Acrobot_ER_Boltzmann.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Boltzmann: Acrobot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "10\n",
      "11\n",
      "12\n",
      "13\n",
      "14\n",
      "15\n",
      "16\n",
      "17\n",
      "18\n",
      "19\n",
      "20\n",
      "21\n",
      "22\n",
      "23\n",
      "24\n",
      "25\n",
      "26\n",
      "27\n",
      "28\n",
      "29\n",
      "30\n",
      "31\n",
      "32\n",
      "33\n",
      "34\n",
      "35\n",
      "36\n",
      "37\n",
      "38\n",
      "39\n",
      "40\n",
      "41\n",
      "42\n",
      "43\n",
      "44\n",
      "45\n",
      "46\n",
      "47\n",
      "48\n",
      "49\n",
      "-90.78\n"
     ]
    },
    {
     "data": {
      "image/png": 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vqcked+5ce34djlu6ZIldZ8stZZsgsA6q1rPec/49q9mGH3wQ+MQngBdesMtaWoDx4+VzdbVk4K2vl+vV0WGTO2mf1tmOE/3hh/mdexQbN8pUr4uPP6yPosMuafKtYvdr7anf296ip8KDHwNwkjGm2hjzUQA7AHgVwGsAdjDGfNQYMxCSrOmxHioDIYQQstkS1UB57LH4ZYAItxEjbBhfT3HJJcCvfw3cf3/P7H/jRmkI+w33f/xDpgMHZp5jXAMzF488Arz/vjSEt98+nGhFG+1AuCyuONHQ0MmTw+KtNWVo84EHikD00UY+IELCGODWWzPXiyII5Lz8bKsqwNatA+68Uz4PGZJ9X67wPfFE4KijbDnc81aRcv/9wB/+ANx4I/DznycrLwD897/A4YdLupEf/CD7uk1NmYIckOt27rnheUsdi2XhQvtZRWuUSFTcY7jruSLzppvkfAERNStX2uu5fHn4BUx7O3CxM/6G3ivu/jZFhAPHZUhuawO+8hXg0EPjzyEbetymJiu0Vq+W58Jn6dKwaO3qkudVy6v3qz47a9ZIPfz73+HlysyZ9nNzM7DjjvJ5663lXnfHZlXRqvuOKl8x0ONUVUUvV1Hrk020zpyZ/R5LQtQ90ZcodMib44wxiwEcAODvxph/AkAQBLMAPABJsPQPAN8KgqAzCIIOSP/ifwJ4B8AD3esSQgghpIjMn585TxtBHR2ZywDg7belARq17SuvALOK9B9bG21xjkM+LFxoG+96nm6jb9Mme17r1mWK1lzjSsZx3HHAzjtHC8G33wb+9Cfg4IOBG26w89vbM/vQfelLwNe+Zr8vWZK5v44OK7xz0dkJ3H67iENlxgyZXnll/D3gsmmTda39+YDUo4qJlSuz9wucO9d+VmH62msydcVWVINeRUASVNTcdhvw299mXzeqjgHgiScy573rJNVasMB+Xr9eptkEha7jr6euonLTTeKu3nabXD8VrXPmhPcBhO9frT9X/EcJlHfeAf73f4FbbgnP1/r9IKaP8ttv23snCj1uS0v4XnFdUGXJEvvybKutZNrUFM4eDIRF69ChVnz6KW7mz7f12NIiL92GDRPRCoQzBrvD6LS0yPkec4zMc6MdCkWPE/eSwHdQ77xToiQWLJDyjh0bXq+tTSIyjj1Wnpnbb8+vXJu1aA2C4OEgCLYJgqA6CIKtgiA4wll2TRAE2wVBsFMQBFOc+U8EQbBj97JrCjk+IYQQsrnz5z8Djz+eOT/KRVBBECcCtJEUNY7h/vsDu+6aXxl9VKwOKFK8V1eXNOpUpOh5uALBDQWMEq1RjluS4wIiAOfNy1x++eXAqadK490NzVy0SM797rvD6y9ebB1fP2wVkOs8cWKyAQu+/33grLMk7PGKK2Tef/8r09bWsAsMyHc/IZDeB75oVad+3TobUrpunQiOKVNkjE4fFa1r19r9adivK7ZaWjLFrysu580DPv3p+JBhPa+2Nmmkuy9IfPda9zt0aHh+1PM0a5Z1ztI6rXGi1b8H339fynzOOfJdn7czzgDOOy+8rit4VcjFOa1nninbv/eejF36rW+FE4L5iYp8dtkF2Hvv6GX+cVetEgcVAJ5/PnPde+8FfvpT+azrbdgQHR48b54I7REjgLo6me87rb/8pWRNBuS5r6sDDjkE+OQnZV6caH3sMTnf884DLr20uKGzepy46A3/XjnjDPn9+vBDGaJHz9V/+fbUU8C++8pzHce0acAJJ0S/lNqsRSshhBBCSssppwBHH22/65AXc+bEbxMnWrUx1dNjBKYVrevWAQcdFN/vdONGEQYqAqKc1lyi1XeyspVFG/euK5hrkANXJKqAu/768Dp1dXbojaj+hSqWopxwn2nTJNxzwQIJlQVs/bW2ZvZrPuooGQPUbbznEq2rVolgOegg+T57NvD5z0tfYSBc/3o/umWPE63+SxP32t18M/DsszaU1sd/+aCu7vnni5vmhmbri4Eddghv849/ZIZ2zpoF7LmnuGdpnVa3TG6dLPWyuviiYuedZTicESOsOxmF1mOcaN1xRwk5bWuz7t9110l/7tWr7e9BVORDEjHnXr/ly8UpHD06WgS7L0ZUtDY1RYcHX3mlPGMXXxwvWl1aWoDaWnGTNaQ8SrSuWyeu9rbbAocdJu52Z2ey6IMk6HHi9ufeK+4Lgw8/FAHui9aoeysuSuXrXwceekjEvg9FKyGEEELKBm3wZBM2+TitLr/8pTT28iVKtG7aJGGIfnk++ED6e774oiT8icIX21GNPW0sV1YCV10liW9ckjitnZ3Sd/OEE8LHATJF68CBMp00SZzBqPL6DfBsovWnP5UkW7qspUVeUNx8c3g9vbYbNogoMAZoaJCGuTq0UaJVw3w1ZNc9P70fVPD5jV/tC+nec83N4eQ2c+ZIHV97rXzffvtMsbXVViJSVOAPGCDO0vvvyz3wyCM2dDJqmBgg00FW0XrTTTJ1X1ao07r99jJVgbNuHfC5z4X3s3EjMGaMCJ040RrnVOo6o0eH70lXtPrJqgARMAsWiAjJht577j3suso1NdaNVCF1//3AH/8o/X6zOa3uiyL/uk+ZIvewK5ZXrBDhuPvu0WV1X0DkCg9eulRc3n32kX26y306O63T6hIlWgFJXHbiiXKPacKrtP3I49A6zvU7639e3j3Wrp6r3itRojXuxeK4cTJ95pnMaAQmYiKEEEJI2aDu39Kl4uRFZVHN1ZjK5bReeKE0ivLpk6oDMADhsn3729JAdRul3/2u9OvTMMOPfUymHR3AEUdIJmQVcIAVV3GideutRXhEkUS0qiCaPFnc0myiVUXCiBEiVly0ke/3aayrs0LeDQ/u7JQQX81MvHixLctFF4XrUfe9fr3N8muMlEfro6srLN5cwfTMM/azOqwbNkjirMpK2a/f+N1ll/D6gIgTV7R++KH0xVMBts8+Yad1iy2kvC0t9tzuv19CJ1tbpc/vccdZQaDip6UF+MlPrOCIc1pVvLihvYsXS2jwsGHy/aMftcsOPTSzT+JWW4loXrhQnOx16+w5d3XFiwIt06hR4ZcFS5cCBxwgz4Pe2y5bbin3g1uuKNx7T59/tyzV1VK/LlofU6dmFzMvvWQ/f/ih9L08/3xxoz//ebkvo0TrvvvK92wJuj7SPZ6IGx6s9dneLi8V9NrkcloXLZJ6VMHnn6eKVvea6ssW7c/a2mqzGReC/r7mimjRcilpnNa4yJDttpPpd78rydnc3wY6rYQQQggpORrepo2Uhx4SF+Uvf5Hw4d/9zq5biNPqNhqTJC/yG8QDBgAPPCCf3UaUJm1x+7Tdc480zv74x/A+3nkHePJJES6vvWadL190u6LyvfckTNJvvCvLl+d2Wlzn4vDDM/sVqksK2Mb6yJGZQjmuP2Ztra0TNymOL4gXL7ZlbWkJl1v3vWGDFa2AFdGK9m8FwsOnqEi57DIRVIDcU+rovvdeZuNXBZf/kkCF8dChUh7XBd1hBxGUjz8uGYKbmuT8Xad1yBCbDVbR+08TI02dKmGkzz4r3+OcVhUCrku6cqUIURUtI0dakbPffpmCa9QocVrnzJG6+fSn5f7W6x4Xxqmu+ahR4f65S5daUeYOrwPIi4YRI+SzJhWKw315pKLVFStRolXXW7w4PpttZ2f4d2PpUgn9/vWvJdswIM+zK8Q7O6Wu99tPvvvXQ1mwwA5P44YHu8ybBwwfLp8rKyV6IU60ash9LqdVhTIgog6wdf/22/LMDB+ef2I2IN5p1eO4v0vub+3atXI/FiJa3fto9uzwtaVoJYQQQkivceKJwAUXSGPT7RO5alV04/PnPxdhcOmldl5bm/Rx8xPmJOnTquIAkERDfobQZcvEBZ0zRxq41dWSWXfdunAGViAstrShpgJtyhQ5H1dsaQPPDVn84hetY6LLdarn09oqIm233eJF6+2320Z0HOooff/7Egqr4bq6zO0bqX0iR4yworWhIbwfHzdZkBtq6/e/XbQoXHduo3bVKjtUjStaNWxQefHF6DKsWSP71jBeRRvDs2dnvojQ83Yb0u++a8u9ww4iApYtEwH7wQdSL0FgX2BMmiTisaXFCs0o0fryyzJtbJR9aohtVIisng8QLVrXrpXyqGitrRUBWlEhz4d/r3zsY7JchdMbb8jUTQTk85vfiKgGRJD4Q9eoaPWz144cae+hNMMxtbVFiyX/XFxR6zriV11lhfZjj8nLh0sukWXLltl6VKHa1pZ5P9fWWtHqouc4eLA41iooTzghfO9ov/zWVls/gBzbrb/aWtt/WvtMxzmtGzZIvVRV2bGRtU703tbhc9asseMF50Oc06rHiXNagcKdVvfZ3HVXilZCCCGElIgHHgB+9SsJzXPHoVyxIlq0qlDcc087b+NGyR6qDT7FdVqDQITuRReFG+NuVuKbb5bhXNyG5KOPigu6ww5WFL/5pvSBnTAhfDxXeGljU91Lnb7wggy3scUWthxxCZmam8XlUFGhjb3nnpNzPvJI24g97TRxcl1yjU+rjfMTT5SQX9cB7uy0fSMB67aMHGnDgzV0L060uuNVzp9vwxT9cr31VrjO3euzapV8D4KwaNWhPQBpPD/1VObxt99eyjB1auYyFVDvvmvLeNJJ0jCuq5N9ui7iggUieAYPlpcBGzbI8u22E7dLHbQPPpCG+iOPyD3w5JO2rEOGhLOpAuGXJMuW2WOqaI1zWrWO3PDgtWvlGCqmKirkeLvvLmXxhd4JJ4TddEX7Zj72mAgu1yWfNs1+dq+HopmLfdHqh5QnpaXF9qdWopxWF9e9/PGPJRx/222B44+Xefo7cfrpmb8xGzaIgHXDbmtr5aXEqFHAD39o5+tLIX15o8+ij3vuep8AmS7qrruKyAaSO61VVRJm70YvqJh0+5HrC4ko5s0DfvGL+OW5RGtcn1ZA6mz4cLmP9GVCvqK1qio66VNfhaKVEEII6YOoK6AsXx4f5geEG2Rx4b9uWO2KFcDPfiZZRt3wUTeRiuImitFkP8bIuIITJkjjyx1iQ4kSrdpQU/ExbhzwiU+IuNBy//e/4case15f/KLNltveLn8PPigNxkMPtYJr333FDYrLYPzCC+GMrW1t1qXbckvgC1/IFEiu06oNVtdpVVGbRLS2tNiGtS9a164N90N1r8mqVVbQuiJJx2sdM0ZeNPhcc43U88aN0eHL6mi+845t/P71rzbMuK4u3A+3pUUy7u6yi4gUdUU11FVDX+fNk+XGZAq3IUNkvu+2umXScqnw8p3W5cuBb3zD1qHrYK9Zkylab75Zxs0ErNC7/XY7HFGUaFWn9cc/lqnbD9R1730XELACzj93P5w7V79WxRXlSnW1XJ84x9YPuXVfPtTWSt9xQISSK+YqKuS6NjaGw25VOC5bFk6epnWh4cxRIh4Iv9zynVaXAQNsPcWJVv3uitaamvB6vmgdNCi7aD3gABHj+kLExxetGzfK86W/NSokNSLCZaut5HqNGWN/b3T9l1+2wwWpaF2yBPjb3+z2bW3ANtvIi7XmZjqthBBCCCkB2RKEuE6r33ADwu5PXH8t12l1+6m5DbiorK3uGKWvvQZ85jPSYHv4YREpcQ6m24jSBrXbp7W+3jo49fVSvqYmca+0P5rLhg2ZQ4PceacMj3LaaTb8FBA3Z/x4ESNRQuTgg8Pu5MSJNuPw8OHiRPlEOa0jRsgYl6efboVjNtHa2mr7iKrAcuvvxBOl4e0K5gcftJ9XrIgWrXV1kmTpuefC56V85StSP62t0S6OCuh335WGcVWVNMI1lLO2NvxipLVVHOFddpFyqGhVAa+idckSK9x8UaeicYcd5DgqjFTgLV1qBZabddbl738H7rjDfp86Va7DzJnRTuueewJ77BE+/qGHZoptFxVOel2vu07KeuON9n675ZZo0arXKJdonTEj2gH3iRovuKbGZpGOwhetrrAfO1bqxR8CqKJC7mt1WjWrMxB9noAVrfps+I6wovUPZHdaKyrk3IYOjQ8PHjhQ/lzR6qN1ry8mPv1p4NVX439vtb7iulH4fVqvvVa6UugLluZmGVO6sjLzt1HPd9y4TNE6apSM+wyIYL7kEhGoRx1ly9rWJudbVyfHcZ1WilZCCCGE9Pz+jLcAACAASURBVArZGh2u06rhisp220WPv+nj9ml1Ravrks6ebcNcFW1cbdokzts++1gROmpUuM+ci+u0qtDSddetC4c01tVJuf/0JxFV3/pW5v6ihvl58EERqDrkiTY0NQRx9OjsY6xquf71Lztv8OBooeuKVm2wDh8uDek777Siq7ExWvyo06pOkytahw6V8SfvvBP42tfCZXFFmRs67DtZhx4qZTz7bNm364LV1UnjXce8jWPVKimjLzjq6qxoNUYcv1WrJIRz8GDZb2NjpmgNgnjRqgLjlFPEPVfhqM6r67TG9Wl1E05dfrlM//Y3CUf2+7T6rrsmYnLrMVt4sPLGGyKAXnlFnqkxY4BzzknntPrXbuhQEYm5iBKt1dUyjQsR9kWr2wVAxeiSJeEyfeYzcg3Vac0mWvXFhopWfTaMkSy3Pm595nJaAblOKv6iXtjV10vI84cfRotW12kdMUKyVM+eDfz+9/Y397jjpP7dpFdxv6O+0+qPx7thA3DeebIvP3JFr5ErWvV3vbbW3i+vvWbHogXsb6krWpua6LQSQgghpARkS5A0f75tuPiNaN+VTOO0brll2Glds8YOcaLH0pDE5cvFZXBF7ejR8U5rlGj94x8lLFldMEWd1ilTJFwx6TixL74oSXX84UvcxrBSVSUN8AsvtPP8sWOBcGZXF3eejvPpzlOh19gYPre77pLQ3KYm6RurTqsKkGXLpB6PO04arm7D/OtfDx//jTfiRasyYIA0il3nrbbWitZ166Ib94Dsu63NCiFFnR1ARJqKxQkTwuWIcizjhJsyaZIkHdNtxoyR+yGJ0+qy//4yjA4g93FHhw1BBjLDZ1VAuPWkorWiwoqmLbeMPt6mTeGxQ9M4rX42YSBakPlomOzq1fbFjO5L7zn/2vmiddYs+1nFqJsF+6ijpMuAOuiNjeF+qH459Xi+0wpIoir/PnW/53Jadb663FF13NEhobX/+U8y0XrGGfKC59xzZdmUKfKSY8aMsKCP+z12Revdd2c65G4SNF/Q6r02bpyUp6PDvkysrbV14w+X1dwsx1m9Wn5n9PeSTishhBBCep1sonX69EyndccdxWl0XRAgt2htbrb9tT71qUzR6YrS/faT/p+XXmr7QrqCZNSo+MZSlGgFZF9RTquWa+utRYT6QjTuGG644f33i2vnnsO0adLI6+gQN/OXv7TLtAHvC5Mo0aqiYMAACQ19//1wo1tF6+rV4Yb55z4H7LyzFVxDh0r4sQrmt98O92l0G+/ucCgHHihhkirk4kSr4gqjQYPCTmuUqK+ulkZwVLIfVyy4ZRo2LFwOFT61tfb4vtNaWZmZ2RqwdV5fL/uZO9e+XFm5Ulzb9evtftw+xoCU+ctfluOpKzxkiM2k64vW3XaT+8StJxWtw4fbvq/+cfScWlvDojVKdKYRrVH3u+8Oz5sn5++GPftOq98fPIloBWzSKL1egweL6OrokH1qJIFfJj2+3sOuaAUyhebgwfZFgnsf+uvpcWprrQMaVcdu5EA20drRIdfXd4DdxG+uk53EaT399HDXDCBz2COlrs5e43Hj5L684AIrPAcNkuW1tfaanXiiTGfNkmG4pk61TmtHRzjygImYCCGEENIrqKj0nZKDDw47bCpad90V+NKXMvuy5UrE5DqtruBTXFdl991l+rOf2QaYK+iyZUF1RavbsNxnn2intalJGmE6P8qZi3Ja3HPYeWcZZ9JtWO+3n4xLGgQ2kZSiDXg/LDRKtDY0iBuzYIE0HN1wYcA2mLu6wkJu8GA5F31RUF0tbvasWTYL72c/a9d3G+bbbGM/f/KTMn30UbvfbLjCSBMhdXaKaxXV/1GHzWlsjHZaFd91ixKtgK1D32mdNAk4+eTM4+s1UNH62mvyfehQacS3tEjdTpggAtQVHtddZ935hgYbHeCKVl9snXGGvARQAQXIuVRVSVlOPVXuGfecpkyRZDm77ir3d0uLvSd16mbN1brxRao69T6XXSZ9kxX/Os2bJ/eEMXafvmj1X0j4otV9LvfZx37W7VzRqoJq+HB5eXX44ZmJviZOlOk220hGYjdxEBAtWidNsvtV/OujLxnc7eP60yrZ+rQC9p6cNMn2K3bv9WzD1SgqWv1QdcV1Sd0Xgu59ob9ZN9wg61RX2/NtaLD70PK6wlhFKxDu+kCnlRBCCCG9gopKPwnQIYdIQ3PGDPmuolXFXTbR6vbR8vu0GhNukCuuKHEbiepe+U5rHK+/LolygkAE9w9/KCGwra3xTqsrZqNEa1RW4SR9AfU8/PEZtc+Zutj77y/TKNE6YICE+bqZVF1cd7KhQTIQA7Y/qTohNTUiet55R+oHCGcLjnNajzxSQqc1MVMa0ep+X748fM+oWFHXbdWq6D6tgAhI97huSKNfXl+0Rok6F13fGBFA2uDfYw+b8RoQMTlzJnDmmfL9e9+TkG+30a+N/KFD7TOQZDxUY0Swui8x3OtxxBGSRViTWkWFB7v3h++0qhD81Keij3/11XZcYiCzn2pjo32RofvU6xrltA4fnilalX//O/yyJEq0usvGjpUhi3bbLbyfu+6SvtZbbAFMniz9YV2iROt990kEhHt+KqZ1uBkdC9at/yin9ckn7edsTitg77GqKvtiw41wccPPoyJfurrscxyVyRkIZx12nVb3mdp7b3kRCMj1cevIFa16Ld3kbhoeDFC0EkIIIaQEaCPJdSAB24jVMSw1lDVOtLqhuHV1Ev42f36m0+oLEEUdPSDsiEWJVnXnopg1S4TbBRdIg3TwYNtPLs5pzSVaowSPHx4dhTZ2Vfhr2bWPYFOTZCDWOvbdKt95jMJtlA4eLOJywQIRu+65qNO6aZMkS9puOzvsiFtWIFME3n13+BjZ8MusZVixQsTCzTeLa6jjAavYihKt2qjeaqvwubhOa3W1DTHV8rrl1O3issrq+q2t4Wu6114y1QyyDQ3itlZXyz3thnvrcm30DxkiIZZHH22HE8nF3nvLywnFFRTqytbUZDqtmuHVdcf9c9cw7aTos+26wVpPceHB7r07fHi8Y+j/zuh5RInWqJdFSk1NuB+8T5RorauzolS54Qbg8cfl9+L114ErrsjcPsppPfxw6xgnFa2A3IeVlWF31RWZfr01N4fFY5xodXF/i/2y6W/n8uWZolV/q7W8brI712l1M3r3ddGaoDcIIYQQQsqBONH68Y9Lg/T55+W7uptJnFa/z6ceR0VrlHMxfrzt5zV2rAil006TBpIxYWGSTbQq118v08GDRXRu2CDhwr7TqiHE2UTr4MHAE0+IIL7wwnjXzkcbhRoqCojb9cAD4p40NUnDXPuc+Q3MtKK1oUEayyq+okQrIHV6xRVhUeJeE9cJHzQoHM6ZK3GP77RqGZYvlzBqzdAcBNJftrlZhg9qbMx0+/VYW24Z3q8rWrfeOlpc6f2p9RNXl7qf1tbw8fWcNUmOe82zZewF5F4aPNiGVCfBXzeq/6mK1tZWWzfqwO24I/DUU/I5SrSmQc9Fnxt3H3548Pjx4hDrNlVV4WfVx3929N7X80kqWnPhX6O4Z3b8eJvMac89M7evqopPIOau4+NeP/clEBBOMAaERavvtI4cGc7Wm0S0uvgva7QefKfVrXd9hnzHVq/R3LlyfkHQ90UrnVZCCCGkjFmxQhr6jz5qG0lHHx1ep75e3CYNc0wTHuyjQyU0Nooj4wqfU0+1iUh23932Z9UG1aJFso0bZumKlDvusAJVcUN3GxqkQdbYKP3CXNHqNmRzidaJE21W3VtuiT9XF/c8tb72318aeosWiduSTQDHuYMuboPZd0Hdc6mpkRDL88+Xcp1ySnxZ3e0GDQrXvd8H0CdOtK5bF75njJEQdJ2XLTzYd1prauy5+qHmvmjVBD1xolXL64rWQYNEYANWtOYS627dxw0Dk4aoenadVi3P0UcD11wTHqrE789biGhV/H1pvZ13noyzq/dhZWXmCzAX/x5V0aq/M3F9ldOSa7ifXGRLdOWvk0u0+qH92USr/zvqClYgPms6IHXpP39+2eJEq3ue+rIgTrTOmSMvMaurmYiJEEIIIT3Iq6/K9KabbONp0qRw4qKBA8Pib6edxKlTB0obttrojMseDEiDMQikEeSL1jPOCGexVbTR+cEH0X09dZuPf9wO56IceKBtnGl4sOI2qN1y5BKtgJQ9CMJjmmbDbRQ++KDUkY4HetllMs0mWvMJD3bxnVYA+NWvRCD6dR7XONftFi60Tl424kQrEJ2IyS2zf75afyNHhsXSgAHxolUb3HosdYLi6lJdtv32sw71mDF2v0lFq/s8RGVJzoe//lX6ICs1NSJimpvDWZEvvTR8H2lZCxWt7v2r11X3pWKoqkrO1/3ui1bXMfXvd30hotEIxRL/vtubVrT6ia6yrRMlWt2XDlGi1e3HumyZPMcDBoTFrIZ+J6WhIbPO4kTrunXhc3Ovi/7euhmJ3T6tixZZ0UqnlRBCCCE9hg4w777x9zOyGhNO3DJ8uCQ+0aRBuq5Oo0Tr7bdLEqTjjpPvixZlhgfHiQltUMWJ1l/9SqbbbZfZMBsxAjjmGPnc3h5ukOXjtLphg2nws9/W19vsvzr8it+YfuMN6XMK5Bce7OK7k1Gfo8rqoq72ttuGE+jEEdenNap8QPj8fadVr2tDg92Pihw3PNjFd1q1UR3nWmtG5csus07r1lvLfVpdbZNm5QoJ1+NtvXWy5EtJOPnk8AsZV7RmE9F6zQoVre5z5e6rpiYc7eCuW1WVeU+7Qzv518Ef51Vfgrn9e/PhhhskWZaSNKRf0d+fbPWcTbS6+KK1tjaczGjpUjmO9rFXso0PHMXgwfbaaR/nuPBgLYfinmecaPV/zyhaCSGEENKjqHvT3h4WrT5HHGE/++GK2jDdd19pwGpj69lnrdg98EAZo3TffeW7Zu9NIlq1kdzZGS1ajztOnIihQ6OFy403AueeK0mZ4vrJueVQMes38KdMsa5oWtz9a3j12LHAOefY+X5jeo897IuBJKI1aXhwrn3lchKTEpc9GIh2zlwh65dRk9XU19v96H04aBDwzW/aFyKKnzBMEyq5ib58dt5ZhGZdndw72k929GhJJgYkd1rdhEjFpqZGXg51duYehkXXB/IXre4Yrq7THXUvuaLVv6f98YhdLrxQ+lefdZZ815c6P/pRujL7jBwpw1ApucLaffzszNnWySVafee5ri5TtNbW2m4Uih8KHCdElQED7DXT8PY4pxWId1o1UsB9EVldHX4G+ovTykRMhBBCSBnz9tsynTbNJvbQRunTT0sfNUAaPKeeGp1QZsQIGfZh332lUaoNnAkTJOTyxRdt6KU/hqTbWMrltAK5wy0nTJDMnzosyYgRss1vf2uPqbjhpG622CindfDg8LAwaXHPQcWyMcBvfgP87nfyPcoB8pPdZMNtlGZzWkslWgtxWrUBX19v96Piwxjg97/P3N9RR4nD//GPy/dJk8ThTyom7747HCasUQlJndZsSYgKpabG9tFNcr0GDJA6LaZoPf30zOFngOyiNdvzO2gQ8JOf2O/bby/nWCy3Ol+K6bT6rnRdnXXwAXn5pvt6+ml5qThhQrhPKWCvwfjx9jcakGvc1ib1pkMNabK6bKLVffb0PKuro4W6Gx4MiGgdOLDvi1Y6rYQQQkgZ8957Ml2zxgpYFQOHHSYOpXLXXeEhF1wOP1zcs6oqKzBqaoCzzwauu84KJbfhp0NPKHGugdvQzpbYRdlzTzvmou/MxolWNwTRF6333BMe2iEf3PN0G+HuOUeJIe3flyQRk+uu5ErElLSsgLyQUNGfhmyiNUq8VFfbhrV/vtqnb8iQTNEax6BBMpaqKxTSuJ+TJsl4tkD4XsklEvU6FiMJUxxu3SZxWoH0w90A2UXrfvvZDNAu2URrZUo7q9SCFUjXpzXt+dXVSb9yf159vbwk2XlnEaC+aNU63mknO9YyYH/vOjvtb7UO7eNncY+K/gDsNRswQP78844SrUEgY+Q+9ljW0y1r6LQSQgghZUy2pEk+xmQ6BT7u2/zqaglv1RBXIPPtvtv4TuK0JhUCKpx90eoe33XC3HL7onXbbQsXIEmERZRo1TrRUMlcDBwojVxftLpiP63Tevjh8peWbH1a/SFtlMGDZTgkf9uf/lSu0UknyViaQPowz0IYPdp+ziVa1XFK8oIlX/yxapNQW5tetOp974rHXPvIJlrLQYSmJYnTqsvcIa1c7rorLAz97fzjueHAkyfb7zvtBHz72xJBoNtr2DsgURxLl1oXHgC+/GVxW928BED4N88tm38udXXhsWTVsT/mGIm8GTvWCm+NRuiLULQSQgghZcymTSIU0ojXbLgNoSh30HdaXRGcq08rkFwIxIlWP8GUywUXAL/8pW1o63GTOlnZyFe0fuITwJ//bJNJ5cJNWOTvR0nrtOaLHufAA2WaRLQ2NIho9e+d4cNtv8SkTmsxUae1ujq3m6aZt3vLaY26XitXZt7fV10loicNeh+52WtziVZ3rGH/ntZrliRyoNh8+KH03U9Lkj6tej3ihn057bTs+/bnaf9pQJKDrV8vv10aCnz33TKtrw/fj9r1oKNDxO1NN8k6hx0WX3Yg2mnVoYeinFZAchS88op0C7nvPjmmm/ugr8HwYEIIIaRMCQJpxJ13HnDvvcXZpzZoqqujXdm4flS6TRT5OK06xqsfhpptuIvrrhN3wU3w404LIVtfNz2/uL6SX/1q8mE6tP6z1W0up7VYblhFBfDaazZ80a3HKNcJsNcrWxlVIORy/YuJitYkmWfPPhs49ljg+9/vufLkCg8eMSKcaAyQIaUOOijZ/rUfpIoqFTBA4U7runWZIbG9wVZb5ZccK4nTqs9dWlEc1T3CvZ4DBkiW6LVrw79lWsd1deHnVV/SdXRIArqkQ+W4CbJ8p9V/yaXlHDAAOOAAOf5nPtO3BStA0UoIIYSULdrAqq+XsMvXX5eMv4Wgjak40eE7rS5x7kuurLNRPPYY8O9/Z+4zm/gzJuzeFdNpVTQzqos6kcVwOPV8oxId/exn8ct6ir33ttfMvY5xwlhDybO5qKVwWjU8OMk1GjkSePjh6EzXxcKty7TjjibhxRflZYPWtStaczn12UTrgAFy//VEmXuKJKJVz7kQ0arjNtfVyUvEyy6TyJKWFuu0+sfzRasK27gw5TiinFYVvJr3IK6/eX+BopUQQggpUzSUTRshe+4JHHJIYfvMJVqzOa1xjSHXUUsqWocNs2Iw7vi5KKbTCkgj8NZbM+c/+KAMp1MMkRPntALAxReL+EiSiRiQBCvFJJfYAYBPf1qmM2fGr+OP09obpHFaewO3LrMNI5MvY8YAn/+8PY4rgja3Pq1JwoP1uYsLD861bwDYYQd7nJNOAq6+Wup640YRre7LJu2zWl+fKVq1r2kaovq0+qiT2l9FK/u0EkIIIWWKL1qLgTZY4wRKNqc1Sbhnof0Ea2okpO0738m97rHHSihjTzpmgJxTIcPpuFRVhbPw+iQNqZ0/v/iObBJnVF+aZHPiVDSVIjy4WP19C8V9vuJCrYuBvuAoVnhwkhcX5UZvO63uPmprrWh1w731t9t3WisrgUceSVcGQKIDFP+affObwBtv2ONTtBJCCCGkV+lJ0Rrn5lVW2oHo8wkRLDQjqzHASy8lW3f77SV5TV9i4MDiiE3t01hsPvtZ4ItfjF8+ciTwzDN2qJko3D51vcWQIXLflqPT2pNl0iQ/xRCt3/kOcMUVRS1er5BkyBs957ROq7tPdVrXrrXzBg2y4cEf/aid74pWNxFTvk62+3vti3MdA/nrX5dprrFo+yoUrYQQQkiZog2fpOGiScglWgFpFOUrWnsyI2t/YODA8u4v+NRTudc59NDsy7WvXW+KVmPEbS1Hp7Un0Touhmi94Ybilq23GD0auOgi4Oij49fJNxGT+4JJM2qvWWPnuU6ru64Oq1RfH34O0j4Txx8vXRNc4l6CqCBOmtypr0HRSgghhJQp2vApptOq+8rWqK6vl2FNKFqLT1VV7yZaKgXjxonrkyTEu5hce23Ph4onpVj9rHOhQsV18woJD+6LGAP8/OfZ15kwQaYTJ6bb98SJknCposKG6PovCNRpdZ9r12l1w+TTOq2TJ2fOi3sxo/tOm+Spr0DRSgghhJQppQgPBmw/LBW2t98OTJ+ebv8kmvr68nEDe4qKCuAPf+j94550Uu8fM47eclp33BG48ELJeq3hq0nHaa2s7D1xXWp22AFobASGDk23XX29JFwCRKxeeqkMTaTU1soLvubmaNEaNw5uIcS9aIhy3fsTFK2EEEJImVIq0VpfLy6rOgRnnil/pHB+85tSl4D0BipaixnaH4UxMn5x1LHjcJ3W3gzhLjX+mNBpGTAAuOaa8LxBg4AVK+SzG5miUTL+C6piZGeO+39Ap5UQQgghJaEU2YMBaWiVc7/Lvky2BEak/6DPWSnC5dOIVlIYtbXA8uXyOS482KVYQwrdckvmkGEUrYQQQggpCT0pWt3hGXwaGtI3tp99VsLkCCFWwJx7bu8fO5d7StFaPAYNsuG4vRUeDADnnJM5j+HBhBBCCCkJPSFalyyR6QEHxK/z059KYpE06PidhBB56dPUlH0YllLhi9ZvfhPYbrvSlacv417fqOzBPeW0RjFxIvDrX2c6sP0FilZCCCGkTOkJ0TpjhkyzNWz22KN4xyNkc6VcE275olXH+STpcRNZuaJVh53pTdF6+OFAa2vP96MuFZtR92tCCCGkb6Fv64vZCBkyRKbsW0lI/2LcuGTrMTy4eMQ5raedJlN94ahJ7Xo68VV/FawARSshhBBStvSE0/rqq8Azz/TsG39CSO8zc6bNZJsNHfKGorVwXKfVTV53xx3Ahg32u4pW/u7mD8ODCSGEkDKlJ0TrDjvY8RwJIf2H+vr4MTxd6LQWD9dpHT3afq6oiL4WFK35Q6eVEEL6Oe3ttn8N6Vv0hGglhGzeULQWD9dpzfY73Vvhwf0ZVh0hhPRj2trk7e8DD5S6JCQfKFoJIcWGorV4qNM6YkSy9em05g9FKyGE9GOam4HGRmDhwlKXhOQDRSshpNhQtBYPdVrd0OAo6LQWDquOEEL6MR0d4SnpO7S0APPny2eKVkJIsaBoLT6jRmVfzkRMhcNETIQQ0o9pb5cpRWvf4/OfB557Tj5TtBJCisWwYcBhhwH77FPqkvR9Wlpkuv32ydanaM0filZCCOnH0Gntu6hgBeiIEEKKR1UV8PTTpS5F/+C444Af/Qi48MLs6zE8uHAoWgkhpB9D0do/0AYPIYSQ8qGqCrjyyuTr02nNH+p9Qgjpx6hY7ewsbTlIetzx/wghhPRd2Ke1cChaCSGkH0Onte8yeHCpS0AIIaQYMDy4cFh1hBDSj6Fo7bs0NJS6BIQQQooJndb8oWglhJB+DLMH913otBJCSP+A4cGFQ9FKCCH9GDqtfRc6rYQQ0j9geHDhsOoIIaQfQ9Had6muLnUJCCGEFBM6rflD0UoIIf0Yita+i4Z2E0II6R9QtOYPRSshhPRjKFr7LhSthBDSP2B4cOGw6gghpB/DREx9F4pWQgjpHzARU+FQtBJCSD9GxWpnZ2nLQdLT1gbsvjuwcGGpS0IIIaQQ6LQWDquOEEL6MQwP7ru0twPjxwPbblvqkhBCCCkGdFrzpyDRaow5wRgzyxjTZYzZ25k/zhiz0Rjzn+6/3zvL9jLGzDTGzDHG3GiMvnsghBBSbCha+y7t7UBVValLQQghpFhQtOZPoU7rWwCOB/B8xLK5QRDs0f13tjP/dwDOArBD99+RBZaBEEJIDP1FtM6ZA/z2t6UuRe9C0UoIIf0DhgcXTkFVFwTBO0EQvJd0fWPMaAANQRC8HARBAOBPAI4tpAyEEELi6S+i9YADgPPO27ySE1G0EkJI/4CJmAqnJ/X+R40xbxhjnjPGfKp73tYAFjvrLO6eF4kx5ixjzHRjzPSVK1f2YFEJIaR/0l+yBzc2lroEvQ9FKyGE9C8oWvMnp2g1xkw1xrwV8XdMls2WAdg2CII9AZwP4B5jTAOAqP6rQdxOgiC4LQiCvYMg2HvkyJG5ikoI6SMcdxxw9dWlLsXmQX9xWoPu/xRdXaUtR29C0UoIIf0DhgcXTmWuFYIg+GzanQZBsAnApu7PM4wxcwHsCHFWt3FW3QbA0rT7J4T0bd54Axg4sNSl2DzoL6JVoWglhBDSV6HTmj89oveNMSONMRXdn8dDEi7NC4JgGYANxpj9u7MGnwLg0Z4oAyGkfGlr27z6JpYSita+C0UrIYT0D9intXAKHfLmOGPMYgAHAPi7Meaf3YsOBvBfY8ybAB4CcHYQBKu7l50D4A4AcwDMBTClkDIQQvoeFK29h4rVzs7SlqNYbE6ita2NEQmEENIfYHhw4eQMD85GEAQPA3g4Yv5kAJNjtpkOYNdCjksI6du0t1O09hZ0WvsmQSDXjE4rIYT0H+i05g/1PiGk12lrkz/S8/SX7MHK5iJa9XpRtBJCSP+BojV/KFoJIb0Ow4N7DzqtfRN9PihaCSGk78Pw4MJh1RFCepXOThEeFK29Q38TrUHsIGn9C4pWQgjpP6hoNVGDf5JEULQSQnoVbYxTtPYO/U209gWn9Q9/kIZJc3P++6BoJYSQ/gPFauFQtBKSgiAA7roLaGwsdUn6LhStvQtFa+9z9dUyXb48/31QtBJCCCEWilZCUvD888DXvw5cfHGpS9J30QRMFK3JCALggw/y356itffREOZC+i5RtBJCSP9hjz1kymHM8oeilZAUvPaaTPmjkz8Uren4y1+AsWOBF17Ib3tmD+59tIyFhIPpc8LfGkII6fs89BDw3HPAkCGlLknfhaKVkBTMnCnTsWNLW46+RmcncMEFwMKFVkRxyJtkTJsm0zffzG97FaudncUpT6npC6KVTishhBCXjONnAwAAIABJREFUhgbg4INLXYq+DUUrISlQ0dpfXKve4t//Bn71K+Ccc+i0pqWyUqb53nMMD+59tIyFZDqmaCWEEEIsFK2EpED7FtIlTIcmpKmtpWhNi4rWfOuLorX30TIWUlaKVkIIIcRC0UpICjTEkqI1HatWyXTECGYPTouKFjqtQl8SrYWEZFO0EkIIIRaKVkJSoI1RitZ0uKKVTms6Cg0P1noOgr4h+HLRF85Bw4LptBJCCCHFgaKVlCX/+U95CkN1TjZtKm05+horV8p08GCK1rSoaCk0PNj/3FfpC6KVTishhBBSXChaSdmxYAGw557A+eeXuiSZMDw4P9Rp7ewMD8FSSKKazYViJWIqZB/lRF+4Z+i0EkIIIcWFopWUHStWyPTVV0tbjigoWvNDRWtHR7ju6Lbmplh9WgvZRznhC8GHHwb+9a/iHmPlSmDRovy3L4bTynFaCSGEEAtFKyk7tKFXUVHackRB0Zof+iKiP4nWefOA/fYDVq/u2ePQaQ3ji9bjjwc+85niHmPLLYFtt81/ezqthBBCSHGhaCVlhwrDAWV2d7qJbChac9PVBcyfL591yJuOjrBQ7cui9dprJRpg8uTi7/uJJ4BvfCM8rxh9Wgtx/soF9mklhBBCNj/KTBYQUr5Oq9tYpmjNzS9+AYwfD8yaBWzcKPP6k9OqYrBY9+mjjwLPPCOfJ00C7rhDPuvzUGj24EL2UU70JdFKp5UQQggpDhStpOzoTdG6di3w3e8Cra2513UboMwenJvnn5fpggVWqPZH0arhu4Vy7LHAYYdlHqPQcVb7e3hwOVIMp7XY9xchhBDSl6FoJWVHb4rWH/0IuPFG4M9/zr2u2wCl05obY2Ta1WVFfn8KD1ZRUQwnLC4j7saN9jgc8kYoN9E6eTLQ1BSeV4w+rbptuUWcEEIIIaWAopWUHb0pWpubZZqk/yxFazq0TtvbbSPed1o1QVNfpJjhwevXR89vabH3HUWrUE6i9c03gS99CTj7bODOO4Ef/1jmF8NpLde+/YQQQkgp4L9DkpoVK4DHHuu5/auo6Q3RmmZYib4oWufNyy+Uub0dmDu3sGNrY1v7swKZonXffYEpUwo7TqlQAVgMUbFkSfi7hoS6Tmu+IekUrdFs2AAcfrhNFpYP6rDOmweccQZw1VXyvRhOa7n27SeEEEJKAUUrSc1dd0n/uyT9QPNBG+cUrYWxYQOw3XaZWWiTcP75wPbbAx9+mP/xVcy594kfHgwAL7+c/zGKRWsrcPvt6URdoQ6oiy9a9X5sabFlyvd56+iwodr9RbS+9Vb4ZUg+vP8+MHUqMGNG/vvQe9wXp8VwWnUfdFoJIYQQilaSBy0t4iT0VDKizdlpveYaoKGhOPvS0Od//jP9tk8/LdNCxiDVxrZ7n/hOKwDU1OR/jGJx333AWWdJ/efis58FDj7YitVi3Au+aK2ulqkrWjduBO69F5g+Pd2+29ttHfcH0bpqFbDbbsCZZxa2Hzc5WL5EidaOjuJkD6bTSgghhFgoWklqVIT0lGjV/faGw5CvaO2pc7/8cnFIi4GGKKrLVsg+8iHOafVF3qBB0dtv2BAvCJ94IpnATMrgwTK99dbc6z79NPDCC1bs9KRo3bjR3nf/+hdw8snAueem23d/E636IqVQh15fOhRbtK5ebZ+bYjitFK2EEEIIRSvJA22k9yenNcmxyn2c1nHjJBuyUkh4oQrdQkSr7sPv0+qH08aJ1oYGYOLE6GWTJonALxZ6nsuWJRcaPRUe3NkZ7bQqo0al23dzMzBkiN13X0d/d5K8aMpGT4nWVavs52I4rQwPJoQQQihaSR70tGjtjT6tixaFxw9N0rh0w/XKUbQuXAhcfbX9XojTWog7qyR1WrMNGfOvfxVejiS4wiWpCC2m06qh3Po5qk+rkvZFQlOTFa39wWnV+0mFfb70VHhwY6P9TKeVEEIIKQ4UrSQ1/cFp3XZb4KMftcdK0rjUdQYN6nnRWojD6e+jENFajPDgXH1ay0FIudc/qdAopmh199HSEnZa/fKkOV5npzjd/VG0Fjo+bhKnNalT2tVly+OKVjqthBBCSHHgv0OSGm0095RwK0X24FxC5Sc/kfBbYPMSrfk0uru6gAMPBB5/XL7nyh7c03X5xhthJzMK9/onFXa6XjHCg906aG62ovWyy4Annwyvm+ZlUUuLTPuTaNVwcz88OO0zk8RpzXVt3YRLW2whn+m0EkIIIcWHopWkpqcTMfVm6G3S8OArr7SfBw3quXNX0jZ2o9bXeYWE+ubT6H71VeCll2xCqVzhwVHCIKlYzlW+RYuAT3wC+MEPku8nqbArZvZgX7SqIFu4UP7i1s2FjiOqgqqvilb3flAh7ocHpz23JE5rrn3qfRMnWum0EkIIIcWB/w5JanqrT2tvJI1JEx6sDBok6/dk+dLuO+paFCJaCxnX85FHwt/9REy+6IoSYUndy1z34IsvynTZsuzrueeZre7d9fS8ejI82Gfo0M1TtLrlVtfcd1rTXoe0ovW004BLLw0vd51WzdDsJmIq5DeCQ94QQgghFopWkprNXbRq47QYYaFxpHVoykm0Pvdc+LuKjJoaGx7slilKbCQVILnWe+01me6xR/b1kjqtrgBXx68Q0frWW1IX7vAtzc3x/TW32y7dc6d139fDg93r44rWQjJ6x4UHu2HG7rI33gD++9/ocnV12c/FcloLyf5NCCGE9Df475Ckpqf7tBYjq2faY6URrbW14W17grSCPaosxQgPzucaqJhTVGTU1sr+Nm0C6urs8jSidfbs8PnkEnCvvirTXJlmk4pWt2+snmchLy/+9jeZbthghWVzc7zYGTs2P6e1t0Xr974HjB9fvP3FOa35ZH321/frxN2Pu6yjI3Nd12nVZVrnQOFOKwUrIYQQIvBfIklNbzmtvSla0zgiOq5oOYnWqGuh55SPaNXGchohEARyTH8bX7Ru2AAMG2aXpwkPnjIl/D3XPbhggUxzXd+k4cGuIC9GeLB7bVRYRmUM/vjH5Rzq6tI9d6UKD77hBmD+/PTb/f73wIMPZs53y63XYODAcD0Vy2mNE61RXQJcp1XXdd34Qp1WhgYTQgghAkUrSU1vJWIq1/Dg3hCtaRu7xXZa8wkPfvxxYMQIYO3a8HxftK5fDwwfbpdHCdS4uh08ONl6/nL/+rpumL882zkXW7S6TtrQoTJtbs4sb2WlXJOBAwtzWnvjmSqEc84BvvzlzPlx4cGFiNa0TmtnZzKn1RWtdFoJIYSQ4sB/iSQ1/dFpzUe0trYWZ2iaKEqdiElJcw3mzgXWrAknogGsyKirs06riiggd3iwK+B90ZrrHtTluo+2NumbOHgwcO+9dr18woOVbG50Zycwc2b8cleUuOHBUaIVkDDn/tqnNduzFOW0VlfnJ1qfeQa49db8woOTOK3uiw06rYQQQkhxoGglqSlVn9aWFuDZZ3vmWPmI1n33tZ+T8vDDwE035V4v30RMrkAtxOXJx2nVuvRFnDbiXad1662Bj3wkvJ2Luw/XuXL7wgLpRevxx8sQOADw1FN2vXycViXbc/D44xLau3Rp9PKkolXFS6FOazmL1jVrwt9Xr7aCX8f8BawQr6jIT7Qedhhw9tn5hQfTaSWEEEJKA/8lktSUKnvwN74BfPrT+fWVi0PdnXz6tDY2pq+D448HvvOd3Ovlm4hJHTl3H73ltMaJhqjw4GHDgA8+iE8s5I9bqvjnkq3+g8COEavX9/337XJNqAUk79Ma5bRmE0uNjVIOX5AprihpaJDzi+rT6jqtfWnImzSRCEuWhL+fcgqw++7AK68AZ51l5+s1CIJwPSXpfx21frn2ae3spNNKCCGEKBStJDU9LVrjHJC33pLpunXFP2Y+TmtPkm94cLFEq26TJhFT3P2gwqm2Vva3YYMINECcw6hjuPNcoejXSzYBFxVivH69nee6tlFOa2Mj8Je/hPcZ5bRmq6Ncz4p7baqrbfhvnGhVpzWpGGxqkmPU18v3nhat7e3AH/4Q/p4UX7QuXy7Thx4Kz9dr4IvIJGJef0Pc9Ts65B6LygadJnuwlsW9RwpxWru66LQSQgghCv8lktT0dCKmOKdVXYdC3Iuo/cbNi0MT5vQk+SZiKrZoLYbTqvuorZUXDkEQFq1pnFb/Ovn34PXXAy+8IJ+jHC/3hYfrtEaJ1hNOAL72NWDhQrssbXhwrlB6V5QMHGid1M5O4JhjxJkH7L2vQ/ckFYPNzSJYddzXnhat99wDnHmm/Z7GFVbRqkm69tlHpo89Fl5P7wc/XDfJsdzxcF2ndehQYMcdw/N1mZLUaXWTfNFpJYQQQooDRStJTamcVm3gF5oBNarBn6ZxOWZMYcf3ueAC4JprwvPydVpVnLj7KLVoVWprbZisJlSqqsotWrM5V/49+IMfAAcfLJ81NBiwQ/G4QjZOtOrnuXPttkra8OC4Z+XHPwZ22UVcZ2XgQPlTp7WiwopU12mN2l8cTU0iWnX73hCtLvmI1pEjZar1rsMWKXoNXXcz6bG0j2xDg/0daGqSz3r8NKI1qk+re00LdVopWgkhhBChMvcqhITp6URMcdmDi+W0ZhseJgmjRxd2fJ9nnrEN9XzKA/RceHCxRGtlpRVcQG6ntRjhwa5o7ewMiwkAqKmxn/0wUHffbp0WKzz4z38WMXbZZXae77RWVNg680Vr0mevN0Xr8uXA1KnheWlebGmyKv/lVNy5FhIe3Nlp13/ppfA6acKDo5xWd/tCnVaGBxNCCCEC/yWS1OTrtH7728BBByXfvy9QiuW0FipaR4wo7Pg+2frKJaU3w4Pb24Gf/ARYvDi6DFEMHBguW64+rXHhwX69ZLsHfafV7c/q7ysqPFjL5S4rVnjwhAkydfumJnFa9XtS0bp+fe+J1gceyLw+