{ "cells": [ { "cell_type": "markdown", "id": "63434aed-ab9d-445b-8b2d-6911cf90fbc5", "metadata": {}, "source": [ "# 07-Finance Tutorial-Pricing Asian Barrier Spreads\n", "### Modified for Quantum Rings toolkit for Qiskit 2.x" ] }, { "cell_type": "code", "execution_count": 1, "id": "1b3a0b8b-6bbf-455a-9baa-57297d7d9b64", "metadata": {}, "outputs": [], "source": [ "# this example is at:\n", "# https://qiskit-community.github.io/qiskit-finance/tutorials/07_asian_barrier_spread_pricing.html\n", "\n", "# Modified for use with Quantum Rings toolkit" ] }, { "cell_type": "code", "execution_count": 2, "id": "0bd3f7c6-39db-4c79-99a8-c3567d83baf3", "metadata": {}, "outputs": [], "source": [ "#\n", "# Setup your account\n", "# You can also save your account locally using the class method QrRuntimeService.save_account(...) and\n", "# invoke the QrRuntimeService class constructor without any arguments.\n", "#\n", "import os\n", "my_token = os.environ[\"QR_TOKEN\"]\n", "my_name = os.environ[\"QR_ACCOUNT\"]\n", "\n", "#\n", "# Set the backend of your choice, depending upon the task and your hardware configuration.\n", "# See SDK documentation for additional help.\n", "#\n", "\n", "my_backend = \"scarlet_quantum_rings\"" ] }, { "cell_type": "code", "execution_count": 3, "id": "27a80324-8468-497d-85b2-6aee55a1aae5", "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "from scipy.interpolate import griddata\n", "\n", "%matplotlib inline\n", "import numpy as np\n", "\n", "from qiskit import QuantumRegister, QuantumCircuit, AncillaRegister, transpile\n", "from qiskit.circuit.library import IntegerComparator, WeightedAdder, LinearAmplitudeFunction\n", "from qiskit_algorithms import IterativeAmplitudeEstimation, EstimationProblem\n", "#from qiskit_aer.primitives import Sampler\n", "from qiskit_finance.circuit.library import LogNormalDistribution\n", "\n", "from quantumrings.toolkit.qiskit import QrRuntimeService\n", "from quantumrings.toolkit.qiskit import QrSamplerV2 as Sampler\n", "\n", "qr_services = QrRuntimeService(name = my_name, token = my_token)\n", "qr_backend = qr_services.backend(name = my_backend, precision = \"single\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "d9be3d71-56ca-43be-9819-6842ec0c3741", "metadata": {}, "outputs": [], "source": [ "# number of qubits per dimension to represent the uncertainty\n", "num_uncertainty_qubits = 2\n", "\n", "# parameters for considered random distribution\n", "S = 2.0 # initial spot price\n", "vol = 0.4 # volatility of 40%\n", "r = 0.05 # annual interest rate of 4%\n", "T = 40 / 365 # 40 days to maturity\n", "\n", "# resulting parameters for log-normal distribution\n", "mu = (r - 0.5 * vol**2) * T + np.log(S)\n", "sigma = vol * np.sqrt(T)\n", "mean = np.exp(mu + sigma**2 / 2)\n", "variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)\n", "stddev = np.sqrt(variance)\n", "\n", "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", "low = np.maximum(0, mean - 3 * stddev)\n", "high = mean + 3 * stddev\n", "\n", "# map to higher dimensional distribution\n", "# for simplicity assuming dimensions are independent and identically distributed)\n", "dimension = 2\n", "num_qubits = [num_uncertainty_qubits] * dimension\n", "low = low * np.ones(dimension)\n", "high = high * np.ones(dimension)\n", "mu = mu * np.ones(dimension)\n", "cov = sigma**2 * np.eye(dimension)\n", "\n", "# construct circuit\n", "u = LogNormalDistribution(num_qubits=num_qubits, mu=mu, sigma=cov, bounds=(list(zip(low, high))))" ] }, { "cell_type": "code", "execution_count": 5, "id": "3bf78488-876a-40e2-97b6-5b304bb01194", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "<>:13: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:14: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:15: SyntaxWarning: invalid escape sequence '\\%'\n", "<>:13: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:14: SyntaxWarning: invalid escape sequence '\\$'\n", "<>:15: SyntaxWarning: invalid escape sequence '\\%'\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_45424\\2770547151.py:13: SyntaxWarning: invalid escape sequence '\\$'\n", " ax.set_xlabel(\"Spot Price $S_1$ (\\$)\", size=15)\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_45424\\2770547151.py:14: SyntaxWarning: invalid escape sequence '\\$'\n", " ax.set_ylabel(\"Spot Price $S_2$ (\\$)\", size=15)\n", "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_45424\\2770547151.py:15: SyntaxWarning: invalid escape sequence '\\%'\n", " ax.set_zlabel(\"Probability (\\%)\", size=15)\n" ] }, { "data": { "image/png": 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l9VB6SG3Tu3fvbf5fyCTRNhTL9SCoxaw7TQSyJo24OqA8mnWnGdcg33kaTdLIc4NLBpWHdtxxR0caHRwsgCOJDg4G9GKF+W769OlyxBFH+FpIWZTJh4eKg3k5WXBBqrJ8hUASbeiDrYjyuuDWMHDgQNXMutNsXAigQsUjEIafRFXnq+50ImlEtScJOX/zHEJundLo4JA/OJLo4JAi96EfsBAvWrRItZ122kklUPZalq/QCJoNfXBIX3eaTdDy5ctl9erVquIPYx91USuNkMZ8qIzaT1LnYdSv6WeTps/JJI06etrBwSFYOJLoUPRIlvtQ+2/xd6IvVyLw/2KhRa3Za6+92k15qWAjSQwqiMEt1PaDe0T6JSKnURYZs0RLa/P00qVL1fvMyGkiqaO4t8nGoQ5yMd+jSaNWGvUzmxg97eDgkBscSXQoaqTKfeg1OTVVUyCI+B3uvvvunkrrcexCNTcDG/oAbCQJNvXJLMsHCaQNHTpUvU5UPgQS/0DUcZ4LTRrDrDutMwikgx/SaEZP23TtHRziAkcSHYoWLCwsKslyH+qFKhWZ4/WPPvpIPv74Yxk7dqwy43ldhDi2bUpikH1wSI583xs/Zfl03elhw4apsQ5pRGU0606bpLFz586B3PtsFG2TNOpzSkYaE30a3Vh1cMgMRxIdita8zCKSKvdhOiURfy6CU1iI9tlnH6XA+IGN5uYgYUMfbOyLjfBClHg+cKGgkc6JcU+wC0rjmjVrZP78+e11pzVxhDTmw+3BrDmtj2duCFOVEHSk0cEhORxJdCgq+Ml9mCwKGUd/0tsMGjRIldbL5K9YbCTRLbTxQbZjhedCK4gjR47cpu70qlWrVJ5GUvLo9/ipOx10gu90pBHCCHHU5+RIo4NDRziS6FAUMP2WTF8sr6SLhXDevHlqERw/fnx7PrpsYJtPIilHWBSzVX8SkW+iajNsIx5B9CdZ3WlNGs2606Z5OlXd6bCqwCQjjTSdo5HmSKODQ0c4kuhQVKX1gNeasVpJxB8L8zILBrkPcyVTtiiJnBumQvwq+Z2FnIU+37WACxW2keewCBnPCYFcOok8GzNNGomcnjNnjoqu1oTRHGthk8REmHNBMtJI4/fNmzer6jY6EMZvgn0Hh7jCkUSHosl9aFZ58ArMyyxs5D2kCkQQCXxtCFwhXQ/EF+JMChQWPhZColkTawFDHJOVdbOdDNlgfrcZUV0biBXpdmiJdaeJnCb9Dn69jDWt5OULyUgjzwoZDPbff/9tfBo5L600OtLoUKhwJNGhaHIf+i2tx+cxl5HaRi9wQSDfSiIRqix6/fv3V5HZXB/OtW/fvqoBFkMIo1nWTSdbhjSmqtDhFsr4IGrVLl3daU0aKYXJMwsxM/M0ZuP7GwT09eEn/TaVRkof6v8l5mh0pNGhUOBIokPR5D70ChYsVDawyy67BEoQ80kSzbQ948aNU2l79OuJINAgWVk3iCOVOviMXsQhjZgPtQrj1LvUsI042NAfxhobFhrqHKSRccVzSBAMf5t1p/k9StJo5m5MZZ7medCkUVeLcaTRoRDgSKJD0eQ+zAQm+yVLlqg8cJiWURG9JMf2C/qkCWzQx01F0FjAIL6QZ79pe5KVdSPYRVfoWLx4cXvEKyoQ35UvlSoRjrDG69rQJ545vUEBeoNC03WnE0ljmHWc043lVKSR55vGs+BIo0Oc4UiiQ9HkPkwH1IrZs2cr/6jJkycrlWzFihWhLKRR+yRq8zLmPRTEXFUYvgdzM00nW8afkUWcCjSYp/E1yyYFSiHDRlJmG1FJRsgIFKORdspUtWmo2jz3PK9a2U7lCpEtGN9er5MmjWbdaZM0Jvo0mnWnbbsXDg7AkUQHKXbzMn5QkCgWmH333bc90jJZnsQ4mZvpO6oogTemeTnZ53KBLtlGI9BHB/iYKVDMaFZaGAqtgz/Yovb6KcuXTNXWdacxT+NKwWtmup1c6057KRWYDWlEEdX/T1Z32rZ741CccDO1Q6yh1cNszMsmidp5551lyJAh23w+3wEmuRzXj3k5yL7oBQ8/RTMFilZ+iJxGCdKR0zQ/kdMOha1s+iWuyepOJ7pC8B6TNGr/2TCUxGxJI4SR58QkjWbd6TDN6Q4O6eBIokMsoSdWHNuZTElR42ciN1PA7L333oq0JCIsJTFshRKTL8ooATd77LFH5KpdIvng/pjRrBBYvYhjmmZxxK9M52gMylxomxJjo3JnW39yJWTJXCE0acRiwCYF0mXmaESVTPeduSiJXvrrSKODzXAk0SG2uQ91aS2/Cwv1Zimtp1PApFKx4mZuBmvXrlVmN84LZTRqeLkPVVVV20ROk5NRk0ZtLjRN036VH4f4ktag+8QzzAaExkbS9J9lHiDan02UOd4Yn2YfglQScyWNqarBONLoEBYcSXSIZWk9bV5mgvRK5DBNozwSIUlqGx09mQpxMjejzkEOQSplNAr4PTfeDwmkQWq1uZBUO4nKj1Ya/VS8sdGkagtsvDZhE1fTf1bXndak0aw7bZqnw1QSsyWNzIEE1vHcQ34daXQIC44kOsQ6OIWfXtLJQDwwL/N+glMwMcWtxnIqaPMyiwPO/PkiiEHANBeayg+k0VzE9QIOcUxVB9ghMwpdScwE0/QMmEvYbNEgYdRrx8xLvwjKynekvkkasaLgNgOYG7XSyP9N0qijpx0csoEjiQ6xKq2XGJzC33pyTAYmd5RDImzxUdppp50877LDSlUTlBmbvhF4Q25HzMsob/leDIImwKbyAzC7UQcY0ohp2oychjDyPlsjp20z7xajkpgJkCqz7jTjjeAX3Dj0eGODafo05muTohVO013GtLaQL1aTSk0azehpBwcvsHM2dXDwWFovndrH55jUUdp222239pJzXmGzkoiKgDLKT21exmRm48IfJFjkzEXcjJzGvwzzm46cRmVxUdP2ErI49InxxiYEYkh5TsabLiEIedR1p80SgjqFVthgbkoc3zrIJR1p1MTSDISx6Zo72AVHEh1infswlSqH2gSJwgkd8zI/bU967RUohpwbRGnSpEntylm2xw1ygYi6LF+6yGmuk656oZVGFnTnr/U5bCMHtpFEYPokMt7MGucQL52jEf9ZgrAS0zuFpWx7CajxShoTfRptuwcO+YMjiQ6xzn2YSOT4nbyHqEqjRo1SLdsJz7YUOJwbCxEKRpR5HeMEM3JaL9os1jpyGuSSM6+QYONYsZUkpuoTpmZddxqg7OtNiq47HVZOUOYQv6qlSRr1/delTM1qMI40Omg4kuhgDXSqB5rX0nom4WKio7Teli1bZM8992x3Rs8WNkU3M4ETnIIJdcqUKSqlRxDHDRo29EFD+2JBpnXkNGPDzJmXmP7ET+R0tn2yBXEjZPmC3qx6AUEtAwYMUA3wvGrzNDlBmaMginqjwu/ZKtt++pUMZs1p4EijQzI4kuhgBZiYIId+S+tpkkggAyZYJl/My0E4k9uSJ9EsG4hfVCrzlQ3mZmALSUx2nok583BLSEx/olPt0IIMSrDxuti22NtKErPtk647rXOC6rrTEEcC6pjzIIp6vPlJJJ8rSfRCGnWDMEIcgSONxQVHEh3yCtNHRi8QficcnMdnzJghY8aMUaW5giyhlU8l0TQvezk3G1S8OC0WLHZm+hMWbK364LIwZ84cZY7WpNHmyOlskO+xEheSGFSfktWdNhPJU+ecuTCRNKb67qBJYrL+msQxkTSaSqMOguH58Fse1cFuFM6M5xD74BS/BJGABAgUO1wifJOZYHNBpvQ62cJL1LQX83I2xy1W8uEFLHCUMqQBxhWkEZXajJzWpDEXU6EtsG0xz2fi6qj7lCqRvLlRAWbkNIFX+p5Ffa3SkUaeDf0e/ub/KKg6sbdt48zBOxxJdLAu96EXkLcM/0NtngmaIIapzGWKmtam80zm5aD6qyf6IFBIiwGm5sTIae4NC3iiqRDimE71sRGFrNoFiajK8pmJ5LEamD60jLtFixa15w1lzOno5HwhFWkkCTlpx8aPH98eKGOapx1pjBccSXSwLvdhOvAZfMeWL1+uSuth5uDvMBC1TyKvsRDQsjGd22BuBjb0AQS9EBE5PWjQINVMU6FO7A30Ag5pxKxo9sE2AmTLfTJh2zXKp7qZzIdWk8Z169ap30mmz/gzA6/ydf1M0qhJoXYn0koj1zHRp9GRRrvhSKKDdbkP0/keorABglMw0xDUEZaJNcpk2qgCnJsf87KX40YN2yb7sK5HMlMhizYLNipKYuQ0pNFG2Hi/bOtTsqTV+QDzJco1bcSIETJ9+vT2fI1r1qyR+fPnK/XbrAYTdrR+MpjWoWRKI9cTdxqIoyON9sORRIdIoNMqZKMeAsx7BBKwIKOy6Z19mH54YSbTNvtsmpepDJNtxQZbSGK++5APmKoPC7gZOc3YRe3mPfwOgo6cLhRCZmufbPOT1P3CNI0P7ciRIxU502NO150265xHVXc6VUBNos+5Jo30m5YqECabYEaH4OBIokOoYBKAHNKy2SVilia/GD6IEydObPcPC5vIhUlAdZ9N8/Lo0aNVbelcJkNbCJoNfbApcpqE7ozjt956S72uI6cJQjBVn3xETher/1/c+5SMjDG/olhr1VrXOdeR02bdae0WEcZGxavyqsmfPgeTNNJ3/f9En0ZHGqOFI4kOoec+hOTx8I8dO9bXw71582alsDGR7bfffklL64XlNxiFkkjaHkzoe+21lzIhBXHcfBM0N3knh17kyJfHRkeXc6NhJkRFQYU0K3OErV7ZqtrZ2CcblcRMKXCS1TkncppmpngyNypB1J3ONjVPKtLIGkLfU5FGG+9NIcGRRIfQcx/yIPuJxOMz7Hwx0WFG2WGHHVJ+NkySGJaSCPnVu218K4OYmG0hicCGPtiOxHJuOsmyGTltlg8MI3LaxvtkI0mMi5KYCcnqTut0O7qEZRDqNkpgEKq4H9KozdOONAYPRxIdQiutB/RD7pVs8fC///77avLaY489Mjr8x0lJ5FjkdSQiEeB/GOTiY0PFFZsWU5v64rUyh46cRmHWpHHJkiXqXEzfssTI6UIhZLb2yUbikWsy7cQUT6jZmjSaeUE1YaR5MSOHleQ7E2lMVQ3GxnsXJziS6BBK7kPzYeZB9ULkmJwwLzMxYV724i9j+vcFvbgESUB1XWmS5UIOZ86cKUHDKYl29wV4GaO8B0WHRhokxiDjhgAnUp+wyWARNMsHJnPFCKo/UcJWkmhbn8IgrwS1mOo2JFFvVAiCYQ4zXSL4PRlpjCoaPBVpZA1KV0LQkUZ/cCTRIfTch5nMtmYAx0477aRygnmdlM3qA0FP5EGRLk1+8TPDvKyvRdB9toEk2riYxh06WbyOnE4WxQpJNEmjFxeGfI+VuBAyG83N2qUnzH4xpvCh1XWnTdKoXSISSSNjVafAiRrJSKMWLrTSyEaL50RXg9HR0w6p4UiiQ+i5D9Mpckw8KGz4ZGUTwKEnhDBMHLkqiVwbTIWYbohe1uRX73KDXqRtMDfbSj5sQFDXJVkUqy4fiDsD7hrat4z38Eyl8hGzbYG0kSTaaG7WYymq/I3ck0SXCHwYtXma4gasAZikeR3Tddi1pb302bw+9Bk/dyrB6HFG00qjGT3t8DkcSXQIPfdhKnMzpjMIItF3fsrPpSKJQSMXZU6bl0mwDPll8kzW5yAneVuUxHz3odiQrOa0rgTDopgqctrG+2QjScw32UkGPd/ls7qKTiY/ePDgbfxoCcwj8JBmBl+Zdafz1WeILG5MKO2m0qgDK7nPiYEwJZaNx6jhSKJD1uZlHb2cKfdhoiLH76hrlDIbN26c2plm+yCGTRKzOS6763feeUctzPhWJpr+TBO5LQSt2CfCYoichjRintaKD+RRL5a23H+b+mJzn/S8ZAt5Nf1oMUWTGxRztTZPo3DzHpM0QjCjvK6aFOqNeTKlMRlpLE/wabRtLIQNRxIdQi+tZ5JETBH45/H3PvvsoyaVXKBNBmEmvfZrXiawIJ1vpY0ksZD6YDPyscCkipwmVx6kcfXq1YFHTmcDPW5sW4Rt9Em0jSSa0ESMAEQaRQLMutOUUiXlDu8x0+2EPe70NUtlvTFJox6LrZ9Zy8xqMMVGGh1JdPAMrR76La2nSeKqVatUAlcWK0rrBWVqDZMkej0uEwm+YJhaJk+evI15udhIoi2wqS8g3/cmUfFB8da1gFm8deQ06qJZczqKUm42k0QbfRI1cbXtWqVyozHrTuv3MFcy7qg7jWXJrHVOC7rutClsZIK+rmWONDqS6OA/96Hf0np8HpMXZaEmTJjQbgaLQ2UUL8fV5mV2zUQvZ0rdE5b6aQNJBDb0wca+2AZtRtWLd7LIaaol6VJufiKns+0PsG2RtVVJtI24+ukb/9e5F3XdaU0aERPwpWVzYpqns03zlA1J9EIa2z5rEEYz5c5rr72mSOORRx4phQBHEh3SQvtomI7SfiZMTAwsNHx+//33D3x3GGZC7UzHZYLAZMcueMcdd1SLrJ/UPU5JdMg3Eu9XYuS0LuWm/cpQy3WCZW0mDMoiYCtJtFFJtLFPGtmkwDFNz/oYetyZaZ7McedX4eaYQSl9JcY6yDFN0vjII48of0tHEh0KGqYTr1/zsv48aRF4uAcMGKBMCmEQxDBJYjrSxXUhepnd75577tk+uQVx7DiTRGBDH2yFTQTIy31KLOWGaqKDEczIaZ2jUefKy6U/Nl0j4JRE/+tGrn2DeJl1p3WaJ+1Li9uSX4U7zCTfJQZpxOdXV7EpBDiS6BBIcIoJPstDzAM9adIkZX7FOT4sRK0kYo7DvIxflxfzsu0kUfvZ5GrO0X1wiA959nu/UG/Y9NF0gmWipnWuPMZStmlPbCWJNqp2NhLXMPM3JqZ5SqZw69yg2oydSBqjSvJdU1OTc0CmTXAk0SFlaT2/5BDw4BK9jNwOgWJR4aEJq75ymIEridVccjEvR0FssyGJRJtDeFFEuWdaEWKSzSZvpU1kyMZFtJBSu+gEy+TJM3PladLI4q19z/S44v2pvlOPG9sIma0pcGy7Trn6/flBosKtc4Oy/hA5zbxmukXgc6vNzWGjtrbWkUSH4iut5yf9SyKBMn02wphswwpcMXMw0titMgllY162UUlcu3atMpmjCu2yyy7Kf5QFHhKMQqTNiDQmXD9RgQ72I4zxpyOnzbQnjCncTebPn69U91SR07ZsLuJAyGzsUz5T8yTmBk3mFoGlhDWO8QhpDIsw1tTUqA13ocCRRAc1ObMT4wHSYf1+FnseQMgGD0ey9C9hVRgxjx+mkoh5mfPjwSc5djbmZZtIIu+BCKKKQg4hidx/VB7tS0M0eqIZUS/s6XLp2eIXqWFTX2wj0WErZGbaEx3BqiOnGVNm5DTjikXctrQuYW5uC5Uk6jUknzDdIvR8hoixfv16Ne6Y7xiX2mqiqxAFgRpnbnYoxNyHzz//vCJ4qEd+wEMHgeJhw7yczHk47iTx7bffVuooC11Qi0W+UuBA6N977z2lFO69995KIUzWj0QzYnV1tSKNibn0tNIYBHF2iB5Rkh8zcnqHHXbYxq9MmwgB4yvoyOlsYasJ3FaSGJXfn18wnzHXQQ533XXX9ipEOnoaC5omjTSvlpNEaJcLRxIdCir3oXbM9kNaeC+TOWrUzjvvLEOGDEm54IRZOk8fP+hjs4BhXgZMKnpHarOJPBNJZELE/5BJ0E+tbI6rqydQRUYrQpBG6rOS/1L7M0I+w8qjF3fYpmrmuz+JfmV6fPLskRXBVHv8uDwECVuDaWwlibb2KzEFDgo2TW+C2aBo0ki5WF7TATDbf0YavY4BRxIdYg8eZMih6WTsh2ixCyM4hWNoNSod9MMVFkkMWpXT0ctMIkBXCQgSUZqbzYCb0aNHK3+xXBa9xFx6LOYoQpBGGuOKSTefi7uDN9hEfiCNjK2xY8e2J+DXC3eukdPZwswPaxNsJWNhppkJq2/cWza5NMQObTkxU+4Ar3WnnU+iQ0HkPtR+NmZwiSaN6UAqGxS2gQMHKgXRy4SgfVS8HD+fSiLXBGUMR2cK1NOmTp0aeQ7GII8JkccdAOKbqVxgtsDUjC8jjYUeNZHv0Uoj0BGutHQRrkHCtoXdNtjma2f2J5naw8KtSaOOnE4s4xb0+dhqbrYxLY/N5mbgNbrZtJwMHTpUXWuz7vSiRYvao/YT651rc3Mm4SQZbr31Vvn1r3+t1tiJEyfK73//e9lrr72Svvehhx6Sa6+9VlnzWM932mkn+elPfyrf/va3299DXy6//HL5y1/+oggv/vR/+tOf1Hv9wJHEIs19mOggnolo8TnI08qVK2X8+PG+za9hRSAHdWzIFOSXiWCPPfZoV8nCLPkXtk8iE9usWbPU4pltPsdsgBnb9GfUEa6mP6MOgCkmf0YbSVlcro+5cOvIabP2r46c1uOKFkTNaZuVRNv6ZLPCCbJNgVNSUqJ89Wm42+iofV3vHAsNBI2MHvvss4/6Hr/m5vvvv1/OO+88ue2222TKlCly8803y1FHHaXW3GSJuRnnF198sRJqGPePPfaYnHHGGeq9fA7ccMMNcsstt8jdd9+t/OkvvfRS9T/cg/zkxHUksQjgJfdhOpLIDh7zMu+BbGgzrA3BJUEcm8UG87ImU+biEmai7jCVRJyxmQyYuAi6iWpBSSSq5gRr1gaGNOL7Qx91ElwmPhuCFYoJNhENPyQ6We1fbR7UfrLMU2bez2x8ZRMtLrbAVjJms7mZMRLEhrTUiNpnTkNguOaaa1TwJwofQAE89NBD5ZBDDlE/2dikw0033SRnnXWWInoAsvj444/LHXfcIRdccEGH9x988MHb/H3uuecqMvjqq68qIsi4hWhecskl8pWvfEW95+9//7tKEUTZwJNPPtnz+TqSWMDwk/swmbmZz0M2SBnAIEemznZistHcnMy8nHh9wkrpEpa5metAtRtMFrvttlt7UECUSHdeyfwZWdghjTqfGZOvmZ8xlwXaNrXMJtimbOaijiWWcdOR04wrM7myJo1e8+Q5xa5wzM1hEdjy8nI55phjVCPNDoGOf/3rX+Xll1+WP//5z/Ld735XKZAnnXSSMhEngjlwxowZcuGFF7a/xjU8/PDD5Y033vD0HENQmT9/9atfqddwx2AN4BgajHlUSo7pSKKD79J6iUQLYgnZwAcjCLIRppKYjenWNC9TOlAvLjbUhc4WECytjKKIhlUrOx38LqhmElwzWEErjcBMvhyVP6NDvElrsprTOu9nYp68dMFVtvr+2UoSbe1XVAS25jN/xCOOOKLd7ItpGoWPTUuqNHL0TScC1+BvovxTAYsMLj2MbcjvH//4R/W9QJfBTXZMvyVyHUksQOhavH4qp5hKH4MP8zILMs6uQfj22GRuTmdeTkSYSmKQ14PqKeQ/1KaOfJp8sr1eyYIVtD8j54fvD/fKTOodJ39G25S7YuoP44ZgO1riZsSMnNbjSkev2qwk2phqynaSGPa8WFNT06HQAKQRlTFocFzWMdzBnnvuOeXTiDUs0RSdKxxJLEDzso5e9lM5RZubkctZjFOZX20liV5M2VwTFgR2Z/gxkdA30/nZ7pNoVk8ZM2aM8sXK56IW5Hcn82c001KgdOPPaPqd2eoPZSNsM8VHRVrTRU5DGnX0KmNKV4GxDbaSsajqI9tMErv6TH/Tp08f1S8CsEzwd7oAUe4//uYAax8K+XXXXadIov4cx2BjZB6T9/qBI4kFnPvQb+1lIpc5ThC1iRPBQxAmSYQYp4NpPk9nXk6EzT6JidVTUEsgifle/MP6/kS/M9OfUSdf1mkptM+jQ3rYRIDypWymi5xGwWZcvf7669uk2wnCulKIJNHWfkUVVFNdXZ02h2IyYA0howZq4HHHHdfeV/4+55xzPB+Hz2iXI0QQiCLH0KSQMT1t2jT5wQ9+4OucHEks4NyHXqHNeUx8mJfDMGPk09ysU8GgCvg1n9vqk5iseoomytkcN8hyg1EhmT+j9jvDn5H7xnUh+CqsPHp+ke/vL1Zzsx+YkdP4LRIQQBJ6M3IaImCSRq/Vi4KC85W00yextrY2q2ormIpPO+00JdDgLkRkMqqkjnY+9dRTleqNUgj4yXuxhkEMn3jiCfnHP/6h8iACnqMf//jHcvXVV6uAU50CZ9CgQe1E1CscSSyQ0nrAL0HkgSbyDxMzEyLml7D8XPIRuGKal7NNBWObT2K66in6Zzb9Dar8WFjXy48JkaoJemzjFK7z6LE5MPPoxcmfMQzkW3G2lSQmI2OJkdM6qTdjjM0JKqQeV14jpwuRjOmNWbGam6urq7NKEUfkMzkXL7vssvbMFE899VR74AmbXvN+QyDPPvtstb6x+SVf4j333KOOo/Hzn/9cve973/uectPZf//91TH95EgEdt5NB1+5D3VFEz/ARElwCqYUTJUMTC1Vh4GwlcRklUbY8UMS/JiXbfZJNKunJHMJyIUkBol8f7++vkyeTNhUL9D+jCiN2p9RL+wQxygWdhuuSyJsImU2ksRkZIyNtK4wpOdSTRrxC2Ne1pHTuu5v0ITO1oCaoHIRxtXcXJND3WZMy6nMyy+++OI2f6MQ0tKB8fHLX/5StVzgSGIB5z5MBUzLkA0mOXwh2Pmxiwkrj2HU5mbMy5hiUY6IXva7cwq7Moo+rh/S4KV6ig0k0caFK5U/o5kSRS/sWmnMNT9jHGAbKbOtP177xPxiRk5jctSkEQWI10zTtF+ftbgpiTb2S6+bNpNEW+FIYgHnPkz2AONfg0S9yy67KP+EKEhcVMm0zeTfQVUaCbMsn9fjElCE8pXpnGwgiTZ8vxdAsnHsppn+jDTcL7iWZunAoHJO2kSCbLtPNpJEv4od74UE0nB70JHTjCuC5jBPsylPrDldKGTM1oorem2LIk9iV5/RzbbDkcQCzn2YOHgxLwOUqMSBHAVJDDsFDuoo5mUCOUgrEATCUhK9XA/OCX9Kv9VTnJLory/J/Bl1fsZEf0ZNHG3MURf3+2VjMEaufTIjp3XdX9xFUBlXrVqlNu3Z5P60lSTaWnFFCxRRKInbbbedFBIcSbQcWiZnodK1bf1O7FqJGjp0qAp2SPYQJyvLFxeSiC8l4f1cl1zNy7YoiZisMJnrc/KiNujAJb/9DZoo2KZQ5VKblahAXDt0vWnKXVGpJ5sSb7ZdF9uUO9v6E4bvn86/qP2JzbGlfWV15LSe75MFgthKEm3tl2l9CxO1tbUqCrmQ4EhiTMzL+AxCfvzkL9TBG3wW533taJ0MUSiJOgo7SGA6J9KXiXTy5MmBTwL5yJPI/SL/IT5ORK35Oads+xvHFDhRgbFl+jOyKdH5GRP9GWn4JMXhOjjSmn91M3FsYS3SCeOZ1wiKMQOsSCyvc87aSMZsNjfTr7DHV/VneRILCY4kWgpdOUVPBn6TUevSczo3YCZ1LW5KIn2FABOEQ2UYTLJhTJph5klMPK5ZPSXRZ9TPcfO9+Of7+8PuC+ZB059RBypof0ZTLQrSnzEM2ETKbCSJUUcRY2pOFTmNyshGmw0JawPjjt9tumbFbgavra11JNEh2tyH2v/QK0nk80TUYZ72Wnoubj6J7NYgwPiFQYDxA8GkHgbCTIFjVolJrJ6CepAN8k0S8/39USMxUMH0Z2TjwnPIBg2yyP/C3Ij5hW33yUaSmG8/yVSR06iNbCgXLFjQXmUoqMjpQvVJjELhrHHRzQ5R5D7UpMRMju1F6cNUgb8UKiKpbfyUJgsz+jhIskX0MgoiTuBE+nJcIlPDTNQdtrk5WfWUII7rYIc/ozYf8nyRxsj0Z2SBz+eiahMps5Ek2pSP0NyQQA6Z4+kfYyvIyOlCNjeHjRpHEh3CLq2XKno5E4ljoiB6GZ+VVHn08lVbOYjjm+blxEjffFRzCeq4mCdRBCidBPGNa8UTW77fNrBoE2lPI5oVNwKec5RGxjMk0qw3HaU/o22kzLb+2KAkplsvmFMZL8z5qSKntR97VFWGbDY3R5Esv7a2NmsrkK1wJDEmuQ9TkSw+v2jRItVyIRo2m5u1eZkFN5l/ZZjEJKzoZq0A0JJVT4krSbNpkbepLxos0gQpmP6MOqm36c+olcYwlSDbyLyNJNEmJTHxviWSsWSR01rF1pHTkEr9nlSR04Vqbo6iX9UucMUhrNJ6mXIfJjM347+m/dgoCp5LfiZbzc06fQ81iiHByR70sJXEoK8LPmvLli1Tv1NPM8jdfb5JIsj399vaF2A+46b5kPRUjGFcRRKVILPedND5GW0iQDaSRBuVRK+JoU0VW7sj6Y2pGTltpnLK5Vy5VjZeL+B8ErOHI4kxKa3He3jIzTQpJI9mAqA2ca47Qh4g/ZCHMVH7JXJcH9KLkMw4UyLpqOtC5wJNepmUuc5Bm3/yTRJtW+TjBMYa6g7N9Gc08zNiWjTrTee6qNt0v2zrD7CR9GRbPYS5pn///qoBfLk1aWRe0pHT2Zam1P0qVp/EtrY2RxId8ldaT5ubaURMokSNGzcusMSdesIJ62HyQ+RM87KXRNKayIWxyARFQBOrpzBBQ/SDRr5JIsj399sKv9clUQkiAl6bpnU6FAilXtT9+DPaeI9sJIk2BmIEVWKOeZVGqq1E1wfM08AcX1QkSnd/okpYbau5ua6uTl1HRxIdAst96GdCZKJCSZw2bZr6/D777BPoYNQTYViyvFdzthfzcrJjhzWhB0G6klVPgeSHFRDjlMTCBPkZzXQoqBY6PyNKI8+BWW/aS+Uhm+6XraqdjX0yM18EgUTXB+6FTuXEZpZoajNyOtn4iqo+sq3m5pqaGvXTkUSHnHIf6onQ7wOui8TzAI8ZMybwAW8SrTCQSZEzzcuZqsMkQl/LMMhRrkpiquop+Sr3FwXy/f02I8jKNixGNNOfkTlC+zOyGTHLu5n+jPoe2UYSbeqPzX0Km4hxzrg20EaMGKHmZ+0vy0bejJzW4ysb8aOQFOHq6mr1HUGWhbUBjiRGMDghh37Ny4nkiYkfuR8TcxjQO9N8kER2YChtvMdrneLEYwOblLlM1VPyUe4vjM8lO44tsKkvUfozAuYc7W9G/jxMYWaQgo1qh62RxLYpY/lQNyE/WkWkwpUZOU1UPgSJ9YnrtX79+lAip3MB62jQQV+pqq3YNl5yhT13sYBzH+rdqN8JELmf3IcMblQoHREbFsIszZeKJEJ+cchHDRk9enRWD1iYJDEbJdFL9RTbSGKhfH8iirUvLNAEe+mAL13eDaVRByno5PS8J9+VOmxV7Wwkrjb0KVnkNGOJTTE+88yBOsgqiMjpOJibqwsw/Q1wJDGC4BS/BJHPQwiR9JH6Ka1HRv2wS3qFHSVsHtsM5PBrXo5SBfVLerxWT7Glvw7FgcTybpgOZ8yYoZIvU8ZTK0VaacyHycxGkuiURO+R06iHbPqxBiWLnDbLB/qNnI5D4EpNTY0jiQ7B5j5MBj6LsoaUT2obEu9GUREl7FyJmiTqKDptXiYABzNFUMcPGl6Py3mxi/ZaPaVQfRLz/f0O3u6RfubGjx+vxqKu1IEaxOYNlw8zP2MUpkMbSaINql0cSGKi319i5LQOstLmaa6pWQkmU+R0XAJXulqgyAcNRxLzmPswERBDyBP+QlQWMXPohWkKNr8jTCURsNOkHBmpewjACWqyC7t8XjpwzzWx91o9pVDNzQ7pYdsCQn/MSh3a30ybphP9GWmYEcMgKTaSRKck5q7WJQuywpWKMaYjp3GpMklj0Ep2FIErNU5JdAg696H5eVJYMCHvuOOOysSc+PkoSGLYpfkABHHChAntCV2DQljKXKbjMtnNmjVL7Zr91MwuVJKY7++3GTZdl3R9SebPqPPnkcCfOcLMnxeUemIjSXRKYvD94j34KNJ05HQyJdskjbkGnURlbu5mYUBYrnAkMUfoXdFbb72l1D+/A1EHOWCCTVdazzTXhjVphWVu5twgUmDy5Mk5lQ+MmuCmUxJ1TkcmOsi9n/tik08iyhGmcl0CLtcJ2SYy5JAeXsYs4wKzoWk6hDTiJ83GVufP00oj+RwLhSQ6JTF8tY7P6LEDklUagnzpTQkbFL/f4wJXsocjiTmal3X0MhOn38WRVAEQRAY/BDOd30/YZfP0dwRNXAhM4SFngYFMZ7uA5NMnMfG+8j2kJdLVU9KVDPRz3HyQRAj8zJkz1e98DtKLOTFb06JNi7xNfbEN2eZJNE2HJLznWUAFYkFHBeK5wL9Mjx8/qVBsJIlOSYxerUsWOa2VbII5zchpr3NUVObmbk5JdEiW+1ArL153K3yeAAeiCseOHav88zJNRGZFlLAmiCCVRM4RswFqG87xAwYMCK3KSJRKYrLqKdkeN98kce3atWqTAoHHF43P6gmZpk2LpkrE+WYaqzYpiTb1BdhCOIK6LqY/I2DTrFUgfM3wZ/S6oNtIEm1UEm3sU5jkFRce1g8a0JHTemPC95o1p5OVp4xCSaz9LE9iIcAUpBxJDCD3oR6QXggWA4mFGZLpp7SefvjCTAoalJKoiRSASOlIyjB9HsMy35qKX6rqKXEjifwfMyGmHBJ9cz56TCeWftOVfjh3Njb8XxPGZL5Cti3yNsE2whrG/WI8mP6MyRZ07c9IM6NabSSJtiqJtvUpyjrX6SKnmdPMyGldPjAKn8Tq6ur2bCRxhSbTJq9xJDGL0nrAvIj89BJYok2vmmT4eaB0MEyYgSVBkDjTvJxIpMJOsRNW4Ap9JkFsquop2R43Hz6JkEGILhOrTvSt35+4SPM7/6eR0ofrYPoKYZpOjHp1gSvxQFSELHFBZyFlMTf9GfWGg/FlG/mxUbUrdHOzH6SLnMZSoiOntXsX+XjDcnmqqalR82QcoccUnIQ5nhgC1jvEAUcSfeY+1CkjEpGOJOrE0aR/0abXbBB2hHMuJI5rhL8IakGqc4wyWXdQ0BsDakqnqp4SFyWRyRP/QyZUVGy/ijTjj52y3i3jG5RomubYjCHUZC+maYf8IB9E3tx0JPNnZHxCHEn07defMSzYqm7aSBJt6FeyyGk2JAgXCBhYQ1Cvg4ycLgRzM9ft1VdflYcfflimT5+uspBAtIEjiQHlPkxF4Ng5Y3rl/6bp1cYUNdmam3k4KB/I9Up3jnEjiTwknBeAVAW5YIWpuCU7ro7EHjlypKrgE8TCl8w0zfewyE+bNi2jaboYYRPhyHdfEv0ZWZwYK8yjLOak3jGDqCCXUZMQG027NpCxVP2y7RlnTWMMAXLYmjWndeQ040qPw2wip+OeJ/Hll1+Wm2++WZ599lk1h2MBPPLII9VGjufOkcSAch8mkkQ+r6P9uNhU4cj1wY5CSfRLtFDYUJEwJ5EcO90DFheSaFZPwXzAZBK0ohEWSUw0u2uFF/KWbSS2H5UIwoiJAlKdyTQd9kJn2+JuE2xUyACLtI5qNf0Zly9f3h5EpX3Nwq7SAZy52TtYm/JRzjETzOpniT6zWEO0P6OOnEaF1OOsh495Kq7RzSeccIJat3/4wx/KAQccoIQEgmn1uTiSGFBpPZPAsVthUUTmpn6vnvRyRdgkkePzkPg1L+vgBy/Htz1wRVdPYdJg54katmjRIgmLzAW9WCt3iLrlMvedJuk/pI98tHBhe5BUEOUPvXw/55RomtYJmc0ABr9R09nAFv9IW/pha39A4rOQzJ/RzM+oq3RopToMXzNblUTbFDvbyWsq8YIxoyOnGWNmzWm9Melp1JxOFjkdd5L461//WrlSjR49eptz03mZHUlMk/vQT+UUTeDwscG8zIJM7sMgJ64wAz/08b0QLR4kzpH3Qj68SuxhBt4EEbhiVk/RZREhNyAMMhfGcSsaqmX0mPWyYMkGufCcZtl++xIZPrJKNq18S4aN7CNDRg2Wnr16SphIdh8SEzKz4LPY41zuJWraIXjYRn7SPQvJgqh0lQ5Sa+FDxTxkJlzOVf3XmzjbiI+tZMzmfnkxIeua5jSUNDNx/KefmadNFwma3tzyXtyusiGJt956qyJq+ExOnDhRfv/736vCGsnwl7/8Rf7+978rIQPssccecu21127z/tNPP13uvvvubT531FFHyVNPPZX0mKeddlqHTZEZe+FIYkCl9Xg/Cx6TFT5fSLZBT8JhKnFeSSjniHmZnVc2Edq2mptTVU/RD0rQ6R1Mkhgkei+YLiXjh8no0SVy42/K5eKLmmXWjDrVRNaIyBzZbrsSGT6iUoaN7C7DRvaWISMHSveeW/12coWXMW8u+Nq53ExhkQ/TdLERMxvNzX76ZFbpYL5l7tam6aD8GbNNOB42bCSuUeUijLJfyRLHb9myRY0x3KzIeIEvH6TyoIMOUpsWvyTx/vvvl/POO09uu+02mTJlijoehA4rHZHYiXjxxRfllFNOUb7/bLx/9atfKf9B5kyIrcbRRx8td955Z/vfmcQq/ewlG1eOJH42iJhkMgWnpAIJiBk8HAcTpXbEDhpRmJtTES1e56Fg1070shfzsp/j54skZqqeEhaZC+O4zY2N0rl6jZSUbE3D0KdPqfz25gq5/LImWbv28/dt2tQm771br5rIOhGZJ4jBw0Z0kmEjusnQ4dvL4BH9pXe/PlJa5n8x8ntOjAuzwkIm03QUZvNiMO/ahlxMuyjPLKp6YcXaoRUg059RK41e/Bn1PbONkNms2BVyap5SI3IaEYjjojROnTpV/va3v6nx9s1vflOOPfZYOeyww+Tggw/OyAVuuukmOeuss+SMM85Qf0MWH3/8cbnjjjvkggsu6PD+f/7zn9v8/de//lUefPBBee655+TUU0/tYEb3inTPQlGTxMTch9kQRExm5J3jc+RpCosg5tPcbJqX2cFkG8Flm5KYmPQ7WfUUU0kMEkEfl3NZ/fS9MnTYtqbkLl1K5LrrK+Sm3zTJnDmpP19TIzJ3TqPMnfOJiNAWCj7ow4ZXyLARXWXIiO1lyPB+0ndgPykrT70rD0J1STRN6927X9O0bQqQTYi7kpgJPMsoK9psaCaF17nzzI0HriWJ0M+mbdfJRj9J20liGApnWVmZfPGLX1SN72A8/eIXv1Cm4IsvvlipgZMmTZIvfOELcsUVVyQVl2bMmCEXXnhh+2tcv8MPP1zeeOMNz/M+Apeue20qjmyY6NOhhx4qV199ddaJvsuLPTjFnAj8PHh8DufpJUuWqKheFrKwkQ9zszYv9+/fX5UQzOVhs6niiq6ewm6L80o1ucVBSdTnsvvsd6XTybt1+H95eYmc//MK+fvdLfL8896vEe6Y8z9skvkfbhQR2mJhLR0ytFyGDe8iQ0egOPaV/oP7S0Wnz4lakNeK64TZkIZpWqewYMEnoIgNjDZNMwnmI01KHGGjshkWcU3lz8gYSvRn1PkZmeeckmhnxRUb+1VbW6t+Hn/88fJ///d/6nfyIj///PPKlSkZSO7NWGRtNcHf5FX2Akgpm2mIpWlqph+onXCUiy66SI455hhFPFNdh1RjCqW0vJhL62VrXmZhYlFmJ6ATLLNrCFPli9rcbNaXtr3KiD62l2vD/UdJgNx7OS89NoLudxAk0Syvt1u/rtLy4Qop67N/yu879bQyGTS4RO75R/ZjqLFRZNHCZlm0cLOI0JYK887gIWUybEQXGTikmzQ2N0pjfYN0qgo+2pRgBK+maRuJkE0KkE19iVLdNP0ZAfO43niYaVB0fj3bxpGtJDEfFVds6VcNphiRbXwSccnC/BwWrr/+ernvvvuUamimHjr55JPbf58wYYLsuuuuym+X92EGTyS3jPshQ4ZsE7Sin0Weh6IiibkGpwAcVpGTYftEFukIOiYeJpswEZW5GRJMEmm/9aW9Hj8McGzubTpwfzgviIXX6inmQxMkciWfurweZjQcnsv+/QdhL1vapVPa7zziiDIZOIC0B8GNI4bkx0tb5OOlqOlbFfX/PfCkDBoEcewsQ4b3kKEj+sjA4QOlc5eOJv2wTNOoRYCJTitE+Yqato1oFLq52Q8wNSfzZ0ShB6+99to29abzXUnIVpJoa7+iCKipqalRc4ufbCZsdOkXnMIEf2fyJ7zxxhsVSSQBNiQwHUaNGqW+C3EkkSRi7v7yl7+soqH5CXRlORrzaNGQxGxyH5rgczopcbK8gGGrfFF8B9cFIvX6668HYl5OdvwwazenI1w4sON/iMpE7ko/6THCIrfZpu3RqXowkeFLWdZYK5+89o502rGvp3E9fkKZXP+rErns0malDIYBTmvFihZZsaJa5LVq4sdF5D3p379Uho2okqEjesiQ4X1k0PAB0q1Ht1BM05h7UIx5HcXVmabtJa02EVftzwgxpAoMAW2J/ozaHzaVP2MxkjFbzc1RkcQuPpO7M24Qmgg6Oe6449qvIX+fc845KT93ww03yDXXXCNPP/20CpTNBAK3iJ1IFmwKgUQIOumkk5Tqie+kVhUBc2nBk0Q/pfXSDQAIBp9LVXYuKpIYllrJtcFcx/HZmQRhXrYhcMWsnkLVG3yS/N7/fNRZ9pOqp/7ZR6StoVmqJg7xfJyBA7dGPl96SZN8QpxKRFizplXWrKmVt6ahe64Wkfeld58SGTa8SoaN6C5DRvSWwcMHSI/ttwvkeWEzQJLYVKZprQ5phaiYYAMhs5Ekauik8ObGw/RnxBUHf0YsLZow5lLWzU+/bCWJtvYr7HtSXV2dVUAn6W/IUwjZI9chKXDgGzramYhlNizXXXed+puUN5dddpnce++9ajySlQPoVD3048orr5Svfe1rSo1kc/zzn/9crRWk1kkEx/7Xv/6lci9ybFRzjk+aHUCau/JiMC8jqbJQcBP9TkIsJkwERC5zjFQPQRQkMSwljsUTEgxBZFENgyDq/utI8igCVxKrp2QbeR4WufVDEs0KNyRc1aaxtpYWqX32JfV7px38ldzr1q1Ebvh1hVx/XZMsWCB5w4b1bbJhvc7lSK6euSqXo0rJMxzi2EsGjxgg2/fZPicSkco0rXOeYSpCYdQqUdClGIEtJMg2QmZjn5L1J5k/o87PaPozmvkZgz4nG33/dHUO2/qlr1cYz3IQ1VZQ8FCoIWY6DRtJr3UwCxsR85r+6U9/UmOOUnomLr/8cqUCMj5xQ8J8jJ8tcx15FK+66qqUpnDGKyX5IKmolD/4wQ9UwA3kEmGlvBhyH7Lz43c/DysEA3LIDfRS8zYqJTFosqIjYyEd48aNkzfffFPCQthKokm4IAAQX4iBrp6SLcKqFOP1uCw8nAtjOLHCTdPsl6VlNZHHIhUD/CfErqgokYsvqZC//LlFXn89vMh5vyCX4+x3G1QTWS8i81Uux+EjOslQj7kc0z3v6aKmtWk612TMNsM2c7ONiau9pJphXmFBp5ll3bTSCMx600H4M9pIxvQ8Vszm5q5ZiFAA03Iq8zLBJiZwn0kHxhdm6GyAbzv5Gcn5eMstt8i0adPk/PPPLzySaOY+1A8Tuwg/BG7z5s3bEAwvRcvj5pPIQ41/DaZYyCGyMxOc3hGGMVlHlUw7VfWUXI4dxqLq5bjal5IFxgyU0qif+sTnx+telWU/SuR7/1cmCMj/+Y89RDERBBB+MKdRPkjI5ThmSJmcfM5+0r33trnCgoqaJk0KSKw1HWdSZhshs5Ek+iVjycq6JcvxaSb1zmbzaqNZV8+9tvUrKnNzzWckMa6AV3CdUBUxgUMYKff34x//uLBIIicJOUyMXvZKrkz/NRw6aX5rN8fB3MwCSJSvVqa0TK4fpLAeqrBrN3NtIIepqqfYqCSmIg+8DjnBhJXKl7JlzWJpeG+h+r20TzcpyaI6itmXL34Jolgit9wS7jgOEuRyfHdBiyy56Dk57YwdZPTekwIhZ5lM0/zfTOgdtjmrGEy7tpGMXJNWJ6rVzE+o1Wz8WGeYq5h7zXrTXuZdG5Np63XJtn5FrSTGFVwfGkIRG2DEMSq//OY3vykMkmjmPtSTnzlYvRA47Pz4r6EiotgkZjDPhLiYm0ngiXkZAkX0srm4hVWnOAolkXvPQq6rwgQZhBCWkpiKJGqyy71KNxbrpz4o8tnHu0waGkh/9tizTK66ukSuuJzNlsQGm2or5Pe3LpUj310mx37nWCkLMNVNkKZpWxZR25TNQlASvcx/+LzqyhemPyPJk5nDUHK00pjMn1GvdTaRaXPNsOn+RenDWV1dHViquKiguRJFCf74xz/KW2+9pcYgmxVElu985zvy05/+NP4kMTH3YbLKKRChdAETPKQQJyZ6CEY2JgDbzc2meRlySJh7VCXozOOHcWz8KlF3OD75D4OeEMIMXEk8ri4VyHfqIu7J0FZXLXUvv93+d+WYbbP254Jhw7ZGPl98EcRbYoM2KZGnX22TDz96SE7/4X4iXYJP5h2FaToq2LSg20gSw1bskvkz6nrTpj+jVhoZRzYqrsBG4hqlklhbWxs7ksjYJpUaRBDfR3gBVVpw1yIH4xNPPCF/+ctf4k0SveY+TEWuzIoVRC4PGzYs60lBf0eYZpxszc3avGxWiEl1fPqer1yGfmFWTyH6HOUtjIkqrBQ4iQqlDiIinxWpB9KdS8Nr/5O22s/TIZUPDrZmONHFv7mpQq76ZZN8xntigyVrKuW6K6fJV7/YXToN2baWdRjwYppmdw7YrNpgmnZKol0BIqY/o85TxziCMJrR93ochS1IFELEdT7yJMYNd955pyKIv/3tb1WkNfeQzQqmZoJpCGTJ/2wVQe5DBkiikghxYkHmJ06augRTtgjbn09/h1+Spc3LqB7JAh9syGWYDRKrp/A3zuFhIOwUODQkf5oOIkoHpTo88/w2r5X1DF6tqqwskSt/WSF//GOzvP2WXaQiExqayuS+h2tlt53WyYSx46Rz92h2+alM0zyHgET1iSlS8rW42kbIbOtTPn3/GBOME5rpz6irwJCFgrGjlUbel8/IYpuVxKgCV/oG5AMfJVhDEVi+8Y1vqP5rkevss8+We+65R0U423lXPZiXtf+hl+TYiUoiZIKkkezwMenlShD1d4Cwayt7PT7XhgAc5GRUUmo4elEw8lkVxSvYXXP/qHxA4I1eaMMit2Em04ZEcI/Iis9mJRNBBM1z35Dm5Rs+f6GqXEoqwtqYlMg555TLF78Uu6lC4Z2PusqvL3xCPp49Ly/fr03T1E4F5CJDKWZRYYJ+9dVXZfbs2Sr/JTv4Yg9csQk2pZrR/oyYAwGBBSzurINz586VV155Rc0juBPhVx/19bS12kqUPondPZR5tQ1YP6hM9dJLW3Pt6jmBgElECxJyx0pJZCCiGPmtnMJErXMmItvjN+RFsfEDPQjDLpvnxaStVVLy63mtURx1mppskK56SlwUUBMcE4d1NimQXa++sPVP/2+bvzvvNjTUBZ9jn3DC1sjnP99ul5nLC9Zu6iS/+fUH8pUjF8vBpxyVMq9iFMCvDN+lfEdN20bKkgUc5hs2RhHrPmF6ZgGnce3widNBMLoUpVk6MGy/WFvNzTrQJ2wCW1dXF0tz84UXXqiSd5955pkqAbe2fvAaYtrpp58eL5IIvKqHJhggMH2dKBr1MOhwdT+pdrKFHujpSCI1GlEo2HVOmjTJ9yITNtnK9vpkqp4SNyWR3RtjkiTm1JL2Op5b1i+X+pnzt3mtcmzHmpxBg/7tt1+ZDBhQIlf9khykEiu0tJXKQ083yNx5/5Zv/+hQ6dEvWtNQsvGTz4TeNiqJNvXHNiUxnVmX68Z6RjP9GROrCZmbD6wwYffLBmh3nijK8nWLWeAKoAQvPok33XSTsmq88cYb6lpR1YuKK1R2iRVJZBBmMxAx7eDLQWDKmDFjQhvMUZHEZLs2MwiHKCVU0mwmXRvNzV6qp4RlEg6agGo1G/MykwqRjX7uU8OzD4q0bnuenUZkn0TaL3bYoVQFtFxycZPUUn45Zpi7tFKuvfhFOfXbI2TcgZPFJkQdNW0TKbOVJNrWJy/qpunPiHlabz7YYLM+sNlmw6EJYxD+jLaam/VaFoVPYvcYmpsBhPB3v/udyi/MGGEDgZVO+1jGiiT6BQ8H/hrspliQIU9hIkyCpY8P+A5zJ4hZ2QziyGWw2mZu9lo9JQ5KYmJ5Pco++jluW2OD1L04rcPr5X2i3cH27l0iN/22Qq68oklWrZLYobq+Qv74lxVy6Lsr5EtnHSMVVeGkyskVYSb0ttXcbBNsNTf7FTkSNx/MQ9o0zfqo8zPqscRa6fe8bVUSzcIaYaK2tjbWybSJmteR8xpajIodSfS6YGv1CdWJwA3Me2HDb/k/v9BmdpMMYV7G/5CHOxvzcrLvsIEk8j4mMK/VU3Q6mTAWmyCuCTt5HMtZzHWUud/jNr75uLRuqd/2xRKRkqpgTUde0LlziVx9TYXc/NsmmT1bYonnp4t8tOgROf2cvaT/DlsDAsJGtmMzDNO0TQTIVpJoG/EJok/J/Bl1fkb8GTl+Yr3puPokZkqPFwTa2tqUkhhHc3My/03NrzSXiB1JzASznBmTKVGFpJ9Il0w7KESZUNs0L5NTD1+UIB6EMM+BY3shcix4EHze57V6SpjVYnIpy5euvJ5fhbLumWc6vNZp5wF5W1zLy0vkpz+rkHvuaZFnn7G35nM6LFtfKb+6aqZ8/bjFMuUrh1hHVLyqQzwzWh3yYpq2jZTZ1p9iIa6mPyPR0qY/Ixt0U7HWxDGZP6ONhDpKM3hNzEmiJoeJ14qk7gVFEpHN8bdgh42qpssfRUHeojA363PBrExULAtDEDkeo1QSMz24OqE0u1zcA7xOPGGSxGzL8jEWMClzTsnK6/khic0fzZCmRWs6vN55QnAR+tmAc/jWt7ZGPv/97vhFPoPGljK558HNMnfOf+Skc46SLtsF9zxFZd6FBNK8mqadublwAleChF9/RkyUes2w1ScxintYE1OSqMeTvkabNm1SAg33GTevmTNnxo8kplpYGcT45TGAE4MbwjYDR/k9nDskCgJMVGzQKTLyRRLN6im77LKLWuz8QC8wYeUz9HtNdHk9PpuqvJ4fklg/9b9JX++0w1YlKZ/gPA47bCtRvP668BX7sDBjXoUsvuApOeOscTJy0niJK7yYphmPvI9Fgfflm6DZ6v9X7MQ1mT+jNk2zAWZsQRT5SQoY28h+FNVWWlpa1DMVR59ExhJEkLzD06dPVxtKrF7k2mQTMH78+PiRxEToahVMfvgemuY8jUJQEvV5kieSKG1UtjAexjCvVara0InVU7IJvAmz7rRfJRH3Bs4nkxrqlZC3blwrddPnJP1fef/gVa9sMXZsqfz61+Vy8cXN0vh5xcBY4ZPqTnLTzR/JFw5eKkecepSUBbwJy8cCmsw0zXwJQWSc2lBr2jZyYauSmG/fP/wZSQZPM/0ZMUuiXuMjn1hvuhiqrYC4RTeTcxhBDeLPfWPjSHq57373uyqPNG5sqgiHxBicHKqaNrsikadT+MKeiMIiWOZ5slvhAQyzPnSYUcLAPD47UhQ3JpRclFGdiDes8nlejmuW14Mc4iea6bheyGfD8w+JNCf//tJudkXm9utfKjf/rkIuu7RJPqtEFzu0tZXIYy80yYfzH5RTf3igbD84/DyUUYKFm7mSsYdSoBf3RB+0sBN6204SbTSh2nSdTH9GlCd+oioypxMoiiLlxZ+xEOo2g7iZm3nuuT6QQtyhENiw4CUWGYkdSdQPiK5J7MXsauYXDHPCC8PczC6N3b4mUTNmzAiNxIWthnLvzKoxqaqn2EZwOS7+rumAuYXxyGRJ6bVUGxa/JLGtqVFqn38t6f/KB/SQEsuUDtC1a4lc/6sKueFXTTJ/27zfscJHKyrlustek2+eMkgmHr5vTsey1QfQNE2bPmipoqbDMk3bRH5sVhJtJK4mGdOpVBLHkvZnZPyY9abDvr5RKK81NTVKYY2aAOcKlEL4BPci0R3KjAqPHUnkIWGHgrztNWl0VCQxSIJlqlIkACfyLKqqLpkIURCEC+KbqnqKjSQx3XHJto9fBwoN/odey+t5USib3p4qrZ9u3akmomrSULEVFRUlcuFFFXLHHS3yysvxjHwGtY3l8pe718oBsx+Sr/7fsdKpS0ff0jgiFWlNZpoOM6G3zSTRRp9EG/uUKqAmnT8jQRHan1ErjdnkZ7RFSezSpYuV9yXTM6d9/7lOmh9xH81rFjuSiLMsphGSEXuVdzUjZlDC+G0nWPjooUox+BJVqbBJYhQR2hBETBMQqiDvR5jm5lSLKia62bNnKyUURdTPROFFSax75umU/6vcqb/YjNLSEjnzTAJaRO6/L75EEbwys1QWXPConHH2njJo5x2yPo4tC4lXUgYJZCNO01HTpmma/5vmxGw34TaSRFuVRNv65FXhTPRnZH3TaZtQGjkvs950smA/G0lidXV1LINWHnroITn//PPlL3/5ixx11FHbXCfNAWKpJLIQE6Di98ZHEXkcBIHTPnrssCBRiRJ22CQuzIorVE+BqFOvGIfYMJJeRxXdbJbXo/4l5fWC7m/Lkvel8cMVKf9fMXjbDPk2gmt37LHlMmhgi/z2t/FMkaOx6tNKueH6d+Vrxy6S/U883Nf4tc3cDPw+f8lM03qRJzMBgWfaNI0bEI78Xr/DRpJoo2pnK0n0a9bluiLy0HR+Rlx1GEvan5ENiCaMrIfZmHOjClzpFoIKGjZ4huFFX/nKV+TQQw9VPw877DBV2SzWSiK7i2wSY0eZ6DobMEmym9JR2kQwJxt0YZK4sEy2ZvUUdpNI3GE8UGGam81FXpdBRPFF0c52F5lJ+ayb+kjaz5dtl9/IQT/YbfcyuebaErns0maJINFAaGhuKZX7/1cj8+b+W0754RHSrVcwrhJRIwjSygJDJSRdDSmZadpUhtKZpm0kiU5JjK5ffNYsDac3IDTtG5tYb9rL90Xhk1gb05J8uHq99NJL8re//U1uvPFGeeqpp5TgoRuBl8o6kO+ORgXIVdhVV7IliZANTJbI1pmCHqKoDx3k8ROrp4QZeBMWSTTJHI7YWunNtQxiOpLYWv2J1L+xNT1JMpR26yRSbt9ikQ5DhmyNfL70kibZuFFijXcXdJIlFz4rp52xo4zee3eJI4ImZYmmaa0MJZqmtTJkPjs2kkSnJOavX4kbEFRqrVpri5RZOhCSluxesZaF6WIWZ3Mz9wsV9+KLL5avfvWr8thjj8mDDz4o99xzzzbvKyqSaKOSqJOAQwyTmZeD+A4/CFKpTFY9xZba0H6Pq8vrUekGOZ4kxbkuIOl8EhtfeFjaGlPf58qJWwOZ4oYePUrk1zdWyLXXNMnixRJrbKqtkN/fukSOeneZHPOdY6Qsw7Nr0/0Km5Rx7MTKHXqRJ6NBomnaRkJmI3FNVjrNBoTt+4cFMdGfUQfBYIHju838jNqfMSpzc9cYkkQNOMfEiRNVO+GEE9Qah2jFdV27dm38SGK2D61tPokMdKqL4MvjJwUM34HyGBaCIFrpqqeEaS4PK3AF4LBPM8s95opUPoltLc1S+9wraT9bNW6AxBWdOpXIZZdXyG1/apZp0+zz1fODNimRp15tlQ8XPCSn/3A/6T0sfW5MWxC1j2Qm0zTPLe9BJbIhCTNw5mY7+2X6M+KWxXeTGB7CuGLFCkVytGqNKTjs/IU1MS3Jl2xDRCYVGv6JgOsXO5JYCEqiaV6ePHlyux9GkN+RLXI9fqbqKWEriUEvfro6BdfkgAMOCCTiLpOS2DzrBWlZtzntZzsNC4ao5jPy+Qdnl8uAgS3y6CPxjnwGi1dXynVXTJNTTlwsexxzQEEGroRpmmZTSdS0GbSQyjQdFWxUN23sU77JK9+rTc+jRo1SGUZ0fkYIHPM3Vi0z12eQfa2JuZKYWNZWjzGuEal9iookRuGTmIkAafMyA9WLeTkfPonZkjgv1VPiZG7W5fW4V5xLkAQxnfJZ98yTGT9b1jvek5I+/69+tUwG9CuV2/8c35rPGvVNZXLnvRtk3uz/yNfOPkaqutl7j2wypdIPni0WWrIeJDNNY7bWi7yfqOlc4JREb9DEwhYzOGuqVq2x/pB5gr4xphBn6KuZnzGVP2MxkUQNnYvZROxIou3m5lRENFvzchyim/1UT4kDSTQjzfGlJDk25xY0kimJLSs+kob3l6T/YGmJlFTG7tFNeQ323b9EuqzdIDc/0kuZb+OON2aXy8ILHpczvr+rDB2/c/vrtpAyG5VNk7SmM01TRAFowhhUPr24qHY2kkQ959rWL903VGkSeuP2ZPozolwzxzPezATxfgNdampqlK9koaIwVhqLzM0MysRdujYvs6vxa1623dwMKabcktfqKbaTRM6He4WPi440R1GMIrUOqH/moYyfq9xloHWLV67Y7fiBcmXftXLdnd2krjn+09LaTZ3kxhs+kK8ctUQOPvlIsRE2jaF0yqZpmuY5ZB5NzKcXhmnaKYnxJ4mJKXBS+TMynvBnJFUbJlY/46k2Ar/HfCL+s7FHhB3wob+DicWc8HTKFG1e9lqyLR8ky+/xmaw5N3byXqunhF0bOpdrg4/orFmz2s9H3ysvlVGyQeJxW2u3SN0rMzN+rmrCtgXYCwXDD+gn1/bZKNfd0iJra8JNWxEFWtpK5aGn6lVOxa99L7faz4VsbvbTH+aPTFHTQZmmnZLoDXrOtcXc7Cfq2vRnBKY/oxmFv/1nSmMyf8ZCMjcng12jzQOyfWijUhIBE5c2L7/11lvK/IqPXq4EUX9HFHkSM5EiohDffPNNld4GBdGrRG9r4Aq53N544w3lv8L5mPcqivyLoPGVR6StPnNZx04jt9ZCLUT0GttTrrysVHbuWy2Fgg+WVsrNV70ptcvWiU2wiQBlS1q1aZqITBLbEyzHM6w3sK+88oqydDBfseD77ZONhMy2PrFecO9sGk/ZpubR/ozmeBo4cKBSC7EwMZ7wU586darMnDlT3Q/EhWyUxFtvvVWlUkOUmDJlikyfPj3leymdR+CkJrSHH354h/czXi+77DLVX9R13uPHTSplPXcpEkTlk6grcjAxkUzWiwnWNnNzuknbrJ6y2267tfsNeYVt5mbez4NEGo5U5fXCUhJNUsvPumdf9PS58n7bRowXGroM7Co/u6JC7vrNRnl1kf2lB71gS32FPDFVpGHTI/LFs46RipAT/BaqkpgJQZqmnZIY3z5p5BpQ07lzZ9W0PyOEEOUa0nbfffcpcsh6jAWKjYiZ7i0d7r//fjnvvPPktttuUwTx5ptvVvWTGaOUrU3Eiy++KKeccoqycEEqf/WrX8mRRx4pc+bMUWMd3HDDDXLLLbfI3XffrVT2Sy+9VB3zgw8+8OS3q8d64v20885mQLYBH2GTRL2bevvtt9srjARJEKOKbgZJo27r6mTatGnKh4Ndll+CaBtJxP2ACjAkDNUKRBDH9QqTfDa//4o0r/zU0+dKu8bfFJsJFd07yZmX9JET9twghYTnponcdOEjsmZRhuCkIg5cCQraNM2CucceeyglZocddlDfxcYQVQg1CIsPG/rEa2Kjkmhjn2yKbDah4wOC6ltJSYlyX8CX8Q9/+IMSFlADuR/PPvusql5CXuBzzz1XVS9hg5IKN910k5x11llyxhlnyLhx4xRZxBfyjjvuSPr+f/7zn3L22WcrYWbnnXeWv/71r+r8nnvuOfV/zhOieckll6gchwgef//73xVxfeSR9OVdNfSxTA6gxpsUCdgxhpkCR5uX+YkJlqTLQZiXo45u1g9UIhElz9Trr7+ufDIgVAzobBAmSfTjkwjR5XwYFxDedOaCsJJ0mySx7unHPX2mfOj2UlJql7oRFkrLS+VLPxoo/++YwiKKy9ZVyq+umiHTHn0hb2StUJXEIE3Ttl0jW9XNKOojZwO9hoXVt86dO8uxxx6r1o7bb79dBTheddVVyq/xJz/5iSKNyTiHFicwB2vQR/7G5ckLMH/zPSjigGwcWPfMY7JBQqX0esxvfOMb8q1vfUsppJwLfWKsFY25OUwlkZvF5ALxgBhCEsN6kPV5hDWBmZJzpuop2SBsJdHLRmD58uXKZO61vF4YSbrNa9Gydqk0vLPA02c67zZUig17nTJQevdfI9f/vYc0ttqnWGSDxuYy+cd/NsncOf+Rr59zlHTp0SPyPthENvJByDKZpvXGH/NfvhJ6x0G1s9XcHFVATc1ngStYDY8//njVtLCSbMxAwFjDEy1X/E21GC/4xS9+odZiTQohiPoYicfU/0sH1k3S1917773yr3/9S7785S+res5YQ/M/6rNANj5iYZFEiCG7UHYTXFDMsVGYg8Mkidqknal6SjbIZ+AK34t/xpo1a3yV1wtbSWx45kFuqKfPVO7k38RfCNjh0P5ybZ9P5JpbK+TTusIxt789t0IWX/CUnH7WLjJy912K2tycT6KRGDXN3Pfqq6+q/+UzoXcclEQbiaupcIZ9vWpqapKujdm4Y3nB9ddfr9Q+/BSDyhEKmb3nnnsUf3n44YdVe/TRR2W//faLJ0m0oeIKkxqJXefPn6/8XJhYdLbyKAJLwpT4+Q7IL+eWrnpKtsfOh08i/pSQeQCZ91MbNixirgh5c6PUvvSW58+UDyqMQI5s0HfXXnL1JdVy4421svjT7NwdbMSGLZ3kt7+dL188dIkc/u2jpTSiBdcmsmGbaVfPs6grRLwmJvSmr2YC5rASesdBtbPZ3Bx2v5qbm1Wgqp8UOCT2ZnwhVpjgb6yQ6XDjjTcqkogPJH6HGvpzHMNM7M3f+DF6AVY1GgExJ598sjz++OPy5JNPFo9PYpDkDfMyhGPRokUqepl6kXqCi5IkhlliiagpiO/EiRMDNbPkI3CFzPr4H7LbI0G2H4KojwuC7jdjZvDK96WtpsHzZ8p6RLMY2YpuQ7vJRVd2lr2Gpq9tHTe0tpXIf59rkj9c8h/ZuCqzeajQlETbFDJ9fXSftGmasoH777+/WqAhBpim8fkiHRibakyJYfm+67nZNkJmY5+ySX+TDaqrt6bq8mNlwyWNQCodKAJ0EAq+sqlA9DI+j0899ZTiHSZYqyGK5jEJxkIZTHfMZOOLzc9xxx2nIriJlI6lkphtPq1k1VCyNS8zQSDFJganhE0SdQR1GN+hq6dwbCKo2FUEjSgDV8xSiJwPjsTZHlcfL0io7P/vvCder0ZpjyopKbfPrBM1OvWslO9fVi79blknj83e6rhdKJi/vFKuu/RV+dY3BsuEQ71N7oWg3NnWHz2PJOtTlAm9Tej5xzZCVswksaamRv30myeR9DennXaaInsIF0QmcyyincGpp56qNiXXXXed+puUN+RAxGeQdVn7GerqMYyvH//4x3L11Vcr9VunwMFvEcLnh1voPM8o6Icddlg8SWKuClw2yhgXjZB3HJpN83I+y/8FCbN6CpHLYWWQj0pJTFZeL5fjgqD7Xb70XWlY8Ynn93eeVHxBK6lQVlkmJ54/QAbcvVL++lxhJRevaSiX2+9cIwe995B85XvHSqcu4ajHNpEy20iiH0KWWGuayFNNGqlpr6t65GqatrX8na0+iVH0q7a2VqnMfr/npJNOUoEtED+dcxiFUAee4NJg3uc//elPyk/2hBNO2OY4l19+uVxxxRXq95///OeKaH7ve99TVWNQvDmm1/GmSbXmR9S1fu+994qPJEIe/JJEzMuYX3nwkYl12Hmq74mCJAb5HaR84PzYoRDxi/nEllyGfo+tE56S3JQqMEGUQgxLSWx76Rlf76/cuXCLyGeLA04bJH37rZZf399TmlvtWjxzxUszSuWjCx+V0//fnjJo9A4FT8rioiRmAptsmpeE3pBHrwTDViWxmH0Sq6ur1b3OZpycc845qiUDQSkmsIhlAn345S9/qVo2YBziLsF3k6KHqjKso7EkidncEAZLNomoseujsPFge6lPHAVJDCqhdqrqKWGeQ5jJwDk2ph78gzAtI7sHMUkkpgUKAi2frJLGmR/6+kzF0GATsxcKdj5mgFzdd4Nce1uVbG6skELCyk8q5YZr35UTvrhY9vvaYVYRqUImiUFFWyeappPVBvZqms6FuIaJYjY3V1dXx7pus37u2LxQrQXl8LXXXlP/I+Xdd7/73XiSxGzhh/yY5mUCU8zglKC+I5/mZh3ty3ni2Gomx7apKopXcB6QXeR2CG+mKDE/0L4aQSqJDc89KNLiM41Tr8KJ6A0aA/fsLddctFlu+G2zLNvkLzDJdjS3lMp9j1bL3Dn/llN+eIR067V9QZIym/oTViCNrg2cjWla98k2QlbM5uaampp2n8A4Ql+jp59+Wpm0WTepBEMSbszVo0ePLj6S6CXyTAdweDEvJ/sOQuLDRK5EFF8IdgwMiLFjx3aYdMJW+4ImiTqfo5b+gySIYfS7ralB6l7wlgW/HRWlUtKpqB5X3+gxqodccnmd/PHGzfLuyuiTU4eNdxd0kqUXPSunfWcn2Wkvb2kt4hLdbBtJjCpvYzLTNNkYkpmmcZux6Rpp0G8bEo3nw9xcW1ubdfUxG6BJNHmQKTF44IEHqiBP/bq6txJDZPugMJAzkR+/5uU4mZu9Vk/JVy7DbEBgCn4TmGwgvJhwwkCQSmLjtKekdVOdr89UTRhs5QJhG6r6dJZzL6+Q+27eIFPnFp55fmNNhdzy+8Vy9IHL5OjTj5ayiuzN6zaNJ9tIYj5S8pimaWCapkmvo8UH5u98JvROBGtRGCVo42Ju7uYzstlGcA6ku4MXmNeOMRlLkpgt0hE407yM7wgRzNk8gLaam7Xahpk5U/WUuJibdXk9HW3OZBqWQhJkv+umTvX9mapdciuHWEwo61wu3/hFP+n/19Xyj1e9VdWJE9qkRJ58uUU+nP+QnPaj/aX30MGxJ2U29iffZt1E0/TatWvVfIeQEWTUdKGam6NKgdM1xj6J+hqRWuexxx6Tu+66S7lrmWO/6EhiMnMzrxHdC8nwU64tLtHNmM1RR6k/qmoxZjANRGFuzmVRMANuqAZDBnvz2DYric0L35Gmhat8f67TiMIjO2GipLREDv/eQOnXb5Xc9FAvRawKDYtWV8r1V7whp5w4QCYdvX/szc35JmU2J/fWpJFGIm/TNE12CsQNzJ6aMDLXR0XcbA5c8WsJzMbc3C3GSiLch3GCBW7x4sXt/Mgk2EVFEpOZm3nQMFdma1622dzMxMuOkwFApO/w4cM9B9+EqSTqvmUzCRMNyP3i84nl9eKggNZPfSSrz5X1y71udjFi1+MGylX91sl1f+sqNU2FN93VNZbLHf9cL/Nm/0e+dvYxUulD1bCJBDkl0R8ZM03TBFVimkYMoEEYMU3rqGlEjzCDK2xNgRMFea2JuZKo+Q7XinGiS/qZQlIsZ81sB7tJ4JgEMFfOmzcvJ/Nyuu8IC15InBl8Q1Z3zBJeEaaSaDrE+n2A2TVjMu/Xr5/yP0zcKduuJLZuXi91b76f1WdLu9jn8xMXDN23r1zTe6Nc/7tmWV1dmGUNX3+vXBZe8Lic8f2JMmSXMbEkZa4/6ZFuzkRhZF6kaYVL15rWpmmtMtKCVNhsVhKdT2LqsX3fffephNnkRsaSigBDvWYimgECDOMkliQxVwKnzcuQjlzNy6m+I0xk+g6zeko26igPPD6MYSCb6iVey+slluULEkEQ0HrS3jT7P0bFqN7WLVhxw/ZjesoVl9XK727cInPXFqYqu2ZjJ/n1DXPkuKOWyEEnHSGlZaWxMjfbNMZtNDf7UTd11PSQIUPUueDHCGFcsWKFEkaCNE0Xu09iLx/ZT2x61n7729/KW2+9pV5jXPHaueee2+7WQDASrehIIjssKopAnKi9HLTPQlTm5lSpfBKrp2QbfBO2udnr8bUiSpTf5MmT1YSW7thhLX65Kok1WzZL/fOvZvXZzhNdOb4g0HlAF/nZlRXy9998Ki8tSD2O4oyW1lJ58Mk6+WDOA/LNHx4iPQdsLfOVDDaRIBtJom3qWLbElfNg3qSZpmlIozZN8z9NGv2apm02N0dRlq9rzMzN+l6df/75Snjhfl9yySXKxHz00Uer/yM0cW4EusaSJGbzoDAJcdKUneFByZZA2aIkJip9qaqnZIOwzbZeFT92afgfspsh4XcmQq9JYhgLTi7XhDH36fP/lp6fbC0G7xeddsz+Xjpsi/KuFXLGRX2k/21r5IHphRsMNPfjKvnVpS/LEUdWyY5TJqrFn8XMLDFpEylz/YmOuJqmac4TIqBN01hs/JqmbSTUUZHXmpqatJlCbAZ1oHWZ4ieffFJxhhtvvFFtGDA9c19jmyfRL7gQH3zwgXoI8M0jiCMs5MPcnK56ShDHDxpeCNeaNWtk9uzZylyCj4SXh91UKYPeQWZjyjbN5HvO+0Ayp3FPjooBW/OmOQSDkvJS+cI5A2XA/avk90/0Fsssr4FhS32FPPTfFtlv6WvSf/d+UllV1b7wh7UJLBRSZnvgSlDgmudqmi52c3PXmCmJQIspOkDlhhtuUL9zf/lp+lnGliR6Nf9p/zzUKAJUSL4cJhiU9CvM3ZUZWJKpekq2xw9zEUkXGMO1IxobZ+sJEyb4qp4SJkn0a8rm/DCTM9lOGdpLGu5akf139yjMYIt8Y4+TBsrl/dbK9X/vLvUt9i1yQeG1dzvLsJXr5YTTx0trRYXauLC44bSO4z0+2T169MgrSbONJNrokxiFYpeNadpWc3NUJLF7DJVEbdHTz55Oop0MsSWJfpIt459H9DL+egz2MKEHZZgPjlb6IFNM+OPGjVNlnYI+flhIRUIxoUN4cQvIlPA71XFBGATXj5KIsjtz5ky1IyNwqPme32T9vaW9ukhJmgAEh9ww8pB+ck3fT+Xa31fIhrrCjSD/eF2l3PrbeXLS8b1lry8eJNOmTVOLPM8a8yQwTYxRJ2a2jZQVi5IYhGmatQKXGt4bdl5CG2s3d4lhWb6jjjpKrU+33367UpB/8pOfqGhm0iahjEL++UkrL2TzMiqbmWzZS1m+IEkiD00Y4GHFJIDfQDZkygYlMfH4KLwovpwLJvNsrp1eZMLou1clkYh5zoN8U0RiS90W2fLaO1l/b+dJw7L+rIM39Bm/vVx1WbXcdGONLNgQP9ORVzQ0l8nfH9goc9//j4zeb4Aig8yNjOvEmsHaxIjKyMIR9mLrlMTMyLfvXzLTtC6LylpLMuZ8JfROhrAVzra2tlgqidy3Z555Rv1O/zmP3/3udynfX3DmZswnLNKQDKKXzR1xFP6C9CvMPINI/9TxBF6qp8SBJOL7AqnHvEHLdnLWEnoYEc6ZromZuByzP5MoqH/pYWlryNYbUaRqjHdzu0P26Dq4m1xwRYP89cZN8ubSwvYBfeuDCln08Urp/q1KRRJ5ZjA303DJ0SZGSCOWGP5mwYcwsvhDBIImULaRRKckZgZ90QSJYEkQZNR0LtBVvZxPYvL7tmjRInV/sLCChx56SFkVIP1sGBGhaPCp2JLEZNBkg8oiRC8nPlAQqlSpY4JEGGTUJCGDBg1SE3gYBDEKMq1T7KQqr2cjwU1HPrlWOu+mmaanraVFap95KafvLR9SmKlabETFdpXyf5f2kv5/WCePvhOv3Gd+saG6Uv58+wr50oIn5LBvHSWlxmKaaGJk8WBs0/Bj5P+aMNKCmIdsI4k2Kom2EldAv5jXg4yaDqJfUaTA6R4zJRHggmfiuOOOS/negiCJLNKQQwqgp0v/EoWSGMb3JFZPAcj7YSFsJZHJl10MflFBRWSH3fdUx2UixNzC/zkPU7lumv2StKzNLVCqbPv4+bvEGaWdyuT48wbIgH+slNufyX3TYjNa20rk0WcbZd6H/5Fv//Bg6Tmwf9JnVfsmDRs2TM1r5Cxl4UeNYHOEAqlN0yyY2aYos4mU2UrIwhIGgiCJQUdN5wK9/oZ5DxsbG1WLW8UVzSn0GOenKZ5pMUQ/j3aNOB/QJ5DOvFwIJDFZ9RQk4bADS8I8PhMGJvP+/furoJsgJ4colUQmPO4NO2fOI3FCqn/6idy+tLJcSioKN+rWZuz77UHSp/8a+dW920lzq11kIWh8uKxSrrv0Ffn2N4fI+EP2TvtenlXIII1UYvhF8xygMi5btkw9J9moRbaRRBuVRBv7pP3+MvUr7ITeyfqlXb/CNDWDOJLExM1Gus1HbEmiWV2EHS4TVqYBYZo5wxw8QZHEVNVTwqyIEubxtckc4ktgx/jx4wOf9MIqzWeST87j448/VkR3zJgxavwlomXVImmYvSin7+w8cbB1i0IxYfSR/eXaPhvk2j9VysaGwo18BjUN5XLbHavl4Pceki//37HSyWN0M5tX3F9oPB86AAa1CFcSFlAzACbVvGsbSbRVSSyUPgWd0DtfdZtB3HwSsXwdcsghilPw/KL+85xqv2T+1j9psSWJ+OYRTeWnuohmy2FHPeVKEnnwkOOJNEx2fvr4YU2sYVQuMU3mJDRn1xhm38NSErVrAykfMP1zLslQ/8yDIjl2o3LcoNwO4JAz+k/qLVdfvEV+fVOdLN3YWQodL75dKh8tflROP3uyDBw9yvezBxGkabVIq4xsdnl2EgNgbCaJNvWn0EiiH9M0mw2ImB/TdFQl+bp06WLdPckEHZQCWfSyVsaWJLJzRY0it49N6WlyJYleqqfo8wjrQdCDnnMIwgdGl9fjmmMy56EPszZ0WEoi/ifTp09Xfyf6H5poq6uWupdn5PydnUYUbtm4OKH7iO5y8RX1ctuvN8vMFT2k0LFiQ6XccO07csKXFsm+xx+WNVniecelhKbThUAY8admk486pAkjsGmxtdG0aytJDKNwQTrTNPMwG5F0pumolMSuRqnLuAC3PCxhXEf4Bs9lYuPcsArwe2xJIgPDb6Sy9lEIO8I5W5JoVk8hx16qQW6SuDAeBJOE5gqCiTgns7xemIExYR0bnxlKBbIxyeRH2fDqf6Wtbtva2tmgvE/8fF0KFZW9quScy8vlv/+qk0desCdhcFhoaimVfz1SLXPn/FtO/uGR0m373KLsmXuZs2lkn2Du0gs/ZSsBlgbt7xhlupRkcOZmb4ii2ko2pumo6jZ3jZmpGSD86BRtnt4vRYaoEmr7+Q4GPhOl1+opQZK4sCqXmOeE7yHkyjx+WH0PwyeRXRdpeti9ZvKjVJPYM8/n/qUlIiWdw1O7HfyjrKpcjjutmwwbsVFuuTN+i0M2eOejTrL0wqly2pljZMfJEwM7LnMYKa9ozJUvvfSScqshchq/Zf5vLvyUVY0STkm0s09eTdMQRf4XpqJY8xlJtG2ceIFpZtauZalMz7ElidnemCginP1EByP5vvvuu2p35LV6ik4aHdZ55JoQPFN5vTCjp4MkoBxHp1bCvcGLn1LzB69L84rcSz922qlfLCefQkdJaYnsccj2cnW/T+TyG7tKS0vh36NPazrJ725ZJMcc9LEcdfoxUhZwGha9OPGMEQSmK3mw8BMxzTPIHKIJY7oAmCD7VOyEzAui8P3LxjTNuCHy/pVXXslomi42JbGpqUk13KW8RKbHliRmiyhIotfvYDBDEBnEfqunhB3hnC3Z0g6x6crrhW1uDiJwhQkG31D6yXkQRISPRsbPPf0/CQJVE72bAxyix9Bdeslvr94kl1zTSTZXF36aojYpkSdeapEP5z8op/3oAOk1JLigqsS8bDzDBITRqAjBplMHwGCS5pnkf9qf0Y9fepyVRBuJaxRm3WxM07gH8TsRvKZpmnWTsRNEQu/qz3wS44abbrpJLrzwQrnqqqvk4osvlj//+c+qQbIhjpyTjngu2NrN6cAgCdsnEbLHIPVSPYXUPfjo+J2QoqqK4gdey+uF6RcaBAHF5AXRZRHaZZdd1LXwYsZuWfex1M/8SIJA5ShvEfsO+cN2g7eTG6+tkWuub5GlKws7RY7GwlWVct3lr8s3vj5Qdj9qv1BIYiIwNeOnTeO9LM4QRnyESUMFSdSLPgQgCGXLRkJmI3G1Ud0E2swcdNR0opIYxxyJ+nnT941naObMmWoDxoYsEbElidk+LFH4JKYzpyZWT0mVQiXfJNGPSThTyp5kx7Y1cAUzBeeSSN69KJQNzz7EEyhBoHxA4UfRFgIqe3aVyy9vkD/eUi9vz/GWWzDuqGssl7/ds072nf2gfO0HR0tljmpKJpJogvfo/G3kj2U+1QEwLHY6KbNWGbP1GXOELB7m5lRI5ouYLmqaOZ+//Zima2trY0kSf/zjH8tpp53W3nf+/upXv6quGedEgwDzEze42JLEOJqbk1VPsbUqileypc2y9MVreb0wTeXZBq6YdaQnTZqkFpnE46YjiW0NdVL34tb0OEGgtFvhR9AWCso6V8o5Py2Th+7ZLP99Pn6LRrZ4/d0yWXjBY3LG93eTIbuMyfo4ubiHsOlnU0ozI19RGikbyP/NOtNeU5/ZqiTa1ifbzM1+yGumqOlMpumaLH0Sb731Vvn1r3+t1pqJEyfK73//e9lrr72Svpf8opdddpnMmDFDWR9/+9vfKlJn4oorrpArr7xym9co8gDxTQb4hxlIisqaLtq5KEliPlLgpKqekst3hF11JRMJ5WHCp9I0y+azKkq2SiLqgya6kPdkPk6Zjtv4xuPSWl0vQaC8XzcpKbNv4nVIjZLycjn+tO1l4IBP5PZ7MwefFQrWbKyUX98wR756zBI58MQjpDSLcasDwnKdE5NFvuo60yywyepMpyI4TkmMb5+yyYWcbOwQPPXpp59uUz0IczVizxFHHKHcHvwqiffff7+cd955ctttt8mUKVPk5ptvlqOOOkrlf4SsJgI1D9XzxBNPlJ/85Ccpj8v6++yzz7b/7Te/MSoqn0k25ouOJEadAsc0xbJrSDYQ4qYkmj6V7FiGDh3qa0INk+D6DVxhIsAfg4WD9DbpclOmux51z3z+gOaKqkkdy/w52A+egX2P7i0D+m+QX97cPSjPA+vR0loq/3m8TuZ98B/5xg8PlR59+/j6fJiVo7QKpDeDWmVk4ed7zQAYMzm+UxLjb25OVezAC8zgqVGGafqBBx5Qah6bDzYcuFeRyWPChAmexjBBI2eddZacccYZ6m/I4uOPPy533HGHXHDBBR3eP3nyZNVAsv+bvAaf3VwINcro888/r1LX8aygnKI4xpYk2pwCRxNRL9VTskW+fBJRYdmRM9lm61Npi0/i8uXL1Q4RZReFN92YSmdubvnobWlaslaCQuXo/oEdyyF6jNq9t9z0y41yybWVUlNn3wKaK8rLWqVHVaP06Nwk3auapHvnJulR1SQ9OjfKumf+Ij2/dKq0dk+f6zUfJfD0okfjO3WdaTbwKDnMz5pUOiXRG4KqyhU0gs6PWPGZafqcc86Rs88+W2bPni3f+9731GaDCiaYnVEXjzzySPUzGWEjKASzMZHFGtzPww8/XN54442c+odgQwopiDFc47rrrlPppDKB54DrhAoJYZ06dWp7TWoN++6uD2TyE0sGLki6yOMgS7i9/vrrGaun2GxuTjx+Ynm9bH0q800STXV39913Vwl9czGR1039rwSJisG5VbdwyD96De8pN11XLVde0yor19mdFL20pE26VX1O9DTpgwAqIti5cZu/qypaJB1/ap1zp9TtfYnVdZL5PpQg2siRIzsEMbBG4NOIuU/Xmc4nadRzj20k0UbiGrbCWVpaqqyCmKW//OUvK7L45ptvKoKFfyEqIeSRcpQm1q9fr8hr4uv8ncp/0AswW991113Kqseahn/iAQccoAJkM+VdZkyzpmMC5/0c66CDDlKkl/UeN7lYk8RswK6Hkw8LTHjcKCYZJOhM1VNsVhJNUqTL63E+DMZcJoawK66kuy6Qdx4KFFE/6m4qM3brp6ulfvpcCRJlPYNTnB3yh6pe3eSqq+rldzfVy3vzo4187lqpSZ9W+7YSva2k7zPC95ka2KWyWUoD5D+lDZ9K2bJXpGXoAdaSxExBDK+++qqKdEVpXLhwofq/NktjPfHj7xZG2hJbYCtJjLIsX6dOneTAAw9U7eqrr1amaCKoo8IxxxzT/vuuu+6qiB6ZOTCNn3nmmRmfO4JoIIiXX365fPOb31SWNRNFRxLDJFe6eooqil1eHhpBjMonkeOb5fVwjkXSDuLY+VAS8T+EIPIA77HHHr7MJKmUxIbnH8IpSwIDpfjK7Zt0HbJDeZcqOe8XZXLvHdUy9bXsU8VUVTR/rux9pvgpda/9762kj7+7VTVLeWl+HSIrFz8mNYP2lpKyiliQRBM6iAYrEEoj86AOgFm8eHHSAJiw+2+zkmirT2LY/apJkScxFUHEYkWfyO9pgr+z9SdMBr5/9OjR7TXRU0GP2RdeeEHGjh2rzOAQXu6pHm+8pyjNzWGQK7N6CiZM5OcwEYW5GRMMQR08DF5LBnpB2GX5ko0JHV1OBQfMS34n9WTHbWtqlNrnX5cg0Xl3f0FADvajpKJCvnHWdjKo/6dy10PdM/r1bfv31v93Kg/vWQ8DJW3N0mnuvdI0/rTYkcTEPjEXQgZ1WizSfukAGPKq8j4zACaX1GapYC7aNiHOKXByHR+1tbW+UuBAwBAnnnvuOTnuuOPa+8nf+DoGBXwKUb+//e1ve3o/VjUCcLheOmDLvKexJok2pMBJVj0FUzOvhynFh1m1BHBs8jgx+aUqrxcHJZHfcUqHJHpJ9O31uKDpraeldWOtBImqcZ/nr3IoHJSUlspBX+gpI1a9JP12Ks3o11cIqNjwnjRuXi0lPdKrJLYGiaTqE8EBWFRovE8HwJipUswqHkGsATYribb1KSolsbq62rdwgu8fiawJ+iQ3IilwEGF0tPOpp56qLJAEnmjrJFXM9O+MMYJhGWPaLPyzn/1MvvSlLynuwTqH2ZhzP+WUU5L2AW6iN0GaIBJQo68X184c+0VHEoNMgZOqeoq+2GE+QGEG4DDQkMAxqZBYOugJPCqSyEPFA8VPlNBc6mwmU63rpj4tQaPTsK3pOhwKD9XvrZBNL62V4bsUR8lFZo2qD+6Uhr0/j+aMk5LoZe7mPViPaDpVik7IzOLOGpFYZzrbCjA2kjGbzc1R+ST6wUknnSTr1q1TCbIRYSBoTz31VHswy8cff7xNv1mLsUxq3HjjjaoRXPLiiy+2Z+mAELJRQQTZf//9lSUzlSBi5iRF/CHYhlyNENMf/vCHHUzoRUcSgzI3p6ueoh8aJoiw0gOEYW42o34ZtKmSa+aKsANXdI1O/A810c31PiT2uXnxbGn8aKUEjbLexVOxo9iwefoy2byoUTYvaZAeI4qjok5Z/XopWTZN2oZOiRVJzFbdZNFl7qRxXhAJCCPEAGsT64QZAON1XrKZJBajktj2mbk5m7J8mJZTmZc18dMgNVsml7r77rvP83ezLqJaEqAFd4HksnEh1/E111yjNjZYDlHJCepEYIk1SczmIQ6CJGr/NuRdTMyJ/eChCbOqSBi+lfjZ4FOpo34himFFgYetJJKfctq0aWpnTwtiAUpUEuunPiyBo7RESqpi/Ug6pMGmd9ern8ueq5ZdziwOksijV7X4EakdOElKyitiQRKDiiTmnCARNHLWMV/rNDv4jDFP6VrBEMd0tYJtJmO29YtrpfP/hYWGhga1Vgblpx8VUBsffjj12vXPf/5TNRNFtyKxc8vWl89P9ZR8JbvOBkxcqKJmeb0w+68dZINeHDgeZnJ2eEj0QVW3SSS2rVs+kbo3ZkvQqBw7wKrF0kECHZubPtyifv90br3UrGySroPszp8YFErbGqVi3gPSPP6bsSCJYQWJMO8R4arzspp1pvFr1xVitNJIoIPZJ9vImK3mZn3/wuxXzWcCSjZKYj6BQkg0MxyIc8CvkoZlFNWQtZPfiebnd8SjoiOJmqD4fej8Vk8Ju0Z0EOZmzgUfiPnz56uQeXa7emIMW+0LeoLR6YcY8EjoQRLERCWx8YWHRJqCJ9BVE8JLmeSQX9R8sFqaaz5/npa/sEXGfLN4/E87bZgpjVuOlNLufa0niVHlJMTMR5ACTbvI6IhpzH6oVDoAxkbFzlbyqsWNMPtVU1PTXu85TsDdAX9GPyhKczPw89DhT0IiaT/VU6JIUZOL0sdnMZkzKSUrrxd2mpogSSI7H1L1MKlyf6iUEDR0CpzW5iapfe4VCQOdRvmreesQH2ye9vE2f697p06GHdUsnfvEegr2GcRylzROOd96kpiPdDPML0RC00jTxaZXB8AwTyM40B+iW3UATL7BfbORvOro3LBJYteuXa0at0HcS9NdTqM4ZigDZlBJprQuZiLpcePG+UqObbO5GRmZoA5M76iiyQqhh0lyTZKYK4gQo44muQ+ZXCl9FEa/9UPTNPM5aVm/1WwYNMr79QjluA75x6Z3Emp7t4mseHGL7HiC/9rncUV53WppXD5DZMgeVpNEG6qbYGpGlKBpiw8KI+40WH6Ys80AmHyYfPV1stHcHEX6m64FQhL185cqiKroSCIXwwuB0+ZLzMzZJJIOmyRmS+K0KopvQrryemFHIINcjs/AJlqQydP0Dw2r3/o61T8bfNqb9u/oVhzBDEXpjzhvc4fX17xVK8OO7CGdeti1yIYFHvvOix6U2kG7q7yRtpJE2xJX0w/MhKiHZGpA4NABMBBGgihQILU/Y1Tkxdbcjbamv7EVjBXElv/85z9KqWZ8Md7gPGQHiTVJzPZByETgcNrE/5DIM9LbZJM+JQqS6Of4TMRE1FFWykt5vTDNzdoUkO3xyUUGgUcRhcCbzsOpKq4E0edeDZ9I45ylEgbKB/eUkiAL6DpYg/rFG6RxY8ex3tYisuLlahn5xe2kWFDa1iBlH/xHWsd/3VqS6DVHYr58/1iPyIGn8+AxD+oAGKxerA1mAExYdaaj8P2zuSRf15grifq5o+LL+eefrzhPMsSaJGaLVEElZiCHrp6SCxENM3DFD8mCVKEeIpFT/JvdQb59KrMlc5wD/oc8oMkqwYSpJA5bOkfCQtXuQ0M7tkN+senN1BuL1W/UyNBDu0t5F7sW2jBRtX66VFcfIaXdtreSlNlGWjMFiBA8QRsyZIh6HzXqdcS0WWeaxu9BXWudS9Kmexc1SYwr9BjHGkdibwjiFVdcodwcyJd4wAEHqCour7zySnGSxGRVV1JVT8kWUQSu6HxQ6SY0gjrwP2RAo4p63VWGaW7Wx/erJOKPA9klwSgliZKdd1j9bqvbLOXvfIQrWSio2inYaGwHe7Bp1pqU/2tpaJOVr1XLsCOKxx+1pKRNKufcJU1TfmIlKbO1TKDXCjCsXXr9whStA2Dw3eZamxVgkvmjB92nQvZJjCv0NSIdzhtvvKGURMgi5fkuvfRSOeSQQ+QHP/iBarEmiUGZm3X1FOzwidVTskUU5uZMD4RO+p2OVOUz8MYrmTMDiCZMmKCcuVMhrCTmTa/8V9oawlOGywcVj8mx2LDpg01p/7/ylRoZfGA3Kau0b8ENCxV1y6VhxWwpHTzBOpJom7KZCyFjLRs4cKBqnJeuM02uX2ra4+eoCSN+jX7IlY2RzVH6JHaLWY5EE9qKR6olrhVl+QBrrLlJKso8iYkEKFP1lCC+IwzohyCZtM5NZgLACTVT0u98Kolejq9N5TyUXgKIwuh3W0uL1D2zbbmkoFG2Xf5TWjgEj4aVm6V+XVPa9zTXtsrq6bUy+ID4Ljp+wTTbZcEDUjdovHUkMc5KYjpwTpibaWSDYG7VATAUieBvMwAGE3a662CrkhiFubm2tjbWSqKpiJLcXZ+Lvp86kbuKepYiNTcTvQyL9lI9JRswSHnoolASTWBeQBXlu/HZy3Yga7IV1gTuhcwxgDGVs9tN5n+Y6rggyH43v/+KNK/eKGGhtHuVSJl9k61D7lj3/DJP71vxYrUM3KerlJbbRU7CRJnUSsmc/0pb992sImU2Kolh9In5lHWPpmsR6wAYcs3yf00YMVEnzr82VluJiiRWV1fHWknUzxtrqzm2OCc2Ebh2aSW6KEkiFwWnXi6Al+op2YBBilQbFpJFCOvyejzYe+yxR1ZR2X7M2WGSxLVr1yoFkcLjVIPxuoiEUc2lburjEiaqdh9i1SLpEBzWPOktsXvjphZZN7NW+u8Vf3XCDzqvf1XayneQkhJ7SFmhKonpwPkiKNCYc1lXdAAMGTHMABhIIxYdW83NUZDXmpoalf0krtDjm/zPpMUjvzCAN/Tv31/uv/9+Oeyww1R521iTxGweZH1BeBiI9A1rMIVtbja/A9JLolVMzLlGZYdJtrwE9pipejL5H0bR75Y1i6Xh3YUSJqrGDgz1+A75Q+3S9P6IJpa/UC399uxSVKmQSktaZfDqJ2VB/y+KLbBRSYxatdNpdGgAwUMHwLDWAMQVAj6xXgXhxx8UoiCvtbW1vopr2AZ9fQhQmTx5ssrqwnXjfp9yyily5ZVXyqmnnir77bdfvEliYk1dr8EPXAgGeJgPXRQkkRvNQ0rUGsSXXYB+qIM4NuAcwsizlUxJ5FxQD3GuziaBuT4uCMovsf6Zh1R1jDBRMbR4qm4UE2qXb5a2Ru/jsG5ds2yYXS99JhaXf+p2slo6b14uImPFBtiqJIaV79ALiIImty6NvjBHY41DUXvttdeU6GIGwOSTZIe1ZpngvONWtzkZsNLdfffdiuTrMX/uuecqd7xHH31UXnzxxfiTRC9IrJ6CvZ3fw0QUJJGbStoenEyJys4lnUEidP3GMEvzmcfmocP/ULsAaMfZfFRz0Wirr5W6l9+SsFHWq7hMjMWCNf/zr0Ave36L9N61yjqSEiY41VE1L0pL2+FWnLetSqItfaIfmFohhFwrTJZaZcTPn80+PozaNI3fW5T3lXU3yLWwEKObzXu58847q9+5l9w7SD65Er/xjW+owN6CJ4nJqqegukVlCg4LmM0xAZB1H7+BMCaQMKuumCSRc4HEkwyWnU0u58JkFBS5bXjtv9JW0yihoqxUSioL/jEsSnz65krfn6lZ0SQb5zfI9mPCXeRsQ+eyeqme86TI+GPz3RVrlURbSGJin1Dt8GOjQTQgUBBG1lmsd2z8zTrTufjK2+ST2K0ASCKAGHJPEus3U5mNVrDm5nTVU6L0FwwanBeRZzR2aPhFhDV5hJkQXBNQ/A85Fy+lAv0cO9fSfHy+7pnnJWxUTRhk3YLkEAxql3j3RzSx/PktRUcSQZf1L0hN3UFS2jm/yrptKXlsJ4kmuG6QJ9qwYcPUHI9QQwAMcz0WPK1CQhx5X9DXOiqfxK4FkAKHsQ4xRDF89tlnZfny5cryyrnBLUaNGhV/kpgMmaqncFHCLJkXFkkkrQ3+h/iDEHRDbitbEl5nAwYm/fdaKjDKfjfPe1Oal22N+AoTleODIcYOdqFxQ6201mU3x2xa2CiblzRIjxH2BANEFcRS/u7fpXXvH+S1H3EhZPmGF8WO/0MGaQCSqE3T+DRyTmad6WzdjKJMgdP2mVpaCEoiBP2uu+6SO++8U5XgSwTrcsGRRJ1bL131lDgqibq8Hs6y2mcvioTdYRyfXRimCPrPPQpiYgiaJNZPfUyiQOWIrZOnQ2Fh9WO5RcQvf75axn2nuEgiqKpfIFtWL5CyATvmrQ/OJzE8xU5bv2ic0+bNm5XKSMQ0/owQL00YURyzOeeoyvJ1zyKw0jb873//k/POO0+pvdRqRlSDM8E3yDDy1ltvxZ8kmlK11+opcSOJJPxGGU0srxe20heGuRn/QyKYcSxG4Q2aIIJcfRJbNqyQ+rfnSRQo61c8NXuLCZ+8ujy3z39QLzWrmqTrwPxFtOYDTG1VH94rTQMuy1sfbDQ320pccyFjnA9BErQddthBmTm1ysg6zvqZGABjU8WVbjFXEolpINUNRJ0I5yOPPFL5lZqgrnPsSaIerJhevVZPYQBFYW7OtWJJpvJ6NtVXzgSuAzsT/FKIhmMnFtY9yLXfDc89JNIact6bz1DaJXiS7JB/1CzMvULP8he2yJhvBJPSKk6oaNso9XOelbJdDs/L97vAFe99CnKTz7HIi0tjvWCNgDBSWOGjjz5SwoKZZidVAEzYPoltn5mb4+6TiFo4c+ZM+fKXvyzf/va31Wuas+hNCVbL2JNEGD0nykl5rZ7C4IpCSQR8TzbRXF7K64UZfRzk8bWPKJL2XnvtpcwIPPRhBsVkG7jS1tggdS+8KVGgYkTvokqcXCxormmUlurcS3Kue6dOhh/VLFW9Yz9N+wIErcuap2VNv11luz59Iydstqp2thHXMMkY54o5l4ZlkDVEB8CwdqCC6TrTNDMAJmwlsa6uTt2PuJubIbpcJ4pWmFHOiYj97EMEM86V5PrxOjDMSiVhPXi5kEQeBvwPkdrTldcLW0kMwtwMiedcOAfIrvYRDdNUnsuxG6c9Ia2bw82hqdF54pBIvschWqx5YnEwB2oVWf5itez4tZ5SbCgva5XmaXfIq9vt164e8TOKhNI2EjJblcSo+sT60adPH9WArjNNo0CGWSEmbJJYU1OjfsbR3Azn0W4CNNzXENlMC6u+p7yX12JPEiGHfokSJ64l1bAmA52M2k/f/JbX4zxQGm1VEtn1oYYOHDhQ3SdzQgk7vU62x66b+oxEhU479Y3suxyiw4aXPg7sWGveqpFhR3SXTj2iK8lmC4Z1WyelA3rKp6WVSgyYO3euUm90tCy/hzF/26okFnupQBNYDGnk1qUfus4044T7h+UKQglpREQK8trVfKbAhZ2wOwzwvOh7Ro3uX//613L22WfLX//6V/nud7/bQZDCJB17kpjNJKEvBKw5jMCJbJQ+3kd0F4EdXsvrcXxk97CQLZHjIWV3RyLVsWPHqgc5EWEqidkGrjQvmClNi1ZLVCgfGN8C8Q6pUf3hJ4Edq61ZZMXL1TLyi8U3Vpja+634r/Q6+GIV2IALDkRA1w/mOQ86fQpwSqI9+Qi9gD5gdaOxpr/88ssq5y7EkZRxrEdmAEyu5K7ms5J8Npy7HyDYXHDBBUp8QpGHPHNt+PmLX/xCpk2bpgpzEPvANeI8H3/88fiTxFzrEocJryQR6ZwbyMTkp7xeFD6JfskW/WEXx0RO4XD8RoI6tldke+z6qY9KlCjrUVw1eosBrQ3N0rypIdBjrn6jRoYe1l3KO8drUQoCnWSD1H3wklSMO0i5qpj1g3X6FNQjNtimysjCly3R02Y2m2AjSbSxT3o9ZIwgTnAvUcNYj1avXq2KaxAlbQbA+L3X1dXVsTQ1c+5Tp05N+f+//e1vSV+PPUnMZiLQkqsNJJF8gZSkS2aS9XL8sFPg+LlGOPTif8g5pMpRGRVJ9Bu40rppndRNmyNRobRnFykps2uCdcgd655bEvgxWxraZNVrNTL08Hg7ymcDVcFj9ZNSt+M+UmoohYnpU1AZIQKQRqpGaJVRq0d+VEYblURbTeA2kmnunb5W/M6GgUYKOZRGimwwTnDrIu2OGQBDgGime18T08hmUtyQMJs1HaLLeUCg+cl14CfqK5svhCuslLwWe5KYLfJddcUsr0dKGJKL+oVNSqL2PyR9ASbmTBOabUpiw3MPijSHR7gT0XmPoZF9l0N0WPd8cP6IJla8Ui2DDuwqZZ3sIgpRoLysSWTGvSL7nJ7yPWxI2WjTePZZ/DRhNH0Zvfio2UbIdFoSm/pkk7nZRKagFdb9vn37qsY1NQNgWIsxw+qNBSbqiiSBUnwGc7NtG4lMgAzvt99+vj9n1x2OEPlUEiGnKG5MYJSky4Ygpjt+UPBCQrX/IRFSo0ePVjWYvUwcNpHExro6qX3+VYkSlWMGRPp9DtFgywcbQjluc02rrJlWK8WKrvWzpWndCs/PP2m2qDuLy8v++++vTI9YOvBRe/XVV5VLDHl1USBtVxK1VcQ2Qmarudlrn7jHKIIEcJCH+IADDlACB0SSnL6Mk7ffflv9jvqoRaVszc233nqrUjNxJ2Pdnz59esr3kkz8a1/7mno//bz55ptzPmYqZFrjY68kZvsw54skMsAgVPhF6PJ6uRw/nxVXODcGMzv2ZDWy86WC+glc4X6sffKf0v3TaBfgiiHFl9ak0NHW2iZNG8JLn7TipWoZsE9XKS23h8BEBdb9yvf/Ia2HXOD7s8yxWmWEcGlfRooUoDLqUnDal9E21U7PZTYRV5tJYrYmcDONDsDc+slnKuOzzz4rV1xxhcrzC7H0+x3333+/Kn932223KTIH6TvqqKOUyTtZ8Q/USjY5J554ovzkJz8J5Jjpzht/TQgm5mZIMms54tWYMWPiTxKzRVRVV0wixI1gJ5upbGC2x49SkeMBQg0FkF2/EWM2KIlk8qdE4B5zZku4I6EjynrFz6fFIT02vLJMJMRCPQ0bW2TdrFrpP7k4x05VyVrZNPcNqRi7T9bHYM5FZdRKoy4FB2nUkbDMHzRUxnR+1VFBz2W2ETJbfRKD6hNr2qDPAqWIFyCn4JNPPikPP/ywrFmzRnbddVdFyo4++milVqcbKzfddJOcddZZcsYZZ6i/IXZEDt9xxx0q4jgRKOA0kOz/2RwzGSCjt99+uzzwwANqw8QGSgM3ONTMoiWJUVRd0WoZA5fIIszLDKzE+oi5Hj8spDo+kyr+h+xWGEjZTF75DFwxSwTu1rezNH+0UiJFpzIpqbBrcnXIHeueCT5oJRHLX6iWfnt0KcpKPco8uPK/0rDTnlJSXhFKKTh8GbGOoKi8/vrrSjXSPmoQy3wQNRuVRJ2UuVj8JMvLy+WQQw5RDd8+1o4TTjhBnn76aTn11FNVAYyDDz5YbrzxRmWyNsFGZMaMGXLhhRe2v0YfDz/8cFUbORsEdcxf/vKXcsMNN6jfDz300PbqNgTUIqBcddVV8SeJNpubGVjsRvFr4KamKq8XF3OzmewbGRpfjmyvf76URDNFD6aD8gf+IFF7enWeMMSqCd8hGGx+b13o31G3tlk2zKmXPhOKM31SRXmj1E5/QMr3/Wbgx9aRsDoIhmTMWmVkzmBOMSOmo0qmrMmYTXOGrepm2NVWABG/3P+vf/3rqrEusrGAMCZzuYJw0a9EcYi/582bJ9kgl2Pq8fTggw/Kb3/7W2WqRnnEZQzhB96Covjmm2/KXXfdFX+SmC2iIIkwcpyjiaSaNGlSVjWcbYlu5ie5yDDR+vU/zHTsoMGxk1Wi0SZynY+yoqlGPnn9XYkaleMHRv6dDuGChaJhbTTbjeXPbZHe46usIg1RonvDTNm84Qip6O3d78oPdCUuIltZdGm8hv8yhFHn2yPC1cy3FxZhslGx03O3bebmKEhidXW1uu8ajJXx48erFgdoK9sjjzyifl577bVKITWBao4p/YgjjigMkshN8psXL8wUOPQF0zJ+C+xMiZwKY0LXSl9Y5QU1CTX9D/0k+8507LD6nixwRdfDRh3QEdj1z/xT2hqj9kYU6TTi8wnGoTCwceYakdYQHRINVC9vko0fNcj2o+NXFiwIwJcq3r1b5NDzQzl+ssAV5hTS6NCIJmUTqvPtsXlmnmTjrEkjgYlh9iffKGY/ydraWhk2bJjn97Pm0Cf4gAn+xs0hGwRxTDY6WARpyTYjWD9xx7DrDheAkqjNmR999JFyePWSnDNb6IchLEVO14bGx4EIQMyzQZlYdN/9kvtsVEqiGN966y0ZOXKk2u0pn8WWFql97mXJB8r7Fl9S5ELH2icXRfp9qInFjC6lq6Xxw7dDObaXFDiojJjm8D8j9xyWIgQBFmnMdDTWAMzVuc7PtuYj5BrZpmZHca1qfCbThmhRave5555rf40xwd+4oGWDXI6p7xlCGeMTRVx/Xq/HpnhTEEpitiQFphwkdMURbc7E1IyCFRY00QpLYsfvgXNiImTnFOSEoB/kMEwpOnCFhv8kqi41Kdl9aTS/+4K0rP08kitKlHQOxunewR5smrUm2u9b2ChbljZK9+Hh1Z63GUxFXT5+WJpG7xE4UfGr3CWqjFiotC8jEaNstLXKSPOrMtqqJNpmao7SJ7GbzzyJpKo57bTTlKsWYgvpajiOjkwm+IWUM9ddd536G26CQq1/R+ggWJTvJcrayzFTQT8vEyZMUPWaSaXzf//3f9u4w2l3C9b/ojU3B50CR5fXMyuORJGiBgT9HUwATG6QXAYKEU9BwySJYRybe0v0F4M8WcBQ3dQnJR/otGNf63bfDrmjYWV15N+57PktMu6M4nVdqOxUL7VvPCCd9j0p0OPmmkybxRaVkca6xMINYcSfG3URkqiDX7zUDrbVJ9G2Pul+Be37HwRJPOmkk2TdunVy2WWXKZ/W3XbbTZ566qn2wBPqj5vXc+XKlUrY0CBqmnbQQQfJiy++6OmYqaDH9rnnnit33323XHrppbJgwQI59thjVTAqKiXrJsckPU5BkMR8psAx06lADsnsH/R3pIKuURkk0SIaGzWUY+JLSRh8GAiTJGp/ISbivffeu0NppeZVC6Rh9mLJB6omfj4+HAoDW+ZukLaWaPwRTXwyp15qVjdJ1wHFq0z3qHtLqj89Qsq335oAOQgEqdyp2tPduqmm04toX0aiULXKqEmjNv3ZXAHGVhO47lcuBSq8+iR2zSJLyTnnnKNaMmjip4Ei7UX4SnfMTCD345/+9Cf5wQ9+IL/5zW/kX//6l7IYsokhuhmRBRQtSQxC5eOBJwErObWQe4kIijL6GASpVurgDiYrgjvYTYRZFcVPZRSvYGdFDU4mCvyEkk2uDVMfknyhcoe+eftuh3Cw5omFefvu5c9vkTHfCI4gxQ1l5W1SOvNukcOSV6XIBmGSssTawahSmKaxRKHm4POtzdJaZbRRtStWc3PbZ/cM14K4gzF++umnK0L66KOPqjKElNhl4wIJJkE4fo8FQRKzeaBzJVeEwUOoeKjxP0y2e4kizU5QRBS/PUzMVIJhx8s1jSJ6OiiSqGtIM9Hi20FS3GR9bqurlrpXtu6Q8oHyAT3y9t0O4WDj26vz9t3r3qmT4Uc1S1XvgpjKs0K3smXy6UfvSuVOEwM5XlQ+gKbKiIKjVUZII77U+KJBFCGW2sfaFkXRRuJqs0+ibeD+kUgb8/KZZ56pciViEWWzgjURkkjUM5uVop1ZckmB47W8XlT1oXMhWnwWswf+hyhvZv4nPQmEnWInV5g1pCllRMoes7yQiYZXHpW2uo45FKNCaffiTFtSyKhblp8AKIXWrTWddzi+eGuBMzd1XvQfadlx10DmqXyZdxNVRsyazGn4p/E7WSa0yoiJOp9Knq3m5qhS4HSLOUlE5LrmmmvkW9/6liKJmJipnpbsPhctScyGwDEAcTym6oiX8npRkcRsv4MdAxFTkGWCOxL9Yczo6TAmhCCUxGQ1pHEQT3ZcJt66Z56XfKGsbzcpKbNvYnXIHnUra6StMbyqR16wZnqNDD2iu3Tqbp/5LypUVdbIJ288LFX7Hp/zsWyIJlYlCLt2bfd9wxWIlGqQRvLbMXejMmrSyNwdJbEtViWxtbXVdwocG8G6SWUh7SKn13jtB6ndwbiWBUESozA3I/1DqHg4CYbwspOw2dyMHyXkih0puQOTPVhhBpfo4+dybM5h5syZ7T6U+hxSHbf5/VeleeWnki903t17AlaHeGDLgnCfby9obRZZ+Uq1jDh2W5/oYgJrwHa1b0jNpsOkPME33C9sMuua6hgpvGhqs1tXpwgjTftg60TezOlhR/ja7JMYJnmtra1V1z/uPomMF1LnUJ/czPZijnv9HNi3FYgI+qJ4iSDSxd6JkkWt8io1mz59Npmbybk0ffp0ZS5HEU31sOsBExbRzYUkYoLhHHC6Jd+TeQ6pAmLqnnlc8onKMeGUEXPIHzbNWi82YNXrNdJcl19FM98or2gVeevunI6hff9sUskS+8P8hnKIPxlpTw444ADlP8br+GS/8sorSgAgrQpmxTDWH1vNzWEriTU1Nepn3M3NqNB/+MMf1PlgdsaHn40F147GvdX1wgtCScwGeqeVaUeEaRmfPRJYQkj87DBNc21YOzs/aiXnikO0zsFkJpdOBjN4JQxkc2wmPEz+TIBMkPjveCGfLes+loaZH0k+UTE4t3rXDvZh86xlYgNa6tsUURx6WLwVjlzRo2ypfLJorlSNGpvV501zmy3IZNplHtVmZ6126WTeqIyIG6YvYxBrka3m5rAVztraWnX9MNXGEVodZDNx0UUXqet1/fXXq00F1jhcGqgcpF0daEVLEjNVK+HikfGcMkuJAR02kUSv5mZtLudnMv/DdMcPiyT6TYGD8kvCcnY/6Uz+pm+FRsMzD/KESD5Rtr23a+4QDzTVtErNh3aQRLDy5WoZdEBXKetk3+IdFUpKRTrPv09aR16RFdHT85FtJNFPf5jbaeTsZW3AnxHSSC5fzNT4oWnSmG3Z2GI1N1dXV4daajcqkkjp4Mcee6z99Yceeki1ZCgIkpjNDdMDCeKRmL6GBwlCBUhvk22x9rAqovhV44j0xXcPiRnC64ewhpnr0Y+SCDHkHAhMgeQmJshOR2zbGmql7qXpkldUlYuUF+/iXYjY9H6tSEurVaR1zfRaGbR/vE1huaJz1Rb55I3HpGrfL/n+rN5c2qSS5ULITJWRTBymLyMpT5hHdSJvfnpdG2w0N3Pvwiav1Z+RxLhC37MDDzxQnnjiCSUaoY7SMDmTgomfcAZawZTlywbK1p6kIgoPDwSRyGUqqOQy4LS5NmySmO74mJZJD7PDDjvIyJEjfRPqMM3NXlVKfU/Ifzh69OiMk1PicRvfeFxaqxskn+i829DY7j4dkmPTrE/ENqx4sVoG7NNVSsuKd6zxnPWoflnqag+TMo8WE9uVxHSbYj9A8EBhpHFcVEZtlmadwNSoSSWWmlTXIcg+BQW9DoZtbu4Wc39EwIbg6KOP9vTeoiWJiQTLTMZMuRqcgoP6jrBIVjqlj+8kVQJJslP57nk9fr5IIvcE30POI7HkoRcztlYF6qY+K/lG1biB+e6CQ8DYPGu52IaGjS2yblad9N+zuF0bKipbpfrVu6TsyLML3icxW3BMyAJNq4zal3Hp0qXtKqR+j0kKbfRJ1GtJ2IErXSJONxSkmRmSi4JIuV1eGzhwoBx66KGK83D9kq3HBUESs71hmiRmKq8XRBR1WOD4lNExgYSM7x7pejDN5iKPh6mEpiOJ2ieUnIeE6uNw7ee47eaHj2ZI09J1km9UDPfv0+pgL1oaWqX6/SViIyjV129SZykpjddCFjS2K18oG5d8JJUjdvLt/2cTCYiKkKEyYq2haZUR0oh4wlysVUYIYxSVTfyCPoV976qrq2OnJGqC+NJLL8kFF1yg/BHNKG2sjD/5yU/k29/+dlJ3g4IgidmCC8JN5wFIV14vF0RhbiYxpgZ+BEQq8UATwZxrwEw+lETILefA/7gn3Bu/xwUqn9jUR8UGlPeJrx+LQ0dsmlMvbU3hbf5yQd3aZtkwp0H6TCju6j6lZSKdPviXyIjLPH/GtvQ3+eqTqTKS2YM1BoUR0ojKyNzMPE2Ub6LKmC9oP8kwSWJNDBNpcz1wJ/jVr34l06ZNU+rhV7/6VXXvSCOHoHT22WeryObDDz+8Q57QoiaJDCpSwujyemE8iFGamymtxy5h1KhRqgXxsIRNEhMJtBlkk5j/0M9xQcuGlVL/1lzJO0pESqryP4k6BIdN79jnj2hi2Zudpff4/JSXswldu2yU9W8+LV32Psrqkny2B4mwUTdVxrffflsJEBDGRF9GEk3n4xpGEXFdE0OSCKZOnSpPPfWUnHjiiXL11VfLgAEDFMnH/Ey+xBtvvFEeeeQROeywwzrcu4IgiX4HJEwZPzcuEH5uJCINC1GYmzXZJafjxIkTpV+/4JI2R2lu1jWxcyW5ekJtevERkZb8pr0BlTsPsG7hccgNq15fIDaj5sPl8unqidJroB3JvvMaxLLxOWmsP0hKPVgkbFUSbZo/uD6sCyhSBHhCNnTENGsQfTUjpoO2zqVCFCbwmpqa2JmbAaSe+/L9739fCWJAV405//zzFYEkOJQYAESzgiOJfqD99ZDPGcBe8wXaqiQCfClxOvZaLtA2czOTIAFD7EqDILmqlFBrs9S/+KbYgKpdB+e7Cw4BorWpVZrmrUQgthr4Jvb6Zr57kX9Udm6R6hfvlqqj/y92hMzWnISmuonZElMljb5iDYIwQji0L6Mmjfwe1vWNQnGtiamSCHkfNmxYe0Cu9nOFDxHUyppLJTYzkFffp4IhiZxQpvJDul4xgSkEdMydOzf02sphKnHkM4Jccd6cTxgJu8PMk6gHKfeEc5kyZUogNTEZCyM3LpLWTXViAzqNSl/ZxiFeWDd7i5Q02umPaGLzrEWy6ajxsl2f/NUrtwU9K+bLpo8XS+WwkbEzN9vap2SEjNdwFaIREIHKqCOmybShVUZNGoNUGaNSEvtmmSkkn2B9VdVTPuMIXCvuoV7bsaqaYwzrp76WBUMSM4EBCik08wWGHVQCwvoObZplwBJ8E2bZv7CURK4L0cvsLiG5QU4YvT74QGxJc1zev0e+u+AQIOrn2rH58IJlLzXKdl/Ldy/yjzJy2b93j8iwS9O+z9bULjb2yQshQ2XELE3jM5AVTRhZjxEFtC9jripjVCRx5Mj0Gw0boaOyUXuBDjTSvAGxhuuvz80MRCp4kmiW10usVxxHkmjWLt51113VTcZxOCyEpSTqiYJJhBQ3QU6CzYveldbFa8UWlHaLZ51Ph+TYNGulxAUb35gv6/cfJX365zeZvA3o3u1TWffWC9J18iGx8km0kSRmY9rl/VjxaPicQ0x0xDQuYMD0ZfRbHzkKs3xtbW0szc2kySOSedy4ce21mSGNNPxK4RMQdoJaIJKkQ+J9vFbQ5mb8DjFl8nqy8noQLOTwuJBEbjRJMM3axZTRCZPo8mAHHXjDgCTQBhU0jAmwfuojYgvKB20nJZZN8A7Zo621Tba8a2d+xFRY93aV9PmCI4msEd3XPiXNTftLaYqULbb6JNpGEoPoE5YjrTJy3bUvI75xqIysb6bKmOn7ovBJrI5hnkSwfv3WADZS4aR7z+WXX97h9YIhiYlgsLE7wSEzVXm9qJREdkxBDE5Sw7ADMGsXhx0YE1T/Af3k4UfV3WOPPRTZ5fcg0bp5g9S9+b7YgqrdvFWJcYgHqhc3ScumaokTPnn5Q6k7eJR07lorxY7O3Zpl7XN/l65Hnxl7/798ImjVjmueqDJqX0bcqiCRFFTQpDGZyhiFubm2tjYQv/mogTBD3wlw5Sd8gob5n59ca36yJvOart/M3wVHEv2U14uLuRkixYNCdBLh6+YkFvY5BGVu1gEqqJKQXFRdBmzQBLfhhYdEmsK9p35QObp/vrvgECA2ztokcUNbS4ssn95ZdjrEkUTQq+wD2bxihVQOHhwLc7NtfdIZKcLsEyojufxofJf2ZVy5cqXMmzdPqXnaNA2x1JkyovBJ7BJyRpQwwHqbaEn1ioIhiRAnCAjJpCknNHnyZBVhlc8chvo7siVZOjUMpJfE0jwwyY6vH9owdsBBKJU84KigmAxQELWzbNDpddpamqXuuVfEJlQMSj8GHeKFTbNWSxyx9tm5MmzvYVLZ+fPqTMWK8k4iJTP+LjL4wg7/c0piZug5O6o+qVyXPXq0B1bgdqVVRtZ7+gNh5PUwCVxbW5siiXFUEpMhWTYY8zX9e8GQRKTSGTNmqB0ISpUXp1fIiq1KIuQV/0POC//DVANTP6hh7aJyJXKooJwHDzeR5eYEHDRJbJrxrLRssMsUWLZddrs3B/ugFI1ZiyWOaGtokhWzusuofR1JBD27r5N1M16TrnvsZ7VqR39s61PUJDERuFoRbEHTKiOkkVyACESkutNmaa0yFnsy7WRIthlK9lrBkEQGCIEQfsrr2WpuhhhimkUeNv0PUx0/TH+MbM3NPLwLFy6UxYsXqyhsHuhkxw6SJNY985TYhNJunUTK7ZncHXJD7YpmaVq/UeKKNU9/KEP37C8VnZqk2FFSWiJdVz4mbRP3kpLyCmuVRD0/2tQnvR7YQFxNlRGyCIFDTURlJOsHfTV9GSkvWIzRzbmgYEgiwSl+yYyNJJG8gShv+FKOHj064+TQXqc4pPPIxtyMCooPJY6vmVTQoPrdsuxDafzgY7EJVbsNs2pyd8gNG2dtkTijpaZOVr6/vQyfZE96qHyiS/cGWfvMv6TbMae2v+ZUO+/mb9vmNvqFJdFUGRFcIIzkFaYULwRS+zLijubnura0tCiSWChKYtGRxGwGLOZmW3wSGdCEp9PGjx+v0gJ4LkEXclUUPySRYBT8D7m2mRJkB6kk1k99UGxD5biOPqQO8cWmd4KNxM8HVj25UAbvup2Ul9uSaj5/UNU/St+V6jVrpNNnlg5blUQbSaJtSEyBo1Iede+u2ogRI5TPIinjII3kTtYqoyaNmQI7ampq1M9C8UksOpKYC4ELMzeWF5JoKm+UpkM69/sdYaXB8aOE4hdCkXB2cSi7mSaSoEhia80mqXvtHbENnYb2yncXHALElpnxyo+YDM2fbpbVH+4gQ3ZxaiKoqBJpff0uka/+wmol0TbialstaS8uV7htkRKPpoNQIIxY7yhQAUnUibxRGROPVVu7NTtAsSmJ9jwNOSKbh0gPgrDzDKYjWQzUN998sz01jF+C6OU7coFXIodPKIFDO+64o+yyyy6eJtqgSGLjy49IW4N9tXTLeheX70oho25NszSsWCeFgOWPL5aWFntIR76x/XZrZOlzTygSYKOSaJtpN4qk1dnAj18+1xOyN3z4cJk0aZIccMABKrCSY5Bi55VXXlF5lpcvX6786vVajWUsXYxAMtx6661KycQfEhGIyifp8O9//1ul7+P9ZDV54okntvn/6aefrvpvtqOPPlrCQlEriToVi1nMOkq1ct26dWogDhkyRPkfZvvghW1uTndsJjEeqlWrVqmHjZ1YlAooOeBqn31JrENZqZRUFvXjVVDY+K5dUfO5oHntRvloVi/ZeU9XhQWUlpXIgHUvyGtvVqk1gcUZq4hfn7UwYJuyabO5OReFk/tO4CtNq4yMgZUrV8qXvvQlZZbGDQyCSCU3r6l27r//fjnvvPPktttuUwTx5ptvlqOOOkpVHEPRTMTrr78up5xyilx33XXyxS9+Ue6991457rjjlAsX368BKbzzzjvb//ZbwtAP7LvTEUKz8DCDV5Kpldr/ENMstRTZNeTy0IVtbk51bBJkv/322+phQgX1QxAB56xTPGSLptkvS8tq+yJOK3cZaNXu3yE3bH6nMFREjS2vV6sSgw5bsX2fFtmjfpUihsxHVIZCTSKIkDJxEIN8wEZCZrO5OYhrpVVGilfstddeitBRro4xQGOdO+aYY+SWW25RZup0uOmmm+Sss86SM844Q631kEUI5h133JH0/b/73e8UATz//POVy9ZVV12lxJc//OEP27wPUqiTjdMgsWHBrtEXMRgMYUc4mylqtGqJekiZHAYgxbRzRT4CV0g38MYbb6gdGBHM2SQxNXM8Zov6qdtK8baganzHag4O8cXmWUulkNDw8VpZv7yjklHMa0HvkpnSqbFBkYB9991XJf7H/YfIWOa6adOmqeIGBD+E6aJkwjbzd6GYm/2gZ8+eSt370Y9+pEzSpKc78sgj5bHHHlPqHi5Wjz76aFIRBResww8/vP01rht/M56SgdfN9wOUx8T3v/jii0qJHDNmjPzgBz9QvpVhoWDsYdk+SGFXXTFT1ODzgmyMXwOTULrIX5t8EtlZmztaHH0huvhZ8IBke+1zTQTesmaxNLy3UKzEdtvluwcOAaFxY4vULVwphYblUzdInzPDC9qLGyq7iPSZ+6Rs3u9b7WoSTUfGmlU+mBN1VCwtqLk8DqqdjeqmXqPCvFY1nyXSxvJH+8lPfqJeg7BBHhOxfv16tS4n5gjmb1y0koENSbL387oGSuPxxx+vClSQi/iiiy5SyiZEMozzLxiSmC3Crrqi1UoGDHmaUA5h/0E+ZGGbm80drU7Tk6pMYJRKokp7Y6nFrLXE0o45+Man725NfVFoqJm3TD5dvav0GhieChE3DBm0UeYsmi8yalTGKh8QRkzRmKZJiwJZ7NOnj/o9KOJto5JoK3EFYfarurq6Q2QzibW/8IUvSJQ4+eST239nHaZYBSQVsnrYYYcF/n1FTxLDNjdrfzsmEqJ+BycpKm+7kgjYSeu62Nmk6UkGPfllQxLb6qql7uW3xVZ0dTkSCwabZq2XQsXyF2qk1zfy3Qt7UFZeIoNXvyiNjYeqeVXnoU1XSxizIoSRhp+5Ml1/pjCiNvqNhrVdtbPR3BxFFZiamhpf1VbYMDCGKE1rgr9TCSy87uf9YNSoUeq7cIUIgyTadafzZG4Oi2BxXByfedCRp8MgiFH4JAJ8K3DazTZNT9CJwBte+5+01TaKjSgZ0FvKuxTMo1X02DxrmRQqNs9cKJs39Mx3N6xCr/6NUvPsw2pewhUJEsjPVJtZTM0UP8A/bf/991fqDoEFS5culVdffVXNnUuWLFHqo98gPRtJoo19ioIk1vosyce4wK/1ueee2+ba8TfraDLwuvl+8Mwzz6R8PyBNDxsUrwU4ilpJhHT4fQjDqrrCgMLBleOTpDNTNndbzc0oh4CHY+LEiYE/hNrn0Q94f90zz4ut6LLXLvnugkNAaKppldoP7Sr3GDSWvdwsu3w1372wB0oJbH1LGuuPkdJu3dTcypyj1wm9uU2mMvI3gQ40TIBsrLXKCGlkPdAqIxGpOg1bnAiZreZmrfxGaW7OBNLfnHbaabLnnnuqQFVS4KBIEu0MTj31VCUekfIGnHvuuXLQQQfJb37zG2XGvu+++1QGkT//+c/tfbjyyivla1/7mlIX8Un8+c9/rmIDCHAJAwVFEm1RErXZAWaPgkhUXJgm7bCURHYomMk5PhNeGJNVNn1v/uB1aV5urx9VxY7O1FwoWPbaGpECTxXz6evzpfrQnaXbdpvz3RVr0Ll7m2x++k7Z7uTz2kmI2cw5izlMt0SQcxESQONzbLpZH1jcKWEKmdSkkQwRiSTHVpJoW5/CimzOxdwMTjrpJJUP+bLLLlPBJ7vttps89dRT7cEpZDkxryUBreRGvOSSS1RAyk477SSPPPJIe45EzhHr5N13363GEjEORFqTKiesXImOJAYY3cxuk90iuZPIcUSSbP0dYafZwSQS5CRAbigSiZKjSZvMw0A2VVfqpz4mNqOhR6kUV+GmwkXT/DopeLS1yfLXS2XnY/LdEbvQe+AWmf2bB2To8QdKt5EDtgm0Y67XRRL8qIz4KNJY/LE2aZWRYEDMk/iWQRh1WTgbk2lz3pkU0EL0k6ytrc0qWPOcc85RLRkINknEiSeeqFoyYJF8+umnJUrYdafzgKAIHMeYM2eOeuAnT56sHvKgvyMKczMBKqigDQ0Nyg+C3W1Q5fOSwe+xW9Yvl/qZ88VmdO1bxVKS7244BICa9z5PPVHI2PDiPKk/cJRUdd1an9ZBpLzlU+lRvkAen/AP6T1lZxl+4kEy9Pj9papfzw6ZHzRh9KMyMrfShg4dqj5D/kXWD9KjMA9jjrYtshk4JbG4UFAkMVufRB7IXIDZAP9DHhzk4kTZNwqSGMTx8XcgjyMPAgmy9W7RhtrQGg3PPmi3+a9HV6nq7AhiIaC5vlVq5iyRYgDlLZdN7yw7HeJIoolRu22Wd4f3kA3T5qk26xd/kf6H7ibDv36QDP7i3lLRfesmOpnKaJqngVYYk6mMzLGoiDRKtEJIdIod/BpxWdJm6e222y6vJM1mn8QwUfNZnsRiQ0GRxGzAwMql5BIJVlHe8DHAxJzs4Q2bJAbhk6jrSFOKCFOIuYMNU0n0o4K2NdRJ3YvTxGZ03mPnfHfBISBs/qBe2prCS7RvG9Y9O0+G7ztEOlW6ms4aJS31csi1u8t/v7m1PnxbS6usfmamamWdO8mgY6fI8JMOlgGH7y5lnSra5/9ElVGTRz3XpTNLm4m8MWNj1YE8QhqxVnE8M5F3mHV745QCJ+w+VWcRuFIIcCQxSwLHA4/TKQmyCU7BZBD0d0RhbuY8SM9AjiXyOCYrE5iPsn/J0DjtCWndkp8aql7RaWzqceAQL2x651MpJrQ2NMrymT1k1D6FVac6V/TsvkJGHLuDLHli2+pOLXWNsuzBV1Tr1Ku7DD1uPxn29YOk777jpOQzwpJOZfRiluZ9WHQowUbj85AVijPgM47vOJYfncib9GRhm6iL1dxcW1vrSGLckc3DkU0KHAbkBx98oB5UQtszFde21dxs+lESno8ZI9XxbfBJrJv6rNiOTkMYC+Hda4fosGnWCik2rHl6vgzds59UVOTmglNIKJE22fvsfrLkyYUpKzw1frJFFt7xlGpdhvSRYScepAhjz/Ej2telTCpjsuCXRDMqr1HRhaYTeetygViCgJnIO4xygTaam51PYngoKJIYBcHCNI3/ISCwgxQHmcADH2T0cbLj+yWJfs7DhsCV5o9mSNPibTPR24jyXlRXcCQx7mhpbpPq9xZLsaGlulZWzt5ehk9am++uWIXK1rUy5aK9ZNo10zO+t3b5epn32wdV6zF2mPJfpHUdvm1N3kSVMVmKHYij3qQnU+8ggUTc0iCamzdvVuIFVq7EcoGoYEGojDaam8Mmrm1tbYokcj2LDY4k+iCJRJ9BrPr27atMs14flLDrQ/tV+sivxHkwcYwbNy7jw2WDubn+6UfFelSUSWmF8+cqBGz5sEFa64rzXq56aqEM3nU7KS93AVgmRu9bL+/16yJ1a70H92ye+7HMvvIfqvXee6wii0O/ur9U9d3WapPMLA3Zo+HO5CXFDq9hDaKR1xZfRp1iB9LIPG+qjNmmsSlmc3NXpyTGG9nskrzmSeQhw/9jzJgxyv/Qz3fZZG7GjwUTM8Epw4cP93Qe+TY3t25cI3VvfSC2o3ICAT8WR147eMamWcXlj2ii+ZPNsvrDHWXILvYr91GitKVGDrl+sjzxna1BLH6x4c25qs06/88y4PBJyhw9+AtTpKJb5w5zIoGE77//vtrEExSZTYodAlrwMafxuU2bNinSSU5G1gDIpFYZkyXyToViNjd3cz6JxYdMKh8PBP6Ha9euVXUY2YH5RZhKnNfjM8EQZLNs2TKV9R011M/xwySJmfre8NxDIs32qxqV40fmuwsOAWHTrFVSzFj51FIZtHOVlNrFBfKOPn1WyuADh8mKl7Mv1UiE9Kqn31atrEulIooojP0P2xohvWbNGkUQqbKhK3OkSuTtNcUOf+M7T0MgIG2bVhkXL16szNZmucB0hMtWJTEM/0sNhCRctBxJLEKkU+EYFKS34aHAby/b+sv5NjeTBxKnZiYGzsOvZJ5Pc3NbU6PUvvCaxAEVI70Tbwd70dbaJlveLT5/RBONqzbIotk7yY67ubyJJkqkVfb72TB5IAeSaKKltkE+/vfLqhEh3fuoSVI7oZ9MOuko6fcZQTSRKvglkTCmM0sD1jIqgtH4vC4XiJCA/3xiucBi90msrq5WP51PYpGam/VDZn4e/0MIIg8J/oe5DMCwlURNEhPPQUvkJMhmUiBBdkVFRVbHzwdJVH45z/1b5NN4LFQVqtKK3Sl6HDKjelGTtGyukWLHxle3SNuupVJSal/Vj3yis6ySST/aXWbesjXwLygQIb3qXy+J/Etk2p9elGEnHijDv36wipBOBT8pdtIl8taE0CwXiGma1GisHWYib1uVxDD7VFu7dQ1ySmIRQjvvmvUoMclSGsmP3146RJFMO1lNTR5yiC4+lGTxz/Y8OH6uVWnSHTuZT6g28w98/dXYFLgrrXJpQwoBG2dtyncXrED9ktWyfvlu0neYy5uYiHFHi7x/V6U0bg4nuKl22TqZd9ODqm03brgMP+kglVan67B+KT8TVCJvLE00CiswNyOYsJYwH+t1DJ9J8jZ6ye5RCD6JNTU16lxt88WMAkVPEvVN1zsR0gasXr1aJk2apHZOQSAKczPQkwATwtKlS+Wjjz5Sjs+DBw/O+fhRKomYO4i+7rZxubQujIfzfNvQflJa6lLfFAI2vVPc/ogmlj/7ifQ5o6OFothR1rxZDrp+ijxz9suhf9emD5bKe5f/XbU++xAhfbAM/ep+UtkneV5bjVwTeeu1C/91Gp/XmTHw0V+4cGF7Im8aibzzpTCGTRKrq6vVuRbjc1BQJDGbG6h3VPjrobox2Ki/nK3/YarviEpJZAIgco2d3+TJk5VvSRDHjyq6WdePxvdj+NIPpE7ige6Tx+W7Cw4BgIVwy8zi9kc0UfPBx7Jxza6y/YAN+e6KdRg4dLX03b2/rJsV3UZ2/RtzVZupIqR331pD+gt7S3nX9IqeqTLq+TZTIu9kKqP2T0RE4fM6kffs2bPVccxygWEGkuTDJ7FrEaa/KTiSmC14GCAmDGwiyoIebKn8HoOCfqAhugSo8D1eE33nm+Sak5ZZP3qHAb3l01vek7igYscB+e6CQwCoXdYkTRucudnEshdqZPtT8t0L+1DS1iK7nTtAnjk9emtHW3OLrHrqbdVUhPQX995aQ/rQ3aS0Iv2yrslfpkTe+j2JiqReb2hEX9N0Im8I4/Lly5VFDmVRE0Y2/WGqcFH4JHZ1SmJxggHNAMMkO3bs2FAGgWkODmu3wwOiA22CJrph50nk+mMeJ7JO14+u/9/fpK0xPubbigE4NIdXVcchGmx8d0u+u2AdNs9YKJuPHC89ehdv7shUGNSrWnb85mhZ8M/5eeuDipB+4CXVVA3p4/dXhLHPlJ3ba0j7NUtrwpioMuKbnoyMmYm8R40apVyGdIodfPz5v5nIO5sAynz7JHZ1SmJxgQeA4JRVq1YpxQ2fi7B2CabfYxgDmXPgQSZABR/EoM8jTCWRvm7ZskXtQnUd7LaWZql9NnxfnyBRXnyZEQoSm2a5cnTJsOyVZtnluHz3wk5M+WYPWfxgmbTU539Tq2pI//VJ1boM66fM0QS89NxluKfPZ0qxg9lVl5lN58uIqXngwIGq6UTeEMYlS5aoABhURpJ4QxqDUOiiMDd3K8LI5oIjiV4HGuWKUN0gVphltS9iWDBJYpDgwSU4hWowZNdH9g9LCQ1DSWSiQUHkPuy///7tfqBNs56XlvXxUXRKe28npWVORSwEbJm1JN9dsBKfvvahVB88Wrr13JovzuFzlDd/Kgdcs7e8+FO78rnWfrxW5t74b9W2Gz/iM8J4oHQdmjpCOhEmCcTPnfVmxx13VOtMNom8+Sz5h81E3qiKZiJvv+UCdUBOFObmYkRBkUTAIGXQpAI7GqKzCOigggoDMuzoY/3gBPkdECv895DByX/I7/ksnecX9HvGjBnq2vPwaYLIvaub+qTECVWTds53FxwCQN2aZmlY4dK9JEVbm7z/VLXsfXK+O2Inho35RHqO7iUb538iNmLT+0vkPdpld0vffXdRJQFVhHTvHp4+D6F77733VB1p3IGyTbEDsNzh3kUzE3mTkxECydqsVcbERN7JoL/XmZvDQcGRRC91iyl+PnLkyHbVLew8hkF/B7saAm1QD1FC2YmFnaYmyGMzIaDeku2fCYHdKZMMrWnZh9I4Z6nECZ3G5JZiyMEObHzHqWTp0DxrtdR8YYR07e4SxieipLVRDr56gjzy9ezqOkeJda/PUW3mz26XgUdMUil1Bh27V8oIaRRECCI++5iPs02xo39Plcgb6ETemjRCKPX/WSuSEUH9XWGTxG7O3Fy4YNB++OGHiiQmq1scJ5KoCRa7uTFjxmzz8EURgZwrMI1zL5hwIIlMQGZkXdNzj0rcUDGENEMdE4I7xAsbZ67OdxfsRkuLrJrZVXY8yJHEZNiuarnsdOIY+ejfH0ocQIT0yiffUg2COPhLe2+tIX3I5xHSqQii30TeXlLsAJRDGv71OpE3ax7xAwTNYI5GZST4RVuf9LoXprm52vkkFq65Gb83SBU/Ud2SydeYPJNV/bCJJHJOECwigDXBSjy+zeZmM1BIB6joY3NdVNRcQ63UvxZsqasoUL49j5EjiXHH2jfmS/EluPCHtVPnybC9h0inynAqjcQdk0/vKQseKpG2ltQuTzaiuaZelt73omok6SZCersjJ8rSilqVcWLAAH8pvhJVRq8pdtIl8kbNgzCuWbNGrYOs5TrwRRPPsFBbW9u+ZhUbCo4kmiBiFrMsYfkk/0zlEGu7kqhL1JHl3iRYQR0/E3JVKSGAEHUChkyizoNPFBwP9yuvvCLj18+V8vqYlbarrJDSCrdgxh0NnzZLyeqN+e6G9WhtaJTls3rIqL2d72YyVLSsl32v2Fteu/QNiSsa1m+SBX9+XOTPj0vVkD6y9uRDpPNJB8t2Y4dldTw/KXbSJfJGyaNRKpc1RZcLxELIsUjorU3TuGIFiRpnbi48oFi9//77KmcTLd0uA4KF0hgmslX6dCQ2JA2ClaoSTNjmZu0z6He3xsMFUYcYEmCjibr2X4Ek7rfffkrOb7v6X5L/JBL+ULnbGCmReKkGDh2x8d3afHchNljz9HwZukc/qaiI2YYuIoyatFlmDuwqdatqJO6oX76+PUK654SRKuBl+IkHSpch27pseUUys3Q2KiN++NSOplH1BREFEgdhxGJF8m6zXGCuKmNNTY06ZjGi4Egi5AOfNxJ4JvM/zKeS6NekrZVQHHYnTJiQ1jE3bCUxm1xU2n+SKDb8J7UrgLmT1DvHLkvflc0xVHIqdxmR7y44BIBNs5wy5hUtW2pl1fvby7DdXU7JZChtqZe9Lx8rL3z/bSkkbJy9WLX3Lr1L+u63i0rYPeS4/aSyV/bkKVXwi14nvKiMvA/SSDAqzUzkTbEMPmOWC8wmkXeNi24uHKAesrNAdfN6U8NOgZMNiVu9erWSz70ooWH7JGaTDBySzo6OlAk4IQOTHALTj6Th2Sckjug0nKg8pyTGHZtnLct3F2KFVU8tksETekhZeThzTtwxdNBGGX7UKFn69CIpRKx7bY5qM396uwxoj5CeLOVdsi8FmymRdyqVMTFHYmIib10uEJ/+xHKBqI9eVMba2lpnbi4UQKhQrfwk5IxKSfRC4nggCP0nM/3EiROVnO4FOgt+GDB3el76DzlE9scPVKc2MHeI5jHVcdculYZ3FkocUd4H3xcX7RlnNFW3SO18RxL9gPrWq+ePksHjnJqYDLig7PPDAbJ06qKC3kO2NjXLyiemq1berfO2EdLluaWkSZdixxQbdKlAbZlKPAaWOBqp73Df0iojhRzMFDyojal4Q3V1ddEqieHFjOcJsH2/GduzMQX7hZfv4P+YZyFY+O95JYhhK4k6k34mIk3/MY/jTEz/EwmiWRzeRONzD6tkvbFDiUhZlfPLijs2za4TaY3h+MszVj75sbTGzYk4QlS2rpG9LpgsxYLm6jpZ+q8X5OWvXiH/3fE0mfHT22X99Hlpi1t4BWsGaxwqIbkTCUzR6/y6devU66w/EEa91iQDnyN9HO5bBxxwgCpjy3EWLVqkgicptIHiiHlZ97vts8jqbHwSb731VhkxYoTq85QpU2T69Olp3//vf/9bWd94P3184oltLWz05bLLLlMqKfEJhx9+uMozHCYKjiRm46Aalbk5HYlDzn7zzTfVIMdU7ndAhq2Geu0/gxiCqHddpoKYLE1BW0Od1L0cT9+dijEjpKTErZJxx4a31+S7C7FEw6oNsnax941sMWLM/g1S1Tdz1ZBCg4qQvv0xee7Q8+XxCWfJ7Cv/IZvnBafWa9JIKhwsaBAr0y0Kwsjr/Ey1bnEM1MOddtpJrVk0YhiImn7rrbfkO9/5jpx55pnyn//8R5FEL9VfTNx///1y3nnnyeWXX67EEyyDRx11lMpSkgyvv/66nHLKKeo7IavHHXecarjQadxwww1yyy23yG233SbTpk1T6yzHpFJNWChpC4LmWwQ9QPwAH0b8/w466KDQ+gXbR+oeP3580u9nULA7YLBnkxSU3Y9OkRMGnn/+eVXGkHRCqfqfmODbNAukymPV+OK/pfqOBySO6Pb1w6Tn0a7aStzx8jemiixwibSzQedRA2XSD7ZaGhySY+26IfLkmfZXYokCPXcdJcNPOkiGnXCgdBncJ+