iWiI8a00ruOqMtVx/aIQvf/+VQnFhPOKwqiteslzO89n12jBX3PbInNHd8vSAR/cMzBtdD4soT6Q9BifSJfnTEcfBN6Yk6tubiLBl1fw56eVieHQqi+ebqi8eao36LqRVeb3SWDQvepnSaA/pcuoh5HMZ2z0x1mnFtVsUvc2lgbK/m1zK+lIPvQI/LC9MvCYoTNy8kL1aOJraoSh1RYV1ndhzdIwfvnyi8HxtT5wdm/s4O4hIn7KysyKxMhfWxcPlmVeG+O6LA6wLmrUks17BPm593/TYoeEkXTFb2Jg10zGVnA+xiBVe9+0+ynt3rOfoWKYgaq47ZyM7dx0uEdv57Wd9M2sktZ5uGI/uGWDnrsOs6YkXigsPDSc5MZkupFqMp7IcHkkRqbHwbr7oelhEeWVXlKHJLF3x6c6I8ajDWDKHYfoCZmA8ww0Xze0AM9vdgo5IaYpPJcdwtqjvpVtXznkxVGur8noXPVaaF91sBxOlztTqIV3re9Uq5HMZSA5Pd08891fh6S+D54E4QfMWx4rTfLfEXMr+RBLwtfdNFyZuOAcu/wSsP7tRezo/0cS0p7SmdihKXWmosBaRrwDvAQaMMWcFYyuBrwNbgAPArxhjhsWqzjuAdwFTwG8YY3YF69wI/B/BZv/YGHNPMH4BcDeQAL4D3GKMMbO9RyP39a1nrGN4Ksv2dd2cvamPdb316SbVEXXpikXoiruF7oj3PP4qsbLW4QBRR0oasQyM2QhrmbEGBsjkTMGq7+E9x9n9mXeUvO+Ozf2hqRNzRVLrmSsbJmpXdEYZnMgwPJkl5/t4vs0bX9eTQESqKryrJLoedqGwqitO1jOs7ekoHJuoIySi2RmNcSrJSS8Xw7PdLZjvGIZFfS/dupKduw7PKX5rbVXejKLHVnAwUdqcaoW8l7OtxNPjpSb/F99kH5/7B8hMWZF67q/C2jNtTvXoEXtySg3Dq9+3y/ZthktvhtPeuvhRYXXvUJRFo9ER67uBvwK+WjT2KeBhY8znRORTwfNbgXcC24KfNwNfAt4ciOQ/BC7EasJnReS+QCh/CbgJeAIrrK8F7p/jPRrGpaet4sxNvQtuWe6I0BlzScRcOmORiluH510UHvjEtAPEG37/O3PmOBsDPjCWyoVGNYvFSliRY3kktZ65smH7GI845DyDGxVEBIOZsX+VRsgria7PdqGwbW1PidPGFbc9wurueEl6SCU56WFi+LpzNvLVJ17lpYHxEju/SgpAy//PbrjriXnFb63/Z83w6m4FBxNlmeD7NkKdGikV1MVcfNO0wM5jfCumn/gbGGtyYWK0Yzq9I5qYf3lFUepCQ4W1MeYxEdlSNnwdcFXw+z3Ao1jRex3wVWONip8QkX4R2RAs+5AxZghARB4CrhWRR4FeY8zjwfhXgV/ACuvZ3qMlcR0hEXPpDtIL5ksZmU3wdccjJQI5PV+fcyiEsedz2qgkGl3PXNlQi7yxNPGow7a1PcC0k8XgRJreQORVGiGvZH8qFZ0LidSH5X4Lr5bY+dUa26rE8aPW/7NmOHm0SuMdZYmTHLFR6gqaYpVw6Cn4wRfKChPfBxd+cPEKE6MdNiId69GiQ0VpEs34y1tnjHkdwBjzuojkv8E3AQeLljsUjM01fihkfK73KEFEbsJGvDn55AZZPM1C1HXoDKLSiVh1t+XCBF++U13G8wsCeS6KgzAC80YBKxWZ9fIQDn0/32dz/3TkZU1PnMPDSdI5H2NMVRHy2Rq9FEeGKxWdYXMdTWaJuc68RZXlhNn51RqVrbR7ZS3/Z81w8lBbvtagmefNhpKZhKkTNp+6GoZesXnbB743Pbbt7bYwsXfT7OvVg7yLR6xLUzwUpUVopUvasMCcqWG8YowxdwF3AVx44YW1OsNVhCNCRzSf4uESDfKlayFM8EUdIVvmJpEvVhTsP+V3NPNZJh2R0rmERQEX27lhrn3M09MRZXWPN69fNMwsert068oZjV7CPlCViM7yuXbFXITSi5xKc4HrGZWtZ/fKcprh5KG2fK3BYp43G44xkB6zUWovW926UyfgqTvhJ/9a2jHxigYXJopYF494t7YNV5QWpBnC+piIbAg85DO2AAAgAElEQVQiyRuAgWD8EHBS0XKbgSPB+FVl448G45tDlp/rPRYV17H5oN3xCB1RZ8GuIGHkv9UGJzOsLyuYXN0d5fiEjWQXX3L0JyJsXtFZcNro6ywVcrNFARe7o11YmkS5sIq6Ll98/4455/XongE+ufN5JtI5PN8wOJHmmVeHWN0dY9u6nsJyC8nXLZ7rDXc9MeMip9JtN7p7ZW/M5ZUTU1VH0sNoxudBbfmUitn7UOAA8qr1sC53AEmNWXHsz7RHnZNsEp7Pd0wMLnj7ToLLboatP98YoRuJT+dKRxK2aYuiKC1JM4T1fcCNwOeCx28VjX9URO7FFi+OBsL4QeBPRSTfMuvtwKeNMUMiMi4ilwBPAr8O/OU879FwIo61xOuKuzPypevZvrpcKOY8n6grBSs6gN5EjHjEZSyVK3hBv+2MNfNa67VqFLBWYfW5+19kZCpbaIJifMh6hqGJTMnxqle+7kKizvWMypY7fowlsxweSRJx2tdVQ9uVKxWx9yHrWe3EbLfF8WP2ObfDqVfA5GDgO10FxoeffccWJhZ3TLz4Q3BWnQsT3SjEe2x6hxvTqLSitBGNttv7GjbavFpEDmHdPT4HfENEPgi8BvxysPh3sFZ7+7B2e78JEAjoPwKeDpb7bL6QEfgdpu327g9+mOM9Gkp3LEJvR/jJtZ5WYZ+7/0WGJzP4JvCl9gwCHBtNMxw0GMnnDN9+/Tkzor53Pra/EMDesbl/hrVepekUlV4Y1NN7uBZh9cqJKRwBJ8h9EQHxmFHcWa983YUWM9YrKlsu0o8Feffr+zqqtidUlLbih3dYUZ3vshjrhLSBx/4CVp5a/fbCOiae835bmBjvmXvdSsk3aol1T7dFVxSl7Wi0K8gNs7z0tpBlDfCRWbbzFeArIePPAGeFjJ8Ie49G48zSSRFmtwq77YE9VYvOfccn8Uxps7xC/focOcOzivv3nlliHxdGrRcGreo97Ah4hoZE6hcada5XVLZcpBsDm/o76Cm6+FNXDWVJMvKqjVSDzaM2ni3sGz0493rlNLowMe8v3dGnlniKskRopeLFJU1YekDO8zlwYootqzqrEp1evoCvWDkHQ3PlDC/EB7jWdevtPfzF7+4taXP+oStO5eart8+5ztbVXbw0MIEY2xTHBC27N/fFSxq91Ctft5Vygctzv8vdYtRVQ1mS9J9i0z8icfBzgJluL14JUyfgyTvhp98MuioCG86Fyz9en8LESCwoQOxVWzxFWWLoX/QiMZsvcy2iM+IKWc9MW37MUpdfHo1cSO5vrevW0+Xii9/dyx2P7MMRiDhWFN7xyD6AOcX1rdeewe/tfJ7xVI6c5xNxHFZ0RvnjXzi7oa4mrdaiu5pIurYOV9oWY+DCD8G//w/wMtPtxf0snHfj3Os2sjDRcW1kOtatbcQVZQmjwnqRqMSXGSoTnaet7uJnxyZmuH1EywrFy6ORC8n9rXXderpcfPn7rwSi2u6oI5Dzfb78/VfmFNZXnbGWv7j+nBkRZKCkoc6lW1fy+P6hRROTi50mU2kkvVXTdxRlTnJp6/SRHoP1Z8GVt9r24mOv20j1eTfClsvD1/W96cLEycBEKt4HF/82nHX9wgoTox3Q0W/t8RRFWfKosF4kKvFlBis6je+z4zMPzpru8K6zN7B34KUZTV4SUXfOaORCcn9rXbeeLheTGY8yy20csePzMZt1X148vjI4wVMHhljbE2NVV3xRxOSdj+0nk/M4MZEr2OH1dERqTpOpJMpcSSRdW4crbUM2BZkJG10ub+yy5fLZhXQxB4OOiYN1LEws5E73ayGioiwzVFjXiVpETZgv88BYivH0tFAcS+X4/HdfAqbTHR7fP8S63jhjyWlB1puI4IpwfDxdIsiL328hub+1rlvPfOOumD1GxTWivrHj1VIuHsdTORyBsWSO1d0diyIm9x4bYyyVw8HaAOY8w4nJDDlvrOpt1TPKrK3DlZbnp/8f/PCLthixd+Pc0ejZGNpvBfWrP5ge2/aOoDBxY/VzEgm8pjutINcuiIqyLFFhXQcqFTVh4vv68zeVFONNpGdGXw3w+e++xDeePcRJKzp5aWCc9b0dJR7MY8kMh0aSbFnVxcmBSN+56zA