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4IWuIFfIlDQoTFetfJueggInqA1mHz0TCBAApo4AhdioD9wDB8kCoQv7HMwDipGGASDmHKPhcHxUMsWHuQAljvyUYMRt5QsSYJrhn/ieCPivHkj/ES0NBK5WWNlrKDGJPzmSiSFsQCY3GHmWrSAwEDN/Q+++/nxDmUZF6wE/E1CCyXpBoIZck4cjKui69rV+/vkQjAvw6krRO6dn58+cnRDMiWk/27NmtIyV79OhR2edaSOsUrETvcURoXZfcOnK111xzjS1QoEDCRnQkR+K2X79+ElUqHNOnT7c5cuSwTlHKcaeubYMGDSQikHsYiZDkiN9myJDB9u/fX647ZMgQ68jeOtJPuEfuy6lgyWvLli22WrVqcj/kE7yfXLly2cKFC0sa11DI//wqYhspid4Vz0hN9C5F8kgueleyEg2bJvZDou74gTBkMeYAVCcDU96eSrccey3K1MeapPtNWqLT0x0hkg/54LGAHchvqF3suiydEh7bkjyxBXMe10O9PvLII2br1q2y3Mi7774rnhDsQ+GyKCG/XJd749r+HrH1orbp/nM/RFzCk4A8/L2wzhErwvJLEAwG+8iPgCAKhUJxtkiSaOnOskwyYMDJkxVEi9G8TJkyQlYemBk4h6U8IEW66XTRGaDCjEBaIiJBWpgMOB8C5xieAHTLCUQd3jXHbkQePmo9ZgyWAcHWi40WAiQ/SBIDPnZkuuOsyURaiJkuOvlgLmBf+/btpaHgnmgMsO1i1sAcwv94QfCMnIcPMdfGRqtQKBRniySJFrKCbJi4gOrzQGHiSRAkX+CUsfzP6D9KGG8FFqZjH6QKGeLPSpxLbKbYXRnJf+KJJ2RSAZ4IXjUHATFCtHglMIiBWkaRsvw1qpbGADuI6/ZI6DaIHOWKWoX4WRCO6zBARzqIHeXM/bAEMiqbmWOoZsi6Xbt2co369evLtXlWCDgtB8EUCkX8IVlFSzwDXKf8kieQKYZeCBGiDQIyQk2ynhJTZRmQgrRwm0LlQriQLMQHeeO3ircCbl4s44wLVbjZAHAPXI+lMSBH7oWliyFfzudvGgVG71mplLSQLGp16NChMiiGRwPkzmw2PB5QxlwLVYxHAQNzLE/CfeCSgSmBe/WTGxjA454VCoXibJGk1wGTCxjJh7gYPePXEy0qkn3BNac4hp0WP1VUJdHkAYu4QbbezIAixp2JvDmHNarIC+ILKmQP/G5RnZAoqpZzMAMwQkreeEJA8vyNuQKiRIkyjRj7LKYDP30Yl7SgeYK8IGXIGM8HTA+YIvjlGTi2bds28Z3FfKCIbaR0hYV4RWpWWFAkD3goqRUWdCkbRVxAifb0UKJNGyRHtEmaDhQKhUKRdlCiVSgUighDiVaRANz3sKMzGKoWpd+g5XB6UD6nK6MzHQcpSeOR0nTRBiXaOADEiRcFv0mByssAKK5wTLfG3S25tPEEGh0f+Cf4gdMg4e3CwKzf+J908QTKB3dKnj0c1B8Gz/FNT6oMAWkoOwajSXOmkKnkQTquG2tQok3noHLjDoeLG5U0KVDhiVuBKx4TQYheBpnEOwhQRNAhgioFCQCXQCa54P7oN/4/ZW57Ogf1igaZgE+4RAYBEa5bt0581SkbfOm7desmHkGebClPPJgYnPQTmJhMBDEnB9xGKWcEwekIORqhRBsHYIozkzqSU6nsR8kSIxh3txEjRiRMpY5HQAa4CBJkhUkrKC1PEDRATLghqhxui4zQs+GCGC/hBSE5SJZgS5Al5ePBMVw9IVBIs1+/fqZJkyYSapUwjChYQBp84XH17Ny5s/i7z507V3zjGbkPwpM6szZ5L6poFWkKFAAVjCnOtOJMuCCqGF0t/+HzS5eK48RoYIYb5OArI38TIhCfZD6KcFULceD/jC8y/sZMXyZPZvhRqT05s4//8Usmb7qFpOFeIOdJkyaJAuQ6/t64b9KTN3EmWI9u9erVci5p+BA51398HixdxHNfKFXN83Xt2lXu2z+LB/eOLziB4HnepUuXykZDBamkd/CuiHBH0H3qHP7vwTKifAhfSt2dMWOGuIwNHz5cfokMRplCxuxjQhKxTyBaXO+IrkfvCzUcBEROTGp827lW+DuJCbibVkQpHNlY13WVqGNEn7r55psl2lnDhg2tI0+JTOZaf+u6ZRLJrHbt2rZKlSoS0WzChAnWVXaJIkSEMiKkEbGMKGpBuA/DNmrUSI7nzJlT0mzatEnycQpCjgNHPtZ9QLZx48YSCc2RrC1UqJB1H4l13T5bvXp1iZhWr149iQDFvXEPHGvWrJklMlSFChUkmlufPn3kvletWiV5EJHNwxG7bdWqlXUfpkRiSyukNHoXz+mIRKLM9ejRwzplb+fMmSP7gWsEbKlSpWyHDh2sayhkO3bsmHWNghyPVaQ0etfWrVtt0aJFpR7wHqkzRPTz2Ldvny1SpIjk5csMuIbIXnHFFVK21J9y5cpJ3XDKVo5TX6gPRAx0ylf2ASciJBqf6zVYR8TyPlauXCn1JBrhGoPURe9SXHig6FCgKDxWg0ARvPDCC6ICUYgor2nTpkng8oEDB0ocXexlBDjHaZp4EMT5JZYEU5BRnY7sQrn/BqY2Exwdh366e5zPbD4/uIP68EBZsJ99KF0UBitSoFRZAogp2ATvQelxnPNRwQRkR2k7wpJ7wdZG15vYE3S3UeLk6eqjqEXUIc/AjMTzCe6ZGB+DBg0SBYYphVmCQdDlpYeAmiMAfY0aNaRrzPtBxaV3MLsSGz6xprGrhpcP9QNV6xq2U95fgQIFRP1iwsI0wMZsTR9/2k/TZ5aoI1LZx/tgmj6Bp1C01NG0jAl9PqFEG+WgImPLYnowdkDCRWIbxAwAkUG0BC6/++67ZUoyU4aplBybN2+eVHbsrWw+ME8Q5E9+EC7HiAWRUoIjHQMYfDBcm2A83CNTlz1BEyfioYceElIl9CShNLk3upB8tMTGgIAhL85xqlM+OAJ1h3/EkQQkz8ePyYAyZNmb8LICdG0hAKLIESiJAR/MJ7169ZIGj3zSM2gYCUeaXD2hbBAI4dPWqWOQKeYCGmzSkUfwHVPeEClpqAuIDN4H9YslqqijsQol2igHFZFKS6WmolLZ2FANVEYIilFbTwqkyZ49uxAepIDqjRS4J2JVcI/+3lAowcERiBaC5wMiDcvJ8Esa0tOI8D8DTNwryhf7HxHT2H++gBJjxQ2mohKQCBLwgDw9gRKfo3Xr1uJ5gLIjSh2KnOfGzghJpGfwHv37Tgq+rMIbSa9EIVhAmnB1Sp5+wxbMiisMlvE+wpcg8u8jVqBEG+Wg0nmS8uBvX9H426tHD46hKiCy4Hmpgc/XX4e/UaJBkCb8YwkHacLvwf/PuTQIBCGCrBgAo2vJ2nEpVdVpAZ4NhYrpg7XmuDYhPzEjUI70HjDX0LixXBLmG6K6odIgAEwtrKAMOWBaiGdAsGwMigZB2VGXvHmANF4seNDQ8j+qGbMXJi0i89Eo8z78AClmGwZwwwdRoxlKtDEMKivBK7BpeR9FNjwN6M5ij/XhJ/2xlAACRFHSvadicx7dauytKc0jpUDxPvLII2KXZXULuoko9DMReFqCZ/LPhu0bUweqdcCAAaLACExP2E9s0hAAdujgR07D4UNphjcq8Qbfq8EjJUii1EnKl7ECGifS4JESbLyps5AtZjKC7lO/MX8RVpX3QQNHnviEY0NPaqJEtEKJNoZBpYakaOGJ9UtISVp9urCoAhaWhGgxK6AwGGiiMp8JkByO+qhL3LGwueKLS5D2tCYS7g8VCbFzDWzNPNf5BM9LuE0GE6dOnSoDPWy4KaFusRNSvihYPnaW1WcQEKUFMWAuoKGAPAjPGc/gPbJqCXUFV0EaKsoJFzjK0puFmHgA0UKokC3qFrcuGnbqAJNneB/UCf8+mBAC+TLwy/vADBUrUKKNYvjBKT5gD4iJ1SQgUiouZEoLz0AMA0u0/Kgu7I0MQFExGbChwrO6xJIlS0I5/R8QDdchT4iUDedyzucXZ3L8d1lZmEEvrgsZck6wsnMe9mFvX0W5kMaraoDyYxDMPxPpSE8weT5IvA3Op5oF3AP3yQBccENZU36MrjOKzrNSxqgq1qxj4A6CJYg8DRkDYpRPPIP32rdvXyk3iPGTTz4Rbxf8ZRm0xfuA+tClSxep35Qj6/5BqjRiLBuFJwfjEuHvg8aQfOmpsflxiZiAk/OKKIVr5a1TqeKn6eHIyLpu7in+jk4RyErDjgzFJ5VjThmEjlpZPXjDhg3WVegEv8UgHAmLfyg+kI5EEvY5pSYrCZMnf5Mv5zsVJz6uTrGI36AH5zr1aw8dOiTnO/Us9889e+A/yz5+Ael4vvbt29uWLVtGzD/ybFbBXb58ufj9fvTRRwnlyTsZN26cLV26tM2TJ4/4DrNq8oABA055T7GGlPrRBuG69bICtesFhPb8Bvy3hw4dKqtKU36UEytkb968OaEcqZNjx46V8ylDfL1dz0b8vJOrA6y8Tbq1a9dGrJ6cK5Lzo9XA34oLBrrddC8xTTC9csiQIeKTGgngg5nawN8obGzTKHMUPMoXcN8oWLq97oOXrjJK9nybPNISZxP4GxspG8oy2OsClBEDjJgHKBuWuvIeJx6kYXYg5UivBg8WzDPJ9Wi4FmMR3h0xGkF90cDfiqgClbJt27ZiZ6Zrjo9tNAECwSuC3yBB0PWFjPBpxgsB/+BYJtmzRbgZKAjKCNMTkz4wwXhzUhCkwWeZMmRMAJPY6cxGXI/3EYtlrUSruGBAmTCrjJlkrjue5AerUKQHKNEqLhgYVGPwIzgVU6FIj1CiVSgUighDiVahUCgiDCVahUKhiDCUaBUKhSLCUKJVKBSKCEOJVqFQKCIMnRl2gcCsI8LvEUxDEXmwkCBxG5hkoEgM4r726dNHFlEMj/2qSDn4rkePHi0zEYMzw5RoLxAIs0ewFpapUUQeTAVlFhMzixSJcezYMVnRgBlvsRQVK9pAJDKmCXfs2FGJNhrAHHnULL+KyIOpoCg2lttRJAaBzZ944glZM45IZoqzA980YRyJf6FEq4g7nE1QmXjC2QSVUSSGBpVRKBSKCwQlWoVCoYgwlGgVCoUiwlCiVSgUighDiVahUCgiDCVahUKhiDCUaBUKhSLCUKJVKBSKCEOJVqFQRD38TEqmt8bibEolWoUiAD7iTZs2mffee88sW7bMnDx5MnREEQlQ3rt27ZIAS8mBNJMnT5bAQK1btzY7duwwsTahVYlWoQjh119/NV999ZVp2bKl6d+/vxkzZkxMqqdYwtGjR03Xrl3NwoULkyRP9u3du9c888wz8ne1atVkWfJYgxKtQhECpPr++++bgwcPmtdee828+OKL5pJLLgkdTRkggzOprZSkiQX88ssvCRtdekjzxx9/TPRslCsxAIgOFgykRMNG1DBCNHKMyFfh59Kj2L17t7yTzp07mw4dOpgrr7xS0nK+B3+zj/TkwS8hC4PXDt4bvxwnHecdP35cNn8PPj+2IDhGPuTr80oJlGgVCgc+nEOHDslHTSjFzJkzywZ5sD9oQuCD5MPng4NkDh8+LNuBAwfM+vXrRRVz3BMBITE5Rl47d+6UAC6QCyRDGvLZv3+/EIIHHzHkRRjN4LWjBdzf9OnTzbhx48zSpUtN+/btzd13322ee+45UaA+Dc+OWn388cflODGB165dK/t5vlGjRpk9e/aYOXPmmFdfffWUZ6Vsli9fbl5++WV5P1zrjTfeENNB7969zb59+0Ipjbwjomb94x//kDww/XAe50PO99xzjxynnMmX98b/3Dt5PvDAA7K99dZb8n4h4SFDhpjXX3894T2CI0eOmJ49e5rVq1cr0SoUqQUfJ91TFC0f8n333Wfmzp0rHz+2QYjBY/78+XLckyd/T5kyRX7btGkjH/Vdd91ltm3bJh8pv40bNzYjRoyQGMQPPvigadq0qZAF5MrH36JFCzNr1qyEj5ffN9980zzyyCNCCtEG7u+zzz4zI0eOFDNLqVKlTJUqVeSeCbfo1SLmF0j26quvFiKjUWnVqpUQHGrxxhtvNBdffLE0bnnz5j2FvPibGMI33HCDueiii0z+/PklDUQ+c+ZMadw8eA+zZ88W+zrX/eKLL8zYsWOljLk3Ar5DqETU4t64NiEhu3fvLiRft25daVj79esn9mCuzQbZQuIeEDl15Prrrw/tSRmUaBUKB0wEffv2NXfccYfJly+fGT9+vMSuRcFAqEGlhRKFHL2iRZENGjRIlBOEi5JicAcFhhKDpFGwEPfgwYPlQ4aU+WA/+eQT+cAhkOHDh0uegHxJV6xYMSGiaATPRllATl26dDHdunUTkl2xYoWUGwQFEdO4QFg0QjQ2JUuWFHLmWQlbmTNnTlO9enXTvHlzc+mll4Zy/+2dlClTRsqKvyHqJk2amAwZMsj7CCpN/uZ+2AC/EDGq9emnnza9evWSMJDcW7CML7vsMjERcd+8m6JFi8p74hrcN6S8atUqSc81UPFly5YVO3Fq3osSrULhwIdFDNEcOXKYTJkymRIlSkgAbJRUSlCuXDlRsZyHOqpcubL5+uuvE8iADx9CglBKly4tHzErGWzZskVsju3atROzhVfBEDWqjFF27i1agSLleXgWlsApX7683D+2WMwoqM/7779fjkGi2bNnF4VLt59jECiExS/PGV7eHOM89vObVJrkABlWrFjRXH755bJB8DR6EKxXzryr3Llzy/Fs2bKZwoULSy+D47ly5RLinTZtmrw/7hczCO8kY8aMcn5KoUSrUJwBvhuZHPj4IRvUEYAIIGnUkD8PkihYsGBCGsiVj5sPn2OQAN1kVC5qDeWEmkU9QULRChql4HPzLMArSoiSQOJBckTBUi5Bc8y5Iql3xL1QxoDr857C00HGviHjXoNpeDYaiQULFgjJfvjhh9JgsFqHPyelUKJVKE6DpLqH4d1W/xEHESQWwP9J5eXBB9+oUSOxI2JvxG7I4JEnrmhF+HN6sJ/GhnLCjBAEZhcAkZ0NaHggQt6DJ01IO9xDIBzJ3WtyoAHBtMHv4sWLzYwZM8ScBNmmNi8lWoXiNOCjoqvpiZXfSHgCQDqM3GMPZlCMxSQZVItmNXs60Kig8iHbt99+W0gQUoQQWWmXbjpmGk9YlKsnzTOBsvJdeX55F2vWrBF7cVqCe6MBxNwzceJEse9iJz6bxk+JVqE4DQoUKCCuWhs3bhRlhmuW796nJSAmbIKYF3CRqlWrloyyp1Y5RQu4bzwJnnzySRkAY0Bq6tSp4kXBACADjxAtahF7J+5YqHk/UHU6MOJP3vjVvvLKK+JuxQBkau2mKQF5Moi3ZMkSqQvYoM+m8VOiVShCgBz4iLzNETRo0EDci1CXFSpUkEEsSNCPOnMOZoOgyvH7yIe/ScffwQ+UfZwTNDlgT0Qx0bXGNsi50QrujQE/BpM8wbEP+ysz6/zgF2SIyxcuc8OGDZN9LACJdwdlgl0abwXOXbRoUaIGjP2oYlzC8M7gf86BmOvUqSMDVdiCUclt27aVwSvKmcHJZs2aSTl74NmBGx3lzH3gwYBt3KfhXbCIZ7169RLeFb9Vq1aVATNMOcG6kRroKriKuEBKVsGl+4p6pQvKctF81HRNcVPCGwC1BekykEUXGFLhI8W9i48XRQr4pPAgID/Sk5b/+dC9XZK86PqSFyPxgO41BNKpUydx6vf7zwfOZhVcbxOFoDxZQZSYWiBf9lEW/M/AIGVJWo7xS/n645QHpEb5BMkRUI4cp4yD1/G+uuTl82Pjb/ZzPT8YBoL3RjrO55rh98KvbyQ5B/cuSBsfWl8vkgMeC7oKrkJxGvARQzJ03/3HxIfIPtQsTu905yFAfG35iPkgIVC6wR6ciwLiYyNPXJ/4QIMfPR8759EFhkggd8gYJ3u6quyPdvDsbEFihLSCZElZkIYJCyhRr3R9+frjqFUanWBeHr4Mw69DenoW/FKe5OPz5jdY3iB4b6TheFL3Ql6QLZMfMEtg/sB1D9OBT5taKNEqFAHwEfpuowf7+CD5CDnG//5jZfP7gmCfz8enCX6kwfNQUdgxMRfgf4pPbXh+ivML3g+kvHXrVlOzZk2ZNQhRny30bSoUFxh8wKgm3IcYoWcSgOLCAqKlV8IUYgbu6MGcC5RoFYoLDJQtXWDsudh5z0U5KdIO9GAwG2HyONcehhKtQqFQRBhKtAqFQhFhKNEqFApFhKFEq1AoFBGGEq1CoVBEGEq0CoVCEWEo0SriAkw48BMIFImB3yhuZcFJFYrUg/LDFSy8rmmsA0VcgMAjTLlkKqciMZj3T0wGprPSKCnODsRXoByhVaYdeyjRKuICvpqrYkselJGWz7kjqbqmRKtQKBQRhtpoFQqFIsJQolUoFIoIQ4lWoVAoIgwlWoVCoYgwlGgVCoUiwlCiVSgUighDiVahUCgiDCVahUKRABaKZHVbZjgBv9psatztSevTk59fATeeoUSrUCgEkOPRo0dN165dZQVYSJI1zLp3754iouR8lgXfvHlzAjnv2LHDdO7cWZbqJr94hRKtQqEQoF7fe+898+abb8ry5xDjzJkzzccffywr9Z4JkCurxd57771CzJwPwU6ZMkX+9io3HqFEq1BEKTw58QtxsYWTFcd8Ok9uHvwNeSZ1HgjmzS9EOW/ePJmjnzdvXvnt2LGjGTlyZEKgmeTuh99vv/3WzJo1y+TMmVMC+HB+5cqVzYQJE0ylSpUSFjgMns/fQfj8+WVLLl2sQWMdKBRRCIhl9uzZssz1Dz/8YFauXCmRx5o2bWpy5MghpIXK/OSTT2S11uzZs5v58+fLsZYtW0oEqSVLlpgtW7aYjBkzmltuucWUKlUqIXwfn/2JEyfM4sWLzdatW4VYq1SpYurWrSsEuWHDBjEjLFu2zJQvX94UKFBAzkPpLliwwOzatctky5bN1K5dW1bv3b17t5k2bZp5/vnnzW233Wbat28vv+Tvr0++kDl5etME91SjRg0hZvD999/LfRcvXlyecdGiRXKf1apVMzfddNM5r0Z7wQDRKhSK6IEjILtz506bKVMm65SgdURmHSFZR0a2QoUKdvv27ZKONCVLlrS1atWyjght1qxZbePGja0jV1uzZk2bJUsWW65cOZs/f36bK1cuO3PmTOvIWc7dtm2bbdCggb322mtt0aJF7fXXX28daUq6Dh06WKeE7aRJk+SaH3zwgfz/xRdf2BIlSlhHsLZYsWL2mmuukftatWqVHTdunL3uuuusI3JbsGBBycMRpNx7u3bt5LqHDh2yzZs3l/PKlCkjeXDPnTp1so5g5b7Wrl0r99K5c2dbqFAhuTfukY1jTt1KuliDEq1CEWWA1GbMmGGdAhSiWbdund23b58dNWqUkNTYsWOFuJzas07JCgkNGjTIOmVqnVIUwmT/nDlz7MGDB4WYnRoUUuZ/p3ZtixYtbJ48eezkyZOt6/JLXuRz1VVX2alTp1qnPIUAM2TIINc+fPiwLVy4sJD2p59+avfs2WPfeecd6xS0pCPNo48+Kv+vX7/eHjlyxH755Zdy/iuvvCL5PfTQQ0LS48ePt3v37pXrOuUr5M7zQqKzZs2ScyBo7p90/ELg5PPzzz+HSim2oDZahSLKQJcaUwF46aWXTJEiRYxTi8apQZM5c2bjlKV0wTdu3Ci/bdq0MY7sTO7cucUM8Pnnn5sePXoYp2rF3MC5jz32mHEkK2YIpwyNI0vjlKZxCljMDWXLlpX0rLLgyF3souTvVKVx5C62W0em5uWXX5a0mCqckpbBL85zXCL5cn+YO5waN8uXL5dnqFixonGkK/ZbR/DyHNwT13XKV87lfniWpUuXihnBNSZienDkL6YH0gQDaccalGgViigDRIuNFDslNlBssNgm/S8kiH0WOyfk8/jjjxunRGX/6NGjxT774osvis0VkmMgqnfv3uJ6BWFNnDhRrlOvXj1ZUQG7LYNdfnUFpzAlL9y0OJ9rTp8+XQi3evXqQqKckyVLFrk2dmOnYM3+/ftN6dKlJR+ug/2Yc7Hx8jf+uRAzZMz5Pg9st1zP25XZxyAaBAucQpZfnoNzYhFKtApFlMGrSdfVF7KBiAADUQwWuS68kBZESBqUIWkgXwapIN/Bgwebnj17JmwMUo0aNUpIDIKGtPPnz58wuAQJr1692mTNmlU2BrdQsBAteXMtVKz3JgA0CJyPCiY9ihQVyj68HVDXZcqUkUbgm2++EYIl7yBZonTJJ0+ePKK4Dx06JNdkoA1A2GvWrJHzUNf+2rEGJVqFIooAsUBwEGYQkC8qFVKqWrWqqD88CujmQ2QeEBFpGjVqJN10tgoVKoh/7IEDB4S4IUuuAzED8qbbD9GhciFKuv3kgxolT4id/Z7oOHfgwIHmvvvuMzt37jTbtm2T9JgRAETLPlQ150CuXIfrsgHMGDNmzBCiRrnv2bNHyPr2229PIGPy5N5KlCghaluJVqFQnDMgI+yVENmKFStEzR0/ftzMnTtXbJy33nqrqFhvn0UxQlQAlQrBci5pIaW9e/eafv36ST6oTdJCfpyL3RUXLlRlr169hEw5H5JkkgJkV65cOckHcsdPFnJHWb///vtm8uTJYmvFlED3nrwhchoBFOx3330n6hTgmsV+VDXX5Njw4cPF1euuu+4yN954oyhgiBXbL4CQUfCoaezCsWo2ELiHUSgUUQLXhbcdO3aUUXanFsV9qm7dujLaX79+fetIR0behw0bJm5UK1euDJ35m7eC68LbGjVqiEeBI2XxNMD169VXX7WOsMV1DNcuR7Y2b9681pGvuJDhqcA5jiDFLatOnTriSuaIX/LG0wCvA1yyHBlbR4zWKU/xiCBfR9TiEeEIUdzBRowYYTNnziznAaem7T333GPz5ctnnWoWlzT+fvjhh+WauHfh0oWXBd4IgGsvWbJE3NzwVHANiOyPReiEBYUiioCCa9asmcQIYGCILj+KDrusn6yAcqVrT5qGDRuK/dIDVUoXHMWJqsQme8cdd8ggFR4IdP9Rsxyj285kAFQyqhRzBddAlXJd9jVp0kTy5Rxsu++++64obEe40sVnFpi30TJhATXdqlUrUb8M6GFa4B6gGfahYFHQPAMDa5g18CxAyfO8KF2uyb2iblHQCxculH1MjIhV04ESrUIRRaBbzeg6XfVJkyYJwUFeEBM2SogSsI9PF5Lz+zzY78/jGDbZ8G43xEYa0vp8ITbyg8w4F3BdD38O6TgneD8cC94TebCP84Pk6O+LfRzzaTkPk4W/H3+Oz5e04c8ZS1CiVSiiBHyK27dvF3vks88+K1GvgiSliFUY8z/F+sLiMqQt0AAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.1\n",
    "\n",
    "Here is a confusion matrix for a classifier of joke funniness. \n",
    "\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "Considering *funny* to be the positive outcome, calculate the **(a)** recall, **(b)** precision, **(c)** specificity, **(d)** accuracy, and **(e)** $F_1$ score of the classifier."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.2\n",
    "\n",
    "Here is a confusion matrix for a classifier of ice cream flavours. \n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "\n",
    "**(a)** Calculate the recall rate for *chocolate*.\n",
    "\n",
    "**(b)** Find the precision for *vanilla*. \n",
