{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ce8377cb",
   "metadata": {},
   "source": [
    "# Learning Outcomes\n",
    "- Quantum Teleportation \n",
    "- Superdense Coding\n",
    "- Quantum Key Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c96e5522",
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "source": [
    "# Quantum Teleportation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79b7b4ed",
   "metadata": {},
   "source": [
    "This notebook demonstrates quantum teleportation. We first use Qiskit's built-in simulators to test our quantum circuit, and then try it out on a real quantum computer.\n",
    "\n",
    "## Contents\n",
    "\n",
    "1. [Overview](#overview)    \n",
    "2. [The Quantum Teleportation Protocol](#how)       \n",
    "3. [Simulating the Teleportation Protocol](#simulating)   \n",
    "    3.1 [How will we Test this Result on a Real Quantum Computer?](#testing)   \n",
    "    3.2 [Using the Statevector Simulator](#simulating-sv)     \n",
    "    3.3 [Using the QASM Simulator](#simulating-qs)  \n",
    "4. [Understanding Quantum Teleportation](#understanding-qt)\n",
    "5. [Teleportation on a Real Quantum Computer](#real_qc)    \n",
    "    5.1 [IBM hardware and Deferred Measurement](#deferred-measurement)    \n",
    "    5.2 [Executing](#executing)    \n",
    "6. [References](#references)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29592466",
   "metadata": {},
   "source": [
    "## 1. Overview <a id='overview'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94dd1371",
   "metadata": {},
   "source": [
    "Alice wants to send quantum information to Bob. Specifically, suppose she wants to send the qubit state\n",
    "$\\vert\\psi\\rangle = \\alpha\\vert0\\rangle + \\beta\\vert1\\rangle$. \n",
    "This entails passing on information about $\\alpha$ and $\\beta$ to Bob.\n",
    "\n",
    "There exists a theorem in quantum mechanics which states that you cannot simply make an exact copy of an unknown quantum state. This is known as the no-cloning theorem. As a result of this we can see that Alice can't simply generate a copy of $\\vert\\psi\\rangle$ and give the copy to Bob. We can only copy classical states (not superpositions).\n",
    "\n",
    "However, by taking advantage of two classical bits and an entangled qubit pair, Alice can transfer her state $\\vert\\psi\\rangle$ to Bob. We call this teleportation because, at the end, Bob will have $\\vert\\psi\\rangle$ and Alice won't anymore."
   ]
  },
  {
   "attachments": {
    "image.png": {
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nQYS0+pzfPkmIdKOWv8cZgSRExvnu59hHgkArlHwnpJEghDDiwW+Cx3fCe7ZS9CPqj9/a9/FbHxAS1sparrLffvtVjxDHKBVBgEQdU+VRf9RLKTjkkEOqBYVXSRAIbfvKSnGt9ri1nnnmmWWjjTYqu+yyS7XEIGl233338vGPf7wuuTnmmGPKD3/4wyrE2+ujnsin6u9k5+Jaub5S9PS9Ja8oFSw88kyJQCKQCCQCicBCR4BMJKMRIT5hEJDTF5yfzdTW73t8yGn9Iqt5otIf9tprr6rTWN7CMIMACb2nraftb9TnWHx3DbID8cGgI/4ZUmUq/ci1rkM6/PM//3PZf//9y6c//ekaN+2OO+6oHrebb755WWONNcq2225bzj///BqDhT4Y7bZ525+2v4N8V5/66aFwCt3O8SBEHMuUCCQCSxFIQiT/EhKBESAQwoyAQToQQoRjCGSECJIkJtTKjzpFndGXyENxIJi5jwoIxiOENYXXhv7qV/S1336p37iQKVxSBVC1PlewNWNtBXD0rVfd6qBsWOerji222KKSIpSaBx54oAZq3WOPParFxdIbQVzh67oY41T192qz17GoS9+RIfofmMAnl8z0Qi2PJQKJQCKQCCw0BMhDMpZ3ptghLcEQMnsUcncq3Nr6Qz6Ty5awXHvttdWr9dhjj62BT+kKSJtu2R3XdbcTx+XkvA+djUcIHenQQw+tgeSNHbHQ6gPddYWeIFeWQUVMkq222qoGYRVw1TIeRiPeJmKR8CZh6OE1EsuPoi9t37rb6ve3Otyn0O/8luT0LaSIMWVKBBKBpQgkIZJ/CYnACBAgZAhDE+cgQwgbx31CMBGWs5miPbm2TOItgWFBOeGEE6qQtp6VkG8VB30Pod5P/9RPeUCqHHnkkeVzn/tcJUUQLMbaXZfy3ceinTinP9xP7UYjSBmPEIKbssA1VXwTbW266aYFQcILhZIRJFPUN0yuD5GiP/L4bkzh8RLlIo9y8TvzRCARSAQSgURgPiNAroVxhy4R8ttxMpdsdmw2U8hW7dAP6AHXXHNNJULEGxOfgw5AR9Cnto9xbeS9+hnn6Gq8KCy34ZlKvxAk3vijzsi764k64rjf6kM4MEIx8IhfIgab+uhedDDGoy984QuVHHHeWOiO2om21DWT5Pqor62H7ubTixDpHk97XX5PBBYyAkmILOS7m2ObMwRCiBA+lIcgQ3TAubkkRLRN6LJK2OJWNHVbyP385z+vioO+RH975dOBZoyCkXENtfWcIKzWz1ImKCZtnVFXHIvfbR7n5LD7xS9+Udfq7rrrrjVSe1imKETWCYsrghjZbrvtqvWF4sJiZFyjTtE3dVNWepEvUWbUbWd9iUAikAgkAonAq4EAuUbudZMhjgch4vtsJvVrn6EFYSAuCF2DcQQRYlLf6jP64ppen+5+KhP6Gv3BEhnEhG135Yw9bT3d13f/VjZSXEdnsYRnyy23rDvaIHS0SUfTd8TIhRdeWEkYwVrPPvvsaghqPUbaeqP+meTqS0JkJgjmtQsVgSREFuqdzXEtVwgQ2uG6qGMhMGfSyagjcoKW1YaQtVML4UrII0YIQOfb5LpI7fc41ubRhnFQHmxhhwwh7LUpQCoXUS6rUXa6Otv6fY/rKECsKQgPW91ZghMEkzHoA88XS2cWLVpUECf6wvVUX6KeqLO7nal+t9dGOce0H4SI323qdU17Pr8nAolAIpAIJALzGYGQe/IgRLp1ipmOr20j5LwYIYwtlvsyfiBCwkgSsjfyydrvdd4xOhldQ930JR6q6rcbDUJEUm6YFG3qK9KDPoNs6daRkCaMVbx4LQkWfyQCtzoH46hr2L60/VdHEiItIvk9EViKQBIi+ZeQCMwBAibUo4wh0gpI35EIsTxGhHXbw1mvGgSBIc5EmBLKxsBDIwKystKEmypPlEsvvfTfCfthoVUv0sU6W0tjjKNbMQiFSbs77LBD+Yd/+Ie6Y44+TqYwDYuBsfO60WamRCARSAQSgURgHBEgQ8lBS0JGSYio10ediIpHHnmkGlqOP/74csEFF1Sygl4wbOrWH+hjiIiTTz65LtMVs8y4BE9HjvCAnUmK8cgtxznssMPqdr123NNO2x/f9ednP/tZNQLReywdtmy4NcSoaxRJWzCm12RKBBKBpQgkIZJ/CYnAHCDQTYjMtMkQtuol2LhiWhYjKCnPCUK9FbgzFaTqQgjwBLGdLvfVEOrOIURYccL6MYrxsY7w/OBKysvFWNtx+K5t5AfLDsVpnXXWqeuLeclE0LBR4KDtIETaPsx0nHl9IpAIJAKJQCIwXxAg/2aLEFGv5SL33XdfESxVAFLB1nk0aHcmsjeulyNWBGHlgaodxiR6gkR34jEyU0JEXdGmuuko4pPwBEGQxLnIlfExVvqVZTZis9HneK3Qh5QdRaIzJiEyCiSzjoWEQBIiC+lu5liWSwQIMYKeADJ5H0VSJ+FJeSC4RStngRB/g7DvJTh7Heu3L/rOU8O2ui0ZEv0Q8d0HCSHNpK24Xh2UCFvxnnHGGa9QiqJdeXz0UQDZDTbYoAYyu/XWWys+cIoy8kGTa9w/ihJPnGHqGLTNLJ8IJAKJQCKQCCxvCJB/5OCojB8xPjJW4HLLRXh7Mr74HfI78ig/TK4OHwQDY4tA8+KTGFPIdR4ZjEt33333ME3Ua6K+qFPOqMJoJJAqHSr60paN78oiTcRMWXvttat+hySC+ygS0oXXLcwzJQKJwFIEkhDJv4REYJYQCGGoegJulEtmCFOC+/rrr69ESMTvIOBCqLbtt98HGa7rECzqR7gQ5GGpiHb0xbIVCgwhKw3bXvQt6qYAUE723HPPwtU0jk+WI5wef/zxctxxx1VihELhN/z1c5ikrSREhkEur0kEEoFEIBFYSAiEPGyX4850fOSrWGECpvJyNfkPD4ZuWT9sW+qhA1gac+KJJ9ZlxaEbOCfJESTnnHNOXa4Sx4dps73Wdx/tiXvGK4XxKI5HHn3wW19hQOfaeeeda6w0seEcGzapV0pCZFgE87qFjEASIgv57ubYlhsECHxCyIS9FX79djCukZvcUx6QIXZ4ueeee5YJ137rm6pctEUgI3F4XfBA4XHRS4grhzDh2tmen6qN6c61fbj33nvrNniUmMBvsusDH94c+rTVVluVQw89tLrdwi3qbfPJ6orjyrp/3GrTQyRQyTwRSAQSgURg3BAgDxlJYieUQcfveilksAm+JbHihNhSt40BNmjdU5Wnp+jzueeeW4kXMUqMo036hBDRF8Fco69tmWG/q4sxSWDVrbfeuhIu+hQ49GorrhHr5KijjqqBWS25YQxrr+23T9EGPQ0W9JpMiUAisBSBJETyLyERmAMERkGIEIAm5HZT4VYqbofYIdORBMMMj+CkqFhniwyxHCYUIOfaj37pj2CrYTUKwTtM23FNtKFdQc54ibCwhCIQ5do8rlGGyykS5/Of/3yN3i7ILPzi+ig7XV+dd/9YlpIQadHO74lAIpAIJALjhAB5SA5aMkOWDpvUY2JPRiMpyOff//731eCjzunk8iDtqotxhxHJlroIBnpTr4SQ4SFCzxp1H+BlV5u99967nHbaabUPrT7Sqz/6gLixzOf000+vcUXEVmEUG1YfQYi4f92EUK/281giMC4IJCEyLnc6x/mqIjATQoRAJDR5mIg6jqBgwYio6M6PUnADiqAUj4TQFr+DomIM0Vab65slMywfQYjMFOy2fp4d4qQgRK666qplfejVRnud7wT/7bffXq/dcccdy2233VZxbJUQ5aZL+pAeItOhlOcTgUQgEUgEFjIC5CX9YCaEiDqQIQwpApvecccdVVaHXIZfP3J5OpzV4YMMoUPY0lZOl5osIUQQNLFEd7Jygx6PvsDt/PPPLzvttFPVKVq9qledcR1sxFRxrV1oBJEXPJ7XyaDJ+JMQGRS1LL/QEUhCZKHf4RzfcoHATAgRgtDEXpAvZAgrAbfO7iUgoxqo9kz+eXwIAMYrQ/8d9wkBHbljAq7aJpegdXymKepWj++sI5bM7LffflN6xMR1bU5h4JJrd5ztttuukiLd3i7T9RfWlJFhLTLT1Z/nE4FEIBFIBBKB5R0BsnVQQiTksbGRpbw36Rfikt1yyy2Tep/OFAvtktmMO2J3nHfeeXW3ODrLZImhSdwyS3VdP6oUGMCO98nmm29ejTXImqlSXCfXb0YnxqdNNtlkmbfLoKQI71/10OsyJQKJwFIEkhDJv4REYA4QaAkRzU0naFshiGQgnO1Lz3IRk/lucmLYYbR98R35wpPiwAMPrPFDuttp+xbfv/Od71TFJgiRts5h+hX1Rk6AI10222yz6hkzmUIT7cZ1kVNCkCoIlW233baOi0IQY5uuj5Q42+6qJ+qc7po8nwgkAolAIpAILCQEyL9hCZGQozfffHPZd999a5wOsj1kanc+U9zId8YdetMBBxxQjRph3OlVt/Z5rvBEFdjV71Gk7nExaPFWsXwntuCdrJ3ua/2GP8/XTTfdtAaH5SmC+OknuR6BQs9LQqQfxLLMuCCQhMi43Okc56uKQDchMlVnCPH4UBYE9+JWyipg3atzo0ytwKWwIF+4Y9qhZSqPiLhOf6677rqCFGkJEedHlfRLcFdWEfmgglxf9JPyQTHaZpttqussxSDG0ebd/XYtQiTaHeXYutvK34lAIpAIJAKJwPKIANlHL+h3yUzI1ZChPEMOOuigGktjKv1iJmOPNukjyBfb+P7sZz9bpj9NJr/1UUB28dlGSYgYS/RJDjvBUREaTzzxxMA6nTr01RLqLbfcsu5a8/DDD1fvG8cnG19gSu+BDb0qUyKQCCxFIAmR/EtIBGYRgRBMBA/XyPAw0GSc69W8c8reeeed5eijj67khOsdn+q6XnVNdyzqlFMGWFNsW2uJCOHq0yvFdc7bDu673/1uDcQax+WjSuoi8HmtnHDCCVWxGaZu9RijoGbW8ArkhuRo+9yr3+4fPNyTTIlAIpAIJAKJwDgiQD6Sg4PEC3ONOGSMOpbhWsIaZEgre0eFJ52EzLbM+JBDDqntkvOhy/SS8dp23JIZHiK8LiYrN2w/Y6zGTvdYZZVVqgFq0MD4UY/7gPCxaw0jlr7Hucn66DxDW3qITIZQHh9XBJIQGdc7n+OeEwQIH4lwJoQIsDgWeXdHHCe4KQ2iifvwTphOmHfX0+9v7fno24033liOOOKIanloiYJedUU/lbOcxTIbY5ScG2VSH0JCMFkWEcJ80DaU99Hfhx56qOy1116VGKE0hbIUZbr73hIig7bbXVf+TgQSgUQgEUgE5iMC5N+ghEh4auyxxx51VxkeCvSZkKWTyd1h8VGfpTJ2p/vHf/zHf7dNbbTb1u+YPomZxkMEITLKFG3K6RPaWXvttatnrWXQcb6fNpWND2yvvvrquhT41FNPnXYJjvrpaRlDpB+ks8w4IZCEyDjd7Rzrq4aACTfBNdlWb9ExQo5Q5g1x8cUXl5NPPrlur9aSIYMIzqh3qjwEKwVAe93b507WXlxnbKLF8xIhaCcrP1Uf+jmHBLFF3+qrr15EgqdUDJP0z32wFOmLX/xitSA98sgjyxSMXv0PQqS1ag3Tdl6TCCQCiUAikAjMVwTIR3Kw3yUzZK2dXRhaLK0NzxL1xAcWveTusBhpU1u8a++5556+vECjD2KN0b0sHR5l6h4rEoS3jF38eHYMklqsfHcvBILdaqutyje+8Y1/p4e1bWuHnqZ9ulumRCARWIpAEiL5l5AIzAECBA8hFBPq7iZDwCE+uJYSyJatIClmW2hpE1ljTeuhhx5aI7JHf7r72f4OIctadOGFF1bXzZYQ6aeOtr6pvqsLdrw5Vltttbolnt/DpOi3MVvmY32xHWzgjvjo1e8kRIZBOq9JBBKBRCARWEgIkI90kghK3mtsIUPJTbE7yNcrrriienmG/I0yva6fyTH1Pvjgg3UHGyRBEDD91Olaxii70WgEdHEAACAASURBVPDQnc1EVzrllFOql6pdcGaCh2stBf7a175Wd9JjOKLfOO5Dx2vrt/w6PURm8+5m3fMRgSRE5uNdyz7PCwRCAMkpBtxEKRJxPAbhtw+hRUgKTnrsscdWD4bpPEqijpnkiAVWFHE1LJnRh35S9Nv1559/ft12NwiRONdPPf2UUR8MeXJssMEGdY1vv/3srj/6Jmcl4W5qGQ4vF14o7kN36iZEus/n70QgEUgEEoFEYBwQIA9jwt1rvCFjeT4wtIhLxvMiJubOjzJFe3KTfe0JRI+MiTb7ac/1yJRzzjln5B4i3e3T7ehbds7jjQLTYXFxnevhfeSRR5add965EjqT6WMwSg+R7juSv8cdgSRExv0vIMc/awiEcAthRQjxppDac777IEweeOCBKshvueWWKRWOUXWassAzwjpb1gpWhujbdG1Ev40JIXL99ddXMiWOT3f9MOcJ/N12260GmSXQh0mhIEU/jZlFyHreu+66q96H7nopG7bjo8QEPpF3l83fiUAikAgkAonAQkSA3JvOQ4SMNRm/5pprqm6BZIgJf8jdUWITsli72tpvv/2qYaklBPppTz3ii4k9MtseIjBE2Hzyk5+swfNDN+ynn91lAlN1PvbYY2WjjTaqW/ryPOllhEtCpBvB/J0IlJKESP4VJAKzhEAIadUTSiwqSA8pBFjkhKG4GEgJEc4jaGicn6UuVmuKZSif//zn6/KcQYRyjM81XFMtPyFo4/hs9BkpcdJJJ9Vt+wSaHTQFni0pQlFjvdp1112rl4xgZ461yW/EEW+Y2Rxf22Z+TwQSgUQgEUgElicEyD8yf7IYIs6Tk4wL4aURcjPk76jHo14yncFCEHoeIr/+9a9foWf12+ajjz5a43CMetvd7vb1V+DXddddd9ly4+4y/f4OXOXujR1sGHjEg6MnOd4meigdk16aKRFIBJYikIRI/iUkArOEQCuECB7WilgCE+fkBKPJNg8L8SzspjKb1pQYrraRMIcffnhdezrIWlt1uN7H2HhYWHoSbrRxLtpqc+cGTa6BE6+Qb37zm2X77bevysSg9SgffWtzCpu1w5QIQcmefPLJV1TtflAAjXWY/r+isvyRCCQCiUAikAjMQwTIv6kIEXKaDkOXsfscudnK2vjez9BbWdt+b6+N+shwJMamm25ad8kLb844314z2Xdl6QECnQq63u+1yg2aXIOUsAQ4cBq0DuWjj21OTxFPhJHn9ttvr/erPY8QYbzqNvwM035ekwgsFASSEFkodzLHsdwhEAJIxwieIETiuJzyQDCJ4SGI6p133jly1l47Upv7rj8//OEPK7lACaDkON6Wc50+xvVxvs0pItbciureuqgq49q2bPt9qjqjXG24EfrqF7F+ww03rK6hyo0ixX2wre9nP/vZ2kaLRxIio0A561joCMRzO1UOg3inLHQ8cnyJwEJDwLNNNjJO9JLvCBATfHHQLHE1OR8m9XqHdNcTZfRDf3iHIAIsg+3uW/yOPK7tzi1bRojQyZybrnx7ffQvjsXvyXJ6xQ477FCD6OvzKJP6dtlll6pXRtDWGA+dky6VhMgoEc+65jsCSYjM9zuY/V9uEQihKCd4CCHkgeSYRNjGmlWkAuY+ztUCM/yv7UP7XbuWiSAAIhI7awXPCNYd7qbWotrlxlpa7q8+ltf8+Mc/rkSK7z//+c/rsVNPPbVccskltQxyxbIT7qC8Tghe44ZB24fpvsfQ23KsPqxAa665Zl1/OyqBrg116fMee+xRlTnjCGXIOa6nQZJE3zJPBBKBVyLQPq9TfX/lVfkrEUgE5gMCnunJCBH6C71AgHaxPMh95YdNvd4f3XUpo116gdgh2kWO0D3IbMQAT1jyXBn9iw8vEPoMIws9h74j0OnJJ59crr322vpbIHfXW65LRwo9LnSDto/61v72PY519zuO6zP9iT42yoSI4nVsObQdflrvXd9zl5lRop11LQQEkhBZCHcxx7BcItAKRhNqgpQiIYWgJJhuuummut0tYmTUKYQ24ah9hAeyQzAvS0N4Q4gCb5vfr3/96zUA2pe//OVqVTjmmGPKIYccUg488MCyzz771O9HHHFEOeGEE8qiRYvK8ccfX0477bT6WxCvrbfeuhx88MF1CY5I59YPa8MSF3FR7J7zve99ryofoqqzWugL5YXiFH1tcQs84phyFJ6Pf/zjtR6/R5HUr304uR+f+9znar9DiXD/KEQzVfBG0desIxFYXhGI51T/4vtk+fI6huxXIpAITI6A57klRFq5jTgwuRcLjb4R5yavbeozk707tE82k8mIBJ6ulv5aImL5rhgioZvQQ+gqztNl9t1335rTbXixOH/ooYdWEuSrX/1q1XUsu7FTCz3mqKOOqvnpp59ejUdXXnllJRpsbXvHHXdUr15eJYgT5It+6V+MPcYw2UiPPvroWj+9ZpRJu/Q9nscIKgat6JM+ZgyRUaKddS0EBJIQWQh3McewXCLQCsJehIjzSBCExKWXXros4OpMB6MtFhPKAqsIKwjhTZBfeOGF1R2UcrD55pvXgF577bVXtawgMygACA8uo0gSXh9XXHF5+eY3r6gxQqoS8P3v1wCq1qYK3iWYqjpcyxJhLMbEynLRRReVs846qyooJ554YhXOFAwKiuCooWQgS1hqeJwIasZLhWcJggJOkpyiQfH42Mc+VuzEEx41UWZY7FwfH/FcYLD//vvX/lAikhAZFtm8bqEj4PmgYCM3TQy8bxCfLK0+3g8mLJ5tnmMIUM91pkQgEZh/CIQc9hzHBNsxstiSXxNwz3p7bthRqoPMN3m3/Ea92uD5QM+wGwzyhaz+6Ec/Wnbaaaey++67V8IDycGoQ8+48IILyje+cXG5/PLL68eSHkt8vafoMEFu+E5HUgdyRDm/facT0WsQLn7TERAqjER26dMOIobxh26EgEByIGwQE7xbjac7ue6AAw6o3ivd52by2z3RnnfvF7/4xaqHRZw4ZFV6iMwE3bx2ISKQhMhCvKs5puUOgZYQiYm3Cf8NN9xQBTqh6figKYQeYWvtrgkH7wuCnTBHQnDJ3HHHHcu2225b9txzz2rx4PGx8cYb1yjkCAhLRVxvYvPcM38sLz0v4NbiMtGxzEUckKWxQCYqcfAn6y+Bq22kB1IjCArjpcg4F8KX9QRBwz1V9HPKBesMqw2FACHDOyWW35hIWcerf8gdeKmfFcqSme6YJYHdMDgaR1wn/9GPflS397WMSf+TEAl0Mx9XBOL5MH7fPd+eS67mnmckJ8Xbe2WVVVYp73znO8uKK65YPvKRj5TPfOYzyyyuvMY8XyY43g9tva82toiaJ554onrQGZd3z6i80F7tsWX7icAoEIhn34Q65KacDsPL9LLLLqvvhmGea9eQteS8dwvjB4KV8QMxgeRAVvBGFR+D7oCQ2G677aqOw/NVPxhU/kCfeeaZ8vyzfyyLX3y+TEwsXbI78bIuU8qfjCBw0baPZTWIFrlkbN4L3gP6RR9ABsV7gt7jncYApH/0LfqM73QZuhGS5Ac/+EFdgkN/oWt59xkroxF9zDKeUaYYD72JcUuQWySN46GTJTE9SsSzrvmOQBIi8/0OZv/nBQIEHyFEABFIhCzrgUmE3VlMLkKA9RpQKB5RJpQGgpVgJrxZY1ktttpqq7LZZptVrw3KAksKkgQhoQ8suYQ0V00EyCuS/j3xRJl49NEy8ewfysSSl0pVICYmlio/SyZKZ4LisFSBcC3BzjISHhuvqK/5EeOWS3LjILApP7xlbrvttuo1ItCY5TyWrhx00EF1DCZRltlY57vGGmtUbxSWo8CkV940P9BX9SJsuOAicfSTkhWEz0CVZeFEYB4j0Ovd4/ngDYIwXG211cob3/jG8r/+1/8qb3nLW8r73ve+8vd///eVFGG1RYi8//3vL29961vLa1/72vK6172u/vauMglgPY33Yrwb5hIubRqjd7AJ2GGHHVbHsMIKK9SJFrI4UyKQCCxFwPPieaU7hMxFFvDa4CVKRnenKNcr9+ypj2zlnSl2mfcCogC5sMkmm9TnkMGEgQcBoQ3xQegOCBMeqoxLtf7SKYs79JUlZcnTfyiLf/lYef5Xj5clL7xYOvQYz3tVYLp7uVQnQarQZ+hU6pssOafvkfz2DglvFoQqIgQxsuWWW1aPXCSOwK90NfXTxcRxszyH54v6fOo4mgD30cYgeVuHd/Vuu+1W9cMgduiO+pspEUgEliKQhEj+JSQCc4BAECJhEaUAsKpyvURohPCarCtxnrBUl0kEgYvYYB1ZZ511KhHCXZXCwFMk2oprI+fOSelHPrQCvbb99B9K+cqJpWy9denc9r0y8fTTZTHFwoRhYnFVMhYjMl7WE9SpHW6kN998c1VqJhuD48q3eVs2+qdPhLYxUhos20GKIHnEKhEk7G//9m+r9QXJA8tuJSLqausf5LvrWVN41HCV1Yb+6FeMYZD6smwiMF8RiGdJ7jmjSPPOsmztz/7szyoZwvuMlbQlXj0zFG4krMkLpZzXmmfK8/uf/tN/KiuttFKdEHiO4xmea5yMSz9NxExc/tt/+2/lz//8z8tf/uVf1lhFLM6ZEoFEYCkCnhfPNg8RuojfvL14hwhE6lx3ineHPD6ed9cjQpCO9BGEyqc//enyyU9+snzhC1+oxISltN4f0VZcL9cH+oHreG3EOYTIks5LpfPTu0rn87uUzkEHlCW/fKRMvPBsmZh4qUy83G/9jGviu2U5CBHvMuemSnFtlGt/x3fjRNzQ88QcofPRYdZbb72qu22xxRbVwIMkgUX3OKdqf6pz0b5c+wxjdCikr98IrV73aqo681wisJARSEJkId/dHNtygwAhZ2JgQk1AUrKtHeVV0RIXk3XYNa5nGTHx4P5IeUcU2CWGRYXSQMhpo1uohnB0HnlhaYpJiONt6jz11FJC5KMfLmW7rUo57pjS+d5NZfHTT5XOS4vLxBIWjE71EnGd6/UfMUOg6+NUKfoRZeJ3m4eiZAwENiWB4sN9XRwUsU9e85rXVBLIGmHtwrO1WEV90c6guetZq7jOcs/l5govfXEuUyIwLgjEsyQ3cbGtpeUwb3jDG6rVkZLv3ePZRyx4bj3DcV08z855foLoFMeIFwavEgQtT6y5fra0Z3JgieHaa69d/uIv/qLGItC3VVddtU5UkhAZl7/0HGc/CHhmyGWeEPFsI0IsD5nsGY53gdw1PuSr+Ba8Pni1brPNNvU7wwpyEvHq2fTeUL6tI+phMPHuYFzSp1pmYmkbSzpLysRPf1o6W21dyqofLmW/L5TOmWeWJQ/8vHSe+2P1Fok6Y9x+8xChzzA49Zt61RPH5IET3cyYjF39MFt55ZWr95zx87iDCV0jxt1vH7rLdbfv3vBQEe9E/ekh0o1Y/h53BJIQGfe/gBz/nCDQEiIEN1dK3hwm+aEghABrO+Q6y0l4dSAxuFaysLIyWJPK5RJZEERL1NGdq9MxQpgbKgWCwHWsTZ3f/66U888qZffPl7LrLqWcc0Yphx5SOl8/rUzce3dZItApd9SX1+G63iRHf7jMtoRId91tO+33KCePT7cCRIkQT4QVyseSGcuNWIdEk/ddHwRHg6l+qGPYpB/uk2U6ArUJFkuJ6Ie8GrbNvC4RWB4RiGfRkjHPHq+Ov/u7v6ueU94/nv8oE8+vPFJ7LL5796gPwWnHqLe//e3VtRzxOJupu1+IHH1AfvzX//pfa5BpBCuSh9ed90wSIrN5R7Lu+YaAZ4hsZIDw3CM4LX+zmxySpH3GYmyOKUt+ep7IU3EzLI21FMa1lsLSdcjullRVh+u7P3QesTHsGsP7rD2/pLO4erZO3HNPKV86spQvfqGURfuWctixpZx8Qulc+a0y8dijS0kRsUSio6VUPYNOQd8YJEX7k/U3zsMBIWKJjxhqDGOWBSGaxUlBksDT2JAj3pPel4OmaC9yeqI6119//YqXd5/7mCkRSASWIpCESP4lJAJzgEAQIiYPXDsJQhHPCakQWO2kQnluqCb4JvrWyPogAFgwCNRehEY7lKg3csIv1uVyC43jAoJQCPzf+c2/ls65Z5bOKSeVzlGHl3L2mUutLBeeWyauu7Ys+eMz5SWWl86fYqEgK0R6t1SnJQzUP2xqsaBkWb5iMsbtk6Vjgw02KOeff3713LA8iFstbGDFYsRrhkJDWYNlpOhT5HG8O3deH8IVmGXF5I8S5tx013fXl78TgfmKgL91zzhl+oMf/GCND+K7Zyue02HGpl7Ptm2uP/GJT1SiRWDCeCeqc9TPWfRXbmLGW86YXv/619dgsAI+6xPLM7f9JESGubN5zUJGwDNJl/CceI4YDXhqktEha5VpP/QecpshZtGiRTU2l1gaPGQt4VBXXDsddlGvJSjioFne4vo4LgB8jR8ysbh0fvzP1cu1XHR+KTtsVzq33VE6N19fOmefVZY8/FDpCBxf/1UFqDZNl0BO0LNmkv7Unz9hATeGFR41xg87hiTLnmGBpIATLxneqZYC2YkPSSvGGrIo6tU33/tN8FWHpTrqo9skIdIvelluHBBIQmQc7nKO8VVHgDAizAhuZAQvDRYRAikEnFw5ZAfFnEC0f7xlMRQJgjKssf0MqK2X4kLYCvCFSGjX2y4TqoTro4+UzvHHlSVnfb10rr+mlD2+WJY88ovS+ddfl4knf1cmLMepHiIvR2x/eSmPwGCW7YSAXVZnPx3tUcb1+sxiREFB5Ag+y1piHHat0Ca3T2WRQ8YkUC1ihIWFR42YBfpF+AeBpHz76dH8svPuGU8c65rdExPD6a7tVV8eSwTmKwKeQ88ggoBniGDDnjvH41kYdmyu90xdc801lXwQjBUJ7D0407p79Umd3lHeE94RvF0s2RGvwHs5CF2EyLrrrpsxRHqBmMfGGgHPEFmKuPS8IA/oFAwG8cxGrhziEemJvLALlSUbPLDI8mEMDN47PggE3iXkc6tH8V6t76Yli0v5zk2lHLxv6dx5eymHH14mLri4TDz+WFnyb/9SJiwDnmDcoQ+8TIh0SvWitVOOZTvGMUyK8cvjPWmssECGIGKRIfQ5u+lZlssLOMamLN3HUj74ws4yHtsEI2roOoO+I/XFdbFVMK+a0NeGGWNekwgsNASSEFlodzTHs1wiQPBwMSXkTO6tFW0trAShiQEGnzvp/vvvX5UHllgeEN2T+X4HGYJZ+yY1FAgEQa1vwlYxTU2WmDz0UOkceGDpXHxB6Tz2i1IOP6x0zj+3dF7eYq+SIXUi9KfJEKHO7RxhE8JfuzNJ+ovEoPQIakpZCBddhAgrByUsCJEYp5wywXpECQtlAnkiGj381d1PP9WlHPy55bLoIKvi2pmML69NBOYDAp4BJK730bve9a5Kzpr4tM+AMsMm1/p4jj3n73nPe2osAc84hX+USTveDSYU3oN/8zd/U4O7IpxNVKIv8iRERol81rWQEPB80B/oL94FdrJjLGi9Fzy7CBOTfktAEI7KkePdxpj2uesHJ+8eOgfPCV6jbVD6Wlchtzuls3hJKVdfXzq7716WPHhfmbjzn0vZboey+O67yuLnnl267DeWy3iFTSz1uEAU0B3oH+obJrVjggVs6HY8Vy2LEQuOHqJcECJIonivttfTe7yzeMdaGizmCq8S/YSlevpJ6vT+48nDoKQ9/cqUCCQCSxFIQiT/EhKBOUCAUDSxMLk2uTA5J5wIQAKNcuEYS4D1pKywBH03ERKCsp8uR1ltEHzqNOlgmXHu5XUyfxL6jv3mN6Vc+a3S+fGddXlM5yd3lM4u25TOIw+XiRderLvNLK7LZf5kwVU3rwweL61A76eP3WWir6wzrDSsSSYnFCB9hiOsNt544+rC3ypX0XabKyt6vUmPyO48RtwDSoa6AqPufsRv503WrHG2w41+uS5TIjAOCHg3UaARFZapIVPj+arvkAHdtrsxU1fUJ/bP7rvvXt785jdXL5Hwxuq+Zpjf+uo95V0iDpOtfwV0RXIiSaMP8T5IQmQYlPOacUDAM+K9wDhAtlrmhlCMZ5leI/iyZR+f+9znauBlXl/dXmXqcU0kv/tJrhFrCMGifTqSFM/uUg+RpbrCxL33lc5ll5Ylv/tdefHZZ0rnkEWl80+XlCXVm+VPbdOFqkrU6dTdZcR4o38Nm2JsdAU6iuW7lvPSadQbuoexICa233776g0SY+jOlYOraxmCdtxxx6orIqJgHZ5t0/VXu+6Ddzlyhi6YKRFIBJYikIRI/iUkAnOAAAWC1ZOifcghh9TvhJzjFHLbWIq0bkKA+Z+KCCEs+0khVLVBaBKiLB8mBnGu1sNKWz1GWWsnygQPiiWCki0uHR4RRx9aOuedXZb87rdLt6vjWcIC87J1F7lgeY+ArS1Z0G8/YyzKI414suyxxx7VEkLR0v9oC2bwEhjMMiLl41zk6ovvctcox1p11FFHVUWC62l4iyjTndrr3QvWHYEXXQe/TInAQkfAM+C5OfDAA8ub3vSmSqj6LbXPR6/nZxBsoi5KvfeTLXlt4zsTC230MXLkiveKAK7/5b/8l7qzg8lJvD+iXPQlCZFB7mCWHScEPCMm5ybTDCxihzE8xKSdzEaSrLnmmnXyLmaGc/GJZ6z7mXO8n6Sc5bPia/CciOuiXvFDqh7TmViqwyx5sXSW0LWeLxMPPVjKPnuVzp3fL50Xnq9GoUqEFNv0Lu2j94Sd/BC0UXe//WrLBfmAwBCDzLJAOEU/lfVdcFW7BtJP4lzkUSZ+y9ULe0Yanm6W31juFx60yvRKUYf7YLkgPbTFr9c1eSwRGCcEkhAZp7udY51TBEIAadSknoDFyvPUoKATbJQHv3kvUNCx9y0BoA4CLOqKvN+BKM+7gpWXAGRZifrU4Xx3qgrCy2RHETPkgZ+Xsu8+ZeLeu8qSF58rtrPrNIQIgoAbKIHeWip61R1tteOIcjC58847ywEHHFADo3IrpXhFWf2GGQWLyycFI8iJKBP1d+fOw5XSwG1XDBcxRlhutCFNVofjFBnWLm66iBTHMiUCCw2BeAbkiEDPIE8KMXTuvffe+vzN1t++er2fuNe/9rWvrTssxLPZD85t39vv3qneFeKf/Nmf/VmNDcJ67V3QayyOJSHSD+JZZtwQ8GyQw3QKhpvddtutTqrJfR96Btnqw5usnaTHMwmz+N6dT4en8t5LJvRIEV4q/STi2u54nRdeLJ0zT68GnolHHy4TnSVlsTF1Fi/dPW9ior7nLE9hBNHedKl7DH7DSN/oe7w/LIOmN4TuFfXKeaPYORB2/aSoHw5IY8uv6UyWYrf6XZSTxyfap6t99rOfrUuS1SMpkykRGGcEkhAZ57ufY59VBEIIaYTQMaGwdMOEnPJgiYklISb3JgFIBRN0gtREgPAKARZ1Rd5Px6Os+lgRWD24b3bX+e/qIhdf/nSQMc8/W8qpJ5XOSSeWiV8+UhZ3XipLGqKG0iPgV4xLu1Ol6JcyvuuP9caCo1F0wpUzMFAGEaIcUoPQF/CQZYpiFvVM1WacUxcSxURPn1lYtNdLWYlr5K6xk44gt4itTInAQkQgnk057wnK+v/4H/+jbg05F0Sgd0m0iSjmVddvir4r713hI8aBXSje97731XFsvvnmlWhpJ2rd9asnCZFuVPJ3IrAUAc8Hec2bS5BU8tjzZFmM5Wgbb7xx9cJEQpKzEecins/u3HMax6bDmB7gmWbcQSD0S5jSSMQVmaBHPPxg6Rx4QJm49uq6LHhiSad6kNTzExO1Xu8MgZf7Tfof7xx95JHLwGVZD2IIKet4jFMuuUZ8M3qhd06/KTBTp7otu7Hc+rjjjqterPTLKNO2Gd95mDDwWOocy477bTvLJQILFYEkRBbqnc1xLVcImLib8O+00041hgXrCjIEs8/SQfk//PDDqwAVhIwwFVNEvAvKB0IlhFm/A1MegSDuBQ8UQpOgnLaeqj38KeCqNbmdB35eOl86qiz58Q/Lkheer1YV/VCXsXHf5GpKQZmu/jgvJ7QJZ0tRuN/qY7jftuXiu/opKmuttVYt269C1GKmLnhSWpAqFAmKAaIjcG7L+64dhM8222xTSSuKSKZEYKEhEM+Z3PNBUX/DG95QA//Fu2M2x+x9xTL7jne8o1pWTaj0pZ/U9l093hNc99/5zneW//t//291W0dCIzfbyUJ33epJQqQblfydCCxFwPPByHLaaafVTwQ/5xWCSOANIfAn0sLzx4PBshDPFFnPE7R9/trndjqMyWHeXfQm8lo9/aROQbpMVI+QieefLZ1Lv1HKGV8tE488UhAiqlnM87XTqe8NOpntgPtNMQb6g+DyvDUYoLyD6EeT9ZMeQQ+k+9EJ+0nRlly9Pt5p+iuIPOyRU8hk78G2fHxX3rtdXBM6Zhzvp/0skwgsVASSEFmodzbHtVwhYJIvTggXUwo/ISi4KisHwoPwctySkcsvv7wKNh4JlAnum4gC60QpIlMJ2O5Bs9wIvGWfe5aV1krRXTZ+iyhCQC6NMlaDr5eJ518oE9dcVToXnFMmHnusblXHjSSEMUIkLDYhXGsdUWmTx3l9ESSMgiNavLET1HE+rm9/G7t2Pvaxj9V8MgKjaW7Sr/rOCg5XCow4KLx4KGzRdlxMsaBwILREeNfPTInAQkMgnjXPJgV9lVVWqc/aIJOPmWCife84MURWXnnl+u7Sl35S9N07gaedCdrb3va2suKKK9btxpErvSYI3XWrJwmRblTydyKwFAFyk9z2fDEokN90GR6XlgCTn0gSz6AdVMTQoO+Qr7wh6EGWbHin0IuQHOr03E2VnCevDz300GVendNdE/VNFGQIvcY2uxOl8/ijpZx/ZuncdENZIsD6y+fU573HS03/+q1fOboJXcIYeZ26fjp9y3leqpbvej8NkrTZfrzb6JECzTKqIaHcjyCy27Iwp/OIw8KDpT03SB+ybCKwNrWKygAAIABJREFUkBBIQmQh3c0cy3KHQAgaLDxygyWAgsDV9Ic//GEVolFGTjEgwFhSTM5tZ8sSgxwJIYfgYOmklHCXVL7XpEF9FBNLcRYtWrSsLSBFm70Am6hb0f1pF5oaQ5Ul4qEHS+f440vn+mvKxHNLSQNrb5955o/lzDPOrJMXgjbqlvdKxohQQABxq+UdQ5FoBXf3deqK6yhTa6yxRl273E5wuq+Z6nfbRxMoZBHiiXXFfYmlRepQFr6wpLwgb9yfTInAQkMgngvPosnM//k//6e+Oyjazs1F8m4wqXjLW95Sn0kTrH5SPKcmFpYgvvGNb6y749hJxvMdY4u6JhuP40mIBEqZJwKvRIC8JK8ZWUy6xb+gmwQBEORGPI+eX8tqvv/979fnGjnCcwRpcMstt1TDhmeWRxoDzmRGDrLeBN9ub3SAMJ68sne9f3lz0WNe3kqmdMQNu+GGUk4+sUzcf19ZLBDry6QMz1zvH/pJr9TrPUIPc52lycgUugIcpO7ybZ30CgFV4QejYZL6I/lOBxPg/qSTTqrvT+NA1kQ/5N7vDFD77rtvJbT0I85HXZknAuOGQBIi43bHc7xzikAIGQSGHU6OPfbYav1EahBSk6W4jqAKiwsvEUoEQUfJJ3y5RrLE8F4glJWlUBDGPqwd3EtZZRxvkzb6SUv1iMVlyQvPlc5N15XOqV8pE794uNZvJxrkwYknnFi+d9v3lrUR/Y824rfxsPJwJUXyIIdMVkIJCmWqu19xvfHBjlJE0I9KkKvHOC6++OK6bMnyH/0MHPUPCWJZD1dT/Y+xdfc1fycC8xkBf9eeBRbE17zmNdVjzUQlnsHZHhuF3jvN9rvHHHNM3+Sj/nlOLTe05OZDH/pQJYPbJXj99F09SYj0g1SWGUcEEBGWuCJE9tlnn6qLIENChnt+eiXHkRo8Yi0rufHGG6sxhBGC0YfxxyTds0cn8A6iI7mGHNYuknbLLbesxEi016utvo79+lelnHpK6fzTN8piXiIvEyKWxlp6MtkSFuOID73B+0W/eHnwzqCHTYZBd79cz+uUsQwhNKqkfRjTN+lYvgdezsHVUmr3D/kzl+/3UY0x60kERo1AEiKjRjTrSwReRiCEJmHOoiH+hKB+lsRMR4aoohWqbV0m6ggQ1pXjjz++7LrrrnUpjnopFKwolAnlxC1hLXVsMrJh+hsWrqZLysTjj5dy5tdL+cb5pfPcs+WlSoj8vpx44ldqjA1CN1LbZ9+DdOCiySJCAaIcRb8ib8cddUWuPK8SShEPmWgj8ig3aO567bsvSCfB0EzK/HbcuOxuwyJGgYHrVP0ctP0snwgsTwhQzpERf/3Xf11jA03lvTXqfpsAsbC+//3vr5503nXTpXj+vWN444lfYGKDQI3nNPJ+6kpCZDqU8vy4ImDCz3AgGDzDBONAO9me6jmL51ROriI/BWvmDYvItAyHnoRcQJjYFhY5QpdhkEAceC8F6TBVW1PfH9vOvFTK3XeVcszRpXPvfeXFiZeqbyyyByFiXL1SjMGY9enb3/529XgxhoG8Vl4mJmBId0OsjDLpJ72PjhiGJ+9Hx+k1+n7YYYfV8963w2M5yl5nXYnAq4dAEiKvHvbZ8gJHIAQnoU9ofvSjH62ECGEek/9eEMR17bkQVnLX+hBuBJvJi2UeCAYukCK9f+lLX6ptWtdrZ5RuQd2rjba97u+dicVliaBklsTceksphx1SOg/dX17svFSefvqZcu7ZZ5e7fvKTas2Ja6ON6DO3e4QCTxnus3AJHNqyvk+WKA2EO1ICQSHFtZNd08/xqEN/YMWjhgcLIssEDdZwRuaIb3DttdfWY/3UnWUSgfmCQDx7LL577LFH9bRgSfQMxLnZHotn0ATo4x//eH1fcv/uJ8UzHO/FUP7juHr7SconIdIPUllm3BDwbJg8W/prSRsSozVqxLPWjUscnyz3bHrH8FSwfIaxx9JUS4t33333Gn+E7sD4wyu2JTq72+rvt612J8qS3/6mTJx1Rul8+eTSee7pUjoTlQBmFPHe65WMQV+RDTxbeOxa7hKkUK9reh0zZrrg2muvXZfZwHGUST+9A2O5toC3dCbH6Th0KZ7GPIh5w8S9GWUfsq5EYD4hkITIfLpb2dd5hUAIGIJOnAyBQE2kCULnJkvtuaijO3dtHCP0WHApE1h/yrxAZ7wwtthii7LppptWi45goKytysVkYbI+tMd1VYT2zsSSMrFkoiz5lydK55ILSznrjLrjzLN/fK58+5qry4MPPfgKkqDtH+WBFYQAjtgp0UaUizyOt3mcMz5byx144IEDbcnZ1tXre9Qvd3+QNxQI5A3LD7y0TbmwZpqFjFKRKRFYSAjEcyBGgHcHL43ptqQe9fhjcrTBBhuU1VdfvXp6DNJGPMMxljbvpx7lkxDpB6ksM44IWH5h17r111+/kiNBlk71nLXn2u/wa3/Hs0+foTeRt7xeBW0niz/84Q9Xjwa7wjmOnAnvtenuhXaivUKnsQ3vi8+XifvvLZ1Fh5Zy792lvPB8eeD++8tNN99cfl2XsDTXvNwAIxTvUbFQeKzwYAnjznR9aM/TKRApa665Zt3CeNT6ROCKqPE+hx+Sif6nLcGr6WSWzTBQRfm2j/k9ERgnBJIQGae7nWOdUwRCwBB6JvGbbbZZ9TKI46PsTNQpJ5wpEywp2H+xAGwjx2sESeI3bxLLPigcBGQ3SfOn+igsr1RaOi++UDr33Vs6xx5TljxwX3n2D0+X679zc3nwoYeWWZJdr05CX/wU61S5oRLMFIpBU/SHArTXXnvV7eIsC5qtFBYgRBYSB0GCEKFEuJe2q2PdyZQILDQEPGs8o5ARvNp4a8TzNxdjjbbsyPXe9753zr2xtJ+EyFzc6WxjviFApgseuvHGG1ddgiz3vMxW0h7Cgw6FBOEZynvk9NNPr8QIowUvFYYmJAUPCOVDn4l3iTyORV4JkYnFZeLpp0rn21eUctZppfz2N+XhB+4v3/3e7eXX/2YZyVLjVdRDVxIv5IQTTqheHbxGgxAaFAPX0Yc+9alP1bhoiIvZSggQcdEsJbQzEO8QOo14bHRExrIY42z1IetNBJZ3BJIQWd7vUPZv3iIQQtg2sbwKbBfXrzVjmEGHQJNrxxpcu6IgPZAHLDuWfIjBwc3z6KOPrruq2IVGwFaTAAKe8AwPEnVJUffLP8rE739bOldfWSbO+mp55ldPlIsvuKjcd9/PlikHrufWyv2V+ylLivaRNcMk7VNkuLFaY8xipP7ZStrTV2uYEUmW0IhZQiGylAZ2yJlMicBCQ8BzRul/97vfXWMEDENgzgSTeNd47lZaaaXyjW98o7qjz6TOQa7VfhIigyCWZccFAe8Cu6h88pOfrJ6eJvWzmeJdQPbyyAgPB3oKQwvPBktoxRVhqGDwsbSG94ig6yb94b2hLinqtGSmbsH70kul8/hjpRx1WOnc9aPy41tuLVd9+1vl8Sd++aeyL3uN8m5l2LnpppuqgST0pGEwQIDQuz772c/WXWHUNZsJsc0wJig87JBHCBnetnS0IIpmsw9ZdyKwPCOQhMjyfHeyb/MaAYKXkCGgt99++yp0WgEaAnpUg4z65NzceYIIqIXgcMxH+wQjkoR1ILaaZfEQkfzss8+uk38kjjI8TQjuEJa1HqHHXny+dGzDu/fu5ekbbiynHXd8+fGPflTLUpK0T1mxtITyMBNLCny0GxaVtdZaq7rRI31mKwVeiCQWFfEUkEnwEJdFrJbJtuWbrT5lvYnAbCPg797zzuK6wgor1IDMw5KYw/Y1nj3r85EyvLS8w+YqaT8JkblCO9uZTwjwLGAQMIkn0+kFs5k8i9oQ44JxR8DT0KEc967iqUkWWybMc9OWvggS/aTfIHcZNhAA3caeSopYwvz8s6VzxWWlc+rJ5Y5zzy0XnnV2+cUjv6h6hzboQjxRrrjiiuohE3HgQi8aBgPkEv2I18tc7FqnrzCADSMYzMSKgiuiyTjhnSkRGFcEkhAZ1zuf4551BEKY82YQiNOWbK0AnS3ho14C1nZ2SBFtRrvOxccxkx1KDuGon6wsgrAuWrSoWl6QJiYHYoCwtvDKeGkxgmRJmXjyqdK5+KLyzGGLyol77l7++Y7bq8JBUeLWKoK5YLK9luQMCr4+UyBYaFZZZZVq2ZgL6xTli7supYGyhehhsbZzD9fhTInAQkMA0ehdgBDxHphrQgSennfL7BAiJjhI3LlK2k5CZK7QznbmEwIm1HZgE0OEcYAOMZvJs2iizpNCrAvERC9dRjnHvbvIaHoL4w5vCEts7VrDO4LM5qkq7seTv3+y6iuLF79UOkteKBOWyOyzd/nuIYvKGcccV3UoOgfSACkrBgdixTHttZ9hMKAX8TSlJ9Gv1DebKfQ9S2foo8glHrcC5NL7Zh6odjZ7n3UnArOPQBIis49xtjCmCBBAJu2sCjwMCOOwboQwHSU0Uad2KRCW6Mj99onzbZtxLHLKB+LDzg7W7CJVKBSEJguJMRCiv3vy9+Xpp58qL/7Lr8qzB+xazttu2/LDW28tjz/+y7oe9cgjjyh33H77MqtD1N+2Peh33hrWuq666qrV0mFMs530m+Ii3ooYMJQpk8VddtmlElyz3X7WnwjMNQKsqCyXb3vb26rC7p0wXRrF8x1tqMt7khv3iiuuWJesschGG/LZTOpPQmQ2Ec665ysClq7wJEWUIkTm4llEhvL0EP+CLI73QIthHGtz+gHyAvlh8s+ggXzYf//969KaG2+6ofz0Z/eWx594ojz15FPlueefLS/deFX5yU7blUsOXVR+dt/d5eGHH6rX8aBlGAkvirYd34dJ3mmbb755NTyJTzZsPYO0HZjYvYeXiCUzyBC6YrxjB6kvyyYCCwmBJEQW0t3MsSxXCBBwBLh1rZbMIBlicjEbwi/qJPR4ZhD8w26npi71sA5TKHi3CC5qHFtusWU58IADy5XfuqI88osHytPXXll+vNmm5faLLihnn3NOXabz0C8erlHc3RB1tZ9hb1J4Z6y33nrLAj0OW9cg18EBSWTsCJlvfetblRCxFCpTIrCQEPCcemcJVvjWt761PsvxzppqnO3z7btnxieO+95vco1kB4R3vOMddfIlmLEU9dUfs/SfNpIQmSVws9p5jQAPCcGOkROxbGQ2B+RZ5HFK97D8dyZeoerybuM9y0jF69NOWjvuuGP1IPnB979fHn/0F+WJ/fcp3ztw/3LTZZeULx19VPVU4z3Rvs/iPSQfNMW1xmVrcXrEXJAR0a5xIIiM37JmHnh0xbkiZQbFK8snAnOFQBIic4V0tjN2CBBAJtIEjzW3lOyIezGMIO0HQPUS+taEcm01kQhB2G+bbXnC00e/WWoEEuWOeuF555ejjjiqHLno4PLl/fcr562wQvnaJhuVc045tdx//4PlhZeeL2XilURIv+1PNk7ustYFi4rO8jOXidUcprEumcuwOAuZEoGFhoD3hzg5CBETkX4IkXay4FkRg4hn2T/8wz/UGEKD7AgV7wmTlre//e31eUeGzlXSfhIic4V2tjOfECD7eTXwKLDU1nM/m8mzaNt7y3h5icS7YZg2XeuDVKE/ICF4fCIkBGw9ZNEh5YQTjy9f2WC9cv773ltO23mX8u0rv12X4IQe1L7nor5h+qIPjFV28vKujGU4w9TV7zX6G/239MkSJDqMd7zvCBplMiUC44pAEiLjeudz3LOKQAhLSgPlwc4oLBNzQYhg+rl4nnHGGbW96Eu/A47yrXCMY1zZn3/+hfLkU09VV9Of//TecszhR5XN3ve+svdaa5YD9tyznHLqaeW2279b7r3n3koIEfaxVKjfPnSX074da7h3UmD6maR11zGT39qz/Ci2Md55552rp8hM6sxrE4HlEQHEJ/Lvb/7mb6r1sN9nLd4RXMv322+/8hd/8Rflz//8z+tONSzLgyZL0/72b/+2TobCehltDFrXIOW1kYTIIIhl2XFBwHbcW221VV1KN1ceIrwZ7NKHjBk2xXtDLsmRA95tvD8Yrh7/1a/Kd7773bLdRhuWHVf+QPnippuWw444vMZhI/sfeeSRSgLxmm3rizr76VtcRyeyEw49wjKkmXi+9NNulGnbFxNFnCZLoHbffffaj0HGEnVmnggsFASSEFkodzLHsdwhQLiYXAjoxS0zCJHZEjoh7KwLNSFhYSX0pUHajHraa7q/UyR+/a+/Lldfe3XZa8+9y47bbluuuOyfyndvvbVcdvnl5cKLLizHHXd8nVgJQirIqkkRxaPfCVZ7QxEqgoFZ+2p8c6VARB+0L/CsYKomi+4nl/5MicBCQ8A7y9aSb3nLWwYiRODgPYG4ZEX+j//xP9bPBz7wgfrsDooTQoSXCmWdRTPeQZEPWl+/5dWfhEi/aGW5cULAsl+7otipZC4IEXKenOXB4L0yk+S5nuyD5CDfTzr5pLLD9tuVIw5dVG645upy1dVXV88UpAEDky1+LUe+/fbbK0EijgrdoJ/Uts1jTowkS1V4v4XnRj/1zKRM9IEORo856aSTalwVeg0i2/lMicC4IpCEyLje+Rz3rCNAuBC01uPzEBGQNKwLs9F4CDvbxFrSYRu6Ns1E2EXdcl4uv/zlY9VD4vAjDq8Kw1FHHlnuuuvu8vwLL9Rga6Kms+iY1CCECH4R1QXysg0eN1jLb7jnU3qm6xs3fPE7Nthggyq4g+hpxzeb37WnvzxEKBGUQmPLlAgsJAQ8h8MSIq71nHC9tlzvta99bfmrv/qruqMB1/RBUxAirMNBiGhjunfFoO10l1d/EiLdqOTvRKDUHVc8j+S55bizLYd5b4jBZtlxeIkNex/i3RG5vvvQQRA9J33lK+X0075aTvvqqeXMM86owePpOrx877nnnhpHDSEioKz+WD571VVX1YDrlr8gNugprTds+66KduV0CZ7D6lF/nBt2bP1eF+0gRCyX4UlsJx6kcxIi/aKY5RYqAkmILNQ7m+N61REgfAhcQTjtUMJjIwiREEyj6mTUpz0eGXa1IeRHlWIslAeTG2MhTG2Dy+XTbjTWwrbWEtcYL+HPPdQWwK7hqsnCZCeLW2+9tRJF3FF5j3AlDYIkxiSnbCCWxGKZi+j23bjBleJy5JFHVhfTHXbYoVqKusvl70RgviOAEGENtWQG+dePR1e8H+SeYV5cSBEKv8B93huDJoSInW723XffZZOheCcMWtcg5bWRhMggiGXZcUEAKUEG8gAT06uV97OBAbmvPTE+ZrotbLw7Itd3Xi6WASE3vPOQArbnZbiJrXCjfJAndJWbbrqpetHxHBFgNsgR7zrGHtjQUxAqros65NqlQ33uc5+rupr3bZyfDQzbOqMdfdBX+hjvG/GeBM93PlMiMK4IJCEyrnc+xz3rCITw4dlgZxSTA5MFAlIatfBRH0HH3V1EdpbaUaVQBpAsXC1tYUeAIi8oLQJzxbbCbZuBgVwdLCgIFNvYnnbaaVUYW37CWsJicffdd1dXVOSISZTJmOsoEOKH8NAwxrlO2mSl3m677aryYO1v7jIz13ch25sLBEw8zjnnnBq/A9HZLyHSPuu9vg/ad6SrXWa8N70Pos5B6xm0vHaSEBkUtSw/DggwCpDDH/7wh6sMJ/9nMz366KPl8MMPr0YlMtizOWyiR8Q7RF3eKQwyDDRIEO89Zcj1s88+u3qIRPnI2zqMHelhqc2VV15ZPWAFkfY5/fTT67IaniX0HbiFscf7FAlDJ3QeaRL1Dzu2fq+LdvTd0h9LkPWXl8hMPXD67UOWSwSWVwSSEFle70z2a94jQHj6WLqyxhprlHXXXXeZW2IIplEPklC3RIVrJ8vDqBKhbQnMYYcdVgkXJIgxUCy4zrKuiBHSKi3OSzHW7hw2FArXWSdM8WF5YjlhuYAbK40yCBSWDN4voZSMamz91GNcrEfIG/2gRNiKOFMisNAQ8A4RbE9AU55cgxIi8Xx63tvvg+JkV4kVVlihvnNMKKR4pwxa1yDltZGEyCCIZdlxQUDsC7JZfCHECAPHbD2T6mVk4WkmZoffw7YV18qDDBHDgyy3xNg7LsogSegjiIw41itv323Oq4MRiucFo5RlKOuvv36NO+Z9KgYaIxLigdfwJptsUr8jJ6Kuufg70leeu8Zo+RNSxHJm3jKZEoFxRiAJkXG++zn2WUWA4CHoCNhPfepTZbXVViuXXHLJMuHn/CiT+pATvC24myMxZprUybLBgsLrhLeLyUkQH8aHHOExwlU0jmvXtd2f7uOupxDoK48QpIOo8ggdysquu+5a8912263uViH+iLKum8ukj/fff3/ZYostqjVFEDKKT6ZEYCEhEM+7yQLvDCRlP4QIDNpnPTDpdSzOTZa7RrKk7p3vfGd97yBF4/hk143quHaSEBkVmlnPQkIAIWJ5yEorrVQ+/elP16UhZONsJUtTvIMQIzN5/l3rQz+xnIUBxzIczzl9Is7LGWK8/xAiUpyL7+1Y41zk6ve+pDMhGCwdjK1tkQ/0GPFXxJTbfvvtK4GiPH1GHbOdop/umdgs+sK4gxAZZGv02e5n1p8IvBoIJCHyaqCebY4FAiF8eDdYYrHtttvWLetYCFriYFRgEKrWt+699941cKk2+kkhjKO/kRPULBqUA0qQredMTKLvyrkWIWL5SxAi2nRu0OQadVMmCGdtW6JjPe+mm25a3vve95ZddtmlLs+xa41de7StfNun6H/bhzjWb5+ifOQsKsgYMUwEVRO0VvyUTInAQkLA37u/de7UvDPE7/Bbcm4uUrTDbf3d7353fbfwWpmrpP0kROYK7WxnPiHAaEEef+Yzn6kGCqQlI4xnJj6jGo/6GEZ4qdlhxu9+U/SlzekzlqjQVc4777waIJbu0JbxnccIT9TwEOm3ze5y6kI88KJhROLtSodAPqy66qpl9dVXr0uA4UlHdJ7e433rWqm7b92/o0x325P9juuNm55Il0HS6JN7G+1Odn0eTwQWMgJJiCzku5tje9URIGAQBbw2LDcRg0IMDsQCMmGUCSnAksJ7YRCLShAikeszIS5yukkJhcSyllhjG0JVHoSIMbGGjGpMUTflQNvWuFquwtrCG0UwM3iKcSBYqzW5EciMEhLXt331vd/UfZ2xa5cbLIsVJQI+mRKBhYSAv3vvEZbZFVdcsWy99dYj8TQbBKN49jzbLNEmL+HtNsgzPEibbVltJCHSIpLfE4GlCHgOxdjg3YBY2HDDDavsjcl0PLujwMt7yDvAx1KUQepWli4SH/qWZTf0CN6zyI4geqOvUT8PEfGLBIN3bFTJeOgR3q3ih9CZGJssPfrSl75UPxGclTeq9ulhrou+tbl+xe9++xjlGeW22mqrGjSb54p2WyKm3/qyXCKwkBBIQmQh3c0cy3KHAAHEuiHoKMFnmzbWFfEnIrr4qDpN+FvSYqkJcqLfpI+ujZyVgiXlzDPPrIISIRHCMsrI47tgo9xPlVPPKFLUL7dDjV1zkDMUBF4hxkdxsVYXYUNpsraZtYXCof8UCgpIt0LRT//a9l1vjDx8tIOIYVnhwZIpEVhoCHiGWSxXXnnl8olPfKI+Q56HuUrx7B144IHlPe95T53AhFv+XPRDG0mIzNXdznbmEwJkoXeDpaw8Ri23MJk3gW91hFGMiawXP+Sss86qy0/ivdBP3VHWe4PsvvHGG2s/xe5ArvAW6ZVcd91119WlzeS736NK6jImsZEsmREoHpGEnGHAEtND/DfGHrt7ISmQN4gcxhdBYGO5cPRLHt/76aey3u90Kt6udDyECL0pdMB+6skyicBCRCAJkYV4V3NMywUCIXxMzFkDxODgxWCbNl4cdlThujiqRKAJ3sUbRXT2flMIVcoOywFFB8Fhna2+h6CMcm3uHAXD2Cxv8VtSZiYp2qC4sNZYoiJmRxyX6y9SiULhHOFOgdpvv/2qFwchz/01dq7h2hvrhafrW9sOUoXCstZaa1XCyUSN0qK+TInAQkPA375nWYyAD37wg3UyEu+AuRir9rXHgmk3C8vjHJPiuZzNfmgjCZHZRDjrnq8IeC55vNqmVZB1npkm90gLOgeZHM/qTMdomQlZi0BAJAzy7CuLoLEMBalgJxkGFPqCPkbq7qvflgtaqiOe2SiTuulTlqfYLS8MYo776K+4I3atueaaa6qOQVcU5+Pkk0+u/UJGeTfRI11PPwqda7q+akNZOhDjnLrpSIKq2iUn+jFdPXk+EVioCCQhslDvbI7rVUcgBAyPC66RBBDXTYJWTBFeBoQfoabsTBNBz7LAY6Lf9a/RR9ciQ1hHKCEUgnZtsL5FH+MauesQIiwbs0GIwItXBq8XykTbdvd3fVGe5QWJgqSheFje4jvvHMQG/FlbEB2xvKYb+6jbeeUpJEgZyiAFhQLo+kyJwEJDwN++99JOO+1Ug5p6l8Q7Kp6L2RwzpR1RvM4661TXcs/sXCZjTEJkLhHPtuYLAp4NHq90GctXPafkKlIEccEbo98J+nRjJu8RLwiK9v0z3XXOIxfoAYwk9BlEQtQx2fXxbjMeRIH33igTXOw0473K29XvaLNXrr90MKQTfYOhi6csgw9jleDzPHP0E5HiXtCB1NWdon648K611AkJIsg/DxF1RZnua/N3IjAuCCQhMi53Osc55wiEgMHIY/wJM8s9CC0Kt+1lMfUsKzEx7yXM+u24OsS3ED1cO71SW3/0z3WsMQKJ8Vyh6MSa4BDak9XlPMXFOJAFU5XvVcdkx/RNXZQa7rkIibASTddGjNG44CD4KQWCIrLBBhtUcuX000+vXiUsLZQJdVNAou5o3zlrpgVBs1uQ+0YhgZH6MyUCCwmBeCdQshG2b3rTm+rfPEU6zs3meLXh/Yiw/H//7//VuEGCJ89l0ockROYS8WxrviDg2bCUhAGE16v3Av2GfBVXBHnBANTKUdf0m5SNjwDxCBGeHZM8/JdYAAAgAElEQVRN9KNe7cWHHKc30IUsbx0ktpm2EQUIkVEviTUGhjFxmYKAiP5PleuTsSE8eLxY/oMcseMdnYZX7GWXXVYNUoxTPEdCnwnc1OE7oxcjEZ3KO8444WRJTuA+VV/yXCKwkBFIQmQh390c26uKQAgYgsgyFEw8Ie+4yTSrxZZbblktGINGUe81MIoAQUnoUkp6pehT5PqB0LBEhlvpXXfdtWxZSZSR90qOE9QUB14poyRE1Kt+xIO1rtb+6ut0fdLPtox64A8bHh2PPfZYXfZCiaBQbLzxxtVllMWG9QYxFO24hnWG8nDwwQdXnJAiiC1rcLWTKRFYSAjEs8MyKYjwf//v/73G5PHsxLnZHq9JFg+Vt73tbdUba9QTk+n6b5xJiEyHUp4fRwTIU++Gc889t+oaJt6O0TcYGTbbbLPqXep94bhPv3Iy3i+R835AaFiaE8cmw9x5bZHdPMp4sAjGjNgNUmCya9vj6rHEhofsqN87vFctlxF3JfTAtu3JvsfY2zEioegqvHL1lW5Jl6FPGjtSxzs0lgi51j0yto985COVkOH5ypAl9hrPHmUyJQLjjEASIuN893Pss4pACBg5Bl5gVRPqUBIoDWJfEJC8DmYSlFQblBO7oAjORRD2SsrFR3kkhqBoAnghZQja6F+Uk/dKjitLsBL0JhFxba/ygxxTt/4hWgj6FrfJ+tNdv3LtR98oTHCn1FFKBLflVgv/zTffvHqPUPZsjyeYmSVIlutQrFitlWW1GiRobXe/8ncisLwj4Nm7+uqry+te97q6mwRPqXiWZrvv2hYY+c1vfnMNmjwZuTtb/TDOJERmC92sdz4j4NngqUA2koNkIpmKdDCpZliwfIac9M4YhIyAi/olshoRwhDBKBHvnjjfYuiY8ggH7yyynEcub4gwbvS6rq3D92iDQSkIkX6u665nst8IHoHZbXerb/3WHf1qc+OFLfKYrgd77yweOggOO/LZ0ZAnD32QnsnThkeJZTLaDw8c3j3hETxZ3/N4IjAOCCQhMg53Ocf4qiJAkJlQX3zxxdW1lDAL4UaYsWhwY0SM8BqhcDg/SFKniYPYJLwqTPp7JfUqixCgcCBpWIKRGjwiol9t3qsex6IuYxNkNAgdx2ea9FG9vDj23XffGkQs6o28nzaU7S4fxygUsIaFZUvwoFCJN0KZ2GWXXcqRRx5ZyQ/YUCLEDzFWrqnd9fbTnyyTCCzvCPi7NpEQjNjWu6yOrKXx3Mx2/70TeXCtsMIK1T2c0j+XyTiTEJlLxLOt+YQAuRlLWXlcht7gOBlpwm3ib+mucows/aaQqXI75vEQ4bXaHu+uS7u8XMUNQ4YwcpDpjrsuru2+rtdvZS0/oauR8aNK6r3ooouq0QU+g+h4MYapcvqS+4DYQI4gXwSjZtyBCYIk4rzAxj2h71giLWZKEEejGm/WkwjMRwSSEJmPdy37PG8QCCFGCHFjRHwQRnFcjrzg+sjLAqGB0UdQmAg4L0X5+N4NQCgj4pJYYxoCN66LeghOkxtrWC2TCcHveJTprnuy38pHfYgVQtjvUSTjsYTFThMInkGUqunabzGJ7/pNKTAZY0lh/TIRZAmjaDhn/S7XVG6naVGZDuU8Px8RiOdBLr4OQvLtb397JUdi4uPcbKV4n6yyyipl3XXXrSTrbLbXaxzaS0KkFzJ5LBFY6r1BP7E7CQMO/cUz40NuW8rBQ8MknE5juXDETotycOz13bE4x1PDEmBerG2K6+T0HJ6t4p/xhtAfMnxYPUSd9DRtj4IQifF4dzK08Db1btG/ONeObarvyk92TZxrc/qjd7ilQ+uvv3417hiTtvUHEWJ5TRBOk9U9VZ/yXCKwkBBIQmQh3c0cy3KJAEFDaWC5YDlBSLTWC+cJL14Kp512Wtlhhx2qcOcq2m3pCIHXPVATdkrKJptsUifxQaaE4HWdMgQkLwhulSwI4QrfXV8/v9WpfuOxE0x4iPRz7XRlCGwWFfE6BFXU1qhSi0ng6Rjlyhisq3UPKHWUK2XgKW4Ib5V77rmnYjmq/mQ9icDyhoC/eRMb7tT/83/+z2r15YEWz8ts9dczyL37ta99bfUSGcWkZNC+GmMSIoOiluXHAQHPBllpqYwJvt1P6CjxXojcsjfkBAKAcYFXBINJkCe9ZHBcG/nXvva1Sqh0B/yM84wSyBLlLNFRP71B3cMmdYtXhmAZxbsn+spzBg7w8l6N48P2s/u6qK/NIyA8z2PEB6xC7/SepbNZ4kRvlOLa7rrzdyIwLggkITIudzrH+aohQNAQ1LxATKhZTIKwCCEkJ6xMwHlEmJAL5mlNKM8ECgZBH4pE92CQHQiVjTbaqLpCai/qdg0BaM0oQc9qY9KhTmWGTa5Vt6UtlKM2mvtM6lUnJcuSFYHaKF+jTIFL5HA32WMpoTjwsvnOd76zzAtEOYqcqPq23h1FANxRjifrSgRGiUA8u7yyLOd7wxveULeu5v7u2ZytpF0TB3F7XvOa19QtwE165jrpRxIic416tjcfEPBseAeI18FgYJJP/sdE2/kooxxjCeOLnVV4cDAqkOf0H+ejfHfunAk744T3TpyHkXPktd3jlDnnnHOqbtP2YVgstWPJDGOMpSczTdFvMdB4/zJC0dXi+Ezrj+ujPrn6vUd5gMDdLjJ0s7Zd5+k5vEdao5jrMyUC44pAEiLjeudz3HOKQBAW1nSaWIelpBVk8Z3Ax9qzJgj0KegprwSKxGQWkKjfjiwm9iH81IX44GUhQKm1+aKPRz0zEYDRX+uIKSZBFMykTjfFRMxymbXXXvsV3i6jumHRb9hQzCg+FBbKAw8eWLfLmihaCBoKje1/KRNRx6j6lPUkAssDAvF3Lfd8eOestdZa5V3velcNdDrKpWvd4/XOQhqvvvrqZeWVV64Er2dvrpOxJyEy16hne/MBAc+GZ5JOYZLNcONZaeVlvEO8P3xnjCHPeYuYhFtySldAanjmo1xcF7lluOQtQ08cUxYZQ16rj4GH/G7rGBbHaOPSSy+t8UhmaoiJPtG1GMIs/6GHxXHtjSqpy32hV/IC5tlHf+I9Q5dscdY+HceOQJYHh/FsVH3JehKB+YpAEiLz9c5lv+cNAoQVgWQdrUBWvAwI21YwhjCOQflNUHFzFFjsE5/4RBWoEaTM+TYp6xwhR9gRjspQXPwWPIu3BTfQONfdZltfP99dbwysQOqm5ETq7l8c7ydnsRCQjfWJMJ9JXb3ai3EjQ7jjslyZ9CGekB3G1CbY8q75+Mc/Xm644YZlZFZbJr8nAgsBgXg2jMV3z4g19a9//evr88hbLZ7HyEc1bqQjBf6v//qvK2nMW+7VSMaVhMirgXy2ubwj4NnwCUOCmGhkYrsMxPnQbWI8jpHrvF8ZHshbxAPdgW4U9bY5Aw5ChMEl6vROQIJYBsKLM5a0xnXR3rC5eiwp9s6bKSGiLroWnWvDDTesRBAyJ/oqH0VSD7xhIeaZ4KnrrLNOT3yirKUyliPTL9v+jKpPoxhX1pEIzDUCSYjMNeLZ3lgiYFJNaTCx3m233aoXB8vJVALIOdchUgh/AT033XTTussJYkV9oXgoh5BggYm1ohQQ28ciVCgfJhwE9KiS/mmfBYeHCM+TqcYzWbuuiY9xqGe99darrquh8Ex2ba/jUVd3rqxjFDDkEQ8c29CFcsVi1U0WKQ9HEe9hD+NQ4Hq1nccSgYWEgOfbxODTn/50+cAHPlCfyV7ebcOOOZ5REyzvKqTjhz70oWVWzWHrncl1+pSEyEwQzGsXMgLeCTxCGA+QIYKz0wFCF+k1ds8U2cpAo6xlLnQVgVltcdvGF1FWYqgQU43Hg2vtJENm87TgBUs3mKrNXv2Y7pi2BVT1oXfNJKnLe41HjODwlh8OozuoZ6qPZYX0QTvi0VEsX6Znwho+kdTht/JIqQsvvLDewzifeSIw7ggkITLufwE5/jlBwETfxJp75ymnnFI9IGLpxXQdoAwQ/iwlN910Uzn44IOrgOXRgChhZTFJQSQEIaJsBE91jcl+Kxyna7Of8yFgtW8tams97uf6tkwIfBhRsj72sY9V7w24OTdMiv5FTomDCwsTLx1KCoULbvAL5Sr6Ioe9a/bee++qcLTuucP0Ka9JBOYbApR4W1q+973vrTu/xM5L8ZzM5L0SzxgSV8wgO9p4Jj2r8TzONV76lITIXKOe7c0XBDwfjDlkIQ9OBgVx0UzAneuVHPfxTHuf0EcEMEeMiJWGGLGcWCB5OgC5S7+xvJjxwvIc7wW6k9/aUmay9nr1oZ9j6mP8oDMxOA2b1KN/6mB00W+xVgZ9p6nHJ65rfyM2kCyII0ur3Qc7DPJImYx4QdC4hoeO5TL0nkyJQCKwFIEkRPIvIRGYAwRM7LlLUgRYN6wpxeITmtOlEIjKUgQoBNddd10VhJbCIEhYWURHt72a3Ha6gmnZXpfgDEE6XVuDnI9+sdwgRBAHM2mH0IcJj5b99ttvGYmjzmGS6ygGPGNMuEzq1G07QNYUgWWRUqE8RN8j1x94i5a/xhpr1IBo7mGrnAzTr7wmEZhPCHgeWEu9Z1ZaaaWy/fbbv8La6fywyTvNsjXPZdRtkuV4PIfD1j3sddpNQmRY9PK6hY6A5wMhwnNMfuyxx1YPVBPxyZ7ZON7m5C7CwASd/kLm854VO4Qxh9HCshkeFnQZcTHCQ5MMDjk8Srz1D6mAFJkJIaJPSF26HuMOwqjVw7TTTwq8YqwIDfoWncTyQmQSIgR+CCZtRNle9dM/eZDAmU5EL82UCCQCSxFIQiT/EhKBOUCA8OflQYFgASHgRRzvh6EPodjm6uFKak2uyb3gZtaOvuc976meD6ytlApkQAjIfoVwv3CoT908Q2ayZEZ76jImisPGG29ctygm/GPM/fZJOX2iGPBcEYmeayg3W8qDHSwEZGPdauuPdrpzVh1uultssUUdpz4GnoP0KcsmAvMVAc+Ev3kKtHfMiiuuWElFO0Z4f/VD6naPXZ0mDOpEtLz73e+uy3I8/y0ZotxcJ20mITLXqGd78wGBeBd4dhEG3guMLpbNmJDHs9s9lniO5d0f19CNPHNiW1gazKtCcGVLZ8VFszPe3XffXXWE6MNsyGF122XGBwns9zDJdfARW2277barukNg41x8pqtbOXoKnREZxCOYDrP77rsX8VsQIQJRhwdw1CvvTnRQxjTLH+1AQ7dxLFMikAgsRSAJkfxLSARmEYEQUEGIEG6+81Yw0cb29xJe3V1qy0SdcnURvCwRlAYTi7/7u7+r1hXuqNwiKSrIAd4N2g9ForvO7jan+u1a9fgQ1Age7bR1TnV9e841PvrIbdZOLxSAtp+96o3r5CwdlCp4UhAQRZSrgw46qLriI2xiAhf1Rh/aeqIdOWxFx+fOG9HsY2lNXJt5IrDQEYjnwzPGpX3LLbcsb33rW8sGG2xQtwXn1eXZC4V/Kjw8e7yuKOMIYTs3ve1tb6tBAHm9eT9J0eZUdXWfi2fXcc+pSYJ34zCf8ApbZZVVKmkzTB3eYd65/eDSPZb8nQgsrwh4hhEiIaN5iiBEbrvttvrctc9hO4Y43uvZjmOef54m3gXiYVimxzuTBxmdyXNpiSvPTkYP7yT9GUWKPvB29WE0GTbRHewoYwmzfnsPRP3qbL+3bThuPHCAL69b8UEQNALMMuogjBh5nGOgcU2kqDeORe68PugLQgSGcI73bVyfeSIwzggkITLOdz/HPmcIEJDhIULgmfwjRBAZlAuCy/FWgA3SOUq3OrlPXnLJJXXNqhgZn/zkJ6uLu11bTEBYZLmk8xyhUBCIobBru20/vsfxNtc3v/VZQDRW3pYQiWunG0PUqQ+8OUQ+v+iii2rdcS7aCXyUpQiZWFEaCHbKB0sVEsi411133UqEcLc1+QqMp+tPnNcmjCgiApDBluKXhEgglPm4IOBZiOS5s56fO/sb3vCG8uY3v7ku/xP3xzNoEuGZ9K7zrPj4jpxgcUWeeE652fM0ed3rXlc9wkx0upX7aLOfPN4R8niXWDroXTjMB4Gqf+94xztq7IJh6vDu4H4PA33y/sqUCMx3BDxjMWH3N+3D8GKyzTgScjr+3tv3x3RjVzbK837wHJLpDBu8RSwJtrRG0FPvDO8cRhCEJX3A+6n7WYs6e+Vtf5zXZ3FLtDkIIdJdt/fd5ZdfXjbaaKOqb+lXW0a78Vub8KSP0TnoK7xlLNtBBH3mM5+p5DNPYDqSMsbo+qinHUd8b+vXhmC2tiqGqTroM/SiTIlAIrAUgSRE8i8hEZgDBAjE8NAgqPxmhRBsy2Q7hFcIuUG7hHAhSJEBrLgErPYoDLwlLBlBEqy66qp1+Yd1pNdcc009z9pCadcn9YRCQYi2/Wr7FseVQYioXyyAYZK6KBCIEPE9KDjRttxHn/SPAFeWdcQ4YUjIUzxsNcd6QhEx8WqXt0R/2zFM1VdtWttM+XKP4EKJoLToS6ZEYFwR8GwgN5AE73//+8tf/uVf1q1yeaYhZK1tt22lwIQIAe7ZJhj7779/WW211eoWvv/5P//nSjZw//YsxzPV7/PZC/t4xvXv/7N359/aFdWdwFd3OrGNJtHuTrSjjZrYKg5RxEDQKBoVB1BAZVBBEAQRwXnAARUHFASVCA4giqIIIoOIAk6gcSKRgGg0DmhszfRLd6/+B06vT3V/3y5PP/e+d3ju+z7DPmudW889p8ZddWrv+u5du1iZqddv/dZvbfi+3e1uN7g3msfv/M7vDH/+53/e5mVz12baNqm99awosDMoYBz3gIj/fcNAzlh5ZawnXGs9+/gURvyJsGbw/ZhzWGxecsklzbJs//33b85B+cNgDconmO27+HTAkV6ekbe5QdiXk99C8xBARBnr2TIjbfIW2ppCLjG/RRmTON6rlzaRUdRXfKASsMIWm6c97WkN/DnrrLMagAyckUYek+4xfcdxyC22UB9xxBENGFGu9hUgMqZc/b/MFChAZJl7v9q+wyiA+VnI98wRo8fwWW5EYMbINnJhliw/+N/gIyPleB7tA+CF+WUWJ5gjb+M0EBwlxoEZIIA2IUCJPDDx/grD9ZxWSDuE672Sz/e///2mDfnQhz60TVjAxDFtwgKtMvDj9NNPb9ppdWe6bzsLZ2u0RXyq0EZre+qc/PtwLXWUj/L4ZgEqEZQKEFkL5SrOolLAN+QS+h4I1b455tv2/Fv877rrrsM973nP4S53uctwpzvdabjzne/cfu+yyy7Dfe5zn2GPPfZoJyIATQCovrPxt7pR+uUbNyc5wtc8p5z13hZEbvOKcL3pE/9jH/tY05oDm9Up9Nto+ypdUWAWKGAcjwERPJfihc8Myoh8iwnXUm9xeznDt3fqqac2q1bvzDkBEVihkZ+USfaw9c5WEEofssHrXve6VhegLMvVWMUCSuQjv/7K/0LbY1m74PdrvaTLrQzWHYANc5z5DX3MdZQ9rD/Um6wDNOGXSZ0ps7RX2Sx5yT4BdlLnlKFefq92Zc4RTz3QhJWJvkPHshBZjXr1bhkpUIDIMvZ6tXmHUwBTxBAxIxcmhdk5DYbvj97UdCOVwzABGByQ0cgSwnOFiWKQGDNgxjYTAoUjNGl6WYzQ4FrYcCDqBpIAHDBpwsmVV17ZjsSlicHUgSY0Q/YOs6SgvZE3yxRgRm518ds7pq0YsfItpoAdnKXRjHCipizH6wE+1McWGoIC8IOjWL5KmMIDfVimAHnkqV1oEIEqbe7D0D10WS1kmuqoXQJeLE0CiKSM1dLXu6LAolDANzS+8l355sxrvkNzAosQpu5nn3328La3va3dtJw0uCzSbBG0ODEXmBOTTx+Oy1rr/6mn0DerXuaijd7qmPlsI3kov8CQtfZexZsXCvi+xoCIZ3i5bx4QiR/33+Na2yZNbttiIlfkmXyy0LeoJ0Phy+YUIAKgASBJfiA7sBQjOwAdyA9AAfMRX2XkCE5KWZpSepBH3I6xJe+QyXz/vuPIMkLftGfeKZs8Y/5jnUImAcKQWQ4++OAmP/D98eY3v7m1hXx19NFHt/ccoyqHVQ3ZiTzFEsRcg75pZ2jX02D8O3H6MOnV1/Y9NDD/eo52ZSHSU6t+FwWGoQCRGgVFgR1AgQAiBIVcmBoHoJg3htULEYmz1hCTw0gJAEAWDHt7lzQYr7jAFOCGRQ3AA6hCQ0qjABhgCk8LAySxrcVxv44OZq5K4Nhnn30aeCI+gAfAwoRWyGyUFudd73pXAzRsr+EhnXDiPuyww4a99957eMITntD8dRBk7BkGkthGQ8gBUBA2bAsilEwSGLbX3rW81ye0T9rOgRkhyzO0KkBkLRSsOMtIgXwjvkvfp2/IQsEdnyIBLZeRPtXmosCiUMC37juniMAXXZ757vFq/sQADN557l7rlfhC4KotsOSRPF8pH++Bs4BQ8w1LjChbbEWh9CGHkCvILHwgkWPIM4AS5QBfvHvKU57SfHaISzYDoLCeJc8AS+RDrjnjjDPaVmHyDDmGtQcZidUtZ7AHHHBAkyHISRQ5sRijzKEEUj+gBMAi4HBouVI71/McTfQBGYZMxY8cWc/zAkTWQ8mKuywUKEBkWXq62rlTKYDhASwwbAwpFy2D/fYYLyGif5c4awmlkzeGTENDKNjohYlavKhvgBJmp7bb2N5Do6HOhAzAAUsODs8wfk7AWHkE9KAxApIQHgAlQBHaY17p7RGmqaG5YOpq3y7gg3lnTFx78GOj7VlLOvRza7vtOQAfFjGElTy3uCNQiFNXUaAoUBQoChQFlo0C+CH5AD/EC3veGQsLi3+8G0jh/XquxCcLUMSwQO3LWWte8pGO7MWShKzVAyWsY4EuLNdsU7H1j7+wo446qilmADuRZcgxlDjkG/IMOcYNLGEBwpKUZRzAhCyj3qxPbAVmacIilkymHj34sda2bCSe9mszixmASKxDPJ8EiITuGymr0hQFFoECBYgsQi9WG2aSAj2DwYAADASJXN5j2DQFGDHGRYjo0yXuWkKMFhOnwWB6udF8pOvT5v8+jKABhGHlQjDA/LMlhrBE++FmWeE5gQANgAoEA1omFiksMQAk4vRljH+vhQYbjaMsbQIAEXgIQv1eaIKdtqi733UVBYoCRYGiQFFg2SiAV5Jj8HU80x1eja/z52U7CCuIsQJoPbQiFwEWnGC1XmAl9VlrKP8AJ7b3UfawmM2WGPIM2UAYWQbYQJ6hNNFOslv8KVEcybOnzaS6rIce642r/BtvvLFZ7tp+FOWOepBHtUe9c3leV1FgmSlQgMgy9361fYdRALMNINIzHr8xJUKErSm0IoCCPs5aK4n5AlZYm9jPutFL2ZPKz/OEytMu1iM0J7Fw6dMmbh9Kh1lrN80K01Xai5UEiI22Yz3p1InAwBM7M1rWMPrBc3UXEobKQmQ9VK24RYGiQFGgKLBIFMAP8cYAImlbeDw+yULEFhMWIxbfG7kodQArV199dQNg5L/WK3Xpwz7tpLw8w+cppliraocrz/u88jvygf/5AOFzjQVsr5BK3ElhX6dp/6bAse2HsirKnZRBbvN+rKDL+wqLAstIgQJElrHXq807jAKYoAsDyvaPvvAwScyJHxGnmjCvBA7kXR9/td+YM9NPDryAExu9Uuc+ff8sv4Xq6VQa22Vsdekv71e6CVSYNCewfJ4AixJXO3LlWf6fVijf/lIfAg1nsrQ8rFlStlA7CYCxEBmn7/Oq30WBokBRoChQFFhECuDP+CUeGV495pV8fcXBO2Ah/DLhSnTp35MJWLwCJ/xWVv9+pTzyvI+70u8+rjj4vG0vtvKSyTxL2vzO/9LmGflOGj5Ibrrppm1pEiflJOzzyLNphupDFgTQULb5P3UV+p880wMi0yy/8ioKzCMFChCZx16rOs8dBTAgi2kMqGeGfmP0tCgW5Jxz8TzOLNPz9QgB4toXy8yUuepWX+pOgGAhQogAcGzvSnu1zx7c/lhb73JvL5/NvB+XgW68xKuPvbb8l3jWX/4n2BHMtFkedRUFigJFgaJAUWCZKIAX9ltmxm3HG7139DX+bkHeb9cY899x+vxPJuJ3jBWp7R07gufi7bbMsEqJUiT1SageaJDQb9trHJ3LMqYHgJJmq8PQVEjWJJNxVp92pL7eu8RhxdJvmdnqOlb+RYFZp0ABIrPeQ1W/haBAABGalTClMDHMyk1o4IfD0Ww8kQNQEmctRJAHUIWWQnplbvVFgAC+cDq2VqsUTFg7999//7ZFJdtQ1tPWzbQLnVwpj2Bgz7Bj8hx/N0lrIs0YEJG+rqJAUaAoUBQoCiwLBfA9ckyUNpPajV/yJ/KhD32oKUss0AEc0nq3Ft4pDkelHLJP2o47qdzNPiMzcZLKKoUFxaRLvVJ/bUELCiHKFCe67Ai5a1yv1EnZFDrHHXdcoxugJgqcxJFWXxQgMqZi/b/sFChAZNlHQLV/SykQxokBsS6YBIiEUWFcttU4wcUxcECDsUXJapWVDybOysQCH8Cy1Zc62zJjm854y8yksgkQtgQ5wcU2G5qfCEihw6R003yWcoT6xKkyL3zhC4fLLrus0Ux9xldoW1tmxpSp/4sCRYGiQFFgWSiAF5JLVgNEwmNZXjpy1sl3lDU9r18LvZxo5xQ7VibJcy3pNhoHoPC+972vATErASLJW33IdUCH448/fnC870pWJUmzVaG6oC2Q4/zzzx+OPfbY5rCe8mkS3bTTlqCyENmqHql855ECBYjMY69VneeKAmGcvJKPAY4wq4QABiABpsw5qlNY1qpxkAcG55QUjrQwx62+1JdVBedda7EQYWXxxS9+sR0PzLIkAFHar75+b+WVsmiwOE91ogwNDwEoAtu4fGm8L0BkTJn6vyhQFCgKFAWWhQJ4ITkj/HLc7vBXIfkAmOHI2quuuqopQ/J+nG7S/2QElhfXXnvtNkuHSfGm9WytgIg2iMsaA+BzzjnnDPymeIB9mvgAACAASURBVObdjr6UCeCwRYaTehbCObFwEr3VswCRHd1LVd6sU6AAkVnvoarfQlCAJiGAyLhBYVgJLcqZXtKMMN+kgVhpod7nJT0B5JOf/GQ7sYaZavLs403rd8pzMs7b3/72dnzwOO++fEIUACKe2IEh2rWVl/Jdfei3/nBcML8h6Mz/SWicuH29PAPm6EM0nhSnj1+/iwJFgaJAUaAosGgUwPtWA0TS3vBIigdgiK28TnHLVuDEWy38l3/5l6Zs+ehHP9q24CTP1dJs5h25gDKKo3cWMCtd6kEe4ID9mc98Zts2rJ2e514p7TSehw4pi1xyww03NDCE/KcuY3kmcZUPEKktM9PoicpjkShQgMgi9Wa1ZWYpgNHanhH/FGFokyrsHYb113/918PJJ5/cvJezGlnLQhwT5Fj1Fa94xfCVr3ylMcUxY5xU5kaepZ4333xz2686yalqmLC6/+xnP2uaFE5fCTp5t5Gy15pGGX37U2d1ff/739/oBKRRvz7eOH/paMQCiIzf1/9FgaJAUaAoUBRYdArgheSYlSxEJrVfXAt1W4HJNQCVnt/K0z2+LOw5VeWjzPabSXHGaTbzP7mLEsqJf3j9Spf6O03GVlvbgVhjaE/fppXSTuN56CW0Ndq235e97GXNMnh7/SKNdpIptaOuokBR4P9QoACRGglFgS2iQM+0MKD4EFGcdytdSUfoYPp40kknNf8WGHQY7mppmXGyerjwwgu3CR4rxd/sc0ACaxbgAkuWSZc6a/sVV1wxvOAFLxi++c1vbmvHanSYlNd6n4WWCdWXD5Nzzz237fvlCR9YpY6rXdITNLRDHnUVBYoCRYGiQFFg2SiAF7Lu7I/d3R4NpMF3gRssRFlnjq0YxBlf+DI/ItJQvGz1RU5zysw111zTeP2k8tSJcoffNFYvvVymDZPaMSmfzTxTB+WQXWwrIiPaupMT8rZXB+20ZSYKus3UpdIWBRaFAgWILEpPVjtmkgJhkAFEwoBWY1hJI4T+s/Q4+uijG6OWfqXFe9JJw7s7rQohJM+nTSD5AgduvfXWVh5mPL7EUV8ajJe//OVNINKGPBdu5SX/3OoK0OBfJcBM6pJ6JO64Tp4TAGmCChAZU6f+LwoUBYoCRYFloABeuF5ABF2ks03DlpTDDz+8OY0fgyJj+klD4WLBzxLD/1t5ARgAIkCYlbb2kCEuuuii4fnPf35rgzoFoPB7q+uY9iuTjzk+Q97xjnc0hVTKX6kOeU4eteUn8mjyrLAosMwUKEBkmXu/2r7DKDAGRFYrOExLaPFNA8FS5MQTT2zn3K9kEim+G6P88pe/3LQXgIitulI/20/sX1Wv8SXObbfd1rQpnJf+6le/avVTR5f3W3nJ343+ABtgCDNXliExc02c1GdSnTwjIEWA28o6V95FgaJAUaAoUBSYRQrghRbSq50ys1K98WFKmvPOO69tV7V9JsDDSnzXwv0v//Ivm9UrMGIrL/Uja7FgsZ1Enfp6AUw4eAVC2FaTLSeJ18edVj3HefpfPSiiTjjhhEYbFiuTHNSP65B6Rjkkn7qKAkWB/0OBAkRqJBQFtogCYT6yx2gx/p5prbVY4AHrBN7aWTZ85CMfacCCPPsy8lvoxBen1NgaspEy11I35agbQITTNIBDXwfvmGUSZniKJ2RsNQPuy89vZaIHzRT6EXj0hfolzvbamz6oLTPbo1S9LwoUBYoCRYFFpQCeGQsRv9d7WYzzX8GKlVxAmQJcSV7hyQmVRYHx0pe+dPjud7/7a3w7adZbh5XiqxuLXDICXp86CL3jQF6dL7jggm3WtyvlNa3nfR3IIRQ5ZEEWKmeffXZTOK3H0kN+ZMecMuP/uooCRYFhKECkRkFRYAspEGY2BkTWW2QQfcLDi1/84uac1CK/BztSlhAzv+SSS9o2lbWeUrPeOilHuzgXY7JJS5E6eE6z87GPfaxpMfgNwci938or5SekwXHaDo0Up2M33nhj24bUgyFrqZP4hDbWOvqirqJAUaAoUBQoCiwbBfDLzQAi6CUPjtUdd88Pxxe/+MW2ncbzMW/2jNLlDW94Q1NqxHIj+UyT/pQnFCeXXXZZU0IpO3X68Y9/3MCQM888sylYyDjebfXV14FijCzFMT1FE5kr237XUw91t32JxWvyX0/6ilsUWEQKFCCyiL1abZoZCoRhYkBAigAY662gfCzE+QexHYaWgjBhf20EhDA2ofKcnkLYcDTcVjDvlAOkeeMb39iEhNST9oFpqb3Cl1566TaP9N5v5SX/3KxAgCHnn39+O7qPViV0GAtd26uTPAkjBYhsj1L1vihQFCgKFAUWlQJ44Ua3zPQ0wYNtocWf+Qi5+uqrh3/6p3/axqPDx4X4LjmGL7Vf/OIX2yxNvZvmpV1vf/vbmzIJv5c/kES93vrWtzbnrqxEAkJow1Zf6kBusSUZGOLkQc5pWeRuRJ5Mfjllxv/uuooCy06BAkSWfQRU+3cIBTBVgEgY6XoLxbCyiMcEgR1vectbhne/+93DLbfc8v+Zd4rvmDqMk2klbcC0LRuUoV1/9Vd/NfAPQluhDIzbs2OOOaZZsrAUUffUf71tX098dVIH2id1sL3ICThMbQOGyC/0XKtAIz4BSR9Om47raV/FLQoUBYoCRYGiwM6iAF5IjlnJl9la6yUfN/mARQbljZA1CCVPLzPg3ZQbz33uc4fLL798m/XGWstaazztYgGiHng9+YYcxcL0qKOOaoBE7/MkbVhr/huJhxasgQFGrEIuvvjiRrOePuvJV53JMOgeZdp60lfcosCiUqAAkUXt2WrXTFEggAgww7VeRpr4QheGRnDgI8RWEHtsWWUoJ8CDsjgte9azntWYaZjfOK+W4Qb+yEc9lMFaheYmJp1OlHnnO9/ZNDs94079N1DcdpPIW5tpcz75yU82Aeacc85pAo16pt0y6n9vN+P/G58AGAuRrWzHWupTcYoCRYGiQFGgKLCjKYD3TQsQSd1t3WB5YSvIu971rnZ6Cl4bJYYybVml4CDP/OhHP2q8PumnFWrXBz/4wXbsLlmGYsWJMs94xjOGb3/727/mADYyxFbJAvJFl+9///vDKaec0pzBf/WrX/01ECN1WGv7Ex9dWYhky8xa01e8osAiU6AAkUXu3WrbzFAAA4pTVZXaLBOVHtBASPjCF74wHHnkke0ceiAJph7GBySxZeXAAw/8/xyxJs5GiSQ9oIG1CgdptBhf+9rXhuOPP75Zr2y1z5DUX4gWwBD+Ul772tc2oQldos3ZaBuTThk9IJLnFRYFigJFgaJAUWBZKIAX4rUAC3x3WhdZwhaa97znPW2r7ec///nmuJTspBzvbRM5+OCDG0jhtJpplq8dZCegC58mLF5t59l///2HMRAxrTbLp5dj8lu7KLfIU4cddlg7YSdO6cXZ6JX80bT3IbLR/CpdUWCRKFCAyCL1ZrVlZimAAQEIMLkwpc1UVh4REuTLl8ib3vSm4XnPe17z3cEckgCh3J///OfNsekZZ5zRBAzPw1QTrrcuaYP8+RCxfYdZqePobOMBxExbWBnXMTRAU9oOlioXXnhhqwt6TFP7oaxyqjrugfq/KFAUKAoUBZaJAlmsT3v7KB5LnsBnr7nmmrbV97TTThtuvvnm5jvNe0AMcAJI4DQYdZjmxUcbOekDH/hAUzDZJqOcbOFRh2le8hvfQBmKHXIVi5krr7yyWb1qO9pvtg7So3NZiEyzJyuvRaBAASKL0IvVhpmngEU75o2pTePqmSgmiWHTrlxxxRXN4SpQgoknLQ4rCb+ZfXoPLOnTb6Q+0isXY6W5ePOb39xMOp0qE8doG8l3PWkAO7REX/rSl9q+X3t/+VOx55dQoX7TurS3AJFpUbPyKQoUBYoCRYF5pABeiL/ih9PmsZErKHlsFeEzw+kytq3kVD3yjFPtOGKlBJmmTEWOAkC84hWvaDcnpuQ27VQ39zSv5CnUjttuu635COFPhc+QH/7wh20bcq9I22wdpC9AZJq9WHktCgUKEFmUnqx2zDQFMDTgBIY7jatnpGHWQkIKB6L2wbLa4IDr1ltvbWDJxz/+8eG4445rZpjiJY+N1EdaQsv3vve9BkZw3EqQiPNW77fqAoSwQOE3hSaHVQozW8BMNDmhybTqoD32FPf7mqeVd+VTFCgKFAWKAkWBeaAAXojPUqzgs9O+IjsACChXbF8hywBHnLDH4pWDVVtjWXOQQchXm7m0A39nDUKeeP3rX9+UK2ScyBLqlbptpqw+rfy0U5s+97nPtXJf8pKXDFdddVXzX+JdyhWmLn0e6/md+keGmqYV7XrqUXGLArNIgQJEZrFXqk4LR4EeEAlT6hndZhucvOSjLFYS9p++733vayfAAEOcunLWWWcNL33pSwf7czkMC4NNncb16PP1TnxMlK8SggrBgVNX/jrGXudXynNchv/H5eT/PqSVUmdaIdtzmJM6gk5b7C2m9ejzWk/5k+rUP5MXEInQpJxp5t2XU7+LAkWBokBRoCgwqxTA+3pAxP/9Pc16yxco8ZOf/KQduwsAYf163XXXDZ/97GeblQgnrDfddFOLN6lseax0AQZYgNhi60S+E044oeUPZOnBgtXyWCnv8fPQyHNylO05kaMc6UuOIq/9zd/8zTb/LH0a6aZRD/mQYcqHyLiH6v9lp0ABIss+Aqr9O4QCQIpsmcHUMETof7+1Y1rMLg2S9y9/+cttgoNTXwAjzEEPP/zwJgDw1q5eBIMw374eeeY9wcTe1q9//evtON0XvvCFw9ve9ramrSEg9elSh7WEKWNSqFwmssqNjxCaoRe/+MXNjNbJNtqZtGspbyNx5N87VfV/XUWBokBRoChQFFgmCuB9eG4UIP7Hp8kz01YWyNtNXiJ/sAJlDWpLCeenAITnPOc5g1PtbJ21bRiQMZZn5OFKXuqq/oAWwArFzgte8IJ23C7lCnktZW+0b5Ne3VMuulGs2BpDoQTMOfHEE5sFDJ8h/Hqk7km30fJXSxdAJHJb6rpamnpXFFh0ChQgsug9XO2bCQpgQIAHDDFgiO0XASNSSYxpWlfPhFmMYPz24x577LHtFJZHP/rR7fe1117b9ufSGKgTgcINiMC8+engcd1+WltUOBqz9UY6QspmmWnSp75opXwmuQCPb33rW+14YQCM29YcliK90JI8pkW7cT7yRxu3ctWR4FJXUaAoUBQoChQFloUCeGEPiOCDrB3ICp57P60rfD0h2UkZ/Iuce+65zdoVkLHffvsN5BkWJOQFcgP5gQxDllA/spZntuEAVliWsjA95JBDmkP6H//4x83yJWUl3GhbpEcb4It6kK+UwbqFzzVylNBxw2hHpggIkrKFW3GpV5yq+p2yt6KsyrMoMC8UKEBkXnqq6jnXFLCIxhQxR7/5wOi3X2wF4+uZqt+YrTIdk8sp2b777jvc//73H+53v/u1Y3mZbQIbOGAVx5abT33qUy3us5/97Bbf/lqCRO8rZLN1Vy9MGV0ILgAYJqtMWFmCEBxOPfXUVi9CzSShIW3dqkGiTBolgos6oiPtSl1FgaJAUaAoUBRYFgrgteQYygF8kVIE0AB4CG+eFi3C1xPKN7/VgTUH56MUJY985COHXXbZZdh9992boofyhs8R22lsQ2FB4hhdW1Mcpfv0pz99OP3009spNmNLiZQhXM+VdD0QwmrFyThkmKOPPno4/vjjB87nWYmQeaQJ3ZK+D9dT/lrjqh85S9+5I4uuNX3FKwosIgUKEFnEXq02zRwFMD5MB/OJJQZUHuPLFSaY/zcbyi+MVl75X13Uw/5V4AZw5PGPf3wTJu52t7s1kORRj3pUExqOOeaYZs75mc98pmk3ABLSY6jJu2/DWuucNPICMrBA4dDMSTHKZAb7xje+sVm10PYAIcTty5RHf6+17PXGSxkAEVoV9Y3wt968Kn5RoChQFCgKFAXmlQJ4MCsNSp3IM+GH4ZVb0bbk3YcBHvBkSpRPfOITbfvMQx/60OHud7/7cI973GPYbbfdhsc97nHDQQcd1CxK3vve9zZ/asAU9Y51hHz7K+X0z1b7LT5ghYzAAuXSSy9tJ/4deuihzTcJp7CUTeiGfuouzWoyzbhOq5W/1nfyDCACyAJsAZe2oqy11qniFQVmgQIFiMxCL1QdFo4CmEt/R4CAymPeWdz3zNDv3Ek7/j/PE+Z9wjxPuNpzdYhA47haDPyUU05p22lYjzAldbTdOeec08w8OR6zVSXAjjZFmOjLyW+h9+IpB6BAW0JY4OCV9oaDND5NWJ5wkmp/ME2OOGjFqia00iZ5JszvSf+n/ZsN0xbtIMjYeqROEWYWbuBWg4oCRYGiQFGgKNBRIHwUP8T7KChsPaHcwdsjB/TxwjvDp/N/4iRc6Xne92HijkN1itUKf2PXX39921LjxJanPe1pw1Of+tRtlqYXXnhh84PGQgN4QckDGJE++abM/C9UhnaKC0SQllKJBYryyE9Ow2HVyjkrvySOC+ZzjVKH/IBuK9FqXKb/lZvn0wrlqa36L+BMyum6vH4WBZaOAgWILF2XV4N3FAUwMEwUw7W4xxTDGCHzgAWM1e23O9sy+ucAFP/Lx93H904ad9B+7z1PnkJCi7R5lvzFc0tLY8LJmD2t11xzTRMoWGkQKjB5jsxYkwAtzj777Lalhenn5Zdf3m4CwSWXXNKO+qWp4cBVaOuL022k5RCVEzH5sQY57bTTmhmrU2qUS0gJaJQ2JOzbrS3aRMAQpj0JtXPS7/5ZaJG4PX0TT+g9+hK0OKn1myaIEFFXUaAoUBQoChQFFp0C5BnKDfyYYoBVJwVJ5I/w0fDVSc/DyykV8NbIJHkuTLo8S359GHkmcZKPtJ4BK/DrH/7wh8M3vvGNJpfwL/Ka17ymKV84YaX8IYOQZ5xaZzvNxRdfPFxxxRXb5Bn/AzXIMm5giq040pGNbL/hT41cY/sNOYccpEwWK+oAdFAnd+qXtnuW35FltCXP8ju09Tx08Lv/P8+F0k1K65n3AXP0nzwonQK4LPo4rvYVBVaiQAEiK1GmnhcFNkkBDIY2ANgACLGYplHpGSPmFGY5fh5m57l4hIgwNP/nxmSVEUCkzzO/I0Dk/zDTlJ3/k6e8aBA4AaMBYdHBGRjwAwjCuztBwikzBIE3velNDTBh7UHYcLP48J6QwMrkgx/8YBMqrrrqqpYfYQUAEqFK2WHi2pq6pf3qmGd+BxCJcJU2COWV//vf/TPP+7yVnfKTJrQlAAKMhJ4VILLJj6OSFwWKAkWBosBcUYB1BD5InhFmsZ+Ffvgz/umZO7wU78378FlheHD4cWSZpM3zxJNPlCDJr8/bM/lKl7TqSf5ieeq0OhYdnMxT4ABDyCd8fFDaCDlbfdWrXtVkGDIN4IPFh5P6KIPEp+jhY43yiIz093//940uZDx1j6wRuU29xjRJPPUFiKwky2hH8ku7xv+HFt7Lzy1O0grFIW9ROkUeFacAkbn6DKuyW0SBAkS2iLCVbVGABYGFMwYPkceMaFhYjYxvcftn/l/rPSmdZ3164ExfRt4l7Wr/5x1wJ9tftIWQEaAAsEEgsK0G0OE435/+9KcNVAlQQ4iRPiajfX1Sj77eKz1LfVYL+3zWGi8aksRXz5jH9gBNtvDUCC8KFAWKAkWBosCiUgBPzIWn4uFZ8JMB8MLw2jG/zv/hp+Mw6SY9317apBnnkXR9mLgJIwupO/ksvF27KIGAPSxlyTNkGaH75z//eQMSgBgBMNL+1KMvd/w75Sdu/l8t7PNYLZ53iet32pg03tkmk7Zqt/YCYbyL7JO+rrAosIwUKEBkGXu92rzlFMBgLP4xT4KDhTUmiil550q45ZVZoYCUnzB18v9a7nH8ScX0eef99vLu4+V3wkn55Z0weffPNvKbIKH/aE8IgYQGv/Wl3ylrI3lXmqJAUaAoUBQoCswLBfA8fJASRGhBjR/ik9O8tsfflTXm8X2avEvY1y3PxvEnxemf5XfSJeyf93mv9Dvxd3SoPvoP+BEQi7KHlYhnfXv63zu6nlVeUWBnU6AAkZ3dA1X+wlGAkEBzEDAE83ETJDwvpjPbXa5/CHyEPyCW/vTMb2anAURmuxVVu6JAUaAoUBQoCmycAvge/mfhzMo1ygGKHfywZJmN03arU6ZvyCssQ1jqUvJ47hkLEYq6xFOf/vdW16/yLwrMGgUKEJm1Hqn6zDUFMBTgB+ZDYPDbM0AIYaK3EJnrhi5w5QmAvWWI/suzAkQWuOOraUWBokBRoCiwjQJ4n0UzeYaSwP9uC2u80O+6ZpMCUeTEmieypz4rQGQ2+6xqtXMpUIDIzqV/lb6AFMCICAyYjt+uWIgIXSVINDLM5B99o58iUKik30CSAkRmssuqUkWBokBRoCgwZQqEF1pMhx965n/8sOSYKRN8ytnpH3Kou++rAkSmTOjKbiEoUIDIQnRjNWLWKBDhIfViIcJskSDhwpx6BpV4Fc4GBcb9U4DIbPRL1aIoUBQoChQFdhwFwgv7MBYi+GJds0mByJfpt76WABFboMZbZvo49bsosGwUKEBk2Xq82rtTKAAQsYUmPkQmMamdUrEqdE0UIPjFh0isfNaUsCIVBZaEAhHANTe/E/bPxuTIXJgw75M24fh58hy/T7w+TJxxOI7jfeIk/z4cx+//738nn4T9u/pdFJhXChjPeKFtGBx0FiAyXz2Z+SgWInzDzHofqnNdRYEdQYECRHYElauMpaRAP5FbRLMQKUBkPoeCvixAZD77rmq99RSIoL2VYVoxqQzvJj0fPxvHsxgYx1np/3HaxMvzhHneh97VVRSYdwoY076ZshCZv57s56PeQiRz4Cy0qK+j+uT/Wahb1WHxKVCAyOL3cbVwBigAEBmfMmOyr2s+KKCv9B9QhDBRV1Fg2SkQYXU8j+V5BG1hf5sLcwOI3bYS0joz4XbTXLp9c25gsm/PM7/znk8fDh9z52Qvz/k4cEuXfKSTv7LcFnZuv5Nn3ueduqmjOvv23X170s6eDqHBso+Rav/iUcDY9m34rvoxv3gtXbwWpb/MYeZK/Thrc1XqmHolXLzeqBbNGgUKEJm1Hqn6LAwF+omc0Eyg7oXnTPwL0+AFb0gWQ9VvC97R1bxVKWD8BxDwTZjXAmgEWAiIQei2V90dsMJxj7/61a+Gf/7nfx7+4R/+YfjpT386/OhHPxq+//3vD3/zN38z/PVf//Vw4403tvDb3/52e/bVr351uP7669vvb37zm+3dd77zneELX/jC8KlPfWq46KKLhk9+8pPDpZdeOlxxxRXDVVddNVxzzTXDtdde29J94xvfGOQlrTJuueWW4Xvf+14r9+/+7u+G7373u+35t771reGmm25q79THux//+MfDT37yk1ZX9Vb/ADCO5tYui8MANT3Qgi4BUkKz8IWaR1YdZvVyRimQ79+4rjE8o520QrX6uaeXR1eIvkMe9+MJ8ByAGg8BTo/n0BpzO6RblrKQAkSWstur0TuaApnEw5B2dPlV3vQokL6cXo6VU1Fg6ymw1nGbOSphQA8CtNuCn+UFUAA48I//+I8NzAA43HDDDQ2I+PSnP92Aije/+c3DiSeeOLz2ta8dzjnnnOHDH/7wcOqppw4veclLhjPPPHM4/vjjh2OPPbbFOeCAA4Y999xzeMQjHjE85SlPGfz/7Gc/ezjiiCOGpz3tacOTnvSk4cgjjxxOOumk4fnPf/7w3Oc+dzjwwAOHPfbYY3jAAx4wPOhBDxp222234ZGPfOSwzz77DE9+8pOHJzzhCS0v6Z/4xCe2PA455JDh4IMPHo466qhWvvCpT33q8PjHP76V/+hHP3rYd999h/3226/l8YxnPGNbHs973vOG0047bfjABz7QwlNOOWV417veNXzsYx8bLrzwwuEzn/nMALwB6vzt3/7t8IMf/GD45S9/2ejEaiVWLrE6QdsxSB66b6+/tvd+PKLWG3+cvv4vCowpUGNqTJH5/X9n9KUy8RTzIrAZ8Hzrrbc2PvK5z31u+PKXv9xA61/84hfDv/zLvzS+AzCRZmfUd357t2q+FgoUILIWKlWcokBRoChQFCgK7EQKEAA3emfRHSsFYcANmjgAByeJ//qv/zr87Gc/axYTrCkAHBb5l1xyyXD11VcPf/VXfzVcd911wxlnnDGcfPLJwytf+coGUBx++OENRAgIsffeezdg4iEPeciw++67t/vpT3/68NKXvnR4wQteMBx99NEtBHZ49qEPfajld9BBBw3Pec5zhle84hXDW9/61gY0nH/++cP73//+BqS85z3vGS6++OJmBeL5BRdcMLz73e8e3vjGN7b0QgDFueeeO3zwgx9sIIw00gMxgDLveMc7Wl5vectbhte97nXDy1/+8gbIvOhFLxoAHoceeujwrGc9qwEuQBegDDAF0AKsUeeANN4BbrQNgCIecGX//fdvYAwQ55hjjmltff3rXz+8+tWvHt72tre1+mgzq5avfOUrw9e//vVmocIqhdUMixoWJzSktKbpv7X0vyHaLxbGafoh3Mfrn9fvokBRoCiwGQqM5538by6zPfGf/umfmqXe5Zdf3kBxQPTDHvawAc+45z3vOfzBH/zBsMsuu7R5F4gNWH/f+943iP/5z3++gc5AEnkFIEkZfagN/q+rKLA9ChQgsj0K1fuiQFGgKFAUKArMAAV6QW+l3wE7so2F9s3WDgvtv//7vx9uvvnm4Ytf/GIDFgiYgAeLdMABsABAAZQACgAHLP5ZZrzwhS9s8cQBagALCKmAkQASLEHcLCdYgrzpTW9qAAUwwnYW5QJabIlx0wbedtttAw2g0P+sKoAy0QoCBwA1BGgCcLbesFDJlhzbb7wXiu+dNvudO//LI3FZb/z85z9vtzJpKJXvtl1GfVh6qDNtpa042vClL32pgTKf/exnW7uAG2effXazekFH9ASusGB55jOfsJHeOQAAIABJREFU2axRXvziF7ff6MYy5rDDDmvgCcAEKIO+gCI0lR7o9JGPfKSBQsrWb+qFTrSpACxAFuCE1nSStYkhO2mczMBQrioUBYoCC06Bfu4B7JqzWM8BqAHQ+MtjHvOY4R73uEcDQAAhD3zgA4f73e9+w73uda/h3ve+97DXXnu1udL8iK8Als2fL3vZy4a//Mu/bKA4oN5cDhwxD6bckHf8f55XWBToKVCASE+N+l0UKAoUBYoCRYEZpUAEO0IfARPoQQgEAFjoW9RbyFvAMznmT+PjH/94s4wAXLBQIIjapsK6gUWGbSWsHI477ri2lcV2FotyoS0vrCo++tGPDrbBsBgBBvDdYZFOuFUeIEHZwAXAC+HUVho3MEP9LN5Zo8THRvaG0+5pjzC/gTqeuf3ubzTwfx+GLquFSTOOk7xTXh+qT+jMWgOt3bGq0aaAMgFtgC1owNpDP7D+4JsEAMTK5sorr2waTtYtACOAFBCFoA+I0i/oDyhhgaNf9Jt473znO7dZu9imYwuSG9gUHysBlGxnUj/1RevQctz+GR3qVa2iQFFgjilgnjHnmCvNh1/72tea5R6+wprOtkSgMaDYHPeqV72qWfGxRmSViHe58Zr4lDKX4mvmPnMmgATAbAslAJnlCJ9PQGLzuks96ioKrIUCBYishUoVZ2YoEGHOZBcBOoLuzFSyKlIUKAoUBTZBAfOcec1inPY/oAcNG+ADAME5KFDCIpuACLiwwCZYsvKgUSNsCi2u/bZFxC0egdJNy3beeedtW1QDOVgjWNADOCz04zgUKADQCKihflloq2/m4szTsxT2ddM16pYrv/v6Jk7e9XH7eH2+4+cBVNDJjX4WCAR2NLVQYAmDzpy8AjX0Z4CTOIvVP+9973ubBQoABDjCl0q0rNlqpI8917+0sJ/4xCeaVUv8mgBL/tt/+28NoAo4pV5pQ9pYYVGgKFAU2CgFzIP4FmCcVR2ec8IJJzSLOD6bWBSa2wDFnGqbB/E1AK45Ulogbm48xlzqubmT1R8eCJxn5Yjf4XF4nS2UgBPAtLxqbttoLy5fugJElq/PZ77FESpNgiZEk5pJkGBOmDOBOiXApMdUzm+Cnuc0kibVlYS85D3zRKgKFgWKAnNNAXPNpCvPhYQ1N2HPXBfLAw44bYv44Q9/ODhNxTwXbdlll13WFrv8bLAoiE8LW1xszyAYEjiBHbaq2HbBVwXwBIhi4W0eJVTaRhIrAsKmekSATD21we/caVPq3//fx8nvcZj4K+U7fj4pfZ4lL/9PSte/79MkftJMipc4CRNnUpq86+OOf/t/e3c/FsL3bHnC+4AmtJ+28Tg1h6YU4EEzassNqx8LA9uZ+DRhjs6ZrDFCA0uLytLkrLPOalYqfJewYJGfBYkyAG7KxT8DdPXtGLc97c7zPm7/u49Xv4sCRYHFpYDv3hxirmIFx+KN/yV8ikUHKw5zGV5njhF/ezdqjeOYK81TrA+dEgZgecMb3tAsGwHGrBrxO3MaviZ9XUWB1ShQgMhq1Kl3O4QCmegiDNI+WhBAeC0ITGoEN4K9femEPyZ3ThVwugAndjRkzO8sBGjX7JW3n1w+BP2VJt4d0sAqpChQFFhYCmT+SgMDKCTMe3MQwcz8Rhg0N9nWQIsGzLX1BMjrqFjgBUsAAiTgw9YJ+6Zte3n729/e5kG+OliDEAL5r2AlIi2AGOAB7FAOoCUL3BIK00vzG+pDY8t40rcAE4oAPA/YRevqxBuaUr5IWIswU4/jV75L8MrcxhArIQsIPlGcFkTBwHIFD+5BM+NoDJplnCdE2Yz5+aVy1bwoUBRYDwV88+YGlm8sDDm1ZrHGMsQ8xEoNCG8OyfwgnMYlHyAM/0osUvBIfq9sQzSfAU1SrvJS/jTKrjwWhwIFiCxOX85lSzIxEe4AFxYI0F6CGc2XyZTGy8KAputxj3vcsOuuuw53vvOdh9/+7d8e7njHOw53uctdhjvd6U7D7W9/+xY++MEPbtoxiweCIdPvsdXItCbiuSR6VbooUBSYGgUyh/VhFqzmNYIYEMQcxCwY8EE7b6+0I1wtSPmMYEps0QrcjTafRt9v8x9tG+2avdjMheU11uj381pfn/731BpeGe1UCqRPVSK/hcaehYlxZ5EQ5QJLEPvx+RuxncaY4iNGiM/ir447dkKOY4mNOwsKfFgaSgkgCUWDsWxMK2MMkKQuO5U4VXhRoCiwQylg3iG/k7lZq3F6ajsLQMJ8gReO5wb/T+vK3EcJQObn6JoyQX1YWLKAM1eN6zCt8iuf+adAASLz34dz3QKTqP3xTOiuueaaJqAxraMNjSM5whszcfsF3Rwu2VNtsnUzC49X/3322acdfUiwc4zXbrvt1jxUW0zQnJkUgxRPczKe606oyhcFigIbpkA/j5jPALsEQFp74C7ww5YVx7wCPhzFypEpodFC1MkiNGne285gbrMdwlaZnChiUWtxG2sPgh0BU3mrCXipW8INN7ISzgQF0tcJVSq/x6GxkdtYCUhifFo0ANMsYPBeJ+mwTnKUMb8kxiNnhcbqn/3ZnzU+usceezSwBHDHKgmgx9mhMUoDi4/3Cw71qasoUBRYfAr47lmTkcPxNhbcjj+3bcZ8Ez6FEuN5alrUSb7mOnySZZsTwTiiZi3nNzA3c1TqMq3yK5/5p0ABIvPfh3PZApOXScs+eUAIp0uAEHvgIcvnnntuO9HAyQWENgsMApdFAX8i/rdIyG3yswChOWXuC5W2CJEvE2FAiT3VJmzaLpouE6OrBLe5HEJV6aLApiiw0e8+ghchD7hqywJBy7YXWnSnutC8s2wz97D6oHW3tY/m3UKT5l08AC8npj/60Y+2+fWwUDXHESTl3wMfGpzyE/ZEGLcpccbP+zT1e34pkH7t+znPtGr8PP/3QIkxZqzhrcae7VZ8igBJmJ9z1ks5wRfAYx/72GZFwjeJMZ2tqjSxLEns47fdy/Yd5vHyNH77Os0vtavmRYGiwJgCvm/8j+ISgMrSDG8jYwcMWQkQGee1mf8ztyVUL7z5pptuagpVliLXXXddA4C9q6soMKZAASJjitT/W0aBTFQEMGgyMzZmbUALFiE0pI52pFVlyTHWOG2vYvI38ZrsmPMS7mi/CGixIDFhsx7xv32OBDZp6ioKFAWWiwL57jMvrRaKC0A1XwBhbVexYGTJQfgjDPLDQHPO6gOwC+Dl5NKWBItFApm5yLxjXgLiBviQtzLUoa6iwM6kQPgohYXxCdgAkNhyQ3nBuS//AHzY4NvGe/yTHHjggW3vvpNufA/GPNBPWgoL3w7e3GtptbUf9yt9hzuTJlV2UaAo8OsU8J36joEhF198cfNJBAwxP5Dvyfm5+u87z3ZEqFw8G0DLou3MM89svrYoWtVvZ9VrR7S9ylg/BQoQWT/NKsUGKUDgDxhy+eWXN4GKg1TbXvgMYV7H8mNaE5XJDjgCWKH1uuGGG4bTTz+9aW5pby1SaHSBL4S/mhw32LGVrCgwhxTwvU+6A35YuNkKQLhj/QHI4L/DXBX/HwAPWwyAHpxScm5qywtNua0ywF3gR44UpDEzJymjrqLAvFAgvNT4xU+BJBYVxretNr4HpxpRanBszonr4Ycf3oASwCCrTwBJjgG2fZU1J95Li5vvYtL3mGfzQquqZ1FgGSiAjwFDKATI0468xRs968GQnUmLzB1AEb67WJ4DcvHqgDbi1FUUQIECRGocbCkFMtlYAFhgWBzYy/eOd7yjaVMJSE6SIWSJkwks4bQqJz9Cl0kQCOIEB1YiTIFZqdhmY1916jutciufokBRYDYp4FvPnEPTZQ4CgBDomPta7MUBJa/1FntOuaJl4uvDHmn+i2jBga3S0IJbLMqLUJj8Q4HMazXPhCIVzhMF+vGb78c4D0hC8cChodOOfBu20jjyl58cx0Fz1Op4aKHTb/DeK6+8cpujYN9OTkay4Ep580SjqmtRYBkowNoLAGIr3TOe8YzGK32/Y+uvnUmLzB/4MFDEiZWO5H3Na17TrDUpYMOjxa1ruSlQgMhy9/+Wt94kQ7AxGTG7/dSnPtUWEwCJb3zjG20BEo1pJq9xuNlK9vmZ/ALM0OIecMABzb8IU3cm8AQ78esqChQFFpMC5gBCmzmJUAcEsZDjy4O5L42XI2wt6CzmLOCYAjsNhmYJ+CEucNe2PPn04Ec/f/RzT54nXEzqVqsWlQLjsTzpf23P92W7DQUEzaztsfgtEBFI4khMi6hstcGH+dWhILHFxtHR5AULLN+X7zULl0Wlb7WrKDAvFPA9+kZtmXvEIx7RjoNn7RUwZBZ43KT5CQBi2yowllKD5af1QOLOC/2rnltDgQJERnTFdAm34zsMeRR9u//60KSV3yxMEtut8BQjaC960vgwr6VtZbLG2ak9fZmIUuRW0kfe/Q2EsZixJ5pp71/8xV8M9j1/73vfa32VOlVYFCgKzD8FfPvmYXMOEOSXv/xlA0ABIMAPCzVmv4APVmMcSQJv3/ve9zaAhIm/NBZnvea6n1PyO9TK/0JXwryvsCgwTxSYNJ77Z/mtTeOx7n/fH5CEFZXTacgBtpr57h7/+McPj3rUo9ppNnvttdfAaauTbmzDAT4CLPncIUv04ONK9BuXv1K8el4U2AwFjDP8YKPrg82UvbPSavN//+//vVl3+U7Jz77RHrCcpe+vr4vf5P5s2TcHOdhB//XxdhZtq9ydS4GFBEQM7P72oY6F2Elk91E40YSpNGuB/mYGaq+rvLZ3pWxxpbElJFsyMmks+senfdpKgEFPZuaOvuLlGZI8CwCROlog2ULDhJfGygLI3uZ+vGyvv+t9UaAosGMpkPkzYT+vetbf5hrzsJNcAKB8FtFSM+F3Coytc7bwCVmAAD9sf5Em1h/mg5SxY1tapRUFFosCviPfU75LViRkrcsuu2zgU4zjc0f8PuABDxjue9/7NrDElhv+ehwLzOzdtjbWnD2f7r95v/O9+t1f4//7d/V7PimQvu/7PM9WCjfa0j4/vudYMlkfWGgbj4t6pd3ayErSaWlOTuM/iBw9L5d1HuUGx9BOg9MWfad9roTz0p6q5/QosJCASD8pWpATbpltMnHmR8L7SRfhF3L4wAc+cLjb3e72a/dDHvKQ4frrr1+T9UAmDppIe2nvf//7D/e+972HCy64YNuHt+gfnfYRWAg6gBDmsJ/5zGca4BQNz6Q+2NHPjAVjhGO4k08+uXnK5vzttttu2yZQ7eg6VXlFgaLAyhTI/DopJKyZ422DAWyafxwdygs+qw++QPgBsf3FPmLWIbRbHDpbmDGp7U30V+IVK9eu3hQFigJrpYBv2ALFwhIfpiyJDxLAJYDk2GOPbac2sRxhReIkG8+YvbPi8o1zWkzeiKZ3PDestT4Vb/4oYOxQZJLxxzdFJLnfvD6tMSGfrDFs6Xre85437L777m19sMhbrkM/FhWvfOUrhyc/+cnDaaed1iws5oVPpg1kBIoPW+X5MSLv93PH/H0FVeNpUGDhARFnUNsHvttuuw377rtv0y6shOJaqGOuBGVe0t00iACS//yf/3OzbjD5bu/KR0coZ5J1hzvcYbj97W/f0EgTaN5vL595fm9ysU3mIx/5SDNBt1+PVsfzMBN0mIVLfTDMr371q22it68ZiKOv5mWinwU6Vh2KAltNgcydCX2f5m0aHoKafc2s0IDPnKCy/KAFAoYQfL7whS8MeIKtcYQgZvgAEPM6vtDPTZPmp0nPtrrNlX9RYNEokO83ofb5ne8ZOOLbpH1nYep4a9vayGY00/vss8+w5557Do95zGOaHxLKDN83h+0swZj0mxeSf8JFo2O1Z2hyGqCb0nJ8k/uNFScfOfXLli3zvPGw0StjyVgl05IX/8t/+S9N+WncbibvjdZpq9Npk/ainW/RsfLWVfwAAhfmpc1935kjWLeYN1iJmG/C/7eanpX/bFJgIQGRDHpCLs3ggx70oAZI7LLLLm1LxEqgho8BwgttpnFwsxwAimwEECFo33rrrQ1BlocjG03I8zJ5bHTIap8FCudoGJV9wLQ+PQI7SzRQF31vQjRe9t9//+GJT3zi8PnPf74tlmaprhvtk0pXFFgECvgWLXTMo+ZpoOu3v/3tbYKNY7VpjoEhfjOxZ5n2ne98pwEghCACXIDZCEDy7e+eVv1zv+sqChQFNk+BfFdyyneVZwl9n75Vchl5DIhpi6uTnVidBhzhg8RWm4MPPrgpst7//vc3BQeniRRTTPo3uxDefIsrh62gAMs+26n+/b//903WJ7/FYS9rosc97nHtuTHCue9mZfCMTaExOQZEtqKNOztPbfX9AHxsNeFMlXUlQCj02Nl1XGv5qa+5hS9Dfg0pTPo1ylrzqniLRYGFBkQscJlE2bLC3PKP/uiPGsO0lSUfxbg7x8+Z3DGJu+td77puCxF5YcQmbLffPsLtXeM6+H+1a1L8pOnf9c9Wy28j7/q8LThodUyctDpM0zxzJd5GytiKND19CF5M5x3LxTSXnwECmAVY6j5r9d8KmlSeRYGdRYF8j/nOhOZMILZ52/ZH4Ibj/oAdfP4AQDhCBYCYc2h9aIoJOKxG+ALxDcsn+fbtS5njZ/l/Upq8m+Uw7Zrn+u9M+vZ062nZP99I/TabfrUyk3fC1eLO6rvUPWHq6X83Pm1Ryzkri17bZlh02gZ3yCGHDE94whPaIpizR5YB/AKxDiDLkcOkDSAq73E5Kz1LPSqcLQoEEPnd3/3d1t989uETbvIb7b8tVr//+7/f/EaxOgo4Nu77jLH++aRnoYAtXgCRu9/97r9mIZL0CRN/tbwSZ9bC1Nk3g3bvfOc7G4BA2RvrkHE7Z60NfX36upINADuvfe1rm+XLolr49O2v3ytTYKEBEfsJn/KUpwx77713E5b//M//vIEjJszenBJ5+o+kJ9daAZFMGjQZtl8Q3nP7P0x4pXJSB+8J7urn45SH9CaefhJPeX0YgV881ilJmz3xiSvetK8+b4sQk4yJ8+qrr27mq97Pw4VWfArwfO/kGZqo3pQu7ZyHtlQdiwKzSoF8R+PQ3OQ2h5nzzH0EXltc4hDVVkaaYQsemkHzjKNyaf+cRiENACXz4azSYJr1Ch0JeBYBwCA3DRj6eT8vl763XZH1j77cCn61Ei2UZaFNRog/AlYG+IJ3uTdCT+3CS1gsWFykz1aqS/9cfIsvizw0Wal8z8Ulhyhv0a+0l3yFNo7UpIR54Qtf2KwEbJNm7ek0DPMGyxGWq/o34EgPlqZPxuGi03Ge26cf9e3v/d7vtb43Fvr+w0dYFVGIctLLorBfyPdxfd/eycN3JhyPj55WvknWKAAR/Mn8K31kd+l9j/Lty8nvPq9Z/q2+5kBbTp3+xAGytqdds1z31epmjmQJbiseZYq1i7bWtZwUWFhAxIdqMf5nf/Znw7Oe9ay29eV1r3vd8Ad/8AdNg2jCyrXaB7AWQCSTGyGcxsLESIPpVgd77uLJ2Ae4UnmemzwBGYRa+/PkIb+bb765meexMkl5fai98jYB+6jtk1e2j51G1TNtzgS2Uh1Ck/WE8pKvW/1oY5izcopGqE2Z68lzZ8XVFtt90I6pJRNczBQz6Om9s+pX5RYFFoECk74l8wTh07fmGzQHEsAIKixAnARloeO2FQ/oap4jmJl3Mrcm79DJ/4t+pY34j+2ZfCuwcmMm7mjTvJ8HOuh/WxctNMy9K21x3Yq2WMywNLKQDg0POOCAxsf6hdFGysZ/WTWxaOh58VryEt9e96OOOqpZXK6UxjdgWxieH1lhpbiL8jxjWxgZxHY6io0PfOADzcKXcuMRj3jE8NjHPnbYb7/9msUAS1CO8mm90cy46xevPX1SRv+sfs8GBVYDRNTQN8Hy19Z5wAVADGCoT/vbPAOwBCSTYSO3S4sfGRvjcRBAhA8RsrYtJJx580cnvXw4dfX9jvnTOK/ZoObkWviu0IY/Luspa5IAs/PUjnHr1F3/2DbD2Tp5QlvrWk4KLCwgYnLjUI9DVNtmaA45OGVWR7j2cfsY+nvSEFgrIOIjMkE4ylEZ/+bf/Jvh3/7bf9vu3/zN32ynzDgujlCVMsfleW5yZ+Jpiw/wRh6/9Vu/1dBtWlGCTiZm8V3JT/kmYALxPe95z5b23/27f9eYAA2JCRsj2IpLHbQNg3BSD0HEVpkIZanrVpQ97TwxLoyNuS0hioCsX0LneWrLtGlT+RUFNkuB/jvKb98coZHwCTzmjNkxuCeeeOJw6KGHthOgCC0EMdpdoHEWL+be5DMON1vXeUkfGljY4TP8VfGdYhsBIAld5uWyMMWrDzrooKYU2JGAiHHIKSdlhEUNAAOoRA5YjXevhbb4M2smvJEmOWN1LWkpOgCDABEa7pUutLvxxhubZSz/Bosu3Gdch5b5H3381p8scix0bKWztcZ8suuuuw5/+Id/2I73JVedeeaZ7ZthHYSG+Z76/FaieT3fuRSYBIik//Wfvgwgwo8gEKwHRLzHSyjvTjjhhAac3PGOdxx+4zd+Y7jTne40POxhD2uWJ8aGOaC/ekCE1YRvFJDKWoXsLvQ/R9/mZvXp7z6vWf6t3eZFFpmsKVjP9fPhPH8n5lYn0ZHzgWXjPp7lfqm6TZcCCwmImOBMXs9+9rOHhz/84U3bZAIkKGCENGc+7gALq5F0rYCICcGHRJCyzYJA/+EPf7gJ9Y7cdQMzVvvYCDA+Sp6ybe8B5MiDAAXkuN/97tcsFmg+lNczbR/1pZde2toGBGLWJp0JmjmhY8HkSatKwJzmBJa6EPJYtNDeAl9ySss0y1qtr6b1Tn2NF9pJwpJFBZP9jJd5a8+06FL5FAWmRQFzF208YJpwxRLE4pMVH1CZ36aTTjqpzX+EyV/+8pcNcLZYMYdm7hPmt+8y97TqOQ/5pM1CC0DzOyCaEsAR4gCRWbvUddLluf40/9LKGiMrxZ2U3rP1xh/nY3wp11gD6tt2O14AjNOs5f8eEMGvXWutK5pIAwiMkmFSmd4tIyDS0wJNQ1dhvomMKTIdwO1FL3pRk6dYEbtZBQGcaMEtjGzBMQakT37r6bO+TvV76ygQQAR4YbuU7yRjQOibIMvd6173agAY3xe+ce98V751ILvv/D73uU9bNwDOzjvvvCbLctLKssRRs6wWjYdcAUQcuuDUFdaLZHjWXPKwrdO7P/3TP21Wx+aAnl8ln1kPQ0O82fpGu/t29N/HrLelr59645fmTOslwAjFTF3LSYGFBERMWIAJAMJTn/rUBkR4Zi+ws7OhxMzZMMh81Ct1/1oAkaT1cWGggAETH+GFtg7C/F//63/9/wCRfhJRP5YVQAuM+dprr22Tjjwgy/aC24ZCu0HTIb70bm0AknjHosE+WcIwgdLtN6uTRz7ykW0/rcV9X3bqv5kQgwFC0epycuj4ywhu0y5rM/VcS1r1BX7QLAGQmNKxvDFRejdv7VlLmytOUWAjFMj3sJbQPGVOAPzS2AJPCSHmNVZ7HJsBU81f3jFdFtd353vc3ly9kfrPepqeruZY9CCUA4jwmfCBSe0Ql/d8gvpKl/zla4uBfPFI6fq5u69D4psbxad5tSDB99I/ie9/eQO9mCUzJccj8N3ESSg9qzyKCnkKtVE9Jl3jdOqCz1kMhSaJI/QMT0495C3uuM7KSjrvKDHIEOSAAOKT6rOWZwFEjG80sajQVnVBk3G9CerahG7iudEvIFHqicby0ncWexdddFGTI4A5oSfttz4elxG6S4uG4vTfWspYS/vmIY72oJe+AHiQm8hG5iAnZ5C9KI9ssfHd+H5YW9lyjFZj+mmzPHP1v/Oswq2lgPmH5cLv/M7vNECd7Jlx77slSx955JHN8sNi3tzVf/e+HdbA1gXAMPIxZR7Z2/dAhnfMLLDkE5/4RPt20yJzJaeqrMKznc0zcrdvXD0oJG2p4ZcOsNqXnXxmPfS9fPrTn24HDZhXFgk00B/4AoWyNVgseWa9T6p+06fAQgIiBAn+K/74j/+4aQFyNJTJzTYakxcGaCLcHsNfDyAy7h4fmvR77rnnNkCEsDHpMoFCoIEnzDd7YU0+mDiBCNBDKOoZM6ERIr3HHnu0yVc7+0nXb8KORQfrEcfgejbNi0BnkUPrAiEn5PV1nGZZW51XxoRxRCBmqUNbQDgNXbe6DpV/UWBeKDBeBOT7EZoDzE8ETMIhyzELQnOR+c4+fjdLOCfDAH7N1xb75rz+exuXMy/02Ww90cGC7Morr2x864gjjmjCtTmfZnMlnrI9QETfWBzQhtvKYdEg75NPPrltTdJnfV/6jbdwXgskFp8G1GlcFhqE/YDG8sbD9Olpp53WLO2e85zntD4XF9hlfk3/4mnqID/WkLbL2C6Fj0y65G+RjyZMuNVbfPO0ha681Vf+xhKgwOKW5ZF60ORecMEFbUwG6Mj4SpulxdOmCYjgjWiHLny7aC8zfRYLhPKMee1Df9aJ6IwmfKqwmtKvLvVL+3xTFmQWbvvss09b3FmoSacMi3sm/T1d+M7wjFUW+rl9i8BI4y1xQ49J/TCvz9Im9LYAMmYspPmuQXNWAehouwNFkz7jV8zpeeRGoJQ+Sj7CunYOBcwdAJFsLacUdJCCmzU4gOsBD3hA68N+btBn+p/fJRZC5OexIk8csq1tNhyyHn300W3uSn8bC76z//Sf/lNTnvlm810mfwALCxH1AM4oM+l3DsXWV6q6ahflhXnEPG/8L8qlfcaFLblnn312W1+lbfPUT6lzhRunwMIBIiYjyK6Jy/YYAlI0UgQ0ptn/4T/8h2YqSfgWf7VBv9WAiLLdwA7M1yTORDz18i4TLMENE+7feW9SNlE99KEPbSbSEHOLiv4GiDCftnWHP5FoADc+dP5fSnWAhl9xxRVNOCY4QJQ9d8/blXqjtYmSwG3xBoyaN2Y2b7Sv+s4vBfrvxvwSKwLmqLQv5h9AtAX9bPpNAAAgAElEQVSYxaAtMhbXhFBzlXnaHDee31Akec8vdTZWc+22AHaKjoU8cAFPI7hZuFnkZ4E8LmF7gIi5jGWAvnB8MYDFbVFsyyUfJP2izwJZfwEeaFITH8AO4PI/XqT/aNOByfjwW97yll+LC3A566yzfg30J3ADZowJ2zyNE9acAJ9Jl0WsOtO6hib+B84AB/qFCRAH+AFwQTv1NBZZBIirzv34ym/tmDYgwgIKP9F/LBPUJYARUBAQoVw3HkpjafuteOprGzDgJHUU+m5YMchPe/AqC0Am+9K5jR+a7nxfvk90psCggEk8dQHQ6IuAWylrUj/M6zNtypX2oQ3wDNBm4Uqphha2Uhx44IENTDPO0ZifI/HMcWipv/o8k3eFW0+BbJkBiLDEJkcDs/j+4Rj/0Y9+dLP4ARhmK3fmNWsCvMmWGDI0PpS+7MeFuRRoQmHp2zBWXOYOQOXd7na3lnevyJReXuZCoCoLE994vqutp8x0StAGoJM533xuTbRogIgxhPeYn1nk5VtOOB1KVi6zToGFA0QIbTSRrDJsmcH0CWZQYII5AQPSu9tuu7Uj2rLAXWng7yhAhBmaepnIOU1Tn/42KY0n6rwn1DLx5EiVNsm2lfFN6KXpuOtd79pAFwDGSm1e76DFXFhPEBQIV8AddJ3XK3QRAtcIRhYBGOe8MbN57YOq9/xQwHdibjL3WlCYC5ii097TuliIWhTTstKEW0yYoy1aLSYinCYfYe5QYfx/ni96aB61KCeI0uazJCSME7Jpq2nt8KhJ1/YAEfmY3wiA5jX94GaVAVx42cte1soJ7Qn7ngM0LMrF1e8W5PoTn425sXqKy6IBf1JW4rJMoHHVhkk8jbCNH1poTAJE1Mf4OvbYY5s1gzLlrx4sTwjugOyMK/U2JvG81Fl7yQIsRdQ7bUTH/Fa3aQMi+DJttnb5XpShfr4LC7Kvf/3rrS2pQ0L1Zr3AH4yFeJ6PQ+1C2yc84QkNKJtEX8/QjKxgC0BALGUAYchKlEXo2dNj0hib12djuvX/o4/xpF9ow50KpN9sfXDChm01rG6AarYvGyMWVGgvXV07lgKxEInlt3nRnOM2twECAbDADIcVOJoZn9LnAK0zzjijOU8FBPu/Hwt++y7Ep6wkoxsP+JbLHGuesiWGw29jpk+f789phY795ePEnJs4O5ZSGytNG8w5APgAIuauRbn0hfmQ/xDjxIme2lzX8lFgoQARA9uERNBhBfL7v//7zUqEqZqbBYWjtzhfcoIL7VosGVbq+q0ERDIp+vh4tGe9ARAB3OTdamEmW0xb+25/+9u3NkO7V7oh6I4RjAZtpXav5zmhHQgSR1QELExkXi80z4XGtG+0br02Me8rLAosIwUyL/nOLZxo4S2KfSsW6RZ9NNqAEJprwqLFKmHQfJG5K/mEhv23l2cJV3uXOIsWEsTxM9sZCG093dDRIgywMOnaHiAijfzSf6wTgCHmcn1m8a2/UibeChymJQciiI+PiKMOFoPpT8/EBaoAL8Q1RhLXuOn7M+mEABFKgZUAEfXBayxgenDAc/kCYwjsydNzeaKfhStwRDv5EQN0276SuH0o3bQBEeAgPpIFWcqzqENXAAVa5nlCdQkgAoxyeed5fwUQoR3X/3mffMT1DC04SKQwIj/QjFsMkofQKv2TdMJFuXq6jdvVtze/fWfGLRDLYpiFG0sdCiaWI4A5Y50FqfGItmgY2q9Gt5SxWpx6tzoFYiESp6r5tqQKfY3tbJe3sI+VlTmJ/5A73OEOzToggIi+c0svNPexNCE/+0bNmd7FQgQgwqqoB0T68gEi97jHPX6tjNVbNTtvzQWAJTwdEIjP+yYW5dKPvm+ACODTWkyb61o+CiwMIJKJzwRnwrvzne/cwBCWIk6ayc3sjeXIb//2b7eP21aSpJ3U/VsJiCgvZTNFZlK3koVI4iXs05qgtPNP/uRPGsIJUCFQ0rIJ/Z9n0HJtmuaEBi0nLHBAKn//q+ciXNpB28jUGrqP1ovStkXon2rD1lEgc804JCASGHznBEJzDM0K83tmyZyjWvjZpmA+IGyYb/p8tq7Wi5UzqwYAk9OuLLLQMIL69ui5PUBEPvoGn7DIs4i2594efNpU/ii8T3n6XH+yLIiDbibGtlsADvDe9DNAgobW9kya1f32268tPIwJYAogZSWhU9rVABHpbJUBigASXKGLuqa+oY/Fi3nbGLUNR33cTnN77GMfuw0QychJOvlsBSAChLBwyqU8dGbZwqKqf5c46jIGRPKuD7WVhcgYEOnjKA94xSrFdhALvUMOOaRZd7J4wMstKtE5tBAu+xW6oY0FNXAEqGSLBv8TT3ziE9v8Z5wBmQBzvoeMR/Tr6Tn+vez03Wj7A4g44nbSKTPoDCi0pZsVie0r/HroF/OQRTCHrCwYgVnjfvF/ABEyuu8moOUkC5G+Hel7gIhTbmxJU0ae93Fn9bd5wPxpzjX3A/0WyRJK/wLCKAGsHblV0D8u7+paHgrMPSDST14+Ukimk1pYW0D8CJS0Hm5Ch/+ZpQJFCH9OD1ltctpKQCR1N9yUw/GSPY+0rKlT4gg9659nmNLuQG6BPgQaAiVGnLv/3+9o8pJ+syEBAaBjW466K2ORLkyTNRHnqrSd+qKuosCiU6Cfe/KbcGQutWgy1zhRyrYDzipZhABCLGZZBIhnLsictej02or24VcsCgAiAZrTF304qeztASL4IQeaeA5LHv3JGsXCm9ZUn/bCu/KAMiwsmJ3zbWExQYi0GBRaCKZexoq4eKy98xYcLO2AIxaSwAxxxpcxsz1AhPUK3yXySHnyyW+hcYfXATWYehuftLu2Hrk5OEXXWIikHslD+q0ARPRnNMmps77QB4D3rQZE8j0CT3zH5CQ+TfS5RQ+QCDBj/IQWwmW/QouMK/SjUGMZQDZ40pOe1ORKWyNYNwG4WMbZIiZu6J58+nDZabuZ9q8VELGFEyDCYW7mKbKrucnRuOYmoO64n8xRFszWFSzMWZYFEOgBEf5JfLvj9ORwwDAwJWBo+n4z7d5RabUVvcwNFB7GfNq/o+qw1eWQ8c3LeB6gs+dL+qqu5aDAQgEiJiPaEQ6OWFoARwzsTD4mKv/HzA0oQhCA9no36dpqQESZ6kfw9THa+kIoijYwdReqt/2RtBP9pIvZ0tTxi0KoibDVxzEpQ3ZpAy1U5DetC7PADDi0Y4mirEW6LAoAIkwGCTj9ZLlI7ay2FAV6CmTuMd7NMbYZWNyaMzndpC3i6JN1gSP5fPvA2WyfyPwjz+Q1zXmnr+ui/iaw812E1jTOoSk6EkppPictoNFje4CI/gRoALL9xhfkhc8QCvm06MtUtrFgfjceLOItIPQ5M2MOKGlh1Uv9xPVbXPkQOgEYthbwxYBXeze+1gKI2PcPYOm3zChTHc3XwCO/tQf4QZC3+PcOTT3ny8acviMBERpi2yvUQX1zW9T5jlhZqvv40pZpWoikL9HaGMLDjReLd33odBqLIH2ojnX9Hwqkv4Ro6FtAP/3nG2C15Fvlw8UC2pYalnP8jVDEobNvQtrkVbTdHAUmASI9fdEZ3c0Zd7zjHds2PuPcc+Nfv7CuZjXGEkKfpm8Sh18J/kMAG72PCXOlU2ZswY+Ppz6t70dZrO6AKUCZPv/NtXzHpNYG1n6cQfMJpT3G8CJd1l+AMTyMUkCb61o+CiwUIEIw48iNLw3aKsJaPznlN7CBEAjJ9wGYUPOOoEKrBXRw04TZK+pYLSZV9ld7blLwEWVikN4krExbLMSBpPJIzTTX/kGaGCCNd8owSecySdJesRKhXWCaTFiUrzK0jakeSxCarR4wUS4LDc6+TOrKIfj5qL0j/DFTpsUweVu4TPPCFJxIoF7aF5pMs4ydmRdh3iLQfnNa1EVr386kbZU9mxQw75iTzHGEIUCq7Q4cC1q4AV5ZgxDwstDMIjRz6TjU0jybzVbPXq30AWsJiyy8BAhhXkdrdM/pIZNq3gMi6D6+gCC02BbpAT4sEFj3AOVZYeS59OZ5FoB4iefmQc/VEb8CiFu0+997mlTH3faLQGCZZ7bjME3eCCCiTPxO/QB04XVoAiDhKyCOveVvzhYX31Vn9AP+ALfxf4BIf8k/97QtRABQTtBJ/ZSDPzuZjdUM+k4SxvHx9QAiFEL6X7rxJX99T7axAFS+eKGLfiHzUL54ro51/R8KZFz4L7+FaGdsk//4SrKo4nyY7x/giC3NtmsZm75j8iMgZVL/FK3XR4EAIra9oDkgzzzgxrvMN2Rn25pYjuNZ5tH0m/RAq1122aVZcJDbw8v0qW8E37NesL7wXaXv/SZT81/y8pe/vIElvifjwVwKACYX8zECZMw3NU/fVeYLByaYu9DHHL9IFzkHGK19gE39W9fyUWDuARETi9tHy5qD5uk//sf/OFx44YWN0Wfi6rvWMwzr/ve/fzMXBhB4ZgKjvWKpQSCwr5YpsIkQyGKvqL2Anpvc7BUl+LnUweRpPzUmKE7Sqw9TPUJK0iuDiVbqJwQmmFSBIiZZ7wlKNDYEKeWrDwHPhNSnpX1jjmfbjD3BhFxtBI44TooAiimrmwltWpc6EK5MJibMRUSPCc/6gtn1RRdd1MbJtOhX+RQFdgYF+rmj/x3B3uKXYG/+MfbNLQQ7t0UooROoC0CWpq6toYC+AYbrAwtmc7k5nTaSxtMCy3yePiSgAwv0m7mKlQeeYWuMZ4Q9+YkPSGDZgzcAu8QBYrAOwdvwUmXhLYCE8BjAB78myRN/ArZzoEp7ajzgi0Bk/MzYkY/ylceyg2WRBUv4mLpIK44Fi/LxK8CMZ8Yc/ph2AlnkI3+aPfmzpDE+KTuyHQdPB9YARPgXANzLT53VD02VZazLWzstWoAC4rEM5IxdPdIGQNQkIGd7IwAfUWd0UmeADBr6rZ/UwzelHuQJC2baa9aX4gEinSanr/ST9BZzoaF0FnLf/OY3WzwAija4gT7kowBCeDZQE63S98owZsgmxpa81UO+da1MgZ4+fd+RhYBOgGPyJNmMbMdvCyASvZ3m04OLK5dSb1aiQACR293uds1KmuxM9o4M7xABFhqOomZJbez7DvSV27dsziQ36yNWEGRs37ttgb7NXXfdtSkj+R7plZHmUuU5wIEVmn6l2DTPAGHkxRKdBQrw2sI75Qrn4TIHaKc50NyF95tncs1LO1Lfcaj+aZ/58JZbbhlHqf+XhAJzD4hkcjHB+VB5/+Y0CfMnDOX9uD8JNSYwwIY9oD56HzlBiEMywhhEeXznOady0MR+giPAEFBNrON04/+BIyZP9YvQQbDxMUK5wzxzQg4ndyxAWKkQHtOuhIRQGjCCKk0ExmsLDWEux42Z2Gl60Wpal/IJ5PZzs8qBpk8z/2nVczP56FcLEWAS4RFDrKsoMM8UyLxj7nEb0+YV3zLhkDBoMQiItci0kAUW07gRIM038qhraymAxvgYq0P9wV8LQR+goG9YMPR8zsKeJZsFAUEdz+AjJEC89BZh+hy/sQC3YJOffPnZAIgYA7SifGzoc2WIb3yYA4EiABP5AooBItLQjqqzuEAJYAi+gC+rUxYNForGXHgfqxS8Uxx54uF8WVjMeOYkDyCAvN3S4TWAInUG6rCiQRPPs2gRD5BjgcIaRN7qgpYsb2h8WV2a3+UrHR4qL+XyN5B6SOum9IgiZD29j49QHFhYAG+AOcpQFjCE1Ujq7ftibWBLT+iMr7M2YLYvnXY4IpfcEprgvRbiGSfiufWjRV7GihBQBCRCF32Phn4DbYBPqYu861ofBdDMjc7AZUo3Y4wMRr7kb+Sggw5q342xqe/Nv2iebyJ0T7i+GixPbDI4HhUZm4ze32R185tvfQwgoi16U2aaX1hn97I3ORqYot/Mtb5haZIOMMv3CJALSO3kK3OXNA9+8IOb0tVBDrZMmWvDN5PHPPQS+piLzLWhAxkgbUg4D22ZVEf19/3Z7oZ/+F3XclJgYQARHy1tJVCAQLA9Zu69CYqAZ1LzUZisCDqEAYCJm/A4vj0ndEEVI2BITxghBPqgxmnG/ysDo3RlQtEGdYhpMkGVAEm7RbAk7I4n5HFaWigoNqFVWoIQzRJtkvpmQp7WcFc+WkDe+RVAm0UFRDBV/dCj49OiY+VTFNhRFMicYS4wlgmU5ixa5CyQLE5p0GmMLZyyVSNpd1Rdl70c9MYX3HhN+As+h1dlPk+/hAeGf41DVhniJL588UI80zwuf8KuccHaBJ/Cc5QjrnTADmMGUELxAKzBd8z7yVe/id/HxQMTN3klvgWJslNfcfNbqCzARuInlM4ix/hFE23r6yGestCOUC9fPF991c0iVDptFU875afd4zqoh/biz/Jb7yVvsoYy0Rg/Dk1C47QrdVa3vh79b/01prt02qU93oeGkTf68SIu+qkH+omjD/S9d6mLsK61U6CnW36jJ7qSOVn8kJco4yyegVEc6gKhWUkZX/ql76vqg5Xpb7ybG/J9ZswnNHegqXjpj3Gof8wb5kFgJSCSpRSgl5JU+swr4ub7kKf5InOKeNddd107Qlt6SlNWXmP+mfJXbtXsvNFW8xagmFKQnJAtRxmXCWen1muvie/MYQkU0QAtFkR1LScFFgYQyQSzUjipe8XNxDZONym+Z4k3Ttczr5XSjp+vlFee9+Xl2VrCcd36NH2e4/ps5H9lscxx1CatVMxyN5LXrKYhrDI/Zi4o3IgwPKttq3otHwV8sxbBFlMWWEx7nRZjHzUNMeGc1RzhnWA+nk/6/5ePeju2xWg9pnc/n/e/1az/P7/79J7lyvu1pkv81Gmcb/5PmPiTwklljtON/5+Uz6Rn47z7fPp3+e197uSXd/m/D8Xd6NXnM/6deo7LHtdtnG49/4/zXiltL88kzkbbvIzpQrNxqC/R1oKSxQEHu5RWrH+AIyySWBBRalmEmqf7vlhGWm6vzWMa5//x9ySfPEucPlztnXjj9+P/+7wm/Z4Uf3ttm5X3LP9YwBijrNkAp9roSjgrdV1vPYBa/PoAv1jB+O7qWk4KLBQgki4cT0Z53ofjOP3/4q30kSde8sr/CfN8LWHKSNpxmHrk+XhC7ctIHGGucfw+Th8v8TcSygeqDj3mhdoCC5K+SBdAhNbAhEmLYwKtqygw6xQYf+P+N3Zp02ixbBuw9QHQRztiKwAhnSYd6NcL4tImv/73rNNgEerX07v/3bctz8ehOHmW39tLl3jS9b/H+eT/SaF0Y/7TMvu/f/q8N1PGSnmuVKdJz9dbl77M9f5O+WlzwrXSKukTJn3+XymcFG/Ss5XSe17X2igQGk6ib57pb3IS2YLVFisE86+tF3vttVc7mpqPF75zzNeZi9dWg+WMFbpPKwwV+/zSf/2zSb/H8cb/SzMvl7qybuJM27Y6WyApPhdFDmatRx7id5G/JSBkXctJgbkHRJaz22an1SZLJrccSb361a8eePRelIkyVIYYc3xnf6FTABYN8Ek7K5xPCkwSyPpnhG+CN1NQ5ru0kvw+MOnlx4iFCCCE4N1rJOeTGlXrokBRoCgwHxQwTwcYoXXnCJ9jRxYjfE/st99+zTEnR8Pmb/PzGDzLXJ/na2m5NLn8Brgkff8ucSpcXgoYD8Yoi1EWpEARQF38RXk/r2NGvW3j5DyXgohDbd9CXctJgQJElrPfp9pq+8lZTgBE4ixvqgXs5MzsCzVZ0qJzHEhwqKsoMEsUiFCSEFMnxDDNpoFkEsqxmz2yNCGEbv5B+CUChNAARQuZPGapfVWXokBRoCiwqBQw51Ikma8t0AAgTvpxChKnoJzws8C1bYGvlxztmrlaGEBjPTSSjjWgLTp8RfGHUQqf9VBwOeIaW8YcS3DKFOOQ3L/RcbczqdZ/M8Y6nyisv/ldjC+pnVm/KnvnUaAAkZ1H+4UpGRNn8ul0A0eLxQP1ojSQUy5OJpkKOtLQhFpXUWCWKBAmD9SIo0SOwpwsce655zbhmoWT36xEOFHk3JEwHEE6eSScpfZVXYoCRYGiwCJTIPOwOdzik8XIDTfc0BRNTowCijidhvN68zqnoeJJl7TrkU3ElS4LXY5EATEsYosHLPJIW3/bjAeyApmCHGz8sVgC4s3bWFFfl5AfNdYhwEbOjhdt7bL+nl7uFAWILHf/T6X1JhFAAV8Ejjaz0MqkM5UCdmImBAbHjXIYy3EsB7KL0radSNYqeooUMB4J0bbFEKJp+jB5x3oatyxCHO3omFHax0mnSMhjfE+xipVVUaAoUBQoCqxCgR7UMBf7n2zlBBOLNfIHHyMPfehDh7333rsBJXwfWJiKFwu/VYrY9ipzvTIA6LTjHLriGY5yzkJ3W4L6sdQUyHgEllGqkPPJ/ACFjKV5IFDqmpBi6Mwzzxze8573tO0yZR01D724dXUsQGTraLs0OWOejvhjRWFiwaAXZWKBikPDHblr4mRSajKtqygwCxQg0AJCfvWrXw3f+ta3GhDimO3jjjuuaRJ9j7Z5MW/1TfZCd+of4SDjOmHeV1gUKAoUBYoCW0uBfh7ObyX6TcYCdl9xxRXNj8NjHvOYtpXmoIMOaotTVn/e4wXbA0aSd0I8gTP8Y489tlmhOGkj2yG2tsWV+zxQIONEaGxdf/31AxnDFtwcouDdPFxpizHPH48t/rYR893Dmfy8tGMeaD2PdSxAZB57bcbqbHIBFPBJYN8rB4200P3k0v+eser/WnUyYQq1CyJ+6qmnDocffnjbDkTgqKsosKMokPGovIxJIcEEWGd8MmN1FN7xxx8/HHHEEU1g/uAHPzjceOONzVqr1/ZJW1dRoChQFCgKzB8FgNr8HLAYeeUrXznsu+++w5577jkceOCBw+mnn96sAy3s4nxVC8c8ZMwD/E+uodB6+MMf3mQd4Hr4Bjko+cwfxarG06JAxhGLJafTHXbYYU3m/x//439sG2OJMx5j06rDZvNJ/Yxt1rIOg+Af8Oabb27fTN5vtpxKP58UKEBkPvttpmptErEPlUm+bTNOZImGYVYnxtUImEmRIMDyxd5aNxNBC9G6igI7ggKTvh3PCMVMVW+55ZamHaTZO/jgg9v2mPPPP78Bkr7H7WkKd0QbqoyiQFGgKFAUmB4F8ABzu4Uo4OL1r39920LzwAc+sAEkThHDG/CIngdErlmJrzhhg+Jn9913b3nGwWQAkem1oHKaNwpk7BgLwDZAwqGHHtqUMLboZkwl3qy2T/3y7Vx66aVtO/HnPve55lhe22a9/rNK10WpVwEii9KTO7kdENd/+Id/aA6X3vSmNzWnjdEwqFomzJ1cze0WnwlRaOHJ+zqBw55Jx47l/XYzqghFgSlQIONN6Hui/ePTxlYY+71f8pKXNAsm27poOViMsBzB9IvBT6EDKouiQFGgKDAjFOj5gTmeJe4///M/N+er5BTH9D7taU8bnv/85w/vete7GmACHO/T+T3pYiXCP4Tjfvfaa6+26LX4XSn+pDzq2eJRoB87WkeuYCXyxje+ceDs19YZFuKRN2aZAtrie/jqV786vOUtbxk+9rGPDT//+c+bzDRu5yy3o+q2NRQoQGRr6Lp0uZoMLcZYh2DMjrKaN4dLOi2TImHDcaQWmu9+97vbBMpxWV1FgR1JAePRWASE0MSwAGEq7eg7ntE/9alPNWdgLLJydK76ZRwn3JF1rrKKAkWBokBRYGsokDk9If7AMSqFzVVXXTU4Teyoo45q1iLPetazGrDheHUWJb0fqXHt5OPkGo64WZsceeSR2xRb47j1/3JTgKzxpS99qVmIPPvZz25yciySVqKM8bqzLwCfgxHe+c53Nt8hFJ6AwIA5s1DHnU2jZS6/AJFl7v0ptt1EginTUkOOP/rRjzYnX5jsvE0yJkcoMmeUJ5100nDeeec16xfP6yoKbBUF+u/Eb9/O//pf/6tpMK699tom6L761a9ugOOHPvShdhoAIKTfL75Vdat8iwJFgaJAUWB2KUA+sbij8XZ87ote9KJ2Ks1Tn/rU4QUveEGTyZwgA1yP9e6Y50h/zTXXNJ8kj3rUo9rpMxa6WTDObuurZjuSAsYDhaFtJyeccEKzVuVs9X/+z/+54ljpx9qOqmvKFJKTHPhAifTmN7+5OSh2IiY5q66iAAoUIFLjYCoUMOGYWEyStNicOnL2CFiYNyDBxPnTn/50eMMb3jBAvz/96U+3iV4bc0+FaJVJUeD/UiDjShhnqfzXEDKYdbK8otX4+Mc/PnznO98Z/vVf/3WbUFtELAoUBYoCRYGiAAqQtyxM+QTBN/iYAm486UlPar8pq5wOAmzvF4N4j7R8hwDcHfF7zDHHDLfeems71tf7uooCKGAsGDs5TIHFKv+BFKKR+cXJvbOolvKzpd/BD6eddlpbn2SrzM6qW5U7exQoQGT2+mQua5SJx2LO6RYce3G8hPF65v08XAQCGhQgCAHixBNPbIJF2jAv7ZgHWlcd/x8FjCtM27azH/zgB8NnP/vZdmITz//26DpVgGAKcGT2LP68AY3/r7X1qyhQFCgKFAW2ggJ4gxufAHqwCuFPhL8HJ9I88YlPHE455ZRmCcLvG8tei9s+ncUiHwuO933729/eTuSQX11FgZ4CZJaf/OQnbfvJ/vvv33ztAUUAchlT4htbO+NSru09P/vZz5o1CyUnQISy1vOSoXZGr8xumQWIzG7fzF3NTD4mGGZozC4xYSZ18VY+Dw0iHDg2mLkpQAQw0vtC2VkT+zzQruq4MQr4ZvinsQf8uuuua4IoZ6mOtmMR4sSA7P82/nJvrLRKVRQoChQFigKLSoHwByHeEv5iocq/yJOf/OTmONVWGv/zTQVojw8q6Wyd+cpXvjI8+tGPHh7xiEc0gD7Hqy4q3apda6dAP8ZYVJNRyMzHH3982zJvu3m2o4jrSrj2UjYX07inyOQX56yzzhpe/OIXN+WSugYM2dF12lyLKvVWU6AAka2m8JLk30+QkKwOt7QAACAASURBVGGLO1tn7NX7whe+0CagWScFDQi029aEfffdtzmtZBIYpNsEWxPorPfi/NTPWDLmCA40Fk6O4SPkVa96Vdu7zSIkjLtvVcZgwv5d/S4KFAWKAkWB5aUAvpAbFfJbaDuDbZgnn3zywOHqIx/5yOGggw5qWwhY83pP3nE7vQY/2nXXXYfnPe95zVK2rESWd1z1Le/HlOdAEY57KXEoEjnm/fKXv9xkG3KzS5ppXskvYZ+3Z8AQY/rUU09tW98BIjfccEOziPI+d5+ufi83BQoQWe7+37LWmyBtnWEl4shaPjkCLMzSRJS6mLR/9atfNY28/ZA09DQqJtW6igKboUA/xvKbYEnjxhrJN8KU03HV9m7TrvQ+QqSpqyhQFCgKFAWKApuhAF5CNrMt2NGjjm5/2MMeNtz3vvcdbHng+43vKkC8+1vf+tbwF3/xF+3Umfe///2NL4WHFV/aTE8sVlpjIdtnPvCBD7St5q997WvbVl+yDHmnHzf92Mnz9VAkaSaFymLx9LWvfa1Z29r2TslpPQLw68teT5kVd/EpUIDI4vfxTmkhgAHT5e3cHlQ+RRxx1fvimIWJKROq0zpsj4FsO9bUZGobwyzUcad0YBU6NQoYQ7EuAgraguVbuPDCC9uJMYRSfkJoL1gkMVcWr66iQFGgKFAUKApMmwL4Cz5jO4EFLIvY+9znPs0a5JnPfGZTDPEjwqcVDTvQhIN5AImFb/jZtOtV+c0vBcg5xoaTXBz/zFeHLVnWAKxdrQeAcRk7kb030+LkkbJtzydHKdvJSrbxkLOMc+Nd2XUVBVaiQAEiK1Gmnm+KAiYo4AdnRhdccEHbBhDtAz8dmRQ3VcgUEqsHpm8StTA96qij2gTa+w2ZQjGVxRJTwLdgnNFOMOG0hewjH/nI8LrXva45I/vMZz7TtmpxgEe7kW9DurqKAkWBokBRoCgwbQpERqNNJ/+wit1rr72Ge93rXsPuu+/eLBZvu+22tpgFhjz2sY8dzjzzzLYdunjUtHtj/vMzntxkGNuA+aZhVQQUsUUL8OaEvH/8x39sslBvNbLe1qcs45Al0y9+8Yu2Ref0008fnvOc5wwHH3xwk+f5ZFNe1hzrLafiLxcFChBZrv7eYa01YZmsTEQ//vGPt4EirEW+8Y1vtO0C3u/My4QMUWYZ8prXvKbtk6WpB+IUw9+ZPbM4ZfsOaEWMs69//ett+xjv/cDBiy++uG2ZicNUY67fVtZTQT51FQWKAkWBokBRYFoUwHPcFpX8pzmS9xnPeEazCBHaVuPEEM/5GrHYdOIZuS6L0mnVpfKZbwpE5s+4MEbI0qxFbJ/hG832YMogY4iVLD81FJKssVmXRP4ZUyJ5ek/RSrnEqtspScA8p/HxibPffvsNhx12WPPHxi9bTruJPD/Ot/4vCvQUKECkp0b9nioFMolhtjTjkOJDDjmkeaG2JcVEuBmUeKOVjQDA8atF6ZFHHtluvk7sn1Unl/rXVRRYCwXGY8X/GLcxbuxfccUVbR8rJ8M0Jd/+9rd/7QjdfCt9mHLHeed5hUWBokBRoChQFJhEAXzDApI8IxwvCr3Ps/AdC02+084777zGp/7u7/6u8TEaeIvOAw44oC1u/Z+0k8quZ8tFgYyfhFrvt3HH2ho48eEPf7itASgfgSNnnHFGUwx94hOfGL74xS82i5If/OAHzZcfqyVgiZsPElYetnBx3GrbllMsP/nJTzYFE8tuMjwghCXKZz/72WbFZNxnjKpLXUWB7VGgAJHtUajeb5oCJiOgiH18LDDs62MpwpzNfkPosIkzk2kfbqbw5CMPv02OyrGXkJNXewttkXn+85/f9swCSAKGbKbcSrtcFMg4yxgzhmx/oR0xxjlKffe73z2cc845zayTn5BZ86WzXD1WrS0KFAWKAotJAXwID7JtgYLnu9/97mChSeYhb7FWtOCkYWedSItOBmPJiC9JK4zWPvlx9n3cccc1h5kWpOQo7+oqCqxEAePDTfY21vgSAX6wyqYgPfzww9v2FnI46yPbtoBxwA5+B60XyE+e8WXjPXld/GOPPbb95vPPtnxACdnKWiPlrlSvel4UmESBAkQmUaWebQkFMFonubDKyMTmqFETmcmyd9aVCU242SsTMiavHCgzVBqabM8haxVCgUm7rqLAWinQj9F+jMXDOYZ+yimnNMuQz33uc23sT3IqNo0xvtY6V7yiQFGgKFAUWFwK4CfkmYsuumjYZ599hj/5kz8Z/vRP/7T9pknnu4q1x1lnndW2wlic8vdALmL5gX8B9C0ss42BbERTT8vvFD7Hq7J8JNPVVRRYiQKRbSIfJTS2rAUczUsxaUvN05/+9LblBdjhiNynPOUpw5577tmeO4UPGMcKROhEPiAJkK73ESL/3CvVqZ4XBVaiQAEiK1Gmnk+dApkMMWsTGcZ84IEHtgmPXwXbCGg1MNlMasKNXskDU8fklXn22We3RSowxIRKgxKHS4m/0fIq3fJRIGOGwGjsAvcIjY55w7RpOph69lZQ4rqTVlhXUaAoUBQoChQFNksB/ISm/KSTThrudKc7Db/xG78x/OZv/uZwu9vdbrj97W8/3OEOdxjueMc7Dr/7u787/N7v/V67OVIFnABQAB6seFk0OqoUSEKRZBHL2uSlL33psPfee7ftCmUlstneWvz0kW96ecdvMhDZnPztBBoW5LbWfPOb32z+1q6//vqBw3nKpJtuummwfQsIZzyStaSzVuity0PNlJn/KywKrIUCBYishUoVZyoUyIRoArNXlRknUOKII44YHve4xzV0GEjCpA56bMLLZLfWCqQME6W9i8pwqsfHP/7xZnJ3wgknNO2IydYkbEJOmppE10rliocCxgumDuxgjsxZmP2stBvnn39+Y+6AOGMsAEgo14+5GnehSoVFgaJAUaAosFkKkJ04m6RR33XXXYc//MM/HO5617sO973vfYf999+/KaLIXI95zGOGBz/4wcODHvSg9u6P//iPhz/6oz8a7n73uw/3vve926kzjuRlWWKbs+0LeJzTaGjyyWllJbLZ3lrc9GM5Z6X/yfksuFnQAt6MX3IVwM3tmffuMQjS54mS4/8Xl7rVsmlToACRaVO08lsTBUxaJj+aDIybhQiv5o7LsqDkc+Gyyy4bvvKVrwy33HJL07Lb+0pTYYI0WWbCFAI3eJwWVxppaepZgrzsZS9rIYZuqwzv1gAZi9S6igJrpUDPaPvxa8uV4wiNM1YhtoQ5Wcm4rDG2VupWvKJAUaAoUBSYBgXwHdteaNT5+yAL5WSzv/3bv22KIs5THYPqJBlKI1tnHJMK8OD8HlgCTGE9Aky55z3v2f6/3/3uN9zlLncZHvKQhzRtvsVrXYtDAWOnV0SO5Z6V/l8cClRLlpUCBYgsa8/PQLtNrLEWsa0AkOF4N4tKoAizTb5G7Fd94xvf2LxSs/QAdlxyySUN3Lj00kvbPkRbYexDZM55/PHHtyN0LVCZfdqjePXVVzdzTxp7KHMm9RkgQ1VhjiiQcQPMM2Yvv/zyNi6Nz94qpMbYHHVqVbUoUBQoCiwYBfAqi1u8CDjCYpYyKVaxWfjSuIsD2KBwsiWB80tWtICUt771rc3hpe00e+yxRwNCHv7wh7etzkAVvLCuxaCAMUG5SLHI6tV4MD48j+yzUrgYFKhWLDMFChBZ5t6fgbZncjXhYtT2BrLgsG/Q8aScUgJHnvvc5w7HHHPMkCO7Dj300MaQveN9+n+zd99f1hVV3sD/gHet+WVcM05YyxnDGAdFQUABAck55/CQJUoGyRmRIDkKCshDzhnJSZAMkpGooGLAUWecmR/Ouz417sd6jref53b3vd333t611u06fU6FXd86Z9euXbt2bbLJJs3aa69dFCEGcIoQx2/xqh77DUPrHXWKMyQC40UghIY77rijvKO2ytx8883FuRfhsC08jLf8TJ8IJAKJQCKQCEwUgbZs0x6TQgaK8tvp3ZfHVgWTYiem8e1gAYqzVr4dKEzSGX0gOBox5ceDDz5YjsU9/PDDSz//5Cc/Kcqy9jtE1iFbU6CkUmw0+n+mtyIVIjP9DZjm9sfAHDFyMF4rFgZiq/DMOk04r7/++mLaaQLqyC4nxLi+/PLLy+q8gdr2BVtn5B1rchp1dRICphmOrH6AEYj3hmItPKQ7VteKmve1LTBE+gFuUpKWCCQCiUAiMGIIxNhTx9HEuFf/H9cRR5o6Nr7FL+5H+oxHAwGyDcWXo21XXHHFZr311ivbqFgCOaY55BwxJRkFGWtt8pB3IkMiMMwIpEJkmHtvRGivGWkMtO04BmJWJBQdVi7E8b+YdjvygSauI67h6nSvfp7XiUCNQLwvERMIwtlXrQiJPJEu/s84EUgEEoFEIBGYCgSMP3WI8ah9v53G/5HWdT22xf26jPq6LiuvhxMB/Um2phRxNDPLbNbXLLGvvfbahrWIxUaLQOecc07x+8dy2xabeD+Gs+VJdSLQNKkQybcgEWghUDP2GPDj3lhxq4j8NxFIBBKBRCARSAQSgUQgERgaBMi4FGEOHrB9neKDQsQJjfvss0/xK+PQA6dDbrzxxsVHH/80bdl4aBqchCYCf0YgFSL5KiQCFQJtpu5/oX3fgMEJmVNywpSwKiYvE4FEIBFIBBKBRCARSAQSgaFBIGReMi5L2F//+tfFya4jl1dfffVm8cUXbxZeeOFiHXLhhRcWGbj2zxdWRUPT4CQ0EfgzAqkQyVchEagQMBgYBByZWm/BCYUIxm+rxAsvvFCOVz3ggAOKhpxiJAaSqri8TAQSgUQgEUgEEoFEIBFIBAYegZBja5nXNpkf/OAHjcMMFlpooWbRRRctW2lYjzz++OPl