7NvfPENeL3RCkXi4XH7riVO54ZB8538cRK6p9Y8er5eDwFK7A/uMTZDyfnGdwHdstMU+jxWQ2sPsrtgH0fUPGmyVpfg4qjTJXcgGorcOVlsQYSI9bUf3on9jIcrwPJk/AY7cBt1YmrmcrTLziE7BuhsnU/DguJPrtXLRxS3XM18RHUdoQFdZ1oBJREya+P7nzeQRY0xMviOGxVC70PQwU1htP5Yi66RJhfWw8TdRxlvTt+3zEvlpXkDC6Yy77jk8WmsbkMOR8iBcFmRotJmMRh2TGwy9yK8HY8WqpJMpc6QWgtg5XWgbfs6kemUlbWGgMPPt3VlTnUyyiHZDF5lPPJayzSXjuH2DXPUWFiSfDZR+rrTAxmgiKEbum11WhWDlzNfHRY6a0MSqs60AloiZMfB8eSZL1fE4EzV7msMEGKDT1WNEZZWgyS2csUiJ8NveX5vIloi4/OTI6Z752u3Hz1dvrMv9CR8zADNx1hJxvMFgf8MUQk9vW9nDgxERpSk9XlC2rqi9yqiTKXGlUu5XsAlsRdUxZBLwsJIdthNqU3cEZO2Kjw8VEOmyRYhhhhYkdfXDRTXDWL1VfmBjrhMTKmbnTKhSrI6yJTyYY1+OltDEqrOtAJaKmPPUg5jqks37BMU+Y+f0xG6u74+Q8v8SDOeY6JWkMAEdGkoylckRdqcqebjkwns6xqb+DwYkMGc8nHnFYGXMZTeUYTWYb0oGynHxkeH1fZMGR4UqizNXkTi926/B2EavqmNJgculAUE/MvkzvRpv+USxsZ/OoDitMPPcDcMFvVl+YGIlB5+ppIViOCsXqKG7ikyeagJHXmjMfRakTKqzrwIev3Mondz7P4ZFkSTvxP3j3mwrL9MQj7D02XtSG3Jt2ygtp9FJOX0epaF/dHS9Z/J1nrWfnrsMlwmp4KluTPd1yIH8xtHXNdHR4KpPjtLU9c3ahrKewWkhkOEyIfva9Z865rZNWdPLK4ATjqVIXklNX12YDVi8x3E5iVR1TGoAxNt0jNWbTNebjvBttTnWW2T2qT7xsBW09ChPdCCRW2Cj3XKhQrI58E5/iC5VsEvpPbt6cFKUOqLCuE1nPL0Sgc54hHimNHo+nshTXpBXr57BItesInm9wBDoiDqt74oUUhdFkFgGyvikIkZ27DnP9+Zt4fP9QQVjtPz5J1C3NL6nUnq5dIoi1Umsecb2FVS2R4Vpb01+6dSVPHRjCEfs5yHg+xycyfODilVXPu55iuJ3EqjqmNIDkMEwNVb78lsuBWTyqJwfhqTvhp/86XZi48Ty4/BOw7szq5uW40LnSdkesJP9ahWJ1XHaLTZXJYC9AsknwM3ZcUdoYFdZ14LYH9jCZ9ohFnEIR2mTa47YH9hSEwbGx9KzrO4U22/Z5dzzC7s+8o/B6XuSWp32UC5HH9w+VCKsdn3mwJnu6doog1kqt0eJWEFbVCNHiC6SxZJa+jgjpnF9i0/j4/iFubuAc5qMVjmmlqGNKi1DuUZ1NwtNfnlmYePnNcOpV1RUmOk4Qoe6vbj0VitWx/Rrg9qDY8zV7AaLFnsoSQIV1Hdg/OBlEAadt04wY9g9OFpbJBWHp4vN0PlLtOlKRfVw+sD0wnmJD3/wdG2u1p2unCOJCqCVa3ArCqlIhWn6BdHQ0hQCbViTo6bDrG2NqErD1FMOtcEwrRR1TWgzfg5/9W1CYeNyO1VqYKGLFdGJFbbZ5KhSrZ/s1enyUJYcK6wbhG4PnG6647RFOWtGJBLnVYWkfiahb4tqxY3N/odV2d8zlxGSG3kS0ED2eSHsMTqRZ0zNdvBMmRGq1p2vlCGKzU1RaQVhVKkTLL5DiEXun4/h4uiCsaxWw9RTDrXBMK0UdU1qIg08GhYl77XM3BufcUFthYqwLulYvrHU5qFBUFEWFdT04dVUn+45PIr71I8751hM56kx7T7uuYDwDRWkfYuAN63u4/+NXFrZVHmXcd3yCnGfoikcKdnsru6zdXld8fjeJWuzpWjWC2AopKq0grCoVouUXSKu74xwZTZLKeQu2FKynGG6FY1oNi+2YopQRVpi4/Vq45KPhziBz4bjQtQbitRXwKoqilKPCug586p1v5GNf28VkxsMvikhv7O8siOFVXTFOTGZsMxLfJ+JYR4Zbrz2jZFvlUcZ8AWNxlHFVV5ysZ0rs9uopRFo1gtgqKSrNFlaVCtHyC6TeRJR0zmMq481rKVivOVSzPRWrypxMHrcdE1/81sILE0VsykhipXZLVBSlrqiwrhMdUZesZ8j5Pjkf3LJz9eruOJPpLCIO2YwhFnH4tUtOASikfZy0opO9x8bojkcKftd5YV3sUZ3MemybxxZuIbRqBLHeKSrNTitZCJUI0bALpFjE5XP/dUdd9lPFsLIoZJPwo/8HfvTVaTu+/lNsx8RqCxPBpol0rlx42oeiKEoIKqzrwJ2P7SfiirXIM4IjBt8PmsKMCjHXIeoKGQ82r5huX/7VJ15FeLUkf3o0mWVkKkvEcXBFMEGrbTC8+PpoIdJd7JG9UGYTmK0mmuqZotIKaSWNplUvkBSlIkILE/vh4g/Dmb9YvTB2XOheN3uDF0VRlDqgwroOvDQwzuhUFseRgv90vlAxGkSbJzOGFZ2RGS3NMbA+cPjojEVwRMj4hki+HWPg32d/FZujXcXcykXzpVtX8vj+oZLnO3cdbguBWc8UlVZJK2k0rXiBpCjz8toTtjDxxEv2+UIKE8Gu07XaimtFUZQGosK6DmRyPhTZ7RXjG4i5Dr7vkcmVSmLPN/i+KWlz7hlwBSKOkPF8fGOIOFZUn7G+F6BiAfjongF+b+fzjKdy5HyfgbEUT75ygrU9cVZ3xxkYT/HXj77Mis4ofQnrMNLKArOeEdhWdj5RlGXLiZetoH7th9Nj298Jl3yk+sJEsPnTXWu1OFFRlEVDhXUdiLpCMgt+4AqSL2CMONNi+OWBcdK50m6MAnjGuoi4jpALhHbUlUKr7T1HxxAgWpS0XakAvO2BPQxNZgpt1PP/jkxlWdPTQWcsQs73GU/lWFMUBGq0wAxLPQEqyneuVwS2VZ1PlMbQzvn0y4LQwsQL4PKPw7oa096iHdC93rYkVxRFWST0jFMHtq/r5ZXBCcZTOTKebcYiWN/gPH2d1iKvOI3BNwZXmM7tsG585HzDSwPjeL71wsbAhr54YVuVCsB9AxMlbdTzpIoEftx1SGa8kqh5T0eEU1c3JsITltv8yZ3Pk8l6ZIL9HZxI88mdz3P79ec0TPy0qvOJUn+WQz5925KZhB98EZ76v8sKE2+GU3+u+sJEsOskVtgCRUVRlEVGfYbqwIev3Eos4rK+r4M3rOthbU8cROhNRDDGMJXJEXVdPnLVaazt6WA0mWVtTwd9iSibVySIuIJnDBFXWNUdpCcY2xUvEqj0dOA9PJXJVSwAc/782djxqIMPhQuCjOdzfCLDpVsb86VUnNuctyIcncowlvYwPrZg07dR9c/d/2JD5gBBWsl7zyz5//jse89UobUECfvMRV3hzsf2N3tqyxtj4O/fBT/4vBXVHf1w5a1ww9dh61W1iepIDPo2q6hWFKVpaMS6DpTn/p66upsPXGyLBItzgb/13CGeOjCE5xuOjKbo74jMSA8ZTeaIuQ7b1k3nZgxOpJhMV+89PJeszjcImcr4rOyMks75hYh1byLC4/uHuLnG4zEXYbnN+UPgOEUt4X3DKycam++shX3LA82nb1FE4MLfgu98Es75AFzwG+GFiQd+AD+6B8aOQO9GOO9G2HL5zOXyUepaBLmiKEqdUGFdJ8JEWrEw/cS9u/jmc68Xnnu+4cRUtmT5rOcBsLa7VASs6ooTcbJ879a3VjWnqCNkQ6LWAgWRPprMsr63wzqOBBhjGiY6wnKbq3E5UZRq0Xz6Fua8/w02XQCRjvDXD/wAHrsNnCjE+2DyhH3OrdPiOhKzBYrRWbahKIqyiGgqyCJx3+6jQNDKXEqDKoGLXmHsxFSG/ccn2HN0jP3HJzgxma5JBJy+thtXSrfvCpyxvofv3fpWvnbTJWxb20My65Ws10jR8eErt5L1bErLdJqM4Ar4xmAw+MbgG9i6uqshc1CWF2GfOc2nbxEc10ahZ+NH91hRHe2wJ7Foh33+o3vs6x190HeSimpFUVoGFdZ14tE9A9xw1xNccdsj3HDXEzy6Z6DkdW+OfOeOiEtH1KUj4lqnEL8053lgvLac51uvPYOumN2mwX4vdcXckjbqiy06wnKbP/bzp7OyK2YLNz0fAVZ0Rme0e1eUWrjqjLVcf/4mjo+nefHoOMfH01x//iZNA2oHxo7MjGZHOuDEfrjvo/Dlt8I9/wX2PtSc+SmKopShqSB1IMx14Pd2Ps+qrhgTGY+TVnTiFNnwVULMdUpcOmrNeY5HXTJBq/WI4xCPljZIaEZ3vrC0mR2b+7VDoNIQHt0zwM5dh1nTM931dOeuw+zY3K+fsVandyMMH4TsBHhZ221RouClbFpIxwoYPwb3fxK4HbZfs/D33PsQ/PAOGHk1cCi5pT7bVRRlWaDCug7c+dh+MjmPExPWbs8VIZPzGU/nOH1NNwPjKeKukMwZTJj9XdYrRJQNEC/ysYbac57vfGw/vYloobMjhDeXaYUivlaYg1Id7eIN3cpdNtvlGDaMvQ/B9263IjasMHHThXDkOUBAHMhlwExBYtV0a/JYJ2SwYnihAnjvQ1akO7HGiHZFUZY8mgpSB/YeG+PEZIacZ3BFSOd8a2GX8wv2XhtXdLKqM4obOF+4jnDGui4cKbGxBqAzXhpVrjXn+eDwFImyCLW6ISj1IH+XZmA8VeINXZ4C1Qq06t9BOx3DhpAXsRPHSwsTD/xgepnDz0DnKlugiAlyrV3IpUq3FU3AyGsLn9MP77CiOtZpi1Jinfb5D+9Y+LYVRVkWqLCuA9mgC4vjSIm7RjGJqEtnPMLLf/ouDnzu3bz8p+9iRVcHfYkIgdbGEeiOOUxl/LrkPJ+0onNRCxOV5UM7eUO36t9BOx3DhlAQsYnwwkSwOdaJVbDqdFh3pn2MJsBLl24rm4T+kxc+p5FX7faLqZdoVxRlWbDowlpE3iAizxX9jInIx0XkMyJyuGj8XUXrfFpE9onIz0TkHUXj1wZj+0TkU0Xjp4rIkyLykoh8XURijdynWMQBM+1qkcc3FJw9BifSdMXckgLHFw6PMJbKFdJDjIFkzifmSl0al6gbgtIoWjUKHEar/h200zFsCGEiNtIBY9O2pPSfDH7OpoHkifWCE4HMlD1pZqbAz9hc6IXSfwpMDcKJfTDwU/s4NVgf0a4oyrJg0YW1MeZnxphzjTHnAhcAU8A3g5c/n3/NGPMdABF5E/B+4EzgWuBvRMQVERf4a+CdwJuAG4JlAW4LtrUNGAY+2Mh92ra2h9U9MSKO4PmGok7mRc4eaY6MJEtu+06kPbygOUo+0G0dQazSXqi/s3YXVBpFq0aBw2jVv4N2OoYNof+U6TbmeXIp6N1gT4g96+EtvwcmWyqiozF443UweQyOvWAfz/lAfXKgt7wFJo5BLg049nHimB1XFEWpgGYXL74NeNkY8+psKRTAdcC9xpg08IqI7AMuDl7bZ4zZDyAi9wLXiciLwFuBDwTL3AN8BvhSY3bBRsQ+ufN5vCD07Bl7ZzMecfCMIeY6ZPHJ+KakgKokt7pIRadzPj96bZic7zM4nuaWr/+IDb0dBYeR2QqcZiuEaraAaFWWfeHYAvjwlVv5n/f9hKlMjkTgtNEKUeDZaMW/g3Y7hnXnsltsjnXGs24fuRT4WbjwQzZC7EYDsXx74NLxmh3f8hZ4/h+hax30b7Hi/Pl/hI3nL1xcH/gedK6FzBh4GYjEbYT8wPeAW+uw04qiLHWaLazfD3yt6PlHReTXgWeA/2aMGQY2AU8ULXMoGAM4WDb+ZmAVMGKMyYUsX4KI3ATcBHDyyQu71ScAxjp4+GbmrYCcbxAD+49PFGz05sIAEdch5xlSyRzJzCTb1/UUCpw+CyVCIczyL2w5xaLHa2E0w6ZxqdGux7Bu5828aP7e7VY0926AN//vcPYvlXbQ2n5NqWC++z2QzUBm0IpfN2bFbz1cQUZehe41IEX/B8ZojvVcqD2hopTQNGEd5D2/F/h0MPQl4I+wmvKPgP8T+C0CzVqGITyNJe9aFzY+c9CYu4C7AC688MKaMy/Kbe1eOjZOKueTytk8j3yrcowpOIfkvLnfzgm+WHyT34YpFDiFWYW1sqVYK6LHa+G0YhS43WjHY1iv82bZVsGNw9DLtuHLXCJt4EVIj1Gw4POykByEgezCp9F/irXYixWl49SrMHIpovaEijKDZrqCvBPYZYw5BmCMOWaM8YwxPvC3TKd7HAJOKlpvM3BkjvFBoF9EImXjDaO8CCmTT5wOQ4p+KiDM9zqswGnZF0JViR6v5jJfp1JlGZAXZZOD0LkGhg7AY38OQ/tLRVp5V0U/a0+MjmMj245jn/uZhc/pslvsdhpRGLkUUXtCRZlBM4X1DRSlgYjIhqLXfhF4Ifj9PuD9IhIXkVOBbcBTwNPAtsABJIZNK7nPGGOA/wCuD9a/EfhWI3ekvAhprg6L0wWO08raEauzi4bwfYMpUtUxd/rFsAKnZV8IVSV6vJrHsvdvVix5URbvtuI4E0ShU6NzizQ3bh99396L9P3S8YWw/Rp45+3Qsw5SI/bxnbfb1+5+D3zhbPuoLdQtak+oKDNoirAWkU7gGuBfiob/XER+LCK7gZ8HPgFgjPkJ8A3gp8ADwEeCyHYO+CjwIPAi8I1gWbBVJr8bFDquAv6ukftTbuc1F1vXdHPG+l62rukmGhz9qOMQjzhEHQeHQGg74BlD1BUEWNkdm9MqrFUtxVoVPV7VU68o87L3b1Ys5aLMy9jmL15R5DlMpK15A3SvtcWNJih87F5rx+vB9mvgN74NH99tH8FGzsePzR1JX46EObto6oyyzGmKsDbGTBljVhljRovGfs0Yc7YxZocx5r3GmNeLXvsTY8xpxpg3GGPuLxr/jjFme/DanxSN7zfGXGyMOd0Y88uBo0jDKLfzmivLo1jI9XfG6Im7BREtjhXQH3/bNs47aQXrezu44JSVfOLqbWxZ1T2nVdhVZ6zl+vM3cXw8zYtHxzk+nub68ze1Xf7mYtGqFmytSj2jzJqGowAzRZkbC4RyUduBMJF22S1WTPdshDVvtI9utHHpGpruMDuaOqMoM2i2K8iSobgI6Yo/+y6HRmdq+VWdEdb2dBQcAP7g3W/iW88d4r7dR/F86ybyltNXcfPV27m5bN3y5+U8umeAnbsOs6YnzsmBddfOXYfZsblfxeIstGPhWLOoZ7HnSSs6GRhPFbYFmoazLCnY7WEj07FeyA1AR58VadlkuEgLs+BrpBPFyKs2Ul2MpjtYFvv/QlHaABXWjcBxWNMd5cRk1lrvCazqitIRjfC1my4pLPbF7+7lvt1HcQQiEcE3cN/uo5y6ei83X729qrdUlwulkRwcnqI/ES0ZqzXKvOz9mxVLuShbfRps+Q3rGT2fSCu34Gsk6hQyN4v5f6EobYAK6waQj8it75s+EU9lcqzt6ShZ7svffwUweD7kjL3LKGLHqxXW9RQ+ilJOPaPM7erfrDSAUFHWYo1YyiPrs0XSFUVRUGHdECqNyE2kc/hBl0YkcIwydrxa9Pa60kjqHWWuJA1HO2MqLYGmOyiKUgUqrBtApRE5kUBN56sdBTDBeJXo7XWlkSx2lFk7YyothaY7KIpSISqsG0QlEblEVJhImxlNYDqj1Qtrvb2uNJrFLPbUmgFFURSlHVFh3UTO3rSCF18fZSyVKxQ59nZEeOOGvpq2py4XylJBawYURVGUdqSZnReXPR++ciu9iRinru7irI29nLq6i95ETNM3lGWPdsZUFEVR2hEV1k1Em5QoSjjaGVNRFEVpRzQVpEFU6mig6RuKMhOtGVAURVHaERXWDUAdDRRl4ehFp1J39j4U2Oa9ahu/qG2eoih1RlNBGkCxo4GIfYy6wp2P7W/21BRFUZYnex+yjV7Gj9kW5ePH7PO9DzV7Zq3L3ofg7vfAF862j3qsFGVeVFg3gIPDUySibsmYOhooiqI0kR/eAU7MtiYXsY9OzI4rM9ELEUWpCRXWDUAdDRRFUVqMkVdtS/JiognbTVGZiV6IKEpNqLBuAOpooCiK0mL0nwLZZOlYNmlblCsz0QsRRakJFdYNQG30FEVRWozLbgE/A5kpMMY++hk7rsxEL0QUpSbUFaRBqKOBoihKC7H9GuD2wBXkNSsQ1RVkdi67xeZUZ7CR6mxSL0QUpQJUWCuKoijLg+3XqJCuFL0QUZSaUGGtKIqiKMpM9EJEUapGhbWiKAqVd0tVFEVRlNnQ4kVFUZY9+W6pA+Opkm6pj+4ZaPbUFEVRlDZChbWiKMse7ZaqKIqi1AMV1oqiLHu0W6qiKIpSD1RYK4qy7NFuqYqiKEo9UGGtKMqyR7ulKoqiKPVAhbWiKMse7ZaqKIqi1AO121MURUG7pSqKoigLRyPWiqIoiqIoilIHVFgriqIoiqIoSh1QYa0oiqIoiqIodUCFtaIoiqIoiqLUgaYJaxE5ICI/FpHnROSZYGyliDwkIi8FjyuCcRGRL4rIPhHZLSLnF23nxmD5l0TkxqLxC4Lt7wvWlcXfS0VRFEVRFGW50OyI9c8bY841xlwYPP8U8LAxZhvwcPAc4J3AtuDnJuBLYIU48IfAm4GLgT/Mi/FgmZuK1ru28bujKIqiKIqiLFeaLazLuQ64J/j9HuAXisa/aixPAP0isgF4B/CQMWbIGDMMPARcG7zWa4x53BhjgK8WbWAKvaUAAAjTSURBVEtRFEVRFEVR6k4zhbUB/l1EnhWRm4KxdcaY1wGCx7yp7CbgYNG6h4KxucYPhYyXICI3icgzIvLM8ePH67BLiqIoSxs9byqKosxOM4X15caY87FpHh8RkSvnWDYsP9rUMF46YMxdxpgLjTEXrlmzppI5K4qiLGv0vKkoijI7Teu8aIw5EjwOiMg3sTnSx0RkgzHm9SCdYyBY/BBwUtHqm4EjwfhVZeOPBuObQ5aflWeffXZQRF6teYemWQ0M1mE7zUDn3jzaef7tPHdo7/nXa+4PGGOqrkPR8yagc28m7Tz/dp47tPf8G3rebIqwFpEuwDHGjAe/vx34LHAfcCPwueDxW8Eq9wEfFZF7sYWKo4H4fhD406KCxbcDnzbGDInIuIhcAjwJ/Drwl3PNyRhTl9CLiDxTVIzZVujcm0c7z7+d5w7tPf9mz13Pmzr3ZtLO82/nuUN7z7/Rc29WxHod8M3AAS8C/KMx5gEReRr4hoh8EHgN+OVg+e8A7wL2AVPAbwIEAvqPgKeD5T5rjBkKfv8d4G4gAdwf/CiKoiiKoihKQ2iKsDbG7AfOCRk/AbwtZNwAH5llW18BvhIy/gxw1oInqyiKoiiKoigV0Gp2e0uBu5o9gQWgc28e7Tz/dp47tPf823nuxbTzfujcm0c7z7+d5w7tPf+Gzl1sMFhRFEVRFEVRlIWgEWtFURRFURRFqQMqrBVFURRFURSlDqiwrhMicq2I/ExE9onIp5o9n/kQka+IyICIvFA0tlJEHhKRl4LHFXNto1mIyEki8h8i8qKI/EREbgnGW37+ItIhIk+JyPPB3P9XMH6qiDwZzP3rIhJr9lxnQ0RcEfmRiHw7eN5Ocz8gIj8WkedE5JlgrOU/N3lEpF9EdorInuDzf2k7zb8cPW8uHnrebC563mwei33eVGFdB0TEBf4a20XyTcANIvKm5s5qXu4Gyo3NPwU8bIzZBjwcPG9FcsB/M8a8EbgE27nzTbTH/NPAW40x5wDnAteK9Vu/Dfh8MPdh4INNnON83AK8WPS8neYO8PPGmHOLfEzb4XOT5w5sU4IzsM5KL9Je8y+g581FR8+bzUXPm81jcc+bxhj9WeAPcCnwYNHzT2Mb1TR9bvPMewvwQtHznwEbgt83AD9r9hwr3I9vAde02/yBTmAXtunRIBAJ+zy10g+2i+nDwFuBbwPSLnMP5ncAWF021hafG6AXeIWg6Lzd5h+yP3rebO5+6Hlz8eas583mzX3Rz5sasa4Pm4CDRc8PBWPtxjpjzOsAwePaJs9nXkRkC3AetsNmW8w/uCX4HDAAPAS8DIwYY3LBIq38+fkC8N8BP3i+ivaZO4AB/l1EnhWRm4KxtvjcAFuB48DfB7eUvyy2c227zL8cPW82CT1vLjp63mwei37eVGFdHyRkTH0MG4yIdAP/DHzcGDPW7PlUijHGM8aci41iXAy8MWyxxZ3V/IjIe4ABY8yzxcMhi7bc3Iu43BhzPjb94CMicmWzJ1QFEeB84EvGmPOASVr79ut8tNtnZ0mg583FRc+bTWfRz5sqrOvDIeCkouebgSNNmstCOCYiGwCCx4Emz2dWRCSK/XL4B2PMvwTDbTN/AGPMCPAoNt+xX0TynVBb9fNzOfBeETkA3Iu9rfkF2mPuABhjjgSPA8A3sV/Q7fK5OQQcMsY8GTzfif3CaJf5l6PnzUVGz5tNQc+bzWXRz5sqrOvD08C2oMo3BrwfuK/Jc6qF+4Abg99vxObgtRwiIsDfAS8aY/6vopdafv4iskZE+oPfE8DV2EKK/wCuDxZrybkbYz5tjNlsjNmC/Yw/Yoz5Vdpg7gAi0iUiPfnfgbcDL9AGnxsAY8xR4KCIvCEYehvwU9pk/iHoeXMR0fNmc9DzZnNpynmz2YnlS+UHeBewF5v39fvNnk8F8/0a8DqQxV7RfRCb9/Uw8FLwuLLZ85xl7ldgb5vtBp4Lft7VDvMHdgA/Cub+AvA/g/GtwFPAPuCfgHiz5zrPflwFfLud5h7M8/ng5yf5v9N2+NwU7cO5wDPB5+dfgRXtNP+Q/dHz5uLNXc+bzd8PPW82Zx8W9bypLc0VRVEURVEUpQ5oKoiiKIqiKIqi1AEV1oqiKIqiKIpSB1RYK4qiKIqiKEodUGGtKIqiKIqiKHVAhbWiKIqiKIqi1AEV1orSgojIZ0Xk6mbPQ1EUpR3Qc6bSKqjdnqI0CRGJGGNyzZ6HoihKO6DnTKUd0Ii1oiyQoDPVv4nI8yLygoi8T0QuEJH/FJFnReTBotapj4rIn4rIfwK/LyIHRMQJXusUkYMiEhWRu0Xk+mD8IhH5YbD9p0SkR0RcEfkLEXlaRHaLyIebeAgURVEqRs+ZylImMv8iiqLMw7XAEWPMuwFEpA+4H7jOGHNcRN4H/AnwW8Hy/caYnwuWPR/4OWx72/8CPGiMydruwxC0ev468D5jzNMi0gsksR3fRo0xF4lIHPiBiPy7MeaVRdpnRVGUWtFzprJkUWGtKAvnx8DtInIb8G1gGDgLeCg42bvYNsh5vl72+/uwXxLvB/6mbNtvAF43xjwNYIwZAxCRtwM78hEaoA/YBuiXhKIorY6eM5UliwprRVkgxpi9InIB8C7gz4CHgJ8YYy6dZZXJot/vA/5MRFYCFwCPlC0rQFghhAAfM8Y8uKDJK4qiLDJ6zlSWMppjrSgLREQ2AlPGmP8XuB14M7BGRC4NXo+KyJlh6xpjJoCngDuAbxtjvLJF9gAbReSiYFs9IhIBHgR+R0Siwfh2EelqwO4piqLUFT1nKksZjVgrysI5G/gLEfGBLPA7QA74YpA7GAG+APxklvW/DvwTcFX5C8aYTJBv+JciksDmCl4NfBnYAuwSe+/0OPALddwnRVGURqHnTGXJonZ7iqIoiqIoilIHNBVEURRFURRFUeqACmtFURRFURRFqQMqrBVFURRFURSlDqiwVhRFURRFUZQ6oMJaURRFURRFUeqACmtFURRFURRFqQMqrBVFURRFURSlDvz/8uTZkWnAwBwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(data = df, x = \"service\", y = \"salary\", hue = \"sex\", col = \"sex\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Линейная модель с эффектом взаимодействия"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь давайте учтем эту особенность в регрессионной модели. Добавим в модель выше эффект взаимодействия числа лет опыта работы и пола, который будет отражать то, что эффект опыта на заработную плату неодинаков у мужчин и женщин. В формуле в `statsmodels` эффект взаимодействия (*interaction term*) добавляется через `:` или через `*`. Эти операторы используются немного по-разному, пока посмотрим на первый вариант:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.127\n",
      "Model:                            OLS   Adj. R-squared:                  0.120\n",
