{ "cells": [ { "cell_type": "markdown", "id": "677c5e27", "metadata": {}, "source": [ "Starting with MLE and logistic regression model\n" ] }, { "cell_type": "markdown", "id": "2520b517", "metadata": {}, "source": [ "Prerequisites\n", "Make sure you have the necessary Python libraries installed:\n", "pip install numpy pandas scikit-learn scipy matplotlib statsmodels\n", "\n", "\n" ] }, { "cell_type": "markdown", "id": "97cb296e", "metadata": {}, "source": [ "1. Skealearn library" ] }, { "cell_type": "code", "execution_count": 3, "id": "2e1f9bfa", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Intercept (w0): -11.683190353932442\n", "Coefficient (w1): 5.687089258005263\n", "Standard errors: [3.50977855 1.95402341]\n", "95% CI for Intercept (w0): (-18.562229897321522, -4.804150810543363)\n", "95% CI for Coefficient (w1): (1.8572737464039735, 9.516904769606551)\n" ] }, { "data": { "image/png": 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sWQaAvfbaa+V+xnGM27BhAxMIBKywsNA57G4Sp4EDB7LQ0FDnBTqHGTNmMKlU6jIfQrhATfUIqSNdunSBSCSCUqnE0KFDERgYiB9//BEBAQEu4z300EMu73fv3g1PT08MGzYMFovF+WrXrh0CAwOdTeV+/fVXAChzv9SoUaMgFN759sVLly7h6tWrmDx5MqRS6V0uqd3+/fuhUCjK3NTv6N3vl19+cSnv3bs3lEql831AQAD8/f1dmkndyUsvvQSRSASpVIqOHTsiIyMDn376KQYPHuwyXun161hvt/c6CACdO3dGfHx8mTiVSiWGDx/uUjZmzBjYbDb89ttvzrL9+/ejX79+8PDwgEAggEgkwty5c1FQUIDc3FyXz7du3RpJSUllpllSUoITJ05UaflrIjk5GUlJSS7NXlatWgUej4ennnrqjp/dv38/EhIS0LlzZ5fyCRMmgDGG/fv31yimgwcP4sqVKxg/fjwEAgEAe7M5Ho9XbpM0wH7T+7Fjx1xetdGLICvVrHL37t3g8XgYO3asy74YGBiIpKSkMk1fq/Jdqer+7dCuXTuEh4c730ulUsTGxrrsJ7/++iv69u3rcmwRCAQYPXp0lZd9yJAhzvUPwNkTm2M+Fy9eRE5ODkaNGuXyufDwcHTv3r3S6Vd3vwsMDCzzXWvbtm2Vjw+9e/d26YQnPj4eADBo0CCXexwd5bdPNzc3F1OnTkVYWBiEQiFEIhEiIiIAAKmpqS7zGTVqFKZNm4bZs2fjzTffxKuvvor+/fu7jBMdHY3Tp0/j4MGDWLBgAfr164djx45hxowZ6Nq1KwwGQ5WWqTxubm4YNWoU9uzZ4+xc5ezZszh+/DgmTJhQpaaAo0aNglKpdNnf1qxZAx6Ph4kTJzrLTp48ieHDh8PHx8d5jBs3bhysVisuXbpU42VwMBgM+OWXXzBy5EjI5XKX/WPw4MEwGAzlNh8lpD5R5xCE1JENGzYgPj4eQqEQAQEB5bZxl8vlcHd3dym7desWVCoVxGJxudN1tLMvKCgAYD/BuJ1QKLxjm3YAznspKrr5viYKCgqc3Unfzt/fH0Kh0BmvQ3kxSiQS6PX6Ks3v2WefxdixY8Hn8+Hp6em8D6u00uvdEUd52yM4OLjMiVnpRBf4b507pnX06FEMGDAAycnJ+PzzzxEaGgqxWIydO3firbfeKrNMpbdZedOsKzNnzsSTTz6JixcvIioqCp9//jkefvjhcmO6XUFBQbn3sQQHBzuH18Tq1asBACNHjnR2e+/h4YH77rsP3377LT7++OMyPTomJSXVuHOIO3Fse8cy3bp1C4yxcr8DgL2HvttV5btS1f3boSr7iWPfq2jeVVF6PhKJBACc83HEX94yBgQE4Pr163ecfnX3u7s9Pnh7e7u8d6zvisodyYvNZsOAAQOQlZWFN954A4mJiVAoFLDZbOjSpUu58580aRJWrlwJsViMmTNnlhsPn89Hz5490bNnTwD2Hh0nT56Mr7/+GmvWrMH06dMB2BPe0vfEOTjuYxKJRC7lkydPxpo1a7Bx40a8+OKL5SY9dyKXy/Hoo49i7dq1yMnJga+vL7788kv06tXL2flMRkYGevTogVatWuGDDz5AZGQkpFIpjh49iv/7v/+r8na5k4KCAlgsFnz00Uf46KOPyh2n9P5BSH2jxImQOhIfH+/sVa8i5Z3o+/r6wsfHBz/99FO5n3HU0jhOLHJychASEuIcbrFYKj2JdfSQVFFnCDXh4+ODv/76C4wxl+XKzc2FxWKp9RPd0NDQStcvUHYdO9ZbdnZ2mcQxKyurTJyOq7i3y8nJcZnWV199BZFIhN27d7vU4FVUC+L4/J2mWVfGjBmDl156CZ988gm6dOmCnJwc/N///V+ln/Px8UF2dnaZ8qysLACo0fYtLi7Gt99+CwC45557yh1n8+bNzpPKuvb999+Dx+M5T259fX3B4/Fw6NAhZyJxu9JlVfmuVHX/rg4fH587fqdqgyP+Oy1jVT5f1f2OK2fPnsXp06exbt06jB8/3lleugMJB61WiyeeeAKxsbG4desWnnzySXz33XeVzkehUOCVV17B119/jbNnzzrLAwICKnzen6O8dPLarVs3xMfHY+3atXj22Wfx5Zdfok+fPmjRokWlcThMnjwZn3/+OTZs2IDY2Fjk5ubivffecw7fuXMntFottm/f7qx9A4BTp05VOm3HMbF0J0Glf6e8vLwgEAjwxBNPVHhMqs4yEVIXqKkeIQ3M0KFDUVBQAKvVik6dOpV5tWrVCgCcPWM5nknjsHXr1jI9LJUWGxuL6OhorFmzpsyP2e1KX3W+k759+0Kj0ZRJFjZs2OAc3hD06dMHAPDll1+6lB87dgypqall4lSr1fj+++9dyjZv3uy8ggzA+aDj25s66fV6bNy4sdwYzp07h9OnT5eZplKpRIcOHWq2YLe505V5qVSKp556CuvXr8eyZcvQrl27KjW16tu3L86fP1+mKeGGDRvA4/HQu3fvase5efNm6PV6LFq0CL/++muZl6+vb4XN9Wrb2rVr8eOPP+Kxxx5zNo0bOnQoGGPIzMwsd19MTEx0mUZVvitV3b+ro3fv3vjll19ckhqr1Vqr3aq3atUKgYGB2Lp1q0t5RkYG/vjjj0o/X939jiuOCy2lk+JPP/203PGnTp2KjIwMbN++HatXr8b333+P999/32Wc8i44AP81+3PUcAJAv3798Ouvv5bpYZExhm3btiEyMhIxMTFlpjVp0iScP38er7/+OvLy8pw94VXVvffeizZt2mDt2rVYu3YtPDw8XJo5l7deGGMVPvrhdgEBAZBKpfjnn39cyksnmHK5HL1798bJkyfRtm3bcvePur6wREhlqMaJkAbm0UcfxaZNmzB48GA8++yz6Ny5M0QiEW7evIlff/0VI0aMwMiRIxEfH4+xY8di+fLlEIlE6NevH86ePYulS5eWaf5Xnk8++QTDhg1Dly5dMGvWLISHhyMjIwN79+51JmOOE8MPPvgA48ePh0gkQqtWrcq9Kj5u3Dh88sknGD9+PNLS0pCYmIjDhw/j7bffxuDBg9GvX7/aXVE11KpVKzz11FP46KOPwOfzMWjQIKSlpeGNN95AWFgYZs2a5TK+j48Ppk2bhoyMDMTGxmLPnj34/PPPMW3aNOcJ9pAhQ7Bs2TKMGTMGTz31FAoKCrB06dJyaykA+4nS8OHDMX/+fAQFBeHLL79ESkoK/ve//9XKc7wSExNx4MAB7Nq1C0FBQVAqlS4n5NOnT8eSJUtw/PhxfPHFF1Wa5qxZs7BhwwYMGTIECxcuREREBH744QesWLEC06ZNQ2xsbLXjXL16Nby8vPDiiy+We6/duHHjsGzZMpw+fdrlnrDjx4+X+5DahISESr/7er3eeZ+EXq/HtWvXsHPnTuzevRu9evXCqlWrnON2794dTz31FCZOnIi///4bPXv2hEKhQHZ2Ng4fPozExERMmzbNOX5VvitV3b+r4/XXX8f333+PPn36YO7cuZDL5fjkk0+g1WqrNZ074fP5WLBgAZ5++mk8/PDDmDRpElQqFRYsWICgoKBK76Wp7n7Hlbi4OERHR+Pll18GYwze3t7YtWsXUlJSyoz7xRdf4Msvv8TatWvRunVrtG7dGjNmzMBLL72E7t27O+/Rat26Nfr27YtBgwYhOjoaBoMBf/31F9577z0EBAQ4uwQHgLlz52LXrl2499578fLLL6Nly5bIycnB559/jmPHjpVJXB3GjRuHV199Fe+++y48PT3x4IMPVnvZJ02ahOeffx4XL17E008/DZlM5hzWv39/iMViPPbYY5gzZw4MBgNWrlyJoqKiSqfruE9wzZo1iI6ORlJSEo4ePYrNmzeXGfeDDz7Afffdhx49emDatGmIjIyEWq3GlStXsGvXrhrfS0lIreGuXwpCmqaKuiMvbfz48UyhUJQ7zGw2s6VLl7KkpCQmlUqZm5sbi4uLY08//TS7fPmyczyj0cheeOEF5u/vz6RSKevSpQs7cuQIi4iIqLRXPcbsvYYNGjSIeXh4MIlEwqKjo8v00vfKK6+w4OBgxufzXaZRuncuxhgrKChgU6dOZUFBQUwoFLKIiAj2yiuvlOmOGhX0HFU67vJU1B15aXfaDlarlf3vf/9jsbGxTCQSMV9fXzZ27Fh248YNl/EcvbAdOHCAderUiUkkEhYUFMReffXVMl13r1mzhrVq1YpJJBIWFRXFFi9ezFavXl2mVzNHj3PffPMNa926NROLxSwyMpItW7as3OWsSa96p06dYt27d2dyuZwBKLOdGGMsOTmZeXt7u3R/XZn09HQ2ZswY5uPjw0QiEWvVqhV79913y/TcVZVe9Rzdxz/33HMVjnPhwgUGgD3zzDOMsTv3qgeApaSk3HGejt7aHC+FQsGioqLYww8/zLZt21ZhD2Rr1qxh9957L1MoFEwmk7Ho6Gg2btw49vfff7tMu6rflaru3xWtx/L2vd9//5116dKFSSQSFhgYyGbPns0+++yzKveqV97+hFI9njHG2GeffcZiYmKYWCxmsbGxbM2aNWzEiBGsffv25a6721V3vyutvO96eco7vlS0nI5j47Zt25xl58+fZ/3792dKpZJ5eXmxRx55hGVkZLisj3/++YfJZLIyxyuDwcA6duzIIiMjWVFREWPM3o37gw8+yKKiophcLmdisZhFR0ezqVOnlll2xhi7fPkyGzt2rPM46unpyQYMGFCml8nSRo4cWW7PhVWVl5fHxGIxA8COHj1aZviuXbuc39mQkBA2e/ZsZ0+Ut/+2lLediouL2ZNPPskCAgKYQqFgw4YNY2lpaeV+x65fv84mTZrEQkJCmEgkYn5+fqxbt27szTffrNFyEVKbeIxV8HRGQgghTVJubi4iIiLwzDPPYMmSJVyH0yQkJycjPz/f5X6V5kClUiE2NhYPPPAAPvvsM67DIYSQOkVN9QghpJm4efMmrl27hnfffRd8Ph/PPvss1yGRRiQnJwdvvfUWevfuDR8fH6Snp+P999+HWq2m7xIhpFmgxIkQQpqJL774AgsXLkRkZCQ2bdrk0hsjIZWRSCRIS0vD9OnTUVhYCLlcji5dumDVqlVo3bo11+ERQkido6Z6hBBCCCGEEFIJ6o6cEEIIIYQQQipBiRMhhBBCCCGEVKJZ3uNks9mQlZUFpVLpfKgbIYQQQgghpPlhjEGtViM4OPiOz6VrlolTVlYWwsLCuA6DEEIIIYQQ0kDcuHEDoaGhFQ5vlomTUqkEYF85lT1lnlTMbDZj3759GDBgAEQiEdfhkHLQNmrYaPs0bLR9Gj7aRg0bbZ+GjbbPf0pKShAWFubMESrSLBMnR/M8d3d3Spzugtlshlwuh7u7e7Pf4Roq2kYNG22fho22T8NH26hho+3TsNH2KauyW3iocwhCCCGEEEIIqQQlToQQQgghhBBSCUqcCCGEEEIIIaQSlDgRQgghhBBCSCUocSKEEEIIIYSQSlDiRAghhBBCCCGVoMSJEEIIIYQQQipBiRMhhBBCCCGEVIISJ0IIIYQQQgipBCVOhBBCCCGEEFIJSpwIIYQQQgghpBKUOBFCCCGEEEJIJShxIoQQQgghhJBKCLkOgBDSTNhswJUrQHEx4OEBxMQAfLp2UytuX7dKpb1Mra7b9UzbkxBCSE010t8QSpwIIXXv5Elg/XogNRUwGACpFIiPB8aPB9q35zq6xu32dZufb38BgK+v/VUX65m2JyGEkJpqxL8hnKd2v/32G4YNG4bg4GDweDzs3Lmz0s8cPHgQHTt2hFQqRVRUFFatWlX3gRJCaubkSWDhQuD4ccDbG2jZ0v73+HF7+cmTXEfYeN2+bnk8oKAA0Onsr/x8e1ltr2fanoQQQmqqkf+GcJ44abVaJCUl4eOPP67S+NevX8fgwYPRo0cPnDx5Eq+++ipmzpyJb7/9to4jJYRUm81mv6qUn2+/muTuDggE9r/x8fbyDRvs45HquX3dxsUBmZmA0WivZfLxsf8/K8s+rLbWM21PQgghNdUEfkM4b6o3aNAgDBo0qMrjr1q1CuHh4Vi+fDkAID4+Hn///TeWLl2Khx56qNzPGI1GGI1G5/uSkhIAgNlshtlsrnnwzZxj3dE6bLg430ZXrthfkZGASFR2eGQkcPkycPGivX1zM3NX2+f2davX25s7eHv/t569ve3lOl3tredmtj05339IpWgbNWy0fRq2et8+Dfg3pKrrgMcYY3UcS5XxeDzs2LEDDzzwQIXj9OzZE+3bt8cHH3zgLNuxYwdGjRoFnU4HUTkbYv78+ViwYEGZ8s2bN0Mul9dK7IQQQgghhJDGR6fTYcyYMSguLoa7u3uF43Fe41RdOTk5CAgIcCkLCAiAxWJBfn4+goKCynzmlVdewfPPP+98X1JSgrCwMAwYMOCOK4fcmdlsRkpKCvr3719uwkq4x/k2unIFmD0b8PKyV8WXVlICFBUB777bJGooquuuts/t65Yx4K+/ALH4v6t4JhNgNgOdO9t7KqqN9dwMtqfVZoWVWWG1WWE0G/HHgT/QsUdH8Pg8WG1W2JgNVmb/a7FaYLH9+2L2l9VmdY5nYzYwxsAYgw02MDCAwV4OezkA+zj//rMXwDkuePb3PB7PpYwHHhhjznLHe+Dfz/w7HSee489t4+G26f47zBHP7Xg8HupTdebHrAy4BiAK4AnqN87SeOB2/g0RszKwawy8KB7n24eUVe/bJycLWL0WULoBMhkMPAvCLUp0sPrZh3P4G+JojVaZRpc4AWUPqo6DfEUHW4lEAolEUqZcJBLRCX8toPXY8HG2jVq1sh/8jh+3t1++fR9lDEhLAzp1so/XCLohrSs12j63r9u4OHuvRPn5gKenfd2qVIC/PyCXAxcu1M56bsTb08ZsMFqMMFlNMFlNsNgsMNvMMFvN0Fv0MJgN0Fv0MNvMzsTH0XTjePZxMD4rk8TwwAOfx3d5Ocp4PB54PB4EPIH9/7eVA/aTbB7PXnb7e8dfUjU2qw1ZyEKwZzD4gob1nSP/bZ8gzyDaPhxijMHKrP9d6Pn3ZTabkWnMhA/Px+WikcVmcb53jOv4f+nxHMNKlzsuMt0+HavNAltkAayqK7BIFNDxLGjN98K96u6c/4ZU9Te40SVOgYGByMnJcSnLzc2FUCiEj48PR1ERQsrF59u7F01Pt3c7GhpqP5HX6YCbN+0dGYwb1+BOshuF29fthQtASIj9ap2jO3K5HAgOtg+rrfXcwLenxWaBwWKA3qyH0WqE0WKE1qyFzqSDzqKD2WZ21hIxxpw1N3weH0K+EEK+EAKeAGKB2J7wCHnIRz6ClEEQCAWcLBMhpOFijMFsMzsvyJisJpit9ve3l5utZud7i81S7gUcs81sf//v/0uXOce97TjmGF7m/1azS4JkZdY7L0hq/awvAIAYgD8AFAAAtDyz/berAfyGVEWjS5y6du2KXbt2uZTt27cPnTp1oloPQhqi9u2BuXP/e2ZDVpa9dqRTJ/sBsoE/s6FBK71ufX1dn+PEWO2v5wawPc1Wsz1BsuhhsBigNWlRbCiG1qyF0WqE2Wp2Nj8T8oQQCUQQ8UWQC+UQiUUQ8oVVqtWxWe09O1ENECENG2MMJqsJBovB+XJcPDFajeWWlf7r+LwjqTFajTBZbvv/bcnR7YlRY8UDz36xCAIIhf9dOHJeROILIOT993/HewFf8F/Zv+M7//IFzgtRAp6g3PcCngD8gkIIL16CXlWAlhoRUFjYaM4JOE+cNBoNrly54nx//fp1nDp1Ct7e3ggPD8crr7yCzMxMbNiwAQAwdepUfPzxx3j++ecxZcoUHDlyBKtXr8aWLVu4WgRCSGXatweSkhrlU8IbvNLrVqm0l6vVdbee62l7Wm1W6Mw6Z5KkMWpQYixxJkgmi/2khcfjQSqUQiwQw1PiCbFATMkOIQ2Mo3ZGZ9aVeRksBujMOugteujNeuf/HTXIeove+d7RrPb2JMlgMfx3jyCHRHwRxAIxRIJ//972XsQXOd8LBUKI+beV3/ZXyBfax+ELIeLb35ce7rgg5EhyHOM4/893HVbei8/j25tSnshCcAcOmrr2tyH38in4mkVARLdGc07AeeL0999/o3fv3s73jk4cxo8fj3Xr1iE7OxsZGRnO4S1atMCePXswa9YsfPLJJwgODsaHH35YYVfkhJAGgs8HYmO5jqJp4mLd1tE89WY9io3FUBlUuKW5Ba1Za69B+rcjBKlQColAYk+Q5JQgEVLXGGPQmXVQm9TQmDTQmrXQmDTOl9Zkf68z66A1a+0vkxY6sw4akwZqrRqm8yZozdrKm4zVAgFPAKlQ6nxJBBJIhBJIBBL7e+F/7x3DxAKxy3higdilXCwQ3/HlSIjoeFQNPD4QEgrIfYGQxnNuwHnilJycXKYHn9utW7euTFmvXr1w4sSJOoyKEEJIfbAxG0qMJSg2FCNPl4dCfSF0Zh144EEhUlANEiG1wMZsUBvVKDYWo8RY4nypTWr733+HaUwaqI1qZ5KkMWmgNqlhY7X7QFKJQAK5SO58yYQyyEQyyEVySIVSlzKpUAqZ8L+/jrKKXkI+56e2pAmjbxchhJB6Z7AYkKvNxY3iG1AZVDBajZAIJHATu8FL6uXsbY4Q4spxsUFlUEFlUKFIXwSVUeXyvthYbE+SDCXOZOlum7IJ+UK4id3gJnaDQqSw/xUr4Cb69++/5XKRHAqxAgqRAjKBDLprOkS0iYBCooBCrKDkhjRq9M0lhBBSLxhjKDYW45bmFm6W3ESxsRhyoRzeMm+IBWKuwyOEMxabBSqDCvm6fBToC1CgK0CBvgCF+kIU6YtQqC9EocH+f5VBVeMmbwqRAkqJEu4Sd7iL3f/7v8QdSrH9/25iNyglSijF/74kSriJ3SARSKpd82uz2pCVQ93Fk6aDEidCCCF1ymKzIF+Xj8ySTNzS3oLRYoSHxAPh7uHUBI80aTZmQ6G+EHnaPOTp8pCrzUW+Lh95Ovv7fG0+8vX5KNIXVbtGSClWwlPqWeblIfFw+b+7xB0eUg94SDwgElDvw4TcDUqcCCGE1AmrzYpb2lu4VngNBfoC8Hl8eMu8IVVIuQ6NkLvmqEHNVmcjR5ODW9pb/700t5CrzUWuNrfKtUN8Hh9eUi/4yH3gK/OFt8zb+fKSecFH5gMvmRe8pd7wlHpSEkQIByhxIoQQUqsYY8jX5eNa0TXkaHIg4osQ6BZI9zWQRqfEWIKbJTeRWZKJTHUmcjQ5yNJkIUedg2xNNvQWfaXT4PP48JH5wE/uB1+FL/zl/vCV+8JP4QdfuS985b72pEjqBQGfHrRMSENGv2KEEEJqTZG+CGmqNNwsuQkACFAE0JVx0mAxxlCgL0B6cTpuFN/AjZIbyCzJxE21PVlSm9SVTsNH5oNAt0AEuAUgQHHb69/3PnIfumhASBNBezIhhJC7pjaqka5KR0ZJBsxWM3zlvpAKqUkeaRj0Zj3SVGm4rrqO9OJ0ZBRnIKM4AzdKbkBn1t3xsz4yH4S6hyJYGYwgtyAEK4MR6BaIILcgBLoFQiKU1NNSEEK4RokTIYSQGrParLhZchOXCi5BY9LAR+YDhULBdVikmdKYNLhSeAXXVddxveg60lRpuKayNxmtCJ/HR5BbECI8IhDqHopQ91CEuIcgVGlPlmQiWT0uASGkIaPEiRBCSI2ojWpcKriEGyU3oBQrEe4RznVIpJmw2CxIV6XjUv4lnMo6hVsFt3C16CqyNdkVfsZL6oUWni0Q4RmBCI8IhHmEIcIjAiHKEGpOSgipEkqcCCGEVIuN2ZBZkomL+RehNqkR6BZIz2EidcZgMeBK4RVcyL+AiwUXcSH/Aq4UXoHZZi53fH+FP6K9ohHpGYkWni0Q5RWFSM9IeEo96zdwQkiTQ4kTIYSQKtOatLhceBnpqnTIRXKqZSK1ymKz4HLBZZzNO4tzuedwoeACrhddL7dLb7lIjmivaARZg9C2ZVvE+sYi2isaHlIPDiInhDQHlDgRQgipFGMMWeosXMi/gBJjCQIUAXRTPLkrjDFka7JxNves/ZV3FhfzL8JoNZYZ11PqiXjfeMT5xqGVTyvE+cYhWBkM2ICsE1kITggGX8DnYCkIIc0JJU6EEELuyGKz4ErhFVwquASJQIIw9zDweDyuwyKNjNVmxdWiqziZcxKnck7hVM4p5OnyyoznLnFHa7/WaO3XGvF+8YjziYO/wr/c75wNtvoInRBCAFDiRAgh5A50Zh1S81KRXpwOP7kf5CI51yGRRsJis+B83nkczz6Okzkn8c+tf6AxaVzGEfAEaOXTCq39W6ONfxu08WuDcI9wSswJIQ0SJU6EEELKVaQvwtncs8jX5SPYLZh6HiN3xBjD1aKrOJp5FMeyjuFE9glozVqXceQiOdr6t0W7wHZoF9gObfzb0PO+CCGNBiVOhBBCXDjuZzqXdw5GixGh7qHg8+j+EVJWvi4ff9z4A0duHsHfWX+jyFDkMtxD4oEOQR3QIagD2ge2R4x3DIR8OvUghDROdPQihBDi5LgP5WL+RUgEEvsN+IT8y2qz4lzeOfx+43f8fuN3XMi/4DJcKpSifWB73BN8DzqHdEasTywl3YSQJoMSJ0IIIQAAo8WI1PxUXCu6Bh+ZD9zEblyHRBoAjUmDwxmHcSjjEP68+SeKjcUuwxP8EtA9rDs6B3dGG/821KSTENJkUeJECCEERosRZ3PPIr04HUFuQfRA22auSF+Eg+kH8WvarziaedTlYbNKsRJdQruge1h3dA3tCh+5D4eREkIaE8YYjFYj9GY9tCYtfOW+XIdULZQ4EUJIM2eympxJU4gyhO5BaaZuaW7h17RfsT9tP07lnIKN/dfVd4RHBJIjk9EjvAfa+Leh7wghpEosNgv0Zj30Fj2MFiPAAyQCCeQiOWJ9YxHoFsh1iNVCRz5CCGnGTFYTztw6g/TidAS7BdMJcTNTbCjG/rT9+PHKjziZfRIMzDkszjcOvSN7o09kH7TwasFhlISQxsJoMUJv0UNn1sFis0DIF0ImlMFb7g0fqQ/cJG5wE7tBLpI3yvsf6ReSEEKaKZPVhHO555xJE92b0jwYLAYczjiMH6/8iN9v/A6LzeIclhSQhD4t+qB3ZG/qGIQQckeMMRgsBmjNWhgsBjAwiAViyEVyRHhGwFPqCTexPVFqKs2/KXEihJBmyJE0XVddp6SpGWCM4fSt0/ju4nfYf32/y/OVWnq3xMDogbg/5v5G12yGEFJ/bMwGg8UAnVnnTJRkQhkUIgUiPCPgLnGHm9gNCpECAr6A63DrBCVOhBDSzJitZkqamokifRF+uPwDvrv4Ha6rrjvLg9yCcH/M/RgYPRAx3jEcRkgIaagYY85md3qzHgAgE8uglCgR5RXlTJTkIjl4PB7H0dYPSpwIIaQZMVvNOJdnT5qC3IIoaWqCbMyGo5lH8d3F7/Br2q/OpnhSoRT9o/pjRKsRaBvQtlHeX0AIqTvlNb2TCWVwl7gj2isa7lJ7oiQTyppNolQaJU6EENJMMMZwtegqrhVdoy7HmyCNSYOdF3Zi2/ltyFRnOsvjfePxQNwDGBg9kJ7NRQgpQ6VXQcd0YDYGqUgKN5Gbs0ZJKVE260SpNEqcCCGkmcjR5OBywWX4ynwpaWpCMooz8NXZr7Dr0i7oLfbmNG5iNwyKGYQRrUYgzjeO4wgJIQ2F1WaF1qyF1qSF2WwGH3yIBCK0VLaEl8wLSokSCpGCEqUKUOJECCHNgMakwYX8CxDxRVCIFVyHQ+4SYwx/Zf6Fr85+hcM3DjvLo7yi8FibxzAoZhCkQimHERJCGgqDxQCNSQOdWQc+nw83kRtCPULhKfLE6aun0SW0C6QSOl5UBSVOhBDSxFlsFlzMv4hiYzFClaFch0PugsVmwd6re7H+9HpcK7rmLO8R3gOPtnkUnYM705ViQpo5i80CrUkLrVkLi80CqVAKD6kHor2i4SnzhLvEHWKBGGazGadxusn2gFcXKHEihJAmLq0ozfmsJjqpbpxMVhN+uPwD1p1a57x/SS6SY1jsMIxuPRrhHuEcR0gI4ZLRYoTapIbeogePx4ObyA3hHuHwlfs6e7+j4//do8SJEEKasDxtHi4VXoK31Jt60GuEDBYDdl7YiY3/bMQt7S0AgKfUE48nPo5HEh6hzh4IaaYYY9CZdVCb1DBZTRALxM7e7zxlnvCQeNAxvw5Q4kQIIU2U3qxHan4qGGNQSpRch0OqQW/WY+v5rdh0ZhMK9YUAAF+5L8a1HYeRcSMhE8k4jpAQUt9szAaNSQO1UQ0bs0EmlsFf4Y8AtwB4SDyglCjpMQN1jBInQghpgmzMhosFF5Gvy0eYexjX4ZAqstgs2HlhJz4/8TkK9AUA7A+rHZ80HsNih0EilHAcISGkPllsFmhMGmhMGgD2HjMjPCPgp/CDp9QTcpGc4wibF0qcCCGkCbpRfANpqjQEKgLpCmQjwBjDz9d+xoq/V+BGyQ0AQIgyBJPbT8bgloMh5NPPNSHNhcVmQYmxBFqTFjw+D0qxEi29W8JH7gNPqSddQOEQHYkJIaSJKdIX4ULBBSjFSvqBbQSOZR7DR0c/wvn88wAAL6kXnuzwJB6Me5DuUSCkmXAmS2Yt+Dw+PCQeiPSPhJfMi+5XakAocSKEkCbEarPiSuEVGCwG6nq8gbtSeAUf/PUBjtw8AsDeS97jiY9jbOJYetYWIc3A7cmSgCeAu8QdkZ6R8JZ5w1PqSd2EN0CUOBFCSBOSpc5CpjoTgYpArkMhFdCYNPj0+KfYem4rrMwKIV+Ih+IfwuT2k+Et8+Y6PEJIHXLcs6Q2qsHn/1uzRMlSo0GJEyGENBF6sx6XCy9DJpRRs44GiDGGHy7/gI+OfuTs+KF3ZG88e++zCHWn2kFCmiobs0FtVENtUgMA3CXuiPeLh6/cl5KlRoYSJ0IIaSKuF12HyqBCuDs9DLWhuVhwEUt+X4LTt04DAMI9wjGn2xx0Ce3CcWSEkLpisppQoCuAhVmgFCsR4x0DP4UfvKRedHGrkaLEiRBCmoB8XT6uq67DV+ZLT4dvQNRGNVb+vRLfpH4DG7NBKpTiyfZPYkziGIgFYq7DI4TUAZPVhHxdPgAg0C0Qoe6h8JZ5U2c9TQAlToQQ0shZbBZcKbwCG7NRpwINyOGMw3jr0FvI0+UBAPq16IfnujyHQDe6/4yQpshoMaJAXwAGhiC3IER4RsBX7kuPhGhCKHEihJBGLkudhWx1NoKVwVyHQgCUGEvw3pH38MPlHwAA4e7heOm+l3BvyL0cR0YIqQuOhAmw1zBRwtR0UeJECCGNmNakxeWCy3ATu9FDUhuA39J/w9uH30a+Lh888PB44uOY2mkqpEIp16ERQmqZ2WpGni4PDAwhyhCEe4TDV07NpZsy+pUlhJBGijGGa0XXUGIsQZh7GNfhNGvFhmK8d+Q97LmyBwAQ4RGBub3mIikgiePICCG1zWKzIF+XD4vNgiBlECI9I+En96OEqRmgxIkQQhqpfF0+0lXp9IPNscMZh7Hot0Uo0BeAz+Pj8cTH8XTHp6mWiZAmxmqzolBfCIPVgABFAFp4tYC/wp+a5DUjlDgRQkgjZLaacaXwCgBAJpJxHE3zZLaa8eHRD7Hl7BYAQKRnJOb1nIfEgESOIyOE1CYbs6FIXwSNWQM/uR8SvRIR4BZAzaObIdrihBDSCGWps5CjyaEOIThys+QmXv3lVZzPPw8AeKzNY5hxzwzqbpiQJqbEWIIiQxG8pd7o5NcJQW5B9AymZowSJ0IIaWQMFgOuFl2lDiE4su/qPrx16C1ozVp4SDwwr9c89IzoyXVYhJBapDfrkafLg0KsQKJ/IsI8wqj5LaHEiRBCGpvMkkyoDCqEu4dzHUqzYrAY8N6R97Djwg4AQLuAdnizz5v0XCZCmhCT1YQ8XR4EPAFivGMQ6RkJpUTJdVikgaDEiRBCGhG9WY80VRo8JB7UIUQ9ul50HS//8jKuFl0FDzxMaj8JUzpMoRo/QpoIi82CAl0BzDYzgpXBiPKKgrfMm46zxAUd8QkhpBG5WXITxcZiqm2qRwfSD2DewXnQW/TwkflgYe+F9DBbQpoIZ095FgN85b6I8o5CoFsg9ZRHykWJEyGENBJakxZpqjR4SjzpKmg9YIxha85WbD61GQDQKagT3urzFnzkPhxHRgi5WzZmQ6G+EFqzFn5yP7QJaINAt0CqRSZ3RN8OQghpJG6U3IDGpKGH3dYDg8WABQcWICUnBQAwKmEUnu/6PJ1UEdLI3d61uI/MB/F+8dRTHqky+gUghJBGQG1UI704HV5SL6ptqmM5mhy8mPIiLuRfgAACzOk2Bw+1fojrsAghd4ExBpVBhRJTCbyl3ujo2xFByiCIBWKuQyONCCVOhBDSCNwovgGdSQdfD1+uQ2nS/rn1D2anzEaBvgCeUk/MDp2N/nH9uQ6LEFJDtydMnlJPtA9sj2BlMD1zjdQIJU6EENLAFRuKkVGSAW+ZN9ehNGm7L+3GW4fegtlmRkvvlni377vAZa6jIoTUBGMMxcZiFBuL4SHxQLuAdgh2D6ZnMZG7QokTIYQ0cBnFGTBYDPCT+3EdSpPEGMPaU2ux4u8VAIDekb2xIHkBpHwpspDFcXSEkOoonTAlBSQhxD2EEiZSKyhxIoSQBqxIX4QbJTfgI6Oe3OqCjdnw/p/vY8vZLQCACUkTMP2e6eDz+LBZbRxHRwipjhJjCYoMRc6EKVgZDJlIxnVYpAmhxIkQQhooxhjSi9NhtpohF8m5DqfJsdgsWHBwAX688iMA4Pkuz2NM4hiOoyKEVJfGpEGhvhAKsQJt/Nsg1D2UjpmkTlDiRAghDVShvhCZJZnwlVOHELVNb9bjpV9ewh83/oCAJ8D85PkYFDOI67AIIdWgN+uRr8uHVCRFK59WCPcMh5vYjeuwSBNGiRMhhDRAjDFkFGfAwizUNr+WFRuK8dze53Am9wwkAgmW9F+C7mHduQ6LEFJFRosRefo8CHlCRHlHIcIjAh5SD67DIs0AJU6EENIAFRmKkKXOgq+Maptq0y3NLTzz4zO4proGd4k7lg9cjrYBbbkOixBSBRabBXnaPNhgQ5h7GCI9I+nZdqReUeJECCEN0I3iG7DYqLapNt0suYmpP0xFjiYH/gp/fHT/R4j2juY6LEJIJWzMhkJ9IfQWPQLcAhDlGQV/hT8lTKTeUeJECCENjMqgQqY6k57bVIuy1FnOpCncIxyfDPoEQcogrsMihNzB7V2L+8h80Nq/NYLcgiDgC7gOjTRTlDgRQkgDc7PkJowWIwIUAVyH0iTkaHIwdbc9aYrwiMCnQz+lDjcIaeA0Jg0K9AXOh9eGeoRCLBBzHRZp5ihxIoSQBqTEWIKbJTeptqmW3NLcwtO7n0aWJgvh7uFYNWQVJU2ENGBGixF5ujxIhBIk+CUg3COcuhYnDQYlToQQ0oBkqbOgM+vgJ/fjOpRGL0+bh6k/TEWmOhMhyhCsHLISfgpar4Q0RBabBfm6fFiZFeEe4Wjh1QKeUk+uwyLEBSVOhBDSQGhMGmQUZ8BbSrVNdytfl4+nf3gaN0puINgtGJ8O/RQBbtT0kZCGhjGGIkMR1CY1At0CEeUVhQBFAHX8QBokSpwIIaSByFJnQWvSwsfDh+tQGrUCXQGm/TANGcUZCHQLxKqhqxDoFsh1WISQUm6/j6ljUEcEK4MhEoi4DouQClHiRAghDYDOrEOGKgMeEnqI491QGVSYtmcarquuI0ARgFVDViFYGcx1WISQ25itZtzS3YKYL6b7mEijQokTIYQ0ANnqbJSYShDuHs51KI2WwWLA83ufx7Wia/CT+2HVkFUIdQ/lOixCyL8cz2MyWAwIVgYj2juaOsIhjQolToQQwjGjxYg0VRo8JB7Urr+GrDYrXt//Ov7J/QdKsRKfDP4EYR5hXIdFCPmXo1met9SbnsdEGi1KnAghhGO3tLdQbCym2qYaYoxh6ZGlOJB+AGKBGMsGLEOUVxTXYRFC/pWlzoJYZG+WF+kZCalQynVIhNQIn+sAAGDFihVo0aIFpFIpOnbsiEOHDt1x/E2bNiEpKQlyuRxBQUGYOHEiCgoK6ilaQgipXRmqDCjFSqptqqH1p9dj2/lt4IGHhckL0T6oPdchEdLs2ZgNedo8AECwMhhdQrsgzjeOkibSqHGeOH399dd47rnn8Nprr+HkyZPo0aMHBg0ahIyMjHLHP3z4MMaNG4fJkyfj3Llz2LZtG44dO4Ynn3yyniMnhJDaUWQooueV1NAPl3/Ax8c+BgA83/V59Ivqx3FEhBCVQYUbJTfgJnYDALQNaAsvmRfHURFy9zhvqrds2TJMnjzZmfgsX74ce/fuxcqVK7F48eIy4//555+IjIzEzJkzAQAtWrTA008/jSVLllQ4D6PRCKPR6HxfUlICADCbzTCbzbW5OM2KY93ROmy4aBs1bDqjDgAg48sAG2CDjeOIGpejmUex8OBCAMDjbR7H6PjRsFlrbx06plWb0yS1i7ZRw6I361GgK4BCrEAbnzYIkAfgAA7AarHCzKPfoYaGzhH+U9V1wGOMsTqOpUImkwlyuRzbtm3DyJEjneXPPvssTp06hYMHD5b5zB9//IHevXtjx44dGDRoEHJzczFq1CjEx8dj1apV5c5n/vz5WLBgQZnyzZs3Qy6n7i8JIaSxuaa7hteuvAa9TY8enj0wK2IW+DzOG1EQQghphHQ6HcaMGYPi4mK4u7tXOB6nNU75+fmwWq0ICHB9mntAQABycnLK/Uy3bt2wadMmjB49GgaDARaLBcOHD8dHH31U4XxeeeUVPP/88873JSUlCAsLw4ABA+64csidmc1mpKSkoH///hCJ6IF1DRFto4bLZDXhaMZRlKSWIDApEHwBnfRX1S3NLby9623obXp0DOyIxQMXQywQ1/p8bFYbck7n0PZpwGgbcctis6BQVwiLzQJ/N3+08GoBb6m3835N+g1q2Gj7/MfRGq0ynDfVA1DmhmjGWIU3SZ8/fx4zZ87E3LlzMXDgQGRnZ2P27NmYOnUqVq9eXe5nJBIJJBJJmXKRSNTsvyi1gdZjw0fbqOHJ0mahyFQEAQTgC/h00ldFBosBs/fPRr4+H9Fe0Vg6YCmk4rq92Zy2T8NH26h+WWwW5OvynQlTpGck/BX+FXYvTr9BDRttH1R5+TlNnHx9fSEQCMrULuXm5paphXJYvHgxunfvjtmzZwMA2rZtC4VCgR49euDNN99EUFBQncdNCCF3w2Q1IU2VBrlIDiOMlX+AALBfVHv70Nu4kH8BnlJPLB+4HEqJkuuwCGk2XBImReUJEyFNDaeXZ8RiMTp27IiUlBSX8pSUFHTr1q3cz+h0OvD5rmELBPYdlsPbtQghpMqy1dko0BdQL1PV9NW5r7Dnyh4IeAK80/cdBCnpQhkh9cFisyBHk4McbQ68Zd7oHNIZnUM6I0hJD7ElzQvnTfWef/55PPHEE+jUqRO6du2Kzz77DBkZGZg6dSoA+/1JmZmZ2LBhAwBg2LBhmDJlClauXOlsqvfcc8+hc+fOCA4O5nJRCCGkUkaLEdeLrsNN5EadGVTD31l/Y/mfywEAz977LDoFd+I2IEKaAYvNggJdAcw2M9UwEYIGkDiNHj0aBQUFWLhwIbKzs9GmTRvs2bMHERERAIDs7GyXZzpNmDABarUaH3/8MV544QV4enqiT58++