8AJyMfk4FSID38VJ4BgIpEJkDGDy9sxEgJmg/ZAcRTEXtJ8yBgbX7777bnP//feX027WWGONZrXVVitOp372s5/NUYjEgDIzEcxWJwKJQCKQCCQCiUAikAgMGwIh74opN8jEnKoeeuihRQnipMczzzyz+Bg58cQTy6lD/nfwAfmYnCxfhkRg2BBIhciw9VjS2zcEDADvvfdec8kll5S9kQcffHDz3HPPlaPlfvGLXzRPP/108/3vf7/Za6+9mk033bQc8WtAoEBhURIhFSKBRMaJQCKQCCQCiUAikAh0h0DKT93h1K9UoQhh7eFY3Ycffric6LjTTjs1p59+epGJHbX74osvNnfddVdZPKQk2W233YrVtJMeOV/9j//4jznWItmn/eqtLLeXCKRCpJdoZllDhwBGXf8w8XvvvbfhOZsFCIXHjTfeWBQhRx99dLP33ns3u+66a3E09cQTT5T9lU64SYY/dF2fBCcCiUAikAgkAonAgCAQshhy6uv4f0DIHBky2hgHzraLWwS84447miOOOKI4U2U1zRI65F0KEwuBlB8XX3xxY/v4Djvs0Oy4447NcccdV5Qlb7/9dtli3t5+PjIAZkNGCoFUiIxUd2ZjxotADAgRh1acUsRZ7Msuu2zz1a9+tVluueXK/xdddFHZSmMgkDbyjbfeTJ8IJAKJQCKQCCQCiUAi8H8IhDxlywX5KvxRxP3EqX8IBMaUF3ziXX755c1+++3X7L777uWatUgt80Z6fWSbzBtvvFGsRQ488MBmnXXWKf5GTj755OaRRx4pyhWHEET+/rUiS04EJo5AKkQmjl3mHAEEaqaOWf/pT38q22Z++MMfFq34F77wheYjH/lIs/TSS5d9k/ZIBlOPvOIMiUAikAgkAolAIpAIJAITQyBkKnKY0/tY7LJICMXIxErNXPNCIDCXhjKEVQcLj80337xYfdx5551l23j0QaTvFDuQ4OWXX27OOuusZoMNNmiWXHLJZs0112yOPfbYsuX8/fffn3NYwbxoymeJwHQgkAqR6UA96xwIBDD0YPIG4Ndee604hvre977XnHfeec0ee+zRHHbYYSXG3J3FfuuttxYTQHkj1NdxL+NEIBFIBBKBRCARSAQSge4QIEuZVNuqscsuuzT8uHHWaauG+yFrRdxdqZlqfgjAkwzs9ERWIbaL8wnCUppSqptFQGX4Uao4qpfvkVNOOaWZNWtWOXxgq622KoqSZ555Zi7/IkFb9mkgkfF0IZAKkelCPuudMgSCUbfj2tTvoYceak477bRiHnjMMcc0N9xwQ0MzzgzwlVdeKUfrUpDsu+++zS233NI4hiyUKW1GHvVMWQNnSEWdcI4+mCEQZDMTgUQgEUgEEoGRQ8D4bjxnEeKI180226xZccUVS0wmY7XLr4XtGZ0m6CF3teWEkQNqEg0KbGqsXMOUk1SWIeuvv36z//77N/fcc09RbOiT8QZ5lKm/HnvsseKDzyk1G220UbPzzjs3F154YXHOWjtebctyNa3jrT/TJwITQSAVIhNBLfMMJQIYLKZrMOUD5PXXX2+uu+664jQKk+Ys9aijjppzfFicq26AtlWGdciRRx5ZlCL2V9pnGasWMcAEMMHM4/+MJ49AYBpY1/HkS88SEoFEIBFIBBKBRGC6EDCmk89YGDjB5Dvf+U7Zurz11luX2NYLMtubb75ZZLixFCPTRf+g11vLTHHNtwfLEAuCTpL51re+VY7Ztb0l8J1Iu5RP3iYj689HH320HN3LYsR2HCfT6EtyeMjakUe9bQXJRGjIPInAeBBIhch40Mq0Q40AJutMdQyYSaZVB1thnCjjBJlrrrmmeemll5rf/e53ZSDQ2Bg05MXUmRAecsghzZ577tmce+65RauOmWPeGaYGgeiTesB0L0MikAgkAolAIpAIDB8CMa6Lje22cJC5bLGwjZnMxcLAZNr/nHWS5VjrxsknUcbwtX5qKA58AmPy8PPPP18sNpwSc8YZZxTliAXDWr6aCHV1Xa4pXsjXFhNthaJ8Oeigg4pvvvvvv79si2IxYqGRVbajfeXLkAhMFQKpEJkqpLOeKUcgmGkwY86i7r777uaEE05o7GdcbbXVmu22266ZPXt2cQRVa6nl8YtBwTWliMHX3kjKFKfQiGm+adOlFaTN0B8EYGuPqoHz5z//+RxhKHHvD95ZaiKQCCQCiUAiMBUIGN/9arnLeM/BKjmLxQjLAn4uTKq//e1vly3Mjn4lm0kbcthU0DtMdQS2ga+FP9tZ+Ms7/vjji6LCFvFeKZfq+lwL+oYSxvYc26LOPPPM0p8WGSlK7rvvvua73/1uWaC0+EjmjrzDhHXSOpwIpEJkOPstqe4CAYyUuZ7B9IknnigOnbbZZpuiCLE/lfnl448/Xhh0PQC3GXn7/zAxPPzww5v11luv2WuvvYrlSChF2gw88ndBciYZAwEYhoUPc1mDKU/mN954YzkVKDEeA7i8nQgkAolAIpAIDAECMY6L6+B/MhrLBVYGFrEoRWy/YGlw0kknlS3NJvTkMHJfKkZqBP/vGo6URu+9917z4IMPNuecc07ZMn7llVeWBaZaDv7r3OO/E/0ZOaNfxXyMOMiAZbbDCyi4WAGtuuqqzVJLLVW28FCe1HminIwTgX4gkAqRfqCaZfYdgWC0Y8WYPmYaR4BtscUWzSabbNLsvffexdzSnskwC0RslNMt4QbcH//4x8Xkb6211irOWB944IFSprIMLPWAPN7yu6VjFNLBJkLgFPfEFCHMZznosmrgnPsVVlih+dznPlc80evLyBflZJwIJAKJQCKQCCQCo4WAsZ48wCrkiiuuKIoRW2koRyxSXX/99c2rr74658he8kNM9CExU2UF7SYX24ry/e9/v/gKsUWmdp4qzVQG9VGM6C+OVh1a8OUvf7n56Ec/2li8JGNbgGS1En3YprH9/1TSn3WNFgKpEBmt/pwxrQmFA2bY/mGwBsuLL764TJhtjVlnnXWKeR5TPdstJmtaqU5KEfUw+9thhx3KYEzrbrAOmnRIXIszdEYgMKrx0sewtOrj6L2TTz65bHGygsAB7umnn14sfyi26vyda8i7iUAikAgkAolAIjDsCBjvw2KUvwlKEA7xLXh9/etfLxPrCy64oJxkEj7e6gn1TJPFtJfM6/hi8iqMTjzxxObpp5+eszAY+EzluxFyW/TlU089VWS7T3/6081iiy1WFr9YA/MVEwuYkSfiqaQ36xptBFIhMtr9O5KtC0ZIIcHpFvM/zJ4ixHYKp8Fg9k6O2XTTTYtnaxPqn/70p2WCHYw/ypkoSPKj4a233mouueSSshfSNhx7XWMQjjoinmhdMyFfYGRw1Jd8hDhqz/7Sddddt9lwww2LoHPVVVcVU0tboaSTXt4MiUAikAgkAolAIjC6CIScICbLsR6wyEW+Iy9YONljjz3KpJ/FyEUXXVROTfnNb35T5MTIP7oI/aVl0VZyEsURfyGUIXyvPPvssx3l1L/knpqroJEcR+lxyy23FOsQMp+FrzhhyLYeC5C1YmRqKMxaZgoCqRCZKT09Qu2MgdBRuPaSOi6MjxCDIadbPFc785wn8ptuuqkw0bAKCeYrnkyoyzEg07xTxNjLynKBGaIJO0VNnXYydY5yXhjByv5fe4QNfgZt/WgA5wGdxY8VDWlCCVIrt0YZn2xbIpAIJAKJQCKQCPwfArVc5Tom1BbFOOdkIcLPCOvd3XbbrVhGkBFtGbGQJc8oh8CHMsRJPQ4TcKKiRTtbUWLRLjCI9PH/VMVRr1gf2nq+yy67FP98HKweeeSRZTuU04VYAZGzWQ1rV+SdKlqzntFGIBUio92/I9G6NtPzvwENk99yyy2bpZdeulhnHHHEEWUCTSlx2223FcuNqdImm8yzVMHMneN+3HHHlaN9KUow7nrijn4h4pHopC4a0akf4RKWPnyBOJeedY/9o5ylOcXHPVudYoWni6oySSKQCCQCiUAikAjMMATIFGQupwpamHKCilMFN95446IYsYjGOiIsTEMuGXZ5LNoR3Q0HJ+88+eSTZaGOYoiMbFtKyMWRdlBibbDtnD+YNddcs3nooYeKfxELZPvvv3/x1cf5qsVOyi3ytbbEApl2tHEYlLYlHYOPQCpEBr+PZjyFweDEMYFmHeKYrkUWWaT5yEc+Us6mp0nmZMu56o4UCyYZ+fsNpPpM2p2pfvbZZxdLEc6ram38VNHS77Z2W37d3rgWh9DCUSrFFqUHRZJtTn5WAmyNoSRh3QPbDIlAIpAIJAKJQCKQCMwPATKGyTKHnSyFWZzus88+ZTuNBSvyo2Nn33nnnbkWreZX7iA+r2WruCY33X777UWu4oieJTULW37ZYCPdoAU0OfnRghiFCOUIWlmzWBQjWzsZR3vIiyzCKb0ov2rFyKC2b9DwTnrmRiAVInPjkf8NIAKYJAZnawqfIU6OMYGm8f7kJz/ZfPazny3mkBQPMXmOQaGO+920oNPqBJM+zNpeVhYrtPK8ZQejlnYmhLqdrik24GN1hiLk0ksvLUeuOW6NWas9v/yx6GODYCi1ZgJW2cZEIBFIBBKBRCARmDwC5A2/WnZ8+OGHi2KErGHh5Rvf+Ebxq/Hcc8+VrTQm1ax9h01Oq9uKdu340Y9+VCymOZp1gguZdBjaRvajuFp77bWbG2+8sfSFNkU/8tl37bXXNqeeemqxIuZj5Kyzzirb5llpk7NTbpz89zMTS0iFyEzs9SFqM0aPiWPwzixnAcLJ5o477lhMIJdZZpnCPGn5pYuBQSy0/+9X0+t6gnlj3PaxMvXj6IuZZihFpJkJIfpBe61MUGgRPi677LLSb/aF2hrD8zkTSBYjsb+3xjTKmQmYZRsTgUQgEUgEEoFEYOIIkBnIHbUcYaJs0mwrhkk0OdKRvSxSLWCxGOFjxKLNsE2qtdOioW0y2uFIXbInSxjycbQnZKmIJ45wf3Jyps8P3xZbbFGOB27L9fqUjMhKnMKEjzknSVp8tMDGkuT3v/99aW9/KMxSRxWBVIiMas8OcbuCUYtNonkP50iJphvjW2+99QqjP+yww5q11lqrbE/BANuDX0CgnCgz7vUrjrrEBiAOvpj4sWaxGvHII4+UQSvS9YuOQSpXWw3SViyYbVKAbLbZZnOOxoMJIcVg3u7DwEmcIRFIBBKBRCARSAQSgXkhEPJCW37wPxmDbGZbNWf8Jt+ceK6xxhrFaoTlgZMCOW8PeWRedU33s2gjxQGfGrZpc0bP2vbOO+8si1DRjhqX6aZ7rPr1i+3SLHjIzqEQkT7aGv1ofmBLFJ8iTqQhW9oO5aheii39nCER6BaBVIh0i1Sm6wsCweAUHteYN0ZHA8xb+CmnnNJ87WtfK8eucgrFYaqBzP0ll1yymECyIJF/kAJ6aLIdFWY1gmmfrSEsIWofJ4NE83hpCcyj7+rYYGQLk9UKQgbHZhRYYgMdocOgpa9jwB5v/Zk+EUgEEoFEIBFIBBKB8SAQcqbtuxyPUoyQMzlfJac5opaTfNYVY1mthvwznnp7kVa96A+5CX0sqB0xbOHwm9/8ZnPvvfcWZUgoFKaL1vG2lyzv6F3bmsjNrHU60e6eX1jFkCf1IUuRvfbaq8wP9B+LE2UEVlFW5B8vfZl+dBFIhcjo9u1QtKxmSq5tKcHY77rrrjJpZgXCqzSNMQdRr7/+eplk2w/JSRaFSDDNQWuw9mDCmDGlCM29wYrm3tYfCh/MPDCIeNDaMRY9QW8da68+tFJB8WNrjD7cfffdi0UIJdYdd9xRrH6G0Sx1LCzyfiKQCCQCiUAikAgMBwIht1i4IYuYOPMxYusMmYVShJWCU2rILBQj9eJN5BdPdYi6Q95ykAA5GN3o57OOhUutDJkOOieCC4z1g0MSbPvhS25+tAcO5E6KIJbIjhgmd1KSmD/AKCzJ0RUYToTGzDOaCKRCZDT7dShaFQwplAasBViEOGqVlpciBJNnEeL0FppjDF56ZnIY5sorr9xcffXVRYM/aI2O9okxecxaWw466KDCqK+//vriMyMGLfRLOywhaBUTKvQPJQ9FiEHogAMOKKaotgo5T54GSqyF0wAAIABJREFU33PppJcvyhiWNiediUAikAgkAolAIjDcCJA9yJIhh9RyqNNYLGCRXWzDoByxLYPjfn7QyHNkmMg/1UgE7SxwWbecf/75zbHHHlvkLItv4asu2hbxVNM5kfrIw+EQlsWLNsJ5XiHwCDnUwqmDFyizbB/afvvt51jN2MZOBlXm/MqdV535bPQQSIXI6PXp0LQIE2Pqx38Epm4AopHfcsstixWFfYAsQUKrG0wdEzMwcRjFxBHzxEQHLQS9EaOReabVBseG2etojydFiQFWumEK6NUXNPgGGUeiERpYwNgexPntueeeWzT2FCHRxsAj4mFqc9KaCCQCiUAikAgkAsONQMgfEZPPWOyaVIvJpY6AvfLKK5ujjz66KEdYX1i0Y23AaT7lSFj5TiUaaOSXzbG0rCgsQFlsIy/X9ETbxMMSyJQc759wwgll2xLLHe1th05tivZKTy6FB4sRW4jI3BZbzz777LIVitwdipF22fF/lNeprkiT8eggkAqR0enLoWkJ5oJh0fyy9LjhhhuKdpsWl3Mrk+oXXnhhDrMKpqSBkZcCxdFcNPg04oOs6a2ZaSgQKA8MYraQsHAxADDbrNMOYodGX+i/sAjRFqfEcGpFQbXvvvuWdvEd0jbbrNsUZdX38joRSAQSgUQgEUgEEoF+IhDyh5gy5O233y6KDotWoVQgr1mQe+mll5qbb765TKadZHLJJZcUmcfxr5QjlBMW9/othwataORn41vf+laxgnDogBP61F+3K677iWOvy0azgxQskLLwsPgJ2/GEaLc4tqxTGNlKw9qHjxE+Ypw2RDESFjVRR+Rjma5vYzEvnmc8mgikQmQ0+3XaW1UzpLjGrDE2E2lMCDOiFGAVwiwRsxpLEVI3yOBlsr3ffvsVawTWB/0eiOr6J3ONTj8M2D5JZo4Y9EknnVQGVszb88As4snUOd686uwU3Ic9zbv9tFZPmGpSZG2yySZFGUIxYv8qp7HD0ied2pr3EoFEIBFIBBKBRGB0ESDTkFMoPS6++OKynZnio+1IVRqTYrJmnJa33XbblSN7+YW76aabiu87C0ChGAk5ShzXE0Ey8qOBoobiw3Zrx82yfKAMQS/ZbDL1TIS2fuTRBvKjrdfkYlYwsJ9oCPzI1hZgL7zwwiKzbrrppuWgBvMOMislkzRw9D6Qby3WsjBhpQL/UcB3ojjOhHypEJkJvTwNbQwmFDFmYqDgMNWWESaIjl7dZpttiqYd8zHRDqYT+doMyP+YFu/RfIxccMEFxdKknW4amtxVlXW74IFB04TbXmKrib2r7QG1q4L7lKim12Bs4LWVyUBMILC9iUKLGeIzzzwz137PYemTPkGXxSYCiUAikAgkAonAACNATrFAxdpjgw02KIqG2bNnF8vjsAyQJmRT8hkLBhYaZFCLQTvssEO55rfCNg3lsaKt5aeJQhBlmKibmLNQsYBIWRDHA6srgvTDHuBu0XPHHXcsvkAsok6kXYEdPFzrQ8oOFtkWY1dfffVmzTXXLAoS/5O/YXzNNdeUY5j1rUU/1kPR/3WZw45z0j83AqkQmRuP/K9HCATTEFNgYCg33nhjGThYFNCqM4dzcoy9mgaZOk9cdyJHWsySdYWTZihSpB/0EG2KGIPVFtYysOGEFCY04lYaYkCd6nYFfRGjwyBiZcQgrP8oQvQhDfqLL75Y6NWWoDnyTjXtWV8ikAgkAolAIpAIJALzQyDkFLIYmctij20ojnzlc4L/EItAMRlWnjyUEybpFCPkNZNpW4adamJhi0LFpLsXlrLqI1tZPOOcnvxlu/gTTzwx1wJU0BZtml/bB/U5+m1VsXV+qaWWKj5S4Oj+RELgEXHI3bbCsEI59dRTm6222qpZbrnlikKMXLvKKqsU6x94W8SFf+SPeCK0ZJ7BRiAVIoPdP0NLHaZBEcLxFIsQTIe3Z5ptjqkMIpQklBn1JLqbBssjv8k5pslyYVhCm5n6H7NlBsk0j6UFZ1L2O1IUTYcZJJpiwKctt0fWasgRRxxRtveceOKJRYP+7LPPlgEf/SEwRPvEGRKBRCARSAQSgUQgERg0BGpZhfziR7Zk6cq326xZs5qNN964yK4WfcLPROSTPuQksqzFPU7kyboW6xyB639WHLVfkvHgoC5yNJrIuyxRyNG2W1ukCtm5LjPoq+8N0zX6OaslCy+zzDLFmtz/8J5IUJ4QuCgnrvVpLEjyX/ilL32pWWSRRZpPfOITZa7CEp3iJHCOsiZCR+YZfARSITL4fTRQFGIImAhmTBFRMxfP/O95eHemOedkk2khbSsNfCcnRuNppON5mbQZeJSHWQ1zgJuB1QrFI488UgZjA+pll13WOD6s19pp9fnVIe7pU/jaU8mEVJ85CYcnc06oKEZeeeWVORYh8qHPKop+9V7U70RdR14nAolAIpAIJAKJQCIwSAiEPCQmv4Y1hu3ArAfIPixka8VGyExiMijZh2LEQhHZjdwbTuY5YSVTWeSyHSRkJBhE3XEdz9xXpnrJuqxCWBCzjnY/6h8kHHtBi3Y5cIGMv8466xS/LmTSwGUydQRmEeu38FfiBJr11luvbKNZeeWVi3+RI488ssi8Dm6oZdvoqzqeDF2ZdzAQSIXIYPTD0FBhwvzyyy8Xqw/mZpxMmRBjLAYSE2OnjmAurEEMCJQhHFVRkjAzlBZDmmhwxKvzyVmH0NxPpqyJ0tCrfMGYxXChFIkTaEKJxMN5vZd1su2t63RtoNGHBmtmnvaoOr3H/s2DDjqorHxYkdB/BirKG3nQqz8NFhQnfmiN/p0snb3COMtJBBKBRCARSAQSgURgXgiEbETOZR3LutmkmHLDj48QWyjqyXHkCVmKrEYOZvHLGpostf/++xeZ2FYaspTFI5YfMcmvy3BNhiJrsRR2IortOBalnLhS+9OQdtSCNsEGTmRQW8n1RS/kyhrnWPxTj7mERUiHAnCQe/nll5d+33rrrcschs+8u+++u/RbrdCqyxvFvhi1d2t+7UmFyPwQyudzIYAZ0FhTeDAxw/ApJWyNsY2FiaA9eGussUZhJJ4zGcTcOzH/uQrv4h9MR322lTBrNIkf5tBmqDBitmmVwQDI2SorG202SPSC6UadBhhlWvVwuo/jf+2ftSrCNJPjW4osqx71IIDGUKA4/thgwsGq9AZs5UqTIRFIBBKBRCARSAQSgWFAIGQjMRmG8iEccJJ3bYM555xzipWGbRwm1W2ZLPKSkVg2WDg00XYqjAk2xYoTbWyD8ZwMFpP9kK0sNLLMtaho287JJ59cZLReyYCD3BfwgyuZl0xJmcRXS2Ddxnu8bYF1LOQ5ocepMyyAKJ8stsLYc5bQ5i/6YIsttmi23Xbb8r8DIChoapkYTZOla7ztyPS9RyAVIr3HdKRLxEwwcQzdKTEUHzTgTPo22mijZtVVVy2TaX4mDATt/XfBOCIeL1jyMRmkMd9jjz2KJn4UGFGNh0ERs2WJ40gwCgoKIEoLVjiTUTaoRx9i+pRJ/IPYGqO/1OMoY4oYg7FByKCuvqBPXgobJqVXXXVV8StigKcgs9+yrfgab/9m+kQgEUgEEoFEIBFIBKYLAfJOyD0sYi0akYlYwXKcyuGqo29DRpJeCDmpjslMfMSxNiHH7bnnnkU5wvmqrTWsaslNZC1yGUtcC4sWmShQLDh12jo9Xdj0u17YwYyMyTrEViFWOWTiwHWiNCjXFhkOaSm2zFv0I1m7tvpRvv43fyHX2qqkLxzVy2rFFij9Rimmz5SLtgzDjUAqRIa7/6ac+mBWBgjmf7wxL7DAAsUREYdEtliwIGlPjGtGNhnGgUkxRXQcFgUMLfuwhzY2MRBjtCwuKCscT8zyBiOvTSbH03b1GNx58GbZYduRFQ9KEIMO65B77rmnKEqki34K+tBl0GDxYzCn/Np8883L0cdMQGsNfuQZD32ZNhFIBBKBRCARSAQSgelAIGSvqDvkGDH5xqKUY1idsrf22msX2cyW4Zisy1fnqa9jMk72YvVrYs3ygKUzmZmVtbLIe2RqP9YLrBFCHovygr6or/5/FK71AyWFE3XWWmutInOSeyca4AZDi4BkXBY35F0LuxRQ0X+Bbx3rN/MZsrh+42eEbxMLspRVrLltdVd+huFGIBUiw91/faO+ZghxjTFgHPZH2kvpaLIllliiWWihhZqll166bJGxxYIGNjSmkbcXhCoL0+HN24BE046ZuT+KQbvgbWBgcskfCw/jtibBOAbvsTCO+2L9gWlTqGDqzABpu2ngacAxdZY/6muXK797FCnS8m1iUDCg22/pfgzYo9gP2aZEIBFIBBKBRCARmNkIkKMsBrLssCi34oorlomxRaLawqCWvQKxuEexQhazJcQ2DZa2TpDhq4SvCgtUFCUsdclkZKuQyaKsUY9hZas2WdMcA05kXvc7BfdrjCKd2I9cC28KDIu2LJrvuuuuoiCJhbxO5cY9ZUjHYkRfy09R41hgypFvf/vbzdNPP13SyBP1R/6MhwOBVIgMRz9NCZXBPFQWH3Tcw1CYB1KEYFK2y9i2whERSwPMmxkh0zLOhyhNYnJdM6rJNoRZoUk45QANr8l40DrZsgcpf+AuhiPFDzM95pr8e7hmlVErnqLfIi/cWZnYj+r0mrAIUYY+NDjYfmRwVkddVrsMW2vOOuussp+Tky+mn+HtPPINEn5JSyKQCCQCiUAikAgkAr1CgFxEQUFR4YTDI444osjClBgm7WStmGCHDNUpJpuRZVkekKv5sqAMiW0Z/JXYnmOrSGyTrsvpVXsGtRxttc2I4mGxxRYr8w7KiMCgE93xLGJp4AxjFjjkXfMV22QoNShYxrOQpyyyLpma7G1h1oIipZjjgb0LrHmkq2noRGveG0wEUiEymP0y7VTFB22iHCfH0GLTivuZFN9www2FYdOYYxD33Xdf2ZfHEdGNN95Y9tjVlgy9aJTBgVKGlpdSwP9oHbUQ+GuXa/0AY6sJVg8cBcfcj5mlZ4GBGEN2D3PmQZt1SRwfx0HV97///aLMMOB0GmyjbgO7gZ8mnVWJLTu21vDAbaA2MCTzH7U3L9uTCCQCiUAikAgkAp0QIPOYSJtoWyji580CHaUI+cy2Gs9CjlJGXHeKw/LAsbyxaEVe8yO72eJB3lLmTFh8CowoQGxPonC48sori7+OeCZuh/qZa1jx8WEB1WIeuZcfGL5Jamuedjlj/V+Xr2xbeJRFDreF/IILLigWJCkTj4Xg4N9Phcjg99GUUhgfvQm1/XY0qWeffXbZHsPLMsaPubAOqLdKYBCUHzwz05Rj7Dw38/cRZn+9aIhBwYScI0/Hw9Kyo3nUgzYahCkxDLo8lvsx1dMXlBORRr/RiNt/ilFLZ3uRvaqO9LWKoX8x7pp5R9+7F4O9fmRRwpyTAkp/oiE065FHnCERSAQSgUQgEUgEEoFRRYCsE3IT+ZOFB8ecLA9YeVBikMnIYZ3kpFpmqq+VZXHRqTYWG1nhOrDAIhSfF5yycq7Kope8PaohMOG83xZ827NZy5A7PRMirjGIfLCx0Mcfi4XZo446qigt+G6BLwVU9F+ncuoyO11HPZ6pS39YmLRw3LYO6pQ/7w0uAqkQGdy+mXLKMAlaT5YITogxoWZRwCLB9hhMydYLTKVm9EEoRuG+Cfctt9xSBgjacxpaWz5qi4LIU8fzY06eY4oGh1mzZpUjsIIB1eWM4nUwYTH8YcpKZNllly3WOjxeswiBsy1LTAMpQWxj0m8GaNgZdPVzhLpc1/A0kFOcUII48k05lDAGmLAoqfPHdcaJQCKQCCQCiUAikAiMKgJtmYk8xeKAIoOVgG3jFCMW7shlITO188En7gVW/jfJpgxgFXLNNdcUWc7WDPIY62tbdfiVk2ZUFSNwMF/gL2/99dcv21EcidtJkSFtYBkKCr7yKKjgZkGX9Y1Fvjp/G/vog4nEQUPQUf8/kfIyz/QgkAqR6cF9IGqtP1qMhMUHywIKBz5COA0y6WZZ8NBDD83TqVE0SJmYjkm7PI4P4+uDtQjHnWOZ/clX0xPl1bHnJuW8O6PPYBGKmTrdKF4HrhEzBWSqR3tuwICvPZKUWKw6bHExIBsYmB7q37Hwdd+PsoRShVadAmzNNdds7GX1TrD+mVcZo4h5tikRSAQSgUQgEUgEEoF5IUDmJT+xFLjiiivKdhcn8B199NHlRD+ydSzehbw1ljymHs+UaYFSmRa5TOyPO+64sjWH0sWpJ55LN0oh8GHFTPY0D2GZbitSyPuRJnCCAXwt+lGi2N5PdjWXkW8UcRqlPh+UtqRCZFB6YhroqJkKhsEHyIYbbtgsuOCCxbMz6xCMmHIjJsPydBOkUyYliC02zP6YALI8YWJWMzblBS1jlR31Ym6YIz8mnBrNL99Y5Q3b/WinWF/AFhasPzhZdWIM5RXLEHtOKTZiW0zkHWvgdN9gzrLn6quvLtujKJycaKO/2gP5sGGX9CYCiUAikAgkAolAItAPBMhQ5CwxC1tbPci85DJHx9oCw/KaTBbymLhTqJ/HdSxW2bLsWF5baWxNJ0uPJdd1KnsY7tVtNn/YYIMNyqmILHBCFtWOSKf9rHBCGWWbOIxgTqaFXaQdhvYnjdOHQCpEpg/7aa85mDhmweSPw6FtttmmKBx4vcbYMaA6XbdEBwPCjAwEzPxYMFCK0KA7UqutFJlX2VEerThnUwYZ23fi/rzyjsozbdUflB2UHocddlhjFcKWJttaHAVXb02Kdss3VtC3lCucgzEx5OWcrxgOqOyJrPuoLqe+HqvsvJ8IJAKJQCKQCCQCicAoI0Aeil/IVI5hNTlfZZVVmrXXXrtYLZBfbQUR5iVDRVmRRqxc8rQFSkfIkgNrBcGo4Uv2ZBFu2zalCHk/fOXV+Ng6ZDGX/Or0RNYhjz/++BzHqYF1YDlqOGV7eodAKkR6h+VQlhRMgtUBsz6M1qTaJLm2Col0Ec+vsdLFD9O25YJFg+0Y9kLOnj27OGCl2e2mTGkMCJy8OuGGMoCH56hjfvQM83PtDg24bUKcRFGAwIFJIOUVZ7a2I7UVWIFtGyf/G3AovSirHG/mx0mrwcWg21aGRFnDjGXSnggkAolAIpAIJAKJQK8QCNko5Cwym8k7vxdkNlbNJvZ8Wlh4DKtr9Ufempa4F+XVMbmcYoR8pp5IW+cf9mtt0k6LchZAWSzza0f5EVh47sAGJ9DstNNOZYuMbUUW98xfAptIP4o4DXs/Dxr9qRAZtB6ZRnowEEwWo+l1ULZJvQGC9QGnU/ZD2pLDH0Yn5tVmYOjirBWDtIeSOZx8fqMSauatvUwiKZI4UT3jjDPK6Tq2MtGCU2TAMxQhbQzqsupreCmXoylOwPQFZQgTQxp5g84oYdrGJf9PBBKBRCARSAQSgUSgXwiQuSxQ8eHGotdClon9jjvuWPyBmLi3F7BqWuSfyYEMam5g+8uWW25ZFv5g6T5lEyvz6667rmztdngAC+lw/D/TsZvJ781k2p4Kkcmgl3nHhQAmRbNtEu/IXBP7I444okz2basxOEjT/qnEPc8pU/gPsfWGdQPm6NkoBe3RLtpv+0Q5pWURQ4HEeeoDDzxQjl+jCKHACnzaGLRxDAxp3flfOeigg8oWKX0Qx+nqn1HDs41L/p8IJAKJQCKQCCQCiUC/EAj5iyzHYoE/DBYMrEX46uPvzTYQltm1tUfKX3/xD0LGhRlfLLbac5oKL4cFxIENDn3g6y5OUUz8+vVGj365qRAZ/T4emBbGAEGx4ex2k337/mz7YKlgu05M8iNtEO9/WmEKAaaHmCArh3a6SD/MsTaxDnFkG6ZvX6Tj1jB9uMHB827aHmkMyiw/rErAerfddiu+QnhBt3oB9yhzmLFL2hOBRCARSAQSgUQgEZguBELuqmOLTRb+WOLut99+xVLEtmeLU+Q6FtTktJkeasxg4rTENdZYoznttNOKbxCW0SykOZYlH/PLwgci7OTNkAhMFIFUiEwUucw3bgRqRod58SvyzDPPlGNimbxheHfddVfZN9j2xi0vpocROmaWgoDWfRQZoDZRTtB4W0F4+OGHy0BqQA2mX2M5r46QngKKVt0xyKxBOKiaNWtW2YJjO06N9bzKymeJQCKQCCQCiUAikAgkAmMjUMtn9TV5zOITh6unn356cYj/9a9/vcjATlEhE0sjyDcTQ42XxT/bxZdddtmyiEf+54OQtfT1119fLKXDqrnONxNxyzZPHoFUiEwewyyhSwTaDMv/JuP2Al588cXN7rvvXrTmLBhef/31uSbq0tpC4ihYFiKcssZEvsvqhyZZ4GRgDJ8uruO+OEJct2PP5TGgWJUwqNi7ytv53nvvXQYTCpd68I3yo+zJxkHTZMuRv6atl+UGbXX5cS/jRCARSASGEYF+8Eg49KvcYcR4PDTn+DIetEYjbd3n7WuLVI6JPeecc4pShI8MvtwsgLF8tiA2VhjlbzBwipiFiEMDVltttSK77rrrrmUhz5YZzyLdWPFYGOb9RKATAqkQ6YRK3psSBIKJYf6cJzEl3GWXXYrHaKZwL7/88hy/IibuBhAWDo4y43E6Bg3lZPiL0iBwZUHDnNDJMRQhLGs4qLKXlaIk0vUKO+XVipu4Vv5k62qX7f9uQ9Qd9MT/4427ra9X6dr09apc5XTCopflD2tZNebD2oake2YiUL+7roW4F9/7RJGRP8qIsrspK+oXR/5O+SLdvNJ0ytfPe0HT/Gjvhoa6rLGuuykn0/zlnQ4cBwGTibwj8pjUU4JQhvAtwvGqgwMsVkX7OsWD0OZe0dCpfe5ZDISDLfVf/vKXm0UWWaT4XXGiYvjO6xUNWU4iAIFUiOR7MK0IBDPE4MKUkJ8QZnHnn39+8W8RZoS2d9AQ77PPPmUbySAJT9MK4p8rDywpijic5aOF1c3KK69clEwc2dqrGiaGvaY56hfXfVPfdz2REGVEud2WE/nqWP31/2Ndt9NNhO7J5KnbisZehnabe1n2sJZVY6INvcZ8WHFJuocHgfod7nQ9mZa0y+umLHnmx8fa5fp/EELQVdM/EbqinDpWTv2/6wzzR6DGLPpl/rn6nyLoGi9N0lOKWPxjGc2K15ZmChILV55JI0Qd/W/N1NUQbarjwITiAyZO5qEMWXPNNYu/lTh6d+qozJpmCgKpEJkpPT2A7ayZoOtghK+99lpxpHTIIYc0fs5xZx3idBWmhRQiLB/q/APYvCknCR6UHfC76KKL5mxBss3IKsSvfvWrORY3/cAu+lA/hoLL1icDm5NtJuPzRdnMTG3/odjhEyUEhXkBHe1Ej7yc+IYT2XjWjpmsUsLFlizPpyNQbOmzcDTcKxq0B5a2oNVmp70qf1jL8X461i8xGdYenNl0+67xRHzr5z//efPqq6+WsSBOsQg+NxGU8MP77ruvODUMvthNOerEv+6+++7Ce/HgsOyM/EEXnkSRz1eYe9MV1G0cfffddwuWMA0aJ0JT5BVru/6AifbGs4mUO1PzwAyvvuqqq5qrr766LPJMNxZo8t7ecccdxS+evp1fiL4Xe998G9rEStopNCwjWEKznia/RPr5lTtsz6NdYt8aXuMAAacrOolSvM0225STZu68887yTQ5bG5Pe4UAgFSLD0U8jS2Uww2hgCHQsGXiTNoF15Kyjt84666xmhRVWKAoRwl47b5QxE+MYSCg+OJ7aaaedikLE2exOq7FFphbs+oFdlElYcZqNvmMG6si07bbbrrnkkkuKkI6O8QZlE8Stmmy00UbF70xbsB6rTHkJKHBYffXVCz6EjE54uGfQ9b4RiKNN4qkOcKTYspWMAN2roI3azzw3zU//gqr3g6M7q3XT2e9/oSivEoHuEcAPmZjfeOONZSJhZXXzzTdvjj/++OJQ20RjonyMgsV2S8fe40vdliMdXmNMwnuNCyZ37SAdZeQJJ5xQHE52y9vb5fTif/S98cYbzR577FEU+fU4MdHytU85Jr54OutN7XXfL0P3CMDLu+yEFotj+PV0BzR5z8mqnH2SVboJ0fdi750yHnzwwfIdWAz0PVBE+v68O/EudlP2sKTRdj8yGrmfzxDKIO0nhz3++OPNAQcc0Gy99dZlToD/ZEgE+oFAKkT6gWqWOWkECEQmgbbJMJsz0NAS8zbtRBpWEMFIJ13ZkBSgvXWI9hsoDZgGEkf0Gjg4Tr322muLQDdVqwsxqJlY8vWivyixvvvd75ZjkrfaaqsywFM0CEF/Hcf9diwNpQ5nWquuumrz5ptvzllhq9PW13W5MGBtwdqIh3eDaggXdTrXhH7vW/2OuR8h0sf/84ujHukibx1H/rgX/7NUia1jBKUI0gmRPuL6Xp22/dy3ZTVKfxA24v2IPFFOxJG/Hdfpx3sdZdV11Neex//l4s/tjXvt/HWaeBZl1M/iOsqJWFqnOVmReuyxx/4K2yizzp/XicAgIRD8bYsttigm9/guX1wm9ladTaxi5br9bYzVjkiHX1CgOt0tTNbjm4i4XUbcx2uffPLJwntZgOA/8UyeuDaGoZMFH54Uz9rljvf/KD/y+V8Q481xXS6apkw8KW6MMxZegj9GORFH+sgffH6s5+6bKDvq3hijvZFWXIf6fqdnUWedp5vrdrlR9vzu1/VFnrgX/0fcvl/TVddTp6vv19eRN+5FHrKA95kFBUvH+QX5O4VO96OuOo689b249sw1Ovbdd99i3Yy+iQTvEAvFn/zkJ0Wx4ntz+qJFEVbRvvH4NiZS/iDkCdzEgth3QRly5ZVXFj5zyimnFKUhGYwcdOyxxxbns+S3ySh2B6H9ScPgIpAKkcHtm6Tsz8KJU2iuuOKK4hR00UUXLcdvsYSI/ZXBYGvAgtnW94b9um6nawOjweHFF18sAwl/IbvttltZjTO5swI1LyGt13igiTkwqxQmn5QXsaphUKOgYSliBYVQjDaxfox0ygiaCRUGyhCga4WIFTy2QSRqAAAgAElEQVSCeWxv8Szy1TFhHA7oEktvUhBpAkdlSeNHiWPlieIk7smLljpft/ipI9qFTn2mXAo/7a6fq8N9zyl9vvGNbxRLG4IBGvzkr/NFG7RV+/xcB25RN5zlNykh8DutiVBJyFKfZ8x+6zbKqxx0KVeauuxuMWinizYrGybKDkza/RNp0SV99Kk8db9HOt+F+2h2DU9ptb+NSWCm7ttvv71xBCLz/sBDLI1ylJ8hERhEBHwbjrDfeeedy+qq79S77ltynKeJmhVX33p8J74PP+nqoCzvfP0dUohQzpqg+Z6C94rrdFG2e3iJ7ye+Jfna35/60SqNcYwS3fiAR0XeyFfTOJ5rNAU96sIL6m/ac3S55zkrGyb7Fl+MYUGLZ9oLHz9BrA1o9Dx4s/udsKAEwdOtfLNsiDZGvsgTMT4fOKK7E9bdYhHtjHEg+kW7tT/4cN3OoEN70BLtRFPwxEhTx57BSlnyyFtjUl+rG03aF3y6fq7cqN/zwEzZaPesHeCkPeKgSxrXUZ9+a9fjmbYF3Z3S1PToNzSpy3tjIeryyy8v/7dp6vb/oBFulCC+OVZenOOz/qpPYIw2dVv2dKeLvogY3vAja9luxAqNZTFFl372XB/yK2ihj3WV71H+DIlArxFIhUivEc3yeooAxmcwZVVg9egLX/hCWbkxQNg+YdCIQa2nFQ9YYe0BgMBhwHjooYfKihPzaIMxDTtNewgCU4kNGgl5HIIdc8wxfyUwmeDrt/32268IkdITaAidfMTUAha6CciEeQKKtIQOaVdZZZVyX//ffPPNZfXk0UcfLQOlATTaDAMWRlZX7DW2P5ewQsEW+CiXUEOBFGm23XbbcioPxYh7foR0SgnvojzjCdJrG4HJSimarXQwm6aYIHxF2wnMJuRotYrIIS5HaxdeeGG5576tZHyyKNcPLvqcEH/dddeVH3870oQgSrBjuaMdlIsE8sUWW6z0h3dGG+WVr8YGXSZRBBY4ots7Z4Kk3vFiEbjJhzaraqxU1I0GQpF+rzGJdmqDNlGGSo+emLAEftLKS5DUXnwDXtIzRQ5MpJPHOxTvhwkfvL2j0e/ip556qryDQXvGicCgIeDboHDefvvt/8qyzffs5ArKBvwnvifb5fBX/C+CZ3iyb9y3iZ+6FwoRfEO+e++9t/ASvMpqtgltlCuWVxrfD56Fx0ir7EiHLpM7PEkaR5AutdRSxToPj5JXm+SL8oPO8cTqRDPLE+X53vF7PBMPM16I8Th8gkL/uOOOa/793/+9HPGJFvQFvwleAxtjMF7DOhNvFMeYJZ2yTeACC/6vVlpppaK4YsETfEY+vEn6GL8oFOAT48FNN91UeJr+Chpg2U2oMTfmmFgH3//Rj35UrFW8G+rQH65jrNNOk1b50AnDu+66q9CmX+IdUYdreAfdMAmeju5oW02PMQ8N6vUzHnh/ov4o1/jpPQ7M9Av+r752UKb+FMsvRJ3okI8cEPSIfUPkEO+J90Bd+lYfRzplwN495QfNyvOO7bnnnuX98T5NJgSt6kKn94dCc5NNNilKA3WRfeM9mExd05FX+/RvjM8sQHz/vj2Yh+JROth7j8LiGC9yP0Mi0GsEUiHSa0SzvJ4jYJA1iNkOsu666zY77LBDWWVhempgNmGOQbnnlQ9YgQYCbQ3hgEUIvyowMVEkHNSDN/LliV8/m6MONBAKCFZ13WjShxQShPYQMggs9gITcggkQaeB3koBM20CgfuEL4LHiiuuWLbhUAItvfTSDauhr371q0UJYzIcZUh/8cUXF3xM/hdaaKHmgx/8YBlcQ8kiLSHICqo0fv/yL//SfPjDH24WXHDB5ktf+lK5p3yDsoFanvEE6bWXczB9tfjii5dyxf4/88wzi9JBvxKyDPzqXXjhhZt/+Id/aD72sY8V2oO+9dZbr+CsXLgSVNFvRVOZ0i255JKlHyihYEl4mj17dsEJXp/73Oeav//7v28+85nPzGk3LCkd4x1SNuGDYkjZgcUSSyxR/NNQXCh7IgHthGaYoDUwUfZqq61WFECxEhTtZL5uSws60eKHLsJUTN7QTBHiaG4raniGNDDRbkKl/lYmoZU58nLLLVeef+ITn2g+9KEPFUyifPko+Hxv8vhlSAQGDQH8Bb+kbMZn412NmFLP1hmT2bhnOw3Fte8qAh7km+eniVIkJqXu2UYoPf5uUh+8ZtasWYUf+fb8BHzMljzfDz6Gz1A21pN+vNSEMr5P/PYf//EfG9+hbzX4mJVhStkoO2jtJtZWk0kWi3iL79oRnniIcvFO44QJv9XpGE8WWGCB5gMf+EAZA9Dhh078Snq0GEOchLfWWmsVHiZN8HSTav0gnQkenu650zL++Z//ufnoRz9aeDp63F9jjTUKhiHHGAvRbQIcOKPbeEGhrr+jH7vFQXq0W21XjvFQO43HeCjZ6itf+UppJ94Z44DYOOqUDzSgGZbeEVZJylS2oE+t7q+zzjpz0c2PGGtEPDfohg1LT/4hap7uGj3G/Zjwew9tZYRTYPav//qvZTzwTrWDsckCEas/ijd1Rb0WT8gcFOTu+0mjn+ANg3hPLL6wSggslGH7qn6X7vOf/3zBBDbf+973Sj9PxkIkaKxj9MGV/AFH4/9BBx1UFGXknXhn2hgM4v/apT36E9+hBCG7sJryXpMH9UWkCxz0o+/MAQHyuZ8hEeg1AqkQ6TWiWV7PEcDwCSwGgXDOafXcgEcAtHpTW0UEEx1FpgkLgoI2m/TZ2sFhHcsMg4zBRggMojPa/8f9Xsbq4JCUIEwoqut0TaggkHP0F1p+E039aLAnBArSEoQ4uKT0CoUIYYowQ0A0kFqZJBBYZbB6x7KDsBdCFKwIawRT7w+MrEBKWytEpCdwSCMtwZjARNiLe+4HvugbTzDAW5Fj6WG1zOQd3TCwUmm/rGt0qANt6jVx55TWc4Kje36e10KDdhE24UFQDosOW2JYloTwDF+KEc9ZRhAwCN0EvGgnHELAcm0VExaxtQbd6uPHR9+gayJBv1CCUeSxbAka9DWMCKGhuPBOw58yhHLC5E56ChMri3wm8DPknr4hDBOy0Ug5ov3SevekJczCWrn1+0EggzdMAg+xNIHJRNqaeRKBfiNgIkH5Z4z0vvoO6h+rBWMFvil4xhS/k0LEBNNk13cZfAZ/okykhHYfD/O9UXywrDIu4+W+KT/5gqcamznUpuhUdtAlHX6HJ/nOKCeUT0kS/MB3HzxpvBgqH7+isNFWfCv4IzxMYLVF+dIGL9A2PMDEnKWEMtCBzpgYowUflg4vxV+kw7PwF7wX78E3aiyUjedRMpvYKTfKhkVgY2HBuKgsPFbZ8rJcMM6xGgnlQje4RLnaKZ86lUt2MOmHRYwfnkU70c9SwlYs46b+g6G0MNVfrBW0UVpKBeOcMZRFpbR4uvK9P/oYDeiBJz6Np7MK0efGJoseThOs/azIo454V5Rri7D3t5NCRN9QqsA5xgV1opGjUu2mkHfPWGDhQJ+hM94T3xSLGIozcWBinHDP2Ki/vbvecRYrjsylPILxZAPaBLH2ewf0u/GYctE3hy50asMwBG3RN95vfacN+okcpE+1Q5r2j3KWUlPbfW+eZ0gEeo1AKkR6jWiW13MEDIQGPfv7d9111yKEGGQJIwY8gqBVdoOtQcug12aow8JAO9HtnoHCwEuQs9JvNdDk3+QRNoSp6Q7oJDwRLAxwgXnEBE6TYAOb/hMM5ga5WiHivj6kEAkLEfcIGQSn5ZdfvigrQiCUFgYEESs8BLoQutQdP2mWWWaZItgRguN+IaT6c8YZZ5TJNIFJCPqrJOO6pIjQV6x5DOYx6IthQmCrheGojwDkfbeSK02nIC0clOM78b+2Ezqs8hE2tLsO6iWsEt6susGvUyDoUkKEZUxgilb9a8XZFpu4H3R3Kqt9D30EapjAOcpAm2cEX7gpU7soQQjl6NVe6f2ks3rEsiUEXBMRq9l4AlojLaGVEEaRqP/bAT/BY9SRIREYFgR8I95tE2gTzPhu3I9v0tiIzzq9Ie75/ig1O1mI4NGUBTGuUIhwlG0rCV4U35RvkVKSEpzS1LfaDr5RykinzLR5UZ3W5FI5lOr4wGQDGilpKH4ppPFTbXcfRv7vpGzxDA9gEYIHtvlj4Oc+eUN61+7DC/9RJ+V94BdtkRbPo8BFWx3k94MhyzVY65uar5MByDvGE/mDlrqcbq7l04+2QLGQowRAa12ea+1zYh2rBwsP+gV+aDKGG+tN0o25sDS+G7MoTIJueeSl6AirP2UYC2Fhsmv8cs9PnbaTGl9qBUpNm3QsCzqNb9qvP/Q5JUxsE5NHmymkPPNeKtN443+WMvDWR+5LTwkFa9+OCbs2UqgYR8L6UlptNP5QBtkW5bvoZQh60EoG9O0aD8lH5B7jo3cDzdIK4vrXS3q6LauuH234lHfJO2yshaP3Ir7DoL1dvu+RkjYsoZWVIRHoNQKpEOk1ollezxEwUBuwMUMWIVbuDVoGYYODCSNTOntiPTPoGqBqZjwWo+05sT0oMOjG9P0Mgla97a80yeXjgIAJExhEW3tQ9aSKIISYnG6++eZFyFFYtMU1QcfkmhBlYPSMQqRtISKtsjopRAyeVrQIHyFwKceASiC3Ckn4kh92Ub+4rRAZq7G9VIioV/9QIDB3ZRpq1c8qqHsER/3b7kP5ulWIECYJ4YQ6ghJFAIHa6p0JUiifor3q6kYhAk+mzwRPZdY/EylmwlZ+Q5AOrKOeecXymPigkdDqG7baBRMrlzCJ/tM+3zZzafXWdHhHKD8oukxAtA0WJm8ExaBJ7Fsh3FpFJzy2QypE2ojk/4OMgHc6AoUF3sIqyvdSv/euTSzxWXwhgm/BhKRbhQhLEN8pXluXj4epl1WXcbkdaoUI3jxWqBUi+PdkAxqNOdptUm8RwWTVdhaWLSa7xhB8pg7aMJZCpG63fJQStl6wZrA4gx+ZpNta4n4bD/+3FSJ1ma7hKw15h6VFze9cU2TbtqTfpJ9IkI81hv5kQROKiros7TM+2y7q3aJMq2nxP2tNYw4clEdZQImOf9ftwpfx/Biz9S/lCVmAgrou1/gbPD2UbFFW0Ie2eSlEpCcf4fXqUb+fMcL7wJLF/8qhJIGzrSjoR4u+FLPOpOCBgXFUO2MMb7fRM2WT03qtEIl2axcc9YvFMP0HB98f6yE0apd0QuAW/0c5UxGrE75+8NAfMGUVwroHvzBW+0almVcgr+iHsODUxgyJQK8RSIVIrxHN8nqOACGClt/ATYAjgAWjJfwRDGwhYe5ogDAAStMWDHtOWJ8KjEGM8EDIsIJC4WMgsbJk4kawhEuknY4Br918NBBgDFoG65om1wQIChHmsIRR97pViEhrUKUQcRyiSXMM/PHMiiaFCKGAwOV+/ZsuhYh31WQ8VqzsJyfsEmqtgjG9hUO0B67o7kYhIg/B24oL3JXtB2P7oAmnE1WIUFBQQsA7yo1Y+a4pwCaiENE+7zAzbEpO5bHyICgx7fc9m+RJ5zumRCKUrr/++nPRwnTZNhi0mPTBg/IwVs7q/jcxgzUhGbbtkAqRNiL5/yAj4N2OYELrnacAbSsspLMa77uyhS7CRBQi8rTLt1JuAmvsbSsA1DVdChF1473aThFk/PSzMo33UlyQK7SnDtrQjULEBNgEj7JFuXgQfmSSz1fIeBQiQau+oqxlacBXlsWF4LkRWyk3gTee1e9A3Yb5XctHEaA/8V3X7WAMNXbwlUH5Tf6KNkaMH1ucwU/hQU4x5hirYa8ev/ra/8omr/Flsvbaa/9VG40HtgZRXIUSRb4IypuXQsRzOBo3LCBpn36lxPENwC5o8u1QoBsvLVoEztFG7aagIrMYk4zZaDcuRUCbcnxjk/EhEuXNL0a795ZihwLJO8hixAIF2Rf+aKp/8yuz18/Vre9Y1thCTaHKCse3Z3ynAI2+Vbf0YwXyESsdfcJ6iMyRIRHoNQKpEOk1ollezxEw8HCearLLqVlYFwSzN7garJjvG/BCOCPUEMZi4Os5YX0qULswfJN+CgQTOCv1BpIY7Nptmtdg0icy/6pYNDDdjNVCNArRTwQGggRlgH5xnxBloDNAGsQj6NO2U1UCTShEWIiEAkE5hAODbuxTlz/qjbiTQsSzduilhYiy1QEL7dNeE3erlBzPEtbQTPnQXnHqRiEiD2UIDAkKTLytplAKUB76FiaqEKEgIJTaG63M+HkH1SMm7MS72AnLNrbxv7T6yLetX5wG5BunIDGxIxBb8QrcCJkmCRRuQUfEVp5cewekD4WIrWU1bd45AjK8UiESPZHxKCCAD4S/HzzG9xV8x3dGWWzCRIEZ36lvwbfm+4kgrfGVFUJ7y4wJDWsA31mUL/btBc8fNIUI+rTJ9248tbiAT1qdNg5Z0Q/Fa2DQjUJEWhZuJmhwZJkKB4szrNw4nYVfGw//d7IQUV5gCl/8nDWo8TT4XMT4G54Zk96ge7xxKETQg4+3A97pXdIWYwBrXDTg+xHj2xZtTGyVZ5sPhUjwYmVql7GaTBPKc31izKdccApYtC3KjfGllt+UEwFt81KIRJ3GC31MbtAWCib9Ur/D2s6nCGWGdG1afB/kDX1HzqTA1+e+uWif+jzrh4VI3e5ov3t+8EQbyyfKUN8hpQgloHc+FA6RPvJPRQwvsodxnFUNZSGZhJxGFvQO1HS5HitQbhm3WZRa8KyVUWPlyfuJwHgRSIXIeBHL9FOOgIGH+TsnZwZc2uJ2wEwNnvYzW7XBgE0GDYgG6hgY2vkG6X9tMNBj9lbdKA9MDO3nZlYae5JjkjdItKMF/QZAq3EEOgNyDHrwt9pjwNYv0R/6hmCjrQSTwIDAQgDXbisJ7hMAw4eIAd//sFAHawOmqrBijREYyRc/QiQrA5PuWiDyvA69Voigj9CtrWgOTAiJhDQrlvZyEyyDVjH85uVDRBqCBcsQApH33z3lEyCY+1r5GkshYnXPOyV9p0DwtnpIGeEbDEzRDUsCMhprmjuV0+keYQntftGP0ZcmFbbGmBB4T/woN1mCcMbm+5DWT14THaa37qOlk0IEDaEQmZeFiMmBupSTIREYFgR8kyboFJgm/b6Z+EbwVQoAY4lvQ/B+4xkmr6wkgif5LilsWQSwcIgJLP6Fl9hSgI8pWxm+P99LOPpUbzv47rr1IWLS1EsfIviWsQENMApM8H8TM35NTOrdjwAD4wzfGibm8Ux76x8HtSZpxiL4SQcPE2jlmnj7X54IymYFZ7wjx0R5nsc1Osk5lFX4Wt2XthdQvugP9+uyo475xVGPfmQhYvxx3Q7SwYkSgfylzsBQbJzVxhjnpTVW4KGUCtIoAzbGNtYM+sI9WHnvWNZQvMe2Cfe9c8Z8OLbH6aBduvkpRKSlLICjdvouKLDci/ddGu+IhSeTbXXqI/elUb97lEDw9r++sZBR+xCR1jhE6ei70u/9DIGDGBa+ce8zhSVZgvVT+JfTHmmkFSLuF33KVyecbSWj9LKYpw+M7TFOSxe01Ned6IIn3Ml3yvHuZUgEeo1AKkR6jWiW11MEMEqTO8KHlQqTJJr4dpAO08c4CX0sRUygaOwN0iaFMTC0807X/0FzDAYhZBAcDGpWsEyICU8GX+0TpB/EgC6CjRUf+3FtEdFX+o+AxOKD0EFpFW3WX6x+COsEcAM74cnKGKGcYqtWiMhrf7YVGveVTbA0+BOu7OEOoQ1e+pzAYwAl3DL/9T7IQ0g2ONfCEbq8a+rVD9L4KYOgFn3QLf7Kk5cpsX3JhGdKAPSIrUgRnq2WqSdwUT5BkyChTdoqjzSEshCS3fOOe98JG/CAuXpixUi7Q3hWvmvCilVgQpR6lINO/SGNoC7KLUoRwqS+kc4KsrZQbhEWJxKUod+1zfeqbPXpe33JtJYwBW8/z5kFU5LpFzS7ZzLDB0nwBbQrT7rwISK/+8onMKIbTu1AeUqYh4m08Rs0vtGmO/9PBCCAx3q38QMTON+I7wk/thWAgrSejOCleIBtmCa70pvU+bYdq+o7qBUieJgJCQWIcn1Dvj+TL/ybcjd4KR5sLPANUZ6aJPL9hBe5h4dF2b5NPzzBhDWOlY3vT9rx8l3pfbfGFCv6LPKUr41+sMIzOXHVZvVHQJfJejjv1s6gpcbPyjd+oWwKBeXi0xTuZJVwNhqYqAN/1T/4kD5SLp4aPD3owIuM/xRZwfvxOwpslnLqCFqC7nnFUa44xkTlUv5TqLuONqIx8NaPxiYKL1aMFBrw0Kf+N87jxzDTTtfKUy6ZS1pjLYUDBUYom9HhGfmG8tt4r30whAtFk/7xXgrSowVO8JKXYsniSv1OSSNt/KSnjKOoYJ3gXddX8VxsPDR2stSEt2t0eMcpxizuuK8sbeT/i+LOO40+uHn31cOS17gDw6kM0Q7vuDY6QpnswErSeBgKp7rdricaOuX1zvipi1LV1iQyiFOE8Bo4wW8iwTtLfrS9Sj/CO0Mi0GsEUiHSa0SzvJ4igPEawDBVAxYrAANiOwSDFhucDQwEFmaQBilCm0liCBHSRZ52WVP5f9CB4RNKDLyEBMKnyWg9kETaQaC7jVHQZkA00ecEk6NLq2wES9f6gTARAlfk0S+EvyWXXLLsm6YIgQFBhIUIwUpaGFEgKM9+dcIzZYL/7beWllCFBukNzN4XwoE0lCEf+MAHmi984QvlBAECulVPCoSgRWwri/Ic0SufH5rcV6Y04wmENAKClTiCsp+90+pwfB6hgYBZC87qIEBQzsCFZUvQQognGEsjDwUCbKVRrvZ6fwiy2myyAjfp/eBD2LMXvS6XvxCKoPobMVkggOhH9KLBtX3VJhsTFfx8o9qgn6PswAM+vlfCZk0zYZtgG9hJ70dRQogNpU8oRAiDNab4htWlsSxEvIcEXQo37VSPn4kkoT5DIjDICOCPrPAoE1lTxreK95p0UqrH9ySmADVxlU4avChWYPECq/++U2l9iyafVttN6E2EfXvysSDAC/AVQXrfEn7n+8FjPv/5zzd/93d/V/iR+vAkChdpI49JKKW2MqXx47+IQha/ivJLhjH+KC9+MYE2VuDfNd/QVvyfxRmeXgf5TMrxfyfNBC1OjsEL8Dx1GOdM8j3Hw9CKfhYuUR/FhzEpaIKne9JrJ5rkp7AKaz1p8WBjJZyliZ98xoTgjTXd87pWpqBcMoYxQv2f+cxnmg996ENzaDGemniiWcA/KQLcizahFz0xJhqn9I2fd4oCzsQ10knrHaFAqccW6Y2LxgBpvE+BJT7POgZeAt5uDHOKXGDx4Q9/uPm3f/u38k7Jqw6KfmkFbY46LMR4D1k11jREv/h2vMOsJpXlpx7vifGPDBpjiXfRd6M8Y7M0xtKQSSy4THRcLIRP4E+01buLVrKKBQfKKbKAb834B49o8wSqmZNFGXVQrh9FlfeWElIfUmrBHL6eTzTA3gIJOdE3SF7KkAj0GoFUiPQa0SyvpwhgoiYjJmoGWUoOA3Q7BJOP2KBo4LLSYmJtQFSGY2FjJatdxnT8r30ECitS9rESgAiSJrMGd8KaNNGu6aCx2zqDRoMy4ZaAR4jmid7AaEJbD8rKlYfwYOJNYLKqoO3+JwBRCBGypFMuIdTqGIGQ8G+VxoqMAZ9iI4QW6b0DzIs9t7+eVYnVTwKp/1neEF69T9IHPd4bQp3n0vkRIk20lSltpO8GG/2njVbXtIfApGy0+9/7WJcb5WuvPPAIOrSBsonCTzplwwdt7lsdIpDIRzBipWPligAR5YrVp38CG+XDXh/UtBBI0WfiQCBBN2HLqlyNWzc41GnQTTBFl7LhiwZtQJe+REf97hOqKMd802iVxyqsMtAZaePdY70SbfZMGgJ4TPRqelzD0QomDNGirfAmKMc72M6T/ycCg4JAfFN4p3Fy0UUXLZNNfkOMod7/+B7EeCV+6nugPPR9+xalZaUhDn7qW/dd4qfKxwN8g3gxXhCK4ihfXs98R74hk0W8l0IyvvOwepQH7fidcRAt8vgFP4vy54d11K+8+OEHJtcxvuAbMKFEVa421kEZ+DXeoo3oQDN8WMqhUxox3sP3kXR8N8AHrzB2aQcLg5iAqwNNsKl5urKNCcY0zwMPcgG+Hjji1fyTGJ+iL2u653WtTAFPRZuytMtYSMESbdQObQyagxYKElYcFhjQy+KD0guN8Y5EWu8K3mvs0X98PrTH/kiLp1sIsm1Gv6jfmGx80weBhzrgo360+qHbe+Uar+bnRF9Hf6rDzyRdX6KZ/BH9FzTEe+Jd8C4H3frPtxHyYtAiv7HV94BmP9+Nd0E7vFdBw7z6pJfPoq1idesD1lvkLko6iwboRFvd/snSoD5BmWQOfcGCieVU1OddQlOknUidsPdeWsywdQYPypAI9BqBVIj0GtEsr6cIYKQGR6sItPcGHINop1APCjEwGABNnFlb0JZj1AZpAzahYjqDQYRwQ8ixAmPljbUAgcAgjL4YrOu2TSfN86q7phHdBmWKBas+BHTCHaGBoBNpozxYSE94CSFLOn0dg6kyI517nulfeQy6ngtRtv8JOYQkAgyhLn7xP+E1yo98/ndf2kinDPUpU7rxhChXXm1Cs7LFUWZNd5QvRgs8alrkC4E4yva/dOgM/CKv/9vp5UML7KJsebU72hhlKyfSRhr94PlEQ5StLhgot41JpIl6xGiJPpU++t2zoBtt8e7UZURdkadNu+fRTmUHTSHQtdPn/4nAICEQ77r337jCAoKllfHFFhG8LNJEXH/bwUfdw4trxWik8324j08EL2jzFphEmuAtEQc/xcOUFXTEt+te8Ed5/PAvz7sJUV47Ro82odnPtTZFunbZ7vvupQ2aXeM9kUesjOBH8MPL3I92BO+o8+ifaGOUHTw9cIj0Qbd06lf+vOhut6P9v/KjXdEngbM42ljXgRb5YoyJPol+V4c0EVxH/yuvHn8ibbRPudqjTXIAACAASURBVOpCE/yk79Q30quvHq9qul17pt4oO2J4Kx/G6gqMa1rinrTqj/Lki2dRntg9fRH0SBf1xDsQeExFXNPmWkAHBQ8lk+1FFBVOJ6LkCSwmQ1vg4F3HXyioWIXgOeG/pP7Gg66J1CkvZaltQPweWdjIkAj0GoFUiPQa0SyvpwgY4DB1Fh5MIik3DDzzCxho/AykrC2sIMQea2Z3Vi0wbINbpzAZBl6XV5cTNKlXu6wUMb/kM8RqjVUYA3LQFOnr8oblmvBBk29rSxxnx2LECpl2haAxqO2p+21QaZzJdGX/zOTez7a3EYixQmzctM3UuMmXFqtDk5RO30zka5eX//cXgbH6or+1Tk3pndo2NTXPXUu37/ag0Ds39eP7r1Nb8QHylkU2FsisRcjATloKv3qd8rVrbqfxP7maVQgFC8tOFticzbJAotgKpVq7rIn8rz7WVyxdLI5S8rZpmki5mScRqBFIhUiNRl4PHAIUBzTD/Idw7MUMEKPtJmCYEeQJ82CmuywxKCKYOlpNi5WFSC+u89f3x3tdM27KHKs9tkow9+SB2x5P2wCYhKJjVIJ2WzmxnYWyh5UO81n94NmgK0RGpR+yHYlAIjAzEIixBm+1CGBbHsfFtqqEQ8uZgUS2MhGY2QjUvIBFF4UCPsCfEN96th+x7GDhFMoLedohyqljecjirE8scvFXYnHP1rSwMm2XM5n/1c3CmJU3R9CUuyE/dqJ5MnVl3pmLQCpEZm7fD0XLWUvYO8hpJLM/Qh5GOJGAcTIjtI/SfmCnU9iTaJJuP3NYiwTjn0gdnfIoD83Kp/Sw/5qWPjxw21bCRLPX9XaiZarvRdujbXUcA9pU05T1JQKJQCIwagjUvHUsvjtqbc72JAKJQGcEQr4KvhCLcRYBbWvhIJl/sTjtqN4CVZcY+YOnUHjwnxJOW21h4Z/HQp86In1dxmSvlckahczOUpyftFjE9CxDItALBFIh0gsUs4y+IYD5UojwNM8RGKY7XgYY6cV+GClfFsqzr9LJEqwXaKApLSJ9LxqlLNp37aBR5/zLCR1M/9RPwRN7ToO+XtQ7KGVEmyKuB+m4HhRak45EIBFIBIYZgeCz84qHuX1JeyKQCHSHQCceQOYib3KIy5GvxUAOhh944IGyvTlk0XYNyqLs4A+GdbPtMRQTjke2fYUlcLu+dhmT+V/Z6ra1nMyOdrRmSAR6iUAqRHqJZpbVcwTsReQdnIM4zlA5seo2YKKdgvuhpMDcjzzyyLIdx/5HPkpCKTJW/k5l1vcin9hPGziDpUl3VJ19nJyMUu7UpoqRvi5r2K/bbYr/Ix729iX9iUAikAgMCgImPKFoDh7bjgeF1qQjEUgE+ouAb78d8AdyZ8ilfA05zpbVSPjVa/MMi4gsNPgeOfPMM8tx07aeW0QMy5LIo75O9bbpGM//yiOX2+aDTicv2bYTodf1RbkZzywEUiEys/p76FrL34Rj3lZdddWyzWU8CpH5NdbAgMkyGaR55sHafmtOoTD/2vwvmH3E7bLjfh0bROzRDEsUViGOQbOXk7Y7lCHtsvL/RCARSAQSgUQgEUgEEoFEoB8IkH9t1ea/7tvf/nbxBbLffvsVZQNHrORXaZxIw0qbNYiTHvkg4RcuTkIMmbcfNEaZ6kCP7eZOY+T/r95m7nmGRGCyCKRCZLIIZv6+IYDJOXKX06YvfvGLzSWXXFIUCb2sUB1M7/gQwWwpLFiM2ELz+OOPzznxRbr4dao/nokNIkwIOYN1nC5/IbTw9RYZaaTNkAgkAolAIpAIJAKJQCKQCEwlAhblLM4999xzzezZs8uxuVtuuWWRgzlhtqB31113FSWIbetkWVbVrEtiwXAq6CUrU4hw3OrUQtbW/PGF3J3y9FT0wujXkQqR0e/joW0hJoch01ovt9xy5egwioZehlBgYLa2sHAWZeuMfYr2SXJ46hSaYP7BgDvRgF7l0Kjbo+lcdk6gzj///KIcYe3i+bzK6FRu3ksEEoFEIBFIBBKBRCARSAR6hUDIvyylHcNL4bD99ts3a621Vjnelgy81157lW0qHLDaIsMf3lRbN6NTnbbPO3Fy0003bZ5//vk5srTnGRKBySKQCpHJIpj5+4YABvjKK68UEzkOnOxvtF+xlyE0yzEw0JZTZrDs2GqrrZrddtutufHGG+cyD+xUP1ppzQ0YnEyxNnEkmQFGG/rtdKoTTXkvEUgEEoFEIBFIBBKBRCAR6IRAyMAW/X75y18WuZVC5LOf/WzzqU99qvjv+853vlMsMmJhUDlk5qlSRERdTsgxF1h55ZWLI9i4P1V0dMIv740OAqkQGZ2+HLmWsKagYLBlhpbaiSwYci9DzVDjmvKCXxG+S3bdddfmuOOOK0oRtLD+MIBEkIeSxp5LezFPOOGEchwZp6kctI51FFky8EAw40QgEUgEEoFEIBFIBBKBqUQgZF4xedvWcfLuiiuu2Cy00ELNwgsvXA4CsJX8pZdemrOFHI2RN677SXfUZQ5w+OGHN2uvvXZx8Br3xRkSgckikAqRySKY+XuKQM3gmPFRKtgveMQRRxTtda2M6GnFfy4s6qd4CWdSvGlzuIqGu+++uzhz8hwtoTy54oormkMPPbRskeEFm2PWsArpB51ZZiKQCCQCiUAikAgkAolAIjARBELeFf/hD38op7hQhHzlK18pTlT50uNMdY899miOOeaYhl8Rzkzrrd9RxkTq7zYPWdvvrbfeKv5MNthgg+aWW24p96ai/m7pzHTDjUAqRIa7/0aS+mBwtq9QQDCRO+qoo4pCxNaUfgf1C2KM31Ydyo511lmncVLMpZdeWrbHGEA4XjVQzJo1q9lnn33Kue6sRTDvaEe/6c3yE4FEIBFIBBKBRCARSAQSgW4RCFlXegt4jtXdZJNNGouArEUcbfvyyy+XU134FuHP7+abb27eeeeduZQi3dY30XToJFM7ZIG8vfHGGzeXX375lNIwUdoz3/AgkAqR4emrGUFpKBHEtptQPjhhxjnp9jdiiv0ONQ2ubYkxOBgImA7ytI0pO/qLsmb11Vcv57Lfc889RVFCaRMKEbRGef2mO8tPBBKBRCARSAQSgUQgEUgE5odAyKYRU4pwrso62mIgOZb8SxHhlEQn0PCtd+6555YtNNKTd+XvZ1A+Wiw22kK/+OKLF0sRVuRTMSfoZ9uy7MFBIBUig9MXSUmlPMAAMWHno3/+859vTjrppHI82FQwXnXU9bg2KDhthtJj9913L3srP/e5zzVLL7102dLDkSqLlnpwiDLacXZ0IpAIJAKJQCKQCCQCiUAiMF0IkE3bv9gOHot6oRRxSuIdd9xR/OSdfvrp5cAAW8PJxf1WSgSNZGy+/Th9dYKjE2+CzunCMOsdHQRSITI6fTkSLQnGJ3bkrq0yHDxhxFOpDVa/EPRQdGD8d955Z/O1r32tWXDBBZuPf/zjRTHifPb777+/7MGs841Eh2QjEoFEIBFIBBKBRCARSARmJALkWjIwBcSrr77aPPjgg82VV15ZLEUcx/vuu+/OkZX7CZA5gHrXWGONsjDJarxehOxn3Vn26COQCpHR7+OhayHmS+vrpBcKEb47WGCw0giFw1Q0KjTPf/rTn4oZISdORx99dDmK115KpnsYM/M957VT4AR9EU8FnVlHIpAIJAKJQCKQCCQCiUAi0A8EyLR+ceDAk08+Waw1Tj311OaZZ56ZY6nRT9nXHOCaa65pll122WbddddtXnnllZ6fPNkP7LLM4UAgFSLD0U8zikoMlTLi+eefL/46HLH1wx/+sChE+g1EMP2ggUb8hRdeKPsnKT323XffxokyHE397Gc/ay666KJm0003bQ466KDCnCN/v+nM8hOBRCARSAQSgUQgEUgEEoF+IkCuFUK+JZ87VMBRvGRzPvZiATHS9pKeKJMyxsLk8ssvX7ar27JDSZIhEegFAqkQ6QWKWUZPEcD8MD6MlrJhpZVWKsfYcvLU76BujF399is+9dRTzfHHH1+2ybAKueGGG4qz12D+77//fvPcc88VM8I4ZlcZwcD7TW+WnwgkAolAIpAIJAKJQCKQCPQLgVqmDRnXdhWyslio0/SSjiiX3G27DqvxpZZaqnnkkUem3HK8l+3KsgYLgVSIDFZ/zHhqgvHZpsJviBNcNtxww6JwwHjjeb+AUj7FixNubNNx/BirEKfK+N8xZNJ08+sXjVluIpAIJAKJQCKQCCQCiUAi0E8EQuaOOOqqZeC416846qIQ4cPkgAMOKFtmLJqaK7Rp6xcdWe5oI5AKkdHu36FrXTA+5ng33XRTUYZwWsqhaWih+9koTpvsS7QVhjdr+xUfeOCBcu56MN5kvv3sgSw7EUgEEoFEIBFIBBKBRCAR+MtWHbL3b3/724Yj1z333LO57bbbUiGSL0jPEEiFSM+gzIJ6gUAoRFhonHfeec2SSy7ZbL311uVcdNrhfgZ185bNi/Xhhx9efIXYG0k5E2eyB339pCPLTgQSgUQgEUgEEoFEIBFIBBKB/0OA/G2b+uWXX97svPPOZQt7bFVPjBKBySKQCpHJIpj5e4pAKBzeeeed5thjj20WWmihZocddihbVcJvR08rrApTN+3zY4891tx6663lZBkOm6LeoE2cIRFIBBKBRCARSAQSgUQgEUgE+oNAyN1ROoXI7Nmzi/U4S26+/vq9WBp1ZzzaCKRCZLT7d+haF8zvrbfeao444ohm4YUXbg4++ODiOGkqmB4/JSxCMNk43zxoquOhAzYJTgQSgUQgEUgEEoFEIBFIBIYEAXJ3HcjnTnpcZZVVin+/9957b0q209c05PVoIpAKkdHs16FuFQb4xhtvNN/85jebNddcs7nsssvmWGlMZcNqBUibKU8lHVlXIpAIJAKJQCKQCCQCiUAiMJMR4MvvBz/4QbPyyiuXUyh/+tOflpNuZjIm2fbeIJAKkd7gmKX0EAHKh9dee6055ZRTmgMPPLB58cUX5zrVpYdVZVGJQCKQCCQCiUAikAgkAolAIjDgCLDidrqMEyjXXXfdMlewtT1DIjBZBFIhMlkEM39PEaAMsTWGEuTEE09sDjvssIZj07DQiLinlWZhiUAikAgkAolAIpAIJAKJQCIwsAjYyv7ss882s2bNatZee+3mpZdeKifNDCzBSdjQIJAKkaHpqplBaChEnn/++eJDZK+99pqjEEllyMx4B7KViUAikAgkAolAIpAIJAKJQI2ABdNXX321HLu7/PLLN48++mjjpJkMicBkEUiFyGQRzPw9RYDSwxG3t99+e9kfuOOOO5ajcN2PX08rzMISgUQgEUgEEoFEIBFIBBKBRGCgETAP4GNwzz33bJZYYonmtttuK4cgDDTRSdxQIJAKkaHopplDJGZH23vxxRc3q666asNCxFG4QipEZs57kC1NBBKBRCARSAQSgUQgERh9BMYj37/77rvNMccc06y00krNNddc0/zud78bfYCyhX1HIBUifYc4KxgPApiiI2/POeecwuwOOOCA5o9//GMpYjwMczx1ZtpEIBFIBBKBRCARSAQSgUQgEZh6BMYj3//6179uzj///GattdZqzj333OZXv/rVHD+DU0951jgqCKRCZFR6ckTagSlidk6YceTu8ccfP8dhkmcZEoFEIBFIBBKBRCARSAQSgURgeBEg03OSyi/IeBQiFk2vuuqqMkc4/fTTm1/84hepEBne12BgKE+FyMB0RRICAUyROdxRRx1VjtT63ve+V3yKxLNEKRFIBBKBRCARSAQSgUQgEUgEhhMBsv5//dd/FX8gFBp8B7rXTZDvwQcfbLbddtvmrLPOKnMGSpUMicBkEEiFyGTQy7w9RwBDfO2115r99tuv2XDDDZvLL7+8aJBV1C2z7DlRWWAikAgkAolAIpAIJAKJQCKQCEwagf/93/9tXnzxxebII49srr766ub9998vliLdFPzf//3fzWOPPVYWTfkZNGdgaZIhEZgMAqkQmQx6mbfnCNDy/vjHP2523nnnohC5/vrr5zDJbhUi0nWbtucNyAITgUQgEUgEEoFEIBFIBBKBRGAuBEI2//3vf99cccUVzYILLtgceuihZdtLt1YerEnME2bNmtXssMMOzXPPPTfHknyuyvKfRGAcCKRCZBxgZdL+IoBRYoiPP/54s++++5ZjtZ566qn5VpoKkPlClAkSgUQgEUgEEoFEIBFIBBKBaUMg5HWnR9ru8rGPfazZcsstm7fffnvO4uf8iGMN8uabbza77757yfvss882rEYyJAKTQSAVIpNBL/P2HAGM7oEHHmi23377Zp999mlefvnlrusIRivOkAgkAolAIpAIJAKJQCKQCCQC049AyOZiW2QuvfTSZrXVVis+A3/5y1+OSyHC1+DBBx9clCIWUf/zP/9z+huYFAw1AqkQGeruGz3iKUTuueee5hvf+EZz0kknNT//+c+73v6CyWKKTqnhhTqY7+ihlC1KBBKBRCARSAQSgUQgEUgEhg+B3/zmN80ll1zSbLLJJs3s2bOLgqRbmZ0lOTn/tNNOK1tm7r777iLzDx8KSfEgIZAKkUHqjaSlmL1dd911xULk5JNPbpjVdRsw01deeaUw2VtvvbV4sA4GG3G3ZWW6RCARSAQSgUQgEUgEEoFEIBHoHQLk8Xfeeac55ZRTmvXWW6+58847Gz5FupXTpZP+sssua3bZZZfmhhtuKAqS3lGYJc1EBFIhMhN7fYDb/Ic//KE599xzm0033bRof/3fTcAgaY1pirfYYouG5+mwLvGsW0bbTV2ZJhFIBBKBRCARSAQSgUQgEUgE/hqBttwd/4vJ6q+//npz7LHHNjvttFNxkOoo3W7ldOlYg99yyy3N1772tea8884rCpao46+pyTuJwPwRSIXI/DHKFFOIgK0uZ599djGDo/3905/+1HXttttcddVVzRJLLFG0zqxFumWwXVeSCROBRCARSAQSgUQgEUgEEoFEYEwEavmbEsTPPbL6q6++2pxzzjnlZ/HSyTF1+jEL/fMDCpHbbrutWX/99cshDC+99NKc8ueXN58nAp0QSIVIJ1Ty3rQggBnaF3j66ac3X//61xtbZ5xV3k0IJmurDAa53XbbNRik+/HrppxMkwgkAolAIpAIJAKJQCKQCCQCE0Mg5O6QzS12svim+HAizJNPPlksRM4444wi95P1pe02sCj54Q9/2HzlK19pNttss1IeRUvU2205mS4RCARSIRJIZDwQCLz11luFSe6///7FuSoG103ABGmfn3jiiUZe55o7oSaY43gYbTf1ZZpEIBFIBBKBRCARSAQSgUQgEZgbgZC9KTreeOONcpIM5QclBouQ+++/v9lmm22aI488sjhEJb+PJ1CsvPDCC83KK6/cbLTRRs2jjz5aFlCj3vGUlWkTAQikQiTfg4FCgBLj8MMPb44++ujmqaee6lpjHEzQNhnKkB133LF58MEH51KIRJqBanASkwgkAolAIpAIJAKJQCKQCIwQAmTuUIjss88+zcILL9yssMIKzXHHHdeccMIJzZZbbllOmAn/ISGji+cXlGsBlVPWVVddtThmVU6EbsqItBknAhBIhUi+BwOFwMMPP9xgnJilLS/dhmCkPFfbcrPzzjs3N954Y9mrGPsWI00yym5RzXSJQCKQCCQCiUAikAgkAonA+BEgf//xj39s7rjjjnJYwnLLLdesueaazUorrVQUGU6acQRvvd2lGxldepYmG264YaPMm266qdSDwpD1x09t5pjJCKRCZCb3/oC1HePkFHXjjTcu5nU/+clPuqYQA5T//fffL4zx29/+dnP11VfPZULXZpLdMN2uCciEiUAikAgkAolAIpAIJAKJwAxHIOTtkM35ELGl3WEJBx98cPH98fGPf7xZa621yrG5Tp3hYyQUI/ODj7z/29/+tmy7oVxx9G4c3Zuy/fzQy+edEEiFSCdU8t60IMAEjnXHsssu2xxyyCHNT3/603FvmeF5+t57721OPPHE5oILLiin1ISGGvOkqfZ/Msxp6eKsNBFIBBKBRCARSAQSgURgxBFoK0UoO8jg/Ihsu+22zSc/+clm8cUXbzbffPPmmGOOKX4DbYOh2DAfmJecTo6nQNlvv/2KH5Errrii+d3vfpfWISP+TvWzeakQ6Se6WXbXCGB8PE87l3yppZZqWHgwo+s2BON1TO/dd99dTqk5/vjji/dqihUOnC699NLm8ccfb2K/YrdlZ7pEIBFIBBKBRCARSAQSgUQgEZg/AiGTSxnXYoqMF198sThTXXfddZu99tqr2WKLLcq2F05WTzvttOauu+5qfvaznxVZvdMCZpRH3nd0L6eql19+eZkzxDNxhkRgPAikQmQ8aGXaviGAedEKH3jggc3yyy/fnH/++UX7222FwQRplR977LHih2SHHXZoHnjggeawww5rFl100aJFvvDCC8u2mkjfbfmZLhFIBBKBRCARSAQSgUQgEUgExodAyNwUHOErkHXHj3/843JkLgsR2+WdGsMviDmAZ7/+9a/nWHpHGWJBWRY799xzz+aaa64padtpxkdlpp7JCKRCZCb3/gC1HWPD+Lbffvvmq1/9anPxxRc3tr90G4IJUog8/fTTzQEHHFC23tAcL7DAAs0nPvGJZpdddmmee+65OaZ4wVS7rSPTJQKJQCKQCCQCiUAikAgkAonA+BAgc9s2Y1u7kyCPOOKI5le/+lWRyS2IOlnSdvcNNtigzANWWWWVskj6yCOPlIXM8C8S8r7/WZPwQ/LNb36zee211+ayRhkfdZl6piOQCpGZ/gYMQPsxNwqR9957rygtVltttebaa68tW2i6JU8ZzOc4Zjr55JObxRZbrPnUpz41h1Eyp3MkLyVLMNNuy850iUAikAgkAolAIpAIJAKJQCIwMQTI3mTw6667rtlpp52ak046qfj9IP/7keF/+ctfNo8++mhz5plnNltttVWz5JJLlqN1OWOl8Kj9i1CIsDax9Wbfffdtnn/++TnyvboyJALjQSAVIuNBK9P2BQGMC2Pj68O55Ouss045oou1R4SxmBsmyicIR0yY7KGHHtpQqHzmM59pFllkkbIf0TPOlv7nf/5nLmY5VplRZ8aJQCKQCCQCiUAikAgkAolAIjA5BMjcZPFLLrmkKDBsYa8XKT0Pmd6Rug8++GBRmpgX7L777sXxqsVNlt5OlCTT21az2WablcVUihT5JxvQEb/JlpX5hweBVIgMT1+NJKXBdCg/3njjjWa77bZrdt111+L8FGPzXIh09f88TDua1/njJ5xwQtl3SJkya9asZpNNNmnWX3/95vrrr5+jCBlJALNRiUAikAgkAolAIpAIJAKJwIAjQNHh0ATb41mCtxcqg3zyP4uRd999t7nllluao48+uhyWYNGTZQnFCIuQF154oZS13nrrlXQOZ+gUYu7Q6Vl9Tzo0vf3228Wxq1Nxus1bl5PXw4dAKkSGr89GhmJMJn4Y0Kuvvlq0wJgd5Ug8q2OWJM4zZ/VBe3zccccVR0x8hTjG64wzzijWJeedd15hkmeffXZhqsrIkAgkAolAIpAIJAKJQCKQCCQCU48AOX///fcvR+3eeuutxaIj5POIa6rcs/hJ+UExMnv27MYJkvvss0+Jv/vd7xafIyuttFJjW00oMOTrVF5ddqdrcwxKm1NOOaUxj7BNx70Mo49AKkRGv48HtoXBsMQ0wRwnOY/c0bu2z8TzsBSRxv077rijKEKcIsMbNYsQzEt+jlmZ0t1+++3F2oSjJcy0F2Z0AwtkEpYIJAKJQCKQCCQCiUAikAgMKAJk+ieffLIsXpLd77vvvjly/rxIli8sRvgY+dGPflTmCRZBWYJ/+tOfbr74xS+WeQCLEgoMeSYSLM6icdVVVy2LrQ899FCxGJlIWZlnuBBIhchw9ddIURsKDzGtLs3vMsss0xx11FHNO++8UxgaJsgEjlWI7TEcpvIovfTSSzebbrppMb17/PHHi6OlYIJ8imC09h0ecsghxYt1anhH6tXJxiQCiUAikAgkAolAIpAIDAkC5Pm77767yOZ8grz00ktdUR7KDbEy+B3hR+TUU08tSot/+qd/av7f//t/5cheViSUIuYUMSeIuUY3lZk/OAXny1/+crPGGms0FCK1P8Nuysg0w4lAKkSGs98GhupgVBMlKBgVK47vfOc7haGdfvrp5cQZjM/9F198sbnyyiuLQ6U111yzsT2GYoQJHeYVZQQtFCiO3rXn0LFe9gImQ5toD2W+RCARSAQSgUQgEUgEEoFEYOIIkOn59WMdstdee5Wt7yG3z6/UWs5Xjh+r8WeffbZZYYUVmr/5m79pPvjBD5bjem2nuf/++5vf/va3497uYv7wwAMPNMsvv3yxZFF+tzTOrw35fLARSIXIYPfPQFKHOVBEOP4K85gMs5CXFtdZ5HvvvXfj3HHOkliIPPPMM8Vq5Fvf+lbRKG+99dbFeapjtmyNUTem2A7K42jpgAMOaORxtrm0GRKBRCARSAQSgUQgEUgEEoFEYGoRIIdb+Fx99dWLQsQW+IkGcwc/i6YOUfjbv/3b8ltggQWaBRdcsFluueWaAw88sPnBD35QLEZivhD5Im7Xb8sMq3MW5ieeeGLz+uuvT2qO0y4//x9cBFIhMrh9M5CUYSIYhi0p559/fvHbQTkykRAMifUGBYgzx2llWYhcfPHFDUXIfvvtV/7n3IgDpjfffLOYy4UpXKd6lcsREgsRp87ceeedRYHTKW3eSwQSgUQgEUgEEoFEIBFIBBKB/iFgrnDuuecWv3+svFlwTCaQ9c0FTjvttGbxxRdv/j979x1tWVHlD3z9ZlwuxzBjAAMKg4gKCEqQJFlyagQkNEKTgyRBMgiINEjOGSRnaHLOQXKOklGSSNBBXTPOX+e3PjWz3xyv7zXd/e5999x791nrvHPfCXV2favOrl3f2rWLB/mJZo9AGwAAIABJREFUJ55YpsqvtNJK1cILL1zIF30BfRbxR/Rfou/h2Lq5bhB1q622qk466aTiYT7cfa3P5f+9j0ASIr1fhmOaA4rB/D3MKbLBHD7eGtOyhVKiJE1/ERtkrrnmKvP2KKOf/OQn1Zlnnlk8RcwJ5JGCPInn6sfW92OeBVRdYoklqgsvvLCwyK335P+JQCKQCCQCiUAikAgkAolAItBZBMQCRITw6LA6jDgf07rV7X+rTl5zzTVlmowp8lapvO6668pqNmussUYhSizCYNXJhx9+uPrjH/84FF+k9f2m4Yghsv3221fnnntu8S7xrtz6H4EkRPq/jNuaQ4oBgfGLX/yisK9c0pAVU7tJB7nxwQcflMBKPEBmnHHG6jOf+UwhMQRc4iUikCpXt7ryG+536/vffffdMt1m6aWXLuyxlWdySwQSgUQgEUgEEoFEIBFIBBKBsUVAX0HsECu4sO9HM5W93g+IeCLIDL95jRi45Sl+9dVXl8HRDTfcsEKO7LTTTtUVV1xR+h36BTHIGkh47rLLLivxQy6//PISz9C7cut/BJIQ6f8ybmsOKQYuZVzUkA2IkakhRDxPAWGKrUeO1d1nn33KfL+PfOQj1fTTT19if2BxIyBSXfHF78hU6/9xXvqW3jWPcL/99