permutations_test.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Permutations Significance Test\n",
    "\n",
    "A common problem that one encounters when analyzing data is the need to compare samples of data, `sample_A` and `sample_B` in our case, in order to determine whether or not the observed samples are drawn from the same parent probability density function. Are the two samples that you are analyzing actually different from one another? One way to test for differences is to make some theoretical assumptions about the nature of the probability function of the null hypothesis. For example, if the null hypothesis is normally distributed then we can look at our observed samples and make some educated inferences about whether they are drawn from the same theoretcial null hypothesis distribution. It is often difficult to be confident in theoretical assumptions about your particular set of data. Often I find myself analyzing problem sets in which the underlying probability functions are not well understood, and do not lend themselves easily to theoretical assumptions. In these cases I use permutations testing. I have found this test to be practical, intuitive, and reasonably easy to implement with a little bit of custom code. I want to share my use of this test with you because I think it is powerful and widely applicable. \n",
    "\n",
    "##### Intuition and Terminology\n",
    "\n",
    "Ok...permutations test. Well, permutations of what? The testing name refers to permutations of the null hypothesis. The null hypothesis is the hypothesis that your two observed samples are drawn from the same parent distribution and there are no significant differences between them. Under the null hypothesis, your two samples are two ways the null hypothesis could be observed. In other words they are two permutations of samples from the same larger parent distribution. If it is in fact true that we have two observed samples from the null hypothesis distribution, then we can create many more observations using re-sampling techniques. An assumption that must be met in order for a permutations test to be applicable is the observed data points must be exchangeable between the observed sample groups. In practice this means that there can't be any underlying reason why an observation in `sample_A` couldn't have also occured in `sample_B`. You can test any feature of the data that you wish including, mean difference, deviation, or t-score. For this purpose I will use the mean difference between the two samples. \n",
    "\n",
    "##### Steps and Methods\n",
    "\n",
    "The steps to perform a permutations test are as follows:\n",
    "\n",
    "1. Compare and log the observed mean difference between `sample_A` and `sample_B`.\n",
    "2. Pool/Merge the observed data points from `sample_A` and `sample_B` into one set of data `null_observation`.\n",
    "3. Recreate the two groups by randomly sampling without replacement from `null_observation` creating two new groups, `resample_A` and `resample_B`, and log the mean difference between the two resampled groups.\n",
    "4. Repeat step 3 n times. In our case we will re-sample the data 1000 times.\n",
    "5. Compare the mean differences collected from `resample_A` and `resample_B` to the mean difference obtained in step 1.\n",
    "\n",
    "##### Example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1000,) (1000,) (2000,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x126087278>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABq8AAARiCAYAAAA6Hm1PAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvNQv5yAAAIABJREFUeJzs3XuMned9H/jvO1fOGZIznCGpK4eSrUhN42ZVl73YvUSt3YUdWNuLDLttHETdFjKS3RYubGwrI0GBdWB3AXnroqgDC+2u0iTdWpVTJFLjdGu1ky4q1xvaVppLl0pkiUPZkkXOTeScIedw5t0/DqnGtigOyXfmfc85nw/w4pjDmXO+EIwfgec7z/MUZVkGAAAAAAAAmmCo7gAAAAAAAABwmfIKAAAAAACAxlBeAQAAAAAA0BjKKwAAAAAAABpDeQUAAAAAAEBjKK8AAAAAAABoDOUVAAAAAAAAjaG8AgAAAAAAoDGUVwAAAAAAADSG8goAAAAAAIDGGNnNDzt48GB5xx137OZH9q4TJ7qv99xTbw4AAACAHnLqtVNJkiP7j9ScBBg05g9c3Ve/+tUzZVkeutr37Wp5dccdd+T48eO7+ZG96777uq/z83WmAAAAAOgp9z12X5Jk/sH5WnMAg8f8gasriuLkdr7PsYEAAAAAAAA0hvIKAAAAAACAxlBeAQAAAAAA0Bi7eucV1+Duu+tOAAAAANBz7p61pgLUw/yB6hRlWe7ahx07dqw8fvz4rn0eAAAAAAAAzVAUxVfLsjx2te9zbCAAAAAAAACNobxqqoce6j4AAAAAbNtDTz6Uh560pgLsPvMHquPOq6aana07AQAAAEDPeW7xubojAAPK/IHqKK+a6lOfqjsBAAAAAADArnNsIAAAAAAAAI2hvGqqBx7oPgAAAAAAAAPEsYFNtbhYdwIAAACAnnPvzffWHQEYUOYPVEd5BQAAAEDf+Mx7PlN3BGBAmT9QHccGAgAAAAAA0BjKKwAAAAD6xod+8UP50C9+qO4YwAAyf6A6jg0EAAAAoG+89NpLdUcABpT5A9Wx8woAAAAAAIDGUF4BAAAAAADQGMorAAAAAAAAGsOdV031jnfUnQAAAACg57zjdmsqQD3MH6hOUZblrn3YsWPHyuPHj+/a5wEAAAAAANAMRVF8tSzLY1f7PscGAgAAAAAA0BjKq6Z64IHuAwAAAMC2PfD4A3ngcWsqwO4zf6A67rxqKndeAQAAAFyzxfZi3RGAAWX+QHWUV031sY/VnQAAAAAAAGDXOTYQAAAAAACAxlBeNdV993UfAAAAAACAAeLYQAAAAAD6xrvufFfdEYABZf5AdZRXAAAAAPSNn/qhn6o7AjCgzB+ojmMDAQAAAAAAaAzlFQAAAAB9472/8N689xfeW3cMYACZP1AdxwYCAAAA0DfWO+t1RwAGlPkD1bHzCgAAAAAAgMZQXgEAAAAAANAYyisAAAAAAAAaw51XTfW+99WdAAAAAKDnvO9uaypAPcwfqE5RluWufdixY8fK48eP79rnAQAAAAAA0AxFUXy1LMtjV/s+xwYCAAAAAADQGMqrprrvvu4DAAAAwLbd99h9ue+x++qOAQwg8weq486rpnrwwboTAAAAAAAA7DrlVVMprwAAAAAAgAHk2MCmOnOm+wAAAAAAAAwQO6+a6v3v777Oz9caAwAAAAAAYDcprwAAAADoGx/4gQ/UHQEYUOYPVEd5BQAAAEDf+Ik/+hN1RwAGlPkD1XHnFQAAAAB9o91pp91p1x0DGEDmD1THzisAAAAA+sYP/8IPJ0nmH5yvNwgwcMwfqI6dVwAAAAAAADSG8goAAAAAGFidza185RuLKcuy7igAXKK8AgAAAAAG1iee+p188NH/nMePn6o7CgCXKK8AAAAAgIH05G98K//8yyezZ3Qo//u/ey7rG5t1RwIgyUjdAbiCBx+sOwEAAABAz3nw3gfrjkCPeP70ufy9L/yXvH1uOh/77+/JX/unX8n/8Z9eyP/0Z++qOxo9yvyB6hTbOcu1KIq/k+RvJimT/GaSv57kliT/Mslskq8m+dGyLDfe7H2OHTtWHj9+/EYzAwAAAABct/WNzfylz/6nfPu18/k3f/tP59bpifzNnz2er3xjMb/2v/zZzEyO1R0RoC8VRfHVsiyPXe37rnpsYFEUtyX520mOlWX5tiTDSf5Kkv8tyT8sy/KuJMtJ/saNReY7nDnTfQAAAADYtjPtMznTtqbCm/v7v/xbOfHts/mHH7w3t05PJEn+7nvuydrGxfzjf/+7NaejV5k/UJ3t3nk1kmSiKIqRJK0kLyf5c0meuPT3P5vkL1Yfb4C9//3dBwAAAIBte//j78/7H7emwpX9q+On8vjxl/I//9m7ct89h1//+vfdtC8fOHYkP/+fT2ZhsV1jQnqV+QPVuWp5VZblN5M8kmQh3dJqNd1jAlfKsrx46dteSnLbToUcSB/9aPcBAAAAACpx4pWz+alf+q284y2z+ci77/6ev/87f/7uDA8VeeT/PlFDOgAu286xgQeS/IUkdya5Nclkkvds9wOKonioKIrjRVEcP3369HUHHTj33999AAAAAIBK/JP/8HvZMzqcf/RX783wUPE9f3/T/j35G3/qzvzyb3wrv/nSag0JAUi2d2zgu5O8UJbl6bIsO0l+McmfTDJ96RjBJLk9yTff6IfLsny0LMtjZVkeO3ToUCWhB8KJE90HAAAAAKjEV08u50/ddTCH9+254vd8+IfempnJsXzqi/81ZVnuYjoALttOebWQ5E8URdEqiqJI8q4kv5PkPyS5fIDnjyX5pZ2JOKA+/OHuAwAAAADcsJdX1/PNlfX8kaMH3vT79u8Zzd/6c3flmecX8x9/98wupQPg9xu52jeUZfmVoiieSPK1JBeTfD3Jo0n+TZJ/WRTFT1/62j/byaAAAAAAcDU/fuzH645AQ33t5EqS5O1zb15eJcmP/PGj+cf//vfyS89+Mz90t9Ok2B7zB6pz1fIqScqy/PtJ/v53ffkbSf5Y5YkAAAAA4Dp98G0frDsCDfXVk8vZMzqUP3jr/qt+79jIUN4+dyBfX1jZhWT0C/MHqrOdYwMBAAAAoCecWj2VU6un6o5BA311YTk/ePt0Roe3tyT69qPTeeHMWpbWNnY4Gf3C/IHqbGvnFQAAAAD0gh/91z+aJJl/cL7eIFzVv/jKwq59VmdzK7/50kr+9Pcd2vbnXi6tPvPvnsv/+hfftpPx6BPmD1THzisAAAAAoK+9tLyerTKZm2lt+2dun25lqEgWlts7mAyAN6K8AgAAAAD62sJSt4C6lvJqbGQoN0/tef1nAdg9yisAAAAAoK8tLLVzcO9YJsev7RaVuZlWXlpez+ZWuUPJAHgjyisAAAAAoG+VZZmFxbXMzUxe88/OzbSycXErJ145uwPJALiSa/tVA3bPRz9adwIAAACAnvPRd1hT4TstrW1kbWMzR6/hyMDLLhdeX1tYzh+8dX/V0egz5g9UR3nVVPffX3cCAAAAgJ5z/z3WVPhOJy/fdzV77eXVgdZoJseG87WF5XzoTxytOhp9xvyB6jg2sKlOnOg+AAAAAGzbiTMncuKMNRX+m4XFdvaMDuXQvvFr/tmiKDI308rXF1Z2IBn9xvyB6th51VQf/nD3dX6+1hgAAAAAveTDT3XXVOYfnK83CI2xsNTOkQOtDBXFdf383Ewr//Z3vp2ltY3MTI5VnI5+Yv5AdZRXTfXJT9adAAAAAAB62vnOZr792vn8wG2Hr/s9jlw6bvDrC8t51/ffVFU0AN6EYwOb6p3v7D4AAAAAwHU5tdROmeTozOR1v8ft060MDxX52sJydcEAeFPKq6Z65pnuAwAAAABcl5NL7RRJbj8wcd3vMTYylO+/ZZ97rwB2kWMDm+rjH+++uvMKAAAAAK7LwlI7N0/tyZ7R4Rt6n7fPHcgXvvpSNrfKDA9d391ZAGyf8goAAACAvvGTf+Yn645AQ2yVZU4ttXPvkekbfq+3zx3IP//yyZx45Wz+4K37K0hHPzJ/oDrKKwAAAAD6xrvf8u66I9AQ337tfC5c3MrcTOuG3+sPz3ULsK8tLCuvuCLzB6rjzisAAAAA+sazrzybZ195tu4YNMDCUjtJcnR28obfa26mldnJsXxtYfmG34v+Zf5Adey8AgAAAKBvfORXP5IkmX9wvt4g1G5hsZ294yM50Bq94fcqiiJ/eO5Avr6wUkEy+pX5A9Wx8woAAAAA6DsLS+3MzbRSFEUl7/f2o9N54cxaltY2Knk/AK5MeQUAAAAA9JXO5laW1jZyy9Seyt7z7XMHkiRfd3QgwI5TXgEAAAAAfWVpbSNlktm945W95w/ePpXhocK9VwC7QHkFAAAAAPSVM+cuJEkO7h2r7D1bYyP5/lv25Wsn3XsFsNNG6g7AFXzyk3UnAAAAAOg5n3yXNRWSxXPde6lmJ6vbeZUkf+i26fzKb76csiwru0uL/mH+QHWUV031znfWnQAAAACg57zziDUVujuvWmPDmRgbrvR97zq8N6vrnSyubeRghUcS0h/MH6iOYwOb6plnug8AAAAA2/bMqWfyzClrKoNup8qltx6aTJI8/+q5yt+b3mf+QHXsvGqqj3+8+zo/X2sMAAAAgF7y8ae7ayrzD87XG4RaLZ67kLsO7638fS+/5/On1/LH3zJb+fvT28wfqI7yqqk+97m6EwAAAABAz9m4uJXXzl/M7A7svLp1aiITo8P5PTuvAHaU8qqp7rmn7gQAAAAA0HMW1y4kSWYnxyp/76GhIm85NJnnTyuvAHaSO6+a6sknuw8AAAAAsG1nzm0kyY7ceZUkbz20184rgB2mvGqqT3+6+wAAAAAA27Z4bud2XiXd8uqbK+tZ39jckfcHwLGBAAAAAPSRz7znM3VHoGaL5zayb3wk46PDO/L+dx3emyR5/vS5vO22qR35DHqT+QPVUV4BAAAA0DfuvfneuiNQszNrFzK7d2d2XSXJWw9PJlFe8b3MH6iOYwMBAAAA6Btf+saX8qVvfKnuGNRo8dxGZnfovqskuWN2MkNF8vzptR37DHqT+QPVsfMKAAAAgL7x0//xp5Mk737Lu2tOQh3OdzZz7sLFHNyh+66SZM/ocI7MtPL8q+d27DPoTeYPVMfOKwAAAACgLyyubSTJju68SpK7Du3N86eVVwA7RXkFAAAAAPSFxXMXkmRH77xKkrce3ptvnFnL5la5o58DMKiUVwAAAABAXzhz7tLOq8md33m1cXErLy23d/RzAAaV8goAAAAA6AuL5y5k/56RjI3s7LLnWw9PJkl+z71XADtipO4AXMHnPld3AgAAAICe87n3WVMZZItrGzt+31WSvPXQ3iTJ86fP5V3ff9OOfx69wfyB6iivmuqee+pOAAAAANBz7jloTWWQnTl3IT9w6/4d/5zp1lgO7h3L86+u7fhn0TvMH6iOYwOb6sknuw8AAAAA2/bkiSfz5AlrKoNofWMz7Y3NHb/v6rK3HNqb3zvt2ED+G/MHqmPnVVN9+tPd1/vvrzcHAAAAQA/59Je7ayr332NNZdAsrl1IkhzcO7Yrn3fX4b35N//l5ZRlmaIoduUzaTbzB6qjvGqqJ56oOwEAAAAA9Iwz5zaSZFfuvEq6916trneyuLaRg7v0mQCDQnnVVAcP1p0AAAAAAHrG4rkLKZLMTO7ezqskef7Vc8orgIq586qpHnus+wAAAAAAV7W4tpGpidGMDu/OkudbD00miXuvAHaA8qqplFcAAAAAsG1nzl3I7C7dd5Ukt05NZGJ0OM+/urZrnwkwKBwbCAAAAEDf+Lm/9HN1R6Ami+c28odun9q1zxsaKvKWQ5N2XvE68weqo7wCAAAAoG8cmTpSdwRq0L5wMeudzRzcpfuuLrvr8N4cf3F5Vz+T5jJ/oDqODQQAAACgb3z+tz6fz//W5+uOwS47s7aRJJndO76rn/vWQ3vzzZX1rG9s7urn0kzmD1THzisAAAAA+sbPHP+ZJMkH3/bBmpOwmxbPXUiSXb3zKumWV0ny/Olzedttu3dkIc1k/kB17LwCAAAAAHramXMbKZLM1HBsYNItrwCojvIKAAAAAOhpi2sXMt0azcjQ7i533nGwlaEief5V5RVAlZRXAAAAAEBPWzy3kYO7fN9VkoyPDGduppXnT6/t+mcD9DPlFQAAAADQs8qyzJlzF3b9vqvL3npob37PziuASo3UHYAreOKJuhMAAAAA9JwnPmBNZdCsbWzmwsWtzE7u/s6rpHvv1f/zu2eyuVVmeKioJQPNYP5AdZRXTXXwYN0JAAAAAHrOwZY1lUGzeO5CkuRgjTuvNja3cmqpnTsOTtaSgWYwf6A6jg1sqsce6z4AAAAAbNtjzz6Wx559rO4Y7KLldidJcqBVT3l1ubB6cdG9V4PO/IHqKK+aSnkFAAAAcM0sHg+e1fZGkmSqNVrL5x+dbSVJFpbatXw+zWH+QHUcG9hU8/N1JwAAAACAxlte72RidDjjI8O1fP7hfePZMzqUk4vKK4Cq2HkFAAAAAPSs1XYnB2radZUkRVFkbqalvAKokPKqqR55pPsAAAAAAFe0sr6RqZruu7psbmYyC0vuvAKoivKqqZ56qvsAAAAAAG+oLMustDuZnqhv51XSvfdqYamdsixrzQHQL9x5BQAAAEDf+JUf+ZW6I7CLzne2cuHiVqZrPDYw6ZZX5ztbefXshdy0f0+tWaiP+QPVUV4BAAAA0Ddao626I7CLVtY3kiTTtR8b2P3/3cnFtvJqgJk/UB3HBgIAAADQNz7765/NZ3/9s3XHYJestDtJ0oBjAyeTJCcX3Xs1yMwfqI7yCgAAAIC+8fhvP57Hf/vxumOwS1bWL5VXNR8beNv0RIaKZGGpXWsO6mX+QHWUVwAAAABAT1ppb2R4qMjkeL23o4yNDOXW6YmcXFReAVRBeQUAAAAA9KSVdifTE6MZKoq6o+TobCsn7bwCqITyCgAAAADoSavrnUzVfGTgZXMzk1lw5xVAJZRXAAAAAEBPWmlvZHpirO4YSbo7r5bbnbx2vlN3FICeV+9hsFzZ/HzdCQAAAAB6zvyD83VHYJdc3NrK2fMXM92QnVdHZ1pJkoXFdt5221TNaaiD+QPVsfMKAAAAAOg5r61fTJlkeqIZ5dXcbLe8Orno3iuAG6W8aqpHHuk+AAAAAGzbI888kkeesaYyCFbaG0mS6VZTjg2cTJKcXHLv1aAyf6A6yqum+vKXuw8AAAAA2/bUc0/lqeeeqjsGu2BlvXu3VFOODdw7PpLZybEs2Hk1sMwfqI47r5rqC1+oOwEAAAAANNblnVdTDTk2MOkeHejYQIAbZ+cVAAAAANBzVtqd7B0fyehwc5Y4j860srCkvAK4Uc2Z7Hynhx/uPgAAAADA91hd7zTmyMDL5mYn863V9Vy4uFl3FICe5tjApnLfFQAAAMA1mxidqDsCu2S53clN+8frjvEdjs60UpbJS8vreeuhvXXHYZeZP1Ad5RUAAAAAfeOLP/LFuiOwC8qyzOr6Rv7AzfvqjvIdjs62kiQLi23l1QAyf6A6jg0EAAAAAHpKe2Mznc0yUxNNOzawW16dXFyrOQlAb1NeAQAAANA3PvFrn8gnfu0Tdcdgh620O0nSuDuvDu0dT2tsOCeX2nVHoQbmD1RHeQUAAABA33j6hafz9AtP1x2DHbayvpEkmW6N1ZzkOxVFkbmZVhYWlVeDyPyB6iivAAAAAICe8vrOq4YdG5gkczMtO68AbpDyCgAAAADoKSvtjYwOF2mNDdcd5XscnW1lYamdra2y7igAPUt5BQAAAAD0lJX1TqYnxlIURd1Rvsfc7GQ2Lm7l22fP1x0FoGeN1B2AK5idrTsBAAAAQM+ZbVlTGQQr7U6mW807MjBJjs60kiQnF9u5ZWqi5jTsJvMHqqO8aqovfKHuBAAAAAA95wsfsKYyCFbWO7l1ek/dMd7Q0dluebWw2M6feIsyY5CYP1AdxwYCAAAAAD2js7mVtQsXMzUxVneUN3Tr9ESGh4qcXFqrOwpAz1JeNdXDD3cfAAAAALbt4S89nIe/ZE2ln622O0nS2GMDR4eHctv0RE4utuuOwi4zf6A6jg1sqsXFuhMAAAAA9Jwvv/TluiOww1bWm11eJd2jAxeWlFeDxvyB6iivmurRR+tOAAAAAACNs9LeSJJMN/TYwCSZm2nlqf/yct0xAHqWYwMBAAAAgJ6xst5JkWT/RHN/L//obCur653XjzgE4Noor5rqoYe6DwAAAADwupV2J/v2jGRkqLlLm3Mzk0mSk0trNScB6E3N/fWEQffcc3UnAAAAAOg5t++/ve4I7LCV9kamW809MjDp7rxKkpOL7fzg7dM1p2G3mD9QHeUVAAAAAH3j5//yz9cdgR22st7JbdMTdcd4U3Mz3fJqYaldcxJ2k/kD1Wnu3loAAAAAgN9nqyyzut7JgdZo3VHe1OT4SA7uHcsp5RXAdVFeAQAAANA3PvKrH8lHfvUjdcdgh5y7cDGbW2WmGn5sYJIcmWnZeTVgzB+ojmMDAQAAAOgbz77ybN0R2EGr7U6S5MBEs3deJcmRA618/dRy3THYReYPVMfOKwAAAACgJyy3N5IkUw0/NjDp3nv1rZXzubi5VXcUgJ6jvAIAAAAAesLqenfn1fRELxwbOJHNrTIvr56vOwpAz1FeAQAAAAA9YaXdyfjIUCbGhuuOclVHZlpJ4t4rgOvgzqumuvvuuhMAAAAA9Jy7Z62p9LPV9U6meuC+q6R7bGDSLa/+ZM1Z2B3mD1RHedVUjz5adwIAAACAnvPo/dZU+lkvlVe3TE1kZKjIKTuvBob5A9VxbCAAAAAA0BNWeqi8Gh4qctuBCccGAlwH5VVTPfRQ9wEAAABg2x568qE89KQ1lX50cXMraxcuZqrVG+VVkhw50Mqp5fW6Y7BLzB+ojmMDm2p2tu4EAAAAAD3nucXn6o7ADnnt/MUkydSeHiqvZlr5t7/9St0x2CXmD1RHedVUn/pU3QkAAAAAoDFW1jeSpKd2Xs3NtLK0tpFzFy5m77ilWIDtcmwgAAAAANB4q+1OkvTMnVdJcmRmIklyyr1XANdEedVUDzzQfQAAAACAvLbeLa+mJ8ZqTrJ9czOtJMmC8grgmtir2lSLi3UnAAAAAOg59958b90R2CEr651MjA5nbKR3fh//yIFueWXn1WAwf6A6yisAAAAA+sZn3vOZuiOwQ1bXOz11ZGCSTLdGs298RHk1IMwfqE7v/JoCAAAAADCwerG8KooiR2ZaObW8XncUgJ6ivAIAAACgb3zoFz+UD/3ih+qOwQ7oxfIqSY7MTLjzakCYP1AdxwYCAAAA0Ddeeu2luiOwAzqbW2lvbGaq1Xvl1dxMK/MnTqcsyxRFUXccdpD5A9Wx8woAAAAAaLTV9U6S9OjOq1YuXNzK6bMX6o4C0DOUVwAAAABAo/V6eZXE0YEA10B5BQAAAAA0Wi+XV3OXyqtTy8orgO1y51VTveMddScAAAAA6DnvuN2aSj/q5fLqtumJJMnC4nrNSdhp5g9UR3nVVJ/6VN0JAAAAAHrOp95tTaUfrbY7aY0NZ3S49w6S2jM6nJv377HzagCYP1Cd3pv2AAAAAMBAWV3v9OSuq8uOzEy48wrgGly1vCqK4p6iKJ79fc9rRVF8pCiKmaIo/l1RFL976fXAbgQeGA880H0AAAAA2LYHHn8gDzxuTaXf9H551cpLyqu+Z/5Ada5aXpVleaIsy3vLsrw3yR9J0k7yr5P8vSRPl2X5fUmevvRnqvKOd7j3CgAAAOAaLbYXs9herDsGFev18mpuppWXXzufCxc3647CDjJ/oDrXeufVu5I8X5blyaIo/kKS+y59/WeTzCf5u9VFG3Af+1jdCQAAAACgdhsXt7Le2cx0D5dXRw60UpbJt1bO586Dk3XHAWi8a73z6q8k+b8u/e+byrJ8+dL/fiXJTZWlAgAAAABIsrK+kSSZavVueTU320oS914BbNO2y6uiKMaS/A9J/tV3/11ZlmWS8go/91BRFMeLojh++vTp6w46cO67r/sAAAAAwABbXe8kSfb3+M6rRHkFsF3Xcmzge5N8rSzLb1/687eLorilLMuXi6K4Jcmrb/RDZVk+muTRJDl27NgbFlwAAAAAUIV33fmuuiNQsdculVfTE2M1J7l+h/eNZ2xkKC8pr/qa+QPVuZby6q/mvx0ZmCS/nOTHkvyDS6+/VGEuAAAAALhmP/VDP1V3BCq2cnnn1Z5rWcpslqGhIkcOTNh51efMH6jOto4NLIpiMsmfT/KLv+/L/yDJny+K4neTvPvSnwEAAAAAKrPa7mTv+EhGhrd9A0ojHZlp5dSy8gpgO7b16wplWa4lmf2ury0msQ8SAAAAgMZ47y+8N0nyxR/5Ys1JqMrqeidTPXzf1WVzM6187eRy3THYQeYPVKd399oCAAAAwHdZ76zXHYGKra53cnDveN0xbtiRA628dv5iVtudTLV6v4zje5k/UJ3e3msLAAAAAPS1ftl5dWSmlSSODgTYBuUVAAAAANBI5zubuXBxq0/Kq4kkycKS8grgapRXAAAAAEAjra53kqQvjtl7feeV8grgqtx51VTve1/dCQAAAAB6zvvutqbST14vr/b0fnm1f89oDrRG7bzqY+YPVEd51VQf+1jdCQAAAAB6zsfeaU2ln/TTzquku/vq1PJ63THYIeYPVMexgQAAAABAI62ud1Kku2upHxyZaWVhca3uGACNp7xqqvvu6z4AAAAAbNt9j92X+x67r+4YVGS13cm+PSMZHirqjlKJuZlWvrmyns2tsu4o7ADzB6rj2MCmevDBuhMAAAAAQK1Wz3cyNdEfu66S5OhMK53NMi+vruf2A6264wA0lvKqqZRXAAAAAAy41XYnh/eP1x2jMnMz3cJqYamtvAJ4E44NbKozZ7oPAAAAAAygsiyzut7JdB/tvDpyqbw6tdSuOQlAs9l51VTvf3/3dX6+1hgAAAAAUIfzna1sbG711bGBt0ztychQkZOLyiuAN6O8AgAAAKBvfOAHPlB3BCqyut5Jkky1xmpOUp2R4aHcfmAiC3Ze9SXzB6qjvAIAAACgb/zEH/2JuiPzLiH5AAAgAElEQVRQkdX1jSTJ1J7+WsI8MtNybGCfMn+gOu68AgAAAKBvtDvttDuKgX6w0oc7r5JkbqaVk8qrvmT+QHX669cWAAAAABhoP/wLP5wkmX9wvt4g3LDV9U6GimRfn+28Ojrbykq7k9X1Tl/d54X5A1Wy8woAAAAAaJzVdif79oxmqCjqjlKpuZlWkjg6EOBNKK8AAAAAgMZZPd+fO5OOXCqvFpRXAFekvAIAAAAAGme13Z/l1ZzyCuCqlFcAAAAAQKOUZZnV9U6m+7C82rdnNDOTY8orgDfRX7cd9pMHH6w7AQAAAEDPefDeB+uOQAXWNjZzcavMVKv/yquke3TgwqLyqt+YP1Ad5VVTKa8AAAAArpnF4/6w2u4kSaYnxmpOsjPmZlr5jVMrdcegYuYPVMexgU115kz3AQAAAGDbzrTP5EzbmkqvW1nfSJJM9+nOq6MzrXxzZT0XN7fqjkKFzB+ojp1XTfX+93df5+drjQEAAADQS97/eHdNZf7B+XqDcENWXt951Z/l1dxMK5tbZV5ePZ8jM62641AR8weqo7xqqo9+tO4EAAAAAFCL1fVORoeLTIwN1x1lR1wurE4utpVXAG9AedVU999fdwIAAAAAqMVKeyPTE2MpiqLuKDtibrZbWC0stWtOAtBM7rxqqhMnug8AAAAADJiV9U7f3neVJDfv35Ox4SHlFcAV2HnVVB/+cPfVnVcAAAAADJjVdic337yn7hg7ZnioyO0HJrKwtFZ3FIBGUl4BAAAA0Dd+/NiP1x2BG3RxcytnL1zs651XSffeKzuv+ov5A9VRXgEAAADQNz74tg/WHYEbtLreSZJMT4zVnGRnHZ1t5esLy3XHoELmD1THnVcAAAAA9I1Tq6dyavVU3TG4ASuXyqupPt95NTfTymvnL2alvVF3FCpi/kB17LwCAAAAoG/86L/+0STJ/IPz9Qbhuq22L++86u/y6shMK0mysNTOdKu/d5kNCvMHqmPnFQAAAADQGCvr3Z1IU31eXs39vvIKgO+kvAIAAAAAGmOl3cm+8ZGMDPf30uXl8urkovIK4Lv1978AAAAAAEBPWV3v9P19V0kyOT6Sg3vHcsrOK4DvobwCAAAAABpjud3p+/uuLjsy03JsIMAbGKk7AFfw0Y/WnQAAAACg53z0HdZUellZllld38gfuHlf3VF2xdGZVn79xeW6Y1AR8weqo7xqqvvvrzsBAAAAQM+5/x5rKr2svbGZzmaZqQHZeTU308ov/8a3snFxK2MjDsnqdeYPVMdEbKoTJ7oPAAAAANt24syJnDhjTaVXrax3kiTTA3DnVdI9NnCrTL61sl53FCpg/kB17Lxqqg9/uPs6P19rDAAAAIBe8uGnumsq8w/O1xuE67La3kiSTE+M1Zxkd8zNtJIkJ5fauePgZM1puFHmD1RHedVUn/xk3QkAAAAAYFdd3nk1NSA7r47OdgurhaV2zUkAmkV51VTvfGfdCQAAAABgV620OxkZKjI5Nlx3lF1xeN94xkaGckp5BfAd3HnVVM88030AAAAAYECsrHcy3RpNURR1R9kVQ0NFjhyYyMnFtbqjADSKnVdN9fGPd1/deQUAAADAgFhtbwzMfVeXHZ2dzMLSet0xABpFeQUAAABA3/jJP/OTdUfgBqysd3L3TXvqjrGr5mZa+X9fWEpZlgOz46xfmT9QHeUVAAAAAH3j3W95d90RuE4XN7dy9vzFTE+M1h1lVx2ZaeXchYtZWtvI7N7xuuNwA8wfqI47rwAAAADoG8++8myefeXZumNwHV47fzFJMt0arPLq6EwrSfLiYrvmJNwo8weqY+cVAAAAAH3jI7/6kSTJ/IPz9Qbhmq20N5IkUwN259UdByeTJC+eWcsfOXqg5jTcCPMHqmPnFQAAAABQu5X1TpLB23k1N9PKUJGcXFyrOwpAYyivAAAAAIDarbS75dXUgN15NTYylNsOTOQFxwYCvE55BQAAAADUbnV9I5PjIxkdHrwlyztmJ/PiGTuvAC4bvH8JAAAAAIDGWWl3Mj1gu64uu1xelWVZdxSARhipOwBX8MlP1p0AAAAAoOd88l3WVHrVynonh/eN1x2jFnccnMzZCxeztLaR2b2D+d+gH5g/UB3lVVO98511JwAAAADoOe88Yk2lF5VlmdV2J3cf3lt3lFrcebCVJHlxcU151cPMH6iOYwOb6plnug8AAAAA2/bMqWfyzClrKr1mvbOZjc2tTLXG6o5SiztmJ5MkL5xp15yEG2H+QHXsvGqqj3+8+zo/X2sMAAAAgF7y8ae7ayrzD87XG4RrstLuJMnA3nl1ZKaV4aEiL55ZqzsKN8D8geoor5rqc5+rOwEAAAAA7IrV9UvlVWswy6vR4aHcfmAiLywqrwAS5VVz3XNP3QkAAAAAYFestDeSJFMDuvMqSY7OTuak8gogiTuvmuvJJ7sPAAAAAPS5lfVORoaKTI4P7u/a3znbyotn2inLsu4oALUb3H8Nmu7Tn+6+3n9/vTkAAAAAYIettDuZmhjNUFHUHaU2dxyczLkLF3Pm3EYO7RuvOw5ArZRXAAAAAPSNz7znM3VH4DqsrncyNaD3XV12x8HJJMmLi2vKqx5l/kB1lFcAAAAA9I17b7637ghch5X2Ru46vK/uGLW6c7ZbXr1wZi1/9I6ZmtNwPcwfqI47rwAAAADoG1/6xpfypW98qe4YXIPNrTJnz1/M9IDvvLr9wERGhoqcXFyrOwrXyfyB6th5BQAAAEDf+On/+NNJkne/5d01J2G7XlvvpEwyPTHY5dXI8FBuPzCRF8+0647CdTJ/oDp2XgEAAAAAtVle30iSgb/zKunee/XCGTuvAJRXAAAAAEBtltc6SZKZ1ljNSep3x+xkXlxcS1mWdUcBqJXyCgAAAACozXJ7I0XsvEqSOw9Opr2xmdNnL9QdBaBWyisAAAAAoDbLaxvZPzGakSFLlXccnEySvLjo3itgsI3UHYAr+Nzn6k4AAAAA0HM+9z5rKr1mqb2RA44MTJLcMdtKkrx4Zi1/7M6ZmtNwrcwfqI7yqqnuuafuBAAAAAA9556D1lR6zfLaRu46vLfuGI1w2/RERoaKvLC4VncUroP5A9WxF7epnnyy+wAAAACwbU+eeDJPnrCm0isubm7l7PmLdl5dMjI8lLmZVl48o7zqReYPVMfOq6b69Ke7r/ffX28OAAAAgB7y6S9311Tuv8eaSi9YaXdSJjkw2ezy6l98ZWHXPmt0eCjPnlq57s/8a398ruJEbJf5A9VRXjXVE0/UnQAAAAAAdtRSeyNJ7Lz6fQ7uHcsLZ9ZSlmWKoqg7DkAtlFdNdfBg3QkAAAAAYEctXyqvZhq+82o3ze4dz8al4xT3T4zWHQegFu68aqrHHus+AAAAANCnltc2MjxUZN8ev2N/2eylIu/M2oWakwDUR3nVVMorAAAAAPrccruT6YnRDDke73Wze8eTJIvnNmpOAlAfv9IAAAAAQN/4ub/0c3VH4BostzccGfhdplujGR4qlFc9yPyB6iivAAAAAOgbR6aO1B2Ba7C0tpG33TpVd4xGGSqKzLTGsujYwJ5j/kB1HBsIAAAAQN/4/G99Pp//rc/XHYNtuHBxM+2NzRxojdYdpXFm947ZedWDzB+ojp1XAAAAAPSNnzn+M0mSD77tgzUn4WqW1zpJkgOODfwes5Njef70uWyVpfvAeoj5A9Wx8woAAAAA2HXL7e7OogMt5dV3m907ns5mmbPnL9YdBaAWyisAAAAAYNctrV0qr+y8+h4H944nSRbPufcKGEzKKwAAAABg1y23NzI2PJTJseG6ozTO7N5uoefeK2BQKa8AAAAAgF23vLaRA5OjKdzp9D2mJkYzOlzktJ1XwIAaqTsAV/DEE3UnAAAAAOg5T3zAmkqvWG533Hd1BUNFkYN7x/Pq