N///sfVIhBCSJXlaHJQaChEmHsYqPfxqslWZ+PlX16GlVkxKGYQHmvzGNchEdKkWW1WFOoLobfo4a+wd/oQoAighIk0e5wnTgAwffp0TJ8+vdxh69atK1P2zDPP4JlnnqnjqAghpHaVrm2i5zZVzmAx4MWUF6EyqBDnG4fXerxWYedBhJC7Y7VZUWQogs6sg6/cF4kBiQhwC4CQ3yBOFwnhHO0JhBBST7I12f/VNpFKMcbw1qG3cLHgIjylnljafymkwrrtQY+Q5sjGbCjSF0Fr1sJb5o0EvwQEugVCJGjePa0RUholToQQUg8ctU1KsZLubaqizWc348crPzo7gwh0C+Q6JEKaFMYYio3FKDYWw1vqjVa+rRCkDKqT56IR0hRQ4kQIIfUgW5ONIkMR1TZV0d9Zf+PDvz4EADzX5TnqDIKQWlZiLEGRoQgeEg+0C2iHEPcQSIRln3lJCPkPJU6EEFLHDBYDrhVdo9qmKirSF+H1X1+HlVkxOGYwHm39KNchEdJkaEwaFOoLoRAr0Ma/DULdQyEXybkOi5BGgRInQgipY1klWVAZVFTbVAWMMSz8bSHydfmI9IzEK/e9Qp1BEFILDBYD8rR5kIqkaOXTCuGe4XATu3EdFiGNCiVOhBBShyw2C26U3KDapir6+tzXOJRxCCK+CG/3eRsykYzrkAhp1ExWE/J1+eDz+Ij0ikSkZyQ8pZ5ch0VIo0SJEyGE1KFig/3G6wBFANehNHiXCi7hg78+AGB/yG2sTyzHERHSeFlsFuTr8mGxWRCsDEYLrxbwkflQDS4hd4ESJ0IIqUOF+kLYmI2eg1IJvVmPV/e/CrPNjB7hPTC69WiuQyKkUbIxm/3htWY9/N38EeUVBX+FP9V4E1IL6JecEELqiI3ZkK3JhlxIN15XZtmfy5CmSoOv3Bdze86lq+KE1IDKoEKxsRg+Mh8k+CUgSBlEF20IqUW0NxFCSB0pNhSjxFACH7kP16E0aD9f+xk7LuwADzwsTF4IL5kX1yER0qhoTVoU6AvgJnZDUkASQt1DqWtxQuoAJU6EEFJHVAYVzDYzPUzyDnI0OXjr0FsAgPFJ49E5pDPHERHSeBgtRuTp8yDiixDrE4sIzwjqKY+QOkSJEyGE1AHGmL2ZHj0fpUIWmwWv738dapMarf1aY2qnqVyHREij4Oj4wcqsCFWGooVXC3jLvLkOi5AmjxInQgipA2qTGiqDCh4SD65DabDWnlqLU7dOQSFS4K0+b9G9GIRUgjGGIkMRNCYNAtwCqOMHQuoZ/UoRQkgdUBlUMFqMkCqkXIfSIF0uuIwvTnwBAHj5vpcR6h7KcUSENGwakwYF+gJ4SDzQIagDQtxD6GIDIfWM9jhCCKlljDHkaHIgEdDN2eWx2CxY8NsCWJkVvSN74/7o+7kOiZAGy2gxIk+XB4lQggS/BER4RNCDoQnhCCVOhBBSy7RmLQr1hVBKlFyH0iBt/GcjLuRfgLvEHS91f4m6HiekHFabFXm6PFiZFeEe4Wjh1QKeUk+uwyKkWaPEiRBCapnKoILerIef3I/rUBqca0XX8NnxzwAAL3R9Ab5yX44jIqThcTyPKUARgGjvaAQoAugCAyENACVOhBBSy3I1uRDxRVyH0eBYbVYs/G0hzDYzuod1x+CYwVyHREiDojfrkafLg1KsRPvA9gh1D4VIQMcSQhoKSpwIIaQW6c165OvzqZleObac3YKzuWehECnw6n2v0hV0Qv5lsVmQp80DAMR4x6CFVwt6HhMhDRAlToQQUotUBhV0Jh283emZKrdLV6Vj5d8rAQCzusxCgFsAxxERwr3buxcPdAtEjHcMfOW+dFGBkAaKEidCCKlFudpc8Hl8OvG5jY3ZsOi3RTBajegc0hkjWo3gOiRCOMcYQ6Y6E25iN+penJBGgvZQQgipJUaLEfk6aqZX2tZzW3Hq1inIhDK83uN1SioJAZCtyYan1BMdgjrQMYOQRoIeNU0IIbVEZVBBbVTTvQm3uVlyEx8f+xgAMPPemQhWBnMcESHcu6W5BblIjrYBbSlpIqQRocSJEEJqSYGuADweD3weHVoBe1Oktw+/DYPFgA5BHfBQ/ENch0QI5wp0BRDwBUgMSISXzIvrcAgh1UC/7oQQUgvMVjNytDlU23SbX67/gqOZRyEWiPFGjzcooSTNXrGhGCarCW3828Bf4c91OISQaqJfMUIIqQXFxmKoTdRMz0Fn1mHZn8sAAOOTxiPMI4zjiAjhltakhdqkRmv/1ghxD+E6HEJIDVDiRAghtaBQXwhmY9Qr1r++OPEFcrW5CFGGYHzSeK7DIYRTBosBhfpCxPnGIdIzkutwCCE1RIkTIYTcJavNimx1NhRiBdehNAjXi65j05lNAIAXu74IqVDKcUSEcMdsNeOW9haivaMR4x1DvUoS0ohR4kQIIXep2FiMEmMJlGLqHYsxhiV/LIGVWdEjvAd6RPTgOiRCOGO1WZGlyUILzxaI842DgC/gOiRCyF2gxIkQQu5Skb4IFpsFIoGI61A4l3ItBceyjkEikODFri9yHQ4hnGGMIUudhSBlEOL94un4QEgTQIkTIYTcBRuzIVudDblIznUonNOatHj/z/cBABPaTaAb4Emzlq3JhpfMC2382lBzVUKaCEqcCCHkLpQYS1BsLKZmegC+OPkF8nR5CFGGYFzbcVyHQwhn8nX5kAglaOPfhh5wS0gTQokTIYTcBZVBBZPVBIlQwnUonLpWdA2bz2wGAMzuNrvZrw/SfJUYS2CxWdDGvw185D5ch0MIqUWUOBFCSA0xxpCtzoZMKOM6FE4xxrDkd3uHEL0ieuG+8Pu4DokQTujMOpQYSxDvG49gZTDX4RBCahklToQQUkNqkxpFhqJm3xRn37V9+Dv7b0gEErzQ9QWuwyGEEyarCXm6PLT0bokWXi24DocQUgcocSKEkBpSGVQwWozN+sZvg8WAD/76AAAwsd1EuspOmiWrzYpsTTZaeLZArG8sPauJkCaKEidCCKkBxhiyNdmQCJr3vTxf/vMlcrW5CHYLxhNtn+A6HELqnaPb8WBlMBL8EiDkC7kOiRBSRyhxIoSQGtCatSjSF8Fd4s51KJwp0BVgwz8bAADT75lOHUKQZumW9pa923H/NrQPENLEUeJECCE1UKQvgt6sh0zUfDuG+PzE59CZdUjwS8CA6AFch0NIvSvSF0HIF6K1f2u4id24DocQUscocSKEkBq4pb0FsUDMdRicSVOlYceFHQCA5+59Dnwe/ZyQ5kVr0kJv0SPBLwG+cl+uwyGE1AP6pSOEkGrSmXUo0Bc064fefnj0Q1iZFT0jeqJDUAeuwyGkXpmsJuTr8xHrE4tQ91CuwyGE1BNKnAghpJoczfTkIjnXoXDiRPYJ/Jb+GwQ8AWZ2nsl1OITUK0cPelFeUYjxjqEe9AhpRihxIoSQasrT5UHAEzTLEyYbs2H5X8sBAA/EPYBIz0hO4yGkPjl60wxyC0KcbxwEfAHXIRFC6hElToQQUg0GiwF52rxm25teyrUUnM87D7lIjqc6PMV1OITUq1xtLtwl7mjt37pZP7+NkOaKEidCCKmGIn0RNCZNs2ymZ7Ka8MnRTwAA49qOg4/ch+OICKk/KoMKPB4Prf1bN9sLJ4Q0d5Q4EUJINeTr8sHn8ZtlL3Jbz21FliYLfnI/jG07lutwCKk3OrMOGpMGCX4J8Ff4cx0OIYQjze+XnxBCashoMTqb6jQ3xYZirD65GgAwtdNUaqZEmg2T1YR8XT5a+bZCuEc41+EQQjhEiRMhhFSRyqCC2qiGQqTgOpR6t+bUGqhNasR4x2Boy6Fch0NIvXD0oBfpGUk96BFCKHEihJCqKtAVgMfnNbuetHI0Odh6bisA4NnOzza75SfN0+096MX7xUPIF3IdEiGEY5Q4EUJIFZitZuRoc+AmcuM6lHq3+uRqmG1mdAzqiK5hXbkOh5B6cUt7Cx4SD+pBjxDiRIkTIYRUgcqggsakgZu4eSVON0tu4vuL3wMApnWaxnE0hNSPIn0RhHwh9aBHCHFBiRMhhFRBob4QNput2TXXWX1yNazMii4hXdAusB3X4RBS5zQmDfQWPRL8EuCn8OM6HEJIA0KJEyGEVMJqsyJHkwOFuHl1CpFRnIE9l/cAsPekR0hTZ7QYUagvRKxPLELdQ7kOhxDSwFDiRAghlSg2FkNtVEMpVnIdSr36/MTnsDIr7gu7D23823AdDiF1ynEfY5RXFPWgRwgpV/Nqc0IIITVQpC+C2WaGSCDiOpR6c73oOn668hMAqm0iTZ/BYsAt7S1EeEQgzjeOeo4khJSLEidCCLkDxhhyNDmQi+Rch1KvPjvxGRgYkiOSEecbx3U4hNQZrUmLAn0BWnq3RJxvXLO6QEIIqR5KnAgh5A5KjCUoNhbDQ+LBdSj15nLBZaRcSwEAPN3xaY6jIaTuFBuKoTapkeCXgBjvGKppIoTcESVOhBByByqDCkaLEVJF83mOy6fHPwUA9I/qj5Y+LTmOhpC6UaArgNlmRtuAtoj0jKR7mgghlaLEiRBCKsAYwy3tLUgEEq5DqTepeak4kH4APPAwpcMUrsMhpNY59muhQIj2Qe0RrAzmOiRCSCNBiRMhhFRAa9aiSF8EpaT59KbnqG26P+Z+RHlFcRwNIbXLxmzI0mRBKVYi0T+RntNECKkW6o6cEEIqoDKooDPrIBPKuA6lXpy5dQaHbxyGgCeg2ibS5DDGkKXOgrfUGx2COlDSRAipNqpxIoSQCuRp8yDii5rNvQ+O2qbBLQcj3COc42gIqT2MMWSqM+El80JSYBLcJe5ch0QIaYSoxokQQsqhN+uRr8tvNs30ztw6gz8z/4SAJ8Dk9pO5DoeQWsMYQ6YmE55ST7QLbEdJEyGkxihxIoSQcqgMKmjN2mbz/KY1p9YAsNc2hbqHchwNIbWDMYYsTRY8JZQ0EULuHiVOhBBSjnxdPvg8Pvi8pn+YvFxwGYcyDoEHHsYnjec6HEJqhSNp8pB4oF1gO3hIm8+z2AghdaPpnxEQQkg1mawm5Gpz4SZy4zqUerHu9DoAQN8WfRHpGclpLITUBsYYsjXZcBe7IykwiZImQkitoMSJEEJKURlU0Jg0cBM3/cTpRvENpFxLAQBMaDeB22AIqQWOpMlN7IakwCR4Sj25DokQ0kRQ4kQIIaUU6gsBAAK+gONI6t6GfzbAxmzoFtYNcb5xXIdDyF1xJE0KsQLtAtvBS+bFdUiEkCaEuiMnhJDbWG1W3NLcgkKk4DqUOperzcXuS7sBAJPaTeI4GkLujo3ZkKXOgqfUE20D2lLSRAipdVTjRAght1EZVCgxljSLbsg3ndkEs82MdgHt0C6wHdfhEFJjVpsVN0tuwkfmg/ZB7SlpIoTUCapxIoSQ2xTpi2C1WSHkN+3Do8qgwrep3wIAJrafyHE0hNydbHU2Aj0CkRiQ2CzuTSSEcKNpnxkQQkg12JgNOZocyEQyrkOpc1+f+xoGiwGxPrHoFtqN63AIqRGLzQIACFQGIikwqdk8d40Qwg1qqkcIIf9SG9UoNhZDKW7azfS0Ji2+OvsVAPu9TTwej+OICKk+k9WErJIsAECifyIlTYSQOtcgapxWrFiBd999F9nZ2WjdujWWL1+OHj16VDi+0WjEwoUL8eWXXyInJwehoaF47bXXMGkS3dxMCKk5lUEFk9UEiVDCdSh16tvUb6E2qRHuEY7ekb25DoeQajNYDLilvYUWXi1wAzcq3GdtNhtMJlM9R0cczGYzhEIhDAYDrFYr1+GQUprT9hGJRBAI7r6nXM4Tp6+//hrPPfccVqxYge7du+PTTz/FoEGDcP78eYSHh5f7mVGjRuHWrVtYvXo1YmJikJubC4vFUs+RE0KamlvaW5AImnbSZLQYsenMJgDAhKQJzaLLddK06M165OnyEOMdg5aeLXEDN8odz2Qy4fr167DZbPUcIXFgjCEwMBA3btygmu0GqLltH09PTwQGBt7VsnKeOC1btgyTJ0/Gk08+CQBYvnw59u7di5UrV2Lx4sVlxv/pp59w8OBBXLt2Dd7e3gCAyMjIO87DaDTCaDQ635eUlACwZ9pms7mWlqT5caw7WocNF22jqtOb9SjUFkIhUMBmrZ8TLcd86mt+APD9xe9RoC+Av8IfA1sMrNd5NzZcbB9yZzqTDoX6QmfS5Ng2pY9xjDFkZmaCz+cjJCQEfD7dmcAFxhi0Wi0UCkWzODFvbJrL9mGMQafTIS8vD1arFQEBAWXGqep5Eo8xxu4mGKPRCImkZldoTSYT5HI5tm3bhpEjRzrLn332WZw6dQoHDx4s85np06fj0qVL6NSpEzZu3AiFQoHhw4dj0aJFkMnKv6F7/vz5WLBgQZnyzZs3Qy6nNtGEkObByqyYljoNuaZcPBnyJIb6DeU6JELqBJ/PR1BQEIKDg+l3nhACAFCr1cjJyUF2djZKpz86nQ5jxoxBcXEx3N3dK5xGtWuc9u7diy1btuDQoUPIyMiAzWaDXC5Hhw4dMGDAAEycOBHBwcFVmlZ+fn65mV9AQABycnLK/cy1a9dw+PBhSKVS7NixA/n5+Zg+fToKCwuxZs2acj/zyiuv4Pnnn3e+LykpQVhYGAYMGHDHlUPuzGw2IyUlBf3794dIJOI6HFIO2kZVl5qXiuuq6whWVu34VRtsVhtyTucgMCkQfEHdXxHfe3Uvck258JR6YlzfcZAKpXU+z8asvrcPqZjaqIbaqEacbxwivSLB59m3R0XHOKPRiIyMDHh4eFR4UZXUPcYY1Go1lEplk67RaKya2/YRiURQq9Xo06dPmUofR2u0ylQ5cdq5cydeeuklFBcXY/DgwZg9ezZCQkIgk8lQWFiIs2fP4ueff8aiRYswYcIELFq0CH5+flWadumNxRircAPabDbweDxs2rQJHh4eAOzN/R5++GF88skn5R4gJRJJubViIpGITiZrAa3Hho+20Z2ZrWbkG/PhJnXj5ASZL+DX+XwZY9h8bjMAYHTr0ZBL6Cp8VdXH9iEVUxlU0Fl1SAxKRAuvFuWeH5Q+xlmtVvB4PAgEAmqmxyHH/WU8Ho+2QwPU3LaPQCAAj8eDUCgsc05U1XOkKidOb7/9NpYuXYohQ4aUu3JHjRoFAMjMzMQHH3yADRs24IUXXrjjNH19fSEQCMrULuXm5pbb/hAAgoKCEBIS4kyaACA+Ph6MMdy8eRMtW7as6iIRQggAoMRYArVJjUBFINeh1JkTOSeQmp8KiUCCh+Mf5jocQqqkUF8Ik9WEpMAkhHuU32EUIYTUlyonTkePHq3SeCEhIViyZEmVxhWLxejYsSNSUlJc7nFKSUnBiBEjyv1M9+7dsW3bNmg0Gri52Z8OfunSJfD5fISGhlZpvoQQcrsifREYYxDyOe8vp858+c+XAIDBLQfDS+bFcTSEVC5flw8bsyEpMAmh7vT7TgjhXo3q5fR6fYXDsrOzqzWt559/Hl988QXWrFmD1NRUzJo1CxkZGZg6dSoA+/1J48aNc44/ZswY+Pj4YOLEiTh//jx+++03zJ49G5MmTaJ2zISQamOMIUeTA5mw6R4/0lXpOJRxCADweOLjHEdDSOVytbkAD2gX2I6SJkJIg1GjxKl9+/Y4ceJEmfJvvvkGbdu2rda0Ro8ejeXLl2PhwoVo164dfvvtN+zZswcREREA7IlYRkaGc3w3NzekpKRApVKhU6dOePzxxzFs2DB8+OGHNVkUQkgzpzapUWIqgZvYjetQ6szms/Z7m3qE90CkZyS3wRBSiRxNDoR8IdoHtkeQMojTWGw24NIl4Ngx+9/6eCTUhAkTwOPx8M4777iU79y50+X+LsYYPvvsM9x7771wc3ODp6cnOnXqhOXLl0On09V9oIQ0QzVql9K/f39069YN8+fPx0svvQStVosZM2Zg27ZtZXb0qpg+fTqmT59e7rB169aVKYuLi0NKSkq150MIIaUVG4phtBghVTTNHuZUBhV2X9oNgGqbSMPGGEO2JhtykRxJgUnwlftyGs/Jk8D69UBqKmAwAFIpEB8PjB8PtG9ft/OWSqX43//+h6effhpeXuU3rX3iiSewfft2vP766/j444/h5+eH06dPY/ny5YiMjMQDDzxQt0ES0gzVKHH66KOPMGTIEEycOBE//PADsrKy4O7ujmPHjiEhIaG2YySEkDqTp82DWCDmOow68835b2C0GhHnG4eOQR25DoeQcjHGkKXJglKsRFJgErxl3pzGc/IksHAhkJ8PhIYCCgWg1QLHjwPp6cDcuXWbPPXr1w9XrlzB4sWLy71vfOvWrdi0aRN27tzpck94ZGQkhg8fXuWulQkh1VPjvgcHDBiABx98EL///jtu3LiBd955h5ImQkijYrAYUKAvaLLN9IwWI7ae3woAGJs4tlk8p4M0PjZmQ6Y6Ex4SD7QPas950mSz2Wua8vPtNUzu7oBAYP8bH28v37ChbpvtCQQCvP322/joo49w8+bNMsM3bdqEVq1alduRFo/Hc+l5mBBSe2qUOF29ehVdu3bF7t27sXfvXsyZMwcjRozAnDlzYDabaztGQgipE8WGYmjNWshFTfOZRj9e+RGF+kIEKALQL6of1+EQUoaN2ZClzoK3zBvtAtvBU+rJdUi4csXePC80FCh9rYHHs5efP28fry6NHDkS7dq1w7x588oMu3z5Mlq1alW3ARBCyqhR4tSuXTu0aNECp0+fRv/+/fHmm29i//792L59Ozp37lzbMRJCSJ0o0BXYH/zHa3oP/mOMYfOZ/x5425S7WieNk8lqws2Sm/CV+6JdYDt4SBtGLUlxsf2eJoWi/OFyuX14cXHdx/K///0P69evx/nz513KGWNUg0wIB2p0trBixQp89dVX8PT0dJZ169YNJ0+eRIcOHWorNkIIqTMWmwW52ly4iZpmM70jN4/gmuoa5CI5RsaNrPwDhNSjEmMJcjQ5iPSMRPug9lBKlFyH5OThYe8IQqstf7hOZx9eH63hevbsiYEDB+LVV191KY+NjUVqamrdB0AIcVGjxOmJJ54ot1ypVGL16tV3FRAhhNSHEmMJ1CZ1k72/6csz9gfejmg1okGdlJLmzcZsyNHkQG/Ro21AW7QNaNvgmsrGxNjvZbp5E2DMdRhj9vKEBPt49eGdd97Brl278McffzjLxowZg0uXLuG7774rMz5jDMX1UR1GSDPU9NqnEEJIFRQbimGxWZpkE7ZLBZdwNPMo+Dw+HmvzGNfhEALgv6Z5bmI33BN8D6K9oyHgC7gOqww+397luK+v/V6nkhLAYrH/TU21l48bZx+vPiQmJuLxxx/HRx995CwbNWoURo8ejcceewyLFy/G33//jfT0dOzevRv9+vXDr7/+Wj/BEdLMUOJECGl2GGPI0eRAJpRxHUqd2HRmEwCgb4u+CFYGcxwNIfYLFY6mefeE3AM/hR/XId1R+/b2Lsc7dgQKC+0dQRQWAp061X1X5OVZtGgR2G3VXzweD5s3b8ayZcuwY8cO9OrVC23btsX8+fMxYsQIDBw4sH4DJKSZaHqXWgkhpBJasxbFxuIm2UwvT5uHvVf3AqAH3pKGIUeTAz6Pj6SAJER4RjTIWqbytG8PJCXZk6biYvs9TTExdV/TtG7dujJlERERMBgMLmV8Ph9Tp07F1KlT6zYgQogTJU6EkGZHZVBBb9bDT96wr3rXxDep38BisyApIAlt/NtwHQ5p5nI0OZAKpWgb0LbB1zKVh88HYmO5joIQ0lBQUz1CSLOTr8uHiC/iOoxaZ7QYsT11OwDQvU2Ec/m6fIgEokabNBFCSGk1TpyGDBmC7OzsMv8nhJCGzGgxIl+b3ySb6aVcS0GRoQgBigAkRyZzHQ5pxgr1hbAxGyVNhJAmpcaJ02+//Qa9Xl/m/4QQ0pAVG4uhNWsbXBfId4sxhq/PfQ0AeDjh4SbZWyBpHFQGFUxWExIDEhHoFsh1OIQQUmuoqR4hpFkp1BcCQKO5Qb2qzuSeQWp+KsQCMT3wlnBGbVRDZ9ahjX8bhLqHch0OIYTUKkqcCCHNhsVmQbY6u0k20/vq3FcAgIHRA+Ep9eQ2GNIsaU323ioT/BIQ7hHOdTiEEFLrKHEihDQbKoMKJaaSJpc45Wnz8Mu1XwAAo1uP5jga0hwZLAYU6AsQ5xuHKK8o8Hg8rkMihJBaR4kTIaTZKNIXgTHW5O7/+Tb1W1iZFe0C2iHON47rcEgzY7QYkavNRaxPLFr6tKSkiRDSZFHiRAhpFqw2K7LUWVCIFFyHUqtMVhO2X7B3QU61TaS+WWwW5Ghz0MKrBVr5tgKfR6cVhJCmq8ZHuNuvKNHVJUJIQ1diLIHaqIZSrOQ6lFqVci0FhfpC+Cv80btFb67DIc2IjdmQpc5CmHsYEvwSmlxNLiGElFbjxIkxVu7/CSGkISrUF8JsM0MkaDoPvmWM4euz9i7IH4p/iE5cSb1hjCFLnYUAtwC09m8NsUDMdUh1w2YDLl0Cjh2z/7XZ6mW2f/zxBwQCAe6//36X8rS0NPB4vHJff/75Z73ERkhzVuNfWbVaXe7/CSGkobExG7LV2U3u2U1nc8/ifP55iAViPBj3INfhkGYkR5MDT6kn2vi3aXL7ldPJk8D69UBqKmAwAFIpEB8PjB8PtG9fp7Nes2YNnnnmGXzxxRfIyMhAeLhrL4U///wzWrdu7VLm4+NTpzERQu4icSKEkMZCbVSj2FgML6kX16HUKkcX5AOiBsBL1rSWjTRc+bp8SIQStPFvA3eJO9fh1I2TJ4GFC4H8fCA0FFAoAK0WOH4cSE8H5s6ts+RJq9Vi69atOHbsGHJycrBu3TrMnTvXZRwfHx8EBtLDhQmpb3QXJyGkySsyFMFkNUEilHAdSq3J0+bh52s/A6BOIUj9URlUsDIrEgMS4SNvojUcNpu9pik/317D5O4OCAT2v/Hx9vING+qs2d7XX3+NVq1aoVWrVhg7dizWrl1Lt0QQ0kBQ4kQIadIYY8jR5EAqlHIdSq3afmE7rMyKpIAkxPvFcx0OaQY0Jg10Zh3a+LdBoFsTru24csXePC80FCjd+RWPZy8/f94+Xh1YvXo1xo4dCwC4//77odFo8Msvv7iM061bN7i5ubm8rFZrncRDCPkPNdUjhDRpGpMGRfqiJtWbnslqwvZU6oKc1B+dWYciQxHa+LVBmHsY1+HUreJi+z1NigoeXSCXA1lZ9vFq2cWLF3H06FFs327fv4VCIUaPHo01a9agX79+zvG+/vprxMe7XjARCAS1Hg8hxBUlToSQJk1lUMFgMcBf4c91KLXm52s/o0BfAD+5H/q06MN1OKSJ05l1KNAXIM43DlHeUU3/ESQeHvaOILRae/O80nQ6+3APj1qf9erVq2GxWBASEuIsY4xBJBKhqKjIWRYWFoaYmJhanz8h5M6q1VTv/PnzlY7z5Zdf1jgYQgipbTmanCbXVfI3578BQF2Qk7p3e9IU6xPbPB5wGxNjv5fp5k2g9L1FjNnLExLs49Uii8WCDRs24L333sOpU6ecr9OnTyMiIgKbNm2q1fkRQqqvWkfAjh07YunSpeXepHjr1i0MHz4c06ZNq7XgCCHkbmhNWhQaCptUM70L+RfwT+4/EPAEeCDuAa7DIU1Ys0yaAIDPt3c57utrv9eppASwWOx/U1Pt5ePG2cerRbt370ZRUREmT56MNm3auLwefvhhrF692jluQUEBcnJyXF4Gg6FW4yGElFWtvf7LL7/EkiVL0LNnT1y9etWlPCEhAcXFxTh16lRtx0gIITWiMqigM+ma1HNmvk39FgDQp0Uf+Mp9OY6GNFXNNmlyaN/e3uV4x45AYaG9I4jCQqBTpzrrinz16tXo168fPMppAvjQQw/h1KlTKCwsBAD069cPQUFBLq+dO3fWekyEEFfVauPx0EMPoUePHnj66aeRlJSE+fPn49ChQ/j555/x9ttvY+bMmU2/7TMhpNHI0+VBxBc1meOS2qjGj1d+BAA8kvAIx9GQpqrZJ00O7dsDSUn2pKm42H5PU0xMrdc0OezatavCYR06dHC29qGuyQnhTrUbx/v7+2PHjh14/PHHMWfOHCgUCvz5559ITEysi/gIIaRGDBYD8rR5UEqaTjO9Hy7/AIPFgCivKLQPrJuHb5LmjZKmUvh8IDaW6ygIIQ1EtY+IRUVFGDNmDHbu3ImXX34Z/v7+GD16NI4dO1YX8RFCSI0U6YugMWmaTDM9xhi2nd8GwF7b1FRq0UjDoTVpKWkihJA7qNZRcffu3UhISMDVq1dx/PhxvP322/jnn3/Qq1cv3HfffXj99ddhsVjqKlZCCKmyfF0++Dx+kzn5+zvrb6QXp0MukmNQzCCuwyFNjKMjFUqaCCGkYtU6Mj788MN45plncOTIEcTFxQEAFAoFVq5cid27d2Pjxo3o1KlTnQRKCCFVZbKakKvNhbuknGewNFLbUu21TYNjBsNN7MZxNKQpcSRN8b7xlDQRQsgdVOsep6NHj6Jt27blDuvfvz/OnDmDWbNm1UpghBBSU45mekFuQVyHUivytHk4mHYQAPBwwsMcR0OaEq1JiyJDEeJ949HSpyUlTYQQcgfVSpwqSpoc3N3dXZ4zQAghXCgyFAEABHwBx5HUjh0XdsDKrGgf2B4x3rX70E3SfGlMGqgMKsT5xlHSRAghVUCPnCeENCkWmwU56hwoRAquQ6kVFpsFOy7sAEC1TaT2OJKmeL94xHjHUNJECCFVQEdKQkiTUmIsgdqkbjLdkB9MP4g8XR68Zd7oE9mH63BIE+BImhL8EtDSm2qaCCGkquhoSQhpUor0RbDarBDym0aF+jfnvwEAPNDqAYgEIo6jIY3d7UlTjHcMdWtPCCHVQIkTIaTJYIwhW50NmUjGdSi14nrRdRzLOgY+j48H4x/kOhzSyKmNaqgMKrT2a01JUzMWGRmJ5cuX1/jz69atg6enZ63F05QkJyfjueeeq5d5vfHGG3jqqafqZV7lOXPmDEJDQ6HVajmLgQuUOBFCmgy1SY0SU0mT6a7729RvAQA9wnsg0C2Q42hIY1ZiLEGJqQRt/Nsg2juakqYGasKECXjggQfqdB7Hjh2r8gl3eUnW6NGjcenSpRrPf926deDxeM5XQEAAhg0bhnPnztV4mg3F9u3bsWjRojqfz61bt/DBBx/g1VdfdZZNmDABPB4PU6dOLTP+9OnTwePxMGHCBJfxR44cWeE8IiMjXbaT4/XOO+8AABITE9G5c2e8//77tbdgjUCV27IsXLiwRjNITk5Gz549a/RZQgipDpVBBYPFgABFANeh3DW9WY9dl3YBAB5JeITjaEhjVmwohsasQRu/Nmjh1YKSpmbOz8/vrj4vk8kgk91drb67uzsuXrwIxhgyMzMxZ84cDBkyBJcuXYJYLL6rad+J2WyGSFR3TZ69vb3rbNq3W716Nbp27YrIyEiX8rCwMHz11Vd4//33ndvIYDBgy5YtCA8Pr/Z8Fi5ciClTpriUKZX/3T88ceJETJ06Fa+88goEgqbRi21lqlzjdP369Rq9VCpVHYZPCCH/uaW5BYlAwnUYteKnqz9Ba9YizD0MnUM6cx0OaaRUBhW0Zi3aBrRt1kkTYwxak5aTF2Os1pbj4MGD6Ny5MyQSCYKCgvDyyy/DYrE4h6vVajz++ONQKBQICgrC+++/X6b5WOlapPnz5yM8PBwSiQTBwcGYOXMmAPuF7/T0dMyaNctZ2wCU31Tv+++/R6dOnSCVSuHr64sHH7xz02Iej4fAwEAEBQWhU6dOmDVrFtLT03Hx4kXnOH/88Qd69uwJmUyGsLAwzJw506VZWHZ2NoYMGQKZTIYWLVpg8+bNZZaNx+Nh1apVGDFiBBQKBd58800AwK5du9CxY0dIpVJERUVhwYIFLuuxonUCACtWrEDLli0hlUoREBCAhx/+r7fT0uu6qKgI48aNg5eXF+RyOQYNGoTLly87hzvW5d69exEfHw83Nzfcf//9yM7OvuP6++qrrzB8+PAy5R06dEB4eDi2b9/uLNu+fTvCwsLQvn37O06zPEqlEoGBgS4vheK/HmsHDhyIgoICHDx4sNrTbqyqXOO0du3auoyDEELuis6sQ6GhEEpx4+9NjzHm7BTiofiHqNczUiNF+iIYrUYkBSYh3KP6V5ubEp1ZB7fF3DTh1byigUJ8949HyMzMxODBgzFhwgRs2LABFy5cwJQpUyCVSjF//nwAwPPPP4/ff/8d33//PQICAjB37lycOHEC7dq1K3ea33zzDd5//3189dVXaN26NXJycnD69GkA9hPupKQkPPXUU2VqHW73ww8/4MEHH8Rrr72GjRs3wmQy4YcffqjycqlUKmzevBkAnLVBZ86cwcCBA7Fo0SKsXr0aeXl5mDFjBmbMmOE8Hx03bhzy8/Nx4MABiEQiPP/888jNzS0z/Xnz5mHx4sV4//33IRAIsHfvXowdOxYffvghevTogatXrzqbLs6bN++O6+Tvv//GzJkzsXHjRnTr1g2FhYU4dOhQhcs2YcIEXL58Gd9//z3c3d3x0ksvYfDgwTh//rxzWXU6HZYuXYqNGzeCz+dj7NixePHFF7Fp06Zyp1lUVISzZ8+iU6dO5Q6fOHEi1q5di8cffxwAsGbNGkyaNAkHDhyobFNUm1gsRlJSEg4dOoQ+fZpHr69No9spQkizpzKooDPp4OPuw3Uod+1c3jlcLLgIsUCMobFDuQ6HNEKF+kKYrCa0DWiLMI8wrsMhtWDFihUICwvDxx9/DB6Ph7i4OGRlZeGll17C3LlzodVqsX79emzevBl9+/YFYL/oHRwcXOE0MzIyEBgYiH79+kEkEiE8PBydO9truL29vSEQCJy1DhV566238Oijj2LBggXOsqSkpDsuS3FxMdzc3MAYg06nAwAMHz4ccXFxAIB3330XY8aMcdbetGzZEh9++CF69eqFlStXIi0tDT///DOOHTvmTCC++OILtGzZssy8xowZg0mTJjnfP/HEE3j55Zcxfvx4AEBUVBQWLVqEOXPmYN68eXdcJxkZGVAoFBg6dCiUSiUiIiIqrMlxJEy///47unXrBgDYtGkTwsLCsHPnTjzyiL0JttlsxqpVqxAdHQ0AmDFjxh1vj0lPTwdjrMLt+sQTT+CVV15BWloaeDwefv/9d3z11Vc1SpxeeuklvP766y5lu3fvRnJysvN9SEgI0tLSqj3txooSJ0JIk5Cvy4eAJ2gSTZEcnUL0a9EPnlJPboMhjYrZakaeLg8igQjtAtshxD2E65AaBLlIDs0rGs7mXRtSU1PRtWtXl2Nc9+7dodFocPPmTRQVFcFsNjtP8gHAw8MDrVq1qnCajzzyCJYvX46oqCjcf//9GDx4MIYNGwahsOqnh6dOnbpjjVR5lEolTpw4AYvFgoMHD+Ldd9/FqlWrnMOPHz+OK1euuNS6MMZgs9lw/fp1XLp0CUKhEB06dHAOj4mJgZeXV5l5la6ZOX78OI4dO4a33nrLWWa1WmEwGKDT6e64Tvr374+IiAjnsPvvvx8jR46EXF52G6empkIoFOLee+91lvn4+KBVq1ZITU11lsnlcmfSBABBQUHl1pw56PV6AIBUKi13uK+vL4YMGYL169eDMYYhQ4bA19e3wundyezZs106lADsidLtZDKZM/ltDihxIoQ0eiarCXnavCbx0NsSYwn2Xd0HAHgo4SGOoyGNhcVmQYGuAGabGYFugYjyioKf4u46AWhKeDxerTSX4xJjrMyFIcf9Uzwez+X/5Y1TnrCwMFy8eBEpKSn4+eefMX36dLz77rs4ePBglTtRqElHEXw+HzExMQCAuLg45OTkYPTo0fjtt98AADabDU8//bTLvUUO4eHhLvdC3a68Zb39nhzHtBcsWFDufVhSqfSO68SR8B04cAD79u3D3LlzMX/+fBw7dqzMfV8VrffS27H0er59W5bHkQQVFRVV2NHHpEmTMGPGDADAJ598UuG0KuPr6+vcThUpLCx0SfyaOmo4Twhp9IoNxdCYNFCIGveJEQDsubwHRqsRMd4xaOvflutwSANnYzbk6/KRpc6Ch9QDnUM6o1NwJ0qamqCEhAT88ccfLifVf/zxB5RKJUJCQhAdHQ2RSISjR486h5eUlLh0RlAemUyG4cOH48MPP8SBAwdw5MgRnDlzBoD9Hhar1XrHz7dt2xa//PLLXSwZMGvWLJw+fRo7duwAYO/k4Ny5c4iJiSnzEovFiIuLg8ViwcmTJ53TuHLlSpU6JOvQoQMuXrxY7rT5fPtp8Z3WiVAoRL9+/bBkyRL8888/SEtLw/79+8vMJyEhARaLBX/99ZezrKCgAJcuXUJ8fHyN11V0dDTc3d1x/vz5Cse5//77YTKZYDKZMHDgwBrPqyrOnj1bo44nGiuqcSKENHqF+kIAgIDfuLtDZYw5m+k9FP9Qk2h2SOoGYwwqgwolphL4yHyQ4JeAIGUQhHz6WW/siouLcerUKZcyb29vTJ8+HcuXL8czzzyDGTNm4OLFi5g3bx6ef/558Pl8KJVKjB8/HrNnz4a3tzf8/f0xb9488Pn8Co8l69atg9Vqxb333gu5XI6NGzdCJpMhIiICgL0Hvt9++w2PPvooJBJJuU2+5s2bh759+yI6OhqPPvooLBYLfvzxR8yZM6fKy+zu7o4nn3wS8+bNwwMPPICXXnoJXbp0wf/93/9hypQpUCgUSE1NRUpKCj766CPExcWhX79+eOqpp7By5UqIRCK88MILkMlklR43586di6FDhyIsLAyPPPII+Hw+/vnnH5w5cwZvvvnmHdfJ7t27ce3aNfTs2RNeXl7Ys2cPbDZbuc0hW7ZsiREjRmDKlCn49NNPoVQq8fLLLyMkJAQjRoyo8ropjc/no1+/fjh8+HCFz/wSCATO5oB36ia8pKQEZ86cgUKhcCaN3t7ezq7L1Wo1cnJyXD4jl8vh7u4OAEhLS0NmZib69etX4+VpbKpV43T06FGXKw+lqxKNRiO2bt1aO5ERQkgVWG1W5Ghyau0+Ai6dzDmJ66rrkAllGBQziOtwSAOlN+uRUZIBHo+HdgHt0CW0C8I8wihpaiIOHDiA9u3bu7zmzp2LkJAQ7NmzB0ePHkVSUhKmTp2KyZMnu9y8v2zZMnTt2hVDhw5Fv3790L17d8THx1d4P4ynpyc+//xzdO/e3VlztGvXLvj42DvZWbhwIdLS0hAdHV1hs7Dk5GRs27YN33//Pdq1a4c+ffq41LJU1bPPPovU1FRs27YNbdu2xcGDB3H58mX06NED7du3xxtvvIGgoCDn+Bs2bEBAQAB69uyJkSNHYsqUKVAqlRUuq8PAgQOxe/dupKSk4J577kGXLl2wbNkyZ7J4p3Xi6emJ7du3o0+fPoiPj8eqVauwZcsWtG7dutx5rV27Fh07dsTQoUPRtWtXMMawZ8+eu36W1FNPPYWvvvoKNputwnHc3d2dCU5FDhw4gJ49e6Jjx44u3zWHuXPnIigoyOV1e0K8ZcsWDBgwwLnumgMeq8YDBgQCAbKzs+Hv7w/AvlFOnTqFqKgoAPYnGQcHB1darcu1kpISeHh4oLi4uNIvFamY2WzGnj17MHjw4Dp9oBypueawjYr0Rfg943f4yn0hEjSuZbRZbcg6kYXgDsHgC/h4df+r2Hd1H0bGjcRrPV7jOrxmr/T24ZrVZkWeLg+MMUR6RiLKO6pJXDC4GxUd4wwGA65fv44WLVpUeiLdlGm1WoSEhOC9997D5MmT633+NpsNJSUlcHd3d9Zo1JWbN28iLCwMP//8s7NXwaaKMYYuXbrgueeew2OPPVbj6dzN9jEajWjZsiW2bNmC7t271ziG+nSn40JVc4NqXZ4qnWOVl3PV5oPeCCGkMiqDCmabudElTaUV6gux/7q9nfxD8dQpBHFVYixBkaEIAYoAtPRpCT+5HzXlJGWcPHkSFy5cQOfOnVFcXOzs1vpumoY1VPv374dGo0FiYiKys7MxZ84cREZGomfPnlyHVud4PB4+++wz/PPPP5zFkJ6ejtdee63RJE21pdbr9elATgipL4wx5GhyIBNWv1enhub7i9/DYrOgtV9rxPnGcR0OaSDMVjNuaW9BKpSirX9bhHuGQywQcx0WacCWLl2KixcvQiwWo2PHjjh06FCNu6NuyMxmM1599VVcu3YNSqUS3bp1w6ZNm5ps64rSkpKSKn1eVl2KjY1FbGwsZ/PnCjWIJoQ0WhqTBiqDCu6Sxt3k1sZs2HHB3psU1TYRh2JDMUpMJQhRhqClT0t6phepVPv27XH8+HGuw6gXAwcOrPMe4wgprdqJ0/nz5509bDDGcOHCBWg09ofK5efn1250hBByByqDCnqLHv4Kf65DuSt/Zf6FTHUm3MRuGBA9gOtwSAOgN+uhNqmRFJCEcI/wRt9jJCGENAXVTpz69u3rch/T0KFDAfz3wC5qqkcIqS952jxIBBKuw7hr2y9sBwAMbTkUUmHzvZGd2FltVuTqctHKpxUiPSPpd5UQQhqIaiVO169fr6s4CCGkWvRmPfL1+XATu3Edyl3JN+Xj8I3DAIAH48s+yZ40P9nabAQpg9DSpyUlTYQQ0oBUK3GqSj/tp06dalb9uRNCuFFsLIbOrIO31JvrUO7Kz4U/w8qs6BDYAVFeUVyHQzhWoCuAXChHgm8CdQJBCCENTK10ql9cXIwVK1agQ4