kulFsDkMRFIBBKBRCARSAQSgUQgERhDBF588cUyXWbVVVctRIW+wLRuYftP7ogcMYDLY4Sn+A477FCW6d1ss83Ksr033nhj6YcYmI2pNLHAA9Jm0qRJJb6hd+TW/wgkIdL/Zdz2HFIyV155ZVnt5bDDDqvefvvtf3jHcEoKa8tFThwQZAWiAmEx77zzVrPOOmv1z//8z2U9cXP9QjlNqyIKQsQyvltuuWWJZk3u3BKBRCARSAQSgUQgEUgEEoFEYOwQsGILTw27lVw6bZNH/8F79D0QMhdccEG12267VVtvvXW1wQYblFiF+iO8SfQbDMSKHSIeCU+RaQ0JMHao5pvahUASIu1CcoDSoWTuuOOOyrSWc845Z1iF4R5KKI4IDu5pDzzwQJnXt/jii1dzzjlntdRSS1XbbbddYY0tm4Ugsb64Z+P5aYGW25t3/fCHP6y22WaboggRMrklAolAIpAIJAKJQCKQCCQCicDYIKAvwCZff/31S8DSxx57rPQPOvl274w9+hQ8Rt58882y2MK2225bYhaSaY899igLNyBGTjjhhGq99dYrA7e8R3IbDASSEBmMcm5rLimYe+65pxAigqoOt3RWKCEucRhXy1gJxIp1XWihhcryuhMnTiwsMeX09NNPl2BLt99+e2FpR0OGyCwCRqBWK9dsscUW1XPPPVem6rQViEwsEUgEEoFEIBFIBBKBRCARSARGRECfQDyPtdZaq9p1113LIKVzndyiH1I/Ghi1I0b0O8QyOfzwwyvkyKabblpWp7Sgw0YbbVTde++9uSBDJwuoYWknIdKwAukFcSgXigSjamnc559//h/ERmhwP0NKnH322YWUWH755cvxyCOPrG655ZaynBVPDuQF5cQ1zf+tQY7+IfEpOCGNF154objEWcqXR4t35JYIJAKJQCKQCCQCiUAikAgkAmODgD7BJZdcUm288cbVUUcdVb311ltj6iES5EudHBGE1YCtGCP6JOIZrrzyytXss89epvJblYbHyGiCv44NuvmWdiCQhEg7UBywNCgU01rMwfvpT39aheub85hXRIjrlB8FY57e2muvXebtBREicFFMYQlF1U4YKV9Kjozzzz9/kcWyvbklAolAIpAIJAKJQCKQCCQCiUBnEQj73sDnaaedVjzLBThtysqP5AtP9gcffLB4iMwzzzzVTDPNVC2zzDIl1mH0WxAo7h9u7yyKmfpYIJCEyFig3GfvoAx4fghWKo7IQw89VLw8rO3NW+Sqq64qq89Y95vr2d577z20zFUQIdLo5CZ9q9+YlrPAAguUWCetCrjTMnQyf5l2IpAIJAKJQCKQCCQCiUAi0GQE2Nrsb0veis2hjyDIaRM2stkNopJJ4Nfx48dX4hwuueSSZTVNA7qHHnpo6eu89957pb/j/ng2jk3IT8ow7QgkITLt2A3kk/Hhv/zyy2UeIELktttuK0tXich84IEHVpa0mjBhQlEgN998c5m6QtFQIHUl0mkATcHBSCNEuL61RouWl9wSgUQgEUgEEoFEIBFIBBKBRKB9CISNze5/7bXXqnXXXbdMSRFLhLdFE7bo05CFp4iVaMQdFH/Q9H6LMqywwgrVGmusUbzczz///OrRRx+t/vCHP5Qp/mPZp2kCXv0sQxIi/Vy6HcobBfD6669XP//5z8sKMQKrCkokCJHARKbJICJ4kSBCQimG4qkfOyRiSRYjbXngRRZZpLI8MI+ReHcn35tpJwKJQCKQCCQCiUAikAgkAoOIQN3W1mfgebHaaqsVYsEUFFNour2FjHEUK+TJJ58sZAgixG8LMlx00UVlAHidddYphI5lg88888ziMfLuu++W6f/SyK23EUhCpLfLb8ylp9goDUpC/BArxnArs2zV0UcfXd1///1l1RnBUYM5JWQonNbfncqA95meQx7srnXHX3311SGZUnl1CvlMNxFIBBKBRCARSAQSgURgkBEIO1u8wF//+tfViiuuWMgGsTrq/YNuYhRykJXXij7DmmuuWab38ITnNWJBBsFVzznnnDLwu/DCC1dzzTVX6VtceumllaV5I6/dzEu+e3QIJCEyOvz6/mkfOYVhpxjECbnzzjuLG9lss81WffnLX66WXXbZipcI5YEscW8TNspNTBPzFq2G87vf/W5ICctXKrAmlFLKkAgkAolAIpAIJAKJQCLQbwiws/UdTKlfYoklihe5VSqbaIMjPhA3PEDEPjTNJwgTpI6BXv0IQWGRO/PNN18Juvrmm29mf6IPKm4SIn1QiO3MAiVVJzRCmXELu/3224unxUorrVQtuOCCZVmq73//+4UMMR2FC1xTlBw5yENR7bDDDmXuIkWHsGmKjO0st0wrEUgEEoFEIBFIBBKBRCARaAICYWuzu48//viKZ4Up9QZP41oT5AwZECLigxxzzDFlSsw777wzRIiQV99IXqykycvlmmuuKaEBPOd6br2NQBIivV1+bZc+lJQjVhcRYhWZM844ozC7pscst9xy1e67715WmDFVxly6iBXSFKVADoyuwEdWu8FMmwdo6d2myNj2wssEE4FEIBFIBBKBRCARSAQSgS4iwM62IxEQBr/85S9LPD9kgwFUW5NscbKYZn/TTTeVaT0WYtB/CA+Ren78lif9Cce4p4tw56vbgEASIm0AsZ+S8KHzrHjjjTeqe++9tzrqqKOqTTfdtBJMaOONN6722muvatKkSdVvfvObsnKLFWVOOeWUIaLB803ZKCkry+y8886FmcZQ+79JMjYFq5QjEUgEEoFEIBFIBBKBRCARGC0C7Gw7O5xHxcSJE0s/wtSZP/3pT6NNvq3Ph6wIjiuuuKJaddVVq3PPPbeyxG5cc7TV/2/93VahMrExRyAJkTGHvNkv5BXy1ltvlZgbAgsttdRS1SqrrFICqPKwsCSVeXRYUctPmWtnaSqxRerKoQm5JA9FbP1wrnoYankLOZsgY8qQCCQCiUAikAgkAolAIpAI9BMCbG2e2oKOnnTSSdURRxxRpqToP7jWhC36A44IkWuvvbYsEnHddddVVqqM65OTtSl5mZyMee3DEUhC5MMxGqg7kB3m0IkNImAQ75DzzjuvrCrjWigHxMlVV11VbbXVVmVJ29a5dt0GLeQ0lcd0nwUWWKDaZZddSqTouNZtGfP9iUAikAgkAolAIpAIJAKJQD8hEHY2QsTUewOogpH+9re/LdPx43oT8hyyIEB4sGywwQbVDTfckKvHNKFwxlCGJETGEOxeeFUEIjXPj+eHqTHB5obSkA9ucIKUHnbYYdUll1zyd65lTcon2RE3PERM77GuuHyQP7dEIBFIBBKBRCARSAQSgUQgEWgfAtFf0Kd46aWXyvT7U089tRAiSJK43r43TntKIYspMjxZDAjffPPNQx4i055yPtlLCCQh0kulNQayhmKgxHiBxP+tRwpNjBHzAk844YSymguSwX1N2kSEFg3a0sATJkwoAWJDzqbJ2k7c+jlv7cQp00oEEoFEIBFIBBKBRCARaC8C7NC//e1v1f33319tvfXWZUVKy9aGDd7et017auQkE9l23XXXarHFFqtuu+22MuV+2lPNJ3sNgSREeq3EOiwvxTDc7rXOx0Z5IBq23XbbokC4wdWfi/u6fUTqWOLLajgIkbvvvrvMaQxZuy1fO98vT/JrapMdqVUvs3a+K9NKBBKBRCARSAQSgUQgEegMAuw3g3qmfrPpYpCyM29rb6phY5NdXI711luvOvvss/9h5Zb2vnXqUws59Wn0Y/bdd99q3XXXLf0bq86kDT31mPbqE0mI9GrJdVHuUCDPPPNM9fOf/7w64IADiiKJ801QICELTxYBXy2hdfDBB1cPPPDAUKPSBDlHU4yRR0cNpfmPd9xxR8UtUcMjFgx2vn7faN6XzyYCiUAikAgkAolAIpAIdBYBdpsp3zwVTjvttLLqySOPPFKWhu0Fmy5ktLCB+CGrrbZaOYonEtccm7IhRAye7rffftU222xT6d9EuICmyJhydBaBJEQ6i29fpk5xUGTPP/989Ytf/KI68MADy+8mKbmQhayUmgBJgqs+9NBDf0cS9GoBRf4ckT5YeI2llXTGjRtXvGGuvvrqkvfIo3tzSwQSgUQgEUgEEoFEIBFoLgLsNR4KJ554YrXGGmtUP/rRj8rAnrh+4f3bZJuObOxvS+wee+yxZbVK8fz871rs3S6BkIMdLcbgxhtvXJYHhnMMKHZbxnz/2CCQhMjY4NxXbwkF8sILL1S77757tf3225fOeJxvQmZDFkcuhwIkHX300dVNN91U5gXG9SbIOq0yyAMlzjPkiSeeKAFud9ppp2rttdeu9txzz0L+8ByJzf25JQKJQCKQCCQCiUAikAg0F4GwXU03+fGPf1wGufbee+8ysCdIqYE+hENTN/KT7w9/+EN1yCGHVOPHj/+7uByuN8EmDTnYyryqEU+m2MNY36EJMja1jPtNriRE+q1EO5yfUB6OFIalbCkPzG8o5yYokLqc5Lr11lsLeXPmmWcWBd0EGUdbVPL1/vvvV/fcc08JbmveI48dnjAIkpj/WMditO/M5xOBRCARSAQSgUQgEUgEOosA282Al9h3PEUMQG6yySbVcccdV6Z0sPHC7u6sJFOfOtkN2L3++usVIod9Krgqb+Ym2qS8bkyph+8OO+xQ5A5PnKnPfT7RiwgkIdKLpdZlmUOZicgshog1u60vTvnFtS6LOPT6kMcSwVh28wPNE+z1TSOoobzzzjsLKbXVVltV++yzT3XfffeVmCkRfCvy75hbIpAIJAJNQSB10v+VRGLxf1jkr0QgEfgfBMJ+0zF/6623qmuuuaaQIptuummxZZ9++uky8MUejHubhB07VKBSU7l5kj/33HNDXhdNkTfkiHgtgr/utttuBe+wo5uEacrSOQSSEOkctn2bcigQrnCCPfFK4NYXysP1Jm3kefzxx6udd965RJB+9tlne84NLjB31Ph98MEHxevFEmEbbrhhcUl85ZVXytzSJhJTTaoPKUsi0G8IhF4IPdHE/IVs9SNdFsZ8/G6X7PX3DPe7Xe8ZbTrTKlvrc8PJUb8ncB7uvjyXCCQCzUQgvmHfL+8KqzvyFOFxMXHixDLNo9UbuCk5MeUkFl8wYPfaa68N9ROaImPgC8NLL720Wm655YqHyNtvvz00yNsUWVOOziKQhEhn8e3L1EOBiBZ91FFHlZgVgibFfDvXm7KFLAIkbbHFFtWWW25ZvCh6zTgMzMn93nvvVZMmTao233zzimeICN7R0PRavppST1KORKCXEajrh9B5TcxPyDnSsZ0yD/eO0I9xrZ3vm9a0Qpb6cUrSqt/v93Bb6z0j3Tfcs3kuEUgEmoFAfMf0l+V32bOmzYjLYdq61QV5DNf1WxMkR+DceOON1eqrr14WX/j9738/JGMT5CNDYGs1nIsuuqhaeumlq+2226565513GkfeNAWzfpUjCZF+LdkO54sSsZztSSedVP3whz+sDjrooKGIzE0xukLROXLb+9nPflaY39tvv73nmF954IGjQTnrrLMqLpMIEcvrvvnmmz0RdbzDVTKTTwQGEoG6novfTQSCsc7o5MnGddouMLc4SDFXm/zt2gILHnNG/+hOOrRpnQZ5520Jm/DumxIM5M/9XOmNZuoo1TfX63kNPOr35O9EIBFoPgLx7cY3bfUTU78PPfTQ4iEs5gUvbYNlcW+3c0UOetdCBoibU089tYold7stW/39gRf9a6AReSPmiXaJ/sxtcBBIQmRwyrqtOaUo/vKXv1TnnXdeCUIkinQYZBRME7ZQdI4MRvFOeFRceeWVQwZ4E+T8MBnID1sdCUFhN9tssxIP5YILLqheffXVoWjjrbi3/v9h78nriUAi0FsI6Ey/8cYbZRUtHnrRAW5iLpARljUUy4m7t33FFVcsQaCNbrZbX0nPbm645db32GOPMtUwMGr3+6YFczKY/njwwQeX4NhTusxj5M2zjHdz3pFLrVvchzQRMNAxt0QgEegdBOIbjiP9RZciG0xH4Z0tEOiOO+5YFjfwjbve7Y289DqixuCd+Cf0VdO2wJWsl1xySfF4P+yww4rsca1pMqc8nUEgCZHO4NrXqYaS0Em//PLLizLef//9ywhXUzNOEZ9yyiml0aCYp9Tw7FZ+AmONn3XbGfTmi2LazXEUt4XyRu5cd911xYWyPsoaz5M/fju2/h/XWjsJcT7yH8+2/h/nW4/199SfaU03rrUeI71IJ44jPV+/vzWt/D8R6AYC9TpZ/x2ytNbl+D+OcV8c47yjzZEOvvfeewvRi6Cuf8dxv3Nxfzzb+n/c6xhplIda9Ef9+bgeabX+H2nG9fBmuOWWW6orrriitB0rr7xyWS6ce/KHbfX04t44Vz/G+yIfOg5WGVtnnXWKV2N4YXhmSrd6+q2/J5dGvCOOIVs9DSORW2+9dekwjLQCQzxff85vZW4wQvuLMK9fr7/rqaeeKm3GY489NiRu/d7676Eb/rfs6+nUr+XvRKBbCKivrVuci7rsepxrvbf+f/3+eCbO1Y9xrf5s67l4X/25+B33DndPXItjPNN6pLvYsg8//HDRn1Z3POecc4rnM7vQlHCr0Tz//PMl3khd90t7LDey8wjhGbLttttWFjag35q2BcZk5fGuTdJX4DESbUjTZE55OoNAEiKdwbWvUw0FYuRNh9y63djpJrrDRUEYPeUOJxgVEoeyk48mbuSiiMkoNgiXw5/+9KfVIossUs0xxxzVN7/5zWrxxRevxo0bV+Y7fu973ysdIkuaGSW0+o+lzkyl4SZuBJkniXPSM33I/+4zmsBdW4eEu6XdVCgkDMacwU2OOMZvnQydMbgiYjTU9mhAoo7EcbjzsI/r9eNI591TT6f1viaWZco0uAhEna7X2Tg3uWPr/fV63nrNd2gKoM6+b7P1ev3/+u/W97tW31uv1/8fqUTr9xih1B48+uijJaC13/RDffM+3iJGOF23SaN1c64ue9xXf9/kZIcREqaVEGl9z+T+j3fV5YjfcRxOrnjOcbjrnh2JEHFtuGfqacKU7oaf9rh+rf77kUceqQTg5iUSW/361PwOmSKdPCYC7UKgtR62puu6rX6MZ+I7jP/rx0gnzrX+H+c/7Bh2jiO7h/2jk88+qttIdHHs7Cj2lO88bCzfLK9lthl7LHb2GbvM/2G/OTrPZrMgABJk7bXXrr773e9WK620UrEDF1xwwWq22WarvvOd75QBM4NnBtHYf+QLbCLfY3GEpfwdc8wxZbo62Q1ENm2LModVxESEcbdwaxo+gyRPEiKDVNptyGsoD8cgGVZdddXSIae443obXtXWJDQIN998c5FTvBMNElmbuJFLY6qjY7kyU2SWWWaZatlll60+//nPVzPMMEP1hS98ofrKV75S/v/4xz9ejtzP3Yv02XPPPcuoobxaahhhtddeexXXauSKOafcrLkGCs51wgknFNf1k08+uUzLufjiiwuBxPskvFA0EkZ2/X/DDTeUToYOD7dNRMxLL71UGnMNvcafkW5nEBjVkKe64RCEi4aHMa+xZGTYdaiiEY861fq/sotrU1KWcW+U+ZQ8E/fmMRGYGgSirqmz6rbvgEFrDyOVUV2/jz6NWBC+nzCOPRsebe53HxJTWpZdFEfIt++3eeU8BRjViM34ZupyhHHNWPUNhhxxL3njm/W9xv3eiQR1X+vmm2X0I129ny647LLLqh/84AfFq83y4OSub9KZEkKELqA/tC/1vEkvZA4c5YXM7oWPI0yRyjoRMIn81mX5sN/Sl0cdGnjosMDDu5QV3Rbpktf/zse5kA85A1s4Oue6NHmI0K/SrMvu/noa8ktfBs7wsHsX+eI97pNXsrou7Y033rgc1RHYON9at7zLO2Emj4EhmeXLFu/4MMzyeiIwGgTUs+G21vP+b9UD/o9dnVZ37XQG/eb7U899p2Gb+N/37JydPvN9+D59XwaPfBN0Gw8M+taKL3QLe8hAm/3qq68u3l6+OfYTW+rCCy+sTj/99OItccYZZxSbCxHMPgt7zNG0PnbZTjvtVDyCTaXbd999Kyu0uL7RRhuVgbF/+7d/qz72sY8VG/BLX/pSZWcT/vu//3u1/PLLF1KEVwYywgqLdEYrbsNh285z8IcVcoYdS6+FDmnne0abFlzsyteUdDaxqZ319mW078jnewOBJER6o5waJWUoEMpNYzBhwoTSwWZ8xbVGCVxVpXHksid6tFgiIWvT5CQPDJEMa665ZvXlL3+5jASIfcL1kFvkUkstVS200ELVwgsvXH37298ujeH0009fSBEN4iyzzFKeQ55oJD/3uc9Vn/jEJ6pPf/rTlYbU/q//+q/lOSML3/rWt8ozM800UyUdhMvXv/714o3C+2SBBRaoHL1r1llnLfd+4xvfKJ4qRikQYjo+dksAI2QQLBpBU3sEgWUoMBCuv/76svPWEX9GpwnxwwVUIyR6urLReDJEGCsMFQZMK2miwdIJcIzfYfg4ulb/P36HoeQY9TWOTawPKVPvIRB1iyGqXgt+J3r9EkssUchKI/Xqdtynrup8mgv+xBNPFDdoHmCM2wMPPLB8Fwx79/suEJ5LLrlk5fudffbZy3frNy8yu5FDREkQKeo+A54cXILJoYPMUGf4hxy+Ax3lo48+upCft912W7XaaqtV3//+94ux7jv1LdY3zyBgGPoCbJNr/fXXH+qAy48OhXfUN/9/GCHiHiSBToZA0osuumghf7iJIwV89/HtyqOOjDZJ3uhJeEZHZTSECOx1hhDGsEVO022mKx155JGlQ0RPkZcMiGMdniA+nLfrQClPdYLczgUhQh8im+lQGHJ/t3qE8vF+98uvMlAmsKCXtQU6Tjpvkab7uX+T1T08C+n3Oeecs/zvnHpCFh0Bm2d0CO+5556iw5Hw6sk222xT8oPII2/gXS/L/J0ITAkCUXfiGN+Fo/rnG45jtNd0Y32Ptj7O+Z+ecwyyg971HSLyDH6xKehXdhWCgP41QGbasVhsdITVUEynjul8vnWDSTrIvmWDSqYs08trrLFGscXmmWeeYiuxh2aeeeZiE80333zFNmM3+TZ59LKn2GL2r371q8WO8uz8889fTTfddEN2Wdhmn/zkJ4tOZ8PZw66bccYZh86zDen8sAXpaHGZfPe84cjkfjGG6EqYj+Wm/Him0Wf6CMrAuaZtURfpN8vualvUFbLGtabJnPJ0BoEkRDqDa1+nGkpCw3XXXXcVo9bSXxRekzcdAg3cEUccUQz4sW4gphQbcvG4EO06GkikBcaf6zeD1fQYjTqDWQOuY4N40BgadUD6GG1ATiBTTGvSOZCGsjLasP3221eHH354aTB1TNZaa63SiWAE2xnlGn73YfkZAkiYueeeuxjYOmIIkiBJNNDIF433vPPOW4iTr33ta+UZHYhVVlml5EkjzhhwzTMMhsUWW6y8E8GC9HG//Bs5VWZcGbH3lkXTIYADg0ZsgPp+9913l06KegkbHRb3M4IYQy+++GIhW3SydCCMouoExIgRI0u9rhtqUd+Hqy9xbUrLNu8bDATUC/UIoeC78x0aLdRZ982p2/5ntLuXMY8M1Ik3qud7Vr8Z64xJBAPDXpqMfrqM14U0dIZ1bgWv8z4EIx0RRh3DTqfXd8ywD+8uBCu94NuKzjxZuDaT13fnm/N9ISTkY4MNNii6p17vddjdv95665UlwMltDjZD3aio7yw60vXSd24kQkT6Nt8pEsd7f/WrXxVZ5NP/Vg3zPUfasNTB0dknu/vgc/zxxxcCCcE8LR4iMJcHWCkHHSWdJ8YzvQgXS58juMjtiIzikRcjs4GX8jH6S3c7R3aEiKCDzkf5II4RynQwkiRIK7Igl+h/5Sw9o8b0PYM+3iNdxJZ64D5xBehv7YP/YzfSrew9Rw8qO+8Mksf/nuV5aOQ66km9HPN37yMQ9WaknLjeug13zj2RlqN6aFdv6SHEhW+CDvO9qsu+LR5JSFV2D90m1o0pHwaxtOPadXWZzlMn6SR139H/rt93332lM0tP0LG+PySqes+eQPCxOxyRFQaODP6wYxAT9AYdxtvOPYgN5AViwf1f/OIXC3kR5AS7h+3CNkM4SpsepiN8uwhNg0VsG9+UI9uG7qKLDzjggKLbtthii6I/ff/0oe9ZGu5BfNt5iSBm6Gwddl4nBphggmSVd7/pP6QNIoTnMHuMd4kBppHKq7Vc2/W/MlZGykD7QM+pC03bor7ynFMm7GW2ojY5rjVN5pSnMwgkIdIZXPs+1WjsGGY6rZQIQ7rJCoTCE4BOA8EgbaKKeTGvAAAgAElEQVRyVnFgyGjQ6ceua7CNLGiQNdQaToa+EUvGN8PC0c5w1vDoPMXO2NAg6hT5zQDR0bAzSNznmg4Ug0THTIOgPBnVXOvtlskUnI+xEmSMjlKQMQxnnTPGCA8RnRINOWPdeYaKUWSjzzoz8qZjyGDxG/mCbOGJYjRTnk0LYoAwPmJExf3IG6Of8GDMzDXXXIWE0aFcYYUVygiqDhlDRrwVI+1GUFwzim0Exa7ewlOdYJiQVwfKLj+mEzkavWWA2HWGGB+MMMSLURCY6ZwpE3jqXDD+7HWSJb6POEZ5x/9Tcqw/U1c0rc/Wr+XvsUVAWeigqvuMWCN0vlP1wvepw8zQVW/cy/jyvRn1R5pEHdKB1yHQGXfeffSWIxLPN2x0k+Ht29ZhpTtcC4Mu7vcNe3fI4Zv3/fI2IKtOC1l8+wxYxIz3S9MziEWEKkKAsetem44Ljwyd+CAYpcdo941xmx5O1zo3HCEiXbvryF6xL3xvdVnoqZ/85CeFlCAb2ekqnYFzzz13CG/XdLTITG9II/I5pTUCnjpd0tbxgKFyNPpMFxqVpR+8y0YPI5IQ0p6N/LimA4eM1m7aXJOeTgOdY1BBOnbledppp5WOlTKBh/vJD39pkwNRIagqzOsbvaMeuE8d0kHTofR/7OpI4KEu6cjpeIUc0ocZDNXPHDWtIzy2v5V96xZ1K45RR+L/eKb+/3C/68/5rZzVH/VMHVHX1S82gnZOffTdI9YMOmgLff88LBCF9Ju2kw7x7fmtfvuWtbn0ou8A0RZtMT2kneZJp51GICAltOkGUxAV9KM4Gdp7gzPup/uk4TobwXVkB7sB4cFuMvjCtrD71txPH7A5yOP7ISOyAWmoY8x+YRcYYJIHR9+G30FKsMOQNkgJgy7sI/jQtb4hvxE8vh32E13oW4Kl75795bur22r0MnstbLW45l72Xdh8vk2/tSH0D1KVvcPjxBQadhQ9TkfV9XVrHerU/9oN7Qu9yRNNHYr62Kl3Tku6ZFLneTLyhlMvlGO0n02UeVrymc98OAJJiHw4RnlHCwLRoFIilD3DnkGsY2hrqgLRwOiQa+wYuORv4gY/RqoGREOqw8O4ZgBo2O1GInbeeefSQUf06HhHubQeo0xGKpe4Hx7eyxiK3f+t5xlK3sfYjo4BozlGeuCsEQ8iRWdQIx8NO2OAsSBvjAhxSDRAMcKBODEqrF4xmhjyDCcNvt+ICw0sV1ANmKk6yBEkCbd4dZHBxVBChiBNXDdKw6Di/eIIQyM2DC/kCVwZWkGkMJ7C8NKoxyiT93CfZUyFsWZkyUixKVnKRceCAWjEl+eOUXmGk46QPBuZZVwyhhhGDBudlOigwLxeLvF7uGNrHXZPbt1FQBkgDdVX08J04H2nDGI7Uk2d1lH1rSl334P6ZDpFGLDqAaPaaGdMgannzPfHKEcs6kTXy761rvhuGdUMcjJ4H4IPUaguuu4ZnR2EJaLT+23O+76Rnb5N7430dYSMZtL/UW/pBp0E355vWx5bN/dOjhCBge8cmQpL+AWGOhcw0ZGhX+gj7zMdyLW6PoQLjBCh00KIeEa+yUF3RR7ln45DqPIQ8R7b1BIiykSnjCdIHVeYKXsjyojX4Qx0ssCBpwrZRtoQOcisIGLq90U5Kl/ek/SnTi5y1zl6Sd2ovz8wqKeTvzuPQJRV/U3O2RyjXOK++D/add+FjirbQtlql31TdIF2WP1Q13RktcMIDQMCBgrUc4NfPNa0swgI7StvBt8xQkMb6bw2MogLJAWvUJ11nhQ8LrS/2mPkh3ZYOtplbbFz2m660P/qP1vAoIn38vRChCA1tMNko6/YB2wDR7qVbaAtZifwgoupu/SUzi+iINpi9oi2GCaOCAl6xfftN9vF9xXtdRATsAzSyDdi993CO3b/xznlEXuUW70soxyj/OJYf8Zv76Wn6R12B49c9guPFTYNHc3mQBK71zMjva/1/e36nx5kuyoLdYkcYy3DlOSFTPBRL8iqjrHPlKWtiTJPSb7ynqlHIAmRqcds4J+gIGLXWGCnGWSM1jjfRJAYAUYczf02eqmRauIWjRcsycjQ1rAhcTT+OhnR+DEiKHH50slhvHp+arYos+GO0nE+jq33tL6n9frknq0bDH4z1nQIGBsMEAYJo1y+NFA6OkZDkHA6cDDxW71j8Bux8pux4z6jVjDT+TQy68jQ41bKkDCSbCRXJ0DHSqBZnQZGFiKGoYHoYJAxqnQUGHo6L0a6GGiIFqNXOluuMQqVD/dbRiDDj5HompFkJIo0jVLpRDLkkDfIE7IoR6NuDDUd1xhNitEhdUFnU2NdrydRDoF//J/H7iCgHEzZ0EFXP9Qlu3JXjxjzrrlHR1N5qt/qjs6Jc1G+vgHEgJFL30h9G4kQiXrgKB3GKO8AdV2HgQw6NogURKtviQzu903RM4gc/9sc6U/1FDHA2I201VUdovA+8C37hn1r6rtO/XA6ybnJESLqum9E5yem/AWOjjpOvkO6QP541BlZ1ibRm+SzxzWG7rQQInQRopNRj7yMdB2Rv8jq0RIiOm/qgm870oejDhoXep2b+rWoAzBsFyGi7dAp8D740nOIIB5O9KiOM5m8c7jyDJny2DkEom7EUTmo6/SF+uEb9e2pp8gO7YdvG1nIw0zbZxqbKVG+cXVX3aML6CTtGPI/yH66QTuGmPBt0RfaMtfpL+d8G9pL9UYa/ue15Hvz3dI3iAltqz0GDAwWIHnZj8hXccV4mKhr2kDtNZm16Tr/CBv50M4bPHHUzssfGwHx6n961K6+yj994DuCDV1Az8FMXXaEYeDZeqxfi99Ruu5t3Vqf/7B7Wp8f7v9Ik6z0F8KcLlIOyoYtiGhSJogf2Ch79UEe4/nhZBnufe06B3eewuoTYgRx1MQNLnBSt9RNXkHwg3dg10S5U6b2I5CESPsx7fsUQ0k46qhpwLj2Gl2Ia00EQefBnHwNt5GP1s5FE2QO/FqPGmNGD0XNWNCJ1tGy1FoE10KMcFdlIDCK5M9zsUlzuC3e5Vr8jmOci2Ocbz1O7vrkrrWm4//h7h/unHvlr77XDXYNWuxhBMFQw8xY0AHQ6WJk6PQYDdK5YkTphBrVZ4jZGVcMEUaYqQNGl9R3c2SDdNHoM/DULQQK44+HgKOyQYRwxwxPEyPzDE5TfnTunGdgMipNB9AwMyx1Snxf0uaqq6Op8xkr/Ohwkj08TRh98hlYBKYF2PwzJgjAXDkxWpWjUVY7UiN+I+QY7uqo8molRKRhVx9HQ4jQA+orEoQLNVKDDFzEdYqQdnRGGIDqe50Q8X2RAwkShIjORcjn+9G50bnSqVc3EXvqvFgiQSK0Ai/dyREi3ocQ0TFn6AdudRwRndogdd536PtpNWbj2mgIEXLoSEZeIu8IEaPXIxEi3h33yv9wU2bIr1PKi6VOevh+6aUgROgradU3GI6WEJGedKVFNyKUdVJNDzB4oC4oS4Me8k+uVjnqMuXv9iAQZeK7VC7sF9+dOsGjQfukTdKRU6+0PzxgtRMx7UPdVD/UL2SGNoYHAe8LHhu8M5Cwdufdw+ODp0VMhUZwGDDw3akX9Bqiws4W0R4i0qJtpD8QFDEw4Xe0qdpV36d6RG/Ik3qt3tNT9KD8qmOO8VvdHGmHU2Dlnvh/So9RWnH/h6Xh/rg3nq0f41r9GNedm5qNLPChIxA+pusYWDEdxpRiXjjsBTYH4giuMKu/O35PzXtHe693as8QZTyG1JUm2tuRT5jxiiMvvcd+Dj03tWUWaeax9xBIQqT3yqzrEoeCdeRCiN1n9GuUozHpupDDCKDRZTToGJjSoDPcxC3wDdnif0cbRa2BNBIAd6M35syaO6qBxHIzjLjj6+DrWEQjGWnWj5Fu/Zzf9fP13/X7Ws/7v3WPtFrPx7P18/W068/F+bh3ctfq97Q+F9ccY6ufG+l3/X1Rx93rd+wwZrjqBDH2fBuICkZguCSbNuM7MVVBZ5GhqRFGgOgcGqlDnDBMGatcYbkPG42zM1y5Gutou89IruelIz2jbDqlyBoj/cgSxigjWj1gXAVZoh5FXgKLyGf8PxwecS2PIyMAN9+ncuW9pG4E1q4pB50b9cX/ysToZt1DxHlbECI6JO6vb1PiIULPIT/UE0aqd0lbWjozPDDUUTLaghBBrtpCDvVHOnQng9F5O73K4NWJYvwi/XhV6Uyr/+F5EumURP935a86IRLpxX3SVa+9E/EQ35nrfvvGfGvqsbzoEPDY0gGLPLoXRjwsWqfMxHtCnpGO3sMrBjEZcoQMRkF5qSDa4WODN/d855VxvdyNeiNX6oMHdDkc6IQ6gaI8ELF0Al2uQ9Eqs7R5mSErdDSH2zzD2EfMeu9wm3u8L/D0P/zlSR6N3BuB1vEdTo7h0hzEc63lMzkM3Kv81F/YwzX0gukZ2m6kBw8s7Yb64ZvU+dXuq0e8FMPzUHvh+9NORMwNQcp5kbpHe4FcUw/oJfVTveaZ6PtA7qsnMY2E3lGntB3qMdnISNZ62yEf9T3yXD8Xv0e6Vj9f/x3PxdG1+D2540hpDPd8/d74XT96z+S2yV2Pa3GcXDpxzb30F72j/BGliBB2qykxBsBMO0L+IqKRYnSOumSLd8Ux0h3LI1m0LewTctLN8tTEDU7aKDoW+W7QoE6INFHmlKkzCCQh0hlc+zrVULSOGkxu2BphRqDGMq43DQRKz4hGTHnQYe3FDb52RokRAcaSAGAMH9HFESOWajOKwEPByiwM6zRkm1Hayo7B4FvRkdPpYPzobOmYGlnTweSqrvPJPVbHUEOt7uqYREwTZYw0EXg3ltQ0H1vH0H06U57RmTNqr64woHRy7K3Grm8kjF0yhqzxO+recEfoOp/b/yzzjQww/Uo50jXK2jeo02lUl4eIMoAtYxEhwlPIsd6hD0KE+7Hn65vOvhge4ujQBfEOz6tf0la/jHrRETxB3GN3P68K72R4S9v9CBEdLp2vKGfvDGJFcEEdpLim4yafPCh0uHmjIOLcrz7V6w6ZyOZdZECiaD9g5Zxrcb8jjyidN+QS3OI5suvIeZ90pOud6rx6Hnjr1MOYbIga35n6HbLXsRzpt/fqlHD/11mUL+90HunoWzRyDmfpeqfpRrwqEKH+D3KBzDoJSDL5s8uLqVTqifZU2nay8jzREfKe+C4d4WR3H88cZaueBIaRx8AyYoj4/t0Te5SP+71Pp8BUxcij9NUx+ZYf150b1E352uIYvwPnqFf1o2vwVUftsEcuhM4P0pzHH3xNa0EmmmqC8FBvkZYID1MxeYXS+wY/BB1FmCM7TNf0HWonxJBAkAsir87x2lIXeZbQ+Tp8yjW+t5B/UMu1KflWDvQIG4A+MPAhoDx7bvrppy/L96oPSGIeI8rQM03Y6t+E+m4KI1nZIuoeXdPEjdx0GpuLbvbtBa71PDVR9pSpvQgkIdJePAcitXpjrxNn1RAjmwz2MMSaCATZGIYxT5Ah0qtbKGpH+WJgMYiNVCKnRBn/xCc+UZbt9Zs7LMaeMZZbMxCI7yikif8dGTnReYyOjzJmyDJo1V0GNG8QwRjNCecWzYDWcfM9mo7DcDaiZFoOw9n0CMa1UWWu0YxunV/1xuiv0XXftA6R95KBLPaQr/47ztXzEL8H9RjlxwA0qsuohbfOKCJE5xyBwa1dWbof1ogI5ISj/wNbJJkpM8MRIuoEUoPRKWZOuK8H6UU36Iwb+VUnjCj6TRYENnKDx5EOv3Ins853KyFCFoZ6eIjUCRFeJ0adETzyRwa7+qmDT+eoM2TRCZS+uuYe2NDHvKb8L+/qXuRd51yHH+mAHJC+zp0Aj+q6Z8jsfjIhJkwFMPItOKR74WypcWSJ95PD/VO6ud+IPa8tni9IGhj69hCVztUJEfcjhXxfCEnlot0hB3LDeSOmZIALQgTZgPjhBeR+6ZsmpAMs3hW53S9t+axj6Fmkp3oAVxgiayKfnjOdwT1kd0/s2gx1yL2w5jWgDipndQS+CCbEFS8D9ZVOGNQNlnZb/B5OHzoHJ7iq/8oMMYfsVId1dk2HVB+i7H2Hyls9Q3rMPPPMhfBwTpvuXnWep5fnlYtOp46xb1ecDN+O8vROOsS3QQbyhJxxrOdjUMuzafmmYw1gaa8/85nPVJ/61KeqT37ykyVOCNKUJ496FDq1afKHPOodb2ztkvpNZvWwiZvvQBuJiNQe0elBiDRR3pSpcwgkIdI5bAciZQ290TDzTRnbYZw2MfMMAcai0TTGp1GvXt1ajTF5gz2DiDcItttqOlxnESJf//rXS0PLUM6tuwhE2dWPIVGcq/+vbGNnVDC0lTWjiPGrTBElRsUjEK16zvBmQHG31dHyfeq4avR14rhTW0mH8YU84doqzgJD3bzx6ITr7HGn1sHlYWCU0XfPiCAH2UJux9z+x0MELnDSwTXqxDg0h5+uNLVJJzv0pSNsdXqQUnEenu5ThgxlnZz6pj64HxkmJk3sOlVILnXEPeoIcsbUDISYeefKFZkhRoSyFxuAIUh/ILl1turl6ppndMbCYJRH94tpJG/xfkcda3K4P/KqY66OiWHgnqh7OoP+R+ZJL+oUHPxvlJthLU06jecU/R1ykNN3YfoJAsHUAPnUiYAbLxpBk5UHPCJfdSwn91vaRjl5Whn11EGVZ1NgkC3ImvAQkTY9jPQQw4EcZFaGvG48pxMbMpBJm6QdJbtRSgQ2slKZ6eh6v/uVPzLDNwwLmAmsaGUsHoJIL94CvlHYBY7w9/3HM1E+PAlci7QRWDoy5JZHZaoTTn+QWZqB3+Tw6tdrUWaOsFUedLAyQlzyUlLH1Qt1Vswd5CJ7g/cGLw5lq8zoX14ePPqUme+Cd4fprsoKYUnvIqUQKcpUx9K71DXfNB1cJz6UDbnqe13mkX73a3n1Wr6UL13wla98pQxkaA/UIW2IQRBlThfEd93U/PG4oOsQwjwA1VcyN3UjL1sJ2Yi41m76VnIbLASSEBms8m57bhkDGm1GIWNRA91UxUfBcQ1noDDUGX69rPRaZfe/ndGqo8C4ZZxxnTXix1hzLbdmIVAvx/gdZdl6rEveeo0xbGcwKWeNvHqgk2gUWsfHaj1Gr01BEHxPvTAnXadY51FnzIi8TpARdR05HUCGjZFt5+2MNl4pvB3EF5Amg9176ITowNXljd91ueNcvx0jj8pDGTBmdaiN7CM+dIIDI/fSmcoLhqFDIw3GmU6QcmzVre7xnJF+aeu02nWgEGTuj3QYpd6NLKMHpelZRjjZeCGQKTp4SDZbPO+a8g0vAWmTVaea9woCjmeKnQwIC0Yx7wJ6SJ2Ub3Uw5IxjPEdHMfrjnY46fN6LGHE/Wem2VpzcC29yI4nk01E+vRdZSIY6JlNT75SD9yKRyKCs4CloZSsh4h3y4Z3ujfIgi12diDzCVbrwj3wqS/lVZvIU90oX2TIchoGla8ow8imPMFQfYBL3OSp7dSDK2btgpT6RmxzKxLPRSSDLIGx1zNUbZQYHU8SQFOo2ss90NCQyHUk3IvUcEUo8wdgavHN0thDRvgceTPSuzi4SzNQv0ySUue9LHVEf1CG4Kz9lo0yjXEO++jHKpX7O79jqv52r3xf35LF7CChvdQEhzeOO3lAffM9R/spMHWjaVq9bdBQiGomtjtMxTZQ5MPRtI6QNLCAyfW/1/MR9eexvBJIQ6e/y7XjuGKWYVZ0pjTzFQnE3caPgGHo8J4ykGbELWftR+ckTxa6DwNBm1PVjPptY15ook7JnlOiAMbLVC4Y3Iz9il+i4MvbNZWeQMWaMxpuiwGXeiLERTUSJ0Wa/BfJDpFhZxy7mCe8CI+Q6ujqNOvOMPfXR+8lhJ1NrnZzcudZ7m4hzv8sU5UN36rAjyrgbM9yjTB0ZweoSTwf1SbmPtEWaI11vwvnWuud/JGMQIjoBuXUXgahHcQxp6mVXvxbnHUMvKkd1GWmI6NVBRfry2jD1DWGM9Aj9x7vKzsuJFxjSg4cNotBos46hEX7fAtIQyYSIone1y95XJzxCppA9j4ODAL3JplYv6mRoKwJNrCNkil3d9r3Q/eq/b6uJMgeuvveQF7nddHlD7jy2F4EkRNqL58ClpmOl88O1j1u40SVKvYkbhcyA5cInlgJPkWCCm6ysm4hlytRfCKj/vludXMaA74KhzjAL7wYxGcQr4VmCKNER9N2vueaahSzRETD1hks4gsRoi6k3OhC8lKxGRVdw+TeKbYSdIYIo8U7vj731e/R/67n+KoHeyU2UhbIycoksszMklW/sYmyYHqL8dS7d329bEiLNK9GonyMd6Th2C/0m9oZBEiPxCFyDO4hgnnNWcbGb4ob0Q3ggQXiCmN5C7wlaLuYA4sN0MnVevBj1ndcPItggkffRcd7dj99B82pBSjTWCNS/NwMs+gMGSsU2Uuddb+JGLjYOr1crkfEUabK8TcSwX2RKQqRfSrJL+eB1IHCdDpBpM8O5dXdJtH94LcXHDdXcXHPYubHqjDVVUf9DBvJEItBBBFq/g/r/fjMSGPXRmYgpOEZQxazh+m3qjU6EeA1cxLnMIki4jvMqEftAJ4KLOQMEsaITwpOEKzqSRCfF6BgPA/oljBMy1GXqIBSZ9IcgEPVBBw/BJTirqQA6iaYImG6lI8koNipOz/bTFnVReyf4qRglyKHcuotAlEvUT/rDiLt2n76iXyLOB3LXKiwGRhB6Qe6a6hKxPugysT8iBgivD89FEGBTXHjZqd/0YhAeIUer7orz3UUp354ItB+BqNuO2nNEuG9KcOa41v63jj5FstELPGFNdUPg1OX1O7fBQCAJkcEo547lUgcplvQTEIyrHCOgiRvFxmi19C4CR8eModRUeZuIYcrU/wiEMVA3BOrnhvutIxBeJbw+xE7QWdAZNjXNVBqdCl4kRleteCMQpCWDdT6QJ7wJjLaaP20FBc+KARHuwzo2QZBER6P/S6N5OWwtfxLSq8rcSLspAeJPGHVTZupGvS41L0fTJpE8qfPaPNPP5DO37iCgLOCPlEBOKA/lIt6LDhm3fWQG/WLaC7LO9L855pijeIsi8QQaNqKNHEHsWpFHzBVErSku9JC0vSf0T71e+z2le3dQyrcmAp1DIOq+byNsbJ5Vpp3Ftc69fdpTJi9CRAxEU91iBTAy2+I47W/IJ3sFgSREeqWkGion44DCQ4YwInSGKJgmbhQbA9aINoPIEoOMpjRkm1haKVMTEKgbA35HR4Bs/h9uj3vifqSpDjPykSut0SOdlNNOO618h0ZleJeZYsPDwHS2xRZbrKzOYVUUhoq4JDxJTLXR2fEdR8dkSvUNeYbbRjo/3L157n8QCMwCe/9Pbu833CLf8hVY9Fsem5afVpz9rxzCaw1hITApDw6eZ2Ka6ZCZ5oJ85RXqfyttIWfFAXEUHJVNgMRDfPBOCyIvyjnqdmDSKku9HsS99XuGOxdp5TER6AcEoo77Hq2yxDvEt2ZQI641MZ9kE+fMgAyZLXkeW5PlDhnz2D4EkhBpH5YDmZJOiWj1RoB5XDAqKMQmbpQbeY1gGiXi4m0EyKhzKr4mlljK1C8I+L50Lnx/9ANCw2irToy59tzZGU46JuKNiD3Ck8TyoDoysaSrKTcMF2SKjo8gsDox9cCEMIv3xXc90jHudT23RCAR6DwCrd9a67dJgtZz8T/9wQsEKYpcRayaqscLjWcHbzP6QnDTiPlhSVuEKy8RS4fzXKNz6A3TXZC19BG9JH16qlXGzqOSb0gEeheB+D7lwLckXphYO6bFmgJbv960XJINkWpqnOXaTQHNbTARSEJkMMu9bblmPCBBeIhwg9ehQTA0caP4yIsNNno0fvz4wgYzsEJhO+aWCCQCnUUgvrdWksTIrE6Kzg7iUoBOwQotUUnHiE0RAVvFJaFzzPMXw8J93F25vyJbpB17vG+4o5zmd9/Z8s7UE4FAYLhvbbjvMnQDkoLXhtgfViviLWbqi/hEVriiE8QsMuWF1wdPVUFOJ02aVAkEbdoMncBDLeISJfkRpZHHRKB9CPiOtb3aa6SkGFK+u/i+2/em9qVEz1giHnljYJeeyW0wEUhCZDDLvW25pugQDAISGdE1YoMhbuIWSplxJE4Bea+66qriHhvXHHNLBBKBziMQ35w3xXcX53SCEKsx1YYHiZUbLF9p6oxlXhkwOkUIEjEAfM9cdA877LAS10gMCyM/jB06ijdKfTSYIRTvi/d3Ptf5hkRgsBGIby5Q8B2G1xhPL9NYdUp8tzw4eXNwwde54tWJALEahHgfvFJ971Z3oRcQor51aVjxDgEibe9o/d7JEedCljwmAonA1CMQ37SjAQ1enLw6BZy2ylJcn/qUO/8EHWDa/wknnFA8T/UPchtMBJIQGcxyb2uudTxOPfXUYqD0AiGic0XeZZZZpsw1ZoSFwnbMLRFIBDqLQOv3Ft9d/Xz8JonfDBdkKy8So06CHZoyIyq8mAFWrrHrOBkdNprst+WBjzzyyOr0008vS+oZNRaw1fPceZEkyBckTMjR2dxn6onAYCLg+wqyU7uL7EB+mLdvtTpeXmeccUY1ceLEMq1VhwrJYalv01zF/TKKa6U49yNN2B/Sohd8x0Fy1L9lvye3D2ZpZK4TgfYgUP+2TEXjzWn6msDE2uz6t9ieN7YvFfqIZ7vVphA5luHObTARSEJkMMu9rbmmALmomqtrOTpTUJq4hdI2UmyEefnlly+GV9Nd+pqIZcqUCLQDgfgmW4+RdhhSrdfjf8YMg8s3bJoNj5B77rmneJJY/cro8c4771zc6AVQNK/ZctuCtTJ+ECWm5SBWrJCCLDWyzO033OrjXSFTHhOBRODvEah/I/EbMRHfJ8JC3A8rEQmqjJC0kpSVXxAdvLzEDTLlBYGJ2NSpMnBh9Bb5EYFPESCm0NTJj5Am3u3Yug13Lc613pv/JwKJwNQhEN+SgQbT1jbffPPStsLW/fMAACAASURBVGpH49rUpTg2d5OPh5ng7la7o6NyG0wEkhAZzHJva651IgRC5LYuYjs31SZuoZQZZzpBYhAwusgfo0pNlDtlSgQSgZER8F3H5jvWUaKDkBo6TzpURqDPP//8ao899hiaZjNu3LiyAoVAaqbeMIYQuzpqiF1TdMKLBEliBBr5opMXuuTDjiFXXcY4l8dEoKkItNbXej0nc/1/v313Oha+D9/d+++/X4KWCmCKADGdhdeWFaOs8Gbqy7rrrlstt9xylUDJMf1FbBDBkpEfYgiZ+uJbNshS/+6ailvKlQgMKgKhE8TsQYiwrQ1QhG3tetM2MtFZ+i10kKn/dFdug4lAEiKDWe5tzbU5g6JKW9LuggsuKB2Htr6gTYmFwtaxEYtAQDaB2Ljs6kTllggkAv2BQHzrcWSU6VQxdpAcYhOIS8AlX4BlI9I83OgDHTRxCgRrDU+Sc889t8Ql0cGztLh50QwpncC6wRfvaz32B6qZi0FBQP21DVePnVPnERTqv++Kx4aBBcti33777cWzA/koxgey0eCD78qy2kZieWfx3rI6jGm2yEeu6q2eH63vD7kGpRwyn4lAryDg26QTfP++dZ6YvC7jm41j0/LD9r/uuuuKJ6mAzQjd3AYTgSREBrPc25prHhfc07mfGwWiUJqm/MgTu44MF3mEyAorrFCW2XKOkZdbIpAI9C4C8Y0Pd/R91ztyDCHxQ7jyiyViJPumm26qkB+W4EOQmFa3+OKLl32VVVYprv3IEyPd119/fRkBEwcBQSK9eEe8v3eRTMkHHQF1OLaozzo82koeUwiMhx9+uLT5Bx54YFn2FtkhmKJvZokllqhWXnnlMk3N/HwBzHWWkCZIRWnU4/dIe7jvJ94dsuQxEUgEmoeA7xRBKlaXoMemw/HQ9E3XdUnTJOeBxkPElFqyGzDNbTARSEJkMMu9rblm2HCJ1YkQRKmJhIgMh2FFaVsqWIeH4Sb4IiUY19sKTiaWCCQCHUWgbmzFN1w/evnk/mew0QkxzQZBorOHINGBE2/ouOOOK14kRr122mmnojvEO+BmK8gjMpjuu+2228r0HCtdIIqNnku7LmNHwcjEE4FRIBD11BHB55sQnweJwatSAOPTTjutOuSQQ0qA0wkTJpRvwbQzAU9NhUF+mEKLAPEMbyxxxnh/sA0QKsiPIECIW/8+R/pdz1bIWT+XvxOBRKB7CITOEAB54403LkvvmvIW32ocuyfh8G+m4+gq7bgBXW12boOJQBIig1nubc01Q+eaa66pjKDW1x1v60vakBiFbNcB0uGxbKdI2Iy8IHGaqrTbkP1MIhFIBKYAgdARdQ+SmA7wyCOPlKCtyA/zpHUABW21m16jMyiYnKk4PE0uvvjiol+slMF9OJb+lXZ0CEMvjXQMkeN6/J/HRGBKEIh6M9JRPURS8HLiKWXlFjF3uJGbCqsea9dNf7H6CxJQ3d9mm23Kbt69jgSvS98HMpAHCLvAQEN4Tnl/bolAItCfCLCrkQumwQmQrI00uBBbU79/egqJw8tNbEG6MLfBRCAJkcEs97bmGplgJJWbnFEixlBTlV8YhWQ888wzi8xc35u+VnpbCywTSwQSgSlGgM5g7Ok46tzp5CE2xB4S/JHu43JrVPyII44oHiSm1TAKd9hhh2qXXXYp56ymwdsEeWzkXMC56DzyJmFMekfoqJGOUyx43jjwCNTrUHhCqb86AaZ6vfTSS9Wjjz5avCSttKBjwHWcF5S2XBwd/6vP9hNPPLF4iLjXyi+etbqTjo+R1SA/Bh74BCARGDAE6Bp6QHwggwKCI9M1Td/EFTv++OPLoAYPTx6duQ0mAkmIDGa5tzXXDCGGUYyQIhsYX03dQnFbTWLhhReuTjjhhNLBIbNruSUCiUAiEAhEp9L/8dsxSBJEhg6m4NI8z4ywW6UG+YF0Pfroo8tSolaxQZrwTNPJdORJcsYZZ1RXX311IVdML7DsX6snSf29IVceE4HhEIi6Uvf84LqOuHjqqadKENPLLrusjOSKhcNVXN005//YY48t7bhz2kWjvO6tT33RgYjpYMMReMPJlOcSgUSgvxHQHiJZeY4JpIxcQJDSR03e6EbtMBIYyUun5TaYCCQhMpjl3tZcY1QZWhQhV9pYxratL2lTYmEsMugobIHfKEIdmSRE2gRyJpMI9BECYdCF7pC1+D3ckR6JmCSIEvETxCziTfLggw9WF110UdGTRtx5jTAe6U4uu3vttVfpmJqmYNqCaTavvfZaiePAEy86oH0Eb2alTQiodzogvB0RalZEQrBp5wQLPOCAA8qULkcxPyx/i/gw3UtMEKScIKnqKO8nHQVpGfBorXfD1fvhzrUpa5lMIpAINBwB+ofHozhb4gmaQteqN5qWBTrLAISV5njE3XPPPY0ezG0afv0mTxIi/VaiXcgP45/hzjXcXGMKpqksaxhtotub72x5TYQI4zEJkS5UnnxlItBgBEJfxHEkUevX43cc4xn/B1Gis2n5XzrIUuXHHHNMGbHfdttty/Lllv81XcGu02oqA2MtglPyStH5bbrBGXnP44cj0FpfPuwJ9wcJoj0T/FQ7JiYWTyREh46JODfrrrtuWe1lzz33LFNe1DdTtwxkINwQKK3ER7SHrXK1/h9yuj+3RCARGEwE6AXt2frrr1/tvvvu1dNPPz00cNBkRLTDvON4yxm4kI/cBhOBJEQGs9zbmmtGOaNK9HmjT1hihn9TNwqP8Sdyvmk+RmWNiJE5lWFTSy3lSgT6BwF6xh4dWgSH1brEdEAuW/53//33r9Zee+1q1VVXLbslTAVtjeXNdWZ1ZGPVjkgv0g60/B8Edeu1uCeP3UNAmdiibFqP9WshpXqjzgiCyqPD1BZGvalYlpMfN25cCXJuJSTkB28j7Z12eqTpLpF2HhOBRCARmFoE6C0kq6Xqxc5CLvTCFn0XUwTpyNDHvSB7ytheBJIQaS+eA5kaY9v85IMOOqgEU3rssccaHamZwkN+UIRGYI2gMRiRJKkMB7IKZ6YTga4hQOfo4NJJvD4QHKbHvPHGGyU204033lhG/Ln0CtRqtH/11Vcv0x6QJuedd1513333FTKFl0CM9EtT2rHLYPx2zK05CNTLZbjf2lgBCsXnQpiZBmMAgsfH+PHjS33YYIMNSv3gUWTKlWC/SDPeSDxI1KvwKoq60RwEUpJEIBHoZQToFDGzlllmmRIfS5+gFzaeLNpWZPKTTz6ZfYBeKLQOyZiESIeAHaRkKULTZAQPtCSfJSYZ5U3eyMxQ5B2ic2H+dCy922S5U7ZEIBHoHwSG6/w6Rz8hSHgBGNGnq3iPiENiKVRLnYoBYYoNY870CPFI6GDXESQvvPDCUGdYWtKM9/UPgv2Tkyh35AfyQvwOU6QQIMiNs846q7h1I0EEQRWDJubr8xqyqgOXdR0RnkPasyDHotzrx/5BLnOSCCQC3USAXtFW8VIzZQYxgrzthQ25rN9iyv9zzz2XhEgvFFqHZExCpEPADlKyDG2Gmwj1m2yySVnCj3Js8kaBWyKMO/Fqq61WTZo0qXQ8mixzypYIJAL9g0B0Tus5inN18sI5/+so06tW+RArAjmCyEWAcPfVQQ6PNyQJ7xH6zWo34kpwYTbFQkcbQSLd3LqPgHLguSEAr4EFHpaWgj///PNLsFOrESFABN9FfJk2deqpp1YXX3xxdd1115X7PWfKFQKkte5EnYpj5DjLP5DIYyKQCIwGAboEAWuA0TR0U2cQ+U3fyE3WDTfcsLSfpvunXmx6qXVOviREOoftwKRMgWCDrZ5gtQRLTvbC+uM6BoIVrrLKKiWgoVG13BKBRCAR6DYCdGoYZvXfIZdOr040IxRBYpUsnnmWEreE4B577FGCRfMg0JEWS4IHyfHHH18MQK7ByBGd8HonOtJ3jPfXz+XvqUMgyq6Opd8xBQaJYWqUOCBIeYH9kB/Ky1RO5YcEsXrbySefXIgShIkBCIS+drZObtXfE5KGDPF/HhOBRCARaCcC2iP2M5218cYblyl9TR8UlX9y82YRq2vixImlHR1Oh7YTq0yruQgkIdLcsukZySgQhp1RSFHt77jjjp4gRMyrRuIstthi1c9//vMyOpfKsGeqXQqaCCQC/4sAvcW4izgTXH8R04JtHnbYYWV6DUNVR5t7sNXAxB7hYSJ+Eo+TmGZhuoa0pBl7Aj1tCES5IEAQT0ZNEVGmwWgnEVhIeR49vCvXW2+9Uj5IkeOOO66sQGR1IeWD+NLJiLKZNonyqUQgEUgE2osA/WaqHv2lndGmIOybvpH7pJNOKkHLTUXkaUdn5zaYCCQhMpjl3vZcM6YtH4lpFQTQyKWtyQY14/KWW26pFl988TJ/0Jz7VIZtrxqZYCKQCIwhAvVOOB3Hk4Ar8F133VWdfvrpZSqNpcatBLDllluWoJym2wjEeffdd5fOd6v3QejFJuvzMYR4xFcFPlEGOgWId+2jKUvaGwa4qU3IKe7lysJ+8MEHlzb0oYceKoZ5eO8w2uvpxu8RhcgLiUAikAiMIQK81JDwG220UdFlTzzxxNDKZmMoxlS/itxiL/Fs5533+9//PvsAU41i/zyQhEj/lGVXc2J1Ay6/vC0EeGMAxsaAa+JmJJTiXmONNcrqOAxRxmduiUAikAj0EgJ1HRsd5tYjzwI6j64WoBX5oXO+5pprlqVaN99882rChAkl2v6vfvWrcv2tt976u2kZkWYvYTOWssIHzgxt3iCIKAMEpirBlxeI1WBWWmml8j8PxYcffnhoOVzPeT68QKRnS9zHshTzXYlAIjA1CGhXTNmk26w2qX0J3TU16Yz1vQhrOtgUUzGbtI29IPdY4zQo70tCZFBKuoP5pECMKF577bXV0ksvXQLBWRUhFEscOyjCNCXN+OQiJ0id0VKuyc7llggkAolALyJA19Z3eaj/H51teo73CAOQZxxy5NJLLy3GrHngPP3WWmutMpXjkEMOqS6//PLK8oRiRZmWI51IuxdxmlqZJ9eGuYZI5xWJQEJwMK7NSbeU47hx4wqeVgQSePyqq64qAXFfffXVEuA2VoKRxnBEyHCyTk6e4e7Pc4lAIpAIdAoBbYL2Y4kllihL7vZKcFJEjqDjpieaYiquYOrWTtWS5qebhEjzy6jxElIgRsMY1SuuuGJxmXvttdeGjLumZoDxaV62+CHjx48vwQYZp7klAolAIjAICNCBMa0DOSI4Kz1+2mmnlRUDdOh5kHCF9ltgVivX3HDDDcWrgQHJqKx35MOgdKzvvYZnyE7u+B1H5IW2wkAAQklnwJQXI42ID0tPmk9vKoz2BUGCKBEM1VQYHQi4Sy+3RCARSAR6GQFksGXBrdh4yimnFGK46fmhe7VfPNpNGRXTSVuWOrnpJdc5+ZIQ6Ry2A5MyBYIQoVBMmTEvHUMcRnJTgSAfRS7A4A9+8IMSbZqCzC0RSAQSgUFBgP6OPTwdePiZE25p3zPOOKMs88oVmvcIXSn+hWCtlvsVmPXRRx8tq6XQn7xPIr36sVfwrMscv4M4QoDw7IALV+sTTzyxtB86AqZebrfddtXRRx9dOgWWxX3kkUeGAtbyyIGvNHNLBBKBRKAfEKDPLKrAy0K7ICaHgcambnX9++677xbS2rK7N910U08Egm0qrv0gVxIi/VCKDcgDQ/i+++4rDPF+++1XRg8ZkU3eKEaMsPndXMSNiholzS0RSAQSgUFBgB4MIzF+092IDfqRcWuqzPPPP19dd9111YEHHlhWrbGc77rrrlu8R6yKgjC57LLLhqbW8KCQTqTZK3iGvI4IDEFReXbw8DAKqn3jLWO+vA6ApXEF5UOEGBSw2gK8dBJ4gcCgjoN0Y6v/jnN5TAQSgUSgVxCg2+g7UwR5xv36178eWlSh6XkwxZFHH28+U/7p69wGF4EkRAa37Nuac6NflhJkKB566KE9QYgAgMErGKylwriCizKdWyKQCCQCg4JAvVPud+ytnfjwHmFECkZ9zTXXlJgY3I2RI4xKJMHee+9dvO0ef/zxssQs78GYVtN0TOVdPmN1HlM/Gfhif5j+ggCSR6vDyOepp55a3XbbbaXt0ymoe4EEjvVja/5dyy0RSAQSgV5FgL401XLHHXcselHb0CtTz+l3ZDZi2zTQnMbYq7WwPXInIdIeHAc+FYqEUjziiCMKIfLyyy8PuQeHQdhEkMh2xRVXlMB3u+++e4mO3UQ5U6ZEIBFIBMYCgeH0des5/9P5yA5TSMQdOfvss0vcER4TCBIxNSzlizAQZ4OnidgZMaWmnpfW9OvX2vnbe1o355A/5DKF8u23366efPLJ6vrrry/LFCM+uFRvvfXWZRRUEL6IB+L+VuIo8jLcsfXd+X8ikAgkAr2MAL354osvVrvssku17777FhvauSZv0Q5ou8TF2nPPPcsqOcO1TU3OR8rWXgSSEGkvngOZGuVCkTAkESKCyD3zzDNDAYrCMGwiOGS76667ypQZDDd2O+SNYxPlTpkSgUQgEWgKAkgBo4Jij4ivgRzhKSg+E4PTb4FF77333hJrBJGgzfDccISCfNG/o9nqz4curx+91+gmuRE7prrccsstlSWHTQuy+pi27KijjirxQrQNplTmKOJoSiWfTQQSgX5CgP4UQ0pAafGmeFnTq03c6vrfb0S96Z4HHHBA6bOQ2/ncBhOBJEQGs9zbmmsKhHHJGOY+vfLKK5cARUYDQwG19YVtSixks5ykqT4UujgooRRTMbYJ6EwmEUgE+haB0KOOdKfpMQgGHoN2JIiAezxHzNfmOXLhhRcWI9r0G+2E9sMWabULrEiv9UhOca/IZ0rM6aefXmKDCBq7/fbbF88WRr7rDHxxROQrSJx2yZfpJAKJQCLQqwjQq/SowNqWaT/88MML4R36vOn5EvTadHmDofQ9uXtF9qZj24vyJSHSi6XWQJkZmIzbIETMLzcKWDdEGyh2kY/cRgKRIty7625z5M8tEUgEEoFEYGQE6nreb0YlTwo7g1lAVgFXrUyDeKZrTVHcddddq5NPPrl66KGHqvfee29I90Z6I79xyq9EWiETguP2228vxrv323fYYYcSE0SskBtvvLEQIXUSpE6SSy+3RCARSAQGHQG60MpbvOrmn3/+olPp16aTCqHDtQOrrLJKWRnzscceG+qvDHq5Dmr+kxAZ1JJvc74ZjBQh97PllluuBCo1ShjGaCigNr921MmR64MPPigrBBjBFGCVC2DT5R51xjOBRCARSATahEDoy0gu/ndkHNOpppvEkrWXXnppddJJJxVD1Aid6SliOfHWM3UFma5NGe3m/UgZRru4Vk899VSZziNAqrggjlYXM8LJIH799dfL6jARBLaeD79zSwQSgUQgEfg/bz5E9pFHHlkIkQsuuKAQ203XlaHXDdyOGzeukPSmzzRd7qx3nUUgCZHO4jswqTN6QzEyNC+//PJCNITiaSoQ5OOybX4745hCD88WeUoF2dSSS7kSgUSglxCgS+vkiOkovDF4iFj6/IQTTihTayxtaxrLG2+8UdoQnhq8TJAayGvkSl03Sxd5Qo+7x3K3nrEjYRAhVhBAfPAAMX3H+8x3v+eee4bek7FBeqk2payJQCIw1gjU7eHQ55Yk/+Uvf1ktvfTS1a233jpk94+1bFPzPrLbBf021YfnohVnchtsBJIQGezyb1vuKRfGqrnhVhjgHs0wdb7JG/mMBt58881lBQHBABnRtrrR3eQ8pGyJQCKQCPQaAnQvEgORbkoNHUz/Ii5OPPHEEsjUCB4j2xFZffHFF5cg2EgOz2ljLHf73HPPlYCoDFxtkBViPIeYP+ecc0p6CBC/kS08Vej5IFd6DbuUNxFIBBKBsUIg7HjH+o6I5lkh7hJiwepbiOi4f6zkm9L3tMqunVl//fULGW/qfG6DjUASIoNd/m3LPUWDEGF0rrjiitUpp5wy5DrXVOUYmRcz5I477ihLb1kNgdt0XXHGfXlMBBKBRCARaB8CoWfpYIa0wNxWc9F+cMM2BfNHP/pRWQVs7bXXrtZdd91qwoQJJVaVexAkxxxzTIkBwrAdP358McwZ5zwVrXAjHSQJwx0J8l//9V9/Fzg7ZJCrprdV7UM+U0oEEoFEYMoQqOtIJDYvagOJdiTI6quvXi2zzDLV448/XvTrlKXanbsiLzwCDzrooNK+IOLffffd1P/dKZLGvDUJkcYURW8LQskYreP+vPjii5eVBMQUafIWipEniNFJBveWW25Z5pnHNcfcEoFEIBFIBNqPQF3P+k0XM7J5f4gnoj1BbAh8t8EGGxT9PN9881Wf//znqy9+8YvVl770pfJ7xhlnrJZaaqmyWgAyxEpn2223XSVWCSJE2xTBslvf2f5cZYqJQCKQCPQHAnV9ST/Ty1ZjNMVEnEC2s7iBYnG89NJLRX83OefRziBELKaw6qqrlqCw2pzIa5PlT9k6h0ASIp3DdmBSDiVCOV500UXVAgssUEbmKMy45tjELeSz5BYyZKONNirzyuN8U+VuIpYpUyKQCCQCU4NA6Nn6M3GO8c3r8De/+U2JAWJp3J133rn69re/XX3iE5+oPvKRj1T//M//XH30ox+tpptuujKHfeLEidV5551XpstEcFbpRJqtx3iv87Y4xvk8JgKJQCIwyAiEzqRHTZExDXHPPfcsQbB5U7P5DYKyn007cU/T9ai88HThgcij3XRMbU20FYNc3oOc9yREBrn025h3CpCCMT/baJ6lDM3zDsUYxza+si1JkctuDrp5kJtssklhvCl1W1yvH9vy4kwkEUgEEoFEYFgE6FsbA5XHiKkud999d2VFmplnnrn67Gc/W80wwwzV3HPPXS244ILVd7/73WrJJZcsS+fyCEHOGwGsG7iR5rAvzJOJQCKQCCQCwyJQt38ffPDBaq+99iorMxpIFIdj4YUXLtMYxXOq69xhE2vASTIK1M3mX2ONNQq54//IZwNETBG6gEASIl0AvR9fSZGYm20+4XrrrVfmdBvZC+XYVGM0FKAVDcwnRIgIvJfu1f1YSzNPiUAi0HQEQifHESHy4osvVkcccUS1xBJLVIsssshQHBG62rSYXXbZpfr+979frbTSSmW07+233y46PPIaacX/eUwEEoFEIBGYcgRCh5oWY0VGpIhVwg4++OBqscUWqw455JCyylfcN+Upj+2d5NMvQbKbVmkqpiDcBnRzG2wEkhAZ7PJvS+5DAYrY/+yzzxZSgfucAEu9QogI5nfAAQcUg1pg1Qi8J0/2XnADbEthZiKJQCKQCHQRAe2JzZHetTyvZXIF7hMfxCo0RiYZ5uZ9v//++9Vjjz1WDHLeiT/84Q+LW7cgeXVPvy5mKV+dCCQCiUDPI0An07lHHXVUmRZvVa899tijxG86//zzi9dF9AeamlnyBSGC1NFXsagCOz+3wUYgCZHBLv+25D4UTIzkWRXASgAPPfRQUTxe4p4mbqG8//SnPxUlby313XffvTDdVj0QQOrJJ58s8wvj3ibmI2VKBBKBRKAfEIi2wtEoHg8Qq8twbbZaDIOcBx+jNnYEtimaxx133NB8dlNswg0aLpFuP2CUeUgEEoFEYKwRoEMRB1dccUX1i1/8oniHIBSWXXbZ6vbbby9eFu5pqq4N2bQbiPR999232nbbbUvcQP2Xpso91uU8qO9LQmRQS77N+aZIzNk2mmf5Qyu23HPPPUOeFU1VNKEgucthuLlc//jHP65MoREU9thjjy1LCfufEm1qPtpcnJlcIpAIJAJdQSB0MpLjrrvuKvqYd4hldluXRox7HbU/dPY+++xTAuXtt99+xWMxDd2uFGO+NBFIBPoEgbB7HdnBpsqIEygGh1XA1lxzzTJwGLo27m9i9snGc9AqmPJgAPSRRx4ZmibfRJlTprFBIAmRscG5799CyRi1M/UEoUBB3nLLLcVIda2pCjLkIvt1111X3K3NKeQZcv/991dbb711WfqR8ox8xDN9X6iZwUQgEUgExhgB+pXRLW6IOd7mp++2227VK6+8MqSDhxPJc0iRp556qho/fnwJsiruSK+sfDBcnvJcIpAIJAJNQoCefeaZZ6rDDjusTDexbO0666xTpjDSv67bm7qRLaZimibPq1AgbueaLntTMe0XuZIQ6ZeS7HI+KJIgRHbcccfiJYJF5l7XZCVDNhvZb7vttqLYkTncrc8+++xiWF9yySXVf/zHf5T7mpyXLleBfH0ikAgkAqNGABnCO0SsEEFUxQ259dZbJ0uu08vhwedZS/Sa/miazQ033FBWqnE9t0QgEUgEEoHRIWC6iaVqDRjSsxtttFEZDGVHhy4e3Rs69zT5yIlwF4ybFziyPQiRzr05U246AkmINL2Eekg+BifiwLy8TTfdtCxf2wuESChwgfmMSCJEzFs/5phjqi222KIQJeKJuC/2HiqWFDURSAQSgZ5BIKbKiEVl9FHgPgZ4EB50cOsWetnRfbxCjP4JsmpFhCeeeKLo7tbn8v9EIBFIBBKBqUPgr3/9ayFEfvCDH1SLLrpoNXHixMq5yenoqXtD5+7WRvBk4QFuKubee+9dPf/880mIdA7ynkk5CZGeKarmC0oZ/vnPfy6GqEBLpswwbsNYbWIOQjZHbnPmE66wwgrFHVDQKEuJCdbXC66ATcQ3ZUoEEoFEYEoRMHInDoi56aa9HHnkkWX0LkYe6emRtroup68tAb/nnnuWgKxWRfjggw+SFBkJvDyfCCQCicAUIkC/8rxDiMw333xlQQLxQ3qFECErL3BtjIFPsQ+j/ZhCCPK2PkQgCZE+LNRuZIkyoQx5UnBB22qrraqrr766/N9kRVOXTeBU8yJXXnnlaueddy55MAf97bffHlL03cA235kIJAKJQL8iEDrYkYfhZZddVn3ve9+reIgwWrUp07JZOYxbN6PdUrxGBINYkZ735ZYIJAKJQCIwdQiw9e+9997iTT3X2SlPXgAAIABJREFUXHOVOBx0a9MJkWhrECIPPvhgiYFy8sknV6+//noSIlNXBfry7iRE+rJYxz5TFA1laIrMpEmTytw8hAiPkaYbniGfFQxOOOGEavnlly+Rsy3HdfHFFxcjPRTp2CObb0wEEoFEoH8RCN1q1JGXnqDc3/rWt4p3SKzuNS25Z6ALjr3DDjtUCy20ULX//vuX9ijmiofen5a085lEIBFIBAYVAbrTKpJWZfz6179enXTSSUNTTkKfNxGbkE0/5aabbiqxDhEib775ZhIiTSywMZYpCZExBrwfXxdKxpFRa7WWPfbYo4zOGaVzvhc2o5MCqS611FLVuHHjSiwUy3FRnrklAolAIpAItBeBetvxl7/8pbrmmmsKebHAAgtUd955Z5mXPq1vlLbYI6eeemolPZ5/CJemx7Wa1vzmc4lAIpAIjAUCdOsVV1xR9OoMM8xQHXzwwSVwdejzsZBhWt9BRlP5xQncZJNNqrPOOqsswdsLsk9rnvO5KUMgCZEpwynv+hAEQpkYlaNo1l133TJ15p133ukZ5pWStDIOF+uFF164xBN56aWXCslTz7685pYIJAKJQCIwOgSi3XAUCPXQQw+t5p577mrjjTcusUR4c0zrJk0E/X333VeC5/ESufzyyyvES26JQCKQCCQC04YAO59XyKyzzlpNN910ZYq5GE1N976L9sY0zPPOO6+sKnnRRRdVvMPj2rQhkk/1AwJJiPRDKTYgD6FMKEqkwtprr108LATIc63JW8hHdsazuevmRe61115DqxuQP/LY5LykbIlAIpAI9BIC9Krplk899VQZsZtzzjmrc845Z9TTLUNfmx/+85//vJptttlKkNU6SR+6v5fwSlkTgUQgEegmArzsxNubeeaZq89+9rPVhAkTqt/+9rddXXxgSnR5tAmm8vMM2WCDDUqsQ57strjeTWzz3d1DIAmR7mHfd2+mTBi2d911V4khctppp5W1yXtFyZBdoCVkDuPZCgdGE8mfWyKQCCQCiUD7EaBfGdhWJbPM7oorrlg9++yzxa15NG+LdsfIJc8QgVoFVzVtBvkd10fzjnw2EUgEEoFBQ4CHBft4wQUXrGafffbiES5odTenI4Y+rx+HKxd2PgLEggmmUV555ZUZJ3A4oAbwXBIiA1joncoyRRSEyGabbVaWrMUaO98LGzkfe+yxEmjpq1/9apnyM60rHPRCflPGRCARSAS6iUAYr+I3WRFm9dVXL5H///jHPxb369HKJn0rCjz66KPVGmusUQiRBx54oPrP//zP0SadzycCiUAiMJAIIJTF1zvuuOOqHXfcsSxCIHYgezl0+lgDE++tH1tlcM20HlNkfvaznxXy/dprrx1akj2ebX0u/x8MBJIQGYxyHrNchpfF1ltvXR1wwAHV888/3zOECEVpyoxRyumnn77aaaeditv2mIGXL0oEEoFEYIAQCANUlH+B+VZZZZXqoIMOGhppHC0UYQAj5q02s/TSS5dV0BAwuSUCiUAikAhMPQL06l//+tfKKmDXX399mYp4ySWXFHtZH8D1sd68UxxAgbRHItTdQz6EiGmU2ptbb7215MW1bsg91jjl+0ZGIAmRkbHJK9OAAGVjLvg222xT7b333mXZw24pyKkV30ii+CeLLbZY9alPfaooy/feey+V5NQCmfcnAolAIjAFCIQR+uKLL1bbb799tfjii1fnnntuW4LzRdqOf/jDHwrRMsccc1THHHNMFXFEpkDEvCURSAQSgUSghgCdyq4XtPqVV16pjjrqqMrytfRsTEes3T4mP8nz8ssvlykwltQdaYVLA58I+G233bZ4DRoERaREezEmwuZLGolAEiKNLJbeFYpSYtz+5Cc/KUvvmoIyJYQIZdTtzVxzkafnnXfeQogsuuiilYB85M8tEUgEEoFEoL0IhBGKRBfgzpz0q666aqjNGG27EOkjto899thqxhlnrPbbb79iEI827fYikaklAolAItAbCIReZRsjQcQL3HXXXYdiP3VDt5JFf2P//fcv02G0KcgZW10eJA7PdfGkrIZp6o/B0MhTb5RAStkJBJIQ6QSqA5omhUIpYYwRInbs6+QY41BCdYU1lvDFex0t+4jpZpTPMsss1QorrFDyglHOLRFIBBKBRKC9CNC72oyHH364LIG4yCKLVEb3nAvdPNo3SocL9emnn15WRdhll12q3/3ud21Lf7Ty5fOJQCKQCPQSAnRq7KYfTpo0qcQSuf3220e9Oti04kAeev3www+vxo8fXwY3TeuJtiTkjZhSpsbzZEecIEls7sltcBFIQmRwy74jOadQzNfecsstq4022qi64YYbhpRN6wtDQdWPrfd0+v9QgI48W375y19Wa665ZrX55puXkUTzESnU3BKBRCARSATajwD9ypBmoMaIXd2IHc0bo22xWpjgebz+LBFppZnQ/aNJP59NBBKBRGDQEAi96oh0uPnmm0uMpksvvbTijTfWNnPII1i2mCDs9+222654eMeAbNxjeoyBWnb+PvvsU+z+8CQZtHLM/P49AkmI/D0e+d8oEaB0eFpQRggRMTmwr84Pt/G+wNiG0hrunk6fIxsFjim2tjpSBDliCk16h3Qa/Uw/EUgEBhUBupfuZ8Suttpq1UorrVRZBSYIkdHgUm9z/vznP5eld+ecc85q4403rp577rkxN9pHk5d8NhFIBBKBpiBQ163sd1NQ2M6W4jUg2g2CIez4V199tQR5FTD1nnvuKSvfwC2uI3AM1C6xxBKFxHnppZeGYlY1Bd+UozsIJCHSHdz79q2UjmBG5mmbE3711VePSIhQpJQXF2lrmIfb2liBQ9bYyYI1FnDvsssuK0q0HUb5WOUl35MIJAKJQK8hQP8ynhmoK664YrXeeusVMjp0r+vTuoVud7Qc5K9//etqoYUWqtZaa63qmWeeSUJkWoHN5xKBRGDgEQj9SleLI2IJXkvZiuPRrWXNyWQFmZNOOqm0JwgastXbE96CbHyLJxj8jDiBkR/H3AYTgSREBrPcO5prCscSilzSfvWrXw2RC60v5Vp35ZVXltVozjnnnLYttdj6nsn9H0rQ1JgLLrigBGS64447hhjjVI6TQy+vJQKJQCIw7QjQrwgRxPkyyyxTAt0ZbawbsNOe+v+MCnoHQuTOO++s5plnnmr11VevnnzyySRERgNsPpsIJAKJwP96XoTXBbv/7rvvLt7VYw1O2PLIGOS3aTPiGD777LNDfQv38BY0tYeHyAEHHPAPhMhYy53vaw4CSYg0pyz6RhIKyRJcRuIEKTX1hCKKzW9TUSgqEaE322yz4iXSDTc7MpGHm98JJ5xQHXLIIdWjjz465DlSlzvkz2MikAgkAonA6BGItsAc9KWWWqoYqYiLmKo4Wv3rebugqueff34Jqoqo/81vfvN3bdLoc5IpJAKJQCIwmAjwsH7ooYeK/cz74u233x5z/Rq6Xtvx+9//vnisrL/++tV1111X9H9cR4gY/Pze975XpvlYgte13BKBJESyDrQdgb/97W/F+DRXG8HAEySUkZf5jVE2KogMEdjojTfe6IpSIovRSCOGyJujjz66TOMJeR1zSwQSgUQgEWg/AuEJgoS2DOI3vvGN0h4gMBi2o9G/ocO1R8h37dEXvvCFyiozr7322qjSbj8SmWIikAgkAr2JgMFMcZn22GOP6tBDDy1Bq4PUHqschb53NCh77733lsUdDHRafSbaEx7sSBIDtjzTTbEZTTszVvnL93QegSREOo/xwL1BLBAMLNdkcwqDga0rLPP2KE5zxi+++OIR44x0GjwyMZhvueWW6ogjjqguvPDCyvSZkJXBnlsikAgkAolA+xEIPWtET1C+2WefvcT5EIzbSN5o9K+0Y7SQUTzbbLNVgqpeccUVlaUiXc8tEUgEEoFEYHQI0NOIBR7fe+21V/Xggw+WxRJGl+rUPR1tiSOCxiDr3nvvXeR55JFHCknimnYFIYK84Y3o/9wSAQgkIZL1oO0IUI5WDdh0002rXXfdtXrllVf+bk44I5XC3H777atNNtmkKCXPdMNA9U7G8RlnnFFNnDixuu222/5uvmE3ZGp7gWSCiUAikAg0EAH61c6Affrpp8uI3iyzzFJWm4ngfHFPHKc0G9oU0zURIIsvvnjxPmGwR5C9KU0n70sEEoFEIBEYGQG62XK2p5xySrXTTjsVwqEbREO0EXS/9yPC9TMMdNL7rvM+PPvss4t3uuXetRG5JQIQSEIk60HbEaCMMLDjx48vytEStqGoHAW4o6CQIYIaWaY33NnaLsyHJEge3iqiUp911lnFKA9ZXMstEUgEEoFEoDMI1NsF0ygR0ssuu2w1/fTTl6ktSBLtRV0n1/Vy/fnW31yj77rrruIajWSx6tnLL7885quZdQa5TDURSAQSgWYgQPfS0RdddFG1xRZbFMLhnXfeGRIudPPQiTH4QR5T4Q3MGuwUN8o5Huv77rtvtfPOO5e4J9qX3BIBCCQhkvWg7QggRATJW3vttasf//jHZf62l4RSZJSKG7LddtsV4sSUFde6sZGV0X3ssccWkgY5EnJ2Q558ZyKQCCQCg4JA6FrHMFaR5J/5zGeqz3/+8yXIqqURGbZGIOv3+x1bnKfPESuIkJ/+9KfVvPPOW0033XTVHHPMUZ177rklDe/JLRFIBBKBRKA9CIT+ve+++8rqLnS4mCJ0bejpOLbnjR+eivfxCtl9991Lf0OboG2wgAIyxHR9sau6tUTwh+cg7xhrBJIQGWvEB+B9FNEDDzxQXNX222+/MirnnJ1rtGW5KCQxOygnRqxrY715J4V9zTXXlKk93OjqAZa6IdNYY5DvSwQSgUSgWwjQsfUd6WEkT+BT8UQEQZ111llLPCr62eheEBp1/ey3Z3kjik215JJLVjPNNFP1pS99qVp00UVLsGxxSqKtqT/brbznexOBRCAR6BcE6FT2PN1tuVtL34on6Hw39K13GmzVbmy77bZlWry4Ii+99FIhbawyI/Bqeoj0Sw0cfT6SEBk9hpnCMAhgh4888sjq+OOPL0yxWxij5vWJ7IwQmTRpUvk/FOZYK03yUIannnpqIURM88EgxxZyxf95TAQSgUQgEWgfAqFj40gnIzbEnbJMLg/DhRdeuCyXO8888xSvD4S6lcsY2+5n9PLsu/LKK6sJEyYUAsUUmWWWWababbfdquuvv36ISIn3tC8HmVIikAgkAokA3cq+P+6444qeZk/zvuimztU+8ALhJWKaDA+WZ555prQTCBFLBaeHSNbdQCAJkUAij21FwLSYgw46qOLu/PDDDxelyDvE6B/FtOeeexZ2NhhkL6c4x3Iz0silTqA9nizkJGNuiUAikAgkAt1BIAxo5PQLL7xQCPQVV1yxeHvw+Fh++eXLcu5WCLB6AMID8cHA/dznPld9+ctfrjbccMMyHdNyi2GUdyc3+dZEIBFIBPofAXqb/XzVVVeV1SWtNCmAaejzsbbvIe6dZDj55JMLSXPeeeeVfof2AWH+1FNPFUK9/0snczglCCQhMiUo5T1TjQBD1DKKDNUbbrihuDkb+bv22mtLkCMxO1577bUhZTnVL2jDA8gYBI1YJkiR559/vow4tiHpTCIRSAQSgURglAgwaP/0pz+VZdE333zzslLMpz71qWqGGWaoFltssWrVVVeteI4IwooMmXvuuctyilaoEVTVCGE3DPFRZjsfTwQSgUSgpxCgZ+1PPPFEWSyBd7h+QJzvhh6m/5E0VpPZcccdi6fIJZdcUlYzE+MQ4a4fkFsiAIEkRLIedAQBnhdIj6233roEs/vv//7v6v333y9MLTdoLDKDNZRlR4T4kESNHN54441l9QHTe8wv7IbS/hAx83IikAgkAgOLAJ2MTDcNk8fhV77yleojH/lI9U//9E9l/3//7/9V//Iv/1LNP//8ZaUwbU94Htb1ef33wIKZGU8EEoFEoAMI0K92cZ7Y/jzEkSPdJKVDJoOde+yxR/WjH/2okDVbbbVV8RgxKJte4R2oDD2aZBIiPVpwTRfbnO5dd921BMMTM0SsDgatc6L/P/74411VRBSlkUdECKb44osvLv83HdeULxFIBBKBQUGAnmZQI8/N995+++3LqjEf/ehHq49//OMVb5GPfexjhRD55je/WR188MEl/kjrymXSyS0RSAQSgUSgMwgE+fDBBx9Up59+epmGblojwiGudebNk0/Vu02/vOOOO0rAbcsCr7nmmiWOoUHQCNI9+VTy6iAgkITIIJRyF/L49ttvl+ky5umdeOKJJVaHZQ832mijof9blaT/x2qjBMkolokI1A8++GCZSziWMoxVXvM9iUAikAj0IgLIEEbrSSedVC2yyCJlOd5Pf/rT5bcpmdyfkezf/va3K+ct1bvSSiuVlcPMHa+PTvqdWyKQCCQCiUD7EQjbmTf4TTfdVKah088CrXZL90YfAyljENYU/oUWWqhCnm+yySalbemWbO0vgUxxtAgkITJaBPP5YREwPcZa5CussEJ1zDHHFO+QvffeuyzHJdJztwPdUdoCvzKmjSpaLiyZ4mGLMk8mAolAIjAmCIQB68ir8Lbbbqu22Wabaq655irBUr/73e9W++yzT3X//fcXQpuXH7dnKxq47xvf+EYhRaxMI1B2BM2LdMckE/mSRCARSAQGDAE61saONsBo8QR9gG7GCgy972gqDxL9O9/5Tpl2yfY3KJqEyIBV1MlkNwmRyYCTl6YdAW5zRx99dLXOOusUwuHyyy8v8/dMUXnrrbeK0gwFOu1vmbYnvZcLHaOad4ho2AgcirFbMk1bTvKpRCARSAT6BwH6l0FNP5vGiFCfccYZy1K6pjbyMmRgiykS+tr92hvLKR511FHVsssuW8iTr33ta2V5RW7b3Sbg+6eEMieJQCKQCAyPAP1tf/bZZwshLZBprDLZDds65HFEsItduOSSS5b2QUyRd955J23+4YtyIM8mITKQxd75TDNozz///BLN2bSUAw88sBo3blx12WWXDQVT7bwU//iGUJAIEO585qSLQE3ebijsf5QwzyQCiUAiMJgIhOHKM2TxxRevvvCFLxTvEG3IAw88UJZQDCIkdHn8z+vPiJ9nTc386le/Ws0000zVeuutV5bnTQ/AwaxTmetEIBEYWwQMevIMt4AC7z26t1v2dbQTZLD6GGLd8u1Wl9RedEuusS2RfNuUIJCEyJSglPdMNQJG5BAODNMJEyaUqTITJ04sy1wxXLu1UX4MaAr7uOOOGwrw2hqEr1vy5XsTgUQgERhUBOhhS6ELejfddNNVCy64YFmxwPTG+soxYeQOd9S+mC++++67l7nis8wyS1lhwOozafwOas3KfCcCiUAnEQjd6ihuiMFPMTvOOuusIY++Tr7//7N33tFSVOneXuuuuXdm7syoM6OODjpmncGECTNGEEzkKBlUclQkieQoWQUBBQVBRBQJKiiSgyISBRHEhAFzmnvXuv/sbz3vfO+ZojnncEKf7uruX63VqzpU7dr7qa5de//qDQWVHa3Xhx9+aFbhJ5xwQmjQoIGlBZZQXhC53PtegkjunfOUtJiB7bPPPhuqVKkSKlasaO4y8+fPN7M1f6KXkorkcxAG1nv37jWrFXwc8S1Mp4KdTxX1lQiIgAjkFAH6YLKTIZxjGYJ1B+kbv/jii8P8vBnkFvbiHkOqRSwAy5UrFy6++GIbmGMJyG9aREAEREAEkkvA+2TG2Fj0jR49Ojz66KPhm2++SUu/GxVDaCmW4VOnTg3XXnttqF69el6MqeRSUGmZSkCCSKaeuZjXm6jOixYtCtddd50FMMJdBl/u6FO+VDbBO2rW+JuTgov4IajXP/zwg3XW3nmmsl46lgiIgAjkKoFov0yAVNwsEUJ+/etfhyZNmlgw7pI+weNes3z58nDDDTeEo446Klx22WXmOoNYn25RPlfPt9otAiKQ/QTo1/fv329uM8TqQJxmTpDuhToQg2rUqFGhVq1aNkfhvuNjf78fpbueOn56CEgQSQ/3rD8qg9hXXnkl3HjjjYHgdm3atMmL6JzuTgfTaQbejRs3DnPnzlX8kKz/N6qBIiACcSXA/QCBgowwuMr87ne/CxUqVAjr1683i0IfrBa3/uxH6t3p06eHs846Kxx99NHmukn/z/FkKVJcotpeBERABIpGgHTpWIjgNv/aa68FhOh0L9wTfv7557BkyZJQp06dMHz48IAbDUIJv/kr3fXU8dNDQIJIerhn/VERRBYvXmwWIhdccIF1jHSI3uGwTvXCMRkEo1zTURPbhEwzceioU81CxxMBERCBOBCgX2aQ+swzz1jaXIKhzpgxIy+AaknrSLkMdIk/0qdPn3DcccdZgNbNmzdbn8/vvLSIgAiIgAgklwCW12QKu/fee81NhbgicehvsRx0d0pStePaQwYa3Q+Se/4zsTQJIpl41jKgzogMDHDJ+Y3/9vPPP5/X4aSr4+G4DJC3b99uOdLJQ/7RRx8dog5nAFpVUQREQASygoDfC3iaSBDU448/3vy7PYhqaRrpZTMQ54kglop//OMf7b4UNZMuzTG0rwiIgAiIwOEESI2Om3y7du1C3759LRZUSd0fDy+95N/wUBSxhiw4WInMmTPH0u/yPfcMLblLQIJI7p77pLc82plgqjx+/Hgb3NavXz9s27Yt6ccrboHUj+w3mGIPGDDAgj0RT8Q7wmj9i1u2thcBERABESgeAfpcXjt37rR0iH/+858tTS4ihvfLxSvx31tTLmW4CH7VVVdZbJJ+/fpZlrF/b6l3IiACIiACySRAv/vee++ZdV6rVq3Crl27QjozTNI2v99Qj3Xr1oWWLVuGQYMGmbsm3/nvyeSgsjKHgASRzDlXGVNTBqFkcUEVpsOZNWuWBTJNdwPo7Igy/eKLL1oaRmKceJBX6qbOMN1nSMcXARHIJQLe5+LGQtT/k046ycRqBtOlFUTg6OV//PHH5stOfJJu3bpZYL1c4qy2ioAIiEAqCdD3fvnll2HKlCmhbdu24a233rIHknzP4n1zKuvkx8VS5euvvw4DBw605Aq492M1kq46pZqBjpc/AQki+XPRt8UkEO3kPLo/WVweeughU4n992IWm9TNGWDjIoPlCn6Na9assQ7QD6LO0EloLQIiIAJlT8D73LfffjuQiez0008Pjz32WF4a9NLeN7x8Uvfef//94Q9/+EPo0qVLQCApbdllT0dHEAEREIHMJED/iqXf66+/Hvr37x9WrFhhsaK8T/Z1qlvHcZkLME9BCOnevbvFOOGekAwRPtXt0fGSR0CCSPJYqqT/r/rin03u8datW4fJkyebVQadULoXnjq+8847AZPp3r17W2Alr1O6Omc/vtYiIAIikEsEvM9lEIobIxnJTjnllPDkk0+aIFJaFl4+a55UEliVdL4tWrSwwNqlLV/7i4AIiIAI5E+AfhcXdYKW8mCUAKvffPNNnhUGv6dr4Z7D8umnn4Zhw4ZZ/dauXZt2l5508dBx/0VAgoj+CUkjQAdHR4O7TKdOncxMjqBKCBHp7Py8gQR5evXVV61uQ4cODQg3LHGom9dRaxEQARHIFQLe9zJorlKlSjj55JMt2B0mzf5bSVmwv78+//zz0LVrVxNESAGPpWBpyy9pvbSfCIiACOQCAeJy7Nu3zyxEJk6caAIE8wGWdPW/0eMyJ8CFHisR0rO7YJML50ZtPJyABJHDmeibEhCgk2EQS3aZhQsXhrvvvjuMGDEib+AZ7YRKUHxSdqGzmzp1amBATOendLtJwapCREAERKDEBLg3kAYRi8Jy5cqZawsD6dKaL1MuL8oha03t2rXD73//e0u5jsVIHO5JJYamHUVABEQgxgToXz1WB3FEHnnkkfD+++8fkvI83X0w9wZc55kTIJhv3bpV94UY/6fKumoSRMqacA6UT6fGC+WXJ3FkcCG/N6kOf/nlF/st3R0fp4G64crzwAMPhDfeeCMpZtk5cHrVRBEQAREoEwJ+7/jwww9tUHrccceFW2+91frqaMDrkhycshnwYra9cuVKSwGPIEKMEn8SGIf7Uknapn1EQAREIM4EvG9nDkAcESxEyOwSDV4ah/6X2CHMWXClnD9/fsBqxOseZ76qW/IJSBBJPtOcLJEOhIEnkaQJWjdy5EgLpuruMnHo+Pbv328RrxFFcOuJQ51y8s+iRouACIhAJNMAEf/HjBkT/vrXv4YzzjgjLF++PE9MLyko+ncEEaxBRo8eHUjpi0vO0qVLLbgfv2kRAREQARFIPgH6X15YYm/bti08+OCDFh/qwIED1i8n/4glK/Gf//xnmD17tlm1jxs3Lhw8eNAK8vqXrFTtlYkEJIhk4lmLYZ0RPkhpO23aNBNEFixYYDE6GHTGoWOhHtu3bzezPYL2eacXQ5SqkgiIgAjkBAG/N/BUDhHkyiuvDMccc4y5z+BG40/rSgKDsn/++eewevXqcNttt1mGmdtvv93EcKxPJIiUhKr2EQEREIGiEaAPZm7Aw8i+ffuGQYMGhXfffde+K1oJZb8Vbj1kOcNyvGPHjvZQNy7zlrJvvY4QJSBBJEpD70tEgE6PgSsDWPzwyO29c+dOi9jsA94SFZzEnVCpcZMhojTRrhkoaxEBERABEUgfAb8/MADFbaZnz55myYGlCJkJuKfQd7NdcRa258nfxo0bzRT6hBNOCH/729/sCWXUZLs4ZWpbERABERCB4hGgb//uu+8spmCPHj0soxh9c3H79OIdtehbUw+sViZMmGBCPA9ziWHF93GpY9Fboy1LQ0CCSGnoaV8jQKdBh0dHUq1aNYvTgQVGVGVNV8fix/3xxx/DCy+8EDCJIx96af3TdepFQAREQARKT4A+mheDZLKS3XTTTWbNcdJJJ4XBgwfb00Xvr70/jx7V94/ebxjQkmK9ZcuW4S9/+Yu54jRp0sSCfFMWS35lRcvVexEQARGmGSTSAAAgAElEQVQQgdIRoJ/FnX7mzJkWW5BxONbk3m+XrvTS7009/N6DO/3ixYttPuOZznSfKD3jTClBgkimnKkY15OOA5M4nuhhmkyWGSww4tCReB3wI3/55ZfDs88+a08d+d5/izFaVU0EREAEspqA98UIGgTgw6oDUeToo48OZ555psUWof+ODlB9Hwfjn1mzHdYm7dq1CyeeeKKJIW3btrVMM9GYVmyrRQREQAREoGwIeB9Ln7xp0yZzm5kxY4al3/U+u2yOXPRSqQf3HqxEEG2IdUIQbnfX9DYUvURtmakEJIhk6pmLUb3pON58800zNyPdLikOo0/h0tWheIdLZ7d+/Xp72kiH5ykX01WvGJ06VUUEREAE0kbA+2hf01fztA6Xy3r16pmYce6555rvOdkA+L2gfpvvue+89957di869dRTw9lnn22+4X5P8uP4Om0N14FFQAREIAcI0NfSb3/66aeWaebxxx+3h5IuTqcbgd8LsCJftGhR6NSpU6COWLG4CJ/uOur4qSEgQSQ1nLP2KHQmCAwIDU2bNg2TJk0KP/30U96gld/TtXhHjPk0cUN69+5tazo+7wTTVTcdVwREQARynUBU4PA+me8Q2RGxa9WqFYj/QeYZ0iI+88wzYevWrXbPIbYIg2qsShhss/3kyZND9erVbR8yynTv3t2C+HEPYPFjJL7P9fOg9ouACIhAWRDwPpfYTVOmTDELjLVr15YoNlRZ1g8xfffu3SagN2rUyCxa4hTrpCzarjIPJSBB5FAe+lQEAnRwvqCgvv/++xastHnz5hbR3wefvk261tSTwTUdMTnQ77//fgus6qZw6aqXjisCIiACInA4AR8802/jdok/NwJHuXLlzFrkggsuMHeae++912JVIcQPHz48EB+kUqVKoXz58uHYY48Np5xySsBNhuwBPqiN3rcOP7K+EQEREAERKCsCCA5z5syxOCJPP/10XhyRsjpeccr1uQIPd0eMGBGuv/76MHXqVMtGyb1IS24QkCCSG+c5qa30QStrgiWRY5wnc6NHjw6fffaZmZkl9YAlLIz68QTxo48+Cn369LEYJzxddDM4ftciAiIgAiIQHwLR+8v3339vInu3bt1ClSpVwsUXXxyw/CBQKlYj55xzjmWPwYrktNNOs7S9xLEimxhp1rEeoTwGterv43OOVRMREIHcIkAfvGzZstChQ4cwatSo8Mknn8SmT/Z7DtbtxEC84447zHVm165dsbFkya1/S3paK0EkPdwz+qjeedDBff755+H55583CwwyBJQkRWJZwaCeWKsQzAnrEBRfTKs1OC4r4ipXBERABEpHwO8vvuaegtBOsFVcZohT9ec//zn86le/Cv/xH/8R/vM//9NihZDSkcHsli1bwjfffJOXSczLYa1FBERABEQg9QTofxGpe/XqZTGhiBMVhz45en9gvrBv3z6bL9SvX98EHET5ONQz9Wcs944oQST3znmpW+wdCJ0Hg9T+/fubX+DevXtj1XFQTyxYyC4zdOjQ8NprrwXFDyn16VcBIiACIlAmBPzeEl27gI21x1tvvRWaNWtmgsgxxxxj7jFHHXWUZaPp27dvXkDv6P7R92VSaRUqAiIgAiJwRAI8QKWfxp1xxYoVZsF9xJ3KeIPo/YH3WIm89NJLoXbt2mHs2LGBYN58ryX7CUgQyf5znPQWeufAUzhSaLVv3z5Mnz7dxAf/LekHLUGBuMag7j7yyCMm2CDeePwQ6hmnupagedpFBERABLKOgPfN0TV9OdljiFP1+9//PiCG8ARv4MCB4brrrrMUvcQNwTUS0dtFlGgZWQdKDRIBERCBDCJAXKjx48dbgOxZs2aZS2Ncqu/3CtzsCa5KnCqsEcmg6Vkz41JX1aNsCEgQKRuuWV2qDzbfeeedcM8994SGDRuGJUuW5MXmiEvj6cSIH4LPIlYsBH9lYM3inV9c6qp6iIAIiIAIHE6AvppBKubWd911VzjrrLMsHhSD1q+//jqsW7cutGrVKhBwtWvXruG7777L6+cPL03fiIAIiIAIpIMA/fjq1avNSgTriy+++CJ2DyaZ33AP6dmzp81tcMMkMQP3IS3ZTUCCSHaf3zJpHR0DlhZz584NDRo0MH87BqdxExnILoBVCE8Sx4wZY37o3qn5ukwAqVAREAEREIGkEKCvZpCKKfOOHTtMAGEgTWwRBG5caT788MOwYcOGsGfPnrzYIUk5uAoRAREQARFICgH6cQKVYrVNYFWfNySl8CQVwv2Gh6mLFi0KxKVi7sB9hbqz8LvmD0mCHbNiJIjE7IRkQnXoDAhOOmDAADNhfuqppw6JzRGHzoI64C6Dutu0adMQtzRfmXCeVUcREAERSDcB+nJeiB/ErXIhxL/33/iegax/n+566/giIAIiIAL/JoCocODAAXObIdEB1iJxFBqoEyI7LpmdO3cOr776al76dlrDPUZL9hGQIJJ957TMW8TAlI6sZcuWZvqG6wymcL7EobOgQ+Mp4oQJEyw40iuvvBIrf0VnpbUIiIAIiEDhBFzk8HsL/Xv0u/zeF16ifhUBERABEUg1AdxPZs+ebdYXPLBE5I7236muT37Hoz5YHj7++OP20BeLFjKdxa2e+dVd35WcgASRkrPLyT3pEHCXmTRpUmjcuHGYPHlyOHjwYOxY8KSQmCH4lDdp0sRSMdLxahEBERABEcg8Atx7WKKDUv/OW+O/+WetRUAEREAE4kMAS75ly5ZZooMnnnjC4nNEBe441JT7iD/4ve+++ywsABnO+E73mDicobKpgwSRsuGataXSIWB5QcChFi1aWEpbBJK4LcQPoQNr165dePjhh03dpdPVIgIiIAIiIAIiIAIiIAIikDoCiAlYk69fv96sywcNGmSJD/gubkID9SFo97hx4w7JihO3eqbu7GX/kSSIZP85TloL6QgQP1atWmV+dfjX7dy5M88HMGkHSkJBxA/B7w/hhpzimL9pEQEREAEREAEREAEREAERSC0B5hA8mCSFOjEI27RpEzZv3pwX+ym1tSn4aC56MN+ZOXNmaNasWejdu7eJN/5bwXvrl0wlIEEkU89ciuvtHRmK6bBhwyxHN0LDjz/+mOKaHPlw1BV/P8zxsBBZs2aNCTlH3lNbiIAIiIAIiIAIiIAIiIAIJJOAzyO++uqrMG3atNC6deswZ84cG5/zW1wWrwsW8Vu2bLEHwLVq1bLMM+42E5e6qh7JIyBBJHkss7IkOgZ/oZaS9pDYIe3btzdl1wMixanxKNAffPCBpfXq1q2bqdHEFNEiAiIgAiIgAiIgAiIgAiKQWgIeKwSX9pdffjk0atTILC++/fZbc6VxISK1tTr8aD7nYU2MxBEjRoTKlSsHXHwICiv3+8OZZcM3EkSy4SyWYRu8Y6AD+Oabbyw6dIMGDSxtFlYYcVNLqS9Bm8h8g0keHRhWLdRTiwiIgAiIgAiIgAiIgAiIQGoJMD5nLsEDyk2bNoW2bdta0oN9+/blZZtJbY2OfDTmEwsWLAhYiDRt2jRs27bN6n/kPbVFphGQIJJpZyzF9XVBhA5s7969gYjLd911l8URIS6H/57iauV7OK8LbjxLly61uhIQiXpK0c0Xmb4UAREQAREQAREQAREQgTInwDidB5RkgSTGX40aNczaHAt0fovbQp2IldihQ4dw/fXXh6efftrmFHGsa9zYZVp9JIhk2hlLQ3258BEZVqxYEerWrRs6duxonZlHhk5DlQ47JHX0F1lwZsyYYXFOnnvuudgqz4c1Ql+IgAiIgAiIgAiIgAiIQBYS8HH6559/bq4od955Z1i4cKHNMfgtjgvW8ZMmTTJBpHPnzuHTTz81F5841lV1KjkBCSIlZ5cze2Jd8dFHH4XRo0eHatWqWTCk7777LlZWF96RUtfdu3eHwYMHW0BVIljHza0nZ/44aqgIiIAIiIAIiIAIiEDOE3AxhDWZILG2uPHGGwMZKxFI4uraTqzEDRs2BMIF3HzzzWH16tWBOChasouABJHsOp9JbY13XvjQrV27NtSvX98EEXKI853/ntSDlrAwrwsd1/Llyy16dY8ePSwgEiIJv2sRAREQAREQAREQAREQARFIDwHG47jIrFq1ygSGO+64wxI2MK+I40J9v/zyyzBx4sRwyy23mLUIsQl93qH5RRzPWvHrJEGk+Mxyag8udMzFZs2aFapUqRLuvvvuQMqsqJIbh87A64BrD6pzw4YNLcuMxznJqZOmxoqACIiACIiACIiACIhADAkwh3jvvfdC1apVw6mnnmpZZ8jgEseF+cX//M//mIBDthksRXbt2iV3/DierFLUSYJIKeDlwq5YVxBQqGvXrmbaRu5wrDDc6sKFiHSzoB683C+xXr164Zlnnsnz84tLPdPNSccXAREQAREQAREQAREQgXQRYEz+ySefmDX3H//4x9C/f3+LzZGu+hR2XOqKgPPhhx9aZhxCB7zxxhvhp59+kvV5YeAy7DcJIhl2wlJdXVTRRYsWBQSGOnXqhC1bthxiJhYnoYG6ELmajrVly5Zh2bJlsRNuUn3+dDwREAEREAEREAEREAERiBMBrM+J93f00UeH6tWrh+3bt8cqNqGzYm7BQ2AsWGbOnGmhA4ipiKDD9yxxmgt5vbUuHgEJIsXjlXNbHzhwIAwdOtTcZfr27RsIpsrCxe+vOEChLmS9WblyZWjVqpVlmMGyxevIWosIiIAIiIAIiIAIiIAIiEB6CeDiPnXq1ICFyPnnn2/jdyzQ47pQt3fffTc0b948L2kD3/k8I671Vr2KRkCCSNE45eRWmIht2rTJ8m83adIkvPrqq3kuKHEDQoeE+RqpsQh69MADD4Ro0KO41Vf1EQEREAER+DcBF62jax9osuZ+RNA9ntKRoYCni5999llAtKevZ3BNoD4GqGybWI4fyb/3z1qLgAiIgAikngAW6K+99lo4/fTTw5lnnhnmz59viRC+/fZbc38nu+XevXvtRapb+ngefLJ4P+7rVNQeaxAeCvfr18+s5l988cVAXalDKuuRirbm4jEkiOTiWS9im0krRYBSXGX69OljA884XvTeGdF5EvT1sssuC8OHD7cgSHGsbxHxazMREAERyGoC3nfnt2bgiwDCoJmBMP07ftuTJ08Ojz76aBg7dmzo1atX6NatWxgzZkyYM2eODa7ffvttS73OAJrBKvtTVn7HyGq4apwIiIAIxIRAtP+lSnxGvCaw6lVXXRVOPvlk68uxGOE1bNiw0Lt3b3sg2759e+vr586dGz744INDslxSTqoWr/Pzzz8fatasGR588EG71/zf//2fBJFUnYQyPI4EkTKEm6lFe8fFkzeUUHz7Hn/8ccu77f5ycWsbdSY3OB3rJZdcEmbMmHHIIDhu9VV9REAERCDXCfi9xtdYdjBI/vnnn836A/Pkd955x4SQRx55JNx5553hlFNOCX//+9/tieLxxx8fjj322HDuueeG2267zX7v0KFD6NSpUxg4cGB48skn7b6AmELGMQau3MP8eLnOX+0XAREQgVQR8L6Xfp7+GAu/FStWWMKGP/zhD+G4444L5cuXDxUrVrTvbr311nDllVeaOw2CyQUXXGBzkv379+f14anoy6PHoA179uwxt5nGjRuHBQsWKLhqqv5AZXwcCSJlDDgTi+fip8Nat26dxeNo27Zt2LBhwyFmyHFrF/UlA84//vEPy2vOk8RoJ8Z7LSIgAiIgAvEg4P0zawaZiBW4wzDYXLJkSRg3blzo0aOHBcnGGuS+++4zM+Wrr77a1sSKqlWrVmDQTBBtrBhx7axfv3644YYbwhVXXGEvhBJcKDHNxvway0fuFz44jwcN1UIEREAEspsAfS5Wf2SDJOkB/ft1110XTjvttPCb3/wmHHXUUfaZ78kSuWbNmrB48eLw1FNPmUUGgsnZZ59tQrdbZaRqbB+9X3EPwQr95ptvDsRWxGolVfXI7n9IelsnQSS9/GN5dC5szIwRGO66667w2GOPpd1PrqDOxjspOqju3buHv/zlLxYB2rPh0AFrEQEREAERiBcB77txZyH+E9Yg3HMQLxgQM9AcNWpUePbZZ02QJ4MYlh5E9idmCL7crL/66iuLJ4J7DE8cEVQQ8F944YUwYsQIM7lG1Od9z549w8svv2zpHYk3Er2vRN/Hi5RqIwIiIAKZTYD+lT4bi4qOHTuaNTdCyKWXXmpCNmN3LP+eeOKJ8MUXX9gcBGtBXozvech5zTXX2BgfV0msCFlS0W9zjOhxENTXrl0bateubQI8Vi58pyWzCUgQyezzl/Tac9FzYdMhMXhs0aKFDSBRddP1RI06cWw6Rszs8CdnAI1ow3cMqOloifx80kknhXvuuccGvF7fxM4s6dBUoAiIgAiIQKEEvB+OrhElPvzwQxskT5gwwaxBJk6caKnet27dav04fTsDYu/r6e+9b2cdfXHvYjvuDVibfPnll/b0juDgBAUn/sj06dNNaMFPnWMwsPbyqFt0Sfwc/U3vRUAEREAE/kWAvjLaj3o/z3f0x4gGPLSsVKlSuPDCC826omvXroHApFij4xqD6+P48eMPSYjg5SB0M7avUqWKxTZkTuK/pfoccFzE986dO4ebbrrJ6kygb5Z01SnVDLLxeBJEsvGslrBNXMh0XgxSX3nllVC3bl17Urdjx45DOroSFl+i3agTnSkpdPEHHzRokPkQkrscM2oGtwsXLgzPPfecmdqdddZZgfzgCCbsy6IOqkTotZMIiIAIJI2A98OsMXdGrECo4F5D8G7iPuHWgn94YjDUklSC43A/41gIKliT4DLDk0YG4sTGwnJk9uzZZnUSDbxakuNpHxEQARHIVQLR/t37XuYSWPW99NJL5vJCDBBcGel3sRTB6g/BmxfujmeccYYFVkUkj5ZHH844v3Xr1oGxP4FY3SLDt0s1d+YlWM9XrVo1tGnTxiwcvS6stWQeAQkimXfOyqzGXMQ8XcM6ZMCAARakjidqDCTTdaHz9G7jxo2hadOm4aKLLgoXX3yxCR90QpirseZFJ/unP/3JOlTMrOlQGQSnq95ldpJUsAiIgAhkIAH6Yn9auG/fvjBr1iwTtbnHLF261AbHWHVEhQn2KekS7fs5Li+eKnI/43gEXWUQ3qxZs4B1yu7du+1hQGmOWdK6aj8REAERyFQC3tfSx/IesYK06CQ6IFsMAsgtt9xiMQl5iLlt2zYTQdiOfejziRlCPKiHHnrIBOpomWQMI6MLD2mx7OM+weLbsE71Qr1xzcSKnrkIoo/HNUl1XXS85BCQIJIcjllRCp0KLimYrxGIrlGjRuYn577W3vmkqrF0OAQrwkyOCNT4F5JWd+TIkWb6TMdIoD0yD5x44onhv/7rv0K5cuWsUyXAHooywgjWInS86eg0U8VKxxEBERCBOBOgP0ek5unelClTLKUicT2wECHIHoNJtvH7jK9L2yYvx9deD0QZ4pPgz16vXj0buBPHREJ6aYlrfxEQgVwi4H0ra/px3EnoWxGccZGpU6eOWQCSMQzrv0TRm/3Iakkw7TfffNMED75j3I71CGUROBuXm/Xr19uDW/hGj5tq3hz74MGDJurXqFHDrNcRgfheS2YSkCCSmeetTGodvcCxxOjfv/9hsTjK5MAFFErHinVIhQoVwm9/+9vQpUsXe4qHwMGglTXK8cqVKy1F19FHH21puQi8hGkeHTF5zPFR/Pjjj20fOtiCFu9cC/pd34uACIiACBSfAH0rfTaCA08I6ZdJ5c4AmZhQLlh7H+zr4h8p/z2i5fGehWMSkBVrEYL0USdEdoK2Rgfs+Zeob0VABERABJwA/Sr9JmNtUqTXrFnT4oTce++9FuC6ICHE+2bW9Ml+L6AsxBBEEoQQxv/01Xzn+3Ds6HuvSyrWHJc6ItDgMoNgs3379rx7RyrqoGMkl4AEkeTyzOjScJfZtWtXaNiwYbj88sutE/NIzuloGILI5s2brVM99dRTzaSOwbN3gKypM1YgKLSnn366xTzBH51OmCBNCCMIKmQtQDjJr1OmbV5mOtqpY4qACIhAthHwPhWLDPytMZPGPQaTaEQRhId0BsaDt1uLYLUyb948E2m45yTeJ7Lt3Kg9IiACIlBSAt63+5pyEDKw8iC234033mhu7LjeE7cJ4YC+Nr8lWoa/pyyClBIIu1u3bpZ5jKxhuPNTDtule/G68lAWl8v27dvbPQSL+rjUMd2MMu34EkQy7YyVYX3xy0ONJR4HJsQEMqUjS9dCh+MKMSINKRndJM07I5464qdIMNXy5cubHx+WI3ScBM/D3ebMM88Mf/3rX8PVV19tA143z6ZdXk50na726rgiIAIikC0EvE/lHoLggBjSr18/M3/GpJrvfRtvM59TuXA8Bq+I71iLMOhGrGEgzn3Cn1amsk46lgiIgAjEmYD3276mn6T/xAWScTbW2WSLIaCqiyEF9e3+fbQsxv0E2MZqD8sLUqUT+ym/e0a6OHl9mYMQS4TYhbiCIqbrvpGus1K640oQKR2/rNmbi5vOC0X3qquuskwtXNjeWaWroaitpEbEAqRx48ZmnhaNaULMEwavZ599tnWcBMajM6LjxLqFjAXz58+333CladCggXVcmN5hbeJKbrrbmS6+Oq4IiIAIlAUB+lT6YvpkxBAyhBF4Dr9rLPvoe31h23T0wX5c1twzsFohcwABV0kTyT0kHfVyLlqLgAiIQJwJeL+J2+H1118fqlWrFp566ilznaGfp/+M9vWJbYn2wQjT3C+w8mYu0q5dO8sgSUYyfotLXxytM+2nztSX5A/EYEQkiUtdE3nrc8EEJIgUzCanfkFk4EImkCriw9q1ay3ifrohMKDG2mPIkCHmk0hKXYLh0QnR4dDh4rPIgJsBLFYu3ln5kz/UZnz76GSJdo05H21EwWYA7B1tYgeW+DndLHR8ERABEcgUAvS/DGQRGPABJ2067o359bfe1/o6VW3keNEXLjzcBx9++GEb1G/ZssUCjaeqPjqOCIiACGQCAfpN+ngenNK3X3jhhWYZQvr0xHF1Yf26l4MFCNbeWJngJsP4/PXXX89XQI8DH79vwIA5ysSJE22O4lYifK8lswhIEMms85XU2voFzRpzN9JekbGFNFm4piBGpHuhbvifYyVC5pgOHTqEJ554wiw/GFjT6XgqRVRZF0rYzxfesy1tJI7IAw88EG6//XZLA4YJN2IJx/B9WPNSh+YEtRYBERCBIxOI9qGI1WvWrAl9+/Y1qzz6WbfuO3JJ6dmC+iOgI4owyCfIKlkP8hNx0lNDHVUEREAE0kvAx8iMvQmMjVvL+eefbw8ueWBJ3++Lb5vfmjkGVngebJvUuozPH330URvz84CTcTj7xm2Jtoc2YHWOaz8PXXERhY2WzCIgQSSzzldSa+sXNJ3S+++/b+lsSWtL7A0fACb1gCUojDrSISJYYAGCgEGHibUHliHU3dvhHad/Tjwcv9Nx0VnhJ161atVwySWXmNBCp477jZfh68Qy9FkEREAEROBQAt7nsmZBmCZOCNkGsOpDYIgGxD5073h9ou9HPJ85c6ZlD8B9JhpPxNsYr1qrNiIgAiKQGgL0gd5PIhrjJtOsWbOwY8cOG0f7/YDaeH/p37Ef9wdi/X3wwQcWtwkLQvYn+QEpdpmP8IAzU8bhtAfrx/vvv9/chohFFYeQA6n5N2TPUSSIZM+5LHZLvINCbMBFZvDgwWb2hblbnDoirydqMSmucJ9BFJk9e7YNVFFivb6+LevExX9D7GGwPmvWrHDrrbdaNhrKe+uttw4RRXz7xHL0WQREQARE4FAC3l/SFyN+8MTsvvvus37aswOwR35986ElpfcT9eOe8vbbb1s6Xp5+YrrNfdLvM+mtoY4uAiIgAukjQB/Jw0gycrVq1cpEAIQMRA6/DySu6TuxHOHBI0LI4sWLzXKwTp06lkmSAKo89CTGFGN072spJxMW5ieI6DfccINlUiN+IYy0ZA4BCSKZc66SXlPvsHj6hd9bx44dzfKCwaD/lvSDlqBArwsdJKm4iDiNksxgG0sRVGnUZDqfonSilMd2mEYvWrQo1KpVK1x33XXm5455NJ22H5O1FhEQAREQgYIJRPtL7h979uyxOByI16Tbjbokeilx7Vu9LQxwyXTQpUuX0L9/fxPRuTdw79AiAiIgArlKgD6Sfh5LCAKp3nLLLeb2Ep070E8yJqfPxFWSGCEEH8VtHbf85s2bWxbI1q1b24NYfotaacPWx/OZwJl2MhfByh63GR6w0m4tmUNAgkjmnKuk15ROjQ4LdxEEhnvvvdc6Kx8Qso7DEq0P71GhN27caC4+mNp17drVgjEhlhSkyCaW4Z9RopcvX25BVs8991wThVCvWXybODBQHURABEpPQNd06RnmV4JzZY2QgEUFWWXIAMbnTBMRaAf3EjKvkU6xbt26ZvGCy6UWERABEchlAvTniB/07yQoIPYgFnVuRUff6SIILupsx1gdi+yaNWuGu+66y6y8ly1bZq4mbJsofkTvKXFn7fcLXC07d+5siRsWLFhg9z6vO9toiTcBCSLxPj9lXjsU2blz51q6KNxGiMsR9wuXjhOLEII3zZkzxwKtIuhMmjTJFGh+887UO1n/7GvA+nvMu3GfwdTt5ptvtuwCdND8rkUERKD0BPxa8msuvxKjv/E+v2s3v/2K8p2XfeDAAbNcqF69ekh8MYFnQOPbstZSNALOzH2pidFEphZ8wRk4Z9LibWHNvYFBOynfeaqJOylt1CICIiACuUqAvhHRA6sOMsJcfPHFZmk9btw4sxohrgjBtLECueOOO2xcXalSpXDTTTeZxd3ChQvNbQaBmf6U8jJ9YbyCIERq+SpVqgRcgHbu3GmcoveUTG9nNtdfgkg2n90jtI2LlAEryi1PwHA/4YJm8Qv4CEWk5WfqRueDaMEEB19EolMTlAlrEbLlYLLtoivm0tAAACAASURBVIa3paA1ZSEEEfzvtttuM1ccrER8+7Q0UgcVgSwh4NcRa7JXEWiT4GP0O4kvBle8/Hvesy2TUVK4cq2WdOH4BD7r1auXBVMmoDKvs846Kxx77LEWIZ4Jb7S+JT1Wru3nzBCjsThkYEw/jHVIQVZ7cWXkbaF+mEFzL8FtplOnThZrizZqEQEREIFcJcB9mBeCMRbWuNsjAhBctUWLFuYywpwC6xEsQtq0aWOJDEjYQH9KwNFsdD90q0IYIATxsBnL9eg9JVf/M5nQbgkimXCWyqiOKLM8/cJ8rV27dmHTpk15E444X8BeNzpkOlU6V8z1EDTq168fateubZMeVOhdu3blmfH5fvmtKQc3HNyGEEVI7euBncoIv4oVgZwgEL3eiFdEkMqKFSvmiRI8XbrgggvCSSedZC9c1y699FJ7IViwLQMrgpSVVBDxOjCAw4QXP+ZVq1bZi/gQJ5xwgg3ccJHwwR77aCkaAVjBDT9x+l2sQ+iTsQ7h+0xi6f8VWk7dub8QY6tp06Zh3rx5FnuqaFS0lQiIgAhkHwHvIxEAuKdiCUHfOHHixDBt2rTw4osvhueff94eViKCbN261YKlIiYz7/B7QibdF4pyFmkPD2KxkGEeQlZMBCBvb1HK0DbpIyBBJH3s03pkLlxicZDvmyBAEyZMsA7LOyhfp7WSBRycuiW+6IToeJ566qnQvn17m3ThRsPTYBRsTPuYjOEi5CZ6iWV8+umnYcSIEeGKK64wgYiOno5MiwiIQOkI+LXGNbV69WobMM2fPz/weu6552wAcfrpp5sggrDJYIoXvxO4jZgU/qSlJDXx4+e3xpLhjDPOyBNEotuU5Fi5uA/MEJDfffddGxTjvohFDwNm55kpXBLri9Xkhg0bLAAgQrlnYcuU9qieIiACIpBsAt5PsmZMjfsLgjgv7tV8RgBBFM/vPsB+2bQ4D+YM27dvN0vXe+65x+KnuLV6NrU3G9siQSQbz2oR2sRFi/k4pumNGjWyCQodVyZ1UtG68p5OF5P8LVu2BAIajR8/3nwYcaPB3Hno0KHm30ckaAa1bEunTWdFx42bDAH08HUkMFImBgMswqnXJiKQcgI+WIhes14JBlNYZlx00UVmKUKmp+j2RXnvZfm2/pm1f1fQujBBhH2OtHi5fizfvjj7Jm6bX5lF2caPXdDay/Wyomt/X9C+hX3PvojNZGXBvQmm9Klepq8LKyOuv/H/JE07Wc14kT0Ai0ItIiACIiAC+d9jE7lwD8jk+0Bie/L7TPuYW2FVSEwy3GZGjhxpDwdyof35Mcmk7ySIZNLZSlJduTAZ0BH5mZSz+P+haGZ6Z+UdDsII1i979+41M76ePXtawNSrr77aomHjFtOnT5/w+OOPh1deecVchdatWxcmT55sPIiEPWPGDGOU6UyS9JdRMSJQZgRcEKlQoUI4//zzA4JIQYtf46wZeLAv1zrWCMQTYuLKYMSj3fv2BZXH91FBhFhC0SW6v7+nf2Hyj6DK8bAs4/hYv9Cvsh0La+rIGusJnpodPHjQnpiR8huLNZ6mIRzwO+2gPL7nPW3zY3o5rBFw2f+LL76wNrNGvOXYvl1iGyiLY3M82FAGnDgeL8rju+iTPG9HtKyC3rMtPDCVxtpwzZo1eWUVtE+mfE/bEM4Ry4lThUsQn7WIgAiIgAiIgBPw+zX3YqzVcfXFSoTU8/6bb6t1/AhIEInfOSmzGnFBsvjgGCGErCr4/DEg9t/LrAIpKtg7HiYHdExYgyB8YDHCgBaXGOIWEKeAQFBEwr799tvD5ZdfHhBNCOSI6Xd+k4sUNUGHEYGcIUB/hIVIcQQRrk0s2ri2yRBF7CCuX/qzAQMGBARORAuf4BcGszBBhP28X2RNXRESli5daqLqtddeGy677DLzF0ZgJWaRiyLeD7GmnjwxqlevnsUwYXJduXJlCzZHXRFBaMf1119vL+qEwBAtg/e0mdgc7F+1alWLr0LKQ3y36bNcCIq2FwYINjBq3bq1+XMT+PShhx4K1J8+j7rxHRN9jhNtd7Ssgt6zD8IM9cblCTG6uGUUVHa6v6dtnFOEENwxn332WcURSfdJ0fFFQAREIGYEuFfwYnxCzDNiaTGfwE24KGORmDUn56ojQSSHTrlfrDyRJK7GLbfcYkFEGWDzhJLfM3Xxtnn9/TMdE5MYJhI8oSWrDkGemHw8+eSTFvl67NixZgrNpGDRokWWcSY6qfEytRYBEUg+geIKItSAPgwrhBtvvDGceOKJoXz58uZyg4XJaaedFi688MIwZMgQm+DTBxS2FCaIRPtE6skgBxe8cuXKhbPPPttEHFx9zjnnnPC3v/0tXHXVVRaolf6DxfshBAIm0wSPJQML9WYfysGslu9w1UMU+tOf/mT1X7JkifVblEEbaDN9FtsQb+W8886zNrM+5ZRTbB+i2ieK29QbQQYBGMGIuFFNmjTJC2xLPTgmwg6uhi6KeN0LY+e/sS19K30pLjNw8qU45fg+cVszmMVyiYxH3DuwtNEiAiIgAiIgAk6Aex0L92usPHkQywMCYqFhxem/+/Zax4uABJF4nY8yrQ0XIwM7TKd5wsgTQ6Ih8/SQCzjTL9Zo/f09a3/RdoQRBvyIIzyBZWCLqT0TBjjQibk45PuV6UlR4SKQ4wSKK4iw/ebNm63/QghB+Fi/fr0FVSY+EE/wcQVEfJg+fboJCYUhPpIgQj9A/4jQQFBNhIMOHTqYqEzGGoI58wSod+/e4cwzzzS3PNxQqKf3IYgFBK8+9dRTrX5E5SdQLFYeCBLEpiDLFxYmCCeUw9Ml+inK8PgctIl9aBdmuJRLzKSZM2ea4IG1B9YrWIr4Qj1wBUJIoe4IFitWrLDMANSdgKE8xULQIeMYdfB6sy7KAh8sTDgXpFXG4oWlqPsX5Rjp3IZ7B4G5yUhEenqsYbSIgAiIgAiIQJQA9zzuh9wzGKcMHDgw9O3b1+7XfK8lvgQkiMT33CS9ZlyoDJRJgcWEAfNtBuU8eeS3bBm8FhWct5lOileutb+onLSdCJQlgeIKIl999ZVlg8IahPhACJoInVzDlIXISWYa3OJwCSFYMt8XtBQmiET3IcYGk2LECIQQ+k3vO+hXSdtdrVo1ExYQGdje+xiEC2IXkVIYMYT6Uk9iGWHhMXz4cNuees6ZM8ey3hDY2cVqBNvGjRubZcjs2bNtQo5wy/FZI3IzUcdqhQDSBMz2Y/O7CyIwwfWDeCcM2NifeiKuuPvPyy+/nCfmRNtf2HvKWrt2rbkrYcWCW1E2LbSPWDFkz+H84+Ll9wtfZ1N71RYREAEREIHSEWBs8thjj1nWS+6L0TFB6UrW3mVBQIJIWVCNYZk+OGagSjpLTLt5EskTQgbhGtTF8KSpSiKQAwTof4oTQwQrkAYNGpjLB1YV3rf5mskrAkTbtm3D8ccfb8GjES8KWooqiFA+rjCICd5n+jERFnATIS7TUUcdZVYaWHX479SnTZs2JtIgTrA/v5PmG1cWApGyLeWQqYU0wFiUuNiD2IIlCTGPcL9hf7b18p3hddddF3ghTvjvUUEEtxzK8v1YwwvLOASXf/zjHxZTCsHGtymIW/R7jr9y5UoTeBANMA/OlgUOsER0wl2GgNucA75n8XW2tFftEAEREAERKD0B7vEEGm/RooU9vMFykvttce6tpa+FSigqAQkiRSWV4dv5oA5TbnzImVDgb+5+bRrUZfgJVvVFIEMJ+GS+qEFViQF0zTXXmKiLNQMTfOI78OI9L77HIuM3v/mNuXDgelLQUlRBhP2ZGDPIQaggiCnxl/y4ixcvNlHh97//vfkOs52LElFBBGsP2oxIQ0q+ihUrWlBU76Ox2kMQIQAqx0GAweLl2GOPtXTguGv4gMrXLmpg+YcbEW5DHgcpKogQQyQ/EYlt4fX3v//d7g9YvHjZBXGLfk97Vq1aZa43BHilztmy+HnBomfMmDEWJwVLIc6tFhEQAREQARHIjwD3RTJ44hLbsGHDnLbIz49P3L6TIBK3M1JG9WFQx6AXixCyrTAQ5ykXg+XiDHzLqHoqVgREIEcJFFcQ4YnLWWedZYFAialxySWX2At3EF585nvidfzxj3+0vq4wF46iCiKIDsQdIlAawTXr1KljGav8+LjDnHDCCeF3v/udbRMNTuouM9QvURAhrodbiHAMLEQImooggpsGdZ8yZUr47W9/a0+ZcBmK9tk+YUdgwQ0SNmzPZ36Dr7vM3HTTTSbi+P6+L/cBLGoQRIgB4vsW9S/JMRCqcGEi2w4WJ9myOCMsRMhghD84g1wJItlyhtUOERABEUg+Ae4d3DdIwUs2uB49epi7K/dLftMSLwISROJ1PsqsNlx8POF66aWXLEsCwQF5iudPMHVxlhl6FSwCIlAIgeIKIkRsx4KCDC3E7KhevXq+rxo1alg6XCzhEi0WvL9jTUwOgpjWrFnThIOCqoo1HfE9EA3IykIAU9J1+/FxZ0GMcEEECxE/TqIgggCB6EBwawQRrCrYlv440UIEEQY/ZKxdevXqFVwQidaT/bDqIFC2CyJ8ZolaiLgg4vtyTF4uiOAygwUhdWPx+vv2Ba05h6QPHjx4sLmUJPIuaL9M+R6hCiGLuC5dunSxQLYuiBSVUaa0VfUUAREQAREoPQHuDcQNwZ2U8QjZ5YjhWFwLzNLXRCUUhYAEkaJQyoJtGNDhe9+vXz8za8bHnEGwFhEQARFIJ4HiCiLLli0zMYInLkxSGVwU9qKfiwq/DFKir6gg4sEyo7/7ewYyiCak+SVOBlYXWIH4sbG4Y7IcFUT8uFFBBKsP2hwVRLAQYeFYCCJuIYLLDEIMLjDEJsEyhSdObOdl+3vKq1u3rgk2xLogDghLYYKIbRCC1YcYJ1GXGf+tKGvqgivOQw89ZCKP15F9qV+mL7Rv3759FhyPoLUEoeU7X7Khjd4WrUVABERABEpPgPsCcy/u+UOHDrW09zxUwepT94zS8012CRJEkk00puXxtJJ0jK1atTILESYS0QFdTKutaomACGQ5geIKIqSyQ5ggMHRiilgGGT4IQajg6Qz9nH+f3zpREGH7xH34jCvLhRdeaBYdZJnxzDZeJgIJvsIuiCCWMBji99IIIv6E6ZRTTjGzW0SbaP34e3AcLEcqV64cLr/8cksJ7MdOhSBCGxEJcCnhRZabbFloG+6mPERo1KhRePDBBw8Jqpot7VQ7REAEREAEkkuA+4dblxLUnFhdxKBi3KMlXgQkiMTrfJRJbbggEUDGjRtngX3wL2eywPdaREAERCCdBIoriBAYGksEYnYMGzbMgpxGBQLKo7/D9YNYSd99912eMEGfl/iKxhApyEKE8jF7JSMMMUOwFkBo8LI4JhZ4uKy4IOIuM2xTGkEEYYPUwbjmkFaXgLHR+CSUj3UI6XT5vWXLlhYryuuWKkEEEQTmgwYNyhOq0vm/Stax4YggsmDBgtCsWTOLkUI6ZC0iIAIiIAIiUBgB7h88PMGCkqDmuNbycDrb3EoLY5Apv0kQyZQzVYp6MpjDDBvrEALnedrFUhSpXUVABEQgKQTyE0QYROS38D0WE6tXrw533HGHBVElCCjuLIgZpL7lST6CyRVXXGHiAO4bbi2BOLJmzZrw9NNP573atWsXjjvuuECWG0Rjfps5c6bFC8HUlf6T4yJ4kJr2pJNOMiGGz1iFII5wTIJVd+3a1VxbHnjggfDcc89ZlhiOXVxBJJplhmPzhIl06cT4qF27tmWdIUA2wg9Pm8hCQ7pd4pGwHds7w6IKIh5UFVEDwbw4C8ciRtW8efPC6NGjjYcz93oUp7w4bUv9+c8Ru4a28d9D7Ioumd7GaFv0XgREQAREIDkEuDdwL0REx6X2yiuvDCNGjDArSh60aIkPAQki8TkXSa8JFyIv/NUY6N96660WIZ8gfVpEQAREIA4EEEQQHm644YZw7bXXhnfeeSfPJSSxft6n4R7CBJX0u1htkG4WseKuu+4Kt9xyi32HYEIqWCb3bkGCFQOBST0zDFlfzjnnHIsLQlYaz1pDmZTN5Net6eg3CdDKPlin+DGxGmjatKmlZMV6gwEP5dDfvvXWW2ZJgoVH9+7dLagacUFoM+UiPvDUaOrUqdZU2scxOT4BPD///HPrw9meARV+yAg9BGfDGqVJkyaWWQZ21AtRhvKjAy325bvrr7/eXI1wbXGOHJT3bEN8Esom4La3OZF/QZ8pA6uVFStWmGiAKIOQ5Nz5PVMX2sDTPDIFEDuGWDHw0iICIiACIiACBRHw+yz3EKw4Fy1aZPdhrD25Vxb3PlvQcfR9cghIEEkOx9iV4hciyiR+9t26dTN3GZ7g+RPP2FVaFRIBEcg5AgwWsNxgsskr6raSCMP7Nd8HNxbidmAdgUhx3nnnWeYXLESwhIu6tbDvF198YRYUBJcu7MX+Q4YMCdFYIfSlWJtg+YEActFFF4Xy5csHMrfwxId+lnZgjUe2FURonzyzH4OhyZMn57nw0A9jrYIYsmHDhjyRgn0QNtjeLT2oux+fgKmk5EXU4fiIGARERYRAKEqcrDsrMtUwqceqxDn6mn1wuSHbDXVxMSORf0GfKQfW7777bpg2bZq1ibpzbD9GQfvG/XvYINiREWjGjBnGj3ZpEQEREAEREIGCCPi9jzX3ER5M8CCDhxc8DIkGHy+oDH2fOgISRFLHOuVHYtCG7xoDeMysO3bsaKblGsyl/FTogCIgAkcgEB08+PvEXfx7X9OX8ZQFC4ydO3eaKMGgw5+8sB2Lbx9dJ5ad32ffnuP4ewY2WIsglnBMJss8/YluE33v+7EuqC7Rbfy918c/s6Zcjo/VH646HJ91UcQHL6egcv336Nq3PdLa64ZFC0FqEYRwE4oKUkcqI66/4y7z9ttvmwUNaesRvbSIgAiIgAiIwJEI+P2UezfzMR6UYNHZp08fG0PwvZZ4EJAgEo/zkPRa+EWImXXv3r3NFL1///7m5+2/Jf2gKlAEREAESkjA+6XoOrGo6G/R91EBIr/30e+i+xXnfbQMf5+4Lqw82lLY7/xGeV5mftsm/u6fE/dJ5OafE8tM3C/xd9/vSGvfD7cZLHN4+kUQ0qhQdKQy4vI7bfGF94hfBCInpfErr7wSfvrpJ/9ZaxEQAREQAREokIDfG9mA99wfGzRoEOrUqRMWL15sIkmBO+uHlBKQIJJS3Kk7GBceg12C/eHrXq1aNQsSGE0Vmbra6EgiIAIiUDiB6MChoC19m+j6SJP66LbFeU8dotvn9znxO98+sU7R9rBN4n7+2ddejq8L+t5/T1yzfeKSuI1/Zjt/n986sZz8Pvt+uNpgtULwUQR4rHWwaOH3TFywNHrzzTctNg1BZ3EJoo1aREAEREAERKAwAn5f9DXbEny8Q4cO4aqrrrIU9dwjC1sy9d5ZWJvi+psEkbiemVLUiwuIATmR8PFtJzggAfq2b9+el21BF1kpAGtXERABERCBPAI+4CPOCS5ExEpp0aKFBY7zFMF5G8f8jbeFeygxZ4i9QoBeYr0wmOV7LSIgAiIgAiJQGAG/l0TXuJFicUhGuMqVK4fly5cfMi+Lbht9X9hx9FtyCEgQSQ7HWJXCRcRTLHzLa9asaUokFyC+z36BxarCqowIiIAIiEDGE+D+gkvJG2+8Ee6555689IIMAjNl8Xsk1iGbNm0KPXr0sHSJWIcQT4TftYiACIiACIhAYQT8XpK4Jvsc2eX+9re/hQceeMBS8OKa+f3331v8M7eqZD+3Ni3sOPotOQQkiCSHY6xK4SLCd3vp0qWW4qlRo0bmOpNJg9JYAVVlREAEREAECiXAfYeFwZxnZWnXrl1YtmyZpa313wstJAY/Uk8sXbAOIaMP6YjJzoPQo8FpDE6QqiACIiACGUCAe0n0xRwM0QOhvUaNGuHoo48Of//738ODDz5oDw+wRnzmmWfsd6wRuQ/5/hnQ3IyvogSRjD+FhzfA0zMOHDjQohkT8Z8BKheWL9H3/p3WIiACIiACIlASAj5wY40gv379+tCzZ09LpUxGnkyJvYHogbsp8bcGDBgQhg0bZhlzok/tSsJH+4iACIiACOQOAe4lxG1ETMcCZPPmzeHpp58O9913n6Xe/e///u/wu9/9Lpx99tmhQoUK4corrwznnntuqFevnj1I4D7k99XcoZa+lkoQSR/7pB058YLB1Jc0gTfeeKO5y5Aq0P24/QkX+2gRAREQAREQgWQR8HsR95kff/zRUvAOGTIkPP/884GUvIj1cV94irdnz54wfPjw0KZNmzB37ty8bDl+/4x7G1Q/ERABERCBsiNQ2ByK33gAgJXHtm3bwqJFi8ITTzwRWrdubUkuiB+CZcixxx4bfvOb34RTTjnFfmvSpEk444wz7EVQ8sQH2WXXGpUMAQkiGfg/8EFndO3N4LuDBw+GRx55JJQrVy5wgTG4i5pe+X6+j9YiIAIiIAIikEwCiAd79+4No0aNsowzpKz94YcfYvnEy++JrBmEYrbMgJTgsGQBoC1aREAEREAERAAC3Ct87fcP7hO8iDW1Y8cOsy7ENebCCy80K5CLLrrI3GMmTJhgWT+bNm0ajj/++HD11VebcIIVyZNPPhluvfVWy0SDRYnuPan7v0kQSR3rpBzJL7zEizF6IZImkAvst7/9bcBtBoHE92M7f5+UCqkQERABERABEUggwH0Gc2H8pUnDi+vJqlWr8gKT+j0sYbeUf/T7IfdGTJuJF8KTvJEjR1qaXY+95dulvII6oAiIgAiIQKwI+P3A1zx0xioSEQNX0apVq5r7C5Ygt9xyS3jooYfCypUrTWBnO+41xNeqVauWxRPZunWrWZXs2rUrdO3a1QSRjRs35j3MjlXjs7QyEkQy9MRyEXIBkjkG95jFixfbUy2eaHXr1i386U9/Cscdd5ypkATxYduoGML+WkRABERABESgrAhwz8EqZMWKFWYp8vjjj5vIgDlxnO5BPpidN29ewMWHwSt1dldT+MSpvmV1vlSuCIiACIjAkQlwP+D+xr0Dyw4sIJl7XXHFFeHkk082NxjStU+cONEeCnz22WcWmwqBnf14sR+xtki9++2339oDhJkzZ5pI0qVLF7Ma0X3nyOciWVtIEEkWyRSWwwXiFyGmV6iP1157bahUqVKoWLFiOOuss8KvfvWrcMwxx9iTrmnTpoUNGzaEr776yi449tVFlsITpkOJgAiIQI4SIBgpGVuIZcX96oUXXggff/yx3YvSfR/i+AxQiW9CsLsWLVrY07mFCxeGL7/80gatOXra1GwREAEREIECCCBoEDycdOy4hTL/Ou2008I//vEPc3kZOnSoWUQihOBCw/bcb6Iv7o3EfER45yHB/v37LeBqw4YNw5QpU+y+lO57ZAHNz8qvJYhk2Gn1i4kLEXOqypUrh5NOOilcc801FpkYdfIPf/hD+PWvf20XJ8F7MMlq27ZtePTRR8Nrr71mFiUMUP0iBYEuugz7I6i6IiACIpABBLi3IDoQm+PVV181H2mCrL7zzjtm4cigMDpY9Cb5vc4/J2vt9zrWuPR88skn4cUXXww8kevevXvASoS4IZ5VJlnHVTkiIAIiIAKZS8DvSdyvCJhKsNQOHTqESy+91OZhiCIPP/xwWLdund3vEDv8fuOt9jJ8TVk8pMbanwDeiCFkoXnrrbfy5miJZXhZWieXgASR5PIs89K4MLiAMK+aNWuWWYTUrFnTBnSrV68OvXr1ssjFRC3u16+fBfDp3bu3XWQ333xzqF69uj0Fc/WSp2AMCv3iTFyXeYN0ABEQAREQgawngCjC/QZXFFw7sRZ5/fXXA0/QGDhyX+OV7HtQYnl8RuzAlXT37t1hyZIl9rDgscceC8TfwoyZukb3y/qTowaKgAiIgAgUSID7Afcn7g0I5tzDCH6KRcgll1wSOnXqFLAsJGYj1h5sW9DiZfm9iPkcLjd9+vQJ9957r1lRcq/0e1BB5ej75BKQIJJcnikpjQsN9xdMqhA4nnvuOVMXuYDILnPVVVeFVq1amZkyKiaR/ufPn29PvxBFiHRcvnz50KhRIwt2hw8bFiM+KI1erClpkA4iAiIgAiKQ1QR88MeTMFw4EURIbYvP9M6dOy0gHYPNqCiSTCB+fO5zWKsQd4s64CqD5STB7KL3QB+MstYiAiIgAiKQmwS4B3Bf4v7AfGrSpEnhpptuCuedd16oU6dOmDFjhrm7uJDOtn4fy4+Y31vYnrkc87OWLVtaVlCsRHhI4BaKuv/kR7BsvpMgUjZcy7RULhCeYpGeidghgwYNMsWSJ15vvPGGDfIwR45elFxcDES3bNliv99www3hxBNPNGsS1E1MtHhyR7keY0QXYpmeRhUuAiIgAjlFgHsK9yXcNblHYV7MvYcsNDwh++ijj+w3vweVFg7H82My+OQeiRUIge7atGljLwSZqIuM7xNdl7Ye2l8EREAERCAzCXAv+OWXX+zegRU+saZ4oIylPUktCGHgAojfNwpqqc/LmJPxEJv7DxlpeJA9duxYi6/lwsqRyiroGPq+ZAQkiJSMW1r34iIhCA8uMg0aNAjNmze3dE5clJhqsY5eUFSWfbgQ+Z50TzwNIw0iMUaIQVKuXLlQoUIFCyhHYB/fP60N1cFFQAREQASyioDfi7hXYZlIKsKpU6eGvn375gkjBF11a43iNp7yfeE9x+Ep3I4dO8wapF27dqFz587mToqVCCbOUQGGfRJfXp7WIiACIiAC2U0geg+hpaTJxbWSeIwkrqhbt254+eWXTdBw95ii3jPYjrkYIjzCfLVq1axM7n/RYONeXnaTjlfrJIjE63wcsTZ+kbi6iMkxqZ0GDx4c9uzZc4iZFdvmt/A9cUMYCKJu4juNL9wJJ5wQTj311NC0aVML7oO7TdRsy4+dX5n6TgREQAREQASKSoD7CfcXBHruXQRaZYCI1ciIESMsuCn3J9xbGJByZbIsuQAAIABJREFUz0q8H3EsyvGnbggb/lAAsYXAdNOnTw89e/a0lIgjR440t9Jly5aZ6TMpgdlHiwiIgAiIgAhAwO8prLn3cG9inkXwVB5Ar1mzxuI4Ru9HBZGjjOiLfbjfEYOkWbNmoX79+oF09DyI5h7HvUxLeghIEEkP91Id1S8uzI4Z8BEdn4A+s2fPtoj5/rTLtyvoYFx4lEHKQdxlCL5KlpozzzzTzLeGDBlivt2ejYbytIiACIiACIhAMghwT+E+hDUIAj1BTnH7xHR43Lhx4YknnrB0vQgYWJJs2rQpEPMK60juWQgmuN4Q1Z8ArWxHYDt8shlwIqxQDuWRZW3VqlVh37595jrjT/aS0Q6VIQIiIAIikB0EfO6EGMK8qnbt2uH666+3ORLxr4oqpHs5rJmXEbaAe9hDDz1kQggZarhXkenMxZXsIJiZrZAgkmHnLfEC48IkIFyPHj0sOjGDQAZ8fnGxfUELA1F+Z40Lzvvvv29KKP5x5557brj66qstaw2DTp7i6UlaQST1vQiIgAiIQHEJRO9n3IcQKTz7CwNP4oqQEhc/ayw9CCT+4IMP2kOA1q1bhwceeMAi8/NAoH379haPhEj9Y8aMsRfbk+oXdxnik3AfK8q9sbjt0PYiIAIiIALZQYD7Eg+CcanEMoTQAri0EPzbXTmjc6vo+ygBvmfeRBiDDz/80MpDpMcyhBTv3N+II8I9SUv6CUgQSf85KHYNuMiiL1xbXnjhBbvIuHgJskokZOKAMMgsaKEMF0X8wkUR3bp1a8C0GH85LlwGmOTbxg9bokhBNPW9CIiACIhAcQhE72PR99yXGJDyRA2XmXfffdcsQxigEm+EJ2y4wTC4xG10wIABFuCOBwLz5s0zCxJEEJ68IbBgisy9K3oM3msRAREQAREQgSgB7hXcPwicysPhevXqmZsMgn30HsI+/jm6v39PIFZcYRYsWBDGjx9v86pRo0aZwM+DZtLtRudgBZWVWLY+lw0BCSJlwzWlpXJBEaCHrDO33367pYPymCIMBPMb+PmFF11TaT7TGSB+YIKMGw0RkAkiRKop/LL9Ak5pI3UwERABERCBrCIQvf9E39PI6GfuOQxGsWQkExrWHrwQS7j3scb1EwGFQSjb5ieARMvMKpBqjAiIgAiIQKkJcK/hwTAWIRdccIHNp+bMmWPiRX73j8Tv+Mz9hznU8uXLrRweVNesWTMghmzevNnK8sQVbM+SWE6pG6ICik1AgkixkcVvBy4kBn8MCmfNmmVqJml1sfJINPE60kUX/R3TMGKUIIpUqlQp3HjjjZayF1UzOtiMHxHVSAREQASKRoA+T4sIiIAIiIAIiEBuE0CoQLS4+OKLw+mnn26Zz5hb+dwIOv4+ukZIYV/cMrEuIf4VFibEZSSTDKnlCUsQjcno++c28fi0XoJIfM5FiWviFxUXJObBBI4jtSCZY/CrJgAdiie/+7asExe+YxsW3w6l01P0kicbXzosRXDTiZaXWJY+i4AIiEBcCBTU38WlfqqHCIiACIiACIhAeglgYcgc57jjjjMxg+DdUWsOnxv5/Ic1MUCYY+HaScaYxo0b2/yrTp065tZJ0G+sF9nW9/Ny8hubpJdA7h5dgkgWnHu/sKIX5pYtWyzgHKZaBJx76qmnLNWTu9AUdhF6eaDhPYomAYGwPkEUOe+88yxVr4siWYBQTRABEchiAtE+jWZGP/NeiwiIgAiIgAiIQG4TwAKeB8pHH310uO222ywrTFTEgI7PtbAGee+998Izzzxjgb4bNmxoViF33nmnWdYTNPXjjz+2oKpuVc/+Pv7wdW4Tj0/rJYjE51yUqiZ+YbHmwkPlRK0kOv+wYcPCww8/bMolKZ4++OCDPMUz8aDRcqLvsRQhew1+dSeffHLAJYeyUEXZTosIiIAIxJWA92UMZIj4ThwK4lH493Gtt+olAiIgAiIgAiKQGgJY2Xfp0sUEEQKqEsSbuQ/ZYBA3SDpB5jLEjgkTJti2CCCEFMBFhvTuZP5MTO+eONbwz6y1xIOABJF4nIek14KLDBHj4MGDYfv27WbdgaUIJlxc7KQyJAgd2yRekP6ZdfSFyEJk5Pr164ezzjrLMtC8+eabJq4kvQEqUAREQASSRMD7MazdsJ7Dv5dAaQQ+i6Zh9e18naTDqxgREIEkEPDrMr91EopXESIgAjlOgNiJZO2sUKFCKFeuXKhYsaJZjPTq1SvwuueeewKWIB06dAhNmza1V9euXS2LDEFUyWzGw5aoRUiOI82Y5ksQyZhTVfyK+qCBSQBqJdYi+LYRIJWUuqibBE1FNHFXGo7i+/naj8xnTMRIfYjrTPny5S1QEL5xWkRABEQgrgS8L2OwQ4yl1q1bh+rVq5swwpOfgkSRuLZH9RKBXCPg13BB61zjofaKgAgknwBCBuEApk2bFmrXrh0uvfTScNFFF4Vbbrkl3HXXXaFly5YWm7F///62zdKlS8O2bdvsATPji0T3muTXUCWWFQEJImVFNs3l+qCBavCeAT8DfxTMAQMGmMLJxY7KSRAgLD1IqYvgQQChgi5qOgt87Nq2bRtOPPFEsxbBNSe6cDwtIiACIhAXAt4f0g/iMogbIdHfq1SpEmbPnn2ItZxvq34sLmdP9RCBf41jGJfw4gHODz/8YEHko2KmOImACIhAaQnQxzAXwrr+2WefDWPHjjXXGR4Gr1y50rJ3EleRh8FY2UfnS4wb/HNp66H9U0tAgkhqeafsaPkN5vmOgQTCx5IlSyzoD6IIr44dO1qObFxp9u7da7FB2BZxxE2//EKnAxgyZEg44YQTwrXXXmu+dPkdL2WN1YFEQAREoBAC9E/+ol9DFBkzZkyoXLlyIPA0UeU/+uijPBdC37aQIvWTCIhACgn4Ncn1u2fPnjB9+nQTM/H59zFKCqujQ4mACGQpAfoaRA1e9C3Meeh3EF+9r/H+KLoGR+LnLEWUlc2SIJKVp/XfF2X0AvX3XORc2Agjr7/+uj0tJbYIZmE8NSXCMoMNrEYQR7AsIX4I4ggdA+Zk9913n6WlIg0vwVXpBLSIgAiIQBwJRAcpvGdQQ782aNAgM4mlH0PkRRTxpzustYiACKSHQOKYwq9brtHevXuHc845xwRNxBHGJVpEQAREIBkEEscL+X3mOPl9z3daMpOABJHMPG9JqTWiCD5vxBDZuHGjxRQhSFC1atXMXw4/++bNm4cWLVpYdhnMxshWw3ennHJKOOaYYyxI644dO5JSHxUiAiIgAqkgwKAFgffAgQMWDO26666zuEj0cQSbzu8pUCrqpWNkF4HogDm7Wlb2rYmy4z3jlf3791sWB6y6Lr74YrNsjcYAKvta6QgiIAIiIALZSECCSDae1WK0yQcaWIAwESA4EO40xBV58MEHQ6tWrSyVFEFYb7/9drMiOfXUU8N5551nWWZIP4WvnRYREAERyCQC9H08WcZ9ZuDAgRZNnojy9Ht855YiiROzTGqj6ppeAn5/Za2l6AQSrznM1ckORewfHtQQ+wwr1vfee8+uYb9Wi34EbSkCIiACIiAC/yYgQeTfLHLyXXTgwVNRBh4//vijiSO7du0yy5Fly5ZZisopU6aEPn36hH79+tlnLEMIbCbT8pz866jRIpDRBHwShSiyc+dOCzZ9+eWX25Nn0uvxNBorEvpI3zajG6zKp4wA/xkeMhB477PPPsv7H6WsAhl+IB+XMCYhhSWuvZ06dbIsDz179gyMSbAM0fWZ4Sda1RcBERCBmBCQIBKTE5GuajDw8MUHIb5mMMKA45///KdFc//qq68sxzaWJMqz7dS0FgERyEQC9HMudCAEIwAPHz48XHPNNYGYIqNGjTJRhN+8T8zEdqrOqSfAfXP37t1h8ODBFqeGuBd8p6VoBLjecJH55ptvwssvv2yWqgRAvv/++8OaNWss051fu75mHy0iIAIiIAIiUBICEkRKQi3L9/HBf1HWWY5CzRMBEchiAtFJFJYiBJGeMGGCxVCqUaOGxRfBfcZFEVD4Pt4/ZjGeUjctysjfO79SFx7jAvi/MHGvWrVqKF++fJg2bVrggQKTdy2HE0jkghhC8HbSXOIigxiCZci6devyrFJz6f90ODF9IwIiIAIikEwCEkSSSVNliYAIiIAIZCQBJlg8xcfFYfbs2ZZt68477wwTJ060mCJMcv1pNA2Mvs/IBpdxpaMTVlg5r+j3ZVyFtBWPdSXuMmRDOe2000LdunXD6tWrzdrS25+2ysXswPCI/jcQJsmAt2jRotC9e/dQr149S5GNWxvWqmyvRQREQAREQASSSUCCSDJpqiwREAEREIGMJOATM0QRTPXnzZtngaTJQEN6XgI48ptPaH2dkY1NQaV9kgszJrJkNEMocG6ss3nx2DS33nqrxaXp37+/uWA5F+eQzQyK2jZnwX8FIenpp58OXbt2DcTymTNnjmXCw2rEF9/eP2stAiIgAiIgAqUhIEGkNPS0rwiIgAiIQFYQ8EkWaybu33//vaX4vOKKK8IFF1xgE7Q9e/Yc8jSbbbXkT8A5bt26NUyaNCksWLDAmEY5579ndnxLO4m1RQDQSpUqWVpnJvoeiNw5ZEdrS9cKrjcED0RHYvc0adLEUuq+9tprFuQ9UUiDnRYREAEREAERSBYBCSLJIqlyREAEREAEMpqAT1JZMwkjgPSTTz4ZiCfCk/4RI0bYE2x/yp9fYzVZ+xcV+BGThTTGDRo0CJMnTzbLG2ecH7ts+w4G3333nQXrJYMRE30m+e76of/Kv2LyYBmCcIYY0rlzZ/vPwAl2MExcxC2RiD6LgAiIgAiUhoAEkdLQ074iIAIiIAJZS4Cn1gcOHAgvvvhiaN++vU3sx44dG7AU8UCrPsGPrrMWSCENi7afCS6xWGbOnGlxNB555JGwbdu28L//+795MSBKO6mNHi+/94VUNWU/US8m9O+++679f6666qrQsmXL8Oabb9r3pWWQsoYk8UDRcwUbLGZWrVoV+I/gmjZ9+vSwefNmyyTD7759EqugokRABERABETgEAISRA7BoQ8iIAIiIAIi8G8CiCJkCCH9JxkvsBQhHgSTXOJiuLWIT9xyfZJL7AzEkJUrV4aHH344LFy4MLz//vvhl19+OYzVvykX/53z5vzgmsLEGiHGvy9+icnfw+vC/wTXmUaNGoUqVapYkNBvv/02TxxK/pHjW6Iz4VwRPHX+/PmhQ4cOllKXeCGJ/5X4tkQ1EwEREAERyBYCEkSy5UyqHSIgAiIgAkknwASOJ9VffvlleP7550Pt2rVtUjt69Oiwe/duE0V8kpf0g2dIgd5+F0OWLFlirkazZs0Kn3zyiVnTJFM48uOxRgjZsGFDeP311/Pic8QFW7SeBOole1GrVq0se8r69esDvNgmlxbaS7s//fTT8Mwzz4R7773XLK9wTSPFtVsRObtcYqO2ioAIiIAIpIeABJH0cNdRRUAEREAEMoCAT8wQRQ4ePGjuM0zi6tevH4YNG2axDzwmBM3JtQmut9ndZLCkIVUxYkhBVjSlPe1RcQXBZerUqQFXpl27dsXKFcX/O6ypMxlUnnjiidCtW7eAoIY7FhYuufSfcTEEd6p27dpZzBCsRLAqcoHIeUT5lfY/o/1FQAREQAREoCACEkQKIqPvRUAEREAEcppAdELGe495QMDHmjVrWuaQHj16hO3bt+dN5rIZmPPwNvpnuHz99dfhlVdeCUOHDrXsPGQMIc5KVLzw7X3t5bDO77vo79H3vi1rRIWnnnoq9OzZM7z11ltlJjBEj1lQXaLb8J62w4Y1Lyb8WBURnBcx4KWXXspz9eH3bF8Qzfbt22dpdbt37x4eeOABs+xBUKT9UX7Owr/zz1qLgAiIgAiIQLIJSBBJNlGVJwIiIAIikJUEfJLLBG7RokWhadOm4Y477ggjR460iR6TX5/ARdeZDMPbHG1P9D0TWcQQRCI4DBgwIKxbt87ieSROchP3i34u7nvK5rV//34TGO655x4LxukWF0Utz8the3+f35pzy4vyeSV+RvzxF24fxA356aefLG0sbj3+wvVq9erVASENSyPSEROk98cff7QyqUe2LbQJZmSS6d27d6hbt65ZycCB2DJaREAEREAERCCdBCSIpJO+ji0CIiACIpBxBJgwf//99yYC8JS7WbNm5gKBy0Z0Qu4Ny+RJLnXn5SKBCwG+Rgx54YUXwpAhQ8xthYwhsMEaAIsIRALW/pn3/j2iAS8mxQRGRWjiPUICAgJpV4m9gasSMSc+/vhjW5MOmYCcuFkQP6Rv376hRYsWYfny5ZYqmd8RSkj7i0sN22JJ8tFHH9lnAncyOWdfYnmsWLHCguZSd+KfIHYtXbrU3KNw7cDNhbKJU0LcC+JdEE8GMYNtcQ/q16+fpYslUwoWIAhDXbp0sXghHTt2DG3btrXgoVhG8L5hw4bhoosuCmeeeWa48sorw7Rp06y9mfxf8f+7r/1/w3nFegcmd999t/1PyDrEOed/pUUEREAEREAE0klAgkg66evYIiACIiACGUUgKhAw8X/jjTcsDkL16tVtvWnTpkNcRTKqcflU1ie1iAxkSkH8QDTgRZBQJrlM7nnqf99994XHHnssPP744+bGQmwIBAUEA9bE+iC+CJN/hIVHH33UJsfE0xg/fnyYMmVKmDFjhm0/efLkwAuhBXeYrl27mpsJIgMCSJ8+fczlggl2pUqVQsWKFW2yPXjw4PDQQw+ZGIEVBu/Zn8xAY8aMMeGKzwMHDrT348aNs9+ICUNqZcSKxo0bW0YY2lWvXj17derUydLCUibb1qlTx1Lo0mbqQ7Dd22+/3SyGqlWrZmu+w4KoSZMmtg9ZZnCVwZqF9xUqVAhHH310OPHEE826BnEpmwQRRDMyNCEaETcFdvw3du7cmZd1KJ+/nL4SAREQAREQgZQSkCCSUtw6mAiIgAiIQCYT8AmrCwVYMLz66qs2Ob7mmmts4o4owlNx3zaT20vdsXrBvaFz585mDYOVAwJB1apVw4UXXhjOP//8QNtr1apl4kiNGjVC8+bNzToCkYHJMEIGLiKIDfzGd3xGgKA8BAqsLLCuQBjB0oJAqQghbN+mTRuzAqEc9mFfxIUGDRqESy+9NJx77rmWwcUFEKwyECt69eplggjlI7BQ/qhRo8zqgwCwiDzE8uA7fsf6Y/jw4SakIPYQOBfRBBEHMejZZ5+1ST3CDuIN3xE7Zd68efYZkYcX2yMC8XrxxRdNQMLqBNciLFL4zyAQ3XbbbeGKK66w7bNFEOF/jxUQ1jlY0nAOOGcIY1jt+LWRLddHpl/fqr8IiIAI5DoBCSK5/g9Q+0VABERABEpMwJ+CM7FmEo6VAE/CeQrOxC8bXAJoI4FjEQaY3CIYtG7d2oSIKlWqmFiBEIF4gEUHVhpsy4R/+vTpJiJgJYBogECACwrWJQgFiBK4qrz55pvmwoIbC++JQ4KwtHLlShMPcFnhxfesEWhwd8FtBbGEesyZMyds2bLFXm+//XZ45513zDUG9wyCmZLlhQk5ayxeECCw8uHFZ1xzsGhw9xpcbHDLIe4H3+PCw+vbb7+1F+9x78H1gxduPvyGSEaZfCY2CG5AxBXh5S5EvGdbAsK2bNnSeFFHhASEgkwRC6J19fe4QeGWhGCEgHX//fcHrIU8BXOmtK3EnYJ2FAEREAERyCgCEkQy6nSpsiIgAiIgAnEjgGDAxJgJPFYJiCIEGN28ebNNiBNFkUyaEEYnuYgDO3bsMKsIrEUIKouwQUYZBAVidSAeICwgCiAYIAogCDBJRiDyeCEuEiAAEF8EKxReHmvEv2Pt730b1jCHK7FFcNNBjEIMYVu+93pH13H733j9ceXB2gXxCMbR+setzl6fKNfoe4QeYulg3cN/BHHwueees/8D50yLCIiACIiACMSNgASRuJ0R1UcEREAERCBjCEQng0zyCR6JxULlypXt6ThWDHwf3Y73mbBE68xkFoEDaw4sRIibgbsIVhYIFNE2+X7eRv/sa/8+ui7st+h2vGdbXyPA4IqBywvCDHWJCgrFKTfxOKn4DFeEHILz4gaE+w3/F76Pa929XtE1zBG9sIzCOqhVq1YW54X/C6KYb5sKpjqGCIiACIiACBSHgASR4tDStiIgAiIgAiIQIeATPV9j8bB27VqLpUH2EGJtbNy4MeNcIbyJTHR54fqB2wsBQYnpgRjCxN3FB9/eOfCZ97727xPX+e3n30XXvl+0PI6NIIMFAulccbXBQsSPG90/ru+pK240ZLAhrgrCCP+XOAsiieeAutIGLKQIkEs7cJ/ifCCSJP5H4nouVC8REAEREIHcJCBBJDfPu1otAiIgAiKQBAKJE3Umf7iGEL+CQJLXXXeduXNk6mSd9iGGLFy40Nw6yLxC0FDcYmirL1EO/l107b/7Ovqbv+e3whb/3ctgTRwOrComTJhgcUKwEMmkhTbAEVcZYm7gcoW7FS5IUb5xa5OfA8QQLIeI6+KCDu0gVgtiiG/n67i1Q/URAREQAREQAQki+g+IgAiIgAiIQBIJMPnDemLNmjVmIVKzZk1L+YprRDRopk8SfZ3EKpSoKK+Hr5mQ0w4sQ8j2QpwOsrDs37//MDeZEh2wlDtRT1xmiL2BZUUmi05YWOzZs8eyzZB1hwC0BGrlHPj5iK5Lia5Eu3N8Fq8H4hNxY+bOnWv8CZ5K0Nx9+/bliSElOpB2EgEREAEREIEUEpAgkkLYOpQIiIAIiED2E2DCyESWTCNkSSGwJJlE+vfvbzFGEie6EPHJZjrp+ESXNU/+CRSL9QViCNYuCA+IIYmiTrrqTD2xrHjkkUfMegVXpUx0mXHu/C/4v8CbgKQIaon/Fd82ncypAwIO2XoQQxBCqO/ixYvDxx9/LDEkXSdHxxUBERABESgRAQkiJcKmnURABERABEQgfwJMGBFEeOFOwEQdC4YaNWqYxYgHmoxbnAifbFMv3GSYkHfo0CE0btw4PP744+GDDz7IE0NouW+fP4XUfItrCXXDeiVTBREnBXfa88wzz1icFgQ0rEYQH5y1r32fVK05Lgv/aayGCJ46ZcoUc5Mh5TJWRKQmdkHKt09V/XQcERABERABESgpAQkiJSWn/URABERABEQggYBPWH3NBJIsGwTK7NevX6hSpYpZjGzYsOGQp/8JxaTlI3Wmvogh1G/QoEE2MWfi+/777wdSqnq7qGD0faorzLFZcJmhfgR7RcBhQp7JC9Y3uJyMGDEiNGjQIDz11FMmkngmn3Qx9+NSP+LjEDQVsWzw4MHhjTfesP94VODz7TP5XKjuIiACIiACuUFAgkhunGe1UgREQAREIEUEfLLO4Xxi6ClJH3zwwdCkSRObUDKxzC9TS4qqedhh/Ok/sTh46k82mfHjx4dPPvnksCf/3q7DCknhF9QBiwpcZkjzirtJpgsitIn/yttvvx1at25tFkXLli0zwYHzk46FOnFs6sV/YdKkSeaiNGDAAHMBSxTKqCP7aBEBERABERCBTCAgQSQTzpLqKAIiIAIikNEEmCD60/9evXqF6tWrh549e4Z169ZZVhp+90mkr8u6wX5MX+OagUjTp0+fUL9+fUuhirUC9WZJVb2O1G6vB+sDBw6EiRMnmrWCB1U90v5x/x3xgfgts2fPDvfee6/Fntm2bZudB37z9qeiHRwLyw+snOD79NNPh7Fjx5pbz+7duw9x50lFfXQMERABERABEUg2AQkiySaq8kRABERABEQggQATSyazWDAQF2Lo0KFmgdGlSxdLWZoYJyJh9zL5SJ38xaT3o48+spS6uJ/gsuFiCNvEbfF6E6OF+BVYtOCW5K4lcatvcepD22gHYg/iw9133x3GjRtnAUtTIYg4W68Hbknz5883oYz/K+8JnpqO/2xxOGpbERABERABESgKAQkiRaGkbURABERABESgFASik0xcDBAbSGHLBJPJ/JIlS8wlIRUTXm+G1wmR5r333rP6kDEEMQSLhMQJL9vHYfF6sEYQWbhwoVlREPeEtvjvcahrSepA/Xm5xQ5uVmRxeemll8xypKzb58d3iybimBAUuHfv3uH55583oYa6+X/Vty9JW7WPCIiACIiACKSbgASRdJ8BHV8EREAERCDrCUQnsbxnQokIMXr06FC3bl2zFom6z6QCCPVg0rt9+/YwZswYm/Q+8cQT9pnYJj7RjdY9FfU60jG8Xmz37bffmmtJ+/btLe0r7YlbfY/UnsTfvX0IDriqkHWmWbNmJoqsX7++TOOk+LER7bZs2RKGDx9uKaMRRF577TWL2eKMfdtM553IX59FQAREQARyi4AEkdw632qtCIiACIhADAgwiUR0IGbHwIEDQ7169cxSZPXq1eH777+3uA1lMdGMTmKZ9JI9Bvedli1b2uR3x44dZqni28UA1WFV8LqxRhBBMCAAKZYiTNazacGVae/evWHChAmhRYsWdo4+/PDDvP+Hsyhtm70c1vwvOOaMGTMsqCuxbl5//XWzxkl0SfL9Snt87S8CIiACIiAC6SIgQSRd5HVcERABERCBnCbAZPLnn38OiBDEiGjcuHFo27atPYn/5ptvkhoPwyeurLE8YNLLxHratGmhTZs2lhKYoJkE84y6QsTxBEXb8vXXX4fp06eHhg0bmkuJWy/Esd4lrRPWRLt27TJXJkQR2ovlSDTNbUnLZj/nidhBuZs2bQozZ84Mjz32mAVR9f+F/3dKcyztKwIiIAIiIAJxIyBBJG5nRPURAREQARHICQI+ESWdKe4zw4YNC5UrV7YUslg7YP0QFSfYvqSLT2ZdDCGGyaxZsywuBFlaSPOKGOJ14jilOV5J61mU/bxerL/66qswefJky9qzYMECsxDx34tSViZsQ3v++c9/hjfeeMOsRJo2bRqwJEpWymbKJ/YK4hL/u27dulkAVeKFfPDBB4fEkvH/YyZwUx1FQAREQAREoCgEJIgUhZIFx57eAAAgAElEQVS2EQEREAEREIEkEmASGn1h2UCWF2I1XH311RZTZOXKlWbJkYxJqB+LiS9iyKOPPmrZS+bOnZuXMcSP49uyjvtCBhQsGciMQ4yLbHOZgT/ngXODRQ8Bb6tWrWouQliNYD1SmvPEvvwnyGhDmt9GjRrZi/d85y4ybBd9xf1/ofqJgAiIgAiIQFEJSBApKiltJwIiIAIiIAJJIhCdXPp7XCCY9BLIEvcZRIv9+/ebdQATYha2LelCGYguuMkQMwRXma1bt+ZZVXg9ouuSHqus93MOTNrhVatWrfDss8+aQFDWx051+X4+ED8IgEtmoooVK1pckc8//9zEkuLUydmxD4LHJ598YlY2xLFp1aqVuR4hNLkY4mX7fr7277UWAREQAREQgUwmIEEkk8+e6i4CIiACIpAVBHzS6xYcpDodPHiwTXqxFMFlIj8LjoImp16er9kX8WDq1KlmGUJ6XSwqKNe3ySSQ3u4vvvgijB07NtSsWdMm8qW1mIgbAz83rDmHP/74o5232rVrh/r161tmHb4r6hItD1a4auFyROya++67L6xduzYQv4b/oTP2dVGPoe1EQAREQAREIJMISBDJpLOluoqACIiACGQtAZ+sMlHFrYUUuB06dLB0q2T8OHjwYN5Te982PxjR33jPRJon/mRjwSVn0KBBYcWKFZY1xEWW/MqJ63e0yReYPPLII6FOnToB9x+CxUZ/9+0yee3nkzVCBW1G2EIUQTTDdcYFDN+2oPb673AiwxHBfLt3726Zhkj7TBwZD9ZaUBn6XgREQAREQASyiYAEkWw6m2qLCIiACIhAxhNg0kqgVVKfEvgU15Y77rjDBA2CiLorA9sVtPjEl4ky+yCu9O7dO4waNSqsX7/+EDHEty2orLh9H2034gAxRG6//fZAcFi4RX+PW91LUh8/P6wRsDinuD4hhvTo0cNchT777LM8IcO3z+9Y7A8jguiOGTPGBLKHH344bNy48ZAMQ/ntq+9EQAREQAREIBsJSBDJxrOqNomACIiACGQsAZ/QYilCTBFcGm677bbQoEGD8OKLL1o2EBdF8muk7+/WBGQLITNJr169AlYA33//fZ6bjE+yWWfaQp1xmRk/fnwg/gWcslEQ4bz4OfXzxfknPS6iSJ8+fcyNJpolKL/zieXHd999Z/8BgrN27drVRKRt27ZZ+udMtBbKtP+s6isCIiACIhA/AhJE4ndOVCMREAEREAERsEkwrg24z+DacOutt4aOHTtaatSopUgiKibDTJhJ2/vKK6+ETp062evll182MSVx4uuT7cRyMuEzrkCTJk0Kd911l1nQZKPLjJ8HP0++RgDhnPbs2TMMGTIkvPXWW4e5DPm2ZN/BimT+/PlmFUK8EOLUEEPEmfm2rLWIgAiIgAiIQK4QkCCSK2da7RQBERABEcg4AkxOsfTAEoI4It26dbPgl88995zFBfF4D9HJLN9hBbJq1SqzHmjfvr0F38Q6IFEMyTggkUw7tJkAoE8++aQFVYVPtlqIJJ4nP9+4zgwbNsxiqOASRVYiP8e+DWLIxx9/bNmFSKvbuXPnsGDBgkCGGoQzLSIgAiIgAiKQywQkiOTy2VfbRUAEREAEYk3AJ7UucvBUv2HDhqFGjRoWOwNLkegEmPdkHSFo6oABA8yiZPHixSaQuHji28e64UWonAsiTz/9dGjXrl2YM2dOzgkiCBrvvvuuuc4QWHb69OmWetjPMWIasWhI4cz/Bk7Lly/P+z8UAbM2EQEREAEREIGsJiBBJKtPrxonAiIgAiKQqQSY8PvEljWCBk/1sYi48847LW4G7iJYSbjY8csvv1jQ1OHDh1s2maVLl5pAwsTZxRV48D5Tl2jdPeNK8+bNLfOKpyfO1LYVtd7+3+B/8cMPP4QXXnghtGrVKrRu3Tps2LDB3GCIQbN7924Tzrp06WLWQghlbO//h6IeT9uJgAiIgAiIQLYSkCCSrWdW7RIBERABEchoAi5guADA2jOMkDWmSZMmoVatWvb0n1ga7iYzcuRIsxjAMuTrr782UQUQ0fK8zEwEFK07gghBVa+//vowevTogCAS/T0T21eUOkfPJeLGJ598YtYhuMNMmzYtHDhwwCxBxo4dGwYOHGhZhrZu3XpIWt1c4FQUltpGBERABEQgtwlIEMnt86/Wi4AIiIAIZBABJrEeE2Lu3LkWT4QAmVOmTAl87tu3b+jfv78FzySIJpPlbF1gQeBY3EQIOMvkPxcFEc4vgVH37Nlj1iD333+/ZY8hne6ECRPCkiVLLLZIrsRXydb/u9olAiIgAiJQNgQkiJQNV5UqAiIgAiIgAkkn4JYBHmh12bJlFmgVS5GaNWua2wQxNQiiyTbZagXgHAgUi7UMbSdOBi5D2drm6J/J2x9d4zo1b948s5apVKmSiWWIIVgPIaLlApcoI70XAREQAREQgaIQkCBSFEraRgREQAREQARiQCA6AUbwIKvIiBEjwmWXXRYqVKgQunbtGt588808YSCbJ8G0DRHg/7V3H1BSVnn6x8/5786ZOTs7O7M7SXfdnRmd5DjOjI5hdAiCCjIqSXIGkSQ555wzgiBJsqCSRRAJEiU3OdPEBpqGJjUZZ3//89ydt2kaKLrpqq633vrWOXWqusL73vu5hee8j/f+rpaIFClSxHr27GlpaWnpS4R8MFwRa4I3rnpUHRHN/tAWulo29MILL9jjjz/uiqhqpyGvror3nYg1igMjgAACCCAQgwIEIjE4aDQZAQQQQCB+BbyL4IsXL9rKlSutYcOG9tprr1n+/PmtbNmybqaEtmP1Cq0G9UJY/fICkUKFCrlddeIpEFH/dddyGe00o1oqKqpau3ZttwvRiy++aAMHDnT1RSiiGr//vaDnCCCAAAKhBQhEQvvwLgIIIIAAAr4R8C6CtYNIQkKCWxZRuHBhUyFVzQ7Q89dff92mTJmSPkvEN40Pc0NkoRoiI0eOtLx581q/fv1cnzVjIug373egWUL79u2zYcOGWdWqVa1Vq1a2YsUKN/7PPfec/fnPf3bvyUnf4YYAAggggAACtwsQiNzuwV8IIIAAAgj4VkAXtVoesWnTJldAtVy5ctarVy+3dEZb8ioI6dKliy1YsCC9wGgQL4S9Pl24cMGmTZvmQiAVk9WsmXgJRPQ72LVrl6lmTIcOHVwBVYVkWiKj3YUaNGjgls5UqFDBNm/eTCDi23/VNAwBBBBAIJoCBCLR1OfcCCCAAAIIZENAM0NmzJhhRYsWtYIFC7rtdTVDQK9rtoAuhLUFq2YExMMyCV38f/HFF65ehnZViYclMwp8zp8/bzNnznShmHaVmTRpkttlxqsXorFfs2aN23JXs0e0hMoLkbLxc+OjCCCAAAIIBF6AQCTwQ0wHEUAAAQSCIqAL/u7du5uWQ+j//K9fv96FIbrY1V11Q7x7PFwAa1eZRYsW2bvvvuvqZQQ9ENGYKvRYtmyZ1apVy6pVq+aKyiYmJrqZQ3pfgYkeZaFwTNsv6zvcEEAAAQQQQOBOAQKRO014BQEEEEAAAV8KqICmttrVzjLz5883LRnxLoB1EZz5rk7otaDeFIjIo1mzZm77Xf0d5CUzXtAxd+5c69ixo1sipTBEv4vMY+/97f0+gvoboF8IIIAAAgjkRIBAJCd6fBcBBBBAAIFcFNBFri76z549m1401bvw9R695nh/6zGoN2+2hOqHqH6Kt2QkqP1Vv7Q0SktgduzY4ZZIeUujMo9zxr8zPg+yDX1DAAEEEEAguwIEItkV4/MIIIAAAgggEDUBXdx7dwUg2npYu6u8//77cVVUlZkfUfsJcmIEEEAAgQAJEIgEaDDpCgIIIIAAAkEX8MIQ9VOByOLFi61mzZrWunVrO3fuXKCXzGQeW2Z+ZBbhbwQQQAABBLInQCCSPS8+jQACCCCAAAJRFMgYiKhw6KxZs6xy5co2YsQIt4woyDVEPPaMBt5rPCKAAAIIIIBA9gUIRLJvxjcQQAABBBBAwAcCmiGyYMECK1u2rHXp0iVulsz4gJ4mIIAAAgggEAgBApFADCOdQAABBBBAID4EMi4TUYFZ7bjy+uuvW7t27QhE4uMnQC8RQAABBBAImwCBSNgoORACCCCAAAIIRFogcyAyZ84cK168uLVt2zZ9G+JIt4HjI4AAAggggEAwBAhEgjGO9AIBBBBAAIG4EMgYiFy5csW++uore/vtt90MkfPnz8dVUdW4GHA6iQACCCCAQAQFCEQiiMuhEUAAAQQQQCC8AhkDkWvXrtm6deusffv21rVr17jbZSa8shwNAQQQQACB+BMgEIm/MafHCCCAAAIIxKyAF4joUYHIpk2brHv37ta3b1+WzMTsqNJwBBBAAAEEoiNAIBIdd86KAAIIIIAAAg8gkDEQUVHV+fPnW7Vq1VwgcvHiRZbMPIApX0EAAQQQQCBeBQhE4nXk6TcCCCCAAAIxKOAFImp6WlqazZ4920qUKGEtWrRgyUwMjidNRgABBBBAIJoCBCLR1OfcCCCAAAIIIJAtgYyByOXLl23hwoWuqGrHjh0JRLIlyYcRQAABBBBAgECE3wACCCCAAAIIxKTA1atXbdmyZVazZk3r168fNURichRpNAIIIIAAAtETIBCJnj1nRgABBBBAAIEcCGjb3aVLl1qdOnVs+PDhRg2RHGDyVQQQQAABBOJQgEAkDgedLiOAAAIIIBAEAc0QWb16tTVt2tSGDRvGDJEgDCp9QAABBBBAIBcFCERyEZtTIYAAAggggED4BLTt7qpVq6xu3brWqVMnO3v2rH3zzTfhOwFHQgABBBBAAIFACxCIBHp46RwCCCCAAALBFfACEdUQadasmaWkpBCIBHe46RkCCCCAAAJhFyAQCTspB0QAAQQQQACB3BBQILJ8+XJXVLVLly6Wmppqf//733Pj1JwDAQQQQAABBAIgQCASgEGkCwgggAACCMSjwPXr123FihVWpUoVt2SGQCQefwX0GQEEEEAAgQcXIBB5cDu+iQACCCCAAAJRFLhx44Zt3rzZWrRoYb1796aGSBTHglMjgAACCCAQiwIEIrE4arQZAQQQQAABBEyByJo1a6x+/frWvn17O3PmDEtm+F0ggAACCCCAQJYFCESyTMUHEUAAAQQQQMBPAloys2HDBmvcuLF1796dGiJ+GhzaggACCCCAQAwIEIjEwCDRRAQQQAABBBC4U8BbMqPZIaNGjbLz58+zy8ydTLyCAAIIIIAAAvcQIBC5BwwvI4AAAggggIC/BbxARDvMDB061NUQYZcZf48ZrUMAAQQQQMBPAgQifhoN2oIAAggggAACWRb45ptvbP/+/S4Mad68uSUnJ9vNmzez/H0+iAACCCCAAALxLUAgEt/jT+8RQAABBBCIWQGFH1u3brXWrVu7GiIUVY3ZoaThCCCAAAIIREWAQCQq7JwUAQQQQAABBHIqoCUzKqrasGFDGzhwoKWkpFBDJKeofB8BBBBAAIE4EiAQiaPBpqsIIIAAAggESUCByPr1661GjRrWsmVLO3HiBIFIkAaYviCAAAIIIBBhAQKRCANzeAQQQAABBBCIjIACkdWrV1vJkiWtYsWKduzYMWqIRIaaoyKAAAIIIBBIAQKRQA4rnUIAAQQQQCD4AgpEVqxYYUWLFrUSJUrYoUOHCESCP+z0EAEEEEAAgbAJEIiEjZIDIYAAAggggEBuCigQWbt2rZUtW9ZKlSplBw8eNL3GDQEEEEAAAQQQyIoAgUhWlPgMAggggAACCPhOQNvu7tixw9UP6dixoyUlJTFDxHejRIMQQAABBBDwrwCBiH/HhpYhgAACCCCAQAgBBSIHDhywQYMGWadOnQhEQljxFgIIIIAAAgjcKUAgcqcJryCAAAIIIIBADAgoENm+fbs1a9bM3n33Xdu/f79dv349BlpOExFAAAEEEEDADwIEIn4YBdqAAAIIIIAAAtkWuHnzpm3YsMFtu1u5cmVXVJUaItlm5AsIIIAAAgjErQCBSNwOPR1HAAEEEEAgtgUUfqxfv94FIpUqVWLb3dgeTlqPAAIIIIBArgsQiOQ6OSdEAAEEEEAAgXAIaIZIQkKC1apVy6pUqWKHDx9ml5lwwHIMBBBAAAEE4kSAQCROBppuIoAAAgggEDQB1RDZvXu3NW/e3AUiiYmJ1BAJ2iDTHwQQQAABBCIoQCASQVwOjQACCCCAAAKRE1AgsnXrVqtWrZoVLVrUdu3aRSASOW6OjAACCCCAQOAECEQCN6R0CAEEEEAAgfgQUCCyefNmK126tL300ku2bds2u3btWnx0nl4igAACCCCAQI4FCERyTMgBEEAAAQQQQCAaAgpEtmzZYnXq1LG//e1v7jmBSDRGgnMigAACCCAQmwIEIrE5brQaAQQQQACBuBdQILJ9+3Zr0qSJqyGyc+fOHM0Q+d///V/LeI97YAAQQAABBBAIuACBSMAHmO4hgAACCCAQVAGvhkjt2rVN2+4qHMnJDJGMYYj3PKh29AsBBBBAAAEEzAhE+BUggAACCCCAQEwKKBDRtrvly5e3YsWKuQKrV69efeC+KAT5+9//bjqu7vqbGwIIIIAAAggEV4BAJLhjS88QQAABBBAItIBCCxVVrVChgr3xxhuuqGpOA5Hr16/b6dOn7cSJEzmabRJoeDqHAAIIIIBAQAQIRAIykHQDAQQQQACBeBPQbI49e/ZY27ZtrWLFijneZUYzQpKTk2369Ok2YsQI279/f7yR0l8EEEAAAQTiSoBAJK6Gm84igAACCCAQeYHcqr+hQGTfvn3Wpk0bt8uMls/kdIZIYmKiC1i0BOfjjz92S2i8/rCEJvK/Hc6AAAIIIIBAbgoQiOSmNudCAAEEEEAgDgQyBgiRDBEUiOzdu9fq169vBQoUsPXr1+c4EElJSbHBgwdboUKFrFevXu54Oo/XpzgYPrqIAAIIIIBA3AgQiMTNUNNRBBBAAAEEckdA4cGNGzfs8uXL7jFSoYiOqyUz2mXmmWeesTVr1tiVK1ceuJM63qVLl2zGjBlWsmRJN/PkwoULt80SeeCD80UEEEAAAQQQ8J0AgYjvhoQGIYAAAgggENsCmlGxe/duW7RokWkJisKRSNx0Hm21q/ohTz/9tK1evTrHgYjaunbtWjfrpEmTJnbw4MH0HWciFexEwoZjIoAAAggggMD9BQhE7m/EJxBAAAEEEEAgiwIKDVTHY8KECdaqVStbvHixmymSxa9n62PaZWbLli1ul5k8efK4IEPnVhvuFl54r3uPmU+m1xWyHDlyxMaMGWMtW7Z0IYt2nvG+c7fHzMfhbwQQQAABBBCIDQECkdgYJ1qJAAIIIIBATAgoUDh37py1bt3aypUrZ3Pnzg1LIKIgQjcvkNBznWvbtm1WqVIle/nll23jxo0ujPE+4z1m/J73mveY8T0dT/ezZ8/avHnzXCAybdo007IZBS3eXbNIvM/qONwQQAABBBBAIDYFCERic9xoNQIIIIAAAr4UuHnzppthUadOHatRo0b6DItwNNYLMbxHhRJaktO+fXsrXbq0bdq0yS2Z8cIKzSDRXW3So4IM3TXjQ/dr166lhxx6fvHiRRd+HD161O0woz507drVVqxY4eqTrFq1yp3j0KFD7vteO8LRN46BAAIIIIAAArkvQCCS++acEQEEEEAAgcAKKHDQVrht27a1gQMHuhocCihycvOCh8yPOq5XVPW5556zL7/80lJTU12woVkeZ86cMe0ac+rUKVPIsXnzZhfQfPXVV/b555+70ENLe+bMmWMLFiyw4cOHW8+ePa1jx46uLsmf/vQne+yxx+ypp56yv/71r6ZlOSrgqqKrOqbXnpz0je8igAACCCCAQPQECESiZ8+ZEUAAAQQQCJyAlpVo+9v33nvPlixZ4pafKDjIePOChIyPmsGhWRq6a6eYtLQ0F24o0FCwofuxY8fcEpmVK1fawoUL7bPPPrMhQ4a4HWZ+9KMfuaUz/fv3ty5durhQQ48NGzY0vda9e3crU6aMFSlSxIoXL+5mlLz66quWL18+e/PNN91r1apVs6pVq7rPlSpVyp544gl76KGHXMHWYsWKmV7TMZctW+Z2o8ncr4x95DkCCCCAAAII+F+AQMT/Y0QLEUAAAQQQ8I2AF2JodoaWomRchqIwQwGG6m4MGDDAFFwcPnzYTpw44ZbR7N2713TX0hYVQ9U2udoZRo/Tp093IYoCjh49ergAo3PnzubdNeOkZs2a9vbbb7u76pOULVvWXnnlFfvpT39q3/3ud+355593oUWJEiVc/RIt2Slfvry98847VrduXff9Ro0aWadOnVz7Bg0a5M45evRomzRpkqsbopkius+fP9/69etnBQoUsFq1arnZJ5phoiU6mn2iAMez8M3g0BAEEEAAAQQQyJYAgUi2uPgwAggggAAC8S2gEECzQLQ1rXZimThxogtAZs6c6ZagKFyoUKGCvf766/buu+9amzZt3GwN7TjTtGlTN2NDszDq169v7dq1sw4dOphCCm2dq5BDszh019+asaElKprloSBEr+k4CkcUlGh5i777hz/8wR599FFr3ry5ffDBBzZ+/HibOnWqm0GicEMzVRS8rFu3zs0wUSijoEYzThTWJCcn2+nTp10xWBVQVS0RLb3Rd9QXtVfFW9VvBUHMDInvfwP0HgEEEEAgOAIEIsEZS3qCAAIIIIBAxAU0M0IBggqOKohQfQ3N0lCIUa9ePTdD41e/+pXp/swzz7gZFq+99pqVLFnSqlSp4kIOhQwKSrSspm/fvi7c0KwN/a1AZdy4cTZlyhRXq0O7vSxdutQtU1HtD83S2Llzp+3fv9/VJ9G2vkWLFjXVENGONsePH08PNi5duuRCDM1c0UwWzWhRoOGFGt4Mj8yPQtRnNRtE/dTxly9f7nbLyRyGZP474gPACRBAAAEEEEAgbAIEImGj5EAIIIAAAggEW0AX/woKFDpo9saTTz5pefPmdUtXNONDu71oNsdLL73kdphRvQ2FHAo4NINEMzW0Y4tmlyjQ0OyMpKQkN1tDx/QKomqGhsIM1RLxwgwFMbpnDDT0d0JCgqsBonBGS3QuX76cvpQlc9CRlb81gt7nNGukd+/eplojmnGipTJ6L+Mt898Z3+M5AggggAACCPhbgEDE3+ND6xBAAAEEEPCNgBcUKKTYvn27251F9T+0q4x2cdEyFBUcVe0NzahQIVQtM9HsjMxhRsZOecf1wgXvUZ+523ve+wpHVI+kUKFCbsmMZoioGKt3877r/e0dz/vbe987Xsa/9VzBzKeffuoKr6oo65EjR9IDEe+z3rF4RAABBBBAAIHYEyAQib0xo8UIIIAAAgj4RsALBvSoGRTazlbhgZa2KAzR65G66di7du1yu8toRxjNQskYiOT0vNevX3dFYFW/RMuBNm7c6MIdr0/eY07Pw/cRQAABBBBAIDoCBCLRceesCCCAAAIIBEJAoYDumgGiWSLDhw93u8QcPHjQFChEMjTQDBEtmdESnX//939359aym3Dd1CftmqNlQG+99ZYrGquiq9wQQAABBBBAIBgCBCLBGEd6gQACCCCAQFQEvEBEy2K0pGT27Nlu5xnV31CgEOlAREtmVMfkX//1X10golkq4bopcFEtE+2Eky9fPjfzRTVPMt4i2b+M5+E5AggggAACCIRfgEAk/KYcEQEEEEAAgbgR8AIRFTPdsGGDjRw50mbNmuWWrihQiGRgoGOrlkmRIkXse9/7ntty99y5c2Gz1/FVL+Xjjz+2PHny2DvvvOO23/X6Fcm+ha0THAgBBBBAAAEE7ilAIHJPGt5AAAEEEEAAgfsJKBTQ/fz586Ytclu3bm0LFy5Mrx8SydBAx962bZu9/vrr9vDDD9uIESNcO+7X5uy8r111VDtE5yhXrpzbyUazYbx+Z+dYfBYBBBBAAAEE/CVAIOKv8aA1CCCAAAIIxJSAFwxoR5np06db27Zt3ba6Xv2QSAciqlWic1aqVMkWLVrklriEE1CzQbQlcIMGDdw51Ecto/H6Hc5zcSwEEEAAAQQQyF0BApHc9eZsCCCAAAIIBEpAwYBCgxMnTtjUqVNtwIABppDCqx8SyUBEkFeuXLFDhw7Zzp073ewQzegI50190zm0FKhKlSo2ePBgO3XqlOszoUg4pTkWAggggAACuS9AIJL75pwRAQQQQACBwAgoFFD4oVBi8uTJNm7cONNOL7kViHiBTKTqenj90/a+HTt2tG7dutm+ffvcDBGdkxsCCCCAAAIIxK4AgUjsjh0tRwABBBBAIOoCCgxUU2PHjh02duxYmzFjhptR4QUUudFAtSHjPZzn9I67Z88ea9WqldWsWdM+//xz00wUvccNAQQQQAABBGJXgEAkdseOliOAAAIIIBB1AYUC2mFm5cqVblnJqlWrAhUWeIGIlsn06NHD3nrrLXv//ffdLjree1EfBBqAAAIIIIAAAg8kQCDyQGx8CQEEEEAAAQQkoFBAS2S0w8yHH35omkkRpKDA64tCnwkTJljx4sXdTjqqmaL3uCGAAAIIIIBA7AoQiMTu2NFyBBBAAAEEoi6gpTGHDx+2SZMm2fjx411xVTUqSGGB+qIlMosXL7batWtb8+bNbfv27emFVaM+CDQAAQQQQAABBB5IgEDkgdj4EgIIIIAAAghIQMVTt23b5nZfGTNmjGn73aDdFIion3v37rXevXtbw4YN3Ra/1BEJ2kjTHwQQQACBeBMgEIm3Eae/CCCAAAIIhFHg+vXrtnTpUrf7ypQpU1xtDe/wQZgloj5495SUFBsxYoS1a9fOZs6c6YrHBqGP3njxiAACCCCAQLwJEIjE24jTXwQQQAABBMIocP78ebdUplmzZjZnzhy3tCSMh4/6obzAQ4+XLl2yJUuWuO13+/btaydPnnTLZqLeSBqAAAIIIIAAAg8kQCDyQGx8CQEEEEAAAQQkoFBg6DQYed0AACAASURBVNCh1rVrV1uzZk2gaodkHmHVS9HyoAYNGlj58uVt48aNbilN5s/xNwIIIIAAAgjEhgCBSGyME61EAAEEEEDAdwKaNeHV1RgwYIDt378/0IGIBuDQoUNuhkj+/PndrjpaMsQNAQQQQAABBGJTgEAkNseNViOAAAIIIBB1Ac2YWLlypduGVrNEjh8/HvU2RaoBCn90P336tA0bNswUiHTp0sW0Ha9e54YAAggggAACsSdAIBJ7Y0aLEUAAAQQQiIqAFwp4J79x44arG9KiRQvTDjOpqaneW4F9VB2RefPmWfHixd3SmVOnTgWubkpgB4+OIYAAAgggkEmAQCQTCH8igAACCCCAwN0FvEDEmxFx8eJFGz16tJshMnfu3LiYLaGtdlVHpHHjxlamTBnbtGmTXb169e5gvIoAAggggAACvhYgEPH18NA4BBBAAAEE/CPgBSJqkZ4nJydb//79rWfPni4YUFjghSX+aXV4W6L+JSUl2aBBg6xYsWJuhkxaWtpt/Q66QXhFORoCCCCAAALREyAQiZ49Z0YAAQQQQCCmBHShn/F+4MABt7uMCqomJibeFgrEVMey0Vj1/+zZs/bpp59ajRo1bMSIEW6pkOqpeDbZOBwfRQABBBBAAIEoChCIRBGfUyOAAAIIIBCLArrwVwCwatUqV1h08uTJbvvdWOxLdtusvquQ6urVq61SpUpWu3ZtUzCkeip6TzfvMbvH5vMIIIAAAgggkLsCBCK5683ZEEAAAQQQiHkBXfArAJgyZYo1bNjQPaqgarwEAVoapBBExWSrV69ua9eujYv6KTH/w6UDCCCAAAIIZBIgEMkEwp8IIIAAAgggcHcBBR66f/PNNy4AmDp1qnXu3Nm++uqruAkE1H/NjtH2u6NGjbK8efPaBx98YCkpKemBULwEQ3f/lfAqAggggAACsSNAIBI7Y0VLEUAAAQQQiLqALvY1Q0IzQlQ7pGvXrrZ169bbloxEvZERbIDCEN3Pnz9vM2bMsGeffdZatWrlaqjodfkQiERwADg0AggggAACYRQgEAkjJodCAAEEEEAg6AK62NdymYMHD1rHjh1t8ODBLgzQrJF4CQPUzytXrtiaNWssf/78Vrp0aVdT5Nq1a4QhQf8HQP8QQAABBAIlQCASqOGkMwgggAACCERWQGHA9evXbcOGDdayZUubOHGinTp1Km7CEE9XodCRI0esRIkS9sILL5gKy2rWiHy4IYAAAggggEBsCBCIxMY40UoEEEAAAQSiLqCLfS0LuXr1qpsd0a1bN1u8eHF6EBBPYYActP2uCqs+99xz1rdvXzt+/LjziSeHqP8oaQACCCCAAAI5ECAQyQEeX0UAAQQQQCCeBHShr6Uxmgkxbtw46969u23atMkFJHrPu8eDifqqYGj27NmWL18+a9Kkie3Zs8cFIvHQf/qIAAIIIIBAEAQIRIIwivQBAQQQQACBXBBQCKCCqmfOnLEJEya4QGTXrl3pBVXjKRARt5bNJCQkWMGCBa148eK2cuVK5yMHbggggAACCCDgfwECEf+PES1EAAEEEEDAFwK60Ff9kP3791vv3r3tk08+seTkZDdrxAtDgh4GeP3UgGjZjOqnVKtWzYoUKeJ2nbl8+TJ1RHzxa6URCCCAAAII3F+AQOT+RnwCAQQQQAABBP4hoGUi27Zts/79+9vatWstLS0tbgMAhSPy6NmzpxUrVsw++OADtx1x0EMh/jEggAACCCAQFAECkaCMJP1AAAEEEEAgwgK60L9w4YItWrTIhQBbtmxxgUCET+vrw2uWyLx586xcuXLWqlUr27dvX9wGRL4eKBqHAAIIIIDAXQQIRO6CwksIIIAAAgggcKeAt0REBVXbtm1r27dvt2vXrt35wTh7RXVUqlatalWqVHF1ROTEDQEEEEAAAQT8L0Ag4v8xooUIIIAAAgj4QkAFVQ8dOmS9evVysyESExNdYVFfNC6KjUhJSbF27dpZ6dKlXV0VQqIoDganRgABBBBAIBsCBCLZwOKjCCCAAAIIxLOALvQ3bNhgjRs3tr59+5qCAGZDmFs2pAKzdevWtX79+rlCs97vhHoingSPCCCAAAII+E+AQMR/Y0KLEEAAAQQQ8KWA6ofMnTvX3n33XVc349KlS9TL+MduM3v27LFu3bpZ586dbffu3ekuBCK+/CnTKAQQQAABBJwAgQg/BAQQQAABBBDIkoC2mB09erRVr17dFixYYFeuXMnS94L+IYUeBw4csBYtWjibJUuWpG9FrL4TigT9F0D/EEAAAQRiVYBAJFZHjnYjgAACCCCQiwK6qD969KgNHjzYLQ3ZtGlT3O8w4/HLRsuHtIyoVKlSNnz4cBcW6XXCEE+JRwQQQAABBPwnQCDivzGhRQgggAACCPhOQLVCtKXs0KFDrXfv3nbs2DEKqv5jlBR6aLaMZs1ot5n69etbUlKSC0MIRXz3U6ZBCCCAAAIIpAsQiKRT8AQBBBBAAAEEMgt4MxxUUHXjxo3Wv39/Gz9+vKl+yDfffJP543H5t4wUGG3ZssUaNWpkFStWtISEBGaHxOWvgU4jgAACCMSSAIFILI0WbUUAAQQQQCBKAmlpaTZ//nxXNPSzzz6z69evs8PMP8bCC0RUR6RDhw5Wvnx5V3xWgZEXKEVp2DgtAggggAACCIQQIBAJgcNbCCCAAAIIIPB/RUFVI+Pjjz+2QYMG2ddff31b0dB4N9LsEAUfp0+ftrFjx1rp0qWtV69edvnyZUKjeP9x0H8EEEAAAV8LEIj4enhoHAIIIIAAAtET8GY36PHgwYM2cOBA69ixo+3atSu9Pkb0WuefM8tH96tXr7qwqGXLlta8eXPTrjw3b970T0NpCQIIIIAAAgjcJkAgchsHfyCAAAIIIIBAZgFd1G/evNl69uzpaogcP36cQCQDkheIyGnHjh2uqOorr7xiGzZsMNVe4YYAAggggAAC/hQgEPHnuNAqBBBAAAEEoi7gXehrBxXVD9HskJEjR9q5c+ei3jY/NcBz0qO2JlZwVLBgQZs6daqp9ope54YAAggggAAC/hMgEPHfmNAiBBBAAAEEfCHgXeifP3/eJk6c6JaBTJ8+3S0N8d7zRUOj3AivhohMFBap6GyDBg3svffes9TUVOqIRHl8OD0CCCCAAAL3EiAQuZcMryOAAAIIIICAEzh58qQNHjzYmjZtaosXL04vqMrMh//7gXjhkB5VR0Tb77Zv394FSImJiXbjxg1+SQgggAACCCDgQwECER8OCk1CAAEEEEDALwK6yNd2sloG0r17d9u2bVt6/RACkVuj5Floq10VoNXyIm2/u3LlSrt06dKtD/IMAQQQQAABBHwjQCDim6GgIQgggAACCPhLQBf5Wg6ydetWGzJkiE2ePNltLavXvbu/Whyd1nhhiM6u58nJyTZgwAArUqSIjRs3zs6cOROdhnFWBBBAAAEEEAgpQCASkoc3EUAAAQQQiF8BXdxruUdCQoKNHz/eFi5caJcvX3YgGUOA+BW6e89Vc2XGjBlWtGhR69GjhyUlJVFY9e5UvIoAAggggEBUBQhEosrPyRFAAAEEEPCngAIP3bXDzLp162zOnDkuGLl+/bo/G+yjVilE2r9/vyus2rp1a/dcS2m4IYAAAggggIC/BAhE/DUetAYBBBBAAAHfCCgQOXHihNtqd9SoUbZjxw5XUNU3DfRpQ27evOlmhWinmW7dutnOnTuNIMmng0WzEEAAAQTiWoBAJK6Hn84jgAACCCBwdwFvhsiePXusQ4cO1qdPH9Nzva6b9/7dvx3fr8pG2+9qZ55atWrZrFmz3N/xrULvEUAAAQQQ8J8AgYj/xoQWIYAAAgggEHUBXdSroKp2SalXr56rhXHo0KGotytWGqClRvPmzbM333zT2rZt65bNyNMLkvTIDQEEEEAAAQSiK0AgEl1/zo4AAggggIAvBXTBrloYmt1Qu3ZtGzZsmJ06dcqXbfVjo7RERjNq6tSpYzVq1LAVK1a4ZTMEIn4cLdqEAAIIIBCvAgQi8Try9BsBBBBAAIEQArpwv3r1qo0dO9aaNm1q8+fPT99hJsTXeOsfAiqieuHCBRsxYoRVrVrVPv30U0tLS2OGCL8QBBBAAAEEfCRAIOKjwaApCCCAAAII+EVAgYjqYGjb2MaNG9vq1avdjBG/tM/v7ZCfiqtq+9369eu7YCklJYVAxO8DR/sQQAABBOJKgEAkroabziKAAAIIIJA1AdW7SEpKsr59+9qYMWPSa2Bk7dt8ylsas3TpUqtYsaK1a9fO9u3b5+qyeO+hhAACCCCAAALRFSAQia4/Z0cAAQQQQMCXAprdsHHjRtPWsUOGDLFjx4652Q2+bKwPG+WFHqojoiVHzZo1szVr1rhti733vEeFT17BVXVFr2d89GH3aBICCCCAAAKBECAQCcQw0gkEEEAAAQTCJ6ALctUPmTNnjtWsWdNGjhxJQdVs8nphR2pqqo0bN846d+7sls9krCOiEER/r1u3zpYtW2bJycmEIdl05uMIIIAAAgjkRIBAJCd6fBcBBBBAAIEACuhi/uLFi+5CvkmTJvbFF1+4AqEB7GrEuuQFItpt5rPPPrNatWpZr1693DIkbzaIPqMZJK1atXJ1RtauXetmikSsURwYAQQQQAABBG4TIBC5jYM/EEAAAQQQQEA7pJw8edLat2/vlnps2LDBrl27Bkw2BRR4KPzQUplq1arZ22+/bZs2bUpfHqP3tB1v4cKF7Y033rCvvvoqfYZINk/FxxFAAAEEEEDgAQQIRB4Aja8ggAACCCAQVAFdxCv82L17t5vV0Lp1a/dcIQm3rAt4M0T0mJiY6GqxlChRwi1DUn0WLyyZPn265cmTx/ReQkJC1k/AJxFAAAEEEEAgxwIEIjkm5AAIIIAAAgjEvoB3Aa9ZC1euXHGzGrQ7yvDhw91sEe/92O9p7vRAXrrpUdvtduvWzYoVK+Y8L1++7F6/ceOGjRgxwvLmzWv16tVzwUnutI6zIIAAAggggIAECET4HSCAAAIIIICAE/BCj/Pnz9vMmTOtatWqNmvWLDt37py7gPcu8uG6v4BnpUcVqP3oo4+sfPny1r17d1egVsGTXlddEQUiHTp0cEVV739kPoEAAggggAAC4RIgEAmXJMdBAAEEEEAgRgW8IEQX6V79kJ49e7plHF9++aXbCcW7wI/RLuZ6sz0vPcp15cqVVrt2bXffuXOnC5jOnj1rjRs3tkKFCrkCttpxhhsCCCCAAAII5J4AgUjuWXMmBBBAAAEEfCvghSIKRI4ePWq9e/c2LZlRXQvNZPDe920HfN6wQ4cOWb9+/axhw4a2ePFiFzwdPnzYFVotXry4ff7556YdabghgAACCCCAQO4JEIjknjVnQgABBBBAwNcCCj10Ua6tYLt27Wpt2rSxI0eOmFcEVO9zezABLTvSMqSmTZvae++952bdaKaIdp5p1qyZC54oXPtgtnwLAQQQQACBBxUgEHlQOb6HAAIIIIBAwAQUeKig6rp169xF+qhRoyw1NdXNDglYV3O9OwqaNNumSZMmVr16dTt48KCtXr3a1Wnp0aOHK6hK4JTrw8IJEUAAAQTiXIBAJM5/AHQfAQQQQAABCehiXHfVtZg9e7a98847NnfuXOqHhOnnIVvNvKlfv77bZveLL76wadOmWdGiRa1z586m5TMEImHC5jAIIIAAAghkUYBAJItQfAwBBBBAAIEgC3iBiJbIqKCq6losXbrUvC1ig9z33OibfDUrpGXLlvbUU0/Z4MGDbdiwYVamTBkbMmSIHT9+nEAkNwaCcyCAAAIIIJBBgEAkAwZPEUAAAQQQiEcBLwxRDYsdO3a4ZR1VqlQx1bi4du1a+uyReLQJV59lfPr0aRs+fLg9++yzrnaIwpFSpUrZ5MmT3cwcfYYbAggggAACCOSeAIFI7llzJgQQQAABBHwh4AUg2g7We65HhR8rVqywSpUqWa1atezEiRNuNxRfNDqGG+EZqz7LkiVL7I033rC//OUvzrlu3br21VdfMRMnhseXpiOAAAIIxK4AgUjsjh0tRwABBBBA4IEFvIv0jI+qHzJx4kRX16Jdu3Z2/vx5U2jCLecCctZuPVu2bLGSJUvaY4895kIR7TKzfv16t7uPPsMNAQQQQAABBHJPgEAk96w5EwIIIIAAAr4Q0IW3lsdcvXrVzUzQc7128uRJV9tCyzimTJmSvlzGF42O8UbIV+GSaoVo290XXnjBfvGLX1jlypVt8+bN6Vsbx3g3aT4CCCCAAAIxJUAgElPDRWMRQAABBBDIuYAuzC9cuGDLli1zSzjOnDnjApIDBw5Yly5dTPVDvv76ay7Sc06dfgQFIrqnpaU584IFC9ojjzzidp3Zu3evC0v0PjcEEEAAAQQQyD0BApHcs+ZMCCCAAAII+EJAM0KOHTtmrVq1sjp16timTZtM9S20dKN27dpuy10u0sM7VF4gcv36ddu2bZu9/PLLLhAZOHBg+g4zBCLhNedoCCCAAAII3E+AQOR+QryPAAIIIIBAwAQ0Q0SBSKNGjeyVV16xL774wlJTU23GjBlWrFgxF5KwDWx4B90LRFRHZP/+/VaoUCF7+OGHrV+/fpacnJxe3Da8Z+VoCCCAAAIIIBBKgEAklA7vIYAAAgggEEABXZyrYOrUqVPdbBDtLJOUlGR9+/a15557zm27q/eZsRC+wfcCEc3OOXLkiJUuXdp+/vOf29ChQ+3UqVNYh4+aIyGAAAIIIJBlAQKRLFPxQQQQQAABBIIjoC12d+zYYV27drWZM2fazp07rXv37la8eHEbO3as3bhxIzid9UlPFIooENHsm+bNm1uJEiVs+fLldunSJddCAiifDBTNQAABBBCIGwECkbgZajqKAAIIIIDALQHVsti3b5/179/fJkyYYIsWLbLq1avb3/72N1u4cCHb7d6iCsszb4aIgiaFTypcW758eUtISGA3n7AIcxAEEEAAAQSyL0Agkn0zvoEAAggggEDMC+jC/MSJE26GyKBBg2z8+PFWsWJFq1ChgtsGltkKkRlibXWs4rWaHVKjRg1T8VrVFcE7Mt4cFQEEEEAAgVACBCKhdHgPAQQQQACBgApo6ca5c+dc3ZBmzZpZvXr1LF++fFa3bl07dOgQF+hhHncv8NDymMWLF7vZId26dXO1W1Tk1ptBEubTcjgEEEAAAQQQCCFAIBICh7cQQAABBBAIqoAuwrXV7qRJk6xmzZqWJ08ee/zxx03hyJkzZwhEwjzwXuBx9uxZmzx5shUpUsRGjRqFdZidORwCCCCAAALZESAQyY4Wn0UAAQQQQCAgArpA17KZJUuWWKVKlew3v/mN/f73v3c1RS5fvkwgEoFxlrm2O1YhWwVQ06ZNc7N09Do3BBBAAAEEEMh9AQKR3DfnjAgggAACCPhCQLUrtm3bZlWrVrWHHnrInnzySfvoo4+oaRGB0VHooWVKKqhauXJle+GFF2zlypXmhU96n2AkAvAcEgEEEEAAgRACBCIhcHgLAQQQQACBIAp4F99aNnP06FErV66c/fjHP7aCBQu6GSNcmEdm1DUjZ8OGDVasWDF78803bc+ePek7zHhjEpkzc1QEEEAAAQQQuJsAgcjdVHgNAQQQQACBgAvoAlyByOnTp90MkV/84hfWokULO3z4MDMVIjD28tYOM8uXL7fixYtbmTJl7MiRI+mzcQihIoDOIRFAAAEEELiPAIHIfYB4GwEEEEAAgSAKeIFISkqKuzj/r//6L2vUqJGdPHnSBSJcoId31OWpHWYWLVrkdvJp2LChyV7LaLghgAACCCCAQHQECESi485ZEUAAAQQQiKqAF4icOHHC3njjDdMMkQ4dOrgZI3qPQCS8wyPP1NRUt8NMqVKlrGPHjq6gqmbpcEMAAQQQQACB6AgQiETHnbMigAACCCAQVQEvENE2sH369DFdpGfcBpZAJLzDI0+FT3379rUCBQo467S0NIKn8DJzNAQQQAABBLIlQCCSLS4+jAACCCCAQDAEdIGuu7fzyQcffGDjx4+3pKQkV1uEQCS84yzPgwcPWqtWrSxv3rw2a9YsV1ME5/A6czQEEEAAAQSyI0Agkh0tPosAAggggEBABHQh7t2Tk5Nt3LhxNnz4cLcNr0ISlnKEd6DluWPHDlc/RLv5qLjq9evX08cgvGfjaAgggAACCCCQFQECkawo8RkEEEAAAQQCJuCFIXo8f/68zZgxw0aPHm1r1651s0b0OrfwCdy8edNWrFhhFSpUcMuT9u3bl77DTPjOwpEQQAABBBBAIDsCBCLZ0eKzCCCAAAIIBEQgY+Bx7do1W7dunVsyM3/+fLty5Qq1LcI8ztpyd/r06fbqq69a5cqVTbNymIUTZmQOhwACCCCAQDYFCESyCcbHEUAAAQQQCJqAlshs377dhgwZ4kIRFVrNGJgErb/R6M+FCxdMdVpUULVx48amvzGOxkhwTgQQQAABBG4JEIjcsuAZAggggAACcSmgC/PExEQbM2aMjR071u2GwsV6eH8Kp06dsn79+lnx4sXdTjOaMYJxeI05GgIIIIAAAtkVIBDJrhifRwABBBBAIIAC2hL2k08+sQ8//NAOHDjAxXqYx9jbYaZYsWKugK1qinBDAAEEEEAAgegKEIhE15+zI4AAAggg4AuB1NRUtxXse++9Z+vXrycQCfOobNu2zapVq2baYUYFbKkfEmZgDocAAggggMADCBCIPAAaX0EAAQQQQCBoAhcvXrTFixfboEGDbMGCBW4HlKD1MVr90dKYNWvWWNmyZe21115zW+4SiERrNDgvAggggAACtwQIRG5Z8AwBBBBAAIG4FdBOM8uXL7cuXbq4ZTPaaYbbgwt49UH0qKK12nK3Vq1a1qhRI9uzZw8zcB6clm8igAACCCAQNgECkbBRciAEEEAAAQRiV0AX7fv373f1LVRY9dy5c1y0h2k4FTZNnTrVFVStV6+eHTlyBNsw2XIYBBBAAAEEciJAIJITPb6LAAIIIIBAQAS0hOPYsWM2bdo0F4qoyKo3yyEgXYxaN9LS0tyWuyqo2q1bN1O9FmyjNhycGAEEEEAAgXQBApF0Cp4ggAACCCAQvwK6QNfWsJ9++qn17t3bLetQSMKFe85/E2fOnLEBAwZYpUqVbNSoUXb58mVcc87KERBAAAEEEMixAIFIjgk5AAIIIIAAArEvoOBDy2TmzJljzZs3t4ULF9qNGzfchbveIxjJ3hh7Xno8fPiwtW7d2sqVK2fTp09Pd83eEfk0AggggAACCIRbgEAk3KIcDwEEEEAAgRgU0IW7Zi6sXLnSWrZsaVOmTLGrV6+mByIx2KWoNjljILJp0yY3O6R06dK2aNEittyN6shwcgQQQAABBG4JEIjcsuAZAggggAACcSugC3jNCNm2bZt1797dLe24cOECF+85+EXIVHfNtlH9kAoVKtjatWuZbZMDU76KAAIIIIBAOAUIRMKpybEQQAABBBCIUQFduN+8edPtNDNkyBBXR+TkyZPutRjtUlSb7YUhqsMyceJEe+WVV+ydd96xXbt2MesmqiPDyRFAAAEEELglQCByy4JnCCCAAAIIxK2ALuB18a7dZSZNmuRmiSQmJrpZI3GLkoOOe4HI9evX7f3337fChQtbu3btLCkpiUAkB658FQEEEEAAgXAKEIiEU5NjIYAAAgggEKMC3gW8dkSZP3++9enTxzZu3EgdkQccTy9gUl2Wjh07Wp48edysm7Nnz7Jk5gFN+RoCCCCAAALhFiAQCbcox0MAAQQQQCAGBbxA5OLFi7Z48WKrU6eOTZs2zfS3Zo6wBW/2BtXz1M49bdq0sZdfftlGjx5tly5dYoZI9ij5NAIIIIAAAhETIBCJGC0HRgABBBBAIHYEvAt4zWhYv3691a9f39577z1LSUlJD0P0GW5ZE5CVQqSjR49avXr1XFFVbWmsJTQ4Zs2QTyGAAAIIIBBpAQKRSAtzfAQQQAABBGJAwAtEtNOMaof06NHD1RHRBf0333zDRfwDjKFMExISrHLlyi4UWbNmTbolocgDgPIVBBBAAAEEwixAIBJmUA6HAAIIIIBALAp4gYhmNSQnJ9ugQYOsWbNmtn37drt27RqBSDYH1fP88ssvrWzZstaqVSvbs2dPuiOBSDZB+TgCCCCAAAIRECAQiQAqh0QAAQQQQCBWBXShfvr0aRs+fLjVrFnTli1bll73Ilb7FI12y1Eza8aMGWMFChSwDh062JEjR1wg4oUl0WgX50QAAQQQQACBWwIEIrcseIYAAggggEDcCmScsaBCqp999pk1adLEli5d6gqrxi3MA3Rclpppo5k1Mnz66aetV69ebuaNF4Zk9H6AU/AVBBBAAAEEEAiDAIFIGBA5BAIIIIAAAkESuHLliqneRY0aNWzSpEluxoh3IR+kfkayL5odomCpYsWK9rvf/c5tuauZNzhGUp1jI4AAAgggkD0BApHsefFpBBBAAAEEAimQccaCdkLZu3evNWzY0AYPHuyWemjGA7esC9y8edNOnTplZcqUsbx589qUKVNcQEIgknVDPokAAggggECkBQhEIi3M8RFAAAEEEIgxAc1u0Ha7ffr0cffdu3ebdp/JGJrEWJdytblyktfBgwetevXqVrx4cVNxVYrT5uowcDIEEEAAAQTuK0Agcl8iPoAAAggggEB8CeiCPi0tzcaPH2+dOnVyy2e0jIZAJGu/AzldvXrVvv76axeGvP3227Zx40ZXZDVrR+BTCCCAAAIIIJAbAgQiuaHMORBAAAEEEIgxAV3Qz5w5020Xq9kNCki4ZU1Agcjly5dtxowZ9vzzz1u7du3swIED6YESwVLWHPkUAggggAACkRYgEIm0MMdHAAEEEEAgBgVUR0RBSJs2beyTTz6x1NTUGOxF9JqsAElbFysQ6dGjhyUlJaU3hkAknYInF8ZzSwAAIABJREFUCCCAAAIIRFWAQCSq/JwcAQQQQAABfwqoKOiOHTvs3XffdVvGJiYmps9w8GeL/dMqBR5nz5619u3bu0Bk6NChbstdr4UEIp4EjwgggAACCERXgEAkuv6cHQEEEEAAAV8KqLDqkSNH3JKZ7t27286dO42dZrI2VHJKTk62xo0b2xtvvGGzZ8+2CxcuZO3LfAoBBBBAAAEEck2AQCTXqDkRAggggAACsSOgi/rz58+7ZR+a4bBp0ya3c0rs9CB6LdUOM/v27bOSJUta4cKFbcmSJaaitNwQQAABBBBAwF8CBCL+Gg9agwACCCCAgC8EtKxD28ROmzbNLf1YvHix2znFF43zeSPkpl1lXnzxRXv11Vdt7dq1ppos3BBAAAEEEEDAXwIEIv4aD1qDAAIIIICAbwQ0S2TVqlXWv39/V1hVM0a43V9As0FWrlxpr7/+ulWtWtUtN9ISJG4IIIAAAggg4C8BAhF/jQetQQABBBBAwDcCmiVy/PhxGzNmjE2cONFOnDjh2kZR0NBDpHoh2pnnlVdesQ4dOrhaLNRfCW3GuwgggAACCERDgEAkGuqcEwEEEEAAgRgQUPChi/uPPvrIRowY4epi6DUCkdCDl5KSYv369bOf/exn7lEFVjELbca7CCCAAAIIREOAQCQa6pwTAQQQQACBGBFQIDJ+/Hjr3LmzrVixwrQdr3fjIt+TuPUok2PHjlnz5s3tkUcesXHjxllqauqtD/AMAQQQQAABBHwjQCDim6GgIQgggAACCPhPIC0tzaZMmeIu8LV9rAqGEoTce5y0NGbPnj1WpUoVe+KJJ2zevHlsuXtvLt5BAAEEEEAgqgIEIlHl5+QIIIAAAgj4V0DBhwIQXdSrFoZmiqiwql737v5tfXRapuKpe/futSZNmlihQoUsISGB3XmiMxScFQEEEEAAgfsKEIjcl4gPIIAAAgggEJ8CCj20RGbp0qXWqFEj6927t3n1MPQetzsFFCBpZ56SJUtasWLF7MCBA7ctM7rzG7yCAAIIIIAAAtESIBCJljznRQABBBBAIAYEtARkw4YN1qJFC+vWrZslJiYyOyTEuF28eNGmT5/udpgpV66cqyfClrshwHgLAQQQQACBKAoQiEQRn1MjgAACCCDgdwHNBNm/f7/17dvXevToYTt37iQQCTFoZ86ccTvy5MuXz9Vd0Y4zbLkbAoy3EEAAAQQQiKIAgUgU8Tk1AggggAACfhbw6oScOnXK7ZbSv39/N1tEMx689/zc/txsm+dx8uRJGzZsmGl2yOTJk00zRvQeNwQQQAABBBDwnwCBiP/GhBYhgAACCCDgGwFdzGunmZkzZ1rHjh1twYIFdv36dQKRDCPkhSF6PHz4sPXr189atWrlCqqqpgg3BBBAAAEEEPCnAIGIP8eFViGAAAIIIBB1AW9mgwKQRYsWWZs2bWzChAl26dIlApF/jE7GMEQzZ7Zs2WJ169a1t99+23bt2uXCo6gPJA1AAAEEEEAAgbsKEIjclYUXEUAAAQQQQMALRLzCqgpEVEtEdTG8IAAlS7dQcLRkyRK3u8ybb75p+/btsxs3brj3cUIAAQQQQAAB/wkQiPhvTGgRAggggAACvhDwAhE97t692zp16uQKhepCn0Dk1hB5FleuXHE7zOTPn98qVKhgx48fd1vueo63vsEzBBBAAAEEEPCDAIGIH0aBNiCAAAIIIOBDAe9CX49Hjx61oUOHWuPGjW3FihXmFVb1YbNzvUme0/nz5+3DDz807TCjJTPnzp3DKddHgxMigAACCCCQdQECkaxb8UkEEEAAAQTiSsC70NejtpP9+OOPrWXLljZ16lSWgmT4JXhOJ06ccLNonnnmGVdUVTNGtNxI73NDAAEEEEAAAf8JEIj4b0xoEQIIIIAAAr4Q8C7k9ahCqkuXLnWFVd9//327evWqu9j3RUOj3AgvEDlw4IDVr1/fXnzxRRszZkz6chnPMcrN5PQIIIAAAgggkEmAQCQTCH8igAACCCCAwO0CuqBXwdDNmzfbgAEDbNSoUXbhwgUCkX8wyUdLiHbu3GnNmjWz4sWL27Jly9JnhxCI3P574i8EEEAAAQT8IkAg4peRoB0IIIAAAgj4VMC74FcdkSlTptiIESNMy0Nu3rzp0xbnXrNk4/msXLnSqlSpYtWrV7dt27ZReDb3hoEzIYAAAggg8EACBCIPxMaXEEAAAQQQiC8BXfQfO3bMhg8fbg0bNnS7zmjWCDdzM0Fk8cknn1jBggWtfPnytn///vRARHbcEEAAAQQQQMB/AgQi/hsTWoQAAggggIAvBVRYddq0aa5OhpaEqGgoN3PBh2qsKCx67rnnrFKlSpaUlORelw+BCL8SBBBAAAEE/ClAIOLPcaFVCCCAAAII+E7g4sWL9uWXX1qDBg1s3Lhxpm1mudj/v8AjNTXVunfv7rbc7dmzp7Px3QDSIAQQQAABBBC4TYBA5DYO/kAAAQQQQACBewlcu3bNtm7darrg79+/v6WkpFBY9R8zQLScSEFRgQIFbOjQoSYrwqJ7/ZJ4HQEEEEAAAX8IEIj4YxxoBQIIIIAAAr4X0E4qBw8etB49eljXrl3t8OHDFFb9RyCye/duq1atmpshwpa7vv8p00AEEEAAAQScAIEIPwQEEEAAAQQQyJLA3//+dxeCdO7c2RVW3bJli5sJkaUvB/hDmgmyfv16q1q1qpUuXdoWL16cPjuEWSIBHni6hgACCCAQ8wIEIjE/hHQAAQQQQACB3BHQxf2pU6fsgw8+cBf/S5cuNRUTzXjRn/F57rQq+mdRUDR79mwrVqyY1a1b1/bu3XtHo+Ti2XjP7/X3HV/mBQQQQAABBBCIiACBSERYOSgCCCCAAALBE9AFfFpammmHmRo1atiMGTPs3Llzt13oB6/X9+/RjRs3bOTIkfbSSy9ZrVq1bN++fXd86V4hSMYPegFJxtd4jgACCCCAAAKREyAQiZwtR0YAAQQQQCBQArpg11a7mzZtcjNEBg8ebCdOnIjrQEQmKqCqQKR8+fKu2GxycvId454xEMn4XLNLMv59xxd5AQEEEEAAAQQiJkAgEjFaDowAAggggEDwBDQbQsVUu3Xr5nabOXDggKnYqndRH7we379H2n64X79+VqZMGRswYICdPXv2ji/JR+HH1atX7fTp07Zjxw5bsWKFW16TlJRk2qXmwoUL7NpzhxwvIIAAAgggEDkBApHI2XJkBBBAAAEEfCuQMcDwnt/tUR3Q696jwg9d0A8aNMhatWrlZot4W8x6n/NtpyPUMAUaDRs2tDfffNPGjh2bXlfF89CjgpBdu3a5+itNmzZ14UnhwoWte/fu9sknn7iAacSIEbZnzx63c4++430/Qs3msAgggAACCMS9AIFI3P8EAEAAAQQQiEcB74I746NmMGgGiAKO69evuwvzjLM/9Fl9RjMgFIioXsaiRYvSAwA5xuNFvIqoVq5c2QUic+fOdXYZXbXMaPPmzda4cWP74x//aI888oj98pe/tOeff960Y8+HH37ovq+/mzdvbgpYPPd4/G3SZwQQQAABBHJLgEAkt6Q5DwIIIIAAAj4RyHix7j2/fPmyW7axbt06W7JkiWkHmYSEBDty5IhbyqGgxKt3cfHiRZswYYKrI5K5sKpPupirzfj666/djI+33nrLli9fnh5myFauW7dudcHHyy+/bL/+9a+tePHi1rdvX1N4olkjClSGDh1qTz75pD3xxBNulom+J29uCCCAAAIIIBA5AQKRyNlyZAQQQAABBHwr4AUhuujWDAbVs6hatar96U9/chftv/nNb+yFF16w6tWr25QpU+zgwYPu4l4zFzSDRCGAlolMnDjRbcXrHc+3HY5Qw9TvadOm2SuvvGLlypWztWvXulkyclWIpICpY8eOruBqvXr1bPTo0W62iGbg6Lv6nEy1VEYzSB577DEXmBw6dMh9P0LN5rAIIIAAAgggYGYEIvwMEEAAAQQQiEMBL8DQRfsXX3xhb7zxhv37v/+7fetb37If/OAH9vDDD9tPfvITe+ihh9zMBe2g8vHHH7v6IfqOLtjbt2/vioiqsKo3m0HHjaebwgzN7njttdesSZMmbraHDFQzZPfu3a5mSJ06dUw78mzZssWFShmtvHFQKKXZJZplUqVKFfvyyy/dUqR4sqSvCCCAAAII5LYAgUhui3M+BBBAAAEEfCDgzUzQcg4VA3300Uft97//vVWoUMEth9GSmU8//dQGDhzoLtL/8pe/2Isvvmi6uF+1apWdPHnSevfubV26dHEzHm7evOl6FU+BiBd8dOrUydUDad26tR09etSFHhs2bLAOHTpY/fr1berUqW6GjUKSe/nodRWr/fzzz92MEs0mybilsQ9+MjQBAQQQQACBwAkQiARuSOkQAggggAAC9xfQzAZt89qnTx/77W9/a6pvMWnSJDerISUlxVQnRMVTjx8/bitXrjRd9GsJzeOPP+6WdKiYao8ePUwhgJbPxNNOMwovdFeopC13tdTomWeeMe0So6BIM0G0/a7MtNxIs2kyhyF3C0bS0tJs3rx5LlzJmzevW0ajceKGAAIIIIAAApERIBCJjCtHRQABBBBAwNcCqmGxb98+K1q0qD311FM2ZMgQN7tBF+DeBb86oOeXLl1yxT9HjRrlZpMoQGnQoIHVrVvX7Y6ipTQKUDJ+z9edz2HjvH7KSjvCaIaNdoj56KOPnNPIkSNNW+tq9xjVXskchtzr9AqoVJNFy5RUXHXbtm1up597fZ7XEUAAAQQQQCBnAgQiOfPj2wgggAACCMSkgEKOxYsXuwt5FQNdv359+naxmvngXfR7j6oboiUc2hmlbNmybkbEs88+a6+++qrbglczI7zPxiRIFhvt9VGPWia0fft2y58/v1tONH78eBdovPPOO9aiRQv3nmqDeDVDdAp9L+NjxtNqRo5ClB/+8If29NNP244dOwhEMgLxHAEEEEAAgTALEIiEGZTDIYAAAggg4HcBXZSnpqa65TK//OUvrWXLlnb48OHbLta9C/+MfdGFvS7atVxGM0u8uiPNmzd3yzu8ICXjd4L23HPRo2bZeKFS4cKF3RIizZypWLGiTZ8+Pb2Aqj6b+Xa31zQmWnajYrYFCxZ0BVpZMpNZjr8RQAABBBAInwCBSPgsORICCCCAAAIxIaCL8eTkZBeEqJDqBx98YKobkpWbQg8tj5k/f77bavaRRx5xNUW0ba+33CYrx4nVz8hOdzloKczkyZNNM2W0O4xqiZQqVcr69++fXhD1bsHHvfp+6tQpV6j2P/7jP9yuNRl377nXd3gdAQQQQAABBB5cgEDkwe34JgIIIIAAAjEpoIt0zUZ4//333YX8rFmzXIHV+3UmYxigIqoTJkxwhVZVbFV1M1QUNDsBwP3O58f3PQM9atmRiqcqVNIuPNp6V7NtNm/e7AIT77NZ7ceRI0dcbZbvf//79re//c0VY1Xwwg0BBBBAAAEEIiNAIBIZV46KAAIIIICAbwV0ka0ZIp07d3bb7H755ZcuzMhqg/V93bXFrAqrKhDQMhFtNRv0C3gv5FA/tXxIS2R+8YtfuFos1atXd1vsaucZ76bPZ+Wmz+3evdvVZ9GSmbZt25pmjGT1+1k5B59BAAEEEEAAgdsFCERu9+AvBBBAAAEEAi+gi3ltp1uvXj1XFPWzzz5zy2Cy0nEvENBnVTB0zJgxrsCqtp0dNGhQlmaaZOU8fv6MDFRQVYaayaFdYQoUKGB9+/Z1tVT0XnZv+s7q1atN2+3+9Kc/tdGjR7stfbN7HD6PAAIIIIAAAlkXIBDJuhWfRAABBBBAIBACuqDX7IM2bdq4JS/aHUVLaLxbVmclKFhRLREtFfnNb35jNWvWtE2bNj3QchHv3H5/9AIhFVTds2eP5cmTx3784x+7rXdloa1zs+rnHUuPqsuibY012+TXv/61C0cUOHFDAAEEEEAAgcgJEIhEzpYjI4AAAggg4FuBc+fOuWKqf/rTn1whT22pm/ECPSsN1+cVgKiYqAKRv/71r9apUyfTsb0Cq/pMkG6ekcKK5cuXu34rEKlVq5Zt27Ytvd9Z6bN3LAVLWn6krXo1O0QBk/5+kJkmWTkvn0EAAQQQQACB/xMgEOGXgAACCCCAQBwKqADq7Nmz7cknn7RGjRrZ/v37b5vZkdUgQxfuHTt2dDU0/vu//9vy5cvnZjdoBoV3wR8kXq9PmgkyadIk++EPf2gPP/yw9evXz5KSkrLVZ+9YN27csGXLlpm27v2f//kft32vxkdBCTcEEEAAAQQQiJwAgUjkbDkyAggggAACvhTQhfjly5dt7dq1LsCoVKmSrVu3zs1I8C7S9ZiVmwqIjhs3zl566SX73e9+Zy+++KKbcZKdpSNZOY+fPiOb06dPuyDoX/7lX9wskblz56bvspNVO31OoYdm1AwcONAeffRRV6B26dKlppAkq8fxkw1tQQABBBBAIJYECERiabRoKwIIIIAAAmES0AX3sWPHrFq1alakSBGbM2eOC0l0ga57Vi/GtXRk7NixLhDR7JBXX33VqlSpEtglH3LRXVvkFi9e3L71rW+52TEKl7TExXs/K8PkfTYhIcFtf6zZJirSynKZrOjxGQQQQAABBHIuQCCSc0OOgAACCCCAQMwJKPRQmDF58mS3Za52iDl58qS7oM9OIKKlMdOmTXNByAsvvGB//vOfrUSJEm4LXh1fF/1Bu6k+yo4dO+zZZ5+1f/7nf3Z+e/fuTe9rVvusz126dMl69uzpZof87Gc/czvVBHW5UdB+B/QHAQQQQCD2BQhEYn8M6QECCCCAAALZFtDFuC68VbuiUKFCVqZMGVu1alW2ZzkoPPnqq69cCPL000+7gqC//e1vbfDgwW5ZSVbDgWx3IEpfUH80u2b9+vX2+OOP2z/90z9Zhw4dHrh+yNatW6106dL22GOPWalSpUx/e2beY5S6ymkRQAABBBAIvACBSOCHmA4igAACCCBwp4AutjXTQcVUK1SoYPnz57f333/fVBNE72X1Ylyf27lzpzVt2tRefvllK1++vKup0a5dOxcSKDAJ2k0FT7XE6KGHHrLvfOc7brvcM2fOZNtNs0P69u3rCtv+4Q9/sBEjRmRr296gudIfBBBAAAEEcluAQCS3xTkfAggggAACPhDwQg8VP9UOKQpE3nnnHbd1bHaWzKgr2l2lT58+rv5FxYoV7bnnnnPb0O7bty9wW8fK7ezZsy4E+d73vmff//733W49Fy9ezFYgolkmS5YscbNztFRGhW1VS8TbrtgHPxGagAACCCCAQOAFCEQCP8R0EAEEEEAAgTsFvBkgCj9WrFjhlm1o29ePPvrIrl69mj5DxPvcnUe49UpqaqqbXfL888+7pTclS5a0cuXK2fLly92xbn0y9p/JQ7VWunXrZt/+9rfdLBHtCqNde/ReKC/vfYUhBw8edDNzHnnkEVeL5OOPP2Z2SOz/POgBAggggECMCRCIxNiA0VwEEEAAAQTCIeBdnOtYycnJ1qlTJ8uTJ49b+nLo0KH0nWa8z93tQt97T0s/PvzwQ/vjH//oiqvWrl3bFIp89tlnppkTQbqpz/KpV6+e22FGgcbq1avTQ6S7Oan/el3hk3aiUaDSq1cv08yQX/3qV9ajRw9LTEwMGaYEyZC+IIAAAggg4BcBAhG/jATtQAABBBBAIJcFvKUxKq76xRdfuMKoL730ko0fP94VDvUu4vUY6kJfM0pmz55tTz31lLvI11a+2mlm3rx5btZDLncroqeTgwqfanth7TDz8MMP2+LFi0POEPH85K1aI+PGjXNFVJ944gk300RLizRr5F7GEe0QB0cAAQQQQCCOBQhE4njw6ToCCCCAQPwKeBfp3qNmiQwcONDVtGjSpIlpG1mvnoUXnNztgl2v6XObNm1yBVU146Fs2bJuK9oZM2bYuXPnAoUsC/W1QIEC9v/+3/+zH/zgB6blLhmL0d7LScVYP/nkEzeTRvVH6tat67bvvXbtGmFIoH4ldAYBBBBAIFYECERiZaRoJwIIIIAAAmEUyHjRrue6KN+yZYu1bt3aihYt6paEHD582M1cuF8gou/v3r3bqlevbj/60Y/sxRdfdIHBtGnTXAHSMDY76odSX1NSUmzy5Mn26KOP2ne/+11XlPbUqVNuSYxnlbmhWjqknWmKFCliWmajQEW1W/T6vb6T+Rj8jQACCCCAAALhFSAQCa8nR0MAAQQQQCAmBXRRrtkcCxcutLfeesuefvppV9vixIkTru5Fxot2hQK66+Y9V12NZs2amWY+/PznP3ezRBYtWhTIGiJaYqTtit999103Q0T1UjZs2GB63fPwvPSomiGaRVK5cmX785//bKVKlbIFCxa4sMibheN5xuSPh0YjgAACCCAQowIEIjE6cDQbAQQQQACBcAroglwX58eOHbPRo0fbX/7yF/vrX/9qEyZMcDMiMl+4exf+3qMu+rt3727/9m//Zj/5yU/Sd5lRwdUg3bz+artiFY197LHH3L1Fixa2c+dOu3LliguQNONGu++o4Gr//v3drBvNnKlataoLQ7TERmEJNwQQQAABBBCIngCBSPTsOTMCCCCAAAK+EfAu9HUhr/ohWjrzhz/8wc1mUN2L06dPpy/t0Gd1876jR13gT5w40RUZ1SyRggULum13FRAE7ab+qgjq0aNHrWbNmvaf//mf9vvf/94aNGjgZoKomOysWbPcDBvNHlEQkj9/fmvXrp0tW7Ysvd5I0FzoDwIIIIAAArEmQCASayNGexFAAAEEEIiAQMZwQ7M6Nm/ebK1atXJb8VaqVMk+//xzt0OKto3VZzPfFKSoJoaCgW9/+9v2+uuvW0JCgqtNkvmzsf63Z6U+r1mzxtVO0Q47v/71r13B1GeffdYtjdHsEW2tW6hQIRs2bJjt2rXrtu157+YY6za0HwEEEEAAgVgSIBCJpdGirQgggAACCERQwLvQ16PqYezZs8eaNm3qZjeULl3axo4d65bU6D0t98hYJ0PhwPLly92sku985ztWq1YtU1HWIC8LkZNmiqieyIgRI1zBVIUi2mnnd7/7nRUuXNi6du3qgiJtt5t52VEEh5JDI4AAAggggEAWBAhEsoDERxBAAAEEEIhHAc0G0c4zjRs3djMe8uXL55Z9qICodkfR+wo8vGU2ffr0sV/+8pduVsSnn37qlobEg5uCEW2pq2BENUOWLl1qGzdutCNHjriaIkEOheJhfOkjAggggEBwBQhEgju29AwBBBBAAIEcCehCX2FHYmKiTZkyxerUqWOqidG8eXMbPHiw20Z2yZIlNnv2bGvfvr0VK1bMzZIYOXKkK8SqwCQebnJS6KHZIqqZ4t31t17X+9wQQAABBBBAwH8CBCL+GxNahAACCCCAgC8EvAt9hSIpKSm2fft2F4JoFxoVCK1Xr55VrFjRFV4tX768m0kyffp0S0pKcuFAvIQBcrrf3RcDSiMQQAABBBBA4DYBApHbOPgDAQQQQAABBDIKeBf6CjcUjGgr2YMHD9qqVatMu88MHTrUhgwZ4p5rKY2CE6/wqheo6DHIN89Ifcz8PMj9pm8IIIAAAgjEugCBSKyPIO1HAAEEEEAgFwV0wa/ioFoWonDk+PHjbkaIniswyRx+ZP47F5vKqRBAAAEEEEAAgZACBCIheXgTAQQQQAABBBBAAAEEEEAAAQSCKEAgEsRRpU8IIIAAAggggAACCCCAAAIIIBBSgEAkJA9vIoAAAggggAACCCCAAAIIIIBAEAUIRII4qvQJAQQQQAABBBBAAAEEEEAAAQRCChCIhOThTQQQQAABBBBAAAEEEEAAAQQQCKIAgUgQR5U+IYAAAggggAACCCCAAAIIIIBASAECkZA8vIkAAggggAACCCCAAAIIIIAAAkEUIBAJ4qjSJwQQQAABBBBAAAEEEEAAAQQQCClAIBKShzcRQAABBBBAAAEEEEAAAQQQQCCIAgQiQRxV+oQAAggggAACCCCAAAIIIIAAAiEFCERC8vAmAggggAACCCCAAAIIIIAAAggEUYBAJIijSp8QQAABBBBAAAEEEEAAAQQQQCCkAIFISB7eRAABBBBAAAEEEEAAAQQQQACBIAoQiARxVOkTAggggAACCCCAAAIIIIAAAgiEFCAQCcnDmwgggAACCCCAAAIIIIAAAgggEEQBApEgjip9QgABBBBAAAEEEEAAAQQQQACBkAIEIiF5eBMBBBBAAAEEEEAAAQQQQAABBIIoQCASxFGlTwgggAACCCCAAAIIIIAAAgggEFKAQCQkD28igAACCCCAAAIIIIAAAggggEAQBQhEgjiq9AkBBBBAAAEEEEAAAQQQQAABBEIKEIiE5OFNBBBAAAEEEEAAAQQQQAABBBAIogCBSBBHlT4hgAACCCCAAAIIIIAAAggggEBIAQKRkDy8iQACCCCAAAIIIIAAAggggAACQRQgEAniqNInBBBAAAEEEEAAAQQQQAABBBAIKUAgEpKHNxFAAAEEEEAAAQQQQAABBBBAIIgCBCJBHFX6hAACCCCAAAIIIIAAAggggAACIQUIRELy8CYCCCCAAAIIIIAAAggggAACCARRgEAkiKNKnxBAAAEEEEAAAQQQQAABBBBAIKQAgUhIHt5EAAEEEEAAAQQQQAABBBBAAIEgChCIBHFU6RMCCCCAAAIIIIAAAggggAACCIQUIBAJycObCCCAAAIIIIAAAggggAACCCAQRAECkSCOKn1CAAEEEEAAAQQQQAABBBBAAIGQAgQiIXl4EwEEEEAAAQQQQAABBBBAAAEEgihAIBLEUaVPCCCAAAIIIIAAAggggAACCCAQUoBAJCQPbyKAAAIIIIAAAggggAACCCCAQBAFCESCOKr0CQEEEEAAAQQQQAABBBBAAAEEQgoQiITk4U0EEEAAAQQQQAABBBBAAAEEEAiiAIFIEEfkJUlnAAABHklEQVSVPiGAAAIIIIAAAggggAACCCCAQEgBApGQPLyJAAIIIIAAAggggAACCCCAAAJBFCAQCeKo0icEEEAAAQQQQAABBBBAAAEEEAgpQCASkoc3EUAAAQQQQAABBBBAAAEEEEAgiAIEIkEcVfqEAAIIIIAAAggggAACCCCAAAIhBQhEQvLwJgIIIIAAAggggAACCCCAAAIIBFGAQCSIo0qfEEAAAQQQQAABBBBAAAEEEEAgpACBSEge3kQAAQQQQAABBBBAAAEEEEAAgSAKEIgEcVTpEwIIIIAAAggggAACCCCAAAIIhBQgEAnJw5sIIIAAAggggAACCCCAAAIIIBBEAQKRII4qfUIAAQQQQAABBBBAAAEEEEAAgZAC/x/LvBZS8lbGhAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "3823f74d",
   "metadata": {},
   "source": [
    "## 2. The Quantum Teleportation Protocol <a id='how'></a>\n",
    "To transfer a quantum bit, Alice and Bob must use a third party (Telamon) to send them an entangled qubit pair. Alice then performs some operations on her qubit, sends the results to Bob over a classical communication channel, and Bob then performs some operations on his end to receive Alice’s qubit.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "We will describe the steps on a quantum circuit below. Here, no qubits are actually ‘sent’, you’ll just have to imagine that part!\n",
    "\n",
    "First we set up our session:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8cc55692",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "# Do the necessary imports\n",
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit import IBMQ, Aer, transpile, assemble\n",
    "from qiskit.visualization import plot_histogram, plot_bloch_multivector\n",
    "from qiskit.extensions import Initialize\n",
    "from qiskit_textbook.tools import random_state, array_to_latex"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a1b94c8",
   "metadata": {},
   "source": [
    "and create our quantum circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "96994668",
   "metadata": {},
   "outputs": [],
   "source": [
    "## SETUP\n",
    "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n",
    "\n",
    "qr = QuantumRegister(3, name=\"q\")    # Protocol uses 3 qubits\n",
    "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical bits\n",
    "crx = ClassicalRegister(1, name=\"crx\") # in 2 different registers\n",
    "teleportation_circuit = QuantumCircuit(qr, crz, crx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b10255f2",
   "metadata": {},
   "source": [
    "#### Step 1\n",
    "A third party, Telamon, creates an entangled pair of qubits and gives one to Bob and one to Alice.\n",
    "\n",
    "The pair Telamon creates is a special pair called a Bell pair. In quantum circuit language, the way to create a Bell pair between two qubits is to first transfer one of them to the X-basis ($|+\\rangle$ and $|-\\rangle$) using a Hadamard gate, and then to apply a CNOT gate onto the other qubit controlled by the one in the X-basis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "79cb68d8",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def create_bell_pair(qc, a, b):\n",
    "    \"\"\"Creates a bell pair in qc using qubits a & b\"\"\"\n",
    "    qc.h(a) # Put qubit a into state |+>\n",
    "    qc.cx(a,b) # CNOT with a as control and b as target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ecdced8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SWIyXxGK8JBbjJbEYL4nFeEksxkti/R8KTCTsta8oXQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 212.91x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n",
    "qr = QuantumRegister(3, name=\"q\")\n",
    "crz, crx = ClassicalRegister(1, name=\"crz\"), ClassicalRegister(1, name=\"crx\")\n",
    "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 1\n",
    "# In our case, Telamon entangles qubits q1 and q2\n",
    "# Let's apply this to our circuit:\n",
    "create_bell_pair(teleportation_circuit, 1, 2)\n",
    "# And view the circuit so far:\n",
    "teleportation_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66a228d4",
   "metadata": {},
   "source": [
    "Let's say Alice owns $q_1$ and Bob owns $q_2$ after they part ways.\n",
    "\n",
    "#### Step 2 \n",
    "\n",
    "Alice applies a CNOT gate to $q_1$, controlled by $\\vert\\psi\\rangle$ (the qubit she is trying to send Bob). Then Alice applies a Hadamard gate to $|\\psi\\rangle$. In our quantum circuit, the qubit ($|\\psi\\rangle$) Alice is trying to send is $q_0$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da217642",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def alice_gates(qc, psi, a):\n",
    "    qc.cx(psi, a)\n",
    "    qc.h(psi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0dd4296a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 393.51x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n",
    "qr = QuantumRegister(3, name=\"q\")\n",
    "crz, crx = ClassicalRegister(1, name=\"crz\"), ClassicalRegister(1, name=\"crx\")\n",
    "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 1\n",
    "create_bell_pair(teleportation_circuit, 1, 2)\n",
    "\n",
    "## STEP 2\n",
    "teleportation_circuit.barrier() # Use barrier to separate steps\n",
    "alice_gates(teleportation_circuit, 0, 1)\n",
    "teleportation_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dc12b05",
   "metadata": {},
   "source": [
    "#### Step 3\n",
    "\n",
    "Next, Alice applies a measurement to both qubits that she owns, $q_1$ and $\\vert\\psi\\rangle$, and stores this result in two classical bits. She then sends these two bits to Bob."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "96d592dd",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def measure_and_send(qc, a, b):\n",
    "    \"\"\"Measures qubits a & b and 'sends' the results to Bob\"\"\"\n",
    "    qc.barrier()\n",
    "    qc.measure(a,0)\n",
    "    qc.measure(b,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b197db60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 574.11x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n",
    "qr = QuantumRegister(3, name=\"q\")\n",
    "crz, crx = ClassicalRegister(1, name=\"crz\"), ClassicalRegister(1, name=\"crx\")\n",
    "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 1\n",
    "create_bell_pair(teleportation_circuit, 1, 2)\n",
    "\n",
    "## STEP 2\n",
    "teleportation_circuit.barrier() # Use barrier to separate steps\n",
    "alice_gates(teleportation_circuit, 0, 1)\n",
    "\n",
    "## STEP 3\n",
    "measure_and_send(teleportation_circuit, 0 ,1)\n",
    "teleportation_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab7667fc",
   "metadata": {},
   "source": [
    "#### Step 4\n",
    "\n",
    "Bob, who already has the qubit $q_2$, then applies the following gates depending on the state of the classical bits:\n",
    "\n",
    "00 $\\rightarrow$ Do nothing\n",
    "\n",
    "01 $\\rightarrow$ Apply $X$ gate\n",
    "\n",
    "10 $\\rightarrow$ Apply $Z$ gate\n",
    "\n",
    "11 $\\rightarrow$ Apply $ZX$ gate\n",
    "\n",
    "(*Note that this transfer of information is purely classical*.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "d5efcbcb",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "# This function takes a QuantumCircuit (qc), integer (qubit)\n",
    "# and ClassicalRegisters (crz & crx) to decide which gates to apply\n",
    "def bob_gates(qc, qubit, crz, crx):\n",
    "    # Here we use c_if to control our gates with a classical\n",
    "    # bit instead of a qubit\n",
    "    qc.x(qubit).c_if(crx, 1) # Apply gates if the registers \n",
    "    qc.z(qubit).c_if(crz, 1) # are in the state '1'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "216184a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 754.71x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "# Protocol uses 3 qubits and 2 classical bits in 2 different registers\n",
    "qr = QuantumRegister(3, name=\"q\")\n",
    "crz, crx = ClassicalRegister(1, name=\"crz\"), ClassicalRegister(1, name=\"crx\")\n",
    "teleportation_circuit = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 1\n",
    "create_bell_pair(teleportation_circuit, 1, 2)\n",
    "\n",
    "## STEP 2\n",
    "teleportation_circuit.barrier() # Use barrier to separate steps\n",
    "alice_gates(teleportation_circuit, 0, 1)\n",
    "\n",
    "## STEP 3\n",
    "measure_and_send(teleportation_circuit, 0, 1)\n",
    "\n",
    "## STEP 4\n",
    "teleportation_circuit.barrier() # Use barrier to separate steps\n",
    "bob_gates(teleportation_circuit, 2, crz, crx)\n",
    "teleportation_circuit.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7145be3c",
   "metadata": {},
   "source": [
    "And voila! At the end of this protocol, Alice's qubit has now teleported to Bob."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2af71757",
   "metadata": {},
   "source": [
    "## 3. Simulating the Teleportation Protocol <a id='simulating'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02885c0d",
   "metadata": {},
   "source": [
    "### 3.1 How Will We Test the Protocol on a Quantum Computer? <a id='testing'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee5f7584",
   "metadata": {},
   "source": [
    "In this notebook, we will initialize Alice's qubit in a random state $\\vert\\psi\\rangle$ (`psi`). This state will be created using an `Initialize` gate on $|q_0\\rangle$. In this chapter we use the function `random_state` to choose `psi` for us, but feel free to set `psi` to any qubit state you want."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "dc00142f",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \n",
       "|\\psi\\rangle =\\begin{bmatrix}\n",
       "0.19721 + 0.8694i \\\\\n",
       "0.41518 + 0.18133i\n",
       "\\end{bmatrix}\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
      "The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
      "  x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create random 1-qubit state\n",
    "np.random.seed(0)\n",
    "psi = random_state(1)\n",
    "\n",
    "# Display it nicely\n",
    "array_to_latex(psi, pretext=\"|\\\\psi\\\\rangle =\")\n",