    "\n",
    "**(c)** Find the accuracy for *strawberry*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.3\n",
    "\n",
    "Find the Gini impurity of the set\n",
    "\n",
    "$$ S =  \\{ A, B, B, C, C, C \\}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.4\n",
    "\n",
    "Explain why for the binary case $K=2$, Definition 5.5 implies that $H(S)$ is maximized when the two classes are equally represented in $S$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.5\n",
    "\n",
    "Given $x_i=i$ for $i=0,\\ldots,5$, with labels\n",
    "$$\n",
    "y_0=y_4=y_5=A, \\quad y_1=y_2=y_3=B,\n",
    "$$\n",
    "write Python code to find an optimal partition threshold using Gini impurity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.6\n",
    "\n",
    "For the decision tree drawn in Example 5.10, make predictions for each of the following queries, showing the path taken through the tree for each case:\n",
    "\n",
    "**(a)** $(x_1, x_2) = (4, 5),\\quad$  **(b)** $(x_1, x_2) = (-3, 1),\\quad$  **(c)** $(x_1, x_2) = (10, -1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.7\n",
    "\n",
    "Using 1-norm, 2-norm, and $\\infty$-norm, find the distance between the given vectors:\n",
    "\n",
    "**(a)** $\\mathbf u=[2,3,0], \\  \\mathbf v=[-2,2,1]$\n",
    "\n",
    "**(b)** $\\mathbf u=[0,1,0,1,0], \\  \\mathbf v=[1,1,1,1,1]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.8\n",
    "\n",
    "**(a)** Prove that for any $\\mathbf u \\in \\mathbb{R}^d$, $\\|\\mathbf u\\|_\\infty \\le \\| \\mathbf u\\|_2$. \n",
    "\n",
    "**(b)** Prove that for any $\\mathbf u \\in \\mathbb{R}^d$, $\\|\\mathbf u\\|_2 \\le \\sqrt{d}\\, \\|\\mathbf u\\|_\\infty$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.9\n",
    "\n",
    "Carefully sketch the set of all points in $\\mathbb{R}^2$ whose 1-norm distance from the origin equals 1. This is a *Manhattan unit circle*. (Hint: You can consider each quadrant of the plane separately.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.10\n",
    "\n",
    "Suppose you are training to fit the ground-truth one-dimensional classifier\n",
    "\n",
    "$$\n",
    "y = f(x) =\n",
    "\\begin{cases}\n",
    "+1, & \\text{if } |x| \\leq 2, \\\\\n",
    "-1, & \\text{otherwise}.\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "Here is a table of training data:\n",
    "\n",