2fN1R+EamD9QHeVVUx08WHcCAAAAgJ5zsGVNpReUZZml9kbuPDRZd5TGOrRvPKeW2nXH4BqYP1AdxwY21WOPdR8AAAAAtu2xZx/LY88+VncMrmK53cnGxa3M2Hl1RYf37Xn9vxO9wfyB6iivmkp5BQAAAHDNLB73hss7ihwbeGWH940niXuveoj5A9VxbGBTzc/XnQAAAAAAdsSp5Uvl1eRozUma69Dl8urs+dw2PVFzGoDdZecVAAAAALCrXlpeTxLHBr6J2b1jGSqSV8/aeQUMHuVVUz3ySPcBAAAAgD5zaqmd1thwxkeH647SWCNDQ5mZHM+rrymvgMGjvGqqp57qPgAAAADQZ04tr7vvahsO7xvPaTuvgAHkzisAAAAA+sav/Miv1B2BbXhpqZ0Dk8qrqzm8bzz/3yuvZXOrzPBQUXccrsL8gerYeQUAAABA32iNttIabdUdgzextVXmpeX1zLRG647SeIf2jWerTBbP2X3VC8wfqI7yCgAAAIC+8dlf/2w+++ufrTsGb+LVsxeysbmVaccGXtXhfXuSdP+b0XzmD1RHeQUAAABA33j8tx/P47/9eN0xeBOnlttJkhnHBl7VoX3jSZRXvcL8geoorwAAAACAXXNqqVteHbDz6qrGRoYy3RrN6bPn644CsKuUVwAAAADArjm1tJ4kmXbn1bYc3jee03ZeAQNGeQUAAAAA7JpTy+3ctH88o8OWJrfj0N7xnD53IVtlWXcUgF3jXwgAAAAAYNecWmrnyIFW3TF6xuF9e9LZLLPS7tQdBWDXjNQdgCuYn687AQAAAEDPmX9wvu4IXMVLy+v5Y3fO1B2jZxzeP54kOX32fGYm3RPWZOYPVMfOKwAAAABgV3Q2t/Ly6nqOHJioO0rPOLSvW1696t4rYIAor5rqkUe6DwAAAADb9sgzj+SRZ6ypNNXLK+ezVSa3zzg2cLtaYyOZHB/JaeVV45k/UB3lVVN9+cvdBwAAAIBte+q5p/LUc0/VHYMrOLXcThJ3Xl2jw/vG7bzqAeYPVMedV031hS/UnQAAAAAAKnVq6VJ5NTORF86s1ZymdxzeN57feGklZVmmKIq64wDsODuvAAAAAIBdcWq5nZGhIjfv31N3lJ5yaN94zne2cu7CxbqjAOwK5VVTPfxw9wEAAACAPvHiYjtHZloZGbYseS0O7+uWfY4OBAaFYwObyn1XAAAAANdsYnSi7gi8iZOLazk6676ra3Vo33iS5PTZC3nrob01p+FKzB+ojvIKAAAAgL7xxR/5Yt0RuIKyLHPyTDvHjs7UHaXn7N8zkvGRobx69nzdUXgT5g9Ux/5cAAAAAGDHLa1t5OyFi3ZeXYeiKHJ437hjA4GBobwCAAAAoG984tc+kU/82ifqjsEbeHGxnSS5Y3ay5iS96dC+PTmtvGo08weqo7wCAAAAoG88/cLTefqFp+uOwRs4ubiWJHZeXafD+8Zz9vzFnO9s1h2FKzB/oDrKKwAAAABgx7242M5Qkdx+QHl1PQ7tG08SRwcCA0F5BQAAAADsuJOLa7ntwETGRixJXo/Dl8ur187XnARg5/mXAgAAAADYcS8utt13dQMOTI5lZKhw7xUwEEbqDsAVzM7WnQAAAACg58y2rKk01cnFtbzvB2+pO0bPGiqKHNw77tjABjN/oDrKq6b6whfqTgAAAADQc77wAWsqTbTS3shKu2Pn1Q26af94Xlxs1x2DKzB/oDqODQQAAAAAdtTlwuWo8uqG3DI1kdX1TtobF+uOArCjlFdN9fDD3QcAAACAbXv4Sw/n4S9ZU2mak4trSZI7Zls1J+ltt0ztSZK8snq+5iS8EfMHqrOtYwOLophO8k+TvC1JmeR/THIiyeeT3JHkxSQfKMtyeUdSDqLFxboTAAAAAPScL7/05boj8AZePNNOUSRHZpRXN+LmS+XVy6vn85ZDe2tOw3czf6A629159Y+S/GpZln8gyX+X5L8m+XtJni7L8vuSPH3pz1Tl0Ue7DwAAAAD0uJOLa7ll/57sGR2uO0pP27dnNHvHR/KynVdAn7tqeVUUxVSSP5PknyVJWZYbZVmuJPkLSX720rf9bJK/uFMhAQAAAIDe9eLimvuuKnLL1J68srpedwyAHbWdnVd3Jjmd5P8siuLrRVH806IoJpPcVJbly5e+55UkN+1UyIH00EPdBwAAAAB63MnFdu446MjAKtwytSffPnshm1tl3VEAdsx27rwaSfL2JH+rLMuvFEXxj/JdRwSWZVkWRfGG07IoioeSPJQkc3NzNxh3gDz3XN0JAAAAAHrO7ftvrzsC3+W1850srm3YeVWRm6cmsrlV5vTZC6/fgUUzmD9Qne2UVy8leaksy69c+vMT6ZZX3y6K4payLF8uiuKWJK++0Q+XZflokkeT5NixY34dAAAAAIAd8/N/+efrjsB3WVhsJ0numLXzqgq3XCqsXl5dV141jPkD1bnqsYFlWb6S5FRRFPdc+tK7kvxOkl9O8mOXvvZjSX5pRxICAAAAAD3rxcW1JLHzqiIH945nZKjIy6vn644CsGO2s/MqSf5Wkl8oimIsyTeS/PV0i6/Hi6L4G0lOJvnAzkQEAAAAgO35yK9+JEnymfd8puYkXHby0s6ro3ZeVWJ4qMhN+/fkFeVV45g/UJ1tlVdlWT6b5Ngb/NW7qo3D/8/e/cfIed93Yv88uzu7O7PLmV0tLYoUqR9JLDWREgmoc63V4k53di+2a90vCXbRKIiAA2Qk/1SojbYykr8cWCggoy5QOLXQAgoSp2fBdnCVkBh30oU5oHJTp1fJlXoR/UOkSEmkxOXuDLkzy53dffrH7NK/RHFJPrvfZ555vYAHK9qy/AY8/g7wvPfz+QIAAABw7V46/VLqCPyM42dX4kBzKhqTO/09eq7kptZ0/O3bncjzPLIsSx2HLc4fKM4V1wYCAAAAAFyrE4tdKwMLdrA1HStrG3F+dT11FIBdobwCAAAAAHbN8cWVuM3KwEIdbNUjItx7BVSW8goAAAAA2BXdtfV45/xFk1cFu6k5HRERp9u9xEkAdodFs2V1xx2pEwAAAAAMnTsWvFMpkxOL3YiIuE15Vaj65HjMN2rxlsmrUnH+QHGUV2X11FOpEwAAAAAMnace8E6lTE4srkRExK3WBhbuplY9TiuvSsX5A8WxNhAAAAAA2BXHtyavlFfFO9iajrMXLsba+mbqKACFU16V1aOPDh4AAAAAduzRZx+NR5/1TqUsTiyuxP7Zydg3XUsdpXIOtqYjj4gzHdNXZeH8geJYG1hWCwupEwAAAAAMnWOLx1JH4CccP9uNW913tSsOtuoREXG6vRpHbjDZVgbOHyiO8qqsnngidQIAAAAAuC4nFlfiP/5Fv6S9G+YatZiaGIu32r3UUQAKZ20gAAAAAFC41f5GvNVejdtMXu2KsSyLm1rTcbptbSBQPcqrsnrwwcEDAAAAAEPojXPdiIi4dcFKu91ysDUdpzursZnnqaMAFMrawLJaXEydAAAAAGDo3HvTvakjsOX42ZWICJNXu+hgsx7/5/q5WFpZi4XZqdRxRp7zB4qjvAIAAACgMr78sS+njsCWE4uDySvl1e45ODcdERFvt1eVVyXg/IHiWBsIAAAAABTu+OJKzDVq0WrUUkeprAPN6cgi4nTHvVdAtSivAAAAAKiMh7/1cDz8rYdTxyAGk1e3mrraVbXxsdg/OxVvL/dSRyGcP1AkawMBAAAAqIxTnVOpI7Dl9bMr8aHb5lPHqLyDc9Pxxrlu6hiE8weKZPIKAAAAACjUan8j3mr33He1Bw42p2O524/e2kbqKACFUV4BAAAAAIU6ea4beR5x+37l1W47NF+PiIg3rQ4EKkR5BQAAAAAU6vWzKxERcZvyatcdnmtERMSpJasDgepw51VZffjDqRMAAAAADJ0PH/ZOpQyOLw7Kq9utDdx19cnxWJiZjFNLJq9Sc/5AcZRXZfXEE6kTAAAAAAydJz7qnUoZvH62G/ONWrQatdRRRsLN8/U4sWjyKjXnDxTH2kAAAAAAoFDHz65YGbiHDs83ot3rx/nVfuooAIVQXpXVgw8OHgAAAAB27MFnHowHn/FOJbXjiytWBu6hw3P1iAirAxNz/kBxrA0sK3deAQAAAFy1xe5i6ggjr7e2EW+3V01e7aFDc/XIQnmVmvMHiqO8KqvPfS51AgAAAAC4ascXVyIi4nbl1Z6ZnBiLA83peHPZvVdANVgbCAAAAAAU5vhZ5VUKN8/X49RSL/I8Tx0F4Lopr8rq/vsHDwAAAAAMkde3Jq+sDdxbh+fr0V3bsDoQqARrAwEAAACojI/c/pHUEUbe8bMrsX92KmanvHrcS4fnGhER8fKp5ThyQyNxmtHk/IHi+AYBAAAAoDJ+/+/9fuoII+/42W7cvl95stcOtKZifCyL751qxyd/7VDqOCPJ+QPFsTYQAAAAACjM64srcduClYF7bWJsLA62puPlk8upowBcN+UVAAAAAJXx8a99PD7+tY+njjGyLlxcj3fPX3TfVSKH5+vxypvt2NjMU0cZSc4fKI7yCgAAAIDK6PV70ev3UscYWcfPrkRExO3KqyQOzzViZW0jfvTuhdRRRpLzB4qjvAIAAAAACnF8cVBeWRuYxs3z9YiIePlUO3ESgOujvAIAAAAACvH6u1vl1f5G4iSj6QP7pmJmcjy+d8q9V8BwU14BAAAAAIV4fXElDjSnojE5kTrKSBrLsrj75pbJK2Do+RYpq09+MnUCAAAAgKHzyTu8U0np+NkV910lds+RuXj6/zgea+ubMTlhdmEvOX+gOMqrsvrc51InAAAAABg6n7vPO5WUji924zfuOpA6xkj7tcOtWNvYjNdOn49fPdxKHWekOH+gOKp3AAAAAOC6tXv9OLeyFrctmLxK6Z7DcxER8bJ7r4Ahprwqq/vvHzwAAAAA7Nj9T98f9z99f+oYI+n42ZWIiLjN2sCkDs/XY75Ri+8pr/ac8weKY21gWT3ySOoEAAAAALBjxxcH5ZU7r9LKsix+7fBcfO9UO3UUgGumvCor5RUAAAAAQ+T1syuRZRG33NBIHWXk3XO4Ff/TX74b3bX1aEx6BQwMH2sDy+rs2cEDAAAAAEPg9bMrcahVj+naeOooI+/XDs/FZh7x6lud1FEAronyqqweemjwAAAAAMAQOH52JW7bb+qqDH7tSCsiIl4+6d4rYDiZGQUAAACgMj5116dSRxhJeZ7H62dX4oF7DqWOQkTcuG86DrWm42X3Xu0p5w8UR3kFAAAAQGX87q//buoII2mp24/O6nrcvn8mdRS23HvLnMmrPeb8geJYGwgAAABAZXT73ej2u6ljjJzXz65ERMRtC8qrsrjn8Fy8ca4bixcupo4yMpw/UBzlFQAAAACV8YmvfSI+8bVPpI4xco5vlVe3f0B5VRb3HJmLiIjvWR24Z5w/UBzlFQAAAABwXY4vrsRYFnFkvpE6Clt+9eZWjGURL1kdCAwh5RUAAAAAcF1eP7sSh+cbMTnhdWNZzExNxB0H9sXLp5RXwPDxbQIAAAAAXJfjiytx234rA8vmnsNz8fLJ5cjzPHUUgKuivAIAAAAArlme5/H6uytx+4KVgWVzz5G5WOr2441z3dRRAK7KROoAXMYjj6ROAAAAADB0Hrn3kdQRRs67Fy7GytqGyasSuudIKyIG917duuB/n93m/IHiKK/KSnkFAAAAcNW8PN57JxYHUz23KUdK584D+2K6NhYvn2zHP7735tRxKs/5A8WxNrCszp4dPAAAAADs2Nnu2Tjb9U5lL22XV7daG1g6E+Nj8as3t+LlU8upo4wE5w8UR3lVVg89NHgAAAAA2LGHnnkoHnrGO5W99MbiSoxlEYfnlVdldM/huXjlzXb0NzZTR6k85w8UR3lVVp/97OABAAAAgBI7vtiNQ3P1mJzwqrGM7jkyFxfXN+O10+dTRwHYMXdeldUDD6ROAAAAAABXdOJc18rAErv3yFxERLx0cjnuvrmVOA3Azvh1iLJ67bXBAwAAAAAl9sbiStxyw0zqGFzG4fl63DAzGS+fdO8VMDxMXpXVZz4z+Hn0aNIYAAAAAHA57V4/lrr9uM3kVWllWRb3HpmLl08pr4DhobwCAAAAoDJ+50O/kzrCSHljsRsRYW1gyd1zeC7+8rV34sLF9Zid8kp4tzh/oDhOKgAAAAAq49N3fzp1hJFy4txKRIS1gSV3z5FW5HnE904tx32/uD91nMpy/kBx3HkFAAAAQGWcbJ+Mk+2TqWOMjBNbk1e3mLwqtXsOz0VExMsn24mTVJvzB4pj8goAAACAyvitP/utiIg4+sjRtEFGxInFldg/O2UVXcnNz0zGrQuNePmke692k/MHimPyCgAAAAC4JicWu+67GhL3HpmLl08pr4DhoLwCAAAAAK7JG+e6cesNyqthcM/huXi7vRpnOqupowBckfIKAAAAALhqq/2NeLu9GrcuzKSOwg7cc2Rw79VLVgcCQ0B5BQAAAABctZPnuhER1gYOibsONWNiLHPvFTAU3KRYVp/9bOoEAAAAAEPnsx/2TmWvnFgclFe3KK+GwnRtPP6Dg/vce7WLnD9QHOVVWT3wQOoEAAAAAEPngTu9U9krJ7Ymr26zNnBo/OrNrfiLV05HnueRZVnqOJXj/IHiWBtYVq+9NngAAAAA2LHXzr4Wr531TmUvnFhciX1TEzHfqKWOwg79yqFWLHf78eZyL3WUSnL+QHFMXpXVZz4z+Hn0aNIYAAAAAMPkM88N3qkcfeRo2iAj4MRiN25ZaJjgGSJ3H2pGRMSrb3Xi8Lx1j0Vz/kBxlFdl9cUvpk4AAAAAAJf1xrlu/MrBZuoYXIVfPtiM8bEsXn2zHb9x102p4wBclvKqrO67L3UCAAAAAHhP6xubcWqpGx+7WwEyTKZr4/GLH5iJV97qpI4C8L7ceVVWL744eAAAAACgZN5ur0Z/I49bb7B6btjcfagVr77VTh0D4H0pr8rq858fPAAAAABQMicWuxERcevCTOIkXK27bk6pPR8AACAASURBVG7Fmc7FeOf8auooAJdlbSAAAAAAlfF7f/f3UkcYCSfOrURExK0LJq+GzV2HBveUvfpWJ268czpxmmpx/kBxlFcAAAAAVMZHf+GjqSOMhDcWuzE5MRY3NZUfw+ZXtsqr/++tTvz9O29MnKZanD9QHGsDAQAAAKiMl06/FC+dfil1jMo7vrgSt9zQiLGxLHUUrlJzuha3LTTilTfde1U05w8Ux+QVAAAAAJXx2Lcfi4iIo48cTRuk4k4sduPWG6wMHFZ3HWrF995cTh2jcpw/UByTVwAAAADAjuV5Hm+c68Yt7rsaWnfd3IyT53rR7vZTRwF4T8orAAAAAGDH3r1wMbprG3HbwkzqKFyjuw61IiLi1betDgTKSXkFAAAAAOzYG4vdiAiTV0PsrkPNiIh49c1O4iQA7015BQAAAADs2Imt8sqdV8Nr/+xUHGxNx6tvmbwCymkidQAu44tfTJ0AAAAAYOh88SPeqey2E+e6MZZFHJ5XXg2zuw4145W3TF4VyfkDxVFeldV996VOAAAAADB07jvincpuO7G4Eofm6jE5YanTMLvrUCv+zd++E9219WhMek1cBOcPFMc3TFm9+OLgAQAAAGDHXjz5Yrx40juV3XRisRu3uu9q6N19cys284h///b51FEqw/kDxVGpl9XnPz/4efRo0hgAAAAAw+TzLwzeqRx95GjaIBX2xrlufOzum1LH4DrddagZERGvvtWO//DW+cRpqsH5A8VRXpXVV7+aOgEAAAAA/JTOaj/OrazFrTeYvBp2B1vTccPMZLz6pnuvgPJRXpXVnXemTgAAAAAAP+WNxW5EhLWBFZBlWdx1qBmvvNVOHQXg57jzqqyefXbwAAAAAEBJnLhUXs0kTkIR7jrUimNnzsfa+mbqKAA/RXlVVl/60uABAAAAgJI4cW4lIiJusTawEu6+uRn9jTyOnTmfOgrAT7E2EAAAAIDK+PLHvpw6QqWdWurFwsxkzEx5rVgFdx9qRUTEq2+14+6bW4nTDD/nDxTHtwwAAAAAlXHvTfemjlBpp5Z6cXi+njoGBbnlhkbMTk3EK2924tO/njrN8HP+QHGsDQQAAACgMp7/0fPx/I+eTx2jsk6d68bheSsDq2JsLItfOdSMV99qp45SCc4fKI7JKwAAAAAq4w/+7R9ERMRHf+GjiZNUz+ZmHqeWe/Gf/cqB1FEo0F2HmvG//V9vxMZmHuNjWeo4Q835A8UxeQUAAAAAXNHZCxdjbX3T2sCK+eWDzVjtb8Yb57qpowBcorwCAAAAAK7o5FIvIsLawIq548C+iIg4duZ84iQAP6a8AgAAAACu6NTSYDLnyA0mr6rkl26cjYiIH7xzIXESgB9TXgEAAAAAV3Rqa/Lq5jmTV1UyOzURN8/VTV4BpTKROgCX8dWvpk4AAAAAMHS++knvVHbLqaVe7J+djPrkeOooFOyDB2bj2BmTV9fL+QPFUV6V1Z13pk4AAAAAMHTu3O+dym45tdSNm913VUl3HNgXL/5wMTY28xgfy1LHGVrOHyiOtYFl9eyzgwcAAACAHXv2tWfj2de8U9kNp5Z6cXjefVdV9Es3zsba+ma8ca6bOspQc/5AcUxeldWXvjT4+cADaXMAAAAADJEvfWfwTuWBO71TKdLmZh5vLvXiH951IHUUdsEdB/ZFRMSxM+fj9v0zidMML+cPFEd5VVbf+EbqBAAAAAAQERHvXrgYaxubcdjawEr6pRtnIyLi+2fOx2/cdVPiNADKq/Lavz91AgAAAACIiMF9VxFhbWBFzU5NxM1z9fj+OxdSRwGICHdeldfTTw8eAAAAAEjs1FIvIiKOmLyqrA8emI1jZ5RXQDkor8pKeQUAAABASWyXVyavquuOA/vih+9eiI3NPHUUAGsDAQAAAKiOP/6nf5w6QiWdWurG/tmpmK6Np47CLvmlG2djbX0z3jjXjdv3z6SOM5ScP1Ac5RUAAAAAlXGkdSR1hEo6ea5n6qri7jiwLyIijp05r7y6Rs4fKI61gQAAAABUxtdf+Xp8/ZWvp45ROaeWusqrivvgjbMREfH9M+cTJxlezh8ojskrAAAAACrjD//mDyMi4tN3fzpxkurY3MzjzeVefOzug6mjsItmpibi5rl6fP+dC6mjDC3nDxTH5BUAAAAAcFnvnL8Y/Y3c5NUI+OCB2Th2RnkFpGfyCgAAAAAq5E//+o1C/3knFlciIuIH71