aV5s+X1Kc5XVF625QqaDAJg1y26r62tiN31xlI/T2tEh+3cjHXSbfKHTSgghhFjotJLU5Ctab7452Xq5nNZSi9bKIj812RycpBTbaXXL5nPrrcCVV4rI+MUv7Pw0olXDgwt1WtOIVj+Bl3uMqPDgqDB1X/jW1OQXHhwlsLI5re6QN1H7i2PdOhnupljPTjbuv1+uq+topxGt/pBJucqaNjx4+XJJrlVXJ+v662tiLnd+riFv/Htl8GAZqsctY77QaSWEEEIs/JdIUtHZaRtivd2ntSdFa5rGZS73o7MTuPzycOM1Gx0dmSKm1EPeZMsefMcdMh02LDw/2/2QzWktJBFT0vDgKKc1KiTY/Rzl+L36angftbX5idaolwFVVZlOqx8enNZpXbtWROuAAfLXk07r4sXST9clH9GqZcz1DKQND54xQ6Z77hn9zOn9ki08OM5pdUWrX8Z8odNKCCGEWChaSSrcxncx+7SuXi3JiLq64sODy6VPay734/HH5Vy+971k+ytGeHBv9mnVbLp+UqJ8nNYkiZjcey6b0+oPA5NGtEaFB/siqqkJmDYtPORRXV2yPq3+OaZ1WvNNxLRunR2jtaKiZ0VrZ2e4nzCQ7DeivV2iMPR+yjc8ONuxmpuBJ56Qa3fggXKv+OtrnUaJ1iAI91t1y6DLgUzRSqeVEEIIKQ78l0hSEScmCuXcc8WdfPpp2zDsqezBaUWrL4YqKrI3JtMOCVSM8ODe7NOq+/UTG2UTDdXV6fq0uvPc/eqxd9hBpm4d+wLBH/LGDw+OE61uch13vRdflM9HHGHX1VDTONKGB8c5rXq/5eu0AlL/5Shab7hB+rs/+aR8T+q0+iLyjDMykyopn/oUcMstwCc/acesde8PILvTqvdCnNOqFFu00mklhBBCBIpWkoqeEq0aShsEtmEYl4ipt51WX2BUVGTv16rlyyYWXSFcqGidMkWGzQF6LxETkE60pu3T6s6LEq0qcKKWKYU6rf73Dz+U6U472WVJw4MffRT429/s/LROq94vcU5rR0dm6LJmTFanNUq0Fvos+WVQUa1E/Ua88064HO+/H16etE9rVGKkhx+OXveNN2R62mlWCPqiddMmqWf32viub67nVF/GxC1PA8ODCSGEEAtFK0lFT4lW3W9VVXwDsVR9Wv3zrKgA7rwzflsVGNncWF8kFSImPv/5cNn8Y+QjWvUcokRr1HiUQHLRaowNsU0iWqPc1Opq2Y+7zO9/6A95k7ZPq/9d69MVZrW1ycKDp0wBjjrKzk/qtOqx9Lzjhry55BJgv/1sdlzAnm+c03rXXXIMPwt0viRxWufOBXbeOTzUz/Ll4XXyDQ8GgG23zVwvCOQ8L7oI+OpX7TPi3h+AdW6jnNa4F2k97bQyPJgQQggR+C+RpCLOAXMJAmDFinT71YZiZaVtGJZLeLC/fkUF8JWvAFdfHb1tEqc16fiPSXAbtlHDuLjlePllYNWq3PuMuwZBEC9akyZi0vBMIL5Pa67wYHUh40RrU1O00+rWVVqnVaeuaE0aHuyT1mn1BbO/Xw2LXbvWztNw6Din9bbbZKp9lAulszPc3xfIvCf03vvXv+w8/7ciTXiwv057uxxj5Uo7r6VF1tPEYXof+k6rljeNaPW/MxETIYQQ0jNQtJJUuI3QOJFyyy3AVltJGGBStKFoTHyjVRtwUQ7Mhg2y7YMP5j5WWtEa5bRmK4+6lIWI1jQOjTppQPg8osTzJz8JHHJI7n3qfrJlNU7jtNbUWLHgNuzzDQ9WFzIuPHjDBitaBw2yfVq32EL6TwKZolXL598L2URr0vBgn7R9Wn2n1b8nVYC5olEFbJzTqtfPF1r50tmZGR78hS8AP/iB/a517J6/L1rb28PdBLIdz1+nqUnGW91ySzvPr4e48GBA7hlX8PrXPtdzSqeVEEII6Rn4L5GkIkl4sPY3fO+96OVRDTk3JDCX0xrV4F+yRKZu2KFbTjcJTzHCg4F4kVMM0ZrGoXFFazanVZe9/XbufcY10qNEj+LWq+8QDRsWL1qzJWLyRaEvWuOcVle01tbKuTc1ict7443A8OGZolVDW9OEB2v2YD9Zl38efvmL7bS2tMi0qsrOy+W06vVLM+7wm28CBx0ELF2auSwqPBiQREuKOxbrPfcA118fHZUR5aJqn2L3eLrOnnvKtKkpc19+PcSFBwPAAw8A559vvxfDaV2zBnjqKbnn/BD1bNBpJYQQQiwUrSQx8+bZBqYfmumSK2FSNpHiNiTj+rRGOa3aWHbDI5UDDggLu2xO6+TJmY1of309P23sxzmt2VySKNEaJTiTkFS0xvUR7OqSRvVvfgOcd15423xFqx8mmk20xjmt2vc1qWiNc1pVtG7caMvlCzg3iVCa8ODa2uyuoH9uKqCK7bSqaHXLEeW0ustVQKVN+vXii5Lt2ycqERMgdaSou9nRAfz+98Ctt2beR4DUj38dfEHsCtsbbwRGjIgWrVH14JbF5YUXMs8JiH8ekjitw4YBn/ucJJuLe5EXBZ1WQgghxMJ/iSQx220njS9AGmdxojVXwqSkojUue3DU9rquL1rb223mUCVOtK5cCXzpS8CJJ4aXpQ0PzrdPqzuvGOHBvmiNSxj0i1/Idf3+94Hf/ja8rX9u7j7SiNbhw6NFa7ZxWl0Rp2i9qKBzt/UF9caNcu41NbJda2u8aO3szHQ1/f3qfFc8qSCLCwP252uW7KhrUVVlhbifiCmp0+qWPcphjHrpkOZe0+y4jz4q07feCtdPVVWm0Kqrs59VKLa3A3PmAMuWRR+nvT18LhUVYRdZj6fHrqgQF90fOxiId1qjRKuf/bexETj9dOssd3WFXfVc2YP96+wvzwaHvCGEEEIsFK0kL7bYIjq8DshPtGojXPcZNTxHNqc1Luzyuefij+VvryHGOo1bP2l4cBKntasrOmtpGvfLdbKyOa1xonXGjPjyxbmO9fXFc1rjEuqoaI1yWgcMyO60rl8v91JNjVwvdVpVcEaJVtdp9Yckcqd+eLCWNwr/3lmzJn5993x7ymmNSj6V5l5zjzt7NrDbbsCll0p9aTirLy6jnNa1a0WwRrmsQLibACDn7T9P7n2jotV3Wv/4R5tdO5to1eRgen2UqVOBu+8GTj7ZzovqN66MHCl9xk8+WY7jX/80dd3VRaeVEEIIUfgvkeTF4MG5RWsh4cHV1dLAc8VDEqfVx+2/qdv521dVSVkXLZLvrnMJ5O7TWojT6jqacdlscxEndpOKVr+h7pfLRb8PGyYN8rg+zn4o57Bh9vr5ojWqbG1tcl3iRGuuPq1f/KIM5VJTI8ft7Ix2Wo8+GjjiCPns9mmN2m820VoMp1X7tLa22mFa9B7LNeSNG3arqGhVdy/qRZC77yS4z7wOlfPaa2EH3O8jGyVao+453R7IDA+urs4UcG6f1spKuRa+aL3kEvvZT8Tk/raooPW7Bmh9v/tu+LhRnwG5h559FvjrX6Xe/euUaxgfFzqthBBCiIWileTF0KG5+7QWEh6sAsJtUCdxWn3UgQJs6KDfkKytle1VtGoDVsk3e3ASp9WdJgkPnjkzM+mPez75OK1R/YC1LP42+n3oUJm6TplbjijRqvUfJVr9a6LhwXEZgnOJVgCYNi230/r445I4zHVaOzvDLpzvSPp9WqPK756Hiyta/TpSp1XruKIi81nSY8c9e+5zsGKFXCd1PuNEaz5Oa2WlPbeBA8Nhur7TGhUeHIeum8RpdUVrXHjwdtvZz25CKh8V9r5ojXoxl81pdfddDKeVopUQQggRChKtxphfGGPeNcb81xjzsDFmiLPsEmPMHGPMe8aYI5z5R3bPm2OMubiQ45PSMXRovNNaSCImbdRGJcWJclqfekqSBxUiWgcNCotWP7Q1V3hwIU5rnGiNOp8pU4Dddwf+/Of48mVzWuNcnnyc1lyiNapPa9QQK3Hhru3t2Z3WAQNE9EX1gb72WpnOn2+d1jR9Wjs6wuLKvUbGhEVZnGi99FLgoouiRauOdeuOV6t14QriiorMUHs9dtwLCPf6L18uQ08pxXBa3evkilbX8SxEtGp9ap9W/V5dnfk8+eHBUU6rK1r12kcJQVe0jhtnk1RFlTfbc+rue8CAzPs6jWhlIiZCCCHEUui/xKcA7BoEwe4AZgO4BACMMTsDOAnALgCOBHCLMabCGFMB4LcAJgLYGcD/616X9DGGDMlMlqIUIxGTn4DG3a/baHzySclAGud+uKJVP/tCoqYmLFr9hm9PDnmTRrTOmSPTV16R6caNkjjq/fclxPXMM7NnIE7jtKYVrUGQ22mNEq1xiYXiEjG5IZO+aNWyfeQj4XKoaM3Vp9UND3bvGzeUu7Iy7Ka5IsvlZz8DrrtOro3L6tXhfsEulZVWOANhp1WvaxrRumJFeLxS95yzJRPKhl6Lrq5o0RoVHpyP06rhwfo9qdPqP7tuqL8+j9lEa2OjbKPXJs5pXbAA+Mc/6LQSQgghvUVBojUIgieDINCm3zQA23R/PgbAfUEQbAqCYD6AOQD27f6bEwTBvCAI2gDc170u6WOoaIkKUyxGn9aoMTNdp3XECMl0qxlE3cahZgtdty7ciI1zWjV8VEVrtgRDbjlyhQenEa2uCNDvPuoUqaB64gk7RE91tZQnnz6t2cKD47IHjx4t0+XLo9eLSsSk1yJKtPriICoR06JFwKpVtv7jnNaGBitCxo5N5rR2dFhBmM1p9UVZXHjzjjsiEle0+sOjBEFup1WFbFw4clKn1RXlaYSU1nc20ZokEVMcuq6GB+v3gQMzn6ck4cFR93y28GBAwoiNkX1GidaODuCww4CJEzPPx9131HWi00oIIYTkRzH/JX4dwJTuz1sDWOQsW9w9L25+JMaYs4wx040x01euXFnEopJCUdEa1ajLp0+rnz04W3jwqlXiiHzve/YYbuNx1SoR0+PGiQurxIlWTdSjiWU0NFDx3Ztc4cH59GkFwmG6UXWn+9NzdcXBwIFWfPv7yCVao46Vy2n92MdkOneuTKNCrl2GD5ekOMccI0OIKPpywn/5EZWI6ZhjgNtuy+20VlQAo0bJ5512indaoxxcHcs0m9Pqul9xojXu2m/aZK+D77QGQW6nFZB6yddpjRoaKt/wYP3s92lNkogJCPcd1/N2nVY/PNhHs27rcaPCg3X5lVfaeVHupVsWN3FVlMju7LRD4MyaFV5Gp5UQQgjpGXKKVmPMVGPMWxF/xzjrXAagA8BfdVbEroIs8yMJguC2IAj2DoJg75EjR+YqKulB/Iatht1FidZ8woNV6Pl9Wt19qPiaP1+mY8bY5a7IWLNGHC3fQYwLD1aHUpOw+E6rill3fSA+PDifPq0AsNde9nNU3WmDvKVFztGtew2fzMdpjSJuCCEt77bbigDUkGVfdPqitbZWhOQjj4QFQpzTGpWIqbFRprlEa2WlvZ8+9rF4p9V/SaCCq6MjvCyJ0xpXTz7u0EauaN11V3nJEue0ZhOt7mc9blubnIPrtLrjtGpCKCD/IW/0fszVp9XFvV4f/7j9PHy4TLM5rT5JndZttgF+9CM7L1t4sPu5sjLeaR0/Xj77Y0DHOa2nnGK3TQqdVkIIIcQSESgVJgiCz2Zbbow5FcAXAHwmCP6vp9RiAE7PMmwDoPvddOx8Usb4fUs1tLEYovXss+3nbE6r3l3z5sl0661tY/7/s3fv8XJV9f3/3/tcck4uEEhCIDFAggbkjhgEVEC/XBS1YKX61aKAFEWLUh5+aa1V0Wr9VqsPa6uWFr7g7aHWb1t/QuWm2Hqp/VoJCoKAXJRCIAgkkdxPcpL9+2Odj3vNmrUvM7PnzJxzXs/HI4+ZM5c9ey4nZ7/n81lrhZUxaxGWstBS1B68dWt2EB5WWh95xIV0C8EWAssmYmq10hrbhs/C9LZtrt3WV1RpDR/TF85EXLZ/9t7NmuUO3C20xsYJS27Nyve8Jz/A2+1ioTWstPqz6kougMbag4eGstfKQqvNCOyHVgvBdl+roo6PZ5W08LUIK60W0KoubbJrV/Y87HdV3h58AAAgAElEQVTo4IPdrNBSc6XVOhr8CYX8GYalxi9Z7DWwxpS8Ma3+WsTtLnkTC62x9mD/c+hXLo86Svr+9935BQvcuq3+GOFwTGsoXPJm3rzmz7Pf9m2qtAfb7fLGtO63n3Tvvc1faOVVWmNfwpVhyRsAADKdzh78cknvlnRWmqZebND1kl6fJMlIkiQrJK2U9GNJt0lamSTJiiRJZslN1nR9J/uAyeEfbM2enR82pNZmD07TxhbeotBq2/NDa6zSumtXY2hdtKjxNuGB48CA9MQT2Ta3bJF++EPp6qvdZY88Iq1Y0fw88sa02s+tVlp9RZXW2BhUq7TGQqtdFqu0hgE9vG/ecxselp7znPLQuny5myQqT1578ObNLoT4EzGFobWoPdjCwyGHuJ/Hxtzr4LcH+9XGsbHG9uBYaPWrsSavPTgvnPih1Sqt/nsWVloPP1y64Qbpyiuzy4eHGx8vFlptrHE4pvW//ku69lr3mS7b1xj/fbLHLZuIyX9+fmg9/nh3OjKShdNW24PD2YNDO3c2708rlda82YPzxuaGlVZ7vdoJrbQHAwCQ6bT56DOS9pD07SRJ7kiS5O8lKU3Tn0v6v5LukXSzpEvSNN01MWnTOyTdIuleSf934rboc/7B1uhoftiQWpuIKQxFRe3Btj0Lb4sXZ9f7bYFhaLXOcrtNbJkKC61W0frUp9yY2TR1EwAtX978PPLag+05hZVWvwrUSaU1XEtSKm4PjoVWu85/nfzHzts/vwX32c92Y1rDmYOl4uVFfHntwZs2ufDgV1r9UCploXXjRukLX8huNzTk1l99z3tcRWxgIHvv/UqrH9i3bGlsD3788cZWVTsNZw9upT143rzy0BpWWiXpFa9oHBcatgf74zjD0BpWWiXpD/6gMbS2O6bVHjcMj2WV1sMOk26/XXrRi9xle+yRfQ46aQ+OhdZYpbWVMa15473DIQSxbddRaaU9GAAAp7Q9uEiaps8puO4jkj4SufxGSTd28riYfO1UWqu0B4f3r1Jp9dllfmgN24Ot0mq3CbcThtbvf9+1V27d6loWH3kkXi3Maw+OVVq3bnVBOLxNK5XWstCa1x4cC63bt7uDfL9C7d8vr9Jq2xgacl8GbNvmgkxepbWo2uzfLvzyY9MmF2b8A397bH/24LEx6R//Ubr44qwaPjgoHXOM+2e3t/fer7T6tmxpbA9+4gk3bve++4onYmqlPXj+/MYxrdYeXFRpjQlDa6xF2j4jYaXV2ARa/n2q8B/LPo/+ck1hqJeaK61z5kjHHpvt47x52fMuWvLGZ9XdogqvbSe8PHY7/0sBvz04pii05o1ptf2n0goAQHv4HheVtBJaWxnTGoaVcMmbvPVX7boq7cFWafXbg8NwYNuxSuvTT7vT225zgeaAA5qfRyvtwX/+59J739t8m3bag2OveVGl1Sq8saATC607d2avte3ff/yHex1trOTwcPYajo01v4/2/uWNmTV5ldaNG7MKXN6YVnsMe11sgq4wbAwMZM/Tr7T6Nm9ubA9euzZb77WdJW9aqbT6r1Gs0hryq89SPLQWVVolV+m0x+90IiZ/veYqlVZ7DyyQWhu4f5lVWu22YXvwrFnNFd7Y67VzZ7VKq3/Zsce607zQOj5eLbRSaQUAoD78SUQlfmCcPTs/bEj1hNYqlVb/oLVoIqb5890++e3B/kGwf2AYhtbvfc+dLlumJmXtwT5/0h//Nu20B8fEKq12PgygUtaGHQut/nti79X73udek9tucz8PDTUGNjs4T5LGGWTLQmus0pqmWaW1aCImu2/42oahpEqlddu25vbgZz3LPZ+iiZhaaQ+2QGy3tYDWaaXVf+3scZ980v2e+jMU+8/5gQeylvfws3bHHdJ3vxt/7NiYVguYts/23v/937t1cvNC6+zZ7vX1K63+REx+aM2rtPot4+HrZW3uVca02vJChx8unXBC/DFN1dDqV1r9/8/StPz3wvafSisAAA6hFZV02h7sHxjHKn6f/7wbS9ZKaN21Kz57cFhpnTvX/fNDq+2/lB0YDg+7oCJlofU//sOdLl3a/DzL2oPznrN/m3YqrTGtjmmtGlpt/+wg3Z7z0FC80jp3rnsdqx5sx7782LbN7bOFVptEyQ70y0JrlUprbFkWCz47drhK69KljTPuxiZiqtIefOGF0urV2bbsfbCAVjamNVQUWv1K6+LFjdX+8HWxZVvCz9oHPyhdckn8sWOhNay02uMsWuS+MArbg+09GBhwr0FRe7B9ORJWWkdGmmcPDl8v+4KgSqV1YMB9ju64I7ssL7Ru3Zr/e1ul0jowIL3pTfH7h/tPpRUAAIc/iaikldBqYhP/hJfbQfDoaOMSE0UTMfk/57UH+zPszpnTOH4z1h4suYN8O6C27f7kJ+50v/2an19ee7DdN+85+/dpdUxr3hhRq7RKWbirM7RaYLZTW45Gcgfmdp/581sLrbHPkYUhfyImf9/bCa1h23ms9dPGY65b5167RYsaQ2vRREyx0GoBbM4ctwavtaH7ywZJrVdaq7QHP/lk43jW2PYOP7z58SX3u5M3q3TZmFa/0mpBMq/SKrnXKFZptert4KC7LlZpLWsPtv2qsuTN4KBb1ir2hUTIX8NXyoYfhNsumj34y19WKZa8AQAgQ2hFJXmzB8dCa2wMZVloHRlxB4kWpmz7/m2LxrQWTcQ0e7Y7GPYnYgpn+ZTcQatfgfX3e8mS5udZ1h5cVmn99Kelk09u3m54X7N5czw8S1ml1d+fsomYpNYrrfa6+pXWHTuy7e2xh3sf7bVppz3YHssqrWnauMRIq+3B/s95Y1rtdkND2XPcY4/GGWRjEzEVhVabhdY+d2FoXbrUBcu/+Zvsfn47b6eV1jC0hs/5qKMa72M2bsxvfy0b0+qHenut8iqtkmsfXr68eUyrbXNw0M3i/bu/27gfYaU1L7RWXfImdllepdW+ELPt+rerc0zr7t1UWgEAMPxJRCWtVFr9kPS617nlSPyKon8+DK1hRaydMa1he/DAQHOl1T8YtPP+WF3fnns2zi5qytqD/dcsdht/fdpQXqU1DCLGr7Ta61Sl0hpbb7JqaLWD9bGx7H2bP79xX8rE2oP90GrX+19K+LMHS9Uqraao0mrBx57jvHnNlda8iZjCL1fSVDr9dPfz61+fPWbYHvzEE9JrX5vdt47Q+h//Id15Z+MkTLHnnFdp3bjRBdLYFw5jY9l2ysa0Dg01t6yHofXWW6W//Mt4pdUq2x/6UPZamnD24IGB/NBa1B5sn41WQqtVWhcsaNxGbNvh7MGxtZLzUGkFACDT0ZI3mDnyQmtsnVY7CN6+Xfqnf3L/Xv3q7PpYxc/ag+1A2A5s/QpW1TGtYaV1fFzae+9s5tvwYNDO+8/Ll1fdLJs9uKzSWnRA2k5oLau0Vp2IyQ+Qdt6qatY2GrYH2+0uu8w9roXMskqrhUD/c2SPYZXWcD/bmYjJVKm02vbC0GqV1rIxrfa6H3xw4/MPK62x9lNbBif2PMysWY2vh/9+jY9LJ53kzoeflbC13J89eONG99oMD7vzu3a57foB0x5r9mz3WSwb0xpWWsfG3Gvrh2mrRoeh1V7PotfAvrQaGHDPLTamNTYRU9jCmzfhUVmldcEC14bt3zestBp7frEvifIwERMAABkqraiklUqr3faRR+L3r9Ie7M8iatqttO7a5SadsSVR8kLr6GhjpdUO2GOtwVJ5e3DZmNaiA9Lwue7c6Q7k66q02utV1B68557uAN0PXrH2YL/S+uIXS+ee29rB9shIfqXVgoNfaW1nTKsJK61+KLNAas9x7tx4pbWsPdhfs9RnodWuj4XWqrMH+48Xaw+Wmj9z/n2OPbbx8zJ/vhvDmyTZlzuxib/GxrLfTXvcqpXWxx5zp7Hlo8KJmOzzkPca+O3Bdpvw9a5SaX3BC9xp7Hfc3ttwuxZaFy50p/7nKwzExj53sd+3PEzEBABAhj+JqCQMrUVL3lhIeuih7DK/ylcUWm17VSutVSZistD6+OMuFPsHum9+c2O7qV9pfe5z3WlepbXT2YNjB+Rf+lK2zz4L84sWxffFr7RWCa22dE1RaF20yL3+FmKkeHuwX2m11y+cFKrI6GjxmFapMUCFoTX8DBaF1rDS6k+iY1VCe01i7cFhpdXO+69tXmgN24NjodWvhnYyplWS3vrWxvvZ7f7u76Qf/zh7Xez1DidfCse1hmunGpvpV2pc7iistNqXWEWh1QKxvad5a6VaaPUrqVUnYvJv9/GPu9fiyCObH8M+e+HQgLA9eHCw8Xzscez5tRJaqbQCAJAhtKKSMLQmiTuoKwqtDz7oTufOrVZpHRrK7lsltO7end8e7M/wOT6eLe/xq19lB4NpKl17bX578KGHutO8SmtZe3A7ldbf//3sufnsddh77/i+tDIR0/HHS9df784XtQdboLvvvuw6C63Dw/GJmOz1s32pElrzKq02e7BUXGkNFbUH2z77y7L49/Pvm9ce7N8mSZorn2WV1qLQWvQ8zPCw+72x1ykWWt//fuk5z2m8nz9Zlv9crQMhFFZa7XHC0BpWWv32YL/SWhRaw4mY7DNXpT3YblN1Iib/5zlzpOOOy38Mu43PKvt+pfW226T/83/yK622rVbag6m0AgCQ4U8iKglDq+RCQ1FotQP5vfbKr7T6Ycc/iLfHaGf24B07XKX1ooukFSukiy/OQusvf9l8MOiHIH8f9tpLuuYa6W1va36OUueV1tgBqVXa1qxpfk5ScWit2h786ldL99zj2jW3bm2efMoeywLdXXdl11k1Lm8iprwgWST8HLU6EZPUOIFRUaU1bPn0Q2tYRc2biCl838IlaLodWmfNkh54wIX69esbXzsLlrHxmHY7C4ZloTWstNq2wxAXjmnNq7T+93+70/33b36ssNJ67bWN+xiqElqrrNNa9B7Yaxj+fqxd605tTefdu93/L3/wB/mPQ6UVAIDOEFpnqLExNyPn6tXVbh8ueWOn27c3B9ewtfWxxxqrK0XtwaZqpTXWHmyVkCOPdCH12c92/6QstOaNaU2S7PmNjEgXXigdcoiiujGmNUlcKLr6ajc+1NjrZIEjNDxcfSKm5cvd6YYN7nXzJ//xH8sC3Z13ZtdZ5dQPrRs2uDAbzqzr375I2B5swXjevGoTMUmNYb5oyRu/Cig1V1qLQqtVWkOzZsXbg8P9sOVz6qi0mscfd6+d/b5YJS+27XC8uH1eOq20Fk3EFFZa9903/sXG2We76vDSpY2XF7UH22PnhdZnnilf8iZvsiX/uvD+Tzzhfmfs9ya2PJUUr/BTaQUAoD38SZyhHn3ULTdhYxvL5FVav/lN9/OPfpRdn3cQZ4rag8PHyKu0WstxLLTaGEw/yCxa5A7k165tDq1h5c4OMIsOaKX89uAwLIbPw+6TF0rs8jvuyC4Ll84IDQ9Xq7QmSeNkN9u2NYfWsD3YQqs//tNvD37zm6VPfKIxjIQz1RYJ24O3bHHBamAg26Y/3jIWWm1MoVRcaQ1Dq7V42nb99yRvIqZQK+3BZWNaw9vH+Pfbts39DtkXLhaKiiqt9rtl23/44fjjXH65q+iaovbgKmNaH31UWrYs/lgHHeSWtqmypqrUOJ46L7Q+//luvdrwdY7N/lz0GOE+rV3rfhfsvnlrr8bCcasTMVFpBQDAIbTOUDZRURi48vgHZjZWbsGCbEZQv1rTSmgtaw/Oq7TOn984ptW/nYVWP8jY2MNwxlGpcUyr7YsUX7PV18o6rVXbg6X45fb88vYpTauNaR0ebpzAqGqldfHixoA3MNAcjGIVtHYqrTt2ZNveay936k8G1WqlNRZa7bJwiRm73pb0sdCapsWV1tiSN+22B9t7XBbYJPd7vH27ey0GB7Pfp9i288Ydh23A5u67pTe9SfrZz6TrrmsOvaaoPdivtMa+IAkNDDR2ZRTNHmyPnRdaTbvtwXZdeJvx8WqhtdPZg2kPBgAgQ2idodoNrd/8pvSKV7jz55+fXW/rLUrtV1r9g8NwvcZwu/PnN1ZafbHQKmWVrt27Gw8o2620ttIeHLYF+gfboVjQK6u0+kG8qNLqh9axMXcQ7Y8HlbJwYqF1bMwFCXtPhobclwBhgK6r0uqHVnsPf/3r7PpOKq12X3s9bX1gu5+dt9dkaMiF9tmzXXjLW8+zyuzBVUOrvc5VQtiGDe79GRlxt69SaQ1neC4yb5509NFuHLSNKw4/L0UTMfmV1lirbsw992Tny4L72Fh5aK27PVhyX+LY9VUqrUVjWu+8M/vyz0d7MAAAGf4kzlDthtaRkSyQXHhh8/Xh+ZhYaLWqlom1B/thbs89G8e0+vJCq1XNwkqrPYY/VlfqvNLqh+zwYLWoPTisykrFE+zYYxVVWr/0JemTn4xXWufMaQyZ9lh+ZfWAA7K2YgtN3aq0+pPnWAX1ySebt+k/vl9pDQ/07WcL21IW7kZHG0NiGFoHB91YTNs/u35kRLr0Unfebw++8063Tq1/W1NlyRupuX03VBRaiyqtz3ueO42tL5rHr3o+8YQ7DWfTrlpp9ZenKeJ/jvJuX6U92NTdHiw1VlqrjGmNtQf/4Afu9JhjXNv06adnr7F9xqm0AgDgEFpnKFsSpixgGv+g1Oy5p/TTn7rz/oGbf95m2PSFoXXWrKx915S1B9s6jbEDxqLQGmsPtscI24PDUPZnfyZddln2cytL3viz39pt8g5226m0+kuxxCqt552X3S4WWv3Xww/I9pqEldbYvsQqre0seeNXWi2M+u3B9vySJKsG+6E1rPL6odX4ra4rVrjzg4PZzLbhczX28/bt0t/8jTvvtwe//OVu3c/YfbtVafXbg4sqrX//927f7HeySiDyxzHff787DUNrWaXVD61l43jD/SprD96xI9vmZFdaWxnTOjzcOOZYkk4+WfrWt7Kfb71V+t73GrdJpRUAAIc/iTNUu5XWvPGCeaE1NvFKOKbVwk4rS95Y22HsgNGqcjYe0r9PlUqrHRCHldaPfET667/Ofh4YcAeiee3Btr9pGq+0+oG8TFFo/cu/lF760uy9uP9+6TOfiU8I5U9uVBZa/RB05plZpdWvNvrKKtN5YpVWe57Dw+5xY5VW2y9/n2OKQuvoaDaz9OCgdNhh7rx9qVNlYiA/tPr7mRdat21z+1RWac3jfwb8SuvQUPHswbNnN65JmheI/Nv4/z/8/OfuNFZpzZuIaWCg9fZgX1loHRvLtln3mFZ7nWOt7q2OabVJvsL/B9asafzZ3nt7zai0AgDgEFpnqLpDq3/g1kpotQNuqfGA1tYdjVVaP/rRrO3Qf9yBAXefNHUTvsTaAq3CWaU9uGxMq79NX1hpja1lOz5eHLSMBbS8iZgGB6U//dPsuUuu2vfOd2ZLlqxfn91+y5bG0LptW3NoteDjvx+nn55VAP1Q4mu30hqu0+pXzyRXMffHtPqfL2vRfcEL8rdvzy0vtNoavps2SYce6s5b+AwDSSx0DQ9nnyF/3/LagzdudJ/PvHG/9jrnLY/SbntwKBaI5s7NKsVS42f05z931/vj16XmSuu8edmXI2GltdXQWqU9uNXQGpuYq+gxYh0R++zT2phWqzqH76m/xJaUvX9UWgEAaMSfxBmqrtAatqSG5xcvbt6W/5h+aPUPLm1sXBhazzhDeve7s0prGBJsf8LWYNumBV3/YNCflEfKr7TGWPU29vxs38LWYLtNlUqrHeTmVVr9g+7wADcWesLQunWrq+7497X9nT1bevBBN6bTXyrHHjMMXf7r1clETH6lVXKtv1b5lBqD8KpV7r6/8zv5249VWv0xrTYb9i9/mVVazTPPNP5cVmktuq19/jZtKp5F10Jr3kyz7bYHh2KByO731a+6U/95/fznbp3V8H7hmNZzz5X+7d/cZGn+RExV24N9VSZiKgutsWBqFeGiz6k9RuyLl2c9q7UxrTbJV/ie2pdNr361+zkMrVRaAQBwCK0zlIWAqqHVDszyJrnJm4jJAoHPvz6vPXhoqHlWVn+yoVilNTaRji9vIqaqY1pjbJysL6y0xsJj1UqrhSZ/nOnRR2fXx9abNbGwLDWG1u3b3fP2t2MVWmudtXGeYWgNxSpO7S55438W/PGqsccZGSn+giEWWv0vKo44wp0fHm6cfErKvtwxRUvehM81rz24LLRefbX0hjdIL35x/Pq89uBWK61S82fG7vf617txzH5o3bSpObQmSbzSesop2fbtum61B7c6EZPdtuw1Kqq0HnRQa2Na89qDk8S9xvZ5sPcv7/9bAABmKv4kzlB2MN7JREz+z3mV1pUrpXXrGu+TV2n1D2jDSutPfuIOmu0gLjam1Q4MpXjgzJuIqeqY1phYe3A4lrST9mALrX6l9T//U7riiuzxTfjelIXWbdsaq3TGD62+pUsbrw/5XzDUteSN1Fw1j4WIoi8YYqH1M5+RLrjAVe5f9CJXWfyrv3LX/fu/Z8uuhJXWvNC6c2djNTh2W/v8bdrU3GLre/azpa98Jf85tbvkTUz4mfHvZ2HcD05haB0dbR7TGm6/k0prHe3BsW0MDpa/RkWhddmy8tAado7EQqvkXj/7PFBpBQAgrsXvvTFdTNZETHvu2Rw6ytqDbYIjO2jevFl6/vPddTZpTl6l1cJS7IA0byKmsD24lUprUXuw7VssnO7YUa09eOPGxn2cNcu1j+63X/b4pmql1SbI2bzZvVdVQ6vNsuuPkfXFlupppdKapu7927mz8QuDsNIa22ZRRSoWWg88UPrc57KfX//67PxLXpKdt9C6ZIm0dm08RAwPu/1/5JHGy2MBbny8vNJaJgytNn7Ubz9tt9Lqf+ZHRtzz8r+ACEPryIj7jBb9/9BOpdWq0lVmD54/P/7YJvZa+BNG5SlqD/bvnxdarXNjYCBrAw4DsG07r9JKaAUAwKHSOkNN1kRMsYPzstDqL6myc2djdSKstIYzCtt98w5UYxMx5bUHV620ls0eHFZa58yRHnusvUprWJUuqrTmTeRjk7/YZ2B0tDGIlIXWPH5oPfBAd3rMMcX3kdxzSlN3/5//PFsGyYShNW8MYZ5YaG2VTSgW28bChW7iJn9Znthtq7YHl/Ffmy1bultp3by58fP97Gc33mdkxL0f9t7HOjH8SmvV98D2o1tjWqu0B5eNWS2qxErNyybF9s/+rwhDKxMxAQDQiD+JM1Q3J2LyD3LDNsjR0cbHjI1ptW1ae3C4ZIudxiqtRe3BeRMx5bUH1zF78HXXSV/+cuP1hxwiPfRQ++3B9lz8U6m1A9wwtPrbsQptJ6H1xBOl1avdpFlV9kWSfvELN7509eri0FqleuurI7QWrW26cqWb3fjRRxsvz2sPttmD2+VXPrdvr3dMaxhaw6r6297WXGm1/ZCKK62ttAdXXXvVbw/Oe3/zxrR20h7sb7cstNr7VRRaR0bc9qi0AgAQR2idofyJmG69VfrCF4pv326lNQytIyONIc8fv2gH8hZKrNLq375sTKtfpQ3lTcSUt+RNHbMHv/rV0qc+1Xj9wQdLjz/ePF4yxtqD/YmY7Ln4p7YvecJwUhRa8yqt4bq3obA9+PnPrxak7XH8NSv9oGHtn6bVSmtsyZtW2ec4to2VK93p6tWNl3erPdh/ncNxyfblRtVwGH5m/PvNmpX9P/HOd0r33ef2uyi0Fo1pbaU9OG9ZpXC/21mn1bbbTnvwypXSlVfmb9dnnRv2nsT2z97L4eHGpZ+otAIA0IgxrTOQzRoruYOjf/gH6Wc/k84/P/8+7U7EFAutftD0WwYtFPnVonDsZ1hpDZe8seuL2oPLxrTWVWkNJ+YxBx/sTv2D4VNPld7ylubb2msRVlpjB+pFB7g27tIUhdZNm9xpldDui41prcIex5+p13/tw7Dcbntwq5MASdLHPiZ985tZAMmrtErSbbc1Xp4X4OoMrTt3us+RVVpN1fbgskqrfYZf+ELXIRDex5/FVyqvtNbVHtxKaO10Iib/9/T++7PzZZ8nq7Ta/WP74Y9B9kMrlVYAABrxPe4MsWVLFqb8Ct/4eOOSFaE772ysaLY6EVMYfMJKqx8gw3BiEzH5B+mdzB7stwdXmYipSmgL15KVsuf34IPx+1holVxY/exnXbX7f/7P5tvatnbsaHx+rVZawwPmsjGtw8Px7X3xi9I118Qfo93Qaq+3/7mss9LaSXvwn/yJ9P3vF1f+bFmnsNKa9wXP+Hjx7MFlYp+38IuHdiutee3BttyR1Dx7sJTfHtzu7MFlodX2wX4vim5bx5I3r3td84zYZaHXvujwHzNkoXXWLCqtAAAU4U/iDDFvnnTeee68X9EqCq0PPugm0rnsstbbg5ctk/71X5sP9FoNrVu2ZC2y/uOVrdPaykRMfoue7aM9fplwjVGpfJywH1pPO036wz/Mv63tW7gMTKtjWgcH3TIuDz2U7XdepXVsrLk12LzpTdKFF8avO/74/McvUlZpDUNrL8a0FoXWOXOyMa++2JhWU0el1d/e3LmNP7c6EZO9RmFo9bdviiqtsXWc7fc0TetvD/art61UWlttD/7a15q/LKlaaQ332WcTZ+W1B1NpBQDAIbTOIF/9qjuNhdZY0LL1VT/96dYnYlq+XHrVq5q3GU7EtHt3dqAbhtbhYekHP5Be8ILssk7XabWA7h9cf/Sj7nTevGwfpWqV1nZC6+LF2fmyx8gLra1WWgcHpUMPlQ46KNvvvNBql7Xi9ttdFbYdk1Vp7SQAlAWU/fd3pwsXZpfF2oNNJ6HVKng2o7HkAlI7lVZ7bSyU5oVW+93w7yM1jmm1pap89ntqvxN1TcTkX26vcytVyTonYspTpdKaF1ppDwYAoBGhdQbyx1oWVVptbKPkZnaVqldai9ZXbKXSGioa0+qH1ryWwFh78Nvf3lgFOu006YILGsNlHv9A039ORQYHs+daNbSGy8DEQmvsoKcL4WQAACAASURBVD1vDUs/bNcRWo89trEa14pWx7S2W2ntpNXSPk95X0hYpXXffbPLuhVaL7pI+vjHpfe/P7ts7tz2xrRayLSqYDgRk799kxdaYxVN+z2NVYeL2GOHITi2D7bNvNvG2tZbbQ+OqaPSmjemlfZgAAAa8SdxBggP8v0K2/h48wy9xg+ta9e606oTMeUdbLUSWmMHhbFKq39ZO7MHhw4/XPrc56pVOUZGmkNrWaV1aCgLxGXhoqzS6u9jbH9t7GRRKO0ktNp4zk7EKq1F7cHtVlrzQk0V9lnMG7droXWffbLLutUePDwsXX554+vSbqXV/m+wqmC77cHbt8c/f/ZFkf1OtNoenPe7FKu05skLre1MxBS7Pg+VVgAA6sPswTNAeJBvoXXRouyAsiy0PvWUO606EVNRaPUrkX6ADNfjjB0UWvDwx8rNnu3Gvg4NlU/EVCW0tmJ01K3RacbHmyfKie3H4sVuJtKiSuvQUGNo9W8bW8Yl9prnLdUShtbYkjhV3HVX9bV+89hj+ZVWP3SFAS8vtF54YXzt23DcZjvKQqu16haFqboqrcYPRWForVpptdfSqoJVQqv/OPbejY3lh9ZO2oPzXu9OQ2uVMa1l67C2WmmtMnuwLTdFpRUAgEaE1hkgbFf1Q2vV9uCnn3anVdqDwzGjvqJKa9heWtQebAfDu3e7g8MtW6pNxGQtxXUdDIZjWu+80z1GbCkcY6HVzucZHm6cPbis0tpqe7B/vt1Ka6ttxDFl7cHhvuWFiLxZjetsDy6rtFrokIpDaxho2uG/9uFETFW/lKkaWv3ZjluptHbaHpz3BZC/D2XPNbaN97+/fN3hWBeJr44xrWFotf9nmYgJAIBGfI87A8RC68iIq/YUTcRUpdLqH9itWCG94hXFY1rDiZj80Bq2b+aNkbNTq7TaAXcrEzHVdTAYtgf/4Afu9JRT8vfdD622pEjM8HDnEzF1uz24DmWV1lAvx7SWhdYtW7LLitqDw0DTjrxK6/Bw9VZoey3tC6PYmNaRkcYqv/862udr/fr89VCl5hm6y7zxje702c+OX1+10nrEEdJZZzVffs45brmpIvYa5n3eyv4PaWX24HDJm1Yr0wAATHeE1hkgDK0bNrgqg7XLFlVak8T9K2sPHh+XHn5YuummeCXTDgCLKq2hcKyo/3g2Vs4qrXaZXZ83EVM32oNtP9NUuuUWN3PygQcW77tN2ONPihXyQ2veREy9rrTWoazSGmp3TGs3Q+uSJe7Ur7TmfcEj1RNa/ffID61VW4OlamNawzVl/dfRlm+67778SquUdSNUrbRedJH7vTrggPj1/naKtnnXXY0zOrciNvTBV/bFQCdjWlsdAwwAwHRHaJ0BYmNa99orqzwWVVrnz3e3tRa7vNBq63/a44UBwQ76iyqtIb9qFT7ewEC2HT+02kF4XqU1NntwJ/z24L/7O+nmm916uLGA5K+t+q53SW9+s3TJJfnbLqq0xsa0dlJpbXdMax3KlrwJ9WOl1ca0vutd2WVF7cF1V1r92YNbqc4VtQfblwn+cjdS4+t40EHZ5zRvTKvUemj1H9/39a+737PYFzh1W7bMraF8ww3t3b+T2YMJrQAANCK0zgBhFfWZZ1wYtRBn1ccwDGza5FqIFyzILgsPvKwSe8cd7ue5c+OhdelSdxqO9SwaX+pXrYxfrbQA4YdWOwgvag8ual9ulX+g+f/+n1uv84MfjG/fZtpNEhcmr7228bU169a5ynYYWv2D+E4rrYsWZedHRvqj0moH8FJ3Kq11rNOaF1rnzHG/P5deml1W1B5cx+tbR6W1ypjWMGD7n7NZs7IW3iqV1k7bXX/3d90SVZMRWgcGpM9+VjrqqOLbnXBC/PK8Sqv/+lFpBQCgGkLrDBCGVgtAfqVVag4Dmza5KosfrGLBaGDAteFJ0mGHxSdi+u53pauucmGtqNL6q19JDzzgzpdVWi1A2MGhtQxLxe3BdU7EZGNa01TauNG1IiZJtn0/WNx6q/Qv/1JeZVuwwIVKmz34f/0vN1a2zjGt++3XuK1+GNPqC4PXNddIF1/szvdiyZuyNTuLHtd0s9IajmmtqkpoDd8f/3kNDGQtwkVjWp94Iv827ZiM0FrFE09I3/lO/Lrwd8r2058AikorAADVEFpngPBAe+dOd5AUhtYw3IaVVquqhsIlMGKVzAMPlN7ylqy6a8LQunx5VpEsCq1+K7AdcA8NlVda89qc2zU66vZj504XWsOQ6K+lud9+0mteU33bNnvwJz/pfraZRaXqldYqoTV2fS8qrb4weF14ofSBD7jzrYbWOpa8+b3fk976VunjH69+n/B3pey9alVYaS1aozhP+DsUm4ipKLQODmahNfa+2G1f9Sp32o3Q2ssZdvfdt/pM0LGlvWKVVvv/RCK0AgBgCK0zQBhGd+7Mqmt+aL3+eteaasLQmndw6B/E2jI0eQflYXtw0fjSovZgf/ux9uC8Sms3Qqvk2h/90Gr7V7asRhFrD7ZJfm6/Pbuu6phW27/w4LefQuvAQPP7FQtetrZpbDbYsu37p+0YGZH+4R+yCbTaUXe48iut/szZ3a60+s9jcFB68Yvd+Ucead5++Jzrmg23rNL6J38i/fzn9TxWXez/nqJKqwVWKq0AADQitM4AYWgdH49XWl/7Wum007LbWWi1ykCV0Fq2DmoroTU262dsfKLfHlxWabWxdXWH1u3b45XWOkKrVZ5PPjm7rmql1Z/8yReG1rCFdjJDa+zxYuFm3jzpscfcOMNW1BFa61B3AAlfo05mD263PXhwUDrjjPzth695Xa9BbHy37/Wvd0MV+olVVf3/E+z/QlvyRnJBliVvAABoRGidAfy2vVe8wk3EZKHVJmIyNqGSlIVWO8jKC3r+5bt3x8e0mqEhd6Bs+1QUWm+4wbVl+qpWWierPdgOnsPQavvntwe3ykLr2Jj0ghe45YRM1TGteZMQ7bNP4892vX1p4U+KNBnCFuG84LV0aesH8v0SWuuutOa1H9dVabXtFE3ENDDgrj/88PjyNL2qtPb6vY6JhVYzPJxNVvfoo1RaAQAI9eGfdpQ54wzpK1+pfnu/0nrTTdKDD8YrrSELrdaWaYEvFGsPLgu4/jjavNvuv78bRxh7LP8+fmgtm4gpts+dKKu01hFat293B7T+2LlYpdUCyJIl2ePmhda85VhOOcWd+q3Ik6FKpbVd0zW05m2/ndBq3RT+mqxWhS2rtEruy65f/rJ5+92qtJaF1l6Oc/V9/vNu2IVUHloPOcSd/8UvCK0AAIQIrVPQt78tnXtu9duH7cFSeWjdtcuFsPnzs9CaF279A8Qq7cG2rTR1/4oOMMMKXKeV1tg+d8IO6DdudBXROse02uzB27bljyv0n5Otp3nppW4W5scfr77cix9azzhD+tjH2t/vdlSttLajX0JrtwOIvYetzExswXTZMul735POOSe7zmayrRJaYzNQ+9ebyQqtvX6vzfnnS7/zO+68vZ55odUmtCK0AgDQjD+JM0CroXXrVjdT7fi4m823bHxjqxMx2T5ZwCw6wMwLrbFKqz97cKza1I3Qavv31FPuNKy0WpBsx/CwC6zbtze/B7FK6z77uPA8b17WOloUWg8/PKue2+1mz5ZuuaX9fW5X0WQ/napjyZtWHHBAtUmJ6ma/x6tWVb+P/b4MDTWOmZaqhdaycBheX1cFvex3uV8qrb6ySuvIiOsuue++xnWtAQAAoXXKscpIK2JLUcRmDzYPPyz9+tfu/LOf7YJQkTC0lo1pldxjWpguOsDMO2DOq7TaNmOVunDW0zrY/j35pDsNK62x5VyqGh52r31RaA0Paq0qbmw/Yge/d9+dna9jWZhOhMuGtLqsTRH7nZms5/azn8V/Z+w17lZ4Xr3anVqLdxV+aA1ZaM374kiqXsE3dYUw/zXs5/ZgX1lolVyL8C9+IZ10kvuZ0AoAgNMnTVSoKlY1bec+fqU1vP4LX3DjXiUXWsMgFGq3PbhKaK1SaY3NHjxZlVYLk2Gl1fbT9uP001vftj+mtUqlNabV9uBeHewfeWTjz3WGVtvWZD23+fNdxSxk71md43Vf9jLpzW925y0UWeBpRSwcveQl7vTssxsv74fQWrbNfmkP9uWF1oGBbH8PPLBxIiZmDwYAwOF73Cmm7tBqS8CYefOkj39cetvb3G323z+rIuZpZSKmukKr/5hDQ25fy8a0dnMiprDS6lewNm1qr+JaFFpjY1pjpkpoPeEE6dprs5/b+ZznqdKGPhnamSipzM03Z+evv176yU/aG0cd26fjjnOvXd4sxVLv2oN9U6XSaq34/mRXUuP/VfPnu/8vGNMKAECjPvw+GkXaOZiPVa0stFoLoDnpJNdOeeed0ooV7uCvlUpr2ZhWf/bguiqtAwPudmXtwd0c0xqGVv+gc9689g7Wh4fdlwo7d1ZvDw5NldB6/PGNP8+dW9+2+y201jnJlO+5z5V+//fbu2/e5yjWykyltTPhZ9v/v2GPPaQtW7IvEwmtAAA4/EmcYuqstA4ONo+RtVbbX/1KOuIId74stPoHiFXbgw84QPr61935Tse0Dg66YDg62rv24LzQ2snjWJVWap4RtmrItPe3ahtxrw72Dz/cnb7vfW5c3wtfWN+2+yW0dqM9uC6thKNWQiuV1mZFyzvZ/x+/+Y07JbQCAODwJ3GKqTO0xqooFo62bs2qiK2E1qoTMUnS177mTluptNo+h5MqffWrbqbjf/5nd9lkT8QUjmm117yTg87hYWnz5sbHMUninkPZ86hSzfav79XBfuwLlLr0S2jtRntwXdoNrWWvKZXWzMEHS/ff3/z/blhplaQNG9wpoRUAAIc/iVNMXe3BQ0Px0GrhaGwsO2AqW7Yl1h5cNqZVyiYm6XRM68BANmlM1Upr3WNabbZY2986xqQND7tWQf9xfFdcIZ15ZvE2pkpo7Sb7TEzWkjd5ut0e3InJqrR2I4RNlSVv/vM/pTVrsi+iTKzSun69OyW0AgDg8CdxivFD665d1Q7O8iqtMRaOtm9vfYZae6wq7cFSFlqLAmR40BYboxmGZmnyx7RaG68/0VT4mK3y36O80FqG0Dr5S97ksdDcj5XWVvapkzGtk9Ue3Ov3OmbhQvfvrrsaL49VWtevd5+XfnweAAD0An8Sp4j166WvfMVNymOsClemaPbgkD92smrgamUiJn+bNglUK0Epb0yrmex1Wu1xtm51p2Fo7eRxykJrFVVDa9UJm6aifmkP7udlTFr5csWvWLc6e3CdlcOiNYj7+XN85JHSv/6r9KpXuZ/zKq39+DkBAKBXCK1TxFe+Ip17rnTeedllVt0r0+3Q2sqYVv9gskp7cN5j5S274S81E+pGpdUOLO252M91jWk13Q6tdn2vg1039EtotS+cpnp7sB9aezl7cFFo7fV7XeZVr8oCqv95sMs2bKA1GAAAX5//aYexA95/+7fssqqhNW/Jm9gBpx+O2gmt1h5cZUyrVSfrrLQWBZRuVFptO+ESFZPRHlwF7cHZa9DrIGNfCD33ub3dj5h2P6e9nD24aK3iqfA5ttdi4cLsMr89mNAKAECmo8O4JEk+niTJfUmS/CxJkv8vSZK9Ji5fniTJtiRJ7pj49/fefZ6fJMldSZI8mCTJ3yZJr6dHmRpsYXpfOKFHnnYrrVUP/NptD66r0uqf/9rXpFNOic943I2JmJKkceyvfZrrCK3+fQmt7euXSuthh0nXXSddfXVv9yOm3c9pq7MH1/keTOVKq5Tt9377ZZf5S94QWgEAyHT6p/3bko5I0/QoSfdLeo933UNpmh4z8e9t3uVXSnqrpJUT/17e4T7MCFbJ83XSHjw0FD8oyqu0fulL0lVXxbff7kRMFrrLgpJfmcqbPdiceab03e/GH78b7cFSVjHxt8+Y1v5hobUfnttZZ0lz5/Z6L5q1WwFttdJa51eURZ/Zfnivy9j/F0uWZJf5X7YRWgEAyHQUWtM0/VaaphOH5/qRpGVFt0+SZImkPdM0/X9pmqaSvijp1Z3sw0wRq7R22h7cSmh94xult7wlvv1wIqQ0rRZabVmHsgPMe++VLrkk/zHbqQjXeVBrzykWWutqD/Yr4K2oGp5nwphWejrydas9uJvhcaq3B9sXkX5onTUrm5Gc0AoAQKbOQ9QLJd3k/bwiSZKfJknyvSRJTpq47FmS1ni3WTNxWVSSJG9NkmR1kiSrn3rqqRp3deqJVVp/9atq953MiZgsJFUJrVWrgFIWOGLLl1Q9QO12pdUPmf02prVsP6Zze/ALX+hObS1fNGv3fW9l9uB2P8Nl256q7cFPP+1O/fZgKau2MnswAACZ0j/tSZLcmiTJ3ZF/Z3u3ea+kcUlfnrhoraQD0jR9nqR3SfpKkiR7SorVOtK8x07T9Ko0TVelabpqn332aeV5TTuxSut3vlPtvpMZWm3CqLyD4NjlVQ4w7TYWWvNmDy7SrdAaq7T2y+zBe+3lThcvLr7ddA6tJ58sPfOMax1HXLshr+zzYr8Hp5ySjWGvS1FonQpVdQutfqVVysa1UmkFACBT+mcxTdPTiq5PkuR8Sa+SdOpEy6/SNB2TNDZx/vYkSR6SdLBcZdVvIV4m6fH2dn1mCSut++7rxm6Oj5cf3OS1B/trvpp2Zg/2D1xbqbTG7p/HthebVKed9uA6KzGxMa0f+5ibTOWlL+18u1L7ofXNb3an559ffLuVK6UVK6ZvdceCAOpV9rtn/8d043NVFFqngrJK61R9XgAAdEOnswe/XNK7JZ2VpulW7/J9kiQZnDh/kNyES79M03StpE1JkpwwMWvweZKu62QfZoqw0nryyW5M64MPlt+3lUqrH46qhsFYAKw7tFrlJDapTj+2Bx92mPSDH0jz5rW/3TpmDx4clC66qDw0vOEN0i9/OTXaKtE/yiqahNZ8NuIlDK02UddUfV4AAHRDp4eon5G0h6RvB0vbnCzpZ0mS3CnpnyW9LU3TiWl39HZJ/0fSg5IeUuM4WOQIK60LFrjTLVvK79vK7MHttAe30vLbjUpr1aA1mRMx1aGOiZiAInfe2d0leLoZWqd6S/tf/ZX7Mspfp1WS5sxxp4RWAAAyHf1ZTNP0OTmX/4ukf8m5brWkIzp53JkorLRaBW/bNumQQ1yl7IMfjN93Mse0mrwDyU5Da2xMa79UWrsVWvPeK6BTRx3l/nULldZ8b32r+xcitAIA0IxmwCkirLT6ofX++6U///P8++aNaZ01q/ly/7JOQms/jmnt9kRMdR+Y2/YOO6ze7QKTZe+93enBB9e/7dgyTf/jf9T/OJON0AoAQDP+LE4ReZXWrVubbxvKq7TaAaXPP1DqRntw7Ladjmltpz242xMx1WHzZndKaMVUddpp0nXXdWfm5rD7QpJuuKH6+tX9ykLrdJ0UDQCAdhBap4i8Suu6deX3zQutsRlV/WDXaqV1cDB7rG5VWqfKOq112LjRnR53XL3bBSbTWWd1Z7v2f4D//9voaP3rwU42Kq0AADTjz+IUEYZWWxbBZqAsEmsPHhpqngDELo+dr2LWrGwtxlZCayvrtNoBqh86YxXjmPnzs/NTYSKmiy92FeZLLql3u8B08Nd/Lb3lLdLSpb3ek3oRWgEAaMaY1ikirz24SmjNq7T6Ic60U4206qc/HrbuiZjsNrExrfvsU35/STrwwOx82VIdrehWe/Ds2dIf/REHr0DMWWdJv/711K+shiy0svwUAAAZ/ixOEXntwRZaY5MqmbzQGgtu7VRaY6G1H8e0StJ990lvepN00EHV71OmWxMxAZh5LLSOj/d2PwAA6CfUcKaIskpr0TqeebMHx7QzptVCq7/NVoJkp2NaW3HIIdIXv9jeffN0q9IKYOax0Br+nw8AwExGpXWKGBtrDEUjIy7sPfmk+9kOdGLyKq0x3a60zp8vvfe90pe/nF3WzpI3dY5J7VS3xrQCmHns/3Jb4xYAABBap4wdOxqD6eCg+9kqrf0WWvNCZZJIf/EX0vOeV37b8H5S85jWffetto/d1K3ZgwHMPFRaAQBoRmidIsbGmkPr7NnV2oNjoTUvkHbSHlyl0mqqBFxfWGm159RPoZVKK4BOEVoBAGhGaO1zO3e6KuP69fHQakvMFFVaWxnTWtfswd0KrfZY69e7035Y7oL2YAB1IbQCANCM0NqnPvIRF1Y3bswui4VWU6XS+vTT0kUXufMWWn/ndxpvOzCQteJ2cyKmVgKufxsL4Kec4tZovOaaavvYTbQHA6gLoRUAgGaE1j71yU+6U6soSsWhtcqSNwsWZLezgPW1r0n33NN4+1YrhxYkW6metlppPftsd3ruudn9r7qKSiuA6YXQCgBAMw6z+5SFut/8JrusKLRacPzOd6Q1a6Tzz2+8ziqow8PuvlZNnT1bOvTQxsceHHRtya2GMD+IllUdWw2tK1dmFd1+Q6UVQF0IrQAANCO09ikLQOvWZZfFZg82Vk097TR3aqF11y437tXaaxcskPbaq/ixW60cxsa01h1a+xkTMQGoC0veAADQjMPsPmWhrmp7cGyGYMmNWb3pJreuqyRddpn0utcVP3a7odUPqmX3bWfCp35FezCAulBpBQCgGYfZfcpCa1GlNdYebHbscNu46abs9pK0557uXxG7bTcrrdae7D/eVEV7MIC6EFoBAGjGREx9KhZa/ZA6MFBcaX3gAenMMxtvX5WF1aphMjYRUytVx6keWqm0AqiL/T96+eW93Q8AAPoJh9l9KtYe7H/zPjgoPfxw9nNYaf30p6Wbb85+bie0drPS6pvqoZUxrQDqkiT9O+kcAAC9wmF2n7Ig5IfWrVuz84OD0i9/6c4ffnhzpfWZZxp/LpvU49vflhYvducnO7S2Eqj7Ee3BAAAAQPcQWvuUVU6LQus//qN0ww3SXXdJjz7qLt9zT2njRuneexu3VzY+ymYdtm1L3Z2IyTfVK620B2Om+elP8yd/AwAAqNsUr3FNX9u3u1N/TKu/9urgoPTCF0of+Yg7byF3/nx3etddjdtr5QCT9uDW0B6MmeaYY6TnP7/XewEAAGYKQmuf2rbNnVpoveEG6eijs+v9oDc4mIVSC63hGNdW1BFaZ2KllfZgAAAAoH6E1j5lodXag4eGmoOqGRjIQqsfHNtl264aJhnT6k6ptAIAAAD1m+JxYfqy0LphgzsdGmoMReE6p1ZZ9duAL7rIjXttVbuV1nbHtE51VFoBAACA7iG09ikb02rCSqvPbw8eH88uX7TI/WtVu6HV37+ZFOCotAIAAADdw2F2n7JKqxkczA9Ffnvw+Lh0zjnS6adLr3iF9MgjrT82obU1hFYAAACgezjM7kPj440VU6m5PdgXtgePjEgXX+x+fuqp1h+/3SVv/NvPpABHezAAAADQPbQH96Gwyiq11h7sB8bR0dYfv91Kq3/7mRTgqLQCAAAA3UNo7UPheFapuNIatgf7t5s9u/XHt/u3Onuwf/uZFOBaDfkAAAAAqiO09iGrtM6bl11WVmm19uDx8cbbtRNa220PnuljWmfScwYAAAAmC6G1D1lo3XPP7LKyMa1Wad21q3ftweHasTMF7cEAAABA93CY3Yf80Pr44+58UaW1G+3BSVI9eFqVt9XQ9uMfS/fc09p9+hHtwQAAAED3zKB62NRhY1rDSmuSxG8ftgf74WnWrNYfv2h5nZjf/V13unRpa49z3HHS+ee3dp9+tP/+rtp64IG93hMAAABg+iG09iGrtM6fn11WNClSOHuwf9u8oFukqBU55oMfdEvrLFnS+mNNBwcdJG3ZIh1+eK/3BAAAAJh+CK19aOtWdxpWWvMUtQe3o9XQOjAgLVo0s8axhpiECQAAAOiOGRwz+temTe504cLssqIQ6bcHhxMxtaNo/GyRmRxaAQAAAHQHMaMPWWhdsCC7rCy07trlguvu3Z2H1lbHtPr3AwAAAIA6EVr7UKuhdWDAhVVrEe40PO61l/vXKiqtAAAAAOpGzOhD7VRa01TaubP8tlW8733STTe1fj9CKwAAAIC6sbJkH9q0ya2v6q+xWhZaJWnHjvhtf/GL1pa+WbCgMTBXRXswAAAAgLoRWvvQpk3SHns0zkhbFAitwpkXWg8+uN79K9sPAAAAAKgLMaMPxUJr0XqrFmjHxtxpp+3B7SK0AgAAAKgbMaMPWWit2tIbVlp71aZLezAAAACAuhFa+9CmTdKeezZWWouUjWmdLFRaAQAAANSNmNGHWq200h4MAAAAYLoiZvSh2JjWIhYWex1aaQ8GAAAAUDdCax/auLG10Bq2B/cqPFJpBQAAAFA3lrzpQ0XtwX/zN9LcuY2XMaYVAAAAwHRFaO0zu3ZJW7fmV1ovvbT5MtqDAQAAAExX1Mb6zObN7rSdiZiotAIAAACYbogZfWbTJnfazpjWXldaCa0AAAAA6kbM6DPthFYLi72eiIn2YAAAAAB1I7T2GT+00h4MAAAAYKYjZvQZ2oMBAAAAIEPM6DPtVFr7ZfbgJOnN4wIAAACYvgitfaaTSmuvx7QCAAAAQN06Dq1Jknw4SZKfJUlyR5Ik30qSZOnE5UmSJH+bJMmDE9cf693n/CRJHpj4d36n+zCdWGjdc8/q4bNfxrSaN72pt48PAAAAYPqoI958PE3T90tSkiSXSrpC0tsknSlp5cS/4yVdKen4JEkWSPqApFWSUkm3J0lyfZqmG2rYlynPr7RWbbftl/ZgSdq2rXqFGAAAAADKdFxpTdN0o/fjXLkgKklnS/pi6vxI0l5JkiyR9DJJ307TdP1EUP22pJd3uh/TxaZNLoTOnl39Pv1UaR0dpT0ZAAAAQH1qiTdJknxE0nmSnpH00omLnyXpUe9mayYuy7sckjZubK3KKjXPHkxoBAAAADBdVKq0Jklya5Ikd0f+nS1JaZq+N03T/SV9WdI77G6RTaUFl8ce961JkqxOkmT1U089jteZcgAAG5VJREFUVWVXp7xNm1xobYW1B/dDpRUAAAAA6lQp3qRpelrF7X1F0g1yY1bXSNrfu26ZpMcnLn9JcPl3cx73KklXSdKqVauiwXa6aSe09lN7MAAAAADUqY7Zg1d6P54l6b6J89dLOm9iFuETJD2TpulaSbdIOiNJkr2TJNlb0hkTl0GdhdZ+mIgJAAAAAOpUR7z5aJIkh0jaLem/5WYOlqQbJb1C0oOStkp6sySlabo+SZIPS7pt4nYfStN0fQ37MaWtXi3dems8tC5dWnxf2oMBAAAATFcdx5s0Tc/JuTyVdEnOdddKurbTx55OjjvOnR5xhLTvvtnlTz8tjYwU35eJmAAAAABMV9Tk+swzzzRWWhcuLL8PY1oBAAAATFcdj2lFvTZskObObe0+tAcDAAAAmK4IrX1m82ZpdLS1+zAREwAAAIDpitDah9oNrVu2uNNZs+rdHwAAAADoFUJrn/Cro2UTL4WsPXjdOmnePCqtAAAAAKYPQmuf6CS0WqV13Tpp773r2ycAAAAA6DVCa5+oI7Ru3UpoBQAAADC9EFr7hB9aWx3TOuC9i4RWAAAAANMJobUHHnxQ+qM/knbtyi6ro9IqEVoBAAAATC+E1h4491zpb/9WuvPO7LK6Qutee3W2bwAAAADQTwitPWAV1h07ssvqmD1YotIKAAAAYHohtPbA8LA7tXVVpc7GtNIeDAAAAGC6IrT2gAXUDRuyyyzISq1XWhctys4TWgEAAABMJ4TWHrCA+pvfZJf51dJWQ+usWdLChe48Y1oBAAAATCeE1h6w0OpXWjtpD5ak5z7Xnc6b1/5+AQAAAEC/IbT2QJq607ragyXpla90p3PmtL9fAAAAANBvhspvgrrZBEx5ldZ2Quu73y2tWiWddlpn+wYAAAAA/YTQ2gObNrnTOkPrwIB0+umd7RcAAAAA9Bvag3tg82Z3WueYVgAAAACYjgitPRALrQPeO9FOpRUAAAAApiNCaw9Ye/Bdd0nbtrnzu3dn1xNaAQAAAMAhtE6y8XFp+3Z3fvt26aKL3Pldu7LbEFoBAAAAwCG0TjJrDf7EJ6QVK6QnnnA/W2gdGGgc3woAAAAAMxmhdZJZaN1zTxdad+xwP1t78MiIlCS92TcAAAAA6DeE1klmoXXePGnWrCy0WqWV1mAAAAAAyBBaJ1lZaGW5GwAAAADIEFon2diYOx0ZaQytfnswAAAAAMAhtE4yq6gODbnQaiGW9mAAAAAAaEZonWTj4+50cJAxrQAAAABQhtA6ySychqHV2oNnz+7NfgEAAABAPyK0TrKwPdivtC5fLv3v/92zXQMAAACAvkNonWR+e/DISGNoPflk6dRTe7dvAAAAANBvCK2TLK89eNcudxkAAAAAIENonQT33CN98INSmja3B+/c6S7fvVsa4N0AAAAAgAZDvd6BmeCss6SHHpLe/vbm2YMlF1yptAIAAABAM2p7k2Bo4quB9eub24Ml1yJMaAUAAACAZoTWSbD33u706aezSqu1B0sutO7eTWgFAAAAgBChdRJYaH3yyeJKK2NaAQAAAKARMWkSLFjgTvNC69gY7cEAAAAAEENonQTz57vTJ5+MtwevX097MAAAAADEEFonUV6l9dhjpa1baQ8GAAAAgBAxaRLs3OlOn3qqMbSOjDTejkorAAAAADQitE4CawnOaw82hFYAAAAAaERonQRWaX3ssXh7sKE9GAAAAAAaEZMmgVVXH3pI+s1v3HkqrQAAAABQjtA6CazSmqbSbbe587FKK6EVAAAAABoRWifB+Li0337u/H/9lzulPRgAAAAAyg31egdmgvFx6VnPcqH08cfdZQMDVFoBAAAAoAy1vUmwc6cbw7rXXu7nwUEpSQitAAAAAFCG0DoJxsel4WH3T8rCKe3BAAAAAFCMmDQJrNJqIXVooimbSisAAAAAFCO0ToK8SuvISOPtCK0AAAAA0IjQOgms0kp7MAAAAAC0hpg0CcbHG0Mr7cEAAAAAUA1L3kwCaw8eH3c/Wzi1EGsIrQAAAADQiErrJMhrD06SxtvRHgwAAAAAjYhJXbRxozQ2llVaw9mDJemWW7LzVFoBAAAAoFFHoTVJkg8nSfKzJEnuSJLkW0mSLJ24/CVJkjwzcfkdSZJc4d3n5UmS/CJJkgeTJPnTTp9AP5s/Xzr11PxKqySdcYa0YEHz5QAAAACAziutH0/T9Kg0TY+R9E1JV3jX/SBN02Mm/n1IkpIkGZT0WUlnSjpM0huSJDmsw33oaz/8Yf6SN8Yqr4RWAAAAAGjUUWhN03Sj9+NcSWnJXV4g6cE0TX+ZpukOSf8o6exO9mEqCCutQ8H0VxZWGdMKAAAAAI06jklJknwkSZJHJZ2rxkrriUmS3JkkyU1Jkhw+cdmzJD3q3WbNxGXTWrjkTVhRtbBKpRUAAAAAGpWG1iRJbk2S5O7Iv7MlKU3T96Zpur+kL0t6x8TdfiLpwDRNj5b0aUnfsM1FHiK3OpskyVuTJFmdJMnqp556qpXn1VdoDwYAAACA9pSu05qm6WkVt/UVSTdI+oDfNpym6Y1JkvxdkiSL5Cqr+3v3WSbp8YLHvkrSVZK0atWqstbjvmXtwVZRpT0YAAAAAKrpdPbgld6PZ0m6b+Ly/ZLErUKaJMkLJh5nnaTbJK1MkmRFkiSzJL1e0vWd7MNUUFZptZ+ptAIAAABAo9JKa4mPJklyiKTdkv5b0tsmLv89SW9PkmRc0jZJr0/TNJU0niTJOyTdImlQ0rVpmv68w33oezamNZ2oFRNaAQAAAKCajkJrmqbn5Fz+GUmfybnuRkk3dvK4U0EaNDMPDzdfZmgPBgAAAIC4TiutyLFrV+PP/jjWMLxSaQUAAACAOEJrl8RCazIxd/Lu3c3XSYRWAAAAAAgRWrskDK3Dw/mhlfZgAAAAAIgjtHZJrNJq4TQMrRZWqbQCAAAAQCNCa5fEKq15odXag/MmagIAAACAmYrQ2iWxSmteOLUwOz7e/f0CAAAAgKmE0NolsUqrhda8Ma3hfQAAAABgpmPqny6JVVqHh915QisAAAAAVENo7RJCKwAAAAB0jtDaJbH24Fmz3HlCKwAAAABUQ2jtklYqrUcd5U732af7+wUAAAAAUwmhtUvCYDo8nIXWcPbgD39Y+vd/l44/fnL2DQAAAACmCkJrl7RSaR0akl7ykknZLQAAAACYUgitXRIb05oXWgEAAAAAcYTWLmml0goAAAAAiBvq9Q5MV2FonT9fShJ3ntAKAAAAANVQae2SMLQeeCCVVgAAAABoFaG1S8LQOm9e/uzBAAAAAIA4QmuXhKFVotIKAAAAAK0itHZJLLQOTYwgJrQCAAAAQDWE1i7xQ+v8+e50cNCd0h4MAAAAANUQWrvED61HHOFOB3i1AQAAAKAlxKgusdD6utdJX/+6O7/33tIf/7H0ne/0br8AAAAAYCphndYusdB62WXS4sXufJJIf/VXvdsnAAAAAJhqqLR2iYVWG8cKAAAAAGgdobVLCK0AAAAA0DlCa5cQWgEAAACgc4TWLiG0AgAAAEDnCK1dQmgFAAAAgM4RWruE0AoAAAAAnSO0dgmhFQAAAAA6R2jtEkIrAAAAAHSO0NolhFYAAAAA6ByhtUsIrQAAAADQOUJrlxBaAQAAAKBzhNYuIbQCAAAAQOcIrV1CaAUAAACAzhFau4TQCgAAAACdI7R2CaEVAAAAADpHaO0SQisAAAAAdI7Q2iWEVgAAAADoHKG1SwitAAAAANA5QmsNPvtZ6bzzGi+z0DrAKwwAAAAAbSNS1eDuu6Vbbmm8bNcuF1iTpDf7BAAAAADTAaG1BkND0vh442W7dtEaDAAAAACdIrTWIAytaSqNjRFaAQAAAKBTQ73egekgDK0XXyxdfbU0d27v9gkAAAAApgMqrTUIQ+vVV7vT3bt7sz8AAAAAMF0QWmswONg8plWStm2b/H0BAAAAgOmE0FqDoSFXVU1T9/PoaG/3BwAAAACmC0JrDYYmRgbb2qxz5vRuXwAAAABgOiG01sBCq7UIz57du30BAAAAgOmE0FoDQisAAAAAdAehtQaEVgAAAADoDkJrDcLQyphWAAAAAKgHobUGhFYAAAAA6A5Caw3C0Do83Lt9AQAAAIDphNBag8FBd2qh1U4BAAAAAJ2pLbQmSXJ5kiRpkiSLJn5OkiT52yRJHkyS5GdJkhzr3fb8JEkemPh3fl370CthpXXnzt7tCwAAAABMJ0N1bCRJkv0lnS7pEe/iMyWtnPh3vKQrJR2fJMkCSR+QtEpSKun2JEmuT9N0Qx370gsWWnftcqdUWgEAAACgHnVVWv9a0p/IhVBztqQvps6PJO2VJMkSSS+T9O00TddPBNVvS3p5TfvRE1RaAQAAAKA7Og6tSZKcJemxNE3vDK56lqRHvZ/XTFyWd3ls229NkmR1kiSrn3rqqU53tWvyQuvKlb3ZHwAAAACYLiq1BydJcquk/SJXvVfSn0k6I3a3yGVpweXNF6bpVZKukqRVq1ZFb9MPYqH1nHOkf/7n3u0TAAAAAEwHlUJrmqanxS5PkuRISSsk3ZkkiSQtk/STJEleIFdB3d+7+TJJj09c/pLg8u+2uN99JQyt4+PZZQAAAACA9nXUHpym6V1pmi5O03R5mqbL5QLpsWmaPiHpeknnTcwifIKkZ9I0XSvpFklnJEmyd5Ike8tVaW/p7Gn0VqzSylqtAAAAANC5btYDb5T0CkkPStoq6c2SlKbp+iRJPizptonbfShN0/Vd3I+uI7QCAAAAQHfUGlonqq12PpV0Sc7trpV0bZ2P3UuDg+6U0AoAAAAA9apryZsZLTamldAKAAAAAJ0jtNbAQuuuXe50504mYgIAAACAOhBaa8CYVgAAAADoDkJrDQitAAAAANAdhNYa+KE1TRnTCgAAAAB1IbTWwA+tNq6VMa0AAAAA0DlCaw380LpzpztPpRUAAAAAOkdorQGhFQAAAAC6g9Bag8FBd0poBQAAAIB6EVpr4FdabQZhxrQCAAAAQOcIrTWwgLprF5VWAAAAAKgTobUGjGkFAAAAgO4gtNaA0AoAAAAA3UForUFsTCuhFQAAAAA6x3RBNYhVWpmICQAAAJgZdu7cqTVr1mj79u293pW+Nzo6qmXLlmm4hSof0aoGAxP1atqDAQAAgJlnzZo12mOPPbR8+XIlSdLr3elbaZpq3bp1WrNmjVasWFH5frQH1yBJXGWV0AoAAADMPNu3b9fChQsJrCWSJNHChQtbrkgTWmsyOMiYVgAAAGCmIrBW087rRGitSVhpZUwrAAAAgJli+fLlevrpp7uybUJrTYaGpLvvljZscD9TaQUAAADQC2maavfu3V3b/ri1l04SQmtNBgelb31L+r3fcz8TWgEAAABMlocffliHHnqo/vAP/1DHHnusvvSlL+nEE0/Uscceq9e+9rXavHmzfvzjH+s1r3mNJOm6667T7NmztWPHDm3fvl0HHXSQJOnqq6/Wcccdp6OPPlrnnHOOtm7dKkm64IIL9K53vUsvfelL9e53v1vr1q3TGWecoec973m6+OKLlaapJGnLli165StfqaOPPlpHHHGEvva1r3X83GhircmmTY0/E1oBAACAmeeyy6Q77qh3m8ccI33qU+W3+8UvfqHPfe5z+tCHPqTXvOY1uvXWWzV37lx97GMf0yc/+Un92Z/9mX76059Kkn7wgx/oiCOO0G233abx8XEdf/zxkqTXvOY1estb3iJJet/73qdrrrlG73znOyVJ999/v2699VYNDg7q0ksv1Ytf/GJdccUVuuGGG3TVVVdJkm6++WYtXbpUN9xwgyTpmWee6fj5E1prYmNZDWNaAQAAAEymAw88UCeccIK++c1v6p577tGLXvQiSdKOHTt04oknamhoSM95znN077336sc//rHe9a536fvf/7527dqlk046SZJ09913633ve59+85vfaPPmzXrZy1722+2/9rWv1eDgoCTp+9//vr7+9a9Lkl75yldq7733liQdeeSRuvzyy/Xud79br3rVq3673U4Qrbpg0SJp6dJe7wUAAACAyValItotc+fOleTGtJ5++un66le/2nSbk046STfddJOGh4d12mmn6YILLtCuXbv0iU98QpJrA/7GN76ho48+Wp///Of13e9+t2n7JjYT8MEHH6zbb79dN954o97znvfojDPO0BVXXNHR82JMa83uukt68klpwYJe7wkAAACAmeiEE07QD3/4Qz344IOSpK1bt+r++++XJJ188sn61Kc+pRNPPFH77LOP1