      "Method:                 Least Squares   F-statistic:                     18.98\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           1.62e-11\n",
      "Time:                        19:30:25   Log-Likelihood:                -4632.4\n",
      "No. Observations:                 397   AIC:                             9273.\n",
      "Df Residuals:                     393   BIC:                             9289.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=======================================================================================\n",
      "                          coef    std err          t      P>|t|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------\n",
      "Intercept            8.207e+04   7568.722     10.843      0.000    6.72e+04    9.69e+04\n",
      "sex[T.Male]          2.013e+04   7991.138      2.519      0.012    4417.900    3.58e+04\n",
      "service              1637.2997    523.026      3.130      0.002     609.020    2665.579\n",
      "service:sex[T.Male]  -931.7363    535.243     -1.741      0.083   -1984.035     120.562\n",
      "==============================================================================\n",
      "Omnibus:                       24.451   Durbin-Watson:                   1.862\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.606\n",
      "Skew:                           0.586   Prob(JB):                     1.01e-06\n",
      "Kurtosis:                       3.545   Cond. No.                         232.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model2 = ols(\"salary ~ service + sex + service:sex\", df).fit()\n",
    "print(model2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Правда ли, что эффект опыта работы на заработную плату значимо отличается у мужчин и женщин? Да, если мы примем уровень значимости равным 10%, и нет, если мы примем уровень значимости равным 5%, p-value при эффекте взаимодействия равно 0.08, что больше 0.05 и меньше 0.1. В данном случае предлагаю согласиться с уровнем значимости 10%, все-таки вполне логично предположить, что сотрудников разного пола некоторые фактору по-разному сказываются на заработной плате, плюс, на графиках отличия в наклоне регрессионных прямых были довольно заметны.\n",
    "\n",
    "\n",
    "Итак, теперь уравнение модели выглядит следующим образом:\n",
    "\n",
    "$$\n",
    "\\widehat{salary}_i =  82070 +  1637 \\times service_i + 20130 \\times Male_i - 931 \\times service_i \\times Male_i.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Интерпретировать коэффициенты множественной регрессии мы уже умеем, поэтому остановимся только на эффекте взаимодействия. Чтобы корректным и понятным образом объяснить коэффициент ($-931$), нам потребуется вычислить предельные эффекты пола на заработную плату и опыта работа на заработную плату. Специальных функций для вычисления предельных эффектов в случае линейных моделей не предусмотрено, поэтому определим их самостоятельно на основе уравнения выше.\n",
    "\n",
    "Предельный эффект опыта работы на заработную плату (находим слагаемые с `service` и относимся к `Male` как к какому-то фиксированному числу, а не переменной, более формально – находим частную производную по переменной `service`):\n",
    "\n",
    "$$\n",
    "\\text{marginal effect of service} = 1637 - 931 \\times Male.\n",
    "$$\n",
    "\n",
    "Подставим в это выражение `Male = 0` и `Male = 1` и вычислим предельный эффект опыта на зарплату для женщин и мужчин. Получим значение 1637 для женщин и 706 для мужчин. Проинтерпретируем полученный результат:\n",
    "\n",
    "* при прочих равных условиях, если мы будем рассматривать только сотрудников женского пола, каждый дополнительный год опыта работы будет сопровождаться увеличением годовой заработной платы, в среднем, на 1637 долларов;\n",
    "\n",
    "* при прочих равных условиях, если мы будем рассматривать только сотрудников мужского пола, каждый дополнительный год опыта работы будет сопровождаться увеличением годовой заработной платы, в среднем, на 706 долларов.\n",
    "\n",
    "Теперь вычислим предельный эффект пола на заработную плату (находим слагаемые с `Male` и относимся к `service` как к какому-то фиксированному числу, а не переменной, более формально – находим частную производную по переменной `Male`):\n",