vjsKZAniBvrEsoieb/zETemuJkSuRtgs//73//k//+97/y8ssvq7X1wAMPlK9//ety7LHHqgCZTEA5nDx5svzhD39o7xf++T/84Q/lggsu6PD+k046SZ3PY4891v4axJUAXEgh58Ea+9Of/lR+9rOftZcZ7t+/v9x1111y8snh1MwsOCUxG+TT3Ay5o4bx6NGjlfSdbdb4sJXEVCl2iB6j/+zGSPLN+7R6mE5BBPyv/tnnJa7oNKp/vrvgkCMaa5tFlrjI5mxRt2iVbFju1MR06NtvpQzab9viB8WKje8tkncvvlP+t/N35IVjLpKFdz4tDZ9sCYwgAtYbIpgxLfM/XbbWj8rI+1Hx7rjjDiUgAUjigw8+2L5WQ9SwniUDx2ddxBxs9ou/33gjeQ5NXjffD1AJ9fsXL16sAlrN9yDaQEZTHTMIFBxJzGZHm4/AFX6njjQKIwNdRwAHdfygkXh8nWqIRoDKsGHDOvgfgnSZ8FvnvyXNH6+XuKJiQHE6MhcSNr5fK9LsXAZywbJnPgnE76xQUdLWKvv/3KXK2gZtbbL2ldny9g//IP/d4VR59eSr5eMHX5HmuvSFCRhnrJsEkiQjiIlg/cGdjPfpxt9azNCEMZ0vY11dnfoJKcSiRtDL1VdfLRs3bpRnn3026ffil8/xUPlM8DdELxl4Pd379U8/xwwCBRfdnA0YNFqaDstsYhJRXSqQgbnvvvumTJDtB2Em09bH1w8QDxb1PHlQE/0PM5mXTTQ887msHkeUdXMLY9xRM3tzvrsQe9R88LFsXDNBth/wSb67Yi06l6yS3c7ZXd75Q/zKjkYRIb3isWmqlXfvLEO+tI8ySfc7aOI2EdKaIG7ZssUTQQwqxU5Nzdak6HqdI4XO8ccfr1oxoOCUxGxgStFhfgfHZ4AjDSOBIxMHQRDN44cFTULZVSGx6wowiQEqOmdVJoLY+skqqZ8xT+KKsgG9pbQ03Co9DuFj06yV+e5CQWD5i1vVFofUGH+sSKcewZaLKzQ0b6mTJfc+Ly995XL53+jTZeb5f5YNb33YThDJeQhBDKLsnjZLmyoj66gWRLTKuHnzZrVO+3EF69OnjzoWdaZN8HeqOti8nu79+qefYwaBgiOJ2ZqbQZh+iXwHEUgQLCqQ4IzqN1VPvs3NmuBSO5oHVWeuNx2FvRZab3r+YZGW+CpxlbuPyXcXHHJES3ObVL+3ON/dKAhsenuBbP6kZ767YTXKmjfLQdftle9uxAb1azfKgtsfl0/fW6TK7hGkERRBTJdih+PrFDtlZWVy9913q6BTLH9ewXHo63PPPdf+GusjfyOuJAOvm+8HzzzzTPv7CZaBDJrvgcAS5ZzqmEHAmZsNaTksJY5dEGwfkgg5DIP1h60ksqPCcZboawqsAx05pr/XK0Fsa2qUuheTO/zGBW2q0opDnLFlXoO01qf3gXLwjuWvtMi4r+S7F3Zj4LC10mdiP1n/rktCngllVZ1k7zt/Jpt32E4+/eQTlbkjDIKYDHot+9Of/iT33nuvImZ+v5v0N6eddprq91577SU333yzMl2fccYZ6v+nnnqqEoyuu+469fe5556rMqz85je/kS984Qty3333ydtvvy1//vOf1f/pz49//GPlD0mgKKTx0ksvVRHPBNmEBUcSQyZZqJO6VCDKW1iycFgkFxJIcA2De8iQIdsQRLOCik647QXN05+S1s3xNk+V9C++3GeFho3vfJrvLhQUPnn1Q6k5ZIx07eEvWrWYUNLWLAddtrM8+DVHEtOhU6/usv8Dl8q6Hm1q7YRokWA6KrCu/e1vf5OrrrpKHn/8cdl///19H4OUNiT6Jvk1gSUIRE899VR74AmZTUwTNvEJENJLLrlELrroIkUEH3nkkW3S5v385z9Xa/H3vvc9FThDvzhmmNem4PIkAqRhv3jxxRdl1113Vck1gwL+eyTRRLbmhvN7Yoh7UECl5BwImQ8q+AaCS/g/ZmYSiXJtKHtoOvp6VQ9NbLnyR9K0cJXEGQNv/56UVbhyfHHGez+dKRtf+TxRrUPu6HvELjLmqI357ob1eOvBzvLB3W7sJUOXYf3kwIeukJVt1SqSOB8E8R//+Iecf/75KlfiwQcfLMWMgvNJzBZBV10hazv+e9SMJKEmgzzswBgQ1HdAcPF1wA+DCGakdq0c+glQSUTLondjTxBLulRJqSOIsUZba5tseWdRvrtRcFj/wjypr3EqeybsflKVlFXlVtu4ENF15yGy/+NXtRNE/PqiJoj/+te/VLqbhx9+uOgJYsGSxHznSly2bJnyJdhxxx1ll112aXeK1QpcGNCydRDngIxNgA2JOtnF6agvTQ79BKgkovHZ/0rcUTlpDGWbHWKM6oWN0rKlNt/dKDi0NbfIwtcKclkJFOXNn8r+V++d725Yhe5TRkvvG06RtxfMkRUrVqgIYXzhozR2kiwb38AHHnggNKtf3OB8EgOsugJ5mjdvnqxatUolmO7du3dSpS/bqirpYJbCywUrV65UqQYwj+N/CBHU+SOJLsP03K1bt6wIYuumdVL3ZvxNLJVjtyYOd4gvPn1nU767ULD45IWF0nDAUKns7FJEpcPwnT+RnjttLxs/cr6xw75+kEz+049k4ZLF0rRmjSrOQOQuLlqsbRBGGmtqkFlBTDz66KPygx/8QPkFUnrPYSscSQxISWTH8+677yp/SMLRE4uBmyRRp44JEpC2XM4BIrhgwQJZunSpcrCl0Ll+XWeOr62tVYXPMT3z/379+ilzulfC2PTSoyLN4aXpiQoVwyD/8T+PYsbmWa5Wc1goaWqWle9tJyOnuHKH6VDS2igHXbWrPHpycdd1HnPuV2XXX54mHy1YoGokY73S6yeiB5YtKpgsXLhQ+ciz5rD+QBp5XxA++ASnfPe731Xpbr7yFReiX/AkUatfUfkkoq7NmjVLKWz47yXb6eii4vmor5wJfIaHD6WQBN/du3fvUGKPLPOQR/4m2oyHGVIMeGBp7PI0GU5EW3Oz1D//mhQCynuT6d/5JMYVjOvNs1x+xDCx+umPZMikPlJREV7u2UJAzy7LZcfjR8uCh+ZL0aGkRHa7/kwZffaXVQYN0sSZBFGvaQRM0qiZjK88EcOQRkQNBAvIIusP+XuzsdKRi5C0NH/961/lhBNOCPgk44+CJInZIFsVDrJEiTpMs/ggptvVhJ3LMJuE2kRFI+nzWRRQXerIJIim/yHv06SQ97DL4xrMnz9fqagQRRRGHlyzbFLLrGel5ZNqiT3wL610ZrQ4o/bjJmne4MzNYaJlc42smjNahu3mUr1kwsRvdZWFj5ZIW4yLC/hFaadymfKX82To8fsrskeKGIJUEi1wiaDyCaZomhYsII24SOEuBpnUpmkvAS9kBPnmN78pf/zjH+Xkk08O8AwLB44kZumTCEEiuTQSOHmMBg4c6Ok7oij95xUohxBEHigdYAN0/eVMASq8zu6Nxi6P/E0QRvI/kSFfmwUgjS3PTJVCQMW4kVJS4kzNccbSl5fnuwtFgVVPLZLBE3pIWZl7XtKhW/lmGf+TsTL7xg+kGFDRo4vs96+Lpd+BExRBxA8eBVGXePWKRMGiurpaKYzEBBAbgGVPE0aCMBPXsVdffVXlMiTJ9be//e3AUscVGgqSJGZzszERe82vCBEjQTZpbjDPYoq1qb6yF7Bzw8SM+jlixIh2E302FVQA7+OhpJFLEYWSHR6kccPsN2TEvGVSCKiaMCrfXXDIEU3zC0DRjgGa1m+S1fNHyeCxTk3MhN0OKZVF93WTmuWFPTY7D+wlBz58pWy3y3AlsGRLEJOtP7hJ0ahEQowAKXQgje+88456D6lt+C6qk/DdJ554olx//fVy5plnOoKYBi5XgU8CB/khfyC+EZhnvRJEP98RprlZB6hAECdOnKgeKE0QdYJsvxVUkgGpf+jQocqEsPPaj6VQ0GnU1mz5DvFF3WynJEaFpf9bLK3hTXkFg9KWOjnk2j2kkNFjzFA57PlfS8/xI2TRokUqzQ3rQ64EMRlwdcK6N2HCBFXqjp+8dssttygR48gjj5QDDzxQDjjggMC/u9DgSKIPczPK4euvv66IIbUY/dZyzLe5mf8RbLJ8+XIVYIMZGJgJskG2ORCToXnRAql//T0pFLRu7xLgxhm1q5ulceX6fHejaNC6dqMsmN05392IBXr1XCHDjhghhYg++4yVQ5/5lXQd2k+peOQShiBieQobrGX4yv/+97+Xe+65R6mNX/ziF9XrCD1Y0kh989hjj6kMHg7bwpFEjwSLXQ8JsnfYYYdt/PeC/I4wzc0ooNOnT1c/eTCSRTDz+SBzODa+NU02X3u5SKP/Mom2orxr8TiXFyI2vePqCkeNLW/URpoQOa4okTbZ50eDpNAw5Mv7yEH/vUoqe3VXCiIEEbNvFATRBC5iX/rSl+SnP/2pqqby3//+V5mkb7/9duVu9qMf/UjVa3bYFs4nMUMKHMgTkbuQxN133105wWaLfJmbdVJSIr8guDpNTaoI5lzBceuf+K/U3X+PFBLa+vcSn+Kxg2XYNMv5x0WNuoUrZcOK3aTPEJc3MROq2tbI5J9PlrdueEsKATuedazsfuP3pLSsTAV6EtQYlYJoYu7cuYogohhecskl7WsdblFHH320apiiw1yf4wqnJKYhcNQtnjFjhgrAwDybC0FM9R1BItnxyT2FDyX+gfhlmOUBQyGIzc1Se8ftBUcQQdfJ4/LdBYccsfmdwvGPjROWP+uqinjFzgc3SlXv+JvoJ1xxqky66fuKIC5ZskQVaoAgaitWVCAHI+bl0047Ta688sq02TrCquYSZziSmMInkXD6N954QxEozLNBONdGaW6GCOL7QQ7HXXfdVZnJEwNU+D1IgthaUyNbbrxWGl56TgoRlaMLzxRUTGj4pEXqF6/KdzeKEtXvL5WNa3rluxuxQGlztRx8/WSJK0rKy2Sv238s4352olpbIIi0fBBEzNsQRFLdEMkcRkncQkdB0uZczc0ohwR4oL6R/y8oEhWVuZnvILkoiUbNFD3avKz9g4J8YFrWrpEtv7lOWletkEJFxSCuo0ukHVdsfLcm310oaix7sU56npTvXsQD/QaslgF7D5bVb8ZrPi3vWiX73nOBDDxia6Q26iFm5nwQRL77C1/4gjIz33TTTY4gZgl31RKURAY0eZXGjRsnY8aMCTR/UhQkkfxQ1FcmsTUm8kSCCInUJQKDQtNHH8rmKy8qaIIIynu4XFpxxqZ3nE9cPrHprQWy5dOe+e5GLFDS1iJ7nDtA4oTKvj3lkCevbSeI+B+i5EEQ/aSKCwLkX4QgkurmD3/4gyOIOcBdOQMQKWRx0tsMGhS8aTFskogPJcmrccblHHRZIs4LAhy0eRk0vPmabLn+SmnbslkKGSU9ukpJeeFEaRcjNs8sjITuccayV1z1Fa/o03WjTPj+rhIHdNthoBz+3A3Sa9JO7QQRd6dJkyZFThApFHHssceqHIi33XabI4g5oiCvnl8SRFoYzMtg8uTJqoRPviui+AXkkPyHEEOSZCcGqPB7rgmyTXC8ukcflJo/3gw7lUJH1e5jxOmI8UVTdavUznckMd/45NV5UrMlWrNjnDHxy+VS0b2T2Ixee+wkhz1zg3QbtbU0LSluNEEMay1Ntw7ig4h6STobncnDIXsUJEn0g40bN6oAFR2SH2Z0U6o0O7lA15CG5KJ+UgA97ACVtqYmqfnzH6TuwfukWNBp7NB8d8EhB2x6r5aHJd/dcGhtk+VvFKQrfCgoa94kB107RWzFwCP3kIMfv0aq+vVsJ4hU9CJdXNQEkZyHX/7yl2Xs2LHy97//3UUqB4SiJon4LeC/R8Z10sNApDJVXbHJ3AwJJEGoNpFvv/327aRQ+x+CQCOYt2yRLTdcJY2vvSzFhIqhLjIzztj4zoZ8d8HhM6x/fq7U18Y/xUtUGDRirfTZta/YhsrDd5HuF31J1mzcoKxxWLJINwNB7NkzWt9TqqF95StfUWs5NZorKioi/f5CRkFS7UyECBJFgmx2Pbvttpv07dvXirJ5fkCAyqxZs9TxSNGDmZl60pocBp3/ELSsWilbbrpOWteslmJDRS8mHZdoNa7YPMvVa7YFbc0tsvztrrLjgXX57kosUNLWLAdeNlYeOsGewKuxP/+6jPzJcbJ+/XpZtWqVSlYNqJesLVlBrj3psGnTJvnqV78q/fv3lwceeEDVaHYIDgVJEjMFd5A7UEf/mpnfwzAHh0ESt2zZoiqo4BBMDkTtdwEpbGhoULsqpP4gH9KmeXOk+nc3SltNtRQdykqltJNLfRNXNNe3Ss2cJfnuhoOBtc/Mk2FTBkunShcM5gXdO62Qsd/aRebeMyev/SgpLVUJsnf87jFb+9W9uyJlVPUaPny4qn3M2sRaRPEJGnWTwzL9shZ+7WtfU2vhQw891B6s6RAcCpYk6t2MCYghAxi/PdS3REk6n7WVvULncOSB3HHHHduJIMohDwoyPwoj54ZC2q9fP/VaLhFeDa++JDV/+5NIkZYsatlxsJSUuKjMuGLTnHqlXjnYg9a6BlnxTg8ZOcUedcx2TDqli3z4QKm0NuZnLiqr6iT73HW+DP7i3tu4bH344YfKxEzZV70W4euPykgAy+zZs5UrFOsRpLFLly6B9If1/MQTT1Rr3SOPPKLWdYfgUbAkMREMWPIfDhkyJGX+w8SqK0EjF6USwktyUHw+qL+sU/TwuvZBpP/4VvI3ibSJ9OIB5W8eUBq7Oq8RXyqC+aH7pf7RB6WY0dOV44s1Ns1y/og2YvXTH8nQSX2kvCK8ObeQUN7yiRxw9d7y0s9fj/y7O/XqLgc8cKn02Xts+2uYmefNm6dctjRBBAgS/E2jGAXqIusvAgduXpBErTJmK2DgWkUVFda9p556KvJa0MWEgieJJrkiQfbgwYNTvtdWczM7sw8++EA9ZKTo0U7BqSqoQID1Q8j/2NXpBxRfRogiCiP/T+Xg29bYKDV//aM0vvmaFDs6jeqX7y445IDN76zMdxcckqBlc42s+mC0DJ24Nt9diQ2Gj9so2+2wvWxaGF0t7C5D+8pBD18pPXb+PMOD9kMk3ZpJEJN+vksXGTZsmGqIMEQhQxoRMFjbWI+0gOHFn5AgmW984xtKSZw6dWrklVyKDQVLEiFKujwdA9IkV6kQhblZp6bxunuC1KGA4kuJD6WW1PVxMgWo8DpSP22nnXZSNalRGImI5trwOoSRVllZqT7TunmTVN98gzQvmB/g2ccXFX255vX57oZDFmhpapXqdxfnuxsOKbDyycUyaHx3KStz7hxeUNLaIAdfvas8espLkXxfzwkj5cCHLpfOA3tvk6xaE0SInR8gxBBgQmMNw5cRAQMhh/UIX3rEC0hj165dO6xrrIennnqq+syzzz4beZqdYkTBkkQCOGbMmKFIlI7+zYQozM0AIuqFJELo8KFkp0RiUv15M8WNnwhm3sexaDvssIMyA/Cw8dDjV4JP44CSNul2790iG5yvkEZZF2cOiyu2zGuQ1gYXdGQrmtZvlNXzR8ngsWvy3ZXYoGfX5bLDcaNl4SPhbuL7HbSr7HfvRdJpu67tr7FWYNUiYNIvQUy2HkHyaPjXoxBqszTl/FAVybnIunT00Uerv8844wxVzeX555/PqGA6BIOCzZOI+obqNmXKFM8RT1EoicDLd/CwvPnmmzJgwADl86EJok6QHUSKG8wABMCgsh544IEypLZauvz5944gGigfSdCKI4lxxcZ3Nua7Cw4ZsPLpZfJZSlcHj9jrrF5SUhZeiplhJx4oBz50xTYEcc2aNUrtgyCi9gUN1mliBgiCOfjgg2XnnXdWgS8//elPlamaWIJp06bJP//5z1C+X+O6665TayJiSr9+/eS4445TIkom3HzzzaqP8I6hQ4fKT37yE0V8446CJYkob2Z6GC8I2ydRk7pM34H0ToQymeNx/A27ggpoff0Vqbr7z1La4FJSmKjcbcd8d8EhB2ya5fwRbUfD8nWybonz+/WDTi3rZO9L9grl2GN+dJzs/befSlllxTYEkcINYRHERLBuY3K++uqrVTwBIgYuV8QUQCIhcVdeeaW8/fbb7UUjgsJLL70k/+///T8l0jzzzDPqe4888kjlA5kK9957r1xwwQVy+eWXK1M8JQHvv/9+ueiiiyTuKFhzM9K0X8LHwMRMHSbSEVEGO9FiSPp77rmn8hdMFqASaA3m1lap+/e9Uv/4o4Ecr9DQacet9Ugd4ofW5lapfsf5I8YBy6eukX7/l7kQgsPn2HGvWnlvcDepWRFc7trdrj9Txpxz3Dav4cOuCaIuPBEVWBN//OMfK0UR6yAKHeZoIpofe+wxuemmm5SlDWIXFDi2ibvuukspirivQVaT4fXXX5f99ttPBdQAKr+ccsopSvmMOwpWScwGYfskpsuVyG6FQUjqGnwoEwkiDwsTaKA1mBsapPoPNzmCmAYVA11qhbhi7ZxN0lJdm+9uOHhA3YKVsmGFfaXnbEZpS60cfO0ewRyrU7nsc+f5SQkiUcikVssHQcTU/MILL6ggFQgioB/f/va3lVKHW9add94ZekUXkM4Hct9991Xr9/Tp09Xf+FQ+8cQTcuyxx0rcUbBKYjZEKmxzcyq/R2RsBhjRXEQw5xqg4gWtGz+VLb/9lbQsXhjYMQsR5d2dshFXNMxzAStxwvLnNkmf0/Ldi3ih9/YrZOhhI2TZc9lXFKro0UX2+9fF0v+gXbd5HcVOE0SUtCjBmnfhhRcqogVJRJlLBlK4jRo1KnQlc7/99pPx48enfB8KIoR1//33V+s2YtP3v//9gjA3OyUxwsCVZN9Bzih8H0gJYEYwBxmgkojmZUtl8xUXOoKYAaW9esj/b+88wJyo1j/87S4dpIN0BAQERERQBBUrWLDce+00GygoFrChqCgqxV5BsRcUvda/oliwoVKkF0WQXgQBF1jqtvk/7+Gedcgmu0k2yaR87/PMs9nUyWTmnN/5anqGxmgmKlnzNGM2kdi5cJVkbtKM1VBIE0e63LS/sUI4lKtTXU75crRfgUj7WoSRFwKR2L7333/fWBDJfPaK6667zrjaJ06cWOTzvvvuOxk5cqSMHTvWVCShReCkSZPk/vvvl0QnaS2J8epudotEUvnJmiJBhawu3w4qEGmBmD1/rux89nGRvXsi9p7JStn2Lb3eBSVMTA22uSu83g0lRJZ9ninHXO71XiQW5ZxN0vGWDjLrkdkhva5yy4bS9cN7pWKjA0WgLXSNQMR4EevrFrH15ptvmjI3ZAt7xaBBg0zc4w8//FAwPwfi7rvvNi7wfv36mf+xvuIhvPrqq2XYsGElaovrNYm758UQjrCKlSURIUoGFFlbHTp0OEAgsoqyQjWSCSqw9+vJsvOxUSoQg6Ssq8OAkljsWpMjuX/v8Ho3lBDJXrROdvxd2evdSDhanZInZasFV+oNanZuJad8NaaQQMSzhQWR7mReCMSHH35Yxo8fb7KKaT/rBewHAvHDDz80QrVJkybFvoaaw75C0FZWsQmniUrSisRwiEVMIqKPEjdcjCSo2GBYaz1ki3iCSn6e7HrzFdn9+kt8UETeMxUo3bDoDj1K/LJ9rgrERGWddgINmfTcLDn+gaOCem79s4+VE//vfilb/cB2dsxJ8+fPN54t6vPGEua/p556ymxffPGFyaT20sWMJZOyNgcddJCpNsJGv2gLXV+ImbScc845Mm7cOOOWXrlypRG5WBe5P5QyfPGIuptjaElktUEfZcrzIBBjkaDi7N0jO8c+KTnzQnNFKCKlqvL7aCHtRGT7PO0HnKj8PXWJ7DqphVQ8KHKlXVKBeg3+kqrtqsu2+X8HfE6zfmfKUY9eI+k+woWqGlYg1q0b27JfzH8IrDFjxhiBiHfNS9gXoKC3G7KoL7/88oJQMbfl8K677jLzNn/Xr19vMrARiA8++KAkOmlOottCA4DgoqxMKBBD8OOPP8rpp58e8f3hIqRANv2RCQSmSHbUM5j/3ipZj42WvDXhZ76lLGVKS/1xPSUtLSkvj6Rn+nmfSfafW7zeDSVManU/XFp2z/R6NxKOrJyD5YPzf/b7WNvhfaTVLRcWmmOYm6hBSIeTevXCT4IJB+Y/Ck9jdSOTmSxiJb5IWndzuCVwbFxgJFm3bp0pcYMwpN+lLYxt4w+j0UEld9UK2X7fHSoQw6Rsu+YqEBOU3X/mqEBMcP6a8qvs3PFPxw8lOA4qvUmOuMbHVZuRLhWv7yaZXeqbOHhEoZ3jvBaIr7/+ukns+Pjjj1UgxinqbnZhYwcQcZHIRuIiIHsZ8zPlbRCIS5culezsbHOR2gs10gkq2bN/kZ3jnhTJ1vIt4VK2jf+6XEr8s32euikTnbS8fFk1vYwc3j00b5AicsR5peXXN0tJ7q5cKVWxnHR543apdcqRRhDa2ofMPZUrV5bMzExjvPBCIL799tty6623GoHo69pV4gcViX5EItY9inSWBN6DGA/iECmQTaFs+xk8ZgViJFPjufD2fTFJdr/9uiaolJAyh0S/P6kSHbZpPGJSsGPqask+sZ6UKatF0UMhI3ebdB15rPx0/0I54f17pEaH/aFNhDmxMU9guKAFLPHxGC7orEIcHX2Z7VwVTaiBSJHq//73v3LqqadG/fOU8ElakRiOZY7XRCJ5BWFIQU3iDxGIVnBycZYrV07++OMPEy9pL1ou1JLi5OXJ7jdekn3ffFXi91JEStWknMRer3dDCYOsOau93gUlAuTv2ScbFlSVQ45W0R8q9VrnyWlTHpJKzer5bTOH2xkXM+XXyNqlNiJWRu4vX768EYxsVapUiXiNPyyHAwcONJbEM888M6LvrUSepBWJVvSFmpdTUpGI+R6BSIYYF6G9wGyCChcemc1ckBs2bDCrOS5EalLxGBdoqOTv3iU7n3lcchfND3u/lQPJKK9urkRk3995snf1Rq93Q4kQf36+VBocWVNKldYqA8GSX76m5LQfKJXKVSv0GNU1SKCki4mtz8ucQ19kNrxclMJBNFIvEY8X1kXmJsKlSuphowsJBaeJRTz33HNL9F5KbEhqkRjrriskqFAkmyrxjRo1OqCDio1BRDRizmejH+XevXuNYMTcj9mfukzWwhiM2T9v81+ykwzm9WvD2melMKWbN5K0tOjWy1Siw7b5Go+YTOTt2CV//tpCGrZTa2Iw5FeoLdntrxMpW8WvBRGB2KxZMyMIAyVvYrBgY97iNQhGav/Rnq5q1aoFVsYKFSqEtG/UDqSEzIsvvijnn39+2N9RiS0qEiNgSeRiQuCtXbtW2rdvb1Ze9n53goq/DGbcz3YVR0ILFySCccWKFWaFZwUj4tH3tbnLl0nW42PE2bG9xN9b+Yey7bzrFaqUjO1zNas52dgweaXUO/wgyciIbNWJZCO/Yl3Jbn+tSJkDi2QDYg8PFwLRGjCKg/kGUciG5RG3NAYN5ijc0ohEa2Uszi1Nb+NevXqZGoSXXHJJib6nEltUJJaw6wpWR8zyO3fuNPGHlSpVOsC9bN3dwcR1EJtIlhmbNftv2rRJZs2aZcz8VjBy0eb8Ml12Pv+0SIi1IJXiKXNobLsNKJFjx9w1Xu+CEmFyNm+TTX80kXot1ZoYiPxKDST7yAEiZfbPP2527NhhBGLTpk2DFoj+wGjB69ncbmkSNAF3NIKRLmLuOPupU6fKxRdfLE888YTpbxzJSh5K9ElqkRjtmERWVlx8CDgEor0wIlEg2232570oX4CFcf68eVJ74VypM2tayO+pBEepg3GjaEZlopGTlSe7l67zejeUKLD+83VSp3kZiXAORVKQX7mRZLcbIFK6gl+BSI1e+g83btw4Yp9ZlFv6sssuM40punfvbiyQN998s4wePVquuuqqqAnEUaNGyQcffGBi/BGzXbp0MR1cCP0qCmI0qdPIa5ljOUaI2bPOOisq+5mIJLVIjGZMIgkqxHdwkdDKyDdBJZIFstknU56gWlXZ9fP3kq0CMarklVGBmIhsmZOlpZ+SlH3rNsuW1e2ldhO1JrrJr9JEsttdI1KKagwHkpWVZYwYCETi36OFr1ua/suILrZff/3VeL8Qj1gUEW+2HW0k+f77703P5aOPPtrM33feeacRqXx+oNh+wru6detm9u+9996T+vXry+rVq833UP5BRWIY7maykhcvXmyKkGJ6t0LQxh9GpcXerp2y86lHJPe3xRF7T6UwGbWqSRgJ5kocsO5H7S6UzKz74i+pdY2j7sr/kVf1UMk5or9IqbJ+BSIWRCxj0RSI/sB6R2mbZ555RkaMGCGtW7eWTz/9VC644AIzt/LYf/7zH7NFismTJx/w/6uvvmrEH8ega9eufl/z8ssvG+vhzz//XJC1HetjlQgktfE+nMGkKHezTVBhdXLkkUeaC9C6tHlNpC2IlrxNG2XHiGEqEGNA2aOKdk8o8YuzTBO4kpndf6yXrRtqeb0bcUFe9ZaS0+5qvwKR+HjEEQYMrIixhixoytvgZr7rrrtMJvMrr7wif/75pxGL7Nc333wT1X3A/Q3ERwbi//7v/0w5OiyQeAQPP/xwGTlyZInrJCcbakkM0t3MfbQzIsajpAkqoZCzdInsfPIhcbKyIvq+in/KttxfO0xJLHL35Mu+3zUeMdlZP2W71OwrKU1ejTaSc/jlIhml/QpEEh0RYiSqxBpKwJ199tly7bXXmlg/t7GEuRVRxhZN8OTRzYVe0Ai/QFBBBLFK1vVnn31mmlyw3zS6GD58eFT3MZFQkegDJzIniRtqGRLbYU9yd4JKtNzLsO/nqbLrxbEo1Ii+rxKYUg2oL6YZ44nG9sV7TNchJbnJWrBKtm0+XKrWypRUJK/WEZLTpq9IeqmAFkTKqXkhEPGyIRCvuOIKuffeez0LC8AyiDXzxx9/LPJ5zNu4pMePH2/m9g4dOph2hQ8//LCKxFQRieFmFbvNzbZCPYkjxFb4JqhEQyDy3ns/fk/2fPBuxN5TCY5SVejfrSIx0dg+92+vd0GJEeu+y5aqF0rKkVe7veS07i2Szhh1IGQTIxBJvvBCIGKVQyBS6oZM40h71IJl0KBBxqX9ww8/FHSUCQRd0YhFRCBaSELduHGjSWqJRLvcZCCpYxLDwR2TSAzFL7/8YuI62rRpU3DiIwyjJhBzcmTX80+rQPSCCuUkvfQ+r/dCCYMd8zZ4vQtKjNg2Y6lkZRbuKJLM5NU5WnLa9AkoEHExIxAplh1rCx4ZwT169DBxiI899pgnAhHDCgLxww8/NC7kYGIxcUfjYrbNLqw1FPGoAvEfVCQGcDdTUZ4M5nbt2pmMJ5ugYgViNBJU8rN2SNaYEZL989SIvacSPOXatZA00RIqiUZudp7smL/C691QYsjaH1PnOs2t11lyWl0qkpYe0IJIAwYvBCLuWQQi5WbIZvbKgoiL+c0335S33nrLdCfDGshGLWNL37595Y477ij4f+DAgSa7+cYbbzTikL7SJK7wXso/qLvZB05yYjv27dsnnTp1MidcLBJU8v5cL1mPjpL8vzZF9H2V4CnbJvxuBIp3ZC7aJZKtIQKpxN9Tl8juk1pIhYOSu1d3boMTJLf5f5jMCj22e/duIxDr1Klj6hPGWiAiwhCIJ5xwgjz33HOeCUSg3R+cdNJJB9xPVjX9omHNmjUH7COxm1988YUMHjxYjjjiCGOJRTDefvvtMd77+CapRWKokKCCBRFrYSwTVHJ+Wyw7n3pYnF27Ivq+SmiUblSDX9vr3VBCZNei5BYKih/yHVk3o7S0OE2SltxGJ0tus3MDCkRczJRuad68ecwFIt2/iEHs2LGjvPTSSwfE9XlBMJ3V6B/tC/P89OnTo7RXyYG6m111laZNm2aalpO84ttijy0qGcxTv5Wsh+5XgRgHlKpZuOaYEv9sn/un17ugeMDmKUtk357krHz/V+WOsqVGV79LVlyoWBARiDR0iLVApGcz8Yckcr722mtR6aCixA9J/esGe/FgNqcGIjEdNWvWlJkzZ0a9g4qTny973p8oez/5MGLvqZSANJGMsuqyTDTy8/Jl5zyNR0xFnJxcWTe7ojQ7/p+4s2RgW+2uskZayOZ588y8w5xEdY0aNWqYrFssiPzvhUCkHe15551nEkOI/7OdSlIBx0nNbj9JLRKD+dFJ3WcjQYWaSZjxreXQZj1FXCBm75Nd45+V7JnagzleKN2qqaSlaZ29RGPn8hzJ25VcIkEJnk1f/i6NjqkrpZOk33pOs3OlXONThBLQzD+UYNuyZYtJrCBOHqpUqVKQTBlrb9u//vUvY8F89913UyYDeM+ePVK+fPkD2u96GX8Za1JWJCICKbjJyogOKjZBhR/f1Cncu9dcBJwYEc1g3r5Nsp54SPKWL4vYeyolp3Qb7dmZiGybq634Upn83Xtl/fyqcsjRf0mik9P8P5LX8J8+w8xFtJVjI8mCcmzlypUzIoVC0cxZWBTZ6AAWTdFIL2ja6yFQP/jgAylbNjVCc3799VeT7UxiC72mif8kkzyVrIspKRJZkdFBhR+XwFV7wtuyNlWrVjUXIRcn1kW2SKyactetlZ2PjZL8LZsj8C2USLK3VnLGNiU7Go+obJy8TBocWV1KlU5MT4AjaZLb8kLJq9/F7+MYLIhBxO1MsWfmLdzOWBg3b94sq1atMm5fKxirVasWUUsXZXYuvPBCMwd+/PHHxqqWKixdutQYknCtP/300yYDesiQIcawhHZIdoEIaU4waUEJjDXRW+i9jEDkQqKvo83K8u2ggomZDC42XoNwtIKR1Vw45K74Q/ZN+1H24WbO1A4R8UT1Ry6XCtX/KaqqxD9cs9PO+FhyM3d4vSuKxzTu214aHvFXYgrEVpdIXt1OAQUiMYgYLKxA9IV5CyGDYGTLzc0tiGPkb0niBpkHEYiI0s8//7zA45ZK7Nu3zxyHRx55RP7v//7PeCApO0Sf57vuukuSnaQXiZzc9itu2rRJFixYYNoWsbljDIpKUOFCRSzyeuIyKleubMQisRmhrqp4j8WLFknzCuWkxro1kj17huRvWB/Bb6yEQ70Xr5L0dE1cSSR2rsqWORdN9Ho3lDigdO1q0vHmipKRkTjTmZOWLjmtekl+nQ4BxQkCEQMFmcTBWK2Y63ANW8FIzV9ebwVjxYoVg94/5r1LL73UxEV++eWXxtWc6qxYsUI++eQTufXWW40YJ4nnvvvuMx3ZvC4DFC1SQiQi/lauXCnLly+Xtm3bmlUA8NWtBRGCiT/kwuXiQ+yxeiMWBLGIaCzqAuRzcAuwH+wDF60lb8N6yZ490wjGvBXLI/bdleDIqFdL6j5wpte7oYTIug+3yIpRn3m9G0qc0LT/UVKv5abEEYhtLpP82u0iJhADCT0rGOkuQok365ZG9AV6X+bN3r17m9a0X331lbFkpjL5PskqM2bMMG5nyubhdkYonnLKKUmZ0JL0IhEzMeZhLpCjjjrKWAF9C2RDOAkqtO+zgpHaUVyAVjC6A4n5DAJg2Yf27dsXabLP27pFcmb/YgRj7pJf2dESfX+leCr0OF6qn9/U691QQmTx8MWy9fPZXu+GEieUa1hbjrq+lKSnx3ecmJOWITltr5D8muQw+xeIxCAyV2GhilTcG5Yv5inmLOIZwbql8YjZuZF5jS4lWM2mTJlinpOqOH4SU+x9S5YsMeLwnXfeMUKRrjMYgJIt+zmpRSJfjQQULIWIMxtL6I4/5MeOxA/KBcjFh1uaC5BkGAQjsY9cbHzmkUceGVJWWP6O7ZIzd7Zkz5ohOYsX8CEl3k+lMNUGXygV26ZOMHayMP3cSZK9cavXu6HEEXX6NJVD2x0Yhx5POOmlJaftlZJfo5Xfx20dRAwJxMxHKzGC+Qg3MnPW4sWL5YorrpAOHTpIt27dzOevXr1avv32W2PwiCajRo0y2dIILoRqly5dZMyYMdKyZcugXj9x4kTjEsft+9FHH5VoXzj2JOcQUsZxodVhIKxQ5Djhen7vvffkjDPOkM8++yzpsp6TWiTChg0bjMk+UIJKNH5I3h+hyGfzl88hKwrRyL6E85nOnt2SPX+u5MyaIdkL5uJHiPh+pyq1H75KytTQeMREYvefuTLrvLe83g0lzijbrK50HBDZsmWRwkkvIzlH9JP86i2KFYhYEGNpjSJW//333zct9gijwiJGyRc6q2BgidbxRFhdcsklcvTRRxtDy5133mk8f3jeioufJHzr+OOPN/kFuMPDFYnEbf7xxx/GiPP777/L/fffb0LTKH3Tu3fvgK+zQpDnYnn96aefZOjQoTJy5EhJJpLHJhoATOmxFIjA59GqiJVa48aNTY0lPnf+/Pnyww8/yG+//WbM/tbVHQxp5StI2WOPk0qDhki1Z16SSoOHSpmuJ0tapdTLNos0GVWS/jJIOrbN04xmpTD7lv8pf62pKvGGk1FWso8cUKRAxMVMmFKsBSJgtcSggdhinsI6hlA78cQTpVGjRiaTd968eRH/3MmTJxuBxXemocWrr74qa9asMceiKJhPe/XqZdy9iMSSQMYyoWhvvPGG6UdNuRsEKjURs7MDF2lHP6Ap6NT2/PPPG3c9bQptL+hksb+lRJ1Em6ASrRZ7vqxbt86sSChZYAtvIlb5bFZpuKRZLbFP3I9Jn5ZLwQ4MaWXKSJn2Hczm5OVJ7tIl+13Ss2dK/t/qfguFtErlJb1U/LqnFP9sn6u1RhX/LP98qxw8IH6mNqdUOcluN0CcKocUKRARJoi1WAtE5qWbb75ZvvvuO+NippsLho0+ffqY+Mjvv//eCCmSWLC2RRNcvVBcosyIESPMvHnVVVfJ1KlTw/48xGbPnj1NSBgud8LDEIsI0GBIS0szx4/koscff1z69+8vX3/9tamjGI/W7HBIenczQbhsJUlQCRYO5bJly4ybmYusqBPdxoTYWoy2thUuaQRjOOn0xlK6crkRjGz5G7XQcHGUO6G91Lyirde7oYTIzAu/kL2rEyOTVYk9bW5rI9Vqb/N6N8QpVUGy2w8U56CGfh9nbkIgEo+Hi9cLgXjHHXcYVy0iEauYV7AvuLeZF8klCASP4aLGssmciSWS14Trbt64caOceuqppvIIopi4wtNPP91khpctWzZovcDrL7jgAhOniOs52LjKeCd+lltRANH0xBNPmBMA03E06xgh8rAOUp2e+Iri4ik48Vi1sNGonYLdiEXbo9MKRv7iug4G3rNU00PNVv7CnpK/Yd3+0jqzZkjeqpUR+qbJRdnWjbzeBSVE9m3NVYGoFMn6H3Kk2gXe7oNTupJkt79WnEr/tHGLN4F4zz33mFhErwUiEAPIHFqUQKQGJBbOF154ocRZ1zamkMQZQsCIRcR1fdZZZ5ne1LQhtBVSSO7BknrYYYeZ/AIqmfjSpEkTY9kcNGiQEYqIxGRIYElqkYjwIgbw7rvvNhcAGVD//ve/jRs4khckKw5WNYi5Y445JuQK95xE1KxiI6OKQFrK6mAC5+TEIolgxDUd7Hvznhn1G0p5tnPPl7zNf/1TWmfpEi2t8z+cOpW83gUlRDLn7/J6F5Q4Z9v0pZJ1Wms5qKo3vb2dMpX3C8SK+2vyBhKIVNzwQiAiXh588EGZMGGCcTFjqPAShNWnn35q5usGDRoEfB5JIiSsnHPOOQX3WS8h8y9hXsGKXSve1q/f38zihBNOkK5du5pjc9FFF5n9yc7OlpdfftkU0AaSigYMGGA2RKHFikFc1k8++aRJAKJuYrAGnngm8b9BESC6+HExRfOXFQOWRU5CKxhxC5fkAkWIIhBxEUdCfHKicSKyIRixTCIYCeYlkDjcftIZtWpLxhk9pNwZPSR/+zbJnjPLxDCa0jr/KyaeiqRV1qSVRGOHxiMqQbDuR5FWZ8f+c52yVSW7/XXiVPinYYKvQKQ1LK7Mks4/Ye2f48hDDz1krHHffPONiafzCvbl+uuvlw8//NBYM93Cyx9Y8hYuXHjAfbTGw8KIOGvY0L9b34KXjuNuo+xs8gmQsIJQJEYRw0+PHj3Mb8N25plnGosv4WR8DlZMknt8cxx4Ds06+I2TQSCmREyiL5xMxBxgYqcXJT82gvFf//qXdOzYMaQL1rTYW7zYmKjJYo62WXn37t0R7yedt3OnrJk8SWTBXKmyYS1R1JIyZKRL/fF9JS1NezYnEr/0/lb2LF3r9W4o8U5Guhx1d3OpUGlnzD4yv1x1yUEglq8RMCwJgYhHiGxeLwQiIoc+xHRSoTail5A1jTj7+OOPD4jhw8BjW9727dvXuHipqeiPYGMSEX3M8WREuyGHgFI6a9euNc/hs6jbiIU1PT1drrnmGnn22WfNcykujojE3Uy5IoxDvtZE3NJ169Y94L5EJjmkbghgobv44ovNhugiBR/BiEgkhZ3AWUQj2UmBYhjdLfbIRot2wVELJyaZZ2y2n7SNYwynnzQD1sJly2RPvYbSvse5Ui4jXXIWLdifKT13lji7ktutV6bNoSoQE4zsHXmyZ9k6r3dDSQTy8mXd9DLS4rTYfFx++ZrGgijlqhUpELEweWVBHDt2rDz88MNm3vNaIMK4cePM35NOOumA+1955RUj/gAvWkmPFeV9qDoCuJD5DXhPLIFUIKGEzeDBg00WN1D2Bwtl8+bNjQsZLyEucfIbcM3PnTvXvKdbJFoxaAUimdPJ0M855SyJgUB0sbJCMHKiYJIm7gGX9HHHHVdgOuZ5mMe7d+9uMqBsKyMv4aS3gpHWf8H0k7ZxlKxoGbB8Yx2d3FzJ/f03E8NI8ouTmSnJxkG9Tpcqpx7s9W4oIbD5xyz5bciHXu+GkiCklSktHe9uJGXLR7f5QH6F2vsFYtkqAQUiwgLRgAUx1g7zGE4AAF9/SURBVOKBaf7FF180iSp40pjTUg1E32OPPWZ+B39JJXjn8C4iHqkPiUGpfPnypsQO4vCpp54ysYiEq+GB5LlWECYzKhIDiC5MzbTawQwOmKFZ7VALCQsk8Y0lLeIZDdz9pBGMnOS+/aRxuXOhBBtH6eTnH1haZ9NGSQZq3N1HyjdJbFdAqrHsmVXy5+s/eL0bSgJR91/tpNnx+3sVR4Nd6VVlU+NLpXrdxn7DfqxAZJylzqAXAvH111+X2267zcTm+1rtkh0rBnEV03YQLyKJJe4MZX/9lrEEOo5jDEQUGCcpFbc02oDOMA888ICkAioSi4ELnIwrVmGkxXOykRp/4YUXysknnxx2LGCs9h2TOILR9pPG8sltYigRuaHGS5hajOvX7m8POGum5K1ZJYnKwU9dLaUraXvDRGL2VVNl10It56QET3rFcnL0sDpSukzkW2/mVqwnK2udKxu3ZplC0CzEWZBTiYLbiA9czF4KRGL+cKVi8MAilspgISQ867///a8RfP7Eoe8cWup/XsTbb79dHn30UeNuJonUGmVCrWaSaKhIDAKyrhCGV155pbEokonFxqBA1hPxjKeddprf2knxAqsiygOQ7s9FQWa0TXoJt5+0ed+/Nhl3NKIx94+lCVVap/5LV0lamvZsThSyd+XK9NMmmlgzRQmFhpe0l8Yd/4roe+ZXbizZ7a4RKV2hwAPFAhxPDm1XEQ9Mr/wlYcILMYEYov4gf5mrUhUbH4gHkMQTQsWsl7Co2MFd/6suMnz4cGOJRCCSsILbHstsKqAisRgIoCVglXgECmVaWIHMnDnTuKQRjJxInHgkvdC0nFVkvMBPTANzAneJh0EUMogRw8iAhkC0gpHi3uEGCedvyzSldXBJ5/62KK5L62Q0rit1h3fzejeUEPjzp22ybPD+wHJFCYVSVStJx6HVpVSpyIxJ+VWaSna7q0VKlSuy1Z7t/ct8QRwbFsZQGiSUBLJ9aRP39ttvm4RMZX8m82WXXWYEHyVsxowZY+73Z1Gkhe4zzzxjBCIhW3RTefrpp032MhnQJADRzjDZUZFYBKTBUzcJNzOu5UBwghFzgmBkpUIqPZZFBCPV23HxepUGzyqJMj0E5bZv375QIou7nzRbuP2kfcnftVNy5s3Zb2VcMDfuSutUPK+rVDvPfy9VJT5Z/sJaWf/Ct17vhpKgNL7sKGnYtuSdevKqNpecdv1EMsr6fzwvzyQFMrYy5mKlsh21WJQT0069W8ZZtmiELFEImqxcYhFt5xBlP7j/mdfppEJcIfGF/iyKCPxZs2aZWpKdO3c+wFWPwcV645IdFYnFwMUdSgYzh5PWQpj3sTAS/0DldQTj2WefbSx1sRKMnOQE3LJPxMMUV3w7Gv2kzfvu2yc5C+ftF4xzZ4uz2/vSOtVuvlgqtvE/yCvxydyB0yVr9lKvd0NJUMocXE06DKkoGRnhT3l51Q+TnLZXimT4H0sRGoy5/EUg+rMYIhIRi4yx/uIYSzo/fPHFF6Z1HXH09DhW/sFaDDHm9OrVy9weNmxYQKHo7/XMk/Y5yVLmpihUJEYRDi3WSOuSRjzS9ocYRgQjg0K0BCOxFFg3SeOnlmOoJzL7ble/uNLD7Sdd6H0prbNk8f5M6dm/iLN9m3hB7Uf7SZlq8WXdVAKTl5MvP5/yjjj7NIZUCZ9mV7eXui3Ci03Mq9lGctpcLpJRukiByOL6qKOOCmqM9BfHaAUjYUGhenLIvCV7l3qICMVEL+QcLZjfxo8fL0OGDDEWxRtuuMF0Y1MKoyIxRnCY6TtJHUZWMZi8u3TpYiyMxItQbylSFzTuYwYrioRSDLSk78u+00/aCkYuqnD6SRd63/x8yV2+bH+m9OyZkv9XyV1BwVLvhf6SnrEvZp+nlIzMBXtkYb//er0bSoJTrvHB0uG6DElLD21MzKvVTnLa9BFJLxXQwsSYS7ZrsAKx0Gfk5ZmyZQhGNhvHaEN/intP6vkRN4fYIclSBWLR8FtZtzwGEUoDjRgxQtq0aWM8frZ0Tn4xGdDJjopED+CQU0XeCsYZM2aYGky22wv9J8O9wDdu3GjS88nCKqpRekmtlFYwIh7D7SddqLTO2tWmrE7O7BmSt3aNRIu0qpWk/mP/idr7K5Fn1WsbZM2zX3u9G0oS0OL69lK7cfDWxLyDj5KcVr1E0jOKFIhYBRGIkchiZjzEFW0FY3FxjNOmTTONH0aPHi0DBw5UgRgCzJdkgCOyEeOIRdoFUiInI8ldycGgItFjOPxkXCEW2X788UcTy4JYZKPheTAXvLtVIB1UWIHGAqyKiMVI9ZPme6xYsUI2LloorXL2SsbiBZK3fFlE97n8yR2lRh/vmtoroTP/plmy/ef9tckUpSRUaNFA2vfPD2pcza1zjOS2ukQkLT1mAtEfiESb+IJ4pHMIYUQkpfA9CGGiJzFu02gKRPonM08RRkWjBrxhZAi7+y778sILL5gEGsKtgHaAI0eONIYRr7FWQlz9dKIhSXXSpEnmMZJPmzZtauojMg+nKioS4wh+CgQXpQu4EKnPiOnbCkasg/4GANwUXLSc6AhM4hC9wN1PmgSYUPtJc8H+9ttvxuXC97BlhPL/3rq/tM5sSuss5okl2s8q1/5bDurozTFSQic/L19+Pu19yd+1x+tdUZKEVkPaSY16RXdhya3XWXJbXlikQFywYIEZ9xA+saqDyOeRlIKowYKI25Q2e/fee6+JeY/mflDejWSYo48+2sRekvCB+MMaF6gFLAki7B+CEsMBopIYfapuUErGa3zdybTbY98oQr5u3ToT58k8nKqoSIxT+FkQS1Ywfv311ya+ELGIW4F2eghGgp7p/sJK8pprrombDjD++klbwehvMGHAYcAlQQaBGOh75O/M2l9aZ9YMkzEtOaEnMtQadYWUPTh+azgqB7JjyV6Z1/ddr3dDSSIOOrKptOsdOCY5t0FXyW3+b5EAVjmExcKFC40nJZYC0Q3iDNFGmTUW4bTcY9zlf1uvN9oGAyybjOvff/+9EajBgFGDmD9qEPbt21fiBV+xiMU2Ly/PuPlTOS5RRWICYONT/u///s8Ixi+//NLELdJiCNM4t4lv5MKLR2w/aQQj1k4GNCsYEY8MbGRiM9BS7DvYoG9n317JWTBvv2CcN1ucPcFZmuo+d7VklNF2fInCmombZNVjX3i9G0qS0Xbo4VKlZmah+3MbnSK5zc4pViDiAkYghhuHXRLwuNBBZcCAAcbNbBMsaPBAJxHmClzAzBfRhCYNGC84Hri/gyErK8uM/5SJo8pHpChKyKWyyCspKhITEC4yKr/ff//9RoAhEq2FkUErni8G20/axtcgDLmPWEYEYti1GHNzJOfXRZIze+b+0jo7tvt/YukMqf9cb0lL09M+UVh4+zzJ/HaB17uhJBlVO7eQw88/sGZr7iHdJbfJmUUKRCx4JO95JRCpvYtApHMIsX2BxnusnMGE+YQLx4JkS0KLiKUPFpJCqOWISzcUzxedTnD/Nm7cuFARa7cIRCQT187ciFvcNsJQoRgeKhITENwK9J+kfySZbFxwWBKxKlapUsVcuLifO3XqFNfZWVgV6UzAQIabGQtiJPpJO/l5krts6X4LI6V1tmwueKxsx1ZS69qjI/gtlGjC8DTt9I8kd1uW17uiJCFH3tVKKlXdYW7nNDlL8pp0D/jceBCIiB/cyIQYPfroo56KHuYe4vcQiMFW0iD7+qGHHjLx9iRYBstPP/1kkmawoFL8mhqQ1sVvS9XALbfcIhMmTDDl31avXm3mEo4V1lYlPKLfQFKJKMRxDB06VF599VVTEwvIcGNj5fjVV18ZF8NFF11kVmnnnHOOsTASNByLfqHBQoIOK0lcIgwwDMDELnI/2YIl6Sedlp4hpVu2MpvT8zLJW72qQDCWbaOt+BKJXatyVCAqUWPtT2nSqodIzqHnSl6jUwI+DyHCeEXJr44dO3oiEBE9PXr0MF4jrwXioEGDTI3BH374IWiB+MgjjxiRSHx9KAKRBJ1+/fqZ8m5YBX1rRlqBSAHxiRMnmmzqbt26mXAAMpPJWMZoQqy7EjpqSUwgiEukhhMXA70ki4I4P3pOYmEk+YULifgPBCN9K70Y5NyDHYXF27Zta2p++YJgxIVhS+tEqp+0Yd92KVX6L8nI/1MyJIBLWokb1n24WVaM+tzr3VCSlYx0OeqtQZLe/IRiBSIlvrAgli0b+3ae69evl9NPP92UZXnuuec8E4gci+uvv95kJ2MNJB4xGLAePvjgg8brdeyxxwb9eQhKLKeUorn55ptNcmYgV3T//v3lsMMOMwWxK1SoUHDcWrdubbKwEYxK6KhITDDcpvVgIeaP7DPaAyIYce0iGFmR0lc6VoMe+048DStCeknjGg/mNYhjKxhtP2kEI39L4k5Pc3ZLhvPn/wRj4QB2xXsW37NItk6e4/VuKElKnSv/LQ0G9Yxrgch4iUCkjMxLL73kaQgR8YSUhiHuz10bkbHcxj+SsUxpG9zDQMkbQqN4Hd/BQtKiLXPmD1zLeMIweBCDz3wVKLaQ+eE///mP8bLxGmCuwOKIxw2jCJ+fCr2WI42KxBSDi4T4DttPmiQYgqC5AFml2hVYND6XeB7cNZj9w/kcdz9pNuqFWcGIpbEk7vQ0Z+9+wej8KenOVtF+Bd7D7z393EmSs+lvr3dFSUKqn3GcNHngBkkLYJXj/KP+H14NXMxeCETGOcZnCnW/9tprnocMBTJQvPLKK3L55Zeb23i7DjnkEBMSBdzGe+TL8OHDTW3HQIaQhx9+2Fj/+IsV0f2Yvc1mBSPWRNrb+nLbbbfJlClTZPbs2YUEporG4lGRmMJwwdAS0ApGso27d+9u4jdYuRa1ygsFssxIUOFUw4IYCVe3u580G8HkuKJL2k96/5vvkwxno5QygnGLpIleIl6we0OuzPrXW17vhpKEVDryMGnx3D2SXqZ0sQIRC6IX9WepAkEMIha7t99+25NajF5CWBRWVCy5zBkIOgSeW6haa6HFV0Rym1hIXPSU67HgKqfjS7SMIsmEikSlQDDOmTPHCEYSXyg1gGURwchKlu4p4WQbk0xDDUQuRmIQo7Vq8+0nTbKLFYwlsgA4OUYwpuOSzt8kWkEhdmz4LFP+uPcTr3dDSTLKNKwjrV8bKaWq+i80zZRoOz9hQfRCIGZmZpqQoEaNGpl6gl7GkHsBHi7bPQxB5xuaRBcU4hUnT55s4hCtN4zn+4ZkYQAhExuRyG/JHEd1EBJabPKnEhgViUrAUg9WMHJxEbvIRcjKFgEWjGDENYxARKyxGo5V03mEqRWM7AMDDPsQbj9pYmKwhJbKcOSoI+pKmfTNkuFskjTRri3R5LcHl8jmj2d6vRtKEuFUKi9Z154nlZo2NAtINjpAua1PtsWpVwKRGGzKmLFvCBwv3NxewxhOjUMW/zSPsAky/DYUCif20E2zZs1M4gq9q31/MxI4Edy///678ZzRJvCuu+6Su+++O6bfKVFRkagUiR00rWDE9E+nFyyMXHjEBPoTf8SHsBonK43ip7ESiL4Qt4gbHcHo7ifNFoyrwVpCmUjoKFBgCXXyJMNBLG74n2DMjf6XSTFmXPCF7FuzyevdUJKEtDKlpeXzw6VMqyYFHaCwFiIqbCIc4xb34WKOZiHqoixojK2E+iCGvNgHr7GSBOvf+PHjjbUPYUdMIdbD6dOnm8cxWFB+hzqNzDW0qmWewiBhrYmmzuq0aeaYIgzvuOMOGTx4sDzwwAPmPbTAdvGoSFSChlMFqyJldRCMiCey1bAwsvKtU6eOuTCffPJJefnll01x72BraHnZT5rNX/wlAzbfkcnD9sr2i5Mv6c5mKeVsNIkvaRJ6P2nlQPZtyZUZZ2k8ohI5mo4ZItW7HVg6jJg2rIZ2XEA04HUgAYKevbFMasBqRr1bRAtjp78e96kEVj/qIrLQZ3GPV4j4w0MPPdTUaSTTGlauXGmSZqZOnWqSYdjc8HiLFi1MTCNJLNRqBBWIwZH0IpFin2RHsQphlYj5nlVFIBA/48aNM+5FSsW0adPGZGCRyKH8A6cNGWtWMNIzlEBgLjqONZltkezLGet+0lgdOQeICcIaGrQl1AjGv//JlJZ90f4qScnGKdtl6R0fe70bSpJQ/4beUvfy/SVUApXmwtuAWxN3L2MDYwQLRNy+/I1m4ggeCzqDsJCliwmxdamMtQQi/Gg/iJhnPsYSePzxx5tQAHfiCgW3mW+wElJo3F99YYwZNptaBWLwJL1I5IKj5AvuA+ooFScSb7rpJtPShxUMreFI7Sc7ilWNVmz3D6fQqlWr5NJLLzWWN1ZslGzgOHNhUgLBK3dzqP2k+Yv1gAkCNzmr1rD3nfIMkrm/DqMRjHsivetJy++P/CGb3v3Z691QkoBa53eTRnf293sdW4HItc8cYUNQuB9Pgl1IYuUjFtuW24pkrCKWMsZOxAzFpoOpH5sKWCG3YcMGcxsxiLfK4i6Bg5uZLmMU28bIY19r//L7WcusCsTQSHqR6IZBojiR6A+siRdffLEpCKoUhmxiVsFczLhJuJg5zlgYKeLN8bOCkZV6PAtGrKO41BmomSQQjNbCWJJ+0vsF43aXYNwV6V1PKn7p9Y3sWbbO691QEpzKXY6U5k8MlbRShd3GTH3Lli0zZVawTBUVo2yT4RCNeBmw9NkuUO7El1DBcti7d2/j5SLeDiGqBMZfiRsg3nDkyJEm25kyboFeowIxdOKnmW+cwkmFWCA+RSkMA6zNeMa1b1fBBB0PGDDAuHKpzo9bmouY2BDEIqKxyDi/GMNAsmLFClmzZo2xgvJ9bD9pJgfbT5qJAcEYaj9pSUuTfKkq+RlVJcc5TNIkS0oVCEbtTewme1ue7Pljvde7oSQ45Vs0lmZjhgQUiCwGgxGI5r3KlzeeBTaEnfU8EO9G9rG1MIaykMRbQSzd2rVrTQauCsTi8ScQOXYkuFCD11+bQPfvoQIxdNSSGETPSQJdyfBlIFAOhC4ArIBpF1VULS/bXo+MPQQjZQ0YcK1gpIail/1IyY5j4Ecg+ktisf2kbWmdSPaTTnN2utoDaj/pPyatlw33TfF6N5QEpnTt6tLqtZFS5uAaAQUing8EYkkSRAitYSGMhZEN7LhQVOILIS79+vUz1SKo+adzS3D41kAkc5k4RQwUEyZMMG57JbKoSCwCej1SewlLGIWllcj1kyZTDdc0ghEXAdY5MqT//e9/G6EWK8HIIL9w4ULZvXu3iTkNpuSEbz9pLAJ2YtB+0iVnyRN/yF9vaTyiEh7pFcrJYS/fLxVaHOL32l2+fLmsX7++xALR30KSccG6pUm0sIkvLKC5bcccPC2zZs0yhaLdcXZKcPMMx5A4xBEjRpgF/mOPPWbyCXyfp5QcFYkBmDhxolx55ZWm2j3uVCV6EFRMghGCkSw1XDYIRn4nMqajVYbC3S4QgRhO9qL2k448P176heQv1/qIShhkpJsYxCrH+U8yRCDSTYoklUi1HS2qbShiEWshdf7atWtnqmRQ1JnwFQRiLEqEjRo1ysSH4w1jEdylSxcZM2aMqSdYFMx9FJwmKRE3Lq8566yzxGvwWr355psm3h1rLWFMV199tXlMYw4jj4pEP9AnE4GIUMQdqsQOAsRxRTOoffLJJ2ZQO+ecc8xvxuAWqQb3iDnaEPL+RxxxRESEKJcSgtdaGG0/aSsYS9RaK0X6SWdn5cj07u+I5OV7vStKAtJ42NUmm9lLgegPMqgRXS+88IIRjiTzkY1rQ22iafk644wz5JJLLjEdTHBz33nnnaajFr2pA1lSf/75Z+natasRmJSWwauGSGTMpKlAtCjOCogF8ZZbbjEisVu3bibpxwpXFYjRIelFIqs529gbaxFmacrbsAKhBh7xDLgeXn/9dfMcLgbqMlEQmpI5FsSEliaILQSIE++IYMTlz+BhBSMDWLh1yzgnKNXDOUDyTLQGFttPmo3kJ1tCgy0S/aRxSafn/yXp6clzCa//Yassv2WS17uhJCB1Lj9PGtzQ2+9jNikNF3OsBaIVMLSSIyYbQwUu0o8++siE2jAeYIxA8CBgow0ilc/EEsc46g+qeTB+ffrppwX3HXvssSY55LnnniuxCKQ3NbGcbMyr9F+2FCf28ABhiaUVn032UYEYPZJeJGLSRxT6ghCk4DPZZZjTeR5QdJOLJ9DzFW9gYCA4mdU4ghEByQqXwZXfN1jRRfIJArFhw4ZmkEnUftI22WZb5hY55qgGUqFMZlL0k17+/BpZ/9L+a1FRgqVat87SdNRNkuZHKJCBTGkrBJgXRaoRMJRPwzPFPEOFB/e4MGXKFDOmYcSwXUSiCUYT3MfEYgeyCmJAGTJkSEGcH9DJBGGLQAsHK+QokD1s2DD55ZdfTNymFaW036PjjPu5/iyJvl4fjUGMLkkvEpXkg4GCfp0ELjNoYaXD5YBgJMEoUPIJAo34IAZIRKJX+PaTZuKygjGYftJ8f9xFrPRJ8ikQmQX9pIlj3JiQ/aTnDpgmWXOWeb0bSgJRsV1LaTnubkkvVzbuBCLTK32CaVNKFnPr1q3FSxBfxHsz7jCGBoLQGCpXuLOFx44dK/fdd58Zt0rSQYW4TIQetXVpf8iY/NVXXxnXN8IUi6sSP2idRCXhYIA58cQTzUZYAA3fEYyEDlBWgkEIlzR/bczNE088YZ7D5nU2IaIOkcqGRdQKRlb47K8VjP7cYsQUsZJHKOI6OyDOMS1D8tLqSJ7U+V97wC0mhnG/YMyWeCcvO192Ll7l9W4oCUTZBgfLoY/d5lcg4iHyWiBSQu3FF180tfy8Fohw3XXXmQVmUQIxGiAQcflfddVVJjGRLmY9e/YseBxhyLHCW8RinzAgJT5QJ36M4SIgro7Wf1w4WMKChfaCJG4QF6LsB5cECS3EmiKyGIxxI1MagXaABGwTW/rggw8aEem1QPQFkVe/fn1jEUT0ss+4o2kDSfA434n/mXAQlPTFBp5fZCJMWrrkp9eW7Ix2siejm+xN7yw5aYdIvpQgFjLK7Phtnzj7crzeDSVByKhSSZo/faeUrla50GOIQ6yIXCdeCUQWsE8//bRptUdyitcMGjTIxBhi0Swuq5px0tdiyP8lGT+ZvxjPaJ3nFogI1scff9zEJRLWpQIxvlCRGGNwEVIK4dlnnw3pdbgH+vbtK6eeemrU9i0ZBCMZfGThUe4BQW7bXRHTSEwpWXEETcdjlAWJOLhfWAQgGJs2bWrqN1JPjYGUQRYrKo+HlOVtBGNNycloK3sRjBnHSU5aU8mX4mtCxpLtc1OzLqQSOmmlSxkLYrnG9Qo9RoIKVissiJUrFxaQ0YaxBdfsww8/bBJTEKpewv4gEEmYYRHdpEmTYl/TuXNnEyvpBpcw94cL4zHjV58+fQrumzlzpslSZqHMwp7YRGDcJhtd8R4ViTHmzDPPNDEqFI0OBVrcsfoqyUWaSmB1o1MOVjj6s1IPsVOnTmbwZpDk+L/yyivG1RuPgtE2s6c8D5MdbmZEJPGXiEVEMC0DQ9532gOmVZecjDayN+NU2ZNxguSkHSr5ErmiwuGyfd4Gr3dBSRCajBgkB7Vv5VcgIi4QZl4JRNzLjPE0C6DOazy4mFkcU7kDqyqtCNlImrFggMDTYrnxxhuNwH300UfNWHPvvfeaxSpisySLeMJk+I2ABEKSDgmtodQOiSsW9hfRSHFyxVtUJCYAiBlWxmSXKcXDwIIYZzBCUCEKiQciw5CBiUBpBicsi4ceeqjJkqb3JwNnvAlGvovNxj7uuOOMhZHvQgD6ggULzOqcemeUkuC+kEhLEyetquRktJK9GSfLnowTJTu9heSLBxmgufmSNX9lzD9XSTzqD+op1U8/rtD99EC2AtGLcmWMHSR7UICaUjeEwcQD48aNM+MIlTvwVNjtnXfeKXgOYyXWOwv7jqhkXMTzZZMEg6mRaMch3/GIsRaoVUlcNftji2FbC6INFeA+3NvRaqSgBI9mN8d5cW+sYMcff7zJCqN0Ais6LlYsY4p/iAOigwvlcopqu8WpT3A7nV74HXB9UAuM7D+Cp3GBeFlaAeFn64HR57q4ftL8T9FuEl+K6hsbj/2kd/y2V+Zd9m7UP0dJbGr++1RpfNc1ha5LBCLxbpSRITEi1jCWIKrIzqWczSmnnCKpiC1Rg4cGEUqSHhnSjMMsdhlbqe5A6RssvVhcKUNn2bJlizmGjMckG5LooniLisQ4FolccIgWLhTczaAisXg4pTl2ocTt8RpWuBTuZiNpBIsEvw2CEZEWS8GI6CMLkSBukpzC6SdNe0AEYyL0k17z9iZZ9fgXUXlvJTmofGw7OfTJoZJe+sDrmuuWjiZcr14IRGBBilsXixsdTlJZICLY6SZD8h2GDTpnUXaMRSzdXshsZixFDBI/7l4U33XXXcZ6SdyirUusdRC9RUViHItErERUlHdP8Fxo/GTcR/u6VF2xRhOOL65nfhsEI8XVyU60ghG3STQHLTvp8ZlYBsPZf2IXrYXR3U+av+F2qolmP+mFt8+TzG8XROjdlGQjrWFtafDk7VKzYf0DxkO6ZdELGQui7b4Ra1i09+/f3xTLpnJFKmKLXzPe4KpG8FEYnKLZbm8Oz8PogVseQX/99dcbjw2vJZkTzwki+7PPPgtYPFuJLSoS41gkckERb+aGxAsy1FixEmtXlDtVKTlcHgx4uJA45hz7li1bGrFo63lFSjBa9zcbGcyRmPQSoZ80+zit+4eSu31n+PuiJC0ZNapIufv6y5a87AILOecut62L2SuBSEmZK664Qt54440D2rimIiTCUMKGcZLM7sGDBxvxZwWkW/BRlBvrq3t+I+6auZDSQUCyXkhVHJSooCIxzntJ+6LuZu/gUsG6S1A6cYyUhKCuIXE2ZEsT1B1u/1Dem/hTgsejWdst6v2kjZVxs6RJ8Ek0O1dky5xLJob/2UrSkl6+rLR8cYRUbNXUXCOMn5y7jJE2rg1LFKKxROdvGFD/kH7LdFNxJ16kKtSlJH6eRTSLaX/t9dxCkWQZ4hQJk6FLFlUcKPvl+zzFW1SmxxjKCLh7SROX4e4NjUiwJQKU+AKLIaKK34qN8jpYEhCM1K8kY9AKRhYAwQpGBlL6MFPShjqPwbTmCxcsz1ig2Ww/aVzruOzICLWCMVBrw4CklZa8tIayL7euzJ8/W2pU3ifNm5SXUrK52H7SmfN2lOxLKclJepo0HT3YCER7/bF4YnGDlYlFGUKRMZMyLQhGe/5G8xoCClITN/fcc8+Z+LtUgbGC0lz+4gRxFfNb2Ph5fhtf4e4WfhhF2PyNhyoQ4we1JCpKBMDCQUY1MYzUR8MyTHwSghHhF2jQY8W8cOFCI9gQlgV9mGMMA7q1MFJsnMmYyZbEl2AnXGpTzpkzx7iwKZthvnMQ/aQX371Itn4xJwrfSklkGg3tJ7UvOv2A+xAhLKg4vwibcJ+/ZNRy/rLYYjGEdZFzmHM5kjHEVJqgph/Zt1deeWXKJFVQ2ofWeVgJKcflC+MeYx7W1UCeMGtZxFiC1ZBxUolvtE6iokQA+izTsP7tt9828X9MILhRzj//fNNu6uabbzaTCxYQC7GOPI7rjD7MXglEYMVPTBAun65du5q2XYhFsrynTZtm6s8hhANBcgwDP4KSeMoCUUw/6fQ6kp3RXvZknC570ztJblojcWR/LCRr1B1ztT6iciAH9zknaIFoz1/OWdveEku5u1sRlvJIdFriWuA6RyylkkAEavUSB8oxdWOPKZnMjIM8zvEOJBD5HU4//XR56aWXYrbvSvioSFTC6ifNyp3MNUrDMEATm0dsjiLGVUsANqtpJjZKOmBl69WrlykFccMNN5gaYmSm47I+4YQTSpRxHIt+0rj4/PWTBjsZ464mIzugm91PP+m9OxtKCOGLSgpQ7dRO0uDG3oXcnAhEOhD5CkRfuJZstyLOXxZpLM5wh1KpgGL6WB2x4ocC5ziLOmr74VJNFYFor/MJEyaYrGO6sXDsiCcEjgPHF68DTQxw/ZNg6V5UMl8wLjAO0knFeiuU+EfdzYpxk9KZBCsSGXrFFfgGMnuxmDFgUhIGMcRK0Z8bQtkPq3AmKTroIBIZNIlnYuKh+0CsA+9DhYkA6ye/O0VvEZOUseA2kzIB6+FMnE5+vuxauEwyv54mmVOmS/bGrVHZfyX+qXh4c2k5frikl/vnWuB8Q9gh+shsLmnimQ2rcGdKF1caikTBHj16mIUxXoFUEYgW30zjNm3aGNFO8h7x2Bb6PbMY5vhSAoc2foh0CxbYBx980ITWEM+N5VGJb1QkKiF3gaGn5yWXXGLcDxpTEhpMdt27dzfHF3FIDCOWW1bdZ511lrmfQTfkxJEYgyWBeo5kZHPOMMHapAGSe8KdRBmOdv+6XDK/nm4E4751myK+70p8UqZ+bWn12kgpXb1KoaLyCMRwaoYGwp0pbUtDMZbZ89ddWozPx0KGOKT6RLQFIp4dSsjMnj3bLL6DWbRj5UOAcT1i0Wd/eY/irK7B4puljAAkaYdjRp9ldwFxqj9cc8015rdDIJJgRKkwwm2+++47Y1QgBIBjrVnM8Y+KRCVkkcgAQbFn4uioD8aASlbv/fffH/fixkumT59urBG4m+kjbScbBkoes+0BsdYRs8NvgKCMx1qYuIuwrhB8TiwjyQJ2wgWb9MKEW5KyQHuWrioQjHtXbYjwt1DihYzKFeWwVx6U8k3qF9zHuURSV6QFoj8ImeDzcEPffvvtRkAitBjjKPg8cOBAU34sFhbEUD07PJc44scff9yEDRHjjDucGEEWoSXFLeRoXXrMMceY27iNOSa4jRGK7kLieEzoGU0WOMcU8DbgaXrmmWfM2KACMTFQkaiELBJZNbIiPO2004zYwd2IcKS0D65UpTBMQMQj0rie9l1FrdiJfbKCkQG/W7du5vfguFPmw2v4vRcsWGAmIZIF3DCcICCtYGQiiEQ/ad5374p1BYJxzx9aJipZSCuVIS3G3S0HdWhTSCAS48qCI5bQVo5CzxSFJo4RVzSiC8FGUlYsXc3BjMe0uUOQkVzm7l9Pyzus/SXBXeqGECOOzejRo83iFUaNGmVc8CSsEYPtLiiOa5/YZY4h4xouZo4lz1WBmDioSFRCHpQYIHAdEEyOawNYsVIWAreNWhP9Q8IHrpZgYWBFjDFZcXxx7yPMGayxSHLsYx0bZd1/xCRhGQimn7RtDxjJftJ7V62XzCkzjGDcvUSzoxOZJg/cIDXOOqHgfyxPnPdeCEQL1xqLMq41rF90XCJpA/ctYyOlrSgcHW2hE8x4jCWRBTphK1g/ud6IdSZGmKS5SIDFEE8R3WVY6Lp/F0TqbbfdZmKqabdn60YG6piivZgTCxWJSsiDEoWkGZhs5xggiLl169bGDY3FTIksXKa0sLKCkePNxMAkdvbZZ5vJK9oDr+2TG05P6Wj2kyZuMfObGcbKuGvRsrDfR4k99QZeLPX6X3CAQMSCyCKExYQXrF692ghE3KdPPfVUQbgE5yyJGYyP/OV6jPaCOJjxGLB8UpKHfUScse94I8K9rnwFHuEvZCYT+0gVDK5nd9FrWunRho/X4E0ieQXUYpj4qEhUQh6UWJ3edNNNZsK32WmstHE1EMujlsToYlv4WcGIO4cyOghGJgcm10gLRroAsSjA3VbSZKVo9pPO3rilQDDunP87H1aifVWiR41zTpJD7r224FwljIFzmUQHrwQiCyE8JWy4cAPF08bKGhbMeIxYxcOASEPMkexy6623miL+wdQiLOq7EEaEKCT2nEoW1Ih0J7G4b3O8CKXhf4QiHWmUxEdFohJyP2meT7bascceaxq1M7j369fP1CR74YUXPP42qQWXLz1TbQzjL7/8Yn4XBCObrX1Z0vdHJHJu2PCCSCcNWMEYyX7S2ZszZdu3M41LOmv2YpF8HerihYOOaSvNn75D0v9n6SJZC4GIN6K4MIZoQfgMIgs38osvvhgXFrBgRCJiDAsi1kQL2cMsHDds2GDahRZ3/fE5xBviBbLjxddff23EMnMAYSOIRESgr3XQLRQ5bldffbW5Td3cyy+/vMTHQPEWLaatmEQJBACb7SfNbZJSwLefNNZD6mMRmEz2H64F65pRYgsDOhnGWA4IASCWitjQTz75xAh5yungCsKFFup60FosmTz4naMhEIFAdjpkdOrUycR/4X5mwibuFdHLvtO2MFTK1Kpmuna0fH64tPvqBak08ALJbdmQBrJR+R5KcJRr2kCaPXxzIYHI+eqVQGSBQpwvmbssdONBIAYLIs/X4mn3v7hrnuNOtYXOnTubbGrGDgph41rGOkkCDNc/IpHMZvveCEMLn23/x1jw/PPPm9sIfiXxUUuioiQhXNYILawQWBmpvUYpESwSWBibNWtWpIWR1xP3yATO5BFs/+Z46ydtQTyz0KGLTAUnTbb9MNu4pHdMny9OTuF+0kp0KF2zqhz26kgpW69WIYFYnMUrWuAJQSBS0++tt97yvPtRqJ6dV199Vfr3728W6dbdTDgQ4o0uSYFgUUkCDt+f68qWr+I6I76RBBVCh3h//gcym0lS8Vc70f0/vyshJL7PURIPFYmKkuRwiTMRkP2IYKR2GZmPVjAyOboFI+IMtxHxhwhEL3tKW7BskNTARMYERO1IKxi5HUjw8t0pDcKkikD0bQWWt3O3bJu6XzBu/3muOPtyYvSNUg+6qLR88T6p2LqZ+Z/amtTa5PwjLMILWHyQ+EV70XfffbdE8bCRgvJiiEJ/CYMINly4q1atMs+zYPGjuDWhIXRBouUnJXBor+kPxCNdnhByeI4QgRT6Z4wgnhDL/fDhw00BcSyHiOe+ffua44NQxPoIviLQxjdqBnPyoCJRiUvisetAMmDrGNIVAcFI2ADuaoqhY1VgsqQTDGKMuKZ47K9KKR1EL/vIX0QsYhHRyP7ayYnvSrY98Y6I3eKKkuft3iPbf5pn2gNu/3GO5O/ZF6NvlAKkpcmhj90qVU88Om4EIi5Um+hFAli8t8WMFFhuu3TpYq4XWuT17Nmz4DFiGHE3M47ynC+++KLguEycONEIVTKYKYeDuAS1FiY3KhKVuCTeug4kK0yU9FDlGHHMGfARWlgTsDTE++BPED1C0faTxlXIpE+WNIuLcN3l+Xv3yfZp803Sy/YfZkneztBjIpV/aHjblXLwJWea2yxS5s6da6zZgSxd0YYEKcYTznUWTPFgLY8FWAtxYSP0EH0sDn1L3rCwIgmRa2rOnDnGo2ChooLNWqbjCrHQoKVukpfClS4VJQ7ACsgWLNOmTZNDDjmkwA1CIgT9Q3G5KIHB4kriEcfa1kKj4DfWBWKgmESYTCmnEY+TAPuEKLRtvrBQMblhgWb9S5wbmZ/