cO6NixY21MkhBCKsQYQ7Y6GwKeoFFfkbfYLEgpSAFAtU0E0Jl1MFgNSPBLgIfUg+twCCGElHJXvert378fa9aswfbt2xEREYGHHnoIq1evrq3YCCGkXAX6AmSWZMJb1rhrm36/8TsKzAXwknqhT4s+XIdDOGSxWZCny0OcTxyClcFch9NkmawmWGyWepufkC+kmkNCmpBqJ043b97EunXrsGbNGmi1WowaNQpmsxnffvstEhIS6iJGQghxYowhXZUOG2yNviMFR6cQw1oOo5OrZi5Hk4MQZQhifGIadS1qQ2aymnD05lFozJp6m6ebyA2dQzvT/g3giSeeQHx8PF599VWuQ2kQkpOT0a5dOyxfvpzrUJqEe+65B6+88goefLBuW29Uq6ne4MGDkZCQgPPnz+Ojjz5CVlYWPvroo7qKjRBCysjX5SNTnQlfWeN+oOPNkpv4M/NPAMADrR7gNhjCqXydvZOTeL94OsGuQxabBRqzBmK+GEqxss5fYr4YGrOmWjVcarUazz33HCIiIiCTydCtWzccO3bMZZwJEyaAx+O5vLp06eIyzvPPPw9vb2+Eh4fjq6++chm2detWDBs2rErxmEwmLFmyBElJSZDL5fD19UX37t2xdu1amM1mZzwPPPDAHafzzz//4IcffsAzzzzjLEtOTnbGL5FIEBsbi7fffhtWq7VKsTVEPB4PO3furNK427dvx6JFi2o8r9vXH5/PR0BAAB555BGkp6fXeJrlOXDgAHg8HlQqVZU/U5XvRG1744038PLLL8Nms9XpfKpV47Rv3z7MnDkT06ZNQ8uWLesqJkIIKZeN2ZCmSgMPPEiEjbsb8p0XdoKBob2yPULdQ7kOh3BEY9LAaDUiMSCx0T/IubGQCCX1VlttMpmqNf6TTz6Js2fPYuPGjQgODsaXX36Jfv364fz58wgJCXGOd//992Pt2rXO92Lxfwn3rl27sHnzZuzbtw+XL1/GxIkT0b9/f/j4+EClUuG1117DL7/8UqXYBw4ciNOnT2PRokXo3r073N3d8eeff2Lp0qVo37492rVrV6Xl+uSTT/DII49AqVS6lE+ZMgULFy6EwWDA7t27MXPmTAgEArz00ktVmu7trFarM4loyMxmM0QiEby9776puWP9McaQnp6O5557DmPHjsWhQ4dqIdK651gXtWHIkCGYMmUK9u7di0GDBtXKNMtTrW/XoUOHoFar0alTJ9x77734+OOPkZeXV1exEUKIizxtHrI12fCVN+7aJrPVjO8ufgcAGOgzkONoSH0zW80o0BUgozgDGpMGsT6xCHIL4joswjG9Xo9vv/0WS5YsQc+ePRETE4P58+ejRYsWWLlypcu4EokEgYGBztftJ+GpqalITk5Gp06d8Nhjj8Hd3R3Xrl0DAMyZMwfTp09HeHh4pfEsX74cv/32G3755Rf83//9H9q1a4eoqCiMGTMGf/31V5UvoNtsNnzzzTcYPnx4mWFyuRyBgYGIjIzEjBkz0LdvX2eNzbJly5CYmAiFQoGwsDBMnz4dGs1/zSzXrVsHT09P7N69GwkJCZBIJEhPT8exY8fQv39/+Pr6wsPDA7169cKJEydc5svj8fDpp59i6NChkMvliI+Px5EjR3DlyhUkJydDoVCga9euuHr1qsvndu3ahY4dO0IqlSIqKgoLFiyAxWKvUYyMjAQAjBw5Ejwez/l+/vz5aNeuHdasWYOoqChIJBIwxpCcnIznnnvOOW2j0Yg5c+YgLCwMEokELVu2rLTfAMf6CwoKQpcuXfB///d/ZZb14MGD6Ny5MyQSCYKCgvDyyy87Y3bM99lnn4W/vz+kUinuu+8+Zy1nWloaevfuDQDw8vICj8fDhAkTAADffPMNEhMTIZPJ4OPjg379+kGr1WL+/PlYv349vvvuO2eN2IEDB5CWlgYej4etW7ciOTkZUqkUX375JQoKCvDYY48hNDQUcrkciYmJ2LJli8syJCcnY8aMGZgxYwY8PT3h4+OD119/3eW5sgKBAIMHDy7z2dpWrcSpa9eu+Pzzz5GdnY2nn34aX331FUJCQmCz2ZCSkgK1Wl1XcRJCmjlHbRMf/EbfnGl/2n4UGYrgJ/fDPR73cB0OqQcWmwWF+kJkFGcgT5cHmUiGtgFt0S2sG2J9Yum+JgKLxQKr1Qqp1LU2TCaT4fDhwy5lBw4cgL+/P2JjYzFlyhTk5uY6hyUlJeHvv/9GUVERjh8/Dr1ej5iYGBw+fBgnTpzAzJkzqxTPpk2b0K9fP7Rv377MMJFIBIVCUaXpnDt3DiqVCp06dap0XJlM5mwCyOfz8eGHH+Ls2bNYv3499u/fjzlz5riMr9PpsHjxYnzxxRc4d+4c/P39oVarMX78eBw6dAh//vknWrZsicGDB5c5R120aBHGjRuHU6dOIS4uDmPGjMHTTz+NV155BX///TcAYMaMGc7x9+7di7Fjx2LmzJk4f/48Pv30U6xbtw5vvfUWADiTjbVr1yI7O9ulieWVK1ewdetWfPvttzh16lS5yz5u3Dh89dVX+PDDD5GamopVq1bBza3qzyksLCzEtm3bcO+99zrLMjMzMXjwYNxzzz04ffo0Vq5cidWrV+PNN990jjNv3jxs374d69evx4kTJxATE4OBAweisLAQYWFh+PbbbwEAFy9eRHZ2Nj744ANkZ2fjsccew6RJk5CamooDBw7gwQcfBGMML774IkaNGoX7778f2dnZyM7ORrdu3Zzze+mllzBz5kykpqZi4MCBMBgM6NixI3bv3o2zZ8/iqaeewhNPPIG//vrLZfnWr18PoVCIv/76Cx9++CHef/99fPHFFy7jdO7cuc5r22rUq55cLsekSZMwadIkXLx4EatXr8Y777yDl19+Gf3798f3339f23ESQpq5XG0ucjQ5CFAEcB3KXfs21f5DNCJ2BAQQcBwNqUsWmwU5mhzweDx4SDzQxr8NfOQ+8JB4QMCnbU/+o1Qq0bVrVyxatAjx8fEICAjAli1bytTuDBo0CI888ggiIiJw/fp1vPHGG+jTpw+OHz8OiUSCgQMHYuzYsbjnnnsgk8mwfv16KBQKTJs2DevWrcPKlSvx0UcfwdfXF5999hlat25dbjyXL19GcnLyXS9XRkYGBAIB/P39KxzHZrNh37592Lt3r7MW5vbamBYtWmDRokWYNm0aVqxY4Sw3m81YsWIFkpKSnGV9+rj2UPrpp5/Cy8sLBw8exNChQ53lEydOxKhRowDYT+a7du2KN954AwMH2lsBPPvss5g4caJz/Lfeegsvv/wyxo8fDwCIiorCokWLMGfOHMybNw9+fn4AAE9PTwQGBrrEYDKZsHHjRuc4pV26dAlbt25FSkoK+vXr55x+ZVasWIEvvvgCjDHodDrExsZi7969LsPDwsLw8ccfg8fjIS4uDllZWXjppZcwd+5caLVarFmzBmvWrHE2b/v888+RkpKC1atXY/bs2c7aTH9/f3h6egIArl69CovFggcffND57NbExETnfGUyGYxGY5n1ANi3a+kOHF588UXn/5955hn89NNPZZLAsLAwvP/+++DxeGjVqhXOnDmD999/H1OmTHGOExISgoyMDNhstjprsnnXU23VqhWWLFmCmzdv1nn1GCGkebLarEhTpUHIF0IkqJ320Fy5XnQdJ7JPgM/jY0SrEVyHQ+qQ1qRFpjoTwcpgdAvrhvvC70NLn5bwlnlT0kTKtXHjRjDGEBISAolEgg8//BBjxoyBQPDf92X06NEYMmQI2rRpg2HDhuHHH3/EpUuX8MMPPzjHmT9/Pq5cuYIzZ85g5MiRePvtt9GvXz+IRCK8+eabOHz4MJ588kmMGzeuwlgYY7VSE6rX6yGRSMqd1ooVK+Dm5gapVIrhw4dj7NixmDdvHgDg119/Rf/+/RESEgKlUolx48ahoKAAWq3W+XmxWIy2bdu6TDM3NxdTp05FbGwsPDw84OHhAY1Gg4yMDJfxbv9cQID9gtztJ/8BAQEwGAwoKSkBABw/fhwLFy6Em5ub8zVlyhRkZ2dDp9PdcR1ERERUmDQBwKlTpyAQCNCrV687Tqe0xx9/HKdOncLp06dx+PBhxMTEYMCAAc7atdTUVHTt2tVl3Xfv3h0ajQY3b97E1atXYTab0b17d+dwkUiEzp07IzU1tcL5JiUloW/fvkhMTMQjjzyCzz//HEVFRVWKuXTNo9VqxVtvvYW2bdvCx8cHbm5u2LdvX5nt1aVLF5fl6Nq1Ky5fvuzSmYhMJoPNZoPRaKxSLDVRa+mYQCDAAw88QLVNhJBal6vNxS3NLfjIfLgO5a45uiDvEd6jSdSekfLl6/KhMqqQ4JeAdoHt4Cv3pWSJVCo6OhoHDx6ERqPBjRs3cPToUZjNZrRo0aLCzwQFBSEiIgKXL18ud/iFCxewadMmLFq0CAcOHEDPnj3h5+eHUaNG4cSJE87EoLTY2Ng7njxXlY+PD3Q6XbkdZThO/K9evQq9Xo/Vq1dDLpcjPT0dgwcPRps2bfDtt9/i/9u77zi5yrL/45/ps723JJuebLLZJKSARKogQZqIoCgSUECNQRTzk44KFvKogBTpoigiRSD60J4kKKG3VJKQhPS2vc5Ob+f3x2Q32ewmm7Z7Zne/79drYOfMOWeuM/eczbn2vs91L126lAceeACgfSgfJC6U903Ivv3tb7N06VLuuece3nvvPVasWEFeXl6n99+7KEHbPrpa1lalLR6Pc/vtt7NixYr2x6pVq9iwYUOn4ZX76m5YY0pKygFf35+srCxGjx7N6NGjOeGEE3j88cfZsGEDzz77LNB18tt2X5DFYunw877rHChpttlsLFq0iNdee43y8nLuv/9+ysrK2LJlS7cx7/tZ3HXXXfzhD3/g+uuv57///S8rVqzgzDPPPOTCKpAYrpiamnrYn+fBOOjEafbs2ezYseOg1n322Wd56qmnDjsoEZE2/am3KRgN8vJnLwNw4fgLTY5GekI0HmWnZyc2i41pJdMoyyvr899b6X1paWmUlJTQ1NTEggULOP/8/fdONzQ0sGPHDkpKOhcYMQyD733ve9x1112kp6cTi8XaE4+2/++vfPMll1zC66+/zvLlyzu9Fo1GO/T8HEhbL86nn37a6bW2C//S0tIOvWpLliwhGo1y1113cfzxxzN27FgqKysP6v3efvttfvSjH3H22WczYcIEXC4X9fX1B7XtgUydOpX169e3Jyp7P9qGhTkcjsMqpz5x4kTi8ThvvvnmEcXY9hkGAgEAysvLee+99zoUUXjvvffIyMhg8ODBjB49GqfT2eEeukgkwpIlSxg/fjywp2LjvsdlsVg44YQTuP3221m+fDlOp5P58+e3b3Own8Pbb7/N+eefz6WXXsrkyZMZOXJkl38E+OCDDzo9HzNmTIfvzerVq5k6depBve/hOuh7nAoKCqioqODzn/88X/7yl5k+fTqDBg3C7XbT1NTEp59+yjvvvMPTTz/NkCFDePTRR3sybhEZIGp8NdT6ailO7zxWuq9ZtHkRreFWBqUP4vghx0PPTjchvSwQCVDrr2VQxiDG548ny51ldkjShVC054bxHOn7LFiwAMMwKCsrY+PGjVx33XWUlZW132vj9Xq57bbbuPDCCykpKWHr1q3cfPPN5Ofnc8EFF3Ta32OPPUZhYWF7RbsTTjiB2267jQ8++KC9t6DtvpV9XXvttbzyyiucfvrp/OpXv+LEE08kIyODJUuW8Nvf/pbHH3/8oMqR5+fnM3XqVN55552DLl8+atQootEo999/P+eddx7vvvsuDz/88EFtO3r0aJ588kmmT5+Ox+PhuuuuOyo9ED//+c8599xzKS0t5Wtf+xpWq5VPPvmEVatWtRdbGD58OP/5z3844YQTcLlc5OTkHNS+hw8fzuWXX84VV1zBfffdx+TJk9m2bRu1tbXt92F1xe/3U11dDUBNTQ2//vWvcbvdzJw5E4A5c+Zwzz33cM011/DDH/6Q9evX84tf/IK5c+ditVpJS0vjiiuu4IYbbiA/P5+hQ4fyu9/9Dr/fz5VXXgkkhhlaLBZefvllzj77bFJSUlizZg3/+c9/mDlzJoWFhXz44YfU1dW1J1vDhw9nwYIFrF+/nry8PLKy9v+7cPTo0bzwwgu899575OTkcPfdd1NdXd2+rzY7duxg7ty5fP/732fZsmXcf//93HXXXR3Wefvtt9uPvaccdI/Tr371KzZs2MDJJ5/Mww8/zPHHH8/QoUMpLCykrKyMyy67jM2bN/P444/z/vvvdxgnKiJyOKLxKFubt+KwOrBbD6uWTVJpKwrx1fFfxWpJ7rlG5NA0BZpoCDRQllfG1JKpSpqSkN1qJ92RTjgepjXc2uOPcDxMuiP9kH53tbS0cPXVVzNu3Dguu+wyTjzxRBYuXNg+hMxms7Fq1SrOP/98xo4dy+WXX87YsWN5//33O82RVFNTwx133MF9993Xvuy4447j//2//8c555zDc88912EuqH25XC4WLVrE9ddfzyOPPMLxxx/Psccey3333cePfvQjKioqDvq4rrrqqkMaiXTMMcdw991389vf/paKigqeeuop5s2bd1Db/vnPf6apqYkpU6Ywa9YsfvSjHx2wMMXBOvPMM3n55ZdZtGgRxx57LMcffzx33313e3EESAw7W7RoEaWlpV1WIzyQhx56iIsuuog5c+Ywbtw4vvvd73bbq/fYY49RUlJCSUkJX/jCF6irq+PVV1+lrKwMSBRLePXVV/noo4+YPHkys2fP5sorr+TWW29t38cvfvELvvrVrzJr1iymTp3Kxo0bWbBgQXvSN3jwYG6//XZuvPFGioqK+OEPf0hmZiZvvfUWZ599NmPHjuXWW2/lrrvuai8w8d3vfpeysjKmT59OQUEB77777n6P4Wc/+xlTp07lzDPP5NRTT6W4uLjLyXMvu+wyAoEAxx13HFdffTXXXHMN3/ve99pf37VrF++9916Hgh49wWLs3X93CJqbm9m2bRuBQID8/HxGjRrVZ8qpejwesrKyaGlpITNTEw4erkgkwquvvsrZZ5991CYwk6Orr7fRLs8uPq78mJL0kj6fOK2rX8el8y/FbrXzyjdfIS81j3gsTuWySgZNHYTVpkQq2Rxs+7SGWvFFfEwsmkhpZmmf+bewP9jf77hgMMiWLVsYMWJEh/tPwrEw0Xi0q131CLvV3uenTzgS8Xgcj8eD0+lk/PjxPPPMM8yYMcPssGS3tvbJzMxM6omDTz31VI455hjuueee/a5z3XXX0dLScsARb/v7vQAHnxsc9pVIdnb2frt3RUSOlGEYbG/ZjtPq7PNJE8CLaxNFIb4w/Avkpfb9IheSEI6FaQo2MaloEkOzup9UVMzltDkHdCJjFrfbzd/+9rejcq+RSFcKCws7lDXvKYeUXvr9fq6++moGDx5MYWEhl1xyyVE5CR588MH27G/atGkHPXnVu+++i91uP+gxsyLSdzQHm2kMNJLtzjY7lCPmC/v4v03/B6goRH9iGAbV3mqGZw9nePZws8MRSWqnnHIK5513ntlhSD913XXXtZeV70mHlDj94he/4IknnuCcc87hG9/4BosWLeIHP/jBEQXw7LPPcu2113LLLbewfPlyTjrpJM4666xO9dv31dLSwmWXXcbpp59+RO8vIsmpwd9AOBbGZXeZHcoRe23ja/gjfoZlDWNayTSzw5GjpMZXQ25KLmX5ZSo1LiLSQxYvXnzAYXq96ZDGv7z44os8/vjjfOMb3wDg0ksv5YQTTiAWi3UoB3go7r77bq688kquuuoqAO655x4WLFjAQw89dMAbAb///e+3Twr3r3/964DvEQqFOkyG1TZnQSQS6TAfgByafUuaSvLpq20UjUfZ2byTNFsa8VjfLj1nGMaeohDjvooRNzBI3Fradmx9/Rj7qwO1T2uoFeIwNmcsDhx97hzrL/b3Oy4SiWAYBvF4fL/ltqXntd1G39YWklwGWvvE43EMwyASiXTKWw72d/ghJU47duzgpJNOan9+3HHHYbfbqayspLS09FB2BUA4HGbp0qXceOONHZbPnDmT9957b7/b/eUvf2HTpk38/e9/by8BeSDz5s3j9ttv77R84cKFpKamHnLc0tGiRYvMDkG60ZfbKEDA7BCOyHrfejY0bsBpcTLVN5XKZZ3nIqleWW1CZHKwDtQ+H63/qBcjkf3Z93ec3W6nuLiY1tbWw5pIU46u1tZWs0OQAxgo7RMKhQgEArz55pud5pny+/0HtY9DSpxisVj7RFjtO7DbiUYPr0JNfX09sVis05jEoqKi9rr0+9qwYQM33ngjb7/9Nnb7wYV/0003MXfu3PbnHo+H0tJSZs6cqap6RyASibBo0SLOOOOMPlmxbSDoq220rm4dm5s2MyhzkNmhHLHH3noMgDNGnUHZcWUdXovH4lSvrKZ4crGq6iWhrtonbsSp9FQyNHsoEwomaIieyfb3Oy4Wi7FlyxZCoRDp6emqdGgSwzDw+XykpaWpDZLQQGmftl4mj8dDWloaZ5xxRqcqgm2j0bpzSImTYRh8+9vfxuXac89BMBhk9uzZpKWltS978cUXD2W3nRrLMIwuGzAWi3HJJZdw++23M3bs2IPev8vl6hBzG4fD0acuJpOVPsfk15faKBgNUhOoITM1s88nE83BZl7f8joAF5ZfuN/jsdqsff5Y+7O926fWW0tuei7ji8bjdri72VJ6y76/4xwOB6WlpezcubPbuXCk5xiGQSAQICUlpV9fmPdVA619UlNTKSkp6dQJBBz0NdIhJU6XX355p2WXXnrpoeyig/z8fGw2W6fepdra2i4rY7S2trJkyRKWL1/OD3/4Q2DPeEW73c7ChQs57bTTDjseETFfY6CR1nArQzKHmB3KEXv5s5cJxUKMzRvLxEJNCt7XeUIerBYr5QXlpDo0zDvZpaenM2bMGN1/ZqJIJMJbb73FySef3Gf+eDeQDKT2sdls2O32I04QDylxOtAM04fD6XQybdo0Fi1axAUXXNC+fNGiRZx//vmd1s/MzGTVqlUdlj344IP897//5fnnn2fEiBFHNT4R6X1VrVU4rA6slr7dAxM34jy/9nkAvlb+tQHx17z+LBKL0BJsYVLRJArSCswORw6SzWY77OJVcuRsNhvRaBS3293vL8z7IrXPoTN9Vsm5c+cya9Yspk+fzowZM3j00UfZvn07s2fPBhL3J+3atYu//e1vWK1WKioqOmxfWFiI2+3utFxE+h5v2Eudv44sd5bZoRyxj3Z9xE7PTtIcaXxp1JfMDkeOUI2/hsGZgxmWPczsUERExCSmJ04XX3wxDQ0N/PKXv6SqqoqKigpeffVVhg1L/ONUVVXV7ZxOItI/NPgbCEQCFKT2/b/o//PTfwJw3tjzSHGkmByNHAlvyIvL5mJ07mgVgxARGcBMT5wA5syZw5w5c7p87Yknnjjgtrfddhu33Xbb0Q9KRHpV3Iizq3UXKfa+n2RUe6t5e/vbAFw4/kKTo5Ej1RRsoqKkgpyUHLNDERERE/XtmwhEpN9oCbbQ6G/sF8P0Xlz7InEjzvSS6YzI0b2XfV1+aj7DsjRET0RkoFPiJCJJod5fTyQewWnrXCa0L4nEIvx7/b8BuKj8IpOjkSMRjAYBGJkzEpe985QWIiIysChxEhHTRWIRdnl2keHMMDuUI/bG1jdoCDSQn5rPqcNPNTscOQIN/gYACtMKTY5ERESSgRInETFdU7CJllALGa6+nzg9/2miBPkF4y7Abk2K20jlMDQHm9vnalIpeRERASVOIpIEarw1YKHPJxobGzeyrHoZNouNC8Zd0P0GkpSi8SiekIeROSPNDkVERJKIEicRMVUgEqDaW02Ws+8XhXhh7QsAnDzsZA3v6sPqfHUUpxczOHOw2aGIiEgSUeIkIqZqDDTiDXtJd6abHcoR8YV9vLrhVQC+Vv41k6ORw+WP+LFYLIzOHd3ne0BFROToUuIkIqYxDIPK1kqcNmefv4/ktY2v4Yv4GJY1jGMHHWt2OHIYDMOg3l/P8OzhFKT1/UmYRUTk6FLiJCKmaQo2UeurJdudbXYoR8QwDJ5fmygKcVH5RX0+CRyoqrxV5Kbkau4tERHpkhInETHNLs8uovEobrvb7FCOyMqalWxs3IjL5uLcMeeaHY4chmpvNamOVCYVTWqvpiciIrI3JU4iYgpv2Etla2Wf722CPSXIvzT6S/2ipPpAU+urxWlzMrl4MjkpOWaHIyIiSUqJk4iYorq1Gl/E1+eLQtT763l9y+sAXDT+IpOjkUPV4G/AarEyqWgS+an5ZocjIiJJTImTiPS6UDTEtpZtZLn6fgny+evmE41HmVQ4ifEF480ORw5Bc7CZqBFlYtFEitKLzA5HRESSnBInEel1Nb4aWkItZLoyzQ7liERikfZhehdXXGxyNHIoPCEP/oifiYUTGZQxyOxwRESkD1DiJCK9KhqPsq15G2mONKyWvv0r6D9b/kNDoIGC1AJOH3G62eHIQfKGvbSGW5lQMIHSrFKzwxERkT6ib1+1iEifU++vpzHQ2C+KQjy75lkALhx/oSZL7SP8ET/NwWbK88tVdlxERA6JEicR6TWGYbCjZQc2i63PJxqra1ezqnYVDquDC8ZdYHY4chBC0RD1/nrK8ssYmTtS822JiMghUeIkIr2mMdBIjbeG3JRcs0M5Ym29TTNHzSQvNc/kaKQ70XiUal81I3NGMiZ3TJ8fJioiIr1P/3KISK/Z1bqLmBHDZXeZHcoRqffXs2jzIgAunqCiEMkubsSpbK2kNLOU8QXjsVltZockIiJ9kBInEekVraFWqlqryHH3/QlG9y5BXl5QbnY4cgCGYVDZWklRehEVhRU4bU6zQxIRkT5KiZOI9IoqbxW+iI80Z5rZoRwRlSDvW6q91WS7s6korCDFkWJ2OCIi0ocpcRKRHheMBtnRsqNfTHjbVoI8PzVfJciTXL2/HpfdRUVhRZ+fM0xERMynxElEelyNNzHhbX9InNqKQlw0/qI+XxmwP2sONhMzYkwsmqjiHSIiclQocRKRHhWOhdnWkpjwtq+Xf1YJ8r7BG/bii/ioKKygOL3Y7HBERKSfUOIkIj1qZ8tO6v31/aIoRFtv0xkjz1AvRpIKRoM0BhoZnz+e0sxSs8MREZF+RImTiPQYX9jH5qbNZLmy+nwJ6A4lyFUUIilF41FqfDWMzh3NqNxRfb6HU0REkosSJxHpMVubt+IJe/rFvU1tJcgnFk5kQsEEs8ORfcTiMXa17mJY1jDG5Y/TBLciInLU6V8WEekRjYFGtrVsIz8lv8//5b9DCXJNeJt0DMOgyltFcXox5QXlOGwOs0MSEZF+SImTiBx1cSPOlqYtROKRPj9vE8CCTQtUgjyJ1fhqyHJlaa4mERHpUUqcROSoq/HWsNOzk8LUQrNDOWKGYfDkJ08C8I0J31BvRpJp8Ddgt9mpKNJcTSIi0rOUOInIURWJRdjUuAmH1YHT5jQ7nCP2wc4P2NS0iVRHKheOv9DscGQvnpCHSDxCRUEF+an5ZocjIiL9nBInETmqdrXuotZf228uZJ9clehtOr/sfDJcGSZHI238ET+ekIfx+eMZnDnY7HBERGQAUOIkIkeNL+xjU+OmflF+HOCzhs/4aNdHWC1WvlnxTbPDkd38ET8N/gbG5I5heM5ws8MREZEBQomTiBw125q30RJq6RflxwH+/snfATh9xOkMyhhkcjQC4A17aQg0MK5gHOMKVHZcRER6j93sAESkf2gKNLG1ZWu/KD8OiQIXCzYtAGDWpFkmRyOQSJqag82UF5QzOne0kiYREelVSpxE5IjFjTibmzb3m/LjAM+seYaYEWNqyVTKC8rNDmfA84Q8tIZbmVAwgVG5o/pFci4iIn2LEicROWK1vlp2te6iIKXA7FCOCm/Yy4trXwRg1kT1NpmtOdiML+KjoqCCETkjlDSJiIgplDiJyBFpKz9ut9hx2V1mh3NU/Gvdv/BFfAzPHs4JQ08wO5wBrSnQRDAaZHLRZIZmDVXSJCIiptEAcRE5IpWtldT6+k/58Wg8yjNrngHgWxO/pftoTNQUaCIUCzG5eDLDsocpaRIREVPpikBEDlsgEmBj40bSnen9ovw4wOubX6faW01uSi5njz7b7HAGLG/YSyAaYHLxZEqzSs0OR0RERImTiBy+bS2J8uM57hyzQzkqDMPg76sSJci/Xv71fjP0sK8JRUM0BhoZlz+OIZlDzA5HREQEUOIkIoepJdjC1uat5KXk9ZshVEurlrKufh0um4uLyi8yO5wBKRaPUe2rZkTOCEbmjDQ7HBERkXZKnETkkBmGwZbmLYSiIdKd6WaHc9Q8+cmTAHy57Mtku7PNDWYAMgyDKm8VJRkljM8f32+Gf4qISP+gxElEDlmdv44dLTv6TUEIgI2NG3l3x7tYsHBJxSVmhzMg1fpqyXRlMqFggoZJiohI0lHiJCKHJBqPsqlpExYsuO1us8M5av684s8AfGHEF1SMwATNwWYsFgsTCieQ6co0OxwREZFOlDiJyCGpaq2iurWagrT+MdktwNbmrSzatAiAK6dcaXI0A08gEsAb9lJeUE5hWqHZ4YiIiHRJiZOIHLRgNMimxk2kOlKxW/vP/NlPrHgCA4OThp5EWV6Z2eEMKNF4lFp/LWNyxzA0a6jZ4YiIiOyXEicROWg7W3bSGGwkNyXX7FCOmp2enby28TVAvU29LW7E2dW6i2FZwxiTN6bfVGcUEZH+SYmTiByUBn8Dm5o3kePOwWrpP786/rryr8SMGMcPPp6KwgqzwxlQKr2VFKYWMr5gPA6bw+xwREREDqj/XP2ISI+p99ezonoFkWikX924X+2t5qXPXgLgqqlXmRzNwFLrqyXdkU5FUQWpjlSzwxEREelW/7lJQUR6RJ2vjpXVKwnFQpRklJgdzlH15CdPEo1HmVoylWOKjzE7nAGjOdgMwMSiiZovS0RE+gz1OInIftX56lhRvYJQLERxerHZ4RxV9f56/rXuXwBcNUW9Tb3FF/bhi/iYUDhBFfRERKRPUeIkIl2q9dUmhufFIv0uaQJ4atVThGIhJhVO4thBx5odzoAQioZoCDRQlldGaabmyhIRkb5FQ/VEpJMabw0ra1YSjUUpSi8yO5yjrjnYzPOfPg/AFVOuUDW3XhCNR6n2VTMqZxSjc0frMxcRkT5HiZOIdFDtrWZlzUri8Xi/TJog0dsUiAYYnz+eE0pPMDucfi9uxKlsrWRI5hDGF4zHZrWZHZKIiMgh01A9EWnXGGhkZc1KjLjRb+8/8YQ8PLfmOSAxb5N6Pnpetbea/NR8JhRMwGlzmh2OiIjIYVHiJCIAGIbBtuZtBKNBCtIKzA6nxzy75ll8ER+jckZx8rCTzQ6n36v2VpPqSKWisII0Z5rZ4YiIiBw2JU4iAkBDoIGdnp3kp+SbHUqP8YV9PL36aSDR29SfJvJNRvX+ehw2B5OKJpGTkmN2OCIiIkdEVw0iQtyIs615GwBuu9vkaHrO06ufxhPyMCxrGKePON3scPq1pkATMSPGxMKJ/boHU0REBg4lTiJCvb+eXa27yEvJMzuUHtMUaOLJT54EYPa02SpQ0IM8IQ/BaJCJhRP73aTJIiIycClxEhng4kacrc1bsWDBZXeZHU6P+cuKv+CL+BiXP47TR6q3qad4w148IQ/lBeWUZmmuJhER6T+UOIkMcHW+Oqpaq8hP7b/3NlW1VvHPT/8JwA+P/aHubeohgUiApmAT5QXljMgZYXY4IiIiR5WuHkQGsFg8xpbmLdit9n5dJvrRZY8SiUc4dtCxfG7w58wOp18KRUPU+esYmzuWUbmjVOZdRET6HSVOIgNYra+WGm9Nv763aVPjJl7Z8AoAVx97tS7oe0AkFqHaV82o3FGU5ZepR09ERPol/esmMkDF4jG2Nm/FbrXjsDnMDqfHPLjkQeJGnNNGnEZFYYXZ4fQ70XiUSm8lI7JHMD5/vIpuiIhIv6XESWSAqvHVUOOr6df3Nn1S8wlvbnsTq8XKnOlzzA6n34nFY1S2VlKaWUp5QXm/TsBFRESUOIkMQNF4lM2Nm3HZXNitdrPD6RGGYfDHj/4IwHljz2N49nBzA+pn4kacSm8lxRnFVBRW9OuKjCIiIqDESWRAqvZWU++vJzcl1+xQesx7O99jWfUynDYn35v6PbPD6VcMw6CytZL8lHwmFU4ixZFidkgiIiI9TomTyAATiUXY0rQFt93db3ub4kacBz56AICLJ1xMUXqRyRH1H4ZhUOmtJNudzaTiSaQ508wOSUREpFcocRIZQOJGnE1Nm/p9b9PCTQv5rPEz0p3pfHvyt80Op1+p8dWQ7kxncvFkMl2ZZocjIiLSa5Q4iQwQcSPOhoYNrKtfR15KXr+tfhaJRXhoyUMAXDbpMrLcWSZH1H/U+mpx2VxMLppMtjvb7HBERER6Vf8cpyMiHcSNOJsbNrO2fi257tx+Pbzq+bXPs6t1F3kpeXyz4ptmh9Nv1PnqsFqtTCyaSF5q/533S0REZH+UOIkMAJsaN/FZ82f9Pmlq8Dfw8JKHAfj+tO+raMFRUuerw2K1MLlosu4XExGRASsphuo9+OCDjBgxArfbzbRp03j77bf3u+6LL77IGWecQUFBAZmZmcyYMYMFCxb0YrQifUfciAPwWUP/T5oA/vjxH/FFfIzPH8/5ZeebHU6/UOurxWK1cEzRMRSnF5sdjoiIiGlMT5yeffZZrr32Wm655RaWL1/OSSedxFlnncX27du7XP+tt97ijDPO4NVXX2Xp0qV84Qtf4LzzzmP58uW9HLlIcosbcTY1bgIgx53T75OmVTWreOmzlwC4/vPX99t7uHpTra8Wm9XGMUXHqKdJREQGPNOH6t19991ceeWVXHXVVQDcc889LFiwgIceeoh58+Z1Wv+ee+7p8PyOO+7g3//+Ny+99BJTpkzp8j1CoRChUKj9ucfjASASiRCJRI7SkQw8bZ+dPsPk05Y0fVb3GRYsuG1u4rG42WH1mFg8xm/f/S0A5445lwn5E/rE8bbFmIyx1nprsdvsTMibQK4rd0Ce5/odl/zURslN7ZPc1D57HOxnYGriFA6HWbp0KTfeeGOH5TNnzuS99947qH3E43FaW1vJzd1/aeV58+Zx++23d1q+cOFCUlNTDy1o6WTRokVmhyD7YcECQPXKapMj6VkLGxayrmEdqdZULnJeROWySrNDOiTJ2j5RoixZu8TsMEyn33HJT22U3NQ+yU3tA36//6DWMzVxqq+vJxaLUVTUcQhIUVER1dUHdyFx11134fP5+PrXv77fdW666Sbmzp3b/tzj8VBaWsrMmTPJzNQ8JIcrEomwaNEizjjjDBwOh9nhyG71/nqWVS0j1Z5Kqj2V6pXVFE8uxmozfWRuj2gJtfDU808B8P1jv0/5hHKTIzp48Vg86dqnxluD0+akoqiCgtQCs8MxlX7HJT+1UXJT+yQ3tc8ebaPRumP6UD0Ai8XS4blhGJ2WdeXpp5/mtttu49///jeFhYX7Xc/lcuFyuTotdzgcA/6LcjToc0wegUiADc0bwAqZqZntQ8CsNmvSXJgfbY8uf5SWUAsjc0ZyccXFWK197ziTpX2qvdW4nW4mF0+mIG1gJ0170++45Kc2Sm5qn+Sm9uGgj9/Uf6nz8/Ox2Wydepdqa2s79ULt69lnn+XKK6/kueee44tf/GJPhinSJ8SNOJ81fEa9v57CtP3/IaE/Wd+wnhfWvgAkCkLYrUnxt6A+qdpbnZjcVkmTiIhIl0xNnJxOJ9OmTes0tnLRokV8/vOf3+92Tz/9NN/+9rf5xz/+wTnnnNPTYYr0CTs9O9navJWitCKsFvN7L3qaYRj87t3fETfinDHyDKYPmm52SH2WkiYREZHumf7n2blz5zJr1iymT5/OjBkzePTRR9m+fTuzZ88GEvcn7dq1i7/97W9AImm67LLLuPfeezn++OPbe6tSUlLIysoy7ThEzNQcbGZt/VrSnem47W6zw+kVr218jZU1K3Hb3fz4cz82O5w+qy1pOqbkGPJT880OR0REJGmZnjhdfPHFNDQ08Mtf/pKqqioqKip49dVXGTZsGABVVVUd5nR65JFHiEajXH311Vx99dXtyy+//HKeeOKJ3g5fxHThWJi1dWsJRUPkZwyMC19v2Mu9H94LwBXHXKGJWQ+TkiYREZGDZ3riBDBnzhzmzJnT5Wv7JkOLFy/u+YBE+gjDMNjYsJEqbxVDMoaYHU6veXjJwzQEGijNLOXSSZeaHU6fpKRJRETk0PT/GyFE+rEqbxUbmzZSkFqAzWozO5xesaxqGc+seQZIFIRw2pwmR9T3KGkSERE5dEqcRPoob9jL2rq1uGwuUh0DYyLnQCTA7W8mJrM+v+x8ZpTOMDmivkdJk4iIyOFR4iTSB3lCHlbVrKI11EpeSp7Z4fSaP378R3a17qIorYifHP8Ts8PpUwzDoKq1CrfdraRJRETkMCTFPU4icvBqfbWsqlmFN+xlUMagg5osuj9YWrWUZ9c8C8CtJ91KujPd5Ij6DsMwqPJWkeZM45jiY8hNyTU7JBERkT5HiZNIH2EYBttbtvNp3acYhsHgjMEDJmkKRAL88s1fAvCVsq9oiN4hMAyDSm8lmc5MJhdPJiclx+yQRERE+iQlTiJ9QDQeZWPjRtbXryfdmU62O9vskHrV/R/d3z5E79rjrzU7nD7DMAx2eXeR7cpmcvHkAfe9EREROZqUOIkkuWA0yNq6tWxp3kJBasGAKQTRZknlEp779DkAfnbyzzRE7yDFjTiVrZVku7M5pvgYstyaIFxERORIKHESSWKekIfVtaup9lYzKH0QDpvD7JB6lT/i51dv/QqAC8ZdwPFDjjc5or6hLWnKTcllcvFkMl2ZZockIiLS5ylxEklS9f56VtWswhPyMCRjyICZp2lvbUP0itOL+fHnfmx2OH1CJBah0ltJYWohk4snk+HKMDskERGRfkGJk0gSqmytZFXtKqKx6IAqArG3JZVL+Oen/wQ0RO9gecNeGgINDM8ezrj8cQNuWKeIiEhPUuIkkkQMw2BbyzbW1K7BbrVTnF5sdkimaPA3cOsbtwLw1XFf5XODP2dyRMnNMAzq/fXEjBgTCycyMmfkgOyhFBER6UlKnESSRCweY2PjRtbVryPDmTFgb+aPxWPc+sat1PvrGZE9QlX0uhGNR6n2VpPuTOeYwmMGbLItIiLS05Q4iSSBSCzCuvp1bGrcRG5KLmnONLNDMs1jyx7j48qPcdvd/PaLv9VwswMIRALU+msZnDGY8oJy3c8kIiLSg5Q4iZgsGA2ypnYN21q2UZRWhNvuNjsk07y34z0eX/44ALeedCsjc0aaHFHyagw0EogGGJc3jjF5YwZcxUUREZHepsRJxCTBaJBaXy3bmrdR768fkOXG91btreZnb/wMA4MLx1/Il0Z/yeyQklLciFPlrcJtdzO1ZOqALR4iIiLS25Q4ifQiwzDwhDxUe6vZ0bKD1nArKfYUBmcMHtA380diEW76z020hFoYlz+OucfPNTukpBSKhqj2VVOUVkR5QTk5KTlmhyQiIjJgKHES6QWxeIx6fz2VrZVUeasIRUNkubIozSxVbwFw30f3sap2FenOdP7n9P/BZXeZHVLS8YQ8NAebGZkzknH54wb0kE4REREzKHES6WG+sI9Paj+h1luL1WIlx51DSlqK2WEljdc3v87Tq58G4PZTb2dI5hCTI0ouhmFQ66sFC0wqmsSInBFYLVazwxIRERlwlDiJ9CB/xM8nNZ9Q46uhJL0Eu1Wn3N62t2znV2/9CoBZk2ZxyrBTTI4ouUTjUaq8VWS7sikvLKcwrdDskERERAYsXcWJ9JBAJMAnNZ9Q7a0e8PcwdcUT8vD/Fv4/fBEfxxQdw9XHXm12SEmlrdR4aWYp4wvGk+5MNzskERGRAU2Jk0gPCEaDrK5dTWVrpZKmLoRjYX666Kdsad5CYVohd5x+h3rj9tIcbMYb9qrUuIiISBLRlYrIURaKhlhTu4Ydnh0MzhishGAfcSPObW/exrKqZaQ50rj3zHs1BG23tvuZLBYLxxQfw9CsoSoeIiIikiR0RSdyFIVjYT6t+5RtLduUNO3HHz/6Iws3LcRmsfH7M37PmLwxZoeUFGLxGFXeKjJdmUwonKBkUkREJMnoqk7kKInEInxa9ylbmrcwKH2QkqYuPLfmOf72yd8A+NnJP+O4wceZHFFyCEVD1AZrKckooaKgggxXhtkhiYiIyD50ZSdyFPjCPjY1bWJz02ZK0kt0T0oXFm9dzJ3v3wnA7GmzOXfsuSZHlDzqfHWMzB/J+PzxmsNKREQkSSlxEjkCLcEWKlsr2eHZgTfspTitGKfNaXZYSWd17Wpu+e8txI04F4y7gCunXGl2SKYzDIN6Xz0A4wvGM6ZgjIqIiIiIJDElTiKHyDAMmoJN7PTsZJdnF8FokBx3DkMzdSN/V3a07ODaBdcSioU4ofQEbjjhhgH/OUXjUaq91aTZ0ggTZlTuKCVNIiIiSU6Jk8hBihtx6v317GjZQbW3mmg8So47RzfxH0BlayU/fO2HNAebGZ8/nnmnzxvw9361zc80KGMQY3PG8vanb5sdkoiIiByEgX0FI3IQ4kacOl8dW5u3UuOrAQPyUvNw291mh5bUdnp