    "# Show it on a Bloch sphere\n",
    "plot_bloch_multivector(psi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6534cde",
   "metadata": {},
   "source": [
    "Let's create our initialization instruction to create $|\\psi\\rangle$ from the state $|0\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "fde76573",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "init_gate = Initialize(psi)\n",
    "init_gate.label = \"init\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad2169aa",
   "metadata": {},
   "source": [
    "### Exercise 1\n",
    "\n",
    "Let's say the state $$|\\phi\\rangle = \\begin{bmatrix} a_0 + ia_1 \\\\ b_0 \\end{bmatrix} $$ is orthogonal to state $|\\psi\\rangle $ we defined above. In order to find the values for $a_0,a_1$ and $b_0$ we need three linearly independent equations. Solving them can be a lot of work, so I just want you to write down three linearly independent equations. In other words, what are the conditions for $|\\phi\\rangle$ to be a normalized and an orthogonal state to $|\\psi\\rangle$?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9377ec4",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd394ead",
   "metadata": {},
   "source": [
    "(`Initialize` is technically not a gate since it contains a reset operation, and so is not reversible. We call it an 'instruction' instead). If the quantum teleportation circuit works, then at the end of the circuit the qubit $|q_2\\rangle$ will be in this state. We will check this using the statevector simulator."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94d16a5d",
   "metadata": {},
   "source": [
    "### 3.2 Using the Statevector Simulator <a id='simulating-sv'></a>\n",
    "\n",
    "We can use the statevector simulator to verify our qubit has been teleported."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "68c653f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 935.31x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "qr = QuantumRegister(3, name=\"q\")   # Protocol uses 3 qubits\n",
    "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical registers\n",
    "crx = ClassicalRegister(1, name=\"crx\")\n",
    "qc = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 0\n",
    "# First, let's initialize Alice's q0\n",
    "qc.append(init_gate, [0])\n",
    "qc.barrier()\n",
    "\n",
    "## STEP 1\n",
    "# Now begins the teleportation protocol\n",
    "create_bell_pair(qc, 1, 2)\n",
    "qc.barrier()\n",
    "\n",
    "## STEP 2\n",
    "# Send q1 to Alice and q2 to Bob\n",
    "alice_gates(qc, 0, 1)\n",
    "\n",
    "## STEP 3\n",
    "# Alice then sends her classical bits to Bob\n",
    "measure_and_send(qc, 0, 1)\n",
    "\n",
    "## STEP 4\n",
    "# Bob decodes qubits\n",
    "bob_gates(qc, 2, crz, crx)\n",
    "\n",
    "# Display the circuit\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35192a27",
   "metadata": {},
   "source": [
    "We can see below, using our statevector simulator, that the state of $|q_2\\rangle$ is the same as the state $|\\psi\\rangle$ we created above, while the states of $|q_0\\rangle$ and $|q_1\\rangle$ have been collapsed to either $|0\\rangle$ or $|1\\rangle$. The state $|\\psi\\rangle$ has been teleported from qubit 0 to qubit 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "04110edf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
      "The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
      "  x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 3 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sv_sim = Aer.get_backend('statevector_simulator')\n",
    "qobj = assemble(qc)\n",
    "out_vector = sv_sim.run(qobj).result().get_statevector()\n",
    "plot_bloch_multivector(out_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82d01357",
   "metadata": {},
   "source": [
    "You can run this cell a few times to make sure. You may notice that the qubits 0 & 1 change states, but qubit 2 is always in the state $|\\psi\\rangle$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0c984db8",
   "metadata": {},
   "source": [
    "### 3.3 Using the QASM Simulator <a id='simulating-qs'></a>\n",
    "\n",
    "Quantum teleportation is designed to send qubits between two parties. We do not have the hardware to demonstrate this, but we can demonstrate that the gates perform the correct transformations on a single quantum chip. Here we use the QASM simulator to simulate how we might test our protocol.\n",
    "\n",
    "On a real quantum computer, we would not be able to sample the statevector, so if we wanted to check our teleportation circuit is working, we need to do things slightly differently. The `Initialize` instruction first performs a reset, setting our qubit to the state $|0\\rangle$. It then applies gates to turn our $|0\\rangle$ qubit into the state $|\\psi\\rangle$:\n",
    "\n",
    "$$ |0\\rangle \\xrightarrow{\\text{Initialize gates}} |\\psi\\rangle $$\n",
    "\n",
    "Since all quantum gates are reversible, we can find the inverse of these gates using:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8353ccf6",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "inverse_init_gate = init_gate.gates_to_uncompute()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6679bcd",
   "metadata": {},
   "source": [
    "This operation has the property:\n",
    "\n",
    "$$ |\\psi\\rangle \\xrightarrow{\\text{Inverse Initialize gates}} |0\\rangle $$\n",
    "\n",
    "To prove the qubit $|q_0\\rangle$ has been teleported to $|q_2\\rangle$, if we do this inverse initialization on $|q_2\\rangle$, we expect to measure $|0\\rangle$ with certainty. We do this in the circuit below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "6216a97d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1115.91x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## SETUP\n",
    "qr = QuantumRegister(3, name=\"q\")   # Protocol uses 3 qubits\n",
    "crz = ClassicalRegister(1, name=\"crz\") # and 2 classical registers\n",
    "crx = ClassicalRegister(1, name=\"crx\")\n",
    "qc = QuantumCircuit(qr, crz, crx)\n",
    "\n",
    "## STEP 0\n",
    "# First, let's initialize Alice's q0\n",
    "qc.append(init_gate, [0])\n",
    "qc.barrier()\n",
    "\n",
    "## STEP 1\n",
    "# Now begins the teleportation protocol\n",
    "create_bell_pair(qc, 1, 2)\n",
    "qc.barrier()\n",
    "\n",
    "## STEP 2\n",
    "# Send q1 to Alice and q2 to Bob\n",
    "alice_gates(qc, 0, 1)\n",
    "\n",
    "## STEP 3\n",
    "# Alice then sends her classical bits to Bob\n",
    "measure_and_send(qc, 0, 1)\n",
    "\n",
    "## STEP 4\n",
    "# Bob decodes qubits\n",
    "bob_gates(qc, 2, crz, crx)\n",
    "\n",
    "## STEP 5\n",
    "# reverse the initialization process\n",
    "qc.append(inverse_init_gate, [2])\n",
    "\n",
    "# Display the circuit\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7473a1b4",
   "metadata": {},
   "source": [
    "We can see the `inverse_init_gate` appearing, labelled 'disentangler' on the circuit diagram. Finally, we measure the third qubit and store the result in the third classical bit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cbacb6c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1176.11x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Need to add a new ClassicalRegister\n",
    "# to see the result\n",
    "cr_result = ClassicalRegister(1)\n",
    "qc.add_register(cr_result)\n",
    "qc.measure(2,2)\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "820e8f2c",
   "metadata": {},
   "source": [
    "and we run our experiment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "c3dafdc5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "t_qc = transpile(qc, qasm_sim)\n",
    "qobj = assemble(t_qc)\n",
    "counts = qasm_sim.run(qobj).result().get_counts()\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e127d54a",
   "metadata": {},
   "source": [
    "We can see we have a 100% chance of measuring $q_2$ (the leftmost bit in the string) in the state $|0\\rangle$. This is the expected result, and indicates the teleportation protocol has worked properly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "212a1e7d",
   "metadata": {},
   "source": [
    "## 4. Understanding Quantum Teleportation <a id=\"understanding-qt\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5dda1e25",
   "metadata": {},
   "source": [
    "As you have worked with the Quantum Teleportation's implementation, it is time to understand the mathematics behind the protocol.\n",
    "\n",
    "#### Step 1\n",
    "\n",
    "Quantum Teleportation begins with the fact that Alice needs to transmit $|\\psi\\rangle = \\alpha|0\\rangle + \\beta|1\\rangle$ (a random qubit) to Bob. She doesn't know the state of the qubit. For this, Alice and Bob take the help of a third party (Telamon). Telamon prepares a pair of entangled qubits for Alice and Bob. The entangled qubits could be written in Dirac Notation as:\n",
    "\n",
    "$$ |e \\rangle = \\frac{1}{\\sqrt{2}} (|00\\rangle + |11\\rangle) $$\n",
    "\n",
    "Alice and Bob each possess one qubit of the entangled pair (denoted as A and B respectively),\n",
    "\n",
    "$$|e\\rangle = \\frac{1}{\\sqrt{2}} (|0\\rangle_A |0\\rangle_B + |1\\rangle_A |1\\rangle_B) $$\n",
    "\n",
    "This creates a three qubit quantum system where Alice has the first two qubits and Bob the last one.\n",
    "\n",
    "$$ \\begin{align*}\n",
    "|\\psi\\rangle \\otimes |e\\rangle &= \\frac{1}{\\sqrt{2}} (\\alpha |0\\rangle \\otimes (|00\\rangle + |11\\rangle) + \\beta |1\\rangle \\otimes (|00\\rangle + |11\\rangle))\\\\\n",
    "&= \\frac{1}{\\sqrt{2}} (\\alpha|000\\rangle + \\alpha|011\\rangle + \\beta|100\\rangle + \\beta|111\\rangle) \n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "644aa003",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "Let's say Telamon is unavailable, instead his son Ajax is. But Ajax can only prepare entangled qubits in the following Bell state:\n",
    "\n",
    "$$ |d \\rangle =  \\frac{1}{\\sqrt{2}} (|01\\rangle + |10\\rangle) $$\n",
    "\n",
    "- Design the circuit for initializing this state.\n",
    "- Write down $|\\psi\\rangle \\otimes | d \\rangle $."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "047a3382",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ecafe73",
   "metadata": {},
   "source": [
    "#### Step 2\n",
    "\n",
    "Now according to the protocol Alice applies CNOT gate on her two qubits followed by Hadamard gate on the first qubit. This results in the state:\n",
    "\n",
    "$$ \n",
    "\\begin{align*} (H \\otimes I \\otimes I) (CNOT \\otimes I) (|\\psi\\rangle \\otimes |e\\rangle)\n",
    "&=(H \\otimes I \\otimes I) (CNOT \\otimes I) \\frac{1}{\\sqrt{2}} (\\alpha|000\\rangle + \\alpha|011\\rangle + \\beta|100\\rangle + \\beta|111\\rangle) \\\\\n",
    "&= (H \\otimes I \\otimes I) \\frac{1}{\\sqrt{2}} (\\alpha|000\\rangle + \\alpha|011\\rangle + \\beta|110\\rangle + \\beta|101\\rangle) \\\\\n",
    "&= \\frac{1}{2}  (\\alpha(|000\\rangle + |011\\rangle + |100\\rangle + |111\\rangle) + \\beta(|010\\rangle + |001\\rangle - |110\\rangle - |101\\rangle)) \\\\\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Which can then be separated and written as: \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "= \\frac{1}{2}(\n",
    " & \\phantom{+} |00\\rangle (\\alpha|0\\rangle + \\beta|1\\rangle) \\hphantom{\\quad )} \\\\\n",
    " & + |01\\rangle (\\alpha|1\\rangle + \\beta|0\\rangle) \\hphantom{\\quad )}\\\\[4pt]\n",
    " & + |10\\rangle (\\alpha|0\\rangle - \\beta|1\\rangle) \\hphantom{\\quad )}\\\\[4pt]\n",
    " & + |11\\rangle (\\alpha|1\\rangle - \\beta|0\\rangle) \\quad )\\\\\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b845d16a",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "\n",
    "In order to use the entangled qubits produced by Ajax to perform quantum teleportation we must modify our protocol. According to the new protocol, Alice will apply a C0NOT gate to her two qubits followed by a Hadamard gate.\n",
    "\n",
    "- Explicitly write down $ (H \\otimes I \\otimes I) (CNOT \\otimes I) (|\\psi\\rangle \\otimes |e\\rangle)  $\n",
    "- Decompose the resulted state like the one above. That is $|00\\rangle \\otimes (\\text{sth})$ for 00,01,10 and 11."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca739d37",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf0fd426",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b0ea7d70",
   "metadata": {},
   "source": [
    "# Step 4\n",
    "\n",
    "Bob, on receiving the bits from Alice, knows he can obtain the original state $|\\psi\\rangle$ by applying appropriate transformations on his qubit that was once part of the entangled pair.\n",
    "\n",
    "The transformations he needs to apply are:\n",
    "\n",
    "$$\n",
    "\\begin{array}{c c c}\n",
    "\\mbox{Bob's State}                 & \\mbox{Bits Received} & \\mbox{Gate Applied} \\\\\n",
    "(\\alpha|0\\rangle + \\beta|1\\rangle) & 00                   & I                   \\\\\n",
    "(\\alpha|1\\rangle + \\beta|0\\rangle) & 01                   & X                   \\\\\n",
    "(\\alpha|0\\rangle - \\beta|1\\rangle) & 10                   & Z                   \\\\\n",
    "(\\alpha|1\\rangle - \\beta|0\\rangle) & 11                   & ZX\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "After this step Bob will have successfully reconstructed Alice's state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d96a2dc7",
   "metadata": {},
   "source": [
    "### Exercise 4\n",
    "\n",
    "Which gates should Bob apply to his qubit to successfully reconstruct Alice's state? Fill in the table below according to your results from Exercise 3.\n",
    "\n",
    "$$\n",
    "\\begin{array}{c c c}\n",
    "\\mbox{Bob's State}                 & \\mbox{Bits Received} & \\mbox{Gate Applied} \\\\\n",
    " & 00                   &                    \\\\\n",
    " & 01                   &                    \\\\\n",
    " & 10                   &                    \\\\\n",
    " & 11                   & \n",
    "\\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "371047bc",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2be3836",
   "metadata": {},
   "source": [
    "## 5. Teleportation on a Real Quantum Computer <a id='real_qc'></a>"
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "e6aa9ae6",
   "metadata": {},
   "source": [
    "### 5.1 IBM hardware and Deferred Measurement <a id='deferred-measurement'></a>\n",
    "\n",
    "The IBM quantum computers currently do not support instructions after measurements, meaning we cannot run the quantum teleportation in its current form on real hardware. Fortunately, this does not limit our ability to perform any computations due to the _deferred measurement principle_ discussed in chapter 4.4 of [1]. The principle states that any measurement can be postponed until the end of the circuit, i.e. we can move all the measurements to the end, and we should see the same results.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Any benefits of measuring early are hardware related: If we can measure early, we may be able to reuse qubits, or reduce the amount of time our qubits are in their fragile superposition. In this example, the early measurement in quantum teleportation would have allowed us to transmit a qubit state without a direct quantum communication channel.\n",
    "\n",
    "While moving the gates allows us to demonstrate the \"teleportation\" circuit on real hardware, it should be noted that the benefit of the teleportation process (transferring quantum states via classical channels) is lost.\n",
    "\n",
    "Let us re-write the `bob_gates` function to `new_bob_gates`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "47cae343",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def new_bob_gates(qc, a, b, c):\n",
    "    qc.cx(b, c)\n",
    "    qc.cz(a, c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9cfc0c2",
   "metadata": {},
   "source": [
    "And create our new circuit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "9b80e582",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1049.8x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(3,1)\n",
    "\n",
    "# First, let's initialize Alice's q0\n",
    "qc.append(init_gate, [0])\n",
    "qc.barrier()\n",
    "\n",
    "# Now begins the teleportation protocol\n",
    "create_bell_pair(qc, 1, 2)\n",
    "qc.barrier()\n",
    "# Send q1 to Alice and q2 to Bob\n",
    "alice_gates(qc, 0, 1)\n",
    "qc.barrier()\n",
    "# Alice sends classical bits to Bob\n",
    "new_bob_gates(qc, 0, 1, 2)\n",
    "\n",
    "# We undo the initialization process\n",
    "qc.append(inverse_init_gate, [2])\n",
    "\n",
    "# See the results, we only care about the state of qubit 2\n",
    "qc.measure(2,0)\n",
    "\n",
    "# View the results:\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17e61ded",
   "metadata": {},
   "source": [
    "### 5.2 Executing <a id='executing'></a> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "d06141c3",
   "metadata": {
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [],
   "source": [
    "# First, see what devices we are allowed to use by loading our saved accounts\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='ibm-q')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "dce71f47",
   "metadata": {
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-41-9873ace37c62>:8: DeprecationWarning: Passing a Qobj to Backend.run is deprecated and will be removed in a future release. Please pass in circuits or pulse schedules instead.\n",
      "  job = backend.run(qobj)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# get the least-busy backend at IBM and run the quantum circuit there\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "backend = least_busy(provider.backends(filters=lambda b: b.configuration().n_qubits >= 3 and\n",
    "                                   not b.configuration().simulator and b.status().operational==True))\n",
    "t_qc = transpile(qc, backend, optimization_level=3)\n",
    "qobj = assemble(t_qc)\n",
    "job = backend.run(qobj)\n",
    "job_monitor(job)  # displays job status under cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "6e94ba6c",
   "metadata": {
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'0': 977, '1': 47}\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get the results and display them\n",
    "exp_result = job.result()\n",
    "exp_counts = exp_result.get_counts(qc)\n",
    "print(exp_counts)\n",
    "plot_histogram(exp_counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c05a102",
   "metadata": {},
   "source": [
    "As we see here, there are a few results in which we measured $|1\\rangle$. These arise due to errors in the gates and the qubits. In contrast, our simulator in the earlier part of the notebook had zero errors in its gates, and allowed error-free teleportation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "919ba828",
   "metadata": {
    "scrolled": false,
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The experimental error rate : 0.046%\n"
     ]
    }
   ],
   "source": [
    "print(f\"The experimental error rate : {exp_counts['1']/sum(exp_counts.values()):.3f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "996cb515",
   "metadata": {},
   "source": [
    "### Exercise 5\n",
    "\n",
    "Now that all theoretical work for using Ajax's entangled pairs is completed, let's try it with a real quantum computer! Complete the below parts and run the next cell and see if you have done it correctly!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50a4d363",
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = QuantumCircuit(3,1)\n",
    "\n",
    "# First, let's initialize Alice's q0\n",
    "# We don't need to change this part!\n",
    "qc.append(init_gate, [0])\n",
    "qc.barrier()\n",
    "\n",
    "# Now begins the teleportation protocol\n",
    "# Initialize 1st and 2nd qubit to |phi> = 1/sqrt(2) * (|01> + |10>)\n",
    "# Your code here!\n",
    "\n",
    "# Send q1 to Alice and q2 to Bob\n",
    "# You don't need to change this part.\n",
    "qc.c0x(0,1)\n",
    "qc.h(0)\n",
    "qc.barrier()\n",
    "\n",
    "# Alice sends classical bits to Bob\n",
    "# This is the part where we Bob applies the transformations you found in Exercise 4. \n",
    "# If you need to apply Y gate if a specific classical bit is 1, you can achieve the \n",
    "# same effect by applying a CY gate where the control qubit is qubit 1, for classical bit 1.\n",
    "\n",
    "\n",
    "# We undo the initialization process\n",
    "qc.append(inverse_init_gate, [2])\n",
    "\n",
    "# See the results, we only care about the state of qubit 2\n",
    "qc.measure(2,0)\n",
    "\n",
    "# View the results:\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "476b8833",
   "metadata": {},
   "outputs": [],
   "source": [
    "# First run this cell to test your code!\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='ibm-q')\n",
    "\n",
    "# get the least-busy backend at IBM and run the quantum circuit there\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "backend = least_busy(provider.backends(filters=lambda b: b.configuration().n_qubits >= 3 and\n",
    "                                   not b.configuration().simulator and b.status().operational==True))\n",
    "t_qc = transpile(qc, backend, optimization_level=3)\n",
    "qobj = assemble(t_qc)\n",
    "job = backend.run(qobj)\n",
    "job_monitor(job)  # displays job status under cell"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d86be1a4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Then this cell !\n",
    "# Get the results and display them\n",
    "exp_result = job.result()\n",
    "exp_counts = exp_result.get_counts(qc)\n",
    "print(exp_counts)\n",
    "plot_histogram(exp_counts)\n",
    "# If you get mostly 0, that means you did it correctly!!!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b215d73",
   "metadata": {
    "colab_type": "text",
    "id": "OQYW8N5rPyGC",
    "tags": [
     "remove_cell"
    ]
   },
   "source": [
    "# Superdense Coding"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b21e361",
   "metadata": {
    "colab_type": "text",
    "id": "OQYW8N5rPyGC"
   },
   "source": [
    "This notebook demonstrates the Superdense Coding (SDC) protocol. We first use Qiskit's simulator to test our quantum circuit, and then try it out on a real quantum computer.\n",
    "\n",
    "## Contents\n",
    "\n",
    "1. [Superdense Coding and Quantum Teleportation](#difference)\n",
    "2. [The Process](#process)    \n",
    "    2.1 [Step 1](#step1)    \n",
    "    2.2 [Step 2](#step2)    \n",
    "    2.3 [Step 3](#step3)\n",
    "3. [Simulating the Superdense Coding Protocol](#simulating)    \n",
    "    3.1 [3.1 Visualizing Our Measurements](#visualising)    \n",
    "4. [Superdense Coding on a Real Quantum Computer](#real_qc)\n",
    "\n",
    "\n",
    "## 1. The Difference between Superdense Coding and Quantum Teleportation <a id='difference'></a>\n",
    "\n",
    "Quantum teleportation and superdense coding are closely related, to avoid confusion we need to clarify the difference.\n",
    "\n",
    "Quantum teleportation is a process by which the state of qubit ($|\\psi\\rangle$) can be transmitted from one location to another, using two bits of classical communication and a Bell pair. In other words, we can say it is a protocol that destroys the quantum state of a qubit in one location and recreates it on a qubit at a distant location, with the help of shared entanglement. Superdense coding is a procedure that allows someone to send two classical bits to another party using just a single qubit of communication.\n",
    "\n",
    "| Teleportation                                     | Superdense Coding                                    |\n",
    "|:-------------------------------------------------:|:----------------------------------------------------:|\n",
    "| Transmit one<br>qubit using two<br>classical bits | Transmit two<br>classical bits<br>using one<br>qubit |\n",
    "\n",
    "\n",
    "The teleportation protocol can be thought of as a flipped version of the superdense coding protocol, in the sense that Alice and Bob merely “swap their equipment.”"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "2db5c8ee",
   "metadata": {
    "colab_type": "text",
    "id": "N5LyBKFXYG41"
   },
   "source": [
    "\n",
    "\n",
    "## 2. The Process <a id='process'></a>\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "### 2.1 Step 1 <a id='step1'></a>\n",
    "The process starts with a third party, who we'll call Charlie. Two qubits are prepared by Charlie in an entangled state. He initially starts the 2 qubits in the basis state $|0\\rangle$. He applies Hadamard gate ($H$) to the first qubit to create superposition. He then applies CNOT gate ($CX$) using the first qubit as a control and the second as the target. This is the entangled state (Bell pair) we mentioned earlier. \n",
    "\n",
    "#### Outcome States\n",
    "\n",
    "Charlie first applies a Hadamard gate. \n",
    "\n",
    "When the H-gate is applied to first qubit, it creates superposition and we get the state:\n",
    "\n",
    "\n",
    "$$|0+\\rangle  =  \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |01\\rangle)$$\n",
    "\n",
    "\n",
    "\n",
    "Then Charlie applies the CNOT gate. The CNOT gate entangles both qubits, i.e. it flips the target if the control is $|1\\rangle$. Note that the control qubit is our rightmost qubit.\n",
    "\n",
    "\n",
    "\n",
    "$$\\text{CNOT} \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |01\\rangle) = \\tfrac{1}{\\sqrt{2}}(|00\\rangle + |11\\rangle)$$\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "55aeb1e8",
   "metadata": {},
   "source": [
    "### Exercise 6\n",
    "\n",
    "Let's say we want to implement a superdense coding protocol but Telamon and Ajax are not available but Ajax's step brother Teucer is. However, Teucer can only prepare the following entangled state:\n",
    "\n",
    "$$ |f \\rangle  = \\frac{1}{\\sqrt{2}} ( |00\\rangle - |11 \\rangle ) $$\n",
    "\n",
    "- Design the circuit for initializing this state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed90fdd4",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "622c0194",
   "metadata": {},
   "source": [
    "### 2.2 Step 2 <a id='step2'></a>\n",
    "\n",
    "Charlie sends the first qubit to Alice and the second qubit to Bob. The goal of the protocol is for Alice to send 2 classical bits of information to Bob using her qubit. But before she does, she needs to apply a set of quantum gates to her qubit depending on the 2 bits of information she wants to send:\n",
    "\n",
    "\n",
    "#### Encoding Rules for Superdense Coding (Alice protocol):\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "\n",
    "Thus if she wants to send a `00`, she does nothing to her qubit (apply the identity ($I$) gate). If she sends a `10`, then she applies the $X$ gate. Depending on what she wants to send, she applies the appropriate gate, then sends her qubit to Bob for the final step in the process.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e82e1e8",
   "metadata": {},
   "source": [
    "### Exercise 7\n",
    "\n",
    "Let's say Alice does the following operations according to the message she wants to send. Fill in the last column.\n",
    "\n",
    "|Intended Message:              | Applied Gate:           |  Resulting State($\\cdot \\sqrt{2})$:  |\n",
    "|:--------------------------:|:--------------------------:|:---------------:|\n",
    "| 00  | I  |     |\n",
    "| 01  | X  |     |\n",
    "| 10 | Z   |    |\n",
    "| 11 | XZ  |    |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d62bfec",
   "metadata": {},
   "source": [
    "\n",
    "### 2.3 Step 3 <a id='step3'></a>\n",
    "\n",
    "Bob receives Alice's qubit (rightmost qubit) and uses his qubit to decode Alice's message. Notice that he does not need to have knowledge of the state in order to decode it — he simply uses the restoration operation.\n",
    "\n",
    "Bob applies a CNOT gate using the rightmost qubit as control and the leftmost as target. Then he applies a Hadamard gate and finally performs a measurement on both qubits to extract Alice's message.\n",
    "\n",
    "| Bob Receives:              | After CNOT-gate:           |  After H-gate:  |\n",
    "|:--------------------------:|:--------------------------:|:---------------:|\n",
    "| $|00\\rangle + |11\\rangle$  | $|00\\rangle + |01\\rangle$  |  $|00\\rangle$   |\n",
    "| $|01\\rangle + |10\\rangle$  | $|11\\rangle + |10\\rangle$  |  $|10\\rangle$   |\n",
    "| $|00\\rangle - |11\\rangle$  | $|00\\rangle - |01\\rangle$  |  $|01\\rangle$   |\n",
    "| $-|01\\rangle + |10\\rangle$ | $-|11\\rangle + |10\\rangle$ | $-|11\\rangle$   |\n",
    "\n",
    "When Bob performs the measurements, he is certain to get the message Alice sent him. Note that the last outcome has a negative sign $-|11\\rangle$, writing it as $|11\\rangle$ is also correct as this is global phase and is not measureable.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e93807d7",
   "metadata": {},
   "source": [
    "### Exercise 8\n",
    "\n",
    "After Bob receives the state in Exercise 7, he should perform three operations to get the classical message. He should first apply a CNOT gate, then a Hadamard to the first qubit, then a X gate to the first qubit. Fill in the table below to see if this procedure allows Bob to receive the classical message correctly. Note that the first column of the following table should be the last column of the table in Exercise 7!\n",
    "\n",
    "| Bob Receives:              | After CNOT-gate:           |  After H-gate:  | After X-gate:   | \n",
    "|:--------------------------:|:--------------------------:|:---------------:|:---------------:|\n",
    "|   |  |     |   |\n",
    "|   |  |     |   |\n",
    "|   |  |     |   |\n",
    "|  |  |     |   |\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b757ee46",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "369c7470",
   "metadata": {},
   "source": [
    "## 3. Simulating the Superdense Coding Protocol <a id='simulating'></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "32137ad8",
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "u6m-M5G0X4HO"
   },
   "outputs": [],
   "source": [
    "# Importing everything\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit import IBMQ, Aer, transpile, assemble\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96f3f249",
   "metadata": {},
   "source": [
    "We saw that to create an entangled pair, we needed to do a H-gate followed by a CNOT. Let's create a function that takes a `QuantumCircuit` and entangles the qubits with indices `a` and `b`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "c3e673d1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function that takes a QuantumCircuit (qc) \n",
    "# and two integers (a & b)\n",
    "def create_bell_pair(qc, a, b):\n",
    "    qc.h(a) # Apply a h-gate to the first qubit\n",
    "    qc.cx(a,b) # Apply a CNOT, using the first qubit as the control"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05f82a7a",
   "metadata": {},
   "source": [
    "Next we need to encode our message. We saw that there were four possible messages we could send: `00`, `10`, `01` or `11`. Let's create a function that takes this message and applies the appropriate gates for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "9f1b9765",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function that takes a QuantumCircuit (qc)\n",
    "# a qubit index (qubit) and a message string (msg)\n",
    "def encode_message(qc, qubit, msg):\n",
    "    if msg == \"00\":\n",
    "        pass    # To send 00 we do nothing\n",
    "    elif msg == \"10\":\n",
    "        qc.x(qubit) # To send 10 we apply an X-gate\n",
    "    elif msg == \"01\":\n",
    "        qc.z(qubit) # To send 01 we apply a Z-gate\n",
    "    elif msg == \"11\":\n",
    "        qc.z(qubit) # To send 11, we apply a Z-gate\n",
    "        qc.x(qubit) # followed by an X-gate\n",
    "    else:\n",
    "        print(\"Invalid Message: Sending '00'\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5ee41f0",
   "metadata": {},
   "source": [
    "Finally, we need to decode our message, we saw we could do this using a CNOT followed by a H-gate. Let's create a function that does this for us too:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "cbd4aebd",
   "metadata": {},
   "outputs": [],
   "source": [
    "def decode_message(qc, a, b):\n",
    "    qc.cx(a,b)\n",
    "    qc.h(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "286d7093",
   "metadata": {},
   "source": [
    "Finally, we can put this together to complete our protocol."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "b69dab73",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 185
    },
    "colab_type": "code",
    "id": "_HMTtQ8IYh19",
    "outputId": "2d05d830-a863-49d9-c522-5a0e331d2fe1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 718.879x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the quantum circuit with 2 qubits\n",
    "qc = QuantumCircuit(2)\n",
    "\n",
    "\n",
    "# First, Charlie creates the entangled pair between Alice and Bob\n",
    "create_bell_pair(qc, 0, 1)\n",
    "qc.barrier() # This adds a barrier to our circuit. A barrier \n",
    "             # separates the gates in our diagram and makes it \n",
    "             # clear which part of the circuit is which\n",
    "\n",
    "# At this point, qubit 0 goes to Alice and qubit 1 goes to Bob\n",
    "\n",
    "# Next, Alice encodes her message onto qubit 0. In this case,\n",
    "# we want to send the message '10'. You can try changing this\n",
    "# value and see how it affects the circuit\n",
    "message = \"10\"\n",
    "encode_message(qc, 0, message)\n",
    "qc.barrier()\n",
    "# Alice then sends her qubit to Bob.\n",
    "\n",
    "# After recieving qubit 0, Bob applies the recovery protocol:\n",
    "decode_message(qc, 0, 1)\n",
    "\n",
    "# Finally, Bob measures his qubits to read Alice's message\n",
    "qc.measure_all()\n",
    "\n",
    "# Draw our output\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45f8fb3b",
   "metadata": {
    "colab_type": "text",
    "id": "ODWmbUKVY2a5"
   },
   "source": [
    "### 3.1 Visualizing Our Measurements <a id='visualising'></a>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "aca05180",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 352
    },
    "colab_type": "code",
    "id": "caUnckbWY0Sd",
    "outputId": "f2347fd0-8027-435d-dcab-0fd3a0044c92"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'10': 1024}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "qobj = assemble(qc)\n",
    "result = qasm_sim.run(qobj).result()\n",
    "counts = result.get_counts(qc)\n",
    "print(counts)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b4229b2",
   "metadata": {},
   "source": [
    "Our simulator simulates a perfect quantum computer. We can see that, without errors, we get a 100% chance of measuring the correct message."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d1ac76c",
   "metadata": {
    "colab_type": "text",
    "id": "fMHrapgKZCpp"
   },
   "source": [
    "## 4. Superdense Coding on a Real Quantum Computer <a id='real_qc'></a>\n",
    "\n",
    "\n",
    "We can now see this working on a real quantum computer. First, we want to load our account to get the least busy quantum system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "9bcb8fdc",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 85
    },
    "colab_type": "code",
    "id": "CVZk6LPJaQXa",
    "outputId": "91fc343f-5c01-428f-a324-888a641b4c55",
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2021-05-22 19:29:13,732: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "least busy backend:  ibmq_manila\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-50-4c5440f57654>:16: DeprecationWarning: Passing a Qobj to Backend.run is deprecated and will be removed in a future release. Please pass in circuits or pulse schedules instead.\n",
      "  job = backend.run(qobj)\n"
     ]
    }
   ],
   "source": [
    "from qiskit import IBMQ\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "shots = 1024\n",
    "\n",
    "# Load local account information\n",
    "IBMQ.load_account()\n",
    "# Get the least busy backend\n",
    "provider = IBMQ.get_provider(hub='ibm-q')\n",
    "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 2 \n",
    "                                       and not x.configuration().simulator \n",
    "                                       and x.status().operational==True))\n",
    "print(\"least busy backend: \", backend)\n",
    "# Run our circuit\n",
    "t_qc = transpile(qc, backend, optimization_level=3)\n",
    "qobj = assemble(t_qc)\n",
    "job = backend.run(qobj)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "520d7434",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "rtFSdEg-bE0u",
    "outputId": "5fb9cd41-db14-4298-882f-9fee155158d9",
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# Monitoring our job\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "job_monitor(job)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "2c4b28cc",
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 335
    },
    "colab_type": "code",
    "id": "ufD9dKRded1X",
    "outputId": "87a43f61-0d3b-40db-8107-d925414b0f5d",
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Plotting our result\n",
    "result = job.result()\n",
    "plot_histogram(result.get_counts(qc))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fc9aa64",
   "metadata": {
    "colab_type": "text",
    "id": "idsn5tuwfG_4"
   },
   "source": [
    "As we see that there are a few results from the other three states when run in a real quantum computer. These are due to errors in the gates and qubit decoherence. We will learn more about these errors in later sections."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "28597999",
   "metadata": {
    "tags": [
     "uses-hardware"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 81.74%\n"
     ]
    }
   ],
   "source": [
    "correct_results = result.get_counts(qc)[message]\n",
    "accuracy = (correct_results/shots)*100\n",
    "print(f\"Accuracy = {accuracy:.2f}%\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee7ba07d",
   "metadata": {},
   "source": [
    "### Exercise 9\n",
    "\n",
    "Now that all theoretical work for using Teucer's entangled pairs is completed, let's try it with a real quantum computer! Complete the below parts and run the next cell and see if you have done it correctly!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "4ef5b6af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 478.079x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the quantum circuit with 2 qubits\n",
    "qc = QuantumCircuit(2)\n",
    "\n",
    "\n",
    "# First, Teucer creates the entangled pair between Alice and Bob\n",
    "# Your code for initializing |f> = 1/sqrt(2) * (|00> - |11>) here !!\n",
    "\n",