q1bp/vuu0+HH364JGnTpk1asmSJdu7cqS9/+cu5j3HyySf/9vqbbrpJGyZmpH388cc1Z84cvfGNb9Tll1+un/zkJx0/HyqtNdt3X4klmgAAAAD0yj777KPPf/7zesMb3qCxsTFJ0l/8xV/o4IMP1vHHH69f//rXOvnkkyVJRx11lBYvXvzbqumHP/xhHX/88TrwwAN15JFHalM4ec+ED3zgA3rDG96gY489VqeccooOOOAASdJdd92lP/7jP9bAwICGh4d15ZVXdvx8Epvlqd+tWrUqXb16da93I5cF1V27pAHq1wAAAMCMce+99+rQQw/t9W5MGbHXK0mS29M0XRW7PfGqZgRWAAAAAKgPEQsAAAAA0LcIrQAAAACAvsVETDV57DFpYskiAAAAAEBNCK01YV1WAAAAAKgf7cEAAAAAgL5FaAUAAACAaWrdunV66Utfqnnz5ukd73hHw3W33367jjzySD3nOc/RpZdeKlsOdf369Tr99NO1cuVKnX766dqwYUMvdv23CK0AAAAAME2Njo7qwx/+sD7xiU80Xff2t79dV111lR544AE98MADuvnmmyVJH/3oR3XqqafqgQce0KmnnqqPfvSjk73bDQitAAAAADBNzZ07Vy9+8Ys1OjracPnatWu1ceNGnXjiiUqSROedd56+8Y1vSJKuu+46nX/++ZKk888//7eX9woTMQEAAABAXS67TLrjjnq3ecwx0qc+VesmH3vsMS1btuy3Py9btkyPPfaYJOnXv/61lixZIklasmSJnnzyyVofu1VUWgEAAABghrHxq74kSXqwJ+WotAIAAABAXWquiFbx2c9+VldffbUk6cYbb9TSCutxLlu2TGvWrPntz2vWrPnt/fbdd1+tXbtWS5Ys0dq1a7V48eLu7HhFVFoBAAAAYAq75JJLdMcdd+iOO+6oFFgl1/a7xx576Ec/+pHSNNUXv/hFnX322ZKks846S1/4whckSV/4whd+e3mvUGkFAAAAgGls+fLl2rhxo3bs2KFvfOMb+ta3vqXDDjtMV155pS644AJt27ZNZ555ps4880xJ0p/+6Z/qda97na655hodcMAB+qd/+qee7j+hFQAAAACmsYcffjh6+apVq3T33Xc3Xb5w4UJ95zvf6fJeVUd7MAAAAACgbxFaAQAAAAB9i9AKAAAAAOhbhFYAAAAA6FBs3VM0a+d1IrQCAAAAQAdGR0e1bt06gmuJNE21bt06jY6OtnQ/Zg8GAAAAgA4sW7ZMa9as0VNPPdXrXel7o6OjWrZsWUv3IbQCAAAAQAeGh4e1YsWKXu/GtEV7MAAAAACgbxFaAQAAAAB9i9AKAAAAAOhbyVSZ4SpJkqck/Xev96PAIklP93onAPFZRH/gc4h+wWcR/YDPIfpFP38WD0zTdJ/YFVMmtPa7JElWp2m6qtf7AfBZRD/gc4h+wWcR/YDPIfrFVP0s0h4MAAAAAOhbhFYAAAAAQN8itNbnql7vADCBzyL6AZ9D9As+i+gHfA7RL6bkZ5ExrQAAAADw/7dzN6FWVWEYx/8PmplGqUVRaqgklQSlhNkHIRpmJdnAyCgSM5oEWRRhTaSBgyCyonDiRxZhhUlJg0JMqElSJpRloVjoLVPBj6Igk54Ge129XW/W9XjP2Z2eH1zOWWuvwTrw3nef9+y1VtRWnrRGREREREREbaVoPQUkTZf0jaTtkha0ej7RviSNlLRB0lZJX0qaX/qHSVonaVt5HVr6JemFEpufS5rQ2k8Q7URSP0mbJb1b2qMlbSxx+IakAaX/9NLeXq6PauW8o71IGiJptaSvS268Jjkxmk3SI+W+vEXSKkkDkxOjGSQtl7RX0pYufb3OgZLmlPHbJM1pxWc5kRStDZLUD3gJuBkYB9wlaVxrZxVt7AjwqO3LgEnAgyXeFgDrbY8F1pc2VHE5tvw9ACxp/pSjjc0HtnZpPw0sLnF4AJhX+ucBB2xfDCwu4yJOleeB92xfClxBFZPJidE0koYDDwFX2b4c6AfMJjkxmuNlYHq3vl7lQEnDgIXA1cBEYGFnoVsXKVobNxHYbnuH7cPA68DMFs8p2pTt3bY/K+9/pvpyNpwq5laWYSuB28v7mcArrnwMDJF0QZOnHW1I0gjgVmBpaQuYAqwuQ7rHYWd8rgamlvERDZF0FnADsAzA9mHbB0lOjObrD5whqT8wCNhNcmI0ge0Pgf3dunubA28C1tneb/sAsI7jC+GWStHauOHAri7tjtIX0afKcqLxwEbgfNu7oSpsgfPKsMRn9JXngMeBP0r7HOCg7SOl3TXWjsZhuX6ojI9o1BhgH7CiLFVfKmkwyYnRRLa/B54BdlIVq4eATSQnRuv0NgfWPjemaG1cT7+M5Ujm6FOSzgTeAh62/dOJhvbQl/iMhkiaAey1valrdw9D/S+uRTSiPzABWGJ7PPALx5bB9SSxGKdcWUY5ExgNXAgMplqG2V1yYrTa38Ve7WMyRWvjOoCRXdojgB9aNJf4H5B0GlXB+prtNaV7T+cSt/K6t/QnPqMvXAfcJuk7qi0RU6ievA4pS+Pgr7F2NA7L9bM5filTxMnoADpsbyzt1VRFbHJiNNONwLe299n+HVgDXEtyYrROb3Ng7XNjitbGfQKMLSfEDaDaeL+2xXOKNlX2vCwDttp+tsultUDnSW9zgHe69N9bToubBBzqXC4ScbJsP2F7hO1RVDnvA9t3AxuAWWVY9zjsjM9ZZXytfsGN/ybbPwK7JF1SuqYCX5GcGM21E5gkaVC5T3fGYXJitEpvc+D7wDRJQ8vKgWmlrzaU/5HGSbqF6ilDP2C57UUtnlK0KUnXAx8BX3BsL+GTVPta3wQuorp53mF7f7l5vki1mf5XYK7tT5s+8WhbkiYDj9meIWkM1ZPXYcBm4B7bv0kaCLxKtQd7PzDb9o5WzTnai6QrqQ4EGwDsAOZS/SifnBhNI+kp4E6qU/43A/dT7QlMTow+JWkVMBk4F9hDdQrw2/QyB0q6j+o7JcAi2yua+Tn+SYrWiIiIiIiIqK0sD46IiIiIiIjaStEaERERERERtZWiNSIiIiIiImorRWtERERERETUVorWiIiIiIiIqK0UrREREREREVFbKVojIiIiIiKitlK0RkRERERERG39CbtTtFHjZJqMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "env = gym.make('Acrobot-v1')\n",
    "import random\n",
    "\n",
    "#n_actions = env.action_space.n\n",
    "#n_states = env.observation_space.shape[0]\n",
    "#print(\"Action space size: \", n_actions)\n",
    "#print(\"State space size: \", n_states)\n",
    "#print('states high value:')\n",
    "#print(env.observation_space.high[0]) # 1  cos of first rotational joint \n",
    "#print(env.observation_space.high[1])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[2])  # 1 cos of first rotational joint\n",
    "#print(env.observation_space.high[3])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[4])  # 12.566371 angular velocity of 1st joint\n",
    "#print(env.observation_space.high[5])  # 28.274334 angular velocity of 2nd joint\n",
    "\n",
    "#print('states low value:')\n",
    "#print(env.observation_space.low[0])   #-4.8\n",
    "#print(env.observation_space.low[1])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[2])  #-0.41887903\n",
    "#print(env.observation_space.low[3])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[4])\n",
    "#print(env.observation_space.low[5])\n",
    "#[cos(theta1), sin(theta1), cos(theta2), sin(theta2), theta_dot1, theta_dot2]\n",
    "\n",
    "class Qlearning():  #change the buckets #(self,bins=(1, 1, 1, 1, 12, 24) #(1,1,3,3,6,12) #(2, 2, 2, 2, 8, 12), (1, 1, 1, 1, 6, 11)\n",
    "    def __init__(self,bins=(1, 1, 1, 1, 6, 13), max_episodes = 2000, max_steps = 500, min_epsilon=0.01, gamma = 1.0, epsilon = 1.0, decay = 25, action_space = env.action_space.n, env = gym.make('Acrobot-v1')):   #max_env_steps=None\n",
    "        self.bins = bins \n",
    "        self.max_episodes = max_episodes\n",
    "        self.max_steps = max_steps #per episode\n",
    "        self.min_epsilon = min_epsilon #\n",
    "        self.epsilon = epsilon\n",
    "        self.gamma = gamma  \n",
    "        self.decay = decay\n",
    "        self.action_space = action_space\n",
    "        self.env = env\n",
    "        self.QTable = np.zeros((self.bins + (self.action_space,))) \n",
    "        self.alpha = 1 # learning rate\n",
    "        self.beta = 0.5\n",
    "        self.actions = None\n",
    "        self.tau = 1000    # tau --> 0 pure exploitation tau --> infinity pure exploration\n",
    "        self.tau_decay = True\n",
    "        self.decay_factor_tau = 1.0\n",
    "\n",
    "    def discretize(self, state):\n",
    "        # observation = obs, reward, done, info = self.env.step(action)--> in training\n",
    "        # define upper and lower bounds for each state value\n",
    "        #it is necessary to give finite bounds and reduce the range of the cart velocity and pole velocity at tip – i.e. [-0.5, +0.5] and [-50, +50],\n",
    "        #respectively – in order to be able to discretise.\n",
    "        upper_bounds = [1.0, 1.0, 1.0, 1.0, env.observation_space.high[4], env.observation_space.high[5]]  \n",
    "        lower_bounds = [-1.0,-1.0,-1.0,-1.0, env.observation_space.low[4], env.observation_space.low[5]]\n",
    "        descretizedList = list()\n",
    "        for i in  range(len(state)): #state = tuple (0,0,X,X)--> aka the state space  #scaling factor\n",
    "            ratios = (state[i] + abs(lower_bounds[i])) / (upper_bounds[i] - lower_bounds[i]) # (state+lower / bin_width) = bucket size\n",
    "            new_obs = int(round((self.bins[i] - 1) * ratios)) # makes the first two buckets 0, and #bucket_lower := min_x + bucket × bucket size\n",
    "            new_obs = min(self.bins[i] - 1, max(0, new_obs)) #no matter what the buckets-1 is going to be 0 or greater than 0\n",
    "            #this makes sure that the first two components of the tuple is 0\n",
    "            #why are we taking the min between the bucket-1 and the new_obs\n",
    "            descretizedList.append(new_obs)\n",
    "        return tuple(descretizedList)\n",
    "\n",
    "\n",
    "    def Boltzmann(self, state, tau):\n",
    "        qList = self.QTable[state] #moves = self.q_matrix[pos_index]\n",
    "        self.actions = [i for i in range(0, env.action_space.n)]\n",
    "        if self.tau > 0.0:\n",
    "            action_probs_numes = []\n",
    "            denom = 0\n",
    "            for q in qList:\n",
    "                val = math.exp(q / self.tau)\n",
    "                action_probs_numes.append(val)\n",
    "                denom += val  # summation of the values\n",
    "            action_probs = []\n",
    "            for x in action_probs_numes:\n",
    "                probs = x / denom \n",
    "                action_probs.append(probs)    \n",
    "            prob_sum = 0\n",
    "            action = random.choices(self.actions, weights=action_probs, k=1)[0] # the weights give a weight to correspond \n",
    "        else:\n",
    "            action = np.argmax(self.QTable[state])\n",
    "        return action\n",
    "\n",
    "    def action_policy(self, state, policy):\n",
    "        return policy[state]\n",
    "    \n",
    "    def Q_Update(self, state, action, reward, new_state, step_size):\n",
    "        ''' Update the Q-values'''\n",
    "        # self.QTable[old_state][action] += alpha * (reward + self.gamma * np.max(self.Q[state_new]) - self.Q[state_old][action])\n",
    "        self.QTable[state][action] += step_size * (reward + self.gamma * (np.max(self.QTable[new_state])) - self.QTable[state][action])\n",
    "        return\n",
    "    \n",
    "    def decay_tau(self, t):          \n",
    "        if self.tau_decay is True:\n",
    "            #print(t)\n",
    "            new_tau = self.tau - self.decay_factor_tau\n",
    "        if new_tau < 0.0:\n",
    "            self.tau = 0.0\n",
    "        else:\n",
    "            self.tau = new_tau\n",
    "        return new_tau\n",
    "\n",
    "    def decay_step_size(self, t):\n",
    "        if t == 0:\n",
    "            step_size = 1.0\n",
    "        elif t > 0:\n",
    "            step_size = self.alpha / (t ** self.beta)  \n",
    "        return step_size\n",
    "\n",
    "#1-ln(time unit/decay)\n",
    "def learning(Qlearning):\n",
    "    rewards = []\n",
    "    alphaList = []\n",
    "    epsilonList = []\n",
    "    for e in range(Qlearning.max_episodes):  \n",
    "        state = Qlearning.discretize(env.reset())\n",
    "        tau = Qlearning.decay_tau(e)\n",
    "        step_size = 0.01 \n",
    "        i = 0\n",
    "        for t in range(Qlearning.max_steps):\n",
    "            if e % 2 == 0:\n",
    "                action = Qlearning.Boltzmann(state, tau)\n",
    "            if e % 2 ==1:\n",
    "                action = Qlearning.action_policy(state, policy)\n",
    "            new_state, reward, done, info = env.step(action)\n",
    "            new_state = Qlearning.discretize(new_state)\n",
    "            Qlearning.Q_Update(state, action, reward, new_state, step_size)\n",
    "            state = new_state\n",
    "            i += reward \n",
    "            if done:\n",
    "                break\n",
    "        ########### Policy Extraction ##########\n",
    "        stateTuple = list()\n",
    "        stateList = []\n",
    "        actionsList = []\n",
    "        states = []\n",
    "        for list1 in Qlearning.QTable:\n",
    "            for nextList in list1:\n",
    "                for nextList1 in nextList: \n",
    "                    for nextList2 in nextList1:\n",
    "                        for nextList3 in nextList2:\n",
    "                            for nextList4 in nextList3:\n",
    "                                actions = np.argmax(nextList4)\n",
    "                                actionsList.append(actions)\n",
    "        observations = np.argwhere(Qlearning.QTable>=-500)\n",
    "        j = 0\n",
    "        for obsList in observations:\n",
    "            stateTuple = (obsList[0], obsList[1], obsList[2], obsList[3], obsList[4], obsList[5])\n",
    "            stateList.append(stateTuple)\n",
    "        del stateList[1::3] \n",
    "        del stateList[1::2]\n",
    "        policy = dict(zip(stateList, actionsList))\n",
    "        if e % 2 == 1:\n",