2MvuV2VR7qxmSOYQ/nPkHUh2pZodlqqZAE76Ij7K8MsbkjcESH9g9byIiIn2JEieR/YjFY9T5dydM3hpsFhsFqQW6h+kgbG/ZzuxXZlPrq2VY1jAeOuch8lPzzQ7LNHEjTo2vBofNwZSSKZRmlmKxWIjEI2aHJiIiIgdJiZPIPmLxGLW+Wra1bKPGW4PdaqcorUiV8g7SlqYt/ODVH1Dvr2dk9kgePOfBAZ00RWIRKr2VFKYWUl5YTm5KrtkhiYiIyGFQ4iSyWyQWoc5fx7bmbdT6apUwHYaNjRuZ8+ocGgONjM4dzYNnPzigE4VgNEiNr4ZhWcMoLygnxZFidkgiIiJymJQ4yYAXjAap8dawtXkrjYFGXDYXxenFA76IwaFa37CeOa/MoSXUQlleGQ+c/QDZ7myzwzKNN+ylKdDEmNwxjMsfpwRcRESkj9OVoQxYraFWqr3VbG/ZTkuohTRHGoMzBqss9GFYW7eWq1+7Gk/IQ3lBOX88649kujLNDss0zcFmfBEf5YXljM4djdViNTskEREROUJKnGRAicajNAebqfZWs8uzC3/ET6YrU3MwHYF3tr/DLf+9BV/Ex8TCidx/1v2kO9PNDss09f56YkaMyUWTGZql75WIiEh/ocRJ+r1wLExzsJnGQCNVrVV4wh4wINudPaCLFhwpwzD4x+p/cO+H9xI34kwrmcZdM+8asEmTYRhUe6tx2V1MKppESUaJ2SGJiIjIUaTESfodwzAIRAN4Qh7qfHXU+mrxhr0ApDvTKU7T/UtHKhKL8Lv3fsf8dfMBOL/sfG484cYBex9PNB6l2ltNtjubisIK8lLzzA5JREREjjJdPUqfF4wG8YV9+CN+WkItNAYaCUQCBKIBrBYr6Y50StJLdO/SUdIcbOaG129gadVSrBYrP/7cj7mk4pIBOyTNG/bSEGhgUMYgJhRMIMOVYXZIIiIi0gOUOEmfYxgGLaEW6n311PoTvUnBaJC4EceKlRRHCqmOVHJTcnVT/lG2tXkrP1nwE3Z4dpDmSOM3p/2GE4eeaHZYpogbcep8dRgYTCiYwMickQO2x01ERGQgUOIkfUY4FqbeX88uzy7q/HWEoiFSHam47W6yXdnqUephH+z8gBv/cyPesJdB6YO4+8y7GZ072uywTNE2P1NeSh7jC8ZTmFZodkgiIiLSw5Q4SVIzDIPmYDO1vlp2enbSGmrFYXOQ7c7GneY2O7wBIRqP8sjSR3hixRMYGBxTdAy/P+P35KTkmB2aKRoDjfgjfkbljGJs3lhNaisiIjJAKHGSpBM34nhCnvay4Q3+BsKxMJmuTAZnDtbwu160vWU7t75xK5/WfQrAV8q+wvUnXI/T5jQ5st7XVgAi1ZHK1JKp+i6KiIgMMEqcJClEYhFaQi00BZqo8lbRGmolFAuRYk9J9C7Z1bvUmwzD4H8/+1/ufO9OAtEAGc4MbjnpFr448otmh2aKtgIQQzKHMC5/3ICe3FdERGSgUuIkpjEMg6ZgE9Wt1VR5q/BGvGBAij2F3JTcAdmrkQxagi3c8c4d/GfLfwCYVjKN20+9neL0YpMj632GYVDvrycaj6oAhIiIyACnxEl6XSweo95fz07PTqq91URiETJcGZpfKQksqVzCzxf/nFpfLTaLjR9M/wGzJs0akIU3IrEI1b5qslxZHFNwzIBMHEVERGQPXaVKrwnHwtR4a9jesp16fz1Wi5XclFwNw0sCzcFm7vvwPv73s/8FYGjmUH592q8pLyg3OTJzeMNeGgONDM0aSll+GenOdLNDEhEREZMpcZIe1xpqpdZXy7aWbTQHm0mxp1Ccrt6lZBA34sxfN58HPn4AT8gDwAXjLmDu8XMHZLU4wzCo9dViYFBRWMGInBH6noqIiAigxEl6SCweoyHQQGVrJTXeGvwRPxnODEozS1WJLEmsrVvLvHfntVfMG5M7hhtOuIFjio8xNzCTeEIemoJNmptJREREuqTESY4qX9hHnb+OHS07aAw0YrFYyHZlk5+ab3Zospsn5OHBjx/khbUvYGCQ5khj9vTZfK38awOydyUYDVLrqyXVmUpFYQVDs4Zq+KiIiIh0MvCukuSoC0aCNIQaqPPVJarjhb2kOdI0HC/JhKIhXlj7An9Z8Reagk0AfGnUl7j2+GsHZGIbjUep9dViwcKInBGMzBmpMuMiIiKyX7qqlUNmGEZiXhtvAwDv73wff9zf3ruUm5mLxWIxOUppE4lHeH7t8zzxyRPU+moBGJE9ghtOuIHpg6abHF3vixtxGgONBKIBitOLGZUzivzUfH1nRURE5ICUOEm34kacQCSAP+LHG/ZS7a2mOdhMIBTAhg2nzUlOWo7uXUoy0XiUlz97mUfWPkJdpA6AorQirpp6FeeNPW9A9gbufR/ThMIJlKSXDMhS6yIiInLoBt6VkxxQ3Ijjj/jbHy3BlkSSFA0QioaIG3FS7ClkujLJd+dTSSVpzjQlTUkkGo+yaPMiHl36KDs8OwDIT8nnO1O+wwXjLhiQEwsHo0HqfHWkOFJ0H5OIiIgcFiVOA5xhGPgiPlpDrbSEWqj11eKP+AlGghgYOG1O3HY3Gc4M8lM6DmeKx+ImRi778oQ8/Gvdv3ju0+eo9lYDkO3O5oLcC/jOF79DqivV5Ah7Xyweo85fR9yIMyx7GCNzRpLlzjI7LBEREemDlDgNMJFYhGA0iD/ixxPyUOOtwRvxEowEsVgspDpSu0ySJHltadrCM2ue4ZUNrxCMBoFEwnRJxSV8ffzXaV7VPOB6VwzDoCXUQkuohaK0IkbnjqYwrVDfaRERETlsSpz6oVg8RigWIhgNEowGCUVDtIZb8Ya9BCIBQrEQkVgEALfdTbojXYlSHxM34nyw8wOeXv007+98v335mNwxfLPim5w56kxcdhfxWJxmms0LtJftnTBlOjOZUjyFIZlDcNgcZocmIiIifZwSpz7KMIz2xCgYDRKKhfCHE71I/qifSCxCKBYiHo+DBewWOw6bA5fNRbYrG6fNqUSpD9ravJVXNrzCaxtfax+OZ8HCycNO5psV32RaybQB2a5xI05LsAVP2EOmM5OJhRMZlDGINGea2aGJiIhIP6HEqY+IxWPtVe1aQ63UB+rxhr0Eo0HiRhwMsFqsuOwuHFYH6c50cqw5qhjWD7QEW1i4eSGvbHiF1bWr25enO9M5b+x5XDzhYoZkDjExQvPE4jGag834Ij6y3FkcU3QMJRklpDhSzA5NRERE+hklTkkqGA3iC/vwRXw0B5tpDDTij/gJRUNYLVbcdjcp9hSyXdlKjvohX9jHezveY+Hmhby9/W2i8SgANouNGUNmcM6Yczhp2EkD7t6lNpFYhKZgE8FokNyUXMryyyhOL8Zld5kdmoiIiPRTSpySQCQWwRfx4Qv7aA230hhoTNyPFA1gGAY2i41URyrZrmxcabow7K/q/fW8vf1tFm9dzEe7PiISj7S/NjZvLOeMOYcvjfoSeal5JkZpLl/YR1OoCYCC1AIqMisoSi8akCXWRUREpHcpcTJZ3IizpHIJDf4GIvEIVqsVt029SQOBYRhsbtrMuzveZfG2xayqWYWB0f760MyhnDr8VM4afRZj8saYGKm5YvEYnpAHT9hDmiONYVnDGJwxmNyUXJ0fIiIi0muUOJnMMAz8ET8pjhRK3CVmhyM9rMZbw8eVH/Phrg/5aNdHNAQaOrw+oWACpw4/lVOHncrw7OEDstBDm2A0SHOwmUgsQrY7m8lFkylMKyTDlWF2aCIiIjIAKXFKElaL1ewQpAfU++tZWbOSpZVL+ajyI7Y2b+3wusvmYmrJVE4ZdgonDzuZwrRCcwJNEtF4FE/IgzfsxWV3UZBWwJDMIeSn5ms4noiIiJhKiZPIURKNR9nYuJGVNSv5pOYTVtWsotJb2WEdq8XK+PzxHDf4OD43+HNMLJyoggaAN+ylJdSCYRhku7OZWDiRgrQCMl2ZA7rXTURERJKHEieRwxCNR9navJV19etY37Ce9fXr+bT+U4LRYIf1rBYro3NGM7l4MscNOo5pg6aR6co0KerkYRgGvogPb9hLKBYizZnG0KyhlKSXkJuSqwlrRUREJOkocRLpRnOwmc1Nm9nctDmRJDWsZ1PjJkKxUKd1053pTCqcxKSiSUwsmsiEggmkO9NNiDr5xOIxfBEfraFWYkaMVGcqRelFFKUVkZuSq8lqRUREJKkpcRIhcVFf66tlh2cHW5q3sKVpC5ubN7OlaQtNwaYut0lzpDE2byzj8sdRllfG+PzxjMgZofvVdosbcQKRAIFo4mHBQroznWHZwyhIKyDbnU2qI9XsMEVEREQOihInGTCC0SDV3mqqWqvY2bqTHS072OFJPHZ5dnWYN2lfgzMGMyJ7BKNyRzEubxzj8scxOHOwkqS9RONR/BE//oifcCycmKjZ4SbDlcHw7OHkpOSQ5crSPV0iIiLSJylxkn4hGo9S76+nzldHnb+OWl8tVd4qqrxVVLdWU+Wt2m/PURu71c6g9EEMzxnOyOyRjMgZwcjskQzPHk6KI6WXjqTvCMfC7YlSLB7DbrWT4kihOL2YvNQ80hxppDvTcdvdKvAgIiIifZ4SJ0lahmHgDXtpCDTQGGikMdDY4ed6fz11/jrqfHU0Bho7TB67P6mOVIrTixmSOYTSzFJKM0vbfy5KL8Ju1SnRlbgRJxQNEYgG8Ef8xI04TpuTVEcqw7KHkePOId2ZTrozXYUdREREpF/SVaL0imA0SGuoFU/Ik3iEPR2eNweb9zxCe36OxqMH/R42i42CtAIKUgsoSCugJL2E4vTiDv9XeevuxeIxgtFg+yNmxBLD7uxu3HY3gzMGk+XOak+UbFab2SGLiIiI9DglTiaKx+Gzz2DdFshIh/EjwXoUrunjBuzYAV4vpKdDaenB73fvbd2pUfKK/YSiATyBAK+/GaCqwUd6jo9xk/xU13kJearxvWHDlhKgrsWLJ+glZPiIWr14w4nn/oiXiBE+7ONJtaeRYc8j151LSXYuuSl52EK5hD25ZNoKmTC8gAkjC/DV5bB5c+Keo+HDoaYGGrZAcxxyR0JzFqQNhp07YOMmiEZh506IRqC4BM45GxyOxGewfVtinXgcfF6w2aEgH449LhHTxx9BXT3EopCWDlYrjB4FQ4ft/7Pet10GD4Zdu/Y8H1QCH30M69dDTTUUFsG4cfC5z3V+z5QUaG6G/HwYOSrx+ubNgAEpqZCVmdgn8cRJvmMHDC7d834pKbCzMkptfZhQPMTg0hCu1CgGccJBGzkZbkYPS2VQ5iAyXZmkOlJJdaSSYk9JysQzHoeNG6GlBbKyYPToRJuIHKyuvkMiIiJ7U+JkkuXL4a9/hU/XQrUbXE4YPRTOPRfGlXVePxaPEYlHCMfChGNhIrE9P4diofafN28P88HHYWrqQ4TjIayOEFl5IUaNDZGeHSQUDRGKhTr0KASjQQLRAB5/kBZfiHA8QNzqx7B20dtjBVqAtw/9mC2GjXRnBjkpmWS4MshyZZHhyiDTlUm2O7vTo35XNm8vymLnFjehcOIzcmTBrlbYshm8vsR+X3YmEp5IBELhRCIU3R26YYDFAnZHIsmwWsDng9ZWCLflchawWeGP98PMmYkLp5UrE4lJKJzYh82aSDbSd1cW93ohEEgkQ5CILTsbJk+GWZd1bsN16+Hll2HrlsQ+IxEIh8DpSsTe6oHqGgj4IRbbs53Nltivwwne1sR7xuKAARZrIi6rdU+SEIuDhcR+nc44GRkh7r0Bfvm7Zjz+KA53BK8/TmMDRMM24hEnlpgbazSPNFsmqS43+VkpFGSnMmGci29fbmHolENv697Udi6tXQvBILjdMH48XH45TEny2CU57O87NGuW2ZGJiEgySYrE6cEHH+T3v/89VVVVTJgwgXvuuYeTTjppv+u/+eabzJ07lzVr1jBo0CCuv/56Zs+e3YsRH5nly+GXv4T6eth4/LkEXFuJGRFWxeL86/UIaR9GwBptT5QisQgxI9b9jtukAkM7LvpkO7D9ILa17n7sLW6DSCpEU7BEUjHCqRBOxxZP4aTJFpasyCfYmobTksagvAwIp7NrSzqWSDqjhqZTnJ1B1J9OY00aOdkWrvpu18nh3tath/l/SyQvhYWJpKWmFt55B0IhcKckelVCYWhqTCQMNiukpu1OduK7d2QBpyORpOzckUg2YK/XAYzE9s0t8Nw/E0mQzbZnPxZrIkEKBBIJEyRej+21j1AYWjzw/vuJdv3J3D3HuG49/OmxPccSCiUSZp830VuVlwtbtyUSvn3FYtDQsNd7xnYHbI1hWKJELVGw7n7YI9hsMQzDIBwHW9yCNZY4xWuqHLQ0ZmOPZRD0uomFXcTDbiwxNzbcRCMWWoBYOjgCUJINy5Ymet5+/vPkTUD2PpeGDIG0tERivHQpbEvy2CU5HOg7VFkJ3/qW2RGKiEiyMD1xevbZZ7n22mt58MEHOeGEE3jkkUc466yz+PTTTxk6dGin9bds2cLZZ5/Nd7/7Xf7+97/z7rvvMmfOHAoKCrjwwgtNOIJDE48n/rJZX5/4i+aSlGUEbbUd1gl2nle1AwsWnDYnDpsDl82F0+bEaXPS0ugiHHCS4nRiw4nNcGEzXFgNF36Pm/wcF58/zoXb7mq/X8Vtd+Oyp/Dqv93s2uZmcLELB6nYDDfWaCqL/i+FaNCB3Z5IVoJBiMcSvThOZ5xrv1zJ7CcGkeey4vWCkZ2IMWV3AbuABdKywZIGWSMSPS6vvAJjxx54SNvLLycSjeEjEu9lGFBXm0gc2nqRHI5EsmIYe7bzene/bt2THMV3rw/7JEyW3fveJ4kKhRJJCiR6qtoSq717gmKx3T09tsTr0ViiF8nthm3bE/GPHZtYd+9jAdi0CWIxg/yCOB5vnI3b4kSJgzMGlihY4mCPgREDayzxHNjz9haI2xMJrWGDmAPCaRBJxUIqlpiTeNiBYTix5diANwlv+jyleU42b018B+32Pb1yMfZ8xuFwoo137YLjj4d16+Bvf0v0pCXb0Ld9z6W2Ns7MTDxfuzZ5Y5fk0N13aNOmPeuJiIiYnjjdfffdXHnllVx11VUA3HPPPSxYsICHHnqIefPmdVr/4YcfZujQodxzzz0AjB8/niVLlnDnnXfuN3EKhUKEQnuyEY/HA0AkEiES2f/cPT1h48bEY/jwxIX/F1ofptG2GitOXEYWoYCDoM/OpZc4GDrYid1qTyRJVkd7gmSz2DrdZ7JjB9x7L2RkJP5iui9fGFo3wjnnJO552ndbYxuUZUD7phbYVgUOC7hS44lExQY4d19cWMBpT1xNuJ1xXK7E635/YvPc7N0X4iEIBRP3cAEMHgS7dsCObZ3j2Dueyp2JdZ27v6Gt3sQwNrcTUlMS+zbiYLdAijsRU9wAI24keswMdv9n93MM9hTd2/2D1QCLsddre1XlsxhYrUaih8piEI/HE/u27Nmv1R7f3YNlYBhx4hi4sgwgztrt8PFaAwuwpcZC7jCDiBP8AQjYLWSWgM1mwW23EjKsOAxrIhGK28BwQdwBUTfE7BBz7U6U7GDYsJD42YjuXhZzsDswrNbEZ2GxJKK07P5+u11RwmELrt1TKFksiSTPMBIJlH335xyPQ2pqInkKBBLf0w0bEvddJds9H/ueS/tK5tjbtP3+6e3fQ5LQ3Xdo6NBEu2zYEKGsm15yMYfOoeSm9kluap89DvYzsBiGYXS/Ws8Ih8Okpqbyz3/+kwsuuKB9+Y9//GNWrFjBm2++2Wmbk08+mSlTpnDvvfe2L5s/fz5f//rX8fv9OLr41++2227j9ttv77T8H//4B6mpqUfpaEREREREpK/x+/1ccskltLS0kJmZud/1TO1xqq+vJxaLUVRU1GF5UVER1dXVXW5TXV3d5frRaJT6+npKSko6bXPTTTcxd+7c9ucej4fS0lJmzpx5wA+nJ2zcCNddBzk5ieEgAD5LNXFLItP1eRPDz26+GYYPO/j9bt0Gd9yRuO8nbXfvjoU9vVJeb6LowS23JP662mHbrfCb3yQqSbUVP4BElbalSy3tvRhOZ2Iol4W2oXIxHr9nNT/5eQUpKXaiMfDvLtiQmgbsHvo1ZQpkZiRi8foScfzsVhgxomOvWVu8m7fCr3/ZMZ5Wj4UPP0p8PlZbojslKwuaGi2EI4ltEz1OlsQwPQMwLGAknmNYMOKW9ncCEr12RqL7zIi3/bz7dcOCzQZWa+LnWMxCPLZnfUj00rQNAYvHE4+CgsTzESPggQcSP+/d3i0t8OGHic/S4Ug8r909UnPvP2FYdx9DV3/W2Ps9u3qtvcfJgPT0CA8/vIg5c87A6XRQV7f7CC173mPfHqfCwsRQxc99LrFeUxP8/vfJ12vT1bm0N48neWNvE4lEWLRoEWeccUaXf/SRntXdd8jvj/CVryxi1KgzKCtT+yQjnUPJTe2T3NQ+e7SNRuuO6UP1gE7DzgzDOGDJ467W72p5G5fLhattjNJeHA5Hr39RysoSF3FLl+4ZU+8iMWbNMGDLRpg+HU6dcmj3ZQzPhf8t7bjfNoYBm3fv95Qu9jssB/49NLFt3l7blpXAx80QCCUu8u1pEN5d9S2RSEWA1USbhhILOfC0JCrXAdTtSPy/sBDyXWCJJOKo2R3Hicfs//gGZUH5sI7HkuuGbAc0NiWSsYwMcKaB4Ydga+KCv/0+pt33NLUtczgSP7fd09OmLcHYd1tIJBKh3fcCGUbimPdNVGy2xKMt+XA4EkMV7XaYNIn2oT17t3dqamKIXH19IvHz7/48w+HOiVNXidG+7bqvtq9zNJrYR1viGQo5SE93EAp1vscp8Xpif05nIqaCgkRBjnXrEu1VVpZ89wl1dS61MYzEHwSSNfZ9mfG7SLr/Dm3fXVBnzBi1T7LTOZTc1D7JTe3DQR+/qZcT+fn52Gy2Tr1LtbW1nXqV2hQXF3e5vt1uJy8vr8diPVqs1kSZ5Pz8xM3rHk/iAtbjSTzPz4fLLjv0C70j2e/+tvX5oKgo8Xrbxb3DsSdRaLvIcDoT1adsNhg1KjE/USSSeAwalNj2UI6vq3hiscR+7fY9vSmhUCIRaYvDak0kI23J0N77a0sy9i7dbRidkxOLJZEwpKQknofDe4pC2Pf6M4Pdntg2EtnzWTidiZ/Hjk3E3/Zeex9La2viM7LZEp+ZwwETJnS+v6KrpKktieuuJ2rvY22TlgZVVYmE027fU2Rj7/1C4hhcrsRnvW7d4X8fe0NPnUsycHT3HWr7J0XfIRERAZN7nJxOJ9OmTWPRokUd7nFatGgR559/fpfbzJgxg5deeqnDsoULFzJ9+vQ+ky1PmZIok9w2b0hlZaIXYvr0xIXe4ZZPPpL97m/br341cSHxzDOJYWXxeOIiwuXaM+Rv8ODEBbnbnRga5XbDl76UuBhvaEgMhznU49tfPOeeC42N8OmnifeCxEVP2zDCtjlY2u7xa+stcruhpCQRu8eTqHIXDCbWsVgSiUxODlx8cSLmd99NbBcM7p7HyZZIPrKzE89bWhKJZVuC43ZDbi6ceCL89Kcdj3HfYwkGE4Ux2mJ1OhN/+W6bHHfvniC7PdH743QmYvb59iQ9VuueXq/2eZx29wZmZCTaqG340fDhifjc7sR+du5MfF7xeGJfLlfi+NLSEp+nYRz597E39NS5JAPHgb5Dl16aOFdEREQgCYbqzZ07l1mzZjF9+nRmzJjBo48+yvbt29vnZbrpppvYtWsXf/vb3wCYPXs2f/zjH5k7dy7f/e53ef/993n88cd5+umnzTyMQzZlSqJM8r4z1R/pXzaPZL8H2vauu+DJJxNDV4YOTcxtsmULfPYZPPwwjBmTuCdq7+3gyI5vf/FA4n1Xr078XFGRWL5x455l48YlEpHq6kRyUF6e+OvxyJF71otEEuWGw2EYNiwx2aXTmVi/bf9tvWV2e6L37PTTE/v/z38SF1jRaCI5sdkScYwd2/UxdnUsI0d2/MyGD0/sd/nyROxDhsDUqXDGGZ3fMy0tMdyvpCTRYwWJZDJxX1MiScrKSsS/cWPnNkpLS8xztPfnk5OT2E9r69H7PvaGnjqXZODY33coFlPiJCIie5ieOF188cU0NDTwy1/+kqqqKioqKnj11VcZNixRGaGqqortbQPNgREjRvDqq6/yk5/8hAceeIBBgwZx33339Yk5nPZlte6Z6ydZ9ru/bZ1OuPLKjstGj04kGKNHJxKLrrY70uPbXzzjxiUeB1pWUdH1Prvadt/37G6dM8/c/2sH2u++x7Lv87POSjwO5z3Lyzsvi0QSF4NdtVFX6/dVPXUuycDR1Xdo77nbRERETE+cAObMmcOcOXO6fO2JJ57otOyUU05h2bJlPRyViIiIiIhIggaziIiIiIiIdEOJk4iIiIiISDeUOImIiIiIiHRDiZOIiIiIiEg3lDiJiIiIiIh0Q4mTiIiIiIhIN5Q4iYiIiIiIdEOJk4iIiIiISDeUOImIiIiIiHRDiZOIiIiIiEg3lDiJiIiIiIh0Q4mTiIiIiIhIN+xmB2AGwzAA8Hg8JkfSt0UiEfx+Px6PB4fDYXY40gW1UXJT+yQ3tU/yUxslN7VPclP77NGWE7TlCPszIBOn1tZWAEpLS02OREREREREkkFraytZWVn7fd1idJda9UPxeJzKykoyMjKwWCxmh9NneTweSktL2bFjB5mZmWaHI11QGyU3tU9yU/skP7VRclP7JDe1zx6GYdDa2sqgQYOwWvd/J9OA7HGyWq0MGTLE7DD6jczMzAF/wiU7tVFyU/skN7VP8lMbJTe1T3JT+yQcqKepjYpDiIiIiIiIdEOJk4iIiIiISDeUOMlhc7lc/OIXv8DlcpkdiuyH2ii5qX2Sm9on+amNkpvaJ7mpfQ7dgCwOISIiIiIicijU4yQiIiIiItINJU4iIiIiIiLdUOIkIiIiIiLSDSVOIiIiIiIi3VDiJCIiIiIi0g0lTrJfb731Fueddx6DBg3CYrHwr3/9q9tt3nzzTaZNm4bb7WbkyJE8/PDDPR/oAHWo7bN48WIsFkunx7p163on4AFm3rx5HHvssWRkZFBYWMhXvvIV1q9f3+12Ood6x+G0j86h3vXQQw8xadIkMjMzyczMZMaMGbz22msH3EbnT+851PbR+WOuefPmYbFYuPbaaw+4ns6hA1PiJPvl8/mYPHkyf/zjHw9q/S1btnD22Wdz0kknsXz5cm6++WZ+9KMf8cILL/RwpAPTobZPm/Xr11NVVdX+GDNmTA9FOLC9+eabXH311XzwwQcsWrSIaDTKzJkz8fl8+91G51DvOZz2aaNzqHcMGTKE//mf/2HJkiUsWbKE0047jfPPP581a9Z0ub7On951qO3TRudP7/v444959NFHmTRp0gHX0zl0EAyRgwAY8+fPP+A6119/vTFu3LgOy77//e8bxx9/fA9GJoZxcO3zxhtvGIDR1NTUKzFJR7W1tQZgvPnmm/tdR+eQeQ6mfXQOmS8nJ8f405/+1OVrOn/Md6D20fljjtbWVmPMmDHGokWLjFNOOcX48Y9/vN91dQ51Tz1OctS8//77zJw5s8OyM888kyVLlhCJREyKSvY1ZcoUSkpKOP3003njjTfMDmfAaGlpASA3N3e/6+gcMs/BtE8bnUO9LxaL8cwzz+Dz+ZgxY0aX6+j8Mc/BtE8bnT+96+qrr+acc87hi1/8Yrfr6hzqnt3sAKT/qK6upqioqMOyoqIiotEo9fX1lJSUmBSZAJSUlPDoo48ybdo0QqEQTz75JKeffjqLFy/m5JNPNju8fs0wDObOncuJJ55IRUXFftfTOWSOg20fnUO9b9WqVcyYMYNgMEh6ejrz58+nvLy8y3V1/vS+Q2kfnT+975lnnmHZsmV8/PHHB7W+zqHuKXGSo8pisXR4bhhGl8ul95WVlVFWVtb+fMaMGezYsYM777xT/2j1sB/+8Id88sknvPPOO92uq3Oo9x1s++gc6n1lZWWsWLGC5uZmXnjhBS6//HLefPPN/V6c6/zpXYfSPjp/eteOHTv48Y9/zMKFC3G73Qe9nc6hA9NQPTlqiouLqa6u7rCstrYWu91OXl6eSVHJgRx//PFs2LDB7DD6tWuuuYb//d//5Y033mDIkCEHXFfnUO87lPbpis6hnuV0Ohk9ejTTp09n3rx5TJ48mXvvvbfLdXX+9L5DaZ+u6PzpOUuXLqW2tpZp06Zht9ux2+28+eab3HfffdjtdmKxWKdtdA51Tz1OctTMmDGDl156qcOyhQsXMn36dBwOh0lRyYEsX75cXe89xDAMrrnmGubPn8/ixYsZMWJEt9voHOo9h9M+XdE51LsMwyAUCnX5ms4f8x2ofbqi86fnnH766axatarDsu985zuMGzeOG264AZvN1mkbnUMHwayqFJL8WltbjeXLlxvLly83AOPuu+82li9fbmzbts0wDMO48cYbjVmzZrWvv3nzZiM1NdX4yU9+Ynz66afG448/bjgcDuP555836xD6tUNtnz/84Q/G/Pnzjc8++8xYvXq1ceONNxqA8cILL5h1CP3aD37wAyMrK8tYvHixUVVV1f7w+/3t6+gcMs/htI/Ood510003GW+99ZaxZcsW45NPPjFuvvlmw2q1GgsXLjQMQ+eP2Q61fXT+mG/fqno6hw6dEifZr7bSofs+Lr/8csMwDOPyyy83TjnllA7bLF682JgyZYrhdDqN4cOHGw899FDvBz5AHGr7/Pa3vzVGjRpluN1uIycnxzjxxBONV155xZzgB4Cu2gYw/vKXv7Svo3PIPIfTPjqHetcVV1xhDBs2zHA6nUZBQYFx+umnt1+UG4bOH7Mdavvo/DHfvomTzqFDZzGM3Xd9iYiIiIiISJdUHEJERERERKQbSpxERERERES6ocRJRERERESkG0qcREREREREuqHESUREREREpBtKnERERERERLqhxElERERERKQbSpxERERERES6ocRJRERERESkG0qcREREjkBDQwOFhYVs3br1kLb7/ve/zyWXXHLU1z0cF110EXfffXeP7V9EpD9Q4iQiIv3Gzp07+cEPfsDo0aNxu90UFRUxc+ZMVq1aBYBhGGRnZ3P//fd32vaaa65h6tSpAEyaNIlf/OIXXb7HHXfcQU5ODnV1dQDMmzeP8847j+HDhx9SrPPmzeOxxx475HWvvfZavvKVrxzSe3Xn5z//Ob/5zW/weDxHdb8iIv2JEicREekXtm7dypQpU6ivr+fJJ59k3bp1PP/885SXl+NyuQDYtGkTLS0tTJ8+vdP2S5YsYdq0aUAicWpLtvZWXV3NvHnzuP322ykoKCAQCPD4449z1VVXHXK8ubm5pKWlHfK6H3/8Mccdd9whv9+BTJo0ieHDh/PUU08d1f2KiPQnSpxERAaQp59+Grfbza5du9qXXXXVVUyaNImWlpaj8h6nnnoq11xzDddeey05OTkUFRXx6KOP4vP5+M53vkNGRgajRo3itdde67Dd//3f/3HiiSeSnZ1NXl4e5557Lps2bQKgrq6O4uJi7rjjjvb1P/zwQ5xOJwsXLgTg/vvvJy0tjWeffZYZM2YwfPhwTjrpJO655x7Gjh0LwNKlS7Hb7RxzzDEd3jsajbJy5cr2xGnixImsXr2607HdfPPNDBs2jDlz5gDw2muvYbfbmTFjRvs6hYWF/OlPf+qw3ccff4zL5Wo/nq1bt2KxWNi2bRvxeJw77riDMWPGtPeSzZo1q33bvdd1Op2899573HLLLVgsFj73uc912x41NTVYLBbuvfdepkyZgtvtZsKECbzzzjsd1vvyl7/M008/3e3+REQGKiVOIiIDyDe+8Q3KysqYN28eALfffjsLFizgtddeIysrq8O6d9xxB+np6Qd8vP32212+z1//+lfy8/P56KOPuOaaa/jBD37A1772NT7/+c+zbNkyzjzzTGbNmoXf72/fxufzMXfuXD7++GP+85//YLVaueCCC4jH4xQUFPDnP/+Z2267jSVLluD1ern00kuZM2cOM2fOBKCpqYlgMMj27dv3e/xLly6lvLyclJSUDsvXrFlDIBDokDht2rSJQCDQvs7y5cv561//yn333Yfdbgfgrbfe6tR7VVFRwZo1azosu+mmm/je977HqFGjAFixYgXZ2dkMGzaMefPm8Y9//INHH32U9evX8+KLL3Lqqae2b9u2bmlpaXuys2LFCqqqqliwYMF+j3XvuAEefPBB/vCHP7By5UqGDx/Ot771LeLxePt6xx13HB999BGhUKjbfYqIDEiGiIgMKC+99JLhcrmM3/zmN0ZOTo6xevXqLtdraGgwNmzYcMCH3+/vtN0pp5xinHjiie3Po9GokZaWZsyaNat9WVVVlQEY77///n7jrK2tNQBj1apV7cvmzJljjB071vjWt75lVFRUGIFAoP21pUuXGkOHDjUsFosxbdo044YbbjDWrFnTYZ+nnXaaccUVV3R6rz/96U+Gw+EwgsGgYRiGsX37dgMwli5d2r7OySefbFx44YUdtjv//PM77e9HP/qRMXPmzPbnCxYsMNLT042ampr2ZbfddptxyimnGIZhGCeddJJx/fXX7/dz2Hvd+fPnG3l5eftdtyv/8z//YzgcDmPz5s3ty5YsWWIAxvbt29uXrVy50gCMrVu3HtL+RUQGCvU4iYgMMOeeey7l5eXcfvvtzJ8/nwkTJnS5Xm5uLqNHjz7gY9+emzaTJk1q/9lms5GXl8fEiRPblxUVFQFQW1vbvmzTpk1ccskljBw5kszMTEaMGAHQoQfpzjvvJBqN8txzz/HUU0/hdrvbX5s6dSqbN2/mjTfe4Etf+hIvvvgikydPZv78+e3rLFu2bL/3N02YMKH9XqjS0lKys7Pb73N6/vnn+fjjj7nrrrs6bBcIBDrEAB17nAzD4Oabb+a6666jsLCwfZ0VK1YwefJkIDFE7s4772TmzJk8/PDDNDY2dtjf3usuX768/eeDtWLFCr761a+2f55A+3Hura0t9+4FFBGRPZQ4iYgMMAsWLGDdunXEYrH2BKYrRzJUz+FwdHhusVg6LLNYLAAdhoqdd955NDQ08Nhjj/Hhhx/y4YcfAhAOh9vX2bx5M5WVlcTjcbZt29bpfW02G6eccgq//vWvWbNmDYWFhfzjH/8AYMeOHTQ3NzN+/PhO273++ut8/vOf77Cs7T6nUCjE9ddfz/XXX8+wYcM6rJOfn09TU1On7Xbt2oXH4+G5555j586dzJ07t8M6K1eubL/P6qc//Slr167li1/8Ivfffz+jR49my5YtXa67dxJ1sFasWNHpnq5ly5aRn5/P4MGD25e1JWwFBQWHtH8RkYHCbnYAIiLSe5YtW8bXvvY1HnnkEZ555hl+9rOf8c9//rPLdWfPns3Xv/71A+5v7wvvI9HQ0MDatWt55JFHOOmkkwA6FS8Ih8N861vf4uKLL2bcuHFceeWVrFq1ar/JXzweJxQKtScCkUgE6NyjsmjRIjZu3Mjjjz/eYXlb4nT33XcTi8W44YYbOr3HlClT+Pvf/95hWUVFBRaLhZUrV/Kzn/2MX/ziF6Snp7e/7vF42Lp1a4cEaOzYsVx//fX8+Mc/Jisri08//ZQRI0Z0WnfVqlVccMEF+/8g9xEIBNiwYQOxWKzD53Lvvfdy+eWXY7Xu+fvp6tWrGTJkCPn5+Qe9fxGRgUSJk4jIALF161bOOeccbrzxRmbNmkV5eTnHHnssS5cubS+KsLfc3Fxyc3N7JbacnBzy8vJ49NFHKSkpYfv27dx4440d1rnllltoaWnhvvvuIz09nddee40rr7ySl19+uf14TjvtNIqKiti8eTN33HEHhmG09/aMGDGCcePGcdNNN+F0OikoKODDDz/klltu4dJLL+Xkk0/u8H4TJ07kueee49133+XPf/5zl8MSzzzzTG666SaamprIyckBID09nWHDhnH99dcD8N3vfrfDNitXrsRmszFhwgR+97vfUVRUxLHHHovNZuNPf/oTOTk57b1fe68LiaTnk08+obKykrS0tE4FPfa1atUqLBYLf//73znttNPIzs7m5z//Oc3Nzdx6660d1n377bfbC22IiEhnGqonIjIANDY2ctZZZ/HlL3+Zm2++GYBp06Zx3nnnccstt5gcHVitVp555hmWLl1KRUUFP/nJT/j973/f/vrixYu55557ePLJJ8nMzMRqtfLkk0/yzjvv8NBDDzF16lRefvllzj33XMaPH8/s2bMZN24cK1euZPTo0UBieOArr7zCqFGj+MY3vsHJJ5/MI488wq9//WueeOKJTjFNnDiR+vp6pk+fzkUXXdRl3BMnTmT69Ok899xznZZ/8MEH/OY3v2mvwNdm5cqVjBs3DpfLRTAY5I477mDatGmceOKJbNiwgf/+97/tSdje6wL8+te/5tlnn2Xw4MH88pe/bN/nE0880T78cW8rVqxg3Lhx3HrrrVx00UVMnz4dq9XK+++/T3Z2dvt6wWCQ+fPnd0ryRERkD4thGIbZQYiIiPRVr776Kj/96U9ZvXp1h6Fvvem2225j8eLFLF68uMPyq6++mqampvb7vPbngQce4N///nf7nFgiItKZhuqJiIgcgbPPPpsNGzawa9cuSktLTYlhwYIF3HvvvZ2Wr1ixgvPOO6/b7R0OB/fff39PhCYi0m+ox0lEREzz+uuvs2rVKn7yk58c8PXzzz+fNWvWHFQSIAmGYZCVlcUzzzzD2WefbXY4IiJ9nhInERFJeg888AB+v5/rrrvO7FBERGSAUnEIERHpUR988EGHnqKXXnqJK664AoCzzjqLtWvXAvDII48wdepUKioquOSSS9pff/PNN7n11lt57LHHmDJlCoFAoPcPQkREBjz1OImISI/yeDxMnz6dzz77DIAZM2bw1FNPMXLkSEaPHs26detobW3li1/8Ih999BE2m43m5mays7PbX//CF77AP/7xD9PuIRIREVGPk4iI9KjMzExCoRCRSISXXnqJCRMmMHLkSFpaWkhPT8dut2O322loaOCGG25gzZo1ZGdnd3h9586dSppERMRUSpxERKTHjRkzho0bNzJv3rz2iVdXr17dPrFrRkYGq1atYvLkyVx00UW8/PLL7a/v3LmTwYMHmxm+iIiIEicREel55eXl3HnnnUycOJHhw4cDicSpoqICgA0bNpCRkcGsWbM46aSTCIVC7a9v2bKFQYMGmRi9iIiIEicREekF48eP5+9//zu33HJL+7I1a9a0J06/+tWvKCsrY8qUKbjdbi644IL21ysqKtiwYQMTJ05k3bp1Zh2CiIgMcCoOISIiIiIi0g31OImIiIiIiHRDiZOIiIiIiEg3lDiJiIiIiIh0Q4mTiIiIiIhIN5Q4iYiIiIiIdEOJk4iIiIiISDeUOImIiIiIiHRDiZOIiIiIiEg3lDiJiIiIiIh0Q4mTiIiIiIhIN5Q4iYiIiIiIdOP/Ax+2Ha5LPPdxAAAAAElFTkSuQmCC", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from sklearn.linear_model import LogisticRegression\n", "from scipy import io\n", "from scipy.stats import norm\n", "\n", "# Load the data\n", "data_path = \"../data/\"\n", "suv_file = data_path + \"suv_percentilesSLOthenUWM.mat\"\n", "flags_file = data_path + \"flags_combined.mat\"\n", "\n", "# Load .mat files\n", "suv_dict = io.loadmat(suv_file)\n", "flags_dict = io.loadmat(flags_file)\n", "\n", "# Extract relevant data\n", "suv = suv_dict['lung_SUVperc_COMBINED'][0:58, :, :]\n", "flags = flags_dict['flags'][0:58, 3]\n", "\n", "# Choose percentile of interest\n", "p = 94 # For lung and bowel, use 94 (0-indexed)\n", "X = np.nanmax(suv[:, :, p], axis=1).reshape(-1, 1)\n", "\n", "# Handle missing values\n", "valid_indices = ~np.isnan(X).flatten()\n", "X = X[valid_indices]\n", "flags = flags[valid_indices]\n", "\n", "# Fit logistic regression using sklearn\n", "logr = LogisticRegression(penalty=None, solver='lbfgs')\n", "logr.fit(X, flags)\n", "\n", "# Print model coefficients\n", "print(\"Intercept (w0):\", logr.intercept_[0])\n", "print(\"Coefficient (w1):\", logr.coef_[0][0])\n", "\n", "# Design matrix with