    "qc.barrier() # This adds a barrier to our circuit. A barrier \n",
    "             # separates the gates in our diagram and makes it \n",
    "             # clear which part of the circuit is which\n",
    "\n",
    "# At this point, qubit 0 goes to Alice and qubit 1 goes to Bob\n",
    "\n",
    "# Next, Alice encodes her message onto qubit 0. In this case,\n",
    "# we want to send the message '10'. You can try changing this\n",
    "# value and see how it affects the circuit\n",
    "# You don't need to change this part !!!\n",
    "message = \"10\"\n",
    "if message == \"01\":\n",
    "    qc.x(0)\n",
    "elif message == \"10\":\n",
    "    qc.z(0)\n",
    "elif message == \"11\":\n",
    "    qc.z(0)\n",
    "    qc.x(0)\n",
    "qc.barrier()\n",
    "# Alice then sends her qubit to Bob.\n",
    "\n",
    "# After recieving qubit 0, Bob applies the recovery protocol:\n",
    "# Construct the circuit that applies the receiving protocol decribed in Exercise 8 here !!!\n",
    "\n",
    "\n",
    "# Finally, Bob measures his qubits to read Alice's message\n",
    "qc.measure_all()\n",
    "\n",
    "# Draw our output\n",
    "qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "9c1c234c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ibmqfactory.load_account:WARNING:2021-05-22 19:36:14,960: Credentials are already in use. The existing account in the session will be replaced.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "least busy backend:  ibmq_manila\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-55-338de7cda6aa>:18: DeprecationWarning: Passing a Qobj to Backend.run is deprecated and will be removed in a future release. Please pass in circuits or pulse schedules instead.\n",
      "  job = backend.run(qobj)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Run this cell to test your code!!! \n",
    "\n",
    "from qiskit import IBMQ\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "shots = 1024\n",
    "\n",
    "# Load local account information\n",
    "IBMQ.load_account()\n",
    "# Get the least busy backend\n",
    "provider = IBMQ.get_provider(hub='ibm-q')\n",
    "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 2 \n",
    "                                       and not x.configuration().simulator \n",
    "                                       and x.status().operational==True))\n",
    "print(\"least busy backend: \", backend)\n",
    "# Run our circuit\n",
    "t_qc = transpile(qc, backend, optimization_level=3)\n",
    "qobj = assemble(t_qc)\n",
    "job = backend.run(qobj)\n",
    "\n",
    "# Plotting our result\n",
    "result = job.result()\n",
    "plot_histogram(result.get_counts(qc))\n",
    "\n",
    "# If the result you obtained is mainly the message you wanted to sent, than you did it correctly."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a18bffa0",
   "metadata": {
    "tags": [
     "remove_cell"
    ]
   },
   "source": [
    "# Quantum Key Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baed5eb5",
   "metadata": {
    "tags": [
     "contents"
    ]
   },
   "source": [
    "## Contents\n",
    "\n",
    "1. Introduction\n",
    "2. Protocol Overview\n",
    "3. Qiskit Example: Without Interception\n",
    "4. Qiskit Example: With Interception\n",
    "5. Risk Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e916266",
   "metadata": {},
   "source": [
    "## 1. Introduction\n",
    "\n",
    "When Alice and Bob want to communicate a secret message (such as Bob’s online banking details) over an insecure channel (such as the internet), it is essential to encrypt the message. Since cryptography is a large area and almost all of it is outside the scope of this textbook, we will have to believe that Alice and Bob having a secret key that no one else knows is useful and allows them to communicate using symmetric-key cryptography.\n",
    "\n",
    "If Alice and Bob want to use Eve’s classical communication channel to share their key, it is impossible to tell if Eve has made a copy of this key for herself- they must place complete trust in Eve that she is not listening. If, however, Eve provides a quantum communication channel, Alice and Bob no longer need to trust Eve at all- they will know if she tries to read Bob’s message before it gets to Alice.\n",
    "\n",
    "For some readers, it may be useful to give an idea of how a quantum channel may be physically implemented. An example of a classical channel could be a telephone line; we send electric signals through the line that represent our message (or bits). A proposed example of a quantum communication channel could be some kind of fibre-optic cable, through which we can send individual photons (particles of light). Photons have a property called _polarisation,_ and this polarisation can be one of two states. We can use this to represent a qubit.\n",
    "\n",
    "\n",
    "## 2. Protocol Overview  \n",
    "\n",
    "The protocol makes use of the fact that measuring a qubit can change its state. If Alice sends Bob a qubit, and an eavesdropper (Eve) tries to measure it before Bob does, there is a chance that Eve’s measurement will change the state of the qubit and Bob will not receive the qubit state Alice sent.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "6e65cd43",
   "metadata": {
    "scrolled": true,
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Imports Successful\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, Aer, transpile, assemble\n",
    "from qiskit.visualization import plot_histogram, plot_bloch_multivector\n",
    "from numpy.random import randint\n",
    "import numpy as np\n",
    "print(\"Imports Successful\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e28d019b",
   "metadata": {},
   "source": [
    "If Alice prepares a qubit in the state $|+\\rangle$ (`0` in the $X$-basis), and Bob measures it in the $X$-basis, Bob is sure to measure `0`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "27c88b8e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 314.126x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1,1)\n",
    "# Alice prepares qubit in state |+>\n",
    "qc.h(0)\n",
    "qc.barrier()\n",
    "# Alice now sends the qubit to Bob\n",
    "# who measures it in the X-basis\n",
    "qc.h(0)\n",
    "qc.measure(0,0)\n",
    "\n",
    "# Draw and simulate circuit\n",
    "display(qc.draw())\n",
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "job = qasm_sim.run(assemble(qc))\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5211e765",
   "metadata": {},
   "source": [
    "But if Eve tries to measure this qubit in the $Z$-basis before it reaches Bob, she will change the qubit's state from $|+\\rangle$ to either $|0\\rangle$ or $|1\\rangle$, and Bob is no longer certain to measure `0`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "2ba36a0a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 374.326x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc = QuantumCircuit(1,1)\n",
    "# Alice prepares qubit in state |+>\n",
    "qc.h(0)\n",
    "# Alice now sends the qubit to Bob\n",
    "# but Eve intercepts and tries to read it\n",
    "qc.measure(0, 0)\n",
    "qc.barrier()\n",
    "# Eve then passes this on to Bob\n",
    "# who measures it in the X-basis\n",
    "qc.h(0)\n",
    "qc.measure(0,0)\n",
    "\n",
    "# Draw and simulate circuit\n",
    "display(qc.draw())\n",
    "qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "job = qasm_sim.run(assemble(qc))\n",
    "plot_histogram(job.result().get_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d9e7d4e",
   "metadata": {},
   "source": [
    "We can see here that Bob now has a 50% chance of measuring `1`, and if he does, he and Alice will know there is something wrong with their channel.\n",
    "\n",
    "The quantum key distribution protocol involves repeating this process enough times that an eavesdropper has a negligible chance of getting away with this interception. It is roughly as follows:\n",
    "\n",
    "**- Step 1**\n",
    "\n",
    "Alice chooses a string of random bits, e.g.:\n",
    "\n",
    "`1000101011010100`\n",
    "\n",
    "And a random choice of basis for each bit:\n",
    "\n",
    "`ZZXZXXXZXZXXXXXX`\n",
    "\n",
    "Alice keeps these two pieces of information private to herself. \n",
    "\n",
    "**- Step 2**\n",
    "\n",
    "Alice then encodes each bit onto a string of qubits using the basis she chose; this means each qubit is in one of the states $|0\\rangle$, $|1\\rangle$, $|+\\rangle$ or $|-\\rangle$, chosen at random. In this case, the string of qubits would look like this:\n",
    "\n",
    "$$ |1\\rangle|0\\rangle|+\\rangle|0\\rangle|-\\rangle|+\\rangle|-\\rangle|0\\rangle|-\\rangle|1\\rangle|+\\rangle|-\\rangle|+\\rangle|-\\rangle|+\\rangle|+\\rangle\n",
    "$$\n",
    "\n",
    "This is the message she sends to Bob.\n",
    "\n",
    "**- Step 3**\n",
    "\n",
    "Bob then measures each qubit at random, for example, he might use the bases:\n",
    "\n",
    "`XZZZXZXZXZXZZZXZ`\n",
    "\n",
    "And Bob keeps the measurement results private.\n",
    "\n",
    "**- Step 4**\n",
    "\n",
    "Bob and Alice then publicly share which basis they used for each qubit. If Bob measured a qubit in the same basis Alice prepared it in, they use this to form part of their shared secret key, otherwise they discard the information for that bit.\n",
    "\n",
    "**- Step 5**\n",
    "\n",
    "Finally, Bob and Alice share a random sample of their keys, and if the samples match, they can be sure (to a small margin of error) that their transmission is successful.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9d322fe",
   "metadata": {},
   "source": [
    "## 3. Qiskit Example: Without Interception\n",
    "\n",
    "Let’s first see how the protocol works when no one is listening in, then we can see how Alice and Bob are able to detect an eavesdropper. As always, let's start by importing everything we need:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f03487dd",
   "metadata": {},
   "source": [
    "To generate pseudo-random keys, we will use the `randint` function from numpy. To make sure you can reproduce the results on this page, we will set the seed to 0:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "83037bec",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb6e0f49",
   "metadata": {},
   "source": [
    "We will call the length of Alice's initial message `n`. In this example, Alice will send a message 100 qubits long:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "0e2dc2e7",
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 100"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3a1ac54",
   "metadata": {},
   "source": [
    "### 3.1 Step 1:\n",
    "\n",
    "Alice generates her random set of bits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "9b29f077",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0\n",
      " 1 1 0 0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 1 1 0 0\n",
      " 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "print(alice_bits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c3add8a",
   "metadata": {},
   "source": [
    "At the moment, the set of bits '`alice_bits`' is only known to Alice. We will keep track of what information is only known to Alice, what information is only known to Bob, and what has been sent over Eve's channel in a table like this:\n",
    "\n",
    "| Alice's Knowledge |Over Eve's Channel| Bob's Knowledge |\n",
    "|:-----------------:|:----------------:|:---------------:|\n",
    "|     alice_bits    |                  |       &nbsp;    |\n",
    "\n",
    "### 3.2 Step 2:\n",
    "\n",
    "Alice chooses to encode each bit on qubit in the $X$ or $Z$-basis at random, and stores the choice for each qubit in `alice_bases`. In this case, a `0` means \"prepare in the $Z$-basis\", and a `1` means \"prepare in the $X$-basis\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "ff932d2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 0 1 0\n",
      " 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 0\n",
      " 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "## Step 1\n",
    "#Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "print(alice_bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "190ecfb7",
   "metadata": {},
   "source": [
    "Alice also keeps this knowledge private:\n",
    "\n",
    "| Alice's Knowledge |Over Eve's Channel| Bob's Knowledge |\n",
    "|:-----------------:|:----------------:|:---------------:|\n",
    "|     alice_bits    |                  |                 |\n",
    "|    alice_bases    |                  |     &nbsp;      |\n",
    "\n",
    "The function `encode_message` below, creates a list of `QuantumCircuit`s, each representing a single qubit in Alice's message:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "ca81ded9",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def encode_message(bits, bases):\n",
    "    message = []\n",
    "    for i in range(n):\n",
    "        qc = QuantumCircuit(1,1)\n",
    "        if bases[i] == 0: # Prepare qubit in Z-basis\n",
    "            if bits[i] == 0:\n",
    "                pass \n",
    "            else:\n",
    "                qc.x(0)\n",
    "        else: # Prepare qubit in X-basis\n",
    "            if bits[i] == 0:\n",
    "                qc.h(0)\n",
    "            else:\n",
    "                qc.x(0)\n",
    "                qc.h(0)\n",
    "        qc.barrier()\n",
    "        message.append(qc)\n",
    "    return message"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "6bbfe1c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44f422fd",
   "metadata": {},
   "source": [
    "We can see that the first bit in `alices_bits` is `0`, and the basis she encodes this in is the $X$-basis (represented by `1`):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "a1713cea",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bit = 0\n",
      "basis = 1\n"
     ]
    }
   ],
   "source": [
    "print('bit = %i' % alice_bits[0])\n",
    "print('basis = %i' % alice_bases[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f2e2ee7",
   "metadata": {},
   "source": [
    "And if we view the first circuit in `message` (representing the first qubit in Alice's message), we can verify that Alice has prepared a qubit in the state $|+\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "6188d843",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 193.726x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "message[0].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "803deea3",
   "metadata": {},
   "source": [
    "As another example, we can see that the fourth bit in `alice_bits` is `1`, and it is encoded in the $Z$-basis, Alice prepares the corresponding qubit in the state $|1\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "a9967a35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bit = 1\n",
      "basis = 0\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 193.726x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('bit = %i' % alice_bits[4])\n",
    "print('basis = %i' % alice_bases[4])\n",
    "message[4].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcea833e",
   "metadata": {},
   "source": [
    "This message of qubits is then sent to Bob over Eve's quantum channel:\n",
    "\n",
    "| Alice's Knowledge |Over Eve's Channel| Bob's Knowledge |\n",
    "|:-----------------:|:----------------:|:---------------:|\n",
    "|     alice_bits    |                  |                 |\n",
    "|    alice_bases    |                  |                 |\n",
    "|      message      |     message      |     message     |\n",
    "\n",
    "### 3.3 Step 3:\n",
    "\n",
    "Bob then measures each qubit in the $X$ or $Z$-basis at random and stores this information:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "3b2b3a83",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1\n",
      " 0 1 0 0 1 0 1 1 1 1 0 0 0 1 1 1 0 1 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 1 1 1 0\n",
      " 0 0 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 1 0 1 0 0 0 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "\n",
    "## Step 3\n",
    "# Decide which basis to measure in:\n",
    "bob_bases = randint(2, size=n)\n",
    "print(bob_bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "776256cc",
   "metadata": {},
   "source": [
    "`bob_bases` stores Bob's choice for which basis he measures each qubit in.\n",
    "\n",
    "| Alice's Knowledge |Over Eve's Channel| Bob's Knowledge |\n",
    "|:-----------------:|:----------------:|:---------------:|\n",
    "|     alice_bits    |                  |                 |\n",
    "|    alice_bases    |                  |                 |\n",
    "|      message      |     message      |     message     |\n",
    "|                   |                  |    bob_bases    |\n",
    "\n",
    "Below, the function `measure_message` applies the corresponding measurement and simulates the result of measuring each qubit. We store the measurement results in `bob_results`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e8ce2123",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def measure_message(message, bases):\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    measurements = []\n",
    "    for q in range(n):\n",
    "        if bases[q] == 0: # measuring in Z-basis\n",
    "            message[q].measure(0,0)\n",
    "        if bases[q] == 1: # measuring in X-basis\n",
    "            message[q].h(0)\n",
    "            message[q].measure(0,0)\n",
    "        qasm_sim = Aer.get_backend('qasm_simulator')\n",
    "        qobj = assemble(message[q], shots=1, memory=True)\n",
    "        result = qasm_sim.run(qobj).result()\n",
    "        measured_bit = int(result.get_memory()[0])\n",
    "        measurements.append(measured_bit)\n",
    "    return measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "9b61f82f",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "\n",
    "## Step 3\n",
    "# Decide which basis to measure in:\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f68035a7",
   "metadata": {},
   "source": [
    "We can see that the circuit in `message[0]` (representing the 0th qubit) has had an $X$-measurement added to it by Bob:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "8a8018c3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 314.126x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "message[0].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01abca62",
   "metadata": {},
   "source": [
    "Since Bob has by chance chosen to measure in the same basis Alice encoded the qubit in, Bob is guaranteed to get the result `0`. For the 6th qubit (shown below), Bob's random choice of measurement is not the same as Alice's, and Bob's result has only a 50% chance of matching Alices'. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "0a0daae2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 314.126x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "message[6].draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "b3880eca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "print(bob_results)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4df72224",
   "metadata": {},
   "source": [
    "Bob keeps his results private.\n",
    "\n",
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "\n",
    "### 3.4 Step 4:\n",
    "\n",
    "After this, Alice reveals (through Eve's channel) which qubits were encoded in which basis: \n",
    "\n",
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "\n",
    "And Bob reveals which basis he measured each qubit in:\n",
    "\n",
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "|     bob_bases     |      bob_bases     |      &nbsp;     |\n",
    "\n",
    "If Bob happened to measure a bit in the same basis Alice prepared it in, this means the entry in `bob_results` will match the corresponding entry in `alice_bits`, and they can use that bit as part of their key. If they measured in different bases, Bob's result is random, and they both throw that entry away. Here is a function `remove_garbage` that does this for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "ddc88545",
   "metadata": {
    "scrolled": true,
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def remove_garbage(a_bases, b_bases, bits):\n",
    "    good_bits = []\n",
    "    for q in range(n):\n",
    "        if a_bases[q] == b_bases[q]:\n",
    "            # If both used the same basis, add\n",
    "            # this to the list of 'good' bits\n",
    "            good_bits.append(bits[q])\n",
    "    return good_bits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e48cb94",
   "metadata": {},
   "source": [
    "Alice and Bob both discard the useless bits, and use the remaining bits to form their secret keys:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "dc36559b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "\n",
    "## Step 3\n",
    "# Decide which basis to measure in:\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "\n",
    "## Step 4\n",
    "alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)\n",
    "print(alice_key)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6a21589",
   "metadata": {},
   "source": [
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "|     bob_bases     |      bob_bases     |                 |\n",
    "|     alice_key     |                    |     &nbsp;      |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "9bd01169",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "\n",
    "## Step 3\n",
    "# Decide which basis to measure in:\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "\n",
    "## Step 4\n",
    "alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)\n",
    "bob_key = remove_garbage(alice_bases, bob_bases, bob_results)\n",
    "print(bob_key)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e16278a",
   "metadata": {},
   "source": [
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "|     bob_bases     |      bob_bases     |                 |\n",
    "|     alice_key     |                    |     bob_key     |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd297796",
   "metadata": {},
   "source": [
    "### 3.5 Step 5:\n",
    "\n",
    "Finally, Bob and Alice compare a random selection of the bits in their keys to make sure the protocol has worked correctly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "1390928d",
   "metadata": {
    "tags": [
     "thebelab-init"
    ]
   },
   "outputs": [],
   "source": [
    "def sample_bits(bits, selection):\n",
    "    sample = []\n",
    "    for i in selection:\n",
    "        # use np.mod to make sure the\n",
    "        # bit we sample is always in \n",
    "        # the list range\n",
    "        i = np.mod(i, len(bits))\n",
    "        # pop(i) removes the element of the\n",
    "        # list at index 'i'\n",
    "        sample.append(bits.pop(i))\n",
    "    return sample"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a404c02c",
   "metadata": {},
   "source": [
    "Alice and Bob both broadcast these publicly, and remove them from their keys as they are no longer secret:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "1b9af94c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  bob_sample = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n",
      "alice_sample = [0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=0)\n",
    "n = 100\n",
    "\n",
    "## Step 1\n",
    "# Alice generates bits\n",
    "alice_bits = randint(2, size=n)\n",
    "\n",
    "## Step 2\n",
    "# Create an array to tell us which qubits\n",
    "# are encoded in which bases\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "\n",
    "## Step 3\n",
    "# Decide which basis to measure in:\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "\n",
    "## Step 4\n",
    "alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)\n",
    "bob_key = remove_garbage(alice_bases, bob_bases, bob_results)\n",
    "\n",
    "## Step 5\n",
    "sample_size = 15\n",
    "bit_selection = randint(n, size=sample_size)\n",
    "\n",
    "bob_sample = sample_bits(bob_key, bit_selection)\n",
    "print(\"  bob_sample = \" + str(bob_sample))\n",
    "alice_sample = sample_bits(alice_key, bit_selection)\n",
    "print(\"alice_sample = \"+ str(alice_sample))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61d9f7b5",
   "metadata": {},
   "source": [
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "|     bob_bases     |      bob_bases     |                 |\n",
    "|     alice_key     |                    |     bob_key     |\n",
    "|     bob_sample    |     bob_sample     |    bob_sample   |\n",
    "|    alice_sample   |    alice_sample    |   alice_sample  |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6e4c74a",
   "metadata": {},
   "source": [
    "If the protocol has worked correctly without interference, their samples should match:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "d0bdbd16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bob_sample == alice_sample"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "32fad42a",
   "metadata": {},
   "source": [
    "If their samples match, it means (with high probability) `alice_key == bob_key`. They now share a secret key they can use to encrypt their messages!\n",
    "\n",
    "| Alice's Knowledge | Over Eve's Channel | Bob's Knowledge |\n",
    "|:-----------------:|:------------------:|:---------------:|\n",
    "|     alice_bits    |                    |                 |\n",
    "|    alice_bases    |                    |                 |\n",
    "|      message      |       message      |     message     |\n",
    "|                   |                    |    bob_bases    |\n",
    "|                   |                    |   bob_results   |\n",
    "|                   |     alice_bases    |   alice_bases   |\n",
    "|     bob_bases     |      bob_bases     |                 |\n",
    "|     alice_key     |                    |     bob_key     |\n",
    "|     bob_sample    |     bob_sample     |    bob_sample   |\n",
    "|    alice_sample   |    alice_sample    |   alice_sample  |\n",
    "|     shared_key    |                    |    shared_key   |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "2162cad5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "[1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0]\n",
      "key length = 33\n"
     ]
    }
   ],
   "source": [
    "print(bob_key)\n",
    "print(alice_key)\n",
    "print(\"key length = %i\" % len(alice_key))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22db8544",
   "metadata": {},
   "source": [
    "## 4. Qiskit Example: *With* Interception\n",
    "\n",
    "Let’s now see how Alice and Bob can tell if Eve has been trying to listen in on their quantum message. We repeat the same steps as without interference, but before Bob receives his qubits, Eve will try and extract some information from them. Let's set a different seed so we get a specific set of reproducible 'random' results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "9d4f3e23",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bce8f8b8",
   "metadata": {},
   "source": [
    "### 4.1 Step 1:\n",
    "\n",
    "Alice generates her set of random bits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "ff66999b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 0 0 0 1 1 1 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1\n",
      " 0 0 1 1 0 0 1 0 1 0 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 0 1 1 0 0 1 1\n",
      " 1 0 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "print(alice_bits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fde5b77",
   "metadata": {},
   "source": [
    "### 4.2 Step 2:\n",
    "\n",
    "Alice encodes these in the $Z$ and $X$-bases at random, and sends these to Bob through Eve's quantum channel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "5159eb3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 1 1 0 0\n",
      " 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 1\n",
      " 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "## Step 2\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "print(alice_bases)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4558352",
   "metadata": {},
   "source": [
    "In this case, the first qubit in Alice's message is in the state $|+\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "47c202c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 193.726x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "message[0].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "031f710c",
   "metadata": {},
   "source": [
    "### Interception!\n",
    "\n",
    "Oh no! Eve intercepts the message as it passes through her channel. She tries to measure the qubits in a random selection of bases, in the same way Bob will later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "6fa5baa1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "## Step 2\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "## Interception!!\n",
    "eve_bases = randint(2, size=n)\n",
    "intercepted_message = measure_message(message, eve_bases)\n",
    "print(intercepted_message)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b89ea700",
   "metadata": {},
   "source": [
    "We can see the case of qubit 0 below; Eve's random choice of basis is not the same as Alice's, and this will change the qubit state from $|+\\rangle$, to a random state in the $Z$-basis, with 50% probability of $|0\\rangle$ or $|1\\rangle$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "461c0ce4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 253.926x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "message[0].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea2dbad1",
   "metadata": {},
   "source": [
    "### 4.3 Step 3:\n",
    "\n",
    "Eve then passes on the qubits to Bob, who measures them at random. In this case, Bob chose (by chance) to measure in the same basis Alice prepared the qubit in. Without interception, Bob would be guaranteed to measure `0`, but because Eve tried to read the message he now has a 50% chance of measuring `1` instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "298af3a6",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 374.326x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "## Step 2\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "## Interception!!\n",
    "eve_bases = randint(2, size=n)\n",
    "intercepted_message = measure_message(message, eve_bases)\n",
    "## Step 3\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "message[0].draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d841b459",
   "metadata": {},
   "source": [
    "### 4.4 Step 4:\n",
    "\n",
    "Bob and Alice reveal their basis choices, and discard the useless bits:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "699625cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "## Step 2\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "## Interception!!\n",
    "eve_bases = randint(2, size=n)\n",
    "intercepted_message = measure_message(message, eve_bases)\n",
    "## Step 3\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "## Step 4\n",
    "bob_key = remove_garbage(alice_bases, bob_bases, bob_results)\n",
    "alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42990178",
   "metadata": {},
   "source": [
    "### 4.5 Step 5:\n",
    "\n",
    "Bob and Alice compare the same random selection of their keys to see if the qubits were intercepted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "01afa28f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  bob_sample = [1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0]\n",
      "alice_sample = [1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(seed=3)\n",
    "## Step 1\n",
    "alice_bits = randint(2, size=n)\n",
    "## Step 2\n",
    "alice_bases = randint(2, size=n)\n",
    "message = encode_message(alice_bits, alice_bases)\n",
    "## Interception!!\n",
    "eve_bases = randint(2, size=n)\n",
    "intercepted_message = measure_message(message, eve_bases)\n",
    "## Step 3\n",
    "bob_bases = randint(2, size=n)\n",
    "bob_results = measure_message(message, bob_bases)\n",
    "## Step 4\n",
    "bob_key = remove_garbage(alice_bases, bob_bases, bob_results)\n",
    "alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)\n",
    "## Step 5\n",
    "sample_size = 15\n",
    "bit_selection = randint(n, size=sample_size)\n",
    "bob_sample = sample_bits(bob_key, bit_selection)\n",
    "print(\"  bob_sample = \" + str(bob_sample))\n",
    "alice_sample = sample_bits(alice_key, bit_selection)\n",
    "print(\"alice_sample = \"+ str(alice_sample))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "394db08e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bob_sample == alice_sample"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "e480e150",
   "metadata": {},
   "source": [
    "Oh no! Bob's key and Alice's key do not match. We know this is because Eve tried to read the message between steps 2 and 3, and changed the qubits' states. For all Alice and Bob know, this could be due to noise in the channel, but either way they must throw away all their results and try again- Eve's interception attempt has failed.\n",
    "\n",
    "## 5. Risk Analysis\n",
    "\n",
    "For this type of interception, in which Eve measures all the qubits, there is a small chance that Bob and Alice's samples could match, and Alice sends her vulnerable message through Eve's channel. Let's calculate that chance and see how risky quantum key distribution is.\n",
    "\n",
    "- For Alice and Bob to use a qubit's result, they must both have chosen the same basis. If Eve chooses this basis too, she will successfully intercept this bit without introducing any error. There is a 50% chance of this happening.\n",
    "- If Eve chooses the *wrong* basis, i.e. a different basis to Alice and Bob, there is still a 50% chance Bob will measure the value Alice was trying to send. In this case, the interception also goes undetected.\n",
    "- But if Eve chooses the *wrong* basis, i.e. a different basis to Alice and Bob, there is a 50% chance Bob will not measure the value Alice was trying to send, and this *will* introduce an error into their keys.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "If Alice and Bob compare 1 bit from their keys, the probability the bits will match is $0.75$, and if so they will not notice Eve's interception. If they measure 2 bits, there is a $0.75^2 = 0.5625$ chance of the interception not being noticed. We can see that the probability of Eve going undetected can be calculated from the number of bits ($x$) Alice and Bob chose to compare:\n",
    "\n",
    "$$ P(\\text{undetected}) = 0.75^x $$\n",
    "\n",
    "If we decide to compare 15 bits as we did above, there is a 1.3% chance Eve will be undetected. If this is too risky for us, we could compare 50 bits instead, and have a 0.00006% chance of being spied upon unknowingly.\n",
    "\n",
    "You can retry the protocol again by running the cell below. Try changing `sample_size` to something low and see how easy it is for Eve to intercept Alice and Bob's keys."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "d0c0afdc",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eve's interference was undetected %0.2 of the time.\n"
     ]
    }
   ],
   "source": [
    "trials = 1000\n",
    "undetected = 0.0\n",
    "for _ in range(trials):\n",
    "    n = 100\n",
    "    # Step 1\n",
    "    alice_bits = randint(2, size=n)\n",
    "    alice_bases = randint(2, size=n)\n",
    "    # Step 2\n",
    "    message = encode_message(alice_bits, alice_bases)\n",
    "    # Interception!\n",
    "    eve_bases = randint(2, size=n)\n",
    "    intercepted_message = measure_message(message, eve_bases)\n",
    "    # Step 3\n",
    "    bob_bases = randint(2, size=n)\n",
    "    bob_results = measure_message(message, bob_bases)\n",
    "    # Step 4\n",
    "    bob_key = remove_garbage(alice_bases, bob_bases, bob_results)\n",
    "    alice_key = remove_garbage(alice_bases, bob_bases, alice_bits)\n",
    "    # Step 5\n",
    "    sample_size = 15 # Change this to something lower and see if \n",
    "                     # Eve can intercept the message without Alice\n",
    "                     # and Bob finding out\n",
    "    bit_selection = randint(n, size=sample_size)\n",
    "    bob_sample = sample_bits(bob_key, bit_selection)\n",
    "    alice_sample = sample_bits(alice_key, bit_selection)\n",
    "\n",
    "    if bob_sample != alice_sample:\n",
    "        #print(\"Eve's interference was detected.\")\n",
    "        pass\n",
    "    else:\n",
    "        undetected += 1\n",
    "        #print(\"Eve went undetected!\")\n",
    "print(\"Eve's interference was undetected %\" + str(undetected/trials*100) + \" of the time.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c19ad547",
   "metadata": {},
   "source": [
    "### Exercise 10 \n",
    "\n",
    "There is nothing unique with X or Z basis states while we are trying to perform a Quantum Key distribution. Let's say instead of $|0\\rangle, |1\\rangle$ set we use $|R \\rangle, |L \\rangle$ which we define as:\n",
    "$$ |R \\rangle = \\frac{|0\\rangle + i|1 \\rangle}{\\sqrt{2}} $$\n",
    "$$ |L \\rangle = \\frac{|0\\rangle - i|1 \\rangle}{\\sqrt{2}} $$\n",
    "\n",
    "Instead of $|+ \\rangle, |- \\rangle$ we use $|U \\rangle, |D \\rangle$ which we define as:\n",
    "$$ |U \\rangle = 0.92387953|0\\rangle + 0.38268343|1 \\rangle $$\n",
    "$$ |D \\rangle = -0.38268343|0\\rangle + 0.92387953|1 \\rangle $$\n",
    "\n",
    "- Plot $|R\\rangle, |L\\rangle, |U\\rangle, |D\\rangle$ states on the Bloch sphere using the cell below.\n",
    "- Design the circuit for preparing these states.\n",
    "- Design the circuits for performing measurement in these states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "4840fd6e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.38268343+0.j  0.92387953+0.j]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.8/site-packages/qiskit/visualization/bloch.py:69: MatplotlibDeprecationWarning: \n",
      "The M attribute was deprecated in Matplotlib 3.4 and will be removed two minor releases later. Use self.axes.M instead.\n",
      "  x_s, y_s, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Write the state you would like to draw in the array format below.\n",
    "# For drawing |0>, write [1 0], for drawing |+> write [1/sqrt(2) 1/sqrt(2)]\n",
    "out_vector = [1 0]\n",
    "plot_bloch_multivector(out_vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cdc903cf",
   "metadata": {},
   "source": [
    "### Answer\n",
    "\n",
    "?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6a193d3",
   "metadata": {},
   "source": [
    "After completing this exercise, you can actually modify the encode_message and measure_message functions's relevant parts for preparing and measuring to implement Quantum Key Distribution using these states. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "57150602",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}