EVoXi/sI1Wu3kY8yWn50jO2YuNC7pbd/NlLwdu6L6nZKN2peeVSAQSXZDILJ480ogUnKJUi4IQxafqSIQrQBEELJxjViR6La+02aT64nryHeRSGILCzHGDApskzSDWzoexwYlMsS3mUBRgoTsPLLw6IrAQMcAx6r3rLPO8nrX4h4sblgOmBzIYMQNTdLLE088Yaw+uJ9JLLjllluMCxoxFo8wUdlgeUQh9faY5CjOTC9Z6slhbXRnZgZDepnSUvX4o6TJvddKu69elOZj75Ka/zlNSlXzvkVivFP1pKOl4ZC+hQSibzvHWEGsHR1BOAewIMZjX/RoQkgJcYeAy9haArl2WEwhFknwoqIAyTwku/lCHDPldohdpgQaCW5K8qLu5hQHtwvEY+yZ110HUgEmA8rkEH9EXTN/bbRspwmOJRMrz+HY8ntQUy5ejq9tY4gQwMVskxAC9ZMmJgtRGXY/6bw8yZq7xMQwbvtmpuRsyYzwN0ps0pvWl0ZP3i416tUxYQ0IRKzULEa8gPP4kksuMf2EibWLVkmneMWdTMJimoQdIBOaDGrg2uGaJtnr2WefNRbDQEkovAfPZxGpJC8qElMUgpfffvtt8xcLHLXpWDleeumlnq3yvew6kKogmqgLR1mNYOIPSRohqxIrLRYJBBeCEesCMYxeZYeyH5zL7B9ZzIGEq7ufNBvuddtPGsHoTyQHg5OfLzsXLJVtU6abOMbsjVsllck4uLqUuecq2bxvtznm/D64l4lD9CLOFatX7969jYeBZC0KtqcidrpnTLXFsoFx89FHHzUCkdAdXMl4DoLtnqXZzMmLisQUhBU9K8QlS5aYcgmsqIktsaVFiDuhaj7WmHAnzUTrOqCEDtZajjHHHMHIOYR7H8GIYI9VrBcChExZ/hKUH6xl091Pmg2rCEIRwViSftKm7eDiP2TblBlGMNJbOpXIqFRBDnv1ASnftKFxMZP8ULlyZXN8EfFuK24sxhc+k/ItlI355ptvUr7agVsoEoZBuRzuwziwbt06IxCvv/56I6RV/CkqElMMAvvpx0lNMCZyXAq4gIgrobvFm2++aVyL3EdtLDptJIJIxOXBhPPOO+8U3MeKGDcqmc5eldlIFRBoHG/bHpDz7IwzzjC/Wbdu3aIW+4VQZdHDOUIWZklEB0WMEYtYm0huIHHHZkqHayFleN2zdJVJekEw7l21QZKZtFIZ0vyZYVL5mLbGrUtyBCWWKK3kFuUcYxZ17p7d0Qhb4Py46qqrzPiGQOSzFDmgdA2VIRCKiGmuIWoo8ltgfU2VskBKYFQkpgh2RUj9QeL2cLPRPslfBjHlTwhIpqI/ZWWSueuAEp3JhwWHFYxYcnFrYWHkfItU/CuTGlYqJrR27dpFNMMSq6gVM5HqJ801uHfFugLBuOePf1pdJguH3Hed1DznpEICsShRzsbtSPXsdi9cKIPFOUIBea9a/iWCUGSBR2wywp1aiMwBvqVxlNRERWKKwWCAdYeJj0GcrFWbrYqItH04eR6Fbr1yzcSi64ASfTiXiBUkhpFajPxmWLApvUEMLKEO4bizWORw/hIzRQZmNOPcmDitYCSekX22YibYmC2/77tqvWT+zyW9e8lKSXTqXn2h1B9wUcHYQkkqtmDAFW0FYySOMWMa5bAIh2CM0DGgeKGIRZ64Yn4/SgRZr4wKxdRGRWKKgfWN4HGsMFgLr7vuuqAtOwwWWGs0RkUJB4YaivkiGLEwEhPLQgALI5mWWImDObdwgyFCKlWqVFDmxut+0mzhuNRt28AN83+Vxn/vk91T58quRcsk0ajRo6scMmKQsQjy22A9pFZpuMfYtmAkbIHf2X2MiztHED10AyExAwtiIEtmKlFcVxT7+KJFi0w5LM5tmhhwrYLGJqYuKhJTEFox3X333eY2Frl+/fqZ2D3foOaiYFDhuVpEVQkH2zIPlzQWRqyNJBlh5SZbGkHg7xxEhJCkgqW4TZs2nk5c4faTdh8DQipwxxP7a0Vm9sYtkvnNDOOW3jn/d54o8cxBHdtI82eHye59+2TWrFklEojBtGC0gpFkGN9jzLg0dOhQU6oJCyLu7mTHV8DZbHKsf8Ri4mYPJpvbdk1h8YbrmZAd5gWssUrqosW0U5Bhw4aZnsYM5LhuCezmf9w8/ia26dOnm7ivBx54oOA+Vp1WIOo6QwkVzjMs2nfeeaeJX2RiItGFskwUWyZ2cdy4ccbybc8vyhwdc8wxxh3mtUAEkllwYxIzi5sO1yoilhjYn3/+2fQQJzbP3/XBfTzOROwWiOZ969SUg3v2kMNevl+OmPy8NBrazwgxSY8/S065Q+pLs0duKRCIxAtHSiAC4w6VCYg55RiTUIf7nzjDqVOnmrjqSZMmGcGOQGTxi5UaK2KsBCJx3ixsSI7jnLTFqouzljIOI6iJv+TcoU5pONjrgGREspX5H4HIcSHkhvdFbBcH4zlCkTAj3of3aN68eVj7pCQPaklMUZjMWG3TzJ0JDbDkTJgwoVCdRNzSbNQZu/jii00GNIM37ggGRwaXVHBHjBo1yli9EDTESbHKJuYRsVMUlIhh8iIej0GX12gnGP9wHlG3k+PMxrlJrUu2N954w4jH8ePHx3VPadtPGusXlkauFWthtAWcsaIS44hADLavdE7mdtn27S/Gwpg1a5E4ud52vilVvYq0eu1ByalS0biYGTeaNWsWk89GEOKKxiuCOOJ/xCTHFAsiojJe+8wDIRbsKwtvhC+LBb7DcccdF9Y+YO0jyRCBh0hlwd+pUycjlFlsUWEgWKxFkfJFWOyDcVcryYuKxBTC34XOChPR99BDD8nvv/9uxAuTsy35weMUWMXag8uCSY4VJiVCGNhIPqCMDhaEZAdLFx0bECzEZ2IFI4YHC1egeDREDoM3ApO4O8oKIRKxhBBPpwSGoYlz7JlnnpFHHnnEHHOsdkzATLIIknhfmNh+0jaOkcnXlhfhPAq3NFDu9izZ9v0sk/iyY/p8cXJyJZaklysjLcbfK2lN6hkLIhZVxI4XMEYNHDjQjFvEtbIA5lpDsHHNEtMYT+W6Jk+ebMaRFStWmP2NBFhSqW1IYXwsuXRSwiLPuMO1EiruRb8KxNRGRWKKws/OZi9+SsxQYZ9sZlbGtj4ibc6onQUU2KYqP4MGcWG4qD/99FPzutGjRxcbGM1WXJZcsDGR8QBWIixEuGYClQrC8oqg5jhZjj32WHNMycRWigYxTfmcG2+80ZQzYQImjpGEBDLzmQCZkLHmJoJg5HoiKcBeKza+DrEQ7kScm7VLtv84x1gYt/88V5x9xbsWS0RamjR7+GYp0+nwAoHolWBnvKDHOOMS9V25rjhnEIycJ4glSmLRdSkWlRqCEYnUqcWSzBiLdZyFAtn+9FIuSba8HW/43oyzt912m4wYMcLcrxnKSrjo8iAFYGXNIMnA5E46cU9KCEAsGwTguxu20+PUNoZH1DCgkdGJa/q1114zlkVqaiGY/E2KZG7y+XxWMIMUg2y8T/YWXDpQlDWAUkKUfHHDpMX9StFwjIipIhEBdz0FlzlPscRs3LjR1MGkbAduf2IVmWSx7HJ+xxtcb1jqWTB07tzZZJDiEuW6wBLNQoN9t72lQ6HUQRWlxpknyKGP3ipHTnlJmo4ZItW6dZb08tEphNxgcN8CgUgcnpcCES8GVmbOCazM7AduX9zQhIUgGHHhxlMbPiyIuIf5vRGUiFyyiBGPJYEEKDwXWKuxLOKGJzYTGHvVHqSEg4rEFADRZy2FiDkmJisQ7YTKwLJw4UJz21oRWX2yIgfcOcAEZgcbXoNYpMYZFhILAxQJCFiAKHFCUDaWNlbNTJLgHrDs7SeffNK4iAjoj3c4bogUJqCi3MaIGWLR3PA/9yuBITmBWm1M9py3bhACCPMrrrhCPvnkExPbRXF1RBjJDYiF4cOHGwEZD4KR85trELczAgZrEd8B4UIMGdcQ/aYJ8WAhh2DkeuIc4RoMhYwK5aV6t87SbMwQIxibPXqrVD/zBMmoVDILlaX2xWfIQf8+2cQgIhBxMXslEHGtcn6QoMEiwR9Ym+nhHk/uUs5Jjhnx3+w3IT6Mzyy6GUvDhbF50KBBJqSFRRXn0jXXXFPgxeAzVSgqoaL25xQAVxwDES4ZCg8j+HBvtG7d2kxMBNmTDMDEzOM2EYNJl0zNtm3bGusH2IxmJi9KUPB62/cZmAgpak2iCwMz8Yxk77GqpxA2EyCDu3tisbcRljNnzjQleUjwiOdkGOpLYgnQ8hDRgVIniDysh8WBNZukKjYynz/77DOzuCEejR7MnOu4/7CUx1oscA5jKSQJgMWXv37WnON8BzbOeyzvCF8sTtSVDLd1XXq5slLt5GPMlp+dIztmLDAxjNu+myl5O/Yv1kKhStcOUuPai41ApKyKlwIRQXXPPfcYAWTLdyUKJNjgordJTFbM8r3onRxKRrF7jGzYsKEZl4jBpE0pYF0nVpG4TbxBPNe6njnPiI1N9V7WStGoSEwBEHPEpzCI4DImToWyCAQ2M6AQt8OEjIWDlaidSL/66ivzl3IjuJndAczWdWzdpkzA8OKLLxr3CdYyLIMXXXSReR2CCmsPn0uSCwM8MEiRGQi4r3DD2cxfBjYmxXgTihwjJidKX/hmgvvCZMqE74b/tUVY8QQjEH0hFIK4LDYWL4RLEKPFBMljCEbiGFn0RLvGpy0eTlgCFkR/AtEXznX2kw0RZlvXrVmzxohNLKg2jjGUftLpZUpL1RM6mC0/52rJmrXYdHrZ9u1Myc3cUezrKxzWROrefY3MmTfXXNsIGa8EIpay22+/XT7++GPP2oaWBLwPVDzgt7VJNVj9GFuLG08sdiz2/Q3cSTos1DlHsCoS04ul8YILLjBjNx4lWphScYFEOu1trwRCE1dSDOq2MWlSHxH3MtZDVrYMOLg8KJXAZMZqE3cx5SQYZBhw7ArUlkgg/gVLIZZH3GlMhqzqsRoSp9i3b98DPptkF+LxEEjEyiACcC3TcxnBZQdQ9o9JMBjsvvC9EMPRhEuFVTlxRByXYFb8VqzgFrVwjLDYauJK7OA855zj3KL0E5MnGbCIR865UCx0wU7iCEQsmwjESPQitv2k2TjfKU+CYOM6CkaA+oMyOlnzlkjm19Nk2zczJWdLZqHnlKlTQw55frjMX/WH+SyvkoS4/hBXLNKI4cNSHA+E2mee52M5JIGNcRVPDt4TFsh4WYId8xB6VKZgkc35zfnAsWFcclsHqVxBXC/jPPGbLJSo0YhIxMJuQ4oUxS+IRCX5yc/PN5ubnTt3OjNmzHB+/fXXA54Hv/32m5Oenu6ULl3a6dy5c8Hjubm5BbevuOIKJy0tzRk2bJj5/8MPPzT/H3fccc6OHTv87kfDhg3Nc1asWGH+37Ztm/PBBx84Bx98sJORkWEeY2vcuLEzZswYZ/v27UF9v6pVqzpt27Y1r1m9erUTDQYOHOhUqVLF+e6775w///yzYNu9e3fBc/r06eMMHTq04P+ffvrJKVWqlPPII4+YYzp8+HBzTBcuXBiVfVSKJzs72/niiy+c/v37O7Vr13Zq1qzpXHbZZc5HH33kZGZmOrt27SrRlpWV5UybNs356quvnL///rvE7+dv27p1qzmfOBc//vhj59tvvzXX8ZYtW8J+z51ZWc7Gn2Y7v933rDPtxD7O9y3Pcn7scL6zbuY8Z/Lkyc7s2bPNmBGN7xPMNmHCBKdixYrOJ5984sQTHHumUt+Ncwr4e+KJJx7wGn670047zSlfvrzToEEDZ8iQIQeMI4Gw4+/69eudI4880oyVZcuWdSpXrmxu16hRw7n++uud+fPnH/C6J598smBsZazl7xlnnFHweF5eXoSOhpJsqCUxBcEi6E5e8Rff8vjjj8vNN99sihfTMo2agL169SqIoxk5cqQJGseyiKuaoq0kcrA6pUAsz/eFIskkI+DioMwOq27rfsXNQhA/n4mF88svvzSfhfua+4tyuWChJPDfDSt1Osmwz1hbIhHfGOj1WE1pbwi28waWWgvWj7vuuqugmDYrey2mHT/XAp07sExRhBhrHbU/cUnTmixUC50NrSBBCwtiKC7hcLG9jrmOKK+Dy5FzPtx+0sD1smvxHyYJ7dfdmcYyxXXoVegH4R0kKmE5w/qbyhD3jdWRMCHiy/HYYF1kHCJECK8OFkI8QLZ8GeCeZ8xmXCXZjjEetDyOUhR6ZqQg7gHBLZ7cEwAuOSCWkeQVMkwpM4GrmKxLBm0mIeIbEYhMJiSv8B7EOrqxn0FhZAL4ccO41yZM0AxyCCcrtojBYjAMJBDdIvGdd94x/5PJx+TOvlMzjX2mDATCNVD2YygEs57CDe0LwphNic9rAdcgG+cJIRS4pDl3OFdxaTLhEoZRXGcUzkcWOAjNWAlEwJXNIouNOF4rGCk/ZftJsyEegxV5prXboQ1l3qxZ5nr1UiASV3rllVeaeOZUF4hAcXlCGRCBZPHbxT6uZBbX/GXBg3uZ8dmW/2FsZBHLeWDjcW2PZ0UJhJ4dKY6/gZ/4GqwrTHRsJK6QdUdGITFWBNUT+D948GATCA1MiAxKCCnib9yxM/YzsEhiTWPixdrmXuHyHBuEzmRLLE9xXVzs4GZFIpZM4qWY0JkgyeYmxgcrHpY9Dc5WisKWdGIjroxMewQjkzFxs8ToMtFy/nINuCEmjFhVul3EUiD6Qmwl5zkbFiIEIzGMXHdYRa1gJH63KNHH95n1P4GIVd4rgfjNN99Inz59TPwuSXDK/gQ/zj8WxQhEW1KH8xfPD3/5zSk5xjFjXLXPcf/ujNXRTt5SEp/4KR6lxA24LBhUsK6w6qSMCFYWElOwtJCEQaKJFYi2Fh3N6q1b2d0wHpikEHMMajao297Pe5HIYfuWBlPPy34mK2reg0kRgcj9fC7WTLKssXKSsGALhCdbdAVtt8gsZ9Jg8sfqRemiokA4I4SwMLBR7BtBpPwD5ymJBXQVIvOUcxRrGsebBQ4JSWTZYm3EckgyAOebrXcYD7CIYuFG0W4sSGRLI/4oYUPpJs4T9t/3mrDP4dzwUiByzC+99FIz9hA2Em9VDryAMAasxBwLW1PRZjnb35HFDElZLOgpNg7+vEV6PJVgUJGoFILYFiDuBXAlW7HHxMnKFCFmByXr7jjnnHPMRDR27FjTVJ7BjOfhnsYag1UAKwwxX25ByvsjWsjOs67p4gYwKxJxJ4O1MthuMva2zcSk5hxwO9SOFvEMdSepjTZ9+nRzLHE3MknYouWBXOJMvrS2o4QRpZF4jbUAKwfC+Y34Iw6XxQaCmv8RLwhGFiRYromXi3SWdKTgOiROkZqnCEYEL5ZG4nkRY7bYtxWIXIvUUfVKSHBeck0Tv0ssogqa/RA+QMgP2e0UEXcXi3cLRcJ2+A3JnLaPKUo4aOKKUggmCYQELdCwULnjFotLAEF4UDQbwUEcIHFcBFgj0hjciGvEamhhxUvxY1zOiMxQm8kjAimjQxkIXOBMfNbFjducVlfsEwW+6f3ri+/3sS5ygrrZf2vdTBSC6SftC98ZqxGxTr5li5TAYEFk0bNy5UpjGUdosdjBmsu5TLmYeJ+cud5IdsE9yaKORQb1UrmuSFbxolPJL7/8Ytz6xNNRcirej2E0cI9Ldky0YxMLY2I0WahQVscdumOfw6KFpBXcz3YhrSjhoJZEpRDEVJFlbOOuQnFR4EpG9GHdwoJIID8ChJUt1i4Eol2XMMliXWRCsoklwUwIdvVMPUYEIqLIdoRx9yjFQkIcJJO1bTWIWLRJOe7PY3C1rmomTL4/2a2JZnUMpp+0L/wOiINQXpPqcMwQg5wfhDxgkUMkUgeUdmtksTNBE0tHT914XYsjPhCD9F/GCsptwku4tkrSTzpcqJTAcSWOOFUFIsfa/b2xGoKNH2QsY/FKyAB1EVmk2N+H5zCOURUCb4Kt+hCv558S/6glUSlEqNa8oiBekGBpK0Ds6cYgSNY04g5XJxbGYLElG+69915jbSAGDEFHKyp6PyN4SLwZMmSImaBp18agyWDLfhBnSfcK/icjm31wZ/ixzyTlUCaCtlZ2dZ4IvxuxccSZhdIuEGsrGaSInXCLMqeaQMRSSJgECyLfJBbOcbLzKVLMhuuURRDWMTbc+/EkfvgeNhmCc966Lbk+rIWR5yAeWZDxNxoZsSwoqXDAAo0C1PF0jGKFe6yhXA2iGcFOXCmLdyz9HH+OFXGaiHhCgC655BITW8yCnHAfQiGIEWehjNtZUcJFRaISFbHCVtxEguWF0jDEzRB7RPcWEk2CdcWQdc17IBBJLrAJM/RFtfF1uFyx5hCDhQURKwWra9tPGkFJHBYJCogld0yZHbDjuYe0G2qmUX8SgRhse6/Ro0ebY094gTsMQAkM5xx1QMkedbdB8wfnDgsVMp/JlOa3wQ1oBSPnu5fnFuKP8BJi3RCI/haHfAfbTxrRSMJEuP2kA8GiDYHINUhZl0S43iKNe5yxYTgsgBlLWRgDiUQkAPJbccxYCLMg5jchTIDfDwsi8aSUwyGhL1EWuUp8oiJR8RRi/5gUmIQQKayUKYJti3YHsnIS40iSDJMVbu0FCxaYhAJW3ohOMvtYWbPCxnIDxCSOHz/erMS5v1OnTsbiwyDLbfaD+CyEK24cBGWiwP4S14nlgDIswUA9NQqfk/1t3fFK9GCoRWRRww7BiDBnMkcscq6RABNLcRSMQCwqw5bvwnUbbj9pCws8XPOEpJAclIoC0Q1WVDLl8YBwm9+JTHSuV2KvyVjnWueapTQZ4xcLYDwgjIcstkn2IVFJBaJSUlQkKp5DTA11DCdOnGisfFhoAlkhrauZpvQMoPQ8Rfi5H2fi8nWx4IJFhDKoEshNUV47eDLpEcvHqvull14yNfEQiqzYA1kRrbXUXQfSC8LpJw1YD3Fn4WbGXaXE/ncjm5jJHpc0Qp24QAQj5yYWo2gmjWBBRyBifSLjOdzP8tdP2grGYEIXSLBAIFJSCGu+F4kyXuPb8YRkKLroMP64e9gz3lCVgA5OeAqIGXUvCBnH3B12VCAqkUBFohJXMNEQwxhInNn7aelHUgqZy5TqYbWN28s3I9BCzCPuLLJPGVztc2y5Hfu+FOKmWwuuHgZr3wGcyZXN3X3DHWcZa3DPUa8PsUECkAVLLAIAsM7igqfGHyCw77nnHvM6d/Y2rtPi3KdKdGARQ/1RBCPCHRFgBSOLm0iKp0gJRF8I27CCke/DdYzIwaJlz0U3WL4QiMR3EkOXigLRDdY/vB4sYikZRsyhFXrucci6orn2aRjA/SoGlWihIlHxHE5B3+4s/rDCj9hDgrIJ0ibxJBjoTkARaeo3ctu9yrYCEQskExuCChcYE5v9TOLKSH4hYBzLJ24dJjfc1rivvSKcftLcpiyRL7jbSQZSvIVQCUQALmliTDm/rEsaF2NJxJQViFj5Ii0+3bBos4IRiyluaMQvtQ9JwiBmmIQ1Nq7JWAlEwjGwWHIMaBOKBT7YsBJcvSxIcc2TzR4OeCz4fSkH5l58EqtK/DSLAwQ2yTtcj25xaG+TYEYVCcZAFrzFtYtUlJKgbfkUzzF9YoPIlrSCCLc0kLASjFuFQZnJllgeBldwT0rWbYw1DrAmWssHn0nmJ6t3JjwmbCZYYrIoXo3blj6/xFG6XT3u9w6mOHgs+0ljwVHiF7KMcb+y4c7FCo5gRMywiCGDHdFImEAoFiQE4pw5c0zSVjQFIiAK3f2kiRmm/iEdQLAssiBDcPF/LC2IuGQRqdQZpBJCsCDcsMgz5nDthwPijhJcJJQQ6oGV2LrkiSNkEUeoC8eL2GpgXLQLVTtGMo5xDPkteU86LilKtEht+76SUFihhSUQl+ltt90W1OsotUMsIpMqyQHu93JDfTtwWxYoX0LMHwIR9w//k+yCpYf+vojJ22+/3STP+MPdMivRai4q3oOVCDHDuck5hqhCYCEgOZfpV441yWa/BoLHER6IN0RSLIUZYSCUb0EcIRQRQYQ1sMgicYfYYu6PhVML9zbJWgi0UCDprWfPngX1WEOFdqa0MSV+Ghe8v+oPiFC69vAbkYhCrUjgt+L3s/VhSRTCi4IARzAqSlTB3awoycygQYOctLQ059lnnzX/5+XlFXrOnj17zHPq1KnjZGVlFdw/YMAAc3+/fv2c9evXF3rdn3/+6TzxxBPO33//XXDftm3bnJkzZzqPPfaY89xzzzm///571L6bkprs27fPmTx5sjkva9WqZbbLL7/c+fjjj53MzExn165dBdvatWvNefz99987O3bsOOCxWG6rV692Dj/8cOfCCy90cnJyzH0ffPCB06tXL6dy5cpOo0aNnDFjxsTsGDL9ffjhh8U+7+WXX3aOPvpos8/Dhw932rVrF9Ln/Pzzz+b7NW7cOKjvxz6VL1/ejDv33HNPoccnTpxoHjvhhBOcLVu2hLQvihIqKhKVhCM/P9+v0PMHgq9hw4ZO/fr1nV9//dXc535tbm6u+fvuu++agbdPnz4FjyH86tWr55QqVcqZNWuW+Vz3PtjX7t27t+D2p59+6nTq1Mm8l3vr3LmzmdRL+r0TiZEjRzodO3Z0KlWqZETMeeed5yxZsiTo17/99ttmIud1SmAQL1OmTHEGDhzo1K1b16lWrZrTu3dv57333nOWL1/utGnTxoiczZs3eyYQ161b5xx55JHmt0Tg+sI1NGnSJOe///1vXInEpUuXOrVr1y5Y6IUqEnkd4w/v8dZbbxXczxhU1PX80UcfmeuGsQNRzf+LFy92Ro8e7bRq1copW7asEZ+KEm1UJCpJzcKFC81Ae/zxx/t93Iq7c8891zzPPUl9/vnn5r6uXbs6u3fvLvazGMixRPKaIUOGGME4fvx458orr3TKlCnjHHbYYc6iRYtKLAgShdNPP9155ZVXzHeeN2+ec9ZZZxlr0c6dO4t97cqVK42wx1qiIjF4OJ+xGN5www3m+KWnpzvVq1c3v4NXInHDhg1Ohw4dzO+PGIwXihOJHEsWOePGjSu4LxSRyOuHDh1qxoMHHnjggPt9BaIdh9x89tlnTtWqVc3rsSzWrFnTXD9dunRxvv32W/OcYBfLihIumt2sJD3EAhJHSE0xfy0Hifch9ouyMfSCtjUWiR+iiwkbpSYI+PfFvh+ZkiQU0I3j5ZdfNlmcbsiipG0gAfO0zQql6DCXKO9LDBd15Qiip4MMyQt0nUkUNm/ebOKxiKEjk7Oo34vHOVYUCub7UoBaCS1Bg5JPJL506dJFPv30U5NwQW9pzhvKO8Wi3BFJY3weCTfE2cVT20dihYvKbua8I/bPnRzE9c71yH3EWJ5yyikB35/YSyoL/PHHH6a7E+9F1rf72idjmnN80qRJZnwiztTGIgL1M6mgQFY0MY3EpHIsbY/6VC88rsSAsOWloiQA/lbovo/ZGJ+ePXsecP93331n7sciVtx7jB071lhtmjZt6kydOrXQ84hTxN1WsWLFA2IeA2EtBMSXjRo1yriX2JcqVaqY9+Cz+B+rAjFTW7dudeKdZcuWGesN1t2iIA7rX//6l7l92WWXqSUxRLDUnnTSSc7JJ59sLHn2fCJkAstWixYtjGXqnHPOcV588UVj6eM1kbYg/vXXX8aCz77Y/YgnirMkcsw4V90bLv2WLVua28VZxIkFxdWM23j+/PmFHnv66afNdWyv5YyMDPP30ksvNTHSFkIJsAbz2F133eVkZ2cnnFdBSVw0u1lJaooqEWIfw8JlS9+ANa6TOYj1kJIx9jnubitgrZLUgON11H/DCkYdNIrdTp8+3TyOlZIyF1hv/NUoDAR1C+kTTDcOLJtYJajxRiHsq6++2pQWofwOJTXCLc0RCzheZOJSvJs6c4GgXhxdb6hpqYQOlkPqd3IuUpzb1tDjPCXDmILqWLXI+KeHNO3fqJuJler11183NQ0j4Vyil7C1prv3w2vIDKfGoa1zSM1TbuNpADKtyTK2x4xz1b3ZTjLc9lfyyg3ZxxxjrLpkLdvr/r333jOVGW644QZzrLH4YjW/9dZbjZWREl+MHRaslVg8KXvDdT5s2LCCmol2HFKUqOG1SlWUeMHfyvzaa681K/irrrrKWFz8gRWvffv2xsKHVe+OO+4wsXQ2Q7FGjRrGIta8eXOnQYMGzty5c4NKRNm+fXuBdQGrpj94L+Kmunfv7vz2229OvEJ2LdmdWFACQebtIYccYmKxLGpJDA1iZ7EWBmOttucgCV0jRoww53Dp0qWdU0891Vi5iAsNx8LI9dCtWzfn2GOPNRb0eIJYPqY9343zDPh74oknBnx9sDGJ9tp+4403TJwyY0OzZs2MV4LrGeshSUZkO7vHAbwQjBtkQ9txwvLTTz+ZOFM7HlmLoqJEE41JVFIe39Z7vpYH2mVRzJj4P1b1xANSHxGrGBY+rC/ENdFSkDqKWBiw6mGhsDFH3CZGCcsCVseirBA2zhGLA9YYPpfX0FvaPu62Yrrfm5p08cagQYNMoXK6Xbh7zfrC96Ddom8MmP2uv//+uzneSnRgKiDmlXOd9oAUayaekZhC4m2xrBcXA0fP4d69excUmycOL5VhTKCeKv2WiSsGjiE95xkzqNtoj72tdUnBbizqXPPWu2GhsD+eCn6LRYsW+W13qCiRREWiogTABoZTiJs2d7Tloz2fTa4gqJwOLjyHhAAmRTbbCcayZcsW4yJGQOKCYoIIJuicgt19+vQxLkRczrTqwm0X7S4ukYLvSCFyXGV0fWnevHmxvX9xp7shiJ/khyeffNIE9YeS8KOU7LfDBWsFI+7pY445pqDbCz2Gfc8/Fiq4anGr0v+c1pWpjL3GuX5p88kx4fo96qijzGLInsu+1zNjCmEkHPNDDz200PvSZYUFIwLcXyKeokQSFYmKEgK//vqrzJ8/30yAWBWtBZK4KyZPrCi01wo0cDORBmvtwyrTo0cP+eabb8znILgGDx5shGYiQFwVsZNYEVu2bFlwP/GZ1gKCqKBXNrFy/qD/tGY3ewtTBIsjxCIbVi5EDuc7G9ZhFk3ExmIt+/bbb6VWrVpe73ZcEGgx6L7ffZv2oVzzLDSJYyQGMtBisLh2pIoSCVQkKkox2ESVovpLYwUbMmSIPPfcc9KxY0eTVEJvWms9w5qAMArV+kfJjPvvv1+ef/55Y5GkjRmfQ1u24gLnvSbQd8Uqi/gDSoSQOIGw9oeKxPiC6QJXMr8HghELcatWrQosZoQUkLSlBIdbIOJKZhFIC793333XlMxSFK9RkagoIWAvF38CiFqJZB/ilkbcEbtIn1Ush8R2IRwbN24c9GdZVxLikIzHhx9+WNauXWsypKnb2L9//4DuJuKbsDKE65LmfVesWGGslvFU206Jr2uBeFysxaNHjzb1L/25R5XC+F63uKJHjBhh4pfpS0+mM2gtRMVrVCQqSoQhJuvtt982Az+lc3AxU5aEsheIxpIEwWNpwBLHxMGkTFkd65pGQCLoIuGOxlJE7CSilokrXkqYKEoygWuejeQWRCMlr/AUgMYbKvGAikRFiRD+EkpwlVIzjhitQO5qOxkgKHFJYyl0TxBcosQf8Xpivshu3Lp1q0yYMEEuvfRS8xy6PxDXR51GBCMTDZbGUMSdtVogcK+77jqTVc3kdfTRR5f42CiKciAs8m6//XaZOXOmWexRBcDWllSBqMQLehYqSoRgUEdkWVHHX1r8Ua6iqHhGKypxVVNUl6xSt0C04tN+Bm5k3pesXwuubSYaEglIMmACIk4yFPgMEnNwi1NE/I033igkEO2aku8HJNVQLDiR1pqIab7XQQcdZBIDKEVCeZ3iQPAjnm2RdbKtyUBXlHA44YQTTMtPyuMQk6sCUYlH9ExUlAiD2AolHpDnYf3DOkhtRALW6XOLBdK+l81iJKD9r7/+kqZNmxb0bUagNWrUyCS4XHbZZUb4UF8tWNe2rUVI1jbWDATtAw88YBJKrBh07ytiye7PaaedZvpdc7/vc+MVBDRij244lCwiHKB79+5G7AaCGFOOKd13+I0QlXSFITNbUUKFaxYhyPXK9c717L5fUeKFwOYNRVFiBpYphBm1z2i/17NnTyNKyJQmo5lYQ5JXcAXb8jI8Bgg0RAx119555x0jDtu1axd04Lt9/JlnnjHZqtQmvPDCC819TFjWskEiC+KVIr+4tanVhkWTIt6QKOU4Jk+efMD/WHEQ1tSyxJXvj5dfftkkaZB5aksYIaIVJRwCXZOapKLEGxqTqChxBFYtLF1kSFNfEAujm7Zt25o4xKFDh/p9PW5U3KBPPfVUSMWMcTPTjxaRStcNxJ8vuGURiYgkElqwqpFFjTWNUjXUyfMnnLA8ZmZmFtltxUso4E2pooULFwbsK01/XcQ3MZ78LsSYIuSJKUsUcawoihIqaklUlDgCAYYLl42YQrq60H0BwYcAw6pItwu3ldBa+mjTRYYzXVpC7XaB6xQGDBhgBKJvoV6K/CIQsVASQ4V7jKLYZEBjgSOeEjFIGQ/bis3uH5Y7BBUZ03TsiCc4djfddJNpsRhIIAJWVOIve/XqZeIQEZZYcxH1w4cPj+k+K4qixAoViYoSZ9jYPlzMZ599ttn84e7YABQ3RhzSDcPeH4z7CgGEgCOr2hbwta+zApQWYbZDCrXw6LPMc8aOHWtiJKnthmByZ1Pb98AtXrlyZRO76H7PeIDYRMQ1XUSKgn3GJU0oAOK5Q4cOxuVO7UoVidGBwtwcXxYh1CClvSPW7EBw/o8bN86cm1jgidmlpAwtMxVFCY/4GKkVRSnAnaiCOLEiMFBkiLul1xFHHGEynd33FwdldajtSLYlfWXBijj7HvSvdgtYeinjggXEExnDWNaIrfQFqyPvs2TJEvP6eBGIJOl8+umnpk5dcbUlyWjGje+2rtJpZOPGjSYeVIk8JBJhuX722WeDFpXE8WLpRVjSA5n6pHPnzo36vipKsqKWREWJY9yCKlAPWJ6D+5MYQRJOgu2bay16JGPAsccee8D97s/ErUzyBskt9JUlLg/3KxCXSNKMFae+IDBpIbh48eK4iN/jmNEHG8sUiTrBxErijqaziPvYLF261IhHvrsSec4880yzBcsTTzxxwP8jR4405yl91a11XVGU0IiPJb2iKCGzc+dOmTZtmvlL5jMxgsccc4x5LJh8NCsAeQ/bRzkQnTp1kkceecT05+UzcOchjvgcSubYMjr+4HGEqy0S7nWuHC7mN99804g+aiViDWSj5JAFt/odd9xR8D/17MhuvvHGG404nDRpkhEhvJcSn3CuUUu0JF2OFCXVUZGoKAkKYoUEF1zMxG4hxHD3FiXYfEUiApPe0CTM+LqafZ97ww03yEsvvSTNmjUzggrX3uuvvx7wNRYSWRBhtBXks7wu80Hc2vbt240oxhJoN8oHWShoThychWQhSv/88ssv5nhzLBCMgbLMFe9hUcP5bYtUK4oSOloCR1ESmJUrVxqLGIknxGEhZiiRg5UrmNg/ki9IVkH04T4OJiv64IMPNvGIxIDx+ZTrueKKKwqJP5s4w3MQliR7ILIUJVQ4j4pLXHHDNUFbStzNLKQURQkPtSQqSoKCCCOebtiwYUZ80Y6PiZG4P1sEuyh4nBqHxBTiErbuVrtupAQPlj+wyRkkuWARfOWVV0zZG3j00UfNff72D+hsAjZmMVhLp6KEA6EXxNDSnUgFoqKUDE1cUZQExd0nGlFYp04d0y3FUpwlkcdttjLu4Jo1axa8L+Bufeyxx4zwxMUKuJtPOeUUc9tmQ2MpRCQSE+n7/mCth0W5sxUlEtCRiP7nCMUePXp4vTuKkvDoaK0oCQyCDisgwssKxmDh+VgdEW8kofizPr7//vsm9pAyJCSr4Ma7+eabC+orYm2kyLevJdFaEelHTTFwaj7aXtNK0VBOiM45JNVQXggXK72ig8nubdmypZQvX96EHQwePNj8PokK8YTUPGQDFiPcJl4USCwiwcjCucn/WLZJtLIJScSfKooSHioSFSWJBGM4JWawQCLmKHbttvLhyqYTC8WziXE844wzTOFsNrquIEJo54fFxrcdnxWbP/30k3E309+ZuESleGjLSNY0x+2rr74yRcq7d+9u6gYGAoFEEg2FvQkJwOJLIs6dd94picqsWbNM6RpbvmbIkCHm9j333FNg6baCESh0TugEx86dkESCkaIo4aGJK4qS4kyZMsV0paAYN1ZDX5iMaQ942223yaZNmwruJyOamokTJkwoaMXnm7RCT2cyoEePHm0meayeSmhs3rzZWBQRj127dg1YGBxxyG9pweJLp5ziuskoiqIEQkWioijGTY3FCrdwILAEEvOIG3T58uVGsNB1hF7P/lrtYWWkHzKP020FoaOEDoXSmzdvLgsXLgzYXxpLIh1vvvzyS1PHklAALLz08U5ka6KiKN6iy3pFSXEQiO5WgP4sgohCYsIodeMPKxDt88mKfuihhwosWgjEeOrZnChwzG666SbT8SWQQISePXuaY3788ceb3wC364ABA1QgKopSInTEVpQUp6g4RpvpjBWLPrhQVDKEff7YsWPljTfekF69ehUkF3hdRDsRIb5u0aJFJlu3KGgvSNwox33OnDnywQcfmK4w999/f8z2VVGU5EPdzYqihIS1FgaCItuUySHhZebMmVK5cuWY7l+yQJwhxaA5nsX1l6YcEb236bxjofXg1VdfbbKE1YKrKEo46MihKEqx4L60+BOIdq2JMCFZpXXr1ibbFIEYSlkeZf+xRCDSYYQuOMUJRKCntq8QtBZitQMoihIuGpOoKEqxFJeVjHDEDU0cIsIQsWhj6MIpy5PqLmYSUbAikiRErT+gWDk1EAEXPt1yqKkIhAJQ+JwSMdQIJNnl7rvvNvfr8VcUJVzU3awoSkTJzMwsVBJHCZ5ArnxaIWKlhZNOOsnUpnz11VcLLL20SSQOlH7ctWrVMgKR+8guVxRFCQcViYqiRATNXlYURUkuVCQqiqIoiqIohdBlv6IoiqIoilIIFYmKoiiKoihKIVQkKoqiKIqiKIVQkagoiqIoiqIUQkWioiiKoiiKUggViYqiKIqiKEohVCQqiqIoiqIohVCRqCiKoiiKohRCRaKiKIqiKIpSCBWJiqIoiqIoSiFUJCqKoiiKoiiFUJGoKIqiKIqiFEJFoqIoiqIoilIIFYmKoiiKoihKIVQkKoqiKIqiKIVQkagoiqIoiqIUQkWioiiKoiiKUggViYqiKIqiKEohVCQqiqIoiqIohVCRqCiKoiiKohRCRaKiKIqiKIoivvw/g4rT9Srg2PMAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot PDF of uncertainty model\n", "x = [v[0] for v in u.values]\n", "y = [v[1] for v in u.values]\n", "z = u.probabilities\n", "# z = map(float, z)\n", "# z = list(map(float, z))\n", "resolution = np.array([2**n for n in num_qubits]) * 1j\n", "grid_x, grid_y = np.mgrid[min(x) : max(x) : resolution[0], min(y) : max(y) : resolution[1]]\n", "grid_z = griddata((x, y), z, (grid_x, grid_y))\n", "plt.figure(figsize=(10, 8))\n", "ax = plt.axes(projection=\"3d\")\n", "ax.plot_surface(grid_x, grid_y, grid_z, cmap=plt.cm.Spectral)\n", "ax.set_xlabel(\"Spot Price $S_1$ (\\$)\", size=15)\n", "ax.set_ylabel(\"Spot Price $S_2$ (\\$)\", size=15)\n", "ax.set_zlabel(\"Probability (\\%)\", size=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "25c4c7aa-9498-474e-a76e-3702782a67e6", "metadata": {}, "outputs": [], "source": [ "# determine number of qubits required to represent total loss\n", "weights = []\n", "for n in num_qubits:\n", " for i in range(n):\n", " weights += [2**i]\n", "\n", "# create aggregation circuit\n", "agg = WeightedAdder(sum(num_qubits), weights)\n", "n_s = agg.num_sum_qubits\n", "n_aux = agg.num_qubits - n_s - agg.num_state_qubits # number of additional qubits" ] }, { "cell_type": "code", "execution_count": 7, "id": "44e0c9c7-3932-47d5-9c6d-c5de3d254b47", "metadata": {}, "outputs": [], "source": [ "# set the strike price (should be within the low and the high value of the uncertainty)\n", "strike_price_1 = 3\n", "strike_price_2 = 4\n", "\n", "# set the barrier threshold\n", "barrier = 2.5\n", "\n", "# map strike prices and barrier threshold from [low, high] to {0, ..., 2^n-1}\n", "max_value = 2**n_s - 1\n", "low_ = low[0]\n", "high_ = high[0]\n", "\n", "mapped_strike_price_1 = (\n", " (strike_price_1 - dimension * low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", ")\n", "mapped_strike_price_2 = (\n", " (strike_price_2 - dimension * low_) / (high_ - low_) * (2**num_uncertainty_qubits - 1)\n", ")\n", "mapped_barrier = (barrier - low) / (high - low) * (2**num_uncertainty_qubits - 1)" ] }, { "cell_type": "code", "execution_count": 8, "id": "72e56797-ddc7-4f38-a75e-65dabd9d6e63", "metadata": {}, "outputs": [], "source": [ "# condition and condition result\n", "conditions = []\n", "barrier_thresholds = [2] * dimension\n", "n_aux_conditions = 0\n", "for i in range(dimension):\n", " # target dimension of random distribution and corresponding condition (which is required to be True)\n", " comparator = IntegerComparator(num_qubits[i], mapped_barrier[i] + 1, geq=False)\n", " n_aux_conditions = max(n_aux_conditions, comparator.num_ancillas)\n", " conditions += [comparator]" ] }, { "cell_type": "code", "execution_count": 9, "id": "75e06666-79ac-40fd-a2c7-9c8e3750ca1c", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Users\\vkasi\\AppData\\Local\\Temp\\ipykernel_45424\\1379351012.py:10: DeprecationWarning: The class ``qiskit.circuit.library.arithmetic.linear_amplitude_function.LinearAmplitudeFunction`` is deprecated as of Qiskit 2.2. It will be removed in Qiskit 3.0. Use the class qiskit.circuit.library.LinearAmplitudeFunctionGate instead.\n", " objective = LinearAmplitudeFunction(\n" ] } ], "source": [ "# set the approximation scaling for the payoff function\n", "c_approx = 0.25\n", "\n", "# setup piecewise linear objective fcuntion\n", "breakpoints = [0, mapped_strike_price_1, mapped_strike_price_2]\n", "slopes = [0, 1, 0]\n", "offsets = [0, 0, mapped_strike_price_2 - mapped_strike_price_1]\n", "f_min = 0\n", "f_max = mapped_strike_price_2 - mapped_strike_price_1\n", "objective = LinearAmplitudeFunction(\n", " n_s,\n", " slopes,\n", " offsets,\n", " domain=(0, max_value),\n", " image=(f_min, f_max),\n", " rescaling_factor=c_approx,\n", " breakpoints=breakpoints,\n", ")" ] }, { "cell_type": "code", "execution_count": 10, "id": "c9cdd402-289d-44d4-a670-8128124eb142", "metadata": {}, "outputs": [], "source": [ "# number of qubits per dimension to represent the uncertainty\n", "num_uncertainty_qubits = 2\n", "\n", "# parameters for considered random distribution\n", "S = 2.0 # initial spot price\n", "vol = 0.4 # volatility of 40%\n", "r = 0.05 # annual interest rate of 4%\n", "T = 40 / 365 # 40 days to maturity\n", "\n", "# resulting parameters for log-normal distribution\n", "mu = (r - 0.5 * vol**2) * T + np.log(S)\n", "sigma = vol * np.sqrt(T)\n", "mean = np.exp(mu + sigma**2 / 2)\n", "variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)\n", "stddev = np.sqrt(variance)\n", "\n", "# lowest and highest value considered for the spot price; in between, an equidistant discretization is considered.\n", "low = np.maximum(0, mean - 3 * stddev)\n", "high = mean + 3 * stddev\n", "\n", "# map to higher dimensional distribution\n", "# for simplicity assuming dimensions are independent and identically distributed)\n", "dimension = 2\n", "num_qubits = [num_uncertainty_qubits] * dimension\n", "low = low * np.ones(dimension)\n", "high = high * np.ones(dimension)\n", "mu = mu * np.ones(dimension)\n", "cov = sigma**2 * np.eye(dimension)\n", "\n", "# construct circuit\n", "u = LogNormalDistribution(num_qubits=num_qubits, mu=mu, sigma=cov, bounds=list(zip(low, high)))" ] }, { "cell_type": "code", "execution_count": 11, "id": "02a2d394-772a-4365-821a-a813e0eefa24", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " ┌───────┐┌──────┐ ┌───────────┐ ┌──────────────┐»\n", " state_0: ┤0 ├┤0 ├─────────────┤1 ├──────┤1 ├»\n", " │ ││ │ │ │ │ │»\n", " state_1: ┤1 ├┤1 ├─────────────┤2 ├──────┤2 ├»\n", " │ P(X) ││ │┌──────┐ │ │ │ │»\n", " state_2: ┤2 ├┤ ├┤0 ├─────┤3 ├──────┤3 ├»\n", " │ ││ ││ │ │ │ │ │»\n", " state_3: ┤3 ├┤ ├┤1 ├─────┤4 ├──────┤4 ├»\n", " └───────┘│ ││ │ │ │┌────┐│ │»\n", " obj: ─────────┤ ├┤ ├─────┤ ├┤3 ├┤ ├»\n", " │ ││ │ │ ││ ││ │»\n", "conditions_0: ─────────┤2 ├┤ ├──■──┤ ├┤ ├┤ ├»\n", " │ cmp ││ │ │ │ ││ ││ │»\n", "conditions_1: ─────────┤ ├┤2 ├──■──┤ ├┤ ├┤ ├»\n", " │ ││ cmp │┌─┴─┐│ c_adder ││ ││ c_adder_dg │»\n", "conditions_2: ─────────┤ ├┤ ├┤ X ├┤0 ├┤ ├┤0 ├»\n", " │ ││ │└───┘│ ││ ││ │»\n", " sum_0: ─────────┤ ├┤ ├─────┤5 ├┤0 ├┤5 ├»\n", " │ ││ │ │ ││ F ││ │»\n", " sum_1: ─────────┤ ├┤ ├─────┤6 ├┤1 ├┤6 ├»\n", " │ ││ │ │ ││ ││ │»\n", " sum_2: ─────────┤ ├┤ ├─────┤7 ├┤2 ├┤7 ├»\n", " │ ││ │ │ ││ ││ │»\n", " work_0: ─────────┤3 ├┤3 ├─────┤8 ├┤4 ├┤8 ├»\n", " └──────┘└──────┘ │ ││ ││ │»\n", " work_1: ──────────────────────────────┤9 ├┤5 ├┤9 ├»\n", " │ ││ ││ │»\n", " work_2: ──────────────────────────────┤10 ├┤6 ├┤10 ├»\n", " └───────────┘└────┘└──────────────┘»\n", "« ┌─────────┐\n", "« state_0: ────────────────┤0 ├\n", "« │ │\n", "« state_1: ────────────────┤1 ├\n", "« ┌─────────┐│ │\n", "« state_2: ─────┤0 ├┤ ├\n", "« │ ││ │\n", "« state_3: ─────┤1 ├┤ ├\n", "« │ ││ │\n", "« obj: ─────┤ ├┤ ├\n", "« │ ││ │\n", "«conditions_0: ──■──┤ ├┤2 ├\n", "« │ │ ││ cmp_dg │\n", "«conditions_1: ──■──┤2 ├┤ ├\n", "« ┌─┴─┐│ cmp_dg ││ │\n", "«conditions_2: ┤ X ├┤ ├┤ ├\n", "« └───┘│ ││ │\n", "« sum_0: ─────┤ ├┤ ├\n", "« │ ││ │\n", "« sum_1: ─────┤ ├┤ ├\n", "« │ ││ │\n", "« sum_2: ─────┤ ├┤ ├\n", "« │ ││ │\n", "« work_0: ─────┤3 ├┤3 ├\n", "« └─────────┘└─────────┘\n", "« work_1: ───────────────────────────\n", "« \n", "« work_2: ───────────────────────────\n", "« \n", "objective qubit index 4\n" ] } ], "source": [ "# define overall multivariate problem\n", "qr_state = QuantumRegister(u.num_qubits, \"state\") # to load the probability distribution\n", "qr_obj = QuantumRegister(1, \"obj\") # to encode the function values\n", "ar_sum = AncillaRegister(n_s, \"sum\") # number of qubits used to encode the sum\n", "ar_cond = AncillaRegister(len(conditions) + 1, \"conditions\")\n", "ar = AncillaRegister(\n", " max(n_aux, n_aux_conditions, objective.num_ancillas), \"work\"\n", ") # additional qubits\n", "\n", "objective_index = u.num_qubits\n", "\n", "# define the circuit\n", "asian_barrier_spread = QuantumCircuit(qr_state, qr_obj, ar_cond, ar_sum, ar)\n", "\n", "# load the probability distribution\n", "asian_barrier_spread.append(u, qr_state)\n", "\n", "# apply the conditions\n", "for i, cond in enumerate(conditions):\n", " state_qubits = qr_state[(num_uncertainty_qubits * i) : (num_uncertainty_qubits * (i + 1))]\n", " asian_barrier_spread.append(cond, state_qubits + [ar_cond[i]] + ar[: cond.num_ancillas])\n", "\n", "# aggregate the conditions on a single qubit\n", "asian_barrier_spread.mcx(ar_cond[:-1], ar_cond[-1])\n", "\n", "# apply the aggregation function controlled on the condition\n", "asian_barrier_spread.append(agg.control(), [ar_cond[-1]] + qr_state[:] + ar_sum[:] + ar[:n_aux])\n", "\n", "# apply the payoff function\n", "asian_barrier_spread.append(objective, ar_sum[:] + qr_obj[:] + ar[: objective.num_ancillas])\n", "\n", "# uncompute the aggregation\n", "asian_barrier_spread.append(\n", " agg.inverse().control(), [ar_cond[-1]] + qr_state[:] + ar_sum[:] + ar[:n_aux]\n", ")\n", "\n", "# uncompute the conditions\n", "asian_barrier_spread.mcx(ar_cond[:-1], ar_cond[-1])\n", "\n", "for j, cond in enumerate(reversed(conditions)):\n", " i = len(conditions) - j - 1\n", " state_qubits = qr_state[(num_uncertainty_qubits * i) : (num_uncertainty_qubits * (i + 1))]\n", " asian_barrier_spread.append(\n", " cond.inverse(), state_qubits + [ar_cond[i]] + ar[: cond.num_ancillas]\n", " )\n", "\n", "print(asian_barrier_spread.draw())\n", "print(\"objective qubit index\", objective_index)" ] }, { "cell_type": "code", "execution_count": 12, "id": "e9278bc6-84c5-4cd3-8ddc-ef11579c7076", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot exact payoff function\n", "plt.figure(figsize=(7, 5))\n", "x = np.linspace(sum(low), sum(high))\n", "y = (x <= 5) * np.minimum(np.maximum(0, x - strike_price_1), strike_price_2 - strike_price_1)\n", "plt.plot(x, y, \"r-\")\n", "plt.grid()\n", "plt.title(\"Payoff Function (for $S_1 = S_2$)\", size=15)\n", "plt.xlabel(\"Sum of Spot Prices ($S_1 + S_2)$\", size=15)\n", "plt.ylabel(\"Payoff\", size=15)\n", "plt.xticks(size=15, rotation=90)\n", "plt.yticks(size=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "de333051-5cd9-4b82-8847-2d3076bdc43f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot contour of payoff function with respect to both time steps, including barrier\n", "plt.figure(figsize=(7, 5))\n", "z = np.zeros((17, 17))\n", "x = np.linspace(low[0], high[0], 17)\n", "y = np.linspace(low[1], high[1], 17)\n", "for i, x_ in enumerate(x):\n", " for j, y_ in enumerate(y):\n", " z[i, j] = np.minimum(\n", " np.maximum(0, x_ + y_ - strike_price_1), strike_price_2 - strike_price_1\n", " )\n", " if x_ > barrier or y_ > barrier:\n", " z[i, j] = 0\n", "\n", "plt.title(\"Payoff Function\", size=15)\n", "plt.contourf(x, y, z)\n", "plt.colorbar()\n", "plt.xlabel(\"Spot Price $S_1$\", size=15)\n", "plt.ylabel(\"Spot Price $S_2$\", size=15)\n", "plt.xticks(size=15)\n", "plt.yticks(size=15)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "id": "cd08e93a-b480-46ef-9827-236bdbc48216", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "exact expected value:\t0.8023\n" ] } ], "source": [ "# evaluate exact expected value\n", "sum_values = np.sum(u.values, axis=1)\n", "payoff = np.minimum(np.maximum(sum_values - strike_price_1, 0), strike_price_2 - strike_price_1)\n", "leq_barrier = [np.max(v) <= barrier for v in u.values]\n", "exact_value = np.dot(u.probabilities[leq_barrier], payoff[leq_barrier])\n", "print(\"exact expected value:\\t%.4f\" % exact_value)" ] }, { "cell_type": "code", "execution_count": 15, "id": "0cd80879-a8e1-48c3-9677-15c00d28bf2e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "state qubits: 5\n", "circuit width: 14\n", "circuit depth: 5515\n" ] } ], "source": [ "num_state_qubits = asian_barrier_spread.num_qubits - asian_barrier_spread.num_ancillas\n", "print(\"state qubits: \", num_state_qubits)\n", "transpiled = transpile(asian_barrier_spread, basis_gates=[\"u\", \"cx\"])\n", "print(\"circuit width:\", transpiled.width())\n", "print(\"circuit depth:\", transpiled.depth())" ] }, { "cell_type": "code", "execution_count": 16, "id": "5c579c3c-0776-476a-a95a-a6b344031119", "metadata": {}, "outputs": [], "source": [ "asian_barrier_spread_measure = asian_barrier_spread.measure_all(inplace=False)\n", "sampler = Sampler(backend = qr_backend, run_options= {\"performance\":\"HighestEfficiency\"})\n", "job = sampler.run([asian_barrier_spread_measure])" ] }, { "cell_type": "code", "execution_count": 17, "id": "9d237769-19cd-490b-a5d2-56be9290e177", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "DataBin(meas=BitArray())\n" ] } ], "source": [ "result = job.result()\n", "pub_result = result[0]\n", "print(pub_result.data)" ] }, { "cell_type": "code", "execution_count": 18, "id": "92af5d1c-f237-4c82-9919-ebc910176033", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact Operator Value: 0.6309\n", "Mapped Operator value: 0.8332\n", "Exact Expected Payoff: 0.8023\n" ] } ], "source": [ "# Quasi distribution is not supported in SamplerV2\n", "# Here is a workaround\n", "from qiskit.result import QuasiDistribution\n", "result = job.result()\n", "pub_result = result[0]\n", "counts = pub_result.data.meas.get_counts()\n", "shots = 0\n", "for key, val in counts.items():\n", " shots += val\n", "quasi_dist = QuasiDistribution({outcome: freq / shots for outcome, freq in counts.items()})\n", "\n", "# evaluate the result\n", "value = 0\n", "probabilities = quasi_dist.binary_probabilities()\n", "\n", "for i, prob in probabilities.items():\n", " if prob > 1e-4 and i[-num_state_qubits:][0] == \"1\":\n", " value += prob\n", "\n", "# map value to original range\n", "mapped_value = objective.post_processing(value) / (2**num_uncertainty_qubits - 1) * (high_ - low_)\n", "print(\"Exact Operator Value: %.4f\" % value)\n", "print(\"Mapped Operator value: %.4f\" % mapped_value)\n", "print(\"Exact Expected Payoff: %.4f\" % exact_value)" ] }, { "cell_type": "code", "execution_count": 19, "id": "3dfb8024-dd3e-4f4f-9136-e74c1873140f", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Exact Operator Value: 0.6367\n", "# Mapped Operator value: 0.8482\n", "# Exact Expected Payoff: 0.8023" ] }, { "cell_type": "code", "execution_count": 20, "id": "36c10c59-e8f2-4e10-bb65-61b48bfc9fc1", "metadata": {}, "outputs": [], "source": [ "# set target precision and confidence level\n", "epsilon = 0.01\n", "alpha = 0.05\n", "\n", "problem = EstimationProblem(\n", " state_preparation=asian_barrier_spread,\n", " objective_qubits=[objective_index],\n", " post_processing=objective.post_processing,\n", ")\n", "# construct amplitude estimation\n", "ae = IterativeAmplitudeEstimation(\n", " epsilon, alpha=alpha, sampler=Sampler(backend = qr_backend, run_options= {\"performance\":\"HighestEfficiency\"}, options={\"shots\": 100, \"seed\": 75})\n", ")\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "3d737e11-f6a9-42d5-a807-d6b6e5d0ba5e", "metadata": {}, "outputs": [], "source": [ "result = ae.estimate(problem)" ] }, { "cell_type": "code", "execution_count": 22, "id": "d0c9a299-be29-4a47-9ade-cd19fb2cac4f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact value: \t0.8023\n", "Estimated value:\t0.7545\n", "Confidence interval: \t[0.7341, 0.7748]\n" ] } ], "source": [ "conf_int = (\n", " np.array(result.confidence_interval_processed)\n", " / (2**num_uncertainty_qubits - 1)\n", " * (high_ - low_)\n", ")\n", "print(\"Exact value: \\t%.4f\" % exact_value)\n", "print(\n", " \"Estimated value:\\t%.4f\"\n", " % (result.estimation_processed / (2**num_uncertainty_qubits - 1) * (high_ - low_))\n", ")\n", "print(\"Confidence interval: \\t[%.4f, %.4f]\" % tuple(conf_int))" ] }, { "cell_type": "code", "execution_count": 23, "id": "1956b5c7-e1cd-44b4-99f2-9310fd150c54", "metadata": {}, "outputs": [], "source": [ "# Example output:\n", "\n", "# Exact value: \t0.8023\n", "# Estimated value:\t0.8274\n", "# Confidence interval: \t[0.8219, 0.8330]" ] }, { "cell_type": "code", "execution_count": 24, "id": "19f87528-1e81-459d-a563-bfd70f5a1e61", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

Version Information

SoftwareVersion
qiskit2.2.1
qiskit_ibm_runtime0.40.1
qiskit_algorithms0.4.0
qiskit_finance0.4.1
qiskit_aer0.17.1
System information
Python version3.12.9
OSWindows
Thu Oct 16 11:23:38 2025 Mountain Daylight Time
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "

Quantum Rings Version Information

SoftwareVersion
QuantumRingsLib0.11.0
quantumrings-toolkit-qiskit0.1.10
" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "

This code is a part of a Qiskit project

© Copyright IBM 2017, 2025.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.

Modifications Copyright Quantum Rings Inc, 2025
Modified from the originals
Added support for Quantum Rings QrEstimatorV2 class.

" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import tutorial_magics\n", "\n", "%qiskit_version_table\n", "%quantumrings_version_table\n", "%qiskit_copyright" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }