{ "cells": [ { "cell_type": "markdown", "id": "8859d627", "metadata": {}, "source": [ "# Comparison: Numerov - Whittaker\n", "This notebook compares the Numerov method (with and without model potentials) to the Whittaker method for calculating Rydberg wavefunctions and matrix elements." ] }, { "cell_type": "code", "execution_count": 1, "id": "2cdbdd1b", "metadata": {}, "outputs": [], "source": [ "import logging\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "from rydstate import RydbergStateAlkali\n", "\n", "logging.basicConfig(level=logging.INFO, format=\"%(levelname)s %(filename)s: %(message)s\")" ] }, { "cell_type": "markdown", "id": "56558508", "metadata": {}, "source": [ "## Wavefunction" ] }, { "cell_type": "code", "execution_count": 2, "id": "97528603", "metadata": {}, "outputs": [], "source": [ "states: dict[str, RydbergStateAlkali] = {}" ] }, { "cell_type": "code", "execution_count": 3, "id": "983266d8", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING wavefunction.py: The wavefunction for the state RadialState(Rb, n=21, nu=np.float64(17.86825962895559), l_r=0) has some issues:\n", " The wavefunction is not close to zero at the inner boundary (inner_weight_scaled_to_whole_grid=1.24e-04)\n", " The wavefunction has 17 nodes, but should have 20 nodes.\n", " The integration for l=0 did stop at 0.14 (should be close to zero).\n" ] } ], "source": [ "state = RydbergStateAlkali(\"Rb\", n=21, l=0, j=0.5)\n", "\n", "state.radial.create_model(potential_type=\"model_potential_marinescu_1993\")\n", "state.radial.create_wavefunction(\"numerov\")\n", "states[\"Numerov with Model Potentials\"] = state\n", "\n", "# Using Numerov without model potentials will lead to some warnings,\n", "# since the resulting wavefunction does not pass all heuristic checks\n", "state_without_mp = RydbergStateAlkali(state.species, state.n, state.l, state.j)\n", "state_without_mp.radial.create_model(potential_type=\"coulomb\")\n", "state_without_mp.radial.create_wavefunction(\"numerov\")\n", "states[\"Numerov without Model Potentials\"] = state_without_mp" ] }, { "cell_type": "code", "execution_count": 4, "id": "31441087", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING wavefunction.py: Using Whittaker to get the wavefunction is not recommended! Use this only for comparison.\n" ] } ], "source": [ "state_whittaker = RydbergStateAlkali(state.species, state.n, state.l, state.j)\n", "state_whittaker.radial.create_grid(x_min=state.radial.grid.x_min, x_max=state.radial.grid.x_max)\n", "state_whittaker.radial.create_wavefunction(\"whittaker\")\n", "states[\"Whittaker\"] = state_whittaker" ] }, { "cell_type": "code", "execution_count": 5, "id": "3f9cc4fe", "metadata": {}, "outputs": [ { "data": { "image/png": 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33XVXi+e09/2yePFiEhISOPbYY1v8TBs/fjwWi4VvvvmGc845p8U9kpKSfjc7DztLBFR92NNPP82QIUOw2+28+OKLfPfdd61+EJ555plcf/31LFq0iHnz5mG32/noo4+44YYbmn847N27F4DBgwe3eG5aWlrEBNAD21osFrKyspqXeXbs2AHA0UcfHfb5Nputxd81Gk2LQLBpXCqViv79+7e4Hmm3zqGHHso777yDz+drnh5//PHHOe2001i/fj3Dhw8P+7wmbreb+++/n5deeomSkpIWy5d2u73N50LnXnN9fT2ffPIJV199NTt37my+fsQRR/D222+zfft2hgwZ0mZ/Ho+HWbNmMX78eN588000mtY/Dj766CPuvfde1q9fj9frbb4ebcKo0kYOx7x58zjyyCNxOBy8++67vP7666hU4bMSsrOzW206aHq9e/bsiSqgMhgMpKWltbiWlJTUKtfjiCOO6PS99xcMBjnrrLPYvHkzn376KdnZ2THdL1oDBgxoM+gLpym42v+90KQpn3L/ACwW0XydjUYjPp8v7GMejyeqsQ0aNIg//elPvPPOOwSDQdRqdafvAbTIOQNISEgAIC8vr9X1eL/nAM4991zuuece7r777rA7lJt+jh900EGtHhs6dCg//PBDi2sd+X7ZsWMHdru9RR7q/sJt+FEUpVcmpIMIqPq0CRMmNOcazJ49m8mTJ3POOeewbdu25hyapKQkTjzxxOaA6q233sLr9XLeeed16diatlAvXLgw7Jb5Az/89Xp9xA/fztLpdBx66KEceuihDBkyhLlz57J48WLuvPPONp93zTXX8NJLL3H99dczadIkEhISkCSJs846q0NbwjvzmhcvXozX6+XRRx/l0UcfbdV20aJFrX6bPFBTUvT777/PZ599xoknntji8e+//56TTz6Zo446imeeeYasrCy0Wi0vvfQSr732Wruv50ApKSlhE1GbjBo1qnnWdPbs2bhcLi699FImT57c6kOnK3T0g7KqqqpDieoWiyVs8dRLL72Ujz76iEWLFkUMnruDw+Fo3nzQFrVa3fzBmZWVBYRqZR2orKyM5OTkuMxOQXRf56ysLILBIJWVlS0+xH0+HzU1NVEHr3l5efh8PpxOZ6tf5joq0vsr3PUDf/GI9T3X1M/tt9/ORRddxPvvv9+BEbetI98vsiyTnp4ecbPMgQEZhH5ZPHADR28hAioBoDkJcdq0aTz11FP87W9/a37sggsu4E9/+hOrV69m0aJFjBs3jhEjRjQ/3pRkvGPHjha/8VZVVUX8AN2xYwfTpk1r/rvD4aCsrIyZM2cCNC8vpqend3hX2IH69euHLMvs3r27xYzY/jM67WkKOPf/AIn029Nbb73FhRde2CLA8Xg8rZI5Iz2/M6950aJFjBw5MmyQ99xzz/Haa6+1G1BJksSiRYv405/+xOmnn86nn37K1KlTmx9/++23MRgMfP755y0+JF966aU27xvJ0KFDwxYYjOSBBx7g3Xff5R//+EerHXylpaWtSmNs374doMsrbh966KHNv8235c4772yxkxTgpptu4qWXXmLBggXNmwl6yiOPPNLuewRC30dNM8c5OTmkpaWFTdJetWoVY8eOjdv4ovk6N/W/Zs2a5p8lTX+XZTnq8f36668YDIa4ni7QGbG85/Z33nnnce+99zYnxu+v6ef4tm3bWgX627Zt6/Bmkv0NHDiQr776iiOOOKJDs4MlJSX4fL7mTTq9jQiohGZTp05lwoQJLFiwgOuvv755Hf2EE05orlH17bff8vDDD7d43vTp09FqtTz55JMcd9xxzQHDggULIvb1/PPPM3fu3OY8qn/9618EAgFOOOEEAGbMmIHNZuO+++5j2rRprerUVFVVhf3tZn8zZszg73//O8888wyPP/548/VwVZO/+eYbpk6d2irY+eSTT4CW0+Bms7lVkAShoPTA3yyffPLJVr9ZNgUBB96jo6+5qKiI7777jrvuuitsrRyfz8e5557LypUrmThxYqvH96fT6XjnnXeYMWMGJ510EkuWLGHChAnNr0eSpBbj37NnT9RV4idNmsR//vMffv311w4tNQ0cOJA5c+bw8ssvM3/+/BazdoFAgOeee44bb7wRCL3m5557jrS0tOadQl0l2nyWhx9+mEceeYTbbruN6667rquG12HR5FABzJkzh//+978UFRU1zxwuWbKE7du3c8MNN8RtfNF8nY8++miSk5P517/+1SKg+te//oXJZGqxw7dpZ1x+fn7zLstwP1d+/vlnPvjgA0444YS4zYJ3Vjzy9qDlLNWBDjnkENLT03n22We5+OKLm3+J+vTTT9myZQvz5s3r9LjPOOMMnnnmGe65555W+bSBQACHw9GiVE1T7tj+eWy9iQiohBZuuukmTj/9dF5++eXmhEOtVstZZ53FU089hVqtbvWbdVP9kfvvv58TTzyRmTNnsm7dOj799NOIU7c+n49jjjmGM844g23btvHMM88wefLk5t+abDYb//rXvzj//PM5+OCDOeuss0hLS6OwsJCPP/6YI444gqeeeqrN1zJ+/HjmzJnDggULqKmp4bDDDuPbb79tnsnYP3i65pprcLlcnHLKKQwdOhSfz8eyZct44403KCgoaFV48auvvuKxxx4jOzub/v37M3HiRE488UQWLlxIQkICw4cPZ/ny5Xz11VekpKS0GNfYsWNRq9U8+OCD2O129Ho9Rx99NOnp6R16za+99hqKokRMlJ85cyYajYZFixa1G1BB6APzo48+4uijj+aEE07g22+/ZeTIkcyaNYvHHnuM448/nnPOOYfKykqefvppBg0axIYNG9q974FmzZqFRqPhq6++6nDxx5tuuok333yTBQsWtEjezs7O5sEHH2TPnj0MGTKEN954g/Xr1/P888+3CESnTp3Kt99+G9e6PtHks7z77rvcfPPNDB48mGHDhvHqq6+2ePzYY48lIyOj+e/33nsvQHP9sYULFzbnsNx+++3N7ebPn89dd93V/AtBZ0STQwWhch+LFy9m2rRpXHfddTgcDh5++GFGjRrV4vsEfpstjOaYpWhzqO655x6uuuoqTj/9dGbMmMH333/Pq6++yj/+8Y8W9b2eeuqpVl+7M888E6PRyOGHH056ejqbN2/m+eefx2Qytdo8EMvXvrPikUPVpCmX6sBaT1qtlgcffJC5c+cyZcoUzj77bCoqKnjiiScoKCiIKlieMmUKl19+Offffz/r16/nuOOOQ6vVsmPHDhYvXswTTzzR4pfCL7/8kvz8fMaNGxfry+wZPbjDUOghTdt4V69e3eqxYDCoDBw4UBk4cKASCASar69atUoBlOOOOy7sPYPBoHLXXXcpWVlZitFoVKZOnaps3Lix1Xb6pr6//fZb5bLLLlOSkpIUi8WinHvuuUpNTU2r+37zzTfKjBkzlISEBMVgMCgDBw5ULrroImXNmjXNbfYvAXAgp9OpXHXVVUpycrJisViU2bNnK9u2bVMA5YEHHmhu9+mnnyoXX3yxMnToUMVisSg6nU4ZNGiQcs011ygVFRUt7rl161blqKOOUoxGY4uyEHV1dcrcuXOV1NRUxWKxKDNmzFC2bt3a6mugKIry73//WxkwYICiVqtbbWdv7zWPGjVKyc/PD/t6m0ydOlVJT09X/H5/u2UTmlRXVyvDhw9XMjMzm0sxvPDCC8rgwYMVvV6vDB06VHnppZeat1vvryNlExRFUU4++WTlmGOOaXGtqe3ixYsjvhabzabU19crihIqmzBixAhlzZo1yqRJkxSDwaD069dPeeqpp1o9d/z48UpmZmabX6tIXw9FUcK+1mi0V6LgwK9TW23399e//lWRJEnZsmVLm/1H+veI1saNG5XjjjtOMZlMSmJionLuuecq5eXlrdqlpqYqhx12WLv3C1c2IRbPP/+8ctBBByk6nU4ZOHCg8vjjj7coWaAov/2b7P81eeKJJ5QJEyYoycnJikajUbKyspTzzjuv+fthfx392kf6eXtg2YImbf0864z9yyZEGlO4/t944w1l3Lhxil6vV5KTk5Vzzz1XKS4u7tAYI32/PP/888r48eMVo9GoWK1WZdSoUcrNN9+slJaWNrcJBoNKVlaWcvvtt0f7knucCKiEDlm/fn3E+jO9zbp16xRAefXVV3t6KH3Od999p6hUKmX79u1d3ldDQ4Oi0WjCBlp/FIceeqhy2mmn9fQwwtq0aZMCKB999FG7bc877zxl4MCB3TCq+Pk9f+17o3fffVcxGo0tgqzeRlRKFzrk3//+NxaL5Xd9FlQ44fIOFixYgEql4qijjuqBEfVtRx55JMcddxwPPfRQl/f13XffkZOTw6WXXtrlffWEhoYGfv7559/tQbLffPMNkyZNCnsywYHKysp61c6u3/vXvjd68MEHufrqq5t3kvZGkqLEMblA+MP58MMP2bx5M3fccQdXX301jz32WE8PqVPuuusu1q5dy7Rp09BoNHz66ad8+umnXHbZZTz33HM9PTxB6NM2bNjAe++9x7333stNN93EP/7xj54ekiBETQRUQpsKCgqoqKhgxowZLFy4EKvV2tND6pQvv/ySu+66i82bN+NwOMjPz+f888/n73//e9hCloIgdJ/58+fz5JNPMmvWLJ555pkeK0sgCPEgAipBEARBEIQYiRwqQRAEQRCEGImAShAEQRAEIUYiiaQbyLJMaWkpVqu11x76KAiCIAh9jaIoNDY2kp2d3W6lfBFQdYPS0tJuOdxVEARBEIT4KyoqIjc3t802IqDqBk0744qKiqI+qVwQBEEQhO7V0NBAXl5eh3a4i4CqGzQt89lsNhFQCYIgCEIv05F0HZGULgiCIAiCECMRUAmCIAiCIMRIBFSCIAiCIAgxEgGVIAiCIAhCjERAJQiCIAiCECMRUAmCIAiCIMRIBFSCIAiCIAgxEgGVIAiCIAhCjERAJQiCIAiCECMRUAmCIAiCIMRIBFSCIAiCIAgxEgGVIAiCIAhCjERAJQiCIAiCECMRUAmCIAiCIMRIBFSCIAh/EIqisPnXn3C4Gnp6KILQ52h6egCCIAhC7Ooaqrn2f8ez3uDlaIefKyc+zdBDjunpYQlCn9HrZqiefvppCgoKMBgMTJw4kVWrVrXZfvHixQwdOhSDwcCoUaP45JNPWjz+zjvvcNxxx5GSkoIkSaxfv77VPaZOnYokSS3+XHHFFfF8WYIgCDFZvegWjEo9eX4/91WXk/rRxdhrK3t6WILQZ/SqgOqNN97gxhtv5M477+Snn35izJgxzJgxg8rK8D80li1bxtlnn80ll1zCunXrmD17NrNnz2bjxo3NbZxOJ5MnT+bBBx9ss+9LL72UsrKy5j8PPfRQXF+bIAhCtKrLC5la/i7PlVdxbcZlVEs5pFLP5nce6OmhCUKfISmKovT0IDpq4sSJHHrooTz11FMAyLJMXl4e11xzDX/7299atT/zzDNxOp189NFHzdcOO+wwxo4dy7PPPtui7Z49e+jfvz/r1q1j7NixLR6bOnUqY8eOZcGCBVGNu6GhgYSEBOx2OzabLap7CIIgRPL8lz9TsfQ5plmKmHzrh/z02cuMW3Ed3+lSGXv9ehJM1p4eoiD0Sp35/O41M1Q+n4+1a9cyffr05msqlYrp06ezfPnysM9Zvnx5i/YAM2bMiNi+LYsWLSI1NZWRI0dy66234nK5On0PQRCErrB45ypekKdTfMzTAIydfh7HZI3n6hwTz635rIdHJwh9Q69JSq+uriYYDJKRkdHiekZGBlu3bg37nPLy8rDty8vLO9X3OeecQ79+/cjOzmbDhg3ccsstbNu2jXfeeSdse6/Xi9frbf57Q4PYcSMIQtfYWF5IuemfWIZomTjoSwBUGg2pyZOodHzKd3s2c/NRPTxIQegDek1A1ZMuu+yy5v8fNWoUWVlZHHPMMezatYuBAwe2an///fdz1113decQBUHoo5av/RCDz4RalUz/5JTm6zce+hfOeu5Q9uiM+AIyOk2vWZAQhF6p13yHpaamolarqaioaHG9oqKCzMzMsM/JzMzsVPuOmjhxIgA7d+4M+/itt96K3W5v/lNUVBRTf4IgCJGM/nUlq0u28pA/r8X1CfnZXG1YyivKbexY/XkPjU4Q+o5eE1DpdDrGjx/PkiVLmq/JssySJUuYNGlS2OdMmjSpRXuAL7/8MmL7jmoqrZCVlRX2cb1ej81ma/FHEAShK6TX/QyAtf8RLa6rVBJTrUUcrNqJ/ZdPwj1VEIQ46lVLfjfeeCMXXnghhxxyCBMmTGDBggU4nU7mzp0LwAUXXEBOTg73338/ANdddx1Tpkzh0UcfZdasWbz++uusWbOG559/vvmetbW1FBYWUlpaCsC2bduA0OxWZmYmu3bt4rXXXmPmzJmkpKSwYcMGbrjhBo466ihGjx7dzV8BQRCE3zTU19AvuBckyBs1tdXjJQUH8++Kn6lXvuXw7h+eIPQpvSqgOvPMM6mqqmLevHmUl5czduxYPvvss+bE88LCQlSq3ybdDj/8cF577TVuv/12brvtNgYPHsx7773HyJEjm9t88MEHzQEZwFlnnQXAnXfeyfz589HpdHz11VfNwVteXh5z5szh9ttv76ZXLQiCEN5XP73Jq7kZjHZLzM/u1+rxvOFHsazxdTSKTF1DNUm21B4YpSD0Db2qDlVvJepQCYLQFR5YdDGLAqsZ59HzyuVrWj0uB4MsfHwoh3nr8E37L6MOn9UDoxSE3usPWYdKEARBaGl8nYenyis5WjU07OMqtZpRDOUgvx/Hjh+7eXSC0LeIgEoQBKGXyrXvYYrbw8jMIyO28WVPAMBU3noGSxCE+OlVOVSCIAhCiKIoXO+/kjzfbm4ZdnTEduZBE3ivKIUf9G5GKwqSJHXjKAWh7xAzVIIgCL3Q9upyfjXs5FtDBvkFAyK2yx1xOLdnWPg8qZ4tVSXdOEJB6FtEQCUIgtALLSvciCHrHUw5b6DXqCO2SzJbMfrH4K8fz8bSmm4coSD0LSKgEgRB6IUCJZvIctooUNLabTvZ9lc8ZadTVRU58BIEITYioBIEQeiFRpbv4ovKjdzmMbXbdqZmDSv0V3H4upu7YWSC0DeJgEoQBKEX0jXsBUBJ6t9u2+zMLDKlOsye7V09LEHos0RAJQiC0AsluIsBMKQPardt2kHjOC4vmzn9jBSV7ejqoQlCnyQCKkEQhF5GDga5IsvDGdmZBNPbz6FKT81GVkI/7tds+aqrhycIfZKoQyUIgtDL7C3fQYVWTQVqBg4Y16Hn/LU+ncnOdWw2Nnbx6AShbxIBlSAIQi/jLi3iveJStmqSSLR27MDjJMswrI6foHJLF49OEPomEVAJgiD0Mp7qYob7A/iVjgVTAOrM4VAOloadXTgyQei7RA6VIAhCL/OzcSLHeh/i3ewbO/wcXf4I5tsGcp9V24UjE4S+SwRUgiAIvcza2g3stlVQn5LS4efkDT2Ut1P8bLBVsaumvAtHJwh9k1jyEwRB6GU2Ob7AmL0apzoBOKZDz0k2WdC7jqLBoWdXlZOBHY/FBEHoADFDJQiC0MsMa6wly5nACGNip5431nQRmpojqKuwd83ABKEPEwGVIAhCL3Nn1Qa+qPyFoxPzO/W88wLvsNlwMQUbnuiikQlC3yUCKkEQhF4k4PeRotQBkJzV/rEz+7Ok5eOSJBwucQSNIMSbyKESBEHoRWoqisiQZPyKmuT03M49N9XKxII8kgMNHcy8EgSho8QMlSAIQi+yatdSJufncHlmJmpN534nHj34SABkSaG6tqwrhicIfZYIqARBEHqR4tqd2NVqGtSdryeVldaPD/Y28H1hCXV7xSHJghBPIqASBEHoRYa7dLxTXMY5zqyonu/W5AFgLxZH0AhCPImAShAEoRfROWoZ7PeTo+9c/lQTh6UfAP5KkZguCPEkAipBEIRe5EPb2Uz3PsS2/hdG9fyN6YM5P3kE/6E2ziMThL5NBFSCIAi9yEbPOvbYyvElWqJ6fkPeGNYnNLJOqojzyAShbxMBlSAIQi9SLH+EMfstvFJxVM+flDcGb9UxeKqmoihKnEcnCH2XCKgEQRB6kdEuH9nOBIaYE6N6/sE5Bahrp5Jbb6OyRiz7CUK8iMKegiAIvUQwEOA/1T+hkWSqUvKiuodWreJz/a3kK6Vs3JpDxuST4jxKQeibxAyVIAhCL1FfU45GkpEVicTU6MomAFQYctmh1bKneHUcRycIfZsIqARBEHoJe1UJAPWSFa1OH/V9/pei4tTcLJY4VsRraILQ54mAShAEoZdYUfI9R+bncEtGYkz3yTTlYw3KaHz2+AxMEAQRUAmCIPQWVQ1F1KvVOKI4dmZ/x+efxI+FxVxXVR+fgQmCIAIqQRCE3mKs28w7xWWc4c6J6T6Z/UchAZlyJX6fNz6DE4Q+TgRUgiAIvYTeGTp2JjPKY2eapGbm41Z0aCSZikJxSLIgxIMIqARBEHqJd23ncYz3YX4dcF5M91Gp1fxf6iEcmz6Sr8q3xml0gtC3iYBKEAShl9jkWc9eWxlemynme/1iS6fc3MD6BnEEjSDEgwioBEEQeolSPsaY/RZuqSTme41JOB536elofUPjMDJBEERAJQiC0EuMdvnJddoYpDfHfK/DMw6lX0MmtorSOIxMEARx9IwgCALwc9kevti5mssOnUWCIfYltXhTZJlnq9djkPyUJkRfJb3JqMAmluhvYm9FLnB+7AMUhD5OBFSCIPR5xXVVnPfpuaBu4JPdn/LNBS/29JBacbsaMUl+AGwpGTHfLylvCL9qNfyqqSPL50UXQ+V1QRDEkp8gCAK7vvg3f66tJ8uew95dR1BS7+7pIbVirykHwKdoMFsSYr5fWvYA5uRkcUNmCpt3izP9BCFWIqASBKHPS9zzDdc5ijm5Mp0j/JWsX7Gkp4fUys8lazgyP4eLszKQVLH/6Nbp9AzwwTCvj9LiTXEYoSD0bSKgEgShT1NkmXz3FgCOspSyUPcA6Vv+28Ojaq3aXky9Wo1drY7bPefVZfNmaTkptY1xu6cg9FUioBIEoU/bvH0lvxj9VEg6vOPOZ7VBz1rl9zdjM8Bv4t3iMq6ot8Xtnm5rPwCUml/jdk9B6KtEUrogCH3aqp1f8VhmOv198MjQMcwpz0BSFM511mM1J/b08JqpnXYG+f3YDWlxu6eUPAAqQd+wJ273FIS+SsxQCYLQp7nrSijw+cmUzQzKHcVQj5+pLje7d63r6aG1sCpxJsd4H+a7vCvids+yrAEclz6S/0tU4nZPQeirREAlCEKfNt7u5cOSMuZKE1Cp1dxXZeGfldUEy2OvRh5Pvzi2sNdWSr1FF7d7pheMpszcQIW2gkAwGLf7CkJfJAIqQRD6tFKfkV1yFqr0IQDYTaG8Im/5tp4cVis73EswZr9NPZvjds+x2QPwlp2Gu/BiKhu9cbuvIPRFIqASBKFPe9R/Gsf4HkUacw4AgYQCAFT1u3twVK0NczSQ60zgIE38CnCatHoOloZwpLee8qJdcbuvIPRFvS6gevrppykoKMBgMDBx4kRWrVrVZvvFixczdOhQDAYDo0aN4pNPPmnx+DvvvMNxxx1HSkoKkiSxfv36VvfweDxcddVVpKSkYLFYmDNnDhUV4oR2QejtfIEAtQkPY8x9mRSrDMCKjHwmZg/jDsvva8bmpuodfFr5C0fFMSkd4O/Kv3lZ9zDB7b+/2luC0Jv0qoDqjTfe4MYbb+TOO+/kp59+YsyYMcyYMYPKysqw7ZctW8bZZ5/NJZdcwrp165g9ezazZ89m48aNzW2cTieTJ0/mwQcfjNjvDTfcwIcffsjixYv59ttvKS0t5dRTT4376xOEvkYOBnngzWu56qMFePy+bu//17py1MZi1JZt5CSEyhHo0wfj0jupVBq6fTxtsch2AIyJ8Q2oSq1ZfGc0sK32p7jeVxD6ml4VUD322GNceumlzJ07l+HDh/Pss89iMpl48cXw52498cQTHH/88dx0000MGzaMe+65h4MPPpinnnqquc3555/PvHnzmD59eth72O12XnjhBR577DGOPvpoxo8fz0svvcSyZctYsWJFl7xOQegr1n3xCofufpNvK17nli+f7/b+g8U7uK/MwZ+rjRi0oWTvidljcO29lGD5Rd0+nkgUWSZhX4BnSY79HL/9rbZJXJWZztfy9rjeVxD6ml4TUPl8PtauXdsi8FGpVEyfPp3ly5eHfc7y5ctbBUozZsyI2D6ctWvX4vf7W9xn6NCh5Ofnd+o+giC0ptr4FiZFxhpQsaqs+2dI/LUVnOSp5US3v/naoJQ0JnscnOBai8v5+6ggXl5bzDH9MjkpJwtTYkpc752fNIyDvD5yfL+/8wsFoTfpNYU9q6urCQaDZGS0/O0sIyODrVu3hn1OeXl52Pbl5eUd7re8vBydTkdiYmKH7+P1evF6f8u/aGj4fS0dCMLvgSLLDHCuQy35SC46iW3yGFy+ACZd9/1Y8taGSiM4dL8to1n1Gp7RPoFZ8lBUej6mwWO6bTyRFFfsol6txitJWC1Jcb33lEEncMGah3AoRhRZjss5gYLQF4nvnC5w//33k5CQ0PwnLy+vp4ckCL87vxZuZIshgAs1UzVlPKh+msIta7t1DIUN21ll0FNh+i1IkVQqlppSWWw1s73495FXZHIHea+4lAfK459nltHvIGRFwiK5qa0qjfv9BaGv6DUBVWpqKmq1utXuuoqKCjIzM8M+JzMzs1PtI93D5/NRX1/f4fvceuut2O325j9FRUUd7k8Q+oofN3/EpVkZzM3OYqZuPXPUP9C4e023jmGpvJVLsjL49oAdfa8m6bg7NYWN1eu7dTyRBBvrGegP0C9gifu9DUYzlVIqAFV7t8T9/oLQV/SagEqn0zF+/HiWLPlta68syyxZsoRJkyaFfc6kSZNatAf48ssvI7YPZ/z48Wi12hb32bZtG4WFhRHvo9frsdlsLf4Iwu/dE8ve5/pPn+62itkNNbvJ8/vJlS2sSEzh76nJLKn+ulv6bpLo89Lf5yfdkNXi+oCgjSkuN2ZP9+88DKfQOpZjvA/zbMotXXL/mzPHMSFnKG/V7uyS+wtCX9BrcqgAbrzxRi688EIOOeQQJkyYwIIFC3A6ncydOxeACy64gJycHO6//34ArrvuOqZMmcKjjz7KrFmzeP3111mzZg3PP//bbqLa2loKCwspLQ1NdW/bFqqOnJmZSWZmJgkJCVxyySXceOONJCcnY7PZuOaaa5g0aRKHHXZYN38FBKFrLPnpS/6z/Q6QFG7+Ah474aou7/OQRri6sozlWcewxNrIB7KFQzzFXd7v/ubW+hgULGP9kUe1uH6SMoTDKtezXPX7+BG5pbGQQlspWdbELrl/jS0bt38r25xVXXJ/QegLfh8/LTrozDPPpKqqinnz5lFeXs7YsWP57LPPmhPPCwsLUe2XUHn44Yfz2muvcfvtt3PbbbcxePBg3nvvPUaOHNnc5oMPPmgOyADOOussAO68807mz58PwOOPP45KpWLOnDl4vV5mzJjBM8880w2vWBC6h3nFYp5urOBB81C2eEzd0me1T8ceOQOS+jPKrCJz+zdYgtpu6bvJHiWTgOzDmHJAnqMplKSudld363gi2Vy/AkP229SqaoAz4n7/w9NOZuvygZgH9XwCviD0Vr0qoAK4+uqrufrqq8M+tnTp0lbXTj/9dE4//fSI97vooou46KKL2uzTYDDw9NNP8/TTT3dmqILQayTWbmBowMN79sP4GQWv14Neb+jSPp9Vn8VG30z+M/IQhvu2M3h1A1Wou7TPA13tvwaPX+a7vHEtrqusoYBK763p1vFEkttYRYUzgaEJ8Tt2Zn8TUvuxzbOSAWXLgCld0ocg/NH1uoBKEPqKjT98AN8/SnDStYyZOqfL+gkGAvTz7wIJHtM9C8DuXaPoP/zQLusToFD3OIYcHQbDUJKSCwBIUerx+7xodV0TOOyvzuVElfMExqAZk6FlELE5JZ2rc4ZhkjQs7fKRtO+k2nLuqf+F5eaj2m8chUG6Gl7RPYi90Qzc2iV9CMIfXa9JSheEvkSRZdK/uo6R3vXkLr2eYCDQZX1t37uep1NM/M9iZatmMMUaNb/u6tqitXUuB4phB1rbJvolJ5Kclk2VpGGHTkNJafckRu+1V6E2lqA27yTZ2HKZ05TSD7fOSa3k7JaxtEfrCx07ozbFtwZVk8yC4SwzGvjIJlFcJg5JFoRoiBkqQeikuqoyynauZ9jEGV1WBHH35tUMoJZHkxJ53ZzBHdtWc/KIju9O7YzNe1fx3wQbWX6FH2Qj3+lz+FP1txzDtV3SH0B92R7mlbspVNvIsSWhUqk4LncYAY2dvzfUUNBlPf9GU76Hf5Q7KFKntsi9BBidfhCuPZehkxK7YSTt0wdCxYHV5q4JqIxmK39PTaVao8K6Yym5WQO7pB9B+CMTAZUgdIIcDGL/13EMlwtZvvlSJl3ySJf089HGhazMymCDQQ+4+bF4Y5cFVNq6Wi6wN+BUpeM1p6BV6vD76rukrya+ukpOd1dRDs3BjFZKxxfwU2Kv69K+myiN9ZzsrmW3ytrqsbyERKZ460mRCnG5HJhM8a//1Bn3pNhpUGfxZ42L8V3Ux0ivAZW3Hl9V9+60FIQ/CrHkJ/xhKLLM/f89l+v+PZ36xq7ZnfXLz1+TqYQKtQ4oegdFlrukn72OnWww6En16nEVzkXjGdUl/QCk2Ru4qbaemcHBnGg9kjV7ijinTuqy/gA89aGCu42ahOZr4zS34dwxjzRN9+w08zaGSgS49htDE5NOzdPaf/Kw9nnqK3o+wKjQyBRqtRi6aIYK4PzAMJ6orCanThyVJQjREAGVECIHqX7/Cv72+gzcga45JHXxV08w9/mJfLXq9S65/5bVX3FJ4af4Anv453vXdUkf7296mcn5OYwtyOPPadlsLO2afJMZ9gCPVFRxfOMIJrgD2IrXdUk/AL9IB/FC4ARqMo/EltYfFWDzVXZZfwCl9bv4Sa+nSPdb0dujgit4RPssqbs/7NK+m8fQsJuVBj3FBnOrxySViq9MSbxtMbO3vOerh/+zrJaXSysYnD68y/qQkwYAoLXv7rI+BOGPTARUQsjWj7BW7eALfyUf7Pwg7reXg0Fe2PM8B3kqSPjqgbjfH6Du549ZY9CzW6tli3tzl/RR6S7Gq1IRlCT2WOx8X7KtS/oZ6ixlhsvNFIuV/+n+wZk1XVey41tlEPcEzsUx8ERsGQUApAa7NqBa4fyFC7MzeDPR33xtQHAXp6m/I7m2e87PW+7ZzJ+zMvjI6g37+H+S9cxPS2FnXdf8G3eUz+tlZMDFeK+XtOTcLutHnzEEAKtrb5f1IQh/ZCKgEkJ+Xcqbjp0E5SCrK1bH/fabNi3FJgdYbjQwwr+H6vL4n2/4svo0VjbM5KmKKp4oreyS5bjLqwN8UlRKQfVgPOUn4XakxL0PgJsDV3Kl7zqUYcez0qBnjbGxS/oB2MKDWIbeTnXwF6yZucxNGsH5aYOoc3Zdnzqfmzy/nyTVb8ttO4wyt6Wm8LnUPbvMTD4fA30+klWtl/wAhvj0THG50Xo83TKeSOxemWO8D3Oqdz6WxNQu68ebN4iJOcM4M0eF3EVL2YLwRyYCKiGk5CdObrDz5ei/8vBRD8f99t7dW3mztJxXysoxKQqlW1fFvY+fnd/zhm4IWf4g6TioqSyJex/pvjLyAgEONpxISt1QVLXx31Zf43KyRu/ic30mOUPH8uesDO5Kt1Fa1TUzB4pShyTJZJkTSLSlstrmYpfVzq/1XTdLdZxDzyfFZfxJd3DzNbtBw4dWM5u1XRfI7W+mQ897JeWcYAyf5n22O4unKqoo8HVtgdP2FDXUUmgrZUciqNVdV/h0WP/ROLUugmoPu2or2n+CIAgtiIBKQJFlFvhK+NhsJrh9OXx4HfjiGyjUNLopktPQKvCz1sD2io1xvb/d7cZlex1t/qvsVIV+i6/cHd8+PP4gkz2Pc7T3EY6xFLLCcA1T9zwe1z4ANlfsxZj7Kqb8F8lPz2WYx89hbjelXbC8qMgyPxRuZ0lhCeMtofIFescJeMpPwuPtumNgqmUru+QsSPhtCWto4jBuqK1jtr3ram7tr1xJZouch5QQfhnNr0sEQHF3z67DSHbU/ooh+21Uqe93aT8JBhPmmmtw7PgbdY3dewSQIPwRiLIJAvb6PbxgMwJGTtjyDhJemHAZZI5s97kd9bH6GC73DSMh/QPklGX0l+2cFre7w969mxjosFGrVbHUZuUVJYnR9iLimcK7s6YcKW0JpcEkzFmDqChUUyOXxbGHEHvlryS7baAKJUs/WKGnv1zGL3ZH3PtqbKjDJgUwB8GTng9Anjydyrpigg5/O8+O3tO6uWz0zeHFgw5pvjYgbQTH2hup7qbjZ57RXcQm36m8NDB8RXjFkAiA1MMBlbqulDxnAjqVrf3GMZpuNCDVrqZxVxL0n9nl/QnCH4kIqATkhiLOszdQpTLwhimDekMjM0tWMjqOAdUq5z8x5LhJteRQ7rfiUuJ2awDUlUW8X/0Lv6r6cXn/YZTLhTh8DVwYxz62Vu1Bn/oNUiCJausQLsrPITngZXoc+wDIrC7j2/KNbNaFSiU4tYngBa89/ktw9upSbIBDMWLZV2vpbvd9jDasYdWuf8Do8OdmxqpE+wzG3CCyagAQOtzcmpIJQKLSgBwMourC5S2AMv2zGPPcuJQ8IL3V4x+npHGtNIx8XYC3unQkbSuw1/FJ5S9s1I/t8r7+FPySCdr3Wb4bQARUgtAZYslPINll55baes6ttPCNRcuiBCsri9fHtQ+nahta2yYmZRyLc+ffMTaeGtf7e+rLAXBokulvHoevbiKSPzuufWgrd3FovZWxvhQG5oxBqyhokfF4XHHtJ1AfmvVy60MH9Hp1odpDAUdVXPsB2FG2gceSEnnD9lt9o0Z9IqUaNXWNhXHvr4lfvw2NdQsJpt+WlhJTs6hUq9mjU1NTE/+Zv1Zj0O5EY9mBSRf+cZ8lE7fOSYXi6/KxtCXgDM2Q+bRdP0NVlZjBG1YLqzwburwvQfijETNUAtiyKR58Ph9uhgLHZg7z7yRTE788FjkQ4I6qGorUBsYOVDFBuwBrrQx8Ebc+/A2hJFqvPoXDM2bwxapcdMnJcbs/QGZNBS/WbWKdKYGCrINYtbsYjaRQXV+NITM/bv0o+wInvzEUUL2Sls81lhGMVTk4LG69hOys3cpLiTaGeFVcsu/a21YHXybncJxvAzPi3B+Ax+PijqpGqiUD/farQK7TGzgmtz+ofDznaiStC/puosgy91TWUK3SMcBgDNvm4LTDeWuFn/4ZeV04kvYp7noAArrwuxHjqSLRyuNyMv19VXRNJTdB+OMSAZWAL2s0S/r/lRd/2cx1dhc3aNeyUR+/4p4NtRWc4S5HViQq8grIUi8nKEsE/H402vgkv77vWc3duVkcofiZ4V7NJv3VFBUOAFbE5f4AcmMoaPMZ09BotdRJVpJooLG2gtQ4BlQfsoWnszI4VOfmMKDekk6j0sheOf4FV5M8Ac63NxBQ/RY0WLWJ6OVigsH4zrw1cdprONNViaxIkNAybJJkC0HZQ427aw8ldjobmO0JBa7uxMywbfobzRztrSbH3gCc3KXjacsHwZ+5NzeLw3EwoYv7GpF/GFOL/ssAn4Iiy112VqUg/BGJ7xaB+1bex6M7TkGb/B0VhJZ+VI7yuN2/vjpUvqBespCW3Z9bU1O4NCuNXcWb4tZHjVxPkVaLX2/CZLFhlrxoZXvc7g8guypQANkcyvlp2Jck7KqLb25TGY38bNDj0oV+3zk49WhchReT4j8+rv0A5Hokbq6tZ3rgt4DqBNME1uwt5iK7Ke79QSigAnBIxlZ5UlmNd+PcMY9ETb8u6buJoz40Bp+ixmBsXSkdICVQwb91j3G1+9kuHUt76hQHhVotPm2Etck4Gjf0KBZU1HBDfQ01lT1/5I4g9CYioBKoc5ShEESStZgS0vEDnkD8djaVVu7gJ72eHdokNFoty4xGVhsNcT3S4+w6Nf8trWCSdSz1+iCH9svl/Nz4vr3/o9vOwQV5/KgPfW0eTxnCKamjWO6Ob27T6XY1CyqqGGMJ7VEcZk5hktvLoLpf49oPwG79UP4dmElx8m+LiTpLaKlU5++aelBVdcX8pNezVdv6UOIz5M94WPMsquKVXdJ3k+q6YlYa9GzQWSPOwmhtCXxlMvK1RUYOBrt0PG2Z02Dk5dIKJhpGdHlfOr2BClUoQb9yT9ecNiAIf1RiyU/g4aLd1JaWcLs3SPHQdA4O5qMLGlkbp/uvrV7D89kZjPBoeB24qF5FmlyNOT9+1Zj7ee0MkL38kjQYQ0o+HpUKr6Lg9brR68PnyHSWW/IRkCQM+lAuyzqLjVp2sjnOZx8e5HUxMOhmQ0LobLUc7y5e1d1PYUMOEN9dd+u1I3gzkMQN2UObr2nNoYDKGOyagGpL7SYezM6gvw8OPOTo4MB6xmmWsbJ6KnBil/QPsKNmC/OyMsj2K3weoY0pIYEbMkJLksc0VpESYWmwq+V4XQz3e1lrjd+ycluq9blkeCqoLdkExH9WVBD+qERAJaBz1ZAZDNIQTGFUegHLy8BH/I7bUNyN5Pn9pBBaIpvoTWC4r5A1rvj1cbPmZqTGcu7MPYR+mRl8WlRCUlDGUV+DPiM+55/dXqmQopRQdESouvcAwxRK92Rjyxgcl/s3uV99BZK7gmuzxwKgttr4wWigWnIT74/UNc5nsAxdzW7f5UDodThsCVyYNAKf2sz/4twfQNDTSL7fT2qw9ZLi92aFN80p5Lg2MbEL+m7idzcy0OcjIRi5CnqyNYNxbi82RaamtqzHAqoHDNficJRyc94R3dLfP3OGsSpQw6hABZO7pUdB+GMQAZUAztCSVQ02JuQcxAtL56FSDARlBbVKivn2Ezxmri0pY0Va6APBq7WBDwLOmpjv3WSLdhdeiw6d1YpOZ8AWMGDGSXV9NSlxCqhSAg6yCNKYkAXASOshbKtTY3PEt17ScpULjz6ZmxND5wQGTXquzExHoyicHOf6TMFALZJaIUH7W2AhJWfxU2Ijihz+0OBYDfUn8HFxGevMrQOE3XqZr7Rmjg/EL4cvnAEBC++VlLNRPy5iG5VazWPlXlKpZ5eza74WHbFJtRe7RUFlbb1E2hUMSYNRar6jxBP/Mh2C8EcmAqo+zu938bQRknRWaipNDM2wcY3qc5JopL7uMFJSYt+83igb2Cun4zeGkrlr9RY2+nSUu+NzXpjT50GVvhgjYNBdGupTsmJTnLjq43cm2cnKo2i8dl7LHQvA5Np3+KvhcdbsPQaYFpc+nD4vqqyXMAF63VkAZKbkMczrwyrLNDhqSUyIX0GBZ0qLyJCL2Zn5W5CWn5iBt2o6StCALxBEp4lvwOiQteySs2jUt64TNlqVy+jazWj18Z31CzeGLXI+tYa2g22nykqqXI+7oeeCC2/i6xiT/Siq+NZui2RGv1l8vDKF7JSeLRchCL2NCKj6OLu9kBcSE5AUBUellXSbkcs0H2PFxa9VxXEJqD5KOIv3dx/F7YOHcSTw78wBbErYwmC9ltkx3x1qayvIcyTgUkGmNZTf9FpCfyqUBCY6KhkWhz48fj9269coZiMmY+iDLWBKoESjpk6OXwJ/VW05SW4bHnWQTEtox2WyLZ1FJVVopSCVDkerUgOxsAWdpCoylQm/LWdlWBLQVE8mASeNTjcpCZY27tB5qxOO5xLfYC4Z0J+jDnhsmHEghxU2stbStUngG21TuMiXxZl5ea3GsD+3ygIy+Bz1XTqeSLw+D3luEx6VQpaxa3ZdHmhUWjJny+sYUPsFinyUKJ0gCB0kAqo+TuNzcba9Eaek5W2tDqNOzbO2ROwaHeMqNjFgaOQlkY7a5HkNY+5e6uW5wAASDRnIDTYC8Zr5aKjjk6pfaFBM6DSht/T7icnYpRK0QS+nx6GL0oZa9GlfA5BguhuATeparsjLYYi3lmPj0AeAVF/Ld+UbsWNufi2SSoVDMpNEA66GGsjpH6fewKSE6j0Zrb9VSlerJFbqr8IquSmqHENKwpi49Qfwk/0djLnrqFVOhgNOW1SbQuPQ+Rvi2ueB1tR9iDHvB2qk44DREdvNyyhgDzBbtnNwl44oPE+jnU8rfwHAZ0vplj5zki3crXkJjSRTWbaX9Di+3wThj0z86tHHJcoKt9XWcWW1jNUQKrL5uUXLqwk2Cu0749KHXd6OxroF1KFCkVMz5+DceRup/tlxub+roRYAp/RbPaFM7cH46iaiU1qf0RYNZ20Zh9RbGdaYgkETqgdkMyajl2W0SvxmU9wN1QA4pJazQk2vzbPvtcaDHAzySqKKFxKsYG5Zi6lSZQnNvtXHP5ep2rcLjXUrAVXrmT3JZKNSraaOrg2oKj270Vh2EFS1/fWs1ptx65yU9lDZBGdjPQAeRYtOHzmBPp60Oj2LLZk8kpzI2m1fd0ufgvBHIGao+jpjIuUHXcD7m+qx6kNvhyM8Zo5yl5Bkjj0hHeAvNVU0IDFycOj+eb6dPKV9AioygIUx39/jCH0wu9S/Je0OtxzPml+GYRs2MOb7A2gb6nmpbhMV0m+zBOPTxrNm2Xwqid8RN57GUKK+S93y3LbrMw6iVErmYl8tQ8M9MQoNzjpeTAp9zU7cb4YK4PpsI3t0OdxSvZ7RcT6A5vyaUlwBSEtp/f7akZLG3Pwc1AEb6+Paa0vnVJfg8QYwmNo+pXuY8VT2bj6YnMyurlEenmffUqNTMtE94VTIRzYTGwwaLqhYxQnNhxIJgtAWMUPVx8nJ/dk45u88HDgLiyEU8BzjT+eGOjtZ3vjE2yc5S7jOuZcCSyj3J1FycaJ6JaO98al0tbJ2NbNys3gq5be38/TqV9miv4jJOx+OSx/NgY7qt6DNlBAKrixK/I5JWVW7lnOzMnglseW3ZoleT6OhkRK/P259NdZXc569gZMbnaQdUBLAqKjRyQpOd/zyw5oc4azmKmchQwyprR5Ls2WiKBJBJT7BfCRjXHX82VXKQbqkNtuNUms5xltFhr3rDopuy6bqXzgxN4vb0rtnh1+T0WRznr2B7IauqUUmCH9EYoaqj3t3x7vcvfoeDNkjsRpCRSNlXWi5SfbGZ9nFojhB+i0AadDJ3JieSkCR+Wcc7l/rqaZQqyVN/i0nS6fVYpR84IvPB4K3sRYFcO83c2SyhmamTJKXgN+HJg5Hg1R5q9hg0KM/4HedAdpTWbG7jLQBI2Puo0nQ5eKW2nrqsbQqxXCTPYtDnctYOTz+eTvGoAMAnaV1MDMidQiOrfehUalQFAVJ6prASr9vDFpz2wHVGPsSrtA9y6qyE4E5XTKWttQ6K9mr1aJueyIt7qYmHcXEzd/xs7G6ezsWhF5MBFR9nMNVhUwQFQqWfUt+is6GH/B5Yp+dcDjt7DRI2GQNybbQh5fGZOZLswmTHJ9K6eN8icwoK+dXy291jZZrq7iqXx6jfHviUiDym8aVXFGQx2EeH//ad81sS+KC5JE4VBJP2KvJS21dBqCzRgcSOayyigrjgBbXx6gTUbl3k1Afv3MDG2Q9/w7MxGzUc84BjynaRADkLpih2qv14Fa0qE2tZ10sWpl5moVYcOP1TIl4zl6s9mgcBFRaMLW9g7FWr+FLk5FKKrv8YOJwCmQbL5dWUKiNz9J1R1lyhsNmSPXs6dZ+BaE3EwFVH3dWTQXHF5bwdmAgv2aFktJfSk3hO0M++ZKKo2O8f2nVbs7PzkRSFH7al6eTldSP26prscgywUAAtSa2t6HV42ac14cvMaP5mlZnweeT8EjxWSJz+e0EJAlF9dsslE5v4CerG0nlp9TlJB5Ve1K9QSa53KywZLS4fpT9A27WLWJFyTkQp5ymSimZfwTOYZQtqVVAJev3zcR54r/kc12WGZ/KwkJ962kXs8HAxZrPAKhpqOuygOqedBX16iye0LRdsHOHppEXMtIY5a3h3C4ZSdsMXh/jvV5U6sRu7Tdj4GjkL0FR1eBw1GOxdG//gtAbiRyqPk7vdZIRDCIHbc0zVAZz6MPcIccejNgbqsj1+8kKyGg0oYAtLTmbsxsdnOR04Wioj7mPrxNO5VTvfLbnn9F87ZCEMXxeVMJtcZrQme5N44vCEmYHWs4caRtOwFN+Ioocn5ThVQnHc6nvRrZnndTieq1Byw9GA3sDZXHpB2BZ+RIsQ/9OreXZ1o/ZkrkwaQQfhAl6YuH1uEgPBkgOBkmxtT7KRaVW80BSKn9PTaa4Ov6HQTdJCwTJCARI2Vf1PmI7YwYHezwUeLt5zW2frYlHcYr3Lr7M+HO39puSnsMheUM5IT+bH0u67t9BEP5IxAxVX7cvT6pRMWHdl5Q+JWsWb3+XxaDcjLae2SFWr4pPi8solX4rX6A3mPAqWvSSH1djLQnJrZOTO2NToJQNFi/TLL/lNyVaM8gOBJElV0z3bmLwuckKBtmtbbmjL8d/BLV1VeCJzwfuL0qAb/TJjEhsuXz4s9bOa5npHOot48y49AQNzkokSUEfJk9puzWFnwKNlKoCceotxOt08GlxKCj0R6jE/ZnFQI1GxVENxcS3AlaIz+vhndLQGOxpQ9psOzZ5DOeurWSvKvb8uGhs91bxi8VLP0t8i6u2R1KpUEsZ+JRCfqksZMZBPVGFSxB6FzFD1cd97NzLyzYrJTq5OaDKlWu5TvqEo+3vx3x/ty/AXjmdanXLelA7tWY267TUNsR+NMze4McYcxdR6d/cfE2/b3nRpMQnoHov7XIO8zzJloKWCz+Peu5imeFa9IXfxaWf7b63MRU8T4lvTYvryboUhnl9pPnjN1Pyp5pqvtlbzN/rWu9SHGAbibdqOjZ5fNz6A3B63PwqZ1KspKLV6cO2ObUBbqytw+zvmoR0t8vFVjmPIjkNo7nt3XP6fUtdJjl+Ozk7Y3PjNxhzX6Vc/qHb+55k+T8cW+9G4x3efmNBEMQMVV/3dqCK1SlJDPP6sehDS3JJ/nJu0L7NDm8+8EhM9y+zjeYU3wIOzU5i8X7Xz83qT1BTw22ywoiYeoACj5cyJYF81W871SSLjX9YB1Kv0hGPwgnbveuoSd5Lg7Zl1eh6rYlS1Nid8TkzMN3rxouZTFXLXXcTbKO5fNN/2KqNX80rjd9Nqixj0SS0euyghBHoqhtJsbR+LBaNmmSO8z1GslnHTxHaHO80MSRQzHpfXLtu5pSMHO97EK1aYkc7xTKbdnKa4xSYd1auq556n40Cc3zPU+yIyWY3wzRvkrktF6Y/0O39C0JvIwKqPu6IgESG18lOX0pzHSqnTs2/Em00Kj5ujvH+66uXY8h9nUb9KODw5usakvD7/Ti8sX9q3le5kwK5kA0jfptt0Cem8XqqH/Bzu8dFgiG2c9BKgt9gyNhCXXA4cGTz9ecT3awy5HCW42emxtRDyP2Vuxkc2MH6gS2XeDTG0HKmPhi/D3bJF5p1UXStl5P61f7IRsPlbK8eAhwXtz631u7AmPsyKlUGRDiwx6s2QwACLnvc+t3fHnsRxrwX0SgJwMw22wYtNiZnjcCnkvnO58UQYVatq8ytKeNg50ZWJp3UfuM4O0hfyxjNh+yq7Q+IgEoQ2iMCqj7uEocH6ms41ZvTvOTn16t5JikRS1Dm/2QFlSr6pZcyVyFa6xZ8UmKL64OCN7Pi11oyDo19OUGvuAHQmn7LoUozJ+BvGIMSNGB3+2IOqA5xeSmTExgktZwp0Es69HIjQcUT0/2bGIKhIEdnajkz1PTa9HGcKVlPCRsTbFh0AQ474DG1wUKDSsIZpxy0JmWOcjTWrQQDkXcPOjVGKgNqGt1dUwOp0lmLxrIdKZDYbtuUpDTshtBYK10N5OvidzB1R2gDoXpZKoOtnZbxZ84bzONJCezROHg04G/eVCIIQngioOrrRpzKFyvWUa4kN+/yy0rK54yGRixBBbcvgNkQ/Q/SSXVlDKqUkG0ta06d5P2Y87SrMBddCGNi25Bu3BdQ6fera6RRq9FWn0+jN0AgEPvb/P9qdtFPLuIXbcsPtvMCQ3imdDHLs2MtMBFi2PdadKaW/dSbrRydMRJF0vFNXHqC1ZpaVpkTOUvdOmgqVTVwTr88UgIyS+PUH0BBTQmXVYJTFzl9896MLPYqORyhVzMtjn03Sast55oKGbum/RRSk1ZPoPRifD4dgUD3J6br9gXYTTOU3Smv/wgWJtjwSxIbti/j4OFTun0MgtCbiICqrzv2Lv6+6iuq8GLShWZfMpLzuaMmVNCxymHHHOaIkI4a6HRyjnMvy8yHt7h+kH8rh6hXsqJ+UvRj3+eiHCs6xcJ8bcuE7TdVt1KgL6K45B1IOzLCsztGL+8LdMwtZ44kXSiIa1o+i9UtGTp0pHH1AStL+oQ0qkwNKHL8vmVHeFRk+RzkpbcuX5BkCW0iCMQ5LzzZ4+EaZyEbgpEPrdboUlA8Es4uOpDY7PVwmauYHRpjh9ofHtCi9lbhb6iH1PjmlLXnwRQXbnUG52qcjOvWnkGvM3K6XSI/WIurZDeIgEoQ2iQCqj7MH/Qz8bWJ+LO04LwZky70dpC0RvyKGq0UxNVYB6nRB1SSvylPp2WBxh9NPv6nTyHHu63VclNnuN2N7NKFZtCslpYJ2ybJi1Hy4XPFXpzSRCigMpgPmCnYl3+k9sceUPl8XlabQpHU/x2w5JdjTcNdfA6KrMcXCKLTxJ6kfLwDhvtqWTug9XHLBamDWbu7EB0gB4OtjqaJlryvUGhAE7lg56TEi1i/dAoDD+8fsU0sgp7QMppP1bGAar78NHm6UjZXTIQB/bpkTJHs0SlUafRoDN1bNqHJDH9/DnYUsqJyb4/0Lwi9iQio+jCXrxG/7Ae1H2QtRu2+D01Jwi0ZACcuR2yJwdXBOnZpNXgOOOeuRBvkC6OZY3yx5cl4XA5eLq3ApZJISWxZN+vvGWq26XK5qm4tI9pJPm6LHAxyXL8kdEoiz2lbLl1utFj5V/JIkgx6Do26hxCn087jFVU4VCoyknNbPJZsMjHSYcIsuXG5XOhssR+Wu1w9gQ2BVAYlFbR6zGpLpulfzOVswGJr+8y7jqrzVLNDq6VeGzm5e4hnC3do3sJSPhpi3gPaWq2rki06LRVafYfu/ovRxFaMSPa9dHcBgXsr7ATUfjImDurmnkN8iYPA8S2q6u090r8g9CYioOrDLJ4GviwsoV7ScjxqjLrfZiGOzuuPV9PA7X4nw2LoY7GhlDWJ2ZyrqeKY/a6PUecxrno9si62WQif08F4rxefokFnbPlbvF9S41EpuLyxzVA5XHacKhVOIMHWcrau0JbOuoQGrErsVeV9zkamu9z4FTWaA3KoNGoVb+juQS/5Kas7hUTbQTH3t1B9MnsCLt7Kal0+02A0E1Qk1JKCq9Eet4Dq6+A2bsrNYrq/PuKxRtm+XzlF8yk/2R1x6fNAKz1buTEni4leZ4eOVlqYqLBRn8aljVuZ3iUjCk8OBjl83+He1YmxnxMZDXX6EKrKVJT5dvdI/4LQm4iAqg9T+z1kBoPoldDSR/MMFSBLRqABuz+2sgZ6RSYxGMR8QIAwSJ/LxEYHa6yx1ZZ1aBK5yjuPZL3C8wc8dqk9mWHedeweGjlfpyN8TgefF5XglFSkJbY8qmRAwhC866eTaSuIqQ+ARizc7ruRZL3Mg6rWX5ef9BZktZsEezlZxB5Q1STdgSXZQ63vBaDlcqmkUvHXpFHUS0GudtSQTkHM/QFogn6SpCCmNpbbijU+vk5OQqGKrqjPrQ76SQ8GsNCxEgg5QSNaTyMGbXyrxrfH6QtwoXc+VsnNc4ndu7uwSfWAYVxclwvBICfJMqow70tBEELEd0dfti/vx4kBtUpCq/4tA3lg4GYat80jTRfbB/cNNRq+LyzhcFvLj0bVvtwjbSC2bfklbgfrLX5+trZOFk5S2cgJBNH4Yitp4HM5yA4Eyfap0B6wdXxQwkD01YeT7Ig936fc6+VrfQrfmcN/zeelW7giM51f63bE3BcAKheS2kuCIXxw87UV1iY2UhiIX4XNU5xJfFdYwkmayIfK2LVBXkuwssbgjlu/+5vqS2NJUSlnBdo+dqbJGd58XimrZLSve3faVbmcbLD4WG60otd3b/2rJpMGHoKiqJADJvbW1/bIGAShtxAzVH1YsX0vS2xWFL8ek0uNtN+ZbkcHfmGStBl9dSKQH3UfDYqRGsXaagkroNdTqNFQTWzLOjvrdmDMXYQvkAVc2uKxoCZUe0rxxdZHvS6T0zz/JMsMbx/wWJr9F34x/JmSxgzg5Jj62VK7GVPBc3gC2cA5rR7P9UskyD5kX+yBhhwM8nXxbpySCqM2fDkAi28K1XUOtMQvkHAqeqqUBBRj5CXEfEsBl/5qxxjsmgDGhYFiJRWfIaVD7WV9aBxKjEvHnbW3vgRj7qsQNCFJ13Rr300SjWZSqx9hT7WP4hqF/vEr1C8IfzgioOrDdjbs5pGUJAZ4JAyBlru4jnJ+wQjtCr6tGUmkitYd8VfdPAodLt7Ob1keYU1SGpflZaMPJrEmwnM7QtNYSYrbhkXVunDnz2YbXwYGYpN8xFKcochRSVXyFjC0PixaazRjV0k4pNgLeyoNFZh8ZmxS+ONQbqm1MNS/mXX5sSeku5wNpAVl0pDxJIQPLDLlGdirKzAE47fD7IWEq/i+8kweGxh5hqogeSDT6+xU0jXHrXyWdC6X/DqFm/ofxFEdaK/sC6hUvoYuGU8kXns5KW4baim2orSxOse8gVz7ZwTXnQiDr+vRsQjC75lY8uvDUtEwy+FkqEvbIn8KYLVR4V+JNnZ498TUh93yCobsN/BR3+K61ZiEEtQjy7FVXx7W6GBp+Ubur6lv9djSpAxeT/WzRB/bB/NO+04MGR/jsXzR6jG72s/kfnmcmxv7bMq4xkZWlmzh0erwM2o+deiDNeCJPVnbs2/3ZlCR0BvClzCY33gnmwyXkLj745j7a7JHfgND9uvYg5G34ev31foyKV2z5LfV8x6GnEVUBzZ2qP2SxCSOzBrBE5buPU8ve997+98Vld3a74FG6cqYqV6FuXR5j45DEH7vxAxVHzZSm8ADVTV8GezHzykHBFQGD99pEzkxWBJTH0HjerSqAFp1y6KbB6ePx7H9LrIS2j6ctj3NdY3UrX+LzzIMZG3JGIxpeTH1kWivYEhjAuYwtZOSbKGEd1kK1ZHSxXDWm+wL5ZMF1OFzmppqNzW95liU1xfxfoIVY1DDORESjX1qE42ShNtdF3N/TRyqX9AmlCNLkYNCgzkBlyThVnsxBgKoNfH9MVUb3IbW9gveFvtOI2swp1Df2AjEvpOzMwLuUNDrVUeu2dUdajKy+KsnBYe0JebSIILwRyYCqr4sqYDSfiezYqcVwwEzVMOUFDIaCknWRX/cht/n5eIamUZJR5a+ZeBkDdTygOZ59F4JOvjBFo7sDX0wB7StP3RGJR3JW6XJJKdktXqsM4Y0NvB29S+sN7buIzMpl592F6IFGlyOmAIqZV9AJavDB5n/Tcni/8wjOUztY2LUvYSU1BeyIDmJ1IAcJlsr5D8Jdn5Mz+MU788dWhrriIvqnNglLQepIs/2aKwJTCwIBcFfuhrJjFPJhibn1NXiCqoYkNGxSuzDkw7l7dUXMTAj+lzCaARcoSVGXxtFULtDSv4Ivqgxo5eDMf/SIAh/ZCKg6ssGTGV1w2Be2LaeSQcEVJM1BYyt+ZpvkjpWTToct6uRGx17APBYWn4oGtUyZ2mW4lNiewt+49/CE9kZjFAcrX57HlzzNav0d7G3ZBTwUdR9BNuo7m0wmAgqKpBkPM4GbIkdS3QOZ5l/B//NSKO/5OSQMI8XGm1UqRrYTexHsmh8AU5udKAokT+s9VIomPYF47f0dpFjDwk42WuKnN2cYLKiKKENEvUeZ9wDquMcVQwO7uFnXcfu219v5VCXTIGjJq7jaM+Prg08np3BkICPyBlnXW/80Glc91UDw/weSvdsomBIVxSzEITeT+RQ9WFPrXuKf2w8A13qV83n+DVR6WM/UsW9L0/Hr6jRHzBDpdbrmZeazG3pCTjd0fdRLdvZpNdjDxOXGTQS6VI9Zn9sS1bKvnP6ZG3rZUVJpcIlhYJOjzO2qvJlcj0/mIyUacIHTEOt03AXn02mOvbzD1ODev5RXctce+Ql11Pkg1izp5A/eVqf9RcNRZYxKaHkfYMl8pl4KpUK9vwDx9b7MKjiG0wB6PflZmmNHUu2T3Xu4HXdvfyl8Z9xH0tbqv21bNTrqdbE+UDFTtLp9ExxpnKE20Ptrxt6dCyC8HsmZqj6MLu7BnewAZAxtAqoQjMXqkD0wY69sQanVoMiGxh4QJ6OyZLIu9bQB9r1DVWYwyyndcRRngRm16ynKr314cc7qOHGvBzSAo0sjuruIR/Im/lbfg5HBmuZEObxeYlDqZe8zHXVx1BgAg712TiirgZn4viwjw/RpjPSYSbTGXtdqHpNCm8EpqK25jE4Qhu9zopeAXUgPjNULreDMp0Kswwmc9uHDP9Z9SVmTRW+2gGQGt8DX8rVHlBpkCLU3zqQYtCzzGCgRvLF9O/bWRN8No6tr6IisbuPRW6t3joY6nfiLelYIr8g9EW9bobq6aefpqCgAIPBwMSJE1m1alWb7RcvXszQoUMxGAyMGjWKTz75pMXjiqIwb948srKyMBqNTJ8+nR07WhZOLCgoQJKkFn8eeOCBuL+27vaX8mLeKy7lrIbGVrv8PkuwMrpff25NjT6HamfNNv6Um82l2YmtHjObrFxTY+dvNbUEvdF/YOd4gxzl9pCjaz2LojNYqNGoaVDLYZ7ZcU7FTa1aTUAd/ttlqVXN2sQGdgdjq6Rd4FMx2+FkgCb8jNDw2i95Tz+PYyv+E1M/AKXGg7glcBmfpV4UsY2kawqq4xNQVdYVc0puFsfl52A0t136YY7yJZdqPiFYVxSXvvd3XZaRWXnZ1Ks7VuqiURvk8qx07k3v3tyhTG+QqW43+brYcgDjwZU6mJU6E2vce3p6KILwu9WrAqo33niDG2+8kTvvvJOffvqJMWPGMGPGDCorw28rXrZsGWeffTaXXHIJ69atY/bs2cyePZuNG3/7Leuhhx7in//8J88++ywrV67EbDYzY8YMPJ6WP2zvvvtuysrKmv9cc03PFNqLp6SAl4H+AHLQ1mrJT2tOQ1EFiaWOucfTgC0YxCyHX7I4qyHAuQ0OcHuj7uMD65lc5LuJ6tzWie1DEg/ireIyHimPfpYN4CR3Cm8XlzFVGhj28cTAZLxVx2BURZ8/BfCDbSY3+q6gLH1K2MddOjXr9TqKib0e0o+V72IZMp8S1aKIbbabzVyTOIw3jfEJJOyNNSQGg9iCcruJze/adDyQnMSv9bvi0neT0LKjjEmWSbB07DiXVFsmg3w+hvj8yMHY89c66nPbHC703UJJ9gnd1mck2wcdwp9zUnnBGL8dn4LwR9OrAqrHHnuMSy+9lLlz5zJ8+HCeffZZTCYTL774Ytj2TzzxBMcffzw33XQTw4YN45577uHggw/mqaeeAkKzUwsWLOD222/nT3/6E6NHj+aVV16htLSU9957r8W9rFYrmZmZzX/M5p7deRMX+3KDXIq+1QzVIRlH4NhxC4bauVHffgDJ/FhYwqMV4ZdW3ITyd3zu6OsqrZc8fG+00GhpneScYE3jIL+f/v7YZlgS/UGG+P0k6sInUmdzLNrqyZjktpex2rNOZeM97SDqEsMvLG2lhvOzM1lkiy1XC8DprUNSe1CrIwcIu23pLE1y8r0hPmfY2YI6vi8s4f3C9v+9vzdLLEqwUuKK7wyVz+dhSVEpK/cWk5tc0KHn5KT0492SchaWVeBxd1+19A2Kix8MZhoTUttv3MWOHDge2Z+A15OM09u95SMEobfoNQGVz+dj7dq1TJ/+23nvKpWK6dOns3x5+IJzy5cvb9EeYMaMGc3td+/eTXl5eYs2CQkJTJw4sdU9H3jgAVJSUhg3bhwPP/wwgUD3HpTaFT7zV/GW1UytRsZ4wAxVuuJirrKCEz1Lo76/zx+gTrHgVodf3qnSGCjSqGlwRr97qkz9Jqb8F6jwbmv1mGHfspIJD4oc/bLf4qTLOdb7EEV54Y+Wucl+D5sMl5D+67tR9wGwS16EecA/KXSHrx1vMySS6/eTHFDCPt4Z51eV8kFxKX9piBzc5Fn746uZjNEfn11dHo+basVGvSqx3baTPCYurbeTJsdWp+xAbqeTMiUZu2LC1M6yYxOjyYq8b9ehy9F91dILlcWY+v2HKt/mbuszkoNSczCU3Ym76CK2V8ReWFYQ/oh6TVJ6dXU1wWCQjIyWx39kZGSwdevWsM8pLy8P2768vLz58aZrkdoAXHvttRx88MEkJyezbNkybr31VsrKynjsscfC9uv1evF6f1vGamjo3iMrOuoF7GxNTWGg29NqhsrirWSediGlwVTgkajuvyd1Kmd4n+fo/umEm0O8OCsPt0bNFRKET8NuX6ZPoVZlJSNMXSOt2cLT5nwaJQ1/cTVia2NnWVu2KbvYYyvHrg0flHnVBholCU+MR5MkBDx4VAaSpfAB09iEUZy7qoy9qtgKlQKY/V76+wOUayOXLxiSOBRv5SzMEY7C6axq2whmep9lWJaNT9tpO8WbwnjnJlZmxjdvyaEyM9n7FDqNiu0RzjA8kKRS4cSABXfzztXukOnzU6WykBnnwqbRkCSJG61fcbD/E+pXXgT5f+3pIQnC707Pf6f2AjfeeGPz/48ePRqdTsfll1/O/fffH/YU+Pvvv5+77rqrO4cYlQl+yAy42O1PbDVD5dWpWGiz0ghcqSgtDk7uqI31KzBkfUi9eiyEqbEsqcwoshZnIPolhH9XbCNLqWLLuNYlDUzmRJ5NBwhwutcddUBVJn2KIftXagMjCBf6vWKt4fvUPGb7NxM++6ljniwvZFBwFz8PCL+c3LTNXy/Hfm5gU6K5pI+8dJ1i/4Vf9edR1pAObI+5z211mzBkvYHH1B9ovStzf/K+g61lb2z5bwcqtJdgyH4NnZQIdDw36eyMUdSrncxz1xN7ONsxz1ZsI1upZNvBid3UY9sGmt0Mqy9kZenanh6KIPwu9Zolv9TUVNRqNRUVFS2uV1RUkJkZfldUZmZmm+2b/tuZewJMnDiRQCDAnj17wj5+6623Yrfbm/8UFcV/p1JHKErbS0M3NXh4srKaoC+r1QxVUKPmoZQk/pNsxBuIbrmszLULbeI6nNKvYR8fxi04tt1DgSn6ut96JVRCQGNoXVNIq1YjO0bit4/G7Yt+yW+YWyHPkUBehK+ndl8BTG+MgY5WCc1qaiIEObqmgIrYA6oNqhretFqoUEcOZvUGE0gKMtFvGthfqbMIbeI6PJot7bYNao24JQlfnA8kLnNWoU3YAKbObf8v0svUGxop9cdesqKjTEpoS4jBkthtfbalNDOHM7IzedgoSicIQji9JqDS6XSMHz+eJUuWNF+TZZklS5YwaVL4QoeTJk1q0R7gyy+/bG7fv39/MjMzW7RpaGhg5cqVEe8JsH79elQqFenp6WEf1+v12Gy2Fn+62zNLdzLmri9Yu7eNXTlDjmON4TBqFSv6AwKq1IQsTnA4ObnRidMV3V6/wxqqObVazzHe8MHMNM/X3Kf5N4ml30V1fwD9vg97XYQ6Vobai/GUnoNG6lgRx3Duqv6VT6p+YVSEM/bmKENYu7uQU2IsgKmXQ69FG+GwYpfRxKy0UZyVHn63YWd8bajnntRkflVHDlhqJRdj+uczJz/6r93+htorOK1ax0x3+7OdT6cmM6Egj6fN8f0RlVpXzrnVak5p7Fw5kDTfGbiKLiBR0z3zU4osY95XgNRojX9x02gUDD6cLXodu3Qyjc76nh6OIPzu9KolvxtvvJELL7yQQw45hAkTJrBgwQKcTidz54Z2ol1wwQXk5ORw//33A3DdddcxZcoUHn30UWbNmsXrr7/OmjVreP7554FQXsD111/Pvffey+DBg+nfvz933HEH2dnZzJ49Gwgltq9cuZJp06ZhtVpZvnw5N9xwA+eddx5JSb+PH3ThPPRZKEl7wVfbWXhJhBmgk5/kH8U/UlFfj0HT8oMrwZrBQ1WhZPEytwMSOpbAu79RTieXNO5gmTl8/8O9P3Oo5huW143o9L0h9KFzWVYCesXGLRFqTT2vzCdbX4q99L+QGd2JdLp9M0faCDNHWq0VHaAKxDZz9GCaGjUpnBNh1khvTabQEsrhCQSDaNSRz8Nrz1CfRFrQRUZCRsQ2tn07Jz2SRDAQRK2Jvj+Afi4XZzbuZA392m2r1qeAF5xKfMsUJLg9/K1xN9s12k49b6SSSrKzEYMzvkuQkdQ7ark6OxWzInO/Kfrjn+Jp7ODD+ccHjRzsa6Bs+was4+J1wqMg/DH0qoDqzDPPpKqqinnz5lFeXs7YsWP57LPPmpPKCwsLQ8dW7HP44Yfz2muvcfvtt3PbbbcxePBg3nvvPUaOHNnc5uabb8bpdHLZZZdRX1/P5MmT+eyzzzAYQom4er2e119/nfnz5+P1eunfvz833HBDi7yq37OKhvAf8u6Am+PfPh67QQLpulYzVKi1BFChQcYT5dEwUlNBSE34pObVBi8fpyaTEthNNIepeH0uNhhCOWxGY/iALwU7WVItNe7ok4n1StuzYJI29IEXawHM701avCod54TJywNIMyXiKTsVRdbh8gWwGaMPcM6yw+BANRuGDonYJispj2/3FmNUFDweB+Yoc9CaKP59hz9r2g8QJiafytJVwxgwqv3gqzMC+85l9Klb59y15QLHfxinX8bKYgno+srlVXUlbDDokRSFBGts9c3iRaVW0z9YQG5gHSt3rQERUAlCC70qoAK4+uqrufrqq8M+tnTp0lbXTj/9dE4//fSI95Mkibvvvpu777477OMHH3wwK1asiGqsPUWWf8v1iZRG5fG7qfXUghpQNOgPmKFCkvCiR4Mbf5QBlSPYSIVajTfCbqrdWi+fGS1M91dHdX+v28k/K6rwSBJJlvAfOvekqdmty+Zi+y+M5KSo+jkn14IaEw+owufPbDWbWZg4DIvRECb1vmPkoMzfa2pxqSTSrOGXDi16Pfn2HEx48Xm9EEPBzdWqsWwPJpFrzYnYxmxOQLWv3ESNszHmgMrhr6dcrcbTgd11Bf5irld/SELtQKLfA9pao6eWYo2a+ghBfiRlOg1eWU+lpyxuY2mLyhPgyfIqaiU9mk7OpnUlR/IoKFsHZet7eiiC8LvT6wIqoX0u/2/LJGpV+HwVq6eRt4vLqFfpOQNV64AKOCZ3CC51I/N9jUSex4jsVWMJqxJzOEtVxrQwjw9XZTG49he0uuhyggJeL9NcboKKhBThoNtGtUSVRkOjN7qCjMFggFKtGlBHnAXbZU3juyQn1hiWp7weF6c4QoGr0xa+grdKJfGh7nZMkpfSuumQGH1u3tOqcyjxu3kvc2TENiq1Greiwyj58Lpirz30sbSLG/NzOCFQSXtzG2me3ZygeYeNjWOB22Puu8kPnk1cm5fDYZ5GJnfieZ+YHXyblMFJ/p2Er0YWX4rbxVS3mwo6N5PW1fy5w/l3QzabqCX6rSSC8MckAqo/IM9+AVVADj9FpQn6GOL300BotkAfJj/Go1KhqAI0RHvchhJErSjoIizxDNPmcZi9gdUJ0f0G7labucT3V0xqmScjnLN3UUMiA3wbqbBFV2064PezuKQMjySRbA1/plq+dQC+msmYrf2j6gPAHYQ7/JdjwMddEYJDgG06I2qVgsZRTXbUvUFD6j8wp3qp9z8PJEZsd1/CEBqkAOe56mLqD0CR/WgUBZ26/dmhao2fJxMT8NFA5JAvijEEvBiR0Uude8+lSBYG+UoxE9u5kB1Vq8/lIt/N5CQY+Ee39Ngx2lHT+Gf1MyhyCU6fF3M7RwgJQl/Sa3b5CR23f0Dl9kUIhvYdx+JpCqi0rd8Keb7rcey8mVRtQVTjuLHWxPo9RRxpGhP2cUkXCrTUUSZz1/r8LDUk8J058s6rTMXCUJ8fgz+6oNDjdjLU52es14c1wpLXoMSh+CpnYnFHvzRl9wd5R3MQb2oPRd1GIcebMq2cm53JrrodEdt0iLoOldaOWdf28tv7CRq+TnaxW449OfwCRzLr9hQxUzO63bb1Kh/PJyXwtTm+JxIc68tk1d5izg0e1KnnHa8ezrsl5Ux3x7bs2VFFHhffG6ystxV0S38dNTF3CLgOwl83kU1l0S3VC8IflZih+gPaP6ByeMN/IFU5yvjeYiYYNICHsEt+0wJ7GC/vQmcfAB3YmXWgoCLhU9QR6yoFNQbqVCqcSnQ5Wrvqd2Pq9x+UQBJwSdg28r7ZEMUXXekHr2TgeO8DmFU+3oqQ+5Neu5bdhvPYW58LbIqqn732IswDFkDQCJwbsV1qANRKgKAv+gR4RZZ5r3QvHklFUoSZvSZm/0RqGxrQ0fldngfyyRIeRYta334ZhmxbHmdvbcQcjO/RMz4ZGhQjaDv3eqR9Y1b7u2eX34ba1Zj6/Zs6eQQwp1v67AiVSsVY3U38uLeS3XtrmNAvcg6eIPQ1IqD6A/L4f1uWcPnCB1Q7G3ZzZ1oK+V4F6sIv+c1yvM1B2g18XzMaOKLT47jddi8biu282C/8zM13iQlc3i8XS9BG+NMY2+Gqxey1YCDyrrFNJgurg3nocXNYFF1UuRvZaavEoLIgqcIHH1q9mSAgK9GXTfA4a9AE9GiUtmeM7q4yMiSwnZ8LIh8Z0x6vx8lAf+h94QxzqPT+0oN/oqyiDrMqfM21zngm6Wa+r76YBQPDz1jur19Cf46qraMuDoHc/j5I+TMX7j2eWwYN7dTOUpU+NA5NoHsCKr2jCrPXQpb295OQ3uRc/Q/8S/8QW9ccCUe91dPDEYTfDbHk9we0/wyVP6jgDbRerrEpKqa43Az2hAKpcEt+a40Si2wWijzRVXqv1LyDPuM9HHJV2MeNhsTQGKM863eQ082K0s38uyL8/QHeT8zgmXSJL/SdK+TYpLCxBGP2W0ipkQ8+rqCesf3zOT8v+tmUfi4P64p28E5J2wdF+1WhPgLe6JPE3c7fnmtoI18LYF7j3ezUn0/S7g+j7q9Jkfwh+oz3qA+2/37SmUIBjDGGIDWcnd6P0We+TZ0c/vzPSDbarBybPpJ7E+NT5LQ9R9fXsaJ0M7fYf3+HsGfn9sMkeZDdv/T0UAThd0UEVH9A+89QAWGPjhlhSOGpiirOrArtIgq35LfE6OWBlGR2+oqjGodLtxpd8gr8hP+tfnzaJBq33Edyww1R3T+475y3piAjnFR9PgHHQRiIXMCyLarGWnKcCfTzRf4gNZtCBV49UZx32CTgCb0Wn6rtJF//vmrtsje6JUyA2sZyFlvNfGCytpmvBaFdompJxu+Jbpfk/hrUa9Elr8CrtFG9fx+jOQEFkFR+/L74HH0DUB38BV3SalxyZaee57KmU25uYLc2tlpjHbZvV6qsi+8MXTxkjjyMKfk5XJKrY2ehOIZGEJqIJb8/gIoGD9srGjlycGi7vfuABGyvX4YDYw5zGt4Bx/HT9tADujC5NINlC8mOKlKM0b1NZtfLOCQTeRHiDJuvmr9rXkPnNEMUxwoH9wUVgTaCkNEJx/HFygIyM6M7MiTH4+Wzyl/Yo4r8/Nykfny3txiDoiAHg6iiqGAe2Pda/FLbs1wvJWexyzeKIyVv1DWvyuwl3J2agi0ot1sC4LmEBn5Mz+MM9/qoiq/ub7bdQwNGBndgRlJtNjO6oB9ICp+7HWTHaTfZn+obqJP1jMnq3G69g5KG4i45E5s5fEmLeFP5QrOIiv73F1Clp+ZiDapwSzJrN3zMoPx47sMUhN5LBFR/AMcv+I46l583L5/EhP7JLZb8gLBLfvQ/iqrEQ3j4wW/Qa1RIYWZXjpdzGVu1hq+zoqt3dKt9O0bJR9G+pb0DmYMNXKr5hKpAdEf4rHVv5dnMNHIDPiLtGxtR8zlLdE9RXDwJeKnTfQS9oRkJfxtBm8WcgGlfAUyX24EpigKYmx3b+V9aCilBmaFttNtqNFOqs5MVob5Yh/j8THO6oJ18LQBJ0qBIEp5g9DNiTa6w7yGdWnYa2v/6mPUmFCQkFGrdTrIT4lMtfE5jKQODv7JB27l/o1xTIgc1JpEebQmRTvpQvZsXMtM4WNcYcyDbFa5xD2V67ZesiXL2WhD+iMSS3x9AnSt09tvnm8oBwgRUrX8bf3Pbm8z96lR0aZ+FXe4DYN+RKlI0R6ooCkYpVFlcH+HIFo9G5qHkRJ5Nji6ur/LXssJopEgbebbBhJeBqjJs3oqo+ujIsuL+eUieKAtglvkq+dRiZrO+7embAYYpeMpOIaMDpQciSZYN/LOymv+raT8oOzUwgG/2FnOcL7aDnwEMhPKhIr0f9qdSqZCKbqdx23wMqvidmamTQ2PQmjo382PzV/Kx/jaeDsyP21jaUqhystxopFETQ+DchVJyJqMFEmrW9fRQBOF3QwRUvdz+x8w0VUX3HBBAef2tA44aTw3lrhIktbv1OX5NNNEHVF6Pg2q1ikZJQquPUO1Zp2Vhgo13bNElc48MJvNAZTVT/JGXYTZIlZyUk8Vzts7lzDRZ3riBk3KyeCEx/IHFEKoofpttGNcmDKXCWR9VP/2DVm6uqeMIX9szJ4N1/cmz55HmjX4JzCmZ+TR4KD9rx7bb1qxNIFWW0fljz2NqVPlD74d2EuGbnMNarpU+wV9XEnPfTRpUHupUKtSG9oO6/WlNFjbpdGw0QiAQ+b0QL7MbNdxXVc1w86Au7ysaGSNCte77e7fFNcdNEHozseTXyzn3K4ug2rds5zmgmKcv2DqgmlO+l8PKa/nEY+dTQ/i4+s3kRObKQ8iX1Ezt5LiqGso4IT8XgOXG8AFTsjWdi+vtGBQFn8+LrpN5Mhl+FYc5XSw3Rq6CLms07NFpMUSox9WehkADe3Ra0uW2Zwo+TFRA7WK2HGRYFP1kB3RMamhkVWLbOTqTqhdzo/55VpbMhk7/q4TUWAZzpf8GDk1Kavd0Q0kbCjxUgdiW/FweJ8f3C1Wa/yTMjtJwzlU+IF9bwuba06DNhdCOuzjXhEtl4T+qzv2SoDObOSsnNEv3ZX05manR5eR11Gi3l0FBFz9bC7q0n2jlDR7DXdYR/GiUuGzT95w2bnpPD0kQepwIqHq5/Qt3yvtOQj4wgPKGqRKeLiukux38GDCit4T/gPMZEwloPNRFOL6mLY1OO5KioAbMhvAzVEnWVG6os4fau52dDqh+STqG1341MSZtXMQ8k+GWIby8pYIGoitAeLCcznGlFRSZJrTZTuc6DIffi0qJXBOrLbush/K5/wL6p4ylrZ7cWi27tBpq5Pqo+gFYXbUU88B/UakZCRzeZtudJhMfWweh1avbHFd76hurUCkKsiSRZO1YPtRnFh0+VQIDGn5leAx9N5GDQZreyYmWzh1FZDMlkeMPYFBkGhpruzygelI7F9ldzp8zRnVpP9FSqdV8kzqEGtbyyd7VIqASBERA1et5wxTxDARbBkDhcqjwh2Yc3Io+bFFPgIlpx/LOj2YGZHX+FLdExcDPe4qoUUxhE94B9PsFWh63A2tC54pVbpX0fKTLI90W+cMt2ZzOCK+XvSpfp+7dxOaXGe/1EjQnttku0XsKNVUODFLb7SLZpk3nVdUE5iaNaLPdKnUF1+Vmc4innJlR9QR2bx0qXR1KhHIW+9uYmMHHbh+JisK8KPsD0Pph/Z4i3IoKg6FjS35fWWCLPoG/uKKrg3Ygn9fNqr3FBAHX7M5V/lep1bxZbMeGk8JoC6d1wvcqHfW6fC5LjO4Myu4wLeckXl2bS4Nf7PITBBA5VL2ef7/ZKLcv9P8Buf06VGs9FXxmNlGtDWKIsASTr3iYE9jGuMbNnR6X1+tGUSQUKfJOMkmlog49dpUKt7PzdY42ud/F3P9p9vi+i9hGu+/YG70cXZ7H+pRZzPHeyaqsc9ps90/3rezSn4excGl0/TgWYxn0EDu8H7fZzqSxkBAMoo/hbL0Z1cUsLKng+vqGdtvmmAvw14/HEIhmIfM3HrcTv6JGRt/hshLjvCbObGgkORCfauEuZyMOxYCkSJjMnd+56tpXkd/rbP/rFitf2rOY+z+FT7F3eV/ROmfUcVjrRpCzdw1eT+y7QAWhtxMzVL3c/st7TYFUqyW/MGUTFnpLWJKeyuiKxogzVMn2TTysfZ6f3SOA/+vUuBpsQxjgfZV8m4bI4Q5Myy8gqHazQPaR36keINHnoipoJFWJPGMQ0Ov4nzGDepWVKzt5f4BtwXp+tvgYFiEPrIlKkpAkJeoCmHqfHUlWY5Paro802TqWaze/zGZt9LMCVn+QsT4vPkv7idnDkkbjKfNhyo3tUOBGYx5HeheSadGwooPPOc6bxnjHJlakRreMeiCnOoGDvS9i1MKWdgqahuNRGUEGr6trgxy3x43Fb8CvCpLewQT+njAozcwXhr+RSj2b1x3G8Ekn9PSQBKFHiYCql/PtN/vUNFvVaskvzC6/gbIGu9tDwG9BG2GGyq4O8K7FTK3iov3T11raVf8r+owP8ekygeMjtpMVA+DG7uv8ESO3VpUxxrWNFYmRZ8GcCancl6lHkZWoAqrt7i8x5i6l1K8AR0ds90Cql58M+fy58WcOiaKf26qqOdixm5VD264Npd63XKaTY6jYvW+5V9ZE2H25n4z6dfys/zOVtZlA9Fvkd9v3oM94H1mXDszo0HOC+8an+KI/Zmd/hfZS9JnvoJeSgFmdfv6daYMoUxI5199AVy5yeR12VpSGZoUD1viVjIg3SaViq20Msn8lO7a8KQIqoc8TAVUv598vePIFQv8faDVD1TqguiZogvJKrvTlIUeoQ1WmOJmXlkKeL8AlnRxXiaMIXfIy/IG2c1VS6v/O7iov2UcO6WQPoAmGgjC1PvLsUZLBSsBVALIOWZZRRTjgOJI8jwu310Z+O2WLJCk0y+eJ8vBc1b7XotK1HeRomwKqGM642xWspNZswtNG/a4mOp2WBMmFU4ktqClxlKBLXo4/0PHNAcq+sh2yLz4HEpc4ytElrUIJRFckdLtBi0NlZ28bM6Lx4GqsJxFwKXpM2ujOoOwuyzIzWOhPZ5h3Xad/RgjCH40IqHq5/XOomv7fLx+YlB4m3yZrNGUNXiorEsmJsOSXbk7nKJcbm7/zOSw5DdUcXWtGrW37uXPkb9Fo9iJVp8CAIzrVh2ZfXpRKG3npKsuagnvvFQD4ggoRKkREdHlNBQc7N7Iy5U9ttrvAmcUj5d+xZcApnetgn6bgUBWpZtc+NUYDp6eMApWRxVH1BMvUZXyXnspspZ5T22lbQQMX9svFIMPSKPsDyLBXcmytCUnT8QDh+ZQk/mzpx3CdTOfeGeEl1Vcws8ZAQBNd3bMc1QmsLxlD6oCD4jCayNyOegBckpH25xB71rTRZ/LVyh8Y63HQaK/t9MYSQfgjEQFVL+cLE1B1ZIaKEx7kPeMu1n62lQERZqgGJQ/k6YoqqpQEFEWJuFsvnHy3hyfsW/hZ33aezjG+bxim2cy6uuOgkx+bLyS48KpSOUbVwPgIbQwaifd1t2PEi8d+CIbUzh2SrOngzJFZbSNVltFEWQDzHUsjb0nJjJdcEV8LQMCWylabHYLR7VoEyAyomSh7SLO0v5xkMibhVKn4reBAdHLcHh6zb2VjG7OJB5INKeBTaFTiUy081e3mwYbtbNNEV9NqmKYAZ6OHBE/XHj+zrWYTD2ekkRrQc2+X9hS7Q0dO5z9vQ75Sy7oVHzJuxoU9PSRB6DFil18v5+9ADpU/TED158//zOul16PSVaCPkEOl25cQa8AXtjhoWxRfKE8nqG77A/RrMzyalMgO5+5O3R/gZ4PM12YTPnXkD1y1Ws0wqZAhqhI87s4njGvkpoCq7cCwaXkKf3S5TauMAd62WXBq2v6wzrZm4KmYib862qIJcKLDwH/KK5mobz+wyE3qx8dFpXxYVIoid+49sD953/shoO54gvn4pBNx7LiVAunsqPvdX9ATWrb0dWIM+zux9r98qr+VAUVvx2U8kVQ6S/nRZGSjofOHbPeE0rTJAPi3ft7DIxGEnhXVDJXX62XlypXs3bsXl8tFWloa48aNo3///vEen9COFjlU+/7/wCU/f5hgaEf9Dmr9tSApEXf56ffl6xjx4vQFI7YLx+Nz4JIkfOq2i3WuMgb4yWDjAm9Zh+/d5M+1XhS1i7xhbedp/TkrjXo13Fa7i8y8zh3l8XhSI3Z1JmdS2+bM0c9mKx/aBpOgkaM6zPaUhgABtYOcQblttksz2kiqHYVR8hIMBlF3sATB/nZrBuAINqC2td0XgMWSiCUQqm/mdjsxmjt3Bl4Tt8eOU5LwtxNg768gWMvFyo+k1ZVCHI4IdnnqsKtUeKIMqOxaLZt0Oqr81TGPpS3ZATP3VVVTrS7o0n7ixTxyJnz9JobGFQSDAdRqsfAh9E2deuf/+OOPPPHEE3z44Yf4/X4SEhIwGo3U1tbi9XoZMGAAl112GVdccQVWa3Q/eIXOaZFDFWi55KfTqPAF5OZAa39PlJVT6/dzhz8Y8XBkn97A5JxhBKQgH3g9JJg6nv/yuX8TVxbkcaS3hsPaaDfOb2O0p5LMlM5/yB3rcpGIg92Wtg/uLdSqqdGoaHDVdrqPYq1MsVZHUNv2t8rKhFRW4yVPI3Fzp3uBkxvdpNHALmvbFbiNkp9VhqsAcLrmYLYmdrqvRcZzWVs5k2dz2goR9/W33yHCbmdD1AHVV/5NXF2Qx2RvLYd28DlZrq2cqH2VjQ1j6WzZjnCWen7hqn65TPLaOzyGFs/X1/BhTiZTfLs5OebRRJbgk5nocLHO9Pvd4be/wYcex5FbRlFvsHPf9p84aVgsNfUFoffq8JLfySefzJlnnklBQQFffPEFjY2N1NTUUFxcjMvlYseOHdx+++0sWbKEIUOG8OWXX3bluIV9wpVNaJq1MunULa43UxTG2qs42lmDXzZFnqHS23DrnPi1Hhq8nVvK8u1LGNdKbSelHx5I56919QwIdj799h75Ym71X4I6se1K7jdXybxYVkGq0vk+/q/axzPllfS3tj37mm0cjK/+EMzK4E73AfCsMoeH/GegSWp7F5zeYKZcrWaPRkNjY11UfRVqn8TUfwHl3m3ttlVrNDxsGcid1kFURnnwM4Bv39Kpro1CrweqUQd42WblW0N8yib4gk1jiO5gaavGSkYggLGTy9+d9av1EK71Xc3ytNO6tJ94MRjNSIYBKIqKz3b81NPDEYQe0+EZqlmzZvH222+jjbBra8CAAQwYMIALL7yQzZs3U1bW+SUcofPCJqXvy3UxadXU42+VpE7QD0ooV8eDLmIOlUalQVN+DXYXIHdu+/Yp3izurPyeVRmT22wXbe6RLMu8r8pDRsu17VS9PsivZ2DQyy9hzjRszxiPh1Q8/GppO5l9eOIEvGVGEhI7l/Te5L/KeAKKlvOsbR81olKrODE3G69K4r/1hWRmd36Z3SdVoDZUodV0LNH8lWQtqF1MkYNRH1E825PJ/KrvWZl1ZIefU6328mhKEv18Pq6Kst/9nejN5M7yJazIiG758BjjWG7d9T7rTAVxGE1k22Q1H2n7YUqMz4HQ3eGcQVfxwMeF7M5oe7ZYEP7IOhxQXX755R2+6fDhwxk+PB7HmQrtaVk2oakOVei/xn0zVAcu+fm8dr41GdErCh6PNuKSnyRJHBeowe+vJ+huBDq+BKEOeDApCjpt25WeFa0BP+D3d67WUKPPhbH/k6G/qNouVeCXQnk7AW/nj8e4XvkrKr+De5IL2mw3qHoJG/S38WvZCOCrTvXh8nsxDrwfgCBHQzub5a2ygk5RcHqiOwLliYoSZMlN8qiOzbRoPWNx+T0owehrIqkCXoyKgkHb8SXDDHMWJzqc2ALRzSgdSA540QIaXeePnQFQG0Jj1wa79piV9Q0fYB7wGYXBU2jv8OrfizPHjqPo0zc5qeZHirY/S96QsT09JEHodlHt8rv44ov573//2+p6Q0MDF198ccyDEjpu/4DK17zkt2+GSqdp1QbA7qzkxow0rslIw4emzWTzWwL/4jHds8j1nTugdnHGDQz1vMSGgovabPefZBsH98/ncWvnElkbHQ3o/EbUQR0JurbzrzYYLSw2plPi69yRIYqisErv5UejEbWp7SBHo9Fgk1zog50vQml32pHk0LdioqH9XLL/FXlZVlhMBtEFBuN8jRzttZNk7ljNoCT32XjKzsCkTouqP4D/pV3PEM9/2TxgboefMyBpIPdX1XBZXXwKe76Vfg39Pa+yccCfo3q+2hgKqHRdHFBZvfXo/EbSpN6xyw8gyazjTMvPHKbaQtGPr/X0cAShR0QVUL388sv85S9/4dprr0Xebyu12+0OG2gJXWf/XX6/Lfm1nKFqlUMVcHOwx8MobwBQRZyhAvjeaOJ9i5kaR3mnxrXb9z1y2lJqlZI226n0oarVnf2I0nvdrC3exqq9uzHq2p45eTI1i7szDXzfyarTTr8Hfc4rmPJfRKUKtNl2m1zOxH653JbW+Q9/rcvNhr17WPtrEWZt+7MxXlVoxs3vji63yKiE8tv0po6dE/eA517W6S/DFOXBzwC7fUshbQl1tP1+2J/OGAoYjTFUhd/fr54l6NI/o47O/XLQpMRkYnbqKG5NiT6w7IgbKstYW7yNc4LxOcOwuxQPPpr/S0vhMf+nPT0UQegRUdeh+vjjj/nkk0+YMWMGdXXRJccKsWuRlH7ALr9ISelpaiP/LavkqYpQ3lKkHCqA55O03J6WQrFzb6fGVR5ciT71GxqCbX94HZp8Eo3b5jGAizp1f68rFLh40LdbcNSqyiHoykfdybrTjU47yW4bVo+VBH3bgY5Wb8alUuFRdT5h2buvPpIfPaoOlEHw7UuqDng7H7x5vW6+tuj41mhA08Eim2Y8JEkOAu7olhgBquSV6FOX0hDoeEDVFPCZJC9yMPZimpXB1ehSvsMpl0b1/EBCBrusdnboozsAu6O0gdD7QW2Ibgayp4w64iyWmE1s08OP6z7u6eEIQreLOqAaPnw4K1euxO/3M2HCBLZs2RLPcQkdtH+w1DQz5Ttgl1/TGX/N1DrIn8QOTej8vP9n77zD5KjrP/6asrO9XC/JXXpPSEILARSEICggKCIoShHBAtJUREVEVPCHqCBSRBRFRREVREQ6SEuBEEhISCHtkutte5nZmfn9sXdJrs+WEBLn9Tw8mp3vzHf2srl576e8P6Ol/GaqIkclUziHsV4YjQ/E0ywK+5k5hhlkg9rCV4UnOCScX1eoms6JiYyFjq05rk+T3P4VximL8trDkcrw37a3eallHR7H6OJjZmgGj+9o4Wct+Rt7qn2RprTF7rNflk/g7Iq5vGXkL6h6Y118o7qSS2urkd3WIiC/qMhwZON4XooVPhz5mHiaI8I+ZprWBafg8bGgcSoHTZhIb7r4Tr8lsQQf6PUyq8BZfI3B8aTbTsPsPqXoexmN/rSx7Anu1X1KTUPtZM6LhvhLcyvCa0/s69uxsXnPKUhQ9UcEKioqeOaZZzjmmGNYvHgxjz76aElvzmZs9oxQ9Quq/giVyzFCyq9yGnz+Cb7nvQ5g1JTfF6N+7m7vZLyZ3y/388M7uLd3LfOk0aNClanNfM3xNxZH83NZ3hrdwlXVldxRPrYoODb8Dx5WrmNm04N57dEfOUrjRBhjqLLfHaIhm6XWyH/0TFNkOz+sKOP3IWsRtNe8TtYGomwi/5EsqVSUQ1Np5qQzBDwhS+dkBJGYJJLOFi5qvhBu4te965gjWy9KD3oD6JKKKRr0pIqvWzo/0sSd4XeY4ygs8lPvDVETnsL4cLAo1/ix+FUoxdeqKuiUCx8vtK84ZsZFzFE1prc8iqbtf/dvY1MMBVnamnt8w5NlmXvvvZfZs2fzla98pWQ3ZmONPcWSbpiYprlLWI2U8lvZvpKbX7uZTlcQOG1UQZXtc7Y28uyQc/QJC2mMgvEuIc1doQAqcebkcf3ORDtPez1MsPA7u0LvZKH4LstS1tNNAGqqL60oOBl98Aw4+sf0mPkLqrZECw8G/DSoJldZWF8nHk1XWwNlE/O3TFA0gfvaOkiYLkvpRYBPpeu5rutFtjUUZgkBoPT5UMmusX6Su5Eliez2b5BWJWSs1XuNhtPIRQ8d7sLMST1ChpedVwCQznwOl9v6e8mHlW6TbtnLic7Cuyr3FXOOPYvupd+lkjCrXniIhSecs69vycbmPaMgQfX8889TXj6wQ+iqq67ioIMO4pVXXinJjdlYY7AlQtYwx+zy60n3sK57HZI4GQCnY+QHa7+gMvP0iTKNDCZjP0B7pDR3loWYqGpcnsf1q00v3+nqISaM/ZB/WenhtvoaprJ5VNf2wWwKb+Tb9TVUajK3j7XY5eb/fJNICBLXZbPIsvV/WmWmky/3RshgretuiuNQtveUUa6HLO/RT0qHV/Q5ICuWR1GXiwEmaVnaNC3v/XaTxmT3fEirfMJ8F8XsIRtbDJXFTV/IkkEDFE9hESqPN0CTLJMQBcojnXtNUF3eHSMp6zSWT94r19+bKE4XK+pO4tnkKjY3/ZuHsQWVzf8OBQmqY445ZtjXlyxZwpIlS4q6IZv8GCyWsrq524dqV8pvoOha2NPMHWGVt1IpfsroKb9bK2tZ65/NUQ6ND+ZxX58fL9EjNXCz0c3cUdbVeuo4MxrDm6dTeshwcFwszlrH2FGaqGTytuQklGeUrSfZzdtOJxOEsWtuHL4Qf6zSAZ0r1TRlsnXhUJF18eFwhHVKo6X1Z3T+kptdj7J0+5eA+Zb3AYg56zhH+w7jfW5etnjObvPVwtNuZzV4iIte7jJj5DNN8RL+TL2jg/XdH4dJxQmMTzX6SIoB7hOSFHIlSZY5Y1wdaVHg9z3bqamdWNT9DIeezfLxZM7eoyc0umv++xXvCZfx5EufxjTfZnnTRhY1Tt/Xt2Rj855gWVD9+Mc/5vLLL8dtoZB1+fLldHV1cfLJJxd1czZjM1hQaYax2yl9hJRfpW7wwd42NHJz40YTVN1OH0nitI/RSTcYVQBTEPC6Rq+9agxM5LruXjryrAfq8M7gWu0CqisbxkwVHuKYzPE7XiCsjD0MeE/GE+SXbR10CqOPtgEIujxo0XlgKCQ1PQ8LVOj2TOKn2icJlk/Aih1uWlbokCTiefpqAaztXoNn0m2ownjgOEvnbPB4ecU3EVnKFjyiOC0KmIKA35vffLrnvS6yop+GaFPBLu0A2axGqu8zHPBVFHydCt1AM0ziyXARdzMyCVXjWvUS/EKK60KF3+e+5IOT51L93xPZ3lLJv99Is8ja9wQbm/0ey0Xp69ato7Gxka985Sv85z//obOzc9exbDbL6tWrufPOOznyyCM566yz7OHI7xGDxZKum2PP8tNy9SxJIzdGaLSU3zz/qSS3Xcw42frIEIBHmzp4vmknjaHRI0gOVy6S4yS/2qMdUoA/SQtY5T94zLV1zmqOSaWZoOXX3eXJmhyTSjNbGzt6psgyRvvnSLeeCWZ+tS87lTpuNz/CitCJltY/7mrn+MZxPCa+m9c+AD2pXiRXK4bcYfmcV8pq+V2VwePuggLaZDWVl7fv5PntOxlfNvrw58H8LSBwS0UZ2xJNBe3dj5pOsnLbDl7evpP68vzuYU/ubdZ5dkcL1Ub+cyGt0JPK8JhjIg85DsHp3L98qPbkhg9cQ1lsPPVv/IxwV34edjY2+yuWf0Pef//9vPXWW/zyl7/kM5/5DNFoFEmScDqdJJO5VMDChQv5whe+wPnnn4/LZc3jxqY4BlsiaIaxq8vPvauGauCabclWWtwudqRz39hHi1DNMEyWZLppiLdbvifT0KlEBR1Mz+jC2tlXh6KY+XUErep5Gt+U+9ghHgl8aNS1opJ7+Ml6fnVgrcEFnK9+g6nVdZYiR4/L36BS6iHS/jiEFlje57Xux/DP+B1bhaOAsa0dFNGNaJqYZv41TXN6mrmlNUq7w7pZZq1rAlp0Dq5QYaGGVDKO3zTxmCZpbyivcw9SnUzXuvEF8u9o3JNkPEol4NdNKLCGCiAjukEHLVm4J9dovNu7He/k20H3Ap/dK3u8Fxw5pYL7vb9glr6BpY9Ws/jzN+/rW7Kx2evk9ZVz/vz5/PrXv+ZXv/oVq1evZvv27aRSKSorK1mwYAGVlaMPdrUpPeowNVSaMdiHauCaf0U2cE9tNQvCcUiBMoqgmtXzNJ9T7uaVrlOBMy3ek8nB6d/gQuX5YPWoa1NuDwdNmIQp6qzMZlEsFnPLmV5E3UFQHDvqlFRknnUGaXMIo9ZzDWabrvGSy4/hG/099BMgQUhI0JWnZ5Ke7gbAazGt+hHHPG7Y9BQr/fnXpvi1LIenw7yVRwp3bvli7m/2UuYrzCE8hZtD07/DK2RYmWfU5ePJChYkN7Kiprguv6SjginpP1CuZHnNYnfjcKiiJyeo0nvH3DMRacORdeEwSzO/cF8hCALxhV/gqXXX8RvtUepbvsCEeruWyubApiAfqvPPP59Vq1Yxd+5czj77bJYsWWKLqX2ENkgs6Ya5R4Rq+JRfOSIzMipuLRdFHC1C1eUweMbjZivW3fB7Ugm0ypeIVbyBcwyBFPAGMMWcC3ZMtR5B+kxvhLeaNvON6NiCal1ZHVfUB/lpWX4P87fDL+GZcC+tgjXX58vqvBzZOJ63e9bmtc/5PVHe2NrEVTFrESdJ8SIAUp4RNwBTzUWTdcl6BHlCz6u87LyMr7R9L+/9AFrj3ZhVL6BWrRnTz2swupT7OzPU4ub5NUVbkKqeQit/o6jr3F3RyOmVc1lagKmqFSbF4ryxYyMPtO6dCNh7ycKTLuD2sirWuRzc+Xg+Pbw2NvsnBQkqRVG46aabmDZtGg0NDXz2s5/l3nvvZdOmTaW+P5sxGCyWMlmDvgAVnhGMPc9R6vhbSxuzenNF2oo08sdgtdDDlTVVPOvusnxPnclenFXPoVQ+M2r0CyDk9BLfdA3xjd/F1B2W9xD6bBwMx9giqcwVRE/XIOj5if5gKowv46POsBbNSYgCMUkkkcmvWFzKpnAADoudgZKzsBQmQGu6jRfdLnaOMm5oME7JZLzQRZneOfbiYWhJtOOsfA4h9Hze5+py7r2aRQqqnbEWnJX/xfQXZ+uy2uNhsz/KRgpzWx+L/lRiRto7lgzvJbLs4Kxx5/Cl3ghX73ydlm0b9vUt2djsVQoSVPfeey8bN25kx44d3Hzzzfh8Pn76058yc+ZMxo/Pr5PKpjgGi6W0tnvm2e4I1aBf/v461Mo5tFKOIoujzsKrdJSxMJ2mTrOeIhJjPRwa9rMgFhpzzp4kiVwgrOArPI2asB4FE7I5MSHIYwuq2eVzSW69EqX7fMvXBzgtEmVpyzq+ErcWObqy282/drQwWcgvNbbrvTisFTpv93j5fNkc7gzm1zEHsNzYxiW11TztsR4B2UYPSxrq+U5VYUOK3dEuDg/7OTSRf6PK3ZUVLGyYxq9dxc3yC0baObrXy+JUccXkE5QPkm77GJXyrKKuMxJ6KifG1QNAUAGcc9LVHJucSAUqnQ9+da86zNvY7GsKa9vpo6ysjIqKCsrKygiFQsiyTFXV3p3EbjOQTHZkQbWrhmpwl98xV9M85xL+essL+J2ja+pDfbP4/Nu/ZrWj1vI9eTNp7utdS6dF84DLpYcISgm2Ry6B2jpL5zwvt/JoZTmT5diYrfz+TBt/cNyIkJGB4y1dH0Do64bEQhQMoNp0MzGbpStPA8xXpQ5eLgtRIycsGY92BCp5LRTDoec/6y2QhVmmSoWQh2O500O7LEMec/j2pCKZ5je9a9kiTsz73LQzRDaboaegnXdTm0xxV/gd1justBeMzHTnHN4NQ3lm7zTdvJ58h79WVVCHzoK9ssN7iyCK+D5xK+qflzA/tZzn/3M3HzrZnqhhc2BSUITq29/+NkceeSQVFRVcc801pNNprrnmGtra2li1qvABqjb5MzhClRoQoRreKf3m127mmle/jOTdOGZKTnbmHryOPGbUaX1z16wMLgb4h8/LPcEAbdGdlvdYL8X5p99HhzT2fSkSfEB6m0PMdZavDyD0p9QsRMEAsv31PnkaiL7piHBfKECzZC2F1+hvJNN1HM7k0XntA3Bcpoy/trRxkmC9QHhqcCp/aW7jZ22FzfLTM7l0nSbmX2i9IHgKic1XMkH6WEF795PtaxRQpeKsCD7U9Udedl7OIU33FXWdkdiZ7eBJn5etSnERufcTE2YezH8bP8cnKmdzefv9rG3fsa9vycZmr1BQhOrHP/4xVVVVfO973+MTn/gE06fb3Rv7isHRp5S6R4Sqr4bKNHPF6pKYS79t6NnAut5VCNJMnMJYgir3AOqfxWYFrf/hZVFQ/SXkpMXh4gdx67P2jkkqfCDZTKBh7BSzJsMXaqtJCQK/z2rIsrVarX/JO/h1bTWHOHotRY6WeoI8I06kykhwuKUdchyWkpmbidIwfmwDUYAJ/vGIncfg9+f/fahLrOJNYzJpj7W9AAK+SupVlVSBZUNqOoYJaAWImclmkjP0d5gYVoH8vNAG3kMUnd1F7oWSVlw0yTLhrPX0dD7MUz3MSfSQ8c/bK9ffVxz+mRv55p8/iSG28PV/PcJjn7901+8jG5sDhYIiVKtWreI73/kOK1as4KijjmLcuHF85jOf4Z577mHjxo2lvkebUdAG+VD1R6hkURgQfdozSnVJVyc3RgXmpzNjRqi2ut0cXTeHL9RYT/mtiLzFgokNfLvG2i/MxUmBM2Jx3Lr1j+PhKfh8JMZE99jeSB6vn+VuF6tdTmKJsOU9dopJlrtdxERrqa5/hir5fZXBy4r14nqA4xLw9Z4w073Whh37E9tY77qAv2n5p07+Ezqb09UfsnXCGZbPcXpyxfJuQcXQ84+cvJh4k4UTG/h5Wf5F9I2xN/mJ4x6O6nk473P35JnMmyyY1Mg9wfzd5fdkmdzOyQ31/NWV36Btq0xJwznROLMcB5a9eNDt5dYP/RSj+StsfHcC//jjHfv6lmxsSk5BEar58+czf/58LrvsMgDeeustfv7zn3PJJZdgGAZ6Ab90bQpjcISqv4ZKlgQce3TvqbqBqy9idXC0m4O7t/Ng1o1THsOTx1dOxBWDrPVvk2k1gS4ImGNEv/r5dNTNjGwTb5rW63oec53MI4k5HFMxdk1MyFfJ/3V04TJNshnrqcuT404+FW1Cn2RN6FQqU9jW3o07NPbA5j15xvEh/puazMFl1qbcKW4vCUEgIWjka1G5QfsT7gkbaclcAFh7X4rHw2889cREBxekogR9+RXDp7O5zwNi/v5PPQ6dv/u8hMVIUTVFaT0NIshCfmJ3MG5HAI9qIJt753fcy74P82hHFYtqCo/GvV/54KTZ/N/JAZx/P5cPb1nJK3/o4KjP3bCvb8vGpmQUJKhM02TVqlW88MILvPDCC7z88stEo1EOOuigEQcn2+wd+n2o3A6JlKaT1nJ/dogiDkkYsi73h1yNT8pUxoxQTQw0kmw6H4dgPVWyQKjjmaZm1jkXWFqf7autyebRGv+0NIt3hQkcVTa2KHA4FJbEVRQhS1vGeupydsZgjppkpcdaofwc30d4+Y0Z1E7Jb/TuP6Rj2JpVebDS2rQ6VTY5YmJufMprmSQup/XOtbixA9mzDV2wXufl9gS5tUYGTE5Opwnm6bH5Ab2Oi5seY3XAekNAPy1Cgp9XVTAtk+TCvM/ezcnpaq7u/C9vVFtJ3o7MBwMHc8W63/OOY6wJkoWxQqhkuXgIcyx+FvY3Tl0wnmVrjqZr6ypuT/2FZ+7fxPfO/fO+vi0bm5JQkKAqLy8nHo8zf/58jjnmGC666CI+8IEPEAqFSnx7NmOR0XcPQk5p+u6UnyQgCAIOSUDbY74fwBtmGtGpkFQFPGMIqgqni8UpDScJTNMc0wYBQNY0anSdnYK1B322z2TSyMPYs8P/c3yhblrT44Cx05FpwYlCFjVlvbD6j+7PEYvv4OzqsecFAizq+jufc97H1m0nAnda3qc79EP8lWFa078Gxh6IG/SXAyCYJpF4b16C6vLuNjAyhOqsj/qRJQkjMRPdEMlo+Xf6KZpKta7jl/K3Taj2VHPsjiTl2eJqn5RsmjLDwKuEirqOw52LCSpG/ulLK2zm1/imbmZn+nvAlL2yx75m0TnX84P7VrNW3kyn9ibP3nUhH7zwThzK/u0Ob2NTkKD64x//yAc+8AECgcJnYtkUj2mau2qj3IoEid1F6XJfuk8WRTRdH1BD9dWARDRUS/mWDGVjCCqXmeSPyk0ApNVrcDnHHvy7tuZULnmjniVT6jnEwvv4bnUN25jMSXLGcjG3w9DIiAJ+i2NEVisedEEimOzFanXKMsnNdmUcn/BbMwT1kGG80EWr2m1xhxyCkMYEAg5rD5SAp4zlW3fixqBbyy/1dFgqyhS9nTXOUF7nObsvpieh4hDy/zf/fPW5XPruYXx2wlQLkwoHMr1sJqd0dNFKcXYsD1ZdxheaT+HKibMtNRiMhMOdE4VOI79OTqt49CSqIFPpKMrR5n2NIIpcd+EjiL//NGe3Pc1U7W+885N1BD9zH/WTDszInM3/BgUVpZ988sm2mHofkDVMzH5X9D7PqXQ294B19HXQ9Kf99qy1Gq9lGa9pqLp3zJSf4nTzqtvFcx43sbi1gt5NyY30lq+mXbE2UDnt8GGKWSKm9Y/jczu3sHrbduYq1uquLqlp4NL6EO8I1ut4eny/wTvpTrrUJkvrl0ltLGmo53eu/NrCX2jaxkvbdzJNtiaoREnCNB0IQCaZn4O40md/IbvyM4680/wR/1WugNa38joP4N30W8TK36Rbsu6234/izuUXXRRmKtrPlsyrpCuWE5byE7uDiXq9nFM+l69V7B0D4webt/DW9i0cVWQkbX/g2vP+TPSQW4iZbmZp63jioTO54B830p3cO3MSbWz2NgUJqn3JHXfcwcSJE3G5XCxatIgVK1aMuv6hhx5i5syZuFwu5s2bx+OPPz7guGmaXHfdddTV1eF2u1myZMmQETo9PT2cc845BAIBQqEQF154IfF4YZ48pWTPqFO/51R6UISqXzDtWmvoPNjSyn92tpLJVo46dgZyPlRfrK3m8poquhPWBNLWxEpcNf+h27A2N22u+zPE372aqa4TLK0HcJkZBMDptlbQ4zCr0TPVZPMI6IQ0Eafqodzi/DldkmmXZaKC9XSaoeuUoRIyDDwe619S+j2+1DwHMa93qrzhdGLk2YlYRxcTxA60ZP52ATsyy3DW/IdufX3e5yp9ESGXab2ZYDjajJdxVj9FVLcmjkdCCFazOhhlrXfv2CZ4yEW+XL7QXrn++42DTzqf6HnP8rpzHrdXuHg99meOv/tWfv3Ea3Q0b93Xt2djkxf7laB68MEHueqqq/je977HG2+8wfz58znxxBPp6OgYdv2rr77Kpz/9aS688EJWrVrF6aefzumnn87bb7+9a83NN9/ML37xC+6++26WL1+O1+vlxBNPJJ3e/Y34nHPOYe3atTz99NM89thjvPjii1x88cV7/f2OhbpHoXm/51R/Ubos9Ueo+gRVv72CrkH1bKLuBlIoOB2jR2xESWZ2WuWgdIZMylo0ZGYiyuxokLm6tc7AuVob5xkrqO99e+zFgJ7VUIScMrIqqMZnLiO55SpqXTMsrQd4rOUdXm9ezwyntT0O9szkL82tfD5i3UU7k96dOnJ5rFd73xiaxkVlc9ie59zA71W7OK++hl4hv4jPjVUSJ46vZ1V4TV7nASxMxpkTDTBz8AgkC6huD4eNm8mRjRNQs9m8z+/nyHiaBRE/04qcwVfnryTTcSKZjpN2DSEvFaZh4DVznwdPnp2U+zPjJs/h4Kv/y8cnX46sTiHceRCRl35F5T0L+dPPjuSHfziXZaset8fW2Lzv2a8E1c9+9jMuuugiLrjgAmbPns3dd9+Nx+Pht7/97bDrb7vtNk466SS+8Y1vMGvWLH7wgx9w8MEH88tf/hLIRaduvfVWrr32Wk477TQOOugg7r//flpaWnjkkUcAeOedd3jiiSe49957WbRoEUcffTS33347f/nLX2hpaXmv3vqwqAMiVANTfrI4SFD1/zJyuOArS3ngiH+SwjVmhArg160x/tTajs8Yu34K4CPRbh7sXsNHLQZqZsVe4XrH/Uzpes7S+nC0i+9VlnNjeRmy05p4+Vzqj9zvuAlv88vWbgpwkXsDVkVbmbuSOapGvWp99ExPtINby4LcHQrgzCMN94xfYlkoxrY8nzETtCwTVY2gJ78Hdq8k0OKQiecp4AA+19vCX7rf5kjyH9cSCpSTVpJk5Qy96cIHJF/au50/9Kxlnpz/uJ49qXT7cHcfRlXvDFIZ65FIK/TGurimupzrK8px+A6MWX5WESWJ6z70WV77/D+49VOHcoi/F1Ewec7TyYPGKt59/mIiNzSw9sYP8Mwd5/G1f9/GHUsfZ21LhO6eHrJaaf8ubGwKYb+pfFRVlZUrV/Ktb31r12uiKLJkyRKWLl067DlLly7lqquuGvDaiSeeuEssbd26lba2NpYsWbLreDAYZNGiRSxdupSzzz6bpUuXEgqFOPTQQ3etWbJkCaIosnz5cj7+8Y8P2TeTyZDZw+8oGrU+iDYfZFHkI3NrMczdtVS7itL70lT9NVT9tgldqS6uefEa2sMCcDpOx9iCKoMTSOxyQB8LIds/A89a99kOOcPmgJ8M7ZYKhnvjXfzDnxM533Rb6xybqm9mvrSG12LWxttoagZHnlGw3WN6rEd/umPt/CYURDFMvuSwnoYLZI+iLdyNWyq3fI6ezfLn1jYAessmWj4P4HPRIBPVdXTNtFagvyeynvt5SHnWbQEEnG6S276CaSgYeuG/rpxmrivPkUcUcNjryCIrnV9CFgw6ez+I32PNy8sKnT3NPOHzIpgm13n/dyJUeyJLIqcvHAcL/87OzeuY8MoPSKU3sDCZJUSKkLqaplgTT3W9gb6zjp/80+R+x018UFrDF2pq2KI4uLRbZI7qRhccvONU+HllHR6hjumOczgx/CC1mW085u6mQ8zwIbWSiYYXE4EWyeC35dW4hBCz3GdwWPc/qUpt5b+OTtrEFIv0KiYauc9Pj5DhN6EaHKKPOZ4zOKjrcWpSm3hZaqdZTHKIXsFUI5fCj6JyT1klouhhnucs5vQ8TX1iHcukTraLcRbo5cwwckI/gcbdZWWYgpP53s8ys/d5GuKreV3qYrMYY55exmwjBEAanbtCfrKik/mezzE98goTYytZJXWzUYwySw9ykJH7/ZDF4JdBD5rkZp7n00yLvsHk6HLWiL2sl8JMNQIs1Hd3GN8edJCRvMzxnMnU2DtMi7zMO2KYt6VeJhl+DtV3/x64K+gkIbmZ5f44U5Jbmdn7AhvFCG9JPTQYXo7Qq3etvSfgIiq7mOE+lcmpNub0PM0WMcZKqYs6w8PR+m4Pv98GXPTILqa5PsLkTJh53f9huxBnhdxJtenimGzOzkYA7ve7CTsrObzsTK5Ysu8mt+w3gqqrqwtd16mpGWiaWFNTw/r1w9dmtLW1Dbu+ra1t1/H+10ZbU11dPeC4LMuUl5fvWjOYm266ie9///sW31nhlHsV7vpsro/ukj/l6pXSfcLJMTjl15duiakxlrctRxG8wOmWIlSqoIAJWtpaZ5PU9wAVHNYiEuvlGA9VlHFEptua15CW5bKeMElBRhrLmLSPR31p7ghWsSC1gcMsrO+OdnJdbRUuw+RGC52NAAnFwa8944lLAa60dAagZvlsJEqG/Gqaas0P097Zjt+CzUI/6XSKLcZE3KiMy1NYjCPAPFVluZp/2q1fYEoWU6d7IooiH9G7cWZjaPEIBAuL3Ch9gsqZR53acAiiSLPkQRRTZGKdVFk0R7WCmUpzTXcPEcGJaLF79UBm/JTZXDcl51GVSSd5d8Mqere+weae9ZQRJyuU4fYq1Gm50dndskCnLDLOaGdGNveFdotURkTooifVy8Z3Wvms8l8OE9/hF54a3nQ6+WR4E4cnc5+NV5xetvkq0DPVvPbmoRzjeJojpFX8traKpU43x/Wu4YhE7nfgWkVho7sWQwux7I2D+aXjaY6QlvHn6kqe83pYHFnLEbHcF9AtDpkNnnqMrIcVbxzOzfKzHCH/l0eqKnjG52VhdB1HRHOF+C2yxHrPOExD5vVVR/F9+XmOkJ/myYoyngn4mRl/hyPCuS/ovaLIOk+uOWLlqqO5Rn6RI+R/8d/yEM8EA0xIrOeI3lxEOS0IrPU0gAYr3zycy8SXOcfxN14rC/J0KEh1ZAOLe3bXBV7saQQN3li9gC/wCuc6/szaYICny0N8IhZncdfuceVfck3GELO88fYczjFWcoHjz2wO+Hm6ooyPxBMs7tzdCPIVZRpZOcOqddM4XdvIF5Q/0+Lz8nRVBccmkizu2N24cpk8k7SSZNU7EzhRbeVi5c/0ej08XV3JolSaa9pf2LX2Smk20ZSTdzcusgXVgca3vvWtAZGxaDRKQ0PDXt2zfy5Wv1N6/58HF6VXxnv4v6RMm+7gBnLfuMfiqzXT6aKSi/QEViaM3eZvZWP5eD4ttLLYwvpxchUf6UlQZVr7Vu7QDC6KRAlj/QG902Gw1OlmnN4z9mIgHO9kqduNZJp4XNb26QhW84saEUE3LQsqjy7yzZ4wHViPNAF8O/w9FrhW8Nq2H8GCSy2dk0LhVPVGALZYjLr1o0u5aKOh5m8XcEWtSo80nqvNLubnfTZcL/6aSiXM5p6PwzjrMwj35CMTgggEuCfP2rHhuGBciE65nFu6NzI1r6mNoyOmVc6JxmmjOM+tAxGny8PU+UfB/KM4DNjzE6+pq+iN9HBt+3o6oy0wQeZNTcfIZpC0GKe6vch4mTRvNonmz7I03c5CczuTSBGrPoalfRMaukizwFeJM+hn9sSpZDo+xtLUfKYJzQSzKZKhQ1gazEXEe0kzx1ODIvqYc+wUjK6PsjQ5nQliGydlk2iBg1nq3x2hmuuuQBQ9HHTsFJTuE1mamEC92MFJ2Tj4F7C0rwkhgcY8dxBTdLHg2Cn4ek5gWbyOKrGTk7JRFO98lvWl6zPoHOTyootOFhwzhYrwcSyLlRESuzgpG8Hnmccyd+4LVxaDBU43muRi3gemURc9lqURDx6xh5OyvQTdQZbW7Y46LXTKZCQvc4+cwcS4ydKwjCT2clK2hypngKV1u21MDnY5SMoeZh8xk0kJF0t7dUwhwknZLsYpPpbW7Q5YHOpxEpVdzDxsNhPTFSztTpIRopyU7aTW4WVp3W5PwUO9TnocLqYfOpeJmQaWdX2OuBDnxGwH1bKbZXV1mH01kYf4XESUKg6fPKE0H7gC2W8EVWVlJZIk0d4+sNOsvb2d2trhjR1ra2tHXd//v+3t7dTV1Q1Ys2DBgl1rBhe9Z7NZenp6RtzX6XTidL63JnX9Rei7R8/0p/xy/9tfb+XXNT7avoVuZZxlQbXDCWkxSofFet6UkCUmiYgWfZUOck/lws5u3nJZcxhPyiH+Tzsbj0vhq9ZuiaOzNZwS2YxWYVW0wY0dXSRxWI4WVHnLyManIWPdwDIhBfh19qM