    "            rewards.append(i)\n",
    "            alphaList.append(step_size)\n",
    "            epsilonList.append(tau)\n",
    "            mean_rewards =  np.mean(rewards)\n",
    "    return rewards, alphaList, epsilonList\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    ''' Run main program. '''\n",
    "    #main()\n",
    "    solve = Qlearning()\n",
    "    listof_100 = []\n",
    "    trajectory = []\n",
    "    for i in range(50):\n",
    "        solve = Qlearning()\n",
    "        rewards, alpha, tau = learning(solve)\n",
    "        trajectory.append(rewards)\n",
    "        print(i)\n",
    "    for episode in rewards:\n",
    "        listof_100.append(-1*100)\n",
    "    a = np.array(trajectory)\n",
    "    final = np.mean(a, axis=0)\n",
    "    meanRewards = []\n",
    "    print(max(final))\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.title('Acrobot-v1')\n",
    "    \"\"\"plt1 = fig.add_subplot(311)\n",
    "    plt1.plot(epsilon,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Epsilon')\n",
    "    plt1.set(title='Epsilon Plot',\n",
    "            ylabel='Epsilon',\n",
    "            xlabel='episodes')\n",
    "    plt2 = fig.add_subplot(312)\n",
    "    plt2.plot(alpha,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Alpha')\n",
    "    plt2.set(title='Step Size Plot',\n",
    "            ylabel='Alpha',\n",
    "            xlabel='episodes')\n",
    "    plt3 = fig.add_subplot(313)\"\"\"\n",
    "    plt.plot(final,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='rewards')\n",
    "    plt.plot(listof_100,\n",
    "             color = 'red',\n",
    "             label = \"- 100\")\n",
    "    \"\"\"plt3.set(title='Rewards',\n",
    "            ylabel='Rewards',\n",
    "            xlabel='episodes')\"\"\"\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Continually diminishing Step Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "49\n",
      "-80.56\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "env = gym.make('Acrobot-v1')\n",
    "import random\n",
    "\n",
    "#n_actions = env.action_space.n\n",
    "#n_states = env.observation_space.shape[0]\n",
    "#print(\"Action space size: \", n_actions)\n",
    "#print(\"State space size: \", n_states)\n",
    "#print('states high value:')\n",
    "#print(env.observation_space.high[0]) # 1  cos of first rotational joint \n",
    "#print(env.observation_space.high[1])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[2])  # 1 cos of first rotational joint\n",
    "#print(env.observation_space.high[3])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[4])  # 12.566371 angular velocity of 1st joint\n",
    "#print(env.observation_space.high[5])  # 28.274334 angular velocity of 2nd joint\n",
    "\n",
    "#print('states low value:')\n",
    "#print(env.observation_space.low[0])   #-4.8\n",
    "#print(env.observation_space.low[1])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[2])  #-0.41887903\n",
    "#print(env.observation_space.low[3])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[4])\n",
    "#print(env.observation_space.low[5])\n",
    "#[cos(theta1), sin(theta1), cos(theta2), sin(theta2), theta_dot1, theta_dot2]\n",
    "\n",
    "class Qlearning():  #change the buckets #(self,bins=(1, 1, 1, 1, 12, 24) #(1,1,3,3,6,12) #(2, 2, 2, 2, 8, 12), (1, 1, 1, 1, 6, 11)\n",
    "    def __init__(self,bins=(1, 1, 1, 1, 6, 13), max_episodes = 2000, max_steps = 500, min_epsilon=0.01, gamma = 1.0, epsilon = 1.0, decay = 25, action_space = env.action_space.n, env = gym.make('Acrobot-v1')):   #max_env_steps=None\n",
    "        self.bins = bins \n",
    "        self.max_episodes = max_episodes\n",
    "        self.max_steps = max_steps #per episode\n",
    "        self.min_epsilon = min_epsilon #\n",
    "        self.epsilon = epsilon\n",
    "        self.gamma = gamma  \n",
    "        self.decay = decay\n",
    "        self.action_space = action_space\n",
    "        self.env = env\n",
    "        self.QTable = np.zeros((self.bins + (self.action_space,))) \n",
    "        self.alpha = 1 # learning rate\n",
    "        self.beta = 0.5\n",
    "        self.actions = None\n",
    "        self.tau = 1000    # tau --> 0 pure exploitation tau --> infinity pure exploration\n",
    "        self.tau_decay = True\n",
    "        self.decay_factor_tau = 1.0\n",
    "\n",
    "    def discretize(self, state):\n",
    "        # observation = obs, reward, done, info = self.env.step(action)--> in training\n",
    "        # define upper and lower bounds for each state value\n",
    "        #it is necessary to give finite bounds and reduce the range of the cart velocity and pole velocity at tip – i.e. [-0.5, +0.5] and [-50, +50],\n",
    "        #respectively – in order to be able to discretise.\n",
    "        upper_bounds = [1.0, 1.0, 1.0, 1.0, env.observation_space.high[4], env.observation_space.high[5]]  \n",
    "        lower_bounds = [-1.0,-1.0,-1.0,-1.0, env.observation_space.low[4], env.observation_space.low[5]]\n",
    "        descretizedList = list()\n",
    "        for i in  range(len(state)): #state = tuple (0,0,X,X)--> aka the state space  #scaling factor\n",
    "            ratios = (state[i] + abs(lower_bounds[i])) / (upper_bounds[i] - lower_bounds[i]) # (state+lower / bin_width) = bucket size\n",
    "            new_obs = int(round((self.bins[i] - 1) * ratios)) # makes the first two buckets 0, and #bucket_lower := min_x + bucket × bucket size\n",
    "            new_obs = min(self.bins[i] - 1, max(0, new_obs)) #no matter what the buckets-1 is going to be 0 or greater than 0\n",
    "            #this makes sure that the first two components of the tuple is 0\n",
    "            #why are we taking the min between the bucket-1 and the new_obs\n",
    "            descretizedList.append(new_obs)\n",
    "        return tuple(descretizedList)\n",
    "\n",
    "\n",
    "    def Boltzmann(self, state, tau):\n",
    "        qList = self.QTable[state] #moves = self.q_matrix[pos_index]\n",
    "        self.actions = [i for i in range(0, env.action_space.n)]\n",
    "        if self.tau > 0.0:\n",
    "            action_probs_numes = []\n",
    "            denom = 0\n",
    "            for q in qList:\n",
    "                val = math.exp(q / self.tau)\n",
    "                action_probs_numes.append(val)\n",
    "                denom += val  # summation of the values\n",
    "            action_probs = []\n",
    "            for x in action_probs_numes:\n",
    "                probs = x / denom \n",
    "                action_probs.append(probs)    \n",
    "            prob_sum = 0\n",
    "            action = random.choices(self.actions, weights=action_probs, k=1)[0] # the weights give a weight to correspond \n",
    "        else:\n",
    "            action = np.argmax(self.QTable[state])\n",
    "        return action\n",
    "\n",
    "    def action_policy(self, state, policy):\n",
    "        return policy[state]\n",
    "    \n",
    "    def Q_Update(self, state, action, reward, new_state, step_size):\n",
    "        ''' Update the Q-values'''\n",
    "        # self.QTable[old_state][action] += alpha * (reward + self.gamma * np.max(self.Q[state_new]) - self.Q[state_old][action])\n",
    "        self.QTable[state][action] += step_size * (reward + self.gamma * (np.max(self.QTable[new_state])) - self.QTable[state][action])\n",
    "        return\n",
    "    \n",
    "    def decay_tau(self, t):          \n",
    "        if self.tau_decay is True:\n",
    "            #print(t)\n",
    "            new_tau = self.tau - self.decay_factor_tau\n",
    "        if new_tau < 0.0:\n",
    "            self.tau = 0.0\n",
    "        else:\n",
    "            self.tau = new_tau\n",
    "        return new_tau\n",
    "\n",
    "    def decay_step_size(self, tt, e, t):\n",
    "        num = self.alpha\n",
    "        dem = tt**self.beta\n",
    "        if e == 0 and t == 0:\n",
    "            step_size = 1\n",
    "        elif tt > 0:\n",
    "            step_size = num / dem\n",
    "        return step_size\n",
    "\n",
    "#1-ln(time unit/decay)\n",
    "def learning(Qlearning):\n",
    "    rewards = []\n",
    "    alphaList = []\n",
    "    epsilonList = []\n",
    "    tt = 0\n",
    "    for e in range(Qlearning.max_episodes):  \n",
    "        state = Qlearning.discretize(env.reset())\n",
    "        tau = Qlearning.decay_tau(e)\n",
    "        i = 0\n",
    "        for t in range(Qlearning.max_steps):\n",
    "            step_size = Qlearning.decay_step_size(tt,e,t)\n",
    "            tt+=1\n",
    "            if e % 2 == 0:\n",
    "                action = Qlearning.Boltzmann(state, tau)\n",
    "            if e % 2 ==1:\n",
    "                action = Qlearning.action_policy(state, policy)\n",
    "            new_state, reward, done, info = env.step(action)\n",
    "            new_state = Qlearning.discretize(new_state)\n",
    "            Qlearning.Q_Update(state, action, reward, new_state, step_size)\n",
    "            state = new_state\n",
    "            i += reward \n",
    "            if done:\n",
    "                break\n",
    "        ########### Policy Extraction ##########\n",
    "        stateTuple = list()\n",
    "        stateList = []\n",
    "        actionsList = []\n",
    "        states = []\n",
    "        for list1 in Qlearning.QTable:\n",
    "            for nextList in list1:\n",
    "                for nextList1 in nextList: \n",
    "                    for nextList2 in nextList1:\n",
    "                        for nextList3 in nextList2:\n",
    "                            for nextList4 in nextList3:\n",
    "                                actions = np.argmax(nextList4)\n",
    "                                actionsList.append(actions)\n",
    "        observations = np.argwhere(Qlearning.QTable>=-500)\n",
    "        j = 0\n",
    "        for obsList in observations:\n",
    "            stateTuple = (obsList[0], obsList[1], obsList[2], obsList[3], obsList[4], obsList[5])\n",
    "            stateList.append(stateTuple)\n",
    "        del stateList[1::3] \n",
    "        del stateList[1::2]\n",
    "        policy = dict(zip(stateList, actionsList))\n",
    "        if e % 2 == 1:\n",
    "            rewards.append(i)\n",
    "            alphaList.append(step_size)\n",
    "            epsilonList.append(tau)\n",
    "            mean_rewards =  np.mean(rewards)\n",
    "    return rewards, alphaList, epsilonList\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    ''' Run main program. '''\n",
    "    #main()\n",
    "    solve = Qlearning()\n",
    "    listof_100 = []\n",
    "    trajectory = []\n",
    "    for i in range(50):\n",
    "        solve = Qlearning()\n",
    "        rewards, alpha, tau = learning(solve)\n",
    "        trajectory.append(rewards)\n",
    "        print(i)\n",
    "    for episode in rewards:\n",
    "        listof_100.append(-1*100)\n",
    "    a = np.array(trajectory)\n",
    "    final = np.mean(a, axis=0)\n",
    "    meanRewards = []\n",
    "    print(max(final))\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.title('Acrobot-v1')\n",
    "    \"\"\"plt1 = fig.add_subplot(311)\n",
    "    plt1.plot(epsilon,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Epsilon')\n",
