QSP_detailed_implementation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0b393286",
   "metadata": {},
   "source": [
    "# Qubit-Efficient Quantum State Preparation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "901ffe30",
   "metadata": {},
   "source": [
    "In this notebook, we provide a __self-contained__ circuit-level implementation that prepares an arbitrary quantum state with arbitrary complex-valued amplitudes.\n",
    "\n",
    "See https://github.com/guikaiwen/qubit_efficient_QSP/blob/main/QSP_method_call_demo.ipynb for a simple method call walk-through using the `QubitEfficientQSP` object."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b23f96a1-459b-46b0-b32a-04b3c9226d50",
   "metadata": {},
   "source": [
    "## Overall Structure"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68a8312d",
   "metadata": {},
   "source": [
    "Our goal is to prepare the wave function state vector\n",
    "\n",
    "$U_{\\mathrm{QSP}} |0^n\\rangle = |\\psi\\rangle = \\frac{1}{\\lVert \\mathbf{x}\\rVert}\\sum_{i=0}^{2^{n-1}}x_i |i\\rangle, x_i \\in \\mathbb{C}$\n",
    "\n",
    "via sequence of multi-control Ry and multi-control Rz gates, using the method described in Chapter 4.2 of Schuld et al.'s QML textbook (https://link.springer.com/book/10.1007/978-3-030-83098-4). The protocol was originally proposed in Mottonen et al. 2004 (https://arxiv.org/pdf/quant-ph/0407010.pdf).\n",
    "\n",
    "(Note that $N = 2^n$)\n",
    "\n",
    "In other words, we can prepare an arbitrary $n$-qubit quantum state (with complex amplitudes) from an $n$-qubit product state. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca2bad1e-2202-43ce-b895-bf10d131de02",
   "metadata": {},
   "source": [
    "We can visualize the $U_{\\mathrm{QSP}}$ circuit using the circuit diagram below (the inverse of the circuit in the QML textbook, only with the multi-control Ry gates for real value encoding):"
   ]
  },
  {
   "attachments": {
    "8960221c-ef2c-4bb9-89d3-22f8974aac03.png": {
     "image/png": 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TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KMB27cwAAABxpRE9UAAAAAgAAAAAAAACfAAAAKAAAAJ8AAACfAAB4mXgdM2UAAEAASURBVHgB7N35l1Rlfsfxh32TTZFNWRQRFUUERARUEBV3HTPjZBYdnUwyySQn/0GWc3JyTn5Jfsj8kOTkZCbOGkedcQF1FBF34wJujSLiIKs4bLIIImp4P5MHyrKqurq7urvuve97TtHdVXW313Pr1i2eT32fHp8fmYKTAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAhkR6GHwLSMt5WYqoIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgpEAYNvHggKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAKZEjD4lqnmcmMVUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUMvnkMKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKZErA4FummsuNVUABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUMPjmMaCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKJApAYNvmWouN1YBBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUMDgm8eAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKBApgQMvmWqudxYBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABg28eAwoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAApkSMPiWqeZyYxVQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBQy+eQwooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgpkSsDgW6aay41VQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRQw+OYxoIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgookCkBg2+Zai43VgEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQwOCbx4ACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooECmBAy+Zaq53FgFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAGDbx4DCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACmRIw+Jap5nJjFVBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFDL55DCiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCmRKwOBbpprLjVVAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFDD45jGggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiQKQGDb5lqLjdWAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFDA4JvHgAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiigQKYEDL5lqrncWAUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAYNvHgMKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAKZEjD4lqnmcmMVUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUMvnkMKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKZErA4FummsuNVUABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUMPjmMaCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKJApAYNvmWouN1YBBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUMDgm8eAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKBApgQMvmWqudxYBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABg28eAwoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAApkSMPiWqeZyYxVQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBQy+eQwooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgpkSsDgW6aay41VQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRQw+OYxoIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgookCkBg2+Zai43VgEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQwOCbx4ACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooECmBAy+Zaq53FgFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAGDbx4DCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACmRIw+Jap5nJjFVBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFDL55DCiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgoooIACCmRKwOBbpprLjVVAAQUUUEABBRRQoPkEPv7443D48OHw6aefNt/GuUUNF+jVq1fo2bNn6N27d+jTp0/Dl+8CFVBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRRQQIF6BAy+1aPkcxRQQAEFFFBAAQUUUKCiwGeffRZ27NgRb5988kn4/PPPKz7PO/Mh0KNHj0DwrX///uGEE04IQ4YMCdznpIACCiiggAIKKKCAAgoooIACCiiggAIKKKCAAgp0tYDBt64Wd30KKKCAAgoooIACCuRIgCpv69atCy0tLYEQHIEoglAG4HLUyP+/K6ldaedBgwaF008/PYwZMyYG4fK3t+6RAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKNLuAwbdmbyG3TwEFFFBAAQUUUECBJhagytszzzwTHnroodC3b98wfvz4+NPgWxM3Wjs3jeAbw9pS4Y+A44IFC8LUqVPjcKdWfWsnqrMpoIACCiiggAIKKKCAAgoooIACCiiggAIKKKBAuwUMvrWbzhkVUEABBRRQQAEFFFDg0KFDYenSpeHnP/95HPpy1qxZYeDAgVZ8y+Gh0bNnz7Bnz56wZs2aWNXvxhtvDLNnz45BRx5zUkABBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQW6UsDgW1dquy4FFFBAAQUUUEABBXImQPDt0UcfDffcc08c+vKyyy4LQ4cOjcE3q4Dlp7Gp4Ee47YMPPgjPPfdc2L17d7jyyivDzJkzDb7lp5ndEwUUUEABBRRQQAEFFFBAAQUUUEABBRRQQAEFMiVg8C1TzeXGKqCAAgoooIACCijQXAIE35YvXx6WLFkSZsyYEW644YYwfPjw5tpIt6YhAgQZN2/eHJYtWxY2bdoUCDlOnz7d4FtDdF2IAgoooIACCiiggAIKKKCAAgoooIACCiiggAIKtFXA4FtbxXy+AgoooIACCiiggAIKHBVIwTeGO6X61/XXXx+OP/74o4/7S74EtmzZEh555JEYgFu0aJHBt3w1r3ujgAIKKKCAAgoooIACCiiggAIKKKCAAgoooECmBAy+Zaq53FgFFFBAAQUUUEABBZpLIAXfUsW3G2+80eBbczVRQ7cmBd+s+NZQVhemgAIKKKCAAgoooIACCiiggAIKKKCAAgoooIAC7RAw+NYONGdRQAEFFFBAAQUUUECBPwgYfCvWkWDwrVjt7d4qoIACCiiggAIKKKCAAgoooIACCiiggAIKKNDMAgbfmrl13DYFFFBAAQUUUECBLhX4/PPPv7C+Hj16fOHvZvijdBubYfs6GnxL+8PPzz77rC5i9rtnz57xud1hwLaWbi/bkran1g6kedjPw4cPV91fltW7d+94Y3mlz+f3tD72/dNPP42Pp/t69ep1dD7mZT08h8d5jHk6YmbwDVUnBRRQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUaAYBg2/N0ApugwIKKKCAAgoooEC3CxAo+uSTT2JQKIWHUlCo2zfuyAaksBXbmMJPhKMINHUkyNTRfetI8I19IpRFOOvjjz8+Ggbj/moTbcI+9+/fP/Tp0+doCKza8xt9P9tGG3A7ePBg3P5BgwaFAQMGxG2ptT6sDhw4EHbv3h1v+/fvD9xXGl6jTYcNGxbGjBkThg4dGtuaeXbs2BE+/PDD+Hz2n+dgsHPnznj/cccdF+874YQT4k+ew3HCunbt2hW3j+Vhxq29x4zBt1ot7GMKKKCAAgoooIACCiiggAIKKKCAAgoooIACCijQlQIG37pS23UpoIACCiiggAIKNK0A4SNCQvv27QsDBw6MQaG+fft2KCTUyJ0lxMQ2sn0Epgg9EbgixERYqrumjgTf2B9u7E/aLwJw7CsTIbNUoaz0J/tMG3HDgVtXhBTZHkJ6bOvevXtj8I2/R4wYEQicsQ2VJuZjnwiuEUL7/e9/HwiQ7dmzJy4DQx5Pzxs9enQ455xzYviNABvrW7NmTdi4cWN8Pu09fvz4MGTIkPC73/0ubNq0KYwcOTKcdNJJYdKkSWHixInxmGDbeGzDhg3xWOE5BOS4sYz2hN8MvlVqYe9TQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUECB7hAw+NYd6q5TAQUUUEABBRRQoOkECF+1tLSEtWvXhrFjx4aTTz45hpmorEX4qDunFLiiwhhBp3Xr1sWgE+EnqngRgKsWuurs7e5o8I35CYRt3bo1bN68OYa7qG7GPhPOKg0h0g4YMA8V1gYPHhxOPfXUMGHChBjm6tevX6e1FdtDSO+jjz6K/oTQWB8hMtqBCm2VAojMx/YyH/u3fv36+Dv7QpsR2uM53LZt2xbeeOONGEg777zzwumnnx4IwbHPTzzxRDw+Ccix7wTcODY5Fgi28TvH7ezZswPzEtok+Mb63n777VhRj/URjmN7seM5bT22Db519ivK5SuggAIKKKCAAgoooIACCiiggAIKKKCAAgoooEC9Agbf6pXyeQoooIACCiiggAK5FqAS19KlS8OKFSvCtGnTYniIylmEiborVJbAU3iKCmEvvPBCeOaZZ2Lga/r06THIRMUxqqB1x9SI4Nv27dtjQGv16tXh2WefjeEvAlmE3giUsX9UN2MfCYcRjKNNCJ1dcMEF4fzzz48BMZ5XKXzWCBdCZITXqNb24osvxoAk20bw7pRTTgnjxo2ruG7ajnZjPkJqb775ZgycET6jAhuBtRRAe/XVV8OvfvWr8P777wfadubMmfFYJOzG/djw3BNPPDGG4o4//vi4HSyXIBvbc/nll4eLL744BupS8I1qcYTu2AYCcxzfo0aNOmraFh+Db23R8rkKKKCAAgoooIACCiiggAIKKKCAAgoooIACCijQmQIG3zpT12UroIACCiiggAIKZEaA8NWdd94Zw29UzZozZ06YPHlyrCbWWWGqenFS8I2qdE899VR4/PHHY3DprLPOCqeddloMX1EFrDumjgTfCHQRzmK/du7cGSua/eIXv4jVzTAnGEawberUqTHsRRCOANd7770X3n333VgdjnDilClTwrx58+JzqX7XniE8W7OjKh3BNKoCEmSjTc4888y4braTynuVApI8j+196623YmU7qrcxLCpV6oYPHx7DfewrQb+XXnop/PjHP47DmtKuM2bMCJdcckkM/P30pz8NTz75ZKwyR2ht4cKFcRnPP/98ePnll2PojXkuuuiiGASkGh2+uH7wwQcxdEflN+4nIMhz2X682jIZfGuLls9VQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUECBzhQw+NaZui5bAQUUUEABBRRQIDMChIPuuOOOcPfdd8fwEFWzCAYRrOquamoJj/AUw2wSEHv66afDY489FgNMDFt57rnnxupgVPzqjqkjwTf2i4l9I6T1+uuvh3/5l38J9913X6xsRvDwK1/5SmwPhp6lwhtDjBLgWrZsWfjtb38bg3MEyG6//fbwrW99K4a6GhlUZBvZRwJfHBsED1NojCFFCeWlim3lgbsU7GP40ueeey4OUUrgjSqC3AjypaFGmfd///d/w3/+53+GV155JQbZWP7ixYvjfATfqEZIwJH133TTTTGY+dBDD4Xly5cHQpBUieN44Pd0zGLL9mNGcI8hZXfv3h3OOeeccOmll0YvAnvl217tWDL4Vk3G+xVQQAEFFFBAAQUUUEABBRRQQAEFFFBAAQUUUKCrBQy+dbW461NAAQUUUEABBRRoSgGCb1TbYkhJqmZRaYtQE8NYphBRd244ASaqha1cuTKG36g6xn0XXnhhWLBgQawe1h3b15HgW9reTz75JOzduze89tpr4V//9V/Dww8/HCuoEeD62te+FvePKmdUJ2MY0LVr18bnEJDjb6qYffe7343hNwJlPK9S9bW0vnp+EnjjduDAgVixjSFKCRwSILvssstihTmODdaXwmuly2VehkYlZMYQrlRlS0FF5qFCXDquMPz4448D1dt+9KMfxXUQbiOcRvVBQmkcl/icccYZcahShkFlmNQ0PC8V4Kh6x9CrrKd0m9iWTZs2hd/97ndxGQTgCHRynBPEo2JdvRUDDb6VtrK/K6CAAgoooIACCiiggAIKKKCAAgoooIACCiigQHcKGHzrTn3XrYACCiiggAIKKNA0As0efAOKgBRDZlIRjJ/r16+PVbuuv/76OBRovVW7Gomegm8EsKhQduONN4bjjz++Taugkh1DmBLqI3xIVbvRo0fH6mVf/epXY0CLZVJZbceOHTHE9eCDD8bKcBgQALzllltixTcCXQzl2dGqb1Rr48Zxwfa88MILMTjGjn39618PixYtihXoCN1VmpiXUN6GDRtiO61bty6G1ubOnXu0rVJ7Efpjv6j4xlCvVGUj0EjIjZAcgcclS5bEqnNXXXVVHIaXCn+44fDiiy9G9yuuuCIOgUtlvPLgG+sghMe+UCWOcCDBwmnTpsUbVfPS9lTan3Sfwbck4U8FFFBAAQUUUEABBRRQQAEFFFBAAQUUUEABBRTobgGDb93dAq5fAQUUUEABBRRQoCkEyoNvVNBiqNNmqfgGEgEvglRUHSOIxY0hWQmbMRQowbCOVjpra2M0IvhG6IsgH8EvhhNlaFDcZ82aFYc6JQRG0Isw1+9///s43ClBu9/85jfRg23+zne+E2699dYwfvz4GLzrqEOqQvfee+/FIVVXrVoVw2JUSCP0xrYReqsWFjt8+HAcupV9ot3Y/jREav/+/WOYLVWVY/8JxlHR7YknnojLJMSGAduxbdu2aEMAjqFfWTdBNgJyPL+lpSVuExXcxowZczT4lwxYD9tDBTqqylFRb+fOnbGpqSjHunCjAl1pYK7SsWDwrZKK9ymggAIKKKCAAgoooIACCiiggAIKKKCAAgoooEB3CBh86w5116mAAgoooIACCijQdALlwbd6hzolVMREsCgFmfibQFS68TcTfxMsqhaW+sOzqv9LFbHt27fHyl+PP/54rPZFcOmaa66JQ1yecMIJR4fPrL6Uxj7SiOAbAS4CWVQjW7ZsWRxalEpkF1xwQbj22mvjcJ+EzAiQEbwiJEals/vvvz9WZCPwx1Cnt912Wxzmk2pmrQW4WlNgiFPWRSCPamuEDQngsU1USiMAR7CsWlvi8uijj4Z77rknBtguvfTSGEpjiFOGNWWoWkJtHDOsh+FH33333Rhmo8obYUaGd2VYV24E8BiOlOAbNgxbumbNmlglj99T5TbCdWwb4TqCbGn7UviN9RCWY+hVbgQ8CQxOmTIlDBkypNXjx+Bba0eOjyuggAIK1CNQes3U0ffsetbncxRQQAEFKguUno/57JA+P1R+tvcqoIACCiiggAIKKKCAAs0nYPCt+drELVJAAQUUUEABBRToBoH2BN/oJCCMlaqQ7dq1K1bVogOXoBbho4EDB8ZKbISzqPrFkJIEs9rToUDwjUAW6yEg9utf/zqGnAi/nX322XFoTMJRXTml4BvhMCqRMexqvUOd4ocDwS32hzAfFdKoTDZv3rx4I4DIvhHi4n6qojG055NPPhmeeuqpuK6JR4Y3JRBGAJDwH9Yd7UTHmCAald6okEY47+abb47V0UaOHBnbsdI62CdCkPv27YuV4u68884wY8aM8LWvfS1uE9XbGAKVABltyfMZgpRgG/tI5T6GOMUSm2effTYG3GhTqrkRoJs0aVJYvXp1HPKW8BrbOXPmzDgP81IpjmOvPJjH8UOAjyFlCb/de++9MVT4jW98Iw5TS9U3js1ak8G3Wjo+poACCihQj0B6r+R9nfc6rpU6OkR5Pev1OQoooIACxwQ4F/P5gM+zfKbjdz5D8FnKSQEFFFBAAQUUUEABBRTIkoDBtyy1ltuqgAIKKKCAAgoo0GkCpcE3hg/lNnXq1BgiIpBUOtFJwI2KXXTaEkJavnx5rERGCI5OXAJu3Ahipd8JNZ1++ukxwMRzuLVlSp0TdEw88sgjMfjGMqgMNmfOnEBIrN7QWVvWW+u5pcE3Al5UKqt3G5LjO++8EyujsU9UWMP76quvDgsWLAjnnntumHgk2MZ+EhDjOQ899FAcDnXz5s2xCtv8+fPD3LlzY8CsEdXe2F8q6xF6I4hHSGz//v3hBz/4QbjhhhuOVlOr5MI+cUwQnHvsscfCAw88ELfx61//egzPrVixIob32M8PP/wwLoIAHfOdf/75Ryu6ccwQkmN/qXA3bty4MHny5DB9+vQ4lOnrr78eK7alYBzDr+JF5Ta8CBCUH1+sY9OmTTH8RjW6n/zkJzE4eeWVV8ZtJDzH8VprMvhWS8fHiipAR3G6pfNa6euP33mdl/4sqpX7XVwBXhu8TtJP3ld5X+e1wXsewX1eI75OinuMtHfPS48rfmfiOGMqP6bSuTg+6D8KFFQgnYd5vfCFnYMHD8bPOvzNF7XS5ynPxwU9QNxtBRRQQAEFFFBAAQUyKGDwLYON5iYroIACCiiggAIKNF6gnuBb6iQg2MRQlVTuIki0cePGWLWMTgM61OhAoJoXQ1oSjhs2bFis0kU1LsJhBODKO95YNrfUQVdrD1n+c889F0NRhL+oLkZQ76abbgpUIyuv9FVrWR19rCPBN6oLYEZw8O67745Dg1L5jMovF110UaxgRpUzOsRxJChGxTeez99UJKDaHaG/U089NbqWhxTbun+pHajw9swzz8QbATiWS/CNYB++1SY6jDiWODZeeeWVWJ2OQNt1110X76daHUOUUqWNTn+ez/FE0O7MM8+MQ7sSbhs9enS0YRk7duyI4UaGQOV23HHHhfXr1x8d7pR1nXPOOTGoiRfHAMdX+cS+sR6OWcKD//Zv/xaHN6W6HqFJwnOEKDkGq00G36rJeH8RBTgXp3MTYVdCPHv37o2vXc5vvA45T9GBPGLEiPheQIdyacCniG7uczEFuC7iNcI1C68T3vu4TmLidcJ7P68VbgwLzuuk/FqpmHLudTUBrmu4DuV44hqR6yV+5/oqnYOpXMVQ7lyLpy+j8OWAWtdy1dbn/QpkXYDXDBOfv3bu3Bk/z3IuTp9beYzXDOdjrlf4zMHrx/MxMk4KKKCAAgoooIACCijQzAIG35q5ddw2BRRQQAEFFFBAgS4TqCf4RicaN8JmaRjMF154IXYQMPwkFbm40alLRS5uBLXoLKAi2QUXXBCDb1TvSuEifhJ+Yrl0RtDJ29pwXzz3zTffjBW/Xnrppfhz4cKF4Tvf+U6sDEaHRVd16HUk+EanC2ERnH7zm9+EFUeqoVHljG2n2h4BQXwIlvA8OjPpuCQIx3CehN0IE5522mmxc4bhZSsFvtpyENEW3AgzUm3t6aefjsOQst7vfe97sRJdrfahbRi6lSp2BNLohGVfaH8eI3jGscZP9p/7WBeV5ZgIv1HljjAfATb2mXANwTuCAWkf6dSlo4obbUDnFB1TPF5teCKOL5ZHVcKlS5eGf/7nf47rJIx52WWXxWFqk3l8oMI/Bt8qoHhXYQXoKCZsQZi0paUlrF27Nr6eeX3zuuRcwfmKcz5DNlOR8aSTToohOF7TnN/Se0FhEd3xQgjwvsr7O6Ft3kf4Pb1GeG/ifZ5rJQKiBLx5j+d3XkMdfV8vBHABd5LjhuOKL6Js2LAhVsflixFUyeU6h+sjzrOEKDmeuE7nPEzlZa6ZeMxjq4AHTsF3mddM+jySrln4bMBnkvR64HzM64NzMZ8LuG7hMwnn4676fFnwZnL3FVBAAQUUUEABBRRQoB0CBt/ageYsCiiggAIKKKCAAvkTaC34RgcbYSM6B+hYW7lyZQw5UKGMABbDbZ511lnxdzrcqBZGVTaCU3TmXnXVVTH8RGUuqnIxEWgiJEfnHB0OTKkaRfyjyj90WhC+I2DFcJr33ntvHKrylltuiR17BC0IQHXF1JHgG5apMtp9990XGLaTIAkdkoTFTjzxxNiZSTCM59ERQ8CPUBgBEtypjFatwll79j91CGG7ZMmS8NRTTx2tuHb77beHK664omYwkTYlAPPqq6/G1VMpge1ke+kworoN+8ixhB3PpwIcQ49SZY4KC9OmTYshNEJw1Sa2k2OSWwrPpA6ravNwfwrqEHz7x3/8x3jcsZ7LL788fPWrXw0TjwyTSqdWtTBOefDtvPPOs/O4FriP5VKA1x833jfoOOY9gdf822+/HUNwBF7pWOa1ROiCjmMCF5z/CbYS1iWoSpjVSYG8C/Ba4P2O0Nsbb7wRg0q8x3CdwmuA9zHem3geE68Z3jO5VuI9lACGkwLlAlw/cS3FdcnLL78cq+wyjDzXb1yHc33N8cXxRPiYazGC/pyH+Z1Qj8dWuap/512Az5uERfnMwTULVd/Sl2Z4PXBu5nzMZy6+SMNnMl4vXMdQjTM9J+9O7p8CCiiggAIKKKCAAgpkT8DgW/bazC1WQAEFFFBAAQUU6ASB1oJvhBwIX1HZh0DbsmXLYkfB+PHjA0NTEsYiqEWnAJUnCL5RDY4bAYcbbrghMOQlFSeoYsLyCH6xPDrtqGhGSIIOOarG1fpGfQrh0VlBOOuOO+6Iy7322mvj/FS2oLO4vRPLr3dKwTeCVHQoMhTo8ccfX9fs7DMdlFStYz8YUpSQ4IQJE2JIkFDb888/Hx8n6Edny6233hqHDaUDhpAgQTE6ZqoFterakJIn0S50plIxhCp0Tz75ZOwAYn0ECwmI1WobOooYzpQQH52qhMrYj1S5ho591pGCAPyket+DDz4YwzMMA0dAhpAdobJq+5XaKP3kedWeW7J7cd/o0Lr//vvD3/3d38VjkOMtBd84PnGuto8p+EZ7UCWOY5/nE7pL21K6vkb93hnLph0asdwUOGR5vB7S3+3Zd9qQ+etpy1rLT9vQ1v1L600/a62jyI/xOifESuht+fLl8RxF4JXXB53KnEOw50bglY5jzgdUqCQ8S/VPzgtUkkxtVWRP9z2/ArwGeE1wvUMlVIbvTgFvrplSSJ/XDNdhBDF4fREO5X2X0BLXVZ6T8nuMtHfP+NIIxwzBY4Zv59qcSoJcR3EM8Z7MccP1DMcQXwrhHEz4+NJLL43nYY5FJwWKJMBnL75QxHU8n2s5B6egMdcrTFzfUM2Wz2g8n+DbxCNfjEnnY69b2nfEcD7yvax9ds6lgAIKKKCAAgoooEA9Agbf6lHyOQoooIACCiiggAK5F2gt+EanLJUkqPTGsJQEm6jMRQUywmoMnZTCZnTCEWQiyEUwgs7bm266KcycOTMOF0O4i0oUqcOOYVPpqKMDjs64WbNm1awqRkcy20OA6eGHHw4//elP47oJnrEOwkj1hs9YFp2DLI+OwhTMKm1w7uNxbjyXG1Oaj3Aaw5TOnj077ieBtGrBqdLl0uFC6AtPOi2xorOb4BcV9OgUJ2BIsIRKMayPQNj1118fO2GoBlPPekrX2drvrAMHOujvueeeWPGNMBMdPt/85jdj2KvaOpmXziI8qPTHMXHhhRfG/ag0/CyePJ8KOCn4R6ct+//nf/7n0bPRHSRsI/tDhb2/+Zu/iR1ahN0IsX3961+PrlRIqbaPdJRxbHPMzps3L24rz0/hhdZ8Sx/n2GNbOL648Xe1ie1uxIQnQT22l868Wuusd30sk9c07Unwqb1tRodjqm6ES3snlkOb8JPzTFsmth0bjldCBaU+tBETy037WPp4W9aT9efSPlQa4vxFtUbO9ZyjCPdUmng90SaEkgmZEnwj4EsglseK6pisOJ769D4SoO3V82jwNh1j6Tl5+slrifcZjiNutD/HQd72mf1h33hdENSnwhDv+wybx3vjqFGjYnvTtjyP8ydDnzNUMOdCrmO48XtaVp6Og7QvnG9L33d5v+PGMZKuy/DhuCl9b87b8ZI86vnJvhPM4Ysmr732WrxW5Pqc62Lei8sngjq8dxFA5jrz6quvDpdcckkMJfNY0S05rvBJtyJ68BrjfMzxw2stXfOUH0tZ/Zs25ZYCxulzZ/qSDufldD2CAedszsdc2xAa5XqFsD5Bfl4zeDlVF8CaczufOXhdMaXXWfpMaICwup+PKKCAAgoooIACCijQHgGDb+1Rcx4FFFBAAQUUUECB3AnUCr7xH9Z0hlD964EHHoihKJ6/ePHiODwk34SnmkTqkCTI9eMf/zh2xhFsIiDHMJJU8KITl84UKr0RrqKjjgonLJ+gFwE5OuPSf5JXg06domwT1bsIqdAhQaDi4osvjh3K9XRcpeWkYVzZ3tLOHh6nWgu3NCwr93FjolOW8AfVji666KK4nww9mqqAVdv+1MlNRTyq4xEeoZOFbad6HvtBRwshq0ceeSR2vtDJed1118WQFiE/qqmxnkZOyYMQHsG3J554InoQWPnGN75RNfjG/mBBpyvtzz7R7gsWLIj7Ualzg+fTbnQsUV2OzluGSGS+H/zgB7FCYHkblnY0lT9WjwPz06HF+v72b/82rm/ikVAfYZyvfe1rsUOYEFe1449OZuYlrMdwtFSLI+hIMKEtncdsB8ca+8/t4IEjVbI+/XJnddqn0v1O97XnJ2ZUYKRqBftSeqy3Z3lsF8cgxyoTgcBKbV3PslkO5wc6xAh+tHei7dgeghScZ9pynPBcbDBiXib2kWOVcxT7lkJ1jWqT9u5nd87HMUtwksqQnMP4SScyRpUmXLGjXQgmE5bmnJLCu0W2xAsfgt8D+g8IAwcd+XnkHNSW47aSeTPflyqgEQhjyDleX7zuuTHlbd95byfwxn4RmuB9g5A+QYrSfeX9j6G/CVowD+fnFHxr5vbs6LZxzmU/ObdyLuA9mnNJui7juiJdd3EeSbdSu45uQxbn5xjheOFLKVyT8J6VnMr3BytuvM9yrc11NuFLrptxL7Il+07gHQeu5TgXc4wVbeJ8w+ccblyfVns/z7ILbZ2+dEUb84UlqiBSvZzrE+5L1yNc0/C64vMQ1zzcz/mbW5FfL21pf87t3FLQjWsbXmf8nwG3ap+12rIOn6uAAgoooIACCiiggALHBAy+HbPwNwUUUEABBRRQQIECC9QKvvGf/XROM5znz372s9gZSQcBQ4v+0R/9USDoxURHCR2VVPv64Q9/GMMQdLAR5CL4RiUv/qObTm4qZ9FhR2iC0Bgd4HzrnqpbDIVXz3+GsxzWRRiPUBidVayLqnEMo1dPxwQdrHSqMj8G/EyhNvYpBcF4TuoIYr10EPEY8xP2IcS34EjIi/AU66ZzsVrHGZ7MS/Dosccei1XVCIpx/8033xyXc9ZZZ8XwA9XeqPpGmIwhd+ikodIY62Jf6awrXQ/LZTlsX9pG/iaUmEIF7Fd6HCOsk3faX/bp7rvvjsE39nf8uPHh29/+drjs8suOBhxZTppYB2EGOoqo/sRwpwQd6Vyl06PShCfeDP1GyI7OW7aL+b773e/G4bhYLsbc0vHFNhJMSp0mpftfaT2l9zEvy0rBNzqOCW5S8Q17qr/RKZM8Sufld9oMFwKbhBeoWsX+peBb+fNr/U2nIp1pnxz6JBz8+GDc92rPr+dYrjZv6f1Y0fHE9hJcwrujE8cWrz1+sj/tndi2FJ7t6HJSeJHjsa12qWPu97//fdwVjhnaiuObbWRfS19L7d3frM6HB+8H+BB44/XL6wKj1o4nbHnd0NFMcJfOZtqc13mRJ45RjilunH94/0ivhTy6xHPf/o/C/o/2x/cA3mM4Ntj/PO43QV6qmabQEcc/Q78Tmi49P/E8vgjAez3XSFx3pGB1Ho+DtE+0PWESrmeYOI9wTHDOTdde/M15Ai/enzkXcyvyRJjy5ZdfjuEcjpdqFTfLjTjHzJ07N15Dco2OfR5fd+X7Xe3vdEzx+kzv/0U8trg25jMc11+8BvP4vky7ci7mC0u83/CFJYL4VHvjXJsm9p3rHL6Yw2dVrpc5H6XgWxGPj2TTlp9cL6fPapy3+Z3PTPwfQvqiS1uW53MVUEABBRRQQAEFFFCgtoDBt9o+PqqAAgoooIACCihQEIHS4BsdAQSWqGg18Ug1LDpCGKKL4SF/8pOfxGpqBLB4HkNy8h/YTHTarj9SqYQqbP/93/8dOwoY7pLnUMktVSgjOEEHAh11zz33XAwR0YHHf5ATfCOEVC14lJqDTgk6z6mGduedd8a72VYqpVHFgkoq9Uwsg85CKq2w7ewD25c6fOgQo0OQTo7U2crjsVPosz9Uglrz9poY3qNaGwG/VPGttEO7dFvS8ungvvfee2O4jPAf2/z9738/LFq0KC6D+QmRMXTob3/72xgSJJhFMIzhThccCb8RYKKzjueyzaUdxlRtoCOL9aXOBvaF59CmdCjzN+1HRyjL4LnMQ/CN9qbiG8sZM3pMuO3222JltEptwzLpJMKRoW7ZHyq3cYwQUqs04U7wjJDc//zP/8Rh3ggNEgi48cYbY0AmdcQRYCJos3HjxnjsEAxMlQbT/ldaR/l9dJ7T5gTf/v7v/z5uM8N+EbYktIgvy6vWCUzAh3lfffXVuH2ENXku9qkNytdZ6W+em44p5uf3auvEttpjlZZd6z62EwNu7QnrVVo2bYQpEx2H6bVT6bm17mObOC5ZHp2L7Z3wIiTJctjHtkxsO/vCjXl5PXBj2+gMpp14LdFhWtQJI163vBbpEOb1y++YYV9r4jzDewLvLVStJASXXj+15sv7Yxyr6dyLYWuOWfTgnMfE8dOrZ6/Qp2+f8PmR99ADBw/E+0sDf7zO8jKxv7zXcW3BeYl25j2H6yKuFUpdCGTw/vnee+8dPd/w/sw5Jz0vLy5pP/Dh/Mo1ITZMpe+PvB8z8Ryem94reQ7njry6xJ2u8Q/7zXHCNRpBfK7R6w2ME+7iepXwG4EfjjGu64pqyXHHjfMuxxk/OdY6a0rOnbmO9mw728ON7eN8XP7FmvYss9nmYd84F/NlJdqaczHXIVyXlH5hiuOBzx1Uok5VyTn38HmGa8NKn4OabV+7e3s4ltL1dDq3U2GSsC3DfFPxN4Wdu3tbXb8CCiiggAIKKKCAAnkRMPiWl5Z0PxRQQAEFFFBAAQU6JFAt+EZFHkJpDPXCsJsElBiq7uqrr45DdfFNeTpl+U9twlJUn6AKG8OP0kmQhh696qqrYlApdfiwsQSZCL4RnCB0RgcnVbfqCb7RgUwg66GHHgp33HFH7ECmAhqhMEIVKYzXGgqBAwJbVB4jiEegozR0wD6wXfznPDcCL+wr8zHRcULFI/aBSmxUwCPAVqtThPmZj3DYz3/+87BixYpoQQfMX/3VX4WFCxfGjhXWQccmIatf//rXcV9ZNh00BMMw5RvzqdoWnQzMgw3VCdgX9ovOG+ZjaEE6s9g/HmN/2ScCZASW2GaWweOsl/Z+6qmnYiCN+b/3ve/FdVbaN/aJY4hjhY57AjEEW9iXasE3QnIEyahmR8U3OkiYh+AbloTKCOexDzyPKjhUhaNzl3AgQ8VROYB9Kj2uarU566C9lyxZEv7hH/7haIiOY462o4Ibnem0e6WJgA8VBtlHgn28PvAqPSYqzVfpvtJjimOs2jqZt979q7Se0vtoX0wJGdCmtdZZOl+t39n3FAqjM4t1tGdiPraLY7gjQT/ag31kORx7bd0etoEbxxb7xvzpdYUX7VbpNdCefc7qPCnkTDUUgs6c+3lt4VRrItDI64b3EMLThKExbWsb1VpHFh/jOMOPczfvDdzyPHG+I3xD26d9TcE39rtR57tmMeR8wvUK1zy8R9Lxz7UK50vOJ0w4EHwjZMH7N+EKbpyHsMrzxPk6BfXZT87/3LDhuOB3fDhPcMykW96Ok7a0MfvONRFf/qBiMMOccm1Tz8Q1OxWbqY588sknx+u/jrzn1rPOZn5Oeo/nGOO1yrm4qO9JHAdc36TKd3l6jaV94XXC5x9+ch+ff1LwLZ2POQ44DxOQS1/M4lzMNUyeg8iNfJ3yGsKR83t6n+c9jc/nfP7gVuQvkTTS2mUpoIACCiiggAIKKJAEDL4lCX8qoIACCiiggAIKFFqgPPhGYIlQwrhx444OSUoIipAWVSKoOEaAgdAUnSQEX/hmPMNyUqGMIBjf5qaSFlW/CKVRWSJ1PIDd3uAbIQHCUHQSE876xS9+EcNuhMEIvbHN9XYUsyyCMuk/5+nw4r40sb3c6AziJ/uaOsT4yfPpdGTIUoIcuLQWKGJ9zEc1t//4j/+IQUHWd+6554a/+Iu/iJU4CAbwPPaTUAkBOUKHrJ+Oyuuuuy4sXrw47iud6Gwf25M67rAhpEWnTcsbLeHUSafGdktD+dBhShsRmqOtCcXR4ZOWQyfq448/HreNgN7AAQPDD/7qB+GG62+I25B80k8CL1u2bImBOY6DN954I1a0ISBZLYRImI3nsh2si+ddeeWVYdasWbHyGh0kVABjX1geYTN+so9U1mO7mafe4Bs+dK4TBCT49k//9E+xA50QDsE3OoI5dlKbp30r/UlnGWFL/KjYQ+U5zEqPmdLn1/qd+bgx0a61JrapERMGbCvtVe9rpLX1skyOVcIIHanUxnaVbl9r6632OMtJ7cE2tXViX5g/tQnbxA2zFLhoz3Lbuh3N+nwsOHfzGnjppZfi64FzBO8BrQXfCOqmSkMp+Jacm3V/u2K70rGfjj2M8zzx+knnvvRa5W/ub9S5rln8aEvaldcG7+W8Vvid0BvXCryHsd+ELAiDEyrl/Z8gPNdQvEcTDsibS2qfUh+OhbSf/OTcgA03DJlKH0+/p2UV6Sf7zlDTS5cujVXfGLqRa6V6zh0cc7feemv4yle+Eq/LCYgX+TyMGTeOv3QOLtKxVLqv6TXF8cA5Of1d+pys/87nPUJvVEkkaEzgnC/aUIGTcBv7zHmYLwjxmYG/+VIMn73S+ZhzklNtgXRuL31N8d7Gjc9tvK+l64DaS/JRBRRQQAEFFFBAAQUUqFfA4Fu9Uj5PAQUUUEABBRRQINcC1YJvhNUIaFHVh4ASQQeGQaXDjJAZnQF8m5tvxL/wwgtxSE6ev/5IBTeqwTF8JEE5QnQpdJUgOxJ8S6EugnaE31jHbbfdFgNTdFzwH+tdMRHCIvRGkIpqZYTvCHfUmuh0oUOF6nj//u//HoepwoZwIPvAUK10BtAJRwc5nTO//OUvw69+9avYMU6HAYFCwlq4Elpjf+lk4Pl04tCehNdos0cffTRMPm1yuOzyy2KFMgJlVGRj+FQ6cah0dsYZZ8QgFJ1dLIf5qcRGqI8gIx0Xf/mXfxluuOGGihWvcCDIxnIZdotKUAQer7nmmjh8UGkHB88l+EdHLdUBqeJGhTk6+gmfcdzQMcu20OlEZy7L5Lji+GP/vvvd78bgX6p4V0/nHPtFuABPjpkf/vCHMahFdTnCOHgy1FGtiXAfFVawvfzyy2PVHrbTTrBaaj6WNwFeR4RAOefffffdseol5zRem5UmXp+c0+hcJgy7YMGC+NpJwelK83ifAnkS4P0nhb15rTDxmkjv3bwv8hxeK7yv8Z7M64XHeY9xUqBcgOOJa3NuXKtx/cV1I8dRpYnrFKpVUan2O9/5Trz2I4BJCN5rmEpi3pdHAT7P8BmEz61U7OYzBp9RuKVzLedjXkt8IYhgKJ9P+GKM5+M8HhHukwIKKKCAAgoooIAC+REw+JaftnRPFFBAAQUUUEABBTog0FrwbcWRSm9pWFJCCwTfCCgRuiIMxGMEkxiWkypj3EeYiOExCXTRuUbIqjSg1N7gG+EuglUEslgflcAYsumWW26J38inY6KrOvHoPFm+fHmbgm9UEmDoWMzuvPPOWAWGYXYIvP3xH/9xDNCx/XRecqMKDAE/gmrsL7YE/QhscWPINMJwTKliBeG6vXv3hmefffZIMOWeMGzY0Dg0KJ3pkydPjkEzlkenDmEzOnVwS+1DsIXKNATOCM5RJY2OUkIrBAtpy1JjOolidbkj8xC2Yz6CgLRL6jCiU4n9YVnsA8E/QoNs58SJE2MFQapAEaZM+0MHFftPG9NB9cQTT8S/b7/99nYF3wjrUCWF8NqPf/zjuF72nyF5cWwttMh2p+AbQTmqxbFfpRYdeBk6qwKZEEjnF875BHI5lxFG5rXMOaQ8eEFnMoGLKVOmxHAw4Wle8wRNfe1kosndyA4K8Jrg9UHojRvvsbwXcS3D+xyvDQJJfNmAykMp1E04Lr0vd3ATnD1nAhxDqfLmXXfdFb9IkAI75edgdp1rFa4BuTbjSwlUzeV6zmMsZweGu1NTgNcGn5X4Yg2fL/gsSviNL7TwOYbPddOmnRuHPz3++OHxNUL4jYrGvlZq0vqgAgoooIACCiiggAIKdLOAwbdubgBXr4ACCiiggAIKKNAcAtWCb3zDneElCTZQnYvhTgn7UO0qddQSJiKERuUuOnL5Fj2dCTyHKmGEighKEawqndoTfKOzgk4Jqls8/PDDsTIZf9OBRxiPYT+7cmpL8I3AHtXxqNJB6IuA2IojgUKCYITDGOKToT4JFNLJksJfdJYzJCjVlRgSlHknTZoUh0YlQEJgjk5ynp86yFPHzh+Cb3fHSnC05dlnnx07PbGnSgjBNwJchM0IoKT56RCiChttT3U0OlcJiLE+OucJMpYGVqj0RPsTzKOSG8cBHfgcIwTtqOzEupg41hjyjecRnGFfGTaUbeN5pZUB2R6GeyUoyHMJnRE+a0/wjXAB20Uoj+P4/vvvjxZUJST0hgHV8GpNBt9q6fhYUQQ4D3M+o8IQr0mqQxJO5fXBOZHHeA4ToTfCFZw3qBLKEM0EXHmd05GczjlFsXM/iyvAexCvC97zeQ/mGoD3Ie5LFUT5MkEaLr30Pba4au55NQGuuwi/MVzjPffcE6/puL7impHHOK44hgjrUNWN62O+iMI1OedgzsfpOrPaOrxfgTwKpM9IXKsQRE6fSfjMxLDtV1991ZHXyoXxXJwCb56P83gkuE8KKKCAAgoooIACCuRLwOBbvtrTvVFAAQUUUEABBRRop0B58I2AE51ihBUIMxBwSJXNqNxDtR6qkhBeoFONsAOBN4JFdCLQcUC1rz/90z+NQTnCD+WdBm0NvtFRwXr2798ft+Xee++NnXZsC6ExqqARourKqS3BN1wIk2FJQAwrqiRRPYmhPVMwDfezzjorBrEIhbAOqhHwfMJ+VEmjDfCfNm1avFExjtAYFT3SRKcngTkqttE5yrImHrEiuEinKJUNWA5V48orL7FOtpfA2QMPPBCr0rAOQnl0mlI1pDTIyD6wT4Ty6NznmOA+AnR0GqWhS2lDgmwcb2wf60+BGLaB57EPpWEYOnHp2KXiG/vfnuAb66KDi2UQNmRb03CsVNljyFiOnVK/5Fj60+BbqYa/F1WA1zE3As6EYgnIEswl/Mp5fc+ePfH1j08KvVFl6Nxzz43nEEKmvPZbe70V1df9zqdAet1QlYtrJIJvBJZ4vyOAzXs/rxdC4uXXS/kUca86IsC1FtdqDN/OscSXA9IXD7jm41qZYymdg/kSAtdvM2fODGPGjInXW1yrOSlQRIF0PuZzCp9f169fH1566aX4BaWFCy898oWY6Ue/tMU5uvRzSRG93GcFFFBAAQUUUEABBRRofgGDb83fRm6hAgoooIACCiigQBcIVAu+EVCgg5bgFYEhqn9RrYSJChIpgHXyyScHhvBkeEw6EehsY6jTFCqq1GHQnuAby6ZDj2E66TA+ffLp4ZIFl8QgFlXQurp6RVuCb3ROEnrjRqAMLzpemFJFDoKE7Aedk1RLw43QFh3lBNEIvVGpjeAawTPcJx4JsxFIK6/ewbJZD2E0OnTo2GH5PI8KfLQrFUD4m/tLp9ShSjCPik50qrIdPI/hTqkyR/sTaGQi5MZzqPxHpTdCeOwv6+ex1GnENmFGhyzPI+BHhRt+p9papeOkEcE31km1PbYvhee476KLLgo33XRTDB0SNKi0/lIXg2+lGv5eZAFey5wneH1zfuE8Q+iCCqCc23mf4DkEeglcELYgYJoCrgZ7inz0uO+8NghZMFQw7+Xf+ta34uvD14XHRr0CHENMXBdzrcaXIwghE0AmkEwwmS8TEHLjiwt8YYHwMdeW5V8wqHedPk+BvAmkyolcu/CFGP7mMw6fT9JnnLzts/ujgAIKKKCAAgoooIAC+RQw+JbPdnWvFFBAAQUUUEABBdooUC34RiiJzrV9+/Yfqbq1JrS80RJ2H6nY9fHHB2PIjGpeBKC4EXogmEUYgo41Og6o+kYwq9LU1uAbwSsCeHTwEf4i/Ea1suuvuz5MmDghVrXo6k6KtgTfCHsR2iMQQtUzAiNpInBF+C1V52AoUTosuR9/9p11se+ErzDmMcJihA8JpBFiK63ewXx05FAtjc5QOnToVKfCGu1KOG3s2LFxPtqvdGJ9rINtpWocN6qksf3XXXddHPKUinNUSWM7CJUxRBBDiBJuOf/88+P8VH6iE4ngHstkm3g+28G87CPVSNiP0gpypdvS0eAb62Q/ON4YkpHhYlkfnVoMr8rPZF263kq/G3yrpOJ9RRVI5wleowR5OT/zOtu0aVMcOoxzSAq8MXwjQzJzruE8x3nASYEiCxAWJfhGCOmb3/xmDCb5uijyEdH2fef6hmq2nIO53uL8S2VhKnByvch1Hl+m4EssfMGA60SudwxYtt3aOfIpkIJvfFmHz0l81mJIYD7LlH6myufeu1cKKKCAAgoooIACCiiQJwH2Cl0RAAA4WUlEQVSDb3lqTfdFAQUUUEABBRRQoN0CpcE3KrVxoxIYASkCSQQYqB6xffuOIyG4vbFaGNXVCL4RaqLiBNW0fvOb38Rgw2WXXRZmz54dQ0VU+Kk0tTX4xnqoYkHFNCqlcLviiivCzTffHAiK0WHc1Z3GbQm+0UFZeqtkkrafTsn0O89jPqYUHot/HPkn7XP6me7nJ/PQZoTfsCLwRQcPVeIYdpChYfmdsGC1zh0CbVSKo3IbQ6ZS0W/+/PmxIh2dqVQSYV6qxz399NPxRtCFoXIJtrEftBshPzpnmVgfYT3mS9tduq/xSSX/dCT4hgHH7oYNG+LQrmz/6tWrY/WTRYsWxf2nE7ha6K5kM+KvBt/KRfy7yALpvIQB5ybOF4RjCV4QluW1v3Dhwvg+kM4xtV7rRbZ034snQPCNyrW8/1Adl4pcvj6Kdxx0dI/TeZhzMOdcAjx8CYXh7An3E+Ah9Eb4OF13dXSdzq9AXgRS8I3gPl8S4m++uEWVxHTdkpd9dT8UUEABBRRQQAEFFFAg3wIG3/Ldvu6dAgoooIACCiigQJ0CrQXf6FgjvESwgbAXnWt01nIjXEUH2zPPPBOWLFkSK0vceuut4bzzzouBNKprVZqoEMQ8VKYgKEEgis5fQnPlldvo0GO9BJfoLCYARycFAatrr702VhLqjg7jtgTfKhl09n2EUGgfqrExTC2Vlgi9TZs2LQYb6QjFrZodYTUq1dFWBFmoHkeQjKFSp0+fHgMthNt4zsqVK8Mrr7wSZs2aFYOThCJZLs+n/bhxHNGRxHFTbZ3lJu0NvrEutp9jlm3HgOOW0B0dWgz5RaU8qu3UW/3E4Ft56/i3AscEOB/yeqXSEOcC3jMIURPoqfc1dmxp/qZAvgUMvuW7fbt677jm4ca18bJly44G36hqy5dDqLjpebirW8X1NbtAefCNzwl8cYvK5Qbfmr313D4FFFBAAQUUUEABBRQoFTD4Vqrh7woooIACCiiggAKFFUjBt7vvvjtW9Cqv+AZM6lTjd0JMBJf4SeiN8Npzzz0XVqxYEQNRf/3Xfx3OOeecWP2tUoiN+agkxjwvvvhirMhFGOqrX/1qHB6VanLMl8JRhKcIMFG5jOE0CVrRIcFwNFQgo2pXd0zNHHyjvajEt3PnzjjE59KlS8OwYcMClc4IojDMabVQYrJMbU7HEO1F5TQCLQxlSGU3wmM8h7Z59913YyCR+6kmVzp8Ks9JU2rT9HdrP9sbfOMYY15CewQMqEhH1RMCewz/RbU7jrO2bI/Bt9Zay8eLLECHMdUfqTK5atWq+DvnZzqQDVwU+chw3ysJGHyrpOJ9HRWgmnKq+JaGdGeIU4aV9zzcUV3nz5tAefCNv/lsafAtby3t/iiggAIKKKCAAgookH8Bg2/5b2P3UAEFFFBAAQUUUKAOAYJvP/nJT8Kvf/3rMG/evKNVeiZOnBirc5UugkBRutFBwNAwDINJIIoQ3Pnnnx/+7M/+LFYDI1hEoK10Iiy2e/fuWBWI4VGZj/VTjYxh8QhNpeoUKfxGoIIQFxXi6NBjGM3x48fHYZwYyqm1AFfp+hv5e7MH3wh+EXyjUh6hQSqc4Ttu3LjYCUq1s3omKqcRaGFZb775ZgzAUdEtDWdKMJHH8WBYLdqEtm/E9OGHH8bjiuPk4YcfDoTPbr/99rB48eJYwYTqc5XCaxwzb731Vnj11VdjUJJjdsKECbHaGw5sf3kos7XtNfjWmpCPF1mA1xwh2NLgG+8nBt+KfFS479UEDL5Vk/H+jgiUBt+mTp0aq/sSfOOLD5WulTqyLudVIOsCKfjGl3v4rGTwLest6vYroIACCiiggAIKKFBcAYNvxW1791wBBRRQQAEFFFCgRICOsrvuuisOVcoQLxdeeGGYPHlyDJeVhoOo3EUIKlVgS1XYHnjggVjxi0psDHX5jW98IwaMCBeVDyXJPAzFRIUwQkmEkwi1sZ40BOekSZNiRa40L4GqPXv2hCeffDIsX748BpgYSjVV7iI01x1TMwXfUnU2Al6pwhqhMdp269at8cZQVxjTCUrFvHqH8UnLo0OIUAsBMCqpEazjMTpTGUKUIBzhMgKT9YbqWms32n3NmjWxgtQjjzwS9+O2224LV155Zaz0Vy30yLZSUZDjhSAl+02Vt9GjR8eQZXsqnxh8a621fLzIAgbfitz67ntbBQy+tVXM59cjYPCtHiWfo8AfBPiswJd6+Fxq8M2jQgEFFFBAAQUUUEABBbIsYPAty63ntiuggAIKKKCAAgo0TICAFNXUGJ6O0BkVesaMGRNGjhz5haGRCDkdPHgw8HyqttHBtnr16jiUJkEoptNOOy1WFTv99NPjcJoMr0TAKgWNUvW2Xbt2xeEzd+zYEbiP8BSBLNbJ0KVUp2A+7udxQnV0Srz22mtx29hGns9zS8N5DUOpY0HNEnyjXQi8UXWNECHhRP6mjaimR1CRynvYEv5KldraWv2D5RBEI/BGe3Cj04j2IfhG0JFqao1sE44T2p2QACE2Oqeo+HbFFVfEdbEvlSa2df369WHdunWxuh3HM9tFhbh6A3/lyzX4Vi7i3wocE+A8YMW3Yx7+pkAtAYNvtXR8rL0CBt/aK+d8RRQw+FbEVnefFVBAAQUUUEABBRTIp4DBt3y2q3ulgAIKKKCAAgoo0EYBwmxUYNu0aVMMRxEoI7BGmKk0HEXAKg2fSRWxjRs3xtt7770Xh7kkgDZixIgYriJAR9U4lkXoKgXfWAY3gknc+J2gFo8TSEo31sstPZfOCYaiIXxEKI7KXZUqyrVx1zv09GYKvmFJyA0jtou/aSuChVR6oxIbbYMd7VHarvUi0Bapohw/UyCRsAsV3giVMcQpv7dn+aXbwbq4sf0Mc8pQrc8++2wgCEdFwUWLFsVKbhyn6Vgpn5/jCguOrXQMpuOw9Ln1/m7wrV4pn1dEAYNvRWx197m9Agbf2ivnfLUEDL7V0vExBb4okIJvfHbii1z8PWfOnPgFsPZ+SeaLa/AvBRRQQAEFFFBAAQUUUKBrBAy+dY2za1FAAQUUUEABBRRocgECQgSKCEoRXmL4SMJL5QEpgkiE5HgeVd+Yh6pi/E3QiuAbwadU+YtwWqou1pHAEcsmaMV6qDLG0KYsl/XRMdHRkFV7m6dZgm/Y0IZUN2PoWIz4m3Yk9EbgjWpvKfTWiM6cFILDgBttwTFDO3PraJuw/bT3H4YfWn2kQ6olhjOpasdQvNOnT49D8VLJjeOU9ZdPbCNTR7clLdfgW5LwpwJfFigNvq1cuTJWoJw/f37sQO7I+f/La/IeBbIvYPAt+23YjHtg8K0ZW8VtalaB0uAb1aX5PGPwrVlby+1SQAEFFFBAAQUUUECBWgIG32rp+JgCCiiggAIKKKBAYQQICBEu4ychoRRcKg8MpefxXIJJdBDwMwWMEhjzEU4jBEcoial8Wem59f5kHQS8uJVuX0eXW+/6Kz2P/Wf4zaVLl4bzzjsv3HjjjTFoVum5nXVfcmFb6LShMhqhRNqFYWfZLqruUb2PcFijAyi0R5pSW6Sf6f72/CRguWP7jrB5y+awdu07R6oRboxBONZHoPKkk06K+zd+/PgY1mxElbnWttPgW2tCPl5kgdLgG8NmE8A1+FbkI8J9ryVg8K2Wjo+1V8DgW3vlnK+IAgbfitjq7rMCCiiggAIKKKCAAvkUMPiWz3Z1rxRQQAEFFFBAAQU6USAFnfiZfi9fHWEsAlapGlsjglDl62iGv5sh+IZDqohHMGvDhg2BoUe5b9SoUXGIUyq/paE+m8Gtnm3Adt++fWHPnj2BjlyqvxGsYRowYECsKkig74QTToj7lo61epbd3ucYfGuvnPMVQSAF3xgym4pvnIcMvhWh5d3H9ggYfGuPmvO0JmDwrTUhH1fgmIDBt2MW/qaAAgoooIACCiiggALZFjD4lu32c+sVUEABBRRQQAEFukkgVXhLPyttRgq7pZ+VnpP1+5ol+JbagSpvdOLwNzfCbinw1uhKb53ddoQq2Qd+sl+EatKxxE+CblSwS0Ocpsc6c7sMvnWmrsvOukBp8I2KbwxLbPAt663q9neWgMG3zpIt9nINvhW7/d37tgkYfGubl89WQAEFFFBAAQUUUECB5hUw+Na8beOWKaCAAgoooIACCijQ9AIp+LZkyZIwa9ascP3113f5UKdNj5SjDTT4lqPGdFcaLpCCb5s3bw4OddpwXheYMwGDbzlr0CbZHYNvTdIQbkYmBAy+ZaKZ3EgFFFBAAQUUUEABBRSoQ8DgWx1IPkUBBRRQQAEFFFBAAQUqC5QG32bMmBFuvPFGg2+VqXJxr8G3XDSjO9FJAuXBNyq+zZs3L0yZMiUOfd1Jq3WxCmRSwOBbJput6Tfa4FvTN5Eb2EQCpcG31atXx6rZc+bMidctVJZ2UkABBRRQQAEFFFBAAQWyImDwLSst5XYqoIACCiiggAIKKNCEAgbfmrBROnGTDL51Iq6LzryAwbfMN6E70IUCBt+6ELtAqzL4VqDGdlc7LJCCb9u2bQstLS0G3zos6gIUUEABBRRQQAEFFFCguwQMvnWXvOtVQAEFFFBAAQUUUCAHAqXBt/POOy/ccMMNYfjw4TnYM3ehXKBHjx6B4NuyZcvCxo0bw+WXXx6mT58e+vbtazWrciz/LqSAwbdCNrs73U4Bg2/thHO2mgIG32ry+KACXxAw+PYFDv9QQAEFFFBAAQUUUECBDAsYfMtw47npCiiggAIKKKCAAgp0twDBt8ceeyzce++94dRTTw2XXHJJGDx4cNyszz//vLs3z/U3SIDQG7ft27eHF198MezduzcsXrw4MLwtwTcec1Kg6AIG34p+BLj/bREw+NYWLZ9br4DBt3qlfJ4CIVZ427lzZ7Dim0eDAgoooIACCiiggAIKZF3A4FvWW9DtV0ABBRRQQAEFFFCgGwUIvj366KPhrrvuCscdd1w444wzQv/+/btxi1x1ZwkQbjtw4EDYtGlTDLtdddVVBt86C9vlZlLA4Fsmm82N7iYBg2/dBJ/z1Rp8y3kDu3sNFbDiW0M5XZgCCiiggAIKKKCAAgp0o4DBt27Ed9UKKKCAAgoooIACCmRdgKAHnddPPvlkrPo1cuTIOOyl1d6y3rJf3P5U8e3w4cNh3759MeQ4e/bscPrpp4devXpZ8e2LXP5VUAGDbwVteHe7XQIG39rF5kytCBh8awXIhxUoETD4VoLhrwoooIACCiiggAIKKJBpAYNvmW4+N14BBRRQQAEFFFBAge4V+Oyzz8KWLVvC5s2bA78TgurZs2cMQhl+6962afTaCb/RxrQrVf3Gjh0bhg8fHtu80etyeQpkUcDgWxZbzW3uLgGDb90ln+/1GnzLd/u6d40VMPjWWE+XpoACCiiggAIKKKCAAt0nYPCt++xdswIKKKCAAgoooIACmRcgBHXw4MGwf//+QDUwJgNvmW/WqjtA+I1gY+/evcOgQYNCv379qj7XBxQomkB58I3z4vz588OUKVPi66ZoHu6vArUEDL7V0vGx9goYfGuvnPMVUSAF37Zu3RpWr14dDh06FObMmROvW/gyk5MCCiiggAIKKKCAAgookBUBg29ZaSm3UwEFFFBAAQUUUECBJhUg8Pbpp58aeGvS9umMzUrhN346KaDAHwRKg28rV64MH330kcE3Dw4FqggYfKsC490dEjD41iE+Zy6YQAq+vf/++6GlpcXgW8Ha391VQAEFFFBAAQUUUCBPAgbf8tSa7osCCiiggAIKKKCAAgoooIACCnSLQAq+bdq0KaxatcrgW7e0givNioDBt6y0VLa20+BbttrLre1eAYNv3evv2hVQQAEFFFBAAQUUUKBxAgbfGmfpkhRQQAEFFFBAAQUUUEABBRRQoKACBt8a0/Dlw2UzxHJbp44uo6Pzt3V7i/h8g29FbPXO32eDb51v7BryI2DwLT9t6Z4ooIACCiiggAIKKFB0AYNvRT8C3H8FFFBAAQUUUEABBRRQQAEFFOiwgMG3jhF+9tlngU74AwcOBIbQ5u+BAweG/v37h969e4d6hlamDQ4ePBj4yTL69OkTBg0aFPr27VvXxjFsN0PUsgzCb4TuBgwYELeB9dezDXWtyCcFg28eBJ0hYPCtM1RdZl4FDL7ltWXdLwUUUEABBRRQQAEFiidg8K14be4eK6CAAgoooIACCiiggAIKKKBAgwUMvnUMFL8tW7aEbdu2xfAZIbQxY8bEGwE4wmu1qr8RVNu9e3ecf8+ePTFAN2TIkDBx4sQwfPjwujaOwBtD1b7//vsxOEfQjW0YPXp06NevX90BurpWVvAnGXwr+AHQSbtv8K2TYF1sLgUMvuWyWd0pBRRQQAEFFFBAAQUKKWDwrZDN7k4roIACCiiggAIKKKCAAgoooEAjBQy+tV+T0NrevXtDS0tLWL16ddi1a1es+HbmmWeGs846K4wYMSIcd9xxoVevXlVXwjI2btwY5+cnyxg3blyYO3duOPnkk2O1tlrBOSrMffjhh2HVqlXhjTfeiNXnCLtNnTo1TJkyJQwdOjRWj7PqW9UmaNMDBt/axOWT6xQw+FYnlE9T4IiAwTcPAwUUUEABBRRQQAEFFMiLgMG3vLSk+6GAAgoooIACCiiggAIKKKCAAt0mYPCtffQE1gidpcDK448/Hn/nfkJr8+bNi1XbqLrG0KXVJpbx+uuvh0ceeSQG6LZu3RqmT58ebr755nD22WfHeauF1piXG/MsWbIkLF++PFaMI2w3f/78cOGFF4aTTjopnHjiiTXDd9W2zfu/LGDw7csm3tNxgXQeeeedd2JoleAqr9thw4bVrBjZ8TW7BAWyJ2DwLXtt5hYroIACCiiggAIKKKBAZQGDb5VdvFcBBRRQQAEFFFBAAQUUUEABBRSoWyAF3zZv3hxWrlwZh+skNEW1sGqBq7oXnuMnEnBjWNMPPvggLF26NDz44INxyFOCaJdddlm8TZo0KQbPWgu+4X7fffdFf6q+XXDBBeFP/uRPwnnnnRd69+5dNbTGutgGhjm95557YviNCnSDBw8OixcvDgsXLgzjx48PI0eOjMvJcXN02a4ZfOsy6kKtyOBboZrbne2gAME3qqMyvDeVTg8dOhTmzJkTr1tqVVjt4GqdXQEFFFBAAQUUUEABBRRouIDBt4aTukAFFFBAAQUUUEABBRRQQAEFFCiaQGnwjeEy9+/fH6uFGXyrfSQQfGOi8/25554Lzz//fCA8SIc8wcGLL744UO2Nik21OuJZztq1a8Ozzz4b3n777diRj/111113NHxYbajTtA3bt28PVJxjGQx72rdv37h+ggBUjaICnCHG2u1Z76MG3+qV8nltETD41hYtn1t0gdLgG0ON87fBt6IfFe6/AgoooIACCiiggALZFDD4ls12c6sVUEABBRRQQAEFFFBAAQUUUKCJBMqDbx999FEcptPgW32NdODAgRhYI7S2bdu22AF/zjnnhGnTpsXQGyG0WqEzwmtUrWGIQ4Ys3bFjRxg7dmyYNWtWrBZXz1bs27cvDpPKNhB8I2jHMKkMlzho0KAYhKsWnqtn+T7nmIDBt2MW/tY4AYNvjbNMS+Lcyi1VxuQ8zLmRc2E950PmS7c0D8uodT5P604/mf/w4cNH18lymL+e9adl+PPLAin4xnsuFd8Mvn3ZyHsUUEABBRRQQAEFFFAgGwIG37LRTm6lAgoooIACCiiggAIKKKCAAgo0sYDBt441DqGG3bt3xxshOIIOxx9/fBgxYkRgiNMUtKi1FqrsEVhj/oMHD4aBAwcerdRWa770GG1IYG7Pnj1xyDfuZxtOOOGEmkOlpvn9Wb+Awbf6rXxm/QIG3+q3qveZDAPN+ZlQFOdYQsicW/lZqwonyycwx3mV+VJwjXnS/PUE11gG53OWwe8E3vr16xcGDBjQ6vrr3ceiPq88+EZbzZ4926FOi3pAuN8KKKCAAgoooIACCmRYwOBbhhvPTVdAAQUUUEABBRRQQAEFFKgsQOdo6S1VBqmnkzUtkeANE8thShVG4h91/MN8LIOfzFt6q2N2n5IxAYNvHW+w0tcsS2vPa4750ms2LYPl1Dt1dBvqXU/Rn2fwrehHQOfsf7Xg29ChQ9tUYaxzti57S+V8SPXSvXv3hp07d8YhqRnyedSoUQHTWuE3rn8IzTE/FcUIJTMRWGN+QsXp2qyaDOtnOVTzpJInvxN6Gz58eAw1p0qgbTnHV1tXEe8vD75Z8a2IR4H7rIACCiiggAIKKKBAPgQMvuWjHd0LBRRQQAEFFFBAAQUUUECB/xco7ag9dOhQrDJCdZHBgwfHDtN6KkcRYqKzlspR/E7n7JAhQwIdvvV0sLINdBRzo8oJU9qGVL3q/zfXHzkRKA2+rVy5Mh4/8+fPj5VTOH6cFFDgmIDBt2MW/tY4AYNvjbNkSQTXNm7cGNasWRPefffdsGnTpjiE9PTp08OECRNiRc7+/ftXXCnXPlRp27JlS3jllVfCunXrYuU2KmhedNFFcRjpFFyruIAjd7IMrsV4T33mmWdiJc5hw4aFM844IzAUNsuqFb6rtlzv/4NACr4RLGxpaXGoUw8MBRRQQAEFFFBAAQUUyKyAwbfMNp0broACCiiggAIKKKCAAgooUEmAiiB0tNJBS4UROk2pLjJx4sRYoYRO2taG56KzdvPmzYFOdH7v3bt3OO2008LJJ59cV9UYOmtZ//r162N4jm1iG5ifTtvWOnsr7Zf3NbeAwbfmbh+3rrkEDL41V3vkZWsMvjW2JbmWee2112LojPDaW2+9Fc4888xw+eWXx+Da+PHj45cKKq2VUBXXYG+//XZ49NFHwwsvvBD/Hjt2bLjlllvCokWLag5XyhcIeF9l6OkHH3ww/OIXv4jBuTFjxoS5c+fG+bmmGjRoUKvXdJW2z/tCDLpRyY+KfAbfPCIUUEABBRRQQAEFFFAgywIG37Lcem67AgoooIACCiiggAIKKKDAFwToKKWz9c033wwvvfRSHB6L4NukSZMCFUroJGV4LYJntabt27eHV199NXby8jsdq5dcckmYNm1aoGJbrQpehNyoFMf8zz//fNi9e3esEjdlypS4DQTgqD7X2jbU2j4faz6BFHwj8Lhq1SorvjVfE7lFTSRg8K2JGiNHm2LwrbGNSfCN97MVK1bEa6o33ngjBt6uueaaeD1zyimn1Ay+7dq1K15HEVx7+umn43Cp48aNC9///vfDVVddFWp9ESEF3wjP3XfffeFHP/pRvLYiOLdw4cKwePHieE3H9RRfTnBquwDXywbf2u7mHAoooIACCiiggAIKKNB8Agbfmq9N3CIFFFBAAQUUUEABBRRQQIF2CNBJSuiMCm0MifXAAw+E3/3ud/Hvc889N1x66aVh6tSp4aSTTopBtlqreO+998Jvf/vb8Oyzz4YNGzbE4by+/e1vhwULFtSsLsI