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) 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g5NLLIEXi8otcDQcUts0D8eQ1iVDRAMBTsYiNdRIxE09EIBJO9A2xqgERTaW86BUFn0OD2xFO97FAgFhF6OoQ7prYt4XwSeUgQHiJyDbeke9IdQntciLQ1FlJMaYcUNvZBg+FB1ubjlnRNvl3o6IEU2w7fdNPhm/hh+FLysUu6++DLHkOkrSHYEjH0tEPe7WdD3uyDgvAgK/m4szFFR7ch0toUgBTdWHr7EpaWru6+6dmbbnqWEbV2EtxAsXiZAPTtGPSbHsotI2leoM8TePEqgSQprs7AGFf8kuOkPdZPXGb55POAW1d/jLST9v5YflasP6v/CO7+GNAPC2BMZWmsOjp2NNbfHwMCJD+LPVL+D/OYlWEEI/9jpPddOFkB5d1GSuKZYggmCCd7JUxD7EXAzxyirYnNDLdDZoFdx14kivkvGc3579Jm36reTTvDgBnaO6vzyQ6chQmlsMoIkIQ2+bBDWBud1Va4pcCn8CPqxlh/fgtG8IPaPH8C5wk6/nZDv69jurV5QhtwE0x2iqOsj9Mx8B9/0EaUdiPfOYYDCi/q9jhWRuupMDEU0+CtX0sDFxv07T/K5niBPqN9+tQjgEc31NGCXFeMcCEuQBIc/BK4CO78u7EPYvl3yaEfK3vcb6qP1R2tI7vUjVDDUdKubsSrNjYKY1qBEa2P50SJoaXiksIoLiCwnxS6EBuBde87botNfdEWwYvF/R0/u5yCqhGeEOR2ynSeyXjt6ka7neyye8kryBSWE52y+RBgogrXPZ8E1yIHoHIFUM+AbJhE7lbMtt8ApL+xmZW7PwbjAO0fAVoXQOuiSP/ksIVdFZ0aulsamKUzwPZ/NYDMJRBPCxsBqLzqHyneXF6Ej9HlIFo7+pg+jUb3unRmGpstGkm6etOuDBGA5wCMefp1gTHcdZlvPBXlOslvYTp1cd8UjYLVd/J5awNrIOKLnIt9MD9qdrKrWCvA6ALm3QV9VrsPm60Q7+RHJHP+2hqfugo/MvI2H/mqr4b9tFnKSRY1Y5Ek80Nm/WIhr1ikKnxGz9TWXrokf9xwujfvcOTtNTWnxd0F37Y2W79tteBqZ4G5qLCuomw+nSr28QESCRVLTyYKILGJOPfcnaIFOsewhRdvv+rWa/Wih0vlbX6Zb75T5C0qNKVFvH1QL/vazSWgC2s6oWXXIuUxQelKiJbowuJDQViatLmLijg9CQBMg8WiPgiw3LEeYRmm5f+XdnvkDnxLLjMLxtvX74C3OlwPQqx4xwIdpPx38LrlDphiyWUWHWKAzzxurS/xTo+P5wGFak62ap1PVFFN4v/y+xuR39WnIO7lsWfwgVsK17wxrs9K8ltIKuhkw7f/6dhK6gQokFKhWX3urrjk/rnI0pgfpGMeuQIUaEM7+GF5q2iMkCaMQwxxOzcvU0eXbsnS9XknXvP7Gtw5dwPXlFu2ecvSHEZgNDsU6x/GdXBYXyOQjzZReSedeEPY6nEv9gJR4oBQJtFO6Kd0fwC6BO4LNHDeBujB6dSNcUQC9zIv2LnAzGk99bUDrdFY+9yGFQtEo0GQPNv6vS2drj4+1jHbv3aJSMUWP+QTZrmbNTjU8wyG/iXNNpskybLcJ3CiTF5Ir+JYzmJwE0mSVhlxbtbmvweB3ulB6Til5UuUZydpgiFVeobhU0WaBqpJ198d+