intercept\n", "X_design = np.hstack([np.ones((X.shape[0], 1)), X])\n", "\n", "# Predicted probabilities\n", "pred_probs = logr.predict_proba(X)[:, 1]\n", "\n", "# Variance matrix\n", "V = np.diagflat(pred_probs * (1 - pred_probs))\n", "\n", "# Covariance matrix of parameters\n", "cov_matrix = np.linalg.inv(X_design.T @ V @ X_design)\n", "\n", "# Standard errors\n", "std_errors = np.sqrt(np.diag(cov_matrix))\n", "print(\"Standard errors:\", std_errors)\n", "\n", "# Combine parameters\n", "params = np.insert(logr.coef_[0], 0, logr.intercept_[0])\n", "\n", "# 95% CI for parameters using normal approximation\n", "z = norm.ppf(0.975) # 1.96 for 95% CI\n", "\n", "ci_intercept = (\n", " params[0] - z * std_errors[0],\n", " params[0] + z * std_errors[0]\n", ")\n", "\n", "ci_coef = (\n", " params[1] - z * std_errors[1],\n", " params[1] + z * std_errors[1]\n", ")\n", "\n", "print(f\"95% CI for Intercept (w0): {ci_intercept}\")\n", "print(f\"95% CI for Coefficient (w1): {ci_coef}\")\n", "\n", "# Define logistic function\n", "def logistic(x, params):\n", " return 1 / (1 + np.exp(-(params[0] + params[1] * x)))\n", "\n", "# Generate bootstrap samples\n", "n_bootstraps = 1000\n", "bootstrap_params = np.random.multivariate_normal(params, cov_matrix, size=n_bootstraps)\n", "\n", "# Generate x values for plotting\n", "x_vals = np.linspace(X.min(), X.max(), 100)\n", "\n", "# Compute predicted probabilities for each bootstrap sample\n", "predicted_probs = np.array([logistic(x_vals, bp) for bp in bootstrap_params])\n", "\n", "# Calculate mean predicted probability across samples\n", "mean_predicted_probs = predicted_probs.mean(axis=0)\n", "\n", "# Calculate 95% confidence intervals\n", "lower_bounds = np.percentile(predicted_probs, 2.5, axis=0)\n", "upper_bounds = np.percentile(predicted_probs, 97.5, axis=0)\n", "\n", "# Plotting\n", "plt.figure(figsize=(10, 6))\n", "plt.title(\"Prediction Probability of AE Depending on maxSUV Value\")\n", "plt.xlabel(r\"$x = \\max_{visit} SUV(visit, p)$\")\n", "plt.ylabel(\"P(AE | X = x)\")\n", "\n", "# Scatter data points\n", "plt.scatter(X[flags == 0], flags[flags == 0], label=\"NC\", color='blue', alpha=0.6)\n", "plt.scatter(X[flags == 1], flags[flags == 1], label=\"AE\", color='red', alpha=0.6)\n", "\n", "# Plot the mean logistic curve\n", "plt.plot(x_vals, mean_predicted_probs, color='green', label=\"Logistic Regression (MLE)\")\n", "\n", "# Confidence interval band\n", "plt.fill_between(x_vals, lower_bounds, upper_bounds, color='green', alpha=0.2, label=\"95% CI (Parametric Bootstrap)\")\n", "\n", "plt.legend(loc='center right')\n", "plt.grid(True)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "92b70025", "metadata": {}, "source": [ "My question? You mentined that it would be better not use regulization. Whay? Also, what about penalty? " ] }, { "cell_type": "markdown", "id": "16b21d5a", "metadata": {}, "source": [ "2. Statmodels library" ] }, { "cell_type": "code", "execution_count": 6, "id": "36e9c0c3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: inf\n", " Iterations 8\n", " Logit Regression Results \n", "==============================================================================\n", "Dep. Variable: y No. Observations: 58\n", "Model: Logit Df Residuals: 56\n", "Method: MLE Df Model: 1\n", "Date: Tue, 15 Apr 2025 Pseudo R-squ.: inf\n", "Time: 19:18:54 Log-Likelihood: -inf\n", "converged: True LL-Null: 0.0000\n", "Covariance Type: nonrobust LLR p-value: 1.000\n", "==============================================================================\n", " coef std err z P>|z| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -11.6839 3.510 -3.328 0.001 -18.564 -4.804\n", "x1 5.6870 1.954 2.910 0.004 1.857 9.517\n", "==============================================================================\n", "\n", "95% Confidence Intervals for Parameters:\n", " [[-18.56416559 -4.8035785 ]\n", " [ 1.85686085 9.51707004]]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "c:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\statsmodels\\discrete\\discrete_model.py:2385: RuntimeWarning: overflow encountered in exp\n", " return 1/(1+np.exp(-X))\n", "c:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\statsmodels\\discrete\\discrete_model.py:2443: RuntimeWarning: divide by zero encountered in log\n", " return np.sum(np.log(self.cdf(q * linpred)))\n", "c:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\statsmodels\\base\\model.py:595: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n", " warnings.warn('Inverting hessian failed, no bse or cov_params '\n", "c:\\Users\\zahra\\anaconda3\\Lib\\site-packages\\statsmodels\\base\\model.py:595: HessianInversionWarning: Inverting hessian failed, no bse or cov_params available\n", " warnings.warn('Inverting hessian failed, no bse or cov_params '\n" ] }, { "data": { "image/png": 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WgwcPdlu2bdu2ol69esJut5d9oP5f8efKihUrXNP2798vAIhnn3221OcUf8YtWbJEKBQKcenSJde8a0mc+vbtK+rWrev6B12xyZMni8DAQLftEEmBTfWIakiHDh2gVCoREhKCm266CXFxcfjxxx8RGxvrttxtt93m9vfq1asRHh6OQYMGwWazuR6tWrVCXFycq6ncL7/8AgAl+ksNHToUAQFX7754+PBh/Pvvvxg3bhwCAwOvcU+dNmzYAK1WW6JTf3F1v59//tltevfu3RESEuL6OzY2FjExMW7NpK5m6tSpUCqVCAwMRNu2bXHq1Cl8+OGHGDBggNtyVx7f4uN2edVBAGjfvj0yMjJKxBkSEoLBgwe7TRs+fDgcDgc2b97smrZhwwb06tULYWFhUCgUUCqVmDZtGnJzc3HhwgW35zdt2hQtW7Yssc7CwkL8+eefFdr/qujWrRtatmzp1uxl3rx5kMlkGD9+/FWfu2HDBjRp0gTt27d3mz569GgIIbBhw4YqxbRp0yYcPXoUo0aNgkKhAOBsNieTyUptkgY4O73v3LnT7VEdVQTFFc0qV69eDZlMhhEjRri9F+Pi4tCyZcsSTV8r8lqp6Pu7WKtWrZCUlOT6OzAwEI0aNXJ7n/zyyy/o2bOn22eLQqHAsGHDKrzvAwcOdB1/AK5KbMXbOXToELKzszF06FC35yUlJaFTp07lrr+y77u4uLgSr7UWLVpU+POhe/fubkV4MjIyAAD9+/d36+NYPP3y9V64cAETJkxAvXr1EBAQAKVSieTkZADAwYMH3bYzdOhQTJw4EU888QRefPFFPPPMM+jdu7fbMqmpqdi7dy82bdqEmTNnolevXti5cycmT56MG264ASaTqUL7VJrg4GAMHToUa9ascRVX2b9/P3bt2oXRo0dXqCng0KFDERIS4vZ+W7hwIWQyGcaMGeOatnv3bgwePBiRkZGuz7iRI0fCbrfj8OHDVd6HYiaTCT///DNuueUWBAUFub0/BgwYAJPJVGrzUSJPYnEIohqyZMkSZGRkICAgALGxsaW2cQ8KCkJoaKjbtPPnzyM/Px8qlarU9Ra3s8/NzQXgvMC4XEBAwFXbtANw9aUoq/N9VeTm5rrKSV8uJiYGAQEBrniLlRajWq2G0Wis0PYefvhhjBgxAnK5HOHh4a5+WFe68rgXx1Ha+UhISChxYXZlogv8d8yL17Vjxw706dMH3bp1w/z581G3bl2oVCqsWrUKL730Uol9uvKclbbOmvLQQw/h3nvvxaFDh9CgQQPMnz8ft99+e6kxXS43N7fUfiwJCQmu+VWxYMECAMAtt9ziKnsfFhaGG2+8Ed988w3ef//9EhUdW7ZsWeXiEFdTfO6L9+n8+fMQQpT6GgCcFfouV5HXSkXf38Uq8j4pfu+Vte2KuHI7arUaAFzbKY6/tH2MjY3F8ePHr7r+yr7vrvXzISIiwu3v4uNd1vTi5MXhcKBPnz44d+4cnnvuOTRv3hxarRYOhwMdOnQodftjx47F3LlzoVKp8NBDD5Uaj1wuR5cuXdClSxcAzoqO48aNw5dffomFCxdi0qRJAJwJ75V94ooV92NSKpVu08eNG4eFCxdi6dKlePzxx0tNeq4mKCgId955JxYtWoTs7GxERUXh008/RdeuXV3FZ06dOoXOnTsjPT0d77zzDlJSUhAYGIgdO3bggQceqPB5uZrc3FzYbDa89957eO+990pd5sr3B5GnMXEiqiEZGRmuqnplKe1CPyoqCpGRkVi7dm2pzym+S1N8YZGdnY3ExETXfJvNVu5FbHGFpLKKIVRFZGQktm/fDiGE235duHABNput2i9069atW+7xBUoe4+LjlpWVVSJxPHfuXIk4i/+Le7ns7Gy3dX3xxRdQKpVYvXq12x28su6CFD//auusKcOHD8fUqVPxwQcfoEOHDsjOzsYDDzxQ7vMiIyORlZVVYvq5c+cAoErnt6CgAN988w0A4Lrrrit1mc8++8x1UVnTvvvuO8hkMtfFbVRUFGQyGbZs2eJKJC535bSKvFYq+v6ujMjIyKu+pqpDcfxX28eKPL+i7zup7N+/H3v37sXixYsxatQo1/QrC0gU0+v1uOeee9CoUSOcP38e9957L7799ttyt6PVavH000/jyy+/xP79+13TY2Njyxzvr3j6lclrx44dkZGRgUWLFuHhhx/Gp59+ih49eqB+/frlxlFs3LhxmD9/PpYsWYJGjRrhwoULePPNN13zV61aBb1ejxUrVrjuvgHAnj17yl138WfilUWCrvyeqlOnDhQKBe65554yP5Mqs09ENYFN9Yi8zE033YTc3FzY7Xa0a9euxCM9PR0AXJWxisekKfbVV1+VqLB0pUaNGiE1NRULFy4s8WV2uSv/63w1PXv2hE6nK5EsLFmyxDXfG/To0QMA8Omnn7pN37lzJw4ePFgizqKiInz33Xdu0z777DPXf5ABuAY6vrypk9FoxNKlS0uN4e+//8bevXtLrDMkJARt2rSp2o5d5mr/mQ8MDMT48ePxySef4K233kKrVq0q1NSqZ8+eOHDgQImmhEuWLIFMJkP37t0rHednn30Go9GIF154Ab/88kuJR1RUVJnN9arbokWL8OOPP+Kuu+5yNY276aabIITA2bNnS30vNm/e3G0dFXmtVPT9XRndu3fHzz//7JbU2O32ai2rnp6ejri4OHz11Vdu00+dOoWtW7eW+/zKvu+kUvyPliuT4g8//LDU5SdMmIBTp05hxYoVWLBgAb777ju8/fbbbsuU9g8H4L9mf8V3OAGgV69e+OWXX0pUWBRCYPny5UhJSUFaWlqJdY0dOxYHDhzA//73P1y8eNFVCa+irr/+ejRr1gyLFi3CokWLEBYW5tbMubTjIoQoc+iHy8XGxiIwMBB//fWX2/QrE8ygoCB0794du3fvRosWLUp9f9T0P5aIysM7TkRe5s4778SyZcswYMAAPPzww2jfvj2USiXOnDmDX375BUOGDMEtt9yCjIwMjBgxArNnz4ZSqUSvXr2wf/9+vPHGGyWa/5Xmgw8+wKBBg9ChQwdMmTIFSUlJOHXqFNatW+dKxoovDN955x2MGjUKSqUS6enppf5XfOTIkfjggw8watQonDhxAs2bN8evv/6Kl19+GQMGDECvXr2q90BVUXp6OsaPH4/33nsPcrkc/fv3x4kTJ/Dcc8+hXr16mDJlitvykZGRmDhxIk6dOoVGjRphzZo1mD9/PiZOnOi6wB44cCDeeustDB8+HOPHj0dubi7eeOONUu9SAM4LpcGDB2PGjBmIj4/Hp59+iszMTLz66qvVMo5X8+bNsXHjRnz//feIj49HSEiI2wX5pEmT8Nprr2HXrl34+OOPK7TOKVOmYMmSJRg4cCCef/55JCcn44cffsCcOXMwceJENGrUqNJxLliwAHXq1MHjjz9eal+7kSNH4q233sLevXvd+oTt2rWr1EFqmzRpUu5r32g0uvpJGI1GHDt2DKtWrcLq1avRtWtXzJs3z7Vsp06dMH78eIwZMwZ//PEHunTpAq1Wi6ysLPz6669o3rw5Jk6c6Fq+Iq+Vir6/K+N///sfvvvuO/To0QPTpk1DUFAQPvjgA+j1+kqt52rkcjlmzpyJ+++/H7fffjvGjh2L/Px8zJw5E/Hx8eX2pans+04qjRs3RmpqKp566ikIIRAREYHvv/8emZmZJZb9+OOP8emnn2LRokVo2rQpmjZtismTJ2Pq1Kno1KmTq49W06ZN0bNnT/Tv3x+pqakwmUzYvn073nzzTcTGxrpKggPAtGnT8P333+P666/HU089hYYNGyI7Oxvz58/Hzp07SySuxUaOHIlnnnkGr7/+OsLDw3HrrbdWet/Hjh2LRx99FIcOHcL9998PjUbjmte7d2+oVCrcddddePLJJ2EymTB37lzk5eWVu97ifoILFy5EamoqWrZsiR07duCzzz4rsew777yDG2+8EZ07d8bEiRORkpKCoqIiHD16FN9//32V+1ISVRvp6lIQ1U5llSO/0qhRo4RWqy11ntVqFW+88YZo2bKlCAwMFMHBwaJx48bi/vvvF0eOHHEtZzabxWOPPSZiYmJEYGCg6NChg9i2bZtITk4ut6qeEM6qYf379xdhYWFCrVaL1NTUElX6nn76aZGQkCDkcrnbOq6sziWEELm5uWLChAkiPj5eBAQEiOTkZPH000+XKEeNMipHXRl3acoqR36lq50Hu90uXn31VdGoUSOhVCpFVFSUGDFihDh9+rTbcsVV2DZu3CjatWsn1Gq1iI+PF88880yJ0t0LFy4U6enpQq1WiwYNGohZs2aJBQsWlKhqVlxx7uuvvxZNmzYVKpVKpKSkiLfeeqvU/axKVb09e/aITp06iaCgIAGgxHkSQohu3bqJiIgIt/LX5Tl58qQYPny4iIyMFEqlUqSnp4vXX3+9ROWuilTVKy4f/8gjj5S5zD///CMAiAcffFAIcfWqegBEZmbmVbdZXK2t+KHVakWDBg3E7bffLpYvX15mBbKFCxeK66+/Xmi1WqHRaERqaqoYOXKk+OOPP9zWXdHXSkXf32Udx9Lee7/99pvo0KGDUKvVIi4uTjzxxBPio48+qnBVvdLeT7ii4pkQQnz00UciLS1NqFQq0ahRI7Fw4UIxZMgQ0bp161KP3eUq+767Ummv9dKU9vlS1n4WfzYuX77cNe3AgQOid+/eIiQkRNSpU0fccccd4tSpU27H46+//hIajabE55XJZBJt27YVKSkpIi8vTwjhLON+6623igYNGoigoCChUqlEamqqmDBhQol9F0KII0eOiBEjRrg+R8PDw0WfPn1KVJm80i233FJq5cKKunjxolCpVAKA2LFjR4n533//ves1m5iYKJ544glXJcrLv1tKO08FBQXi3nvvFbGxsUKr1YpBgwaJEydOlPoaO378uBg7dqxITEwUSqVSREdHi44dO4oXX3yxSvtFVJ1kQpQxOiMREdVKFy5cQHJyMh588EG89tprUodTK3Tr1g05OTlu/VX8QX5+Pho1aoSbb74ZH330kdThEBHVKDbVIyLyE2fOnMGxY8fw+uuvQy6X4+GHH5Y6JPIh2dnZeOmll9C9e3dERkbi5MmTePvtt1FUVMTXEhH5BSZORER+4uOPP8bzzz+PlJQULFu2zK0aI1F51Go1Tpw4gUmTJuHSpUsICgpChw4dMG/ePDRt2lTq8IiIahyb6hEREREREZWD5ciJiIiIiIjKwcSJiIiIiIioHH7Zx8nhcODcuXMICQlxDepGRERERET+RwiBoqIiJCQkXHVcOr9MnM6dO4d69epJHQYREREREXmJ06dPo27dumXO98vEKSQkBIDz4JQ3yjyVzWq1Yv369ejTpw+USqXU4VApeI68G8+Pd+P58X48R96N58e78fz8p7CwEPXq1XPlCGXxy8SpuHleaGgoE6drYLVaERQUhNDQUL9/w3krniPvxvPj3Xh+vB/PkXfj+fFuPD8lldeFh8UhiIiIiIiIysHEiYiIiIiIqBxMnIiIiIiIiMrBxImIiIiIiKgcTJyIiIiIiIjKwcSJiIiIiIioHEyciIiIiIiIysHEiYiIiIiIqBxMnIiIiIiIiMrBxImIiIiIiKgcTJyIiIiIiIjKwcSJiIiIiIioHEyciIiIiIiIyhEgdQBE5CccDuDoUaCgAAgLA9LSADn/d1MtLj+2ISHOaUVFNXuceT6JiKiqfPQ7hIkTEdW83buBTz4BDh4ETCYgMBDIyABGjQJat5Y6Ot92+bHNyXE+ACAqyvmoiePM80lERFXlw98hkqd2mzdvxqBBg5CQkACZTIZVq1aV+5xNmzahbdu2CAwMRIMGDTBv3ryaD5SIqmb3buD554Fdu4CICKBhQ+fPXbuc03fvljpC33X5sZXJgNxcwGBwPnJynNOq+zjzfBIRUVX5+HeI5ImTXq9Hy5Yt8f7771do+ePHj2PAgAHo3Lkzdu/ejWeeeQYPPfQQvvnmmxqOlIgqzeFw/lcpJ8f536TQUEChcP7MyHBOX7LEuRxVzuXHtnFj4OxZwGx23mWKjHT+fu6cc151HWeeTyIiqqpa8B0ieVO9/v37o3///hVeft68eUhKSsLs2bMBABkZGfjjjz/wxhtv4Lbbbiv1OWazGWaz2fV3YWEhAMBqtcJqtVY9eD9XfOx4DL2X5Ofo6FHnIyUFUCpLzk9JAY4cAQ4dcrZv9jPXdH4uP7ZGo7O5Q0TEf8c5IsI53WCovuPsZ+dT8vcPlctXzpFDOGBz2Mp82IXd+dNhh138/8Nhh0M4/pv2/z8dwvHfz/9fpvhRPL34ISD++12U/L14fom/ISCEcJt/+bTyfgKAEAJ2hx3Hso7htw2/QS6Xu5YBUOL3///F7fmXzyvteWXNv9zly145/2rzrlTaNiv7vMq42jqv+rxKbM/hcODcuXP45rtvIC+nf1FV43FTWAjY/gDaqwCls1l5U1sEphhbOedL+B1S0c8QmajqGa0BMpkMK1euxM0331zmMl26dEHr1q3xzjvvuKatXLkSQ4cOhcFggLKUL/MZM2Zg5syZJaZ/9tlnCAoKqpbYiYiIyHtYHVaYHWaYHWaYHCbX72ZhhsVhcT6Exe13q8MKq7DC4rDAJmywCuffxdNt4v+THGFzzndYXb8XT3f9xH9JULVcdBLVQq1DWmN66nSpw4DBYMDw4cNRUFCA0NDQMpeT/I5TZWVnZyM2NtZtWmxsLGw2G3JychAfH1/iOU8//TQeffRR19+FhYWoV68e+vTpc9WDQ1dntVqRmZmJ3r17l5qwkvQkP0dHjwJPPAHUqeO8FX+lwkIgLw94/fVacYeisq7p/Fx+bIUAtm8HVCqcD5Hh71AzjMIKhcUGNG4EyORAkQ4YNwaIS6h6wNnngAWLgJBgQKMpOd9orJ7teAlhFxDHBGQNZJApZFKH4zdsDhuKLEXQWXTQW/XOh8X502A1QGfVwWA1wGA1wGQ1wVBkgElpgtFmhNFmhMlmgslmgl3Ypd6Vcskhh1wuh0KmgFz238/yHjKZzPk73P+WQQaZTAaFTAGZTAYZZP/NhxyQwbWMDM7XtMw50cU1Tzh/v3yZy59b6rQrtyNkUBQpIEIFZHKZa5+L1+tarpT1FW/XLQa4x3T5c66M021frtjP4mlX/n55TJdvq8xlrzxmZbhyPWXNu3IdV1tnVZa77AkAAOEQ0GXpEBwf7Do/NcEVX0EB8OuvgFoNqFQAgGYFYRjw73rnfAmvCYpbo5XH5xInoOQLsPimWVkvTLVaDbVaXWK6UqnkBX814HH0fpKdo/R054ffrl3O9suXv0eFAE6cANq1cy7nA2VIa0qVzs/lx7ZxYyAwEGeM57EvRg25RaBejtHZXE8R5jzOTTKA9DbOJKqqwuKAuI3AwX+A+iklz+ep3OrZjpdw2B04h3OID4+HXOH7+yMVi92CS8ZLrkeuMdf1e54xD/mmfBSaC1FgLkC+KR96q75at6+QKaBRahAYEAhNgPOnSqGCOkCNQEUg1AFq598KNdQBaijlSqgUKtdDqXD+rZQroVQonT////cAeYDrp+sh++93hVzhNs+VIMkVruSmooQQ7k34/v93AeE2rbg5XvFzZDKZW1M4mey/BEcmk0EhV7j+lv//+7Y4QVPIFFDIFZDL5QiQ/X/8cue8AHkA5JD/9/zLErfihM1hd+DPzX+ibde2UAYo3RKsq/0E4DYNKCXhu+L34mXKmkclWa1WrFmzBgP6DfDMNYLDAex4FPjjymsCm+TXBBXdf59LnOLi4pCdne027cKFCwgICEBkZKREURFRqeRyZ3nRkyedZUfr1gWCgpz9bs6ccRYyGDnSr5OmKrvs2Ip/DuJU/Qjsz82GKr8QEWa5s7xrdJTziyg8HBg48NqTGZkcuOkmICsbOH4CiIlxbsdkAi5cqL7tkM8w28zI0mUhW5eN8/rzuKi/iPP687igv+D6vcBcUOn1yiBDiDoEIaoQBKuCEawKdv0eonb+DFIGQaPQwHzWjLoN60Kr1iJIGeR6FCdJSoV3/mPP5rDBZre59WG6vL+TqyfFZXdJihMXhVwBBf5LaDRKjSvhK07qipMzVxIkr/xdrWtV3G8kVhvLf7BSrbgm8LnE6YYbbsD333/vNm39+vVo164d35RE3qh1a2DatP/GbDh3znmx3a6d8wPSy8ds8GqtW8Px3P9w7NN3ceDsXwjW1kGYsQgIhDOJEXDeARo4EEhvXD3bTG8M3HcvsHq1M3nKuQio1NW/HfIaBaYCnCg4gdMFp3G26CzOFp7FuaJzOFt0FhcNFyu0jgB5ACI0EagTWAeRmkhEaCJcj/DAcISpwxAaGIowdRjCA8MRogqBQq4od70OuwPnDOeQkJTgNXcFHcIBq93ZL6q4+IPVbnX2dRLCmQgJuN2NUsgVUAWoEBIQ4nYX7PI7VZffwSq+E1T8k8hn+Pg1geSJk06nw9GjR11/Hz9+HHv27EFERASSkpLw9NNP4+zZs1iyZAkAYMKECXj//ffx6KOP4r777sO2bduwYMECfP7551LtAhGVp3VroGVLnxwl3JvZHXYcSdLi0L03Izy3F4LNAgjSOmca9EBwMFCvXvXfAUpvDDRqBJw+Deh0Nbcd8hghBM7rz+PfvH9xIv+E2yPPlHfV5wYpgxAfHI9YbSxitDGI1kYjVhvr+hkVFIUwdVitaTIlhIDF7iwkYbFbYLE7C0kIh7NZHGRwa84XrA6GJkADTYDG1fRPKf+vmV/x70yAyG/48DWB5InTH3/8ge7du7v+Li7iMGrUKCxevBhZWVk4deqUa379+vWxZs0aTJkyBR988AESEhLw7rvvllmKnIi8hFzuvNimamFz2HAo5xCO5B5BpDYKQeFJng1AJgeSkj27TaoWNocNpwpO4VDuIRzKOYTDuYdxKPfQVZvUxWpjkRyWjMTQRCSGJCIhJAEJIQmoG1q3ViVFl7ParTDbza7kyGq3ugoHKBVKqOTOflJRQVEIVgW77hJd2UeqNh4bomvmo9cEkidO3bp1u2rN+cWLF5eY1rVrV/z55581GBURkXc7U3gGh3MPI0Ybg8CAQKnDIS+Wa8jF3vN7sff8Xvx1/i8czj0Ms91cYjmFTIHksGSk1ElB/fD6SAlPQUpYCpLDkxGkrL1Dd9gddlclPrPdDLvDWY2vuCiEOkCNGG0MQtQhrgISlxeSYGJE5D8kT5yIiKjyLugvQK1QM2kiN0IIHMs7hj3n92BvtjNZOlt0tsRymgANGkY2RHpkuuvRoE4DqANKVqCtTWwOmytJMtlNcDgcUMgVzop7Sg0SQhMQrAouUYGPyRERAUyciIh8jtlmRoGpAFqVVupQyAvkm/Kx/ex2/H7md/x+5vcSBRtkkCE1IhUtY1uiRWwLNItuhnph9Vylp2srIQTMdjOMViMMVgPswo4AeQA0ARqEqcOQrEl2VecLUgZBrVAzQSKiq2LiRETkY4osRTDYDAhTh0kdCknA7rDjr/N/YduZbfj9zO84mHPwv3F6AKgVarSIbYGWsS3RMrYlmsc2R7AqWMKIPUMIAZPNBL1VD6PVCMicxyJIGYQGIQ0Qpg5DsCoYWpUWKoVK6nCJyAcxcSIi8jE6iw5CCFbh8iM2hw27s3bjp+M/4ZcTv+CS8ZLb/IYRDdGhbgd0qNsBrWJb1fomd8XMNmdfrXNF5yBkAoHKQISqQ5FaJxXB6mDXHaXafneNiDyDiRMRkY/JMeRAKee4dbWdzWHDn1l/4qdjzmTp8rLgoepQdKzb0ZUsRQVFSRip5wghoLfqUWQugtVhhRLO90FqnVREBkciVB2KIGUQm9wRUY1g4kRE5EMsdgvyjfnQKtm/qbY6nnccK/9ZiR+P/uiWLIWpw9AtpRt61e+F6xKvQ4DcP77C7Q47dBYddFYd7A47tCotEkISEBMcgyBFELYc3oL0qHQolfxnAhHVLP/41CUiqiWKzM7+TbHaWKlDoWpkspnw8/GfseqfVdidvds1PUwdhh71e6Bn/Z5ol9DOr5KlIksRdBYdACBYFYz64fURFRSF8MBwaJQaAIDVapUyTCLyM/7xCUxEVEvoLM7/uvvLBXRtd/TSUaz6ZxV+OPIDiixFAJzjKd2YdCNuaXwLOtTt4DfnurgZXoGpAAICIeoQpEelI0ITgfDAcBZ0ICLJ+cenMRFRLZFryOUFpI8TQuCPc39g0Z5F2HFuh2t6fHA8hqQPweD0wYjRxkgYoWeZbWYUmAtgtBmhVWmRFJ6EuOA4RGgi+FonIq/CxImIyEdY7VbkmfIQpAySOhSqAodwYPPJzVi0ZxH+vvg3AOfdpS7JXXBr41vRPrG931RKFEKgyFKEfFM+VAoVIjQRaBraFJGaSI5PRkRei4kTEZGPKLIUwWA1+NXdiNrA5rBh/b/rsXjvYhzLOwbAOb7QkPQhuKfFPYgPiZc4Qs+xOWzIN+XDYDUgRBWCjOgMxGpjER4Yzkp4ROT1mDgREfkInUUHm8PmN31efJ1DOPDDkR/w8Z8f42zRWQCAVqnF0KZDcWfTOxEZFClxhJ5jtpmRZ8qDzWFDeGA4Gkc1Row2xlXkgYjIF/Dbl4jIR1wyXuL4TT7ij3N/4O3f38ah3EMAgDqBdTC8+XDc0eQOBKuCJY7Oc0w2E3IMOVDIFIgJjkG90HqI1kYz+Scin8RPLiIiH2Bz2HDJeIn9m7zc6YLTeGf7O9h4ciMAZxntca3H4Y4mdyAwIFDa4DzIZDMhx5iDAFkAksOTUS+0HiI0EWyOR0Q+jYkTEZEP0Fl0MFgMiAqKkjoUKkWRuQgf7/4YX/79JWwOGxQyBW7NuBXj24xHHU0dqcPzGLPNjBxjDuSQIyk0CUlhSUyYiKjWYOJEROQDisxFsDlsUCrYVM+bCCGw6tAqvL/jfRSYCwAAHet2xCMdHkGDOg0kjs5zLHYLcgw5EBBIDElEcngyIjWRTJiIqFZh4kRE5AMuGS/5TalqX5Gty8YLm1/A9rPbAQANwhvgkQ6PoGO9jhJH5jkO4UCOIQcWuwUJIQlIDk9GdFA0EyYiqpWYOBEReTm7w87+TV5ECIFvD32Lt39/G3qrHmqFGhPbTcSdze70q6IHReYiXDJdQqQmEi3jWiIuOA5ymVzqsIiIaoz/fMITEfkonUUHg9WACE2E1KH4vfO683hpy0vYemYrAKBFTAtM7zodyeHJEkfmORa7BRf0FxAYEIhmMc2QHJYMdYBa6rCIiGocEyciIi9XZCmC1WGFSqGSOhS/JYTAD0d+wBvb3oDOooNKocLEdhMxvNlwv2lC6RAO5BpyYbabUTe0LlIjUhEeGC51WEREHsPEiYjIy+Wb8iEHm0BJRWfR4fktz7tKjDeNbooZXWegfp360gbmQQarARcNFxGpiUTz2OaID4lnszwi8jtMnIiIvJjdYUeuIRdalVbqUPzSadNpvPbdazhdeBpKuRL3t70fI1qM8Ju+TEII5BhyYHVY0TiyMRpENPCr8aiIiC7nH5/8REQ+Sm/VQ2fRoU6g/4wF5C02nNiAGYdnwOQwIVYbi9d7v44m0U2kDstjLHYLsnXZqBNYBy2jnMUfWC2PiPwZEyciIi9WZC6C1W5l53sPsjvsmLdrHhbtWQQAaBvfFq/0fMWvBrLNN+WjyFKElPAUNIpsxDueRERg4kRE5NUKTAX8L78HFZgK8L9f/odtZ7YBAIZED8HUvlOhUvpHYQ6bw4ZsfTYCAwLROq416oXVY18mIqL/x8SJiMhLOYQDFw0XoVXyv/2ecDj3MJ7IfAJni85CrVDjfzf+D80LmvtNfyaj1YgLhgtICElA46jGrJhHRHQF//g2ICLyQXqLHnqrHmHqMKlDqfW2n92Ox9c/DqPNiMSQRLze+3Wkhafh3J/npA7NI/JN+dBZdGgc2RgNIxtCqVBKHRIRkddh4kRE5KWKLEWw2C2sYlbDfjn+C57Z8AysDivaJ7THrJ6zEBYYBofdIXVoNU4IgQv6C5DJZGgV1wpJYUlsGkpEVAYmTkREXqrQXMiL2Bq2+vBqPL/5eTiEAz3q98CL3V/0m4GG7Q47snRZCFYFo3lsc8RoY6QOiYjIqzFxIiLyQkII5OhzoFFopA6l1vpi/xd4Y9sbAIDBjQbjmc7P+E1/JovdgixdFuKD49E0pilC1aFSh0RE5PX84xuCiMjHGG1G6K16BCmDpA6l1hFCYP6f8/HRnx8BAO5ufjceuf4Rv7m7p7fokWvMRf3w+siIzmBTUCKiCmLiRETkhXQWHUw2EyI0EVKHUqs4hANv//42Pt//OQBgQtsJGNd6nN8kTQWmAuisOmREZyAtIs1v7rAREVUHfmISEXkhvUUPh3BwDJ1qZHfY8eKWF/H94e8BAE90fALDmg6TOCrPyTflw2g1okVsCySHJftNskhEVF2YOBEReaFcYy7UCrXUYdQaQgi8tvU1fH/4eyhkCkzrOg0DGw6UOiyPyTPmwWw3o0VcCySFJUkdDhGRT2LiRETkZax2KwpMBdAoWRiiunz050f45uA3kEGGF7u/iN6pvaUOyWNyDbmwCRtaxrVE3dC6UodDROSz2AaEiMjL6Cw6GK1GFoaoJl/+/SXm/zkfADC101S/SppyDDlwwIFWca2YNBERXSMmTkREXkZv1cPqsLLjfjVYe3Qt3tjqLDk+oe0E3N7kdokj8pwL+guADGgZ2xIJIQlSh0NE5PP4rUxE5GXyTflQyBRSh+Hztp3ehukbp0NAYGiToRjXepzUIXlMti4bKoUKLWJbIDY4VupwiIhqBSZORERexCEcyDXkspneNdp/YT+e+OkJ2IUdfVL74PGOj/tNFbnzuvNQK9RoGdcS0dpoqcMhIqo12FSPiMiLGKwGGKwGFoa4BsfzjuPhtQ/DZDOhQ2IHzOw602/KuucacqGQK9AirgWTJiKiauYf3yRERD5Cb9HDbDezFHkVXdRfxOQfJ6PAXIBmMc3wWu/XoFQopQ7LIwpMBbA6rGgW0wwx2hipwyEiqnWYOBEReZEicxEg4DfNyqqTxW7Bkz89ifP680gJT8HsvrP9psmj3qJHkaUITaKbIDE0UepwiIhqJSZOREReJMeYg8CAQKnD8ElvbXsL+y7sQ4gqBLP7zkZ4YLjUIXmEyWbCJeMlNI5qjJTwFKnDISKqtZg4ERF5CbPNjCJzEfs3VcH3h7/H1we/dg5w2+NFvxmzyGq34rz+PFIjUpEWkcY7lURENYiJExGRl9Bb9TDajLzjVEn/5PyDWb/OAgDc3/Z+dKrXSeKIPMPmsOGc7hzqh9dH46jGUMhZwp6IqCYxcSIi8hI6iw52h50D31ZCvikfT2Q+AYvdgs5JnTG29VipQ/IIh3AgS5eFxJBEZERn+E0BDCIiKTFxIiLyEnnGPCjlvACuKLvDjmc2PIMsXRaSQpPwQvcX/KbseLYuG1GaKDSLacY7lEREHuIf3zBERF7O7rDjkvES+zdVwtw/5mLH2R3QBGjwWu/XEKwKljokj7hkvAR1gBpNY5pCq9JKHQ4Rkd9g4kRE5AWK+zdpApg4VcTPx3/G4r2LAQDTukxDWkSatAF5iNFqhMFqQEZUBupo6kgdDhGRX2HiRETkBfQWPcw2M9QBHPi2PCfyT2DmppkAgHta3IPeqb0ljsgzbA4bLhguIC0izW+qBhIReRMmTkREXqDIXOQ3/XOuhc1hw7RfpsFgNaBdfDs8cN0DUofkEUIIZOuykRiSiIaRDVl2nIhIAvyWJiLyAhz4tmIW7VmEAzkHEKoOxQvdX/CbCoQ5hhwEq4LRJLoJVAqV1OEQEfklJk5ERBIzWU3QWXTs31SOAxcP4OM/PwYATO00FdHaaIkj8gydRQe7sKNpTFOEqEOkDoeIyG8xcSIikpjepofRamRFvasw2UyYvnE67MKO3g16o29qX6lD8gir3YpcYy4aRTZCXHCc1OEQEfk1Jk5ERBLTW/QQEOzjdBVz/5iL4/nHEamJxNROU6UOxyOKB7mtH14fDeo0kDocIiK/x29pIiKJ5ZvyOfDtVezK2oXP9n0GAHiuy3MIDwyXNiAPuaC/gAhNBNKj0qGQK6QOh4jI7zFxIiKSWL4pn/2byqCz6DBz40wICNzS+BbcmHSj1CF5hM6iAwBkRGcgSBkkcTRERAQwcSIikhz7N5Xt7d/fxjndOSSGJOKR6x+ROhyPsDvsyDXmIjUiFTHaGKnDISKi/8fEiYhIYla7lSWmS7H55GZ8e+hbyCDD9K7ToVVppQ7JIy7oLyBWG8t+TUREXoaJExGRxORyfhRfKd+Uj5e2vAQAuLv53WgT30biiDxDZ9FBJpOhUWQjJtNERF6G39ZERBIRQgAAAhUc+PZKb217C7nGXDQIb4CJ7SZKHY5HFDfRS4tI85sxqoiIfAkTJyIiiZhsJgBg/6Yr/Jn1J9YcXQMZZJjWdRrUAWqpQ/KIC/oLiAuOQ/069aUOhYiISsHEiYhIInqrHgD8JjGoCJvDhld/exUAcHPjm9EsppnEEXmGzqKDXC5nEz0iIi/GxImISCIGqwEAOPDtZb76+yv8m/cvwtRheOC6B6QOxyNcVfTqpCIqKErqcIiIqAz8tiYikkiBqUDqELxKjiEHH+76EAAwuf1kvxno9rz+POKD49lEj4jIyzFxIiKSgN1hR54pT+owvMo729+B3qpH0+imGJI+ROpwPEJn0UEhV6BhZEM20SMi8nJMnIiIJKC36mG0GqUOw2v8mfUnfjz6I2SQYWqnqX7RfNEhHK4qemyiR0Tk/Wr/NxMRkRfSW/Sw2q1Sh+EVLi8IcWvGrWgS3UTiiDwj15CLSE0kksOSpQ6FiIgqgIkTEZEEigc6JeDLv790FYSY1G6S1OF4hMVugdluRsPIhqyqSETkI5g4ERFJINeQC7WCF8wX9Rfx0a6PAAAPtn8QYYFhEkfkGRcMF1A3tC7iguOkDoWIiCqIiRMRkYeZbWYUWYo48C3+KwjRLKYZBqcPljocj9BZdFDJVWhQp4Ff9OUiIqot+IlNRORheqseRpvR75to/XHuD6z9dy1kkOGpTk/5RRIhhECuMRcp4Smoo6kjdThERFQJtf9biojIy+gtetgddgTIA6QORTIO4cBbv78FALgt4zY0jmoscUSekWfKQ5g6DCnhKVKHQkREleQVidOcOXNQv359BAYGom3bttiyZctVl1+2bBlatmyJoKAgxMfHY8yYMcjNzfVQtERE16bAXACFTCF1GJJa/+96HM49DK1SiwntJkgdjkfYHDboLDo0jGzIZppERD5I8sTpyy+/xCOPPIJnn30Wu3fvRufOndG/f3+cOnWq1OV//fVXjBw5EuPGjcPff/+N5cuXY+fOnbj33ns9HDkRUeU5hAO5hlwEKYOkDkUyVrsVc/+YCwAY2XIkwgPDpQ3IQy7qLyI+JB4JIQlSh0JERFUgeTuRt956C+PGjXMlPrNnz8a6deswd+5czJo1q8Tyv//+O1JSUvDQQw8BAOrXr4/7778fr732WpnbMJvNMJvNrr8LCwsBAFarFVYrx1GpquJjx2PovXiOvI/BYoDBbECwKhgOuwMAXD/9xcqDK3G26CwiNBG4M+NOr93/6jw/RqsRwi6QHJIMYRccw6ua8DPOu/H8eDeen/9U9BjIhBCihmMpk8ViQVBQEJYvX45bbrnFNf3hhx/Gnj17sGnTphLP2bp1K7p3746VK1eif//+uHDhAoYOHYqMjAzMmzev1O3MmDEDM2fOLDH9s88+Q1CQ//7Xl4jI04x2IyYenIh8Wz7G1x2PAVEDpA6JiIj8nMFgwPDhw1FQUIDQ0NAyl5P0jlNOTg7sdjtiY2PdpsfGxiI7O7vU53Ts2BHLli3DsGHDYDKZYLPZMHjwYLz33ntlbufpp5/Go48+6vq7sLAQ9erVQ58+fa56cOjqrFYrMjMz0bt3byiVSqnDoVLwHHmfE/kn8PeFv5EYmgiH3YHsvdmIaxkHuULyltMesXDPQuTb8pEYkohRPUdBqfDe12V1nZ8CUwEcwoH2ie2hVWmrMULiZ5x34/nxbjw//ylujVYeyZvqAYBMJnP7WwhRYlqxAwcO4KGHHsK0adPQt29fZGVl4YknnsCECROwYMGCUp+jVquhVpcs+6tUKv3+hVIdeBy9H8+R9yiwFkClVLldiMsVcr9InPJN+Vi6bykAYGK7iVCrfKMc+7WcH4dwoNBWiJaxLRGuDa/ewMiFn3HejefHu/H8oML7L2niFBUVBYVCUeLu0oULF0rchSo2a9YsdOrUCU888QQAoEWLFtBqtejcuTNefPFFxMfH13jcRERVYbVbUWAq8NuKaov2LILeqkejyEbok9pH6nA8Is+Yh4jACNQNrSt1KEREdI0k/RenSqVC27ZtkZmZ6TY9MzMTHTt2LPU5BoMBcrl72AqFs6yvhN21iIjKpbfqYbKZoAnwv8QpW5eN5QeWAwAmXzfZLwa7tTvs0Fl1qF+nvt8PdkxEVBtI/s316KOP4uOPP8bChQtx8OBBTJkyBadOncKECc5xPZ5++mmMHDnStfygQYOwYsUKzJ07F8eOHcNvv/2Ghx56CO3bt0dCAku8EpH30lv0sNqtXt2vp6Z8uOtDWOwWtI1vixvq3iB1OB6RZ8pDpCYS8SFsCUFEVBtI3sdp2LBhyM3NxfPPP4+srCw0a9YMa9asQXJyMgAgKyvLbUyn0aNHo6ioCO+//z4ee+wxhIeHo0ePHnj11Vel2gUiogopshRBJi+9/2ZtdizvGH448gMA592msvqw1iZ2hx0GqwFNoptApVBJHQ4REVUDyRMnAJg0aRImTZpU6rzFixeXmPbggw/iwQcfrOGoiIiqjxACuYZcBCoCpQ7F4+bsnAOHcKB7Snc0j20udTgeccl4CVFBUYgLjpM6FCIiqiaSN9UjIvIHJpsJOqvO7/o37Tu/DxtPboRcJsekdqX/g6y2sTlsMNqMqF+nvl82yyQiqq2YOBEReYDeqofJavK7inpz/pgDALip4U2oX6e+xNF4Rq4hFzHaGN5tIiKqZZg4ERF5gN6ih0M4/KKaXLG/zv+Fned2QiFTYHzb8VKH4xE2hw1WhxX169RHgNwrWsMTEVE18Z9vcCIiCeWb8qGU+1ezrUV7FgEABjYc6Dd3X3IMOYjRxiBWW/pYhERE5LuYOBER1TC7w45Lxkt+1UzvcO5hbDm1BXKZHKNbjZY6HI+w2q2wOWxICU+BQq6QOhwiIqpmTJyIiGqYwWqA0WZEYID/VNQrvtvUq0EvJIUlSRyNZ+QYchAbHIsYbYzUoRARUQ1g4kREVMP0Vj0sNovfJE4n80/ip2M/AQDGtBwjcTSeYbFb4IAD9cPr824TEVEtxcSJiKiG6cw6qUPwqMV7F0NAoHNSZzSMbCh1OB6RY8hBfHA8orXRUodCREQ1hIkTEVENyzXl+s3dpqyiLKw5sgYAMLbVWImj8QyL3QIBgeTwZL+qmkhE5G/4CU9EVIMsdguKTEV+Uxhi6V9LYRd2XJdwHZrHNpc6HI+4ZLyEGG0MooKipA6FiIhqEBMnIqIapLfo/aYwRK4hF98e+haA/9xtsjlssDlsSApL4t0mIqJajp/yREQ1SG/Vw+aw+cVgqMv2LYPZbkbzmOZol9BO6nA8It+UjwhNBCvpERH5ASZOREQ1qNBU6Bd3IgrNhfj64NcAgDGtxkAmk0kcUc1zCAf0Vj2Sw5P9IjEmIvJ3tf/bnIhIIkII5BpzoQmo/f2bvvz7SxisBjSMaIjOSZ2lDscjCkwFCFOHIVYbK3UoRETkAUyciIhqiNFmhMFqqPWFIQxWA77Y/wUA/7nbBACFlkKkhKdAHaCWOhQiIvIAJk5ERDVEb9HDZDPV+sIQKw6uQIG5AEmhSehZv6fU4XhEkbkIwapgxAXHSR0KERF5CBMnIqIaorfq4RCOWt3HyWq3Ytm+ZQCAUa1GQSFXSByRZ+Sb81E3pC60Kq3UoRARkYfU3m9zIiKJ5RnzoFKopA6jRv10/CdcNFxEpCYSA9IGSB2ORxisBqgVaiSEJkgdChEReRATJyKiGmB32JFnyqvVzfSEEPh83+cAgDua3AGlQilxRJ5xyXQJ8SHxCA8MlzoUIiLyICZOREQ1QG/Vw2g11uqKen9d+AsHcg5ApVDhtozbpA7HI8w2M+SQo25oXalDISIiD2PiRERUA/QWPSx2S62uuFZ8t6l/Wn/U0dSROBrPyDPlITY4FhGaCKlDISIiD2PiRERUA3QWXa0uy52ty8YvJ34BANzV7C6Jo/EMm8MGm8OGpLCkWl3wg4iISsdPfiKiGpBryEWgovb2b/rq769gF3Zcl3Ad0iLSpA7HI/KMeYjURCIqKErqUIiISAJMnIiIqpnZZkaRpajWDnxrtBqx8p+VAPznbpNDOGC0GZEcnowAeYDU4RARkQSYOBERVTO9VQ+jzVhrK+r9cOQHFFmKUDe0Lm5MulHqcDyi0FyIUHUoYrQxUodCREQSYeJERFTN9BY97A57rbwz4RAOfPH3FwCAO5ve6Td9fYrMRagXVq9WF/sgIqKr849vPCIiDyowF0AhU0gdRo34/czvOJF/AlqlFoMaDZI6HI8w2UxQBah4t4mIyM8xcSIiqkZCCOQacmtt/6bP9ztLkA9JHwKtSitxNJ6Rb8xHjDYGYeowqUMhIiIJMXEiIqpGBqsBRlvtHPj2eN5xbDuzDTLIMLTpUKnD8Ri7sCMxJLFWl5cnIqLyMXEiIqpGeqseJqupVhaGKO7b1DW5K+qG1pU4Gs8JU4exBDkRETFxIiKqTnqLHgBq3d2JAlMBVh9eDQC4q7l/lCAvlhiaCKVCKXUYREQkMSZORETV6JLxUq28yF75z0qY7WY0imyENnFtpA7HI4xWIwAgSsu7TURExMSJiKja2Bw25Jvya13/JpvDhuUHlgNwDnhb2+6mlSXflA8ACFGFSBsIERF5BSZORETVRG/Rw2Qz1bqKer+e+hXn9ecRHhiOPg36SB2OR9gcNgghpA6DiIi8CBMnIqJqorfqYbFboFKopA6lWq34ZwUAYFCjQX4zAGy+KR9hgSw/TkRE/2HiRERUTYrMRZDLatfH6rmic9h2ehsA4NbGt0ocjeforXrUC6sndRhERORFatc3PBGRhC4ZL9W6MuSr/lkFAYH2Ce39JpHQWXTQqrSI1ERKHQoREXkRJk5ERNXAZDNBZ9HVqsTJ5rDh20PfAgBuzfCfu0355nzEB8dDq9JKHQoREXkRJk5ERNVAb9HDaDPWqop6m05uQq4xF5GaSHRL6SZ1OB5htVsBAPHB8RJHQkRE3oaJExFRNdBb9XAIBxRyhdShVJsVB51FIQanD0aAPEDiaDwj35SPyMBIRGgipA6FiIi8DBMnIqJqUGAqgEJWe5KmM4VnsP3sdsggw83pN0sdjkcIIWCwGZAUnlSrEmAiIqoeTJyIiK6RQzhwyXipVjXTW/nPSgBAh7odkBiaKHE0nqGz6BCiCkFUUJTUoRARkRdi4kREdI0MVgMMVkOtGfjWarfiu0PfAQBuy7hN4mg8p9BSiLjgOAQpg6QOhYiIvBATJyKia6S36GG2m6FW1I7BYX858QvyTHmIDorGjUk3Sh2OR9gcNgghEKONkToUIiLyUkyciIiukd6qhxACMplM6lCqRXFRiCHpQ/ymKESRuQhh6jAWhSAiojIxcSIiukY5hpxaM37TyfyT+CPrD8hlctzc+Gapw/GYIksREkMToVQopQ6FiIi8FBMnIqJrYLFbUGgqrDWFIYqLQnSs2xFxwXESR+MZZpsZKoWKRSGIiOiqmDgREV0D18C3taAwhNlmxveHvwfgZ0UhzIWI0EQgLDBM6lCIiMiLMXEiIroGeqseNoetVvQF2nBiAwrMBYjVxqJjvY5Sh+MxBpsBCSEJkMv4lUhERGXjtwQR0TWoTQPfFheFuLnxzX4zAKzeoodWqUVkUKTUoRARkZdj4kREVEVCCOQac2tFM70T+SewO3s3FDIFhqQPkTocjykwFyBGG4NgVbDUoRARkZdj4kREVEWugW9rQWGI4gFvO9br6DdjGTmEA3Zh95siGEREdG2YOBERVZHeqofZZvb5UuQ2hw0/HPkBADCo0SCJo/GcInMRQlQhHLuJiIgqhIkTEVEV6Sw6CPj+wLe/n/kducZchAeGo3NSZ6nD8ZgiSxHig+OhDlBLHQoREfkAJk5ERFV0yXgJKrlK6jCu2XeHnc30+qf195sBYG0OG2QyGWKC/aNZIhERXTsmTkREVWC1W1FgKvD5whD5pnxsPrkZgH8108s35aNOYB3UCawjdShEROQjmDgREVWB3qqH0WpEkDJI6lCuydqja2Fz2JAemY5GkY2kDsdj9FY96obW9Zuy60REdO2YOBERVYHOooNN+P7At8XN9PzpbpPJZkJgQCDHbiIiokph4kREVAWFpkLI4NtFIQ7lHsLh3MNQypXol9ZP6nA8Jt+Uj6igKISoQqQOhYiIfAgTJyKiSnINfOvj4zd9f+h7AECX5C4IDwyXNhgPEULAYrcgISTB56shEhGRZzFxIiKqJKPNCIPV4NP9m6x2K348+iMA/2qmp7fqEawKRqSGzfSIiKhymDgREVWSzqJz9ZPxVZtPbUaBuQBRQVHoULeD1OF4TIGpADHaGJ+vhkhERJ7HxImIqJL0Fj2E8O2Bb4ub6Q1sONDnC1xUlEM44IADMVqO3URERJXHxImIqJIuGS/59ECxOYYcbD2zFYCfNdOz6BGsDEYdDcduIiKiymPiRERUCTaHDfmmfJ/u3/TDkR/gEA60iGmBlPAUqcPxmEJLIWKDY326iSUREUmHiRMRUSUU92/y1Yp6Qgh8f9jZTG9Quv/cbXIIBxzCgWhttNShEBGRj2LiRERUCXqLHha7xWeb6u2/sB8n8k9ArVCjd4PeUofjMTqLztlML5DN9IiIqGqYOBERVUKRpQhyue9+dH53+DsAQI/6PRCsCpY4Gs8pshQhNjgW6gC11KEQEZGP8t1vfyIiDxNCIEefA43CN5vpmWwmrP93PQBgcKPBEkfjOQ7hgBCCzfSIiOiaMHEiIqogo80IvU3vs2MAbTyxEXqrHvHB8Wib0FbqcDymyFyEYBWb6RER0bVh4kREVEF6ix4mq+8OfPvj0R8BAAMaDoBc5j8f/0VWNtMjIqJr5z/fnERE10hv1cMhHD6ZdOQacvH7md8BAP3T+kscjefYHXYIh0B0EJvpERHRtfG9b38iIolcMlyCSqGSOowqWX9sPezCjibRTfxq7CadRYcQdQgHvSUiomsWIHUAADBnzhy8/vrryMrKQtOmTTF79mx07ty5zOXNZjOef/55fPrpp8jOzkbdunXx7LPPYuzYsR6Mmoj8ic1hQ74532fHb/rxyP8300sbIHEknlVkLUJanTSfTXipdrHb7bBarVKH4TFWqxUBAQEwmUyw2+1Sh0NX8Kfzo1QqoVAornk9kidOX375JR555BHMmTMHnTp1wocffoj+/fvjwIEDSEpKKvU5Q4cOxfnz57FgwQKkpaXhwoULsNlsHo6ciPyJ3qKH0WpEhCZC6lAq7UT+CRzIOQCFTIG+qX2lDsdj7A47IMBqeiQ5IQSys7ORn58vdSgeJYRAXFwcTp8+DZlMJnU4dAV/Oz/h4eGIi4u7pn2VPHF66623MG7cONx7770AgNmzZ2PdunWYO3cuZs2aVWL5tWvXYtOmTTh27BgiIpwXMCkpKVfdhtlshtlsdv1dWFgIwJlp+9N/fqpb8bHjMfRePEfVp8BQAIvFggBNABx2R7Wss3g91bW+sqw+tBoA0KFuB4Spwmp8e96i0FQIrUKLYEVwld4DfP94P185R+fPn0dhYSGio6MRFBTkFxepgPPCXK/XQ6vV+s0++xJ/OT9CCBgMBly8eBF2ux2xsbEllqnoZ4hMCCGuJRiz2Qy1umqViiwWC4KCgrB8+XLccsstrukPP/ww9uzZg02bNpV4zqRJk3D48GG0a9cOS5cuhVarxeDBg/HCCy9Aoym9Cc2MGTMwc+bMEtM/++wzBAUFVSl2IiJf4BAO3H/gfly0XsTjyY/jxjo3Sh0SkV+RyWSIj49HXFwcQkJCpA6HyG8VFRUhOzsbWVlZuDL9MRgMGD58OAoKChAaGlrmOip9x2ndunX4/PPPsWXLFpw6dQoOhwNBQUFo06YN+vTpgzFjxiAhIaFC68rJySk184uNjUV2dnapzzl27Bh+/fVXBAYGYuXKlcjJycGkSZNw6dIlLFy4sNTnPP3003j00UddfxcWFqJevXro06fPVQ8OXZ3VakVmZiZ69+4NpVIpdThUCp6j6iGEwLYz22C2mau1yIDD7kD23mzEtYyDXFEztXr+zP4TF/dehFapxeCug322lHpl2R12nNedx3V1r6tyRT2+f7yfL5wjs9mMU6dOISIiosx/8NZWQggUFRUhJCSkVt/R8FX+dn6USiWKiorQo0ePEjd9ilujlafCidOqVaswdepUFBQUYMCAAXjiiSeQmJgIjUaDS5cuYf/+/fjpp5/wwgsvYPTo0XjhhRcQHV2xL6srT5YQoswT6HA4IJPJsGzZMoSFhQFwNve7/fbb8cEHH5T6oaRWq0u9K6ZUKr32g9aX8Dh6P56ja6Oz6GB0GBESGFIjCY5cIa+xxGndsXUAgB71eyBI7T932AuthQgJCkF0cDSUimt77fP94/28+RzZ7XbIZDIoFArI5f5VzNjhcDYLlslkfrfvvsDfzo9CoYBMJkNAQECJz4uKfn5UOHF6+eWX8cYbb2DgwIGlHtyhQ4cCAM6ePYt33nkHS5YswWOPPXbVdUZFRUGhUJS4u3ThwoVS2x8CQHx8PBITE11JEwBkZGRACIEzZ86gYcOGFd0lIqIK0Vl0MNlMiNJESR1KpZhtZmQeywQADGw4UOJoPEtn0SE9Kv2akyYiIqJiFU6cduzYUaHlEhMT8dprr1VoWZVKhbZt2yIzM9Otj1NmZiaGDBlS6nM6deqE5cuXQ6fTITg4GABw+PBhyOVy1K1bt0LbJSKqDJ1ZB4iSd8e93ZZTW6Cz6BCrjUWb+DZSh+MxNoezymqkJlLiSIiIqDap0n05o9FY5rysrKxKrevRRx/Fxx9/jIULF+LgwYOYMmUKTp06hQkTJgBw9k8aOXKka/nhw4cjMjISY8aMwYEDB7B582Y88cQTGDt2rN+1HSYiz8gx5Phk36AfjzrHbuqX1g9yWe1vhlFMZ9EhVB2K8MBwqUMhIqJapErfpK1bt8aff/5ZYvrXX3+NFi1aVGpdw4YNw+zZs/H888+jVatW2Lx5M9asWYPk5GQAzkTs1KlTruWDg4ORmZmJ/Px8tGvXDnfffTcGDRqEd999tyq7QkR0VSabCYWWQmiUvvWPmXxTPn47/RsA/xv0VmfRIT4kns30qNZxOIDDh4GdO50/HTU8ssDo0aMhk8nwyiuvuE1ftWqV2x14IQQ++ugjXH/99QgODkZ4eDjatWuHd955BwaDoWaDJPKgKo3j1Lt3b3Ts2BEzZszA1KlTodfrMXnyZCxfvrzEm6siJk2ahEmTJpU6b/HixSWmNW7cGJmZmZXeDhFRZeksOhhtRoSrw6UOpVIyj2XC5rAhPTIdqRGpUofjMXaHHQB8cqBioqvZvRv45BPg4EHAZAICA4GMDGDUKKB165rbbmBgIF599VXcf//9qFOn9Kqi99xzD1asWIH//e9/eP/99xEdHY29e/di9uzZiImJwV133VVzARJ5UJUSp/feew8DBw7EmDFj8MMPP+DcuXMIDQ3Fzp070aRJk+qOkYhIMjqLDkIIKOQKqUOplB+POJvpDWjoX3eb9FY9glXBbKZHtcru3cDzzwM5OUDduoBWC+j1wK5dwMmTwLRpNZc89erVC0ePHsWsWbNK7cP+1VdfYdmyZVi1apVb//SUlBTcdNNNOHPmTM0ERiSBKjd679OnD2699Vb89ttvOH36NF555RUmTURU61wyXIJS7ltNvk4XnMZfF/6CXCZH39S+UofjUUXmIkRro6FSqKQOhahaOBzOO005Oc47TKGhgELh/JmR4Zy+ZEnNNdtTKBR4+eWX8d5775WaBC1btgzp6emlFvWSyWRuVZCJfF2VEqd///0XN9xwA1avXo1169bhySefxJAhQ/Dkk0/CarVWd4xERJKw2q3IM+UhSOlb4x+tOboGAHB94vWICvKtEurXQggBh3BUecBbIm909KizeV7dusCVhT1lMuf0Awecy9WUW265Ba1atcL06dNLzDty5AjS09NrbuNEXqRKiVOrVq1Qv3597N27F71798aLL76IDRs2YMWKFWjfvn11x0hEJAm9VQ+j1QhNgO8UhhBCuKrp+WMzvSBVEJvpUa1SUODs06TVlj4/KMg5v6CgZuN49dVX8cknn+DAgQNu04UQPjdUA1FVVSlxmjNnDr744guEh4e7pnXs2BG7d+9Gmzb+M1YIEdVuOosOVofVp6qz7buwD2cKz0AToEG35G5Sh+NROosOkZpIn6uASHQ1YWHOQhB6fenzDQbn/JpuEdelSxf07dsXzzzzjNv0Ro0a4eDBgzW7cSIvUaXE6Z577il1ekhICBYsWHBNAREReYt8Uz4UMt8qCrH26FoAQLeUbn6XQFjsFsRoY6QOg6hapaU5+zKdOQMI4T5PCOf0Jk2cy9W0V155Bd9//z22bt3qmjZ8+HAcPnwY3377bYnlhRAoqOlbYUQe5D8jIhIRVYJDOJBryPWp/k02hw2Zx5xDNfRP6y9xNJ5ltBqhUWrYTI9qHbncWXI8KsrZ16mwELDZnD8PHnROHznSuVxNa968Oe6++2689957rmlDhw7FsGHDcNddd2HWrFn4448/cPLkSaxevRp9+vTBr7/+WvOBEXkIEyciolLoLXoYrAafumuz4+wO5JnyUCewDton+ld/0yJLEcIDwxGsCpY6FKJq17q1s+R427bApUvOQhCXLgHt2tVsKfLSvPDCCxCX3fqSyWT47LPP8NZbb2HlypXo2rUrWrRogRkzZmDw4MHo0aOH54IjqmFVGseJiKi201l0MNvMCNQGSh1KhRU30+vdoDcC5P718W6ymRAXHMdO6lRrtW4NtGzpTJoKCpx9mtLSavZO0+LFi0tMS05Ohslkcpsml8sxYcIETJgwwW26w+FAYWFhzQVI5GH+9c1KRFRBReYin7oIN9lM2HhyIwCgX1o/aYPxMLPNDJVCxWZ6VOvJ5UCjRlJHQeS/2FSPiOgKQgjkGHMQGOA7d5s2n9wMg9WAxJBENI9pLnU4HlVkKUKYOgyh6lCpQyEiolqsyonTwIEDkZWVVeJ3IiJfZ7KZUGQp8qnxm9b+62ym1ze1r0/dKasOBqsBccFxkMv4v0AiIqo5Vf6W2bx5M4xGY4nfiYh8nc6ig8lq8pnCEAWmAmw97SwP7G/N9GwOGxRyBepo6kgdChER1XL89xwR0RV0Fh2EED5zB+Pn4z/D5rChUUQjNKjTQOpwPKrIXIRQVSjCAmt49E8iIvJ7vnFVQETkQbnGXKgUKqnDqDBXM720vhJH4nl6qx5xIXF+V0WQiIg8j4kTEdFlLHYLCkwFPjPwbbYuG7uzdgNw9m/yJ3aHHQAQoYmQOBIiIvIHTJyIiC6js+h8auDbzGOZEBBoE9cGccFxUofjUTqLDsGqYJYhJyIij2DiRER0Gb1FD5vD5jNNv348+iMA/2ymp7PqEKON8almlURE5LuqnDhdXu7W30rfElHtlWfK85mk6VjeMRzOPQyFTIGe9XtKHY5HCSHgcDgQFRQldShEROQnqpw4CSFK/Z2IyFfZHXbkGnJ9pn/Tun/XAQA61uvod83V9FY9glRBfrff5OccDuDwYWDnTudPh8Mjm926dSsUCgX69XMf7uDEiROQyWSlPn7//XePxEbkSVX+t2pRUVGpvxMR+Sq9VQ+jzYhwdbjUoZRLCIG1R53V9Pxt7CbA2b8pPjjeZ/qiEV2z3buBTz4BDh4ETCYgMBDIyABGjQJat67RTS9cuBAPPvggPv74Y5w6dQpJSUlu83/66Sc0bdrUbVpkZGSNxkQkBd9oj0JE5AFF5iKYbWaotWqpQynX/gv7cbboLDQBGnRJ6iJ1OB5nsVsQrY2WOgwiz9i9G3j+eSAnB6hbF9BqAb0e2LULOHkSmDatxpInvV6Pr776Cjt37kR2djYWL16MadOmuS0TGRmJuLiSxWkcHrojRuQpLA5BRPT/8k35PjPobfHYTd1SuvndXReTzQR1gJqD3pJ/cDicd5pycpx3mEJDAYXC+TMjwzl9yZIaa7b35ZdfIj09Henp6RgxYgQWLVrELhrkt3zjCoGIqIY5hAM5hhxolVqpQymXzWFD5rFMAP7bTC9MHYYQVYjUoRDVvKNHnc3z6tYFrizGJZM5px844FyuBixYsAAjRowAAPTr1w86nQ4///yz2zIdO3ZEcHCw28Nut9dIPERSYlM9IiI4L8b1Vr1P9G/aeXYnLhkvITwwHNcnXi91OB5nsBqQWieVFV3JPxQUOPs0acv4p05QEHDunHO5anbo0CHs2LEDK1asAAAEBARg2LBhWLhwIXr16uVa7ssvv0RGRobbcxUKBZvqUa3DxImICM7+TRabxSf6NxVX0+tVv5fPlE6vLjaHDQq5AuGacKlDIfKMsDBnIQi93tk870oGg3N+WPU3XV2wYAFsNhsSExNd04QQUCqVyMvLc02rV68e0tLSqn37RN6mUk31Dhw4UO4yn376aZWDISKSSr4p3yfuYJhsJvxy4hcA/ttML1gVjDA1+zeRn0hLc/ZlOnMGuLJvkRDO6U2aOJerRjabDUuWLMGbb76JPXv2uB579+5FcnIyli1bVq3bI/IFlUqc2rZtizfeeKPUToHnz5/H4MGDMXHixGoLjojIE3ypf9Nvp3+D3qpHXHAcWsS2kDocj9Nb9YjRxkCpUEodCpFnyOXOkuNRUc6+ToWFgM3m/HnwoHP6yJHO5arR6tWrkZeXh3HjxqFZs2Zuj9tvvx0LFixwLZubm4vs7Gy3h8lkqtZ4iLxBpd5ln376KV577TV06dIF//77r9v0Jk2aoKCgAHv27KnuGImIapTOooPOovOJgW+Lx27q06CPz1QArC5CCDgcDkRqOD4M+ZnWrZ0lx9u2BS5dchaCuHQJaNeuxkqRL1iwAL169UJYKU0Ab7vtNuzZsweXLl0CAPTq1Qvx8fFuj1WrVlV7TERSq1Tj+Ntuuw2dO3fG/fffj5YtW2LGjBnYsmULfvrpJ7z88st46KGHfKKpCxHR5YrMRbDYLVAHeHf/Jp1Fh99O/wbAP5vpGawGaFQaliEn/9S6NdCypTNpKihw9mlKS6v2O03Fvv/++zLntWnTxtX66GqlyVkcgmqbSvcqjomJwcqVK3H33XfjySefhFarxe+//47mzZvXRHxERDUuz5QHhUwhdRjl+uXEL7DYLagfXh8NIxpKHY7H6Sw6RGmjfOLOIFGNkMuBRo2kjoLIb1X63xR5eXkYPnw4Vq1ahaeeegoxMTEYNmwYdu7cWRPxERHVKLvDjlxDrk9cjK876qym1ze1r1/e3TfbzYjVxkodBhER+alKJU6rV69GkyZN8O+//2LXrl14+eWX8ddff6Fr16648cYb8b///Q82m62mYiUiqnZ6q94n+jflGnKx49wOAM7Eyd9Y7BaoFCo20yMiIslUKnG6/fbb8eCDD2Lbtm1o3LgxAECr1WLu3LlYvXo1li5dinbt2tVIoERENcFX+jf9dPwnOIQDTaKboF5YPanD8bjiMuSh6lLGsSEiIvKASvVx2rFjB1q0KL38be/evbFv3z5MmTKlWgIjIvIEX+nfVNxMr1+q/xWFAJyFIZLCkvyukiAREXmPSn0DlZU0FQsNDXWr609E5M2K+zdpVd49ftPZwrP468JfkEGG3g16Sx2Ox9kddgBAHU0diSMhIiJ/xn/dEZHf8pXxm9YfWw8AaJfQDtHaaImj8TyD1QCtUoswNfs3ERGRdJg4EZHfKrIUuYoOeLN1//5XTc8fFVmKEKWN8vp+aEREVLsxcSIiv5Vvyvf6/k1HLx3F0UtHESAPQI/6PaQORxI2hw1RQVFSh0FERH6OiRMR+SW7w44cQ47X928qvtvUsV5Hv6woZ7QaERgQiPDAcKlDIaIakJKSgtmzZ1f5+YsXL0Z4eHi1xVObdOvWDY888ohHtvXcc89h/PjxHtlWafbt24e6detCr9fX6HaYOBGRX9JZdNBb9F7dv0kIgfX/Ovs3+WszPZ1Fh/DAcGiV3p3gEtVGo0ePxs0331yj29i5c2eFL7hLS7KGDRuGw4cPV3n7ixcvhkwmcz1iY2MxaNAg/P3331Vep7dYsWIFXnjhhRrfzvnz5/HOO+/gmWeecU0bPXo0ZDIZJkyYUGL5SZMmQSaTYfTo0W7LX+21lpKS4naeih+vvPIKAKB58+Zo37493n777Wrbr9JUuBz5888/X6UNdOvWDV26dKnSc4mIaoov9G/af2E/zhadhSZAgy5J/vk5arQZkR6cDplMJnUoRFQDoqOvreCNRqOBRqO5pnWEhobi0KFDEELg7NmzePLJJzFw4EAcPnwYKlXNfUdYrVYolcoaW39ERESNrftyCxYswA033ICUlBS36fXq1cMXX3yBt99+23WOTCYTPv/8cyQlJVV6O88//zzuu+8+t2khISGu38eMGYMJEybg6aefhkJRM83wK3zH6fjx41V65Ofn10jgRETXIs/o/eM3FTfT65rcFRrltV0Y+CKbw4YAeQDCAllNj2oXIQT0Fr3HH0KIat2PTZs2oX379lCr1YiPj8dTTz0Fm83mml9UVIT77rsPISEhiI+Px9tvv12i+diVd5FmzJiBpKQkqNVqJCQk4KGHHgLg/Ef8yZMnMWXKFNfdBqD0pnrfffcd2rVrh8DAQERFReHWW2+96n7IZDLExcUhPj4e7dq1w5QpU3Dy5EkcOnTItczWrVvRpUsXaDQa1KtXDw899JBbs7CsrCwMHDgQGo0G9evXx2effVZi32QyGebNm4chQ4ZAq9XixRdfBAB8//33aNu2LQIDA9GgQQPMnDnT7TiWdUwAYM6cOWjYsCECAwMRGxuL22+/3TXvymOdl5eHkSNHok6dOggKCsKAAQPw77//uuYXH8t169YhIyMDwcHB6NevH7Kysq56/L744gsMHjy4xPQ2bdogKSkJK1ascE1bsWIF6tWrh9atW191naUJCQlBXFyc20Or/a81Qt++fZGbm4tNmzZVet0VVeE7TosWLaqxIIiIPMkX+jfZHDZkHssEAPRL889Bb3UWHYJVwX7Zt4tqN4PVgOBZwR7fru5pXbV97p09exYDBgzA6NGjsWTJEvzzzz+47777EBgYiBkzZgAAHnvsMWzfvh2rVq1CfHw8pk2bhj///BOtWrUqdZ1ff/013n77bXzxxRdo2rQpsrOzsXfvXgDOC+6WLVti/PjxJe46XO6HH37ArbfeimeffRZLly6FxWLBDz/8UOH9ys/Px2effQYArrtB+/btQ9++ffHCCy9gwYIFuHjxIiZPnozJkye7ro9HjhyJnJwcbNy4EUqlEo8++iguXLhQYv3Tp0/HrFmz8Pbbb0OhUGDdunUYMWIE3n33XXTu3Bn//vuvq+ni9OnTr3pM/vjjDzz00ENYunQpOnbsiEuXLmHLli1l7tvo0aNx5MgRfPfddwgNDcWTTz6JoUOH4sCBA1CrnVVLDQYD3njjDSxduhRyuRwjRozA448/jmXLlpW6zry8POzfvx/t2rUrdf6YMWOwaNEi3H333QCAhQsXYuzYsdi4cWN5p6LSVCoVWrZsiS1btqBHj5opplThxImIqLbQWXQwWA2I0HimGUNV7MrahVxjLsLUYbg+8Xqpw5GEzqpDwzoNESDnVxWRt5kzZw7q1auH999/HzKZDI0bN8a5c+cwdepUTJs2DXq9HkuWLMH8+fPRs2dPyOVyLFq0CAkJCWWu89SpU4iLi0OvXr2gVCqRlJSE9u3bA3A2O1MoFK67DmV56aWXcOedd2LmzJmuaS1btrzqvhQUFCA4OBhCCBgMBgDA4MGD0bhxYwDA66+/juHDh7vu3jRs2BDvvvsuunbtirlz5+LEiRP46aefsHPnTlcC8fHHH6Nhw4YltjV8+HCMHTvW9fc999yDp556CqNGjQIANGjQAC+88AKefPJJTJ8+/arH5NSpU9BqtbjpppsQEhKC5OTkMu/kFCdMv/32Gzp27AgA+PTTT5GcnIxVq1Zh2LBhAJzNB+fNm4fU1FQAwOTJk6/aXefkyZMQQpR5Xu+55x48/fTTOHHiBGQyGX777Td88cUXVUqcpk6div/9739u01avXo1u3bq5/k5MTMSJEycqve6K4rcREfmdIksRrA6rV/dvWnt0LQCgR/0eUCpqrg28txJCwOFwICLIe5NboqoKUgZB97ROku1Wl4MHD+KGG25w63/YqVMn6HQ6nDlzBnl5ebBarWjTpo1rflhYGNLT08tc5x133IHZs2ejQYMG6NevHwYMGIBBgwYhIKDil6t79uy56h2p0oSEhODPP/+EzWbDpk2b8Prrr2PevHmu+bt27cLRo0fd7roUf0YdP34chw8fRkBAgNu+pqWloU6dOiW2deWdmV27dmHnzp146aWXXNPsdjtMJhMMBsNVj0nv3r2RnJzsmtevXz/ccsstCAoqeZ4PHjyIgIAAXH/9f/+Ii4yMRFpaGv755x/XtKCgIFfSBADx8fGl3jkrZjQaAQCBgYGlzo+KisLAgQPxySefQAiBgQMHIiqqasNLPPHEE24FJQBnonQ5jUbjSn5rAhMnIvI7ecY8yL24qKjZZsaG4xsAAP3T+kscjTQMVgOCVEFspke1kkwm8+qmwhUhhChRtKW4D5VMJnP7vbRlSlOvXj0cOnQImZmZ+OmnnzBp0iS8/vrr2LRpU4WLKFSlUIRcLkdaWhoAoHHjxsjOzsawYcOwefNmAIDD4cD999/v1reoWFJSkltfqMuVtq+X98kpXvfMmTNL7YcVGBh41WNSnPBt3LgR69evx7Rp0zBjxgzs3LmzRL+vso77lefxyuN8+bksTXESlJeXV2ahj7Fjx2Ly5MkAgA8++KDMdZUnKirKdZ7KcunSJbfEr7p575UDEVEN8IX+Tb+e/hV6qx6x2li0imsldTiS0Fl0qBNYx6vLxRP5syZNmmDr1q1uF9Vbt25FSEgIEhMTkZqaCqVSiT///NM1v7CwEEeOHLnqejUaDQYPHox3330XGzduxLZt27Bv3z4Azj4sdrv9qs9v0aIFfv7552vYM2DKlCnYu3cvVq5cCcBZ5ODvv/9GWlpaiYdKpULjxo1hs9mwe/du1zqOHj1aoQJpbdq0waFDh0pdt1zuvEy/2jEJCAhAr1698Nprr+Gvv/7CiRMnsGHDhhLbadKkCWw2G7Zv3+6alpubi3///dfVJLEqUlNTERoaigMHDpS5TL9+/WCxWGCxWNC3b80OrbF///4qFZ6oKN5xIiK/4gv9m4qb6fVJ7QO5zD//v2W2mxGjjZE6DCK/V1BQgD179rhNi4iIwKRJkzB79mw8+OCDmDx5Mg4dOoTp06fj0UcfhVwuR0hICEaOHIlp06YhMTERcXFxmD59OuRyeZnDCyxevBh2ux3XX389goKCsHTpUmg0GiQnJwNwVuDbvHkz7rzzTqjV6lKbfE2fPh09e/ZEamoq7rzzTthsNvz444948sknK7zPoaGhuPfeezF9+nTcfPPNmDp1Kjp06IAHHngA9913H7RaLQ4ePIjMzEy89957aNy4MXr16oXx48dj7ty5UCqVeOyxx6DRaModSmHatGm46aabUK9ePdxxxx2Qy+X466+/sG/fPrz44otXPSarV6/GsWPH0KVLF9SpUwdr1qyBw+EotTlkw4YNMWTIENx333348MMPERISgqlTpyI+Ph5Dhgyp8LG5klwuR69evfDrr7+WOQ6TQqHAwYMHXb+XpazXWnHp8qKiImRnZ7vNDwoKQmios2XCiRMncPbsWfTq1auKe1O+Sn0j79ixwy3Tv/LWndlsxldffVU9kRER1YBCc6FXj99UZC7Cb6d/A+C/zfSsdquzDLmaZciJpLZx40a0bt3a7VGcDK1ZswY7duxAy5YtMWHCBIwbN86t8/6bb76J6667DoMHD0avXr3QqVMnZGRklNkfJjw8HPPnz0enTp1cd46+//57REZGAnCO43PixAmkpqaW2SysW7duWL58Ob777ju0atUKPXr0cLvLUlEPP/wwDh48iOXLl6NFixbYtGkTjhw5gs6dO6N169Z47rnnEB8f71p+yZIliI2NRZcuXXDLLbe4yrCXta/F+vbti9WrVyMzMxPXXXcdOnTogLfeesuVLF7tmISHh2PFihXo0aMHMjIyMG/ePHz