    "\n",
    "$$\n",
    "\\text{marginal effect of Male} = 20130 - 931 \\times service.\n",
    "$$\n",
    "\n",
    "Так как опыт работы – количественный показатель, подставить каких-то два значения и получить исчерпывающую интерпретацию эффекта мы не сможем. Можем только сказать, что у людей с большим опытом работы эффект пола на заработную плату меньше (коэффициент при `service` отрицательный), то есть у более старших сотрудников (рост стажа неизбежно сопровождается увеличением возраста) разница в заработной плате мужчин и женщин уже не такая сильная. \n",
    "\n",
    "Чтобы как-то описать эффект пола в общем виде, давайте вычислим его для среднестатистического сотрудника – со средним значением опыта работы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.614609571788414"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"service\"].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Тогда:\n",
    "\n",
    "$$\n",
    "\\text{marginal effect of Male} = 20130 - 931 \\times 17.61 = 3735.09.\n",
    "$$\n",
    "\n",
    "Итого, при прочих равных условиях, если мы будем рассматривать сотрудников с одинаковым числом лет опыта работы, равным среднему по выборке (примерно 18 лет), у сотрудников мужского пола заработная плата, в среднем, будет на 3735.09 выше, чем у сотрудников женского пола. При желании можно оценить такой эффект для человека с минимальным/максимальным числом лет опыта работы (да и вообще любым оптытом, который нам интересен с содержательной точки зрения)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Точно такую же модель можно было построить, используя другой оператор, оператор `*`. Этот оператор позволяет записывать модель в более коротком виде, запись `a * b` заменяет запись `a + b + a:b`. Для нашей модели короткая запись выглядит следующим образом:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.127\n",
      "Model:                            OLS   Adj. R-squared:                  0.120\n",
      "Method:                 Least Squares   F-statistic:                     18.98\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           1.62e-11\n",
      "Time:                        19:30:25   Log-Likelihood:                -4632.4\n",
      "No. Observations:                 397   AIC:                             9273.\n",
      "Df Residuals:                     393   BIC:                             9289.\n",
      "Df Model:                           3                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "=======================================================================================\n",
      "                          coef    std err          t      P>|t|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------------\n",
      "Intercept            8.207e+04   7568.722     10.843      0.000    6.72e+04    9.69e+04\n",
      "sex[T.Male]          2.013e+04   7991.138      2.519      0.012    4417.900    3.58e+04\n",
      "service              1637.2997    523.026      3.130      0.002     609.020    2665.579\n",
      "sex[T.Male]:service  -931.7363    535.243     -1.741      0.083   -1984.035     120.562\n",
      "==============================================================================\n",
      "Omnibus:                       24.451   Durbin-Watson:                   1.862\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               27.606\n",
      "Skew:                           0.586   Prob(JB):                     1.01e-06\n",
      "Kurtosis:                       3.545   Cond. No.                         232.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model3 = ols(\"salary ~ sex * service\", df).fit()\n",
    "print(model3.summary())  # то же самое"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Важно:** вне зависимости от того, какой из операторов мы используем, главное понимать, что если мы включаем эффект взаимодействия в модель, переменные, которые входят в этот эффект, обязательно должны быть включены в модель по отдельности, иначе смысл взаимодействия и возможность оценки предельных эффектов терятся. С содержательной точки зрения это тоже объяснимо: если мы говорим, что опыт по-разному сказывается на заработной плате в зависимости от пола, будет странным считать, что сам пол и опыт на заработную плату никак не влияет.\n",