/XeNRTZ9/1OPfG7+2hwzd5W3D+hmyjsRcUg/+Cavb++Vh2ls3L7zT/etOnHNxeerv313vzLVqPai4nJv+K1FC6040/4udw7sAb3laSg0XCkAAs0npBO6VJabS4Elk/U+D4gTXW+j0wnrMlqNamq4tMIYB87tE10i0FR3LZNhJsb7/R561btmes8YBCRkhYNByRtKd55mqTas9FYhJnbRGHuOh3M4QTdgQSqmgRxuzGdSvZGcbMxNQGk5C3ebLjoXIOFM4l+WKHmLTJwRv9E8GWJ6dYvf/FmEyEGr+gyrr1p5zrgkz0Cw2j94Hv8Jdx7dIVegBSNtgsqGsRQEYiIBoXwD0LNvQ5d7s5Z00QzwNhqZA0b+tMG1tQq5nd84uq8R0zPvX35G8uRaze4jcOHzz0w1+Q2BIRvf6J6Kgatnrbiem+CFvAxfkrndzD9MFPP1GWTUHclpASUkCNAQkpCCcCgDSUDAhDZ+CuEkgn8J7i9nMA7pA4lISappxILKfAeSAbIcSDuN2bJcfZILqeO5rLs0MnngSHYRdrHjmaz7JEsEPw51ZqDJDmUIOZIe34WaQeegNsJn1qz8AIpT3yCjyEih/xELkuJ0lEMYTLVCiWpo5oYMleMH6USyYJcD+uOe+kWKpn1Qns34iyYDjkSLvgnZXcgVQNeqINXr48m3iS7cjm8tedyY0f1QvTnHHdsrKby/+SSbPY8/NH6vpl/Esq3Ae4ZU1HC44KFiI9o7CEgab/RqHbj7s5KAg06s39ZP/zxI/mVuF/TbTSy+3Fb8If9/cv7+wt91yy8RfP1QXtW5RzQn7qIiZyuFM5QfJ5E9uVnqT85TanFx0lkP3ukBAMprvsRyi/C8NAJL1xbIIirSvnSj4O5netb4JxmNANHPssHAcHMHsFRgEug816gDBeMbdfiuRcghqYcm0+Xxx/5IAEtN3fqFF3LzAXqwoT0PN0OVTNqxo8sxMkd5Ig6k79Zk7VxxX6gMLOZFQgvpW2RrMW1D0BDihaXQ9wVRoBxPLfpknmkeMtoB/qM9cRc9IqmMD2XUmdZ7GSRKPUZvChf8BoykriM2MnKYbOHX8R7cLdNCxSFFVQqoYswnlWtlFS2mNkhswVpZiQW1J/UKFfipHGlUkM6UKBhMz1istELIHJLMSctu3ugzfaVSOjKvUgc/THK4Sdg2Wscz69leKIkkrwuuWiOe9yGYKQXRumkC3qbRcMwrvhjNXgdZk3RxAUEhuSPvn3nnd++U/3vlVOmrJzCD8JLxV1OHRjrZifbcFDOuRNTGqdgQm1tSNJ2OcQ04YiEXuxtII1ECSQRoQGYioEsgCfchB4ghAtw7FfJre4WZ9hkVi9MtjuWqtdNDlpMrfEG9fOT6q21okg+e4As38MfGquNt7oUws6Ysarj1/efE+yst86YUVNvDdts3Pv5c8m/aP0C+f8/Qb+IMnGq09BgwN01oIOAnAdagI8mBSrqk1gxTDUBOtk2ousEtBH2z4Ir2d3f6k8PXXVlt2qN9RODxRuoJT/v27wm09jRYVc/e++iyx2tyzJb/n3J0htXP87eSsQaf2Ly0s6Zmxela88REy1cf4273mI3iXNJ7KxrZibOm9xm6rl4fqy/t27smU8tOfdW2ucBzg2UfmOIVyLIl3kpYlwphDISTXJXsctmiDtN7fNV6zelgxwnWxsVr83Aj/S5ki1jL/a0GC6+2L6Um+aoddlNFuj+bJ8mH/iaLh8I0/U51NspIEfq0dohwyFXKgm4NggwQ4rRhCOUFtxxo8XnitT