++edo2rRpqdtatGgR2rZti5tuugk33HADhBD46quvrnksqfHjx+OLL76Aw+Eoc5nQ0FBXglOWsl5rxaZNm4b4+Hi3x+UJ8eeff44+ffq4jl1NkIlKFPVXKBTIyspCTIzzv4ChoaHYs2cPGjRoAMA5cnBCQkK5t1GlVlhYiLCwMBQUFJR7EqlsVqsVa9aswYABA2p0ADeqOp6jkvZk78GZgjOID4kvf+Ea5rA7cO7Pc0hokwC5wvl/rG8PfYsXNr+ABuEN8OXtX/rlwK/5pnzIZXJ0Tu4saUU9vn+8ny+cI5PJhOPHj6N+/frlXkTXNg6HA4WFhQgNDYVcLoder0diYiLefPNNjBs3TurwatSZM2dQr149/PTTT+jZs6fU4ZTqyvNTVUIIdOjQAY888gjuuuuuaoyw4sxmMxo2bIjPP/8cnTp1KnWZq70XK5obVOob6cocq7Scq7oHVyMiqi4WuwW5hlyv7t+07qhz0Nt+af38MmkCWIacqLbYvXs3du/eja5du6KoqMhV1vpamoZ5qw0bNkCn06F58+bIysrCk08+iZSUFHTp0kXq0GqcTCbDRx99hL/++kuyGE6ePIlnn322zKSpulT7t5K/ftETkfcrNBdCZ9UhXiv93abS5BhysPPcTgBA39Sa7UDrrYQQEA6BOpqSZXyJyPe8//77eOSRR6BSqdC2bVts2bKlyuWovZnVasUzzzyDY8eOISQkBB07dsSyZcu89k5odWvZsmW542XVpEaNGqFRo0Y1vh3+O4+I/EaBqQAOhwMKedmdU6W07t91EBBoEdMCiaGJ5T+hFjLajNCoNAgLZP8mIl/XunVrbNy48ZqbgvmCvn371njFOJJepROnAwcOuCpaCCHwzz//QKdzDuKWk5NTvdEREVUTIQQu6C9AE1D5MT485fJmev5KZ9GhjoZlyImIyPtUOnHq2bOnWz+mm266CcB/A2SxqR4ReSOD1YACcwGCVcFSh1Kqk/kncSDnABQyBXo1qLlSqt7OZDMhLjhO6jCIiIhKqFTidPz48ZqKg4ioRhWYC2C0GhGl8c629Wv/dY7ddH3d6716jKmaZHPYECAPQKia1U6JiMj7VCpxqkhd9D179tRo/XQioqrIM+ZBIVd45V1xIcR/zfRS/buZXrAqmIkTERF5pWrpqVdQUIA5c+agTZs2aNu2bXWskoio2tgddlzQX4BW6Z1lyA/mHMSpwlNQK9ToltJN6nAko7fqEaONYRlyIiLyStf07bRhwwYsXLgQK1asQHJyMm677TYsWLCgumIjIqoWheZC6C16RAV5aTO9Y85mel1TuvptUQQhBOwOu982UyT/ZLFbYHPYPLKtAHkAVAqVR7ZFVFtVOnE6c+YMFi9ejIULF0Kv12Po0KGwWq345ptv0KRJk5qIkYjomhSaC2F1WKFUeN94GnZhR+axTAD+3UzPaDMiSBnEZnrkNyx2C3ac2QGdVeeR7QUrg9G+bnsmT//vnnvuQUZGBp555plqX/fo0aORn5+PVatWVfu6PWHjxo3o3r078vLyEB4eXq3rlslkWLlyJW6++WZcuHABTZs2xZ49e5CY6BtDcFSqqd6AAQPQpEkTHDhwAO+99x7OnTuH9957r6ZiIyKqFhcNF732YmG/bj9yjbkIU4fhhro3SB2OZHQWHcICw6BVeWdzSqLqZnPYoLPqoJKrEKIKqdGHSq6Czqqr9N2toqIiPPLII0hOToZGo0HHjh2xc+dOt2VGjx4NmUzm9ujQoYPbMo899hgiIiKQlJSEL774wm3eV199hUGDBlUoHovFgtdeew0tW7ZEUFAQoqKi0KlTJyxatAhWq9UVz80333zV9fz111/44Ycf8OCDD7qmdevWzRW/Wq1GYmIiBg0ahBUrVlQotqvp1q0bHnnkkWtez4kTJyCTyRAQEICzZ8+6zcvKykJAQABkMhlOnDhR4XXedNNNmDJlyjXHVhUxMTG45557MH36dEm2XxWVSpzWr1+Pe++9FzNnzsTAgQOhUHjnIJJERMVMNhPyjHleW4Z8c95mAEDP+j298o6Yp5hsJsRqY6UOg8jj1AFqBAYE1uhDHaCuUmz33nsvMjMzsXTpUuzbtw99+vRBr169Sly09+vXD1lZWa7HmjVrXPN+/PFHfP7551i/fj1effVVjBkzBrm5uQCA/Px8PPvss/jggw/KjcVisaBv37545ZVXMH78eGzduhU7duzAAw88gPfeew9///13hffr/fffxx133IGQkBC36ffddx+ysrJw9OhRV0uqO++8E+PHj6/wuj0hISEBS5YscZv2ySef+Mxdm8uNGTMGy5YtQ15entShVEilEqctW7agqKgI7dq1w/XXX4/3338fFy9erKnYiIiuWaG5EAarwSv7DpltZmzL3wYA6J/WX+JopFNchjwsMEzqUIjo/xmNRnzzzTd47bXX0KVLF6SlpWHGjBmoX78+5s6d67asWq1GXFyc6xER8V9fxcOHD6Nr165o164d7rrrLoSGhuLYsWMAgCeffBKTJk1CUlJSufHMnj0bmzdvxs8//4wHHngArVq1QoMGDTB8+HBs374dDRs2rNB+ORwOLF++HIMHDy4xLygoCHFxcahXrx46dOiAV199FR9++CHmz5+Pn376ybXc2bNnMWzYMNSpUweRkZEYMmRImXd5Ro8ejU2bNuGdd95x3dE6ceIE7HY7xo0bh/r160Oj0SA9PR3vvPNOhfZh1KhRWLRokdu0xYsXY9SoUSWWPXDgAAYMGIDg4GDExsbinnvuQU5ODgBn0vLbb7/h3XffdYut2K5du9CuXTsEBQWhY8eOOHTokNu6586di9TUVKhUKqSnp2Pp0qVu848cOYIuXbogMDAQTZo0QWZmZon4mjdvjri4OKxcubJC+y61SiVON9xwA+bPn4+srCzcf//9+OKLL5CYmAiHw4HMzEwUFRXVVJxERFWSb8yHEAJyWbUUEa1Wv535DQaHAbHaWLSMayl1OJLRWXTQqrTs30TkRWw2G+x2OwIDA92mazQa/Prrr27TNm7ciJiYGDRq1Aj33XcfLly44JrXrFkz7Nq1C3l5edi1axeMRiPS0tLw66+/4s8//8RDDz1UoXiWLVuGXr16oXXr1iXmKZVKaLUVa+b7119/IT8/H+3atavQ8qNGjUKdOnVcTfYMBgO6d++O4OBgbN68Gb/++iuCg4PRr18/WCyWEs9/5513cMMNN7juZmVlZaFevXpwOByoW7cuvvrqKxw4cADTpk3DM888g6+++qrcmAYPHoy8vDzXefj1119x6dKlEk0es7Ky0LVrV7Rq1Qp//PEH1q5di/Pnz2Po0KEAnMnoddddh3vvvdcttmLPPvss3nzzTfzxxx8ICAjA2LFjXfNWrlyJhx9+GI899hj279+P+++/H2PGjMEvv/wCwJmg3nrrrVAoFPj9998xb948TJ06tdT9ad++PbZs2VLufnuDKl1JBAUFYezYsfj111+xb98+PPbYY3jllVcQExNTagZPRCQFh3DgvP68V95tAv4b9LZPgz5emdh5is6iYxlyIi8TEhKCG264AS+88ALOnTsHu92OTz/9FNu3b0dWVpZruf79+2PZsmXYsGED3nzzTezcuRM9evSA2WwGAPTs2RN33303rrvuOowePRqffPIJtFotJk6ciA8//BBz585Feno6OnXqdNXmdkeOHEHjxo2veb9OnDgBhUKBmJiYCi0vl8vRqFEj152YL774AnK5HB9//DGaN2+OjIwMLFq0CKdOncLGjRtLPD8sLAwqlcp1NysuLg4KhQJKpRIzZ87Eddddh/r16+Puu+/G6NGjK5Q4KZVKjBgxAgsXLgQALFy4ECNGjIBS6d7ce+7cuWjTpg1efvllNG7cGK1bt8bChQvxyy+/4PDhw2XGVuyll15C165d0aRJEzz11FPYunUrTCYTAOCNN97A6NGjMWnSJDRq1AiPPvoobr31VrzxxhsAgJ9++gkHDx7E0qVL0apVK3Tp0gUvv/xyqfuTmJhYqX5ZUrrmb+r09HS89tprOHPmDD7//PPqiImIqFroLDoUWYq8suBAgakAv552/rfQn6vpCSHgEA6WISfyQkuXLoUQAomJiVCr1Xj33XcxfPhwt4vrYcOGYeDAgWjWrBkGDRqEH3/8EYcPH8YPP/zgWmb69Ok4evQo9u3bh1tuuQUvv/wyevXqBaVSiRdffBG//vor7r33XowcObLMWIQQ1TKAudFohFqtrtS6Lt/2rl27cPToUYSEhCA4OBjBwcGIiIiAyWTCv//+W6lY5s2bh3bt2iE6OhrBwcGYP38+Tp06VaHnjhs3DsuXL0d2djaWL1/udjeo2K5du/DLL7+44gwODnYlnxWJtUWLFq7f4+PjAcB1N/HgwYPo1KmT2/KdOnXCwYMHXfOTkpJQt25d1/wbbii9AJJGo4HBYCg3Hm9Qbf/eUygUuPnmm8utZEJE5CmF5kKYbWYEagPLX9jDMo9lwuawISUwBQ0jKtY2vzYqLkMepmb/JiJvk5qaik2bNkGv16OwsBDx8fEYNmwY6tevX+Zz4uPjkZycjCNHjpQ6/59//sGyZcuwe/duLFy4EF26dEF0dDSGDh2KsWPHorCwEKGhJZvtNmrUyHVRfi2ioqJgMBhgsVigUpVfbdVut+PIkSO47rrrADiboLVt2xbLli0rsWx0dHSF4/jqq68wZcoUvPnmm7jhhhsQEhKC119/Hdu3b6/Q85s1a4bGjRvjrrvuQkZGBpo1a4Y9e/a4LeNwODBo0CC8+uqrJZ5fnAhdzeV3sIoTR4fDUWJascsTTCFEifWVlaxeunSpUsdOShW+4zRhwgScPn26Qst++eWXpb6giIg8KdeQ67XNv9YcdVad6hbRTdpAJKa36BGmDvPa5pREBGi1WsTHxyMvLw/r1q3DkCFDylw2NzcXp0+fLvXCXAiB8ePH480330RwcDDsdrurjHjxz8svzC83fPhw/PTTT9i9e3eJeTabDXq9vkL70qpVKwDOogkV8cknnyAvLw+33XYbAKBNmzY4cuQIYmJikJaW5vYICyv9H0AqlQp2u91t2pYtW9CxY0dMmjQJrVu3RlpaWqXvWI0dOxYbN24s9W5Tcax///03UlJSSsRa3CestNgqIiMjo0Rft61btyIjIwMA0KRJE5w6dQrnzp1zzd+2bVup69q/f3+pfde8UYUTp+joaDRr1gz9+/fH3LlzsXPnTpw9exa5ubk4evQovvvuOzz55JOoV68eZs+e7XZ7j4jI06x2K3IMOdAqva+Z3pnCM/jr/F+Qy+ToUqeL1OFIymgzIjY4tlqa4BD5IrPNDJPNVKMPs81cpdjWrVuHtWvX4vjx48jMzET37t2Rnp6OMWPGAAB0Oh0ef/xxbNu2DSdOnMDGjRsxaNAgREVF4ZZbbimxvvnz57v1h+/UqRM2bNiA33//HW+//TaaNGlS5oCrjzzyCDp16oSePXvigw8+wN69e3Hs2DF89dVXuP7668u8w3Wl6OhotGnTpsRFP+As/JCdnY0zZ85g+/btmDp1KiZMmICJEyeie/fuAIC7774bUVFRGDJkCLZs2YLjx49j06ZNePjhh3HmzJlSt5mSkoLt27fjxIkTyMnJgcPhQFpaGv744w+sW7cOhw8fxnPPPVdijKzy3Hfffbh48SLuvffeUuc/8MADuHTpEu666y7s2LEDx44dw/r16zF27FhXspSUlIQdO3a4xVYRTzzxBBYvXox58+bhyJEjeOutt7BixQo8/vjjAIBevXohPT0dI0eOxN69e7FlyxY8++yzJdZjMBiwa9cu9OnTp1L7LpUK/yv2hRdewIMPPogFCxZg3rx52L9/v9v8kJAQ9OrVCwsWLPCZnSei2qvQXAi9Ve+VYwOtOeK823RdwnWIUPpv3x6bwwaFXMFqeuSXAuQBCFYGQ2fVlVqNrboFK4MrfQe+oKAATz/9NM6cOYOIiAjcdttteOmll1xNuBQKBfbt24clS5YgPz8f8fHx6N69O7788kuEhIS4XYSfP38eL7/8MrZu3eqa1r59ezz22GMYOHAgYmJi8Mknn5QZi1qtRmZmJt5++218+OGHePzxxxEUFISMjAw89NBDaNasWYX3a/z48Vi8eDEmT57sNn3+/PmYP38+VCoVIiMj0bZtW3z55ZduSWBQUBA2b96MqVOn4tZbb0VRURESExPRs2fPUpsYAsDjjz+OUaNGoUmTJjAajTh+/DgmTJiAPXv2YNiwYZDJZLjrrrswadIk/PjjjxXej4CAAERFRZU5PyEhAb/99humTp2Kvn37wmw2Izk5Gf369YNcLocQApMnT8aDDz7oFltF3HzzzXjnnXfw+uuv46GHHkL9+vWxaNEidOvWDYCzqMbKlSsxbtw4tG/fHikpKXj33XfRr597n95vv/0WSUlJ6Ny5c4X3W0oyUVojxArIz8/HyZMnYTQaERUVhdTUVJ/5j2FhYSHCwsJQUFBQ5oucyme1WrFmzRoMGDCgRCUX8g7+fI6O5x3Hnuw9SAorf3wQTxJC4JavbsGZwjOY2WUmWha2REKbBMgV/ldVr8BUAAGBLsldvHLwX39+//gKXzhHJpMJx48fR/369UuU9rbYLbA5bB6JI0AeAJWi/D491cnhcLj6LMnl3vMZZzKZkJ6eji+++KLMggX+wBvOT/v27fHII49g+PDhNb6tq70XK5obVLnxf3h4eJm3U4mIpHZefx6BAd5XFGLfhX04U3gGmgANuiV3Q94+3xgtvSborXokhyd7ZdJE5AkqhcrjyQwBgYGBWLJkiWsgWJLGhQsXcPvtt+Ouu+6SOpQKq1R6aTAY8MADDyAxMRExMTEYPnx4tbzo5syZ48r+2rZtW+FBsH777TcEBAS4OvoREQGAwWpAgbkAwapgqUMpobiZXveU7tAoNRJHIy2bw4ZITaTUYRCRH+ratWuJAWPJs2JiYvDkk0/6TIs1oJKJ0/Tp07F48WIMHDgQd955JzIzMzFx4sRrCuDLL7/EI488gmeffRa7d+9G586d0b9//3Lr2BcUFGDkyJHo2bPnNW2fiGqfAlMBDBYDNAHelZhY7VZkHssEAAxoOEDiaKRlspkQGBDI/k1EROQzKtVUb8WKFViwYAHuvPNOAMCIESPQqVMn2O12t8HQKuOtt97CuHHjXBVBZs+ejXXr1mHu3LmYNWtWmc+7//77XYOwrVq16qrbMJvNrhGsAWc7RsDZNrq4/CVV3pUlRMn7+Os5yinKgVzIIRwCAlXqxlkjtpzcggJzAaKDotE2ti0cdmfH6eKf/qTIWAStUgu1TO21r09/ff/4El84R1ar1TnQs8NR4YpltUVxN/ri/Sfv4m/nx+FwQAgBq9VaIm+p6GdIpRKn06dPu1W9aN++PQICAnDu3DnUq1evMqsCAFgsFuzatQtPPfWU2/Q+ffq4VV250qJFi/Dvv//i008/xYsvvljudmbNmoWZM2eWmL5+/XoEBXHskGuVmZkpdQhUDn89R+dwrvyFPGjF8RUAgE7aTji/57xrevbebKlCkpQZZvy4r+IVpKTir+8fX+LN5yggIABxcXEoKirySPU8b1RUVCR1CHQV/nJ+zGYzjEYjNm3aVGLsKoPBUKF1VCpxstvtJUZZDggIgM1WtYowOTk5sNvtiI11LxccGxuL7OzSLySOHDmCp556Clu2bEFAQMXCf/rpp/Hoo4+6/i4sLES9evXQp08fVtW7BlarFZmZmejdu7fXVjPyd/54jnIMOdhxdgditDFeNfhtgbkAf/z1BwDgjk53ICEiAQ67A9l7sxHXMs6vqurZHXac151H+7rtERVUdildqfnj+8fX+MI5cjgcOH78OAoLCxEdHQ2lUulTfTquhRACer0eWq3Wb/bZl/jL+Sm+y1RYWAitVovevXuXqCJY3BqtPJW6qhBCYPTo0VCr1a5pJpMJEyZMcI1ADDib9FXGlSdLCFHqCbTb7Rg+fDhmzpyJRo0aVXj9arXaLeZiSqXSaz9ofQmPo/fzp3Oks+kgZAIqpXdVqvr5xM+wOWxoGNEQ6dHpbvPkCrlfJU56mx7aQC0itBFQBnj/69Kf3j++ytvPUYMGDZCVlYWsrCypQ/EoIQSMRiM0Gk2tvjD3Vf52foKCghAfH1/iJhCACn9+VCpxGjVqVIlpI0aMqMwq3ERFRUGhUJS4u3ThwoUSd6EA563EP/74A7t373YNWlbcXjEgIADr169Hjx49qhwPEfk2u8OOc0XnoFVpy1/Yw9YcdVbT8/eiEICzDHl8cDzUASX/oUVUG6lUKiQlJcFms5VoIlSbWa1WbN68GV26dPHqxNZf+dP5USgUCAgIuOYEsVKJ06JFi65pY1dSqVRo27YtMjMz3UZlzszMxJAhQ0osHxoain379rlNmzNnDjZs2ICvv/4a9evXr9b4iMi3FJoLUWQuQmSQd5W4PlN4Bn+d/wtymRz9UvuV/4RazmK3IFobLXUYRB4lk8m8/s5YdVMoFLDZbAgMDPSr/fYVPD+VJ3kHgEcffRT33HMP2rVrhxtuuAEfffQRTp06hQkTJgBw9k86e/YslixZArlcjmbNmrk9PyYmBoGBgSWmE5H/yTflw+qwet2AksVjN12XcJ3fJwxmmxkqhYplyImIyOdInjgNGzYMubm5eP7555GVlYVmzZphzZo1SE5OBgBkZWWVO6YTEZEQAtm6bK8bu0kIwWZ6l9Fb9QhWBSNEHSJ1KERERJUieeIEAJMmTcKkSZNKnbd48eKrPnfGjBmYMWNG9QdFRD5FZ9Eh35TvdXcy9l3YhzOFZxAYEIjuKd2lDkdyBqsBSWFJkMv8pxgGERHVDvzmIqJaId+UD5PNhMCAQKlDcVPcTK9HSg8EKf173DiHcA6wGB4YLm0gREREVcDEiYhqhfP6817Xt8lsM2P9sfUA2EwPcN5t0ig1XndXkIiIqCKYOBGRzzNYDbhkvIRgVbDUobjZdHITCs2FiNXG4rqE66QOR3J6ix7hgeHQKL2rHxoREVFFMHEiIp+Xb8qHwWKAVuld4zd9f/h7AMBNjW6CQq6QOBrpme1mxGpLjtFHRETkC5g4EZHPyzXkQi6Te9XI59m6bPx+5ncAwKBGgySORnpWuxVKuZLN9IiIyGcxcSIin2axW3BBf8Hrylv/cOQHCAi0iW+DuqF1pQ5HcnqrHlqVlokTERH5LCZOROTT8k350Fl0XtVMTwjhaqY3uNFgiaPxDnqrHjHaGDZZJCIin8XEiYh82iXjJQDwqgvy3dm7cabwDIKUQehZv6fU4UhOCAGHw4EITYTUoRAREVUZEyci8ll2hx3ndee96m4TAHx36DsAQO8GvVlBDoDRZmQZciIi8nlMnIjIZxWYC1BoLvSq/k16ix4/Hf8JADA4nc30AOcxCVOH+f0AwERE5NuYOBGRz8oz5sHusCNAHiB1KC6ZxzJhspmQHJaMFjEtpA7HK5hsJsQGx3pV1UMiIqLKYuJERD5JCIGsoiyvawpXXBRiUKNBTBQA2Bw2yOVyNtMjIiKfx8SJiHxS4f+1d9/hcVT3/sffW7XqXbJluRvbuMbYFBMDoZmYQAgJaRDCTYAbAqH5R6hJKElw7g0hpoUWEgihpjj0axzAJnRcsY17t1Wsru11fn+MJVuWZNlgaUbS5/U8+0g7e2b2O3P2rOarc+ZMtJmmaBNZ3iyrQ2m1tXErK6pX4HQ4+coRX7E6HFsIxoJkejQNuYiI9H5KnESkV2qMNBJLxvC5fVaH0url9S8DML18OsWZxRZHYw+BWIDizGI8Lo/VoYiIiHwuSpxEpNcxDIPKQKWtkqZEKsHLG8zESZNC7JU0khSmF1odhoiIyOemxElEep3maDP14XpbDf/6YOcH1IZqyU3L5cQhJ1odji1EEhF8bh+5vlyrQxEREfnclDiJSK9TH65vPSm3ixfXm/duOvOIMzUsbY9ALECuL9d299kSERH5LJQ4iUivkjJS7GreZauT8cZII29vexswZ9MTUzgRpiSjRLMLiohIn6DESUR6lcZII42RRlsN03tt42skUgnGFo1ldOFoq8OxhWQqicPhIC89z+pQREREDgslTiLSq9SF6oin4nhdXqtDAcyJKl5cZw7TU2/TXsF4kCxPlq0SXBERkc9DiZOI9BqJVIIKf4Wt7t20umY1G+o34HV5+fLIL1sdjm0EY0EKMwptk+CKiIh8XkqcRKTXaIw00hi11zC9f6z5BwCnDT9Ns8ftI56KU5RRZHUYIiIih40SJxHpNWqCNWCA2+m2OhTAnBb99U2vA/CNcd+wOBr7iCQipLnTbJXgioiIfF5KnESkV4glY7YbpvfKhleIJqOMKhjFpJJJVodjG4FYgBxvjq3qSkRE5PNS4iQivUJDuAF/1E+2N9vqUABzUoiWYXrnHXmeptzeRzgepjSrFKdDf2JERKTv0F81EekVdgd343Q6cTldVocCwNKqpWxt3Eq6O50vj9KkEC1apiHX9V4iItLXKHESEduLJCJUBarI8drnmpmW3qYvj/qyhqTtIxQPkenJJDdNiZOIiPQtSpxExPbqw/UEYgEyvZlWhwKY8by55U0AvnGkJoXYVzAepCC9gDR3mtWhiIiIHFZKnETE9qr8VXicHttcM/PiuhdJpBKMLx7P2KKxVodjK9FklOLMYqvDEBEROezscRYiItKJYCxITbjGNlNbp4wU89bOA9TbtL9oIkqaS9OQi4hI36TESURsrT5cTygWIsOTYXUoAHy06yN2+XeR5c1i5siZVodjK8F4kCxvFtlp9pj5UERE5HBS4iQitmUYBpWBSrwur22m+26ZFOKsI87C5/ZZHI29hOIhBmQNsM2QShERkcNJf91ExLb8MT91oTrbzNC2O7ibt7e9DcDXj/y6xdHYS8pIAZDny7M2EBERkW6ixElEbKs+XE84ESbdk251KAC8sO4FkkaSowYcxYj8EVaHYyuhuDmcUvdvEhGRvkqJk4jYUjKVZGfTTjLc9ri2KZFK8K+1/wLU29SRQCxAfnq+hi+KiEifpcRJRGypPlxPfaTeNkO/3t3xLtXBavJ8eZwy/BSrw7GdWDJGcYamIRcRkb5LiZOI2FJVoArDMPC4PFaHAuydFOKro7+K1+W1OBp7iSVjeF1eDdMTEZE+TYmTiNhOMBakMlBpm96mHU07eH/H+4CG6XUkEAuY05B7NQ25iIj0XUqcRMR2akO1BGIBMj2ZVocCwLOrn8XA4IuDv0h5TrnV4dhOyzTkLqfL6lBERES6jRInEbGVZCrJjqYdZHoybXHvJn/Uz4vrXgTg/InnWxyN/bRMQ56fnm9xJCIiIt1LiZOI2IrdJoV4Yd0LhBNhRuaP5JiyY6wOx3aCsSCZnkzb3GtLRESkuyhxEhFbqfBXYGDgdrqtDoVEKsGzq58F4LsTvmuLHjC7CcQCFGYUkuZOszoUERGRbqXESURsIxgLUhWsIi8tz+pQAFi4dSFVgSryfHnMGjXL6nBsKZ6KU5ypachFRKTvU+IkIrZRE6ohGAuS5c2yOhQAnl71NADnHXmeelQ6EElE8Ll9GqYnIiL9ghInEbGFfSeFsINVu1fxSfUneJwezht3ntXh2FIgFiDXl2ubRFdERKQ7KXESEVuoC9dRH7bPpBAtvU1njDyDoowii6Oxp1A8RElGia79EhGRfkGJk4jYQoW/AofDYYtJIaoD1byx+Q0AvjvxuxZHY0+JVAKn00leep7VoYiIiPQIJU4iYrlALEB1oNo218o8/+nzJI0kUwdOZUzhGKvDsaVgLEiWJ8s2dSYiItLdlDiJiOVqgjUE4/aYFCIcDzNv7TxAN7w9kEAsQElmCR6Xx+pQREREeoQSJxGxVCKVYHvTdttMCvHKhldojjZTnlPOjMEzrA7HlgzDIGkkKcwotDoUERGRHqPESUQsVReqozHSaItJIVJGqnVSiO+M/w4up8viiOwpnAiT4cnQMD0REelXlDiJiKUqA5W2mRTivR3vsb1pO1neLL465qtWh2NbLdOQZ3rt0UsoIiLSE5Q4iYhlGiONVPgryPflWx0KsHcK8q+N+RoZngyLo7GvSCLCgKwBVochIiLSo5Q4iYhldjXvIpaM2SJJWV+3no92fYTT4eTb479tdTi2FU/G8Tg9GqYnIiL9jhInEbFEIBZgp3+nbXqb/rTsTwCcNuI0BmYPtDga+wrEAmSnZZOTlmN1KCIiIj1KiZOIWKLSX2neC8gGU5BvadjCG1vMG97+8As/tDgaewvGg5RmlWriDBER6XeUOIlIjwvHw2xv2m6b4V5/Xv5nDAxOHnYyowpGWR2ObaWMFIBteglFRER6khInEelx1cFqmqJNtkicdjbvZP6m+YB6m7oSiofMach91tebiIhIT1PiJCI9KpaMsbVhK1meLBwOh9Xh8MSKJ0gaSY4ffDxHFh9pdTi2FogFKEwvxOf2WR2KiIhIj1PiJCI9qjpQTUOkwRY3vK0KVPHS+pcA9TYdjFgyRnFmsdVhiIiIWEKJk4j0mEQqwbbGbaS7020xucCTnzxJIpVg6sCpfGHAF6wOx9YiiQhp7jQN0xMRkX5LiZOI9JiaYA21oVry062fXKA2VMu/1v4LgIunXGxtML1AIBYgz5dHtjfb6lBEREQsocRJRHpEykixvWk7HpcHt9NtdTg8tfIposkoE0smcnTZ0VaHY3uheIgBWQNscV2aiIiIFZQ4iUiPqAvVUR2spiC9wOpQaIw08vdP/w6YvU1KBg4snozjcXo0DbmIiPRrSpxEpNsZhsHO5p0AeF1ei6OBZ1c9SzgRZnThaL44+ItWh2N7/pif7LRsctJyrA5FRETEMkqcRKTbNUQaqPBXUJheaHUoBGIBnl39LKDepoMVjAUZkDXAFhN6iIiIWEWJk4h0u13Nu0ikEra4/8/zq58nEAswPG84Jw872epwbC+RSuB0OinMsD7pFRERsZISJxHpVo2RRnY277TF9THheJinVj4FwA+n/BCnQ1+BXQnEAmR5s8hN0zTkIiLSv+msQUS6jWEYbG3cSiwZI9ObaXU4PLv6WZqiTZTnlHP6iNOtDqdXCMQDDMgcgMflsToUERERSylxEpFuUxeuY2fTTooyiqwOhcZII48vfxyAH039kS2mRLe7lJECAw3TExERQYmTiHSTlJFiS8MWDAxbXNv0p2V/IhgPMrpwNGeMPMPqcHqFYCxIpieTPF+e1aGIiIhYTomTiHSL3cHdVPgrbNHbVOGv4G+f/g2Aq465Stc2HSR/zE9xZjFp7jSrQxEREbGczh5E5LBLpBJsadiC2+m2xX2bHlr8EPFUnGPKjuHYQcdaHU6vYBgGiVSC4sxiq0MRERGxBVskTn/4wx8YPnw4Pp+PqVOn8p///KfTsv/85z85/fTTKS4uJicnh+nTpzN//vwejFZEulIVqKI6WG2L3qb1det5beNrAPzkmJ/ovk0HKRQPkeHN0DA9ERGRPSxPnJ577jmuueYabrnlFpYtW8YJJ5zArFmz2L59e4fl3377bU4//XReffVVlixZwsknn8zZZ5/NsmXLejhyEelILBljU/0mfC6fLSZguP/j+zEwOH3E6YwrHmd1OL2GP+anML2QDE+G1aGIiIjYguVnNXfffTcXX3wxl1xyCQBz585l/vz5PPjgg8yZM6dd+blz57Z5fuedd/LCCy/w0ksvMWXKlA7fIxqNEo1GW583NzcDEI/Hicfjh2lP+p+WY6djaF9W1NGOph3UBeooyy4jlUz12Pt2ZHHlYt7b8R4uh4sfH/Vjy+PZX0s8dosLIBaLUZRW1K/bt77j7E91ZG+qH3tT/ex1sMfA0sQpFouxZMkSbrzxxjbLZ86cyXvvvXdQ20ilUvj9fgoKCjotM2fOHG6//fZ2y19//XUyMvTf1M9rwYIFVocgXejpOnLhoprqHn3P/RmGwe83/B6AMwrPwLnRSQUVlsbUmaoVVVaH0I4TJys2rWAFK6wOxXL6jrM/1ZG9qX7sTfUDoVDooMpZmjjV1taSTCYpLS1ts7y0tJSqqoM7kfjd735HMBjkW9/6VqdlbrrpJmbPnt36vLm5mcGDBzNz5kxycnI+W/BCPB5nwYIFnH766Xg8ujmmHfV0HW2u38zqmtWU55Rbfi3Rv7f8mw2hDWS4M7jq9KsoSO/8nytWSSVTVK2oYsDkAThdlo+cblUbrCXHl8PRZUdbXo9W0nec/amO7E31Y2+qn71aRqN1xfKhekC7P8yGYRzUH+tnnnmG2267jRdeeIGSkpJOy6WlpZGW1n46XY/H0+8/KIeDjqP99UQdBWIBtge2k5eRh8vt6tb36koileDBJQ8C8L1J36Moy/pJKg7E6XLaKnGKGBGOzDsSr9f6GRHtQN9x9qc6sjfVj72pfjjo/bf0L3VRUREul6td79Lu3bvb9ULt77nnnuPiiy/m+eef57TTTuvOMEXkIGxv3E4gFiDXl2t1KPxr7b/Y0byDgvQCLph4gdXh9CqxZAyvy6vZ9ERERPZjaeLk9XqZOnVqu7GVCxYs4Pjjj+90vWeeeYb/+q//4umnn+YrX/lKd4cpIl2oD9ezrWmbLYbDheIhHl36KACXHnUpmd5MiyPqXfxRPzlpOeSkaRiziIjIviwfqjd79mwuvPBCpk2bxvTp03nkkUfYvn07l112GWBen7Rr1y7+8pe/AGbS9P3vf5977rmH4447rrW3Kj09ndxc6//TLdLfJFNJNtZvJJ6Kk+XNsjocHl/+OHXhOgbnDObcsedaHU6vE0qEGJE/AqfDPkMHRURE7MDyxOnb3/42dXV13HHHHVRWVjJhwgReffVVhg4dCkBlZWWbezo9/PDDJBIJrrjiCq644orW5RdddBGPP/54T4cv0u/t8u+iormCgdkDrQ6FrY1b+csn5j9Zrj72alvcR6o3SaQSOB1O8tPzrQ5FRETEdmxxVnH55Zdz+eWXd/ja/snQwoULuz8gETkogViADXUbyPRmWp6kGIbB/777vyRSCWYMnsFJQ0+yNJ7eyB/1k5uWa4vr1EREROxGYzFE5DMxDIPNDZtpjjaT77O+h+L1za/zUcVHpLnSuO746/r1NNqfVSAeYGD2QMuTYBERETtS4iQin0l1sJqtjVspySyxPEkJxALc/f7dAPzgCz+gPKfc0nh6o3gyjsvhojC90OpQREREbEmJk4gcsmgiyoa6Dbgdbnxun9Xh8PCSh6kL1zEkZwjfn/x9q8PplZqiTeT58jQNuYiISCeUOInIIdvauJWaUA3FmcVWh8K6unU8t/o5AK7/4vV4Xbpp62cRiocoyy7D5bT25sUiIiJ2pcRJRA5JQ7iBLY1bKEwvtHzK6pSR4jfv/IaUkeL0EadzXPlxlsbTW0UTUbwuL4UZGqYnIiLSGSVOInLQWu7ZFE1GbXHPphfXvcjK3SvJ9GQy+7jZVofTazVHm8lPz9dNb0VERA5AiZOIHLRd/l3sbN5JaUap1aHQGGnkvo/uA+BHU39ki2GDvVUoYQ7Ts7oHUURExM70V1JEDkrLPZuyvFl4XB6rw+G+j+6jKdrEEQVH8K3x37I6nF4rkoiQ7k6nIL3A6lBERERsTYmTiHQpmUqyrnYd/pjfFvdsWl61nBfWvQDAjTNu1H2HPoemSBMF6QVke7OtDkVERMTWlDiJSJe2Nm5le9N2BmQOsPyeTeF4mNsX3Q7AV0d/lcmlky2NpzczDINoMkpZdpnl9SoiImJ3SpxE5IBqQ7Wsr1tPni/PFkP05n44lx3NOyjNLOWa466xOpxeLRQPkeHJ0DA9ERGRg6DESUQ6FUlEWFOzhmQqaYsZ197Z/g7/WPMPAG496VZbxNSbNUebKcooItObaXUoIiIitqfESUQ6lDJSrK9bT02ohtIse8yi98u3fwnAdyd8l2MGHWNxRL2bYRjEU3EGZA2wOhQREZFeQYmTiHRoV/MutjRsoTSz1PJpqg3D4Nf/+TV14TpG5I3giqOvsDSeviAYD5LlzdIwPRERkYOkxElE2mmKNLG2di0Zngx8bp/V4fDKhld4a+tbuJ1u7jj5DlvE1Ns1RZooySwh3ZNudSgiIiK9ghInEWkjnoyztnYtoXjIFr0RFf4KfvvebwHzRrdji8ZaHFHvlzJSpEhRkllidSgiIiK9hhInEWljU8Mmdvl32eLal2Qqya0LbyUYDzKpdBLfn/R9q0PqE/xRP9nebFskxiIiIr2FEicRaVXhr2Bj3UaK0otscVPZp1Y+xbKqZWR4MrjjS3fgcrqsDqlP8Mf9DMgaQJo7zepQREREeg0lTiICQH24ntW7V+NxeWwxPfWGug08uPhBAGYfN5vynHKLI+obEqkEGFCcWWx1KCIiIr2KEicRIRgLsrJ6JZFEhKKMIqvDwR/1c8O/byCeinPi0BM5Z8w5VofUZwRiAXLScsj35VsdioiISK+ixEmkn4slY6zavYqGSAMDswZaHQ4pI8XP3/o525u3MyBrAD8/4ec4HA6rw+ozmqPNlOeU43F5rA5FRESkV1HiJNKPJVNJ1tauZZd/FwOzBtoiQXl4ycO8s+Md0lxp3HX6XeSnq2fkcIkkIqS50zSbnoiIyGegxEmknzIMg00Nm9hUv4kBmQNsMRnEm1ve5LFljwFwywm3aOrxw6wh3EBJZgk5aTlWhyIiItLrKHES6ad2Nu9kXe06CtILbDG72uaGzdy26DYAvjvhu5x5xJnWBtTHJFNJEkaCQdmDbNGzKCIi0tsocRLph2qCNXxa8ynp7nSyvFlWh4M/6ue6168jFA8xbeA0rj72aqtD6nOao83kpuVSmFFodSgiIiK9khInkX6mOdrM6t2rSaQStrh+KJlKcstbt7ROBjHn1Dm2GDbY1zTHmhmcMxivy2t1KCIiIr2SEieRfsQf9bOiagVN0SZKM0utDgeAh5Y8xHs73tNkEN0oHA+T7k7XvZtEREQ+ByVOIv1EIBZgRdUK6sP1lGWX2eI6l39v/jd/Xv5nAH524s80GUQ3aYhoUggREZHPS+NhRPqBYCzI6rrV1IZqGZQzCKfD+v+ZLK5YzC8W/gKA8yecz6xRsyyOqG9KppKkjJRtkmUREZHeSomTSD+wqmYVNeEaynPKbZE0fVrzKf/v9f9HLBnjxKEnctWxV1kdUp/VFG0iNy2Xoowiq0MRERHp1aw/gxKRbhOOhwGoDdYyKNsePU1bGrZw5WtXEowHmTZwGnNO0WQQ3SkQC1CeU47H5bE6FBERkV7N+rMoEekWoXiIlTUrARiQNQCX02VxRFDpr+Qnr/2EpmgT44rG8buZv7PFPaT6qlA8hM/toySrxOpQREREej0lTiJ9UDge5pPqT6j2VwPYImmqD9dzxatXUB2sZljeMO6ddS+Z3kyrw+rTGiONlGaWalIIERGRw0CJk0gf44/6WV61nEp/JQOzB1odDmAOF/vJaz9pvVfTA7MeIM+XZ3VYfVrrpBA5ZVaHIiIi0ifowgKRPqQ+XM/K6pU0hBsYlD0Ih2H9LGqRRIRr51/L+rr1FKQX8MCsByjNssc9pPqypmgTeb48CtMLrQ5FRESkT1CPk0gfURWoYmnFUpqjzZTnlNtieF4kEeGnC37KsqplZHoyuW/WfQzNG2p1WP2CP+bXpBAiIiKHkXqcRHo5wzDY0byDVbtX4cRJWbY9hmY1RZq49vVr+aT6E9Jcacw9Yy5jCsdYHVa/EIqHyPBkUJKpSSFEREQOFyVOIr1YykixqX4Ta2vXkuHJsM11QzXBGn7y2k/Y1LCJbG82c788l8mlk60Oq9+oj9QzNHco2WnZVociIiLSZyhxEuml4sk46+vWt147lOXNsjokAHY07eCKV6+gIlBBUUYR98+6n1EFo6wOq9+IJCK4cFGeU251KCIiIn2KEieRXigYC7K2di3bmrZRmlmKz+2zOiQA1tau5ar/u4r6cD2DcwZz/6z7GZQzyOqw+pX6cD1l2WWaFEJEROQwU+Ik0stUB6pZU7OGhkgDZVlltrn4f0nlEmbPn00wHmR04Wju+/J9FGbo5L0nxZIxDAyG5A7B4bB+RkUREZG+RImTSC+RTCXZ0rCFdXXrcOBgcM5g25wcL9y6kJvfvJlYMsZRA4/i7pl322boYH9SG6plYNZAJawiIiLdQImTSC8QjAVZV7eObY3bbHU9U8pI8diyx3hkySMYGJw09CTuPOVO0txpVofW78ST8dbeJqdDd5oQERE53JQ4idjc7uBu1tSsoT5cz8CsgbYZmtccbeYXb/2Cd3a8A8B5R57Hdcdfh9uprxUr1IXrKMksoTiz2OpQRERE+iSd4YjYVDwZZ1vjNtbXr8cwDFsNzVtXt47rF1zPLv8u0lxp3DjjRs4efbbVYfVbiVSCRCrBsLxh6m0SERHpJkqcRGyoLlTH+vr1VPorKfAV2Op+PC+vf5k578whmowyKHsQ/3Pa/zC2aKzVYfVrdaE9vU0Z6m0SERHpLkqcRGwkloyxpWELmxs2k0glGJQ9yDZD32LJGHe/fzd/X/N3AI4ffDy//NIvyfXlWhxZ/5ZIJYilYgzNG4rL6bI6HBERkT7LHmdkIkJNsIb1deupDlZTmF5omwkgALY2buXWhbeyumY1DhxcctQlXHrUpRoWZgP14XqK0osoySyxOhQREZE+TYmTiMUiiQib6zezpXELAOXZ5bbpOUikEjy18ikeXvIwsWSMbG82vzz5l8wYMsPq0ARzivpoIsqk0km26ZkUERHpq/SXVsQiyVSSykAlm+o3UReuoyi9iExvptVhtdpYv5E73r6DT2s+BWB6+XRuOeEWBmQNsDgyadEQaaAwo1C9TSIiIj1AiZNIDzMMg5pQDZsbNlMVqCLdnc7gnMG2GfaWSCV4YsUTPLr0URKpBFneLGYfN5uzR59tm1n9xEy8g/Eg44rH2WaKehERkb5MiZNID2qMNLKlYQs7mnfgxMnArIG2GmK1vm49ty+6nXV16wCYMXgGN59ws3o0bKgh0kBheiGlWaVWhyIiItIv2OeMTaQPC8aCbGvcxrambcSSMYoyivC5fVaH1aoh3MAjSx/hn2v+SdJIkpOWw3XTr2PWqFnqZbKhRCpBKB5iXPE4vC6v1eGIiIj0C0qcRLpRIBag0l/JtsZt+GN+CtILbNV7E01EeWbVM/x5+Z8JxoMAnDzsZG744g0UZRRZHJ10pjpYzaCcQZRll1kdioiISL+hxEmkGzRHm6nwV7C9aTuBWIC8tDwG5wy2Te9Nykjx+qbXuf/j+6kKVAEwpnAM1xx7DUcPOtri6ORAArEAbqebUQWjbDP7ooiISH+gxEnkMGqMNLKreRc7m3cSiofI9+UzNHeo1WG1sbRyKXM/nNs6W15pZimXH305s0bNss0EFdKxlJGiLlzHuOJxFKQXWB2OiIhIv6LESeRzShkp6kJ1VPgrqPBXEE1Gyffl22qom2EYvLvjXZ5Y8QRLK5cCkOHJ4L8m/xfnTzzfVtdbSefqw/UUphcyLG+Y1aGIiIj0O0qcRD6jcDxMTaiGnc07qQ3VYmBQ4CugxGOfa5gSqQSLGhbx8gsvs6F+AwBup5tzxpzDfx/13xRmFFocoRysWDJGJBFhQskEJboiIiIWUOIkcggMw6Ah0kCVv4oKfwX+mJ90dzolGSW2updOJBHhxXUv8uQnT1IZqAQg3Z3O14/8OudPOF9TWPdCu4O7Kc8pZ2D2QKtDERER6ZeUOIkchFA81DocrzZUSzwZJ9eXa6sJHwC2NW7jhXUv8OL6F2mMNAKQ687lO5O+w7fGf4tcX661Acpn0hxtxuf2MapglK5DExERsYgSJ5FORBIR6sP1VAeq2R3aTTAWJM2VRp4vz1ZDpSKJCG9seYMX1r7A0qqlrcvLssq4YMIFTAtNY/gXhuN06YS7N0qmkjREGphUMkmJr4iIiIWUOInsI5aM0RBuYHdwN9WBagKxAC6ni5y0HApzCm3Tu2QYBuvq1vHCuhd4beNrBGIBAJwOJ8eXH885Y87hhKEn4DScVCytsDha+TxqQ7UUZxQzJG+I1aGIiIj0a0qcpN8LxoI0RZuoCdZQG6o1kxAH5HhzGJQzyDZDo1qSpTe2vMGbW95kW9O21tcGZQ/i7NFnc/bos9tcv5RKpqwIVQ6TSCJC0khyROEReF1eq8MRERHp15Q4Sb+TMlL4o34aI41UB6tpCDcQiodwOVxkp2UzMGugbW4smjJSrN69mje3vsmbW95kl39X62sep4eTh5/M18Z8jWll02yT4MnhkTJSVAerGZE/gtJMTeYhIiJiNSVO0ucZhkEwHqQ52kxjuJGaUA2BWIBoMorP5SPLm0Vhun2G4TVFmvi44mM+3PUh7+14j+pgdetraa40vjjki5wy7BRmDJlBljfLwkilO1UHqynOKGZ04WjbfDZFRET6MyVO0ucYhkEoHsIf89MUMYfg+WN+IokITqeTTHcm+b580txpVocKQDwZZ+XulXyw8wM+3PUha2rXkDL2DrHL9GQyY8gMThl+CseXH0+6J93CaKUn1Ifr8bq8jC8ZT4Ynw+pwREREBCVO0gfEkjGCsSDBeJCmSBO1oVrCiTCRRAQHDtLd6eSk5VCSaY8b0wZiAVbtXsWK6hWsrF7JiuoVhBPhNmVG5I3g2PJjOXbQsRxddrRtkjzpfsFYkEgiwpSBUyhIL7A6HBEREdlDiZP0KrFkjHA8TCgeMu+tFK7DH/UTiodIppI4HU7SPelke7MpSi+yfIhTIpVgW+M2Pq39lE+qP+GT6k/Y3LAZA6NNuYL0Ao4pO6Y1WbJLkic9K5aMUReuY1zxOAZlD7I6HBEREdmHEiexpZSRIpKIEI6HCSfCBGIBGsONrdcmxVNxMCDNnUa6O52SzBLcTms/zoFYgI31G1lXt44NdRtYX7eeTQ2biCaj7cqW55QzsWQik0snM7l0MiMLRmpyh34uZaSoDFQyPG84IwtGWp70i4iISFtKnMRS8WScaDJKJBEhkogQioVoijYRiAWIJWNEk1GzJ8npxOfykeZKI8ubhcflsSRewzCoDdWyrWkbWxu37v3ZuI2KQMf3S8rwZDC6YDSTSicxqXQSE0smUphR2MORi91VBiopzSxlbNFYy/8JICIiIu3pr7N0q5SRIpaMmUlQIko0GSWaiBKIBfBH/UST0dbXDcPA4XDgdXnxurxkesxJHHp6avBIIkKlv5KKQAUV/raP7U3bCcaDna5bmlnK6MLRex8Fo211Lyixp7pQHRnuDMaXjNfkHyIiIjalxMlCqRRs3AhNTZCbC6NGgfMwnF9/nu12tm4sBk8+Cdu3w5AhcMEFsGmzOfPbirUBhgwz2Lg5Tn1TDF9mjOKyIMF4iI3bwjT546SlxykekMCBAQ7zHkQepwevy0tOWg5el7fD5CJlwLbtEAhAVhYMHmwu374NNm4yfx81EsoHw84de5cNGwbV1VBXZ+7TiBGQnZMiu6iZNVvqWLmlhobYbnY27MafrCHp240zu4baUA114boDHiOnw0mhZxB5jqEUOIdRljGUEu8wjh09nAlH5OHsZIRVyoAdO/buy6BBsGvX3udlA+Gjj2HdOqiugpJSGDsWjj3WXP/jj6CmFpIJSE+HxkYoKoIRI83XN28GDEjPgNwcc5ukzEa+YwcMGrz3/dLTobKy7fHJyTa3EwztPdad7Yvd7H9se1PsYPa8TiqbRJ4vz+pQ+q2OvvtERET2pcTJIsuWwRNPwJo1EImAzwdHHgkXXQRTpliz3aVLDR7/S5JP1yaIxBJ4fQlGjYmTSCb410sJ/ME4SWI4vGF+PCfE4CER7r4aLv7FezSHk3i8KTwe8HggN8uNEw/+JjfxqA+fJ5vhwzycfZaDsWMObl/WroOXX4atWyAagzSveULT7IfNmw0C0RCGtxlPVhPOjCbizmbiziaS7iaS3ibwNWCk14GvAbbVQ1ojOJPt38gJxIB98iVHPBP8ZRjNZeAvwxEoIy1aRlZqMK5gOcFmL/Vh2Lhnjoc0L7yQB5Mnw4Xfp90+7r8v8TjEouBNM4+XvxmqqiEcguQ+IbpckJcHHi8E/BAOQzIFGOBwgstpJrYtiXEyBQ7M7aZ5ITsT5t4Ed94J/oC5POCH6t1mDEYKHA5z/fR085GXZz6GDYezzmq/L3bT0eekN8SeMlLUBGsAGF04mrLsMosj6r86+9688EKrIxMRETuxReL0hz/8gd/+9rdUVlYyfvx45s6dywknnNBp+UWLFjF79mxWr15NWVkZ119/PZdddlkPRvz5LFsGd9wBtbVQXg6ZmRAMwpIlsG0b/OIXny15WrYMbr8jRU1dkkHlSQZmpgiEEny4Isn6XyeZ/f+SjJuQJJlKkkglSKQSrUPnVq6J8difYzQ2JygalCQzPUkokmDex0lq64B08OaAEyexiJtUwk1llTmErr4yl7o6L1mZLsYdaZ68Ln/HjGnceCgfBKGwwZq1UXZWR/jmBRHKh5oTP0QSEcIJc5a8YDxIOB4mGA+yozrE0k9ChBNB3KMCpDwBwknzYQwMwPhgx0nQwYjkQKgIgiUQLIZgKYSKW597YwNwJXKJRByQMhMUgLgDave8pcu1J4HZIxqDpmZ4/32zXq+dvfekfe06+OOjZg9RSQlEo/DpGggGIDMLCgtg6zZIxNuHmkyavUKt77nPLhspSOwTQ0silTLMnpeIa2+vS0Wl+Z90l9tMvlJJs5zDYa4Ti5uPeBxwQF4+rF0DVZVwyaX2TUD2P7bp6eb+2T32QCxAXbiOAm8BTTQxPH+41SH1Wwf6Pq6oMHvXRUREwAaJ03PPPcc111zDH/7wB774xS/y8MMPM2vWLD799FOGDBnSrvyWLVs488wzufTSS/nrX//Ku+++y+WXX05xcTHf+MY3LNiDQ5NKmf/ZrK01/6PpcECSKL7cGCNzUqxbn+LhJ1PcPioFjhQpw3zsm+zEU+aECvFknEgiYk6uEI/x8FNRNjpjlH0hSbUjTsqRwMiM4ShOsmZ3nNv/lWJWPEHKSJLc8zAMg4SR4t8LDKrcBvlHJKlzpIAUybQk9fkpyEvgcMcx0uIkjDg4YjhcMWKeGL/Z0kTNFBcOd5wGYnzgiZFyRUiOiGE4Y3zkieJwR0kSheFm98y7HwEfHcTByj+IMkkPRHIhuucRyYVojvkIFUCkAGesAEL5pAKFEMmD1J6JJRzm8TdS5u8AGGbnk2vPZVVuj7ksmWqbtCSTe3p6XObriaSZdPh85tDCl1+G0aPNsi+/bJ7YD9tzbrxpk5m4FBebvWebNkMi0Xa3HM49ce27q8l94twT676MFOA09wnMz1qLSMgc1rdrl5kwuVxgJPdu1+EAw4B4wuwJq9kNEyfC1q3wyivmvtht6FvKaHtsW/Y7MwuGZZo9UHaLPZFKsDu4G5fTxbjicZRnlvPGqjc0g55FOvo+BsjJMZ9v2rS3nIiIiOWJ0913383FF1/MJZdcAsDcuXOZP38+Dz74IHPmzGlX/qGHHmLIkCHMnTsXgCOPPJLFixdz1113dZo4RaNRotG9U0I3NzcDEI/Hicc7+Dd/N9q40XwMG2YO0XqmYBJBZyUGZrKSGmDwESn+NNccj5UyUhiGQYqD+MudDUyC9R29lg9bgXfe6mTddGA47Nx/+TTzhwHse6QMIAl80AQM2Lt8v/P//c/tAXCkvGR6fWR4ffjc5iPDk0GmJ5MMTwapaDprV2aQ7s4gw5OBx8gmGc5i+4YsYv4sXMksiGWRk55Fc52PRMKBw2GeSBt7eogMY28ALT1GRgrwAnuO5b6XVO2fpICZXLSUSSXbnzzt+7qRMt8/w2c+37wBdmwzf6/YCYPKwOuGQBDiMcjPNXt/EnGIhMHtanuwWvehgwPYZn86eM0B+PYkQo49+5rmTZFMQNqe++g6AGeaWSaZ3JsopgzISDdjjMXMuHftMPel5foyu9ixo+2x3Z/dYm+KNOGP+inNLmVk/kgK0gtav396+ntITPt/H+9vyBCzXjZsiDPGhj2XgtqQzal+7E31s9fBHgOHYRgdndv2iFgsRkZGBn/7298499xzW5dfffXVLF++nEWLFrVb58QTT2TKlCncc889rcvmzZvHt771LUKhEJ4O/vrddttt3H777e2WP/3002RkZBymvflsLlp1EU2JpsOyLSdOXA4XToez9XeXw9Xm9/2fux3uNq+5He5OHy6HC4/DnNTB4zAfbqcbr8Pbutzr8OJ1mg+Pw2P+vmeZz+nD6/TicvTsLHkiIiIiIp0JhUKcf/75NDU1kZOT02k5S3ucamtrSSaTlJaWtlleWlpKVVVVh+tUVVV1WD6RSFBbW8vAgQPbrXPTTTcxe/bs1ufNzc0MHjyYmTNnHvDgdIeNG+GnP4X8fHM4yCzXIkKOGnCY46wiQQf+gJOfXO5iSLkTh8OxNxly7EmMnHsTJJfDhcvpYvt2J3feac6mlpnV/n2DAfManJtvhmFD2762dRsdrrtlC3y0xByS5nCA12v2Qjgwn3s8SR77/adce+s40tNdJJIQ2jNTd0bmnqFfcfjCFyA7u+s4DhSP3w+LPzZ7bFwuc9u5udDQYL6Hw2H2CHXZ47SPLnuc3HuHeCVTZq9TZ6+nDPP9CwvM5+WD4Ve/Mn/fd18Cfli23DyWbpe5X7Utk1Icrh4nx96hd1mZSR7+7adcdv04PB4XdfV7yjnM2A3MWfpce74JUikoLDSP8ZQvmOW6qi+rdPa5bXEwn7WelJ+eT5a3baDxeJwFCxZw+umnd/hPH+le+38f7y8UivO1ry1g5MjTGTNG9WNHakP2pvqxN9XPXi2j0bpi+VA9oN34/pb7+RxK+Y6Wt0hLSyOtZYzSPjweT49/UMaMMae5XbLEHEOfk5hMy99rw4A1a+HYafCdLx7a1OQjCuHFwXu3u++hMAzYshGmTYMvTWm/3WEFHa87ZgB83ADhqDmMxZ0JsdDea2K83jjwKYn6YSQzPDQ3mdfRANRsN3+WlECxFxyxruM4UDw+L+Q5ob7GTN6ys/cMO2uCiN884W+J2zD2JlJmgmf+3u46Ikfbci3rArjdEE2ZP1uGs3U0VK8liUskzPeJJs11jjnN3Edouy8+L2QloXaHmfhFGyDVZO7Tvn2/TmfH11XsX6/7a/k4JxLmNrKLzTqK1w0jp9BDrMbcrtvd/ngYxp7kOGVef1XogbVru64vq3T2uYWD/6zZhRXfRdL++3j/z9D2Pd9jRxyh+rE7tSF7U/3Ym+qHg95/S08nioqKcLlc7XqXdu/e3a5XqcWAAQM6LO92uyksLOy2WA8Xp9OcGryoyJz6trnZPIFtbjafFxXB979/6Cd6n2e7na0bDEJpqfl6Mmme3Hs8exOFlpMMr9ecfcrlgpEjzfsTxffM0FZWZq57KPvXUTzJpLldt3tvb0o0ChkZe+NwOs1kpCUZ2nd7LUnGvlN3G0b75MTh2DstN5j73DIphHuffzO43ea68fjeY+H1mr+PHm3G3/Je++6L328eI5fLPGYeD4wf3/76io6SppYkruXR0XFr2a99n4M5U1hlpZlwut3mPu2bJLb87vWaCemgQWbS9Fk/jz2hu9qS9B9dfYZa/qToMyQiImBxj5PX62Xq1KksWLCgzTVOCxYs4JxzzulwnenTp/PSSy+1Wfb6668zbdq0XpMtT5liTjnect+QigpzNrZp08wTvc96H6fPs93O1v36180TiWefNaezTqXMk4i0NPOCajBPsrOzzfINDebPL3/ZPBmvqzOHwxzq/nUWz1lnQX09fPqp+V5gnvS0DCNsuQdLyzV+Lb1FPh8MHGjG3txszsQWiZhlHA4zkcnPh29/24z53XfN9SIRcxsul5l85OWZz5uazMSyJcHx+aCgAGbMgOuua7uP++9LJGJOVtASq9dr/ue75Qau+/YEud1m74/Xa8YcDO5NepzOvb1erfdx2tMb2NIj1zL8aNgwMz6fz9zOzp3m8UqlzG2lpZn7l5lpHk/D+Pyfx57QXW1J+o8DfYa+9z2zrYiIiIANhurNnj2bCy+8kGnTpjF9+nQeeeQRtm/f3npfpptuuoldu3bxl7/8BYDLLruM+++/n9mzZ3PppZfy/vvv89hjj/HMM89YuRuHbMoU82ap+9+p/vP+Z/PzbPdA6/7ud/Dkk+bQlSFDzHubbNkC69fDQw/BEUfA5s1t14PPt3+dxQPm+65aZf4+YYK5fOPGvcvGjjUTkaoqMzkYN8787/GIEXvLxePmdMOxGAwdat7s0us1y7dsv6W3zO02e89OPdXc/htvmCdYiYSZnLhcZhyjR3e8jx3ty4gRbY/ZsGHmdpctM2MvL4ejjoLTT2//npmZ5hTKAweaPVZgJpOGAVlZZpKUm2vGv3Fj+zrKzDTvGbbv8cnfM/2733/4Po89obvakvQfnX2GkkklTiIispflidO3v/1t6urquOOOO6isrGTChAm8+uqrDB1qXs1dWVnJ9paB5sDw4cN59dVXufbaa3nggQcoKyvj3nvv7RX3cNqf07n3Xj922W5n63q9cPHFbZeNGmUmGKNGmYlFR+t93v3rLJ6xY83HgZZNmNDxNjtad//37KrMGWd0/tqBtrv/vuz/fNYs8/FZ3nPcuPbL4nHzZLCjOuqofG/VXW1J+o+OPkP73rtNRETE8sQJ4PLLL+fyyy/v8LXHH3+83bKTTjqJpUuXdnNUIiIiIiIiJg1mERERERER6YISJxERERERkS4ocRIREREREemCEicREREREZEuKHESERERERHpghInERERERGRLihxEhERERER6YISJxERERERkS4ocRIREREREemCEicREREREZEuKHESERERERHpghInERERERGRLritDsAKhmEA0NzcbHEkvVs8HicUCtHc3IzH47E6HOmA6sjeVD/2pvqxP9WRval+7E31s1dLTtCSI3SmXyZOfr8fgMGDB1sciYiIiIiI2IHf7yc3N7fT1x1GV6lVH5RKpaioqCA7OxuHw2F1OL1Wc3MzgwcPZseOHeTk5FgdjnRAdWRvqh97U/3Yn+rI3lQ/9qb62cswDPx+P2VlZTidnV/J1C97nJxOJ+Xl5VaH0Wfk5OT0+wZnd6oje1P92Jvqx/5UR/am+rE31Y/pQD1NLTQ5hIiIiIiISBeUOImIiIiIiHRBiZN8Zmlpadx6662kpaVZHYp0QnVkb6ofe1P92J/qyN5UP/am+jl0/XJyCBERERERkUOhHicREREREZEuKHESERERERHpghInERERERGRLihxEhERERER6YISJxERERERkS4ocZJOvf3225x99tmUlZXhcDj417/+1eU6ixYtYurUqfh8PkaMGMFDDz3U/YH2U4daPwsXLsThcLR7rF27tmcC7mfmzJnD0UcfTXZ2NiUlJXzta19j3bp1Xa6nNtQzPkv9qA31rAcffJBJkyaRk5NDTk4O06dP57XXXjvgOmo/PedQ60ftx1pz5szB4XBwzTXXHLCc2tCBKXGSTgWDQSZPnsz9999/UOW3bNnCmWeeyQknnMCyZcu4+eabueqqq/jHP/7RzZH2T4daPy3WrVtHZWVl6+OII47opgj7t0WLFnHFFVfwwQcfsGDBAhKJBDNnziQYDHa6jtpQz/ks9dNCbahnlJeX85vf/IbFixezePFiTjnlFM455xxWr17dYXm1n551qPXTQu2n53388cc88sgjTJo06YDl1IYOgiFyEABj3rx5Byxz/fXXG2PHjm2z7Ec/+pFx3HHHdWNkYhgHVz9vvfWWARgNDQ09EpO0tXv3bgMwFi1a1GkZtSHrHEz9qA1ZLz8/3/jjH//Y4WtqP9Y7UP2o/VjD7/cbRxxxhLFgwQLjpJNOMq6++upOy6oNdU09TnLYvP/++8ycObPNsjPOOIPFixcTj8ctikr2N2XKFAYOHMipp57KW2+9ZXU4/UZTUxMABQUFnZZRG7LOwdRPC7WhnpdMJnn22WcJBoNMnz69wzJqP9Y5mPppofbTs6644gq+8pWvcNppp3VZVm2oa26rA5C+o6qqitLS0jbLSktLSSQS1NbWMnDgQIsiE4CBAwfyyCOPMHXqVKLRKE8++SSnnnoqCxcu5MQTT7Q6vD7NMAxmz57NjBkzmDBhQqfl1IascbD1ozbU81auXMn06dOJRCJkZWUxb948xo0b12FZtZ+edyj1o/bT85599lmWLl3Kxx9/fFDl1Ya6psRJDiuHw9HmuWEYHS6XnjdmzBjGjBnT+nz69Ons2LGDu+66S3+0utlPfvITPvnkE955550uy6oN9byDrR+1oZ43ZswYli9fTmNjI//4xz+46KKLWLRoUacn52o/PetQ6kftp2ft2LGDq6++mtdffx2fz3fQ66kNHZiG6slhM2DAAKqqqtos2717N263m8LCQouikgM57rjj2LBhg9Vh9GlXXnklL774Im+99Rbl5eUHLKs21PMOpX46ojbUvbxeL6NGjWLatGnMmTOHyZMnc88993RYVu2n5x1K/XRE7af7LFmyhN27dzN16lTcbjdut5tFixZx77334na7SSaT7dZRG+qaepzksJk+fTovvfRSm2Wvv/4606ZNw+PxWBSVHMiyZcvU9d5NDMPgyiuvZN68eSxcuJDhw4d3uY7aUM/5LPXTEbWhnmUYBtFotMPX1H6sd6D66YjaT/c59dRTWblyZZtlP/jBDxg7diw33HADLper3TpqQwfBqlkpxP78fr+xbNkyY9myZQZg3H333cayZcuMbdu2GYZhGDfeeKNx4YUXtpbfvHmzkZGRYVx77bXGp59+ajz22GOGx+Mx/v73v1u1C33aodbP73//e2PevHnG+vXrjVWrVhk33nijARj/+Mc/rNqFPu3HP/6xkZubayxcuNCorKxsfYRCodYyakPW+Sz1ozbUs2666Sbj7bffNrZs2WJ88sknxs0332w4nU7j9ddfNwxD7cdqh1o/aj/W239WPbWhQ6fESTrVMnXo/o+LLrrIMAzDuOiii4yTTjqpzToLFy40pkyZYni9XmPYsGHGgw8+2POB9xOHWj//8z//Y4wcOdLw+XxGfn6+MWPGDOOVV16xJvh+oKO6AYw///nPrWXUhqzzWepHbahn/fCHPzSGDh1qeL1eo7i42Dj11FNbT8oNQ+3HaodaP2o/1ts/cVIbOnQOw9hz1ZeIiIiIiIh0SJNDiIiIiIiIdEGJk4iIiIiISBeUOImIiIiIiHRBiZOIiIiIiEgXlDiJiIiIiIh0QYmTiIiIiIhIF5Q4iYiIiIiIdEGJk4iIiIiISBeUOImIiIiIiHRBiZOIiMjnUFdXR0lJCVu3bj2k9X70ox9x/vnnH/ayn8V5553H3Xff3W3bFxHpC5Q4iYhIn7Fz505+/OMfM2rUKHw+H6WlpcycOZOVK1cCYBgGeXl53Hfffe3WvfLKKznqqKMAmDRpErfeemuH73HnnXeSn59PTU0NAHPmzOHss89m2LBhhxTrnDlzePTRRw+57DXXXMPXvva1Q3qvrvziF7/g17/+Nc3NzYd1uyIifYkSJxER6RO2bt3KlClTqK2t5cknn2Tt2rX8/e9/Z9y4caSlpQGwadMmmpqamDZtWrv1Fy9ezNSpUwEzcWpJtvZVVVXFnDlzuP322ykuLiYcDvPYY49xySWXHHK8BQUFZGZmHnLZjz/+mGOOOeaQ3+9AJk2axLBhw3jqqacO63ZFRPoSJU4iIv3IM888g8/nY9euXa3LLrnkEiZNmkRTU9NheY8vfelLXHnllVxzzTXk5+dTWlrKI488QjAY5Ac/+AHZ2dmMHDmS1157rc16//d//8eMGTPIy8ujsLCQs846i02bNgFQU1PDgAEDuPPOO1vLf/jhh3i9Xl5//XUA7rvvPjIzM3nuueeYPn06w4YN44QTTmDu3LmMHj0agCVLluB2u/nCF77Q5r0TiQQrVqxoTZwmTpzIqlWr2u3bzTffzNChQ7n88ssBeO2113C73UyfPr21TElJCX/84x/brPfxxx+TlpbWuj9bt27F4XCwbds2UqkUd955J0cccURrL9mFF17Yuu6+Zb1eL++99x633HILDoeDY489tsv6qK6uxuFwcM899zBlyhR8Ph/jx4/nnXfeaVPuq1/9Ks8880yX2xMR6a+UOImI9CPf+c53GDNmDHPmzAHg9ttvZ/78+bz22mvk5ua2KXvnnXeSlZV1wMd//vOfDt/niSeeoKioiI8++ogrr7ySH//4x3zzm9/k+OOPZ+nSpZxxxhlceOGFhEKh1nWCwSCzZ8/m448/5o033sDpdHLuueeSSqUoLi7mT3/6E7fddhuLFy8mEAjwve99j8svv5yZM2cC0NDQQCQSYfv27Z3u/5IlSxg3bhzp6eltlq9evZpwONwmcdq0aRPhcLi1zLJly3jiiSe49957cbvdALz99tvteq8mTJjA6tWr2yy76aab+O///m9GjhwJwPLly8nLy2Po0KHMmTOHp59+mkceeYR169bxz3/+ky996Uut67aUHTx4cGuys3z5ciorK5k/f36n+7pv3AB/+MMf+P3vf8+KFSsYNmwYF1xwAalUqrXcMcccw0cffUQ0Gu1ymyIi/ZIhIiL9yksvvWSkpaUZv/71r438/Hxj1apVHZarq6szNmzYcMBHKBRqt95JJ51kzJgxo/V5IpEwMjMzjQsvvLB1WWVlpQEY77//fqdx7t692wCMlStXti67/PLLjdGjRxsXXHCBMWHCBCMcDre+tmTJEmPIkCGGw+Ewpk6datxwww3G6tWr22zzlFNOMX74wx+2e68//vGPhsfjMSKRiGEYhrF9+3YDMJYsWdJa5sQTTzS+8Y1vtFnvnHPOabe9q666ypg5c2br8/nz5xtZWVlGdXV167LbbrvNOOmkkwzDMIwTTjjBuP766zs9DvuWnTdvnlFYWNhp2Y785je/MTwej7F58+bWZYsXLzYAY/v27a3LVqxYYQDG1q1bD2n7IiL9hXqcRET6mbPOOotx48Zx++23M2/ePMaPH99huYKCAkaNGnXAx/49Ny0mTZrU+rvL5aKwsJCJEye2ListLQVg9+7drcs2bdrE+eefz4gRI8jJyWH48OEAbXqQ7rrrLhKJBM8//zxPPfUUPp+v9bWjjjqKzZs389Zbb/HlL3+Zf/7zn0yePJl58+a1llm6dGmn1zeNHz++9VqowYMHk5eX13qd09///nc+/vhjfve737VZLxwOt4kB2vY4GYbBzTffzE9/+lNKSkpayyxfvpzJkycD5hC5u+66i5kzZ/LQQw9RX1/fZnv7ll22bFnr7wdr+fLlfP3rX289nkDrfu6rpS737QUUEZG9lDiJiPQz8+fPZ+3atSSTydYEpiOfZ6iex+Np89zhcLRZ5nA4ANoMFTv77LOpq6vj0Ucf5cMPP+TDDz8EIBaLtZbZvHkzFRUVpFIptm3b1u59XS4XJ510Er/61a9YvXo1JSUlPP300wDs2LGDxsZGjjzyyHbr/fvf/+b4449vs6zlOqdoNMr111/P9ddfz9ChQ9uUKSoqoqGhod16u3btorm5meeff56dO3cye/bsNmVWrFjRep3Vddddx5o1azjttNO47777GDVqFFu2bOmw7L5J1MFavnx5u2u6li5dSlFREYMGDWpd1pKwFRcXH9L2RUT6C7fVAYiISM9ZunQp3/zmN3n44Yd59tln+fnPf87f/va3DstedtllfOtb3zrg9vY98f486urqWLNmDQ8//DAnnHACQLvJC2KxGBdccAHf/va3GTt2LBdffDErV67sNPlLpVJEo9HWRCAejwPte1QWLFjAxo0beeyxx9osb0mc7r77bpLJJDfccEO795gyZQp//etf2yybMGECDoeDFStW8POf/5xbb72VrKys1tebm5vZunVrmwRo9OjRXH/99Vx99dXk5uby6aefMnz48HZlV65cybnnntv5gdxPOBxmw4YNJJPJNsflnnvu4aKLLsLp3Pv/01WrVlFeXk5RUdFBb19EpD9R4iQi0k9s3bqVr3zlK9x4441ceOGFjBs3jqOPPpolS5a0Toqwr4KCAgoKCnoktvz8fAoLC3nkkUcYOHAg27dv58Ybb2xT5pZbbqGpqYl7772XrKwsXnvtNS6++GJefvnl1v055ZRTKC0tZfPmzdx5550YhtHa2zN8+HDGjh3LTTfdhNfrpbi4mA8//JBbbrmF733ve5x44olt3m/ixIk8//zzvPvuu/zpT3/qcFjiGWecwU033URDQwP5+fkAZGVlMXToUK6//noALr300jbrrFixApfLxfjx4/nf//1fSktLOfroo3G5XPzxj38kPz+/tfdr37JgJj2ffPIJFRUVZGZmtpvQY38rV67E4XDw17/+lVNOOYW8vDx+8Ytf0NjYyM9+9rM2Zf/zn/+0TrQhIiLtaaieiEg/UF9fz6xZs/jqV7/KzTffDMDUqVM5++yzueWWWyyODpxOJ88++yxLlixhwoQJXHvttfz2t79tfX3hwoXMnTuXJ598kpycHJxOJ08++STvvPMODz74IEcddRQvv/wyZ511FkceeSSXXXYZY8eOZcWKFYwaNQowhwe+8sorjBw5ku985zuceOKJPPzww/zqV7/i8ccfbxfTxIkTqa2tZdq0aZx33nkdxj1x4kSmTZvG888/3275Bx98wK9//evWGfharFixgrFjx5KWlkYkEuHOO+9k6tSpzJgxgw0bNvDmm2+2JmH7lgX41a9+xXPPPcegQYO44447Wrf5+OOPtw5/3Nfy5csZO3YsP/vZzzjvvPOYNm0aTqeT999/n7y8vNZykUiEefPmtUvyRERkL4dhGIbVQYiIiPRWr776Ktdddx2rVq1qM/StJ912220sXLiQhQsXtll+xRVX0NDQ0HqdV2ceeOABXnjhhdZ7YomISHsaqiciIvI5nHnmmWzYsIFdu3YxePBgS2KYP38+99xzT7vly5cv5+yzz+5yfY/Hw3333dcdoYmI9BnqcRIREcv8+9//ZuXKlVx77bUHfP2cc85h9erVB5UEiMkwDHJzc3n22Wc588wzrQ5HRKTXU+IkIiK298ADDxAKhfjpT39qdSgiItJPaXIIERHpVh988EGbnqKXXnqJH/7whwDMmjWLNWvWAPDwww9z1FFHMWHCBM4///zW1xctWsTPfvYzHn30UaZMmUI4HO75nRARkX5PPU4iItKtmpubmTZtGuvXrwdg+vTpPPXUU4wYMYJRo0axdu1a/H4/p512Gh999BEul4vGxkby8vJaXz/55JN5+umnLbuGSERERD1OIiLSrXJycohGo8TjcV566SXGjx/PiBEjaGpqIisrC7fbjdvtpq6ujhtuuIHVq1eTl5fX5vWdO3cqaRIREUspcRIRkW53xBFHsHHjRubMmdN649VVq1a13tg1OzublStXMnnyZM477zxefvnl1td37tzJoEGDrAxfREREiZOIiHS/cePGcddddzFx4kSGDRsGmInThAkTANiwYQPZ2dlceOGFnHDCCUSj0dbXt2zZQllZmYXRi4iIKHESEZEecOSRR/LXv/6VW265pXXZ6tWrWxOnX/7yl4wZM4YpU6bg8/k499xzW1+fMGECGzZsYOLEiaxdu9aqXRARkX5Ok0OIiIiIiIh0QT1OIiIiIiIiXVDiJCIiIiIi0gUlTiIiIiIiIl1Q4iQiIiIiItIFJU4iIiIiIiJdUOIkIiIiIiLSBSVOIiIiIiIiXVDiJCIiIiIi0gUlTiIiIiIiIl1Q4iQiIiIiItIFJU4iIiIiIiJd+P85dyxMAgfahwAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import io\n", "import statsmodels.api as sm\n", "\n", "# Load the data\n", "data_path = \"../data/\"\n", "suv_file = data_path + \"suv_percentilesSLOthenUWM.mat\"\n", "flags_file = data_path + \"flags_combined.mat\"\n", "\n", "# Load .mat files\n", "suv_dict = io.loadmat(suv_file)\n", "flags_dict = io.loadmat(flags_file)\n", "\n", "# Extract relevant data\n", "suv = suv_dict['lung_SUVperc_COMBINED'][0:58, :, :]\n", "flags = flags_dict['flags'][0:58, 3]\n", "\n", "# Choose percentile of interest\n", "p = 94 # For lung and bowel, use 94 (0-indexed)\n", "X = np.nanmax(suv[:, :, p], axis=1).reshape(-1, 1)\n", "\n", "# Handle missing values\n", "valid_indices = ~np.isnan(X).flatten()\n", "X = X[valid_indices]\n", "flags = flags[valid_indices]\n", "\n", "# Add intercept term\n", "X_with_intercept = sm.add_constant(X)\n", "\n", "# Fit logistic regression using MLE\n", "model = sm.Logit(flags, X_with_intercept)\n", "result = model.fit()\n", "\n", "# Print model summary and parameter confidence intervals\n", "print(result.summary())\n", "print(\"\\n95% Confidence Intervals for Parameters:\\n\", result.conf_int())\n", "\n", "# Prepare values for plotting predictions\n", "x_vals = np.linspace(X.min(), X.max(), 100)\n", "x_vals_with_intercept = sm.add_constant(x_vals)\n", "\n", "# Compute predicted probabilities\n", "predicted_probs = result.predict(x_vals_with_intercept)\n", "\n", "# Compute confidence intervals using the delta method\n", "# Get the covariance matrix of the parameters\n", "cov_params = result.cov_params()\n", "\n", "# Compute the standard errors for the predicted probabilities\n", "# For each x, compute the gradient (Jacobian) of the logistic function\n", "def logistic(x):\n", " return 1 / (1 + np.exp(-x))\n", "\n", "# Compute the linear predictor\n", "linear_pred = x_vals_with_intercept @ result.params\n", "\n", "# Compute the gradients\n", "gradients = x_vals_with_intercept * (logistic(linear_pred) * (1 - logistic(linear_pred)))[:, np.newaxis]\n", "\n", "# Compute the standard errors\n", "standard_errors = np.sqrt(np.sum(gradients @ cov_params * gradients, axis=1))\n", "\n", "# Compute the confidence intervals\n", "z = 1.96 # for 95% confidence interval\n", "lower_bounds = predicted_probs - z * standard_errors\n", "upper_bounds = predicted_probs + z * standard_errors\n", "\n", "# Ensure the bounds are within [0,1]\n", "lower_bounds = np.clip(lower_bounds, 0, 1)\n", "upper_bounds = np.clip(upper_bounds, 0, 1)\n", "\n", "# Plotting\n", "plt.figure(figsize=(10, 6))\n", "plt.title(\"Prediction Probability of AE Depending on maxSUV Value\")\n", "plt.xlabel(r\"$x = \\max_{visit} SUV(visit, p)$\")\n", "plt.ylabel(\"P(AE | X = x)\")\n", "\n", "# Scatter data points\n", "plt.scatter(X[flags == 0], flags[flags == 0], label=\"NC\", color='blue', alpha=0.6)\n", "plt.scatter(X[flags == 1], flags[flags == 1], label=\"AE\", color='red', alpha=0.6)\n", "\n", "# Plot the mean logistic curve (S-shape)\n", "plt.plot(x_vals, predicted_probs, color='green', label=\"Logistic Regression (MLE)\")\n", "\n", "# Confidence interval band\n", "plt.fill_between(x_vals, lower_bounds, upper_bounds, color='green', alpha=0.2, label=\"95% CI (Delta Method)\")\n", "\n", "plt.legend(loc='center right')\n", "plt.grid(True)\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "e66de4c4", "metadata": {}, "source": [ "#to chech the CI of the parameters" ] } ], "metadata": { "kernelspec": { "display_name": "base", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 5 }