    "\n",
    "В завершение разговора об эффектах взаимодействия давайте посмотрим на пример того, как, используя эффекты взаимодействия учесть в линейной модели нелинейный характер взаимосвязи между независимой и зависимой переменной. Посмотрим на диаграмму рассеивания для опыта работы и заработной платы:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a228d6850>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.scatterplot(data = df, x = \"service\", y = \"salary\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Невооруженным глазом видно, что связь между переменными больше похожа на квадратичную, нежели на линейную: при опыте работы до 25 лет увеличение опыта работы сопровождается увеличением заработной платы, а при опыте работы более 25 лет увеличение опыта работы в большинстве случаев сопровождается снижением заработной платы. Такая взаимосвязь неслучайна. Опыт работы тесно связан с возрастом человека, а возраст человека, действительно, нелинейно связан с заработной платой.\n",
    "\n",
    "Если бы у нас была обычная парная регрессия, где кроме опыта и заработной платы ничего не учитывается, мы могли бы выбрать другой тип модели, квадратичную. Оценивать такую модель мы сейчас не будем, просто построим соответствующий график с помощью функции `regplot()` из библиотеки `seaborn`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a228cf850>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.regplot(data = df, x = \"service\", y = \"salary\", order = 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Функция `regplot()` умеет строить парные регрессии разного вида, необязательно линейные. В данном случае мы добавили аргумент `order`, отвечающий за степень многочлена, который мы хотим использовать для описания взаимосвязи. Раз зависимость квадратичная, то `order = 2`, парабола описывается уравнением $y = ax^2 + bx + c$. Эта функция довольно полезная, встретим ее позже при знакомстве с логистической регрессией.\n",
    "\n",
    "Учтем эту «квадратичность» в модели, просто добавив опыт работы, возведенный в квадрат (обратите внимание, сама модель линейная, оценивается медом наименьших квадратов, OLS):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.116\n",
      "Model:                            OLS   Adj. R-squared:                  0.112\n",
      "Method:                 Least Squares   F-statistic:                     25.95\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           2.59e-11\n",
      "Time:                        19:30:25   Log-Likelihood:                -4634.7\n",
      "No. Observations:                 397   AIC:                             9275.\n",
      "Df Residuals:                     394   BIC:                             9287.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===============================================================================\n",
      "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-------------------------------------------------------------------------------\n",
      "Intercept    9.966e+04   2424.113     41.113      0.000    9.49e+04    1.04e+05\n",
      "service      1786.7949    733.168      2.437      0.015     345.383    3228.207\n",
      "service ^ 2 -1006.5568    724.345     -1.390      0.165   -2430.621     417.507\n",
      "==============================================================================\n",
      "Omnibus:                       25.200   Durbin-Watson:                   1.833\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               28.562\n",
      "Skew:                           0.598   Prob(JB):                     6.28e-07\n",
      "Kurtosis:                       3.546   Cond. No.                         52.3\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "model4 = ols(\"salary ~ service + service^2\", df).fit()\n",