wo/J9NudxxYF+8+MPF2NjMY3wsSx0HGGEmrwAAAACAy1rqrkVExHxjMnESdtsHb5yNtfXNS4UlQCrKKwAAAADgspa6/YiImGvUEidht33wwL6ICPdeAclZG1hW3/hG6gQAAAAAQ+cbn/JOpWhLK2uxb2oiauN+D77qPnjjbEREfP/M+fiNu25KnGb4OH+gOMqrstq/P3UCAAAAgKGzv+GdStGWumumrkbEzNRE3DxXj2NnTF5dC+cPFMevS5TV008PHgAAAAB27OmXno6nX3o6dYxKWer2Y37GfVej4o4Ds9YGXiPnDxRHeVVWyisAAACAq+blcbE28zza3X7MN5RXo+KDB/bFD9+9EBubeeooQ8f5A8WxNrCsjh5NnQAAAACAEXd+dT028tzawBHywRtnY219M04srsQvfGA2dRxgRO1o8irLsuNZlv2/WZa9lGXZ32z9azdkWfavsyz7/tbP+d2NCgAAAADspaWVtYgIk1cj5I4D+yIirA4EkrqatYF/P8/ze/M8/9DWn/+7iHghz/MPRsQLW3+mKE8+OXgAAAAAIJGlrvJq1PzSjYNpq++fOZ84CTDKrufOq38cEX+09dd/FBH/5PrjcMlzzw0eAAAAAEhkqduPiLA2cITMTE3EzXP1OHbG5BWQzk7vvMoj4l9lWZZHxFfzPH8qIg7kef721r9/OiIO7EZAAAAAANipP//NP08doVKWu2uxb3oiauPX8zvw7KU//es3rvufMTs1Ed89fq6Qf9b7+S//o1t29Z+/15w/UJydllf/aZ7nb2ZZdmNE/Ossy/72J//NPM/zrWLr52RZ9mhEPBoRccst1TqMAAAAACiXRq2ROkKlnOuuWRk4gm5sTsUP370Qm3keY1mWOs7QcP5AcXb0KxN5nr+59fOdiPiziPg7EXEmy7KDERFbP9+5zH/2qTzPP5Tn+Yc+8IEPFJMaAAAAAN7DV777lfjKd7+SOkZlLHf7VgaOoBv3Tcf6Zh7nLqyljjJUnD9QnCuWV1mWzWRZtm/7ryPiH0bEKxHxv0fEb2/9bb8dEf9yt0ICAAAAwE488+oz8cyrz6SOUQmbeR7LJq9G0oHmVEREnDm/mjjJcHH+QHF2sjbwQET8WTYYD52IiD/N8/zbWZZ9NyKeybLsn0fEiYj41O7FBAAAAAD2UqfXj808lFcjaP/soLxaNHkFJHLF8irP8x9FxD3v8a8vRsRHdiMUAAAAAJDWUrcfERHz1gaOnOnaeMxMTcTZCxdTRwFG1I7uvAIAAAAARstydzB1Y/JqNO2fmYzFFZNXQBrKKwAAAADg5yxtlVdzJq9G0sLsZCyavAIS2cmdV6Rw9GjqBAAAAABD5+gjR1NHqIyllX40pydiYtzvv4+ihdmp+HdvLMfa+mZMTvgM7ITzB4rj1AEAAAAAfs5Sdy3mrAwcWQszg//tz1kdCCSgvCqrJ58cPAAAAADs2JMvPhlPvuidShGWe30rA0fYwuxURESctTpwx5w/UBzlVVl95zuDBwAAAIAde+7Yc/HcsedSxxh6m3ke7V4/5urKq1G1PXm1aPJqx5w/UBx3XpXVN7+ZOgEAAAAAI2rl4npsbObRUl6NrOnaeMxMTcSiySsgAZNXAAAAAMBPaff6ERHuvBpx+2cmTV4BSSivyurxxwcPAAAAAOyx5e6gvDJ5NdoWZidNXgFJWBtYVu67AgAAALhq9Vo9dYRK2J68Ul6NtoXZqfh3byzH2vpmTE6Yg7gS5w8UR3kFAAAAQGX8xW/+ReoIldDu9aM2nkVjcjx1FBJamBmsjVxcuRgHW4qZK3H+QHHU5QAAAADAT1nu9aNVr0WWZamjkNDC7FRERCxecO8VsLeUVwAAAABUxhf+6gvxhb/6QuoYQ6/dXbMykJ+YvFJe7YTzB4qjvAIAAACgMl54/YV44fUXUscYeu1eP+bqk6ljkNh0bTxmpiZi8cLF1FGGgvMHiqO8AgAAAAAu2djM4/zqerQaJq+I2D8zafIK2HPKKwAAAADgks5qP/IIawOJiMG9VyavgL2mvAIAAAAALlnu9iMiYk55RUQszE5GZ3U91tY3U0cBRshE6gBcxsJC6gQAAAAAQ2eh4Z3K9Wr3BuWVySsiIhZmBnefLa5cjIOteuI05eb8geIor8rqm99MnQAAAABg6HzzU96pXK9L5ZU7r4jB2sCIiMULa8qrK3D+QHGsDQQAAAAALlnurkW9Nh5TE+Opo1AC+y9NXq0lTgKMEuVVWT3++OABAAAAYMcef/7xePx571SuR7vXtzKQS6Zq4zE7NRGLFy6mjlJ6zh8ojrWBZbW4mDoBAAAAwND5zqnvpI4w9Nq9fsxZGchPWJiZNHm1A84fKI7yqqyeeip1AgAAAABG0HK3H7fc0EgdgxJZmJ2KH7xzPnUMYIRYGwgAAAAARETE2vpm9Pob1gbyU/bPTkZndT3W1jdTRwFGhPKqrB59dPAAAAAAwB5Z7g1Ww1kbyE+6YWYyIiIWV9x7BewNawPL6tix1AkAAAAAhs7h5uHUEYZau9ePiIhWfTJxEspk/+xUREQsXliLg6164jTl5fyB4iivAAAAAKiMP/lnf5I6wlBrdwfl1Zy1gfyEhUuTV2uJk5Sb8weKY20gAAAAABAREcu9fmQR0VRe8ROmauMxOzURixesDQT2hvIKAAAAgMp47NuPxWPffix1jKHV7vVjdnoixsey1FEomYXZSZNXV+D8geJYGwgAAABAZbx0+qXUEYZau9e3MpD3tDAzFT9453zqGKXm/IHimLwCAAAAACIiYrnbj5byivewf3YyOqvrsba+mToKMAKUVwAAAABA5Hke7d6a8or3dMPMZERELK649wrYfcorAAAAACB6/Y3ob+Qx15hMHYUS2j87FRERixfcewXsPndeldUdd6ROAAAAADB07ljwTuVaLXf7EREmr3hPC5cmr5RXl+P8geIor8rqqadSJwAAAAAYOk894J3KtWr3lFdc3lRtPGanJmLxgrWBl+P8geJYGwgAAAAAXCqv5hrKK97bDTOTcc7kFbAHlFdl9eijgwcAAACAHXv02Ufj0We9U7kWy91+jGdZzExZ1sR7u2FmMpa6yqvLcf5AcXwTldXCQuoEAAAAAEPn2OKx1BGGVru3Fq1GLcayLHUUSmquUYvvnerHxmYe42M+Jz/L+QPFUV6V1RNPpE4AAAAAwAhZ7vXdd8X7mm9MxmYe0Vntx3xjMnUcoMKsDQQAAAAAoq284gq2CyurA4HdprwqqwcfHDwAAAAAsMs28zw6vX7MKa94H/ONwedjeaWfOAlQddYGltXiYuoEAAAAAEPn3pvuTR1hKJ1fXY/NPKLVUF5xea1GLbKIOGfy6j05f6A4yisAAAAAKuPLH/ty6ghDqd0bTNJYG8j7mRgbi2a9FsvKq/fk/IHiWBsIAAAAACNuu7yaq08mTkLZzTVqsdS1NhDYXcorAAAAACrj4W89HA9/6+HUMYbO9iSNySuu5IbGZCytmLx6L84fKI61gQAAAABUxqnOqdQRhlK714/JibGYrvldd97fXGMy2r3l2NjMY3wsSx2nVJw/UBzfRgAAAAAw4tq9fszVa5Flygje33yjFnn8eNUkwG5QXgEAAADAiFvu9q0MZEfmZwb3oi11rQ4Edo/yCgAAAABGXLvXj7mG8oorm29slVfuvQJ2kTuvyurDH06dAAAAAGDofPiwdypXa31jMy5cXDd5xY606rXIImKpa23gz3L+QHGUV2X1xBOpEwAAAAAMnSc+6p3K1eqsrkdERKs+mTgJw2B8LItWvRbL1gb+HOcPFMfaQAAAAAAYYe3eYILG5BU7NT8zGeeUV8AuUl6V1YMPDh4AAAAAduzBZx6MB5/xTuVqbJdXzbolTezMfKMWy9YG/hznDxTHN1JZufMKAAAA4KotdhdTRxg6ne3Jq2mTV+zMXGMyOr3lWN/cjIkx8xHbnD9QHOVVWX3uc6kTAAAAADAC2qv9mJoYi6naeOooDIn5xmTkEdHu9mNhdip1HKCC1OIAAAAAMMI6vb77rrgq8zODz8uS1YHALlFeldX99w8eAAAAANhFnV4/msorrsJ8YzIiIpa6a4mTAFVlbSAAAAAAlfGR2z+SOsLQaff68cF906ljMESa07UYy5RXP8v5A8VRXgEAAABQGb//934/dYShsrGZx/nVdZNXXJXxsSxa9VosWxv4U5w/UBxrAwEAAABgRF24uB55RDTrfsedqzPfmIxzKyavgN2hvAIAAACgMj7+tY/Hx7/28dQxhkanN5icaZm84irNNyZj2drAn+L8geL4lQoAAAAAKqPX76WOMFTayiuu0dxMLTqr67G+sRkT42YkIpw/UCSnCgAAAACMqO3yqjmtvOLq3NCYjIhw7xWwK5RXAAAAADCiOqv9mBjLojE5njoKQ2Zuq7xasjoQ2AXKKwAAAAAYUe1eP5r1WmRZljoKQ2a+MZjWWzJ5BewCd16V1Sc/mToBAAAAwND55B3eqVyNTq9vZSDXpFmvxXiWmbz6Cc4fKI7yqqw+97nUCQAAAACGzufu807lanRW1+PIfD11DIbQWJZFq1FTXv0E5w8Ux9pAAAAAABhBeZ5Hu9ePVt3kFddmvlGLpRXlFVA85VVZ3X//4AEAAABgx+5/+v64/+n7U8cYCitrG7GxmUdTecU1mm9MxrI7ry5x/kBxrA0sq0ceSZ0AAAAAgArr9AalgzuvuFbzM5Nx/uJ69Dc2ozZuTgIojvKqrJRXAAAAAOyi7fLK2kCu1Xxj8NlZ6q7FjfumE6cBqkQdXlZnzw4eAAAAANgF7dWtySvlFddovjEZEWF1IFA4k1dl9dBDg59HjyaNAQAAAEA1dXr9GMsi9k17Rci1mdsqr5a6a4mTAFXjmwkAAACAyvjUXZ9KHWFotHvrsW+6FmNZljoKQ2rf9ESMj2WxtKK8inD+QJGUVwAAAABUxu/++u+mjjA0Or1+NE1dcR3Gsizm6rVYsjYwIpw/UCR3XgEAAABQGd1+N7r9buoYQ6G92nffFddtfmbS2sAtzh8ojvIKAAAAgMr4xNc+EZ/42idSxxgKnV4/WsorrtN8w+TVNucPFEd5BQAAAAAjZrW/ERfXN6M5rbzi+sw3JmPl4nqsrW+mjgJUiPIKAAAAAEZMpzeYlDF5xfXa/gxtf6YAiqC8AgAAAIAR014dFA3uvOJ6tRqDz9Cy8gookPIKAAAAAEaMySuKMlefjIiIdm8tcRKgSiZSB+AyHnkkdQIAAACAofPIvY+kjjAU2lvl1b5prwe5Ps36RGQRsdw1eeX8geL4dior5RUAAADAVfPyeGc6vfWYmRyP2rjFTFyfibGxmJ2esDYwnD9QJN9OZXX27OABAAAAYMfOds/G2a53KlfS7vXdd0VhWvXapWm+Ueb8geKYvCqrhx4a/Dx6NGkMAAAAgGHy0DODdypHHzmaNkjJdVb77ruiMHP1WpzuXEwdIznnDxRHeVVWn/1s6gQAAAAAVFS7148jNzRSx6Ai5hqT8dqZ85HneWRZljoOUAHKq7J64IHUCQAAAACooP7GZnTXNqI5bfKKYrTqtehv5NFb24jGlFfOwPVz51VZvfba4AEAAACAAnW27iayNpCibH+Wlt17BRREDV5Wn/nM4Kc7rwAAAAAoUGd1PSKUVxRnrjH4LLV7/Tg0V0+cBqgC5RUAAAAAlfE7H/qd1BFKr701HdOc9mqQYpi8GnD+QHF8QwEAAABQGZ+++9OpI5SetYEUbWZqIsbHsmh311JHScr5A8Vx5xUAAAAAlXGyfTJOtk+mjlFq7dV+TE2MxVRtPHUUKmIsy6JVr4385JXzB4pj8goAAACAyvitP/utiIg4+sjRtEFKrNPrR9PUFQVr1WvR7o52eeX8geKYvAIAAACAEdLu9a0MpHBzJq+AAimvAAAAAGCEdHr9aE0rryjWXKMW51f7sbGZp44CVIDyCgAAAABGxMZmHudX16NZd5sIxWrVJ2Mzjzi/avoKuH7KKwAAAAAYERcurkce4c4rCjfXGHym2lYHAgXwKxZl9dnPpk4AAAAAMHQ++2HvVN7PdrHgziuKtv2ZWu7149bEWVJx/kBxlFdl9cADqRMAAAAADJ0H7vRO5f10tsqrpjuvKNh2edXuju7klfMHimNtYFm99trgAQAAAGDHXjv7Wrx21juVy9mevLI2kKJN18ZjujYWyyO8NtD5A8UxeVVWn/nM4OfRo0ljAAAAAAyTzzw3eKdy9JGjaYOUVGe1HxNjWcxMjqeOQgXN1Sej3V1LHSMZ5w8UR3lVVl/8YuoEAAAAAFRMp9ePfdMTkWVZ6ihUUKteuzTdB3A9lFdldd99qRMAAAAAUDGd1XUrA9k1rUYtTi51U8cAKsCdV2X14ouDBwAAAAAK0un1ozmtvGJ3zNVr0V3biLX1zdRRgCFn8qqsPv/5wU93XgEAAABQgDzPo7Paj1+uN1NHoaJaW1N97V4/PrBvKnEaYJgprwAAAACojN/7u7+XOkJprfY3o7+RR3PaK0F2x1xjMiJGt7xy/kBxfFMBAAAAUBkf/YWPpo5QWu3VfkSEO6/YNduTV8vdtcRJ0nD+QHHceQUAAABAZbx0+qV46fRLqWOUUqe3VV6584pd0qxPRBaDyatR5PyB4pi8AgAAAKAyHvv2YxERcfSRo2mDlNCl8srkFbtkYmwsZqcnYnlEyyvnDxTH5BUAAAAAjIDO9tpAd16xi+bqtWh3R7O8AoqjvAIAAACAEdDprUdjcjwmxr0SZPe0GpMjO3kFFMc3FQAAAACMgM5qP1pWBrLL5uq1aPfWIs/z1FGAIaa8AgAAAIAR0On1ozmtvGJ3teq16G/k0VvbSB0FGGIW3JbVF7+YOgEAAADA0PniR7xTuZz26nrcPF9PHYOK257uW+71ozE1Wq+fnT9QnNE6PYbJffelTgAAAAAwdO474p3Ke1nf3IyVi+smr9h1c43BZ6zd68ehudEqS50/UBxrA8vqxRcHDwAAAAA79uLJF+PFk96p/Kzzq+sREdF05xW77NLkVXctcZK95/yB4pi8KqvPf37w8+jRpDEAAAAAhsnnXxi8Uzn6yNG0QUqm0+tHRJi8YtfNTE3ExFgW7a3P3Chx/kBxlFdl9dWvpk4AAAAAQEV0Lk1eeR3I7hrLsmjWa7E8guUVUBzfVmV1552pEwAAAABQEduTVy2TV+yBuXot2l3lFXDt3HlVVs8+O3gAAAAA4Dp1ev2YGMuiPjmeOgojYK5h8gq4Pjsur7IsG8+y7P/Jsuy5rT/fnmXZX2dZ9oMsy76eZdnk7sUcQV/60uABAAAAgOvUXu1Hs16LLMtSR2EEtOq16PT6sbGZp44CDKmrWRv4X0XEv4+I5taf//uI+B/yPP8XWZb9zxHxzyPiDwvOBwAAAAA79uWPfTl1hFLq9NajOe0GEfbGXH0y8og4v9qPucbozDw4f6A4O5q8yrLscET85xHxv2z9OYuIfxAR39j6W/4oIv7JbgQEAAAAgJ2696Z7496b7k0do3Q6W5NXsBdajcFnrT1iqwOdP1Ccna4N/HJE/DcRsbn154WIWM7zfH3rz6ci4uaCswEAAADAVXn+R8/H8z96PnWMUsnzPDq9fjSnlVfsjdZWUTpq9145f6A4V5wVzrLskxHxTp7n/3eWZfdf7X9BlmWPRsSjERG33HLLVQcEAAAAgJ36g3/7BxER8dFf+GjiJOXR62/E+mZu8oo9s11edUasvHL+QHF2Mnn1n0TEP8qy7HhE/IsYrAv8HyNiLsuy7fLrcES8+V7/4TzPn8rz/EN5nn/oAx/4QAGRAQAAAICd6vQGy5PcecVema6Nx9TE2MitDQSKc8XyKs/zx/M8P5zn+W0R8V9ExL/J8/w3I+IvI+Khrb/ttyPiX+5aSgAAAADgmnRWBwVCy+QVe6hZrymvgGu20zuv3st/GxH/dZZlP4jBHVj/azGRAAAAAICibK9uc+cVe6lVr43c2kCgOFc1K5zn+dGIOLr11z+KiL9TfCQAAAAAoCjtrcmrfXVrA9k7relafL+zmjoGMKR8Y5XVV7+aOgEAAADA0PnqJ71T+Vmd3nrMTI7HxNj1LGGCq9Nq1OL86npsbOYxPpaljrMnnD9QHOVVWd15Z+oEAAAAAEPnzv3eqfysTq8fTfddscda07XII+L8aj/mGpOp4+wJ5w8Ux69blNWzzw4eAAAAAHbs2deejWdf807lJ3VW++67Ys9tF6ajdO+V8weKY/KqrL70pcHPBx5ImwMAAABgiHzpO4N3Kg/c6Z3Ktk6vH4fnG6ljMGJaW+VVe3U9cZK94/yB4iivyuob30idAAAAAIAht76xGStrG9Gsew3I3rpUXo3Q5BVQHN9aZbV/f+oEAAAAAAy581tTLy1rA9lj07WxqI1nI7U2ECiOO6/K6umnBw8AAAAAXKPO6qA42L5/CPZKlmXRqtdMXgHXRHlVVsorAAAAAK7TdnHQNHlFAsor4FpZGwgAAABAZfzxP/3j1BFKpbO1NtCdV6TQqtfih++upI6xZ5w/UBzfWgAAAABUxpHWkdQRSqXT68fEWBb12njqKIygZr0W51f7sZnnMZZlqePsOucPFMfaQAAAAAAq4+uvfD2+/srXU8cojc5qP5r1WmQjUBxQPq16LTbziAtbE4BV5/yB4pi8AgAAAKAy/vBv/jAiIj5996cTJymHTq/vviuSaW199tq9Xv6ApwAAIABJREFUQYladc4fKI7JKwAAAACoqM7quvuuSGa7sGr3+omTAMNGeQUAAAAAFZTneXR6/UvTL7DXWsor4BoprwAAAACggnprG7G+mY/EujbKqTE5HhNjWXSUV8BVUl4BAAAAQAW1VweFgfKKVLIsi1a9dumzCLBTFt6W1Te+kToBAAAAwND5xqe8U9nW6a1HRERz2itA0mnWayOzNtD5A8XxzVVW+/enTgAAAAAwdPY3vFPZ1jF5RQm06rU4sbiSOsaecP5AcawNLKunnx48AAAAAOzY0y89HU+/9HTqGKWwfc/QPpNXJNSq16LTW4/NPE8dZdc5f6A4yquyUl4BAAAAXDUvj3+ss9qPmamJmBjzCpB0mvVabOR5rFxcTx1l1zl/oDh+7aKsjh5NnQAAAACAIdbprUfL1BWJtaYHayvbvX7sm7bCEtgZv3YBAAAAABXUWe2774rkWlufwe01lgA7obwqqyefHDwAAAAAcA3avX40TbqQWLM+mP5rK6+Aq6C8Kqvnnhs8AAAAAHCV1jc2o7u2cak4gFRmpiZifCyLdq/6d14BxfHtBQAAAEBl/Plv/nnqCKXQWR0UBSavSG0sy6I5PRGd1epPXjl/oDjKKwAAAAAqo1FrpI5QCtv3C7nzijJo1WsjsTbQ+QPFsTYQAAAAgMr4yne/El/57ldSx0hue8pFeUUZNEekvHL+QHGUVwAAAABUxjOvPhPPvPpM6hjJbU9etawNpARa9Vp0ev3I8zx1lF3l/IHiKK8AAAAAoGI6q+tRG89iuub1H+m16rVY38xjZW0jdRRgSPj2AgAAAICK6az2Y990LbIsSx0Fork1AdgZgdWBQDGUVwAAAABQMZ1e/1JhAKnNNQafxVG49woohvIKAAAAACqms7oezfpE6hgQERHNuvIKuDq+wcrq6NHUCQAAAACGztFHjqaOkFye59Hp9aN1sJk6CkRExOzURIxl1V8b6PyB4pi8AgAAAIAK6a1txPpmfmnaBVIby7JoTtdMXgE7prwqqyefHDwAAAAA7NiTLz4ZT7442u9U2quDgkB5RZk069Uvr5w/UBzlVVl95zuDBwAAAIAde+7Yc/HcsedSx0iq01uPiIjmtBtDKI/WCJRXzh8ojm+wsvrmN1MnAAAAAGAIdUxeUUKtei3+9nQn8jyPLMtSxwFKzuQVAAAAAFRIZ2u6ZZ/JK0qkWa9FfyOPXn8jdRRgCCivyurxxwcPAAAAAFyFzmo/ZqYmYmLMqz/Ko7U1CVj11YFAMfz6RVm57woAAADgqtVr9dQRkuv01qNl6oqS2S6vOr1+HGxV8/+nzh8ojm8xAAAAACrjL37zL1JHSK6z2r9UFEBZbH8mlys8eeX8geKYHQYAAACACun0+tGcVl5RLrNTE5HFj+9kA3g/yisAAAAAKuMLf/WF+MJffSF1jGQurm/EytpGNOsWLlEu42NZ7JueqPSdV6N+/kCRlFcAAAAAVMYLr78QL7z+QuoYybzTuRgRYfKKUmrVa9HpraeOsWtG/fyBIimvAAAAAKAiznRWIyKi6c4rSqhZr1V68goojvIKAAAAACritPKKEmttlVd5nqeOApSc8goAAAAAKuJ0e6u8mnbnFeXTqtdibWMzLq5vpo4ClJxvsbJaWEidAAAAAGDoLDRG+53Kmc5qTIxlUa+Np44CP2d7IrDd68d0BT+jo37+QJGUV2X1zW+mTgAAAAAwdL75qdF+p3K6czGa9VpkWZY6Cvyc1vSgvOr0+nGgOZ04TfFG/fyBIlkbCAAAAAAVcaa9Gs1p911RTq2fmLwCeD/Kq7J6/PHBAwAAAMCOPf784/H486P7TuV0ZzWadcuWKKd9W5/N9mo1y6tRP3+gSL7JympxMXUCAAAAgKHznVPfSR0hmTzP43RnNW69oZE6CrynibGxmJ2aiE5FJ69G+fyBoimvyuqpp1InAAAAAGCILHf7sba+Gc26tYGUV6teszYQuCJrAwEAAACgAk53ViMilFeUWrNei05vPXUMoOSUV2X16KODBwAAAAB24Mx2eTVt2RLl1ZyeMHkFXJFvsrI6dix1AgAAAIChc7h5OHWEZM6YvGIItOq16PU3Ym19M3WUwo3y+QNFU14BAAAAUBl/8s/+JHWEZE63L0ZExD6TV5RYa6tc7VRw+mqUzx8omrWBAAAAAFABpzursX92MibGvPKjvLYnA9ur1SuvgOL4JgMAAACgMh779mPx2LcfSx0jiTOd1TjQnE4dA97X9uRVFe+9GuXzB4pmhhgAAACAynjp9EupIyRzur0aB1vKK8qtOV3dtYGjfP5A0UxeAQAAAEAFnOmsxgHlFSU3OTEW9dp4JSevgOIorwAAAABgyF1c34jFlbW4ydpAhkCrXlNeAe9LeQUAAAAAQ+6dzsWIiDjQnEqcBK6sVa9Vcm0gUBx3XpXVHXekTgAAAAAwdO5YGM13Kmc6qxERcaA5HW8tryZOA++vWa/FqaVu6hiFG9XzB3aD8qqsnnoqdQIAAACAofPUA6P5TuX0Vnl1U0t5Rfm16hOxsrYRq/2NmK6Np45TmFE9f2A3WBsIAAAAAEPudHurvHLnFUOgVa9FxI/XXQL8LOVVWT366OABAAAAYMceffbRePTZ0Xun8s75izE1MXapFIAya259TrcnBqtiVM8f2A3WBpbVwkLqBAAAAABD59jisdQRkjjdXo2bWtORZVnqKHBFrelBefV2u5c4SbFG9fyB3aC8KqsnnkidAAAAAIAhcbqzGgesDGRIbE8Ibq+7BPhZ1gYCAAAAwJA701l13xVDY6o2HlMTY/G28gq4DOVVWT344OABAAAAgPeR5/mltYEwLFr1mskr4LKsDSyrxcXUCQAAAACGzr033Zs6wp5r9/pxcX3T2kCGSqtei7c71SqvRvH8gd2ivAIAAACgMr78sS+njrDnTm8VANYGMkya07U4tdxNHaNQo3j+wG6xNhAAAAAAhtj26rWbWlOJk8DONeu1eOf8xehvbKaOApSQ8goAAACAynj4Ww/Hw996OHWMPfXj8ur/Z+9uY+w8zzuxX8+8n5nhvHCG5Aw5EiVRllLb3XUa50XKdldYO7uxYWFfbNhokyBEF5CRFCiEtYuujAT94MDeAnKbfqhdC9hCaeLtWpCTZiUkRtba0NmsZDdOoqb2xpIt2ZSGnOHLaOYMOXPOvD79cEaK44jikDxn7ud5zu8HPDgSOXPO/wN5DXBfvO6rljgJ7N94rT/yPOLSlY3UUdqmG+sPdIprAwEAAACojPnV+dQRDtziajOyLOLoIZNXlMd4rXU0vVBvxvGJajReu7H+QKeYvAIAAACAEruw2oypkcHo73XUR3mM1foj4q8mBwF+kJ9oAAAAAFBii/WmfVeUzvhe82qh3kicBCgizSsAAAAAKLGFejNmxoZSx4AbUuvvjaH+HpNXwJuy86qo7rsvdQIAAACA0rlvrvvOVC6sNuPdd0ymjgE3JMuymB2vxcJqdZpX3Vh/oFM0r4rq059OnQAAAACgdD793u46U2lu7cTy+pbJK0ppZmyoUpNX3VZ/oJNcGwgAAAAAJXVxdSMiIo5pXlFCs+PVal4B7aN5VVQf/GDrAQAAAGDfPvjEB+ODT3TPmcri3pVrM+OaV5TPzPhQXFhtxs5unjpKW3Rb/YFOcm1gUdl5BQAAAHDDltaXUkc4UAv1RkSEawMppdnxodjezWPp6kYcrcCf4W6rP9BJmldF9fGPp04AAAAAQMFdMHlFic2M1yKiNUFYheYV0D6uDQQAAACAklqsb8TIQG8cGupPHQVu2Oxe03XB3ivgh2heFdUDD7QeAAAAALiGC6vNOGbqipJ6fWJwUfMK+CGuDQQAAACgMt5z53tSRzhQC/WGfVeU1uHhgRjo7anM5FW31R/oJM0rAAAAACrjV//er6aOcKAurG7ET955OHUMuCk9PVkcGx+MxXojdZS26Lb6A53k2kAAAAAAKKHd3TwurDbfuHoNymhmbKgyk1dA+2heAQAAAFAZ7/vC++J9X3hf6hgHYmltM7Z3c80rSm1mvBaLq9VoXnVT/YFO07wCAAAAoDIaW41obFXjCrLrWdybVjlm5xUlNjvemrzK8zx1lFvWTfUHOk3zCgAAAABK6PVplRnNK0psdnwoNrd3Y2ltM3UUoEA0rwAAAACghN5oXrk2kBKbHa9FRMTCSjWuDgTaQ/MKAAAAAEroQr0ZvT1ZTI8Opo4CN+34RKv5er7uuj3gr/SlDsA1fOADqRMAAAAAlM4H7umeM5XF1WYcPTQYvT1Z6ihw0/5q8qr8zatuqj/QaZpXRfXxj6dOAAAAAFA6H7+/e85UFuvNOGbfFSU3NTIQA709sVAv/7WB3VR/oNNcGwgAAAAAJbS42owZzStKrqcni5nxoThfgeYV0D6aV0X1wAOtBwAAAIB9e+DxB+KBxx9IHeNAXKg3Y2Zc84rymx0fisUK7LzqpvoDnebawKI6fTp1AgAAAAAK6urGdlzZ2Na8ohKOT9Ti//nea6ljAAWieVVUmlcAAAAAXMPi3hVrrg2kCmbHh+LCajN2dvPo7clSxwEKwLWBRXX5cusBAAAAgB9yYbXVvDqmeUUFzE7UYns3j8tXN1JHAQpC86qoPvSh1gMAAAAAP+SNySvXBlIBx/f+HJ9fKf/eK6A9XBsIAAAAQGV8+B0fTh3hQCyuujaQ6pgdr0VExEK9GT+aOMut6Jb6AwdB8woAAACAyvjlH//l1BEOxIXVZozX+qM20Js6Ctyy4xPVmLzqlvoDB8G1gQAAAABUxvrWeqxvraeO0XEL9aapKypjvNYftf7eWNi7DrOsuqX+wEEweQUAAABAZbz/C++PiIgzp8+kDdJhF1abccy+Kyoiy7KYnRiKhXq5J6+6pf7AQTB5BQAAAAAls1hvxszYYOoY0DbHx2txfqXck1dA+2heAQAAAECJbO3sxqWrGzEzXksdBdpmdrz8k1dA+2heAQAAAECJXLqyEXkedl5RKbMTtbh4ZSO2dnZTRwEKQPMKAAAAAEpkcbV1tdrMuGsDqY7Z8aHI89Y+N4C+1AG4htOnUycAAAAAKJ3T7zqdOkLHXai3DvePmbyiQmbHW3+eF+rNmJscTpzm5nRD/YGDonlVVJpXAAAAADesGw6P35i80ryiQo5PtHa4nV8p796rbqg/cFBcG1hUly+3HgAAAAD27fL65bi8Xu0zlcV6MwZ6e+LwyEDqKNA2Pzh5VVbdUH/goJi8KqoPfaj1euZM0hgAAAAAZfKhJ1pnKmdOn0kbpIMWV5txbHwwsixLHQXa5tBQfxwa7IuFEk9edUP9gYOieVVUH/tY6gQAAAAAFNBivenKQCppdmIozpd48gpoH82ronrwwdQJAAAAACigC6vNeOeJ8dQxoO1mx2uxUC/v5BXQPnZeFdULL7QeAAAAANiT53ksrpq8opqOTwzFworJK8DkVXF99KOtVzuvAAAAANhTb2xFc2s3ZsY1r6ie2fFaLK1tRnNrJ4b6e1PHARK6bvMqy7KhiPijiBjc+/on8zz/H7MsuzMi/k1ETEXEn0bEL+R5vtnJsAAAAADwVn7p3b+UOkJHLa62plI0r6ii2b0/14v1ZtwxPZI4zY2rev2Bg7SfyauNiPj7eZ5fzbKsPyL+OMuy34+Ifx4R/0ue5/8my7L/PSL+WUR8roNZAQAAAOAtfeSdH0kdoaMW63vNK9cGUkHHJ2oREXG+3ihl86rq9QcO0nV3XuUtV/f+t3/vySPi70fEk3u//hsR8Y87khAAAAAA9unV+qvxav3V1DE65sLe5NUxzSsq6PXJq7Luvap6/YGDtK+dV1mW9UbrasC7I+J/i4iXImIlz/PtvS+Zj4gTHUkIAAAAAPv0C7/zCxERceb0mbRBOmShrnlFdc2OtyavFuqNxEluTtXrDxyk605eRUTkeb6T5/m7ImIuIn4iIn5kvx+QZdlDWZZ9I8uyb1y6dOkmYwIAAAAAi/VmTI8OxkDfvo71oFRqA70xOdwf5+vlnLwC2ueGfsrleb4SEX8YEfdFxESWZa9Pbs1FxLlrfM9jeZ6/O8/zdx85cuSWwgIAAABAN1uoN9+4Wg2qaHa89sZuN6B7Xbd5lWXZkSzLJvb+uxYRPxMRfxmtJtaH9r7sFyPidzsVEgAAAABoTV7NaF5RYccnhuL8SjmvDQTaZz+TV7MR8YdZlv1FRPxJRPy7PM+fjoj/ISL+eZZl342IqYj4V52LCQAAAAAsrpq8otpmx2tv7HYDulff9b4gz/O/iIgffZNffzla+6/ohI99LHUCAAAAgNL52H3VPVNZ39yOemPL5BWVNjsxFPXGVqxvbsfwwHWPrwulyvUHDlq5/vZ3kwcfTJ0AAAAAoHQevLe6Zyqv7wEyeUWVHR+vRUTE+ZVm3H10NHGaG1Pl+gMHbT/XBpLCCy+0HgAAAAD27YXLL8QLl6t5pvJ682pmrJY4CXTO683ZhXr59l5Vuf7AQTN5VVQf/Wjr9cyZpDEAAAAAyuSjT7fOVM6cPpM2SAe8vgfItYFU2fGJVnN2YaV8e6+qXH/goGleFdWnPpU6AQAAAAAFsrj6+uSV5hXVdWxsKLIs4nwJJ6+A9tG8Kqr770+dAAAAAIACWag3YmK4P2oDvamjQMcM9PXE9OhgKSevgPax86qonn229QAAAABAtHZembqiGxwfHzJ5BV3O5FVRfeITrVc7rwAAAACI1s6rWfuu6AKz47X47qWrqWMACWleAQAAAFAZv/J3fyV1hI5ZrDfjb81NpI4BHTc7MRT/4TuXIs/zyLIsdZx9q3L9gYOmeQUAAABAZbz3rvemjtARG9s7sbS2afKKrnB8vBZrmzux2tyO8Vp/6jj7VtX6AynYeQUAAABAZTy/+Hw8v/h86hhtd3F1IyIiZjSv6AKzE60/5wsl23tV1foDKZi8AgAAAKAyHv7ywxERceb0mbRB2myh3oyIMHlFV5gdr0VExPmVRvzIzFjiNPtX1foDKZi8AgAAAICCe30CZWZM84rqm5tsNa/OLZdr8gpoH80rAAAAACi4xb3JK9cG0g2OjA7GQG9PzK9oXkG30rwCAAAAgIJbqDdjdLAvDg31p44CHdfTk8XxiSGTV9DFNK8AAAAAoOAW601TV3SVucnhmNe8gq7VlzoA1/CpT6VOAAAAAFA6n3pPNc9UFlabMat5RRc5MVGLf//CxdQxbkhV6w+koHlVVPffnzoBAAAAQOncf1s1z1QW64245+iR1DHgwJyYrMWlKxvR3NqJof7e1HH2par1B1JwbWBRPfts6wEAAABg35599dl49tVqnals7+zGpSsbJq/oKnOTtYiIOL9SnqsDq1h/IBWTV0X1iU+0Xs+cSRoDAAAAoEw+8UzrTOXM6TNpg7TRpasbsZtHzIzXUkeBA3NiovXn/dxKI+46Mpo4zf5Usf5AKppXRfX5z6dOAAAAAEABLNSbEREmr+gqJ/Ymr84tl2fyCmgfzauiuvfe1AkAAAAAKIDFvebVsTHNK7rHzNhQ9PZkMa95BV3Jzquieuqp1gMAAABAVzN5RTfq6+2JmbGhOFeinVdA+5i8KqrPfKb1+uCDaXMAAAAAkNRivRGDfT0xMdyfOgocqLnJWswvr6eOASSgeQUAAABAZfz6z/566ghtt1Bvxuz4UGRZljoKHKgTk7X42ktLqWPsWxXrD6SieQUAAABAZbxr5l2pI7TdYr0ZM64MpAvNTdRicbUZWzu70d9b/A04Vaw/kErx/8YDAAAAwD595eWvxFde/krqGG3VmryqpY4BB25ucjh281YDtwyqWH8gFZNXAAAAAFTGr/3Rr0VExHvvem/iJO2xu5vHhVWTV3SnE5Otpu38ciNuOzycOM31Va3+QEomrwAAAACgoJbWNmN7N49ZzSu60ImJVvPq3EojcRLgoGleAQAAAEBBvX5d2syY5hXdZ3ZiKLIsYn55PXUU4IBpXgEAAABAQS3UWxMnrg2kGw329cbRQ4NxbtnkFXQbzSsAAAAAKKjF1b3JK80rutTc5LBrA6EL9aUOwDV8/vOpEwAAAACUzuc/UK0zlYV6M/p6spgeGUwdBZI4MVGL519dSR1jX6pWfyAlzauiuvfe1AkAAAAASufe6WqdqSzWm3FsbCh6erLUUSCJE5O1+P1vLsTObh69Bf97ULX6Aym5NrConnqq9QAAAACwb0+98FQ89UJ1zlQW6o2YdWUgXWxushZbO3lcvNJMHeW6qlZ/ICWTV0X1mc+0Xh98MG0OAAAAgBL5zHOtM5UH763GmcpivRnvPDGeOgYkc2KiFhER55YbMTteS5zmrVWt/kBKmldF9eSTqRMAAAAAkFCe57FQb8bPvP1Y6iiQzNzkXvNqpRHvTpwFODiaV0U1PZ06AQAAAAAJ1RtbsbG9GzMFnzaBTjoxMRwREfPLjcRJgINk51VRPf546wEAAACgKy3UWzt+7Lyim9UGemNqZEDzCrqM5lVRaV4BAAAAdLXFvebVsTHNK7rbiclanFvRvIJu4tpAAAAAACrjN//Jb6aO0DYmr6BlbrIW3168kjrGdVWp/kBqmlcAAAAAVMZt47eljtA2i/VG9GQRRw4Npo4CSZ2YqMW///bFyPM8sixLHeeaqlR/IDXXBgIAAABQGV/85hfji9/8YuoYbbFQb8aRQ4PR3+sIj+42Nzkcza3dWFrbTB3lLVWp/kBqJq8AAAAAqIzPfeNzERHxkXd+JHGSW7e42oyZ8VrqGJDciYnW34P55UZMjxZ3ErFK9QdS8882AAAAAKCAzq004rh9VxAnJlvNq3PLjcRJgIOieQUAAAAABZPneSysNGPW5BX8VfNqZT1xEuCgaF4BAAAAQMHUG1vR2NqJ4xMmr2BsqD/Ghvpi3uQVdA3NKwAAAAAomPMrzYiIOD5h8goiIk5MDrs2ELpIX+oAXMOTT6ZOAAAAAFA6T364Gmcq51dah/Szdl5BRETMTdbilaViXxtYlfoDRaB5VVTT06kTAAAAAJTO9HA1zlQW6q3mlckraDkxUYvnXlqKPM8jy7LUcd5UVeoPFIFrA4vq8cdbDwAAAAD79vjzj8fjzz+eOsYtO19vRn9vFkdGB1NHgUKYm6zF1Y3tWG1sp45yTVWpP1AEmldFpXkFAAAAcMOqcni8sNKIY2ND0dNTzAkTOGhzk60pxFeXi3t1YFXqDxSBawOL6syZ1AkAAAAASOT8SjOOj7syEF53YmI4IiLOrTTinSfGE6cBOs3kFQAAAAAUzPl6I2YnhlLHgMJ4ffLq3HIjcRLgIGheFdWjj7YeAAAAALrK7m4eF1abcXzC5BW8bmK4P4YHemNe8wq6guZVUT39dOsBAAAAoKtcvroRWzt5HB83eQWvy7Isbj88HK+8VtydV0D72HkFAAAAQGX83s/9XuoIt+zcSmuyZNbOK/hrbj88HN9fWksd45qqUH+gKExeAQAAAFAZw/3DMdw/nDrGLVmoNyMi7LyCH3JyajjOLq3H7m6eOsqbqkL9gaLQvAIAAACgMj77J5+Nz/7JZ1PHuCXn9yavTth5BX/N7VMjsbG9GxevbKSO8qaqUH+gKDSvAAAAAKiMJ771RDzxrSdSx7glC/Vm1Pp7Y7zWnzoKFModU62pprMFvTqwCvUHikLzCgAAAAAK5PxKI2YnhiLLstRRoFBOHh6JiIizr60nTgJ0muYVAAAAABTI+XrTlYHwJo5PDEVfT1bYySugfTSvAAAAAKBAFlYaMTs+lDoGFE5fb0+cmKzF2SWTV1B1mlcAAAAAUBCb27tx6epGzI6bvII3c/vh4XjFtYFQeX2pA3ANZ86kTgAAAABQOmdOn0kd4ZZcWG1GnreuRwP+pjumRuJ3nz+XOsabKnv9gSIxeQUAAAAABXF+pREREcftvII3dXJqOFab27Gyvpk6CtBBmldF9eijrQcAAACAfXv02Ufj0WfLe6ayUG9GRLg2EK7h9sPDERGF3HtV9voDRaJ5VVTPPdd6AAAAANi3p198Op5+8enUMW7a+frrk1euDYQ3c3JqJCIizhZw71XZ6w8UiZ1XRfWlL6VOAAAAAMABO7/SiPFafwwPOLaDN/PG5NXltcRJgE4yeQUAAAAABbGw0rTvCt5CbaA3jo0NFnLyCmgfzauieuSR1gMAAABA1zhfb8bxcVcGwls5eXgkXingziugfcwfF5V9VwAAAAA3rNZf7qmlhXojfuzkROoYUGi3Tw3Hf/jOpdQx/oay1x8oEs0rAAAAACrj93/u91NHuGnrm9uxsr4Vs+MOwOGt3DE1HE/+6UY0NneiNtCbOs4bylx/oGhcGwgAAAAABXB+pRkRESfsvIK3dPvUSEREvGLvFVSW5hUAAAAAlfHJr34yPvnVT6aOcVMW6o2IiJi18wre0snDwxERcXZpLXGSv67M9QeKRvMKAAAAgMp45nvPxDPfeyZ1jJuysDd5ddzkFbylk1Ot5lXRJq/KXH+gaDSvAAAAAKAAzq00Issijo2ZvIK3MjE8EOO1/vh+wSavgPbRvAIAAACAAlioN+LI6GAM9Dmyg+s5OTUcZ5eKNXkFtI+fhAAAAABQAAv1Zsy6MhD25fbDw4W7NhBon77UAbiGqanUCQAAAABKZ2q4vGcq51cacc+xQ6ljQCmcnBqOL39zMbZ2dqO/txgzGmWuP1A0mldF9aUvpU4AAAAAUDpf+nA5z1TyPI/zK8144N6jqaNAKZw8PBLbu3mcX2nEyamR1HEiorz1B4qoGC1pAAAAAOhi9cZWNLZ2YnZ8KHUUKIWTU8MREfZeQUVpXhXVI4+0HgAAAAD27ZGvPBKPfKV8ZyrnV5oREXHczivYl9enrc4WaO9VWesPFJFrA4tqaSl1AgAAAIDSeW7+udQRbspCvRERYfIK9unoocEY7OuJV5bWUkd5Q1nrDxSR5lVRPfZY6gQAAAAAHJDzK62fFMBhAAAgAElEQVTm1QmTV7AvPT1Z3H54OL7v2kCoJNcGAgAAAEBi5+vN6O/NYnp0MHUUKI2TUyPxiuYVVJLmVVE99FDrAQAAAKDyFlYacWxsKHp6stRRoDROTg3H2dfWIs/z1FGANnNtYFG9+GLqBAAAAAClMzc2lzrCTTlfb8bxcVcGwo04OTUcza3duHhlI46Npd8XV9b6A0WkeQUAAABAZfzWP/2t1BFuyvmVRrz75GTqGFAqtx8ejoiIs0vrhWhelbX+QBG5NhAAAAAAEtrdzePCajNmJ0xewY24Y2okIiLOLq0lTgK0m+YVAAAAAJXx8Jcfjoe//HDqGDfk0tWN2NrJ47jmFdyQE5O16O3J4pXX1lNHiYhy1h8oKtcGAgAAAFAZzy8+nzrCDZtfbh283zapeQU3or+3J45PDMX3l4rRvCpj/YGiMnkFAAAAAAnNLzciImJO8wpu2MnDI/GKawOhcjSvAAAAACCh15tXJyaGEyeB8jk5NRzfu7wWeZ6njgK0keYVAAAAACQ0v7we06MDURvoTR0FSufUkdFYbW7H0tpm6ihAG9l5VVT33JM6AQAAAEDp3DNVvjOV+eVGnJg0dQU349TR0YiI+O7FqzE9Opg0SxnrDxSV5lVRPfZY6gQAAAAApfPYg+U7U5lfbsTbj4+ljgGldPde8+qlS1fjp+6aSpqljPUHisq1gQAAAACQyO5uHudWGjE3WUsdBUppdmwoav298d2LV1NHAdpI86qoHnqo9QAAAACwbw899VA89FR5zlQuX92Ize3dmHNtINyUnp4sTh0dKUTzqmz1B4rMtYFFNZV2xBUAAACgjF5cejF1hBvy6nIjIiLmJkxewc06dWQ0vvH95dQxSld/oMg0r4rq059OnQAAAACADptfXo+IcG0g3IK7j4zG7z5/PtY2tmNk0JE3VIFrAwEAAAAgkfm9yasTmldw0+4+OhoREd+7vJY4CdAumldF9cEPth4AAAAAKmt+uRFTIwMxPGBaBG7Wqb3mVRH2XgHt4adiUS0tpU4AAAAAUDrvmnlX6gg3ZH553ZWBcItOTg1Hb08WL11K27wqW/2BItO8AgAAAKAyfv1nfz11hBtybqUR/9nMWOoYUGqDfb1x++Hh5JNXZas/UGSuDQQAAACABPI8j3PLDZNX0Aanjowmn7wC2kfzCgAAAIDK+Pnf/vn4+d/++dQx9uXS1Y3Y2N6NE5pXcMtOHR2J711ei+2d3WQZylR/oOhcGwgAAABAZcyvzqeOsG/zy42ICJNX0AZ3HxmNrZ08Xl1uxJ3TI0kylKn+QNGZvAIAAACABP6qeTWcOAmU36mjoxERyfdeAe2heQUAAAAACcwvr0dExIkJk1dwq04d0byCKtG8AgAAAIAEzi034vDIQIwM2uwBt2q81h9HDg3GS5c0r6AK/GQsqvvuS50AAAAAoHTumyvPmcr8csO+K2iju4+MJp28KlP9gaLTvCqqT386dQIAAACA0vn0e8tzpjK/vB73zhxKHQMq4+6jo/F/P38u8jyPLMsO/PPLVH+g6FwbCAAAAAAHLM/zmF9u2HcFbXTqyEhcaW7HpSsbqaMAt0jzqqg++MHWAwAAAMC+ffCJD8YHnyj+mcrlq5uxsb0bc5PDqaNAZdx9tDXJ+N1Ee6/KUn+gDFwbWFR2XgEAAADcsKX1pdQR9mV+eT0iws4raKNTR0ciIuKli1fj/lPTB/75Zak/UAaaV0X18Y+nTgAAAABAh8wvNyIiTF5BG82MDcXIQG+8dGktdRTgFrk2EAAAAAAO2LmVVvPqhMkraJssy+LU0dH47sU01wYC7aN5VVQPPNB6AAAAAKic+eX1mBzuj9FBFyNBO919ZDReSrTzCmgfPx0BAAAAqIz33Pme1BH2ZX654cpA6IBTR0fjt//8XFzd2D7w5nBZ6g+UgeYVAAAAAJXxq3/vV1NH2Jf55UbcfWQ0dQyonFN7f69eung1/vZtEwf62WWpP1AG121eZVl2W0T8nxFxLCLyiHgsz/P/NcuywxHxxYi4IyK+HxEfzvN8uXNRAQAAACCNf/31V9r2Xnmex9mltZgZG2rr+wIRdx8diYiIly4dfPMKaJ/97LzajoiP5Xn+9oj4qYj4b7Mse3tE/IuIeCbP87dFxDN7/w8AAAAAybzvC++L933hfaljvKW1zZ3Y2sljYrg/dRSonJNTI9HXk8V3Lx783qsy1B8oi+s2r/I8X8jz/M/2/vtKRPxlRJyIiH8UEb+x92W/ERH/uFMhAQAAAGA/GluNaGw1Usd4SyvrmxERMTk8kDgJVE9/b0+cnBqOly4dfPOqDPUHymI/k1dvyLLsjoj40Yj4ekQcy/N8Ye+3FqN1rSAAAAAA8BaW17ciQvMKOuXUkdEkk1dA++y7eZVl2WhEfCkiHs7zfPUHfy/P8zxa+7De7PseyrLsG1mWfePSpUu3FBYAAAAAym55rTV55dpA6Iy7j47G2aX12NrZTR0FuEn7al5lWdYfrcbVF/I8/+29X76QZdns3u/PRsTFN/vePM8fy/P83Xmev/vIkSPtyAwAAAAApbW8vhm1/t4Y6u9NHQUq6dSR0djezePs0nrqKMBN6rveF2RZlkXEv4qIv8zz/H/+gd/6txHxixHxL/def7cjCbvVBz6QOgEAAABA6XzgnuKfqaysb8WkqSvomHuOHYqIiBcvXIm7j44e2OeWof5AWVy3eRURPx0RvxAR/1+WZc/v/donotW0eiLLsn8WEWcj4sOdidilPv7x1AkAAAAASufj9xf/TGV5fTOmRwdTx4DKetux0ejJIv5yYTXe/5/PHtjnlqH+QFlct3mV5/kfR0R2jd9+T3vjAAAAAEB15Xkey+ub8bYDnAaBovrXX3+lY+89NToY/+4/XYjZ8Vpb3u+//snb2/I+wP7sa+cVCTzwQOsBAAAAYN8eePyBeODxB1LHuKb1zZ3Y2sljcmQgdRSotNnxoVisNw/0M4tef6BM9nNtICmcPp06AQAAAABttry+GRERk8OaV9BJs2ND8Rfz9Whs7kRtoDd1HOAGaV4VleYVAAAAQOUsr29FRMTEcH/iJFBtM3vXBS6sNuKuadd0Qtm4NrCoLl9uPQAAAABUxmtXNyIi4rBrA6GjZseHIiIO/OpAoD1MXhXVhz7Uej1zJmkMAAAAANpnaW0zDg32xWCfa8ygkw4N9cXwQG8saF5BKWleAQAAAFAZH37Hh1NHeEtLa5txeNTUFXRalmUxOz50oJNXRa8/UCaaVwAAAABUxi//+C+njvCWlq5uxN1HD6WOAV1hdrwWX3t5KXZ28+jtyTr+eUWvP1Amdl4BAAAAUBnrW+uxvrWeOsab2tzejdXmdkyZvIIDMTM+FNu7eVze2zXXaUWuP1A2mlcAAAAAVMb7v/D+eP8X3p86xpt6bW0zIiKmRjSv4CDMjg9FRBzY1YFFrj9QNppXAAAAAHAAltZa0x9To4OJk0B3OHJoMHqzLBZXD27vFdAemlcAAAAAcACWrpq8goPU19MTRw4NxkK9kToKcIM0rwAAAADgACytbcTIQG8M9femjgJdY3Z86MCuDQTaR/MKAAAAAA7A0tVNVwbCAZsZH4rV5nasbWynjgLcgL7UAbiG06dTJwAAAAAondPvOp06wjUtrW3GXdMjqWNAV5kdr0VExEK9GXcfHe3oZxW5/kDZaF4VleYVAAAAwA0r6uHx1s5u1BtbMTVq3xUcpJnxoYiIWKw3NK+gRFwbWFSXL7ceAAAAAPbt8vrluLxevDOV19Y2IyJiasS1gXCQRgf74tBgXywcwN6rotYfKCOTV0X1oQ+1Xs+cSRoDAAAAoEw+9ETrTOXM6TNpg/yQpat7zSuTV3DgZsaHYnG1882rotYfKCPNq6L62MdSJwAAAACgTZbWNiLC5BWkMDs+FP/xu0uxvbsbfT0uI4My0LwqqgcfTJ0AAAAAgDZZWtuM4YHeqA30po4CXWdmvBY7eR6XrmzE7HgtdRxgH7SZi+qFF1oPAAAAAKW3dHUjpkZcGQgpzI4PRUTE4gHsvQLaw+RVUX30o61XO68AAAAASm9pbTPumBpJHQO60vToYPT1ZLFQb8aPpg4D7IvmFQAAAACV8Uvv/qXUEf6G7Z3dqK9vxeHbTV5BCr09WRwdG+z45FUR6w+UleYVAAAAAJXxkXd+JHWEv+G19c3II1wbCAnNjtXi24urked5ZFnWkc8oYv2BsrLzCgAAAIDKeLX+arxafzV1jL9m6epmRLSuLgPSmBkfirXNnbi6sd2xzyhi/YGyMnkFAAAAQGX8wu/8QkREnDl9Jm2QH7C01mpembyCdGbHhyIiYqHejEND/R35jCLWHygrk1cAAAAA0EFLVzdiqL8nagO9qaNA15odr0VEdHzvFdAemlcAAAAA0EGvrW3G1Mhgx/bsANdXG+iNieH+OLfSSB0F2AfNKwAAAADooKW1zZgadWUgpDY3UYv55fXUMYB90LwCAAAAgA7Z3t2N5b3JKyCtucnhWF7fiqsb26mjANfRlzoA1/Cxj6VOAAAAAFA6H7uvWGcqK2tbkUeYvIICmJts7b06t9yIe2cOtf39i1Z/oMw0r4rqwQdTJwAAAAAonQfvLdaZytLaRkRETI1oXkFqJyZqkUXE/PJ6R5pXRas/UGauDSyqF15oPQAAAADs2wuXX4gXLhfnTGVpbTMiIqZGXRsIqQ3298aRQ4Mxv9zoyPsXrf5AmZm8KqqPfrT1euZM0hgAAAAAZfLRp1tnKmdOn0kbZM/lq5sx2NcTIwO9qaMA0dp79cLiauR5HlmWtfW9i1Z/oMw0r4rqU59KnQAAAACAW/Ta2kZMjQ60/ZAcuDlzk7X4s1eWY6WxFZPDrvOEotK8Kqr770+dAAAAAIBbtHR1M45P1FLHAPbMTbb+Ps4vNzSvoMDsvCqqZ59tPQAAAACU0s5uHsvrmzE14oAcimJmfCh6e7KYX15PHQV4CyaviuoTn2i92nkFAAAAUEor65uxm0dMjWpeQVH09fTE7PhQzC83UkcB3oLmFQAAAACV8St/91dSR3jD0tpmREQcHhlMnAT4Qa29Vyuxm+fR08Z9dEWqP1B2mlcAAAAAVMZ773pv6ghvWLq6ERER0yavoFDmJofjay+/FpeubMSxsaG2vW+R6g+UnZ1XAAAAAFTG84vPx/OLz6eOERGtyauB3p4YHfTvx6FI5iZqERFtvzqwSPUHys5PTgAAAAAq4+EvPxwREWdOn0kbJCIuX92IqdGByNp4LRlw66YPDcZgX0/ML6/Hj52cbNv7Fqn+QNmZvAIAAACADriwuhFHD9l3BUXTk2VxYqLW9skroH00rwAAAACgzZpbO1FvbLV1nw7QPnOTtVisN2N7Zzd1FOBNaF4BAAAAQJtdurIRERFHD2leQRHNTQ7HTp7HQr2ZOgrwJjSvAAAAAKDNLqy2DsSPjbk2EIpobrIWERHzK64OhCLqSx2Aa/jUp1InAAAAACidT72nGGcqF69sRF9PFpMjA6mjAG9ivNYfo4N9Mf/aesRdU215z6LUH6gCzauiuv/+1AkAAAAASuf+24pxpnJhtRlHDw1GT5aljgK8iSzLYm6y1tbJq6LUH6gC1wYW1bPPth4AAAAA9u3ZV5+NZ19Nf6Zy8cpGHB2z7wqKbG6yFpevbERza6ct71eU+gNVYPKqqD7xidbrmTNJYwAAAACUySeeaZ2pnDl9JlmG5tZO1BtbcfSQfVdQZHOTw5FHxLmVRpw6MnrL71eE+gNVoXlVVJ//fOoEAAAAANyEi6vNiIg4ZvIKCm1uohYREfPL7WleAe2jeVVU996bOgEAAAAAN+HilY2ICJNXUHDDg31xeGQg5pfXU0cBfoidV0X11FOtBwAAAIBSubDajP7eLCZHBlJHAa5jbrIW88uN1DGAH6J5VVSf+UzrAQAAAKBULl7ZiCOHBqMny1JHAa7j9sPDUW9sxcr6ZuoowA9wbSAAAAAAlfHrP/vrqSPEhdWm/TlQEienRiIi4uzSekwM39q0ZBHqD1SF5hUAAAAAlfGumXcl/fzG5k6sNrfj6NhQ0hzA/syMDcVAb0+cfW0t/vZtE7f0XqnrD1SJawMBAAAAqIyvvPyV+MrLX0n2+RevNCMi4tihwWQZgP3r7cnitsO1OLu0fsvvlbr+QJWYvAIAAACgMn7tj34tIiLee9d7k3z+xdWNiAiTV1AiJ6dG4g+/fTE2tnZisL/3pt8ndf2BKjF5BQAAAABtcvFKM/p7s5gY7k8dBdink4eHI4+IV5ZvffoKaA/NKwAAAABokwtXNuLooaHoybLUUYB9uu3wcGQRbbk6EGgPzSsAAAAAaJOLq804at8VlMpQf2/MjA/F2aW11FGAPZpXAAAAANAGjc2dWG1uxzH7rqB0Tk4Nx6uvNWJnN08dBYiIvtQBuIbPfz51AgAAAIDS+fwH0p2pXLzSjIiIo2Mmr6BsTh4eia+9/FosrjbjxETtpt4jZf2BqtG8Kqp7702dAAAAAKB07p1Od6ZyYXUjIiKOHTJ5BWVzcmo4IiLOLq3ddPMqZf2BqnFtYFE99VTrAQAAAGDfnnrhqXjqhTRnKhevNGOgtyfGh/uTfD5w8yaGB2K81h9nl9Zv+j1S1h+oGpNXRfWZz7ReH3wwbQ4AAACAEvnMc60zlQfvPfgzlYurG3F0bDB6suzAPxu4dSenhm+peZWy/kDVaF4V1ZNPpk4AAAAAwA24cKUZbzs6mjoGcJNOHh6Ov5ivx8r6ZkwMD6SOA11N86qopqdTJwAAAABgnxqbO3GluR1H7buC0jo5NRIREWeX1jWvIDE7r4rq8cdbDwAAAACFd2G1GRERx8YGEycBbtaxsaEY6OuJ7y+tpY4CXU/zqqg0rwAAAABK48KVVvPq6JjJKyir3p4sbp8cjldeu/m9V0B7uDYQAAAAgMr4zX/ym0k+9+LqRgz09cRErT/J5wPtcfvUcPzhty9Gc2snhvp7b+h7U9UfqCLNKwAAAAAq47bx25J87sUrzTh6aDCyLEvy+UB7nJwajjwiXn1tPd527NANfW+q+gNV5NpAAAAAACrji9/8Ynzxm1888M+9uLoRxw65MhDK7vbJ4cgi4uxNXB2Yqv5AFZm8AgAAAKAyPveNz0VExEfe+ZED+8wrza24srEdx8Y1r6DsBvt7Y3Z8KM4urd3w96aoP1BVJq8AAAAA4BacW25ERMTcRC1xEqAdbp8aiVdfa8TObp46CnQtzSsAAAAAuAXzK43IIuK45hVUwsmp4djc2Y2FeiN1FOhamlcAAAAAcAvOLTfi6NhgDPQ5aoMquHNqJCIivn/5xq8OBNrDT1QAAAAAuEl5nsf8SiNOTAynjgK0yVitP6ZGBuJ7mleQTF/qAFzDk0+mTgAAAABQOk9++GDPVOqNrVjb2I4Tk64MhCq5c3okvnV+NXbzPHqybF/fc9D1B6pM86qopqdTJwAAAAAonenhgz1TObfS2okzZ98VVMqd0yPxjbPLsVhv7nuf3UHXH6gy1wYW1eOPtx4AAAAA9u3x5x+Px59//MA+b365ET1ZxMz40IF9JtB5d0639l7dyNWBB11/oMo0r4pK8woAAADghh304fG5lUbMjA1Ff69jNqiSieGBmBzu17yCRFwbWFRnzqROAAAAAMBbyPM8zi034p0nxlNHATrgzunR+PZia+8VcLD8kxAAAAAAuAmvrW1GY2vHviuoqDunR2J9cycuXtlIHQW6juZVUT36aOsBAAAAoJDOrTQiIuLEpOYVVNHN7L0C2kPzqqiefrr1AAAAAFBI55Yb0deTxbGxodRRgA6YHO6PidqN7b0C2sPOKwAAAAAq4/d+7vcO7LPmVxoxOz4UvT3ZgX0mcHCyLIs7p0fixYtXI8/zyLK3/rt+kPUHqs7kFQAAAACVMdw/HMP9wx3/nN08j3MrDVcGQsXdOT0Saxvb8dKlq9f92oOqP9ANNK8AAAAAqIzP/sln47N/8tmOf87lKxuxub0bcxMOqqHKXt979bWXX7vu1x5U/YFuoHkFAAAAQGU88a0n4olvPdHxzzm30oiIMHkFFXd4ZCDGhvri69