2MDQYQ5wuW7Ys3HPPPeGDDz6I1UjOP//82Fl7+umnh9GjR8dhV2ttg49lS8DgW7bay63tXgGDb93rn9e1G3xrbMsSfKMSGNdUVHxbvXr1lyq+MQR8pYlQFdXaSiu+8UUArsGo+EbVuH79+lX9IgHXU6yf66mHH344/OxnP4vBNyq+MYw412N8mYFh5A2+VWqB1u9LwTeGOqVt+XvOnDlxiPbWKiO3vnSfoYACCiiggAIKKKCAAgp0nYDBt66zdk0KKKCAAgoooIACCiiggAKdKJCCb1R4e+qpp8L9998f1q5dG4fWmjVrVqwOcvbZZweqjVBlpNaUgm8sh+AbVeJuvfXW2FHLvNU6WUuDbwztRfCNIVOpEEdnIhVKJk+eHEaOHNnqNtTaPh9rPgGDb83XJm5R8woYfGvetsnylhl8a2zr8WUCwvsbN26Mw7czJOaIESNCCvCnodsrrZUvARw6dCjOT/iNayHeJ6nQNmPGjEC1OMJV1Srocj3FjTDWmjVr4pCrzE/QbcKECXH4edZPFd4ePXpU2gTva0WgNPhGwJH2MvjWCpoPK6CAAgoooIACCiigQFMKGHxrymZxoxRQQAEFFFBAAQUUqE+ADiludAwx0fFDJ5IdQPX5+az8CfBaoOPu9ddfj9Xa1q9fH3bs2BGH5mJoLDpLhw4d2uowo1S/YHgvOgK3bt0aO1qvvPLKMHPmzFihpNZrjG04ePBgINjxxBNPxOFWqVpC1bmLL744UK2ECil01jrlR8DgW37a0j3pfAGDb51vXMQ1GHxrfKsTYOMahi8VcONzBtdRXMPU+syRPptwTbZv374YYCPkxnwMH0+1t1rXUuwJy+DG8PFU82VbmGfAgAFHK721tozGi+RniQbf8tOW7okCCiiggAIKKKCAAkUXMPhW9CPA/VdAAQUUUEABBRTIrAAdQQz/s3Pnzhh+owIVVRCopNC3b99WO5Myu+NuuAKtCNAxumnTprBu3boYOmOoLaq8nXPOOeHEE0+Mrw86a2tNdNIyTCqhN15jdNAyf6pQUmteHqOTmNAdVUoY2otQ1Pjx4+MQYVSPo+O3WpWT1pbt480pYPCtOdvFrWpOAYNvzdkuWd8qg2+d04J85uDaivc5rl34zMHPekJnfEGHayJ+8nzm49badVjaE9bNvKyfid+Zl22oZ/1pOf78soDBty+beI8CCiiggAIKKKCAAgpkU8DgWzbbza1WQAEFFFBAAQUUKLhA6oBiCEbCPXQoEXYbPXp0GDt2bAy/1arCUHA+dz/nArw+qEpC4I1OPTpqCYWmwFk9rw3mIfxG5TaqldBJy5BaVGqrp6OVjlmqkxBOZRv4mwonaViuejuMc95Uudq9FHxjOLeVK1fGY3D+/PlhypQp8fjJ1c66Mwp0UMDgWwcBnb2igMG3iiwdvpPrqvKpnmsh5qk0L/fXO3+1ZbRlfpbh9GUBg29fNvEeBRRQQAEFFFBAAQUUyKaAwbdstptbrYACCiiggAIKKFBgATqQCOIQ6iFcsWLFijgEEIGcqVOnhlmzZoVRo0YdHQKowFTuugIKKNBlAqXBN4bJJfho8K3L+F1RxgQMvmWswTKyuQbfMtJQbmZTCBh8a4pmcCMUUEABBRRQQAEFFFCgAQIG3xqA6CIUUEABBRRQQAEFFOhKAYJvVJGic2/p0qXhv/7rv2LAYsSIEWHRokXhmmuuCaeeemqsbkUVOCcFFFBAgc4XKA++UXVw3rx5VnzrfHrXkEEBg28ZbLQMbLLBtww0kpvYNAKlwbfVq1fHCsVz5syJ1y31DkXbNDvjhiiggAIKKKCAAgoooEChBQy+Fbr53XkFFFBAAQUUUECBLAoQfKOS0K5du8LDDz8cfvrTn8YgHMG3Sy65JFxxxRXhlFNOCUOHDo3Dn2ZxH91mBRRQIGsCBt+y1mJub3cKGHzrTv38rtvgW37b1j1rvEAKvm3bti20tLQYfGs8sUtUQAEFFFBAAQUUUECBLhIw+NZF0K5GAQUUUEABBRRQQIFGCXz22Wfh8OHDYd++feGJJ56IVd+oLDR8+PAwY8aMcOGFF4YxY8aEwYMHh969ezdqtS5HAQUUUKCGgMG3Gjg+pECZgMG3MhD/bIiAwbeGMLqQgggYfCtIQ7ubCiiggAIKKKCAAgoUQMDgWwEa2V1UQAEFFFBAAQUUyJcAFd8+/fTTQMhi7dq14bXXXguHDh0K/fr1CxMmTAiTJk2KIbg+ffoEh6nJV9u7Nwoo0LwCBt+at23csuYTMPjWfG2Shy0y+JaHVnQfukrA4FtXSbseBRRQQAEFFFBAAQUU6GwBg2+dLezyFVBAAQUUUEABBRToBAHCb1R+o9Ibld8IwjENGDAgHHfccYHQW48ePeKtE1bvIhVQQAEFygQMvpWB+KcCNQQMvtXA8aF2Cxh8azedMxZQwOBbARvdXVZAAQUUUEABBRRQIKcCBt9y2rDulgIKKKCAAgoooEAxBAi8EYJLt549e8Yqb4TenBRQQAEFuk7A4FvXWbum7AsYfMt+GzbjHlQLvg0bNswvgzRjg7lN3Spg8K1b+V25AgoooIACCiiggAIKNFDA4FsDMV2UAgoooIACCiiggAJdLUDgLU38ngJv6Wd6zJ8KKKCAAp0rYPCtc31der4EDL7lqz2bZW8MvjVLS7gdWRAw+JaFVnIbFVBAAQUUUEABBRRQoB4Bg2/1KPkcBRRQQAEFFFBAAQUUUEABBRRQoIZAefBt//79Yf78+WHKlCmBapxOCihwTMDg2zELf2ucgMG3xlm6pPwLpODb1q1bw+rVq8OhQ4fCnDlz4nVLr1698g/gHiqggAIKKKCAAgoooEBuBAy+5aYp3REFFFBAAQUUUEABBRRQQAEFFOguAYNv3SXverMoYPAti63W/Nts8K3528gtbB6BFHx7//33Q0tLi8G35mkat0QBBRRQQAEFFFBAAQXaKGDwrY1gPl0BBRRQQAEFFFBAAQUUUEABBRQoF0jBt02bNoVVq1aFjz76yIpv5Uj+rcD/Cxh881DoDAGDb52h6jLzKmDwLa8t634poIACCiiggAIKKFA8AYNvxWtz91gBBRRQQAEFFFAgZwKff/750T3q0aPH0d/9RQEFFFCg6wRKg28rV64MBw4cMPjWdfyuKWMCBt8y1mAZ2VyDbxlpKDezKQQMvjVFM7gRCiiggAIKKKCAAgoo0AABg28NQHQRCiiggAIKKKCAAgp0hwCBNyoK7d27N/A7obcBAwaEgQMHhj59+nTHJrlOBRRQoLACKfi2efPmWPFt//79Bt8KezS4460JGHxrTcjH2yNg8K09as5TVAGDb0VtefdbAQUUUEABBRRQQIH8CRh8y1+bukcKKKCAAgoooIACBRH47LPPwoYNG8K6devCoUOHQr9+/cLo0aPDuHHjwqBBg0LPnj0LIuFuKqCAAt0vUB58I5g8b968MGXKFM/H3d88bkGTCRh8a7IGycnmGHzLSUO6G10iYPCtS5hdiQIKKKCAAgoooIACCnSBgMG3LkB2FQoooIACCiiggAIKNFrg8OHDgZAFHcdPP/10HFJvyJAh4YwzzgjTpk0LI0eOjFXfDL81Wt7lKaCAApUFDL5VdvFeBSoJGHyrpOJ9HRUw+NZRQecvkkAKvm3bti20tLQE/p4zZ04M7Pfq1atIFO6rAgoooIACCiiggAIKZFzA4FvGG9DNV0ABBRRQQAEFFCieAMOaHjx4MOzatSs8+uij4Ze//GUc8nTEiBGxutCiRYvC+PHjw+DBgx3ytHiHh3usgALdJEDwjSpvW7ZsiaFkztNWfOumxnC1TS9g8K3pmyiTG2jwLZPN5kZ3k4DBt26Cd7UKKKCAAgoooIACCijQcAGDbw0ndYEKKKCAAgoooIACCnSuAMG3/fv3h507d4YHH3ww3HHHHTFsceKJJ4YFCxaEK664Ipxyyilh2LBhBt86tylcugKFEmB4ZapNfvrpp/HGucjpmECq+LZ169bw6quvxvPy3Llzw+TJk+NQp3ods+K3Hj16hFRRpk+fPqF3795ffIJ/5VrA4Fuum7fbds7gW7fRu+IMChB844tU77//vhXfMth+brICCiiggAIKKKCAAgocEzD4dszC3xRQQAEFFFBAAQUUyIQA4QkCFoTfVq5cGZYvXx6HOh00aFA4++yzw8yZM8OoUaPCgAEDDBJkokXdSAWyIUAH6b59++K5h2pmnIcILzn9QYBQIC6lHcjnn39+OPXUU+MTDL598Ujh2Onbt2/o379/YKju4447zuPpCBHHSd5fV+zjqlWrwl133RUD+t/85jfj0HpF2O+87+MXX+Vd/5fBt643d43ZFTD4lt22c8sVUEABBRRQQAEFFFDgiwIG377o4V8KKKCAAgoooIACCjS9AB3GVFwiZLF+/frw5ptvxt8JEIwdOzZMnDgxhgiooNOzZ8+m3x83UAEFsiHw4YcfxmE8qTbJkJ6cgwhxpKpd2diLzttKPA4dOhSrp6xbty76nHnmmeGkk06KK6VintOXBQYOHBjft0aPHl3IY4nj5sCBA/FGCIFjiKk0KFkpLFX6+JdV/3BPpfnKl11t3nR/6TLqWWel+dJ9pfO3tLSEhx56KAb0r7vuuhgQ5Zql9DmNWHfp8tJ21PpZus70vLYso3T+8vl4jGszrtc47rlZ6TApN+anwbfGOLqUYgik4Nu2bdvCG2+8Eb/QMHv27BhE9tquGMeAe6mAAgoooIACCiigQF4EDL7lpSXdDwUUUEABBRRQQIFCCRCgoEOVIAo3/qbDmKpvgwcPDv369TP0Vqgjwp1VoPMFtmzZEl577bWwadOmGL5ljYQ4uDmFeB7mvJyGoiagPHLkyBhExqc8BFNkMwJAqcOd42f+/Plh2rRphTyWqKLIa2vjxo3xtmPHjnho1ApQ8YTSx6sdS9WOuXrmZZnl89c7X6V5ua90fvaXqm+EK2bMmBEr1fJ46XNK1196P8uqNTVivtLlt3fdLKN0Xn4fPnx4OOGEE8KECRNi2I9Kh06NEzD41jhLl5R/gfQ+bPAt/23tHiqggAIKKKCAAgookHcBg295b2H3TwEFFFBAAQUUUCDXAnTulnfwlnay5nrn3TkFFOhSASpMPvPMMzGck4aopGIRvzsdE6CCF8PAcm4mhJwqOpWeq489u3i/pfcoAl9vvfVWDFFS8euiiy4q5LG0a9eu6LBmzZrw7rvvhu3bt8cwGMcNVrWOm2RZ6SiqNR/PrzVvWl6lZbR3vrTMNP/u3bvD1q1bY0h/zJgxMbhPgD893sh1p2Wmbaj2s9I6eW5H5k/z8gUFfufLCccff3yYOnVqmDVrVhg2bFjdy6+23d5/TMDg2zELf1OgNYHy4Bt/z5kzx4pvrcH5uAIKKKCAAgoooIACCjSdgMG3pmsSN0gBBRRQQAEFFFBAAQUUUECB5hPYsGFDePHFFwNDnY4aNSpWLSLEMWDAgObb2G7cIsIzqSon1axS8KUbN6npVo0JAa8nn3wyvP/+++Haa6+NVd+KGKLk9cSQ5e+9914c5hSbIUOGxCBYOnYqBbLSY601bvm89c5Xuty0jLbOm+ZLyyqdn4AF1RGZqHpG5b/Sx7k/zV9+P4+1NrV33jRfWn57110+HxUgudHeVPWbNGlSmDt3bgzBlT83rdufbRcw+NZ2M+corkAKvvE+zPDTBt+Keyy45woooIACCiiggAIKZF3A4FvWW9DtV0ABBRRQQAEFFFBAAQUUUKALBDZv3hxefvnlGFYhtDF27NhYrYiqb05fFEjhGQMtX3RJf+HC8J5LliwJa9euDVdffXVhg29UfFu9enWsfkYAjKEwR4wYEYYOHZrrIcsJh1IdkddKCr3l+fVC6I1QCcf766+/HsaNGxePeYY9pdKdU2MEDL41xtGlFEOAcxJhXIY6NfhWjDZ3LxVQQAEFFFBAAQUUyKuAwbe8tqz7pYACCiiggAIKKKCAAgoooEADBVLw7aOPPgqnnXZaDL4R0rHiWwORC7Qogm8PPPBAeOedd8JVV11V2OBbqvhG8IBhLxkGc+TIkfFnngNRBN4IvzEReMvzvrKPBN8OHjwYh7VduXJlPH8yvC/tnfd9Z/+7ajL41lXSricPAgbf8tCK7oMCCiiggAIKKKCAAgr8H3tn8hpV1gfQuzAxTolTBpySiGQQoaNiG43QrbiIK/89QXCnuHLjBLqLKKIoTjjGiCYgipEkJirq4uPc+q6k7Upiqupp16vz4FmVqjfce+6QJ/fk94OA4pv9QAISkIAEJCABCUhAAhKQgAQkIIEFCSi+LYjIAxZBQPGtAIuIb6Q6RXxbt3ZdaG5uDq1trVGCy2MENOqUIiIuortU9aFJ8kMyIaoSkTOJmDkwMKD4VuGWVXyrMFAvl2sCSXxLqU6/fPkS+vv7Q3d3dyBVu5sEJCABCUhAAhKQgAQkIIFqIaD4Vi0tZTklIAEJSEACEpCABCQgAQlIQAK/kYDi22+En8NbK74VGjWJbwg7RFBsaW7JtfiWw668YJWS+IZUQppTxbcFkZV8gOJbyeg8sQYJKL7VYKNbZQlIQAISkIAEJCABCeSUgOJbThvWaklAAhKQgAQkIAEJ1AYB0oSxs6hKFBV2/0K/NtreWkrgVxNQfMueOOkQ044kw3s25vX6+vr4yvs8zPOKb4X+pPhW4JDlvynCHM9LjKn03MQ9GUukGuU1qwh7im9Ztu4/r6349k8e/iSB+Qgovs1Hx+8kIAEJSEACEpCABCQggWoioPhWTa1lWSUgAQlIQAISkIAEJPB/Aiyisk9PT8ed9yzcNjQ0hOXLl0dBIqsFXBtBAhKoTQKKb9m2OzIOczoi1Nu3bwOpxz5+/Bi+ffsWmpqaYgrMlpaW0NbWFud45vxqnucV3wr9SfEt23HF1ZNMOjMzEz58+BA+f/4cEEuRSZctWxafm1atWhXq6uoyGVNJfOO+pjrNtr0V37Ll69XzRUDxLV/taW0kIAEJSEACEpCABCRQywQU32q59a27BCQgAQlIQAISkEDVEkCQQIZAjBgbG4uLuizYrlu3LiBGIL8tWbIkkwXcqoVmwSUggbIIKL6VhW/ekxFzEHHevHkTRkdHw8jISNzfv38fPn36FKW3LVu2hK6urtDb2xtTYqYIcPNe+D/8peJboXEU37LtpEhnCGcIb+Pj43GfnJyM44rnpsbGxji+EEqR33h2qnRERcW3bNt49tUV32bT8L0E5ieg+DY/H7+VgAQkIAEJSEACEpCABKqHgOJb9bSVJZWABCQgAQlIQAISkEAkwAIqggSRgG7fvh2GhobiAi6Ltz09PWHnzp1RfiOKCQu4bhKQgAQqQUDxrRIU/30NRGYiUU1MTITh4eHw9OnTKOkwzyPoIEaxOM1x27dvDwP7B0JHZ0ec54nyWa2b4luh5RTfsuvBPC8hlb569So8efIkRlJEgJuamopjjD8gQHLbuHFj6OvrC+3t7VGC4/mpkpviWyVpzn8txbf5+fitBGYTSOLb69evw8OHD+P/L/v7+0N3d3fFBeDZ9/W9BCQgAQlIQAISkIAEJCCBShNQfKs0Ua8nAQlIQAISkIAEJCCBjAmwgIr0RiSgCxcuhBMnTsT0eER6O3jwYBgcHAydnZ1h9erVMW1XxsXx8hKQQI0QUHwrraFThE5emb/ZSFFKqlKkGz579+5dYOGZNIiPHz+OkadaW1ujnENkT6SdR48eRbmZOb7vj77Q1d0VU6CWVqrff5biW6ENFN/K64tpTPHKuJqd/hexjWhvd+7cCVeuXInPTYxDnqGQ30gpzNjr6OgIhw8fjn84QFTF9evXl1eoH86mbNzXVKc/gMngR8W3DKB6ydwSSOIbzxmIb/ys+Jbb5rZiEpCABCQgAQlIQAISyDUBxbdcN6+Vk4AEJCABCUhAAhLIIwEWUFmYIGrJ5cuXw8mTJ+N70pweOHAgLt6SEi+l7MojA+skAQn8egKKb4tjzlzNTqpSBJuUtpTPVq5cGedo5m1SU8OWqFTM60R6Q1xuamoKX79+jeddu3YtnDt3Lkaj+vuvv8Ofe/8Mu3fvjumtF1eq/87Rim+FtlB8K71PJpmUqG68J8ptinTLOGM8Me4QR+/fvx+/a25ujtIp45LPr169Gn/etWtX2Lt3bxgYGAg8Q1VyoyyKb5UkOve1FN/mZuM3EviRQBLfSLOOeK/49iMhf5aABCQgAQlIQAISkIAEqoWA4lu1tJTllIAEJCABCUhAAhKIAgGLmyk1FZFyiJhTKxsLp9Q/LfDC4fr16+HSpUsxTd6KFStitBIWbknbVVdXZ5qaWukc1lMCv4BAueJbmsOSrMJrsW12xKYUwYm5nvfptdh5lf4szbWpnNwbqWZ2+YrdM9WPORqJDfHm+fPnYXR0NEbn5HOkNqJ0bt26Nb4igcF37dq1oa2tLTCfk26RY4kSdfHixRjdkzKQznr//v1R0OHYrLfZ7QYTypB+//K+1E3xrUCuEuJbEqsW2xZpfC3Upxd73Z85Po0vjk39aaHzUj0ZY4wNroEcynv2+vr6uPP8Q50Ye/QzohmNj4/HsUZEN2RTzr1x40Y4depUHHtEWGRcHT16NHAMWxrLvNLX2UthlcptxLeFWrj87xXfymfoFWqHgOJb7bS1NZWABCQgAQlIQAISkEDeCSi+5b2FrZ8EJCABCUhAAhLICQEWNFnc5C/SkQcaGxvD5s2bv0c1K2UhslrQJOmAxQkWcNmRJkjFxULuy5cvvy/4btiwIbS3t0c+PyNoVAsDyykBCfx+AuWKb8zjiCjMW6QaZE7js7TNFqr4jHkdkQUJDFEl7Ugt5QhX6X5zvSK5IMVMTEwEpCTKyc/Mu8yxS5cuLXoqczUbx6dzma9JpZjqSrn5XQYDJJht27bF1NQNDQ1RVkZ8IwpcEpe5JueePXs2HDt2LApC+/bti6nIkJw5NsuN+9NWRM5CKCFy3ezfv7BIEbYWWw7YUK/h4eFw5MiRGLGU9q61rVzxjTZCsKSd2Oir9OFiWxK3GFvIZvDmNT0v/IpnKcrHTp9inFAmorAxvrn/XGVIY4FIbfRF5hKuMT09/T2FcJpPGKebNm2Kn8/MzEQ+fMf4QnCj38II8e306dPh2bNncXzv2bMnim89PT0RH/dirMKXfk+kRlgtts9Tdu6n+FasV1b2M8W3yvL0avkmwPMFc6kR3/LdztZOAhKQgAQkIAEJSEACtUBA8a0WWtk6SkACEpCABCQggRwQYLGQxc27d++GoaGhKAqQ1pPIZmnhNgfVLFqFtKg9OTkZbt68GaO8dXZ2hr6+vig9sFjMIiyLx7BgT4vbRS/ohxKQgARKIFCO+JaklRcvXsToZwhUSf5CBEsSDkIKO3MYcgyiSRJ9iW5GClDSOHMM21ySTAnVi6ek+RaJCDFrZGQk/u5BWiH94Y4dO8KaNWuKXp5j2Jmrx8bG4rkPHjyI8hyiNjIO5yLgkF6R32cdHR0ByYYobr29vVHyS9GqqBvHIt+cP38+HD9+PLI4dOhQIC0jx89VlqIFLOFD6sOiODIJadDu3bsXf++SZjXVp9TfwYpvhQaphPiGAEa/o6/wvES70ZeTSJZeuSPvGV/0M4TLFF0wyZZ8n9VGuZDIkNGYA/hDBsZyd3d3lPmZB4rdn7owT1BP5g1kScYmUin15jzqxHdTU1NxfPT390fJLdWPutJXqSfHUpZbt26FM2fOBOYlnqUYh4ODg98jvtE2SHHcl/kHQS/NP1zjZzfKz/0U336WWOnHKb6Vzs4za4+A4lvttbk1loAEJCABCUhAAhKQQF4J/A8AAP//CRsSCQAAQABJREFU7N2Hm2RVnf/xKzmHGYchyDAyCAMiSEYYkggIo4IYUUR3191/Z8Oz+vi4iCigEgRRQBQcRkBEMggz5CxJSYKIpP3168zvzJZldXV1d/VQ4XN5iupwwznvE+6d/r7re97zvxNbky0EQiAEQiAEQiAEQiAEBpiAR9bXXnut+fOf/9zccMMNzeWXX97sueeezfLly5tFixY1m2yySbPBBhsMcA1mVzT1f+ONN5pXXnmlufbaa5sVK1Y0O+20U/OhD32o2W233ZrFixcXBrO7So4OgRAIge4E/vCHPzS33nprmY/NPTvuuGOz7bbbNptuumn3Ayd+ax578803G+d45JFHmnvvvbe8nnvuuebll19uttxyy2bhwoXNdttt1yxYsKB56623ypz/17/+tcx/W2yxRbP99ts3u+66a7NkyZKy74Ybbtj3uf/tt99ulOmJJ54oZfW1e4wyud+8//3vbzbffPOO9f3b3/5WyuyYRx99tPnjH//YvP76681GG21Uyq786qlOv/71r5vf/e53zfrrr9/Mnz+/OeaYY5rDDjus/F693vOe9xRmL730UvOnP/2p7P/Tn/60lOHEE09sli5dWvj3wr5jYXv84TvvvNP85S9/aZTjgQceaFavXl3Ktc022zTve9/7yv1HH8Bkuvfhp556qvnZz37WPPjgg406LVu2rLDqsWgjs9uLL75YuOovWG63YLtm4fYLG4z1g6k2fdaxeHo9/fTTZUzpe9pE2+h3m222WTmV/md8GZN+Z8wZe/qna+qTvVx3qnK1/9749yxjfDz55JPNCy+8UPrWvHnzmg9/+MNljK233nr/cG31c5x5wvxR66ceyqm86mk/fdRLfT7wgQ80e+21V7P77rs3rmEc29emX2Nw4403Nj/60Y/KGLOfchxyyCHNzjvvXPbTNvfcc0/zzDPPNBtvvHGz1VZbld85v+977fNYu6Y2cT7zqPnz8MMPL2VT72z9IWAs/OpXvyrzygc/+MHGy/zd63jqTylylhAYDgKeW8zFzz77bJmbfH/ooYc2e+yxx9r5cjhqklKGQAiEQAiEQAiEQAiEQAiMO4H3TPzxJeLbuPeC1D8EQiAEQiAEQiAEBpyAR9YaeL/uuuuaiy66qNlnn32aU045pUgQAv+9Bh8HvKodi6f+ArrEt9/85jfNVVddVYLVJAzy27777tuQQrKFQAiEwFwSmI34plzmMfKKAKu5jPxFpCLr7LLLLmU+I58snpB5BV/9nBRlH9IMQWf//fdvjj766BKU3XrrrXuS7nplQkxxXde75ZZbGtKLn5Ht9ttvvyJPmGuJae2beZqcjRGphzjnZ4LH6kY6cq8i3tiP9Ea6sS8Z5oQTTmiOO+645r3vfW8RaogwxBznw+Cuu+4qLyLPSSedVOQb55zre586YIA/Yenxxx9vHnrooVIm8o97kPqRpohF09m0b8S3pvQzfW4m4lt9PtCPtMudd97Z3HbbbaX/aS/9laBIstphhx1Kn3Qd49AzhT5E5vRhAtKXr+dCKFVOH2AgUD788MOlnJ7riH7Gu2c645vI1i7dVemN8LZq1aoyL5BF9T8fAjBmjAPj6Oabby5zi7FrrBHLSKX2JaAaV8qiPxPnrr/++ubcc88tfdz48zxlvDu/rUqJyoyn6ygr8VfZ8Wsvb6cxUMdRxLdOdPr7s4hv/eWZs402gYhvo92+qV0IhEAIhEAIhEAIhEAIjBOBiG/j1NqpawiEQAiEQAiEQAgMKQEBw1dffbUEaokS559/fgnQfuYznxkb8Y14IEgrqCtQK2AsgOtT+UcccUQJwA5p86bYIRACQ0JgtuKbubwGWa+++urm0ksvbe6+++6SwenAAw8sggoBhwhDkiMwkHhk73FtQg4B7fjjjy8CHOGK/NaPzfVILuQaktntt99epCEikMxRhDwZg8y7Xq2bejleZjbZnIh95mxlI6qRc5S9ZptyHRK3DJ6PPfZYyWYlgyn5jfxD0HFOohDpzTmJSs6pLBgQc0g4vUg3rWWd6dfK474jMwxJ64477ijlkUmL3EcGIgJNpzwR39a0RpWrZiK+OUMdK7KSkSmNLX1G3zJGPCfov77WPq4j6yKJjPymDWXF8izhnUhGmJtOW07Vr/Qfcp5Mj+RJZXUNkpnxTs4zXlrHlmP0eeNAXRz3/PPPlzmE+O+lrPqdseUZSVZg9SeeOu6jH/1oySZI/DOu7Oec+rE5xVi/6aabSka8Y489tnByzppJUZ/XT137vvvuK+Ke7GEywsm6qNy9yKe1LhHfpuops/99xLfZM8wZxodAfSarYjHROBnfxqf9U9MQCIEQCIEQCIEQCIEQGCUCEd9GqTVTlxAIgRAIgRAIgRAYUQI14C5TyDiKb5pVoFYwQtCYCGIpL0HkoycyH5188skl+DuizZ9qhUAIDAiBfohv5jIZz6644ooiMZvTyCyWuvz0pz9dZBKZqUg3ArIyw/34xz8uIhqxjBhHULEcoQxVMjn1Q9AxvxK6CG/eiUEEs4997GNFciEHkdc6XYt4JIMUPsQjkhqhh2ikfK1Cj+OJGT//+c9L9k51Itl84hOfKEIfoc11SDzueffff3/z+9//vohuBDNsiDk1u1qn8sxFd6niDk7YEBZlwVLnuvQ4wY9Y1GuZIr6taanZim/aRnZAHxAwXi655JLynCAD3AEHHNCceuqpJZMZWUvf0q+Ii5dddlnpW8YZwfPjH/94c/DBBxe5sl/jSg2NeeUjmclY6/rGk6xpMgbq0/qzsrVutV7mB+Uls5FPyaGEM+81i6I+R1LzwQDXsK8xRHyTIZH4Zl9inbJYithyo8ai8avvkm9lLlSOKrP5HVlNtjfj0Hj0tfLKEOcYS562Cnutdahf1/ET8a0Smbv3iG9zxzZnHj0CVXwjIxOmI76NXhunRiEQAiEQAiEQAiEQAiEwLgQivo1LS6eeIRACIRACIRACITDEBAQMBTRnK74Jvno5n60G51sDln5Wfz5IyGoAWNYTWUdkfrMUnyW8ZL4TOBasba3LIJU/ZQmBEBh+Av0Q38xl5vKLL764+f73v18EFfPWJz/5ySLoLFmypAgtfiYAK4OTpQjNeWRfsgyZ5SMf+UjJSmLum82mPKQ1Mp5rrVixopTPfOoaxLeahW2y+VU5SUeyQskeRayxJKu6yGpVM7PVeRxH9Se/EWhkrpLF7qijjir7qw95g7zjnRhVM0wRhshlylLvV5OVazZcJjvWPVRmGPIbSdCSrSQk0pRsdKQ8IlAvW8S3NZRmK75V1voh6eucc84pkpa+c+SRRzZf+tKX1gpm+rVMaAT6H/3oR0UUI3JpQ/KppUEt96m/9eNZqI53ZfHMcs0115T+cdBBBxVh0hghs+nT7VuVzmRQNP6962PmAP3McbWM9jWG1d/yueRTY8tcoW8S+fRLkoffPTohvhHZXJfspr4YbLXVVmvHlXMrv5fMeERPUqw+T8YzXgm45iDCardx6BzGjjZyXdIdGQ9vY7rbse1c8n13AvqaLKGyZcpg6CVLX2t/6X6G/DYExodAu/jme88+RPtO8/L4kElNQyAEQiAEQiAEQiAEQiAEho1AxLdha7GUNwRCIARCIARCIATGkICA4WzFN0HR+hJ4tPmDfn35vlUiGMQgpKCpADX5Q/D4yiuvLEHTU045pWQWklWoZilRn2whEAIh0E8C/RDfSGaynP3gBz9ovv3tb5e5nZTyqU99qrxIYFVQMFdbEvSHP/zhWvGN+EL4JYyQZ0gnVX6ZSV2rMEPC+uUvf9n89Kc/LaKbbG/OT2Azt9b7Q6druD8RYYhvMqa4r1gqjNRj3vZyT1GfumyjOv3iF78o8o8sW8uWLSvZuaqYJFuXbHjmdFINSYaYQ94h1rmGc9Z72GwYdKrTZD9TFxKQe5HsduQ9S0iqg+xdJBMiTy9bxLc1lPolvskmRvr65je/2eg/+oasZMQ3EoMlQbWVNiShnXfeec3KlStL1j79iySmH+r3iyeWH+1HnzK+lIXoJeObPi27HNG1lomg1ulaxgtJTSYikiVhVgY7S4xuvvnmRfZ3nPq4juVLCaXGlnEi66I6mS+IcvYlRel35E0vY2vvvfcuY94xmNmMLS/HeAY1b+n3Mr795Cc/KeKgTIeyTuKlLsZup3o4X8Q3FOZ2w9hGkPSMLDOyttVO5OXJBMu5LVXOHgKDTcB9wz3IvGj5a+JbXeq0SvuDXYOULgRCIARCIARCIARCIARCIATWEIj4lp4QAiEQAiEQAiEQAiEw8ARmI74RBCx3RUwQtPS1IKngZGtQ09eClpbCkvFjyy23LL8fJDjKXQULWU0sZ7b77rs3RxxxRAnsCSYrf7YQCIEQmAsCsxXfzMfkFZnMLrjggubss88uWZlkcFq+fHlZklD2pc0226wsL0hkqUudkmYcS6ySwUmmJVIDoWU2G7lGvWTSJL4RuSxfaOlRIlcv8yqRj9wjcEzUkeWNnEMAUwf3Hht5xu/Jy+rlmkQjEh85g9gmAK08ziermnNYMlXGIgKeTWCa+EPkcK8iM1Vhp+wwh/9zP3Z9dfrtb39bJCB1Ii+S346eWH5b9qx6f+1WlIhva+jMVnzTJuQF44O4SXzT74yNE044ofnc5z5XJDD9Urvo8zKokU+JpQQwfc+++iOZq7Zht/ab6ndkNM9cpDeivoy1vieVWn6VGNqt73re0UeMF3OG+UM2usUTUp6x5KXu9dmI8HT11VeXrG/2MY7NE67nOs7nPMaWDI1YWOLU/IMNLjbPgiQ4Qp6vbVWuUwdyHW72MTZxcx1jcrIPH9RyZqnTgrOv/6ts9Q989Zdf//rXpZ3Nw6RE/dscqk0j8/QVf042pATquJEpk1xsbiO+mQfNZ55JPF8YM73cz4cUQ4odAiEQAiEQAiEQAiEQAiEwQgQivo1QY6YqIRACIRACIRACITCqBPxxXsBSUFcw6/zzzy+BWUt8yuhB9uoUbKzBUJlp6h/1BZgFK+v+AmX+yO8ahDeBYhmFBE3rPoPCVRmVV8BWNotLL720yA4C1DKOEOCqGDEoZU45QiAERofAbMU3wpTgqqX+Lr/88jKHycRDZrHUp2VFyQkkLnO2perIVTKjEVZs5CpZLskspBWB2Zlu5lSixN13312WKCWzEIJOOumk5vTTTy9CjPtClV8mu86jE8smyn4mm1Rd9tBx7i0CyUQM9yPzt33cy0hB9iGKWVbM135G8KvLOrrv4SELHqlG8Nk+OLoOCdA9C4OpyjhZ2af7c8zURd0s+SjDGIFP8Fw9vvjFLzZ77bVXuX9OJeNFfFtDf7bim/bwnGN8Glff/e53SxsR44899tiSSdFzAoFB33E9Gd8uvPDCMr60nece44qE6Wsi42TZy3rpM3VsuZasciQ70htRTD8x3o3fbs9ZjpVB0dh3PnKa4wmfJDfCqboT4GRc1J9kZDPeXEO2N1IbmZao6efmFP21SmvGl/PZPFspj++9ZMirHyZwfRtJ0DKaxFXlItTh5lokVfsbp+1bHTcR39rJzP57c6I+oB8bB4Rh9w3zsmd544BkaR7VRnUunf2Vc4YQGF4Cxo37uDFT50VZEo0l0rD7uEygsmKa5yK/DW9bp+QhEAIhEAIhEAIhEAIhMC4EIr6NS0unniEQAiEQAiEQAiEwxAQEDKcrvvljviCmP+j7Q76AsHMIkgpmkgRkqRFYtY+ArCCs4Bihwh/815VIMJ2mwULdBPVkJxL8tXTeUUcdVYKvVRqZzjmzbwiEQAj0QmC24ps5+M4772xuuOGGIu9ef/31RbDZZ599iqhC4CUlCMi6lrmbyOJl7iZ7WerQfEdoIYsRWGa6EdEIMSQgMrHlFEkTn/3sZ5uvfe1rRZRwH5hKALJ84xVXXFGEtsMOO6xkF1ImWbeck4Bh7iYdkW/ce9STlEGyI+n4PXmHTEais4+fuV+R25TD9zZCmXuVZVhrhrxuAlE5qI//0xbaSN1IiUQ9gp8sMV/96leLmK5tiFbdtohva+h4Dlm9enWRIrX3dgu2axZuv7DIV1P1PWfQjx9++OEicMoGaylO/YtQeuSRRxYpSx/Sf/RJS/LecccdzYoVK8rXhDLZDWVSNL5Ib7OV6PUR1zKOlcmyqgRNfd0yegQ7zyvd6kd+NVeQZYl7JAxl1ffIa+pc+6LnOFIpaUO/M0eQ0fRDwoZxbe4heKi/88jmWOcQbDxbkTzMLVX4qOJb7cfGqP5unHqRWE8++eQi7Sqj4zsJn86vrBHfKsn+vGPqvkJI1Nf0Ff2CMKn/6MuyvWlr86229b3x0cvc3p9S5iwhMFgEzEdEUePGOCERe5lHjak63xJFvcxrdS7tJPYOVu1SmhAIgRAIgRAIgRAIgRAIgXElEPFtXFs+9Q6BEAiBEAiBEAiBISLgD/TTFd8EkgkG9917X/O7m37XvPLnV0p2OIGvHXfasQS8BMcETwVDBeAFfokEgrKW0PMJ93W1qaOtWxC4lkWQm2Rw0003FfFA9qSjJ7IGfeUrXynBivrJ/Lp/3kMgBNYNgTqOZ3u1XuaB2V5jJsfPVnwjmRHMLHto/iL7CKqSEbzICTUgS2IRkCWymNNk97QEIylZ1ifHzWauE9x1bveKa6+9tsg5pBjCWRXfSGXaYqr2cA/50Y9+VCRkx8qY5dwCyTXjm3OQXsh8MkWRY8g1lnwk6bjHuWfJPucYQrON2NdaT8IGOcryfYTBKjtPVcaZtHe3Y9yHyCWysMp+RWJ0Dz3ttNNKVj5yyVTZ+Kr4hgkB0DKb6jpuWxXfiOwEg+mKb4RKIpu20A7EeJkUSfxkUlkSyWD6ds24SCb1DKR/EeTqsw+hUh+bbTuQ0whm+jLBTmZAGbfqMsWyFRrD3TbHE0qJo0Q5fd4YMjeQzmRHNI7NGYQ0Igdhw/iTAVfd6+/IpAQ8Y8+HItSb3KeexqLvSW7KZTzKEkaO8/PWzTWIrrfddlv58IE5Q1Y9z2DmJnNYJwlVOZS1im+OJ/Kql/GcbEqtlHv7Gk/zkPuE9iXi6tP6jT5iTrVstnY0T7pv6Bee8QlxRJ5OkmJvV89eITCcBIwbL89zxg3ZzRzkfl3Hg+cXc7iXedGc6t/P9VlkXT9vDCfplDoEQiAEQiAEQiAEQiAEQmBdE4j4tq6J53ohEAIhEAIhEAIhEALTJiBg2Kv4Vv9YL/B1+223F4nggQcfKMFLQXUB3rqEV11STqBYNhDZQWRHEQAWYJ3LjG+CDgIKgnbKLBjqZwIPAnXdggr2q0t2WXLrsssua2QZ+tpEhiJyiCW6plt2jG31fdqNlAMGlsBctWm3PjqwMOawYP3kPIhslUmglLBhPhYIJW4JmLZnRWrHjI15S3YkSzFaYpF0TFgglxFiSAjmLecml9hIJ35PWNhzzz2LkOyaNUtT+3Wm873yyPRJTiPjKZfsJzby2pe//OUiS3Q7pznc/E06uuCCC8p8fsYZZxR5xpyuHu5FrkGGIdwQ20hHgs3meqKYZR9lm7IfGcz87ryYe9W+5Wv3CMwxM99PJZd1K/9sfoefNiQgEa5kfiP9fPrTny5iCQlIOZV5sk1df/rTn5YsXMQ3EtB0712TnXuYfi4zGplKn5CZbbrim35M3rT8ufGpfxF9tIFxSmbTh4w/cp0+aZwZXzLdei6yL/mUMNcPCcuzTe0fyuZZhRhpiXrL6HXru8rq9dBDDzWXXHJJKe+nPvWpInoSQs0bnt8Ik/qhcWjM+Lk+t3hC0LBssuc5v8fVGPWsRzJ0boKHelbRAwvzytKlS0v/dQ6yYLvEhrVrub55TPY3z1+EKhkPzVOdpEHXVJYqvskySXyTAY/s2A/mw9Tn+1FWc6Y5Vj/4+c9/XtqX2KiPmz/xNv9oY3Otewmp0b8FfLjF2GgXG/tRrpwjBAaVgPFAlHYvcB8wf5lTib6kYZKojSRtrjSnGkvmNftUKbrbfX1Q6z4o5ars6vuglCvlCIEQCIEQCIEQCIEQCIFRIBDxbRRaMXUIgRAIgRAIgRAIgREnIGDYq/hmP0FkWdBqphCBXCKboLo/3AuAERAEQmVGka1GIPPzn/9884lPfKIIBTWLzlygVR+BWgFUwQXlFagTKFY+8oAg6GSb45WfJEF6O/vss8txMgfJVuL4qUSU1nM7X30JFGYbLAKCI7V9pluymR7X63VaAzetX+u/rt2Prda/H+dqPUe/+7r6Gtez3bDrNv6nc/7WNpnOcfZtPdbXykQqINbUQCkJTdamqeYbrEkKsvAQWWRHM+cKwJIPzM+ywfkZkcH5BVplqvJOkjGPk7xcq2YdmW6dWvdXJvMoKebqq68u4pv5mAhB3vrc5z43pfhmDhdAltVKNimSjOPMw84vYKwu6o6h6916660l2IyjOfz0008vSyUSdkhfmHhN1j9dw34C0F7tYk5rHefya+UjJsmyRGyS0Yu0JaMXEciSmUSTblsV34hay5cvL8e9W/XpVs65+l2dnz0DkMRkLXvv/AnxbeF2hR2JvXUcdiqHdtDHiD/f+9731i6ZaqyQ/IkMzuFa+qPnH2PJc4KxRSolYLmWfcleU12zUznaf+ZaMiHWLHSWLJVpi1DqwwWEu8nmDfOoMUNoIkYSUsmojvc748NY9bynXmQy/ZBMJuOX33me+8IXvlBEOMcYezg7r00dW+tpftP3MDCnefez1n0c59qEEKLid7/73TLuZZbzfEl+k5WyE0Pl1FZVfCOcGB/q5Hqu5ZWtdwLm3kcnsgF6ltdPZBF1H9H3WudPbUh+0y4yUZIbCZjHHXdckR3b+0LvJcieo0agzsmj2ifUy3OHe7d51fOWe4UxYU72bFHvFeY5c7BnJOOGbO85xf6Zq2bW8/G31XtL/X5mZ8tRIRACIRACIRACIRACIRAC7QQivrUTyfchEAIhEAIhEAIhEAIDR8Af4acS3/wRWaCLQCaALKj4y1/+shx39MQSVDJxCEj6RLs/NAswE96Ib/b1x/+vffVrzadP/XQJABMK5uoP0oKwhAlBBSKJT90TAGwCp5Yn6xb8x8M5BFAF+84888ySMUQWCwFlmSwEJ3rZMHMuwWBlqkHhXo7NPuuGQA3Eebe1BnSnKkHNKGi/eny3Y/T51oBMr2OgHudYAeZej+tWltbfTafOrcd1+xqbXph0O0fr75yPXDHbuuNn/ulH2Zxrpps5qJahtqtAqUxHxAKBUoFQ2YqUt9tmjjHHEtuIb+eff34RxkhmxA/iiN+RwrwTV4hTJCrZoYhkliVUjn5ttUzuGe4VxC1Si6xPsksRiYlck23YEC/M4ZY7tGwrWebEE08sMl9rP7Cv78357jcyT1n+0bKTlqgm2hGQsNRmlftk1/bz1vN322+ufmdMKr8MdjLmaVf1lznVvYj8RozsVk73vR//+MflHJaL1A9q4H2uyj1I59UHjSX9AkvPOTtMMNtphx0n3ncoQlQ3fvqJe7bjPQt85zvfKSKQtsGeMGpOcm776N/6mechrL373vjFvdu1pstNuYhoxpZnLXKSDGz/9E//VDLMGVuTiW/K6RmNxEaqNHecfPLJpcz12ah1jOAm86Ax5VrGIsHOtcxRVWLrtQ7dOGgzoiEh5Jvf/GbJsidjnsxttQ+TC9vPobzaxXMbFkRA490zm+e1fs5tvdZzmPfDl5BjuWX9TNv7urVftNfPMfq5saF/6FOkQz/Dv/1Y+2uz9rZsP2++H34Cta21t36gP4zamFRHL89x7tvuCT7k5d/FPnRFxPX7OleZdz3vyYhOdjNWzFmexXp9Thn+ntHfGphrPPeScOsy2/29Qs4WAiEQAiEQAiEQAiEQAuNNIOLbeLd/ah8CIRACIRACIRACQ0HAH+GnEt/sI1hKepP5RPYPwV6ZTGrA1B/3/cGeoGL5Fll+Vq5cWcQzwdSvfvWrZV9BYH/UFwCYi005ZR4hTCinIK0AQxUuLMU0lbAiOCNgrg6yJ/leBhfBbMKBYEYvGxaCuEQTAohACJbZBoeA9hBsn2672J/04NVr8Fa/a39NRcJ1BAiNIUGdevxUx03n99Otey/n1vf7uTkfqWG2G379WH7N/OVcM2XXGvR1Lt+TUWQK0c4EXUsommsERbttJBhzLllElsoqmTlWls0TTjihzNfXXXddCbTKpiQLHFHGfCbzW12Csdt1pvO7Kr4JAlumU5mUU2D3k5/8ZHPKKadMKb45VnZRdSMOq4+yyo7S6f5hfiW8kHm8SM+WOiW+kZQcX8We6dTl3dhXv1J+sgnx7aKLLirZxLQZgdu7DDKdONTyugf+6Ic/am783Y2Fm6UwZ9Nn63mH5d09XIYq91/PBOpuuVHjCjv9oRs/8zr50hLEnnvOPffcklXRMwz58OgJ6d95ZV0jZ8q4SHTzjEF6I5Xqq67bOt5ny0/fMJZk4LKE8I033lj6ifL8y7/8SxHfSBSTzXN4kC28PMcpn2Mtx+rr9s3zoWvVcWVMyuhFbsKSZGfO6seGubnePPhf//Vfpd/LnEfglUHMO/GtvZyYONY8oaye3dTfPOfZTzt3a+t+lH2UzoGVZ1bP0ERC9wzfd7vfVcbuV+45xoH7ivaarP/X86VtRqn3dK6LtvZc4GX8eo1au6uT5xVCm/oSb1s/xKC+fu7l3mQude8wbxkj/g1tvppsvHQmm58igK25R3ZVsrNnzU7LYodWCIRACIRACIRACIRACITAzAlEfJs5uxwZAiEQAiEQAiEQAiGwjgj4A/xU4psAMilDNh3BXwKc4O8+++xTlp6T7c0f60kF/oAvmCpDioD9W2++VZYEIyCctPykvgVIJ8Pj+oLRAqdED0veqZ8gtzIcf/zxPckPgq8C2hdccEERbgSSZR0hHFjirJeADW7EKOxkWhIYF5zNNjgE9H+BOO3i6143+2tbwSvH99IfBMWMkfrqNbjl3AI45ALHOk8/t17KPt3rKWc/z4uVAPpsN21ljujHNp3+0no9x7XOAzipH3GLjCJbBWmGpEMcMLd22wiBgqeCqJYEJX04BxnZkoREM9m/SGGyoZkXzWeuQU445phjigikzXrtk93K43c4E2xcV1Yq9wNzqnnYspu9iG9YkG2MMdlS1AeTTpniMDXvk63dd2SmEoCW8c21iMvrUnxTHgzUub7XMYzxVJwdT1wjvqmT+5A2df/RZr2Jb08255137kS7/3ZCpPxwCcBr43HZ3H/1QeK7l/mThGD5X+LbVPdx7UZ6M7b04YsvvrjMHcakMUX+cm8ndsqKRQ7yO+1DKCXKV/Gtn8zNHcQ3whvRleglw9DHPvax5l//9V8bgqPA/2Tim0xenov0L/3QXOAZjrTXqV96fqoZ38wf+qQx9cUvfnFtJqNW8U3fbd2mcx9wrPo9OrHE5r//+7+X7JWyJREJPbt5Buv04Yl6nLldWYmK+rq2lpFOGaZTjtbyj+PXWHlmdc8gvplLzcO9bDINWprWGKjL/HZ6ZplNP+mlHNlnsAho73o/rM/CozYmzZ81U6Kv3QOIu54/zLO1vuY448ly1ZYiN8e63xDfpptBc7Ba+d0rDbb4Ed4867m/R3x799ojVw6BEAiBEAiBEAiBEBhNAhHfRrNdU6sQCIEQCIEQCIEQGCkCghHdxDeySRXJBFoFf30voCgYKbODYLI/MAtqCAQLANuPtCDwayk9soNgWGuAdC5AKgMRpIoeAtIyVQiWCtQKDvcS/HeeK6+8sjnnnHNKsIJwob4Cr53Ei051EchQFgEOUgtRKttgEagB8/Yg7FSltD/5QIZBQawa0Go9zs9azysQJuDn577udEzr8a1fO26mx7aep/1r5VOWfm/Trd9U11d34g/Ws9kcr936sc2mLK3H1v5AjDV32sgrgqXmGoHQbpv5W4YRAgxZ1xLTBBzLMhN0ZEoy9xB4zGmWQtXu5m1LZ1o+VEY0c30vc2O3stTfmfvIRuZhMh7xzVgR/LXUqSxs3eZR5cPCcVjJ9OSeI6jZvoSjfe0j4ExCUkeZisy7//Zv/9Z89rOfLaKToOhc9PVa59Z39ZftUxnIV+4DMpGov37sftlt/KsTgbxmfLNkqfY5eiIzl4xvMo5NlfGNtHXhhReWJW7tL4ugceTc47BpA2NdP8RCGyxevLgsz+m5RFt06w/EOVICOcG4Ir/hZ1yedNJJRf5yTs8YhDD93EYoxdvY8tygrbtdZ7ptoa8rWxXfjPdVq1b1LL4RmsixMioqn7Ffl1XuVE5zB5mUTEYq86ECHyLwcjzJoD7XKZv+5VX7t3PWr6eqaz3WMqz/8R//sVZ8k+nRs2Yv4hupb+WELOqZj9AnC5Dr91qGqco4Dr/H6uGHHm6umGjz3/72hjKPm8t62XA/6cSTmmM+eszaftXpvtI6D6VteiE73Pto7zo/aO/pzAvDUHN18vrTn/5UnrWMF88c5lbPc+45fl85yCZKKjWfkpR9wCHi2+xa2jOS+cec71XvS7M7a44OgRAIgRAIgRAIgRAIgRCoBCK+VRJ5D4EQCIEQCIEQCIEQGFgC/gg/mfgmwOuPyAKl/kAvi46ltQQsBN9ldCCzyRTiD/r+0E+uEHi0tJ33uo/99t1333JsldMEjX0tQE1m8BKoJgy4hoCxgICfCzj3sqmPFwlCkFaWOgKBP4DLftSL+FbLp65nnXVWCUYQLw444ICS5U42lV42QR7nqnUSrPazbINDQL+dyVb7mfbttLWf1/5+Vn/e+nWn4yf7mXHhXP3aajn6eU5lU85+bs7XKXg+3Wuo52RtNpNzTfeYun8rb22gfnWJLPOELCECpUQvc/Bkm/nEvGuuIxrL0CPzm2ULySLkG3OvzZwoQ9SZZ55ZBGVy3LHHHluWoLYkYGuWKOVzbnO0+bgKnuZhIp45WZnN3a5vjlNOgccqVxFmSMeEIdclINmH9GYunkx8c13nJfNZato9wJLaRD73hPZ7gf2Vj9zkvkN8e3QiY5T+8vWvf71k5iLnONbm3I5Rx9qvahuUHWbxP+d0fpmntKeXQDiO2lLmOtyVp70erZdVPnXQlisnJB4iOXFOe5GqCEDOpdyTbaRDx5Hn3Pdkn8Gkte9Nduwo/Fw9vYiH5AKigQxUXjvuuOPfZeBpr6/j9Cl90HNPfemzMt3KPkbE0n9IWsSwH/7whyWrK0FTG1lm2DjW52vfq9dxfv3Ey3j3vWcU7VP7hZ97+d7vXEt729d4I7rWpU71E5kbLXVK9iL1dcr4pl/JpHjJJZeU+eDoCZFSfYx9Y7e1P7mO/XEzhi+99NKSWY6ge/rpp5elTkkdZA2bedWYNx8oq3rX57pap1r/yd4rF0z/8z//s2Q6NDd5/sLchw9qRqROZTXutJl5UFt5ZjNubMqUrTcC2HqWN5/+euXEUr4PPVg+vNHL0fqD+V3/1z/0xV7bv5fzZ5/hJmBOGdWxaNxU4d+zj7mS0GaOXTwhXbsPmOPMUz4kRqy2n3u5+5KxU5+thruV353Su096+XCB+9+o9rN3h26uGgIhEAIhEAIhEAIhEAJNE/EtvSAEQiAEQiAEQiAEQmDgCfgj/FTimyCkwK8l8mQKEcgiLxAqZHMTxLcJ8q9YsaJkRxGU9Uf/U089tQTrawYjwWSBgccff7wE9gVViRWyjljSShYSS6n647/AJalOVhHf97Kpj+ADyUNGFOWYjvjmeOUTlBBUtrSr61fxQnkEdHvZnEuQx0uAu1/CTS/Xzj7rhoA29up1aw3W93qM/WZ6XC/XcO7p1KHXc/Y76NQvacd47MdmTM9kw6WWAXdSgDaogrGgKHnG0p6kjcnmG8eaU8xVpDdzr+xThAXCG0mK7GSOFnAlpBBYvv/975d9SDUEHXO5wKwMYnWe9Tuylnn0gQceKBl/lEsQl1RX93XvIFaZ+83f5kpiirYyr5O+lIv4Zm63kSKIMwSwTlu9tqxt5l+ZO770pS8Vcbqyaj3O/u4jhB4Z4ohiuFjqSpZPglJlSBhSD+/2ERxVXnyqXNR67ul+7ZyYuPfJFCZrne/rtdw7STyyrwnOTrbpH+675HHZxvDDS3Y+Mvn+++8/Kb96TuIbWcn99OMf/3iRhtoFrLrvKL/LtoqBceKZokoGxlanedW48tJ/CaX6r2cJ/VGWRMvMEv+1o37l/Pb5n//5n3Id59VGlkIloZHK6riqnPUH59c3qjhKevDSL5RLeass6uf6qnFl0+f1DZKnjG++NpbPOOOMck11bL9mfQ4hW5x33nllzCijOcK+zt3Kw/xmnBAzZHszth6dkDGxsYSwMUkgNCbVwVj3+9WrV5d5grBG3sW8vSyVQ/t7vaY57L//+7+LuOnZEWuZK8m8ztV+b1Em9TNnWfZVu2FAlDPm1Ku1bu3Xzfd/TwBf86nnffeWW2+9tTxH4zzZhq/jzFP//M//XDJtaoMqQ092XH4eAqNEwJxpXvc8VzPPEkA9M7kXmC89L3lGML8bN+ZK/wY2t3kOyVw1sx6BrTmoPie23ydmdtYcFQIhEAIhEAIhEAIhEAIhUAlEfKsk8h4CIRACIRACIRACITCwBASy/JGeOCDAbhk8wVoB0ZrxTdD4V7/6VRHf7EPIsMxVzfZGhhBwFKiXScS+gmb+iC8QK+juXAQ5GUEEdAXSBCcF5wVNLQ8mi41zEOwcu3jiE/Iydvi54OV0NkEFAWEZ3wRjBRN6yfgmeKpMym/pMuKA4OlXv/rVZsmSJaUcM5UHugUNp1O37BsCg05gHAJ3/RzPeAmUElgIMQQyUkknaaa2vbmKSExMMVeRYGR+IquZvwltMk4Jupr/BGRlQpIFrApyBCpLj5p/yXauZ2sN3hK43AOUj4RG/CHKmffdO8z3ZBqyD4mmlpncY653z1A2Ap1Ar3vH1772tVI/12rvK8Q0WbrcI2TRcp0vfOELRfYiBalL3bSBe88TTzxRhBtin2Cz7CnqTv5Tt3qfc69xboxdh/RGKnJ/8TK3K0+VhFrL5xxegqmtr1oW77ipc5UYSUA4EHrcY8lFeLsnVhmv9fj6tetjWjP5qZd76CmnnFIkIALWVPdE9zEZm3C3NCcxSv3UYVw2bUlM0w7Gyfx585sF2y0oUlQ38U2b6aukH9KX8aI9MLR8sD5FADUetK39vvOd7xTR3jOO5xZL7BoP5C99uHUzbpXLWNVOxhExwphXLn3cM4h+TRzzc+eo0hfxTWYzmeZqNjpSGNHTmDbm9e3WTZ2MFSzOPvvs8ix2+pdPb5YdsaZfkAVaN9dQRh9SsISwl3LLXKhu+qIy6auet5QVJyxIp0cdddTa+QenXjZlxEKf/da3vlU+fEAS9azpfLhWMbD1fPq0chh/5kBzB2bmJOMkAkQrram/Nm6IytrTPUM/wxVf/d3WOo/oO+YWcymBx3O/D4tg3y5UTn317BECw03A2JCB1tgxL5q3zcfmS+PBM4L7BJnZ/O5ZxbjJWJldu7c/S87ubDk6BEIgBEIgBEIgBEIgBEKgnUDEt3Yi+T4EQiAEQiAEQiAEQmDgCPgDfa/im4Dm9ddfXwKfVZbwx3pBWn/kFxiWGUWATNBY0EtWEMus1U+7C6a+8MILzcqJrDyECQFTwTTL2MnsIQhsWVVbzZwiaF+zyvUKcKbim8CrwLBMcQQKZTl6YjkwgTzCn+Bee4C41zJlvxAIgRCYjIA5lLDRq/hmriJymTOvuOKKkhXMHGw+lXGHYCZDpXnUnFXnNnO0uVyWKoKK7FWEHu8y9NjIDfYXnK1Z3+xvXicCE9+cm2xiLjdnklJI08QYQV6/c3wVJ8ynZB5yjiUZzacCve1SCtnG/E0ClGXK/YX0Yqls95sqLLl3eck0Rc5zfjIQwYwsLUuUMhLxMCJA16VH1YP45txkDVnxCEPuWeZ4baDsNhmL8PAzdfK9l2C241s3YpFrCGyThLSFd2VSRkFwSwC6p3WTgVxPJj3SYBWb3B/dh0hXxL5u4pwyqTPxTfYsmeKq+NZa3nH4uopv+pS+sN2C7ZqF2y9c24/aGehT2tH+hB8M9Ss8ly9fXrIV1qyHJCz7e06QIVZbaefFE9K+NtYP9S3jTFC+9lnPXMa78aCd9WHiKQFCn9U39H/n9ewkm6JzkCSMGWOTjEpM0keIr2RIz2UEOPtXibXWT3/HQl0sIWwM+DDAssOXNdvOn1jqdNO/X+rU/sq3atWqMl+Ymwi5xrhrGI/6v3Gif+v35hbPdfqnpUnVvdanlqPbu7GCu/lEtkfzlPlG38XScyJZpH3DtZP4RpiL+NZOq7fv3Vv0Uc/zxGVtq4393PyEt838bRzI9EZSNI9qL/cD86TfR0jpjXn2Gh0Cxgl51Mv87uVZytgxp3t5VjI/efcckn9bjk77pyYhEAIhEAIhEAIhEAIhMIoEIr6NYqumTiEQAiEQAiEQAiEwYgQEDKcS3x566KEiN8jERnIgBpAk6vKl/lhPKpCtjXghWCYoJvgpU88xxxxTxDUyhD/6y7gje4jMQ64tMCZoa7kXgQFBT8KAYJrsQoK5Ar6kOcd7V26bawsE11cNHAieTjfjm3O6ruNk2BHoFhyWNUgGJYFnW4J4BUP+FwIh0EcCvYpvVfIgYpnnzM/EBC9ilbnw61//ehF0ZJsy7/qZ4wRh7W8JO9k9zaXmXWIZOYqkQlawfxXSzLnm9gsvvLAca64mtJBQyF/uCyQc9wM/q+IbNOQZIhD5jRRE5DGfy6ApgxnBx7VaN/eAKgSZi0k+9lVO1yXnmefrvYCMQQCyxKF7i/pa3lS2LWKOMigfgcO5idfmda/X//Z6856J/8g/xx1/XKm/rCzOoz1cw/fe3aswVGZBavekdvmsim/aRkDbfo7D3b1TGQhBMr4pZ6fNvdP1iE/uQ+rmnkj8+dpEpjzCkTK0S3ft54r4tobIdMQ37au/EbnwI3ER3/QffYIoRtokgGnf2gbGlHYyFmSII2eRrghAso7VrItVftMnjFXPS7L6yarmnPo3qdSzhjGj/xuTRDvn8EzlmvqIYxxPSP3JT35SfudZi/BJPtI/Wzf9vYpMyqg+9j/wgAOLhDr/vfPXjsXKQH81Zi3Za+zog0dPfBBAmZTRfsQ3kgfOPhhBVpVtjSRoPpiO+IaLZ0lynjoZ0541XVO/x6gyb61bnRM9vylzzfgW8a2V0vS+1rbmTu1hHOinjz762IT89nRpa6z9W8A9QF8je+JNVDRfE3s6tdX0SpG9Q2A4CbiHm5cIb+4P7uHu6eRe/64lsHuWqcJb/l05nO2cUodACIRACIRACIRACITAOBGI+DZOrZ26hkAIhEAIhEAIhMCQEvCHecFGgV6ZQzotdWrZNvKCIOxll11WstkIbMnYUz+1TgBwHkuLkiTIEwJhltsT/JV9RDBYsIysQdKwLKogALGApCBDhAABQUJAjbQhOCBIINCrHIIIxAXnsbmObHACb4LCziWAMF3xDQcSiDoQFARvyRUCuLKbCL4KUGQLgRAIgbkg0Kv4RkggmpjjiCHEFNIN2cM8TjaQbYpcJYOUebgun1iPIzKcc845JYOPOZRYQ9Ahr8k8JXuP81SRmKRDVibaELZIOAQHc69MQOZ8maBcj5RVszKZU4kTyikrleuSI9wXXNMcT3Cum3mYcCTLFB7me/KFn9vPPG+OJ1u4J5Bt7OPlnkDGUbYq3JBy3C9IQgQ5kp3z+LljLal4//0PTGTI+kCpP6nP8c5HvsHLvQ0H1/OOi/uCe6D6V5nJu7ZxD1Fvx7me7G/qpJ2wcC9xT1SH9k09q3DiXup+6xgiHaGJgE0AVIYqJrafo34f8W0NiV7Ft8qevKi/kL1kHCOJevbQv0499dQibWoDY8Rzij5BCqvPLp6h9B/PR55fjjvuuNLXjUFjRz/RP4ho2sjYNa70Ff3JODQGjRkvcoRMh/q2/m8/fZG4pk8bV+edd17pE3VZUKJYzd5Y+4N+6Dpr+vz9pf9vteVWzfY7bF/Gi/5sLtCvzC3qTCKzv3oSWgl1rkH6M46UQ3/FTB/17GR5Yvuag6ab8U1buaa+71yEUQKdDx9g4Bmvzkm1Xt61nbIohwx6Ed9a6czs69q25k9ZI8nIT0z0iccn5LcHHnygLB1sDJgLzZnuMzIN1qyc+vpUc9TMSpajQmDwCZiTbJ4hzPPGj6y05igfNPCs5VnGs5J7QrYQCIEQCIEQCIEQCIEQCIEQGHQCEd8GvYVSvhAIgRAIgRAIgRAIgRIwnEx8E8ASCBWMFHwXTLSkHslB8JXgIFAr4EV4EOSSoUbgUZCW2CCLkIB9lQAIB4K1Mo7I6CF4Sp4T7CW/EewsGSagJsjqHM4taCsI7NokDEFWG6HO9QWKvVy3Bm6JegKoyk4UkK3FsqvK3r4JUuCgrupAyhMIVi7BW+fuJCq0nyffh0AIhMBMCPQqvhFwyAjEFPMbcaaKXURiYgjxS4Yk2aNqFjZzMEnFHGxuvPTSS4usYy41j9dlDM3DRAbzXZ0rzdmWfyYDEW4EbAnJ5B6SGkHFtYhjVQbCwPWqeEackz3LfG1eJTrX4G/lRbZ47LHHiiTmOu4xdflDAWS/Vz/3JV8TjszbyuqeUedqgpB9CEgkHvO6ero/eAk+u6fgQMZzH1F+L+fAlgiu7IQl9ynBafcR9SPgKLtzaQ/ZXWzuPQLZyuhrghM2zqd91cE1tI1ztm/uQ8pGYFQ2vLSXeySJ6ugJoYks2MsW8W0NJW0v245+oJ0nW+pUf9KW2OvnREXPPMaXvqL9yaSf/OQnSz8n/JB7jBF9yz7GiGVEZYjTBwhynjm0t7FSxTXncj3X8szj2UZ72WQrJJF6biEc6deOVXbjznn1E31L39d/v/e975W+pUzEUrKYfmLfKlUYw2ROc4Vj9cVnn322/N649bxD7tdvPWMZh8qgXoQm84j6LJ4Yv1Vsde4qeGBHEjzrrLNKObGarvimjLLmyXanzYwrkiyG5qhavjUt+3//VwY8I779H5N+fIWrdjUHvfTixHK2E/3lkYln8Jtuvqn0Edn8PBv7t4J7hr5qvjQmar/rRzlyjhAYVgLmJPegKhL73hzt37YZJ8Paqil3CIRACIRACIRACIRACIwngYhv49nuqXUIhEAIhEAIhEAIDBUBga2pxLcaDBa4lzGETCALDwFAIFegi1QhQGo5PAFjshpxTaYOgoNAqcCkYwVV69J8AryWzxJAcy7LKREyBFkFTmtWHcfJqKIMZAfXtwkEC/YK8gq8yUQyE/FN2ZzX+a+55ppSPsKeZfkEep23SiBD1cApbAiEwFAQMPcQbUg0JDTzGtmlXbglg5j/iGFkGfIKiaVmRiMcOE7WJVmfqgRG2rKZz11LJifn8D0Jy1xK5CJZEUxas4oRwMg55n8yDnHGvG7Odf9wHyFA+L41mOvnAr2OJ5KR31xPmQR/P/rRj5ZyVplH3WRGqUuCKQuBrQoYzuV4+/mZzbH2IckRL9Td/ch9ABcvx5Hw1MtL+dWdZPOLK3/RbLrZpkXuIeq4dxGsCdCu5Xv3L+exkZ2qjOTnBCHncj/EkKTk9753HbzwVl5t6V6Hk9+3b/bBigAkk577pHuPJSkFyt2LXKOXLeLbGkq9im/6lCxsnmP0c+KVdvNcQL60eR4hiRmf2qKOT8caB46TJU6fMB71ScfYnzRmTOszxoi2rse4FinN9UlrxFD9xvlcx7HavXVMuqb+RczTT/RZgpLnLrLYkiVLSn8zDmzEC+PKfGH8GfPmmvrS15XJs5Cx4l1f93xXn7HMKb6v5ywn/v//Uxbi25lnnlnK6kMP+mwvS53W65LyZNs1LtXPfCRzHB5YGjOdhKp6vHGejG+trTK7ryvX2r/1afOKPm6eJkQaD56/zXnmXf27UxvNriQ5OgSGk4B7h3uQe7pslr73b0vPFZ5dsoVACIRACIRACIRACIRACITAsBCI+DYsLZVyhkAIhEAIhEAIhMAYExDY6ia+CdQLctpPYFRg0f4kAH+0F5QX5BIs9kf9c889t4hvApXEBi8ygUCvYCrpTUBXlhJZPWRPEaQV0HXO66+/vohvloL7whe+UAJqjvU7AVvX8bWy2JSvSh4yggi8KY/sLjLmyMAiCO0czjdZxjdle3Qiu4lMLeQ7xxLvTjvttCKPdAr0jnG3SdVDIAT6TKBX8c1cbCOmEBK815+1FsmcZY6uwVXzYt3Pcea8+r3j/L7u72uvugncklIIOuQ8MhDRrYrJ5l6SGjGmXs+x9fzuG5b5Mr8TmM3P7g3mf6JYlcDIM4QK11DGKguR1ZyX2EO+cA9SbxIOOafKROb5Ole7tvuEc9rXz91nvNTduZRH9lH3EXKSl+xF7gMkPee1NKlj3B+ci+BBHHJt9SJ6k0Hce4g6sntVsU1Zq7DtOAIRRq0SU+WsvOqsH7hH4iWjH7HEvQtr5an1q20z2XvEtzVkehXf9AnSIcneM4P+TlKofdi7fkqy1Ne1h7YkZGlDfcO4IJR6ViGxOad+q1/oywQhx+unjtE/PBPpb/oiOY1s78MAyqDPOU52wZp1sLa38ujX+pc+6EWeI7x5piIleT5TZvuqj+chkqY+VZcN9Twl6xzJzu/Uw3GkWc9uxrk66t+t46uWo747bqbim2PrWLnooovK89fiCeFPdkTPguo/mfTm+pVFxLfaGv17x9bm3Usf9+EQc5T+QW40/5sP9fU6n/WvBDlTCAwvgSq+uSf48EAV38zrrc9Kw1vDlDwEQiAEQiAEQiAEQiAEQmBcCER8G5eWTj1DIARCIARCIARCYIgJCGRNJb4JdtoEWb0EKQUYBeAFcQVOCRGCqpYpFbg/7rjjmqOOOqoELokE/sBPQhBclZFD5hFff+ITnyjyg2CAQD0Z7qqrriqBzuOPP74El0kGNUjsus6jHDZlIy0ICitLDY4Kzgkkk9gEj4kLJDbLiNX6lBNM/A8D57RkH9lA4FoAWpadk08+uQS36755D4EQCIG5INCr+DYX157qnO4Rymeel43JnCqTE7mG/GCOJyC3yzn1vIQu87vjSDZehDfLdzqWEGTuNg/LXOX+YM4nvhB0nNsc7vde7gM2cz4ZzP2lXQgzr7tPuHbdqpjhfkNyIji73xCTlMW1iHSkjt/85jclO5z7gOvJwEbOkalF2UlPzk1QsmSlctSMb96dX7Dbu+OIb2Qi53fP8k4oUu56DyLjuf+4DxGwiFMkpaMnljhVxvY61np1eo/4toZKr+KbviL7mTYgrZHA/KyKPN69tIH21Sdr//Nz+xon2tu7fqr9tK39qiypH1fhQT/UR8hr+qFno0MOOaQsdWo/15oqQ6D6WU6X+KbP6of77bdf6TckOGVVDoIdoVT9iGT6sPFax6YPFai/eiivvqm/kpqcs/25qb3PzUR8q2NUmYwjAqAxqT44yF6nDspRmbVf1/f1PMZpMr51ItS/n5GWV6xYUeZI0pv5v4pvdaz072o5UwgMNwFzvDm6im/myYMPPrgIzd3mtOGudUofAiEQAiEQAiEQAiEQAiEwigQivo1iq6ZOIRACIRACIRACITBiBAQMexXf7Fs3wVGbP9wTIsgQgq6W3RLwlbXEMnayoshyI4Ar+O8T76SHRycECIFWGdi8iAOEBxluBD4dU4O3VapwLeepQU7Xr4Ho+u5nyibIoEzEN5lOBG5lzSHk+dp56ibwK2Cq7Oog4G2zHM3RE8KBAHe2EAiBEJhLAoMsvpm7CQ/EFIIOOYuQQ3wQxCWDVVGnEyNztnnWvYbUVZcyJANVeY5oIyjs3mAf87R7gOxaJLEq3jhXvReZ96tsUd9br1/3a/+Z+w2xjKztfiPTG1Fb1iJ1dS9yryJ0uAe4V1122WVFGnJfUGa/Iw4RvwW33VPIe37mfkISdB5l8HN1JcuRimTPklXLz9zXiEnuO8pUxXD7ybZVM9Hh06mOrXVr/Tri2+tP6rsAAEAASURBVBoavYpvtV959wyhv07GW1t7+X3rPvVYx/u6bvapzy+t+3tW0u6yHMo8qC96ZiI76mOkL/2MvOb4TptyGjf6jeWEiXfGi35jKXnH20d/8Oylb8pKuHgio5r9jFu/96rPdbVuxlz9urXcncoxE/HNNTHwvKZs9957b8koZgwdPTHuLKdcy9jt+pV7xLdOLdPfn7kPyNhcM75FfOsv35xttAi0i2++9wyRjG+j1c6pTQiEQAiEQAiEQAiEQAiMA4GIb+PQyqljCIRACIRACIRACAw5AQHDXsW39qrWYKngvkxvgq4CuIK0X/ziF4v4JlMHcUzQsgYlZVYT7HW8wKasHoLThAfBTwKazDuy/dTl9AT9BWG7BT+VT/BV9hAZQ5zH+cgExAOBVJJGXZ5MINn5SAeOufbaa8tSXQKtsqEIDiuDa2cLgRAIgbkkMMjim7nbHE12MM8rq6xRe++9d8nYVuXmqfiYn4nIBDpZOWXWMh+bb0lg5l6CjuxVxC9LPtZscJOJP1Nds/335nvXcN9yz5EJi2QkwxTZzr3J/UM5lU0muGeeeaa54oorSkYs9xBSkQxuBDZs3EfdS4hDAtvqZulvvIhFMrzZ170EKzIf8c0SrspDnnPvJBTWe6N7p/ufd+VwD5vOFvFtDa1exbfpsO3Xvp6BZFnTB4mVxDeiv7FFJvW1PqPtCWiTbfqfLLWy6DqX/uo5zPEyBepn+pU+qb957iLY6Zf6Zz+2mYhv9VnNWFN2gqnnRWOEULV4Qs6r8l23MkZ860anv7+L+NZfnjnbaBOo4ps5mZwc8W202zu1C4EQCIEQCIEQCIEQCIFRJhDxbZRbN3ULgRAIgRAIgRAIgREhIGAo8CooKgvPJZdcUmQGS3wKjMq8UTPt1Co7xuYP+AKXsnRcfPHFRYgQwBe0/MpXvlIyucmgQ2YQtCUICG5a1stGBHANmYMEpwXqZcmRaUewX/DX75xPOaaS3pxTth6iGzFDucgNxD51IBEQHEgWzl+DyTKOuP7KlStL1hVlEhj2ifxFixaVazt3thAIgRCYKwKDLr7JkkZQsVyirw877LCS8Y2YY37uZXPvcM9wvzE3ux+QxUg6BB1CmPnbPcB5XYME3Yv80sv1q5jmuoLQ7n3OLbMWic8mY5b7gTIShtw3ZKS65ppryv2FDO0eQUZzD2vd3EuIISQk5yfWuc9UPt4JTTJ6uTeS+9wzHUNKssSra9rHvY/05/45k/pHfFvTMoMsvumP+gzR0ocHZLyVRVGmNnKl9u+WSbH2vdbnOOOK8O+5R98xrghwruP5ykbyJJXpm/0SSmcivhnrd911VxFEtZPyGIfGHDHU+OqlfOqPZf1whTnKc+Phhx9eztNNGqwM894bgYhvvXHKXiGAQMS39IMQCIEQCIEQCIEQCIEQCIFRIRDxbVRaMvUIgRAIgRAIgRAIgREn4A/zgqSy8MiSJtgqy42MNp2CrgKogvWy2pDYBPgtKSqoKoOJzD2WORVcFcAkM8ikQ1xzjGCnYKafye4h0E9YIxr4vU/G+xk5ze9JEb1mJRF8lUVIEFWAzrufCXw6F1lB+UgHyqBMfq/+ZAtBWKIFQc5+XqSDbCEQAiEwlwQGWXwzPxOpCDreiSZ1uURzcy9yCnaOk3HKy1zvfL42x5J0zPukuscee6xIYSQYc7b5uxfxuVv7EGPUw/lJ0TKPuieQ2Nyj3G+qQESIc1+UEcs9wD3Fvc69j1BTpRyiTmu53EuIfTJXkeXcf9St3r/Uw3W8qtTjnPbDVbYu97uaEc7XrjETcSfi25regK1nE88D2nu7Bds1C7dfWJ4BWtuuW9+Zq995XtInPfPI9qaP6fNelihV3l7bXt/Tl/Q9gqr+R+IkV+rjrkWK0x89mxErjdtezz8VA9e/+uqrmzPPPLP04RNPPLFIfK5DYu20aRPZHfVV499Y92GDuoywsvbSRhHfOtGdm59FfJsbrjnraBLwHGEeNh8n49totnFqFQIhEAIhEAIhEAIhEALjQiDi27i0dOoZAiEQAiEQAiEQAkNOgHggKCpALKglACnwKGAq6NgeeCSJERaIcrLEEQj8YZ8sIAApoE+eI70dccQRJXMb0YzoVq8FmfMKbAq+khKUwUvwVjC2ZiOpglovmGsA1HUEYp3PuW3kAy/ndt262ce+6i9oTDbwIj3MVDqo5857CIRACPRCYJDEN/OoOdS7F/GLlGWONH+a4wkq5OhO94jJ6utctjrfm3fr/Ox6tiqOuf+QzFyr/R5UdpzG/1zDtapsZwlScp3MayQgglG9z9Qyeq/3KMcLYNvcO6qQ0y4NOabec+q9zDGt+7mnOL7+zH71HqSMftd673P8TOof8Q25pvTZQRHf9I/60qf0ecK/5w5L3ZIyZXwj3nv+0Ed6bft63vrsY7x6NvM8RaS06ROegXywwc/0+X5sdXxdddVVzVlnnVWen0444YQi8FXxrVM91JsMYn5RZ0KorIh1fHU6plN51V0ZkvGtE53+/iziW3955myjTaCKb+Rm87HvDz300JJRvF/z72gTTO1CIARCIARCIARCIARCIAQGhUDEt0FpiZQjBEIgBEIgBEIgBEKgKwEBwxqEJbUR1Lxq8LH9YMFFAgRRQ0DZH/QdL/ho88f8minHcqGLJ5bUIjEI5vcayGy/5lx+X+svIKFuyin4qh5VTpjL6+fcIRACITAo4pt5nHxmXpfZk0hDnvEz86EMaMRo2dlkcprtnF6lFfMwAcw8XJcgdQ3z8Uw353ZO9SDZkN0enVh+1LWcVyYsS0qqQ733uab7X5WkZ3rtXo9Tlrr1834T8W0NVc8qgyK+ERv1bS+Z3rx8rc8bY565PC/1Q0rzYQTym2v64IGxQDDzXENG87PZjt06ZpXdGFvxqxXNOeec02yx5RbNcccd11gW2Piqmevar1fnGcfLtDvTMtU5JOJbnUnm7j3i29yxzZlHj4C53Vzsw2JVRI74NnrtnBqFQAiEQAiEQAiEQAiEwDgQiPg2Dq2cOoZACIRACIRACITAiBCogUPvgpM1AN8eqFTdGuz0B/0asPVzx9oc40UcILxVgaCes+w0YP9T9sqg1r9T3Qes2ClOCITAiBAYJPGN9HbnnXcWudkcb+6WBXPhwoVFFvNe5eh+4K/3jjoH1+8nk697vaZ7lfITgCwjSYCSWYvwVpdRVQ9CEDGOeLN4QjyylGk/69drefu5X8S3NTQHSXwjusk66EWGIIvp6/oamVQGRX2PfDnb5yXCJ6HMGKiZhfzMeT2TGVuz2ZTb+Yh1sta9+MKLzcpfr2wuuuiikjX4yCOPbD784Q+XrIrq5nrtdarHOxcRtZZzuuVyvHpGfJsuuenvH/Ft+sxyxPgS8PxhrvdMJbulOTni2/j2h9Q8BEIgBEIgBEIgBEIgBIaZQMS3YW69lD0EQiAEQiAEQiAEQiAEQiAEQiAE1hGBQRHfVJfcULN51iyY5BXCm+UIJ8vgtI5Q9XQZUo0sboLOJL7bb7+9SG9/+tOfmp133rksrUjMJs0QktTT8twHHXRQqedsRJyeCjjHO0V8WwN4kMQ3/VG7eBEhfE9yM7aMK9kU9Uki3KCL98aNbJBeGBNHf//73zc33XRTyfhrGWHZ3nbddddm/vz5HcW3fg2BKr6RSpTh1ltvLcskH3744UUkbBfu+nXdcTxPxLdxbPXUeaYEIr7NlFyOC4EQCIEQCIEQCIEQCIEQGDQCEd8GrUVSnhAIgRAIgRAIgRAIgRAIgRAIgRAYQAKDJL7JREXMkQlN4JaIIxuVjGi+ljFq0MUcmahk1rK86XXXXddce+21zUsvvVREHXLR5ptvvjYDFcltiy22aA477LDm4x//eFl2cdiXuo74tmaQD6r49uSTTxbZUobBRYsWFUHL0sGdMqMN4HRVikR6W5vxbUJ+q9ns1EHmuirLznW9Ir6tux4S8W3dsc6Vhp9AxLfhb8PUIARCIARCIARCIARCIARCYA2BiG/pCSEQAiEQAiEQAiEQAiEQAiEQAiEQAlMSGCTxTeakV199tYg55BYii6VOCWOEt0GX3sCumaieffbZZtWqVeWlXsouA5R3woyNzEd822uvvZoDDjhgbUa78ssh/V/EtzUNN0jiW5UglEkmQn1UpjeCmP5HwByGsVWHhKyKXjImmi9q5kTjy5gil8poV+s1V5nXqviWpU5ry8zde8S3uWObM48egTrnZ6nT0Wvb1CgEQiAEQiAEQiAEQiAExo1AxLdxa/HUNwRCIARCIARCIARCIARCIARCIARmQGCQxDcyyzvvvFNetSo1E9WwiDnKrx4Cz6+99lp5+Vktf30nzdTsbsS+mp2q/r7Wf9jeI76tabFBEt/0v5olzbvvSWFepDD9cJg2Y6dKZ3XO8G7s1PrUsTWX46mWIeLb3PeeiG9zzzhXGB0CreIbAd/3hx56aLPHHnsM3Xw/Oq2SmoRACIRACIRACIRACIRACMyEQMS3mVDLMSEQAiEQAiEQAiEQAiEQAiEQAiEwZgQGSXwbM/QjWd2Ib2uadZDEt5HsaANQqYhv664RIr6tO9a50vATqOKbzLP33HNPxLfhb9LUIARCIARCIARCIARCIATGlkDEt7Ft+lQ8BEIgBEIgBEIgBEIgBEIgBEIgBHonEPGtd1bZc2oCEd/WMIr4NnVfGfY9Ir6tuxaM+LbuWOdKw08g4tvwt2FqEAIhEAIhEAIhEAIhEAIhsIZAxLf0hBAIgRAIgRAIgRAIgRAIgRAIgRAIgSkJRHybElF2mAaBiG9rYLWKb/O2ndcsWLCgWbj9wmabbbZZu+ztNLBm1wEkEPFt3TVKxLd1xzpXGn4CEd+Gvw1TgxAIgRAIgRAIgRAIgRAIgTUEIr6lJ4RACIRACIRACIRACIRACIRACIRACExJIOLblIiywzQIRHxbA6tVfNt2222b9773vc3ChQubrbfeullvvfWmQTS7DioB4tvbb79dlhFcvXp1c8sttzQ77bRTc/jhhzfz5s1LO/ex4SK+9RFmTjXyBCK+jXwTp4IhEAIhEAIhEAIhEAIhMDYEIr6NTVOnoiEQAiEQAiEQAiEQAiEQAiEQAiEwcwJVfHv11VebJUuWNDvuuGOz1VZbNVtsscXMT5ojx5LAe97znkZ/uvzyy5sHH3ywOemkk5ply5Y1G2200djxeP7555u77rqreeKJJ4oAtemmmzYEuC233PLvWGBmI1ENy1bLPKzl7idr53rzzTebJ598snnkkUea3XbbrTnqqKOK6NjKaVjadlDLGfFtUFsm5RpEAhHfBrFVUqYQCIEQCIEQCIEQCIEQCIGZEIj4NhNqOSYEQiAEQiAEQiAEQiAEQiAEQiAExowAMee2225rXnnllWbx4sXN9ttvX5ZjJOpkC4FeCchiRvR55plnivj28MMPN8uXLx9b8e25555rbr755ubuu+8uMqDxtckmm5RXK9MqYQ2TJFXLrB7DWO5+l1nWN0w22GCD5sADD2yOPfbYkt2v39dp7Tfj9nXEt3Fr8dR3NgQivs2GXo4NgRAIgRAIgRAIgRAIgRAYJAIR3wapNVKWEAiBEAiBEAiBEAiBEAiBEAiBEBhQAjJ03XH7Hc0LL7zQzJs/r0hvsr1tvPHGA1riFGsQCVTxzRKfN910UyPj2cc+9rHmoIMOGtuMb/fcc09z7733NiRA4s7666//D8tfzlYic/xMBauZHjvbMr9b/Xe25e7GSya/+fPnN/vuu29z8MEHl6VOZ9ou7xafQb5uxLdBbp2UbdAIVPHt6aefblatWtW88cYbzaGHHtrsscce5T40aOVNeUIgBEIgBEIgBEIgBEIgBEJgMgIR3yYjk5+HQAiEQAiEQAiEQAiEQAiEQAiEQAisJSBD1+rVqyeW6vtD8/pf/9q8/c7bJXOR7EXZQmC6BGS/eu2115rNNtusCEBLly5tNtxww+meZuj3Jxq89NJLzcsvv9xYRvj111//B+lt6CuZCqwloI/L6Lf11luXZU4jDq9F05cvIr71BWNOMiYEqvjm+Y6AHfFtTBo+1QyBEAiBEAiBEAiBEAiBESQQ8W0EGzVVCoEQCIEQCIEQCIEQCIEQCIEQCIF+E5Ch6/HHH29kBpH1jbQkU1G37Eb9LkPONzoECJMyBs6bN69ZsmRJs9NOO41thpl33nmnjKP6PjqtnJq0E6gZD82d9dW+T76fOYGIbzNnlyPHj0DEt/Fr89Q4BEIgBEIgBEIgBEIgBEaVQMS3UW3Z1CsEQiAEQiAEQiAEQiAEQiAEQiAE+khAJiqym5ev33rrrXJ2Ike2EJgJgZr9yvKPm2+++YyX4pzJtQftGAJpXWKzvg9aGVOe2RGoS5pGeJsdx25HR3zrRie/C4G/JxDx7e955LsQCIEQCIEQCIEQCIEQCIHhJRDxbXjbLiUPgRAIgRAIgRAIgRAIgRAIgRAIgXVOIFLOOkc+8hesQtDIVzQVDIEQmFMCEd/mFG9OPmIEIr6NWIOmOiEQAiEQAiEQAiEQAiEwxgQivo1x46fqIRACIRACIRACIRACIRACIRACIRACIRACIRACITAKBCK+jUIrpg7rikAV3yxhv2rVquaNN95oDj300GaPPfYY26XH1xX7XCcEQiAEQiAEQiAEQiAEQqC/BCK+9ZdnzhYCIRACIRACIRACIRACIRACIRACIRACIRACIRACIbCOCUR8W8fAc7mhJlDFt2effba55557Gt9HfBvqJk3hQyAEQiAEQiAEQiAEQmBsCUR8G9umT8VDIARCIARCIARCIARCIARCIARCIARCIARCIARCYDQIRHwbjXZMLdYNgYhv64ZzrhICIRACIRACIRACIRACITD3BCK+zT3jXCEEQiAEQiAEQiAEQiAEQiAEQiAEQiAEQiAEQiAEQmAOCUR8m0O4OfXIESC+vfjii80zzzyTjG8j17qpUAiEQAiEQAiEQAiEQAiMF4GIb+PV3qltCIRACIRACIRACIRACIRACIRACIRACIRACIRACIwcgYhvI9ekqdAcEoj4Nodwc+oQCIEQCIEQCIEQCIEQCIF1SiDi2zrFnYuFQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAj0m0DEt34TzflGmUAV35599tnm7rvvbt58883m4IMPbvbYY49m/fXXH+Wqp24hEAIhEAIhEAIhEAIhEAIjRiDi24g1aKoTAiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAuNGYDLxbeutt27WW2+9ccOR+oZAVwKdxLdDDjmk2X333SO+dSWXX4ZACIRACIRACIRACIRACAwagYhvg9YiKU8IhEAIhEAIhEAIhEAIhEAIhEAIhEAIhEAIhEAItBB4++23m//93/9t+Um+bCdAfFuxYkXz0EMPNXvuuWez1157NQsWLGiq+Pae97yn/ZCx/x4TUmDYrOkKrWPsnXfeGdn+ob2r+PbMM88099xzT/me+Cbj2wYbbDDy8w0Gtd/X95Ft8FQsBEIgBEIgBEIgBEIgBEacQMS3EW/gVC8EQiAEQiAEQiAEQiAEQiAEQiAEQiAEQiAEQmB4CZDeXn/99fIiq4yykDObVnrxxReb3/zmN80jjzxSslYtWbKkiG9bbbXVWsFlNucfpWPJbuSmTTfdtLwsbRn5p2neeuutxngbhzH22muvNS+//HJjqdNVq1YV8e2ggw5qli5dWvrGKPX3yepiHOj73r2yhUAIhEAIhEAIhEAIhEAIDCeBiG/D2W4pdQiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEQAiEwBgQILs9//zzzV/+8pfmr3/9a/Pmm292zcY0HYGpNcNVRdnt+E77O67bMfW89b3TObod32n/ei7v9VgSzx133NE8+eSTzS677NLsvPPOzbx585ottthi7T72r+erx/nZdLepzlF/P93zditTp3N227/92q3Hk3w23njjZtttty2MNtxww7Ff3pLsZnwRwshvXqO8vfHGG82f//zn5rnnnmvuu+++xvf7779/QxgdBwlMHfV742CTTTYpX49ye6duIRACIRACIRACIRACITDKBCK+jXLrpm4hEAIhEAIhEAIhEAIhEAIhEAIhEAIhEAIhEAJDTUAmswceeKAIKipSMxRNJj1N9vNOEFplqPr7yY4nikwmA012TD1n6/t0rum4Tvu3ns+1lY0Y+NRTT5UsVttss03jJaMZqQWz1ixezjmdMrder3KY7Pj6+9Zjev16snM6vhOHbvu3XrOWCQNtSKZ07Pvf//5m0aJFzeabb95stNFGM2bSeq1h/Zr4pf8Qwar8hhF2o7jpB8bMSy+91DzxxBNFqP3ABz7Q7LjjjqXOnfrbKHCo9TIn6PPk2O23376RGTJbCIRACIRACIRACIRACITAcBKI+Dac7ZZSh0AIhEAIhEAIhEAIhEAIhMDYEJhNcHpsIKWiIRACIRACI0vgmWeeaW644YbmD3/4Q7PlllsWSckylcSNXsWnkYXTUjFSF6HLcpWVD2kpnNZA8jxFdrJs7gsvvFBEpw996EPNXnvtVSRBma9GVfJq6SaTfinb2z333FOyn2GkP8kIpi+N2mbe0BfIfupNrvX9ggULSl/w+yqIjVrd6ziocwPRb8899yzy26jVNfUJgRAIgRAIgRAIgRAIgXEhEPFtXFo69QyBEAiBEAiBEAiBEAiBEAiBISUQ8W1IGy7FDoEQCIEQ6AsBWaiuvfba5tlnn20WL15cBA2ZikZRyJkNMM8LrVndnIvcEjlwDVV8LJMrm9njjz9eMn0tXbq0SD+yXW222WZjL77dfvvtzerVq0smMEvkyoRXMwbiNyqbMWGskES9k9+81/qOUl3b24zgp96WebWE9Pz585sDDzywLI3cvm++D4EQCIEQCIEQCIEQCIEQGA4CEd+Go51SyhAIgRAIgRAIgRAIgRAIgRAYWwKCbwlaj23zp+IhEAIhMPYEnn766SK+WZJw3333bZYsWVJkHOJb7o9/3z3ahZ3w+T8+2Mhk9sorr5SsZvqVpU532223ZHybwPTqq682d9xxR3PvvfeWzGc777xzs+222zYEuFHMhKc/1GdsIphNdsRRrGup3P//H/nTOND/77rrrrLE6WGHHdbssssurbvl6xAIgRAIgRAIgRAIgRAIgSEiEPFtiBorRQ2BEAiBEAiBEAiBEAiBEAiBcSRQg3LjWPfUOQRCIARCIAQIGtddd13z8ssvNwcccEARlTbddNOyDGPohECvBGT0Iv1Y1vL+++9vnnjiiZJBcNddd434NgGR+CbjGzaWvyQFzps3r4hRvQqUk+3nWbaXbbLjHdvrOXq5Tqd92q/d7Xrt+3Y6n591O0frMb2er/WYXr+uZajXkPGtZj28+eabS6bDZcuWlbHQ6zmzXwiEQAiEQAiEQAiEQAiEwGARiPg2WO2R0oRACIRACIRACIRACIRACIRACLQRELCqwaq2X+XbEAiBEAiBEBh5AhHfRr6J10kFiW9vvPFGWeL0vvvua5588smIby3kq/j2wAMPlGUvCYEyvlkGdtSzoLVgGPkvZbeztKvlfm+88caGRBzxbeSbPRUMgRAIgRAIgRAIgRAYcQIR30a8gVO9EAiBEAiBEAiBEAiBEAiBEBh2AhHfhr0FU/4QCIEQCIHZEIj4Nht6szvWMwhhjIA/7PJTxLfufaEudfrggw+WjG+WFF6wYMHILnXancbo/lbWw7/97W/NI488EvFtdJs5NQuBEAiBEAiBEAiBEBgzAhHfxqzBU90QCIEQCIEQCIEQCIEQCIEQGDYCEd+GrcVS3hAIgRAIgX4SiPjWT5pTn6vKbkQxL9+T3jbYYIOhlt8ivnVv+4hv3fnMxW+NrfoyxtZFhmfi2+uvv948+uijEd/molFzzhAIgRAIgRAIgRAIgRB4FwhEfHsXoOeSIRACIRACIRACIRACIRACIRACvRMQEFsXgbDeS5Q9QyAEQiAEQmDdEYj4tm5Ye94gxfzlL39pXnjhheaPf/xjef6oy11633jjjddNYebgKhHfukON+NadTz9/a6zV/vjKK6+Ur7fccstmk002KXLpXD73R3zrZ0vmXCEQAiEQAiEQAiEQAiEwGAQivg1GO6QUIRACIRACIRACIRACIRACIRACkxCI+DYJmPw4BEIgBEJgLAhEfFs3zUzEIeE899xzzapVq5pbbrmliG57Lt2z2e0DuzWLFi1qyG/DulXR6KWXXmruu+++5sknn2wWL17c7Lrrrs0222xT6jrsy7nOpm0ivs2GXu/Heq5/++23i2T64osvNk899VTz1ltvlfE1f/78ZsMNN5zTzIoR33pvq+wZAiEQAiEQAiEQAiEQAsNCIOLbsLRUyhkCIRACIRACIRACIRACIRACY0og4tuYNnyqHQIhEAIhUAhEfJt9R/AsUbdO2aSqiCPL22OPPdbcdNNNzcqVKxtZqJYdvqzZ98P7NkuXLm3mzZtXTzN07xHfujdZxLfufPrxW9IZyY3w9swzzxTpjYC50UYbNQcffHCzZMmSIr5ZVniutohvc0U25w2BEAiBEAiBEAiBEAiBd49AxLd3j32uHAIhEAIhEAIhEAIhEAIzIhAJaEbYctAQE0ifH+LGS9FDIARCIARmTSDi28wQen7wInzVr2U0q1nN6rvfvfHGG81rr71WsqDdf//9zY033tisWLGi2W677Zrjjz++OeCAA5u9995rQnybP7PCDMBREd+6N0LEt+58pvptHWOt+9UxVn/217/+tXn55ZeLXHrzzTeXzIMEuO2337459dRTJ8bZAc2mm25a5Ld6TL/fjfXXX3+9lME4d71ly5aV7If9vlbOFwIhEAIhEAIhEAIhEAIhsG4IRHxbN5xzlRAIgRAIgRAIgRAIgQElILuDP8D/7W9/K0Ewny7feOONyx/bO2WDeLeqIZCgrP5Ir7w+Fe+P9IIJc/mJ+HervrluCLQS0P8HaTy2li1fh0AIhEAIhMBcExhX8c39v1Va8yyw/vrrT/lM4Jia1YnM5vnZc7Sfe252js0226zZYost1i6raH/71oxv1113XfOTn/yksfTi8uXLSzaqvfbaq3nve9871839d+ev/waQJUv9Z7MMZMS3v0P7D99EfPsHJD39QB/1b2n/RtVPjTVjzL9X/bvaexXg7Ncqvt19993NAw88UATTM844ozn00EPL2NTP52ojvimrzI6/+93vIr7NFeicNwRCIARCIARCIARCIATWIYGIb+sQdi4VAiEQAiEQAiEQAiEweAT84fupp55qXnjhhfJHeUGwbbfdttl6663X/oH+3S51DXgJyD377LPltdVWW5VPxpPfWoMJ73ZZc/0QmAsCxkDEt7kgm3OGQAiEQAgMA4F+iG/upTbv9eup6l7vve3vUx3Xj98rYxW1yDS+9sxLiOn2oQ/H2Z9c4/keO+9+ZlMXMs4OO+zQ7LjjjuWZf5NNNik/J+yQn1566aXmqquuar7zne8UOe6kk05qDjrooObdEN+UmaTzyiuvlHpXWa+2id/3ulWe6nffffeV7HaLFy9udt1112abbbYpXKqg1Os5R2m/folvvY6vdnYzadP2c0z3+1pW7/X69X2qcznGy9jSp/70pz8VedS/r43VzTffYqJfbV3+bW3MOa9/z/p9FUyJb9dff33Z/0tf+lJH8a21jMrkPL2WsVMdIr51opKfhUAIhEAIhEAIhEAIhMBwE4j4Ntztl9KHQAiEQAiEQAiEQAjMksBf/vKXxh/cH3nkkfJp73nz5jW77LJLs9NOO5VPqs/y9H05vAYUZKGw9NLq1aubhQsXNkuWLClZKLbccsuuAcC+FCInCYF3kYAxMJsA17tY9Fw6BEIgBEIgBGZNYLbiG+GJPPXnP/+58ezrmZLk5f5apZJayCqVtGZs8oELHw4hs/j5XG9EmpoZikxj86EUz7zEL+XotKkTqYX0hpklFMlM6k7o8lJ38o1MbsS3973vfeXdOVufua+44ormG9/4RkOKO/HEE9818U3bPf/8883jjz9envdlnNMePvzSTQDsxCfiWycq//ez2Ypv+k/NfKaP4d0+vurV6nOtNixZ0TacGFsbrD/tNq3nm8l7HS8yInopkzFmrNfyTXbeKrAR3vRPcws508/V2bm99NdFixZNLBE8r4xd8wcu9jc+77rrrubqq68u8txpp532D+JbLaMxXDM3mgOMgZnORRHfJmvV/DwEQiAEQiAEQiAEQiAEhpdAxLfhbbuUPARCIARCIARCIARCoA8EXnzxxWbFihXNrbfeWv6ALgC23377NUuXLi0ZJfpwiVmfQvBAEEEw4be//W1z7bXXlgDCvvvuW95lrJgsADjri+cEITAABIyBqQJwA1DMFCEEQiAEQiAE5oTAbMU3ItkTTzzRPPjgg+XDHpb4I8C1ZkFT8HqvJeMQq8hmPgzygQ98oMhhZLGaHW1OKjpxUvd8UowsbQ8//HARY4g4H/7wh8uHU2QmU4ZOGzHmueeeK5nMLJ8oU3LN7Lb55psXUYZA5mVfz8+e+2VzI/y4NiYEqJ///OfNN7/5zYEQ37SbfwNoH6Kel3ZRp+lsEd+605qN+Kbv2PRbY418qS/VMdZ+ZRLmmnG22YQUtm3JuKcP1sxodSy2H9fP78lkMq8R15TbNY11fatb5j8yGoHUMffcc09z2223lf2NTXUwdzz91NPNqtWrimC6zz77NLvvvnvJLFjHWZVTiW+yKzqnjG+HHHLI3y11SiRUxpr13PfO5QNgxm+3ck7Gyr+r1d08eOONN5byLlu2rFk8kf0wWwiEQAiEQAiEQAiEQAiEwHASiPg2nO2WUodACIRACIRACIRACPSJgD/0/+QnPylLrAjuyfZ2+OGHl+DaoMhkAin+QC8Ys3LlyhIcWLBgQbPnnnsWQY+kJ8CQLQRGlYAxsC4CgKPKL/UKgRAIgRAYbgKzFd9IJU8++WTJHPz73/++ufPOO5s//OEPRXhBhmxDatt+++3LBz/IJZ49vbbbbrtmjz32KK/ddtutfG//6WYb66UFZGIipMkE9dBDD5Uyq7tMxwceeGB5Tpfpqf0ZndBFMCLiyI4skzN5zvMDkcfzvSxRniUIcatWrSrSi2xVxxxzTMnoRtqxOY8Pm1x55ZUDJb4RdNSJ9Ed8s+yqNptOW0R8694LZyu+6W/ES8Km8UXW0mbGk02/1V7+3WbJXuOSuEUG23bbbRv/vpMhzb9J9XO/m4vnX33cODNejBVimb6hHPrVzjvv3FEoUz9lVh/jkuBnnD766KNrP0BmHBFVjbPrrruuyKaW0iW/kdqMZfXCBaOpxDdzAqZPPfVUuZZ/uzufcS2LnDKbi6YjwJnX1EHdI751HxP5bQiEQAiEQAiEQAiEQAgMC4GIb8PSUilnCIRACIRACIRACITAnBDwx/NLLrmkCGUCDj7pTXzbf//9/yGoNicF6OGkggyCET5Zf9NNN5WyCjrI8iBDxUc+8pHyR/8eTpVdQmAoCRgDcxH4G0oYKXQIhEAIhMDYEZit+FafI2U6vvvuu0v2MPIb6cRWxbKjjjqqiDnEM1nGbrnllpIZjpCz9957N0cffXT54EUVTvrVEPVZlwxDFiKmuTY5iIhDdCHjuG4nyYXIQmIj4vzmN78pwpzy+pCIspOIqmhEdqnnv++++5rly5c3n//854tEpj6DJr5hY7lXdSMTrV69ujz3H3DAAeXfLdqu1w/ARHzr3mNnK745O5mMZKqP3XzzzaXNtJ/nWP2XSEpcJMHVTGuyL+qf+rlsZrIberfPTJfznKym+pN/UxrjMp7J2Ob6xgqxVYZE/ybu9NzdOo/oh441tmRMJ+ypX80IaWzVsSi72gc/+MHmE5/4RJFQyX+u2Yv45t+85DcMSbvEVqwIdoRcAhzRzrzQqcydOJgviH+EvYhvnQjlZyEQAiEQAiEQAiEQAiEwfAQivg1fm6XEIRACIRACIRACIRACfSTgj+jt4pulTgZJfFNdgQafTPcHf/KbQIHg5ZFHHtkcf/zxJdjQRyw5VQgMFIGIbwPVHClMCIRACITAOiYwW/FNcd1LCSSEt2uvvbZIKddff33JhEZ6OfbYY5tPfvKTRaKSXenWW29tfvrTnxbRigxmn1NOOaU59NBDi7xCdOlVNJkKF7nFNSxBSpipL0sufvzjHy9CjsxO7Zne1MmLROPYujQqseejH/1oyRLngyI1O53614xvslHdcccdpU6nn356EZKcaxDFN/8GIGWRFn/961+XZRplsbPco8zP5L5eJKmIb9174mzEtzrG9EX/vrT85xVXXNH87ne/K4IZWcsYIrRpM7KWcUY+u/fee8sx5E7C5nHHHdccfPDBRUDTf/s1zvRtfUmGt5oZURmIaD74RTKVGbHKa+20qoDm36HKTCJVJ9kYzQfqRNQznolx+io5zn7EN4IpUc1Y7iS+ffnLXy71dh68Wjf7kwmd13xIpsNKJrkqt/YqCUZ8ayWbr0MgBEIgBEIgBEIgBEJgNAhEfBuNdkwtQiAEQiAEQiAEQiAEZkhgWMQ3gTh/pBfQE0AQtPQuqPeZz3ymBOsERfoVGJkhzhwWAnNCQP9P354TtDlpCIRACITAEBDoh/hWszURcn71q181N9xwQxG/CFQyvfngB6lNBieSiefMyy67rGStspyhbE7EuMMOO6zIJiSdftyb3ePJOJYXrWKXbExEGpLMfvvtV55ziTDtYos6kXlkibv99ttLVjTZqmStkj3Le2uGOOe9+/d3N7fceksRk9Tr5JNPbk477bS1HyIZRPFNPf07gNwnSx9pSUY+mbYs1Uqk0j5TZX6L+NZ9sM9WfHN27aQ/kyovvfTSIpgStmR682ElkphMZcaZDIeksKuvvroIcrXfn3DCCWVMysAmO1x7v+9ei8l/a1wbK/qO8e/6ddlQQl5d6riKoq1n0nfIZsRRLxIc2fL9739/ETAJczXrGvGtLmGq7kS5D33oQ0V8U3cyn3O1Znxz/i996UuTim+4ypBH1MPWGCC8LZ7I1q7/Y0Xg62VTdqxJh8n41gux7BMCIRACIRACIRACIRACg08g4tvgt1FKGAIhEAIhEAIhEAIhMIcEZiO++QN9zQzhD+i+Xm+99UpwQoDC1zZBQV/PNjgoiFAzA8hSsWLFiuboiSWnTj311LL8k0/ndwpUzCG+nDoE1gmBiG/rBHMuEgIhEAIhMKAEZiu+1edVYo8MVD//+c/LUqKyNsksRf466KCDSjYq2Zg84/rd5Zdf3njmtOyoLEzEnSOOOKIcQ5iZ7bMt3K4li7E6us4111xTJK6PfOQjJQMVMY9U0+laZBh1ItDIiOy5Xj1klyIWEWFajyPb/Pa3v22uu/a65tEJ6eWVV/7cnHjiiSXr2/z589c+15Pwrrzyyuab3/xmyX5lH+eVEYuQt6437WezjKYlT7XhxRdfvLZNLHsq+xvpr/77o1MZsfZvFsvCyqpnSU7ikLa0dCRe3Y7vdM5R+lk/xDdt5UXEPP/880t2RYKl9vnc5z5XBNPKm3z16MRymxdeeGHzi1/8onzASX/V33y4SbsSxdqzn02XufJoe8ubGtcEUwKsfzvKLmdp1Zo1rXW81Os43r9DjQvSGSmWyKfvyMro61pG+5JHjUfiH8lOBkbX+OxnP1vmGIKmn01HfFN+ZdB3ndtcQTB0LjKh19Zbb13K0akOtS7ejQFzAfbO5RzEX/XJFgIhEAIhEAIhEAIhEAIhMJwEIr4NZ7ul1CEQAiEQAiEQAiEQAn0iMBvxTbDNH84F6ywZ4w/yAkaCc4KGJDQ/I8EJLAgITPWH+G7Vcq6XX365BPVkBrD8lMCewIiMGIsWLer5k+7drpPfhcCgERBEm83YGbT6pDwhEAIhEAIhMB0C/RDfPLN6jrT8ICFF9mAijOxSZ5xxRsnIJGuYZ1n3XYKMZ03LopJ4yCGWHSW+kcD6Jb6RWeoSpYQcGaI81xJySD9kLmXqtJFX1IHA9eiExOLZfP/9918rC7VmylInYhPB6PLLr5j4ZMr/Ngu3W1jqc+SRRxZRrko7gya+1boTfbQhWee8884r/wbBSJ21i38LqPNkz0z+LRHxrdL8x/d+iW84y6h25plnloxvJK999923iG+ETrKYfy8SxIiMF1xwQcmuKJOa8WDZYR9ukoFRprQqlf1jiXv7iesYG5YJveqqq0rGNkcSvfw70r8nje/J/q2qPvoe6YwwZ4zKEKdO5gwZ3PQ740f5CX0rV65svvvd75Z/t5JF1UXGSNd0nSqs1sxwrtEt45vy2gdL2d7qXEGeI+/KWikDIoFzqg+CVfFNxjcSacQ3dLOFQAiEQAiEQAiEQAiEwHATiPg23O2X0odACIRACIRACIRACMySwHTFN3/Q98dyf/z3B3sBAOewbIw/xlvyRYYJrxqkkCFj4cKFa4MCkwWjpqqKa9fMFr/85S+biy66qAQbZJ8Q8PJJetfNFgKjRkDfn+m4GTUWqU8IhEAIhMD4EeiH+GaZQxnDfHjihz/8YVli0fPsZz7zmebrX/96WSrQs6vnWaKMrE4//vGPi8BDNCG4nHTSSSUzkmdOklU/7s2udeuttxYhh4hCOpPpStYrWbI8W7cKbK2tb6lG2bTIL+pn33322acsD0mQ8VIfGyHHua++6upmxTUrmkU7LyrPz/t+eN+14o/nDUzsR5D71re+Vc5ZM77tvffe70rGt1pn5VMPIuIPfvCDkrVNm5GjTjnllFIP308m/mAR8a3S/Mf3fohv/q2mDxFMv/GNb5Slgn0g6pBDDinim8xksgv6UJS21Of9m052RX3ZeCCjEblIcvpc/TflP5a4t58QRH1Q6+abby6ZAsl2xrBxplwk1m6Z/pTT8c8991yR50imxpl/f9Z6KIn+6VrGj8zkZ599djmv5YoPP/zwUifLqboWgdO4JeCak1yD+KY8/u08WZ3xNR+SZS3ZfP3115e6kFf33HPPsvTqZKJspVXFN/VIxrdKJe8hEAIhEAIhEAIhEAIhMNwEIr4Nd/ul9CEQAiEQAiEQAiEQArMkMB3xTbDIyx/bBQws3SIbhk0w0OaP8T7lLtAmGOiP9u9///ubww47rLx3C0aVE3T5n2CC6zu/ZaeuuOKKElgQ5JPlQVBOICVbCIwaAX2/H8H1UeOS+oRACIRACIwHgdmKb54fiSYyFFvm9Pvf/3754IbsSJ/+9Keb008/vbGkqM0zrH1JMueee25Z2pAoIgubJVFlbvJs60Md/bg3OzdJRgYz191hhx2K/HLMMccUgY301knK8WxA5JP5yQdQyC7qQ+IhzhBqZKYi4ng+r8/o5B1ijqx1yw5f1izaZVFZqpEsVsUdko8PmXz7298uYo8lXgk5MmNZ1rFTedZVT9SWRETlky3Lv0ne9773NaeeemrJwOXfAjJYddocG/GtE5k1P+uH+EbGNM5WTmQ8O+uss0pbaR/i16c+9am1H1TSh6q4eckll5T2JIL5d93y5cuL/EZOM9Ymk8Amr8n//Uaffv7558u/W2U3u+yyy4pcR5Q0lo0XGdm6jWVjiJTnpcy23Xbbrbz8zvmNr3ot9bAkKilNZjiZ3mpd6rLFxrpMjfYjvumbNeObfSarM0GO5CrT489+9rPy72H/Dl+6dGlDflMnomG3TVmVm3R44403JuNbN1j5XQiEQAiEQAiEQAiEQAgMCYGIb0PSUClmCIRACIRACIRACITA3BDoVXz7f+3d+6/8V13v8TlHASGCiFAOlJa2BwoHSssBLT1SpBc8ChS5BxCRoCEYNZj4k3+CmpAYfpCISiGlp5RyraQgVxFFKJeCYC0ot2IrGOkpJwHEaHL246OrnU5nz569v3v63Xt/n59vPt+ZPfNZt+da6zNrfd6v9V4e5BOcMYjYhoYxjaGNNwwGMFu9MGCIjwGKoY1hifFprPDnjWFsI7PX0siHB/62mbH1lC1rrFa3JY5tqhgL5WOV8WKvaRcuAseLgHZfmz5e9Es3AhGIQASON4FjFb4ZOxLjGKPyLEXQxisVr222LyVo44nJZ4QtxGGf/OQnJ09UxClEbrw28fhmzPuABzxg9iM/8iPHjIV3KyI0Yjze1fzW84hlwYhTnpb9/hsXEMoQ3PAWJ7/yaBzsNAYnpiE+Ev9YlELwwkOVsTsx20UXXbhVlpMm0Zx0cFJ+4/kPfehDsyuvvHIS4FhgwrvVKDuR3PESvym7OlE/TsIdW00SvvHgZRvNsSBnsYISvi0SuePfxyp8UzdEmOaKPL5pPzfffPMkytKe9TUCLfNBbdS1X/jCFyZvh0Rp2qmtfQnfLtja6pQoTXvezuPhHXO//C9terQX26/KF4Hor/zKr0we5bSV7YSSI0Zc5M/8V1hbijrl1b2JIM69Q1r+5o2N+E3/JEZ7wQteMJWbIHUITIlLCc8I38xpsXv+858/9X/3FkLWZX3MddIR3pbNV1111cTNnPuSSy6ZTu9XzYfdB+T3K1/5SsK3Ucm9RiACEYhABCIQgQhE4JATSPh2yCuw7EcgAhGIQAQiEIEIHBuBdYVvHrDfeOON04N8YjenFfn3/7H7zx562kOnrZgYMBg3iNIY8KwktxqeocM2Ugwdwix7iL+bUjBaMTAQ11lJz6jHIPeSl7xkdtppp02r3Lfb4mg36XRtBA4KAUauZYbvg5K/8hGBCEQgAhHYJIFjFb4RmBF5WLTxvve9b/aOd7xjEo8QvhFLnXvuuZN4ytj11ltvnYRfPCpZXEGswtubBRzEb8IQWhnTHsthPMvrk3RsK3rZZZdNY9jhtYlHNgK7ZccQvxC88UxnPG8MfMopp0yiL+X9q7/6q0kUp0zG6ARwRG3eK9NTnvKU2U//9E9PaQzhD0HMEAgS+YjbuN14/hGPeMS07STRnPIfr7G2sssjz9PKyIMXlkQ/FtvwsLWdN76Eb8ta0+2fHavwDV99Rr3wzq2v6U+24CTotHWp/uPwuWuHB3FtmOc12/va5tT1RGnDQ9rtuVz/nfzoC9IwXyRe4yVQP/n1X//1KT/a/k5tWT/lYVC5eD10HyAg1ZcI9/QVoj1tUzmI3vQb+T///PMnwaxyS0ee9DN9V77MqYlXHcSo4tbHiN+WeXuUhgO/97znPTPe8qTnc57lzLmJBfXR7ebc0pdf/PP4NuHsvwhEIAIRiEAEIhCBCBx6AgnfDn0VVoAIRCACEYhABCIQgWMhsI7wjcHAqnAr0v/yL/9yWsVPBPe4xz1+y2h28eyM08+YPeCkB0zGOw/QrVq/9NJLpzCMdowXVvgzmu2HeGcYFb7xj9+Ytnf5P1f8n8lI8MIXvnAS1/GOwRjREYGjQkCb34++c1R4VI4IRCACETixCByr8I1AheCFxyfjVF6fjBVto8hDGKGURR7EJLY6dT1hG49OtkB91KMeNY1jCWYIUghKjvV3mQDGghHesT7wgQ9MAhZjWGI0Ai7e1VZ5LjM+J5oj5uH9yQIT4jf5UxZekS0UIXJxKtsQ5RA48ZZMaEMkM7ZGNN4nyDHO5yVL/hy8XOHEAxdRDjHSsQr/9tqCjYmI+JSduIr3PmUz17DYBjf1tKx+MFe3ridYUkbMlEsZt/Oytde8HrZwxyp80+4sTOJV8aN/+dHZJz/1yUl4pm2OU5smxuQNTTsjYtTuhsBUX1OHBIzqY1k9rstVH9H2icuuueaaSWAmTSLOV77yldO2oNuJw6ShrTn0G2JZ944LtjzRXXTRRdN3+goxrTkyIZm8Kpd+o09pW7Z4db3+Iy15Uv7hGY/4jYc4YXlVlDfXEgESym3n7U5duW8QfiqfPNpKludD7ZnXt+22S8Ukj29T1fZfBCIQgQhEIAIRiEAEjgyBhG9HpiorSAQiEIEIRCACEYjAXgjsJHxjIGIc8mCfsdC2ST5jtOAdg4FprCpnlPTg3Yr6K664YjIoMt7xxnbeeefNHvKQhxyT8WKUjxGCceHWW7+95VnumtkbL3vj7EEPftDswgsvnAwlDAb3uc99xuW9RuDQEzgMwjd5HAbCYwHO8HcsRs5jSbuwEYhABCJwMAkcq/CNyIOXYIIc3pVuuOGGSfTG2xtxCBGJsS4hFMEKr1PEI04iFGNdIjjfHasYZxAmEiJ44S2KoIaIxViZgIu3q7POOmtKc1w//zoEXAQ2vFAZq/MUxTPd8JBFUMRTlWuJbXh7w9H10jQ+lxZxDuEfUY5rsXAtcRkRoN92ZRYvcdjwdredIGc+n5t4Lz/qU5nV6Wte85rJ45U5B+9aFt0o0zJB0+CW8G15zcwL34bQkddBdb+M53wso53pX29+85snT2LaN4Ek0RvBpHak/ka70p8INaWhDWr/0nWtueaxtjEix+985zuTOI1wjUhN3etbtjrVz1aNOeXVnJNIzb2DdzRi0ac+9akTD3HrUzyu6c8O25e6vwij/+lnz3ve86a+qfwO7dd3rrnlllsm4ap8YEDw5sRmlfCNeI7w09z8uuuum0Su+gCvb//jkf9jdvJDTt52IRjhm/Bf3VqwRjjL652+o990RCACEYhABCIQgQhEIAKHk0DCt8NZb+U6AhGIQAQiEIEIRGCfCOwkfBtGOQ/wecewZQ2jmofjjIUMB8PzBY8V11577WSEuvrqq2cPfvCDp+1WiOOs3vcQf78O+WLMsO0MTw8MA4wqjF0EeeumxaAxDDXDGOa14+AR2Mngtpjj6nGRyB3/Zsjbz4MRz/1klQFxnfSGh511rt3pGveFvR7y4f7QEYEIRCACx58AgQjBFqGJ8adFDsQ464jQhtDGtoCXX3755GGN+MV4kScmv1/GsDykWcDBW5jFFL4nJuOFTToEcrsdi6wiR4xmfE14YnGJk+COGE0ZjWuJ7ZYdwvodJ3wj/sLFNpLC8GRHMGQcpOxO1xPaEPYRAL373e+eFqVIyzaUyux3zzHCjPA+89vuVP7x3ufH61Aec4EPfehDs1e96lWT6EedERmZdxAsLhsDKNPw+KauCX/MVwh+tKfBDoMT7VCvhG/EYbYF5g3RnI/nMILHndq+OiGmIg57/aWvn33ms5+ZvLkRsPHghq32qi/rf+I0b/OdNig9n1m8pP0eq+hN/ekjRJw8sr3tbW+b+pt86tcve9nLZo997GNXlsu1wus32trnPve52c/8zM9MfZSHOm1QGs4x7+BJ0BbBOOjbPL69/OUvn7ZKNmfWLofHteFdcrQ3ZXafGW0R8+24Yy0d4jdpqTdtnyjv7LPPnupubGG82Jb1AeEJE3lzlyeL1NwHNnGMe4Z7jLT2+166iTwXZwQiEIEIRCACEYhABA4bgYRvh63Gym8EIhCBCEQgAhGIwL4S2En4xhjIoMZYyDjnwb8H41a7P/rRj77NUObBP2MAbxUeoAvzmMc8ZvZLv/RLkyGOpwwP8ffrGEa8P9vyLvfWt751MjgQu8nbT/3UT02eAtZJy4N/hkAcrNDnHWMYLtYJ3zWbJ6Cu1RMj0TAMjdedUtcunYvXM8CsOoaBZtU1898xSjHiDEMOw9VOacyHX/Ve3pVhv+KTljiHt41Vae/mO0Y/246tk8/Fa+brh7iA549jPaShPvZ6yMd8vvYaT+EiEIEIRODYCRCfEJT4fSXwIpbhHYqoZvE3ZT4193HjOuEJX1772tdOnt2IcAilhuemr3/965OIhCCM8IaAxHjyyU9+8pSOdLcToMynt5v3xjXEKsbNBDKf/OQnp+1Un/a0p01bHhKxEcosO4yLeGQzLrfoxN8ENsIQlyzmlYDHGJeg6e1vf/s0rjdmVn6LWGzn6nfvsByjXs0Dfvd3f3eao6gvwjcnwdaysZi2YG5jO0piIYIovHix0yaG+O+wcNjPfA7hGmEaUZQ+RiBGGGhchud2h/ogvrTlLoEr+cM0AAA8SElEQVTqZZddNrVtrLXJSy65ZOL76U9/etoKleCQcMxCKtv6Eno+7GEPm+aKxm6r+vR2eVj2uXKY51336etmV255oSNwvdvdfnBK7xd+4RemMi72lfl45F8fk1/zYF4h5dmpvYx2OOYaXoeYlSBN+yTue+lLXzqxNB8e40u8ncLMHzhjMO4527FQNu2XYNa8G9tzn3Du7H//9P++7f6hXS873C/UF/Gn+6J6s7XsugvHlsW56jOMiXh58sOAVz/8OiIQgQhEIAIRiEAEIhCB/SOQ8G3/WBZTBCIQgQhEIAIRiMAhJLCd8I2hw4pshsK3vOUtsz/6oz+avABYiT+2UfHQ2gNyD+wZBhiQ3vnOd06GO14zGKBe+cpXTg/8id7Ex0DgnD880J//3N/OVYYI4RkMGRX+5E/+ZMqnh/uMoQyZtorZzlAwnzajgS1qvvSlL00Gzy9+8Yt3MkDMX9/7u54AoxDjjLpyLLaf7XLkOu1SO5k3Ku3UttZtf/PpMk7xqsCI4/VYBFfz8XqvHDvleTHMOn/L8zp9ZD6uRfbz4cW3nYFtPg7vF8Wl831dXY26Xgy3+Peq/PhOOvN5nA+/GNZ341rfzbeZ+XC9j0AEIhCBu56A3wXiatv/EaPZopDXN6Kcce9elqshdCL6uvLKK2e///u/Py2WIPTi7YwghwCH8MOY8g1veMP0PU/FxpPPfOYzJ+9hfqe2S8dvxjgXrxufC7sY3vjkr//6r6dtTonXbBFJJPQfwjde7c7cVviGhzIR5RCvSGcI3/weLx6ELq4lyrFlI0GOMbO0eNviIe2uFr7Js/rx6hiM5scEi+UYf48wvFH/9m//9iSmUn6CpAsuuGAS8Zh3LDIf7YGASVh1zsuZz13vPFEPbcq42WksS/ypjZy25Q2P18NVbNSHLTu1McI3W50SmQkjHguhzAVt6UuoRbCFue+cxIraofHzOvW/bh2ZPxC+feqTW9uvbvX/v9+a7+nvj3v842YvfvGLJ89oq9LD5Prrr5+ZHxKa6lsEgRZ3DQHbfF7MWVyvjMqqn5lTv+hFL5rmw8S6xsrapfI7sRttf7yOOBfb7/jcqwUn7h9Es9LySkB48cUXT/dHedxuXD6Eb8Ry5vg8v6ljot9VPObT3817cXpuQNzoHqeutxP17ibero1ABCIQgQhEIAIRiEAEbieQ8O12Fr2LQAQiEIEIRCACETgBCWwnfLP1yzCqMRS+7nWvmwwFtmCyxQsPEVZs84xAHMdzgof8vEgwdDA02D7K1i7iYvggJOFlyoN67z3MJxTy3fxWL4weDJsMJMsevjMQDHHM+9///smQKQwDKEOolfW25VnnYNxhEJF/Ht8YwjoOFgFGIfXEmKTunese2skItxhmO2PSMDpt9/1iPP7WTrXjce6n8E38I0/e79fB8LebMu6ULiMpo9lu6mdZnOrafWmdYzGt+fL4jqhgu2MxrOtGeN/Jx/wxvpv/bP79svjmv/d+VRzLwq+6fjFufx9rHHsJvyzMYt5WlWNZ+FXXL8a9rNw7hV+W5mK8q+JYFn7V9YtxL8uzz1bFsSzNxXhXhd9LmovxL8vDTmnuFMdO4ZeluRjnqjiWhV91/WLc/t5tHMuuX4x3pzzsNo7dXr+Yn+3KuXjdqnwvy8Oq6xfjXpaH+fCEaRZV+IwYx1Z+xqE7bcFoHGBsNzydvfGNb5zGrrwW815M/EbsYRzKa9LrX//6aTtGnxHYveQlL9lWkKPMTuMUvzde/f6PMYDvjEHkgWDG5/NlEoZIRrqEb4QrhCFPe+rTZo//8cdP4q3ttjrFw6INnuoIjoyZH/e4x01bpS4bOxvT88wsHelJl9jIeJ4IhSDnrhS+YYWN+QL22EjfvMDcYp7Tdm0FX8Ki3/md35kEfcPbm4U3OBqTLcYzxpTG/VhgIk31PRYuLOMnrWXHYvyL1+w13IhnWfid0hxhx+s6ceDiVB8EpkRehFNEXvrZOh7fLCTilZEHQ4uSxEPcpD4I37Tl6667bhLG/emf/un0vfiHJ3HvRx2MvB/r6xC+8fj2pivfNPv7v//7KQ3zxZ//+Z/fUfhmjsgTI8+M8k+8ddqWEPDUU0+9rZ+PPOKsTSvjBz/4wamf6dPK94u/+IuTAE54ZXS4dsyJtXnt1X1iWfsbacy/Cqv9WnhGxKk970b45p5ANGvRmrk8j288smlfu2lj67Qv8ZnbWzBnruC8K+8389x6H4EIRCACEYhABCIQgaNKIOHbUa3ZyhWBCEQgAhGIQAQisBaB7YRvjA8MhYxq73jHO2ZXXHHF5FWDUY2hkNc3BgAPshk6rIRn6OBFgjHJg20rzl/4whdOK7sZU3hU8B0jgoftwtqiyoPvW2+9dXro7uG5vxngGFqWGa1c42G/eBhWXr9lpDzllFOmfBHZMXYxYK1ziEveGB/GuU64rrlrCaijvR7LDDJ7jWs+3Cqj0LpGq/n4Vr1fldaqcKu+k8f9jFd8+u6x8hZ+lWBtVZkWvyM22OtxLG1ur2kWLgIRiEAElhMwJrXAgiCHaIVIgzcjgpFVB89Gxqif/exnZ+9973tntjIl4uGF6SlPecq0SMN41u8OT1WEccQkBDMEK694xSsm8c+ytMb40ZjW9eIg7nCt8avfIJ8TUvt9JE6bF7YYd/LARlhjDM1rE89rxGgELLzOyduyw9ibhzjCtyE8J+YjrFk2BjFmJo6xYISAkHDOOJ3HN2kSosjb+N30aozgFJ/y7Nfhd178uKlXnuswI2I0fh+cVqU32BO+vepVr5rq+IItT2/Eb7y+WaijPIuHcNqEeQfx34033jjNIU7bEjPJg0UBJ/JBhMiLGA9gmJhTWUykXpbxHKxw/erWdqDapH76vve9b2r74iB8Mx/kjdsiIwKtyy+/fOqTvtefeVY899xzJ6EcIeIYn2oro71Iw3vHaJPjOu1ptNkxd/SdNqaueTYbXuj0RfNZolYC2mX9ZZSLqPQDH/jAlNchBCQOWya4lT99XfnMh4netDHt8mUve9mUFpbz9wZ5UyZt3r1D3tbta8qmrgjf3Ds+8YlPTPcN9zX3j1Ue39yrzKUJgt173Efd78ynN3GM+4g2NM5V3DeRh+KMQAQiEIEIRCACEYjAUSeQ8O2o13Dli0AEIhCBCEQgAhFYSWA74RvjGaOaFe7vete7JvHb6aefPhklPFB3MhB5cM5oZ6sgD/oZOxiNPHBnfHKdh+ge6jMeMIo4v/nNb06CM+I2xhSGTA//vXoQzmvbWWedNcU1PGeMgjAsMJTddNNNMx4Drrrqqtu2kWEIbRX5INXrUSGg/wzj3lEpU+WIQAQiEIEIrEvAmJSnMgIuY0zCpnW8QxGHEJYRSBG2EeYQehF5DJEUr1REaDw1XX311dP1vBc//OEPnwQ7xqQEOosiNCIXCzqMSW3xaIGHhRvEZ0QsfrcJq+Sd2M7nxrzyTfxBqEMIRGhHlHbNNddM11hgQgRkEYoFIssOY2lCPuF5nyJQGlu/zgtKjB+UTR4tFuHdCUNjeOnw4jzyRQjD8xOxnrLIv7ziQ7Czk8hwWT6XfWYcT3xmzE+ER5iIj/mCMbz3i2P/xXjGVo3mH69+9asnAaA5B9GbusVkmVBrpG3OIV31pm61CeWcF10tpnki/K3ubUOq/dtGWD9TH4RZ8+1qngWm2rL5IBGVfqa/aTtEbfqZtqZuzQWJUC+99NJJsOUa7fa5z33utFUvcdzoO6Ptapf6mTmrtqxdao/OUV/iNbfUrkd+Ccj0UW1amd7ylrdMeRQH4SsvdF6XlUvaykSUSSzr3sADpO103QcI1ObH5a4fbRIDi8bMofU7ZX/pS186iXWlpd3zhidu+TZvxnn0Q2Va53Bvky9zb2kqo/uGxWmEfbjisewwfxd+CBHlwZaztoDuiEAEIhCBCEQgAhGIQAQOJ4GEb4ez3sp1BCIQgQhEIAIRiMA+EVglfPMw3AP197znPdPKdUY1D9R5iLB6nQGMgYTgjaHQanoe4h75yEfOnvGMZ0xbUVltzvubg0HCNQx8jCPCnvnwM2cP/G8PnB6+M8QxEHoY/6xnPWtKw4r6YdQYRWaIYJCxyt3DfqvcL7zwwsmAwXAlX8uMXSN8rxE4bAQY1OYNbIct/+U3AhGIQAQicCwEiMeInIbwzZiUaGYngRSRiW0HjVMJUQjGeHkiYrFlKmEOUc8Q7hDs8KBEvONz40uCENcSU83/FovbWNmYlJiHkIWXNuNgIi7jUeNe2wkan1pUMoRdxqkEQ8bGvGvxkGUhBzGPNEfexhh6kR3R1pve9KZp3E0gZ7GILUuJZ+aFPMpFxMYz3JVXXjl5vTK2Juqzzau0hrhO/o3DiXLMDwiHiMGUmzDHe/ke8RubKINjnou/xzXeLx7CECRJg2CHZyxpKIN0iAd3EtmZQ/BaZw7wx3/8x1NcyqOueH9erKuRB2kPj2+25ZwXvuFC0LQq7yOeo/qqrRBQ2RJ0HeHbaAOYmpfxKGhuZm6oHtUJsZh+pi2PBVNveMMbpjYvPYugnve85019Ur/hUU0djHain5lfyhMRmzat/2vvhKSu1YfML6Ux5p7qUhzSkLe3v/3t0zVEj+4Bv/qrvzrla1l9j3bivkMsaj789Kc/fRKKDhHgfJvHQToEekSshG8333zz1F8I32yrqpzuX/qie4I8u0Z5ecVzf5B/wr91DsI1Xt70AX3I/Y3wkxdHDPQl98hlh/oiKHT/EnYI34hAOyIQgQhEIAIRiEAEIhCBw0kg4dvhrLdyHYEIRCACEYhABCKwTwSG8M1DegYfD7w9NPfw3YN5RgQeKDz098CeUYonBQI4D9w9sLdNCoMEw5+TJ45f/uVfnl4Z+BgIGAQYDxgTed5ggBD+xx//41Oa3//X708GLJ4fGDVe/OIXT8YSRjbGr3njgpX6w3uHdMV7wZYQzzY60mOUm79+n1AVTQSOGwH9pzZ93PCXcAQiEIEIHGcCuxW++d00XiSO4rHJNofGjMaYxFG8g/GKRKhG9EHoQgRC9EOMRcBDcEM8QpTycz/3c9O1hHbj95hwxDjaONj4lhjNWJp4h5c4r4RvBCnG19IyTiVuISqTpjTEYZEJL1jyYpxN+ObkAWukpwqUSzjjaOIhAhpCL56riIt4Z57fKtHWlcR+rrf9IpGMvCmTV+IhYiSCHWN48RHj4eRQXgykIW5iKHkcfAnQHNIkIPK5cbhw8/mYLvrP/+Rf3fB2JT9OQjViHYIm74mWVh3Cmqeoq7e97W2TiOeSSy6ZPeEJT5iEhzjPcxtxSTvh26Bx59e9CN+G9zBzM17CCalGu3zRi140tWeexMzptA/9zNySyNR16kTdaZPagGuHMJTITRvWJokU9SXtlLhUe9cezTPFYy5LROZzbWh4jtNPzS+1f0IxgjN98Td/8zenvC2bN2qfQ9hKNDuEb7yp6b/6wHz7UgZ5VDb5cM9xzTlnnzM773+dN7VL9wb9ihc4fVKesJJPAkH3I/2dmG+dwzyaGNi9Sv7ch4jsLB4jbMVmu3406kw+5IFAzvzffaojAhGIQAQiEIEIRCACETicBBK+Hc56K9cRiEAEIhCBCEQgAvtEYF74ZusWxgYPvhkeeHzgDcHWSLaHIUA75SGnzB69JX571Jah7OZ/vHkypDEYMDB54M/wYGX/b/zGb0xx8NbmeweDhQf0HrAzwDESEKwxug3PDzxmiMeWMFasM2aM8OJgMPGw/gMf+MC0cl84BgJGTMYInjLmDRHCdETgsBPQ7mvXh70Wy38EIhCBCOyVwG6FbwQzRFnGlAQvvKNZrOG3lJczW3xazMETG4GKw7XEcTxWEfAQ2BiDGqu+7GUvmwQ1xrVD/GYc65Q327AS1fCa5ppnP/vZk7CMuMU57z2Lh7UxtpVPAhZCmde+9rWTIIwox1iaEMiiE4KyMQYgyDH2JXQhlDNutliFMM2WkgRBY8GIuHm3Mu42/hbmpptumj3nOc+ZPDMb8xv7E+tcf/310/eEerxSKRd+hDqEb0R4RGVERbaSNBYnkhK/97ZUJHSTpldj80Vx0Kh7Yxqn8MRPhG/4KLe0dhK+CasuiaB4FiM0IvAh+BmCQ4wHs5GuV+VK+DZP5I7vdyt8w1P71WaIP3lVI4AjStR+X/GKV0zthuhNv3DoI9oZ0SJPh67V3p3asPY8+thoK0PESiCqbxJ2EYjazpNYbAg7tU2fE2kSqOkLwhKlSkvflrZ+/1u/9VtTmtIa/XHQ0EbG/YBIT98hlnXv4MlO3Iv9kqBOm8TB/YBXOZ7szHPlS7/AipAPZ3kmyFVGntItKjOfXlf4Jg7zYflzj8H1mc985uz5z3/+NJ8ntNtOfKrPEgQSvslvwrdR871GIAIRiEAEIhCBCETg8BJI+HZ4666cRyACEYhABCIQgQjsA4HthG+2TbLSnTGPoYD4jQGMEctDeQ/9GZQ8wGfkYvhgIGA8I5z7tV/7tcn45ppheGIQYHy0fRRRnQfyVrgzWnztq1+bffkrX562WGJs8NCegWHeaMYwwNjHCCdPb33rW6eV/UR6DH7yTCjXEYGjRkDbH/3oqJWt8kQgAhGIQAR2IrCu8M3vpTEpUQeRFy9IhFEEIry/EbkQbxHZGD8ag/K4RPhi3MsbE6EYMQkRC3EJgRyPb8IZAxOLEZQMsYx4eYojwiL6IQZ7yUteMgnmjIvlwbiZNzNhicTmt1ckQiGUMa41lvY9EYxxMHGaPI/rjbvlkVDNWFjctjc9bctTk7J4b+zsetfy5KYcN9xwwzReV1ZlJxAzDnf4XpmH4G2MNwiSfKec8iEcj1IWmagPY3n5lX9CM8Im74lozjzzzImV+NXJOMQ9uJlX2IZ2CN8IhNYVvtn2Up0S/plfEAgSG5oPyN9284GEb6Mmlr/uRvimronKzCUtbiKgMs+zCEqfIGJ7+ctfPvWb0e71G2loW5/61KemhVX6jPal7i6++OLpekK5sfhptH3h3vve905paG/ai76p3RN+aQ8EaTyPE08O4Zf2ZwtfwlRiO2JL+TFX1aa9X9wS1P1DGII5+SSClUeCu+H5UHuXNxy0ZW1S2fUJc1Ue3Ahs9UnXavt4iZv4jfCNeNW8l2iTsHQd4du4x+mvBLPm6ISgDvcp/UA8yjTYLda2PCd8W6TS3xGIQAQiEIEIRCACETjcBBK+He76K/cRiEAEIhCBCEQgAsdIYDvhmy2TPKD3IN/qeEYChjYP8j1IZ0xg1OJZguGLmM1Dd0Y2XiF4bLOa3gN3D+jFxShx2WWXTUYHK/AZKqxMZ0j40Ic+NBkLXctgRRAnnuEdQDEZqxgTpce4YesZ+XQtY6KH/OLtiMBRIzD60FErV+WJQAQiEIEIrENgXeGbsSJxCVGIcSdBGpEYD8YWTxiXElcZv1owwSuTcSePYQQoxDUEKQQ21//N9bNb/u8tW6KuH5ud/ZizZmdtCeVcT8RmfDrGnMIQoBFh8XhFLMNDHNELEYzTmFiaRGnEP8bF45BfeSR+E5ZgT96e/vSnT+Nb4+7huYmQjcCG2IuoTtrDuxqBnHyNLR6N2V3vVDZCISchji0hHQQ4BEHG8cRCBHHiM+7AgbhOWt/97ve2vCv/r8mDFUESr1mYEgdZAGNbV4I98waipIsuumhKy3dENuLDHrNRfmkP4Rvh2joe38SjjqV/5ZVXTnkQH7bmFOYW8jHqZjAerwnfBonlr9qTPqONzXspVOeLIir9SX0Pj4Hakfmcv7Vp87jnPve5k5BN/Zo76mfqQDpElZdffvk0pxO3fkXsKZy5IU9urieU1F/MMbVT3gvFr52bBxK6Ed5Jn2c1fZQATl8QVpvRB4jXiPMIxbTLF7zgBZPHcO1+0UOg/Lnead7Jm5r0HfqyUzvT5zDwvXuAUzl9rz0T5hHxjXwIT3Am/uG1cbfCN/z0KWkqyzvf+c6pPHiZE7vvuKct1pe0x5HwbZDoNQIRiEAEIhCBCEQgAkeHQMK3o1OXlSQCEYhABCIQgQhEYA8EthO+WaXuYT7DAuMHTxGMBoxoHqQz3DEcOj/3uc/Nrrjiitktt9wyPexnsLDanCHBwbjgoT5Dyutf//rJWMUQIA3eABjYeLkgsGOMI6hjeGMwmDcQiocxkAHOtQwfttFh6GJwc+3wIrEHFAWJwIElwGg3byQ/sBktYxGIQAQiEIENENiN8I2og7DEeJGQjPDMGNY40jiRMIXwiziFByd/E0oNQYnt/4xZb/z6jbP/9+3/N4lvCGqMNQmrLLQgqjFOdhAAGU8bK7/uda+bxqi2OCTikRen8bK0CHkWBSnSJdwhJCOe42HqtC0PbsJLb4h4jAVwIPAhxhGXfBtHKxdhjrSG6MvfRDbCya/0lZmISd7xINoh7pG2cTuvW+KTJ+N7C00I4G688WtbAqOfmL34xT8/pftnWwtilFe5lWcI36RHRGRLSGXwvfmBtKSJHZbySPhGKMXj27rCN2UiasSAaMp7jP7n/3zcJMwjmMJiu/mAcpmTWEijzLjLJy5DmLVYPxtozgc2Sv1mHeGbNqXd85I42q52ZM6IrfrW5nlJVD9EdARgRJzGs+aXRJOElTy+qVftkhdG4kxe1bQVbXwIJaWnTRI9av/CmE+aM5qf6u/6tfmjuhROXcqrdm4Bl7DveMc7JtEYwZy5qDxqN2Oc7XrlIsyz9bE2M+LQvwjueImTtyHIw00evCqrvmZOO8owX+GDm7zsxeMbdhjzmmfrVwz1P4I/XuOIAYnyVh3KgR+RYludriLVdxGIQAQiEIEIRCACETg8BBK+HZ66KqcRiEAEIhCBCEQgAhsgsJPwzYN+D8YZDBioGIsYERisCM089Ge0+r3f+73JyMEA8ZM/+ZOTpwdGLAcjmAf0DHlveMMbpofsz3jGM6YV/YxN4mS8sv0M4wMDBoMHgwHjm4f3DAuuY1Rh9GCMYLDiUcK2LgwL8jWMFhtAVZQROG4E9MPa9nHDX8IRiEAEInCcCexG+EaoQtgxRFfGocQifksdBDHGscQxRGXEOIRSfmeFJWDhTcmrsafDeJfghajLq+vF4yDyMVYmknnNa14zbZNqYYbxsOulQ1hlzEv8tfh7Ll8jTWNlYjNpEOUQ8QhrPOz46pYoj9DF9RaKEKsNkQ+xjvG6siuHcbE8Gkc7xTnyLg+uU74h2iE8wgMbZTLmtn0rMR7veURxL3rRi6ayE9zwbuUwHyBm8yqc/Mg7oZPxuniIfeRBHGNhi3r5sy0B3brCN5zUKbGOrVkJmJTnqT/71Mnr10NPe+gkSFK2RcZTRrf+w0WZE74NInd83Y3wDUftTZ1YmISp8NqVQ3vieUyb0j6IxbT/IUazHSqxmrD6j/rVZvQZ4jEezFw/+qb0XK8tmgPqC8R12ppDXsw99Qv9Zb4NyJP2ZitS27ESxIqbyO5pT3vaJKDztzyMewABoLYmT8qgL/leXp2jn02Jb/2n/WuPo8zKry8tijD1Bf13rx7fhJevG/72htlH/uIjk1DRvcY2xO4xxH/KsurAEg8M9SX3wPPPP38Kvypc30UgAhGIQAQiEIEIRCACB5dAwreDWzflLAIRiEAEIhCBCETgLiCwSvjmYb3DQ/5hCGA4ZLBwjhXrtoN69atfPRk4nvzkJ0+CNgI2RgKHh/u8AVjR/5a3vGVaRW8rVA/pGRKtwH/jG984ecggejv33HMnQ4bV64wNDGjD0MD45gE97x2EeE984hOnB/2MKR0ROKoEtP95A95RLWflikAEIhCBCCwjsK7wbYxXCbAIO4wVlx2u4wWNWIWgxbh2/M4OUYhX495xGBcTiBCVjLGw70aaxCh/+Id/OHvXu941CUgIvB796EdPQhzbOA4hz4hv/tWYWl6Jeng15snMGJmIhydlCzzkj/Dn6quvnspGqGKLzyFmIzoSj3zL0xDnKaN8K+cQEY084+RUTt9jIh3iHyIhojSCPh7zeOOy2ITo56qrrpoETw972MOmcfpIExvCH9cSHxHW8Ezle3Hz/sW7lvyI58/+U/hG6ESERMhEzKfs4xh5FQexHU9ZPIvdfPPNk6erJ//Uk2dnPuLMKR/SWHUkfFtFZzYJ19b1+KbNOLVVcz31oy2pL4e2pj0MQRjho8/0Hde4nliOYFO7FVYbVPfmftqPv7VHJ6GZOtceicbk0/yPdzXth+htnIvtQHpObVE4Xgx5LBSe8G0INaUtH0R5Q/hmPqr/ErIpj36qr43yj3uBfuh03bivyPfioax7Fb7Jm7Dy/+lPfXp28z/ePN0L3CPcDwgMlUGeVh3Y639DRJrwbRWtvotABCIQgQhEIAIRiMDhIJDw7XDUU7mMQAQiEIEIRCACEdgQAcI3HhMYnjz8P21rpbgH57ZJGcK3kTRjEaPBeIhPfPbVLYOWsIRrDFVPfepTJ69tjFdDjMZrBkMeLxauZfR4+ctfPl1ndT5PEG9+85snQx+D2DnnnHOblwur/onfPOhnaOAVjoc5cRDW2aaGyI6hoSMCR5XAfL87qmWsXBGIQAQiEIHtCKwrfBPeb6bDuNX4cfw9fTj33xDhDGHN+Eq4MeYVdoQnJhHGMS8sGd8T5bzpTW+aPEq5jhjn4osvnhZ6EIMZz86HG+l5HXlVTqKusaUjkdhznvOcyROycTnhm0Uk0nz6058+earyuTIo62J5fU48JN35co48ex2n70f+xMPbG5GdrUrl3/jcghPj/z/4gz+Y8iwPBH1ERK4jVlJugj8iJOJDpzTETRDk9N64fmx1KszwbrcofMOHSIfAiuDngx/84CSCcj1hII945gRDkOj67Q6ch+CqrU7vTGldj29CqlM8CcDG62KM6tk56ma0wdHmiNmEH38LP66fF735XJu0WMpiKuLQv/iLv5jS1TYtprrgggumtrhM+CV+h7aoHRF1vu1tb5uEd0960pOmeac5sHmndAg9CSylRYzpJMYjEBt9dcQ5Rbz1nz4vz6O/KceyY6/CN/nSds3dP/zhD09blN7/x+4/O/2M06f+Zg49+hbOq46Eb6vo9F0EIhCBCEQgAhGIQAQOJ4GEb4ez3sp1BCIQgQhEIAIRiMA+EbCinWcKgjIP9BmbeFw7++yzlwrfPOwf28UQrDFAfeITn5gEbVbc/+zP/uwkRmOIInzz0N8DesI3RjGvVvwz4hHH+Y4Rj9c4cVlVz3sE4xovFoyEjAwe9vMI8JGPfGTaAsqKdt9Lx+majggcVQKMazsZsY5q2StXBCIQgQhEYDfCt+NFiyiHmIYwy/iXmOvCCy+cnXfeeZMgbAjUtsuf33oLQiwYIXwj7OG5ygIP42OiMqKz97///dMY/ZJLLpkEL/s5PpAH4iBjbp6a3/3ud09lsSDGePv000+fvGZdfvnlUx6e/exnT16mzAW+8Y1vTHk8+eSTJxEbL1lDKLhYZmInnqvMP5yEa8RF5hLSUO4RVp4IkXjrMpfAxpzFQh3Xmm8sevhaTG/8bR6T8G3QuPPrboRvdw692U/MBc1b3Qv0DeIvgjr9jPDN9sJj0dVOObFwy/yXxzPeFM1/zSuJNbU7bZPwzTasRJy+0+a0s2Ptb7sVvmn/+otw7g3EeLzR8XxH/GnO7P5AgDr6zE7lT/i2E6G+j0AEIhCBCEQgAhGIwOEjkPDt8NVZOY5ABCIQgQhEIAIR2EcCDAi8LdgyhsiM8YDojXFr0ePbWJVvWxoP3j10twUSARwjhJXmVs0zjp111lmTdwir3hlReMEQRlhGAw/qTzrppMnbA0Mh0ZsH+cP4wGhG3CYPjIce0DPCfexjH5vEb1bljwf9wjB8dETgqBJg9DpWQ9tRZVO5IhCBCETg6BM46MI3v9PGuddcc83s4x//+CRCIeSy5afx8TIvVIu1NgQuRC4EN4QtxGREXxaNELcQ/xB/GbNfsOXhilBsv8YH0icMUw4iM4tVzA+IgS666KLbREHyRqxmPG/cb2vHz372s5Moz2fG7xa3GMsv83olDSIeHuKIi3iEtoDFeN78Ay+enIfHL9dbJEOIR5BkbjA8xA1Pb+sKfhK+Lba6O/59kIVv6o63Nu2TxzeLoQjWCEP1A/1jnYVQ2rn5qDZF+HbjjTdO7Z64jYdFAlPzTm3f/HXMa/XBxbnxHemt99duhW/KzTuiPOuT5t3EqfKin5lTE+Wtc48ZOTSnH1udmlvjRkhqft0RgQhEIAIRiEAEIhCBCBxOAgnfDme9lesIRCACEYhABCIQgX0iwLME0ZmH/7ZHsVLeQ2/Gg0Uj0lgdzlDFEGebGMYqBggP0Hl28ADeyXjAGMVo5TsP6z1gZ8wjUrMtjfSGJzeGBSI8W8z4jtHB94x5DBTikFfGPukypjGMuZbBbTGv+4SnaCJwIAjoA/tl2D4QBSoTEYhABCIQgV0QOIjCN7/NTmNbQhQLOYjeCNaG9zLjaQs9djNOFScBEsGbRSG2PiV+IQwTj88JXSxUMR7ej/HBKIexujTNC3hlJjQjBuINWprK6XMeswhtCI68fuUrX5nG+vJnDE+QZIy+LG/KQvxDxCQeYc0XjOfNJYQ1BxjCN3lzDXGdsDxbOYnfiJF2cwhvPmNe0landyZ3kIVv5ozao3knUZr5IC/hPCoSW2p36/Yz7W8szNIOtAcCT33MXFSb+/znPz+lpZ+Z2xKHrRv/ncne/om0LeYi+rz00kun9visZz1r9oQnPGFKXznmD+Ue9wPzYEI9fUUf0DfdY3YjehO3ebW+rP8lfJun3fsIRCACEYhABCIQgQgcXgIJ3w5v3ZXzCEQgAhGIQAQiEIF9IODBNwMaQ4KH+Tw18LLggfqilwaGIg/JCd8YHWy3xPjlM4YkxicP6xmiPIgnomO0ckiHYZAhQbzjAf0wtFnJ7nur153EcSOsa8Tve2kTyElrbG3k2mWGtX3AUxQROBAE9IHa+IGoijIRgQhEIALHgcBBE775XXYa3xrDGg8TvvGG5m+LM4jfjKmNrXf7G07sYnxNIGOcbgxuXDzSJAwz3ub5bT8O42xpGWMT1hDEEPoQ1hHYEAQZu8uXvFiMYt6gfMb1wmLhvXG5/Ll+2aEM0nO9ePByCCdNp7KOeYjr5Usb8BkBnnnKuG5ZGtt9Jt2Eb9vRmU0CKx69iS21L22YqGzZvHD7WPbvG3U/DvNAfcHiKwum9DmLtWxFqh9oj+v2M+1YfNqt+Sxhmbalr/7Ifbb61H+Z3Sbm5IXwjDPOmOan68Y/8rzsdbce30Y+CUXdY+SVOM8CM/Nuc2J5303e9L2Eb8tqp88iEIEIRCACEYhABCJweAkkfDu8dVfOIxCBCEQgAhGIQAT2gQADkJMBwAPz8eB82Yp2D8k9fLcqnqGAocpnjBLzYT2E5+XBg/h5w9WxZFcaTvl0yqe4pbubB/3HkofCRuB4ERh97HilX7oRiEAEIhCB40ngIAnfhmjLWJgAx2KQMSYm9jIOtgCEcGg3YpxlfI15CVSItQhmxnjAIhFiJK/7cUhHWXhWIzKTHrEbj1rKY9ztGuN+ZSI6I1RzyJNjU+Nx8csPxtIe3uCmRHf5X8K31cCIqg6K8E17U+fEkQ5tj9jN6dDX9DFeAgnWdntoV+a1yqxv6WcOcWlno19LQ1/QB/bjUB4LuWzde/nll0/96pnPfObk8U1ai2LWeQ7yKM/En0Pst5d8YZnwbT9qszgiEIEIRCACEYhABCJwcAgkfDs4dVFOIhCBCEQgAhGIQASOEwFGoGFIk4XtxGSuc3rgzgA1RG/z2RaWEY4xYr+FafLolAcP+bfL53x+eh+Bo0Bgvn8ehfJUhghEIAIRiMBuCBwk4RuRDHHYV7e8or373e+effGLX5ydtuV5yrafj3zkI2enn376JBYjDtuLKGVw8dvvIHwZY/AxHjAGNs4m0NmPw5j+c5/73Ozaa6+dRDWPetSjJo9SvCtLnzjI+e1bvz2J3k459ZRJeCcfjpHX8fd+5GnEIW6n+Yf4lXmvXHE0h2mr00H3jq8HSfimnxFifv3rX59EWuqOh3JiOMJSnth4PbPQaq/9QJza1ehjaIy4pK9fEJjuRVh3R7K3/0X05t7xiU98Yvb2t799So/wzZatti0lapvvR6Pty6PTIY/m266bv/b2VFa/0wcI3772ta+11elqVH0bgQhEIAIRiEAEIhCBQ0Mg4duhqaoyGoEIRCACEYhABCJw0AgMI9divvbyAH4xjv6OQARuJ6Cv1a9u59G7CEQgAhE4sQgcROEbwdvVV189+7u/+7vZ2WefPTvnnHOmV9siEqVt4hhj7/0YE4iLkIbnOt6trrvuukkE86AHPWj2Ez/xEzOiNwIbIhmCIwIhQqH7/ej9Zg97+MPuJNDZRHn3O86Eb6uJHiTh2/e+973Z3/zN38xuuOGGyeub9kfwSFBKYEqcuZdtPpcRGP3Kd6Nvjc/G38vC7eazIVyzXamtZD//+c/PPvrRj06eE5/0pCdN94/TtgS0vKZLc1m6+5UnfRpfwrePf/zjE9Pzzz9/Jv2OCEQgAhGIQAQiEIEIROBwEkj4djjrrVxHIAIRiEAEIhCBCEQgAhE4YQgwdC0zgJ0wACpoBCIQgQic0AQOkvCNgIVw5Fvf+tbs+uuvn7y/2aLQyQOVrUEP+m+2cQURGK9PymDbRQIjHrYIi2ztyMuVcrjW6bNHPOLMLXHMGVueqR4ylfOwNcqEb6tr7KAJ377whS9M7fLb3/725H3t5JNPnjwqPvCBD5wEYgSme/X+t5rE/n/Lgxy+hG+82LmnEZzKv/LYstXWwieddNJtXtP3Pxf/EWPCt02RLd4IRCACEYhABCIQgQgcPwIJ344f+1KOQAQiEIEIRCACEYhABCIQgTUIJHxbA1KXRCACEYjAkSVwkIRvAzLxiG0LbYdI7Da8Tx0GIY5xBQ9ato0kevvzP//z2U033TR5diPs4+ltiPfGtoqPeMQjpu0YebQjziGQO2xHwrfVNXaQhG+EYjfeeON02lpYPyMM0w7vda973aGNri7V8f9Wf1MenhPdM/75n/958mInZ+N+ce9733vawpV4Vp8bn28i9wnfNkG1OCMQgQhEIAIRiEAEInB8CSR8O778Sz0CEYhABCIQgQhEIAIRiEAEdiCQ8G0HQH0dgQhEIAJHmsBBFL4Nz2/EVHe7291u89I0BGMHvUII33h8Iy7i6Y3oiSBmHMPbGxGO8hG7nXrqqZOnLaI3nx22I+Hb6ho7SMI3dWUbXnkiGjMWJjC9733vu3Fh2GpKu/9W3t0viPf0OeXR/+aPu9/97jPit3vc4x6T6HST9xH5GFudfuxjH2ur0/mK6H0EIhCBCEQgAhGIQAQOKYGEb4e04sp2BCIQgQhEIAIRiEAEIhCBE4VAwrcTpaYrZwQiEIEILCNwEIVv47fZq2OTQpVlTI7lM3kmLCKAIS5yEuaMsszHzfOULSVtfTqEOT7bpEeq+fT3833Ct9U0D5LwbbF/jb8PUz+bpz3yv6yPzV93V5RPvye+I3hN+DZPv/cRiEAEIhCBCEQgAhE4vAQSvh3euivnEYhABCIQgQhEIAIRiEAETggCw1h2QhS2QkYgAhGIQAQWCBxE4dtCFg/Vn0N8M8RvRDCrjiF+I4Db9DaMq/JxrN8lfFtNcJnwzdabBI+HUei4urQn7rfD89xXv/rVhG8nbjOo5BGIQAQiEIEIRCACR4xAwrcjVqEVJwIRiEAEIhCBCEQgAhGIwFEjkPDtqNVo5YlABCIQgd0QSPi2G1q7u3aI4NYJdVd4o1onH3u9JuHbanJD+PaFL3xh9pCHPGR2xhlnzH70R390Er4RPHYcfgL6u21WbXVqm+Nrr712dq973Wt2/vnnz0477bTDX8BKEIEIRCACEYhABCIQgROUQMK3E7TiK3YEIhCBCEQgAhGIQAQiEIHDQiDh22GpqfIZgQhEIAKbIJDwbRNUT7w4E76trnPCt+uuu272t3/7t7MHPvCBs1NPPXUSvv3wD//w5Olvdej/+HZdIeUqEeWyOFZdv5ivZeFdM+LY7vvFeMb1i5/7ez/imI933fjmw6zzflkZxlan//AP/zD7zGc+M7vPfe4ze+ITn5jwbR2gXROBCEQgAhGIQAQiEIEDSiDh2wGtmLIVgQhEIAIRiEAEIhCBCEQgAv9BgDFsmeEqPhGIQAQiEIETgcAQvt1yyy2zxzzmMbOHPvShs3ve854zW292RGBdAoRvtnUl8PrSl740065OP/302Zlnnjm7733vO7vHPe5xQm/pOS98w+Okk06aRFGEb7vd6nSVkGudMe18+HWuX9YGdopj/vvF8OukuSq8+NaJYzHdneJcvH6nv5flQT/47ne/O/unf/qnqR/c7373m5133nnTfXWn+Po+AhGIQAQiEIEIRCACETiYBBK+Hcx6KVcRiEAEIhCBCEQgAhGIQAQi8J8EGMGWGa4CFIEIRCACETgRCBAoffjDH57ddNNNkycqopy73/3ua3uhOhEYVcb1CPzrv/7rtM3jN7/5zUn8c9ZZZ82c2hQx5W4FXuulejiu+s53vjP7/Oc/P7vhhhumDBMCYuJ1t+PQ7QRc68YzH37dMIuURxzbhR/fL4bb7vrF6/y9H3HMx7tdfPPXrPt+u3L8+7//+2x4fSOAI3B87GMfO3vwgx+8btRdF4EIRCACEYhABCIQgQgcMAIJ3w5YhZSdCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAKDwDe+8Y3ZtddeO/vyl788CZN4evuBH/iB6f124o4Rdq+vBCjzIpSRznjda7y7CbfbPIz8jtdlacn/fBl2SmO33y+mOdIar4vf+3unNJaF2ctnPF0N0Q/BD5HbOeecMzv77LMnz2YnuvDte9/73uQBjDc8Irh/+7d/mxjpa6vqby91UZg7E9AP7grO+oG01Os9f+ies//2oAfN/vt/P2N2//vf/86Z6pMIRCACEYhABCIQgQhE4FAQSPh2KKqpTEYgAhGIQAQiEIEIRCACEYhABCIQgQhEIAInIgFbMH7ta1+bfetb35qES4QbBCLORQ9diyKqdXgtxiH+u+KYT3e3ac6HlddV4YeYBptxDH4j7LhmvI7rvM6H8/e4Zj7N8dnita4fx2Kej6Wu5tMe8e/0OtIT1slr4IO2RD8nn3zy7Id+6Idmd7vb3XaK4kh/zwuYPnbrrbfOeMYjEhz1ulPB171uMZ7t2st28W13/Xy8I+w61+42nLhXxbvT9/Ppzb/fa57n41j3vfz794P/9QenPnDve997dr8fu9/k3W/dOLouAhGIQAQiEIEIRCACEThYBBK+Haz6KDcRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABG4jQIBDiPMv//Ivs+9///srRV63BepNBLYhQPjD2xXPgby8Eb0R5Q3x0TbBjvzHuOhrQxi4WODtBF/7wW0x7p3iXLx+5HUx3HbXjevH62I4ny+GXbxmt9+PtJa9zse9GO+y6xc/G+F3G1a40RdGHItx93cEIhCBCEQgAhGIQAQicPAJJHw7+HVUDiMQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIETlAAxh5Mox7lbcccJiq1iryBA5DNEP23leTuo+b41//72K3p3lAgMsdt4PUplqywRiEAEIhCBCEQgAhE4kQgkfDuRaruyRiACEYhABCIQgQhEIAIRiEAEIhCBCEQgAoeKwKIAZ/HvQ1WYMnsgCMwLfebfH4jMHedM1L+OcwXcxcnX/u9i4CUXgQhEIAIRiEAEIhCBDRBI+LYBqEUZgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgApsjkPBtc2yLOQIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQ2QCDh2wagFmUEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIbI5AwrfNsS3mCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEdgAgYRvG4BalBGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCKwOQIJ3zbHtpgjEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEYAMEEr5tAGpRRiACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiMDmCCR82xzbYo5ABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBDRBI+LYBqEUZgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgApsjkPBtc2yLOQIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQ2QCDh2wagFmUEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIbI5AwrfNsS3mCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEdgAgYRvG4BalBGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCKwOQIJ3zbHtpgjEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEYAMEEr5tAGpRRiACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiMDmCCR82xzbYo5ABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBDRBI+LYBqEUZgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgApsjkPBtc2yLOQIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQ2QCDh2wagFmUEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIbI5AwrfNsS3mCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEdgAgYRvG4BalBGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCKwOQIJ3zbHtpgjEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEYAMEEr5tAGpRRiACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiMDmCCR82xzbYo5ABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBDRBI+LYBqEUZgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgApsjkPBtc2yLOQIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQ2QCDh2wagFmUEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIbI5AwrfNsS3mCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEdgAgYRvG4BalBGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCKwOQIJ3zbHtpgjEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEYAMEEr5tAGpRRiACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiMDmCCR82xzbYo5ABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBDRBI+LYBqEUZgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgApsjkPBtc2yLOQIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQ2QCDh2wagFmUEIhCBCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIbI5AwrfNsS3mCEQgAhGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEdgAgYRvG4BalBGIQAQiEIEIRCACEYhABCIQgQhEIAIRiEAEIhCBCEQgAhGIQAQiEIEIRCACEYhABCKwOQL/Hw3R++Js/g5LAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "id": "f0eb170a",
   "metadata": {},
   "source": [
    "![qsp_circ.png](attachment:8960221c-ef2c-4bb9-89d3-22f8974aac03.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6537b3a9-7503-4542-8fbb-e8d887671b35",
   "metadata": {},
   "source": [
    "This operation has the following circuit complexity numbers:\n",
    "    \n",
    "A. $O(N)$ depth using generalized multi-controlled Ry gates\n",
    "\n",
    "B. No additional ancilla qubits required (total of $O(\\log(N))$ qubits)\n",
    "\n",
    "Note that this circuit can only create states for which all amplitudes are positive real numbers. To also include negative real amplitudes and complex coefficients, we need to add additional multi-control Rz gates, which fortunately does not change the overall $O(N)$ circuit complexity. See the full printed circuit with both multi-control Ry and Rz gates in the later part of this file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fbb223c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import Braket libraries\n",
    "import braket\n",
    "from braket.circuits import Circuit\n",
    "from braket.aws import AwsDevice\n",
    "from braket.devices import LocalSimulator\n",
    "\n",
    "import numpy as np\n",
    "import random\n",
    "import math\n",
    "\n",
    "# Import some helper functions\n",
    "from helper_functions import row_to_column_vector, nicer_array_display, generate_normalized_complex_array, generate_normalized_real_sparse_array, binary_to_decimal"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "185bd99d-7987-4799-ace7-f3411c2446b4",
   "metadata": {},
   "source": [
    "## Circuit Implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bb750cb-beb5-4c75-9acc-52f0a70d33f9",
   "metadata": {},
   "source": [
    "### Classical Part - Compute Angles"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae694d34",
   "metadata": {},
   "source": [
    "We first classically compute the amplitude rotation angles $\\beta$ for the Ry rotations using the equation:\n",
    "\n",
    "$\\beta_j^s = 2\\,\\text{arcsin}\\Bigg(\\frac{\\sqrt{\\sum_{l=0}^{2^{s-1} - 1}|a_{(2j-1)2^{s-1}+l}|^2}}{\\sqrt{\\sum_{l=0}^{2^{s}-1}|a_{(j-1)2^{s}+l}|^2}}\\Bigg)$\n",
    "\n",
    "These $\\beta$ angles are needed for the multi-control Ry gates, as it exactly appeared in the circuit diagram above.\n",
    "\n",
    "The letter $a_q$ is the amplitude of each basis (e.g., $a_0$ correspond to the amplitude of $x_0$, $a_1$ correspond to the amplitude of $x_1$) You can get it by calling `np.abs` on the complex number coefficient, as shown later in the `qsp_qubit_eff` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a3c18cb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_ry_rotation_angle(s: int, j: int, amplitude_array: np.ndarray) -> float:\n",
    "    \"\"\"\n",
    "    Function to compute a particular \\beta_{s,j} angle according to the equation above\n",
    "    \n",
    "    @param s: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param j: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param amplitude_array: the entire wave function array vector amplitude values to be encoded\n",
    "    \n",
    "    @return: a float/double value that holds the computed angle \n",
    "    \"\"\"\n",
    "    sum_top = 0.0\n",
    "    for l in range(0, 2 ** (s - 1) - 1 + 1): # compute the sum on the numerator\n",
    "        current_var = amplitude_array[(2 * j - 1) * 2 ** (s - 1) + l]\n",
    "        sum_top += current_var ** 2\n",
    "    \n",
    "    sum_bottom = 0.0\n",
    "    for l in range(0, 2 ** s - 1 + 1): # compute the sum on the denominator\n",
    "        current_var = amplitude_array[(j - 1) * 2 ** s + l]\n",
    "        sum_bottom += current_var ** 2\n",
    "        \n",
    "    if sum_bottom == 0: # edge case: arcsin denominator is zero\n",
    "        return 0.0\n",
    "    else:\n",
    "        return 2 * np.arcsin(np.sqrt(sum_top) / np.sqrt(sum_bottom))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "861dbf6f-b4bc-4983-b8f7-155a089edc61",
   "metadata": {},
   "source": [
    "If our coefficients $x_i$ are complex number, we need to compute the phase rotation angles $\\alpha$ for the Rz rotations, using Eq. 5 from Mottonen et al. 2004 (note that the index $s$ is replaced with $k$ to maintain consistency with the QML textbook). This is not covered in the QML textbook."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c885af6b-8c32-4d9c-9468-5c5c4f30f713",
   "metadata": {},
   "source": [
    "$\\alpha_j^s = \\frac{\\sum_{l=0}^{2^{s-1}-1}(\\omega_{(2j - 1)2^{s-1}+l} - \\omega_{(2j - 2)2^{s-1}+l})}{2^{s-1}}$\n",
    "\n",
    "These angles are needed for the multi-control Rz gates.\n",
    "\n",
    "The letter $\\omega$ is the phase of each basis. You can get it by calling `np.angle` on the complex number coefficient, as shown later in the `qsp_qubit_eff` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ceafbfd6-dc48-467e-a37e-8f44672a3a6b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def compute_rz_rotation_angle(s: int, j: int, phase_array: np.ndarray) -> float:\n",
    "    \"\"\"\n",
    "    Function to compute a particular \\alpha_{s,j} angle according to the equation above\n",
    "    \n",
    "    @param s: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param j: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param phase_array: the entire wave function array vector phase values to be encoded\n",
    "    \n",
    "    @return: a float/double value that holds the computed phase angle\n",
    "    \"\"\"\n",
    "    sum_top = 0.0\n",
    "    for l in range(0, 2 ** (s - 1) - 1 + 1): # compute the sum on the numerator\n",
    "        current_var = phase_array[(2 * j - 1) * 2 ** (s - 1) + l] - phase_array[(2 * j - 2) * 2 ** (s - 1) + l]\n",
    "        sum_top += current_var\n",
    "    \n",
    "    return sum_top / (2 ** (s - 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ec0d597-c3b1-44b2-b4af-9b791c0252bf",
   "metadata": {},
   "source": [
    "<span style=\"color:orange;\"> We note that the above two functions require the entire input wave function vector array to define the particular rotation angles. In practice, one could also utilize the tree structure to get a square root speed up on the classical pre-computing time. ($O(2^{2n}))$ to $O(2^n)$). \n",
    "    \n",
    "<span style=\"color:orange;\"> This speedup is not currently implemented since the majority of the CPU time are spent on the quantum circuit simulation rather than the classical pre-computation for small $n$. Once we get to the regime of say $n > 50$ (which is probably beyond the scope of classical simulation of quantum circuits), we can try to implement the tree structure approach once we can get a very good quantum hardware.\n",
    "    \n",
    "<span style=\"color:orange;\"> We note that in `QubitEfficientQSP.py` the functions uses Numpy's vectorization, which provides some constant factor speedup. We keep the original format here for better readability."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2ff615c-b25f-420c-b951-8e4a3955458a",
   "metadata": {},
   "source": [
    "### Quantum Part"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd1b265a-6a18-4cda-8d3f-6da644051162",
   "metadata": {},
   "source": [
    "#### Define Multi-Control and Multi-Anticontrol Ry gates"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "781f55de",
   "metadata": {},
   "source": [
    "Now let's construct the multi-control rotation gates.\n",
    "\n",
    "\n",
    "An easy way to define the open/close controlness is to use the binary representation. A binary 0 would mean an open control; a binary 1 would mean a close control.\n",
    "\n",
    "(Note that the most natural way of representing the open control as binary number is to use 0-indexing. Therefore the converted $j$ values are shifted down by 1.)\n",
    "\n",
    "We will need to \"sandwich\" the C-Ry gates with the corresponding x gates in order to realize the open control operations, as illustrated in the figure below."
   ]
  },
  {
   "attachments": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "1cc95efc",
   "metadata": {},
   "source": [
    "Whenever there is an X gate before and after the control, this would indicate switching from close control (conditioned on 1) to open control (conditioned on 0):\n",
    "\n",
    "![anti_control_equivalence.png](attachment:aae9b5e1-a1c4-4e9b-beaa-bd8b3afc03a9.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8b5b7f3c-a592-4412-bed6-0927bdb087f0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def x_gate_sequence(s: int, j: int, n: int, circ: braket.circuits.circuit.Circuit):\n",
    "    \"\"\"\n",
    "    Function to add x gates to help emulate the anti-control operations\n",
    "    \n",
    "    @param s: as it appear in the equation above\n",
    "    @param j: as it appear in the equation above\n",
    "    @param n: total number of qubits for the state being prepared\n",
    "    @param circ: quantum circuit to operate on\n",
    "    \"\"\"\n",
    "    binary_j = bin(j - 1).replace(\"0b\", \"\").zfill(n - s) # get the binary representation of the current j\n",
    "    for i in range(n - s):\n",
    "        if int(binary_j[i]) == 0:\n",
    "            circ.x(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d882e4-b829-4c77-9ba6-9a2783d93506",
   "metadata": {},
   "source": [