    "    plt1.set(title='Epsilon Plot',\n",
    "            ylabel='Epsilon',\n",
    "            xlabel='episodes')\n",
    "    plt2 = fig.add_subplot(312)\n",
    "    plt2.plot(alpha,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Alpha')\n",
    "    plt2.set(title='Step Size Plot',\n",
    "            ylabel='Alpha',\n",
    "            xlabel='episodes')\n",
    "    plt3 = fig.add_subplot(313)\"\"\"\n",
    "    plt.plot(final,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='rewards')\n",
    "    plt.plot(listof_100,\n",
    "             color = 'red',\n",
    "             label = \"- 100\")\n",
    "    \"\"\"plt3.set(title='Rewards',\n",
    "            ylabel='Rewards',\n",
    "            xlabel='episodes')\"\"\"\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Restarting Diminishing Step Size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "-113.88\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1152x648 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import gym\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import deque\n",
    "env = gym.make('Acrobot-v1')\n",
    "import random\n",
    "\n",
    "#n_actions = env.action_space.n\n",
    "#n_states = env.observation_space.shape[0]\n",
    "#print(\"Action space size: \", n_actions)\n",
    "#print(\"State space size: \", n_states)\n",
    "#print('states high value:')\n",
    "#print(env.observation_space.high[0]) # 1  cos of first rotational joint \n",
    "#print(env.observation_space.high[1])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[2])  # 1 cos of first rotational joint\n",
    "#print(env.observation_space.high[3])  # 1 sin of first rotational joint\n",
    "#print(env.observation_space.high[4])  # 12.566371 angular velocity of 1st joint\n",
    "#print(env.observation_space.high[5])  # 28.274334 angular velocity of 2nd joint\n",
    "\n",
    "#print('states low value:')\n",
    "#print(env.observation_space.low[0])   #-4.8\n",
    "#print(env.observation_space.low[1])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[2])  #-0.41887903\n",
    "#print(env.observation_space.low[3])  #-3.4028235e+38\n",
    "#print(env.observation_space.low[4])\n",
    "#print(env.observation_space.low[5])\n",
    "#[cos(theta1), sin(theta1), cos(theta2), sin(theta2), theta_dot1, theta_dot2]\n",
    "\n",
    "class Qlearning():  #change the buckets #(self,bins=(1, 1, 1, 1, 12, 24) #(1,1,3,3,6,12) #(2, 2, 2, 2, 8, 12), (1, 1, 1, 1, 6, 11)\n",
    "    def __init__(self,bins=(1, 1, 1, 1, 6, 13), max_episodes = 2000, max_steps = 500, min_epsilon=0.01, gamma = 1.0, epsilon = 1.0, decay = 25, action_space = env.action_space.n, env = gym.make('Acrobot-v1')):   #max_env_steps=None\n",
    "        self.bins = bins \n",
    "        self.max_episodes = max_episodes\n",
    "        self.max_steps = max_steps #per episode\n",
    "        self.min_epsilon = min_epsilon #\n",
    "        self.epsilon = epsilon\n",
    "        self.gamma = gamma  \n",
    "        self.decay = decay\n",
    "        self.action_space = action_space\n",
    "        self.env = env\n",
    "        self.QTable = np.zeros((self.bins + (self.action_space,))) \n",
    "        self.alpha = 1 # learning rate\n",
    "        self.beta = 0.5\n",
    "        self.actions = None\n",
    "        self.tau = 1000    # tau --> 0 pure exploitation tau --> infinity pure exploration\n",
    "        self.tau_decay = True\n",
    "        self.decay_factor_tau = 1.0\n",
    "\n",
    "    def discretize(self, state):\n",
    "        # observation = obs, reward, done, info = self.env.step(action)--> in training\n",
    "        # define upper and lower bounds for each state value\n",
    "        #it is necessary to give finite bounds and reduce the range of the cart velocity and pole velocity at tip – i.e. [-0.5, +0.5] and [-50, +50],\n",
    "        #respectively – in order to be able to discretise.\n",
    "        upper_bounds = [1.0, 1.0, 1.0, 1.0, env.observation_space.high[4], env.observation_space.high[5]]  \n",
    "        lower_bounds = [-1.0,-1.0,-1.0,-1.0, env.observation_space.low[4], env.observation_space.low[5]]\n",
    "        descretizedList = list()\n",
    "        for i in  range(len(state)): #state = tuple (0,0,X,X)--> aka the state space  #scaling factor\n",
    "            ratios = (state[i] + abs(lower_bounds[i])) / (upper_bounds[i] - lower_bounds[i]) # (state+lower / bin_width) = bucket size\n",
    "            new_obs = int(round((self.bins[i] - 1) * ratios)) # makes the first two buckets 0, and #bucket_lower := min_x + bucket × bucket size\n",
    "            new_obs = min(self.bins[i] - 1, max(0, new_obs)) #no matter what the buckets-1 is going to be 0 or greater than 0\n",
    "            #this makes sure that the first two components of the tuple is 0\n",
    "            #why are we taking the min between the bucket-1 and the new_obs\n",
    "            descretizedList.append(new_obs)\n",
    "        return tuple(descretizedList)\n",
    "\n",
    "\n",
    "    def Boltzmann(self, state, tau):\n",
    "        qList = self.QTable[state] #moves = self.q_matrix[pos_index]\n",
    "        self.actions = [i for i in range(0, env.action_space.n)]\n",
    "        if self.tau > 0.0:\n",
    "            action_probs_numes = []\n",
    "            denom = 0\n",
    "            for q in qList:\n",
    "                val = math.exp(q / self.tau)\n",
    "                action_probs_numes.append(val)\n",
    "                denom += val  # summation of the values\n",
    "            action_probs = []\n",
    "            for x in action_probs_numes:\n",
    "                probs = x / denom \n",
    "                action_probs.append(probs)    \n",
    "            prob_sum = 0\n",
    "            action = random.choices(self.actions, weights=action_probs, k=1)[0] # the weights give a weight to correspond \n",
    "        else:\n",
    "            action = np.argmax(self.QTable[state])\n",
    "        return action\n",
    "\n",
    "    def action_policy(self, state, policy):\n",
    "        return policy[state]\n",
    "    \n",
    "    def Q_Update(self, state, action, reward, new_state, step_size):\n",
    "        ''' Update the Q-values'''\n",
    "        # self.QTable[old_state][action] += alpha * (reward + self.gamma * np.max(self.Q[state_new]) - self.Q[state_old][action])\n",
    "        self.QTable[state][action] += step_size * (reward + self.gamma * (np.max(self.QTable[new_state])) - self.QTable[state][action])\n",
    "        return\n",
    "    \n",
    "    def decay_tau(self, t):          \n",
    "        if self.tau_decay is True:\n",
    "            #print(t)\n",
    "            new_tau = self.tau - self.decay_factor_tau\n",
    "        if new_tau < 0.0:\n",
    "            self.tau = 0.0\n",
    "        else:\n",
    "            self.tau = new_tau\n",
    "        return new_tau\n",
    "\n",
    "    def decay_step_size(self, t):\n",
    "        if t == 0:\n",
    "            step_size = 1.0\n",
    "        elif t > 0:\n",
    "            step_size = self.alpha / (t ** self.beta)  \n",
    "        return step_size\n",
    "\n",
    "#1-ln(time unit/decay)\n",
    "def learning(Qlearning):\n",
    "    rewards = []\n",
    "    alphaList = []\n",
    "    epsilonList = []\n",
    "    for e in range(Qlearning.max_episodes):  \n",
    "        state = Qlearning.discretize(env.reset())\n",
    "        tau = Qlearning.decay_tau(e)\n",
    "        step_size = 1 #0.01 \n",
    "        i = 0\n",
    "        for t in range(Qlearning.max_steps):\n",
    "            step_size = Qlearning.decay_step_size(t)\n",
    "            if e % 2 == 0:\n",
    "                action = Qlearning.Boltzmann(state, tau)\n",
    "            if e % 2 ==1:\n",
    "                action = Qlearning.action_policy(state, policy)\n",
    "            new_state, reward, done, info = env.step(action)\n",
    "            new_state = Qlearning.discretize(new_state)\n",
    "            Qlearning.Q_Update(state, action, reward, new_state, step_size)\n",
    "            state = new_state\n",
    "            i += reward \n",
    "            if done:\n",
    "                break\n",
    "        ########### Policy Extraction ##########\n",
    "        stateTuple = list()\n",
    "        stateList = []\n",
    "        actionsList = []\n",
    "        states = []\n",
    "        for list1 in Qlearning.QTable:\n",
    "            for nextList in list1:\n",
    "                for nextList1 in nextList: \n",
    "                    for nextList2 in nextList1:\n",
    "                        for nextList3 in nextList2:\n",
    "                            for nextList4 in nextList3:\n",
    "                                actions = np.argmax(nextList4)\n",
    "                                actionsList.append(actions)\n",
    "        observations = np.argwhere(Qlearning.QTable>=-10000)\n",
    "        j = 0\n",
    "        for obsList in observations:\n",
    "            stateTuple = (obsList[0], obsList[1], obsList[2], obsList[3], obsList[4], obsList[5])\n",
    "            stateList.append(stateTuple)\n",
    "        del stateList[1::3] \n",
    "        del stateList[1::2]\n",
    "        policy = dict(zip(stateList, actionsList))\n",
    "        if e % 2 == 1:\n",
    "            rewards.append(i)\n",
    "            alphaList.append(step_size)\n",
    "            epsilonList.append(tau)\n",
    "            mean_rewards =  np.mean(rewards)\n",
    "    return rewards, alphaList, epsilonList\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    ''' Run main program. '''\n",
    "    #main()\n",
    "    solve = Qlearning()\n",
    "    listof_100 = []\n",
    "    trajectory = []\n",
    "    for i in range(50):\n",
    "        solve = Qlearning()\n",
    "        rewards, alpha, tau = learning(solve)\n",
    "        trajectory.append(rewards)\n",
    "        print(i)\n",
    "    for episode in rewards:\n",
    "        listof_100.append(-1*100)\n",
    "    a = np.array(trajectory)\n",
    "    final = np.mean(a, axis=0)\n",
    "    meanRewards = []\n",
    "    print(max(final))\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.title('Acrobot-v1')\n",
    "    \"\"\"plt1 = fig.add_subplot(311)\n",
    "    plt1.plot(epsilon,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Epsilon')\n",
    "    plt1.set(title='Epsilon Plot',\n",
    "            ylabel='Epsilon',\n",
    "            xlabel='episodes')\n",
    "    plt2 = fig.add_subplot(312)\n",
    "    plt2.plot(alpha,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='Alpha')\n",
    "    plt2.set(title='Step Size Plot',\n",
    "            ylabel='Alpha',\n",
    "            xlabel='episodes')\n",
    "    plt3 = fig.add_subplot(313)\"\"\"\n",
    "    plt.plot(final,  # epsilon_hist,\n",
    "             color='b',\n",
    "             label='rewards')\n",
    "    plt.plot(listof_100,\n",
    "             color = 'red',\n",
    "             label = \"- 100\")\n",
    "    \"\"\"plt3.set(title='Rewards',\n",
    "            ylabel='Rewards',\n",
    "            xlabel='episodes')\"\"\"\n",
    "    plt.legend(loc='best')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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