4cnGfT93IS8FaT85XE3H5LMY4zIEPL1hw443wz+1UmhTJyJGxZzw+wsKkKZgUiVtKOKMEb2AKHTv61FNc01PQFwKnvsZ/9pPA4RKTASWahmh+8MxwzHxKy74IRn5LGRjsPUUwTu64UYNY38caqd7HKucZ/tHnODtENw/2UfHRMaq1UUPDJQ0OKkWCeet5fYOhII1VRz8+/Elg5j4Gxur3J8o2PJ4rg+2d08T/fwEzSVbyZ9XPro95T477lRKqUSRXQnauHNsISAl27oWi6Fv9z48JMv8r/aMMj8onCP/DuDZOuN+GPPr/+p7bx+7JlbYdppcNhzKU/1Px5aiaGDn/s1iGMaBcleKUo/v9rcxkZj7DBEKOfrayytXNLYiUdBY+pleQXdnscKlQcpzuWluxsieeyuXIK6SdxozitWyGOV3vOHHjguyCQ6fpIYy2JwvrQEF/Qa9Pdf/QqOSqCiE/EE1/XIVKTc2tzWbHnimrEd+Vyz311Ml3P0GVTj7PD5aDnsvCvH36alEaPMePcMegXs7x8igTu4B9v7G9vTHvhCu/kzIdx+BxC0ay9zRSvoS0F2lIxI+X7klU63I40gLQ3w5ep5na+SFnba3z5D64zv+QtM4n4ffG3tq4aNHGRfxgrXPMim+5487abL7xhdseIRn1KDl+7aINixdv0OD+JSPwKf5+xoP6aiTeQIDVlIhMcL1H5R9PYXvprs3fv2bO7MOplCmweuiq2JRZ1zz+9a/v2PH1Hfz9236w+ZrPXvWfAxlj4NLLHpq3c/PQ3uvmvbrjG7fe+o2y/cLdtE6VUlXi0ASb1VLUBVSUWSU4HdvAraTyS8xzM8NxvxFkXV6pUVRiJwcgC5zEeht4rwcp7ki0k41G0qlQhG1Vzlq8alEmnFi58caB5Q9vn988MLhqyVlHvLEWjtQFeupdiocF/tkkOGPW2ibWaBTkeZ/dvPWazXfOnnvL6jkRXpi85sFzZt+55ZptW3bl1cCCHZPD06MhySha7UFzjcjbp8fOecFCirzAG/yVjBX6OFIaadSjQq1nNhyIe8tVbaaSdHlXIWKacMeuZA1uxS95zILhyrxAdsXTL6m7kNQlx2P9uZf2qhufePFFbpI6/OU0WcP99RrCsrwseVot5mtytpf6Y0gm9sdeyKnPQ7onyK4nXlR/rg7H95M1upzu89DH6pgUcikoiihJ6NJKmRxV1x+MJiOA3YwhDRQrWU0u/0rvq0VYXnyCwsLeTJYBq3dAtJDavuzyoVpzZ99Z0+a0uoiFH/xcqgDR7rUFeOrUn6Cywb8ZeNMbhLV5ugP9l0zv9UN5b5mFkjzxUcpPJCn3V402pRxtJd2GrnLdhtVk9ZSZh9W91fCSH5B7ofxPiWL+j3D/uwhBRdyAyozeZwvQzs79soi+BKSnafLviZCcfrpBpLyimfLfTyJtbyruIQKD01tUwJyKEo/ybaxkSNFUMdMkhQoJyRBQFhnUkDQSXhTM+3NmY0EDM7ffLIjqWEGt8lCO6mLia3PukFnghosJD5p5SIho/VDkzQfLE+IrYoJXkD19pdP7OwG/voIUtagiWiZ4PAFTHHlTVhRZ7dYmPar+NJ+8JhmR6DFK5DV1foHoLNO/pHrvZfmWZ15RQlwvoVDKhCWNK3CCch9lfFBuAqUgpFSShmNaPj+i5++WZfKeViJfW5HnUakVL4UCNVkA4+ETfIqx4B5xSaP2L1yn0zn2ltPn4+OqZGmwwEVCaCSqG53ldtL1oLGAhdMLd09MpCCF6tD6ZnAZBY9hDaYsP0jzZ0j5ZjKsF4i1UmLuhbJMCnYJPt5VwFNvmZawXjEvLJqIH8STonZjq7BZ8gKgR20C9MDFqJAX1H64QW2NEup6qgzLP8cvppL/NNTOBTCJABOHeWoXzLhw4Wuy7gaBtjKr9kgKq8ZlRYBS32Lpxc8vIhpNDTfyNXWybMJbn2RyQ5EmWc2QF9wmSZ0KYCE+cPuYO6b15Uotj2Kd4MItLS7gtFbkTdrFND6pvEZqv5Yv7jXAus7Pg7avo7KDot50NX3CPkP+Kps8J9/3mGQIteY/LGPC+L7872SPR2br5fy8MtKBMHedGuM28/MZmPJMrGgi3Gb1S+Si1/L/zrZwO9XH1ce/z7ZQ1WSoY/+pMb5FT4ua0Wm+Jf/298nFmChEQ+Ti71est4mq9VYI6RsymoRJKYidElT2FGnDTZvqtfhGAFTbeqEw68GqtfmbVa/1IFO1/jdWr/8BDRRtQh9XNjubEm4aWVpVonpTGR7PVGc+KJNoBIWF7kYi4gUV3r1U6723i6TxUl3n3/tM27aZfKb7THiHW9VzFSwHJ05VfK6Ar7kaB0XgPPE0BSkSFKsBUpaLihEWoA9wBt8qirh2VSOkZwXEwyrxZ5jyt2rJmSo9gX7cg6jsEUGJU9z9xJPOEM3uQQxKgkh35DNATnVyrmJ3mbCNyIB/yox4wH1bg2DwN7q9kov4pFqny8oSm3RQbGgJ1QQTs6ZMLilOVYJ9v6Wha3HcJ9jddsXp9YhGUXLXt/qMDnvLpPNTXfNa60z5/yjXQOMq+lNmwh5egpYrdfZQZV9rI47xlRkuyTjpzsmCBSWNkAXVoK8sgYWqQJWbo1RLo6QH0YW6pxqfCnRgkd+RiFjUQUQ7poIaYoakgXxwFd9BuuI38H1xBxXSFb/pBDIKQFn7YB3dB36l7sG1FLaKiBdp1KxLvfswap/30lnVESgNnvjbUoT6w9N+Xoio0qcYOIM+heg940YimsucQVvli9NEcft2UZwGQwLuilj1fFr1i3NP94X+PE7Hpvtj6lBJfJ4R6NvWiaL6MgzWHxiN66DExa+dAdAbMYX6HVF8A+7rjEZIXAVbDe7PVI9rmN69JOLV1DOSvRPxWNPZBZf/Nf+Ny65BhYxxxV+77XJ2wfQ389/IQPgajXbwMsuAz/0IaQcXJavKbRqR2IqyZruXjVC2+hdee/5vdnYOedpmVtR3NGXldxSzDSIiBVpkGb9by89UpEPKrSLZmyFDzMab/wXl2CNe7s/qCtTvWgG5kpBmCBlSzDS/r8N4uwBwohRW63JTS1y32f0TQsPfXVGEHQrV8/NCfiOUVirYcBbIeA2+iF68rQIo3B/S628vYESr79ehzS7Q9LEL9UXmik9XVHb1yBO3Ngvt5935+k1efkV51mzzrM0LL3/20avnwMeKuWyOUZg2TasSqZ+KcZQiOn1Iu2Vh497ALUVZiCKt/gh6IvTIj1ZLRjWAkpHKOKovNwp00eqPROiAbiNEKieXwMLcXhVJ1/uzmLP4tfxaHR59cBdJVG1kTAgl9ze9QKUEQ946Hkb+okJ5JRDyf54Axur1D+WS49cLr0tTPEu7UmXrxcSr3XNvumv4yXzInXKH4F7Tc7p17Zt+t/qW2+93k063X7VW6lALxTY7i1nBXMxcxmzQbabxz+tJo+wijYaIGMNS8AoSMgAPt84DdHOoMPfjXhF+kuH1tZvuFQrRCN07xGcXRX9MYxYchDe5BcHj+Z4i+42WyPc8Xofi7bbZJN5nJLJ5qr6IqRtzqNlM17SpFsnkEyTWoABEjz4JXOQvzWYuwdnV5LNGOwTM5v9r4RpQ8ZXsYodks3o31JBlzbYtNotisnm22MxiwGFXam5oN1n0TA/hRvshvTSDwHff4nNzRo9Dum6PaJbMXzDz+x+Fkj4L4bFNBb1asqsgH7Dyh4DvbkPtf5yMDKzEwyoaESMSNS9P9gJVA3/RTlwoMwZvxECFWxIPNw9gi01nOHjP32esZTtmXHnxvZd8ZtakqQ7ekajbXetpNa6ocTVxJtY+uSe69OLz77zh5bDR3xjZMzUz6fxrz1nqrZGcHQHfPVefN+fiK86LeXj+Sc5lPKy+k/vCUI/DaLFYCWHr6nbXuILTIsb5imNKY/rCm28fSMxPhkN1XbNMNZGuqwOBhtTSxWuTk6bw0ZaG86b1hKddePOKuBvmiguYBn4T/yOqOyGRBt7bKUI1GjioBC8aUKwF7Q319UgcmtFGIzCJGBqwQij0ynDsfdFGc3TS3BlNfJ25xmzniMkpXXTPvCaD3ZaZvyzjmZdudBostmhb0ORZNN2sJBeed1HXkrUsywueQH+L0eCPxmsa5ZpgRJSDZ11yDv+jmbd86vxZfc1WcZJ3UkMq1BOOOVtvu/+pB+en186d3GTwWAw2jheaJs09/+LNfZft37DALyrNj1wABMuUKbODyTVnT/KYbJ3Tpq8IrNh92dkxOj5P/YpZx4/ycyiVcDYdn4JbEoKdQi9054iBKsygLW46FRGxAb0NPNCm8BSNCPjoKcj6EAus4SuP3rB+cV99/eTF6294dA8+TK6v74MHVpYNRt/I30e8QGTOOdfGWzzxcy+87a7bLjw37rHw1nPzp0KyyRSeZO+QQhInt3dYgvycjrPOv+T8s1rptaP84VeywdWX2T4ysr0/7TLIs6+x9zib56ye1dM9e/XsZmePY3NDs9zlnNVt4+WgHJbbz3Livg4P9WWgviOMm4kCRT6I8vw0NbUUEnFvOuFKoxQW1gTsvFirsF5pb7qTUCx4i7VmtToveaDxvK9uOaedVvPRpVOnNz0Q6bry7uiSdQ8t7Vy4JQKVS+XPplV2ts4bvCwZu+KzgITtxepaPRzWdpv74muvv6RO0SorX6cu/dqKn/XWnrtp/Zragz13DUCl5myiFW2Ycvb0PtsXnU+tx8pvLFbUspLX68mdegwmOif/NPDONajTGoUh6tU56HBJCTBASVvNUB5VIiKpc9kd7kludodSFz7xQbiOmMk5dOYk56gzL6uaf7N8a6MQOHm0ae6snZpFDfuT3/jdYzjzwkXXIVHoXNuCfQslQZqBZjTsoHMqrkE4jaYdgkGz2ATOgB3cPkSukD01DnV3ttb1wx+6arPqbkcNAHoFPzKUUQ+qL0k97pjbZv1I/egC9zTFbrrlFpNdmea+gIgfWW3wqkcis8ky5FAcRd1If5nNZrl2FFpungc8wpoCl1BpQV/ScS+zjlASyUTVv/AJ46gkJI4bHX4lTnloctxPZE1ckS3+jG2fKIjkQFyzuo8jvYQG1OrGvJPSTu/nSp9PHNTl4z5hK/8gtXVKF6gEKiglgcKiRlCESsQCV5QIlKWKpr34lt/wkSx/JCmP5/cBKQfl/5gd+rOS/+p91/+YCg5CXK2W4M9fu+/6xxX+vnelVuldIDCG0VQTpU9Dw4pRfei+6zWx0MLie0gPbyrkmRU7OwT16JGeyXLHqOLqAfVN1GPlBzWtFNzj0TRTCjogtP1NjIvu5habN5Aoa1k66wGpqriVetJgiGdwDZtKhnN0y4n9sXYnsqGmZfDSR15+