    "print(model4.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Сама по себе оценка коэффициента при `service^2` не является статистически значимой, это нестрашно, мы добавляли эту переменную в модель не для того, чтобы оценить ее эффект, а для того, чтобы как-то учесть нелинейный характер взаимосвязи. При этом коэффициент при `service^2` отрицательный, что логично, отрицательный коэффициент при квадрате независимой переменной означает, что зависимость описывается параболой с ветвями вниз (выпуклая вверх, как на графике выше). При этом интерпретировать коэффициент при `service`, без квадрата, мы можем как обычно: у человека с опытом работы на 1 год выше заработная плата, в среднем, выше на 1786 долларов. \n",
    "\n",
    "Как эта история с возведением в квадрат связана с эффектом взаимодействия? Очень просто: `service^2` – это то же самое, что эффект взаимодействия опыта работы с самим собой! Единственное, если записать в `ols()` уравнение через `:`, Python нас не поймет, он автоматически уберет «дублирование»:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.112\n",
      "Model:                            OLS   Adj. R-squared:                  0.110\n",
      "Method:                 Least Squares   F-statistic:                     49.85\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           7.53e-12\n",
      "Time:                        19:30:26   Log-Likelihood:                -4635.7\n",
      "No. Observations:                 397   AIC:                             9275.\n",
      "Df Residuals:                     395   BIC:                             9283.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "Intercept   9.997e+04   2416.605     41.370      0.000    9.52e+04    1.05e+05\n",
      "service      779.5691    110.417      7.060      0.000     562.491     996.647\n",
      "==============================================================================\n",
      "Omnibus:                       25.187   Durbin-Watson:                   1.843\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               28.656\n",
      "Skew:                           0.593   Prob(JB):                     5.99e-07\n",
      "Kurtosis:                       3.570   Cond. No.                         36.9\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(ols(\"salary ~ service + service:service\", df).fit().summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чтобы он понял нас правильно, нужно использовать явное возведение в квадрат или дописывать вокруг такого эффекта `I()` и все равно возводить в квадрат:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 salary   R-squared:                       0.116\n",
      "Model:                            OLS   Adj. R-squared:                  0.112\n",
      "Method:                 Least Squares   F-statistic:                     25.95\n",
      "Date:                Sat, 15 Oct 2022   Prob (F-statistic):           2.59e-11\n",
      "Time:                        19:30:26   Log-Likelihood:                -4634.7\n",
      "No. Observations:                 397   AIC:                             9275.\n",
      "Df Residuals:                     394   BIC:                             9287.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==================================================================================\n",
      "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
      "----------------------------------------------------------------------------------\n",
      "Intercept       9.966e+04   2424.113     41.113      0.000    9.49e+04    1.04e+05\n",
      "service         1786.7949    733.168      2.437      0.015     345.383    3228.207\n",
      "I(service ^ 2) -1006.5568    724.345     -1.390      0.165   -2430.621     417.507\n",
      "==============================================================================\n",
      "Omnibus:                       25.200   Durbin-Watson:                   1.833\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               28.562\n",
      "Skew:                           0.598   Prob(JB):                     6.28e-07\n",
      "Kurtosis:                       3.546   Cond. No.                         52.3\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(ols(\"salary ~ service + I(service^2)\", df).fit().summary())"
   ]
  }
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