+7fvPqoOoPdAPNKwAAAAC4QfMrjRjo7YkjhwZTRwE6KMuyuGN6JL7+8lLkeZ46DnQNzSsAAAAAuEHnlhtxfGIoerIsdRSgw+6cHomLVzbi+0vrqaNA19C8AgAAAIAbsLObx/mVRpyYcGUgdIPX9159/eWlxEmge2heAQAAAMANuHilGdu7eZyYHE4dBTgAR0YHY3p0cF97r4D26EsdgGs4cyZ1AgAAAIDSOXP6TMc/49xyIyIi5iZNXkE3yLIsfvKuw/G1vb1X2TWuCz2I+gPdwuQVAAAAANyA+ZVGDPX3xOGRgdRRgAPyU3cejoV6M159rZE6CnQFzauievTR1gMAAADAvj367KPx6LOdPVM5t9yI4xO16LnG9AVQPT9511RERHzte9fee3UQ9Qe6heZVUT33XOsBAAAAYN+efvHpePrFpzv2/ts7u7FYb8bchH1X0E3ednQ0pkYG4msvX7t51en6A93Ezqui+tKXUicAAAAA4IcsrjZjJ8/jhH1X0FWyLIufOjUVz7301nuvgPYweQUAAAAA+3R2aT0iIm7TvIKuc/+pqVioN+P7e3UA6BzNq6J65JHWAwAAAEBhvHzpahweGYiJ4YHUUYADdt/e3qtnX7qcOAlUn+ZVUdl5BQAAAHDDav21qPV3ZipqN8/je0trcdf0SEfeHyi2O6dHYmZsKJ596c33XnWy/kC3sfMKAAAAgMr4/Z/7/Y6998JKM5pbu3HXkdGOfQZQXFmWxf2npuKrL156071Xnaw/0G1MXgEAAADAPrx8+WpERNx1xOQVdKv7Tk3F0tpmvHjhauooUGmaVwAAAABUxie/+sn45Fc/2ZH3fvnSWkyPDsbYUH9H3h8ovvtOXXvvVSfrD3QbzSsAAAAAKuOZ7z0Tz3zvmba/785uHt9fWjN1BV1ubnI4bj88/KZ7rzpVf6AbaV4BAAAAwHWcX2nExvZu3DWteQXd7v5TU/G1l5diZzdPHQUqS/MKAAAAAK7j5Uuv77saTZwESO2+U1Nxpbkd3zpfTx0FKkvzCgAAAACu4+XLa3H00GCMDvaljgIk9ld7r/7m1YFAe2heFdXUVOsBAAAAYN+mhqdiari9Zyqb27t7+65MXQERRw8NxduOjsZzP9S86kT9gW7ln4oU1Ze+lDoBAAAAQOl86cPtP1P5i/mV2NrJ7bsC3nDfqal48k/nY3N7Nwb6WjMinag/0K1MXgEAAADAW3h9uuJOzStgz/2npmJ9cyf+Yn4ldRSoJM2ronrkkdYDAAAAwL498pVH4pGvtPdM5bmXl2JmbChG7LsC9vzknVORZX9971Un6g90Kz9xi2rJsj8AAACAG/Xc/HNtfb+N7Z3407PL8WMnJ9v6vkC5TY4MxNtnx+LZly7Hf/eet0VE++sPdDPNq6J67LHUCQAAAAC63p+/shIb27tx1/Ro6ihAwdx/aip+49mz0dzaiaH+3tRxoFJcGwgAAAAA1/DcS0uRZfZdAX/TfaemYnNnN/707HLqKFA5mldF9dBDrQcAAACAZL728lK84/hY1AZMVQB/3Y/fcTh6e7J49qXLqaNA5bg2sKhefDF1AgAAAIDSmRuba9t7Nbd24s9fWYlfvP9k294TqI5DQ/3xt+bG49mXliKivfUHup3mFQAAAACV8Vv/9Lfa9l5/dnY5Nnd2475TU7FY32jb+wLV8dOnpuNzX30pVptbba0/0O1cGwgAAAAAb+K5l5eityeLH7/jcOooQEH99N3TsbObx9dffi11FKiU6zavsiz7P7Isu5hl2Td/4NcOZ1n277Is+87e62RnYwIAAADA9T385Yfj4S8/3Jb3+vffvhjvum0iDg31t+X9gOr5L05OxFB/T/zH715ua/2BbrefyavHI+Jnf+jX/kVEPJPn+dsi4pm9/wcAAACApJ5ffD6eX3z+lt/n1dfW41vnV+MfvP1YG1IBVTXY1xs/cedU/IfvXGpb/QH20bzK8/yPIuKHZx7/UUT8xt5//0ZE/OM25wIAAACAZP7gP12IiIh/+I6ZxEmAovsv756Oly6txeb2buooUBk3u/PqWJ7nC3v/vRgR/gkKAAAAAJXxB99ajHuPHYo7pkdSRwEK7qfvno6IiHpjK3ESqI6bbV69Ic/zPCLya/1+lmUPZVn2jSzLvnHp0qVb/TgAAAAA6KilqxvxJ99/Lf7BO/x7beD6fmTmUEyNDGheQRvdbPPqQpZlsxERe68Xr/WFeZ4/luf5u/M8f/eRI0du8uO60D33tB4AAAAA9u2eqXvinqlbO1N55i8vxm7uykBgf3p6srj/7unYaB6Lt029LXUcqIS+m/y+fxsRvxgR/3Lv9XfbloiWxx5LnQAAAACgdB578NbPVP7gPy3GiYlavOP4WBsSAd3g79w9FU/9v78c//1P/N3UUaASrjt5lWXZ/xURz0XEvVmWzWdZ9s+i1bT6mSzLvhMR7937fwAAAAAotbWN7fij71yOn3n7sciyLHUcoCRe33v1x9+5nDgJVMN1J6/yPP+vrvFb72lzFn7QQw+1Xk1gAQAAAOzbQ0+1zlRudgLrqy9eis3tXVcGAjdkbnI4Nkc/F//T1/vjv/k7v5M6DpTezV4bSKdNTaVOAAAAAFA6Ly69eEvf/wffWozJ4f748Tsm25QI6Bb9Qxdi/spGbO3sRn/vdS89A96C5lVRffrTqRMAAAAAdJXN7d145tsX4x++Yyb6HDwDN2i81h8XVpvx/Ksr8eN3HE4dB0rNT2EAAOD/b+++w6O67vyPf87MSKPeJSQhARIgOsY2AeMGrrEdEycx6yTeZON1ejZ50pwnidN2U5xsqtM2G6fZG6fY8S8F3BIbGzfigsHGiCoEFipISEK9z8z1jMEAACAASURBVJzfHzM4whFGZWbuHc379TznGWbmzr2feXjOmdH9zjkXAABIerq2Td0DIywZCGBSslKTJMN1r4BIoHjlVtdeG2oAAAAAAACIib/tPqrUJK8umF/gdBQAccjnMcpI9umpGopXwFSxbKBbtbU5nQAAAAAAACDurCheManXBYNWf6tu1tqqQqUkeSOcCkAiWFG8QiOD7drxcoe6B4aVmZLkdCQgblG8AgAAAAAAwLRx6xW3Tup1L9R3qKV7UK9fOiPCiQAkiluvuFVba1p1/c+f0bOH2nXJIsYTYLJYNhAAAAAAAAAJ72/VzfJ5jC5ewMlmAJN31uxc+X0ePcnSgcCUMPMKAAAAAAAA08Y7/vgOSdKdb7lz3K+x1uqv1Ud1TmW+stNY5gvA5JwYf1ZVfITrXgFTxMwrAAAAAAAATBv1XfWq76qf0Gu213XoUGuvrl5eEqVUABLBifHnvHkF2t/co+auAacjAXGL4hUAAAAAAAAS2t3PHVFasldXn1HqdBQA08AF8wskSY/vP+ZwEiB+UbwCAAAAAABAwuodHNG9Oxv1hmUlyvBzhQ0AU7eoOEsFGX49foClA4HJongFAAAAAACAhHXfzib1DgX01teVOx0FwDTh8RhdOL9ATx44pkDQOh0HiEv8nMSt1qxxOgEAAAAAAEDcWVM2sXMqd207osrCdJ09OzdKiQAkitHjz4VVhfrjjgbtaujUGeU5DqYC4hPFK7f6+tedTgAAAAAAABB3vn7p+M+p1LR06/mXj+vmqxbKGBPFVAASwejx54L5BTImdN0rilfAxLFsIAAAAAAAABLSXc8dkc9j9JazypyOAmCayc/wa2lpth7bf8zpKEBconjlVtdeG2oAAAAAAAAYt2vvvlbX3n36cypDI0H9cXuDLllUpIIMfwySAZjuXj3+XFhVoB1HOtQ1MOxgKiA+UbxyqzVruO4VAAAAAADABLX1tamtr+202z2yt1ltvUN66+vKY5AKQCJ49fhz4fxCBYJWW2taHUwFxCeueeVWN93kdAIAAAAAAIBp667njmhGll8Xzi90OgqAaeqs2bnK8Pv02P5WXbG0xOk4QFxh5hUAAAAAAAASytHOAT22/5g2nF0mn5fTYwCiI8nr0blz8/X4/mOy1jodB4grfDq71bp1oQYAAAAAAICIuuf5Iwpa6bqVLBkIILourCpUQ0e/alt7nY4CxBWWDQQAAAAAAMC0cUnFJa/5fDBodde2I1pTma/Z+ekxSgUgEYw1/qytCi1N+vj+Y5pbmBHrSEDcongFAAAAAACAaeMLa7/wms8/dbBVR9r79cnLFsQoEYBEMdb4U56XpoqCdD22/5j+/bwKB1IB8YllAwEAAAAAAJAwfvpYrYoy/bpyWbHTUQAkiLVVhXq6tk0DwwGnowBxg+IVAAAAAAAApo0rf3OlrvzNlWM+91J9p56sadWN51fI7/PGOBmA6e5U48+FVQUaGA5q2+HjDqQC4hPFKwAAAAAAAEwb/cP96h/uH/O5/33soDL9Pl2/elaMUwFIBKcaf86pzFey16PHDxxzIBUQnyheAQAAAAAAYNo73NqrB3Y16V/Pma2slCSn4wBIIGnJPq2ck6vH91O8AsaL4hUAAAAAAACmvdueqJXP49GN581xOgqABHRhVaH2Hu1Wc9eA01GAuEDxCgAAAAAAANNaS/eA7nm+XteePVNFWSlOxwGQgNZWFUqSHmP2FTAuPqcD4BSuvtrpBAAAAAAAAHHn6qp/Pqdy+1OHNRwI6r0XVDqQCECiGGv8OWFhcaaKs1K0ZV+LrltZHsNUQHyieOVWN93kdAIAAAAAAIC4c9O5J59T6R4Y1q+ffllXLi1WZWGGQ6kAJIJXjz+jGWN00cJCbXqxSUMjQSX7WBQNeC30EAAAAAAAAExbv3u2Tt0DI/rA2rlORwGQ4C5eOEM9gyPadrjd6SiA61G8cqt160INAAAAAAAA47bu9nVad/s6SdLgSEA/f+KQzp2br+VlOc4GAzDtjR5/xnLevHwl+zzavLcldqGAOEXxyq1uuCHUAAAAAAAAMCl/3tGglu5BZl0BcIW0ZJ/WVObrEYpXwGlRvHIrilcAAAAAAACTNjAc0A8212jZzGxdML/A6TgAIEm6ZFGRDrX2qvZYj9NRAFejeOVWra2hBgAAAAAAgAm78+mX1dDRr09fsVDGGKfjAIAk6aIFRZLE7CvgNCheudWGDaEGAAAAAACACQkErX78aI3On1eg85l1BcBFyvPStGBGJsUr4DR8TgcAAAAAAAAAIuW6Jdfp4T3NOtI3rE9fsdDpOAASyHVLrhvXdhctLNLPn6hV18CwslKSopwKiE/MvAIAAAAAAMC0sWHBjdpzYI2uXl6iZWXZTscBkEA+9LoP6UOv+9Bpt7tkUZFGglZPHuCyMcCpULwCAAAAAADAtPGdh3dqMNCnmy5f4HQUAAmmb7hPfcN9p93uzPIc5aQlafMelg4EToVlAwEAAAAAADAtHGrt1Q9efI+K8vyaU/AWp+MASDBX/eYqSdKWG7a85nY+r0drqwq1ZV+LAkErr8fEIB0QX5h5BQAAAAAAgGnh23/bJ4+RynJTnY4CAK/p4oVFausd0ov1HU5HAVyJ4hUAAAAAAADi3s76Dt23s0kl2SlK8nLKC4C7ra0qlNdj9Ohelg4ExsInOQAAAAAAAOKatVbfeGCv8tKTVZLNrCsA7peTlqyzZ+Vy3SvgFLjmFQAAAAAAABzx22fqIrKf3Y2d2nqwTVcvL9EjrUMR3TcARMvFi4r0jQf2qqmzn8I78CoUr9zqhhucTgAAAAAAAOB6w4Gg7nupSUWZfq2uyNewf4PTkQAkqBtW3DCh7S9ZGCpePbr3mK5fPSs6oYA4RfHKrSheAQAAAAAAnNaTNa063jesd59fIa/HaG3ZvzgdCUCCmmjxal5RhspyU7V5TzPFK+BVuOaVW7W2hhoAAAAAAADG1NE3pC37WrSkNEtzCzMkSd1D7eoeanc4GYBE1NrXqta+8Z/TNcbossUz9ERNq3oHR6KYDIg/zLxyqw3hKe5btjgaAwAAAAAAwK0erD4qa6Wrlpa88tj3d3xQkvT51Xc5FQvANDSe6+h99Zm3SprY+OPzeDQ0EtRX7t2t5WU5k843GrO4MB1QvHKrT37S6QQAAAAAAACudai1VzvrO3XxwiLlpic7HQcAJmV2fprS/T5VN3ZFrHgFTAcUr9xq/XqnEwAAAAAAALhS0Frdu7NROalJunB+odNxAGDSPMZocUmWXqzv0HAgqCQvV/oBJK555V779oUaAAAAAAAATvLc4XY1dQ7oymUlSvZxegtAfFtamqWhkaBqWnqcjgK4Bp/ubvX+94caAAAAAAAAXtE3NKKHdjeroiBdS0uznI4DAFNWUZiulCSPqhs7nY4CuAbLBgIAAAAAACBuPLS7WQPDAa1fXipjzD89f8msdziQCgAmP/74PB4tKs7SnqZuBYJWXs8/j21AoqF4BQAAAAAAgLjQ0NGvZw+165y5+SrOThlzmzUlXEccgDOmMv4sKc3WjiMdqm3t0fyizAimAuITywYCAAAAAADA9YLWauMLDUrz+3Tpwhmn3K6tv1Ft/Y0xTAYAIVMZf+bPyFCy16Pqhq4IpwLiE8UrAAAAAAAAuN6OuuM6crxfVy4pVmqy95Tb/WTnx/WTnR+PYTIACJnK+JPk9aiqOFO7m7oUtDbCyYD4Q/EKAAAAAAAArtY/FNCDu45qVl6aVszKcToOAETF0tIs9QyO6OW2PqejAI6jeAUAAAAAAABXe3hPs/qGAnrjGaXyGON0HACIigUzMuXzGO1u7HQ6CuA4ilcAAAAAAABwrabOfj1d26bVlXkqzUl1Og4ARI0/yat5RRmqbuySZelAJDiKVwAAAAAAAHAla602vtio1GSvLltU7HQcAIi6paXZ6ugfVkNHv9NRAEf5nA6AU/jkJ51OAAAAAAAA4KgXjnTo5bY+veXMmUpN9o7rNVdVvDfKqQBgbJEYfxaWZMpjpOrGLpXlpkUgFRCfKF651fr1TicAAAAAAABwzOBwQA9WH1VZbqrOmp077tedVXRpFFMBwKlFYvxJS/apsjBDuxo6dfniGTJc5w8JimUD3WrfvlADAAAAAABIQFv2H1P3wIjWLy+VZwInbxt7Dqqx52AUkwHA2CI1/iwpzVJb75CaOgcikAqITxSv3Or97w81AAAAAACABNPWM6gna1p1ZnmOyvMmtmzWL6tv1i+rb45SMgA4tUiNP8tKs+U1Ri8c6YhAKiA+sWygW91yi9MJAAAAAAAAHHH/rqPyeoxev7TY6SgAEHNpfp+qijP1Yn2HrlhaPKHZp8B0wcwrtzr33FADAAAAAABIIAdaurWnqUsXLShSVkqS03EAwBErynPUPTCig8d6nI4COILilVtt3RpqAAAAAAAACSIQtLp3Z5Py05N13tx8p+MAgGMWFmcqJcmjF+pYOhCJieKVW918c6gBAAAAAAAkiKdr23Sse1BXLSuRz8tpKwCJK8nr0dLSbFU3dWloJOh0HCDmuOYVAAAAAAAAHNczOKLNe5s1vyhDC4szJ72fN839SARTAcD4RXr8WTErR9tePq7dTV1aUZ4T0X0DbkfxCgAAAAAAAI57eHezhkaCesOyEhljJr2fpQXnRzAVAIxfpMefOfnpyklN0gtHjlO8QsJh/jUAAAAAAAAcdbRzQM8dbtc5lfkqykqZ0r4Od1XrcFd1hJIBwPhFevzxGKMzynNU09Kj7oHhiO0XiAcUrwAAAAAAAOAYa63u39WklCSvLl5YNOX93bnny7pzz5cjkAwAJiYa48+K8hwFrbSzvjOi+wXcjuIVAAAAAAAAHLO/uUc1LT26eGGR0pK5wgUAjDYjK0WlOSl64UiH01GAmKJ4BQAAAAAAAEcEglYP7GpSfnqyVlfmOR0HAFxpRXmuGjr61dI14HQUIGYoXgEAAAAAAMAR215uV0v3oK5cWiyfh9NUADCWM8qyZSRmXyGh8K0AAAAAAAAAMdc9MKyHdzdrTn66FpVkOR0HAFwrMyVJ84oy9EJ9h4LWOh0HiAkWEnarW25xOgEAAAAAAEDU/M+Wg+odCuiGZSUyxkRsv9dVfSpi+wKAiYjm+HPmrBzdva1eL7f1qaIgPWrHAdyC4pVbnXuu0wkAAAAAAACi4kh7n37x5CGdWZ6jmbmpEd13Ve7KiO4PAMYrmuPP4pJs+X2Neu5wO8UrJASWDXSrrVtDDQAAAAAAYJr55l/3yWOkyxbPiPi+9x/fpv3Ht0V8vwBwOtEcf5J9Hp01K1cvNXSqZ3AkKscA3ITilVvdfHOoAQAAAAAATCM76o5r04uNeu8FlcpJS474/u/e/y3dvf9bEd8vAJxOtMef1ZV5CgStth1uj9oxALegeOVWP/1pqAEAAAAAAEwT1lp95d7dKsz06/1r5zodBwDiSlFmiuYWpuuZQ+0KBK3TcYCoonjlVgsWhBoAAAAAAMA0cf9LR7W9rkM3XV6lDD+XYgeAiTqnMl+d/cPae7TL6ShAVFG8cqtNm0INAAAAAABgGhgYDugbD+7RwuJMbTi73Ok4ABCXFhZnKTs1SU/XtjkdBYgqildu9Z3vhBoAAAAAAMA0cMfWwzrS3q/Pv2GxvB7jdBwAiEtej9HqijwdPNarlu4Bp+MAUcP8bAAAAAAAAERVW8+gfvRIjS5aUKjz5xdE9VjvWPTFqO4fAE4lVuPPyjl52ry3Rc/Utmv9GaUxOSYQaxSvAAAAAAAAEFXf33xAfcMB3XzVoqgfa07WkqgfAwDGEqvxJ8Pv07KZ2dped1yXL54hf5I3JscFYollAwEAAAAAABA1NS09+s0zdbp+1SzNn5EZ9ePtan1Su1qfjPpxAODVYjn+nFOZr8GRoHYc6YjJ8YBYY+YVAAAAAAAAoubr9+9RWpJXH7t0fkyO9+eDP5QkLS04PybHA4ATYjn+lOemqjQnRU/Xtml1RZ6M4VqCmF6YeQUAAAAAAICoeKqmVZv3tug/Lp6n/Ay/03EAYNowxmhNZb5augd1qK3X6ThAxFG8AgAAAAAAQMQNB4L60sZqleWm6oZz5zgdBwCmneVlOUpN8mprTZvTUYCIo3gFAAAAAACAiPvVU4dU09Kj/1y/RClJXqfjAMC0k+T16JzKfO1u6lJTZ7/TcYCIongFAAAAAACAiDraOaDvP3xAlyws0qWLZzgdBwCmrfPnFSglyaPNe1qcjgJElM/pADiFn/7U6QQAAAAAAACT8rX792g4aPWl9Utifuwbl9wS82MCgOTM+JOa7NX58wr08J4WNRzv18zc1JhnAKKBmVdutWBBqAEAAAAAAMSRrTWt2vRioz60bq5m5afF/PilGXNVmjE35scFAKfGn3PnFig1yauH9zTH/NhAtFC8cqtNm0INAAAAAAAgTgyNBPXFjdWalZemD6x1poC0veVhbW952JFjA0hsTo0/KUleXTC/QPuau1XX3hfz4wPRQPHKrb7znVADAAAAAACIE7966pBqWnr0n29crJQkryMZ7j/0M91/6GeOHBtAYnNy/FkzN19pycy+wvRB8cqt7rkn1AAAAAAAAOJAU2e/vr/5gC5dNEMXL5zhdBwASCh+n1drqwpV09KjZw+1Ox0HmDKKV25VUBBqAAAAAAAALmet1Zc37VYgaPWl9YudjgMACWl1Rb4y/D5996F9TkcBpozilVvdfnuoAQAAAAAAuNyfdjTogV1H9dFL56s8L83pOACQkJJ9Hq2tKtTTte3aerDV6TjAlFC8ciuKVwAAAAAAIA7UtfXpi3+p1qo5eXr/hXOdjgMACW1VRZ5mZPn13b/tl7XW6TjApPmcDgAAAAAAAID4NBII6mN37ZAx0nffeoa8HuN0JH1w+fecjgAgQblh/EnyevSRi+fr83/epT9ub9C1Z5c5HQmYFGZeAQAAAAAAYFJ+9GiNttd16GtvXqayXHcsF5ifWqr81FKnYwBIQG4Zf96+apZWzs7Vf22qVnPXgNNxgEmheAUAAAAAAIAJe/7l4/rhIzV685kz9cYznD9Ze8Lfmzbp702bnI4BIAG5Zfzxeoy+uWG5BkeC+tyfdrF8IOISxSsAAAAAAABMSPfAsD521w6VZKfov65Z4nSck2yuu1Ob6+50OgaABOSm8aeyMEM3Xb5AD+9p1sYXG52OA0wYxSsAAAAAAABMyH9u3K2G4/269a0rlJWS5HQcAMAYbjy/QmfOytGXNlbrWPeg03GACaF4BQAAAAAAgHG77fGD+n/b6/Xhi+Zp5Zw8p+MAAE7B6zH61obl6hsK6At/ZvlAxBeKVwAAAAAAABiX3z1bp1vu36s3LC/RRy+tcjoOAOA05hVl6uOXVunB6qO676Ump+MA40bxCgAAAAAAAKe16cVG3fynl7RuQaG+d90KeT3G6UgAgHF47wUVOqMsW1/8S7Vae1g+EPHBxHKq4MqVK+22bdtidry41toaui0ocDYHAAAAAABIeI/sbdb7/u95nTUrV3fcuEqpyd6I7Pe3z9RFZD+jdQ+1S5Iyk1nSEEBsuWX8uX71rH96bH9zt9b/8EktKM7Ub96zWplcrxAOMcY8b61debrtmHnlVgUFFK4AAAAAAIDjnq5t0wfv3K5FJVn6xQ0rI1a4ipbM5DzHTxwDSExuHn+qZmTqx9efperGLr3njm0aGA44HQl4TRSv3Or220MNAAAAAADAIX8/2Kb33LFN5XlpuuPGVXHxS/3H6v+gx+r/4HQMAAnI7ePPpYtn6LvXnaFnD7frP36zXcOBoNORgFOieOVWFK8AAAAAAIBDhkaC+u8H9+r6nz+toky/7nz3auWlJzsda1yeaLhHTzTc43QMAAkoHsafa1bM1JevWarNe1t00x9eVDAYu8sKARPhczoATmHLFqcTAAAAAACAODTV60gd6x7U3duOqKGjXytn5+oNy0v0yN6WCKUDADjtnefMVvfAsL754D5lpvj0lWuWyhjjdCzgJBSvAAAAAAAAIGutnj3crvtfapLP49G/rp6lJaXZTscCAETBh9bNU1f/iP73sYOyVvr8Gxa7/pqGSCwUr9zq298O3d50k7M5AAAAAADAtBYIWu072qWnDrbpUGuv5hVlaMNZZcpKdf/1rQAAk/fpKxYoaK1ue7xWWw+26VsblmvlnDynYwGSKF651733hm4pXgEAAAAAgCjoGhjWtsPteu7wcXX2Dysrxaf1y0u0ujJfHpaPAoBpzxijm69apHVVhfrUPTv1Lz/9u248r0I3Xb6AWVhwHMUrAAAAAACABBAIWjV19quuvU+1x3q192iXglaaV5Sh9ctLtKA4S15P/BetPrXydqcjAEhQ8Tr+nDuvQH/9+IX6xgN79IsnD+mRvS265c3LdE5lHtfCgmMoXgEAAAAAAEwj1lr1DgXU1jOott4htXQNqK69Tw0d/RoOWElSVopP584t0KqKPBVk+B1OHFl+b6rTEQAkqHgefzL8Pn31Tct01dISfeqenXr7z55WZUG6rj6jVOuXl2j+jEynIyLBULwCAAAAAACIM4MjAdUf79eR9j4dOXHb3qe69j7VtPRocCT4yrZeY1Sak6JVc/JUnpemWXlpyklLdjB9dD1U93+SpMtm/ZvDSQAkmukw/pw7r0B/+/iF+ssLjbp3Z6N++MgB/WDzAS0sztRVy0q0sDhTpTmpKs1JVW5a0rhnZo0EghoYCSoQtLLWylopaK2sJL/Po/RknzzTYPYvIofiFQAAAAAAgAtZa9XYOaCDLT061Nqr2mM9qm3t1aHWXjV09Mvaf2yb7POoLDdVs/LSlJWapPz0ZOWn+5WfkayctCT5PB7n3kiMPdN0n6T4PnkMID5Nl/En3e/T9atn6frVs9TSPaAHXjqqTS826rsP7T9pO7/Po9KcVKUlexW0oc+tQNAqaK1Gglb9QwH1Dwc0MBx4ZebvqXhMaPZXZkqSMlN8yk1LVmlOqmbmpLxSLJuZm6ry3DQl+xLnMy2RTal4ZYy5QtL3JXkl/dxa+42IpAIAAAAAAEgQgyMB1bX1qba1VzUtPTrY0qOaYz2qaelR31Dgle0y/D5VFKTr7Nm5uvasMs3OD82iKs9LU2GG/5VfrP/2mTqn3goAwAUi/TmQ5PXoLWeV6fVLinW8b0id/cPq6BtWZ3+oDQeCMsbIY4y8vtCtx0iFGX4l+TxK9nqU5PUoyRt6TpKMkYyk11XkaWA4oO6BEXUPjKhrYFhd/SNq7x3U1oOtau4aUHBU3ctjpPK8NFUUpKuiIF2VBemqKMjQnII0lWanMntrGpl08coY45X0Y0mXSaqX9JwxZqO1dnekwgEAAAAAAMQ7a63ae4fU0NGvhuP9aujoV/3xfh1u61XtsV7VH+876cRcSXaK5hVl6LqV5ZpXlKF5RRmqLExXYYZ/3MszAQAQael+n9L9PpXlRm6f16+e9ZrPDweCau4aUGPHgOqP9+lwa+8rs5CfPdR+0o88/D6PZueHCluz89M1Myc11HJDM7eyU5MiFxxRN5WZV6sk1VhrayXJGPN7SddIongFAAAAAADi0oklj0bCyx4FgqE2NBLU4EhQQ4GghkZCrXdoRL2DAfUMDqtnMKDewRF19g+rrWdQbT1DausdUlvvoI51D2pgOHjScdKTvZqdn67lZdl605kzVVmQrsrC0K/IM1M4uQYAgBSa9VWWm6ay3DStqsg76TlrrZq7BnUoXMw68aOQg8d69ei+YxoaOfmzN8PvU0FGsvIz/KHldcO3WamholxGuKX7fUpL9io5PGss2ed55d9ej/lHM6FbflgSHVMpXs2UdGTU/XpJq6cWBwAAAAAAwBmf/eNL+t2zU1tqyecxys9IVl66XwUZyZqTn6b8DL9Kc1JVlhv6BXhZbujX35zsAgBg8owxKs5OUXF2itbMzT/puWDQqrV3UI0dA+FZz31q7BgI/bCkZ1B17X3aXteh9t7Bk2Y/T8YnL6vSRy6ZP7Wd4J8Yayf3P2OM2SDpCmvte8L33ylptbX2w6/a7n2S3he+u0DSvsnHdYUCSa1OhwDgCPo/kLjo/0Diov8DiYv+DyQu+j+QuOj/0TfbWlt4uo2mMvOqQVL5qPtl4cdOYq29TdJtUziOqxhjtllrVzqdA0Ds0f+BxEX/BxIX/R9IXPR/IHHR/4HERf93D88UXvucpPnGmApjTLKkt0naGJlYAAAAAAAAAAAASESTnnllrR0xxnxY0l8leSX90lpbHbFkAAAAAAAAAAAASDhTWTZQ1tr7Jd0foSzxYtosgQhgwuj/QOKi/wOJi/4PJC76P5C46P9A4qL/u4Sx1jqdAQAAAAAAAAAAAJA0tWteAQAAAAAAAAAAABFF8WoMxpg8Y8xDxpgD4dvcU2z3oDGmwxhz76serzDGPGOMqTHG3GWMSY5NcgBTNYH+/67wNgeMMe8a9fjbjTEvGWN2hseIgtilBzAVEej/ycaY24wx+40xe40x18YuPYCpmGr/H/X8RmPMrugnBhApU+n/xpg0Y8x94c/9amPMN2KbHsBkGGOuMMbsC5+3+8wYz/vD5/Nqwuf35ox67rPhx/cZY14fy9wApm6y/d8Yc5kx5vnwOb/njTEXxzp7IqJ4NbbPSNpsrZ0vaXP4/li+JemdYzz+35K+Z62dJ+m4pHdHJSWAaDht/zfG5En6kqTVklZJ+pIxJtcY45P0fUkXWWuXS9op6cMxSw5gqibd/8NPf05Si7W2StJiSY/FJDWASJhq/5cx5i2SemITF0AETbX/f9tau1DSmZLOM8ZcGZvYACbDGOOV9GNJVyr0nf3txpjFr9rs3ZKOh8/rfU+h83wKb/c2SUskXSHpf8L7AxAHptL/JbVKWm+tXSbpXZJ+HZvUiY3i1diukXRH+N93SHrTWBtZazdL6h79mDHGSLpY0j2nez0AVxpP/3+9W4xTkAAABGdJREFUpIeste3W2uOSHlLoi6sJt/TwWJAlqTH6kQFEyFT6vyTdKOnrkmStDVprW6OcF0DkTKn/G2MyJH1C0ldjkBVAZE26/1tr+6y1j0qStXZI0nZJZTHIDGDyVkmqsdbWhvvt7xUaB0YbPS7cI+mS8N/410j6vbV20Fp7SFJNeH8A4sOk+7+1doe19sQ5vmpJqcYYf0xSJzCKV2ObYa1tCv/7qKQZE3htvqQOa+1I+H69pJmRDAcgqsbT/2dKOjLqfr2kmdbaYUkflPSSQkWrxZJ+EcWsACJr0v3fGJMTvv8VY8x2Y8wfjDET+f4AwFmT7v/hf39F0nck9UUtIYBomWr/lySFvwusV2j2FgD3Om1/Hr1N+Pxep0Ln+8bzWgDuNZX+P9q1krZbawejlBNhPqcDOMUY87Ck4jGe+tzoO9Zaa4yxsUkFIBai1f+NMUkKFa/OlFQr6YeSPit+hQ24RhQ//30K/dJ6q7X2E8aYT0j6tsZeXhiAA6L4+b9C0lxr7cdHXxMDgHtE++//8PLhv5P0A2tt7eRSAgAAtzPGLFFoKcHLnc6SCBK2eGWtvfRUzxljmo0xJdbaJmNMiaSWCey6TVKOMcYXrs6WSWqYYlwAERSB/t8gad2o+2WStkhaEd7/wfC+7tapr5kHwAFR7P9tCs24+GP48T+Ia14CrhLF/r9G0kpjzGGF/r4qMsZssdauEwBXiGL/P+E2SQestbdGIC6A6GqQVD7q/ljn7U5sUx8uTmcr9H1/PK8F4F5T6f8yxpRJ+pOkfztx7g/RxbKBY9uo0IXXFL79y3hfaK21kh6VtGEyrwfguPH0/79KutwYkxu+UPPl4ccaJC02xhSGt7tM0p4o5wUQOZPu/+HP/036x4mtSyTtjm5cABE0lf7/E2ttqbV2jqTzJe2ncAXElal8/5cx5qsKndj6WAyyApi65yTNN8ZUGGOSJb1NoXFgtNHjwgZJj4S/72+U9DZjjN8YUyFpvqRnY5QbwNRNuv+Hlwe+T9JnrLVPxSxxgjOhsRejGWPyJd0taZaklyVdZ61tN8aslPQBa+17wts9IWmhpAyFKrDvttb+1RhTqdAF3/Ik7ZD0DtbABOLDBPr/jZJuDr/sa9baX4Uf/4Ckj0oaDr/+BmttW4zfBoBJiED/ny3p15JyJB2T9O/W2roYvw0AkzDV/j9qP3Mk3WutXRqr7ACmZir9P/wL7COS9ko68Tf/j6y1P4/pmwAwIcaYqyTdKskr6ZfW2q8ZY74saZu1dqMxJkWh7/VnSmqX9LYTS4IaYz4n6UZJI5I+Zq19wJE3AWBSJtv/jTGfV+jSIAdG7e5ya+1EVmzDBFG8AgAAAAAAAAAAgGuwbCAAAAAAAAAAAABcg+IVAAAAAAAAAAAAXIPiFQAAAAAAAAAAAFyD4hUAAAAAAAAAAABcg+IVAAAAAAAAAAAAXIPiFQAAAAAAAAAAAFyD4hUAAAAAAAAAAABcg+IVAAAAAAAAAAAAXOP/A6NZFqj0/DZiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1250da3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "# Using the numpy normal distribution function where loc is the mean, \n",
    "# scale is the standard deviation, and size is the number of observations.\n",
    "\n",
    "n_observations = 1000\n",
    "\n",
    "\n",
    "# Make the distributions non-equal to see if the permutations test\n",
    "# shows the difference.\n",
    "sample_A = np.random.normal(\n",
    "    loc=1, \n",
    "    scale=0.1, \n",
    "    size=n_observations,\n",
    ")\n",
    "\n",
    "sample_B = np.random.normal(\n",
    "    loc=1.1, \n",
    "    scale=0.1,\n",
    "    size=n_observations,\n",
    ")\n",
    "\n",
    "observed_mean_difference = np.mean(sample_A) - np.mean(sample_B)\n",
    "null_observation = np.concatenate((sample_A, sample_B))\n",
    "\n",
    "# Print the shapes of the above arrays to make sure everything is as expected\n",
    "print(np.shape(sample_A),np.shape(sample_B), np.shape(null_observation))\n",
    "\n",
    "def resample(input_array, output_size, n):\n",
    "    \n",
    "    sample_mean_differences = []\n",
    "    \n",
    "    for i in range(n):\n",
    "        # Shuffle the null_observation array using numpy suffle method\n",
    "        np.random.shuffle(input_array)\n",
    "\n",
    "        resample_A, resample_B = input_array[:output_size], input_array[output_size:]\n",
    "\n",
    "        sample_mean_differences.append(np.mean(resample_A) - np.mean(resample_B))\n",
    "    \n",
    "    return sample_mean_differences\n",
    "\n",
    "sample_mean_differences = resample(\n",
    "    input_array=null_observation,\n",
    "    output_size=n_observations,\n",
    "    n=1000\n",
    ")\n",
    "\n",
    "significance_cutoff = np.percentile(\n",
    "    sample_mean_differences, 99\n",
    ")\n",
    "\n",
    "plt.figure(figsize=(30,20))\n",
    "\n",
    "plot = sns.distplot( \n",
    "    a=sample_mean_differences,\n",
    "    bins=10\n",
    ")\n",
    "\n",
    "plot.axvline(\n",
    "    x=observed_mean_difference, \n",
    "    color='red', \n",
    "    linestyle='-.'\n",
    ")\n",
    "\n",
    "plot.axvline(\n",
    "    x=significance_cutoff, \n",
    "    color='green', \n",
    "    linestyle='--'\n",
    ")\n",
    "\n",
    "plot.axvline(\n",
    "    x=-significance_cutoff, \n",
    "    color='green', \n",
    "    linestyle='--'\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Results\n",
    "\n",
    "The red line is the observed mean difference. The green lines are the 99th percentile significance cutoffs. If the red line lies between the two green lines then the observed results are not significant. If the red line lies outside the green lines then the observed results are significant at p<=0.01. The above process can be repeated and the the p-values can be observed in order to understand how often the results are significant. \n",
    "\n",
    "Set the `sample_A` and `sample_B` distributions to be equal to each other to see what the results of the permutations test will show."
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}