    "| $x_i$ | $-5$ | $-4$ | $-3$ | $-2$ | $-1$ | $0$  | $1$  | $2$  | $3$  | $4$  | $5$  |\n",
    "| ----- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- | ---- |\n",
    "| $y_i$ | $-1$ | $-1$ | $+1$ | $-1$ | $+1$ | $+1$ | $-1$ | $+1$ | $-1$ | $-1$ | $-1$ |\n",
    "\n",
    "**(a)** Here is a table of testing data:\n",
    "\n",
    "| $t_i$    | $-4.75$ | $-3.75$ | $-2.75$ | $-1.75$ | $-0.75$ | $0.25$ | $1.25$ | $2.25$ | $3.25$ | $4.25$ |\n",
    "| -------- | ------- | ------- | ------- | ------- | ------- | ------ | ------ | ------ | ------ | ------ |\n",
    "| $f(t_i)$ |  $\\,$   | $\\,$    | $\\,$    | $\\,$    | $\\,$    | $\\,$   | $\\,$   | $\\,$   | $\\,$   | $\\,$   |\n",
    "\n",
    "Fill in the second row. \n",
    "\n",
    "**(b)** Add a row to your table from part (a) showing the predictions of a kNN classifier with $k=1$ trained on the given training data.\n",
    "\n",
    "**(c)** Add another row for a kNN classifier with $k=3$. Then add another row for $k=9$.\n",
    "\n",
    "**(d)** Find the testing precision and recall for the rows with $k=1,3,9$, considering $+1$ to be the positive outcome."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.11\n",
    "\n",
    "Here are blue/orange labels on an integer lattice.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "\n",
    "Let $\\hat{f}(x_1,x_2)$ be the kNN probabilistic classifier with $k=4$, Euclidean metric, and mean averaging that returns the probability of a blue label. In each case below, a function $g(t)$ is defined from values of $\\hat{f}$ along a vertical or horizontal line. Carefully sketch a plot of $g(t)$ for $-2\\le t \\le 2$. \n",
    "\n",
    "**(a)** $g(t) = \\hat{f}(1.2,t)$ \n",
    "\n",
    "**(b)** $g(t) = \\hat{f}(t,-0.75)$ \n",
    "\n",
    "**(c)** $g(t) = \\hat{f}(t,1.6)$ \n",
    "\n",
    "**(d)** $g(t) = \\hat{f}(-0.25,t)$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise 5.12\n",
    "\n",
    "Suppose you have written a kNN classifier with $k=5$ to predict whether dad jokes are funny. Here are the votes for 6 test jokes:\n",
    "\n",
    "\n",
    "<style type=\"text/css\">\n",
    ".tg  {border-collapse:collapse;border-spacing:0;}\n",
    ".tg td{border-color:black;border-style:solid;border-width:1px;\n",
    "  overflow:hidden;padding:10px 5px;word-break:normal;}\n",
    ".tg th{border-color:black;border-style:solid;border-width:1px;\n",