43T7OtXwWZCUnKUEgk7GeTt4ZbcPd+CtE04sonpzHbrDJ7WGtVgdm0pJI3pOEaBKTRFyu/I09AV70uBFEjZrozoKsLlU1Q1oUAIGA33pEbyTchoDbMEikipsLOJiwo5prtQuoDHi5oqRXPrBxKE7Kquo4pGr4iQYfGfCnnBQb6TN82oA/zRh17UcH/GnmqGtPzGPtkgF/yq0dqRRi4FySWaOuPXrAn+YBnxvxHga+vhD4tMW1hwFnWlwLcDqLgc9YWnsKRwCfsrR237DfFKUrisIhhxzCs88+u+s1wzB49tlnWbx4+B/n4sWLB6wHePrpp3etnzRpErW1tQPWRKNRli9fvmvN4sWLCYfDrFy5ctea5557DsMwWLQoX5vCvYejr2aqv4Zqd8qvz4eqvyNQy4W31b5xL2P5UAGMM88gueNcqpzWZs1d1SXz6M4W5nutmfSJSn61R72il7s5jr+7T7W0HmCqUMWpiSR1mrWPvKhlOTWR5ISE9a6wxsA4UjsuJNNytuVzeh3V/Cj7Gf7iy0dOwT3BXg6f2MBzGWudkQA9qQiydyuie0teewE8XF7HT2scPOa2lv7ck3tbwjy6s4UpocKcv+8rc3BdVQVbY4W10WdSCV7YvpP/7GimpmxcQdfYk5+2u1ixfSdT8owqjkWzofAn8RBeCHyopNe1sbF5b9hvIlQAV111Feeddx6HHnoohx9+OLfeeiuJRIILLrgAgHPPPZdx48Zx0005Z+/LL7+cY445hp/+9KecfPLJ/OUvf+H111/nnnvuAUAQBK644gp++MMfMm3aNCZNmsR3v/td6uvrOf300wGYNWsWJ510EhdddBF33303mqZx6aWXcvbZZ1NfX1j6YW8g9Ueosv0pv4ERqmxfl1841U2TUyEh5Wp2xhyODMzVA7iTHfiT1gRPdVZlkpEl6rYWDZCduRSHVUG1uusNfNN/SFQfD3zY0jnIuXouMWttj4RSzWXqJZR5nVithnMbCZ5UrsZNhqy2Dtkxtvh4reNl/LO+T5c+HbA+EFfpG/Kb0a2nsMoinVzTphIWrY+q6adSGU+2awqKK3/H8oZsOjdH0VdYdGhGRqYxG8NZoGtCJhWn0jDQdQHRYhPDaOh9Pz8tXVoDypWdL+Kb+jM6zbkMjlPY2Ni8/9mvBNVZZ51FZ2cn1113HW1tbSxYsIAnnnhiV1F5U1MT4h4mjEceeSQPPPAA1157Ld/+9reZNm0ajzzyCHPnzt215uqrryaRSHDxxRcTDoc5+uijeeKJJ3C5dhdU/+lPf+LSSy/l+OOPRxRFzjjjDH7xi1+8d2/cAo5dNVTGgD8rg3yolvWs5Rv1tcxRNei2FqE6I3IfC5UXebXVAAs1I1e7vkd3bw8311oZPAPrvG7Ob5iO2wzxqoX1ajJX5Og0rflcAcQdEmsVhVbT2kOwwzB5TJlAo9e6CHC7XMwQc12E8VQCnwVBlU7nCkEV628FgE9mp3Jzy5usqrU+jNyZUTkn1UaTmH/B84KyE/nPsgnUVuQX4dENk6Myt+ERMjxcYHTovFiQeZktvD6usA69uFTG8el7qHTqPGvRpHU0VNkLKhglFlRGoh3BkPCX4B5tbGzee/YrQQVw6aWXcumlwxfhvvDCC0NeO/PMMznzzDNHvJ4gCNxwww3ccMMNI64pLy/ngQceyPte30v6a6Z2O6UP7PLrr6FyGDr1WpagnhOMVgRVi0NCdTnpVDst3ctW51oiQQ3VYc0kSfJWkJXTJLLW/JuOjCW5dGsTbzmtt5b/s3I8/xVqqRaDnG5h/bqe1Xgn/ZKY3gh80tIeitPN6eNqSQkiv+zdybTA2Pd3fDjMJdt3ssY9fP3HSDhlPx7TRNasF4lrmdxaVcjfD2pG7/M8rvyC9paDgd9ZPi+cThIuX0PYUHAqhf26yfYVxOuZwnyodsQ6SFW8Rq9cGiuCh0O1/NQ1h4VCuoQl6XBqb5gbt29lWdnsEl7VxsbmvcL+KnSA0G/kudvYsy/l1yeY+muojvc28uTOFr4QyVlBWClK/48nzBfqalhuWKthyQT+havuETSL0aCpoWkktlyO3PllS+sNNYUICKL1biifEsTQggiGtXSXkOhG0dyEDOsiQJQkmmUHLQ6ZWMJaN6GoZSg3DHxinnYASu69C9mU5VN6U5286VRoynPsDIDHTDFb3E5FxpqPVz+diV5cNY/jrP0n7gIH/upy7r2aaqGCagfO6ifRA8+OvdgCb/iCvBWMsTrPqOKYZPr+vSj2nFQbm/2R/S5CZTM8/RGpfr8peVBR+q5ZfrIbQo10q7lv61YiVGV4mKq24hWsFWjPjrtJiU4qJGsfr3JJ4IzsBrwpgLPGXG/2RWV0yXqk5fDKD/OX52qom2bNmPLweIpLdm5gtUXLhH5uaYtTbiZwHmqteLuQ9wLwjsfLg8GZ+D2K5SjJ6vgGfl1fy7y0xnF57QYbhB5uGldLTbaHu/M4LxvtYVY0gCbKA9Lx+XBXZTVr/DM5wqFZMn4djC/SwUGRALJUGvfxCe7D2NgsUhacVZLr9SOqOd8i01l8nZeNjc17jy2oDhDkQQ+r/j/vqqHqF1QLz4GF5/CrO1+BnrAlY8+TmcYPml9hadXYRdOmnuXB7rcA6HJb+6btMeL8xHEPmikBPxlz/ZrMNl4oDxEQVaxVaUFtbB13Om5F62kExu7O7Pdb0sX8hM6MjEwtKhstjiVZl93J28EAilPLK320PlDFs+VJQlifPSPpOuM1jZCZf1G66ZB5V1Ewzfwqw73pFH/tfptuCh/5EnYGSZlJ2guMCI1PJvlTz9u845hT8D3syXTfwbzU7aBi0vC2KYXyvLSD/1SUM1lJv2/awG1sbKxjC6oDhP6U3+A/90eg1L7I1cObHub5Hc/TQwMwe8zhyAA4cikXKx1ymXRi18Q2l8daREB0Kjzs85ISBD6eTuAeY0TJZqODx4IBjlWtd7h5jTBHSivYlLaWijP7BZWcn8liRnSCAZrFuXNrzXaeLg9xYja/dFaDdzJqz5F4A9asLAAOMaq5ZGcrr/vzr9GZ5p/GPWvaSZv5dfllUrmoS0Yo3Jdtrv8k3lzfQONBc8dePAx638gkTcpfSA7Hoo6/crnrZ7zWdAJwZEmuCbBWivKm18f5cuFDoG1sbPYdtqA6QJAHRZoGF6X3R6g29m7k+R3P4xFPAGZbilAJfTP5RAv1OplkfLegcll7gDlcbq6rynXTHRfvGVNQTcu6uTAZQXFb87kCaCfBldWVSEaGWyysX6Ft5sHqSsYLSQ4de/kuXvKU8axh0KBGsBIPmaw5+UQ6TpUnvxl508vmkmnP4FOsp4eSuNhs1JFw5m99UOGrYXo6Qxv5OY1n+wRVIYXw/UwTRJZkOmiM7ijofCOTu4dsnuJ4xOs5PPSKIkm9tDM6P5SQOCoVpnbyxJJe18bG5r3BFlQHCP21Urv/PNCHqn848km9nUzWvCyNpfkHWBqO/Krfx7XV86hVvPxhjLVN4W18pXEcAd3k37K1j5ffE+KDyRQuwyBjYV7gnIybRb0RlnrHW7o+gOYQeMbroUazliLbafTwjNfD8aq1zsN+flFeSUqKcK4kc4KF9YvSLg6L9LBsSn4z4eq6l7PJeQFNPY3Am5bOWVV5Kp9XZ3FewwSsmy3k6B8Q7SQzxsqBvB5ZzRcbxzFdFbkvzz37mRZ5hc8qt/JG5weBz+Z9/hPpN7lswngWq1EOLvAe9mSl1MYXJ4xnTqYz75/jaByTUJmiR1kdKMwA1cbGZt9iC6oDhMEpv12z/Pqd0vsiVPMTMebvfIdW6bC+42MLqh5PGW3eCAlzbHERTfQSliT0PGp7REnilrYIbkGlxUK2Y53nMF7LZmkotx47Gudv4NquHiTDWuppoebnkN4eMv4FlvcA8AqTiCUERKxF595xzWdTt0ZVKL8CZ4fThSzoCIZ1gbMm+gTu8S/TapwA5Jk+czr5p7uSsODivDxOS6hRopJEqghvpV6HyZMeN11iuCBBlNaTJCURowD/reHw9nXhGegluV4/D0inoaRb+WjlvhvuamNjUzi2oDpAkCym/OjrKosbuS40K7YJ04LzSa04iwmVYw94rsTHIztbaBdCVm8dgLTgxI2K1pciGo3XXAt4XK/l2qqDLF+/2l/HglichMWi6smqzKJYnKVl+flDTZPOYWtTO3WHWBkjDc+7TuD57AJurrP+XiAXQTt7YgNluskLFs/pUrci+9eTNvMfUZwNVnJtbU4kfjqbRbEYfZxrVPHPnS1schYyFjnHViHCnTVVzMrEOKeA80/IVPHl7ldYW1WaUu/Dyg7mzZU/Y4dY2oHn/2A2veYcTqvctwNebWxsCsMWVAcIjkERKscQH6pcUXqTFkVzyET6mtCsjJ5pdAaZHQsw2TO2bYKpqkzRsihCfjPfVHLr1czYKb+3tbvwz1zFhuSlYHFcrtJXl+Uig2kYCGNETJb7TuCfbZUcWm19HAzAJyL3c6XyPJ3bL4RFV4y5/h1+gm/6FrYmvgVYf0B7PSEMQUC1aGUB8PFwB6kE+JT80pgA5W4/emo8pqEQUzNUWBRUTi3LZC1LbxFWABXuSg7pSFObLayo3KdlaMxmaVZKY+zp8gaRAJdh3QPMClrdjfhFnbR5GBTRFWljY7NvsAXVAcLgonRp8OiZvgjV97PNrBhfz+zWHshY86GqirzNo87vsjU6ATh/1LXhwGyOz/yESRVu7s3j/s+un0pEquCb2QTTxlgr6FGQwJdHGkl2e9jqkEkLAhPSCTye0R/wbzqqeF46iMll+dWzVBhdzBKbiCQ7LK03zTiCpOKykHrdkwmhyTzXtBNRt57GWpiMcXCiieV5GKL2E3J7SG7LTSgwdOu/NtZUfZRvra7m+GmNli0uBjM3OJtPtXWwXbReM7cnf6/4Ile1LuGLEw4qiR2B05tL+bkpnaCKp+KIgAlUj/HZtLGxeX9iC6oDhME1VP1F6v0Rqn5B5TFNQoZONo/RM1mHgzWKQoeQYazS6e2pTpqCOxG9+c1ti8gSmpSm1xi79uqO1nYmZXfwdrV1YyLF4+dj43PDrP+janjGCHZsyN6Pb8oatiavBKzbDPzHHeZGTy0L9fWWTCjvadlJOc20T8qvHsfrDRLSDcAgq6mWBjFLfYOUBSX/SI8gCPzR+WOCZhS1ezr4x5K9Od5Nb2dnsIk2V35djHvi6Bto7LQ4PHswm7JraQ/tIOKYUfA97Inu8fLl0CwSosTvDKNgw9I9UWNRVm/figYIHtsp3cZmf8QePXOAIA/q8uuPWCmDnNJvTzl5qakZVyJXp2GlhqqDGJ8ZV8sPqsfW35uj7+Cqe5io8+m87r9e/TyJLZdR6xzbCsFlZPCaJi6X9bSIW3FiZj0Ymp9YZuzIgi+bQtIVQnmaScYkeFdR6DXHrgUDqNIzNGR1fO7yvPZxeXY7uKeS1vZqFxJsdDhQLabrBjNb2MY8cRuqxbE6AO8mluKqe5gO47WC9gRQ+joMC40ItRrP4qp9lJ7s5oLvYU+cgQpeLkuwKhglrhUm8gaTiocBUE0XsiP/0UA2Njb7HjtCdYAw1Cl9YFF6ps82AVcQw11OMmM9QhXwllGXzRLSx67XKY/3MCEeotyRn5HjIj3MdO1dfLE5wORR1zrMXGeb7LQ+SkQQBGi6gUQmi1sKjbn+9radTM++y5uN+aXHjhIm8cnW1+n0WYtqOfveiyPPETdOl4frAtOICyKXJcL4g2MLsrtDcTY567iSLo7Oa7cc36n20yl7+ELvBiZZcJsHmJqMoiaDzHAW/t0t4fFyVN0cdAGWFXD+/KRKmxlkEqUZvlfpCZDpOgZMhURGJ1C4Z+ku+gVVQvBQmgE5NjY27zW2oDpAGMkpfUiX3+f/Q1c0zaobn0UUhp43HBNCk3lqRwuqOfbH5eB4nC91rmalN78C4I/F/8Z8ZRkr2usYy336oYCOkyCHitbGu/TzbfH3BBzdZLsnQOXotgGykbu27MwvPVarVLEoneE1pzXbiH8ERDz4ONSR38NeEEX+UWYiiCnOyupMtHCOzzAp13V8BRaIb3dI7FAkwsluy+ec2dvBodE1LA0uKWhPAK+/jKgrNzg4pam4LaQ39+Sa7i1MNJp421Ga2iRFlpHDH0HSkmRV600Bo7GlZyMPVJTh1z1cWZIr2tjYvNfYguoAYaSU325BlfvF/52Xv0MsrSLIB6MIoVzkZgz6TR0VIYue1ZDkkVMSppZLy+Q77He9E7ZJXrR0y5gz7f4ZkAhLQebJ+T3MjuU16qUO1sfGLhhXzFwqJ58oGICg5CJakoUxPZgmd5Z7yQo+HlTy90iSEoeT1rIYFoQuwE3tGcaZ7ayfZ83SYTBfCDuoNZox6qynWiU993kQC6jb6qfSGyTZdAEYCinVwJ1nRszZ142nlLA26SXpy1RIEba2PwWV1qJ1o7Ez1sRDAT/TMoItqGxs9lNsQXWA4BjUJdZflK7IA2uontz2JBk9A8y3ZOoJ4HLvFhXpZBxvYJToU98MPEPOT1A970nwirOCT2Sb+OQYaz8RTZISTap8+XlE3VvmJCJVcFzkXWZy3Khrb68AmXI+JubnDB5WZB5xV9LtMMc0ocyoKU6OJ0gLAmW+/MfB+BNnEulN4bLo+dVNENnM4LA4tHowMzQvc9Q0r2vWC+j7C+FFpfBElsehsDidxW3G0FIJ8Ob32XL1jcvp/2JQCmKCC1mIEY/1luR6VbrCJb1h0kJ+zRw2NjbvH2xBdYAgDXFK7y9Kz0U+1KwBhsE3Mg4iuLhdF3C6rUVFFKebU6oOQhXg7lSMyaMIqseM9XxvfD2LzG5LXW79jDP9HJVso8I5+j2ZhsHlvb2IgklXqD6PHeANt8hmxcu8dPuYa//rlUmICqfkGTl6o2wcD9R68BhOLhxjbSaV5IdduQJvNVid1z4A96jXMMW5hU077oPGU8dcf47xQ2KZLM/XWpkyOJSslIu+mRa8wvr5WaibVrmez9DBYQXtmqt/u0v+GX4hxY7e06GyIq/zT28IIOPnVim/FPFoXFbvZKsynmvCq5nHSUVfr1oVOTUc5Q1v4QaoNjY2+xZbUB0gDJ3lJwz4X003IJvmrB3rALjVdFmOUEmyzDZPHEHM0qOpo5aMR80kzYpMWs+vCPkEYwJHtL/KstrR00kZLct9+im4UPmkNz/zw5PjLrxGM+UVY9fSXNYdISNBdSA/0VbhLkdPNSBJNWOuzWgmD2aPxS2onJpnXRCAQzBwChrZtLUuP73qd7gMiax5GBRQ+rzZ6WKHWY6qRSyLo15Jp8UhIyjFVW4vdfsQRKiIttGAddGRUVP09JnXBnyFWzcMRjFFwCCZKc2A5Cb3LP6rfYrasjklmTdoY2Pz3mMLqgOEoV1+A53SNd0EbXfbeRrFkmVCP1LPGSQyJoowetrko6kyLuxaTVPt6Cm1IThy0Q9hjNqjdBb+L3smIPHZPA0QF2X8HJSOsyI7ehGOpmb4TDxXBB3xjy2M9mRu+cEkt13C+Jqx00sJwcM3sxfjc8p8rAAvox9U6axxNnBx5E0W8OlR1ya1DJL/7ZzDt6OwmXa/qhxPi76VI1wuPmHxnGs6dXx0kp4yth3GaPy00kWLw833I1vyEhzpRJzHdrSQFAWqQrVF3cOeXN1bzsLUG7y5oDTX3CjX82vzw5xbVRqvLBsbm/ceW1AdIAwuSh/slK5mDTQ1yk6HjAsJIy1askzoZ3pmIslYGFEdvX6mMmtwUEYloeQXDTB3CarRvYZ2xtrwz7oW05BxSKfktUd/obypjp6ySms639cuwE2Gr3nzqzcKJbfykHI9aiwAPDvq2g09G/FN/x6iXgGcmNc+AAYiWUEgpY2dgkvHI3yhQyAuSpQ7C4sWBR217IiPQwxar0WarKapQeVdb3HRocmqSI2eQlTzG5ujJuNMyGbJmiJSntYUoyFLPhyAkbEWHRyLFeEH8M94is3ZM4D85jra2Ni8P7AF1QHC4AiVY5jhyM2RJj42vh6fYcAGa6ae/fxM+xENzhbWtU2BSSMXzv49dCE3dB7D58aNbn0wmCcDAS4fN4tG2cnfRlkXSYYBEMk/yhKRHWyXZaLq6IXEsazBn8SFCCh825lnAbRoMFvcSJcRGvt+0hEEKYNgFmYOeUG8mjkdy9k0bewoiZFKcXliO7opIOZpBdHPwsCZrFh1CA3jx/LL380X+B5mJspt1cVFXi7r9TJL284bE/ITuDG5jI9nbqXKmeXhEjia96PLuZSpkY6V5oJqFwBB0f6VbGOzv2L/6z1AGNk2Ife6qhtktQR+3cBnQivWBiP3s9OhEMMxpgfROtpY648Tceb30Up4ykgpCToY3b+pOh7nle07aLPY2bYnP62qY1t5PYd5vZwwyrodkRZ8U2/BNJwIwuiptMHEhAyfratBR+TPY6ydGu7hsR0tNBX4nA+IPmp1nW3ZsYutM+kEAGmceAsUFgt6n+YvygOEd34QuNnSOZvc28gqMoIr/xqxPdEkN2ig970Pq7QkemgPbSbtyM+JfixeDFRwH7NolLIlmQ94fXsnc5JNvDbb/pVsY7O/Yv/rPUBwjOCUruwxy2+qq5JXm3aS8DQwB2su6f3cUgkbnXVcFt84qu1mi/Av3OM206VNBxZavv7csiP4xzKNmeMbRl2nZ5IEDJOYUEARtyOIqTrRjNG9t5KJHkTdgWjR32lPFLeXt1xOJNPE0HVEaWTRKmoqE7JZMnlaTPRjyH1dd2OkMAGiyR7SDhnVcDGroN2gzOjmCPEdXk9aG1Kc1lQctX/DAYjCRQXumkPv6zA0MvkJqq2R7bhq/0k2Ww1cVdQ97MnKQAVrpART8/RCGwmHnkABnO78DHFtbGzeP9iC6gBBGhyhGlRDpekmGFlwBcnIuWLufARV0JCozqqQHb2GZWrapJ0gdeT3oGkQBZZkOhkfH/28bF+EQhXyFyGLgufzxqoPMO2o0VNW41Jp3mraTCv5e0NVBuq4tb0Tt2miaSpOaeTRNXqfONDEwmqaVnkCPKFOJWghSrK5912+Nb6eGs3gmYJ2g9VSL3fVVVOjt3KohfXxRITGeBBVhDJXfiN8BnNXRR3rAnP4oJyxOPQmhzvWwZRYEKdU2oEuDZ65rGzqJlBfXLF9P04991lwePLrXLWxsXn/YAuqAwTH4NEzg5zSdcNEb1iMdE0T/166Df65Nq8aqssjlcxPLWf5GJ1SP+58l0ZjJ28flN8DrCK2gV8pt/JudArw1RHXNcW382IoiGzIXJzXDjAztpwfy//A0bYIGHnWnpbKFRpnxPxFW9BfzvHJXGF9JJXAOYqQ2J7cyUa/D1MQKMQZ6qVQJatllcmKyBVjrFUzCUK6js8ovI4oKZm84XJxUNpizVcyyb8712CYAoKrOEHT4vIRkWLsyPO8SfEkj3StYZ1SmDv8SMwOHc5fO9yEqvMX3cPxkD+FixCHOayNLLKxsXn/YQuqAwR5BKd0xx6iaWXbKv655e/09lYC0/OKUOl96SVjjPSS0j+4OM8HaEaGpz1uegWVqaOs25bayV1lQWZljLwFVU1mK0fIL/B6bHTbhF2RowKiYA6HQtYUkQUDNRWHspG72zZktvFAZTmHplU+k/dOUOeaysqdC/FWj10kPkWs4qWmZjbJ0wrYKcdsz1R+tu0hUsIES+vTfcI0VUTdVj8zvR/mndUNjF+Qn0uTkckVjWcLEMej3k/Hv9nq+jardx4GBcf8dvOkD3rkAPPyrD20sbF5/2D/6z1AGOyU3i+W9jT83BLZxqObH6XBtRCYbtnYE8CQcmkpUxvd1sDZJ6gceQqqTiHBNTVV1GgGnxplXYXh5KxoDIn8xs4AbJJiPF5ZjouOUVNW6+Pv8rfKcoK6wNfy3EMQRf7rLCcpGsxI9FI1ytjiSt3BCYkkZUL+LukAc0JH8bfWMsqrxv5ZqFmDTjNAXCo8pVTjrWd+MsW7kjXrArVfUAmuAmxEBzJD8nN4Sqc+HsnrvP6aq6xc+CzB4XA4PWhA1sivpmskzoomSEgm40LWxKqNjc37D1tQHSAMdkrvF0t7FqvPDHdwFWVEkgLrAKfDuqD6R6iaG+SDOMhhjFqU/vl6LwgevifmN+Yj5K7g4HSaYHb0e5qo+ziru5c3vPmncDrFDA/7fcwfo1OsOd3Wt66w9MsVtTUgxbgFk+mjrJurBbioo4vlFUcXtM+MzqdY6fwBW5oXAv8adW1TxdGcmbmbYyZU8fuCdgNH36BoxaLNwzs96/jK+HrqNYHfFrhnP/N6n+Yi5TZea/swcLrl857OrOY7DfUcosVK6kC+jg7Om9TIJDXOo0VeK6tpfCWSs/IIV9iCysZmf8UWVAcIg32o+iNUoijgkAQ03WRyKs2CrW+xtqKWW9k9588KGz0+tgphnKPoHdMw2KzImIKAK88I1aSyKfy+tYOEOXpqpsM1ifuzJ+Dyz8/7ATnF3cDlLWFEc/RxMg2Gj8t7wqjSaMnHkZGz9WTUOGp29HVtygQe048A/8j1XKOhyAIVQozW7NjjT9aGV+Cqf4SwPA84vKD9DKfCUqeHNlGi0cL6SKqHZodMKRrhIg6BV90umgnnNRMwpsdpl2XSRmHu8CPhc4UAyAjFv7lEWuVX2qfwCyku9NtdfjY2+yu2oDpAkEdI+UGuMF3TdYw+R+2MkEvf5ROhmupdzFtbZSonjyxjNDXF/a3tpAWBykB+KTnFlUvJOFExDQNhhJqbzZ4F3Jr18pmaxlFTg8MxwTuB0yJRNsqjF9aPzzr5ZCTK64H8hvD2U5X4Khvb41ScMLrseMP/If6gTeay+sKE21qzjcsbxzFeC/PgGGvbkttxBFeRFArvtussq+Gy+krQPXzcwvqJlPGHljZ2SsVHXd4Re/hNbTUHpXs4M4/zjk+Xc254KVsq8+kNHJtZFXN5+aWdpIz8xh8NR1jVudM8Eafg5ssFutjb2Njse2xBdYAgDhJUzj2iT7lOP51IOkxGkoj0uYy78jD2nO6ayLhwJ7XqyOM70qkECzK5VF/Gl1+tjuLJXVcWDFRNRRnBoXxp+H58Mx5jk3YqkF/aT1ZyYsJhZEZdt823gOe1T1NfPt+SPcBgvpq5l2plI3LLdTDl5BHXvZH4Ld6py9mSOQfI30ncobiJShIpfezU5GGRDuq6HLiChUdUyt0BjEwlGNbqkRQty4KMiqwUb1lQ5qxgelilZow5jIMJaVnmqBoxpTTdeP34fOUEDQNHgS73e7K+ZzP+Gd8H3QeM/HmxsbF5f2MLqgOUwREqgN8n1vFQ4ziOz7QD+UWo5nU8ygvOW1jRdjzw4WHXpHFzfuZ6PILKH5T8vmnLLg9H180hK5j8PRll3AiCStdiCKKOUkCqRXC66BJFIuLoD8GNynju41jOLS/MY2iysZU54npWxjpGXZfO9iA6ooji6PMRR2JWYCb/fL2FmDm2WJiZTHBBbDPL3IcUtBdAY6COxJavA5DVjSGdpYPZXraYGzI/YEF9DXML3jXHwsBczlvVxmZpcl7nPVJ+Ad9rO4pzGw7hiCLvYU/cvtwIHI+QwchmEeXCf5VGorl/jw4zP7FoY2Pz/sIWVAcoewoqpa9g3TA0JNNE6PvF7crDNiHjcLBNlukxRx4G251JsdqXRhE9CMLobuSDcSkuws44gmAS1VRGmhZ4WWcb06PNrGkYvdtwOJp8Qc6eMB5B97F6lHVvRB/EN/0JNqmfABbkvc+fA1maHNV8ILGW0eTLdzp2UKu10uwd2+l8OPzeCiZrWToZO0rSP3TalAtP+bklg3sdP8FDhlTiSPyB0et9tmR6WOeLU+a15qw+GrI7F8FUjPwiQhuN7WzydxN1lW6OH4DT6+eawHRiosT3E2Eqg4UPf54ZjbFyaxPvFCHKbGxs9j2l/S1j875hTxuFfi+qr5r1vLltB0ekc15ELof1lN8qWjm1oZ77/V0jrmmK7sQ9/gGkmrEqeoYiiiJm6+dJbr8ImZFTSl5do1bX8TlCee/h73OhNs3RxZ6k5TqufPlpwl00O0xWuVx0a6MPYa7RVGarGmXuwmq1FHculeZk9BQmQEyP0iZJZByFR0GcisJx4pscKa0jkxh7KPD66DLc4/9MB88VvGc/Sp+gcuaZYttp/Af3uL/SqW0q+h72xO328Vh5hhfLErSn8xf3e6IlIyiALJbWzd3Gxua9xf5K9D9Af8rPMAwQJNJmLh2Xj6DyOPz4dQOnOXKqTUj0UJUMIguFef4cmRUw02FIJYHhh9mK2dwDVVTy32NyaAKxd24a0hE5mG919HJIrImlUwv7vnGCWsk5kZWk6kYfyOvoi7bIzsIepKbLxa2+CUQFhevGWPtX5w6uahzHmWIbxxa0W85j67KaKmIiXBHeRmXd6EX3tcleqpMBJvmK/94W9ng4vmYuhuDg+TzOm57SaCNIo1igOh4BURQRokehZkEbw+pjLPRUrktTlYsvcLexsdl32ILqf4B+T6p3Ft9C1Xm/5193vgKEceVRQ3VEcD4XrrqdjaNYCYxLpHiufQ1bRStN9UO5wbidOqWTjd0fhAnDp4mWKWFWy37KpbGjMoPxCBrflf+ImwyatgSHY/gBy5KeQqBwoTOFChYlUywd40G73JVmPV4qCvQVEPzl/KbKBDJ8Q1Nxj/B+AERTx2Gao84WtMJbLoVeSaRnjPowgFPDPfyo422WisU7QDn9FXR4opimiGmallPKP+h6lwnGTtbKpZ+R50t8ktZICslikf5IvJ3ayMtlIfyimcc4cRsbm/cbtqD6H6A/5ffkzj/zUk+MqDkJCOLMI0Il99kajNYht3tkS2Gt32+5nLwjuHHG20c0xHzOk2S9s4xLxZFruUbC5ZC4UP4PALFkHEdw+AiS1Bc5Ep2FPSh31Slpo9dG3R8yaXNU8COxsJRRyOVDi80GQyGuji6oLun1clB6PSvmf6mgvXZdp1snZHYTmDHyXv30121RQDRxMDW+ClLNn8Y0HGSyOi6HtV9dLiN3D05P6aM/v9O+wTTnFt7Z8QA0fLTg62zSWngsFOBDan5muDY2Nu8vbEH1P0B/UfqbPS/TtOMdgsbFQDAv24T+UTL9o2WGQ++b86cVODftrnKRLUoV34hv5qgR1hySMpmqJaipGd1LajicLg//Vx4iJYqcG23FP4Kg+rcnwuOeMuYUKHR6ZJFXnD5axhhLsiCtEdV0KryFjZ7xO12ozedimGDqo/9T1gyJlKnsKu4ulMNTCpOMFGvUsaNqUjb3eRAdxUXFAMrcHmbF/HiFNOlUCpfDmkBys/cElSiKmIZJOhku6jpTNCefi0fxeorthbSxsdmX2ILqf4D+GqrTEiqqVM1LqQw7yc82odfl5OyKeeg4eWiENSvia7mxvpZJmsbNBdxnoybjMxI4siM/rD8dyTLB6GbtwvzNMAVR5G9+P2lR4NTYyMX1S90qWxU/3xStzawbzN+rJrBCKadB9o5qQnl9ZxivkKa5LD8rgH4EQeA/yjWUE0HtehICs0Zc+13vdayLRvndpHx8xoeiii4wdkcjR+OP7hZ+7KvleKmbYm01HZLI35XrUYQs7eHTITC2QDJ0nU+ND+EyA/xkLzgSfL9K5y1XI1+KruKQgsZb55ifkjgsHGZpqDCDVxsbm/cHtqD6H6BfUH26YzP+RBOrpJzPdT4RKtNfwdpABFMfOZ3Xq4VZ71TwFugdeXEkxLzMFl4fpZj7BWERPn0Ss/J0Yu/ns+E0bjKjiraPxgxUKUb9xMLa/QNKGUamElEaORpkmibPGwvwkWKOt/BxI5VChAoibE2NPn6mS/k7ztoECX0iUFhEDGCnw0FEdBNJd4+5tkPMsMGp8IE87DlGY5XTgyFmCMU6qWHamOtjqQjNfalBv7+wTsrREAUZyJLKjN3xOBpvOBexMisxqXJBSe7LxsZm32ALqv8B+gWV1FfTEs3m/trzKUqv81WS6TgJ03Ci6caua+7JfL2CD7R10OwqLAqSlXKpQj0zcu3RL/g03ZrKk5WFfZs/K2JSS5SNoxSMnx5NU0uETYHCiusPq/gID784nvrZNSOuyWQNLtUuA2BNsHAX70vq/LQ4fFzds45Jo8SB0s7XUDxRDKEwz6t+rq+ZQFiIcrLTxQljrD0vIuMPN5OeN9qIaOt8qyZApyxyc3gzs0Yd0Z1DSyb5S3MbSVGgIjjy30WhfD5Rz4K2F3l7cv7p5z15wXEwS7NTua2+lOObbWxs3mtsQXUA0VDuZkdPigUNoQGvO/siBBEzjSkIhLV+QWU9QlXhDhDsno9bUEmrGg730EhVmS5yRCrNcldhERejT1CZ2si1S5lx38VnmsSyfwbyr4tRRScYoI2SsrpfOAWXFuaU0Ej2oqMzPvoGv3HcSrpzKnDvsGs6Ej14p96EaSg4pOGd560QE0V6JUikI6OuO6NXJya6aRzD3Xws3FIlPekK9DFqtgCmZjSm6Gne8hQnOPoZpwkEDRU9Y82LSk3EmaOqpExlxI7OYvBIAUKGgawWJ1I3iT/BP2s7TakfwYiWtjY2Nu93bEF1AHHf+Ydx8xMbuPKEgRGBnKAy+Wh9iKxQhmtTrpsoH0HlFDRec10CQGfiVPzuoVGV1WUn8suNIY6snV1Qzcy95TVc4Z3LUYo+7JgQQ9cRxAQI4FMKe0DGRCc9iKRGKST+jXE0GV3m48HChIBPD3OwtIp30iN3bfUk44iOCKYh4SrCbPPKboWJ+na660dOaZmGwXeiG5AFgw7v6N5YYzHfdSEb1+5k4tSxZw/epHyVZKSTr9csKGrPfr7XqTBV38FbU6xZIMSUCk7O3Ei1x+S+ktzBQAxHn62Gmn/H6QDMXMowpBTWzGFjY/P+wBZUBxBTq/3cc+7Qcb5Oh4QDlf6JcWkjV9uTT8pPkF20ixKqKKDHI1RVDhVUG8wUS90KE7yFef60uLyExSg7R7AYymRSPLGzmYwgUFZgxOGiunpicpbzZHPYwcdaNosy+QYUQDWPBPL3otohRLmnpgq3EefnI6zxR7v4c3MbbUIg7+vvSZ3hZqqmEdFGFm+qmsYp5AYoF9vttjj2JB92PEF258nA10Zd+6YjRq9bxvAUb5sAoIoe0CGbHrsgHmBnIsIGfy89nsLHwozGGl+Af6am4XcYRc0JfHTHNpxilM4FxXdD2tjY7DtsQfU/gMsh4kbjrW07yAgC84zcQ9yZR1E6gsApDfWkRYF7ojuYyNAapvXJJ/A0Pk+zmgaOyfs+Z3iX8PbmWsYdNLy9oZZKMi6bk4VagaINMScmE/rwA4kjexR3l7kKe8CpksgrHjfjNWPENWYmw1xVpZqR11ghK/bXnY0sMhLxMGFJwmMYeLzFCap6rYkjpJUsi41dFJ4J/QlPRYqkcRJQWBPBnmiSCzTQLRaBvxvZiHvcg6Sz44Di/LeG441QLS8bGWpF+HYR1wmZKTyGQSZQeC2djY3NvscWVP8DuBwSblRAwClIaDhwSMKAeX9WcJsmomGSTA/fUVabSRJW/dT7C2vzmyb6ODxpMi4xvDhIp+IEANWUUJTCzENnilfw3DtdTJs5f9jjYirFm1ubyAgCzgKNPSf4J/DDzm7QR+7y0/qiLBmhuDTPa94QL0qNlOsJDh9hzc6ebZzTOA6HafJGgT+3flY6ovyhpopaYduYUZnqjJOMKFNRREpzT+6uHMe7WpoPiZkR3+ueuCOd1CaC+KXSRMgGM947BXXzYXjLCi+619QMHiHn7eYdY9i0jY3N+xtbUP0P4JRF2innOwe9yEWL6+C2FXlZJvTz0I40NWYXa+YMn6b6alcrCxJrWVZ2ekH3Oa/nKS5SfsFr7R8BThtyvDPaypMBPw5d5uyCdoCjMstYLK+grD0JDO3iy6TiSIBoyEhyYf88qgN1HB5P0MvIP+O2WDPvej3opkJDQbvk+GtZFa36Bo5UHJwzwppYohfJNHEZBfpZ7EG3nOVFyc0RY0SJNDXDs+2rAYi4SzP2ZYvLS5sjwlaL62fF4zzdsYbVruGSu8Uzt/xQMm0yXl/hlgxdvS38uSyE3zA4z1f68Tg2NjbvHbag+h/A5ZAQ5F7eTD7HX7ZMASbkNXamH1VwgTlyh5yk57qvBEdhEYGwDMtdTnYSZjjjhdZYCzdXlFGeNQoWVPOSKzhcfpylvZOAs4YcV1O595YWnBQaO1JcucjUaK7ymxJbub26khkZOL3AfQAq5EnsCHfjKh85XVSNn1XbdtBM8V5Mc5WJzNv5AhlpdC+rVDJOf1zKVWSasZ8pruPZvHEcdZXW7AWMTK5YPLu3IlQ9y1jtvISWtonAsoKu0dqzg/tCAZyGyUVOuyjdxmZ/xhZU/wO4ZBHREWGH/hTPNo8HLs2rIL2frKjkXLLTw7eJS31z/iSlsNqjtWInv6urYWGmmzOGOS5ndT4STyCYhT943nRmeKE8hD/bxOJhju+MNvFgeQh31slXC9xDcrpYrziIIHGYriNKQ8WrJ2tyRCpFSC8uzTPHdwpL35xD7eSR3dYzmRSqKe+ypSiGBvd4DosnWO0aPdqVSeYiWLopoJSoe22GUsv2WCtVaWuRNrNPUOny3hFUTqdCQEjRZRTe5Wem0nw2EiVFcalYGxubfY8tqP4HcDkkpuphDo4HqFEC3Ep+lgn93F4+ibaslyVGctgI0h2hGHGpmo+J0WE76MYi4AgxNaZSmR3+4VJpuLm5s5ttYmGGmwAblBRPeQJ8WOsc9nhbrIU/BAOM18yCBRX+EGeOyxVhv6SmCbmHdgpOM8r4bFsnqzxjF3ePxuLuf/BZ5X62bz8RuH3YNR2hBZySuZ/59T7+WdRuIPfVlTn00eccbuvexFfqaynT4R6xNE7ph3f9k8udv2J582nAkjHXP5Vdy/+Nq2WhER3281osO4nw+QnjCegmzxR4Dbdq8M2eMDuE+pLem42NzXtPaX7TvQf09PRwzjnnEAgECIVCXHjhhcTjo38zTKfTXHLJJVRUVODz+TjjjDNob28fsKapqYmTTz4Zj8dDdXU13/jGN8hms7uOv/DCCwiCMOS/tra2vfI+9wYuh8TErMpNnW9zQXdH32v5/9Wv8DpYE4zw7gi17FsUnTdcLnRHYTr9UP9cHm5u4+Le4YuYY1KQh/WjeMNZ+ONxhlDN58MRZmrDR9ECusyF4QjHxfMXnP0EXR4MzY+hVhBXhzehjEjlvKjPo9VdnIu4hxQTxXbcmZFnE27oXYuz5p8kPUuL2gsg63Cy0eGgWRrdXLM71sl6p8ImpXTf2eIOiTWKQqvZa2l9rxHnXUUhXqLRN4PxectIiSLJIi4fFsu4O3sKL7jHFog2Njbvb/abCNU555xDa2srTz/9NJqmccEFF3DxxRfzwAMPjHjOlVdeyb///W8eeughgsEgl156KZ/4xCd45ZVXANB1nZNPPpna2lpeffVVWltbOffcc3E4HNx4440DrrVhwwYCgd3F2NXVhc9De69xOUQ85NJxWl+bfSFF6ePkD9LR0kBg/IRhj1/RlUYQ45TNLmwsjNyXKnQYwz+sOzzTuFK7hCPLK/hEQTvAQXIjR/RGeC04QhTMdHJFb4R3HIU7VrscCtrW76LqBhLDp5s2ho7mFq2as+sb+GjBO8FyqYPvj69nWrZpxM63HfGtKOVLSZpFGlACG8qq+L/xdYjZMt4aZV2F4eKutg46hNJ5QL0hdfHHcbUckm63VHe2JBXg7K43aa3N38LDChPLp/D4jmacugimCUJ+XbMAbY46fpw9m6PKq/jcXrhHGxub9479QlC98847PPHEE7z22mscemgumXT77bfz0Y9+lFtuuYX6+qHh8kgkwm9+8xseeOABjjvuOADuu+8+Zs2axbJlyzjiiCN46qmnWLduHc888ww1NTUsWLCAH/zgB3zzm9/k+uuvR9nDjbu6uppQKPSevN9S43RIOMUkSUEg3SeoPM78/+qnKYfzbncZZSPU/SxOJwmQYpu/MIdxyZVLjTmM4Yu5l3U8gXfar2mTD4UCrRQFJSdwpBFSVt3ORu7IfgxfqJFZBe2Q48eOe/CLYdTuqRAc6ir+eu8jeCY9SZN+AnBQwfvoskSzQ6ZKH9nYc0a0g3SPG4+78KhbP2WeEEbWi2iMXpekqCqHpdJskktnVhlQgtSlsvh1a95dtarOIekMy5TSjL4Zcj+BKgJZHdDJZFI4XfnXar3S9m/8s+6khUUU+pm2sbF5f7BfpPyWLl1KKBTaJaYAlixZgiiKLF++fNhzVq5ciaZpLFmyO5Q+c+ZMGhsbWbp06a7rzps3j5qa3YNTTzzxRKLRKGvXrh1wvQULFlBXV8cJJ5ywK8I1EplMhmg0OuC/fYlTFtkZ2saiiQ38WMnVDnmV/B+uZ7T+jJWuLzNz54PDHr9Mv5wvqVfgKBtf0H22u10sqZ7HxdXDR4di6V5EOYEojiwexsThJiOAZgxfWL9TaeAn+id5pfz0wvcAjuZNTpDeIBsfPhUX0TqRXO2YgjXX75FY4JnJH1vaOD8yclHzjHiCn0U2cFpaK2ovgBnlM0ls+i5m8+gVZq2+eZyjfos/Bb9Y9J79LPLP56kdLVzSa+3LwEOBczkr8106xhc+K3E09jRJTcVGn6U4EslULgXvFosXuzY2NvuW/SJC1dbWNiTFJssy5eXlI9YytbW1oSjKkKhSTU3NrnPa2toGiKn+4/3HAOrq6rj77rs59NBDyWQy3HvvvRx77LEsX76cgw8evn37pptu4vvf/37e73Nv4XJIiEJOhMh9zeyeAmpbVIeTblEkpQ0ViGlN5SXFAUY1P/SObGg5GoK/knZvBPThH/wf727h8pZW1gcKe3gBPBvw8IWJjQR1Hy8Pc3xZ9z/xz/wd24SjoYhS5l9UuOmVqzgt/C5TOGrI8c93bscXD9NTX5ygKndVMj+jskEeWSyZWm4PowTRIq8R5+eOO3AbGnDiiOu2qQmWuRVMf+ncvx19EUxljIL4ftbQy3qvyccL/DyOhexQuNk3lYgo8LlED6Gq/N3gP9PdxQ9bd/JGhbWBzzY2Nu9f9mmE6pprrhm24HvP/9avX78vb5EZM2bwxS9+kUMOOYQjjzyS3/72txx55JH8/OcjTWmDb33rW0QikV3/7dix4z2846G4ZInFvRUs37aDM7VcfZPXmf834r87Ozh2wnieEDcNOdaVjOJpvA/PxLtxK/nXkgA0BGpJNZ+F2vapYY97VZVpmkalXLjVgMudq+lJjzDyRU3lIkqeIiMGb7okXvS46UoN301Yp2X5UCbKOLk4M0d5V5p05AdyRouREASyjuIFlcch8HHpFU4SV6CpI/tsrQm/iqfxPtqlfxe9Zz+OPn8vxbQmPtqkv+NpuJ8ubXPJ7mEwfyhXeLQiww6tsOifkolTYRj4ncV7hNnY2Oxb9mmE6mtf+xrnn3/+qGsmT55MbW0tHR0dA17PZrP09PRQWzt8fURtbS2qqhIOhwdEqdrb23edU1tby4oVKwac198FONJ1AQ4//HBefnm4+EYOp9OJ0/n+8ZXJzfJT8ZgmRl+RdCERKqeUeyDrxtCUWyLeiz/tRxfA4yjsvVd5/cyKBfEKaVRVQ1EGdvsJfZGWQo1DARZWHcEvHr+e+uryYY9/obuHX3Ts4LWaItKKwBlRhZDZSrBm+OiIlM2lHPtrugol7VT4vaeOqOgb0ebhIeldvjqxgY8ZbcPEyvJDdru5uqqClCDwnWgHtZXD+7yHEj0E0n7Gl6Buq58uj5tTq+aB4OJfFtY3ZAy6RT+1JbJtGA5n5mBiahLDKGxYt6j1NQq4SmN+amNjs+/Yp4KqqqqKqqqxUwKLFy8mHA6zcuVKDjnkEACee+45DMNg0aJFw55zyCGH4HA4ePbZZznjjJxN5IYNG2hqamLx4sW7rvujH/2Ijo6OXSnFp59+mkAgwOzZs0e8nzfffJO6uuKHvb5XuBwS38+ey8/Nz3BaxTjY2omngBqqU5T5fH/DM7zmG+qd5EkkeLV1LWF8CAV0OwF4JPiX81oAIrFzUSoGpmPXmR3s9HkRHIUPFC7L9nKF+BjupB/40JDjUjaFzzRxKaGC9wA4TPUxN5NgZXb4n/MGKULE7UYv4O9hTzpCNdxS4wCdEQWVRk4cukpg7Ol2ennS68EQBL4yiqA6JdzNj1rXsrSm8IL7wYiBKrb5IpijROP25J729VTTw7tH7L2RLpWZs+hqi+ERC0ttLpfaeSsYoEIpfiyQjY3NvmW/qKGaNWsWJ510EhdddBF33303mqZx6aWXcvbZZ+/q8Gtubub444/n/vvv5/DDDycYDHLhhRdy1VVXUV5eTiAQ4Ktf/SqLFy/miCNy3TQf/vCHmT17Np/73Oe4+eabaWtr49prr+WSSy7ZFWG69dZbmTRpEnPmzCGdTnPvvffy3HPP8dRTT+2zn0e+uBwSUnAVKaWL7eljAFdBgkpxBxEBOTu07ieTzNVVpQse2AKy4uQth5uMZFAV6SA4SFC96Ozi9UAF58iFF/n7sr1cIf+DDrUc+MWQ41J/FMw51IwzH7J93ZTGCGN6HvTHeddZxZXi6DPxxqLSHSKbmIxsjhzh+FI4wC9S63h91meL2gtAlCSu7I7jQ0VU9ZHXqX3vWynu57gn4/zVpFs/DqYT0zTHFO5uMwUCOD17L/rz/dSNzHK+xbtbfgLT8v/5vuiK8o4zxJdlu4bKxmZ/Z78QVAB/+tOfuPTSSzn++OMRRZEzzjiDX/xi9wNR0zQ2bNhAMrm7e+vnP//5rrWZTIYTTzyRO++8c9dxSZJ47LHH+PKXv8zixYvxer2cd9553HDDDbvWqKrK1772NZqbm/F4PBx00EE888wzfOhDQ6Mb71ecsojDvwbZv56OTAMwG28BtglSXw2LQx/aIaelcqmLtFBcFOSSugoiksgve7cyiXkDjk3JCHj1FDWVhRc6p2W4IxQkhcjXhzn+itzJ8lCQGrm4lF+3Q2ZD1kGv2j3s8UmagdtUKfcU59PUGBxHquliZHFkcSHrGi7TxOUafqh1vpwSM6kkwbvaKIKqT3QLJRRU5W4f4yKNeMiQUTVczpHTbKZh4CEnUtzeUMnuYTAeQSUgJNFThTVKLEqazFDj1NcW1hlrY2Pz/mG/EVTl5eWjmnhOnDgR0xwYNne5XNxxxx3ccccdI543YcIEHn/88RGPX3311Vx99dX53/D7CLdD4phkGlX3o5k5oVBIhKrZ6+H2sjkIYhn3DDr2dngt/1dbTZ3m4KYi7nWcZlKpq6ipoVGoM6Iis7RO3phUhEOU08HdZUFk0+SqYebsLXPFeNsZ5GLJWifZSNxSNZ6dRhOLvQGGa9r/ZmeSGrrZdPjcovbxGCkeU76NmwyaejwOZWj92vXBG1jT1MUvJ1obKjwWGcEJJmRTIxuFPuRs5o7aao6SIyVzV/I4RF5wfg2A3ugncI3SVRdJ9PD58TV4DJNb3XuvnvFXoRQrnOP5RGJlQT2hZ0XSjDd7WH94Ma5nNjY27wf2G0FlUziiKHBJopl5yc1cxikAeAsoSg8Ha1kWiiFmhxZSd6W7WOl2MXuUSIkV/q9dYqLRzNszh6ZpVkuz2Zl2Uh4o/Nt8VWgcn4rG8BomqXQCr3dg1GZRUmBOJkZDZXERA6ccwkj60PXhC6LXMIVmo4xyX3HdXS63i7niNgCiyfiwgqpd+A9CVYQEk4Dha57yoVV2kcJBJDl89A1gp5RmjcvFwXJxn4c9kWSZ9bILXTTwRDspG0VQdYXb2dRnzBvwFjeAejSyokRKFEllh/c1G4vHOIZAtpNFZcX/vdjY2OxbbEH1P4JHVMGETjX3V15IhGpCcByZrmNxCaEhxybrAX7S0UWnXNxsuozoAQPU1NDaorvlz7JVS/BQfeGRlspQDd/tzs2C60nEhwiq06MaE41e3l5Y2Picfg4Pns+bb32QqR+cPOSYaZp8Sb2SrGGyrHpKUfsoiotP1dcSFwV+3ruDQGioQIsrr+D0dKFyZlF79XNJXSNJyeR82cHwLSFwdkTk3GgX0pzihj8P5gv1lbmUcHgbk0ZxmJcyOve0thMRnCjDiMxScbo2ke90/IfNBY63+Zl6GqoOr1QNP87JxsZm/8EWVP8jOMhgAmkz963d58r/r35ScDxC53E4paH1RWVZODyR5HVfcdEATXJDFvT00HRSd/AmvME0PertwPC2B2MhyQ5SpoJbUEknosDAsUX/Fo/Fq7ZxeFlxD7jZ0Ze51fEPhNajge8MOBbNpFAm/AzFcCJKH4AiCvkFUWS7QyYpikQSw0eMTogaREUfjUJpLAwkIYCR9aCOMgJmXlplkpHkbX9pa4MqsuAys2TSoxfzm+kUi9MZuov42Voh5CijIZuleRRPrpGIZVIo076FYiiI0lFA6cb02NjYvPfYgup/hHMaFKJiAxVbE5CBkDt/3xyv2sUG1/lkTRFV+ySKY/cDelPwKH6nXsbsqhkcOso1xuKOygY2a1mOJzWkJsWUuxHFDL5RipGtkBTcyKgk4r1Djv3a+AjhrMnTlUMjS/lQozaxWHqV12JDW/a7kzEkV87vLFTA/LfB/Kg9SYUZx7Vw+J/LDeF38AgZmr2FidDBzBav5JkNHUycN2/ENT+RL8aId3JJ9ZyS7NnPbW0CE40W3p45eoF9xFXP2eq11Pod3FrSOxiEkktNi1r+jvftkU4EwQQpQ+Ve7ES0sbF5b7AF1f8IKUHAEATSRu4Xd9DjGOOMobi9fjICJEQwEzEq9jBM3WTCE846vIHGou5zs8tLqxJhqzAw+mEaBg+1bCcqSIyXivvYntQwkbTcy3e0BIMTUtmG7+ATTBLGI0DhD7mNcpyHqyrw0jxEGIrhTm5ridApelDk4v8Jzs44qDdV1qtDI4dZTcMj5KInHn+o6L0APpR6io84luJvORM4b9g1r8gCMWcNl5Zoz35U0Q0GZFOjC5imVIzXPAKTSjj6Zth9PG5e9E3CVAQOz/NcJRLm+e076RTcOCR7lp+Nzf6OLaj+F9A1/tu0k4QoskSrQhTAX4Btguj0cvDEnGD6a++OAYJqdexxvBP/w47sx4EPFnyrU9zHs2XjeKqrFg54PZNOMFPLCYZ4oLhCbl3wAr30agPTNEk1hSBmASgvMnIUcRj8x+dlXnrog99MJTguE6GH0pg5qv1dd8PsFYv14hQE3KaJx18ag8tpmbUcLr3E0vDIESq96td4RR2NjwDFWUPsidbn75XNjJ7yW9vzFp6G3xMzpgPnlGz/wbxZVs+/UjpB0+SbeZ6rJqM0GgYG75+pCjY2NoVjC6r/BTIxvKaJV9dJ4iHgdiAW0I0nyQpOwyQjCoTjXQOOhdJRXKqHmiIzWDOUcTTF2qlODfQ4Ssaju6ph3EWmRyaqV/BGU5SGhfMHvK4mEryyfQdJQSTkLm6g7lTvZK7e8XdEo2bIsUwyJwZSQmlqZpa5Q7xiZKhKhxlswrCjewvnTGzAaZi8XoL0IsByV4p/VFVQq29h8TDH05kUAdWDJupUOktbw3R3RQNNWZPjzdSoqWVXrINQ2k+1vHfFyjhfI1p0Hoo7/yaGdF/KOSmWzqvLxsZm32ELqv8F3GX89NBnefDl9WSRCbnzT/f183BTlHozwob5Ax+Ul3a1cXBsPUs9pxZ1q0d0PcIVzl+xvPljwAm7Xu+OtPFfnxenLvLRItNkx+rrOFp4G2eHF9hdNJ1JRqkxTFwmKEWKj8bAJD4ajbFNDA051hFtpt3tImO6GFfULjl+XllNUgxztiwP8bzqjeZqtVxm6UabNMkqT7i8LNF6hj2eScR5tXUtAGqRTQqDWet202lGaBzj+8CR4TBXta7l9cDeHRE1p3w+6eZzcNfnb5q6Nfwuy4IBnIaTiaW/NRsbm/cYW1AdKKTCYBrgGVp43JnqYk32cXrLVOhdTMhTeFG3JLiRzAhacqDxptznni66iovsJBQHaxUH7ebAgvHmSBPXVVUQ0g0+WtQOcFTqBQ5xvMCyzsmwx9XS8dx7Sgkuiit7B2efO7fLGGoQuj62kdtrq5mREYY1/cwXn9BANKEhmkMjHdWGlxXbdrBVrC7BTjnmifXM7X4LQRne8iGViBAEVFNGKXGEqlE5hh3b66iqHb3Y3czk/i6zyt4t9q6Or+dl52XEwyFgZV7nbopv5r7yEPPT8Lm9cnc2NjbvJXtvDLvNe4eehX9cDC//bNjDzfFmVkYeQil/CYBxocJTTaqYO1cb5BMlZ3PCQSpyBt4bUhdnj6vjb31dcP2YmQwfSKaYny4+0vKW2+CuUIB1ma0DXm+JbOeuUIC/+4sThQAOj48WWaLNMbSd3qFlmZPJUK8XK9tyzHaeR6rpi1Q7hvoyackYbtPEZZauJX+60sB50Riz1eELqTPx3BiWZJFjiIZjhnMGdeHJVKqjX1voq7EyHXtXUDkVhfFCF1VG19iLB1GhCZweizMrW5qRQDY2NvsWW1AdAKx6/S62bX0WvWnpsMfLYh2cJtQwN5YTO+PKCn+43heawMVls3k7O1BQ3RuM8NXqSprl4ka2+JUgNdks/kEeR1W6izvbO/laV/FB1dXONHeWhXhHbxnw+o5oE3eWhfhboHihkwyUcWLDOD47rhzDGPheZull/KWlnfMTtUXvA3BS7O88qnyHyVuGjmZqLj+C6enf8/3Kn5RkL9g9n0/KDv93val3I5+vreZHlaUXCsd2/pEXnVdy8I7fjbruX+K7nFtXzeuu4oZPj0VMUjm+oZ5PNuT/RWJ6RuEHXT0sMYrrjLWxsXl/YKf89nOSWpJz198DDfXMU1v5k2EgiAN18oRMih9ueY0Vxgw+BUytLjwC85zfQ5g4ZYM61N52GrQ6PHxIKU6MLA4u5EtrfsXGQY7rUdPNM/pCNPd4JhW1A0wTqiiPbqLKMfBefbrAp6IxDDNU5A5QHajANGRMw0U4naTcs/tnHhX8rDKm0uMqjTt2hdHDQeJWliV2DDm2vvdtqHqOsHsGlCTBCIai0CpJRMzhZ/l1xdt4ze2isbj50sOScjjY6pDpzYZHXdciJFjlcjFb3rvfGb2+Mjr6avqyWQ1Ztl6fuM0xla3ZD+EvK82MRRsbm32LLaj2cxJagmp3FR2pTtYoEtFoE8HQxIGLMrkHX01lJSdX1HHyvMILdesci2hvrcBbN7Cc+qs9CVQxw8SDihs1IrtzKRrnoNqjnd7ZXK19g2Orq/hIUTvAIY4pHNH9b14LDhRU1ZrCd7t7WasUHzGo8PhJbvwhhglZfeA/s7dCx3OHOpHzGyeypOid4FVnhJ/V1zLZ3DRkEPGW2Ds4K58nJuRvPDkSrwTLubhxHG49xIphjtfqntwYIrF+mKPF8arcweXj61mU3jnq5+DjMYVzItvJTC1uFNJY1JaN56/NrXgNk3Qihi9o3Tx1hfMIHs42ck3DzL14hzY2Nu8VtqDaz6nyVPHsp57jgdunU5aO4Uh0wyBBpWeiiMCEumruOLO4b8MzPEtY1TmJoDFQlH04EcMpaLSUFzfkVfHk0kSDBdWrHf/GO+UvdMpHQt4WigMRXDnRJmcHioxOuY77syfgKp9Ksf7egiBwnfMBgnovqa7p4N8tNN+IPIxnwiu06CdD0TtByiHzjqjgH8aHakakg1TYR5WvdP/UfZ4yTENCN4evofJkshybSLLaVRrfqz1xyz78KQPFHHnsDcCMdIYZ2RRv+vduOs3nDTI9k0USTLoS0bwE1evpn+Gb/g471cuA4mY62tjY7HvsGqoDhM/IVXwkkcSTHDpO5TcdSzl4YgM3ZluL3udjrbexyXUuB2//za7XtKzOldqX+aZ2EZ7QUN+lfIh6PJxWOY8Lqwc+CHvTXYhKN4KULOr6AFJfJ6I4SFBtdc7kuuwFLK/9dNF7AHyEpXxcegU10jbg9V51J5JnO7oQHeHM/DjYM4O72jo4Iza0UPuQWC/39q7jY2r+vmMj7le1iPiGH+HvuWzY49t8C/myejnPV3ymZHv2c4xvIa827eQrvaMXpd+mfIGL1KvI1u3ddJogiiT7HNJSifz+PnU9giBl8CqF25jY2Ni8f7AjVAcK/lpofxtiLUMOJbQEWUFAKoXJocONCmjq7odHbyrFE8460F380FdcV5UjWMkWfwTTFDEMA7GvHuzTHZv5ck8XO6rSRV0fYHnAz+cnTMJnuHh1j9df6v4DvhmPst08BZg/0umWua/MQ48Mx/S8wzQ+sOv1C7t3YqbT4NGK3gOgxtvAwak064fpKBTVvjonpfjOxX6Cepjvyb/HkxSBDw05vlHXeVKpwxkqLv07HJI7F8FU9NGF9QpJo9dZyZcDpZlfOBoP+BqICSofSHSTT3z2rpZtBGmhfULpxK6Njc2+wxZU+zlvdrzJfW/fR62U4GNOF95o0xCTwC85G/jMuudRjvh40fs9rrTz+UmNHJl+l+P6XtsabsY78S5MQ8Ehfb6o648PVJFuOxVT95DUsrsGIVdkMhymJjEdoeLeAODyVWOKOqlB3XcZtRtB1HGXaK7aCrfIJqeXmYmBkcGZyQjzMh287ixuhE4/u9Kk+jBjbrQYJiA4Syeo/HKWC+QnSRvDR1bejDyOd9JjNJunAseUbF/Y7e/l1ocviO8nXX4fnsoMGXMJUDoPruG4qzyALndQbRgsyuO8mmyCWrKogdLXmtnY2Lz32IJqP6cl3sJzO54D4IH6as50Glw3aI1bTeHWdfAUP1PNqwQgA2l2R0PikQ5cqgehBDPJytwe6iPT8Zlx4vHkLkElabkHqOAsvhV/XuUC4pu+Sd2gwb1XtbUyOdnM2gmlaU9bkvRyenwHFYGBP5d+4SN7QsOclT+628OTrjJaRceQDsg7vTv4YnkD50ntQwrWC0X2+vhhRRlxUeTaZBSfZ+DfSTDVi1P1UOsp/cDfmC/AZ8rnokou/jbCmqymUaY6yYgy1e7SjNsZDa8xm+5oNUKeXl8+MwECuN+DKJqNjc3exxZU+zlzK+fy3SO+y0vNL7Guax1OaRhRc8rPYMn3wFH8w+VDwUO4+LWH2CzunhpXH4vxWvN6tgnjRznTGoIg8IhyLWXE2Nq+GCoOAWCd2EOXxw0FDHUeTKXD4DxzOaFUFjhl1+u+bJL6rM4OT2kiGkdoFRycWMdybWCp4gZHgpjkRHCXxmwzUlHP1+v8oIucP+hYRshiCALOEkaoQsFKHgzkUrsXde/A5xlYWH9JZwsHx9ezzHdayfbsRyqrZU0wimmMnPJLxCO81Po2AJkiB2lbocH8DM3NPYTkiZbPSWeS/CXkIGBIHOu3jT1tbA4EbEG1n9MYaKQx0MinZnxqxDWPND1NOB3mQ40fYoI7VNR+fn8NAcPEx+6Ui5oIA5CRSjPkdZvspVVMkwzvZBI5QfWwL8pGZxWXy6OneqwQkLJc77gfwxQw9F8i9qX4lGzu2rK7NA84Xc79PIz0QHPJn1QJ9Eo13ObIlmSfGl8ZeroOU3cPqDsDuLZDoNbcydbFQ13UC0VRnFzUkyBoqmQTQ/8+HH0/R9Fd+i6/hmAVmY4TMQ0XaS2LyzH0V1gq1rtr9I2zRAOhR+Pi2F3c4nyFHVuugvmXWDqnvXsnt5WHADg1uPdFn42Nzd7HFlQHCpGd8NS1YGThrD8OOPTg+gd5u/ttJgYnMiFQnJmkqy894TF2P0izydyokYxUmijI92ucbFbq+FrPag4lF+WYohr4zAyV3uLdxf2hSv4Y8BMTBU7vbqaur6PweXeU111+GpXSNL+mFDctskQ00z3g9UYtS8AQqAyWYjQyNAZrSG69PLenZuB17r7/kJ6iyjTo9FWVZK9+zopADTE2pYYWwu8Spp7SC6pKrx9392EEhATxZBpXcOhnLhXLDW2OCx7ei2RagDjjhS52poYfFj0cyVgPp8fixAUZt6s0X0RsbGz2Lbag2s/pSnURyUQoU9OUr30YRBkMA/aIUhyj6kxwjWM8xbdn6/4Q3wjMICK6+JVpIggCr8XX8rvqSsYZOqWIg4R0mepsCi29W7R9vStBNT1sWjSv6Os7XW5uKwuRFgUO69yyS1A97Ndpd5TxI2V0jyOr/Lqqljd945iquDix77V0KsEfW3M2CtGa0phOuhwi9ys/JkicRPc8vPW7LSfOFn9COhHlj+MOKcle/SRFHxjdpONDbTruLEtiCJWcMkzXoRV0XUfTRu6AfK7iJ3iFNK1th+JzDv0ZburezG2TFlCuyVydLr4rdCyernRyS80hHMpOFljcT0hm+U7aSzdB0u/BPdrY2IyMoigDIvuFYguq/ZwHNzzI3W/dzVnTzyRaVUGnJPHz3i2EKqbuWvOlTa9Bqgc+VPz3daWinicqUkCKaFol6HbSonXwgtfD0ZnSCJHL4uM4OP4iy/s6ugDeMKdTbvZSFyxNfdMJ8Swu0mSTu9NxxyUyhGWDumBpzCA9rkrMhERG3z2mJx5P8I4xFR8ppgwqii8UQRA4SNxCiDjbo13QJ6gMw6DH+zRZpxPFfVJJ9uonLHto0yWisbYhx95ymXTLHk7NM91mmiZtbW2Ew+FR12lH/xhBMDBSWdJbtw45XuabzKmzr0M2Yeswx0vNMbO+xOFCFrcpWd5PFX28fdQdCIJI9D24Rxsbm5ERRZFJkyahFDk6zRZU+zmyIBN0BvE7gzzt8dAjCrT3bNgtqEwT0rmUHK5Q0ftVeYLo4UVksy56k2mCbicHZTwcFOsm5i3e9Rsgq+RqmIxUGADdMPlSJmci+XrVxJLscVGvwiSjlTWpnAg0DYOre7qRBYPOqtL4Jx1bewZPvjqT2pm7zU4jePi4egN+l8yaEtkzAHy3Kki7w8fnO99mwsycmWU4nUSueA4Z8Lm+U7K9AK6sa6BbTHCqJHDUoGNf746SknQaj5ic1zX7xVR1dTUejwdBGN6faVtPFk2AajlEmX9oKjMe7YJMFxoOyqqKnfw4NhW9ThQtQlb04qu0JsZjKZWWSBq3Q6Kxwk752djsKwzDoKWlhdbWVhobG0f8vWMFW1Dt53xx/hf54vwvAjDp9T/iiOykNqFSmkIAAEXhSURBVLu72NnMxMDUEQBKMApEkRU8sbOIxhOk+yJSE1MZDo0leLW8NA8vQ+m7zz4huCPShXfKzZi6F7/rxFHOtE5a8oEBajxX95JMZ/iHfhx+IcmH8xgfMhrjsy18X/4dro4q4DAA1nVtwDPhLhzUAqV5LwDbFIltikRPsn3Xa5HuFhaFfURFmSpPcYarg5HlMkxdJKYNtJjIqhlOSeZMX3vLrUf6dF3fJaYqKkYv0nY4REzBxCGLuFxDHdOzSRlf1iQpOoY9XmqyTjc+M0JCFCzv15WJIfu6MPHictlF6TY2+5KqqipaWlrIZrM4HIWXxtiC6gDiY+7x0LIR9qg9auvZxEcnNlCuGzzrKE2b/iP6VxnvamVN86NQfwzPej7C3zrqObr+gyW5/suhKn6cncc4FywGmnrbEZUe0JM45dJ8ZDOOAGigxnMF4xHV5LvZC5BFkU0lEh/lRPiA/DTb07vtJFpi7Uie7ZjZ0nT49fO5iJs6fTtG5R7RjmiYe3vX0UugJPUBe3K478s8sPxjTDp+YA1TXNX5lno5fiHJj0LWhUJ/zZTHM3aasC4r4zGTJKThPwsZyUeXUYNbUdj7PX4giLn7EE3d8jm6kQVMivgybGNjUyL6U326rtuCyqYPX18HXHx3XUs03kZWEMiKIqX67a2LCqoOyVgHAK+abtZIczm8emZJrt8SrGZzJkKYXLFusGM79zZ3sVkunaP0jTXjWG9M4ig5wWLgzfZ1+GZei6jVIAgfLckeGY/MDyvKSJDlpr7Xpnbu4Nq2DJ3O0j5JpxvlLEhtYEVqd4FzOpoTi3HBR1lJd4P5mdVMk/9NoGUxsFtUdSbTPKnUoYgebnbkX49gJdxuChKYYBrDC5i0aRATZeThPNn2AoYo0ik60AUBq19ZyrMqtZpGWrYuwmxsbPYOxaT59sQWVPs5D296mOVtyzlhwgkc6i1jh9OFM9FKfxXQFIePZ5qaSZdPLNme36oRWeNs5Eu9K1nEmTTJ9+Cd0kaPPg6GeHXnz8zQAv61+lQCfXVgZjzKIjVJuVE6EaI5KzAzOj16LjLSHm5FEHQksTSF9QBOfzkPBvxIpsmPdB1RkvCnEhyfaudN8qsvGgu1bySPntht0ZCKdWECqRLZWexJo/oui+UnWdEzMPK1sXcL3kl3gu4Hziv5vtAnqABGEFRJPYyoxNAoA0qb6hwOTVbokAUwwaqph2AaODHRBHswso3NgUJp8wA27zlvdb7Fv7f8m3d73+VfddP4dH01d7t2d5XJ6Rg1us4EZ+kceeQ++4VYOtcy781qSLpCvbs0D6/pwUZqw1Opj+fqUdRYFwApuXS+RoeVnUH83atpFHM+V7O7Wnm6qZlbuoo3Du1nfPUkvtQb4es9YaJ93kj9gkdzhkq2D0Bn3/iZTdpuG4MXwytYMLGB/6s0RzmzMLYpKj+sKONZR/OA11PhNpyqB7++95JtcVlmi+QmLAz/viRTRzRFHLw3+TRFcmAaTjCtR8SEfjEoln48z/7C+eefz+mnnz7qmhdeeAFBEMbs/NwXWLn/PXk/v5dC+d3vfkcoFMrrnIkTJ3LrrbfulfvZ19iCaj/nxIkn8vVDv84R9UdQG2ig2lONX9lD2Ez7MFz1DnzytyXb88J0Iy9v38ERagWmYfB882rebHqXhYHSWBrUJjfykvNKvhfOTSVsim/hKY+brSUa1QIwU0hwnrGCGZ0v515I9FKr65SLpROeQX8FF/Ym+Ww0RiqSE1QtqSZWOp30uEobNfpH7TS+XufnAdduERHPhDEEAUEsfRSk26HzYMDPW8pAATo53Mvrzeu5rz02wpnFk5ZkUpJOcgRBVaupzNLSlAl7X6ycf/75+F1ufv3zP2CoIUwzd0+PPPLIqGmEpJClRxTJ/g/XUN1222387ne/2/XnY489liuuuKIk1xYEAUEQWLZs2YDXM5kMFRUVCILACy+8UJK9SsnEiRN33bvX6+Xggw/moYcesnx+viIv33sbLITOOussNm7cuFf22x+xBdV+zuL6xZw35zzmV81nyYQlPHvms1x/5PW7jq/qWcvvmp7itXT7yBfJE5+7jqBhIia6ScbDOITct+1geWncuH3ldbTIEi1KAkPXWaFu5Gs1VTznKZ0BYkNqPdc77mdR76MAGImc4NGcpa02igo5cZsI56JsT4tbOb++hlfdpYuEAdR46tHTtZj67rE5x6iVPNe0k0+ppbcOmOyfzBd7IyyJDRQ12XjufaYdpXdJ78cpejCyASRzeLuB/uLw/mLxvY3L5eL+u26lOrIWQ7dWExURdVplGU0sffRwLFS1NMO/iyUYDOYd3ciHhoYG7rvvvgGvPfzww/h8pU+Bl5IbbriB1tZWVq1axWGHHcZZZ53Fq6++uq9va1jcbjfV1aX5In0gYAuqA4lkD/z1XPj9x3a99HLzy/x05U95ctuTJdtG8Od8lZRUJ9GeXGF62nTgLlF3nLeiihMbxnH+uErae1so1wwWptPUyqVrL096XPwp4OM5V05Iva1u5g8BP1vdpX0Id0s+WmSJ3nAuNRbMZpmgaVQ4SzsK5ui6D5PcegX+5Km7XlPSUap0A79SWdK9ACaXTefScISPxgcOKdb7hKmqhIq6vmmaJNXssP9hOFBTLrSMMOzxtKaR1AxS+vDHx/qvP8pklSVLllBbVcFP77gHQx++e/P6669nwYIFu/7sNeCvd/2eQ+Yv3vVaf3ThxhtvpKamhlAoxA033EA2m+Ub3/gG5eXljB8/fohI2LFjB5/61KcIhUKUl5dz2mmnsW3btiHX/dGPfkR9fT0zZswAYM2aNRx33HG43W4qKiq4+OKLicdzQv+pp57C5XINSU9dfvnlHHfcccO+x69//euccsruYeO33norgiDwxBNP7Hpt6tSp3HvvvQPuq/////e//+W2227bFaHZ8z2sXLmSQw89FI/Hw5FHHsmGDRuGvYc9Oe+88/jLX/5CKpXa9dpvf/tbzjtvaG3faD8LyHV/XXXVVYRCISoqKrj66quHfE4Mw+Cmm25i0qRJuN1u5s+fz9/+9rcx73Mwfr+f2tpapk+fzh133IHb7eZf//rXmPd5/fXX8/vf/55//vOfu36G/VE4q5+RW265hbq6OioqKrjkkkt2dd8ee+yxbN++nSuvvHLXtWFoym/z5s2cdtpp1NTU4PP5OOyww3jmmWdGfK+maXL99dfT2NiI0+mkvr6eyy67LO+f2fsFuyh9P6c71U1GzxB0BvFKCqz7Z+5AJgZOPzMjHZzsGsdBQulqWtrLqvhmYAYJh8ipO1fwg5oqxqky3ylRp0RZsIqQbuAyDVraNvLhmMQ1iQ6WzVxYkusDpH0uflxRTkU2y+XACqGFZRVlnCmU9tv7F8ZNJCrBZ8wshwEX9uhMz7ay6shFJd2nTt3GHx0/wuz2Aznx/FD5F7lkx/FcOnkmi0c/PW+8ZTlRHTCiA17/b+ZtHqiuZJqs9zlvFUZK05l9XbFfAoa6uFth3Q0n4lGs/2qUJInLvnM5V375m1xwxdeZ9f/t3Xd4VFX++PH3nZlMek9ICCEJhBaqElpoCUXpS9FVMPqjKago3e/q7tpQyqq4wOraEHAVJCqgK6wiYgoEBQxdYxCkkxBKOplMu78/YkaGVEjCEPi8nmeeJ3PvueeeuWcy85lzT2lV/fJIgRYLvlYrylX9vL777jtCQ0NJSUkhNTWVyZMns2PHDvr27cvOnTtJSEhg6tSp3HXXXYSGhmIymRg0aBAxMTFs27YNnU7Hyy+/zODBgzlw4IBtOPjWrVvx8vJiy5YtABQVFdmO2717N9nZ2Tz88MM88cQTrFq1igEDBuDj48O6deuYPHkyUBpUJCQkMH/+/ApfU2xsLMuXL8disaDVaklOTiYgIICkpCQGDx7MmTNnOHr0KHFxceWOXbp0KYcPH6Z9+/bMmzev9BoFBtq+9P/2t7+xePFiAgMDefTRR5k0aRKpqalVXuPo6GgiIiJYt24dDz74ICdPniQlJYU333yTl156yZauumsBsHjxYlatWsWKFSuIiopi8eLFbNiwwS64XLhwIR999BFvv/02LVu2JCUlhQcffJDAwEBiY2OrLGtldDodTk5OGI3Gass5d+5c0tPTyc/PtwXdfn5+NX6PJCYm0rhxYxITEzly5Aj3338/d9xxB4888gjr16+nU6dOTJkyhUceeaTS8hYWFjJ06FDmz5+Ps7Mz//nPfxgxYgQZGRmEhZWfl27dunX885//ZO3atbRr146srCz2799/XdfqZiAtVA3col2LGLRuEJ8f+RycPXiuURATghtx5txBAO7K+o1F6d/zJ6XuRjtdDGrB//yL2eaax/ELv7DNzZU9rnU7RH3NKQtbTp3FtdDEUTWEH62t0AXU3ci45o3bcVfRZQYXFWExm4kywJDCIkJdQ6s/+BpotX6oVi15xtLblWfUAI5aG+PiW3dTQAB4O2vorf2Jduafbdt+NqSQ57efEre6nfMKwMsvmGJFoUBn5PIVy/ecUC+S5O5Gdu1WcGhwBgwbSJv2bZj/0sJq06qqSp7qTjH6cv2s/Pz8WLZsGa1bt2bSpEm0bt2ay5cv89e//pWWLVvyzDPPoNfr2b69tO9fQkICVquV5cuX06FDB6Kioli5ciUnT5606yPk7u7O8uXLadeuHe3atWPNmjUYDAb+85//0L59e/r3788bb7zBhx9+yLlz59BqtYwdO5Y1a9bY8ti6dSu5ubncc889Fb6uPn36UFBQwN69e1FVlZSUFObMmWMrR1JSEk2aNKFFixbljvX29kav1+Pm5kZwcDDBwcFor1hJYP78+cTGxtK2bVuefvppduzYUaM1ECdNmsSKFaX9R1etWsXQoUMJDLRvHa7uWkBpa9szzzzDmDFjiIqK4u2338bb+4/b2iUlJSxYsIAVK1YwaNAgmjdvzoQJE3jwwQd55513qi1nRYxGIwsXLiQvL4/+/ftXW04PDw9cXV1xdna2XUO9Xl/j94ivry9vvPEGbdq0Yfjw4QwbNoytW7cCpe9LrVZraz0LDq54PGunTp2YOnUq7du3p2XLlrz00ktERkby3//+t8L0J0+eJDg4mIEDBxIWFka3bt2qDNhudtJC1cBpNVqctc5of++Au8fFmRNayLyUQZOwnlB0vjShe93dYooKbIYxpysacwBN3FRePH+Rc/q6mYOqTKHOF0yZFOdkssQ6ljPGkWxo1bPO8m/WJIrXzl1Eo6hcvJjJyLzLRFousr9ttzo7B0B3txl8mnaWkLDS2yzTLTMpMJrZGlG351E93Hg4uBF5Gg1rLWa0Wh1Z6lZcgk5j1vSu03MBuHv5cmd4GCgqa/NzaPf77d5+RTr6FVyCJrVbvsfVScvP8yqeSb7wcj6nLp9Bg0rrgLZ2+8wmE5cv/YIV8Axsi/Y6RtG5Ol37MY0sCq/+9UmG/Hkqf/vrs1WmtaoqZ1R/ctTyP3LatWtnNwlrUFAQ7du3tz3XarX4+/uTnV16q33//v0cOXIET0/7vAwGA0ePHrU979Chg906Zenp6XTq1Al39z/6ofXq1Qur1UpGRgZBQUHEx8fTo0cPzp49S0hICKtXr2bYsGGV9nvy8fGhU6dOJCUlodfr0ev1TJkyheeff57CwkKSk5Ovu6WmY8c/ll1v3LgxANnZ2RW2elzpwQcf5Omnn+a3335j1apVLFu2rFya6q6Fi4sLmZmZdO/+R6uyTqejS5cuttt+R44c4fLly9x11112eRuNRu6889pa1v/yl7/w97//HYPBgIeHB4sWLWLYsGHMnj272jqrSE3fI+3atbMLYhs3bszBgwevqeyFhYW88MILbNq0iczMTMxmM8XFxZw8ebLC9H/+859ZsmQJzZs3Z/DgwQwdOpQRI0agq6MJnG+0hllqYbOozyLo88fzJxV/1OwMmqmlH8rWouzSZkiPuus42K5RBCVZ9+CKAS/Xb+lbWMQPgXU7r5JB7w8mKMnNJNd/FW4+7ri6dK6z/HVOei4qXviTR272Gb61diHdEkSbxnWzjl+ZrmTQQbcO72OdKCr5PyxBy3C1uOHuXLdBTkBAE3a6lk4zkXnxNKGNIuhdYCBT400bV69qjr52Op0OrO6oSjFnCi7RLrj0i63DZQNRpkLSvFrXKn9FUSq97abFjfNmDRpUXHQKmiuCJqNqwksLFlVB63JjJvYE0Kta7uremYH9+/HMM88wYcIEu/0ajcb25WswG9G6nMWi5pTL5+pZmhVFqXCb1Vo6X1phYSHR0dGsXr26XF5XtsRc+SVcU127diUyMpK1a9fy2GOPsWHDBrtReRWJi4sjKSkJZ2dnYmNj8fPzIyoqiu3bt5OcnMycOXOuuRxgf13KWvXKrkFV/P39GT58OJMnT8ZgMDBkyBAKCup+BGpZP6ZNmzbRpEkTu33Oztf2PnzqqaeYMGECHh4eBAUF1XrSyZq+R6p6n9XU3Llz2bJlC6+99hotWrTA1dWVe++9t9KBEE2bNiUjI4Nvv/2WLVu28Pjjj/Pqq6+SnJxcqxnLHUUCqlvMII8IOLEXDEUA9PY04eTRhI8VqKubTC46DXtdpuJLAfOK/som0yP0CK3bXjqb/JvygmsH/Ixn0egvoao5hPnW3ZQGAHkaX/yseVw8d4KFxSMBDXubRtXpOcLV03TXbWHfpSJ+vXgWrdtJVFVLgHvdjjTy9vDjpXO5BKpGTPm5qAFWFl/aj5NiIcuvSfUZXIdGuS9yNNuIe58/bpOudLofzeWT/Dmk7vq7XU2v0xNVYkSjgMlitguoLGg5bg3CSQP186orVjZ7+4vPPk3PuLttHb/LBAYGkpWVhaqqGM0mQCXjUHqtz9u5c2cSEhJo1KgRXl41D5yjoqJYtWoVRUVFtmArNTUVjUZjV/b4+HhWr15NaGgoGo2GYcOGVZlvbGwsK1asQKfTMXjwYKA0yPr44485fPhwhf2nyuj1eiw1HCV5LSZNmsTQoUP5y1/+YtcCU6a6a+Ht7U3jxo3ZuXMnffuWLq9lNptJS0ujc+fSH3lt27bF2dmZkydPXncrXJmAgIAKb4vWpM4quobX+x65Wk3qJzU1lQkTJjB69GigNJi7svN7RVxdXRkxYgQjRoxg2rRptGnThoMHD9qubUMifahuNVcsP2MozqFAo+GSVound80Xqq2WolCo9aFQUUgzneITTQcIq00X5PLOBrbiN888jhpOs+pMNv93ToObU922OExv0opO4RG8mXMQjzZ/xz3yNXzc6vZXUY6nK/P9fVnnmol6Kp2Xsi4z/qIHugo+2Gurx2VnehUbMOZeIj/3om06C5+AxnV+LoAxyg+8oPsA9eRO27Zv8SRB2wGngDp8v11F0WiwKr+3wF61JmKJtXTZmUJt3c1ZVhMGjZbzGieaR7UiPj6+3K2luLg4zp8/zyuvvMLpw4f59t2PSP0updbnjY+PJyAggJEjR7Jt2zaOHTtGUlIS06dP5/Tp01Ue5+Liwvjx4zl06BCJiYk8+eSTPPTQQ3a3juLj49mzZw/z58/n3nvvrba1pW/fvhQUFLBx40Zb8BQXF8fq1atp3LgxrVq1qvTYiIgIdu7cyfHjx7lw4cI1t45UZvDgwZw/f97W2f1qNbkWM2bMYNGiRXz++ef88ssvPP7443YjID09PZk7dy6zZs3igw8+4OjRo+zZs4d//etffPDBB3XyOmpSzoiICA4cOEBGRgYXLlzAZDJd93vkahEREaSkpHDmzBkuXLhQYZqWLVuyfv169u3bx/79+3nggQeqrMdVq1bx/vvvc+jQIX777Tc++ugjXF1dCQ8Pv7aLc5OQgKqBW52+mhe/f5F92fsAKHDz5aCLK+nF2Tgb8kk8eZrPMi/g4Vm3naD/0ciDmIim/BaajEeL13Byrbt5rgB6NO6BIWs44dnBRBsNdDXX/RekxSUYVWPlSOEvKIoVnabu1nQqo3p5s9bLk+1uJtSLWYwqvsBwQ90tb3OlPF1pC97lS2e4dP4UFqBAdcXF9dpv99REjHk3E3Tf4HS+tJ+F1WrF2GgpHpGLQZdfzdG1Y6U0IL16moJicxEa/Xms2osVHVZvcn9ffiZPozBv3rxyXyJRUVH8+9//5s033ySmd1/27D3EzEcn1fq8bm5upKSkEBYWZuswXXZ7q6rWCDc3NzZv3sylS5fo2rUr9957LwMGDOCNN96wS9eiRQu6devGgQMHiI+Pr7Y8vr6+dOjQgcDAQNq0Ke1X2bdvX6xWa7UtN3PnzkWr1dK2bVsCAwMr7XdzrRRFISAgwK4P2ZVqci3mzJnDQw89xPjx44mJicHT09PWClPmpZde4tlnn2XhwoVERUUxePBgNm3aRLNmdTMPXE3K+cgjj9C6dWu6dOlCYGAgqamp1/0eudq8efM4fvw4kZGR5Tr2l3n99dfx9fWlZ8+ejBgxgkGDBlXZ0uTj48N7771Hr1696NixI99++y1ffvkl/v51N0XOjaSo1zrpirhm+fn5eHt7k5eXV6sm14o8uuVRUs+mMr/3fP4U+Sf+e3g9f/v+eXo07sF7UY/A+3eBdxjMurbOhdV5ZuVwNmpOAKBYdaSM3YaPa93dxjpyLp8H//k5S/T/pocmnV2+w+g2Y031B16DV7Z+z1uJR7lH3cfTzu/zg2t7hj+1rU7PcfTEQTZ9Powgk4XwoMn0OLqUNM/+RM/ZUKfnAfhm8RAspnTyIx9G5+/HvJP/plWJyqdTf6rzcwG8+9ZIss378XHvzROTPiLzYiYj14+iRGckZVwq3i41n6rDYDBw7NgxmjVrhouLS7XpT5/7FSMWvFwDCPD6Y56tzNwsck056BRnWtbhqNDqnMo9T54xD1etB5H+Va/oV3gxE4+SLIo0HrgH122fPSHEtavq8+davr+lD1UD96fIP3FHozto7Vt6Dz3EKwx/F398XXwhtCvMPQKX6/7X+j1NhvPX75/GU1U5pgmr02AKoKm3jhTnWXzu5UKRxRWtX91/OXb18aJQ3cU8pw/ACoGudf/lFtEkiscvFaBTrKzT7eJHF2cuudfPr6+3QtpyxHiathjom3sMq6KAUn//4kedrfzPzZN+xrMAGLPPsuvML+Thfk3B1PUo1GqxYER/1e9BT7OZxiYDhdob1yEdwE3nRU6hE1qX6m8ZG6wlGDUa0Gion7ZDIYQjSEDVwA1tPtTueXRQNEn3JwGQcjqFI7lH6BbcjfYVHFsbHXvej3nH84CB3LC76zh3cHZxY49LOwo0v7HU149nI+u2szhAc/cS+jld0b8hsHYj0yqi1ek4qQkmTD3Lt/qjbPcN4gGdhbq/YhDiEUHG2WBMOlfuNEPiidPs9OpT/YHXqY0+gtAL+/HQlLbIFFwo7Y+Ro/Gj/haeKaVXPCkyOaG5ul+dtXRmZ+ph/cKqOFsv01I5i8WkB6oOzC9TQoFOhzdW6naYhRDCkSSgusUoigKb5sCZNLY078jnZxJ54o4naB9QtyGV3sOXwrGfcfa3vdxx96N1mneZve368a9Ll2hf4szd3cfWef6hLTrylasvH/no6VlsoH+rHnV+DoDzrhFgzMasUWliMhMZcke9nOfupmPYlNocfXM/FON7BFit+LnX322vDt7t6XLkP/ykL51g0ZBT2lJV6FT//R9ctR4UF2vRWO27gSrW3/tU3aB1/MpoFHBVjJTUoAOFXgVP1YqTtuENCxdCVE4CqgYuryQPq2rFw8njjw/ozP1wdi+9DJkUBzUjyrl+vuD82vTBr039tYBM/tOLDD0/iUDfEDT1MCpOq9PxlV8kB/TZ5Gj0TO1QdxOHXmlZWFv2lJzmnvxC3ss6z/nho6s/6DqEc5YPnRagP+fE203+wZOGgTwT1a5ezgXg9vtIPh9T6SST23N38UGjAJqpTnXeIno1T/MlGmuyKTJ6AX/cbr6kMXFRo8PjBi86bNHAEScnQKX8gHd7XhZwU80UOdXvbVEhxI0lo/wauGlbp9E3oS8pZ/4Ygr3VN4j4xkH8rBp4Lf17+gZ0cmAJa6dxYDg6Xf39kn9p3Kc86jmEJXevqbfz3BnWB6xazqgBHFaaExhcP1MKhDZqRB/tIbqY95F++VPy/Pbj4lt/0wf4BDejRIFiTS5Wi4UTxjMkubtxxvkG/E7TaDEDFtV+lJ9BUSnQaKAeAvCqaLVOlCgKRkWpdnHly4oruao76G5sPy8hRP2SFqoGruzDW3NFbGwMbMmBwgOlT1y8wS/SEUVrELw9/Jg25pV6PcfD0YP5MFHLlgINUf0imV1P5/EPbspTAY3Y46qjSLcZF08I959WT2cDr+BQuoSHgQKf52TTu1BLjOUSpqB+9XbOMsUaCyf0epxVM1eOu2lktmBRVJzdbuw8VM5OLoSbTGgBq8WCtoqlMy7gg1G1EqmXLulC3EokoGrgPhr6EVbVajd/Up87pzLtwBoevJgN3aaCRhoiHcnD2YV1U/uz/3QuwzrUzySbUDrh5XG9O9k6C01NJvQlIbRtVLeLPV/Jw9UDrJ6oioHDF7NoX3iR1uZC9rSr/xmOdZqyOYX+aA1SrVa8VQuoYHaqfuqFuqTV6nC1glZRMVpMVQZUFu1ZNFpQiUA+goW4dch/cwOnKIptYeQyHp6NefT+L+H4dug0zkElE1eKCHAnIqD+WyT6K1H8JXMrdxpKOOQaZrfQbn0Iv/wih06XoOsewqvWeIJMx/l/zeunc/+V3J09iCo8DWrpLTZFUTBbVc5Yg9ApFprU423iylgVLVrMpbO3V3I3z2K1gmJBAZxu8G1JIUT9kqaLW1Vga+g6GfTS8fV2MqjXLDoXG9ECpvb31fv5huiPMl+3gqK9H5OIyhpNZ5qEV9ctu/Z0Tno0gEZRsfw+W7rRYqFAoyVf417nM97XRIFGx3mNEyWWiheCBbCajbQwmgg3mdHf5gHVhAkTGDVqVJVpkpKSUBTFbpmX20FERARLliypcfoXXniBO+64o97K4wg1eX9c6fjx4yiKwr59++qtTNWRgKqBe//g+7yy+xVO5tfNMg2iYWveths/3/0R+3q/Q5dhD9f7+TrrjhKv28rFs1twC38fj2b/xuMGdErXaLSYf//4sphKA5hC02U0+gvgdOOWnZkwYQKKorBo0SLO/b78TCEqn3/+eYVBncVsxhkVZ1VBUW7vj9+lS5eyatUq2/O4uDhmzpzpkLLUNHArS+fr64vBYLDbt3v3bhRFcUgwX52yYKPs4e/vz913383evXtrnMe1BnnXWrarA6Gr3x8NQYP5j7506RLx8fF4eXnh4+PD5MmTKSwsrPIYg8HAtGnT8Pf3x8PDg3vuuYdz5+zXnJs+fTrR0dE4OztXGuEfOHCAPn364OLiQtOmTXnllfrtxHwt/nv0v3z484ecu1y3a+mJhqt9r+HcMbDu5+2qSH5QKAv8fPnS5wgeJR74EVT9QXUkS+vKUa0rRebSgEo1G9CoGnQ3+GPNxcWFf/zjHxTlFaNanUGt/PxWS+nEoxYc1zplNFbegnYjeXt74+Pj4+hiXBdPT082bLBfPur9998nLKz+FgWvC99++y2ZmZls3ryZwsJChgwZctO2/jXE90eDCaji4+P56aef2LJlCxs3biQlJYUpU6ZUecysWbP48ssv+fTTT0lOTubs2bOMGTOmXLpJkyZx//33V5hHfn4+d999N+Hh4aSlpfHqq6/ywgsv8O6779bJ66qte1vdy6T2kwh2r3r9MCHqg294ez729uSkkxPfZqazwFR/neCvVqDVYdBaKFYtAHiYjESZDIRYb+zH2sCBAwkODmbF0hVYjQFoKT/CsOyWTIm5mEsaDZc1WpYsWUJERIQtTdktjgULFhAUFISPjw/z5s3DbDbz1FNP4efnR2hoKCtXrrTL+9SpU9x33334+Pjg5+fHyJEjOX78eLl858+fT0hICK1bl64IcPDgQfr374+rqyv+/v5MmTLF9iP1m2++wcXFpdyX7YwZM+jfv3+F12Hu3LkMHz7c9nzJkiUoisLXX39t29aiRQuWL19uV66yv5OTk1m6dKmtFeXK15CWlkaXLl1wc3OjZ8+eZGRk2J37rbfeIjIyEr1eT+vWrfnwww9t+ypqAcnNzUVRFJKSkjh+/Dj9+pWOTPX19UVRFCZMmFDhaywzfvx4VqxYYXteXFzM2rVrGT9+fLm069ato127djg7OxMREcHixYvt9mdnZzNixAhcXV1p1qwZq1evLpdHbm4uDz/8MIGBgXh5edG/f3/2799fZRkr4u/vT3BwMF26dOG1117j3Llz7Ny5s9pyxsXFceLECWbNmlWuFW779u306dMHV1dXmjZtyvTp0ykqKrLtj4iIYMGCBUyaNAlPT0/CwsLsvj/LFo++8847URSFuLg4oPwtv6+//prevXvj4+ODv78/w4cP5+jRo5W+1pycHOLj4wkMDMTV1ZWWLVuW+9+paw0ioEpPT+frr79m+fLldO/end69e/Ovf/2LtWvXcvbs2QqPycvL4/333+f111+nf//+REdHs3LlSnbs2MEPP/xgS7ds2TKmTZtG8+YVzyi9evVqjEYjK1asoF27dowdO5bp06fz+uuv18trvVYPtX2IWdGzaOrZ1NFFEbehLlFx3JNn5ZXsCzipKl5RA+r2BMaiSh8uFiesZi8UtXTEn1KSD6ZisJjKpzcV1yzf66DValmwYAEr33sL18w03EuyK01bbDGQqdORr614rqrvvvuOs2fPkpKSwuuvv87zzz/P8OHD8fX1ZefOnTz66KNMnTqV06dLl/kxmUwMGjQIT09Ptm3bRmpqKh4eHgwePNiuJWrr1q1kZGTYfpAWFRUxaNAgfH192b17N59++inffvstTzzxBAADBgzAx8eHdevW2fKwWCwkJCQQHx9fYdljY2PZvn07FktpgJucnExAQABJSUkAnDlzhqNHj9q+MK+0dOlSYmJieOSRR8jMzCQzM5OmTf/4TPvb3/7G4sWL+fHHH9HpdEyaNMm2b8OGDcyYMYM5c+Zw6NAhpk6dysSJE0lMTKy0Hq7UtGlT2+vMyMggMzOTpUuXVnnMQw89xLZt2zh5srSrxbp164iIiKBzZ/sRrmlpadx3332MHTuWgwcP8sILL/Dss8/a3cqaMGECp06dIjExkc8++4x///vfZGfbv4f+/Oc/k52dzVdffUVaWhqdO3dmwIABXLp0qUavsSKurqWBv9ForLac69evJzQ0lHnz5tnqB+Do0aMMHjyYe+65hwMHDpCQkMD27dtt76MyixcvpkuXLuzdu5fHH3+cxx57zBYU79q1C/ij9Wz9+vUVlreoqIjZs2fz448/snXrVjQaDaNHj8ZqtVaY/tlnn+Xnn3/mq6++Ij09nbfeeouAgIAK09YZtQF4//33VR8fH7ttJpNJ1Wq16vr16ys8ZuvWrSqg5uTk2G0PCwtTX3/99XLpn3/+ebVTp07ltj/00EPqyJEj7bZ99913KqBeunSpwnMbDAY1Ly/P9jh16pQKqHl5eZW/SCEaqJ3rl6nq817qzy/HqGaT6bryKC4uVn/++We1uLjYfsfzXpU+ileNUQ+duqhmXsxVVVVVrS81qjz9iqH2+f6jWcXprtH48eNtnw9du0Srk8aOVAszD6sbNmxQr/x4Lft8OZd9RD1x7oB6NvtX9Z///KcaHh5ul1d4eLhqsVhs21q3bq326dPH9txsNqvu7u7qxx9/rKqqqn744Ydq69atVavVaktTUlKiurq6qps3b7blGxQUpJaUlNjSvPvuu6qvr69aWFho27Zp0yZVo9GoWVlZqqqq6owZM9T+/fvb9m/evFl1dnYu95laJicnR9VoNOru3btVq9Wq+vn5qQsXLlS7d++uqqqqfvTRR2qTJk0qvHaqqqqxsbHqjBkz7PJMTExUAfXbb7+1Kydge6/07NlTfeSRR+yO+/Of/6wOHVpa58eOHVMBde/evXZlBdTExES781T22q4uT05Ojjpq1Cj1xRdfVFVVVfv166cuXbq0XL0/8MAD6l133WWXx1NPPaW2bdtWVVVVzcjIUAF1165dtv3p6ekqoP7zn/9UVVVVt23bpnp5eakGg8Eun8jISPWdd95RVbXy768yV1+DnJwcdfTo0aqHh4ealZVVbTlVVVXDw8NtZSozefJkdcqUKXbbtm3bpmo0Glv9hIeHqw8++KBtv9VqVRs1aqS+9dZbFZatzNXvj6udP39eBdSDBw9WmM+IESPUiRMnVnr8lSr9/FFVNS8vr8bf3w2ihSorK4tGjRrZbdPpdPj5+ZGVlVXpMXq9vtw92KCgoEqPqSyfoCD7fiFlzyvLZ+HChXh7e9seV/7SqmsGs4FiczFWteIoXYj61m30k5yfcoCW/5dU5fxLdU2nmminOYFXSen/4Y1dbKa8Z1/4Kx98upHvj/xSaRp3K4SZzXgqFU882q5dO7upLoKCgujQoYPtuVarxd/f39aCsX//fo4cOYKnpyceHh54eHjg5+eHwWCwux3SoUMH9Hq97Xl6ejqdOnXC3f2PqTx69eqF1Wq1tRzEx8eTlJRkuwuwevVqhg0bVmm/Fh8fHzp16kRSUhIHDx5Er9czZcoU9u7dS2FhIcnJycTGxlZ6barSsWNH29+NG5fO5VZ2DdLT0+nVq5dd+l69epGenn5d56qpSZMmsWrVKn777Te+//77ClvuKivbr7/+isViIT09HZ1OR3R0tG1/mzZt7K7x/v37KSwstPUFLnscO3asylteFenZsyceHh74+vqyf/9+EhISCAoKqracldm/fz+rVq2yK9egQYOwWq0cO3bMlu7K+lMUheDg4HKtcNX59ddfGTduHM2bN8fLy8t2u7yslfBqjz32GGvXruWOO+7g//7v/9ixY8c1ne96OHQeqqeffpp//OMfVaap73+K+vDMM88we/Yf82Hn5+fXW1A14vMRZBVlsXbYWtoF1N+6bUJUJTAkvH4y/mvFt/QBTMVFUHQGC0YsFjMZkzcB0NwjAhfnqwKWq0fUzTxY1yWlV+9e9OzXk0Xzl/DE1Cft9mk0GlRVpRgXTKoFrZMLJpOpXB5OTvbzZymKUuG2stschYWFREdHV9jvJjAw0Pb3lYFTTXXt2pXIyEjWrl3LY489xoYNG6oddRUXF0dSUhLOzs7Exsbi5+dHVFQU27dvJzk5mTlz5lxzOcD+upT136nsVs/VygJU9YolgSq69tdqyJAhTJkyhcmTJzNixAj8/etnzdTCwkIaN25su3V6pWvttJ2QkEDbtm3x9/evkw7fhYWFTJ06lenTp5fbd2UH/arewzU1YsQIwsPDee+99wgJCcFqtdK+fftKB1kMGTKEEydO8L///Y8tW7YwYMAApk2bxmuvvXZN570WDg2o5syZU23nv+bNm1cYzZrNZi5dukRwcMWdsYODgzEajeTm5tq9cc6dO1fpMZXlc/XIwLLnleXj7OyMs7Os0yVErVWxPIsGDRmm0laXZoYiwtBhUDQ4e/hDdUPX62HZFxcnV1595kl63jWW6I5d7PYFBgaSlZXFJdUTg+pOhN69TubL6dy5MwkJCTRq1AgvL6/qD/hdVFQUq1atoqioyBZspaamotFobJ3WobSVavXq1YSGhqLRaBg2bFiV+cbGxrJixQp0Oh2DBw8GSoOsjz/+mMOHD1fYf6qMXq+vsjWkqteSmppq1yE8NTWVtm3bAn8ElpmZmdx5550A5a59WevdtZxfp9Px//7f/+OVV17hq6++qrJsV0pNTaVVq1ZotVratGmD2WwmLS2Nrl27AqX9uK4cDNC5c2eysrLQ6XR2gxiuR9OmTYmMLL8UWXXlhIrrp3Pnzvz888+0aHH9c8/V5NpfvHiRjIwM3nvvPfr06QOUdoavTmBgIOPHj2f8+PH06dOHp556ql4DKofe8gsMDKRNmzZVPvR6PTExMeTm5pKWlmY79rvvvsNqtdK9e/cK846OjsbJyYmtW7fatmVkZHDy5EliYmJqXMaYmBhSUlLsftFs2bKF1q1b4+vrex2vum59MfILdj6wkzZ+bRxdFCFuKL2TCxpUdKqK8XIuHqqKh1XnsHmAnHTOdG/TgvjRQ1i2bJndvri4OM6fP8/bb87jzNldvPvOG5V+CV+L+Ph4AgICGDlyJNu2bePYsWMkJSUxffp0W8f1yo5zcXFh/PjxHDp0iMTERJ588kkeeughuy4O8fHx7Nmzh/nz53PvvfdW+0Oxb9++FBQUsHHjRlvwFBcXx+rVq2ncuDGtWrWq9NiIiAh27tzJ8ePHuXDhQo1bMJ566ilWrVrFW2+9xa+//srrr7/O+vXrmTt3LlDa+bpHjx4sWrSI9PR0kpOT+fvf/26XR3h4OIqisHHjRs6fP1/tlDxlXnrpJc6fP8+gQYMq3D9nzhy2bt3KSy+9xOHDh/nggw944403bGVr3bo1gwcPZurUqezcuZO0tDQefvhhW4dxKB1FGhMTw6hRo/jmm284fvw4O3bs4G9/+xs//vhjjcpZnerKCaX1k5KSwpkzZ7hw4QIAf/nLX9ixYwdPPPEE+/bt49dff+WLL74o1ym9Ko0aNcLV1ZWvv/6ac+fOkZeXVy6Nr68v/v7+vPvuuxw5coTvvvvO7i5QRZ577jm++OILjhw5wk8//cTGjRuJioqqcbmuR4PoQxUVFcXgwYN55JFH2LVrF6mpqTzxxBOMHTuWkJAQoHQESZs2bWwjBry9vZk8eTKzZ88mMTGRtLQ0Jk6cSExMDD16/LE0xpEjR9i3bx9ZWVkUFxezb98+9u3bZ2tGfOCBB9Dr9UyePJmffvqJhIQEli5dWm1l3ihuTm64Obmh1dzesy6L24+iKISbdLQ2mTCYFH6zBlOor+dRPFXQ6pxQVZj31GPlgoGoqCjefPNNPl65mnv6jWJvWprdl9X1cnNzIyUlhbCwMMaMGUNUVBSTJ0/GYDBU2WLl5ubG5s2buXTpEl27duXee+9lwIABvPHGG3bpWrRoQbdu3Thw4EClo/uu5OvrS4cOHWw/lqE0yLJardX2n5o7dy5arZa2bdsSGBhYad+Yq40aNYqlS5fy2muv0a5dO9555x1Wrlxp1xq2YsUKzGYz0dHRzJw5k5dfftkujyZNmvDiiy/y9NNPExQUVOOAQK/XExAQUGkQ37lzZz755BPWrl1L+/btee6555g3b57dnZmVK1cSEhJCbGwsY8aMYcqUKXZ9hhVF4X//+x99+/Zl4sSJtGrVirFjx3LixIly/XuvV03KOW/ePI4fP05kZKSt1a9jx44kJydz+PBh+vTpw5133slzzz1n+16uCZ1Ox7Jly3jnnXcICQlh5MiR5dJoNBrWrl1LWloa7du3Z9asWbz66qtV5qvX63nmmWfo2LEjffv2RavVsnbt2hqX67rUqAv8TeDixYvquHHjVA8PD9XLy0udOHGiWlBQYNtf1sO/bNSGqpb23H/88cdVX19f1c3NTR09erSamZlpl29sbKxKaX9Wu8exY8dsafbv36/27t1bdXZ2Vps0aaIuWrTomsp+LaMEhLgdVTXKpioF2SdU9cwe9XTmL+qBM1nqhYJrO76u5Zw9qGZnHlQLivLL7TMZjWrJmT1q4dm9qtlsdkDphBAVqatRfoqqqo4eHHPLy8/Px9vbm7y8vGvq51ATKw6toNBYyLg24wh0C6z+ACFuQgaDgWPHjtGsWTNcXFxqfFxxQS7OBcc4qnXDqDXTzKsFbnrH9V/8+fxhVMVEoEsTGnn42O0rKS7EOedXzGjQhXRyTAGFEOVU9flzLd/fDu2ULmrvo58/4nzxee6OuFsCKnHbcfHw5nKhMyaNBZ3i7tBgCkCruGCyarCqFazj9/uagxZ08sErxC1I/q8buNEtR1NkKsLH2cfRRRHihlMUBX1AC4INBfi4O36QiLsmgEsGI4pL+cDOYL5MsUaDghYZAyzErUcCqgbuyTufrD6RELcwJyc9fk71MwfQtfJU8/FXLmI2eICX/dxcl60G8nQ6PFQFPweVTwhRfxrEKD8hhGgItAq4Kka01vKTDTpZVbysVpwVpwqOFEI0dNJCJYQQdcSoUTni5IRGNXL1cuueFituqpki17qfVFQI4XjSQtXAxSXE0eGDDmRcynB0UYS47Wm0TpQoCial/ODpIlzJVd3BqeJ1/IQQDZu0UDVw6u9LwjpqdmghxB9c9e6EF5rQqaBarShXLHScrXpjUb1o5SwtVELciiSgauA2jNyAVbXi7ezt6KIIcdvT611wsoJGUTGajOidS+e0MZrNoD+NRtWh03g6uJRCiPogt/waOD8XPwJcA3DSSEdXIRxNURTMSunvVIvRYNt+2Vj8+34rOq0WRVH4/PPPK80nKSkJRVHsFsmtS3FxccycObNe8hbidiUBlRBCXKe3334bT09PzGazbdu5YhNO4d0YOGSobZuT0cDZpB20D2zL0aNHq823Z8+eZGZm4u1d2vK8atUqfHx8yqWLiIhgyZIltX4dQojak4CqgfvPT//hvQPvkWPIcXRRhLjt9OvXj8LCQn788Ufbts0/HsS/kT9paXswGEpbqVRzCdt37KZpkxAiIyOrzVev1xMcHNxg+kaWLSYvxO1MAqoG7t2D77Js7zIJqIRwgNatW9O4cWOSkpJs29J27Kbf4LsIDQvjhx9+AECxGEn6Po0+vXva0l24cIHRo0fj5uZGy5Yt+e9//2vbd+Utv6SkJCZOnEheXh6KoqAoCi+88AJxcXGcOHGCWbNm2bYDXLx4kXHjxtGkSRPc3Nzo0KEDH3/8cZWvY9OmTXh7e7N69WoATp06xX333YePjw9+fn6MHDmS48eP29JPmDCBUaNGMX/+fEJCQmjdunVtL6UQDZ4EVA3c8ObDGdNyDB56D0cXRYg6d9l0mcumy1y5hrvJYuKy6TJGi7HCtFbV+kdaa2naEktJjdJej379+pGYmGh7viv1B7p0G0i3Hn1t288V57Jz7yH69O1jS/fiiy9y3333ceDAAYYOHUp8fDyXLl0ql3/Pnj1ZsmQJXl5eZGZmkpmZydy5c1m/fj2hoaHMmzfPth1KF3qNjo5m06ZNHDp0iClTpvDQQw+xa9euCsu/Zs0axo0bx+rVq4mPj8dkMjFo0CA8PT3Ztm0bqampeHh4MHjwYLuWqK1bt5KRkcGWLVvYuHHjdV07IW4lElA1cE93e5oXe75II7dGji6KEHWu+5rudF/TnZySP1pgV/60ku5rurNg5wK7tHGfxNF9TXcyizJt29b+spbua7rzXOpzdmkHrxtM9zXd+S33N9u2L458cV1l7NevH6mpqZjNZgoKCjiwfx/3xjRnaLcWJCUloaoqyXv3UlJipE//frbjJkyYwLhx42jRogULFiygsLCwwqBHr9fj7e2NoigEBwcTHByMh4cHfn5+aLVaPD09bdsBmjRpwty5c7njjjto3rw5Tz75JIMHD+aTTz4pl/ebb77J448/zpdffsnw4cMBSEhIwGq1snz5cjp06EBUVBQrV67k5MmTdi1x7u7uLF++nHbt2tGuXbvrunZC3Epk2gQhhKiFuLg4ioqK2L17Nzk5ObRq1Yqm/p70i+nMw3NeID8/h4PbdhEWHkqblm1tx3Xs2NH2t7u7O15eXmRnZ9e6PBaLhQULFvDJJ59w5swZjEYjJSUluLm52aX77LPPyM7OJjU1la5du9q279+/nyNHjuDpaT+9g8FgsOtQ36FDB/R6fa3LK8StQgIqIcRNa+cDOwFw1f0xu/jEdhN5MOpBdBr7j6+k+5IAcNG52LaNbTOWe1reg1ajtUv79T1fl0s7ssXI6ypjixYtCA0NJTExkZycHGJjYznt5ERRWAghTRqTmpLM7tRdDOjVHa32j3I4OdlPdaIoClar9ersr9mrr77K0qVLWbJkCR06dMDd3Z2ZM2eW6zh+5513smfPHlasWEGXLl1sfbAKCwuJjo629ae6UmBgoO1vd3eZoFSIK0lA1cAN+GQABaYCPhvxGWFeYY4ujhB1ys3Jrdw2J60TTtry865VmFbjVOEcbZWlvV79+vUjKSmJnJwcnnrqKVRFixUL3Xp0YdM3ieza9zPjJ0y67vz1ej0Wi6VG21NTUxk5ciQPPvggAFarlcOHD9O2bVu7dJGRkSxevJi4uDi0Wi1vvPEGAJ07dyYhIYFGjRrh5eV13WUW4nYjfagauGJzMcXmYtsSNEKIG69fv35s376dffv2ERsbi7eTN5EmE3d1u5MPVq3EaDTS6+4/XXf+ERERFBYWsnXrVi5cuMDly5dt21NSUjhz5gwXLlwAoGXLlmzZsoUdO3aQnp7O1KlTOXfuXIX5tmrVisTERNatW2eb6DM+Pp6AgABGjhzJtm3bOHbsGElJSUyfPp3Tp09f92sQ4lYnAVUD99mfPuOrMV8R4hHi6KIIcdvq168fxcXFtGjRgqCgIDzc/XG2qvSOuYOiwkKatWhG8/Am151/z549efTRR7n//vsJDAzklVdeAWDevHkcP36cyMhI2+24v//973Tu3JlBgwYRFxdHcHAwo0aNqjTv1q1b89133/Hxxx8zZ84c3NzcSElJISwsjDFjxhAVFcXkyZMxGAzSYiVEFRT1yvHIol7k5+fj7e1NXl6efCAJUQGDwcCxY8do1qwZLi4u1R/QABRl/YrWWsxvTjo0iittApo5ukhCiApU9flzLd/f0kIlhBD1QO/XFFXRE2xRCPMMcnRxhBD1TDqlN3Brf1mL2WpmZIuReOplFXshbhZOehecGrfBtfqkQohbgARUDdzraa9TbC4mtmmsBFRCCCGEg0hA1cDdHX43RosRN135YeBCCCGEuDEkoGrgXu79sqOLIIQQQtz2pFO6EOKmIYOOhRA3Wl197khAJYRwuLJlWMomrBRCiBulbFmmK5eGuh5yy6+Bu+uzuzBajCQMTyDYPdjRxRHiumi1Wnx8fGyLA7u5udnWlhNCiPpitVo5f/48bm5u6HS1C4kkoGrgLhVfwmg1yq0S0eAFB5f+ICgLqoQQ4kbQaDSEhYXV+kecBFQNXMLwBFRUAlwDHF0UIWpFURQaN25Mo0aNMJlMji6OEOI2odfr0Whq3wNKAqoGroVvC0cXQYg6pdVqa92XQQghbjTplC6EEEIIUUvSQtXAbfh1A1bVypBmQ3Bzksk9hRBCCEeQgKqBm/f9PMyqmd5NektAJYQQQjiIBFQ3QNkIvPz8/DrPu4dfD6yqlZKiEvItdZ+/EEIIcbsq+96uyUh6RZXx9vXu9OnTNG3a1NHFEEIIIcR1OHXqFKGhoVWmkYDqBrBarZw9exZPT886n6wwPz+fpk2bcurUKby8vOo0b1H3pL4aHqmzhkXqq2G52etLVVUKCgoICQmpdmoFueV3A2g0mmoj29ry8vK6Kd+MomJSXw2P1FnDIvXVsNzM9eXt7V2jdDJtghBCCCFELUlAJYQQQghRSxJQNXDOzs48//zzODs7O7ooogakvhoeqbOGReqrYbmV6ks6pQshhBBC1JK0UAkhhBBC1JIEVEIIIYQQtSQBlRBCCCFELUlAJYQQQghRSxJQNWBvvvkmERERuLi40L17d3bt2uXoIonfpaSkMGLECEJCQlAUhc8//9xuv6qqPPfcczRu3BhXV1cGDhzIr7/+6pjCChYuXEjXrl3x9PSkUaNGjBo1ioyMDLs0BoOBadOm4e/vj4eHB/fccw/nzp1zUIlvb2+99RYdO3a0TQYZExPDV199ZdsvdXVzW7RoEYqiMHPmTNu2W6HOJKBqoBISEpg9ezbPP/88e/bsoVOnTgwaNIjs7GxHF00ARUVFdOrUiTfffLPC/a+88grLli3j7bffZufOnbi7uzNo0CAMBsMNLqkASE5OZtq0afzwww9s2bIFk8nE3XffTVFRkS3NrFmz+PLLL/n0009JTk7m7NmzjBkzxoGlvn2FhoayaNEi0tLS+PHHH+nfvz8jR47kp59+AqSubma7d+/mnXfeoWPHjnbbb4k6U0WD1K1bN3XatGm25xaLRQ0JCVEXLlzowFKJigDqhg0bbM+tVqsaHBysvvrqq7Ztubm5qrOzs/rxxx87oITiatnZ2SqgJicnq6paWj9OTk7qp59+akuTnp6uAur333/vqGKKK/j6+qrLly+XurqJFRQUqC1btlS3bNmixsbGqjNmzFBV9db5/5IWqgbIaDSSlpbGwIEDbds0Gg0DBw7k+++/d2DJRE0cO3aMrKwsu/rz9vame/fuUn83iby8PAD8/PwASEtLw2Qy2dVZmzZtCAsLkzpzMIvFwtq1aykqKiImJkbq6iY2bdo0hg0bZlc3cOv8f8niyA3QhQsXsFgsBAUF2W0PCgril19+cVCpRE1lZWUBVFh/ZfuE41itVmbOnEmvXr1o3749UFpner0eHx8fu7RSZ45z8OBBYmJiMBgMeHh4sGHDBtq2bcu+ffukrm5Ca9euZc+ePezevbvcvlvl/0sCKiGEuMK0adM4dOgQ27dvd3RRRBVat27Nvn37yMvL47PPPmP8+PEkJyc7uliiAqdOnWLGjBls2bIFFxcXRxen3sgtvwYoICAArVZbbgTEuXPnCA4OdlCpRE2V1ZHU383niSeeYOPGjSQmJhIaGmrbHhwcjNFoJDc31y691Jnj6PV6WrRoQXR0NAsXLqRTp04sXbpU6uomlJaWRnZ2Np07d0an06HT6UhOTmbZsmXodDqCgoJuiTqTgKoB0uv1REdHs3XrVts2q9XK1q1biYmJcWDJRE00a9aM4OBgu/rLz89n586dUn8OoqoqTzzxBBs2bOC7776jWbNmdvujo6NxcnKyq7OMjAxOnjwpdXaTsFqtlJSUSF3dhAYMGMDBgwfZt2+f7dGlSxfi4+Ntf98KdSa3/Bqo2bNnM378eLp06UK3bt1YsmQJRUVFTJw40dFFE0BhYSFHjhyxPT927Bj79u3Dz8+PsLAwZs6cycsvv0zLli1p1qwZzz77LCEhIYwaNcpxhb6NTZs2jTVr1vDFF1/g6elp67fh7e2Nq6sr3t7eTJ48mdmzZ+Pn54eXlxdPPvkkMTEx9OjRw8Glv/0888wzDBkyhLCwMAoKClizZg1JSUls3rxZ6uom5OnpaeuPWMbd3R1/f3/b9luizhw9zFBcv3/9619qWFiYqtfr1W7duqk//PCDo4skfpeYmKgC5R7jx49XVbV06oRnn31WDQoKUp2dndUBAwaoGRkZji30bayiugLUlStX2tIUFxerjz/+uOrr66u6ubmpo0ePVjMzMx1X6NvYpEmT1PDwcFWv16uBgYHqgAED1G+++ca2X+rq5nfltAmqemvUmaKqquqgWE4IIYQQ4pYgfaiEEEIIIWpJAiohhBBCiFqSgEoIIYQQopYkoBJCCCGEqCUJqIQQQgghakkCKiGEEEKIWpKASgghhBCiliSgEkIIIYSoJQmohBBCCCFqSQIqIYQQQohakoBKCCGuw/Hjx1EUpdwjLi7O0UUTQjiAztEFEEKIhqhp06ZkZmbanmdlZTFw4ED69u3rwFIJIRxFFkcWQohaMhgMxMXFERgYyBdffIFGI43/QtxupIVKCCFqadKkSRQUFLBlyxYJpoS4TUlAJYQQtfDyyy+zefNmdu3ahaenp6OLI4RwELnlJ4QQ12ndunWMGzeOr776igEDBji6OEIIB5KASgghrsOhQ4fo3r07s2fPZtq0abbter0ePz8/B5ZMCOEIElAJIcR1WLVqFRMnTiy3PTY2lqSkpBtfICGEQ0lAJYQQQghRSzIcRQghhBCiliSgEkIIIYSoJQmohBBCCCFqSQIqIYQQQohakoBKCCGEEKKWJKASQgghhKglCaiEEEIIIWpJAiohhBBCiFqSgEoIIYQQopYkoBJCCCGEqCUJqIQQQgghakkCKiGEEEKIWvr/E8HDG46srlgAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.set_title(str(state))\n", "\n", "styles = [\"-\", \"--\", \":\"]\n", "for i, (label, _state) in enumerate(states.items()):\n", " ax.plot(_state.radial.grid.z_list, _state.radial.wavefunction.w_list, ls=styles[i], label=label)\n", "ax.legend()\n", "\n", "ax.set_xlabel(\"z\")\n", "ax.set_ylabel(\"w(z)\")\n", "\n", "ax.set_ylim(1.1 * np.min(state.radial.wavefunction.w_list), 1.1 * np.max(state.radial.wavefunction.w_list))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "e05ac269", "metadata": {}, "source": [ "## Radial matrix elements" ] }, { "cell_type": "code", "execution_count": 6, "id": "128a71d8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Numerov with model potentials: 43.64042739463778 bohr\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "WARNING wavefunction.py: The wavefunction for the state RadialState(Rb, n=10, nu=np.float64(6.864783105371448), l_r=0) has some issues:\n", " The wavefunction has 6 nodes, but should have 9 nodes.\n", " The integration for l=0 did stop at 0.14 (should be close to zero).\n", "WARNING wavefunction.py: The wavefunction for the state RadialState(Rb, n=9, nu=np.float64(6.350837333725099), l_r=1) has some issues:\n", " The wavefunction is not close to zero at the inner boundary (inner_weight_scaled_to_whole_grid=4.07e-02)\n", " The wavefunction has 5 nodes, but should have 7 nodes.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Numerov without model potentials: 43.60588874251313 bohr\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "WARNING wavefunction.py: Using Whittaker to get the wavefunction is not recommended! Use this only for comparison.\n", "WARNING wavefunction.py: Using Whittaker to get the wavefunction is not recommended! Use this only for comparison.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Whittaker: 43.56160364558853 bohr\n" ] } ], "source": [ "state1 = RydbergStateAlkali(\"Rb\", n=10, l=0, j=0.5)\n", "state2 = RydbergStateAlkali(\"Rb\", n=9, l=1, j=1.5)\n", "\n", "dipole_me = state1.radial.calc_matrix_element(state2.radial, 1)\n", "print(f\"Numerov with model potentials: {dipole_me}\", flush=True)\n", "\n", "_state1 = RydbergStateAlkali(state1.species, state1.n, state1.l, state1.j)\n", "_state1.radial.create_model(potential_type=\"coulomb\")\n", "_state2 = RydbergStateAlkali(state2.species, state2.n, state2.l, state2.j)\n", "_state2.radial.create_model(potential_type=\"coulomb\")\n", "\n", "dipole_me = _state1.radial.calc_matrix_element(_state2.radial, 1)\n", "print(f\"Numerov without model potentials: {dipole_me}\", flush=True)\n", "\n", "# For Whittaker we use the same integration bounds as Numerov without model potentials,\n", "# to avoid integrating over the diverging peak at the origin (see plots above)\n", "xmin1, xmax1 = _state1.radial.grid.x_min, _state1.radial.grid.x_max\n", "xmin2, xmax2 = _state2.radial.grid.x_min, _state2.radial.grid.x_max\n", "_state1 = RydbergStateAlkali(state1.species, state1.n, state1.l, state1.j)\n", "_state1.radial.create_grid(x_min=xmin1, x_max=xmax1)\n", "_state1.radial.create_wavefunction(\"whittaker\")\n", "_state2 = RydbergStateAlkali(state2.species, state2.n, state2.l, state2.j)\n", "_state2.radial.create_grid(x_min=xmin2, x_max=xmax2)\n", "_state2.radial.create_wavefunction(\"whittaker\")\n", "\n", "dipole_me = _state1.radial.calc_matrix_element(_state2.radial, 1)\n", "print(f\"Whittaker: {dipole_me}\", flush=True)" ] } ], "metadata": { "kernelspec": { "display_name": "rydstate", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 5 }