4.1_Expectation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d1f85b4f",
   "metadata": {},
   "source": [
    "## Expectation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69c01986",
   "metadata": {},
   "source": [
    "### Descrete RV: Six-sided Die Rolling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "85229702",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3.5"
      ],
      "text/latex": [
       "3.5"
      ],
      "text/markdown": [
       "3.5"
      ],
      "text/plain": [
       "[1] 3.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "15.1666666666667"
      ],
      "text/latex": [
       "15.1666666666667"
      ],
      "text/markdown": [
       "15.1666666666667"
      ],
      "text/plain": [
       "[1] 15.16667"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "2.92"
      ],
      "text/latex": [
       "2.92"
      ],
      "text/markdown": [
       "2.92"
      ],
      "text/plain": [
       "[1] 2.92"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = 1:6\n",
    "p_x = 1/6\n",
    "exp_x = sum(x * p_x)\n",
    "exp_x\n",
    "exp_x2 = sum(x^2 * p_x)\n",
    "exp_x2\n",
    "var_x = exp_x2 - exp_x^2\n",
    "round(var_x, digits=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ede7abb0",
   "metadata": {},
   "source": [
    "### Continuous RV: Uniform Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6d1f416",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.500219067412312"
      ],
      "text/latex": [
       "0.500219067412312"
      ],
      "text/markdown": [
       "0.500219067412312"
      ],
      "text/plain": [
       "[1] 0.5002191"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "6.54538208150943"
      ],
      "text/latex": [
       "6.54538208150943"
      ],
      "text/markdown": [
       "6.54538208150943"
      ],
      "text/plain": [
       "[1] 6.545382"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y1 <- runif(10000) #random samples from a U[0,1]\n",
    "mean(y1)\n",
    "y2 <- runif(10000,-2,15)\n",
    "mean(y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6e5b55c",
   "metadata": {},
   "source": [
    "## Density Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "62fee07b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vhegkEAAhCAQEEIECANf6Ie0C705x6e\nE3tAAAIQqCKBRVTodySPgBq3n2hhLskD/jwmeSRBDAIQgAAECkCAAKn7k7SKDnlRerz7Q2vf\n0TG+mbazmRsb/e0MDAJDEnijNnrzoBY+PLr2VtLDBg/pAxsgAIH6+0Z+n9cjnf65iYev+e+W\nzpA2aNrGIgQgAAEI5JQAgzR0f2I8cMOh3R9WP+K9+t8v87ZTNJT48iPMg8NKTSBcUYMc/lq6\n/Lra2hN/Vfv+NZo/T1JtdUhQXepzT+FySuC/8utv0hHS76RFpcjcsuSPx7p1yYM3uIJtpHar\nDvQIp8PJI+h1EIyF6vYX/nCkznRy3HO12pgptdHP6CXe4SoGO0mOfSAAAQikRoAWpO5R761D\n7un+sPoRu3Rw3Bjt84LkgSEwCDQIhPNoZh/pa9JN0pXL1h5Y4I3aLA9q/hFpR0m11aH/Po+u\n1YKpmmIQgEA6BHZSNgo4al+VzpSekCLzV+g/Ix0pjZdGatvqwE4Cjcu1Xyf3D18jPjBSZzo5\nbnStNrv2W/BdtdFza2DYpzo5hn0gAAEIQAACrQg4QAqlnVttZF0VCYQr609CXTrD+6TNIwKq\nmb3szdqofQeWw1m0zQHS89JVkh5IMAjUCfAdpPT+EFyR4e8hDWVraMMnh9rYp/VutWpcF9ql\nGP5A14lb2u3R67ZX9S1BXadCdQdeode0OB4CEMiEwHjlOimTnDPOlBakGU+AP9Q6ThorLSw5\nWNFDZ83veegBtb6sCQaBNAiE71Mufrn7SklddYI3W+caTNH6w/Tn6XcdLpYu1fwm2n9y6/1Z\nCwEIJEDArf/t7MZ2G1Pe9pDyWyblPMkOAhCAQCEIECBNP01m8XNpN2modznctcnd5PweEgaB\nhAmE7v5yiXS2tKuCnbeHzzBQ155wXe3noOoKza9PkCQSGATyQWAVufGi9HgO3HH3XLV4hfPq\nGuFKQAwCEIAABBoEZoLENALHau5rkvuRryetJC0kLS6Nk/xV9Gcld0lYU8IgkCCBcH4l/hfp\nHEndLTsJjiJ3An/oeAPJ7xj8SQ9AQbSFKQQgkCkBV64dmqkH0zN3C5Jt2YEJ/0MAAhCAQETA\nrSaYRtoRhB2lTSXXvDeba/vcxe5MyV2YtpVukDAIJEAgdMWFApvac9JXFBy5m2eXFqiWOvys\nDnJAv5e0f5cJsDsEINB/AnsryZEO8tNnb+rXCF9jlpFu7nPiJAcBCECg0AQIkAZO39Ka+CH0\n0g7Opt/v8EhFGASSIvATJbyW9H4FR2+MPJNAXWjCnXS8AvtQwwwHnfx9jzw7joQABIYj4G7c\neTLeQ8rT2cAXCEAgNwQIkAZOhVuH3C1pS2niwKqW/5uXu9rd23IrKyHQM4FwdSXxM2lrBTQK\ncHq1QO8vhUcolZM0VbfRoJPhf3vNlOMhUFUCs6rg7pI9VirCID++xrgFCYMABCAAgRgBAqQB\nGO9ocpQ0QdpOOld6SvIIYKMkD9qworS9tJzk2n0MAn0mUH9X6PdKVO8dObDpm+2plBz87yN9\nX8IgAIH+EvC9tIiD/LgFiXdq+/u3QGoQgEAJCBAgTT+J+2nWQ7C6tt0Pk83mF979DtIOkluc\nMAj0m4BHSFxVUutRPy14Xa1H31KKZ2l6ooKvu/qZOmlBAAI1D/KzlaSPNNfOl56W/H6PvpU6\nrYJtvOb9TuA6Ul7eYXWAtK2EQQACEIBAjAABUgyGZi+UlpcWl5aU5pZelp5sSA+aGASSIFAf\nte5ApbyvApjH+59DcJ6Co78r3SOl9fqfPilCoLIEijzIj7vY6X4X6lkgcCUgBgEIQAACIkCA\n1PrP4DGttjAIpEXALZju1vmbBDPcXWn/Ww9Dn9PD0OkJ5kPSEKgSgSIP8uMWpJklVwg6WMIg\nAAEIQEAEZoICBCCQNYFwCXmwq6R3hYIpyXkTTFLabkFSK1XohyIMAhDonUB8kJ92qblCMm+D\n/Lgi0NecZds5zjYIQAACVSNAC1LVzjjlzSMBD+uth6zg3BScO1h5eJj6L0inpJAfWUCg7ATe\nUQELOshPIN/Dh+U/I9mV/a+U8kEAAl0RIEDqChc7Q6DfBEI/mIyXtuh3yq3TC57VA5EHIvmZ\npqfy3kFrSqyFQJcE3EW2qIP8PCTfCZC6POHsDgEIlJsAAVK5zy+lyz+Bn8pFjWwVeACFtOwQ\nZfR16YvSCWllSj4QKDmBog7yQ4BU8j9MigcBCHRPgACpe2YcAYE+EQj9creDlE/0KcEOkwk0\n/HDowSDUtS88WcHZ2x0eyG4QgMDwBPxej1UUe1CO8m2/opwt/IQABFIhMFMquZAJBCDQioBH\nlbtdAcrFrTYmvO63Sn+s1OqbXwlnTfIQgECOCNCClKOTgSsQgEA+CBAg5eM84EXlCIT+dsrO\n0qHZFD2YrHw9SMN3ssmfXCEAgZwQcICkb/6FC+TEH9yAAAQgkDkBAqTMTwEOVJTArir3S9IZ\nGZb/MOX9YT0YrZGhD2QNAQhkS+ABZR9K/kg6BgEIQAACIkCAxJ8BBFInUP8G0beU7e/UvS7B\n7x4NV7DgP9rDL5bTijQcKrZDoLQEgldVtCekFUpbRAoGAQhAoEsCBEhdAmN3CPSBwFZKw91Z\nju1DWr0m4S5+n1UF8uK9JsTxEIBAYQncJ88JkAp7+nAcAhDoNwECpH4TJT0IDE/ArUcnqfXo\nueF3TXqP4BLl4JYkfzwWgwAEqkngfhWbAKma555SQwACLQgQILWAwioIJEcgXFlpf0Q6Ork8\nuk7ZvuykViSG/e8aHQdAoBQEaEEqxWmkEBCAQL8IECD1iyTpQKAzAl/Sbjeo9eiOznZPZa8/\nKRePqrd5KrmRCQQgkDcCDpCWUyVJkDfH8AcCEIBAFgQIkLKgTp4VJRCOVsF3kPLw7lHsHAQv\nasGj6e0WW8ksBCBQHQIOkGaXFqtOkSkpBCAAgaEJECANzYYtEOg3AQ2GUHM3ttP7nXAf0nPQ\n9nHVIC/Vh7RIAgIQKBaBSXJ3qsRQ38U6b3gLAQgkRIAAKSGwJAuBFgTcQjNB3es8rG7OLLhW\nDt0j7ZIzx3AHAhBInED9cwMOklZIPCsygAAEIFAAAgRIBThJuFgGAuGKKsW6Us661w1ia992\nVivSzIPWsgABCFSBgLvZESBV4UxTRghAYFgCBEjDImIHCPSFgN89+pdaj27rS2rJJOLBGvx9\nJnW1wyAAgYoRIECq2AmnuBCAwNAECJCGZsMWCPSJQH1kqO2V2Ml9SjChZOrfZbpAiX8xoQxI\nFgIQyC8BvoWU33ODZxCAQMoECJBSBk52lSSwnkq9qHRqAUrvIG5LdbObqwC+4iIEINA/Am5B\nWlq/fQ8kg0EAAhCoNAECpEqffgqfEgG3yPxD3eueSim/XrI5Xwe/IW3VSyIcCwEIFI6AAyQH\nR8sUznMchgAEINBnAgRIfQZKchAYTCCcTcse3vuUwevzuhS8Jc/8TSS62eX1FOEXBJIh8LiS\nfV1ioIZk+JIqBCBQIAI0pRfoZOFqIQlsIa/9dfpzCuS9u9ldo642i8v1xwrkN65CICsCrmx8\npylzf3jVlSMewfJp6ULJrTQ5tSDUb97vIfEtpJyeIdyCAATSI0ALUnqsyamaBNwSM1GBhmtm\nC2LBdXL0IWm7gjiMmxDIkoDf13tb+lzMCQdFd0knSXtKv5X+Lf1YyrM5gKMFKc9nCN8gAIFU\nCBAgpYKZTKpJIJxf5d5I+nMByz9BPn++gH7jMgTyQMCtsG5B2l0aK60t/VE6QHKrcl7tP3Ls\nPXl1Dr8gAAEIpEWAACkt0uRTRQKfUaGfk64oYOFPl8/j1OVmpQL6jssQyJLAIsp8Denwhjw4\nyz+lr0jXSnlumb1b/q0sYRCAAAQqTYAAqdKnn8InTMBdbty9zt1vCmaBH5TulOLdhgpWBtyF\nQCYE9C5P/X2ks1rk7oqHPLfQ+He/oCpG/MFoDAIQgEBlCRAgDX/qR2mXjaUvS6sOvzt7QMAE\nwoX13/rSaVJRzQ9zBEhFPXv4nTYBfUOoNof0tKRBTmqrSc3me0meBz65V/55sAlakZrPHMsQ\ngEClCBAgTT/dZvET6SbpXMldJFyL9qjk0YeOlm6XDpQwCAxHwKNXuWuNH5SKao3a7rDVg15R\ny4TfEOg3AbcYTZF+Kb0keTAGv3d0hOSKEtv7pYukTaUTpJxa8IYcmyQRIOX0DOEWBCCQDgEC\npOmcD9PsftLL0oek86TjJD/kfl5ywPQH6YfSVhIGgXYE3PJyprrX+eGpoBY8IMdvkWhFKugZ\nxO1UCLyiXOaU3iftKl0q+b4xa0Oa1LaUNpR+Jum6kGtzN7s8dwPMNTycgwAEIFAmArOpMP5A\n5hcahZpd039Ifrj9cGNdNLlcMw6ekrIxStj57pxUBqSbNIFwUZ1CdVMJ10wypym10Ze9WRu1\nb5J5qAx7SA6UsOIS0Dmst4wXtwTF9NzfP4tscc3MGy0kPHUXuR6uC+GB+s1f3A8fX1VLmq5T\n4Ru10Sv0Iz3SgAAEUicwXjlOSj3XHGRIC9LASfC7RTNL0cc8X9P8BOkFyaMOxc0v3i4TX8E8\nBJoIbK3lR9V6dEPT+iIuniGnl9UDk2vHMQhAoHMCruiKzO8dPR8t5HzqFiS62OX8JOEeBCCQ\nLAECpAG+7g5hFh+N4Xaw9HUpXgvozR+X9PCLQWBIAu6C+ZchtxZqQ/CI3PV7eXQrLdR5w1kI\njJiAA6R3q1LEvRkwCEAAApUkQIA0cNod8JwvnSb9RnqX5NYjtyJFtYAf1PwF0mbSsRIGgRYE\nwkW00t0ySxIg1YvoshAg1VHwHwRKT+A/KqHve7Qilf5UU0AIQGAoAg4EsAECHnXsG5KH8/72\nwKpB/++gpY9JP5DOHrSFBQhMJ/BpzbpF8rrpqwo/5wDJ7yWsogbVfxe+NBQAAv0l4AEa1A21\nY3Plm1tmc2qBBp0IXWnoAKlM17Gc8sYtCEAgjwQIkKaflTc0+yvp8OmrBs0doqW9JA/jikFg\nKAJuaVEAXeTR65qL5tHswju01mUjQGrGw3LVCXgY/H92AeFM7btNF/tnses9ypQWpCzIkycE\nIJALAgRIM56Gt2ZcVV8TvXekWvTai9LjQ+zXbrX7dM/Rbgdtm2uY7WzOLYFwfrm2nvSL3Lo4\ncseibnb7jTwJjoRAKQl4IJ+dpaOlqyRXprUztzDn3fweEgFS3s8S/kEAAokRIEDqHu2dOmSi\nNJIaQH+lfOEOs1ygw/3YLT8EtpArz0t+SCqbOUDaVy1Jy6l1jGG/y3Z2KU+vBE5QAh7Q5zjp\nAOlyqd/2ZyXYadDS6/3DAZJbjDEIQAAClSRAgNT9ad9bh7j7wUhsnA6ae5gD3Z/9Vul/w+zH\n5vwR8APFX/Wc9Hb+XOvVI797FDrAdxkP6jU1jodACQkcrzJ9XtL7erUkvoHmrnlLScPZodqh\n167gDpCW0G9e9yO/k4RBAAIQqBYBAqTuz/fPuz9k2hFPa85qZ+6GhxWOQOjA92OSW5HKamep\nYJ+RCJDKeoYpV68E3LNgacn31qm9JtZ0/DlNy0MtOkAaqqv4UMc0r3eA5Bax90g3NW9kGQIQ\ngEDZCcxU9gJSPgikROATyscDfVyWUn5ZZHO2MtVw9+G7s8icPCFQAAIeoe42qd/BUcpFD/ye\nrT9uu2rKGZMdBCAAgVwQoAVpxtMwq1aNk8ZKfl8olJ6XPIrXfY1lTTAIDCKwpZb+rkrXXmtu\nByWas4Wb5c+T0hbS73PmG+5AoAgEVpGTIx3kJ+3y3a4MfS/EIAABCFSOAAHS9FNuFu4+t5s0\n3/TVg+bc1WAXyQM1YBBoEAhn0YxbkL5SbiQeujzUO1Y1B4MESOU+2ZQuGQK+d0yU3BUv7+ZK\nwQ/n3Un8gwAEIJAEAbrYTad6rGa/JnkUovWklaSFpMUl16L5hvasdIu0poRBICLwUc3MJl0Q\nrSjx1O9BqLzhmBKXkaJBICkCHuTnjKQS73O6DpBW63OaJAcBCECgEARoQRo4TX7Y21HaVLpo\nYNWg/x/Xkm8WZ0q+uW0r3SBhEDABt6hcru51L1UAxxUq42uSfyunShgEINA5gV4G+ek8l/7s\n6XvefKoMWUzXNt8DMQhAAAKVIUCANHCqPepQKF3awZm/WPt8tYP92KUSBEKP9LSFVKQHnx7O\nTDBFP5XzlYCDQgKkHkhyaCkJlOkdVr9z64Fn3IpEgFTKP1cKBQEIDEWAAGmAjGvK/N0hP/S5\nf/hQZl7uaufvwWAQMAGN6lYf0OPcCuFwN7s/KlAaVfJBKSp0SilqjwR8byjZO6z+nluo75/V\nA6QqdB/u8U+AwyEAgTIRIEAaOJvvaHKUNEHaTvLD7lPSZEkPgfVBG1bUdHtpOWktCYOACTio\nvlGBwpMVwnGhyurfxQaS5zEIVJ2A32H1R5SPltzC+rT0nDRaUje1mu8f4yW/w7qOVJQu2q48\n9Du4GAQgAIFKESBAmn6699OsHnRrR0h+6G02f9fC7yDtIPmmgUHABDaX/lwtFMHLqlnWO1f1\nroUESNU6+ZR2RgJlfofVQ33vNmORWQMBCECg3AQIkAafXz/sLS8tLi0pzS3pYbD+7Re3ELwu\nYRBoEAiX0cwqklscq2Yu814S7+NV7cxT3mYCZX6H1ZWBK6hCRC1hwZvNBWcZAhCAQFkJMMx3\n6zP7mFZfI7nf9dXSgxLBkSBggwi49eghPTi4n37V7DwVeFE9OL2/agWnvBBoIuAgInqHtWnT\noEVXSBbtHVaXzX6vPKgkLEAAAhAoOQFakEp+gileogQcILklpYLmYX/DW1VwM/B7FRgEqkqg\nxO+wBnoPN3xCJ9bvId1W1RNMuSEAgeoRIECq3jmnxH0hEM6jZPyytUeuqqo5OPT7entXFQDl\nhkCDQJnfYXUr0mqcaQhAAAJVIkCAVKWzTVn7ScAfSn1FchfMqpoDpH1Uw6x39gJ3S8UgUGUC\nZX2H1QGSP2eAQQACEKgMAQKkypxqCtpnAu5apnfUAo9uWFEL1OUmdGBkFkdWFALFhkAzAf8m\nylRh4K51jGTXfJZZhgAESk2AQRpKfXopXDIEwlmU7ickt6BU3TxYgwMkDAIQKCeBm1WseVUZ\n4lE7MQhAAAKVIECAVInTTCH7TGA9pTebxDeABoLE9fXwNFefGZMcBCCQDwIaqbP2gsSIlfk4\nH3gBAQikQIAAKQXIZFE6Ap9Sia5W97oXS1ey7gt0hQ55S9qo+0M5AgIQyD+BIJSPt0oESPk/\nWXgIAQj0iQABUp9AkkylCGym0rprGTbw8ch/CISZYBCAQDkJ3KJiESCV89xSKghAoAUBAqQW\nUFgFgaEJhP5g4jISAdJ0SGahUf1CrifTmTAHgTIRIEAq09mkLBCAwLAEsnqgmXVYz9gBAvkk\n4JaSe9S97sF8upeJVxrNrza/9KFMcidTCEAgaQIM1JA0YdKHAARyRSCrAOl+Ufij5A9tYhAo\nEgEHSLQeDTpjwTNavEEyGwwCECgfAQZqKN85pUQQgEAbAlkFSIfJJ9c2XyU9IP1MWlLCIJBj\nAuECcm4tiQBpxrNkJgRIM3JhDQRKQICBGkpwEikCBCDQBYGsAqRD5eMq0gekv0nfkCZJl0k7\nSHNIGATyRkDv2dSel67Lm2M58McBkn7T4dI58AUXIACB/hO4RUm+v//JkiIEIACB/BHIKkCK\nSPiC+23p3dIm0nPSSdJT0nHSOAmDQF4I+IOoet8meDsvDuXHj+Au+fKwRCtSfk4KnkCgnwQI\nkPpJk7QgAIFcE8g6QDKchaWvS/tIn5H+K50gvVfytxe+KWEQyJhAOEoO+Fs/dK8b+kzQzW5o\nNmyBQNEJOECaV63EyxS9IPgPAQhAYDgCWQVI7kK3nfR36Qnp4MbUH+BcXPqW5HeUDpIOkWaX\nMAhkSWA9Ze7RFy/K0omc5+0ASZzCuXPuJ+5BAALdE3hQh7wguWs8BgEIQKDUBLIKkDwww58k\ntx59R3IXu60lDxcc7750vZZdc+8HUwwCWRJw17Er1b3upSydyHne4lN7Q3JLGwYBCJSKQH2g\nhhtVJIbzL9V5pTAQgEArAlkFSMfLmdWl90lHSJOlVnaJVrr16LlWG1kHgRQJuHWT7nVtgQdv\nafM/JAeTGAQgUD4CHqCGAKl855USQQACTQSyCpA8Wt1DTb5Eix/UjB9Gba9JrpHGIJAhgdDv\nw3l0No+4iLUn4CByU3Wzy+ra0t47tkIAAr0QcK8OVWzW38nsJR2OhQAEIJBrAlk9xPxFVJYb\ngozfP/ruENtYDYEsCDhgv1vd64YK6rPwKa95upvsfJK/F4VBAALlIuAPQrvb+/+Vq1iUBgIQ\ngMBgAu8avJjo0uFKfd1GDnNpepr0emM5mozWzArSMdEKphDIAQF3GaN7XUcnInhWtct+iHJQ\n+c+ODmEnCECgIAQCfQcuvFfOugLEv3MMAhCAQCkJpNmC5KDnzoY8EIMHaoiWo6mb7z1y3Y8l\nDAI5IBAuICfc554AqfOzYVa8h9Q5L/aEQJEI+D0kB0gYBCAAgdISSLMF6d+i+MUGSbcUOQjy\nsKEYBPJM4JNyzoOE+KEA64zAudrtANU0L0O3xM6AsVdpCHjEVX/gfKzkUVpDSa0utTuk+xrL\nmhTaXJG5V6FLgPMQgAAEhiGQVoC0pPz4tuSaZQ/Q4MDoG9JQ9i9tOGmojayHQIoE3BKi92qC\nd1LMs+BZBaoMCSepEGb324IXBvch0AkB30t/Lu0m+R28VnaTVu4iucdEkc2VRUvoN67PcwRP\nFrkg+A4BCEBgKAJpBUi+YWwj3S85QPq0NJc0lHlobwKkoeiwPiUC9ZGaNlZmO6WUYZmyibrZ\nESCV6axSlqEIHKsNW0lHS+dLT0tueXZvCd//VpTGS7dI60hFfn/HvUFeltz1+CwJgwAEIFA6\nAmkFSLeJ3KIxeivF5pmFQF4JfFSOjZIuyquDOfbLAdJXVcs8RrXML+bYT1yDQK8E9Dde21HS\n8PYtrxWPa7272J0pnSFtKxU4QHJrenijyrCWRIAkCBgEIFA+AmkO0lAEerPJybWldaU5hnB4\nw8Y+Q2xmdYkIuIvYFXrAd20p1h2BK7W7R6ncpLvD2BsChSOwtDz2u0aXduD5xdrH95eim7vZ\nuQUJgwAEIFBKAlkGSPOK6EINqvNr6pc+D5ZWa6xLe7KqMrxLulryw93DkrsFNtuPteJbzStZ\nLiUBB0huCcG6JhBM0SEXSmaIQaDMBNw69D9py2EK6R4bvqfcO8x+Rdh8rZz8gOJCdyHEIAAB\nCJSOQFpd7JrBfUIrzpY8UMNx0qnSx6VXpC9Lrpm6R0rLAmV0iuSHuvGN6W6ani65dvAgCasU\ngXCciruERIA08vNudnoHKZxZrXBvjzwZjoRArgmoy1ntKGmCtJ10rvSUNFkaJUXvIG2v+eUk\nd00ruvkbZ7NIa0iuVMQgAAEIQKAPBDzcqR+eNApObRXJ3RN+JM0uXSH9QUrToi4SDtLitr8W\n7NuusZWXaN79yJMy92d3njsnlQHpdkIg/IlOw+2d7JnVPlNqoy97szZq36zyHz7fUA+G4VRp\nveH3ZY8ECeyhtD2CGpYsAXcnvV/y9btZrnxzAOWKl6TNAVsK14XwFhVT18mh7VUNd67rVPhG\nbfQKQ+/FFghAIMcExsu3STn2LzHXsmhB8rs9rkX7vPSktL3km8mJ0muSW5ZcC5emLaLMfFO5\nrilTX/znkn4vPSZdJGHVILC5iknrUU/nOnhOP23XNJvllT0lxcEQyD+BC+Xi8tLi0pLS3NLL\nku9zlt/JK5P5N71umQpEWSAAAQhEBLJ4B2lWZR5IUZcbd7dzH253SbAtKj1an0vvv4eVlVls\n0SLL72jdOZJbjd7fYjurSkfA3/dw//raX0tXtPQLZIYOkDAIVIWAK9OukS6Q3P3sQalswZGK\nVLtK+rAqQbKoaHX+GAQgAIHECGQRILlftpvrvie5FWkdya1Gto0ktx79wwsp2n+V19+kI6Tf\nSQ7SInPLkn1y65JrzNwlECs3gc1UPP9N3FzuYqZSOr+PoRbjcOVUciMTCEAgLQIO/twtnorD\ntIiTDwQgkBqBrGp+vqYS/kX6ovQv6VDJ3RHche1iyS02adtOyvA46avSmdITUmRvaeYz0pHS\neAkrNwG3JJ6nhk53/cR6IhA8oODobiXhViRPMQj0SsC9EN7oNZE+Hj+n0lq2i/Re0L6PdLF/\nTncNVNkZ+qOx60k35NRJ3IIABCAwIgJZBUjuq72I5H7avsBGD6Luz+xaqSwsGqZ1HmX+ZgsH\n/H6Ugyi/j7Rgi+2sKgWB0A87G0ifLkVx8lEItyI56DwwH+7gRcEJ3C//3cvgRCmr+4Wynmar\nac7v2nVqroDbptOdc76fe1X4vn1wzv3EPQhAAAJdEcgqQLKTL0sPSQtIgWS7V1pIcoDyopSF\nuXavnd3YbiPbCk9gY5VginRZ4UuSnwL4PaQfqh5kYf3Un86PW3hSUAKHye9dpJ0lv99zsnSS\n9IiUhV2rTO3L0dJV0iFSO4vet223T1G2ubwaaCmcSb/td4riNH5CAAIQGI5AVgHSODnmG5qn\nrSzPNWyryGEHb4+3cnyYdX7HyS1n7Sw6J3O024ltiRFwVzB19QxatSImlmnJE3alwjOS3+1y\nN1YMAr0QOFQHW373xd20vyHtI10hnSi5+/arUpp2gjJzRZ//vg+QLpf6bT9Wgst3mKhbwtMw\nB0hjJN/Lb0sjQ/KAAAQgkAaB6GE8jbzieZyiBQcKP5McaLwtxS2rmsC4D0PN36kNE6WRdJFw\nzaFvou1sVGPj1HY7sS0JAv6gae2T0neTSL26abpmOTxP5XfwSYBU3T+Efpf8FiVofV/aQNpN\ncsXbkdLpkiukbpfSsuOV0ecldyVdM4FM1UpT8zUqRxbonhbeJ4fWlwiQcnRmcAUCECgeAb/j\n43eOtiie63WPf6r/P5ug72OUtvnsnGAeJN2SgD9oWv+w6fwtN+dsZf4/FBsHFqr1KNR7fOHs\n8bXMp0JgD+VyUyo5pZ+Jum3WdpeuldzF60npcOl6yRVv35TSNN/f/k/KqvLRZTWHfT2TjoUK\nSMPzW+X1Kh+KbYWFdRAoEoHxcnZSkRzul69ZXMT1kFQfgejlfhUi5XR+nnJ+ZJcegS2V1dVq\n5JucXpaVycmjU/rBze94nV2ZUlPQJAi4+7F/q9tLH5ccCHkgkE9J6h47rUfCAZo/RPqj5PtO\nGvaCMrktjYxylId/239SkDRK106P+IpBAAIQKDyBLAIkX0DPkb4kXZZDgrPKp3HSWMm1k27N\neV66Q3JXAi9j5STgh67flLNoWZcqeEM/nQvlxaclAqSsT0ex839A7ruLtgOR70gTpFaVGm5F\n0kN7zdf0tAIkZdXWVtHWF6XH2+5VrI2Xy10zXku6sliu4y0EIACB1gSyCJDsyTXSQdKtDfmG\nEbfbtXByfEUK82bh1qHdpPmGyM/dVHaR7hxiO6sLSyBcXa4vJTl4x5IhYLbq/hTqtxbwjl0y\njKuQ6vEq5BmS7xPt7BJtdJdOBee5Md87RvoOa24KMdiRQPfv8Eatc2seAdJgOCxBAAIFJZBV\ngLS7eLmLnVtpPtmC3Vxal3aAdKzy3Eo6WnJ/ag9H/Jw0WnLAtKI0XrpFWke6QcLKQ2BLFUU1\n0sEj5SlS7kri39UJ0nrSpbnzDoeKQmCvDh3NS6tR3N29tXBPfEVJ5t3NbhPpJyUpD8WAAAQq\nTiCrAGmFnHEfI392lDaV3Ie92R7XCnexO1NyzeW2EgGSIJTIPq2y/KVE5clhUYLnVdN8hRxz\nMEqAlMMzhEuJE3AvhTKaAyQFR+G8qmTS7xyDAAQgUGwCM2Xs/keU/9cld1uzfWBgkvr/SyvH\nUOrkoc03gnVT95AMEyQQ+vyvJp2dYCYkPUDA3ewcIGEQgEB5CPh9Lw1aVx9uvTyloiQQgEBl\nCWQVILkL3d+la6TfSW6RmUNyq4yX/cJnmubWof9Jwz24ucVtG+leCSsPAbcePaSaT94tS/6c\nOkBaVPURWVWGJF9CcqgyAd+71pR8L/my5Hdat5bcRTuQSmr1dwqvUOH8HhIGAQhAoPAEsupi\n91uRe4/kwGhl6cOS+4t/UzpEukLyi6xp2TvK6ChpgrSddK70lDRZGiVF7yBtr/nlpLUkrDwE\nHCDRepTK+QyeUHB0s7Iyc08xCJSBgO+l7j7ngMj3i1Z2k1a6t0RZK2Lcu+LbrQrOOghAAAIQ\nGJ6AW60cDG3c2PUHmnq0ocjcgnRitJDydBPld7/k7nbNmqJ1DqDGSUnaGCXuvHdOMhPSjgiE\nGso9fFtykF4oK9aHYuNowx+J93/ia5hPlMAeSt0P51hyBDyy3ovSQZK7YLvFaEFpMcndd92K\ndL70luQWpiTNFX77JplB67TDFfS71r0rdNnr9iofio1QMIVAUQmMl+OTiup8L35n0YK0gBye\nTXpkCMe93i1LWdiFynR5aXFpSWluyaPtPdnQ65pi5SLglgy3Fl5XrmLlujQeDOOXepBaRb2O\n/p1rT3EOAsMTcKXWjlLFB/kJ7tNv2hWMn5Lohi4IGAQgUFwCWbyD9Ixwueuau6s1m/touwtC\n1hfXx+TDNdIF0tXSgxLBkSCU0Dy0u7rXBar5xNIhEPghyt2MzB6DQNEJLK0C+PrBID+12t/E\nwQESBgEIQKDQBLIIkAzsUGkP6WRJtcj1ARq+pKmDErfguJsdBoGECYTzK4P1JbdoYOkSmKjs\nCJDSZU5uyRBgkJ/pXM/T7NqKF+eZvoo5CEAAAsUjkEUXO1M6UJpT+q40WrJ9SHLL0s7SPyUM\nAkkT2EIZPC9dlXRGpD8DAQel++pBajm13j0ww1ZWQKA4BBjkZ/q5ciWnXj2qfzT2tOmrmYMA\nBCBQLAJZBUi+oewpHSa9Vxor+d0j18S9LGEQSIOAWzD+qgd0DdKApUvA7x6F7krrc+AX2zEI\nFJnAfnL+RukIyUN8N9tUrThT2kHyfa6kFmgwo/AiFc7d7AiQSnqWKRYEqkAgqwApYusRfVx7\nzwNqRIRpSgTCMcroY5JbkbBsCLgViQApG/bk2n8CDPIzwPQ8TX6rQGlmVT71nzIpQgACEEiB\nwEwp5NGchb8Tcbn0tPSC5MEP3MXG7x35ZVcMAmkQ2EyZeLj5Tl6sTsOfKubhAOmDepBasoqF\np8ylJVD1QX7+rjPrCqgPl/YMUzAIQKD0BNIMkOYTzfOlY6R3Sx4h7leSm+EdLH1Fukf6pIRB\nIGkC2yiDc1TD6e9bYZkQCG5Vtg9KW2eSPZlCAAIJEAgmK9HrJVdCYRCAAAQKSSDNAGkvEfJ3\nIr4n+UNyO0l7SO6T/RFpdcl9s8+QHExhEEiIQL173cZK3H9rWLYEfA4+l60L5A4BCPSZwNlK\nz91nMQhAAAKFJJBWgDSr6LiF6GjJQ3y3sru08vPSKGnbVjuwDgJ9IuCXqF+RLulTeiQzcgKn\n69APqJvdMiNPgiMhAIGcEZgof5bZtXaKB2HCIAABCBSOQFoB0iIiM7t08TCEHtL2R6UVhtmP\nzRDohYC7151F97peEPbr2OB2pXSf5HOCQQACpSAQeFTam26vvc+j2WEQgAAECkcgrQBp/gaZ\nxzsg5H0W7mA/doHACAiE8+qgj0t0rxsBvYQOcSsSAVJCcEkWAhkRmPhSbW4CpIzgky0EINAb\ngbQCpGg48Tc7cNcvzaflVwfusEvJCHxG5fHoiZeVrFxFLo6D1f9TN7vli1wIfIcABAYRmDi1\nNvMyg9awAAEIQKAgBAhECnKicLNvBKLudXx7q29Ie00o8PuHd0sM1tArSo6HQG4IBA/NUpvq\ngZcwCEAAAoUjELXspOX4ucpouFakRbWPhwPHINBnAuFCSnADaaM+J0xyvRNwNzsP0rJ/70mR\nAgQgkAcC89Ym+16+Wh58wQcIQAAC3RBIqwXJXZoukvydIw/E0E5Xa/u/JAwC/Sbg1iN/c+vK\nfidMej0TmKAUVlE3u3E9p0QCEIBALgisU/vneXbk57Wf+tMeGAQgAIHCEEirBeleEdmkMFRw\ntKwEtlPBTtXode+UtYDFLVfwgIKjG+W/z5FHtsMgAIGCEzi49o2Ha7XRqpFabwsVpR4sFbxI\nuA8BCFSEQFotSBXBSTHzSyBcVr59SHJLBZZPAn+WW9sqUAry6R5eQQACIyEwuTa/RrMLed4Y\nCTyOgQAEMiHABSsT7GSaAYEvKE918QxuyyBvsuyMgN9DGiut29nu7AUBCBSBwNu1meeTnxsW\nwVd8hAAEIGACBEj8HVSFgAMkt1BguSUQ+P2wSyR3s8MgAIGSEJiz9spVKsoXS1IcigEBCFSA\nAAFSBU4yRQzfJwYrSXSvy/8fg8/RZ9UdZ1T+XcVDCECgEwLL1+7/q/b7jH7Xc3SyP/tAAAIQ\nyJoAAVLWZ4D80yDgmstr1b1uUhqZkUdPBM7W0bNKn+wpFQ6GAARyQ2D/2n6XyZkpkoIkDAIQ\ngED+CRAg5f8c4WFPBEKP1OjudSf3lAwHp0QgeFkZnSWNTylDsoEABBImsHjtQQdHZ0g7JpwV\nyUMAAhDoCwECpL5gJJEcE9hUvs0tnZZjH3FtMIETtajzVv+w7+AtLEEAAkUlcJwc30C/6+WK\nWgD8hgAEqkOAAKk657qqJR2vgp+j7nUvVhVAAcvt7jj/lRisoYAnr6Iut7qXzi4WO0i/kL4l\nrSBV2IKbVHh/BH63CkOg6BCAQEEItLqoF8R13ITAcATCBbSHvr9RO3G4PdmeJwL1D/meLI/G\n58krfIHAEATm0vq3pc/Ftq+o+bukk6Q9pd9K/5Z+LFXZjlHhx6sViUFYqvxXQNkhUAACBEgF\nOEm4OGICfvfoGeniEafAgVkR8IPlanqQ+r+sHCBfCPRAwAG+W5B2l/xtr7WlP0oHSFtIVbUJ\nKvhsEoM1VPUvgHJDoCAECJAKcqJwc0QExuuoU9S97p0RHc1BGRII7lfm/5TGZ+gEWUNgJAQW\n0UFrSIc39JSm/lv+inStVOGuo/VBWBwkfVnCIAABCOSWAAFSbk8NjvVGoN7y4NaHE3tLh6Mz\nJOBzp4fJcHSGPpA1BLolEOoAV8p4NMZmO10r3tO8smLL7ma3vn7XK1Ws3BQXAhAoEAECpAKd\nLFztisBu2vsqtR7d29VR7JwnAh55cJREd5w8nRV8GYrA0trgD6E+LV0jqYvoDLax1jw2w9pK\nrQhuVXGvl9z9EIMABCCQSwIESLk8LTjVG4H619r9/pFrKrHCEgheket0xyns+auM424xmiL9\nUnpJ8mAMfu/oCGlhyfZ+6SJJw9fXTpCqbocKgEb4C+evOgjKDwEI5JOAP6KJ1WpzCsKyXYB4\nQfs+0sX+7Jougc8ru6nSX9LNltwSIHCs0rxFD1IrqDXwvgTSJ0kI9ErAgbzvIatIq0vu2uup\ng6NZJduW0obSz6Qzpaqbux8eLPldpAOqDoPyQwACEMgrgQ/LMdcCdqozEizImIYfOyeYR8mT\nDm/QqXQNZaltSm30ZW/WRu1b6kLWCxferPP5q/KXM7ES7qGU/Q0aLF0CQSy7xTU/b2w5yVm/\n/5SL68KraknTdSp8ozZaFRzNFn5Hv+snpVHNW1iGAARyQ2C8PJmUG29SdIQWpAHY12rigORo\nSe+t1A6R2tlT7TayLUsC4Tjl7hGkxmfpBXn3lYBbkX6hB6k91Yr0Vl9TJjEI9JeAW4x8DXIX\nO7cgudLteekO6XEJm07Aw57vI7nF/2QJgwAEIACBnBJwkOTat49m6B8tSD3BD4/SM4mD3NJb\nhVqQ1H0pfFnatvQnNZkC0oKUDNd4qq5s9DtIk6WheiLcqG2rSklbQVqQjCH8tXS7FG9tS5oP\n6UMAAp0TGK9dK9mCNFPnjCqx5/Eq5SXSgZUobekKGTq4/KKkIAkrD4H6YA2nqDzfLE+ZKEnJ\nCLiV82vScdJ60krSQpK71rlFaRvpWekWaU0JGyDgrtArSpsDBAIQgECeCNDFbsaz4RvZ0pLZ\n+EV/rDgEdpKrHkXqL8VxGU87JOARwe5WTbNGAwv8kIlBIC8EXDGzo7Sp5JHqmu1xrXAXOw/O\n4PdX3RKq9yQx/Zaf0G/6BJH4qfRXiEAAAhDICwFakGY8Ex6h7jaJ4GhGNjleE/pv+RuS3iML\nPOQuVioCwT0qjlt3aUUq1XktRWFcoRZKl3ZQmou1z7od7FelXdw1cTUh/GSVCk1ZIQCBfBOg\nBan787OKDnlRcq1gt7ayDhjuuw9zdJso+9cJfEL/uzvLMfAoLYHDVTLVwod6pyZ4trSlpGBF\nI+DWof9JHsp7Yhvnfb91D4V72+zTbpO7oS3ZbofYtgKNDBc8qt/0SfLdrUjnx8rALAQgAIHM\nCBAgdY/+Th3im6BvdN2au18s1uFBwwVSHSZTmd2+pZKergfnZypT4uoV1A9P6pJT203SqHYY\nBHJBwIMiHCVNkLaTzpU80ulkyYHKfJLfs9leWk5aSxqJbauDXEHXic3dyU452ucA+XKfAqVN\ndA2/MEd+4QoEIAABCHRIwLVcn+1w3+bdAq1wV7B2mkfb3V1jZwnriED4HiHTQ0r4wY52L8lO\n1RnFLn7Cwu/qPKv1Npwlvpb5tgTU4sZ3kNoS6s9GPdzX7pd8/W6Wu/06gPKADUmbA7Z9k86k\nk/RfbfsdpOYUQg10Eap7OyPaNZNhGQIZEhivvCdlmH9mWdOC1D36n3d/yLQjopvmtBUtZrwP\n1h2B72v3f6rm8abuDmPvAhL4o3zeW/qC5G45GATyQsAtH8tL7uq7pORWnJelJxt6XVNsaAL7\naJMDTLfC/UnCIAABCGRGgABpRvSzapVr+cZKzR/6UxeAes2gJlg+CIQ+T+66MtJWvXwUAy86\nJBDo/b/wGO2sVpHwZAXFVCh0SI7dUiPwmHKysK4IBAokw8N0yP6a6l3D4M2uDmdnCEAAAn0k\n4K5e2AABB4seTecJ6XrpbEkjotVf+vfQrP+RPDTrqhKWHwLflisPSH/Lj0t4kjCB3yh919Rv\nmnA+JA+BfhPwO0Sdvofa77yLkN7BcnIO6etFcBYfIQCB8hIgQJp+btX/mQ/9TcdRhLnQXVi+\nLP2KloQinK9++eia5tqfpR/0K0XSgUBKBDzIz6Ep5VXAbIKX5LS7se+lViQGKirgGcRlCJSF\nAF3sBs7kGE12lFwjfdHAqkH/P66lOyQ1+/Ohv0Fksl1wcPSK5IdlrFoEDlFx/62HqDUVHLtl\nF4NAEQj4/Tl/0wsbmoBHBPS13T06dht6N7ZAAAIQSI4ALUgDbJfWxO8yXNoB6ou1Dx/66wBU\nsruEsyl9jWhWU5/14K1k8yL1/BGofzj2PPmlmmYMAoUh4NaRdt9KKkxBknM0mKq0vyHtotvy\nGsnlQ8oQgAAEhiZAC9IAG7cO/U9K+kN/Q58JtnRLwDWMM0t+TwyrJoH9VOyb9BD1fgXJt1QT\nAaXOGQEG+enLCQku1+/6dCV1pKZuJfbQ5RgEIACB1AgQIA2g9sU3jQ/9pXZiy51RvfXohyqj\nXugN9KkNrJoEHBSFHpxjH2mzajKg1Dkh4HupW4fcJWy+IXxSMO9WkZrfQ8KGJ/B97eLBkVwZ\n9vvhd2cPCEAAAhBIikAePvTn96Hc3W/npApZ/HTD7wjR09LsxS/LyEtQzQ/FNvNy61H9I8Ef\naN7C8jQCGhKdD8VOo5HMzPFKVkPQ1w6S3AV7RWlBySPWrSZtLZ0vuTuwWkQSNVf4FfBDsa2Y\nhN/U7/slaYlWW1kHAQgkTmC8cpiUeC45zIAWpMEn5UItevhgPvQ3mEuOluqtRx69TC/pB6/l\nyDFcyYTAtFakvZU9rUiZnIPKZ8ogP8n9CfxOSTu4PE7aKLlsSBkCEIDAYAIESIN5REuPacbC\n8kdANYq1QHKXSAwCJrCPdLNqmdfSn8Z1XoFBIEUC3Q7y89UUfSt4Vv4QdOjeFLdr+iX9vv9Q\n8ALhPgQgUBACjGJXkBOFmyYQum//jyW9nE/rkYlgJhDcqv/8QreH/sYgkDaB+CA/7fJ2heQ2\n0r3tdmJbM4HgAa3xaJW/0j3AwSgGAQhAIHECtCAljpgM+kjgJ0rrGckf9cUgECfgB6h79ACl\nkSiDc+IbmIdAwgT8zo9btCdI20nnSk9Jk6VRkit2/E7S9tJyklo6sS4JHK79PyWdqt/4OvqN\nT+nyeHaHAAQg0BUBAqSucLFzdgTqNYdfV/7b6uY4NTs/yDmfBIKH9ODkh9QDNdXIdvyN5PM8\nldYrtWrXbpSOkPy5iGbzNetMaQfJLU5YVwQ8zHfoAFNd7Wr7Sx7FFIMABCCQGAECpMTQknCf\nCRyg9PSeSXBWn9MlufIQ8IPTTpLeVWBY4PKc1sKUhEF+Ej1VgVrlwh2VhUYDDC/TveCiRLMj\ncQhAoNIECJAqffqLUvhwXXnqvvsfKYrH+JkFgUBdmkIHSfoeTXiGHqDcxQmDQNoEGOQnMeKB\ngtBQ7yK5O2Ooof2DSg4/nBheEoYABKYRYJCGaSiYySeB0EH8kdJJuhlen08UK9H+AABAAElE\nQVQf8SpHBH4rX/yemlscMQhAoHwE9lSR1Jug9lcFSXOUr3iUCAIQyAMBAqQ8nAV8aEfAw3ov\nKtHnvB0ltjUI1F/e9rtqu+rh6YNggQAEykYgeFsl+rw0u6SKszAoWwkpDwQgkD0BAqTszwEe\nDEkgHKtN+0p7qfXo2SF3YwMEBhEILteiuth5ZLGQa9wgNixAoAwEgudVii2kjSQNzIJBAAIQ\n6C8BHh76y5PU+kvAX1G/Vzqmv8mSWgUIfE9lXEH6VgXKShEhUEECwb9V6M9I31ZFyO4VBECR\nIQCBBAkQICUIl6R7IRC6C4W/e7GzWo80xCsGgW4IBE9q7+9LehcpXL6bI9kXAhAoCoHgEnm6\nk/Rr/c49kA8GAQhAoC8ECJD6gpFE+ksgXEjpufVII5IFd/Y3bVKrDoHgDyrr1dLxdLWrzlmn\npFUjEExQiX8g/Um/81bfoKoaEMoLAQj0gQABUh8gkkTfCRytFB+Rftn3lEmwagT8TaRxEl3t\nqnbmKW+FCASHqrB7S3r3MNy8QgWnqBCAQEIEPIQyBoEcEQj9QLuppBHIAn99HoNADwSCR/XA\n9B0loKHiwyv0N/WvHhLjUAhAILcEAlWohTPLvTM13Va/9bNy6yqOQQACuSdAC1LuT1GVHAzf\nq9L6OzbfpWtdlc570mUN/qgczpZO14PTnEnnRvoQgEBWBAJ1y679THJLkivbMAhAAAIjIkCA\nNCJsHNR/AvUP/nlo5gsUHB3V//RJseIEvqzyu3bZ3TcxCECgtASCg1Q0/951Hwl/UtpiUjAI\nQCBRAnSxSxQviXdB4FjtO6u0SxfHsCsEOiQQvKSHpc9p52s1vUZBOIFSh+TYDQLFI+BW4/B/\n8lsDOIQrarqrfvNvFq8ceAwBCGRFgBakrMiTb4xAuKcW/NE/fdMieDG2gVkI9JFAcIsS+5p0\nuB6aPtrHhEkKAhDIHYHgr3JpbWl96Ur95sdqikEAAhDoiAABUkeY2Ck5AvVhWfdT+jsoOOIF\n+uRAk3KdQP19JA8hP1EPTMsBBQIQKDOB4DaVTgP+1PwtPd1fwo+XubSUDQIQ6B8BAqT+sSSl\nrgmEa+iQP0kanpURh7rGxwEjJbCHDrxB+psemBYYaSIcBwEIFIFA8JS8XE86Rfq7fvP7S+8q\nguf4CAEIZEeAACk79hXPuT5inW5WtVMVHP2i4jAofqoEgreVnd9HekW6SA9Lc6eaPZlBAAIp\nEwim6D7zfWX6ackDOKiCJFwlZSfIDgIQKBABAqQCnazyuBouo7L8Q7pU8s0Kg0DKBIKXleEm\n0mySW5I8xSAAgVITCM5T8fw5icckvZMY7iWNKnWRKRwEIDAiAgRII8LGQSMnEK6gY6+Q/L7R\ndqrVc99wDAIZEAg8ypXfSVhcOl8PSnNm4ARZQgACqRIIntZ9Z0tluau0u3S7fvsbpOoCmUEA\nArknQICU+1NUJgfDcSrN1ZJfnFVXB3d7wCCQJYHgCeW+rrSopBbNcL4svSHvwhPwpwrWlPwA\n7tbx3aStpRWlQMJyQyDw+68+LxrhrnaxfvtnS67AwyAAAQjUCJD4I0iJQLi+MrpC0o2otpWe\nFfgmhUBgeSAQuLvNOtJoycMBL5kHr/ChUAT80v8vJQfc10t62K5/lPgYTf0B7P9Ieu+ltqqE\n5YZA8LzuRV+ROx7pbox0l37//sDsYrlxEUcgAIFMCBAgZYK9apmGvgH5naMTJA/nPbVqBChv\n3gkEz8jD9SVPb9QDkr+fgkGgUwL+0PXXpOMkj5i2krSQ5O6b46RtpGclf4vLLUxYrggEt+q+\ntIFc0rf4amtJD+ga8DuJypJcnSecgQAEqkzAtVihtHPxIYSzqii/l9RaFJagPPk6I1Nqoy97\nszZq33x5VXRvPPxveGTjb9aBfRlsDxXipjIUJKdl8DX7bWnjDvw7Q/v8poP9etnF73Xm4rrw\naq02Vtep8I3a6AJ1XQsD/f7VRTJU0BSqMi88VXILEwaBKhIYr0JPqmLBZ6pioSlzGgTqQ6iq\nJr62maSaueD4NHIlDwj0RsCtm8HXlcY3pcP0YHSWxHtJvUEt+9FLq4Cu1Lq0g4K6i7HfecNy\nSyDQuQzOkd4nFx30ziOpe2SoSgZX9IVz5NZ1HIMABPpGgABpRpRq9eAl2xmxdLqmXgPv703c\nLKmbQm013Wj+2enR7AeBfBAI3GXqA9Jy0h16KNo8H37hRQ4J6O+j5hER1erQ1vyekrva3dt2\nLzbmiECgoDf4hBxyl0kPMPQr6SldD06QPirxDCUgGAQgUG4C0Uu2k1VM1wa2kltEVk0YQ4G7\n2IUfErZ/Sc9JqmnDkiRAF7sk6UZp17uJHqy/5ymSW5MWi7YUaEoXu+RP1s+UxVvS2dJOkh+q\n15DWlhxc+xxoOOmaep250ihRo4tdYnjr1wMFueEFklqbw/9KflfJwZKfITAIlI3AeBVoUtkK\nRXm6I+AuYC9KB0nuArGitKDkByLf0LaWzpd8E0zyJdsCBkihatnD0yTdmMNTpIXECEuYAAFS\nwoAHJR/qGhBeL70m/VJyt5ui2B5ylHeQkj9bmyiL+6VWlWsKsGsTpHFS0kaAlDThevqhng/C\nL0tqZapXoDyvqc5xuIM0NhUXyAQCyRMYrywIkJLnnNscHJTk5SXbAgVI4Uq6ERwnKWgMr5Q8\n+g+WEgECpJRAT8um/vL2tvo7f1BSS3O4j7TAtM35nSFASvfcLK7s3HK0qbSOtKw0m5SWESCl\nRXpaPuG8uhZ8QXKA9KykIDm8S3Lr0tYSAdM0VswUjMB4+VvJAIn+swN/qUtr4lq/SwcW2/5/\nsbau23aPUm90n+tQNaXhX1XMuyW3tKnvfbCedF2pi07hKk6g/vL2qYKgioHaXtL20iP6LRwl\nra55DAKzCsG7JQfODpTeI/ll/yWkQMJKSaD+PSUFR4GCpPrw7h/Q9CTJzxaqRKw9qWvEw9Jp\n0vck3S9DV4ZiEIAABHJNwIHiU9Jnh/HSfYwdIPkhKSnLaQtSOE4X9P0lPxC+KZ0u0WKU1F9B\nB+nSgtQBpER3CWfWb2Ab6SpJFSyhBiYJd5cWSzTb7hOnBal7Zt0e4XvDL6Ws32G137QgmUJu\nrF6p6C66X5aOlzzoy1TJ14xJkiobwwOk7aT3S3PlxnUcgUCtNl4Q9HdaPfNFHRu4oagWuN5H\nXBep2rmSAybf7EZJ80krSq4xXk6qQGAQukuIu4dsIn1KWl66RfqtdLJqyjxqEwaBChMI3lbh\nzxhQ6OvDztJ3pMP0kHODphdIF0r63QR+aMXKS+BYFW0r6WjpfOlp6TlptBTdP8Zr3tdQX1f9\n94FVgkD9t6+gyKNh1o4ZKHL9/rqq5lXxWH/H2e81+/qxsCTz4A+1Bxvyw+nDkiona49Jj+t6\nokpKDAIQSJIAAdJ0uvtp1qPUHSGpy9gMphqf2pnSDpIvdCWz0F0BVHtV+6C0tuQuArZrJN/8\nz9JF+SGvwCAAgWYCwb1a88MBhWto6mvIp6V9pZf0wHOdpv4t+QHZAZPeU8BKQmCMyrGj5HeO\nLmpRJj3Q1u8Zvn84oN5WIkAShOpa8LrK7ucNK2b1wV9W0ArL765ZH5OWlBaVZpJC/Zus6ZMN\nuTLXeqYhX1tcgel9FKQHL2uKQQACXRJ4V5f7l3131/a6pWRxyRekuSVfXKILkS9qBTW/YF6v\nnXLZHAwtI7msK0vvkXyTf1G6VbpM8oOdvl8UvKopBgEIdEwgiB589tSDjGuE15Vc6eCg6aeS\nWhVCP9DcLd0jPSC58mGSpIdpv8+AFYiAr6d6aO34HdavFqhsuJoqgeAFZRddP5pyrg8j/m6t\n9D3cwZLnrUWk90m+1iwo+f23UVLD3J2v5muK5Xu881ClzTT5Gcfyvf6VxtTzr8XkZx/rjeny\nO5kYBMpLgACp9bl1M7aVcwsdxK0kzSnNJTnIseaV5pN8oVxI8oXTF9FZJJtrlvxA5gez86Vf\nSbdLD+rhjIueQGAQ6A+B4Gml45YDSxb6N7iKtKrkignLAZQrLOaQZB5KvF4j7GNdK+zfq+UH\nGz+4+Pfshyg/zNys36zXY9kRuENZu8Z+S2liGzd8v91GcmvjSMwVWj73nZgrxLBSEQgc6Dza\n0DAlq7/H5Pu/nwMsPxPME5Mrf62lpLmkORvyNcjzs0uzSW3Mo9fW3mwomvc00pTGvKeW/Y+m\nnm/W21oXydveiS17fbTsaaRovZ9bonWexpc9Hy1H862W49t0SP2YodbFt0fz7aattsXXed7m\n/CKLz7db522t9h3qmCW14ZHGxrt1/3g22pHpYAIESIN5dLLkhxvXwqimt2tzMDJ2mKPchG5z\noDOcHaYdNpX8oGTZL+t5yQ9U+uOvXSH5Qct9mu2zRJO7OJTBfFFsd2EsQxlLVobADwj/aqip\nbPUhwxfTSssVGn4YXlCaX3qv5AccL3u7a3L9ILOH9BsJy46AH8iOkiZI20nnSm4h9DXYNfl+\nQF1R2l5aTlpLGomdoYNW7+BAXxP8t5G56en5tVH6cPjU2lsvZe5MpRyo3+PdKjRp5MWu9zpx\nkBQFS56ftUlqDa+/Z+ep/9bjcmWQlz213hWbej6Sj/X8zA3F5/08FK2P5j2N5G2ed4VAtK55\n2dui7a3mo3XNUx1WPy5aH19uNR+tazeNb2ueb152vs3W6brm4+LLvj5E6Ryg+b3iG5mfTsB/\niFh3BO7U7hMl1wR2a3/WAcPVAPqcjJP8EDWMBZ8ZZgc2l5rA2/uEtalPlrqIlSpcfeCT/6nI\nHfz2KwWmCIXdT07eKB0hbdnC4alad6a0g3RHi+2drHqfdvLD33D2gna4bLid0tg+X73C7i0H\n+FjhCNR7k7wmty0MApUjQIDU/SnfW4fc0/1h9SMmdHCca2gOlrgodQCryrvMUpt6dZXLT9kh\nkDMCF8qf5aXFpSWlfr/D6ppfdynCIAABCEAgYQIESN0D/nn3h3AEBCAAAQhUhMBjKqeFQQAC\nEIBAQQkQIM144tyC4y5uflfI3eFca+d3etwt4r7GsiYYBCAAAQhAoCsCvbzD2lVG7AwBCEAA\nAiMnQIA0nZ1ZuHVoN0ldp1vaTVq7i+T3kDAIQAACEIBANwR6eYe1m3zYFwIQgAAEeiBAgDQd\n3rGa3Uo6WvJocx757TnJI6w4YFpRGi/dIq0j3SBhEIAABCAAgU4J9PIOa6d5sB8EIAABCPRI\ngABpAOAYTXaUNpUuGlg16P/HteQudh6F6AxpWynpAOm9yiMt88vE7vrxUloZdpCPg1J3bXQX\nxzyYh8X0tyQcNOfFfN5elzx0dF7M397wSGx5sWgI2Vfz4pD88N/RNSn6s0SKeZFVewLupZC0\n+VrlCr1nh8loKW33dVajcRfePIy0h6HO0z2sF6ge+c/DxJfB8nZP6IXpPDr4ZakMg6XMrnL4\n2fa/Ujtbtt3GMm8jQBo4u0tr4gfxSzs42Rdrn692sN9Id/FwsL7IHzfSBDgOAhCAQBOBVhU/\nTbuw2AcCeXiH1Q/Wv+pDWUgCAhCAgAm451TljABp4JTfoYlrvf39iokDq1r+b17+/tG9Lbf2\nZ6UDJNcepXlu/KGw9aTNpLyYB8T4oXR2ThzaQn78WlouJ/7YjXOla6UDvZADW0E+3Ch5qOPh\naq/TcvdgZeTBVtxCnBdzy+gm0lUpOuSv22PJEfD12q1DeXiHdRn54RaV4czXVt/L9h5uxwJs\n9weT15c+WQBfh3Pxo9rhdGmh4XYswPa55ONj0rqSn7OKbu45dIx0fNELIv9/1yjDlzooSyXv\nH2k+hHdwDjLb5R3lfJQ0QdpO8oPnU9JkaZQ0n+QuC9tLfkBeS0rSHCRZaZnzMoMX08qww3z8\nLai8+GRfbHnxx764md8Xrrz49Iqdkr0k5cUn8/Hfd178kSt1c7fINxrzTIpP4FgVIS/vsPq6\n0EkXIF/z83T96OWv4E0dnMd72EjKlMd7zUjK4WPcM8fme0PersF1x7r8z39jvm6XoSy+B83c\nKI8mWDMBAqTpRPbTrGu/j5CS+hL69NyYgwAEIACBMhAYo0K4hXJT6aIWBXpc61x7fqZ0hrSt\n5JpoDAIQgAAEckqAAGnwiUn6S+iDc2MJAhCAAASKTiBP77AWnSX+QwACEMgFAQKk1qfBfWYt\nDAIQgAAEINCOgFuH8vIOazs/2QYBCEAAAh0SIEDqEBS7QQACEIAABFoQ8HsJeXqHtYWLrIIA\nBCAAgW4IECB1Q4t9IQABCEAAAjMS4B3WGZmwBgIQgEBhCRAgFfbU4TgEIAABCOSIAO+w5uhk\n4AoEIACBXggQIPVCj2MhAAEIQAACgwnwDutgHixBAAIQKBwBAqTCnbJEHPY3n/6bSMojT/QJ\nHfrMyA/v+5H2xT7lyXzOfO7yYv42xNNS9B2PPPiVJz4Rj0c142+sYRDIkkDerh+9sPB158le\nEsjRsR7woyyDRPn7VP4788exy2D+G/PfWhnM98aZylAQygABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABIpPYEcV4QbpYekv0kelLG0eZX6I9C/pUelSaVMpDzaLnPiHtFdG\nzqyhfI+S7pf+Ln1KyovtLkduzIEzq8sH/x0/IN0rnSItJWVpefuNZcmCvLMjkOfrR6dU2l1n\nilC+QAX9onS19Lh0s/QTabQUt4W0sKfk7b6u7iPNLOXNxsmhv0qPSFdK35dcxrgVpSxxnzfT\ngsu0bHyl5l02nz+X+T7J95fFpbzZmnLowhby31rcivCbifvLPARSI7CRcgqlEyX/6M+S3pKy\nCkjepbyvlyZLv5F2kS6R7OO2Upbm4OiPkn3ZPwNHllCeL0mnSdtIx0lTpS2lrM0+2BcHJFna\nKsr8NelO6TuSA9mHpGelRaQsLG+/sSwYkGf2BPJ8/eiUTrvrTFHK90MV9m3pHMkVJ3+QXpV8\n743bxVr4j7SD9F3J1/6TpTzZ7HLmSckB3K7SQZL9PEaKWxHKEvd3YS08I/lev1J8g+Z3k96Q\nHLxuLzmAdSDlIDBP9gM587o0sUkOYCMrym8m8pcpBFIj4JqQW6QLYjl6nWtFzo+tS3N2c2Xm\ni5JvCpHZp3uku6MVGUzfpzz/Jb0iTZGyCJDOU763SXFzS8kd8RUpz8+j/KKg8QXNZx0guTbP\nNy/7FdlqmvHf1L7RihSnefyNpVh8ssoRgTxePzrF08l1pgjlcwWg7yH2NW4/14KvUa7gsfn+\n5+XlvdCwz2nqdc0P7NH2LKYOEl6TFoxlfoDmfY8c01hXlLLEilB//nHg18zblWwvSi53ZC7n\ny9JPoxU5mZ4qP64Zxpci/GaGKQKbIZAMAV+sN5RWbEreNSLucpeF2R+3jMzZlPmxWvZFKCu7\nXxlfJ5mVA4G0A6S5lKdrHeO1P1qstx7Fb6xel6b5Zuiati9If5CyDpD2kA+uOYvbTFpwi+Tx\n8ZUpzefxN5ZS0ckmRwTyev3oFNFw15milM+BxO+kDZoK/jEt+zr+icZ6V1A234NHa53vgftI\nebFV5UhzWX6odS7LEg0ni1KWhru1r2nGwdF4qTlAitYtqW1xm6CFf8dX5GDelcq/beNHUX4z\nbYrAJgikR8A1IbtLvih8Nb1sh81plPZwF6mrht0zuR3WjCWdRYC0hvL3edky5odnfYPy+k28\nkIG9V3nO3sg3DwFSKwQba6UZfbPVxpTX5fU3ljIGskuZQF6vH51iGO46U/TyuVLQFWBjG0Ae\n0fTPjfn4xA+9brHPo80sp9aWnpYuizlYpLK4de5VyYHqpyTfN+Itdodo+S2p2fbTCnctzIv5\nnuy/J/t7oHSbdK70USmyov9monIkMp0pkVRJtKgEfEH4n/QbyQ+6v5fyYq49nE+KN2un7dsN\naWfYlN88jWWfo7g911hw038WdpcyfS2LjDvM0wGJbxIPSFk/WOT5N9YhTnYrKIG8Xj86xTnc\ndabI5VtXELaXDpf+2wDi8kxuzMcnz2shq2t93I/meT9PuifB1ZK7OH9aiqwoZfE7xg5KT5L+\nHjnfNB2qLL4Pu0Vmjqb9s1p0xanPyU6Sg6XLpQ9Jl0rbSrYi/2YGSpDg/wRICcLNYdJuhZk1\nJl8M4uauUZtKbpL9nHSqlKS561HcH883W6AVv5S+J/1YukZK0oZjlGTew6XtmizblIHJtP+j\nZV8EscEEFtTiRdLi0jZS1oFc2r8xFRmDQJ1A2a8fRS2fa/T9Hogr4OIVgC5Pq5YKX+/zeK33\n/Xw7aXfJ19kbpeUkW1HKsp98dZDT3I3dZYjbUOfF++Tl3Di43kdaR/qW9F1pMelRyYG4W/uK\n+puR68kbAVLyjPOUw/Vy5vWYmgOgh7TtYunb0oHS5yXXQiRleyjhuD+ej/9NOoA7RfqB5B/4\nwVLSNhyjpPNvl35Uszhv005uWbO9NDDh/waBZTW9VnJwtL7kLgZZW9q/sazLS/75IVD260cR\ny/cF/XlcKLnib1PJ98DIntRMdG2P1nnqdXm81jtocFkOlzaXVpB2kGxFKMuH5aefNdzbwIHd\natLSkm1FyfcTW7uyeHtezo17TOwr3WOnGuZzdKq0gOTyFPE3I7fTsXelkw255ISAf/iuUY/M\nPyA3B79f+rfkGofIztXMAZJrH+6MVvZ56mDs1aY0oxoNtyZNlFy79lnpbCkNa8UojXw7ycMX\nZtvYgcm0/xdpzPnhGxsgsIom/vvy3/SGkmvNsrIsf2NZlZl880eg7NePopXvq/oTOVI6Vvq6\n9LYUN5cnurbH1y+shUviKzKe/z/lP0VyF8jI7teMH8z9/GArQlkcILmC1uej2c7RCgexLo/L\nMmdDr2game/L3vZmtCLj6ULKf1GpuWIw/pxnf208Uwxw4H8IDCLgGhIHJb8etHagJsXrN25a\nn9bi35XRc9IaaWXYZT4vaP/9uzymH7vfrESag8XDtM4XPQeVWdsf5MC9GTuxlPL3e1pXSnNL\nWVtef2NZcyH/9Ank/frRKZGhrjNFKd8uKqjvr3u2KfAPte01aa7YPn6I93GfjK3LevYmOeDK\nuXiF+zJafkc6TrIVoSzzyU+3FMX1FS2bt98dXUKyLSc5mP2CFxoWaPqYdGJjOQ8T/23Z97Wb\nnPFvxPfH6HwV5TfTVAwWIZAOgb8pG9eEbC+5xupr0lPStdLMUtr2RWXoH/Zp0pdbyLU8WVtW\nAdK2KvhUyedoHmlryTfRHaU82FAPLmn65tZPM/qR1Pz3s3GajsTyyttvLOYasxUikPfrR6en\nYqjrTBHKt7AK6fvH/VLz9cnLfgC3+fr+sjRRere0snS75GtJnmwHOeP79eHSUpKvsVdJvi+9\nR7IVpSwD3k7//1OaddlWmr6qPneW/n9U+pC0gHSE9Lw0VsqLLSVH/HfmAHZ9aUXp95LL4+eH\nyIrwm4l8ZQqB1An4nZZTJf9wLNf8nC4tJGVhlyvTyJdW01FZONWUpy88+zetS2vxx8roDcls\nHpcOkPJiQz24pOWfb1at/maideek5UhTPnn7jTW5x2KFCOT5+tHpaWh3ncl7+dy1LroetZpu\nF4PwEc0/0tjfAYcfzBeT8ma7y6GXpKg8d2t+7SYni1KWuNtDBUhubbpA8rOSy3yjtJmUN/M5\n8LmIzot7mnyphZN5/820cJlVEEiXgJvyV5FmTzdbchsBAQ9gsazkpn2sOAT4jRXnXJXZ07Jf\nP8pWPnfvmiPnf5DusuVWCreQtbMilKWd//FtY7Tg1r2821g5uPQwTpbtNzNMcdkMAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQyILA7Mp0zhQynkt5zJpCPmQBAQhAAALZ\nE5hZLsw/Qjd8T/I9oxMbpZ3m6WRH9oEABCAAgWoRGKPiPiL9Q/JNqdlW1wpv36B5g5b/KW0Y\nW7+Q5veUbpZulPaRWqWp1S3tPVr7hLRK09attfy3pnUsQgACEIBAOQl8W8U6Zoii7a71vr8M\nZRdqw3cbG/fQ1MvNWrexfV5NfX9buLHMBAIQgAAEIFAn4BtE2NCPWjBZo7Ft06ZtW2n5gqZ1\nF2v5P9IOkm9QL0knS53YYtrpfsm+jGtxwHVa1ypIa7ErqyAAAQhAoKAE3KLzqNQqaNlS66dK\n90qtbDatfF1aubHRlXW+r0xs0ocb2z35nvT72DKzEIAABCAAgVoUIL0mFm9I0Y0lQtMqQJpF\nG33TWS/aSVMHRQ5ulo+t+1xj3Uqxdc2zgVbsJr0ovSANFSD5xniL5P0xCEAAAhAoJ4FDVKzf\nNRXNQdMfJd8ffJ8YKkDaWNscXNneJfme5handuagarLU7j7V7ni2QQACEIBACQlEAdIvVLZn\npBuleLe4VgHSN7WPu8LNJEV2vmZuiBYa09Gavizt01huNVldK10j6BviFtJQAZLTcovU9hIG\nAQhAAALpEfB7PftIf5fOk9x1zRVlkf1AM26FmSNaoekHpT9I6zTW/UrTj0pfktxl+mRpaylu\nS2rBQU10TLTtAM34/vQFyWkOFSAd1tiuSe29ku8nH/HCMPYnbf/rMPuwGQIQgAAEKkQgCpC+\nrTL7ZuUbyo9j5W8VIDkQOjK2j2fdj/vPTeu8eI/kmr+hbAFtWLaxcSNNhwqQvMtp0oWewSAA\nAQhAIBUC8ymXByS38h8l7Ss9Jbnbs1tpbL5PTJEO94LMgyQ8KF0vRYHUfzV/v+R7wtcltxT5\nGHdxi+z7mnlaile+eZuDndk9I/uDNFSA5LQ/651kX5R8P9lOcgB0m3SsNFZqts9ohfedu3kD\nyxCAAAQgUE0C8QDJBM6Q3pR8Q7I1B0ju4uZWoW94Y8x884xujrHVtWu1cH58RZv54QKkn+nY\nx9sczyYIQAACEOgvgSOUnFv5l4wlu6LmHVC4N0Fkvj6/I/n9nhMkd4VbWorMAZLTWTBaoakr\n5rwuqiTzcVdK7WyoAMn+Oa15Ggf/WlP76MBoH+kv0luSW6IWkeLm7nXed634SuYhkFcCzTUI\nefUTvyBQJgKu2XOwc6IU1Q5qdpr5JjSn9Ni0NQMzvrn45tNsriGMav6at3W7/KgOWFQa0+2B\n7A8BCEAAAiMisJmOukbyM5kDHsvX+ruljaXIfqEZtxidJY2XdpMmSXHz9mdjK07Q/MzSmo11\nrphrvrc0Ng07sS/u3eDAzHaZtJf0IWkfaStpA8kB2r5S3KI8V4mvZB4CeSXQ6uEsr77iFwTK\nQsA3r69JZ0o/lC6W4uaaNtsTA5Np/z+pOXfFaDave6h55QiXnYfNPjS/71TfwH8QgAAEINA3\nAu4et7jkirFW1/F4Rfbb2udHkluA7pTcG6HZmu8nrox7VXpPY0df2y9vzHc72UQHxLtgu+eC\nFTcHeu7656ApbvbBvkT3t/g25iGQOwLxH17unMMhCJSYwESV7XTpZ9JqTeV8o7G8cNN6By+L\nNK3zovdrdWNtseuwqxZq7PH6sHuyAwQgAAEI9EpgihJw8DBBcmVXs+KBRqDt+0juSueWoJ2l\nZvM+cRutBfcweKSx0tf26DrfWNXRxBXqG0oXxfZeQfPLxJaj2cnRTGw6m+b9/lF0f4ttYhYC\n+SNAgJS/c4JH1SHwDRXVXRUObipyvBUnvsk1g+tLc8VWui/6gtIlsXW9zEa1e74BYxCAAAQg\nkDwBtwZ9SnLw8HxDr2l6jLSdFNn3NLOe5EESjpV+Ky0rxW3d+ILmN5AcNN3SWO9re3Sdb6zq\naOJ7jbv93Rzb25V8bo1yK1hkDpjWkG6MVjSmDqbsR3R/a9rMIgQgAAEIVI3AvCpwKPll2WZz\nn21vsz7Z2OiKi2ekPzSWo4lfjH1Zmii9W1pZul36mxTZUprxTWuLaEXTdCMtO69xTeujRad9\nX7TAFAIQgAAEEifwMeXg6/I50trSctIJkgOmKJjxNduD+/xasrmi7FHpWmlmyebgx+kcKzlw\n8oAI7u7m7txRy9LvNe+KuXbme8+9TTv4/acJTet207LzO1JyYLSpZH98n1paits2WvC+q8dX\nMg8BCEAAAtUl0C5AMpVTJd84ogDJ606QbvBMk31Ey49I3t81jH5ZdzEpMt98vO1H0Yqm6UaN\n7UMFSA6Oohtw06EsQgACEIBAQgS2VrpPSr5+e6S4q6XPSbZZpbskBy3uqhbZxprx/u6qbXOA\n5HvCbZLXu+veaVL8mE80ti2h6VDWKkByC9SOLQ7YQ+scEDk/y5V275WabX+t8L0LgwAEIAAB\nCIyYwKo60jfJ9w2Rgm9ucwyxzcHR9kNsa7d6Q210//Sl2u3ENghAAAIQSIzAWKXs95BGYg6Q\nogouV5w5sGo2tzY5iPll84Zhln0vmn2Iffx+0vLSUH6P1jYHf9+UMAhAAAIQgEBPBNwV4vQu\nU1hY+98guQtet3axDnA3CgwCEIAABIpHIB4gtfN+A210NzsPmpCGfUmZ3C05kMIgAAEIQAAC\nPRFYUEdPltwfvVPz+0sjCY7er+NcwzdnpxmxHwQgAAEI5IpApwGSnT5b+kEK3vue5K7b7tqH\nQQACEIAABPpCwC+9rt2XlNon8jFtdq0iBgEIQAACxSTwcbntwXs6saW0026d7NjjPq6w+0aP\naXA4BCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgMD/s3ceYHNUZRve\nJST0YoJUIaGX0BQRUAhNUXoEpUaI8EsTpEgTEGkiimABkU4QpINIDQakl9A7hF5iqKF3ksz/\nPPvtJPttdr+drVP2fq/r2Zk5c2bmPffszsx7zpmzEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIBAQwTyDW3FRu0k0E87f0Ea1M6D\nsG8IQKCrCFyn0m7VVSXu3sI+oqIv3r3Fp+QQgECLCYzV/tZv8T4Tv7sZE+9h9znYX0VeRNpf\nGtd9xafEEIBAiwlsof2t0OJ9srvkEnBwdIJ0X3JdxDMIQCAlBBwYDU+Jry11kwCppThburM7\ntDdH7RgEIACBZggsq40JkJohmK5tA7nr4OiadLmNtxCAQAIJzCOfujJAmiGBJwOXIAABCEAA\nAhCAAAQgAAEIxEKAACkW7By0nMAXuf47fpmbyd0KMQhAAAIQgAAEIAABCMRGgC52saHnwL0J\nzLBKLhcs1DuNJQhAAAIQgAAEIAABCHSWAC1IneXN0SAAAQhAAAIQgAAEMkbgs1xuiS9yM52S\nsWJ1bXEIkLr21FNwCEAAAhCAAAQgAIHWEJhp2XwuGNGafbGXuAkQIMV9BhJ9/ECjXwUnSxpu\nPDhJWjXR7uIcBCAAAQhAAAIQSCWB4Bt6zjqj+Mz1K03nTmUxMuI0AVJGTmTrixGco30+KekH\nm/P8ipKGHQ+ulmbSPAYBCEAAAhCAAAQg0BSBYICeqzws/wOS/8fsQmk36RWlj9QUi4EAAVIM\n0JN/yODn8nFrac1cLv9t6ThpbS0vL60sXUGQJAoYBCAAAQhAAAIQaJhAkNemo6SvS/q/uvx6\n0hGad6D0O+nvet5aWlOswwQIkDoMPPmHC/yHkn+U9tGP9M7e/ubdorSOtJJ0uX60/TXFIAAB\nCEAAAhCAAATqJ+AgaBNpIz1zPT5t8/wkLXvdLZJ68QQ8r0+D05E5gHcEc1oOEswiTy+SrtUP\n8/TKXuefV/o60mrSIRIGAQhAAAIQgAAEIFAXgcA9dfaTttQz1yNVNv2Z0peT9q2ynuQ2ESBA\nahPYlO7WP8RB0v/17X/+Oa3fUzpUtRpuccIgAAEIQAACEIAABCIRCGZVNvfW+b2CozHVN8mP\n1zoHUcfoeYv/iqwOquVrCJBajjTVO3SAdKZ+rO/VLkX+YuXxS4Vn60fbr3Z+ckAAAhCAAAQg\nAAEIiMBBkt8/0jvetSyv56zc/6QRtXKyvnUECJBaxzLlewrWUAGGSgqQItseyukXCX8ZeQsy\nQgACEIAABCAAga4lECyioh8gKUjKfxwRwz+Ub4eIecnWAgIESC2AmJFduPVIzbz5l6KXJ/+6\n8vpHfphakeaJvh05IQABCEAAAhCAQFcS+INK/bB0QR2lP095l9Wz1ip1bEPWJggQIDUBLzub\nBnOqLH5ZsMrADH2WdJTWTpAO7jMXKyEAAQh0J4HVVezturPolBoCEOhNoDBk91ZK218V0kHv\ndX0t5V/U2jskWpH6wtTCdQRILYSZ4l1tL98/lK6qvwz5ydrmcEnd7YIF6t+eLSAAAQhkmsDG\nKh0VSJk+xRQOApEJeMCFuxQcSXWbu9ltq2etGevekg3qJkCAVDeyTG7wU5VqlH6wXzZYuku1\n3TOSutphEIAABLqKgEfyfKwP7ap1S5as98hVGAQg0HUEgnlVZLcANXoN8LPWHNKGEtZmAkSh\nbQac/N0Hg+TjN6W9GvfVzcSBW5H04w3Utzb/cuP7YksIQAACqSLwlrx1ZeNy0t3Sc1KprayF\n/tJDxcSXitN6J+qSUwi0am03izIMqZWJ9RCAQMcJ/FxHHC810FvHvubf1zPWvzXjXj9XOwVr\nHwECpPaxTcue15Gj7l53f3MO5/WDD1yL6ubjvZvbF1tDAAIQSA0BD1bjSia/eO3WeL9M/Xcp\ntKM1s7nU7LsDrjm2apmDNY8uikEAAokhELjiQq8i+JWE/JQm3LpW2zbaAtXEYbtvUwKk7jvn\n5SVeVwm36wfrd4matRO1g9MUKP1G+4vwX0rNHo7tIQABCCSCwKfywq3wfng5R9pU2ll6TWqV\n6boaybZRrg8i5SQTBCDQKQI/0YHy0qgmD3ibtldXvWAZ7e7pJvfF5n0Q4B2kPuB0yar1VM7/\ntqisl2g/Dox+1qL9sRsIQAACaSIwWs6uIH0uuUX9RxIGAQhAwM9FZyuocWVKE1Z4heFV7WBY\nEzth0wgECJAiQMpulmB+lU3j6udubk0Z85O0n5Mk1aQyykprmLIXCEAgZQTelr8/lA6WRklU\nGAkCBoHuJRCsqLK7G64CpJaYW5HWasme2ElVAgRIVdF0xQp3r3tHeqSFpfV/KQ2UftzCfbIr\nCEAAAmkjcKYc9gANfr/z8bQ5j78QgEDLCOykPXlo71Z1iXOARAtSy05P5R0RIFXm0i2p66mg\nt+pHO6V1BS68e+Rakn1bt0/2BAEIQCCVBDyi3SYSfxSbytOH0xBolkAwQHsYIbWq9cgO6b3x\n3CLqqTPYC1h7CBAgtYdrWvbqAOm/bXD2ZO1zVf14V2nDvtklBCAAAQhAAAIQSAOB4XJyZuni\n1jmbf0r78t8L0M2udVCn2xMB0nRIuiUhUO1DbjGpDQFS3n8a6/ea/AeJGAQgAAEIQAACEOhG\nAjup0BrAKv9Riwt/h/Y3rMX7ZHclBAiQSmB02azfP3pDP9on21RuDfed21atSHO0af/sFgIQ\ngAAEIAABCCSUQLCgHPuedHYbHLxN+yRAagPYcJcESCGJaVMPMFBqa2phd8l/9DdP6YqUz39d\n/t/XxjL8S/v2cJb+x2cMAhCAAAQgAAEIdBOBrVVYD8l9ZxsK7QBpaVVC6z+RsHYQIECaRnUp\nzV4qXV5MmlPTGyW/DHeKdKX0prS3lAVbSYV4tH0FyX+hfZ8j0c2ufZDZMwQgAAEIQAACySSw\njdy6SD11gja459GHP5ZWb8O+2aUIECBN+xr8WbP+T6ATikl/0vTb0m8kp/tL6DRrOynt5nH5\nWzm8dyUeZyhRgVjwrUorSYMABCAAAQhAAALZIxAspjL52UcBUjssP1l7fUJaoR17Z5+53IxA\nKBAYpE/3E/V7OX7xzfZD6XzpKC8UbaymS0hed0ExLYWTYCE57a6EbWxBMpa8hrgNPAjEztK9\nTsEgAAEIQAACEIBAxgm49ehpPQc93MZy+v/Vlm/j/rt617Qg9Zx+BwxmEQYMec1Pkdy9rtzc\n7c41A2k2tx59Jj3bgUK4m5364QazdOBYHAICEIAABCAAAQjETUCDVLWr9Whq0QiQpqJo/QwB\nUg/TJzXxgAIHSA6O3F/0emmkVGp+yPeXvp01AqXHa9e8AyQ1zRaaaNt1jHC/V2jGTN3qhkEA\nAhCAAAQgAIEMEwiGqnBu2bmwzYV0gOSBGvq3+ThduXsCpJ7TPkmTPaXDpGukzSS/k7Sw5K5h\nv5D2l+6SlpOOldJsei9oamtZm8uRd+B5iTSyzQdi9xCAAAQgAAEIQCBuAq5If1B1w8+02REH\nSA6OPMgY1mICvIM0Degozb4h/Ur6t1RqqxYX/qPpz6TnS1emcH5F+XxmB/0epWPdploOBZz5\nVzt4XA4FAQhAAAIQgAAEOklgSx3s3PYfMP+anqve0XHcWuUBG7AWEiBA6g3T3eqs+aWvSX43\naYA0XnpZmiCl3IKZVAA1yXaqBcm48nfqR+ygcgfpt07BIAABCEAAAhCAQJYITMnN4J5Zy0jh\nX8a0u3iP6QAOkC5u94G6bf8ESJXP+OtKtu6vvDrVqcvKe5/3cECKThVmlA40UiJAEgQMAhCA\nAAQgAIFsEZiUm9HPV+r6lu/EIFiG5252DpCwFhMgQJoe6MxK8js6C0jzSR6w4V3JAYX7k3o5\nzebudWoJy7/d4UKcp+MdI3xr6Nh3d/jYHA4CEIAABCAAAQi0lcCkXH8/V1/R1oP03rkDpO/3\nTmKpFQQIkKZRNIujpV2kgdOSe83dp6WdJTdpptU6OEBDKSK/exTcopQREgFSKRrmIQABCEAA\nAhBINYG7c2vMt1LusX4qRKe615mXA6TF9Hw1qyqfP3EC1hoCjGI3jePpmt1D8uAFa0vuQzqv\n5JHsHFRsJb0lPSCtJqXV3ILU6e51IavzNbO1fsj9wwSmEIAABCAAAQhAIO0ExuS+v8YMuSn6\nD818J5+xPDiDn+X9+gTWQgIESD0w59JkR8lB0EHSbdI4yQHReMlf9kuljaUrpW2ltFqcAZJr\nVWaTfpBWePgNAQhAAAIQgAAEygm8mBv87f65SV+Wp7d3Oe9XQP4n8R5Si0ETIPUAXVQTv1t0\nUwS+Y5RnWIR8CcwSzC2n3Cr2VDzO5d/Xca+W3M0OgwAEIAABCEAAAhkgECz4QW7OpWfMTZoU\nQ2HczW6FGI6b6UPyDlLP6XULkQctGC5d1pNU8dO83Mrk1qVG7C5t5KHDo9hQZRobJWMdeRYr\n5n2hjm1andXd7DQcZTCnmqE/aPXO2R8EIAABCEAAAhDoMIHNBuS+eGeG3OQBHT6uD8dIdm2A\nToDUA1V9RnOnSBdI20tXSR7me6LkL/tAyf8d5JaPJaQ1pEbsKG3kFpy+bBatPFVqR+ueAyQ1\nx+bf68uBNq+7Xvv/WPqRdHabj8XuIQABCEAAAhCAQLsJbD5/7vV7dZA1232gCvt3ryD/OS3W\nQgIESNNgOnjxl/skyS1J5eZmU7+HtIPkFqdGbHSEjfw+lAMkB22tNgdIL7R6p/XtL6/+ucEl\n2saBKAFSffDIDQEIQAACEIBAoggEs8uddVfMPf47TeMIkPxcpwHFAj3T5/2sirWAAAFSb4gO\nYJaUPHLdYEndwHIfShOK+lTTNFsCAqQCPrfU3aof8wL6Mb+WZqD4DgEIQAACEIBAVxPwwFNf\n/jh3WaOV583Ce1E78PDii0gxV4I3W5TkbE+AVPlc6D97clYl87tBHmxgfKWVCU9zgORhyuO2\nO+WA+W4j/SluZzg+BCAAAQhAAAIQaJDAZtruhtlz78fVeuPnKR/bA44RIAlCK2yGVuyky/bx\nmMp7YkrLvLj8TsCPJ+8RAy+StkspR9yGAAQgAAEIQKDrCQT9hGBj6d/xochP1rEdJDlAwlpE\ngACpfpC/0SZ+hyZlVvgRJ6n51d3svqludu7SiEEAAhCAAAQgAIG0EVhLDvvd8WtjdtyV3wRI\nLTwJBEj1wzxam/Q1FHj9e+zMFg6O3KUyAS1ILnDhn6b9D9Bp/tNdFwSDAAQgAAEIQKA7Cbh7\n3R16pnkn5uL7PSQCpBaeBN5Bmh7mzEpaSdIAArn5JHcHe1fyy3fPFJc1SZ35/SP3UX0lQZ67\nFWkH6agE+YQrEIAABCAAAQhAIAoBB0h/i5KxzXkcINkXrEUECJCmgTQLtw7tIvl/jyrZfUrc\nWfJ7SGkzB0gvq5bDfVWTYhfKkd8qBv1GLue4FIMABCAAAQhAAAJpIBAsIy8Xl65JgLe0ILX4\nJMzQ4v2leXeny/k9pDOltSV/8f2nrh7y2y1KW0lvSR4FbjUpbeYfcUK614Xo8v5B3yPRzS5E\nwhQCEIAABCAAgTQQ2FROjlPF87MJcNbPU3pmDWZLgC+ZcIEWpJ7T6BfsdpQ2km7oSer1OV5L\n7mJ3qeQBGvxAP1ZKk7kFKWEBUgGfW5H2l64sLPEBAQhAAAIQgAAEkk9gE7mYhNYjkwqf74Zo\n3u93Y00SoAWpB6BfbAukmyLwHKM8wyLkS1qWpAZIDjgXeia35IJJA4Y/EIAABCAAAQhAYHoC\nwVeU9h3p6unXxZGSf1NH/URioIYW4SdA6gHp1qG3peE1uLrFzV3t1KSaOktogJR/XSRvfia3\n9FKpI4rDEIAABCAAAQh0I4ENVegPJf/xfVLM3ez8rIe1gABd7HogTtHkFMmjqm0vXSX5wX2i\nNEAaKC0tjZCWkNaQUmTB3HLWtR3PJ9TpCyfkFjhpSq7fcwn1D7cgAAEIQAACEIBASMDvH12v\n9488OnBSzAESLUgtOhsESNNAHqXZe6WTpEotSf4R+B2kHSS3OKXJwhqFsI9q0ny/YnKu32n/\nyy341eTGcElDhj8QgAAEIAABCHSeQOBnCw4xaQAAQABJREFU5x9IP+/8sfs8IgFSn3jqW0mA\n1JvXaC0uKXnkusHSnJKbUCcU9ammaTSPYKc/Mcu/n0zn8+8Oyo14ZXxuYXFPaiNXMsnhFQQg\nAAEIQAACHSWwpo42h6QWpESZA6S1E+VRip0hQKp88l5VspUVS+j7R9PwLp57ftyE3ELra6yM\nmRXIfTZtDXMQgAAEIAABCEAgMQQ8ep3ePcq/mxiPehxxLyG62LXopMzQov2wm2QTGCL3XLOQ\nWFs+94T9y0sbJdZJHIMABCAAAQhAoNsJbCwA1yYQgp+j1LIVDEqgb6lziQApdaesIYc9hPb/\nGtqyQxvNlPt80qDcxNd0OP/HFAYBCEAgCwQ8yM/3pV2lFbJQIMoAge4mELhHzjJSUv7/qPR0\nhBXh9hFrkgABUpMAU7K5AyS/R5VoWyg3frwcVNN14L69GAQgAIG0EPC99DDpPsmjoH5Lmkd6\nRfK7radKj0jHSRgEIJBeAu5e95I6vDyZvCLk/c78RIludi04OQRILYCYgl2kIkBaJDf+dbH0\nQBiVRhFMAWZchAAEupTAn1TuoyQ/oKwuXS2dKfmato3kgOkM6SBpSwmDAATSScABUhJbj0Ka\nL2vGA41hTRJgkIYmASZ/88BB8HxS4luQZshNDuTnFZK72Z0nYRCAAASSTmAWObi7NEK6QJpV\nulLaXPqOdJdkc+vSUtJI6XKpXvN/9C0WcaOZI+YjGwQgEJlAMLuyri2dGHmTzmf0qwquFMea\nJECA1CTAFGw+v3zsJyU+QCqyvFDT0epmp+4p+beLaUwgAAEIJJWA3y3yNdZBke0TyYHSqlIY\nHGm2YK4A2q04X+9kmDZYNuJGDtowCECgtQS+p919Kd3c2t22dG9+1iNAagFSAqQWQEz4LsIf\nSloCpFvE04HRj6RTJQwCEIBAkgm4G51b6teVwpGtHCx9IXlkTreMh+YHrFfChTqnHughik1R\npqQNPxzFb/JAIOkEPHrdTfpZf55gR/2s52sR1iQBX9SxbBNwgPSRftDuG58Cy0+WkxdL26XA\nWVyEAAQg4IDHgdFF0p8lVzy+J10ghcGRW5OukzaVTpcwCEAgVQQCV3Y4QEry+0cm6gBpAc9g\nzREgQGqOXxq2doCUltajkKe72emfqgNeNAyJMIUABJJMwC3eR0p+gJpUwdEdlPZd6UDpXxXW\nkwQBCCSbwCpyz68shK3ESfXWz3t+7sOaJECA1CTAFGzuH0qi/wNpeob5sUrzP0JvM/06UiAA\nAQgkjsBn8uiP0tAqnh2v9HkkTzEIQCB9BFz58ZB64yS9wtmDNMymCuY504c4WR4TICXrfLTD\nmzS2IJmDW5G2awcQ9gkBCECgTQS+qLJfd8P7oMo6kiEAgeQT2EQuJr17nSmGAZyf/bAmCBAg\nNQEvJZumOUBaWbUgUUdtSsnpwE0IQAACEIAABNJDIPBfpbiLXdK71xnpm5Lf5SZAMo0mjACp\nCXgp2XQh+RnWKKTEZbtZ+Jdq//O8/xMJgwAEIAABCEAAAnEQcPe6t6T74jh4fccsDHT1hrZh\noIb6wE2XmwBpOiSZS0hrC5JPxAXSdpk7IxQIAhCAAAQgAIG0EHCAdL0qbj2EfhrMleK0IDV5\npgiQmgSY7M2DAfJvkJTCFqQCWb+HtJi62a1eWOIDAhCAAAQgAAEIdIxA4TnK/1+WhvePQioe\nqIEAKaTR4JQAqUFwKdnMTaweuz+lAVL+Vfl+m7S9hEEAAhCAAAQgAIFOEhimg80s/aeTB23y\nWLQgNQnQmxMgtQBigncR1iCkNEAqkP2nPrdWK5L/fBGDAAQgAAEIQAACnSLg0etuV11zmkah\nJEBqwbeDAKkFEBO8CwdI7+iH7f/oSKtdKsfnktzEjUEAAhCAAAQgAIFOEXCAdHWnDtai4zhA\nYpCGJmHGFSC5uRJrPwEHSGluPZL7+ff04aE16WYnCBgEIAABCEAAAp0gUPibkcV1pDS9f2Qw\ntCC14OsRV4D0rHw/S1qrBWVgF9UJZCBAKhTO3eyGq5vdbNWLyhoIQAACEIAABCDQMgJuPRqn\nitrnWrbHzuzIAdIsemaauzOHy+ZR4gqQ/iScHpnsNslfvMOlwRLWWgIp/Q+k6SC49maSpCAJ\ngwAEIAABCEAAAm0n4AApba1HhuJR7Gzhe+g9S3zWRSCuAOlEeTlU+qbkL9+e0ovSf6UdJFoK\nBKEFlpEWpPznYuF3kX7SAibsAgIQgAAEIAABCPRBIPiKVn5HStv7Ry7TW5IrlQmQTKNBiytA\nCt19QDP7SD6JP5A0oEDuXOl16UxpJSkJ5tau7ZLgSJ0+ZCRAKpT6PH1+V03GvHhY55eA7BCA\nAAQgAAEI1EVgQ+X+ULqzrq0Skbnwh7Z+jiZAauJ8xB0g2fX5pJ9LR0hbSG4aPEdaXnpQ2kuK\n2zaWAwfH7UQDx89SgKRhNnOvSmkMVBs4dWwCAQhAAAIQgEBMBNy9brTeP3JLTBqNkeyaPGtx\n/bfMbPLb75OMkDx882TpKslfyBuKy5rkjpWOlzygwydSu2wF7fiCPnbuIG4O6bFiHvu4f3E+\noZNgVjnm4bH9I8mA5QO1Hp2vgrib3QkZKBBFgAAEIAABCEAgcQQK/7voFiRX3qfV/OxHC1IT\nZy+uAOk5+Ty/9JC0r+TgZKJUbvcoYYA0s9TOAOkt7d+tactJd0v2r9RW1kJ/yf7aXip8Jvsj\n7IqWkQCpANvd7A5ToLSianUeTTZ+vIMABCAAAQhAIIUE1pLPs0vXp9D30GX3xiJACmk0MI0r\nQDpbvl4iPVLD5xu13i0hn9XI1+xq99X0gBF/kH4q+UH871JoR2tmc8kDSKTFvlp09O20OFzb\nz/wzCo7uVT63Ih1QOz85IAABCEAAAhCAQF0ENlPuO1QR+25dWyUrsyvHV0qWS+nyJq53kDxa\n3QtVUK2qdHe1s7nVqN3BUeFA+vhU2kv6kXS4dJ0UtsJoNnU2jzz+WD9wlytL9g8VRn8aG/TL\nUqEoCwQgAAEIQAACiSCwqbzwax9pNgdItCA1cQbjCpAul89LVPH7F0rfr8q6TiTrpbzcCtLn\nkt85csCURnMLkrsOZs0uUoEGSRtkrWCUBwIQgAAEIACBOAkEy+noi0tpD5Dcxc6vsmANEuhk\nF7u/ysdhRT/n0NQPuuWtGzMpbSnpNClOc7e0H0r/J42SPpLelNJkbkHKUPe6EH1+olqPrtbS\nSOn6MJUpBCAAAQhAAAIQaJKAu9c9pd43zze5n7g3dwW53t8PZldZ/AyL1UmgkwGSgx7/8ZbN\nEboHQnjHCyU2SfP/kn5fkhbn7Jk6+C3Sn6UPpDRZVluQfA5GSZfph6/vU6r7CLssGAQgAAEI\nQAACySDgACntrUcmGVaQu7KcAMlE6rROBkhPyDe/XG9zS9GvpCRG6Iq4Cy+2LaDpfJKGly78\nee2jmuaLy5ok3jLaglTg7m6Q70nbSH8vpPABAQhAAAIQgAAEGiYQzKtNV5P2b3gXydkwfMXC\nleUvJcet9HjSyQCplMpWpQsJmTcLj1a3izSwik/3KX1nKfw/pCrZEpHsH4VGfcui+Y/bCv+J\nNFKlI0DK4immTBCAAAQgAIHOEthYh1M3/tw9nT1sO46W/1jPSZ9qz34WxBog0KkAabB820fy\nuyMewe53kltqqtnDWnFutZVtSj9d+91SOlW6VnpDchdAt3Y5YFpaGik9IK0ljZWSbG5BuivJ\nDjbp2yht/0tdAJZVw95TTe6LzSEAAQhAAAIQ6G4Cw1X8a/RMMSUjGNzNzs+CWAMEOhUgOcBw\nq9GzkgMkD4DggRqq2axa0ckAaS4db0dpI+kGqdzGK8Fd7C6VLpG2lZIeILnWIGxi1WzWLP+4\ngiMHq/7fqgOzVjrKAwEIQAACEIBApwgEfu78nuSu+1kxPwPSgtTg2exUgPSQ/FuoxMdlSuaT\nMLuonPC7RjdFcGaM8uweIV/cWVxrEL6kF7cv7Tr+Wdrxb3TqDlGNjwf4wCAAAQhAAAIQgEC9\nBDbQBn4O9DNeVowAqYkz2akAqZKLHtGuv/SmNEjaTXJLzvmSW2s6aT6egwk3r17Wx4HNyy1h\n4/rI09eqb2tlrWjetRhNWmCuZpnhFqQCogv0eYK0iXRlIYUPCEAAAhCAAAQgUB8BP/+pB1He\n7+1kxfxcSxe7Bs9mXAHShvL3X9KekofSvlBy0+ZH0q7S6lIn3ytxf9NTJD9wby9dJb0uTZQG\nSAMlv4M0QlpCWkNqxPye09cibuhjNmrhD8I/jgxb/n1V+FyuAnrgDAKkDJ9pigYBCEAAAhBo\nD4Ggn/britb92rP/2PbqSvLFYjs6B26IwDPaygM2LCgNldysebDk1pNbpDOkOOwHOuizkv0p\n15dKcwC1ktROc8uPj71T4wcJVtQutI+gmSCr8cM3sOUXuZn++mVugIOdOi1YR+VU97rA3yUM\nAhCYnsABSrpv+mRSMkrAFX5HZrRsFAsCbSAw9TmiqWemz3IzbarnmA/a4GCDuwwO1bPRnQ1u\nHG42UjMvhgvdNI2jBWk2AXYrjF+EmyC5VcYBwSjpE8ktS9tLcdhoHXRJaWFpsDSn9KFkP620\nNL26BWmy9K6UdbtVBfSPd6R0rIRBAAIQgAAEIACBqATcve52da/zyMVZMrcg1XqtI0vlbWlZ\n4giQZlYJ8pIf4G3ubveo5C5ttoWkVwpz8X28qkNbaTX/INQ9MO/AM+PmMgZnq5A7a/q77ihz\nxk8pxYMABCAAAQh0jsDmOtSfO3e4jh2JAKkJ1DM0sW2jm/q9Htf46z9sCq1Ia2nqViPbBpJb\nj/7jhYTaUPkV9T2iuIrgFqSMv3/UC+0oLQ2W1uuVygIEIAABCEAAAhCoSiD4ulYNkbL4HrOf\nA+dS5XEcjSE6dLotjgDJxPaQtpQ8OMNj0omSu7NpBJHcE1KSv6ihv3IzseYWJNccdInlX1NB\nr5Z27ZICU0wIdDMB90LAIAABCLSCgJ9FH1Dvk5dbsbOE7cPPge6xFQ7clTD3ku1OXFGl3/WZ\nX3KtvwMidZMq2DB9qh9oou038q6TI+w1AqPbWpDM6DRJQVIwn64HbzQCjW0gAIFUEHhWXrqX\nwSgp6fcLuYhBAAIJJrCFfDsvwf4141pYUe5K8/A1lmb211XbxtWCZMgfSi9Ifpift6hxxama\nBBNrR8uzyxLrXY9jXdaCVCi0H5jGSz/tQcAnBCCQUQJ/UrlWl26TnpMOl1zZhkEAAhCog0Cw\nrDJbV9SxUZqyvitnp0i0IDVw1uIKkFaSrw9LH0v+o1jX+JfqDC3HZe6+sZo0XHKXrV2kH0tL\nS26qTIN1YQtSYUAKf29+plaktJynNHyX8BECSSPgLtl+F/Sb0jXSntKL0n+lHaTZJAwCEIBA\nLQJuPXpCj3aunM+g5R0c+b1/V5pjdRKIq4udmzPdxe5wybX+4Yh2mi3Yy+FMB6dm4dYhB0QD\nqxz3PqXvLD1WZX1Skv1jCJtWk+JTJ/w4Wwc5UvqelOSBPjrBgmNAIOsE9N6A3x3I7S+tJ/na\nfa70N+li6STpEQmDAAQgUInAlkq8vNKKDKV5oAZXmmN1EogjQJpbPq4guYXm33X6287sp2vn\n/rGcKl0ruUXrHWkmyQGTW5BGSr4he+S9sVJSzT8G/yi6zPzuUXClCr27RIDUZWef4nYlAb1z\nWBgNdWtN3e3uNcldoL8lPSjtIzlQwiAAAQiUEAgW1YJHsPtpSWIWZ11ZTgtSA2c2jgDJfwb7\nmfRhA/62axO/87SjtJHkkfTKza1cj0qXSpdI20pJD5C6sQVJpyV3inSjAqWF1Wz+qhMwCEAg\nUwRmU2lcweY/GXdrsXsgXCVtIvn6HfZIOFbzx0tnSb7vtNtm0QFWkdx13RVpH0vltr4SPpfu\nKF/BMgQg0FECW+hoz+s5IeutzH4WJEBq4KsVxztIX8hP1/LrXZHEmGsSAummCB6NUZ5hEfLF\nlCVwsNdf6sIWJCPP36KPp6XdJAwCEMgeAQ/McL7k1qN9pQWlH0vXSWFwpNncPdIAye+Vttvc\nK+Jx6XbpVuklaSup3H6lhF+UJ7IMAQh0nICvGZd3/KidP6CfBeli1wD3OFqQ7KZrz34vuQuE\n9b5Uao7o/1Ga0OZ5tw75S+Raycv6OJZ5+aY3ro88ca8Kawq6tQXJ/P8mHamY9ygFTK6txSAA\ngewQ8LuGbsmvVfOrluTcrJJ7LLTT8tr5edKX0sji1O9DXSy58s33OgwCEEgMgcCjXnowrp8n\nxqX2OeJnwSXbt/vs7jmuAGlvIXUXuwWkjSvgnUNpnQyQpuh4p0gXSNtL7q7xujRRcg3kQMnv\nILlLxxLSGlJSLawp6NIWpMJp8cPKcZJriM4vpPABAQhkhcChEQvyScR8zWYboh14ZNYNJPcw\nsPlecozk65DvI2dKzdr62oEf7KKYexFgEIBAZQJ+NnD3ugcqr85UqgOksOI8UwVrd2HiCpCW\nanfBGti/Whty90p+odctSeU2SQmXSjtIbnFKqvmH8JF++O2uNU1q+eVXXuUPztXMnhIBUoLP\nFK5BIAME5lcZXMl2d1lZDtOyK/v+Lr0q3SA1Y+6at0LEHcwdMR/ZINCNBNwTyM9z3WCuLA8r\nzruhvC0rY1wBUliA72hmZckP82dJ35Tul+Ky0TqwmyIXllxTN6fklq4JRX2qadLNP4Rubj0K\nz49bBBUgBfpO5eP8ToX+MIUABLJJ4CUVawZpc+mfUqmF70i5S+B6pSsamPf+o5iDNdcaYxCA\nwHQEgiFKWlXadbpV2UzwtYAAqYFz64t6HOZateulO6STpW2l2aSxxeVOvFSrQ1U11/bZt+uk\n2yU1xebSEBzJzUJTKjfHXP5psfBQ3/sYCgYBCECgTQRe036vkdz7wPezhaTQHKxsL7l16VZp\nqIRBAALxEXDr0XOqOH0oPhc6emRXmKvLbWEAr44eOO0HiytA+ovALSs5MDq6CPETTfeSfipt\nUkxjUj8B1xT4B4Hlcn8WBF0MA49yhUEAAhBoFwHft26TdpeWKDuIR27dQrpUcnc8DAIQiI+A\nAyS36HaLhRXmvIdU5xmPI0DyMbeR3Lx5kfSRZPMw26dI50gESILQoPlHEP4gGtxFZjZzn3/V\nFHXFSDWZOWkUBAIpJOBKqeHSIMnvspabKwAdRK0mnVu+kmUIQKATBILFdZRVJAKkTuBO+THi\nCJDcwjGL9HIVdk5fsco6kmsT8A16Yu1s3ZAj76DbrZUKxgN/5zAIQAAC7STwnnbeV3dsB0/X\nttMB9g0BCFQl4F5L6n6f+T+HLQFQ+KsTN0T42Rurg0AcAdKb8s8P8CMq+JlX2s7SuArrSIpG\n4CvK9m60rF2R6zyV0t+rSt+3rgBAISEAAQhAAAIQyG0nBuUDqXQDFvcqootdnWc6jgDJLp4o\nHSD9QxoqzSb9TPLACEtKJ0tYYwTm1mauxcQKBPLu2nKapNGkAgdKGAQgAAEIQAACXUUgWFnF\n9bvvF3ZVsXsKS4DUwEmfsYFtWrGJ/zxvdmk/aabiDlfX1C1LO0l3FtOY1E/AARItSL25eXSp\nX0p+t+3q3qtYggAEIAABCEAg4wTcejRWHUo8KnG3md+R9OsXWB0E4mpB8tCnh0j+v6H1JA+D\nuqa0qHSuhDVOwF3saEHqxS//mhbd1e7AXsksQAACEIAABCCQcQKF3iMeHOyCjBe0WvH8TOhn\nQ6wOAnG1IIUuevjT26TJYQLTZggEPp/urkiAND3GPyrpSXWzW0M1SHdPv5oUCEAAAhCAAAQy\nSGAtlWlBqZtGrys9je5VNH9pAvO1CcTRgrSL3LpZekPyg7xH/PFQzH7vyC1IWOMEwhoCuthN\nx7Dwx7HuXud33zAIQAACEIAABLqDgLvX/VeVo693R3GnK6WfCcPnw+lWklCZQCcDpIFywcOb\n+oV5R/LXSa7V938hOVjaTXpK2ljCGiMwd3EzWpAq8/uDkjdXK9LSlVeTCgEIQAACEIBAdggE\nfs99K6kbR68LT6MDpPD5MExjWoNAJ7vYHSpfNpL8srxHsSu35ZVwtuQmUL+b9I6E1Ucg/AHQ\nglSRW16DfwR3adXB0k8rZiERAhCAAAQgAIGsENhUBRkgXZ6VAjVQDlea04JUJ7hOtSDNLL/c\nQnSqVCk4stuPS36Jzl/kbSWsfgL+AXypZuRP6t+0a7b4rUqq/0QKBndNiSkoBCAAAQhAoDsJ\n7KBiX6Hnoo+6s/iFUtPFroGT36kAyS+HzSqNqeHjC1r/irRUjXysrkzALUiuKcCqEsiP1qpH\npIOqZmEFBCAAAQhAAAIpJxDMqwJsKHX76MgOkOZUxXA+5Se0o+53KkAKx18fH6F0zjNfhHxk\nmZ6AAyS6103PpTzlGCXspIuF34XDIAABCEAAAhDIHgEPzuC/+fDAYN1sfi708/5c3Qyh3rJ3\nKkAK33X6PIKD6iJWOJERspKljIC72NGCVAalwuK/lfastH+FdSRBAAIQgAAEIJB+Au5ed766\n101Jf1GaKkH4XOhnRCwigU4FSBHdIVuTBNyCFP4QmtxVljfPByqd30XaVa1ItFZm+VRTNghA\nAAIQ6EICwQoq9Nelbu9e53Mf9iwiQDKNiBa27ETM3nS2q7SHWq1ICymPhwPH6ifgL3/4Q6h/\n6+7awqMlHiYdLO3bXUWntBCAAAQgAIFME9hZpbtHrUfjMl3KaIX7UNkmSwRI0XgVcnUqQHKr\nxg0R/fJADQ9HzEu23gRoQerNo48lN7kHRyjDeZoer4vohD4yswoCEIAABCAAgVQQKPz3kUar\nZTCmntPlXjOBn8P9jIhFJNCpAMkR/A8i+kS2xgn4y/9i45t33Zb+XwS3Ih0i7dl1pafAEIAA\nBCAAgewR+KGK5D+IvTh7RWu4RA6QaEGqAx/vINUBKwVZ/eX3jwCLRKDwLtIRyvoz1a74z4kx\nCEAAAhCAAATSTeD/5P5FXf7fR+Vn0K9fECCVU+ljmQCpDzgpXOUWJAKkuk5c/kplf0w6oq7N\nyAwBCEAAAhCAQMIIBIvJofWkMxPmWNzuECDVeQYIkHoDm0WLa0rDpNl6r5q6tL7mnCeJ5gCJ\nQRrqPzMeqGFHtSItV/+mbAEBCEAAAhCAQEII7CQ/Hlfr0diE+JMUN/xs6GdELCIBAqRpoDwk\npH5UudulW6WXpK2kcvuVEn5RnpiQZX/530uILylyI3+jnP2vdGyKnMZVCEAAAhCAAASmEgj8\nXv1PJVqPpjKZOuNnQ7rYTcVRe4YAqYdRXhONZpbzn9SOlLaXnpD8gt9BUgosmFVODpAIkBo7\nW25F2kytSN9ubHO2ggAEIAABCEAgRgLDdey5pX/E6ENSD00XuzrPTKdGsavTrY5nH6IjriRt\nII2RbBdIx0jHSROlpNdIhDUDdLHTyarf8g8qOHJA/Htprfq3ZwsIQAACEIAABGIksIeOrWe3\nPBXF058EAqTpmfSZQgtSD575NdH/4uTuLqN1mJb/Kv1d+n7ZuqQtutbExoWhh0Mjn4dqo28p\nUPpRIxuzDQQgAAEIQAACcRAIltVR15VOiePoKTimA6TwOTEF7sbvIgFSzzl4SROz2Lxnsdfn\nvlq6UrpEWqXXmmQthF98AqSGz0v+BW36F+kPCpL8HwoYBCAAAQhAAALJJ+DWo3vUevRQ8l2N\nxUM/G4Y9jWJxIG0HJUDqOWOvaXKNdJJ0srSQFJpblvxOkluXPHjDUCmJ5i/+x7o4fJlE51Lk\nk7tVzi7tkyKfcRUCEIAABCDQpQQC37N3kGg9qv4NoAWpOpuKawiQpmHxyCe3SbtLS0xLLsx9\noc8tpEsld8dLorkFidajps9M/gPt4tfSIWpFmrfp3bEDCEAAAhCAAATaSWCEdu7nNPf0wSoT\ncIDUX881DiaxCAQIkKZBeluzw6VB0r3TkqfOfaI5B1GrSedOTU3OjAMk/wCw5gl4QI6Xpd81\nvyv2AAEIQAACEIBAewgEee13b+k09aD5vD3HyMRew+dDPytiEQgQIE0Pya0wn06fPDXFwdO1\nU5eSM+MudvYda5pAfrJ2sac0UrUtazS9O3YAAQhAAAIQgEA7CGyonS4m/a0dO8/QPsPnQ95D\ninhSGeZ7elAzK2klaQFpPimQHHk/Kj1TXNYkceZagfAHkDjn0udQXt0tAw/1rotusKpqphw0\nYRCAAAQgAAEIJIfAfnLlIt2j/S45Vp2Anw/9PEuAVJ1RrzUESNNwmMXR0i7SwGnJvebu09LO\n0mO9UpOx4C992ISaDI/S78UBKsI4ye+lefAODAIQgAAEIACBRBAIVpAb60tfT4Q7iXbClbzB\nh3KRACnieaKL3TRQp2vWw0T6/ZO1pWUkv6S/sOQWpa2kt6QHJL+HlDSjBanlZyT/unb5a0mB\nc5DUwTlaXmp2CAEIQAACEEgBgX3l4y1qPXo4Bb4mwUVXovtZEYtAgBakHkhzabKjtJF0Q09S\nr8/xWnIXO49id4m0rTRWSpL5S5/Elq0kMWrEF/dr9vChJ0k/bmQHbAMBCEAAAhCAQCsJBH4N\nYjuJ+3J0rO8pKy1IEXnRgtQDalFN3DfzpgjcxijPsAj5Op3FX3p/+bGWEii8e/R/2uVwfUU2\nb+mu2RkEIAABCEAAAo0Q8LtHz0v+D0ssGgG3IBEgRWOVowWpB5Rbh8Jhvi/rg515uaud30tp\nxM7XRq716MvCczJnX5kqrHMLEgFSBTDNJ7n5PjhB+1FrUnCzmvM/aH6f7AECEIAABCAAgfoJ\nBH7I303SaxF5V25j0QgQIEXjVMgVPozXsUkms05RqU6RPGrZ9tJVkt8/mSgNkAZKS0v+M7Il\npDWkRuxubVTrXRYfzy1Un9V5AAdI/vJj7SFwpHa7pXS8tGt7DsFeIQABCEAAAhCoQWAvrXel\n9oU18rG6NwE/I/pZEYtAgABpGqSjNHuv5HdNhk9Lnjo3SXN+B8nvo7jFqRHz+yy1bC5lOFDy\nv0JHtMBdJb3dexE3IFvdBPL6b6zAIxiqBSm4QrVWN9S9CzaAAAQgAAEIQKAJAsFs2vgX0uG6\nD/u5DItOwM+IS0XP3t05CZB6n//RWlxS8sh1gyV3c/tQmlBUX38gqyyxmf30v0kTILX1FBT+\nG+kvOsRZCpKWF3J4t5U3O4cABCAAAQj0IrCLlhwYnd0rlYUoBNyCxDtIUUgpDwFSZVCvKtmq\nZEOV+L40vtLKmNLCL7y//Fh7CRyi3fufu93S+JP2Hoq9QwACEIAABCDQQyCYVdODpD+qgrLe\n1xCA2PMaRvi8CI8aBBjFrgagCqsfU9qJFdLjTJq7eHBaNNp+FgoXZXez3EatSAwv2nbeHAAC\nEIAABCBQIKBBGQrmd8ax+gm4Ej18Xqx/6y7bghak+k/4b7TJU/Vv1tYt/IX3SC6MrtZWzOHO\n8/cJtwdt0J8LB3pvLf9yuIYpBCDQdQRmV4kXr6PUrsjimlEHMLJCQPda/87cenSM7rmfQKQh\nAr720IIUER0BUkRQJdmOLplPyuwcckTvSjHcZQdPyLE61vrSP3XhXlvsJ3fw2BwKAhBIDoEV\n5cqddbjjwX62qiN/mFXvPeYWDBdqTP1OKgaBLBHwyHUevOq0LBWqw2X5WMebRc8sM+mZ5fMO\nHzt1hyNASt0pq+hwOJhExZUktoNAfoouMh723SMaHiH9WsIgAIHuI3CXiryTdKp0m3S81Jf5\nLyQasTO10dcjbjhfxHxkg0AKCAQepXd/SfdZ3j1q4oSF723No338r4n9dMWmBEjTn+aZlbSS\ntIDkm4y7rrnfph+Enykua5IoK7YgJcqnLnAmrwtM8FMV9ApNVYOcH90FhaaIEIDA9ATOUZJb\nbRzEuHX5ZqnVtnrEHarypvA/fhGzkw0CiSdwsDx8X/LvC2ucwCvFTWdrfBfdsyUB0rRzbRbu\nPuchJAdOS+41p3dPcjtLHqghSeYAifePYjkj+asUHGlEndz5mq6iZyTeLYjlPHBQCMROwMMO\nbyMdJ60Wuzc4AIFMEAgWVjH2kVQZmXcXO6xxAnoVo2DudYTVIMAodtMAna5Zj5DiGgq9U5Jb\nRppX8o/TLUruM/6W9ICUtJsfLUg6KTHaoTq2WxgvU5Ckvr0YBCDQpQR8n9hNovKxS78AFLvl\nBI7RHl0pfXHL99x9O/Q7SG5hJkCKcO65iPdAcv/WHaWNpBt6knp9jteSH4AvlS6RtpXGSkkx\n3kGK9Ux4gIbANccPSqdK7naHQQAC3UfAo0Q91H3FpsQQaAeBwJXTI6T11HoUtOMI3bVPMwzc\nikSAFOHE04LUA2lRTfzjuykCszHKMyxCvk5moQWpk7QrHiv/ppJ/KClQCvarmIVECEAAAhCA\nAASiEjhRGa9VcHRr1A3IV5PAB8rhZ0asBgECpB5Abh16Wxpeg5db3NyFYlyNfJ1e7S+7v/RY\nrAT8/0iF0az+oCBpw1hd4eAQgAAEIACB1BIo/BH7mnL/l6ktQjId97MiLUgRzg1d7HoguU/m\nKdIF0vbSVdLr0kRpgDRQWlpyU+8S0hpSkswB0nNJcqh7fclfqODI/1dykaZrqebr0e5lQckh\nAAEIQAAC9RIIZtMWJ/Qo/2y9W5O/TwJ0sesTz7SVBEjTWByl2Xulk6RKLUmTlO53kHaQkvbQ\n69oAf+mxZBA4TG4sJl2nIEnBdP7VZLiFFxCAAAQgAIHEE/DAR7bf9kz4bCGBD7QvWpAiACVA\n6g1ptBaXlDxy3WApDDwmaN76VEqiuQWJACkxZ6bwIuSOcucGyUHSmgqS/B8OGAQgAAEIQAAC\nVQkES2nVL6URum961DWstQQIkCLyJECqDMo1/mmq9XeA5C89lhgC/r+GwIM23CHpJdNgA13s\nP0mMezgCAQhAAAIQSBSBIC93zpBu1v3SPXaw1hPws6KfGbEaBBikoQaglKymBSmRJyrvIX8V\nGOUWkP6lIGlAIt3EKQhAAAIQgED8BPwfYqtIu8bvSmY9oAUp4qklQIoIKuHZCJASe4LyE+Ta\nd6WhkgduoNU2secKxyAAAQhAIB4Cwdd03OOkQ9R69HI8PnTFUQmQIp5mAqSIoJKbLZhZvvWX\neAcpsScp/6Jc+570bUn/Bh74fGEQgAAEIAABCPQQOE2TJ6STAdJWAn5WZJCGCIgJkCJASniW\nsC8p7yAl+kTln5J760oOktS3miAp0acL5yAAAQhAoEMEAnet8/1xJ7Ue+W9XsPYRoAUpIlsC\npIigEpwtDJBoQUrwSepxrRAkraP5b0lXKkiapSedTwhAAAIQgEA3Egj8H5MnSPsrOHq6Gwl0\nuMwOkMLnxg4fOl2HI0BK1/mq5G3YVEqAVIlO4tLy4+TSMGlZaYyCpLkT5yIOQQACEIAABNpO\noNCT4p86jEetO6Xth+MAJkALUsTvAQFSRFAJzhbWBBAgJfgk9XYt/5yWvyPNJd2qIGmh3utZ\nggAEIAABCGSegAdl8P9O7pz5kiangA6QZtVzR7/kuJRMTwiQknle6vHKAZL+Xyc/uZ6NyBs3\ngfxr8sAtSf4D2bG6WK0ct0ccHwIQgAAEINAZAsGWOs7e0vZ6fnmjM8fkKCIQVqaHvY+AUoUA\nAVIVMClKdoAUfuFT5Dau6qbwrih4dDu1IuVuV5C0CVQgAAEIQAAC2SYQLKXynS39RvfBG7Nd\n1sSVzi1INgKkHg5VPwmQqqJJzQp/yQmQUnO6yh3Nf64bhGrQcidKHrjhUClfnotlCEAAAhCA\nQPoJBK7UvVxSpWDu2PSXJ3UlIECKeMoIkCKCSnA2WpASfHKiu5ZXTVpuK+lg6TIFST6vGAQg\nAAEIQCAjBArvvVykwgyQfqLKwSAjBUtTMcIKdZ4xapw1AqQagFKw2l/ysEYgBe7iYnUC+Su0\nbjVpeelBBUnfqJ6XNRCAAAQgAIFUEXBPidWljYtdzFPlfDaczX+hcnwmzZmN8rSvFARI7WPb\nqT3TgtQp0h05Tv5JHWYV6V7pLgVJe9HlriPgOQgEIAABCLSNgO9lOf8h7BYKjjySKxYfAbci\nESDV4E+AVANQClb7Sx42mabAXVysTSD/UfG9pJ8r7++k0QqSGAq8NjhyQAACEIBA4ggEI+TS\nn6SddG/zoERYvATc64gAqcY5IECqASgFq2lBSsFJaszF/FnazsN/+xw/piBJfbYxCEAAAhCA\nQFoIBJvJ03OkfRQc+U9hsfgJECBFOAcESBEgJTyLH579ZccySaDQFWEtFe146XQFSW5NGpLJ\nolIoCEAAAhDIEIFgIxXmYulIBUcnZ6hgaS+Knxn97Ij1QYAAqQ84KVlFC1JKTlTjbvpPgPPu\nareSNIv0hIKkQySPBIRBAAIQgAAEEkYgGC6H/iX9QfevYxLmXLe7QwtShG8AAVIESAnPwjtI\nCT9BrXMv/4z2tY60p7S39LiCJP5cViAwCEAAAhBICoFgG3lyqXSEgiP/hQWWLAIESBHOBwFS\nBEgJz0ILUsJPUGvd8/9G5N2fe2npekk1dMF/pW+09jjsDQIQgAAEIFAvgeAAbXG+tH+x50O9\nOyB/+wkwil0ExgRIESAlPAvvICX8BLXHvfx7uvm4FWmo9L50v4Ik1dgFy7XneOwVAhCAAAQg\nUI2A/wQ2+JvWHiVtq/vTX6rlJD12ArQgRTgFBEgRICU8Cy1ICT9B7XXP3e7yP9QxviN9RfJo\ndxdKK7b3uOwdAhCAAAQgYALBV/UxRtpa+q7uSe5ehyWXgAMkPztifRCYsY913bpqZhV8JWkB\naT5JXZpy70qPSn4HxMsJscDnzy/t8z9ICTkj8bmRv1vH1o0pWFvTw6SHNX+tpn/UzYr/nRAI\nDAIQgAAEWk0gWE17vEx6Q1pF95uXW30E9tdyArQgRUBKC9I0SA42PFLY/6R7JL3bkTtVOk26\nRHpaGiutICXFwhoAAqSknJHY/XAwlP+e3PBN63PpJgVKD0ojJQfTGAQgAAEIQKBJAoUudYdq\nJ3dI/5HWJDhqEmnnNidAisCaAGkapNM1u4d0puRa+GWkeaWFJbcobSW9JT0g+eEzCRYGSP6y\nYxAoIZC/TzerHylhCekW6U+Sgv/gRGmo5jEIQAACEIBAAwQC31fcM+GX0gjda3aWPmtgR2wS\nDwFXqnsEZKwPAgRIPXDm0mRHyUHQQdJt0jjJAdF4yd3rLpU2lq6UtpWSYOEXnBakJJyNRPqQ\nf0k3rv3k2kKSRhUqvKvk4cHvlX4uue84BgEIQAACEKhBIOive4ZbjR6TPpVW1P3l4hobsTp5\nBFypHlawJ8+7hHhEgNRzIhbVxO8WqTtSTfOLiMNq5upMhvALToDUGd4pPkr+E93Izpbc+jlU\ncu3fIdIEffWvl3aSBmkZgwAEIAABCJQRCDZSwiPSPtIuupeoK3feFchY+gg4QJpR9/xZ0+d6\n5zwmQOph7Rait6XhNdDrC1VoZXLrUhLMAdKXukj5XRMMAhEJ5J/Ud+YAZXb30Q2kV6XjpNd1\nwfQ7S7oBFrpQKAmDAAQgAIHuJRCsovuBK4b/Ld0s6fWD/HndyyMTJXeAZAsr2XuW+OxFwA/8\nWC43RRBOkS6QtpeukvSwmJsoDZAGSv5jTvW1LbzTsYamSTB/ucMvehL8wYdUEcj7e+8bnhTs\nrulakocM30vSO0vBs5r65dsbJHU7zb+vKQYBCEAAApknEKyqIh4u+dWCq6UVdA/wYFVY+gmE\nz41+TeON9BenPSUgQJrG9SjN6r2M3ElSpZakSUq/VNpBelRKgvnL/WESHMGHtBPIT1YJbilq\nbwVHy2r+B5JbmNzHXBUFHg2v0DXvDk3v1M3Sra4YBCAAAQhkgoBHpsttLrkb3ZqSAyMFSvkH\nNMWyQyB8bvQzJFaFAAFSbzCjtbik5K5Hg6UwAJmgecsvJSbJ3IIUftGT5Be+pJ5A/ikVwXJL\nkoKj3OrSutIwya1Nsyn9OU3vkVyx4Bvow7qR6l0nDAIQgAAE0kMgWEy+7iTtKA2Szpd0nc8/\noSmWPQIfqUjuQUKA1Me5JUCaHs7MSlpQmkeaTwqk+SWzeqa4rEkijAApEach607kv1AJ1cWu\nIE0Kf1C8smYcNK0m/VxaStIFN/BvxC/yupXVN1eNmJd7STdaX4wxCEAAAhBIBIFgEbmxpbS1\n5Ov4Y9IJkt4vyk/UFMssgbyeawMHSQRIfZxjAqRpcMziaGkXaeC05F5z92lpZ8kXkiSYA6Sw\nL2kS/MGHriCQd3fT+4s6uafIgb+LX5ccOK0kbSEdKqmlKfdZMXB6WvN+r8l6XnpBek03Y1dC\nYBCAAAQg0DYCgSt/vy1p9LnCe0UraPqSdIm0h67DD2qKdQ8BPzv6vo1VIUCANA3M6Zp1bcqp\n0rXSG9I70kySA6alpZHSA5JfZh8rxW2O/j+M2wmODwHdXP09LGllMpMgr48h0rLSMpJ/Q75B\nuxvHQpLXO3h6RdOXJU9fLep/mrpbq6XfIUGUOGAQgAAEIhIIFlTGb0oeVMpaXeonuUv0xdJP\ndF11az/WnQQcIPkZEqtCgACpB8xcmvihbSPJI3aV23glPCpdKrm2ZVspCQGSo38CJEHAkkig\nENS8KM+s63p7GLjiYdGiBms6RPK7f+sXpwto6jy2LxVEvaGp9WZRb2lqTSzKlRnWuz3iXShx\nwDpPwLX0bkH19zfsou3vpO8fz0iBhEGghQSC+bWzJSRXQC0nDZXcku/vn98JvU+6W/q9dLuC\nInetwiBAgFTjO0CA1APID2q+cd1Ug5dXj5F2j5CvE1kcIL3UiQNxDAi0lkDhv7ue1j6tKhbM\noxV+0LT8EDCv5Ju+p34Q+Ko0qCjXhOWlogUKqnLvSb4JeHhyTy1XKPgBIZx+rPlQfpgI9Wlx\n/jNNPe9pUYUuhlrEIDCVgO+lR0tp6qI91Xlmkkag0Po+t7waKPk6F1773CpkuTLJFUvWbJKf\nX9wC/6T0mHS+9JD0tC6LkzXFIFBOwPdAWpDKqZQsEyD1wHhUk/CPYi8r4VM+a15bSePKV0Rc\ndreiuWrknb3G+tLV/nL7oQ+DQAYJFIYR9+/SN/waVhie9ivKFMq/Mz9geOrfiaeuULCc/jXJ\nvzU/XHg6a1FeditASbClpV4WeMCJz0v0hebL5QDNaZ5afm+rfOo0yw8wpfNeriZfg5aSHpLs\nxw1y9TlNsXgJnK7DbymdKl0rubXzHcmtoH7Ide3+SOkBaS1prFSvuXJgUL0bVc8f+DexUPX1\niVzTx++yor/l+UuXw3lPy+fDtBmK60qnnu8nhVPPW/5tWv1LpgM0b/l7YPnaMktRvub4emOF\n1yafk1Def2h+mPV36jXJ3Y+fkK6XXpKel/Q+Z94VOBgEohLwsyMBUh+0/GPGOvdHsb45+iYX\nxXzRrGV+iPIFM/UW5AL/WH2TwCDQAIFCLamDKatJK9Tehg8ypVPPW37QKVX4AOSpH47ChyLP\nl6r8AcoPSmFa+IAVPmxVm/r4C0t+t8APUG4dI0AShBjND7Q7ShtJClins/FKeVS6VLpE2lZq\nJEC6UdstL0UxB2W17M/KMLJWJtZXJOAWG1dQ+B4cKqzk8DSsGAkrTsIKFQcxYYu0W67flNyi\nHbZq+/dsvSs5wLbeIvgRhRRYv9xkPcf087NMGmyCnPT3GKtCgABpGpijNHuvdJI0fFry1Dlf\n9HyD20Hyza4RW1wbzVpjQz94vSrZl1q2sTL4Qpx6+13ui8PX7nngS31ZKEDaCRTenfJDjIVB\noBaBRZXBDxo31cqo9WOk3SPkq5RlNSXOVmlFWdqLWq4UqJVly+2qhAPLE1O0HOXhrjxP6XI4\n72n5fJjmIMjzpVPNM2hMir4nHXO1f27Src/mJvk5Lw22bxqcjNNHAqTe9EdrcUnJNbSDJTc/\numnbkbbV7AOTa4ysvsw1xBGt8P80EfMmO9sRPTcg34QwCEAAAmki4Aozt1y6Yu2yPhz3/baZ\nLtqfaHurloUP+zXyFe4fap3AIACBVhHQA6RbC1NgvJtW6yQRIFUm5BYcC4MABCAAAQj0RcAV\nO6dIF0jbS1dJr0sTpQHSQGlpaYS0hLSGhEEAAhCAQIIJECDVf3KGahP3ER5f/6ZsAQEIQAAC\nGSTQiS7aGcRGkSAAAQgkkwABUv3n5TFt4m4U7iqBQQACEIAABEyg3V20oQwBCEAAAh0iQIBU\nP+jfaJOn6t+MLSAAAQhAoAsI0EW7C04yRYQABLJNgACp/vN7dP2bNLTF17SVX/zty+bVSg8V\nHPGl3L52Ffs6fxf7SSl5wbEmL482VWtAjpo7SUgGypKQE1Hmht9v8cN4rd/MoLLtWMw2Af+H\nz/zS4jWK6XejPES5h6lOu3nIe/8ePIx2FoxrbjLPokch9mBdWXjm8l9QvCF5iPm+zM+ZXWnh\nn6N1ZeGrFNqjyK0kLSDNJ/mH4P8k8EhFzxSXNWmbOVDwyHl1jGbXNl/YMQQgkA0Ct6gY62aj\nKJSiBgEPEOF7FwYBCECgFQQe105WaMWO0rQPAqRpZ8uBiVuHdpFcs1bJ7lPizpLfQ2qn+fi1\n/i/Jx79WukU6T0q7/VIF8E39wLQXRP7/QNpL2jgDZVlIZbhS2kRybVPa7T8qwHHSf9NeEPl/\novSU5OtWLXMlT1ZaNGuVtdvXu1Uoyp9u/0P5XpVOygAw35dXk3z/TrutrgKcIH0n7QWR/24J\nu0XyCI7jpLTbJSrAxdLlaS+I/P+15P/33DtCWTwwmSvuu8roYjftdJ+u2S2lUyUHHn4Y9L9Y\n+49bHbB4mNaR0gPSWtJYqV3m41q1zF1rxkv318qYgvVvyccBGSnLUiqHLzxZOC/h99AtqH6Y\nSru5O9ELUhbOTXjT8jUAg0BIwN8Lq5Z9qgy+z2Xht7ChyuGuQlkoS1hBm4WyzKlzYntSeqgw\nl+4Pd+F8RcrCuZmocvSTuH8IQiUjQOqh4hq3HaWNpBt6knp9+gvkB8RLJdcgbCu1M0DS7jEI\nQAACEIAABCAAAQhAoNME/GIjlsstKgh+1+imCDDGKM+wCPnIAgEIQAACEIAABCAAAQikjAAB\nUs8Jc+vQ29LwGufPLW5bSVnoS1ujqKyGAAQgAAEIQAACEIBA9xGgi13POZ+iySnSBdL20lWS\nRwJyH02/F+M+wX4HyS8aLiGtIWEQgAAEIAABCEAAAhCAQMYIECBNO6FHafZeySP6VGpJ8kv3\nfgdpB8ktThgEIAABCEAAAhCAAAQgkDECBEi9T+hoLS4pLSwNljwCi4c2nFCUR/3BIAABCEAA\nAhCAAAQgAIGMEiBAqnxiPZxxFoY0rlw6UiEAAQhAAAIQgAAEIACBigQIkCpiSU1i1P+7SEOB\nXJbZ0+BoBB+zdF4+UXndcuppFszn5oMsFERlyNL3LCOnJFXFyNL3x79plycLlqXz8oVOiO8d\nWfmT0SydG/9mGKgtC1cMylCRQP+KqelM9A81SwG7B/fIilGWZJ5J/17yyXQNr1JAIEvfH/8O\nsnQ/5JqbzB9Qls6L/yTWwiAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhEI/AtZTtFela6XtpESpvtLYfv\nreJ0GsqXl+8/kW6Xxkv3S4dJM0mlloay2N8dpbHSS9Ll0rpSuc2rhEMkl9Xn7gipn5Rk21TO\nvSwtXuZkeP7+rfRnpPOkhcvyJGFxNTkxuoL8XQstLWUJ/WXafgKN/laTeL1qtCwrC7OvZc9J\n4yT/xodIcVorfqvVrmlxlKvR74vL4GeX56UzpHWkuK2Zstwq5/0ccLc0UkqK9Zcj/5EOjehQ\nowwi7p5sEGgvgUW0+w+ki6StpDOlSdJwKS1mX+2zb1rllpbyHSTHJ0tXSg4ufJH/WLpCCi0t\nZdlADgfSKMlBn8vwhbSRVGpjtPC0tIO0n+Tv4T+kpNp8cuxNyWVbpszJXbT8meSAb4TkoO9l\naV4pSXagnPlUuqxM+5c4mZaylLjMbJsJNPJbTer1qpGyDBXfT6THpH2lQ6UXpLek+aW4rNnf\nal/XtE6XqdHvixlMkU6XfL+5vri8gqZxWaNl2UwO+/5yrbSD5Puhl/2di9scHJ0l2Z9jIjjT\nKIMIuyYLBDpD4God5qGyQ7mW7NGytCQuzi2nwh/se5qvFCCloXwzyvePJPtaakdrwRcj35xt\naSiLazQfkK6zw0Vz2jOSL/qh+eLvsi0ZJmi6dTGtPPgoyRLrrP2fUMFHPyC9Lzk4Cm0uzXwo\n/TpMSMj0QvlxRx++pKksfRSDVS0k0OhvNYnXq0bL4tYiV4D4nhPaiprxNezIMKHD01b8Vqtd\n0zpclMLhGvm+zKwtX5fOLnP4QS1fUpbWycVGymL/bpBcsdbPC0W7VdNXwoWYpt/QcR+W/Jzy\npRQlQGqUgXaPQSB+AnPIhclSae2xvRoulT6YOy2Jdqycco3+dtIZUnmAlJbyfVW+nyytJ5Xa\nd7Xg87ChlJayONhbX1paKjW3qLjLXWi+MZcuO30m6UPpCClptocccnA0UvI5KQ3iwrTBSi+1\nC7TwRGlCAuafkg9/6cOPkVrn8qWhLH0Ug1UtJNDIbzWp16tGymKUB0hufS21GbQwUSp/OC/N\n0875kdp5M7/Vvq5p7fS70r4b/b5sr535GWZg2U6/omVXUsVhjZbFvt4olVdYuxXJQWCc9qwO\n7u5+vq+7MrpWgNQMA+0+m+YLBpYeAsvKVZ+z58pcfr64vHBZetIW/QA6RPK0kqWlfO6msaf0\n37JCbKPlKZJrbtJSFnd1vEkKg1XfpPaWVpFGSaEtr5ny793nShsvJe1752DoeGln6W2p3NzC\n51o11/yVmsuXpLLMKn+Wkr6QjpN8I75KWlcKLS1lCf1l2n4CjfxWk3q9aqQsJuzf/x/KUH9P\ny34wL3+gLcvWtsVmfqu1rmltc7rKjhv9vrgHgh/efe/4hfRPydc233fcqh+HNVoW+3qutJLk\nSusFpW2lH0ujpDhthA6+hjQuohPNMIh4iPRlI0BK1zmbu+hu+UPfO8V0N+En2R6Xc+4XXs3S\nXL5hKpQvSn+VXpPSWJYN5be/W3+WzpD+LoXm8rj2tdzeVUKSvnf95Y9vur5xuW97JatWFv+O\nXJM2W6WNYkhbQcf0NfqnkoOlm6XVJQe0vhHb0lKWHm/57ASBat+Jvn6r3saWtHtLI2XpKUnv\nTz+AO2hyJchZvVd1bKlaWWpdd6Jc0zpWiOKBGv2+LKTtJ0u+hrmLs6+3+0mPSK6Ui8MaLYt9\nPU+y//5u/U9y5e9F0sFSnDa2zoM3w6DOQ6UnOwFSes6VPXXzvM2136UWLvshKs2W1vK5Rt/9\nd31R8kXflsayuLZpI8lduvx+0YVSaC6PWzLKzd+9JH3vjpI/vumWd0Mt97taWZwvKeWZKF+O\nkNaSXNvqG/HXpFckB+L9JFsaytLjKZ+dINDIbzWp16tGylLO+KtKuEFaWNpK6quSTqvbao38\nVqNe09rqeNnOG/2+DNJ+lpOelRaRNpMGS76P/E2Kwxoti339leTua2dJvnf+WRouxVUWHboh\na4ZBQwdMw0YzpsFJfJxKwC0TNvfXLbWBxYUPShNTOJ/G8m0nzudIN0q++X4q2dJYlhfktzVG\nekM6tqjHNJ0ghd8zzU41p3mbJNi35cSB0m7SEkWHFi1Ol9bUN+Hnpb7K4uxJ+R25tvtIO1Ri\nfsC6UHIN5eJSWsoiV7EOEejrO1Htt5rU61UjZSnF7N/IaMmVHutIbqmIy/oqi32qdN2Jek3r\ndJka/YnZxOwAABMMSURBVL68WXT0r5r6Wmbzvq6QdpZmkcJ7qGY7Yo2Wxd+pw6V/SLsWPXWv\nhZelP0mnSE9IabBGGaShbA37OEPDW7JhHAR8gbUt0DOZ+jl/ca7azW9qxoTPpK18u4vn+ZID\nJNeEfSyFlpayuDvZMMk1e6V2VXHBrRc2lyf8nhUSih/zaZqU750fJnxNO13yg5DlG7HtSmmU\nZ2Quy+xFeTk0/6687vMwIebpvDr+1yv44Jal0NJSltBfpu0n0Mhv1dvYknZvaaQsPSXpGU30\ndi18Jq0hxRkc2adGfqtRr2nefyet0e/L+KKT48qcdYuSzd0JO22NlmV1OTqzdHGZw+5iZ1u/\nZ5KKz0YZpKJwONk9BO5XUf9VVlzXVvihyT/WtNgZcrT8Imnf01I+13a5WfoQO13F0lAWt7C4\nHCeUlcEtMU7/fjH9IE0/keYoLnvim7fzbOyFBNhA+bB0mdyaZB83lBaRbG5dmixt54Wi5TV9\nVRpVXE7CxN8t+75mmTP+Xr0tzSilpSxlRWCxjQQa/a0m8XrVaFmGiK9/I7dKc0pJsEZ+q1Gv\naXGUr5Hvi4MKX9O2KHP4Ti0/WpbWycVGyrKUHHRZ9ihzdKti+o/K0uNafE8HPibCwRthEGG3\nZIFA5whsq0NNkvyjnFv6seQH1x2lNFm1ACkN5XOriS86rvVy03q5fCO0paEs9vMa6SNphORW\nIn+3XpfukvpJNn/XPpQukxaUlpNcI+ttk2ybyDnfxJYpc9JdOl6RfMOeRzpJeldaQEqKDZEj\n/p7dJ60jOfj7u1R+U05DWeQ21iECUX6r/g275tv3j9CSeL2KUhb775fkSyt5rtKy75MHS+XX\n5+8rLS6L8lvdUs753HytipPVrmlVsrctOcr3pVJZbpBHb0s+DwtJfnifIrnSMS6LUpZKvxnf\n/z6QXM5B0jbS09I4aVYpCeZ7SKUAqfw3E4VBEsqDDxDok8CvtPYzyQ9K46VjpbRZtQDJ5Uh6\n+XaXj2ZfTdu7EEVLelns5lekC6WwPL5Z+QY9r1Rq39GC+1c7n4Ny3+yr3cS1KhFW7WFioLy7\nTnJZXZ57pU2lpNmacuhJKTw3EzX/szIn01KWMrdZbCOBWr9VVxj4O3VEmQ9JvF7VKouL8JgU\nvu/hCo/w91JpeqU3iMmi/FYPl2/2e2gVH6td06pkb2tyre9LpbK4F8IF0peSy+nKuAOkuK1W\nWSr9ZnzvPFdyj4Twu3aj5heTkmLVAqTS30zoay0GYT6mEEg0AffVXVxy16AsWpbKl5ay+Mbl\nm3Ktmq9FlGe2jHzp5lI5XDOYdFtADi5aw8m0lKVGMVjdQgKN/FaTer1qpCwtRNnSXWXpt9ro\n92VmEU3aM0wzZVlW5Zmzpd+SeHbWKIN4vOWoEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQ\ngAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAAC\nEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAgZoEZqmZI90Z+sn9QTEV4as6bj6mY3NYCEAAAt1MIM5rfxTucyjTzFEykgcC\nEIAABDpD4Mc6zNnSM1IgvSaNllaVsmb7qECnlRRqZc1fLj0njZPOk4ZIjdi/tZG5lSsMii7R\nuh0b2THbQAACEEgRgQXl68tlelrLV0r7SeE1UbORzQHOJpFzT5+x/Nof5uivmf9Ih4YJJVP7\n+RPJ13bfH31/WFiq18L93K4Nx0v3S4dJM0mh+T58TbjAFAIQgAAE4iXgm4aDouslz28m/VJ6\nSPpS2kHKis2tgrwizVcs0FBNP5Eek/aVfIN8QXpLml+qxxZVZnO8WbqsTOHDwGJK9/6z3kqn\nImIQgEAXE1hEZff18EbpGOm30smS7zNOd6BRr3n7h+vdqJi//Nof7sbB0VmSfbKf5baLEj6T\nDpFGSA5sXpbmleqxg5R5snSltKN0hvSxdIVUandrYb3SBOYhAAEIQKDzBHyhniLtVeHQA5Tm\nlpAJUmktV4WsqUk6Xp76Jhuab9K++fnmGdqKmvHN8sgwIeL0h8XtFqiR/wKt980WgwAEIJBV\nAmGAtH+FAvo67PtOWFFVIUvFJF+vXXHXiJVf+72Pb0gOuD6SXBlYHiC5kux9qfR6PZeWP5R+\nLUW1GZXRx7i6bIOjtex7zdCS9OGaf0AKK9VKVjELAQhAAAKdIvC8DuQavmr2Ta1w9zO3fITm\nYMk3vYul26XzJXcNKLU/amGYtI3k1hTvY2vJtoHkIOFCaRNpBsm2pORata9KR0hjpL9Lvnn0\nk9yqdb30e2k5qdSi+DRYGzgYWqtkwwM0f2DJsmftz0TpbC/UYUcpr4PJWra5Mvim63JiEIAA\nBLJIoK8AyfcFBwbLlxV8Oy37vnCz9FfJ+wjtF5p5VvK12feJMKho9NqvXRT2d7emS0vvSeUB\n0kil2U/fO0rN968nShNqzPtaf7K0Xlm+72rZ+9+wJN3l+UByaxUGAQhAAAIxEHAXAV+cHSRE\nNQcqrsEbL/1FcivLg5L3M1IK7TXNON8zkoOlB6Qpkrd5SzpFulbydutKNgcuXvZ2N0jO+6b0\nouQg60npD5L3+YYUBlZRfXJQV7qdFiva95VqP/aquLZ64lVadZe0p3SLdJvkY9q/UvNLuB9L\nO5cmMg8BCEAgQwSqBUhuNbpVeqSsrH4vdLI0WjpIukNy0PJ1ybaj9Ljka/ixkivUmr32r6Z9\nhFYpQDpeK78IM5RMXRnmIKZZO1M7cJnLex1cpDRzwCAAAQhAIAYCbslwIPC9smMP0PKcRc2l\nqRWOrOMaL7fCrCOF5j7c70iXhwmaOkDyjcxBmG0W6XPJx1tcsrkLwdOSawptYYDkgQxC20Yz\n3sYBVmgrasZpaxYTovp0jvL7xtyXuayPSq6pnLWvjBXWvaI0++Vg7nDpoeJyKRclFczvPJ1Y\nnGcCAQhAIGsEwgDJgcerRfk+4WuklwdKoQ3TjNP3DRM0dfDzoOSKptDO04yvq6G18tpfKUBy\nS5XvZeW2jxLs72zlK+pYdpl9L/1ThW18/xhfIZ0kCHSMwIwdOxIHgkDyCMxexaWDlX5k2TrX\npB0ouTuegx3fHGwOgFaS3pbK93e30twCZPtUcguQb3rPSzbv4wXJ25falSUL9xfnS9PC7VfW\nujukqD4tr7zjivurNHE3CPcRX1haT/pEimoO9hzo+cZ/cXGjozR1K9gvJN/I7WdoDqaGhgtM\nIQABCGSUwH0q1z3Fsvne4evrJtJl0vaSAxAvfyndIi0qhXaTZtwK70DEre7l1qprf/l+S5cr\ntSDZV5sr0Sr5VVjZx8e6Wud72ljpkAr5fH9YSJpLer/CepIg0HYCBEhtR8wBEkzgrqJv39R0\nTImfvnG5ZSe08IE/XP6hZtz9zIHNV6RnJdcGviyVmi/ypeabivOWmtPKrXS7cH2pP2Fa6XZR\nfFpGG9xculHJ/OKaHy35hreO9IhUjznY+2OFDUYpzQHS6lJpgDRByxtIGAQgAIEsE7hBhSu/\nNq6gNF9j95B+Lfn6654IbjGqZA6a3L2ukjV77a+0zzDN1+nSlq4wPUz7IEyoY7qd8p4j+X6w\nleTKw3LzcW2+ZzmIwiDQcQIzdPyIHBACySHwolxx7d3aZS65peeSEpWu3kIL7jL2urSzNJ+0\nlOR9lVulQKY8j5fzZYmTypZrLUb1yTeieSvszC05t0ufSWtI9QZH2qTQqraipnN7ocTeKZkv\nnTU3Hw+DAAQg0G0E3MXYrflh9+73NG/NLzn4KNdTSqtkzV77K+2zNM2ByuxFlaYvoAWv+7w0\nMcL87spzvuQAaTOpWutTeJ/yPQuDQCwECJBiwc5BE0TgJPnyfekPVXxaviz9R1p+U9pW+ldx\n3t0flpbiapGN6pODQdfIldoQLdwqPSt9RyptvdJiZPuacjqwOrJsi22Ky/eWpZtXWEtYtopF\nCEAAApkm4Aoitwr5umtzwOTKpdWld0v0f5r/sxQ+q03RfD8ptGau/eE++pq6i5+P6WAmNFfo\nbSqNCRMiTl2heIp0mLSbNFmqZuF9yvcsDAKxEIjrgS6WwnJQCFQg8DulzSK5m4O7zLnZ/2Fp\ncWktaWvJF+nwZuBgwsHRj6WrJD/onyjNIc0qxWFRfbpLztn3UvurFnxjvl4qX/eS0m6QbH+R\nXJt3sBcqmG/0Zucb+kOStzO7/aRbpP9IobkryWLSZWECUwhAAAIZJeCgZ9di2RzozCf9RHKg\ncbJkO0P6pXS89BVptLSR5PuT39H5UrJ9KA2RHLDcIzVz7dfmNe055fi3dJzk92W9/BvJrUq/\nkkLbRjM/lH4hvREmlkxd5hMkbz9RCnlotmA36dPrQnOA5HvKW2ECUwhAAAIQiIeAH+yvlt6R\nAsm1Zr5A+wbl4Cc0B0EXSO9LkyXfsA6TDpc+kcK8r2neN4RScyvKJaUJmvfN57ZimgMyH9s3\n1NAGa8ZpDshCG6AZp+1ZTIjq04bF7RYpbjdPcdn7qqQri/k8MYsHSpYrzXp/Ll+4r881f57k\nFrZScyDqPKuVJjIPAQhAIEMEfJ0Nr4Xh1IHOq9I10jCp1JbUggOeKZLzO2D4o9RPCm1VzTho\n8PrdpEav/dp0OntPKcdMl9rT3e86pYd+3av5TcvyHatl++SKr0rmrnUhg0rT7cs2ekbL5ffP\nsiwsQgACEIBAJwm4Vm8JyTVkfZmDlEUl1wgmxWr55BvtI5KDvnptcW3gYC6KmZ1rAO1PJTtV\niWFQWGk9aRCAAAS6lYCvn4NrFH6Q1vteFVo7r/3hMebSzILhQoWpAycHbM3a+trBp9KQZnfE\n9hCAAAQgAIGoBNZTRtcUzhl1g2K+czXdrs5tKmWfX4luaftGpZWkQQACEIBAWwg0eu2P4sxw\nZbokSsYIecYoz28j5CMLBCAAAQhAoKUE/qW9HVjnHr9WZ/5q2d16dXa1laRDAAIQgEDbCDRy\n7Y/ijCu+ZoySsUaeVbR+glSrB0eN3bAaAhCAAAQgUD+BIdpkl/o3a8kWe2svvpliEIAABCDQ\nWQJDdLi4rv1RSvpdZXJLFwYBCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAA\nAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhA\nAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEI\nQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAAB\nCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAA\nAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQg\nAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAE\nIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAA\nBCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCA\nAAQgAAEIQAACEIAABCAAAQhAAAIQgAAEIAABCEAAAhCAAAQgAIH/b4eOBQAAAAAG+VtPY0ch\nZMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgw\nYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgw\nYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDBgw\nYMCAAQMGDBgwYMCAAQMGDBgwYMCAAQMGDLwHAorzKvBxQhAHAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow = c(2, 2), oma=c(1,1,1,1))\n",
    "x = seq(-3.5,3.5,length=101)\n",
    "y <- dnorm(x)\n",
    "plot(x, y, type='l', col='blue', ylab='Density', xlab='N(0,1)')\n",
    "lines(c(0,0), c(0, .4), col='red')\n",
    "\n",
    "x=seq(0,50,length=101)\n",
    "y <- dexp(x, rate=1/5)\n",
    "plot(x, y, type='l', col='blue', xlab='exp(1/5)')\n",
    "lines(c(5, 5), c(0, .2), col='red')\n",
    "\n",
    "x=seq(0,50,length=101)\n",
    "y <- dgamma(x, shape=2, scale=5)\n",
    "plot(x, y, type='l', col='blue', ylab='Density', xlab='Gamma(2, 5)')\n",
    "lines(c(10, 10), c(0, .075), col='red')\n",
    "\n",
    "x=seq(0, 1,length=101)\n",
    "y <- dbeta(x, shape1=10, shape2=2)\n",
    "plot(x, y, type='l', col='blue', xlab='Beta(10, 2)')\n",
    "lines(c(0.833333333, 0.833333333), c(0, 4.3), col='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b22bd17d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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