    "Now let's merge the x gate sequence and the buildin multi-control Ry gate together to form a full multi-control rotation gate, depending on the particular $s$, $j$ values (which offers the $\\beta_j^s$ and $\\alpha_j^s$ values for the rotation angles, and the entire wave function vector array (here we divide into `amplitude_array` to hold the real values and `phase_array` to hold the complex angles):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "db00f8b7-d0aa-4026-8177-929d69515a28",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def full_multi_control_rotation_gate(s: int, j: int, n: int, circ: braket.circuits.circuit.Circuit, amplitude_array: np.ndarray, phase_array: np.ndarray, tolerance = 1e-10):\n",
    "    \"\"\"\n",
    "    Function to perform a full multi-control rotation gate based on the s and j values, will anti-control conditions included\n",
    "\n",
    "    @param s: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param j: as it appear in equation 4.30 in the ML with QC book\n",
    "    @param n: total number of qubits for the state being prepared\n",
    "    @param circ: quantum circuit to operate on\n",
    "    @param amplitude_array: the amplitude value vector for wave function array vector\n",
    "    @param phase_array: the phase value vector for wave function array vector\n",
    "    @param tolerance: a float number to determine if a number is close enough to zero in order to be treated as zero\n",
    "    \"\"\"\n",
    "    ry_rotation_angle = compute_ry_rotation_angle(s, j, amplitude_array)\n",
    "    rz_rotation_angle = compute_rz_rotation_angle(s, j, phase_array)\n",
    "    target_bit_index = n - s\n",
    "    control_qubit_list = list(range(target_bit_index)) # get the control qubit list\n",
    "    \n",
    "    if np.abs(ry_rotation_angle) > tolerance or np.abs(rz_rotation_angle) > tolerance: # the tolerance are set to eliminate the rotation gates when the rotation angle is very close to zero\n",
    "        x_gate_sequence(s, j, n, circ) # insert x gate if anti-control\n",
    "    if np.abs(ry_rotation_angle) > tolerance:\n",
    "        circ.ry(angle=ry_rotation_angle, target=target_bit_index, control=control_qubit_list)\n",
    "    if np.abs(rz_rotation_angle) > tolerance:\n",
    "        circ.rz(angle=rz_rotation_angle, target=target_bit_index, control=control_qubit_list)\n",
    "    if np.abs(ry_rotation_angle) > tolerance or np.abs(rz_rotation_angle) > tolerance:\n",
    "        x_gate_sequence(s, j, n, circ) # insert x gate if anti-control"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fcf0f56-a75c-49de-a8bd-a31ed13a4c03",
   "metadata": {},
   "source": [
    "#### Call Implemented Gate Function to Form QSP Circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "294cd9ff-2762-4195-a878-54b648503336",
   "metadata": {},
   "source": [
    "With the full multi-control rotation gate defined, we can now construct the whole QSP circuit using the circuit:"
   ]
  },
  {
   "attachments": {
    "0f35cc10-6af4-4ab6-a904-7c0a2fb9e5d1.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "39503b77-53b4-436e-b8c6-e2d5a117a1b5",
   "metadata": {},
   "source": [
    "![qsp_circ.png](attachment:0f35cc10-6af4-4ab6-a904-7c0a2fb9e5d1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6efccd6f-bcd2-4907-886b-f4efd813096b",
   "metadata": {},
   "source": [
    "We can create a nested for loop. The outer layer loops over the lower index $s$ (in descending order starting from $s=n$ to $s=1$), so that after each iteration, a state on $n-s+1$ qubits has been created. The inner layer loops over the upper index $j$ (which iterates through all $2^{n-s}$ multi-control rotation gates acting on this particular qubit, again in descending order staring from $j = 2^{n-s}$ to $j = 1$), as shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e9cbdbec-94a4-4a24-b683-66a2bfd76e01",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def qsp_qubit_eff(normalized_complex_array: np.ndarray) -> braket.circuits.circuit.Circuit:\n",
    "    \"\"\"\n",
    "    Function to construct the full QSP circuit using the full multi-control rotation gate\n",
    "    \n",
    "    @param normalized_complex_array: the entire wave function array vector values (can contain complex numbers) to be encoded\n",
    "    \n",
    "    @return circ: the constructed quantum circuit\n",
    "    \"\"\"\n",
    "    amplitude_array = np.abs(normalized_complex_array) # get the a values as shown above\n",
    "    phase_array = np.angle(normalized_complex_array) # get the \\omega values as shown above\n",
    "    \n",
    "    array_len = len(normalized_complex_array)\n",
    "    assert array_len > 0 and (array_len & (array_len - 1)) == 0 , \"wave function array needs to have length as power of 2, consider padding it with zeros\"\n",
    "    l2_norm = np.linalg.norm(normalized_complex_array, ord=2)\n",
    "    assert abs(l2_norm - 1) < 1e-10, \"wave function array needs to be normalized\"\n",
    "    \n",
    "    circ = Circuit()\n",
    "    \n",
    "    n = int(math.log2(len(normalized_complex_array)))\n",
    "    for s in range(n, 0, -1): # as it exactly defined in the figure above\n",
    "            for j in range(2 ** (n - s), 0, -1):\n",
    "                full_multi_control_rotation_gate(s, j, n, circ, amplitude_array, phase_array)\n",
    "    return circ"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e36bc19-91c0-439f-9a50-6d2b18d793af",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Classically Generate Random State Vector Array"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a268dc6-59bc-41b9-9db3-353db9e51f11",
   "metadata": {},
   "source": [
    "In order to define the QSP circuit, we would first need to specify the target state vector $|\\psi\\rangle$ we want to get, expressed in the 1D-array form $[x_0, x_1, ..., x_{2^n - 1}]$.\n",
    "\n",
    "Let's generate a random normalized state vector array of size $2^3 = 8$ using the helper functions.\n",
    "\n",
    "You can change `n` to a larger `int` number and see what happens for states on a larger number of qubits!\n",
    "\n",
    "We will display the vector values in a column with all values rounded to 3 digits, using the helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "45bec1e7-246f-4d84-b2f1-f9c8196a1859",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def generate_normalized_complex_array(n: int) -> np.ndarray:\n",
    "    \"\"\"\n",
    "    Function to generate a normalized random complex-valued vector\n",
    "    \n",
    "    @param n: total number of data qubits\n",
    "    \n",
    "    @return normalized_v: an array of size 2^n that holds the generated nomalized complex vector\n",
    "    \"\"\"\n",
    "    array_length = 2 ** n\n",
    "    # Generate a complex array with random complex values that may contain negatives\n",
    "    complex_array = (np.random.rand(array_length) - 0.5) + 1j * (np.random.rand(array_length) - 0.5)\n",
    "\n",
    "    # Normalize the complex array\n",
    "    normalized_complex_array = complex_array / np.linalg.norm(complex_array)\n",
    "\n",
    "    return normalized_complex_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9419a7bb-7190-4895-9779-dea78feb57ab",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.222-0.271j]\n",
      " [-0.392-0.337j]\n",
      " [ 0.109+0.152j]\n",
      " [ 0.204+0.371j]\n",
      " [-0.001-0.406j]\n",
      " [-0.225+0.01j ]\n",
      " [-0.247+0.256j]\n",
      " [ 0.213+0.092j]]\n",
      "CPU times: user 2.64 ms, sys: 1.95 ms, total: 4.59 ms\n",
      "Wall time: 5.59 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "np.random.seed(10) # fix a seed for data reproduction purpose, you can change this value to play with other results\n",
    "n = 3 # number of qubits. We can encode 2^n number of values with n qubits!\n",
    "normalized_complex_array = generate_normalized_complex_array(n)\n",
    "print(nicer_array_display(normalized_complex_array, 3)) # use nicer_array_display() function defined in helper_functions.py to make the array look nicer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21a9c33b-49ce-44ba-9bb9-30ecd68a41f9",
   "metadata": {},
   "source": [
    "#### Construct QSP Circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee58d6ec-08e4-482e-a188-56e6ecc08ab1",
   "metadata": {},
   "source": [
    "With all components prepared, we can call the default circuit construction methods to act on an empty Braket circuit, using the same `qsp_qubit_eff` function. Notice that there is another layer of multi-control Rz gate added on top of the multi-control Ry gate to pump in the phase values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f3cc6403-53cd-43ea-9a63-1ee1e12d88b3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T  : |   0    |   1    |   2    |   3    |4|   5    |   6    |7|   8    |    9    |10|   11   |   12   |13|   14   |   15   |16|17|   18   |   19    |20|\n",
      "                                                                                                                                                         \n",
      "q0 : -Ry(1.36)-Rz(1.39)-C--------C--------X-C--------C--------X-C--------C------------C--------C--------X--C--------C--------X--X--C--------C---------X--\n",
      "                        |        |          |        |          |        |            |        |           |        |              |        |            \n",
      "q1 : -------------------Ry(1.48)-Rz(0.61)---Ry(1.28)-Rz(2.67)---C--------C---------X--C--------C--------X--C--------C--------X-----C--------C---------X--\n",
      "                                                                |        |            |        |           |        |              |        |            \n",
      "q2 : -----------------------------------------------------------Ry(1.16)-Rz(-1.93)----Ry(1.01)-Rz(4.67)----Ry(2.31)-Rz(0.12)-------Ry(1.95)-Rz(-1.55)----\n",
      "\n",
      "T  : |   0    |   1    |   2    |   3    |4|   5    |   6    |7|   8    |    9    |10|   11   |   12   |13|   14   |   15   |16|17|   18   |   19    |20|\n"
     ]
    }
   ],
   "source": [
    "initialized_circ = qsp_qubit_eff(normalized_complex_array)\n",
    "print(initialized_circ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21ee8e06-5d44-4c65-9ba8-40d2d63793ff",
   "metadata": {},
   "source": [
    "## Algorithm Demo - Circuit Execution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b62d719",
   "metadata": {},
   "source": [
    "Now let's test our constructed circuit!\n",
    "\n",
    "We execute the constructed circuit using the Braket's local simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "17ee5e58-cc91-4e66-a23e-2d8c43fc573d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "This program uses OpenQASM language features that may not be supported on QPUs or on-demand simulators.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.109-0.333j]\n",
      " [-0.488-0.172j]\n",
      " [ 0.157+0.102j]\n",
      " [ 0.324+0.272j]\n",
      " [-0.148-0.378j]\n",
      " [-0.206+0.091j]\n",
      " [-0.137+0.328j]\n",
      " [ 0.232+0.008j]]\n",
      "CPU times: user 62.1 ms, sys: 6.27 ms, total: 68.3 ms\n",
      "Wall time: 73.6 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "braket_device = LocalSimulator() # define the simulator\n",
    "initialized_circ.state_vector() # convert the circuit to state vector\n",
    "braket_state_vector_result = braket_device.run(initialized_circ, shots=0).result().values[0] # extract the result\n",
    "print(nicer_array_display(braket_state_vector_result, 3)) # print out the resulted state vector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e90b18f3-da9f-4837-90f4-a0f3d7ece345",
   "metadata": {},
   "source": [
    "Notice that the circuit state vector output looks very different from the generated vector input. Why is this the case? This is because we have a global phase difference! In other words, instead of having the exact state $|\\psi\\rangle$, we instead have $e^{i\\theta}|\\psi\\rangle$. This additional global phase does not carry any physical meaning, nor does it affect the final measurement results on the real quantum computer."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f24af72-935f-453a-b527-74e271924bb7",
   "metadata": {},
   "source": [
    "We can perform the test below to see if circuit state vector result is the same as the input vector but only with a global phase difference. For the circuit state vector result $|\\psi'\\rangle = e^{i\\theta}|\\psi\\rangle$ and input vector $|\\psi\\rangle$, we should expect $|\\langle\\psi'|\\psi\\rangle| = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5f68e2bf-31cd-4e9e-b92b-c77d8629caf1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.0000000000000002\n"
     ]
    }
   ],
   "source": [
    "print(np.abs(np.dot(normalized_complex_array, np.conj(braket_state_vector_result))))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2cff8e55-a9b7-4529-982a-889e4dabae70",
   "metadata": {},
   "source": [
    "We can also try to compute the phase difference $\\theta_i$ between each pair of basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "dc768c43-0066-49e3-ab6c-59d6a8a9b7b0",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.37114178 0.37114178 0.37114178 0.37114178 0.37114178 0.37114178\n",
      " 0.37114178 0.37114178]\n"
     ]
    }
   ],
   "source": [
    "phase_v1 = np.angle(normalized_complex_array) # use python broadcasting to compute each phase\n",
    "phase_v2 = np.angle(braket_state_vector_result)\n",
    "\n",
    "# Compute the global phase difference between v1 and v2\n",
    "global_phase_difference = phase_v1 - phase_v2\n",
    "global_phase_difference = (global_phase_difference + np.pi) % (2 * np.pi) - np.pi # convert to the same number with modular on each phase\n",
    "print(global_phase_difference)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c532491-11a3-44ee-af32-f82c64f4c152",
   "metadata": {},
   "source": [
    "You can see that all the phase differences are the same across all values (and thus a global phase)!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1979c60b-4c01-444c-8729-585a663c5f23",
   "metadata": {},
   "source": [
    "Now we can add the phase correction to the circuit state vector output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "18dd8e16-4e06-46a7-a087-caa913298675",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.222-0.271j]\n",
      " [-0.392-0.337j]\n",
      " [ 0.109+0.152j]\n",
      " [ 0.204+0.371j]\n",
      " [-0.001-0.406j]\n",
      " [-0.225+0.01j ]\n",
      " [-0.247+0.256j]\n",
      " [ 0.213+0.092j]]\n"
     ]
    }
   ],
   "source": [
    "global_phase_corrected_braket_state_vector_result = braket_state_vector_result * np.exp(1j * global_phase_difference[0])\n",
    "print(nicer_array_display(global_phase_corrected_braket_state_vector_result, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60120267-856d-4dab-95b1-eeb64c075677",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Compare Diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "427d2802-9d84-496e-8209-ac15d1018e78",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.77555756e-17-5.55111512e-17j]\n",
      " [ 1.11022302e-16+0.00000000e+00j]\n",
      " [ 6.93889390e-17+1.11022302e-16j]\n",
      " [ 0.00000000e+00+0.00000000e+00j]\n",
      " [-3.75133952e-17-1.66533454e-16j]\n",
      " [-8.32667268e-17+2.42861287e-17j]\n",
      " [-5.55111512e-17-5.55111512e-17j]\n",
      " [ 0.00000000e+00+1.38777878e-17j]]\n"
     ]
    }
   ],
   "source": [
    "print(row_to_column_vector(global_phase_corrected_braket_state_vector_result - normalized_complex_array))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaa5bac7",
   "metadata": {},
   "source": [
    "The result matches perfectly with the desired output!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4bbd236-83c8-4013-9ccd-82b66544835a",
   "metadata": {},
   "source": [
    "### Reference\n",
    "\n",
    "[1] Schuld et al. (2021) Machine Learning with Quantum Computers\n",
    "\n",
    "[2] Mottonen et al. (2004) Transformation of Quantum States Using Uniformly Controlled Rotations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cc354681-f07c-4efd-b62b-eceded57ec10",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.55.0'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import braket._sdk as braket_sdk\n",
    "braket_sdk.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8b8725a4-2e69-4e53-9c5f-479b973c0bec",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.10.11 (main, May 17 2023, 14:30:36) [Clang 14.0.6 ]\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "print(sys.version)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f0fe16f-4718-41b4-a8b3-394d22095bee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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