    "  font-weight:normal;overflow:hidden;padding:10px 5px;word-break:normal;}\n",
    ".tg .tg-1wig{font-weight:bold;text-align:left;vertical-align:top}\n",
    ".tg .tg-0lax{text-align:left;vertical-align:top}\n",
    "</style>\n",
    "<table class=\"tg\" style=\"undefined;table-layout: fixed; width: 604px\"><colgroup>\n",
    "<col style=\"width: 55%\">\n",
    "<col style=\"width: 14%\">\n",
    "<col style=\"width: 14%\">\n",
    "<col style=\"width: 20%\">\n",
    "</colgroup>\n",
    "<thead>\n",
    "  <tr>\n",
    "    <th class=\"tg-1wig\">Joke</th>\n",
    "    <th class=\"tg-1wig\">Funny</th>\n",
    "    <th class=\"tg-1wig\">Not funny</th>\n",
    "    <th class=\"tg-1wig\">Actual</th>\n",
    "  </tr></thead>\n",
    "<tbody>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">Is the refrigerator running? Better go catch it!</td>\n",
    "    <td class=\"tg-0lax\">3</td>\n",
    "    <td class=\"tg-0lax\">2</td>\n",
    "    <td class=\"tg-0lax\">not funny</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">Why did the scarecrow win an award? Because he was outstanding in his field!</td>\n",
    "    <td class=\"tg-0lax\">1</td>\n",
    "    <td class=\"tg-0lax\">4</td>\n",
    "    <td class=\"tg-0lax\">funny</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">What do you call a fake noodle? An impasta!</td>\n",
    "    <td class=\"tg-0lax\">5</td>\n",
    "    <td class=\"tg-0lax\">0</td>\n",
    "    <td class=\"tg-0lax\">funny</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">Why couldn’t the bicycle stand up by itself? It was two-tired!</td>\n",
    "    <td class=\"tg-0lax\">4</td>\n",
    "    <td class=\"tg-0lax\">1</td>\n",
    "    <td class=\"tg-0lax\">funny</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">What’s blue and not heavy? Light blue.</td>\n",
    "    <td class=\"tg-0lax\">2</td>\n",
    "    <td class=\"tg-0lax\">3</td>\n",
    "    <td class=\"tg-0lax\">not funny</td>\n",
    "  </tr>\n",
    "  <tr>\n",
    "    <td class=\"tg-0lax\">What do you call a pile of cats? A meowtain!</td>\n",
    "    <td class=\"tg-0lax\">0</td>\n",
    "    <td class=\"tg-0lax\">5</td>\n",
    "    <td class=\"tg-0lax\">not funny</td>\n",
    "  </tr>\n",
    "</tbody></table>\n",
    "\n",
    "\n",
    "Carefully sketch the ROC curve for this classifier, considering the positive outcome to be \"funny.\"\n"
   ]
  }
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