5NLBlhoDaedEm7sxmpqRija6ZEEg2EAnTiAC8IrmFbGz1q08P9PSkjl/5bqzYqT9hMmptEXDgTqP3Wiye+sD4Wir4jCeoHbbp5hRfpB7BakUIppIlPCD30dR1GtslDz8OsqbXmejFC/v8wu5X2myq7SJ8Avzv9DFUJySf5uNvq4+Ti7W9D/OZrLChdwxmPNiBRqVjnpK/aGxRCDspVYKAW9AN1JANoo8wP4BJUlGqdgw6m1qPQ2QW3+OfU5/ieLS/NuKpDU3uf8bcAXyBal5jMR2NEAbPAZt0K3hvxHBEDlUxfIGcD+N2gNSNx36nfqlAYow0puatNpRz0e4W2oahKzQHsjf2c16ad/3t2KTtPobnX6D8C8pd0MDP+Kx7wnXqGGlLQcvikMErm6TmfsuxJXbSAxqNjOogJLQBLiKEHAE+JGTS3JoEhTrz8/CB+5YlupJ58aOat8Kv4JvregxwcU5Cp8GFAFm1FyOfto6GS2m1NGTS6CPNKkbsTdCBlnN9onMho55BX8IJZtEQ35lk+htwN5A0V3RCPoD/yXAcv6pAtbZczRUA64JmcUf4q7Q89ZHLeJVZ5D1Ps/t+0iCT3AHVtZC7JDCXfR7OSb/Xja5H3zQbZL1B+ULX1BMTEk3AseSpmnKEK4T9ekMIidUCRQFfcbj7z8gNLvzF7mbhQN8h6ZbRset+nQWdS/ZX3k7WpS8P9sfo0iGS64wV516pOhjI6TZ2dApgI5+LhxywYoWxKUrykKJsIoDsR4mSrCTg0egMPnLW/3Q5Nn8BZEuzqEI7HK3n0+zFmuO3TtWQ5WJoG9YqCD6Gc32SxnbnVPfsxvrFXK2dILl7bLthDp6glhcsfp4bYvbSmj/mQ94uBTw0E73x2jbNRCvC6VL6GCFDwU7eWQDcC5FY5s0slieRDwtAbRsbLXbaXAuu14e2OJw1dc6jQ3ZdY8v7rv2/BWZLqvFWVvvcmwZkK9f5jS4muO9yR5res4kfkRxhV03L1RfPOiPtYi8pd7jNEsOpyTwxpaY/yCZu/Amd5Or9uS3DYaeqVOhH7gZN/8I/wi1fEuLXvyNivibjuKvN+1Nc01HF/3h+ef/sOhox8MPd5SFucPjorQwXT+ytA8EmA5mamHNFDVhBI5pjZbQpugBNkO8MvRub8KVDKST1Wag7D3xlin1ZF7LFP/79nbvCXFOY+PUjrT7/otsPXXZ4exdPzuhZuL5LUXVAn7k7PbhG89uz3b41X01gbjP1xwlu5rrvvf9+pbs6E/Vu7Nk642/PYRaAiUBdrmO6CDTBLPQFA1ur0uXoBR1INDMkypKpoTqnSMx5GiEdTEaSHLs0Alvu/19/5QW9Rv1U1ridT22i+53pzumbs+XFFXYC++CGsTj5JUT/GCgRt3n78i2n71FHG4/u6X++9+raya7os3ZbDmgWfXun44e+u2NZKuGZ0HiF8M4TlMPR+EU6rPKRJ8wOU2RFUFLex3egEsz3YqEAq0cqhAAW19dBZIlVzR61tuIdTnpXH7l+uXrbjPUyep+8cl6aXKWhPHpDcXl9KiTWDNr4mBQc8Tq+NzK/OKSbsfl79o9G20R+brBXYvUg0rLHhtrc4TN81TTOWSZ0gL1ZVlOYH2ery/7XVUjFMbzYpg7UswcqJPQwBd0LKLabJ8IaCr2otcjSkIrGwootKECaUd4XH1+SdazRrfddkBU98t1htvWrbjqSqjaCguxrffM/5zDCpBALUycmajhd+R6ww4SWafuZ5eU+tPid4lgd3gt+b/Y9rQoZNmiXYPXyRHbRs8zX/f4WIFjWZJtUdSD55AP3xtXH+ZipC0EqdBGDA4CoYEU6gRLGPU11QhkLTBiEYPiqOeQgwTCl9aok1Qr5pFf71qEeNxjy/8F0GoqYPv75Yh9j3x4DuJ+uEzHRpAq2lMqb+qfTdiq6kGtzfOWsv0c7lSeMXDHBDe1MT+LUgx0Pg/p87u2UicdIvqQi8DkxhcUwUXCedMpb4NQjwY3npTmgsURJavLwCRyEcN2HfWsDVGfv/u9ZUWUx+PYFueUKwaNvbtu+Xps3eVWbN1GcgVrdMnWJ7WmJz9SD66EBidag0NF1Ukep0t5A7sFCWdhzvYwHv6L/BehXuHqfaBwBEU7hfVLcXvS4VQv+T/vaSIl7cbeMc7ekv9i8S3e1L5xxpvMGcu1EYPbKyCiijjGXcDKckm43PqU2qNWlXusZMiqF82cuVzolUHN9NNR0HZPxFPV9V0wLtvq+k4DqOwVWDlzuQLVdqFiP08cRX7aRlBVfR8cb55bWe5LExnlcsDp1vAP8Q9BucPMk1Ulh4GnN0SAdxcNHv3q9ohx1Ati4S/tkWjIDe3hQdkUGrGRaFBiUdiTSkI41UkMuuQHP+EaSQYlPQTFWJF03BNPpTu5KFAdkWgDukzsZKMG0Q1TAQQglScOaP/dsZ8+fP75D/9Uu5Gs3FY/2SxPld0DHOciXI9gqjcEidXjE+3BLosy0OcX3T7O5g65ROGyzQ2BZs7WbZVnO5ydLe32hMwTQ4wnnKXW6XW5LAa7oaXOIHoUl0FgLQLH2by8wSTWeAx2Y5PDazK3BqZbeJZwXGPaYhX87ZNszoDdaRxotXO1nNlpdvAPFWHDm8PqEE0sZxDEqGzxisFNnuCWetPcGrObN0p23tTZwMuRVodSV8+LTrOV3eRvzjQZiSjaLYS1WEJe0kNsJlZu9LFun7++wW4gRDRbaxw2nrOGm+xOj9cmtbp9ZqeTM1m8UXfQQCSTVSQox6pvtjot/FpHvIUjJovFEoYvHYV9C5Y/xN9OfcalvII37UEhTbTg/AQIaPb4Vz6j5u8/aViycMod/fkDcpu8QZbZoeBi/vbzP3XPsZvOubMtaPHkD9jt6+U2O7vqU/9C9SMvgrXpQNG/E0oJxun+CiElUa0IKQSUwERxOntKSV7ekcuh9VBZBBo3VUcB58ofKBHCwLyf9qFosz9Ibf8dGqwaBMjRig4SGOZ2UkWI7UiO9OfUPdxOYFApUZyfpY7mgEc5rtNGGk2H1lPhAk1Hp/VAMqQEHEUfEYkkUQq1JMdzsX7kklRrTrUi1wMcDjmu1YYfATj7Y+pGpPEBXuoQIj8rR9mgCl4C9yqmF7xnVWxGVniNqtpVmXBvQ6iwni5YQ8a1jYrXtc2J13HvgkvqWxuva1sbr+P2S5ceKGyBwDv2DbrToe1u6BkAJV7xnVLUaq0sJB8pFqcUIPi3yuwxi4JuLr+P30f3OkPQ72aO0xYo3/EsmO3QO5qEF8S0qQH0UsKXv0brnl9+8M7jF174+DsfvPOl1au/RL5/9DsbNnwHL2pHR1NTRxMZhJtHktOOxLxErPF6YlLvpC9YP73x+4ofw+3xVdrHcDE0dQQCmCRgvt9b35xINDf1CDcRSfJ+pYl+Sf8YcurfmXP5F/kj6J82jNsrkWiEuhVlgFfyNkB3S5MUzLhoNiwSCYcxQ7Ui4J0Xh7fmqRbaPa1tzujxkBRlsEHy0/OM4pYLPb7g9O6BQJN6l9zQ0OGyCaZz0vMTbHOzXfQ7a2tsterTcqxeInODoemdktw+1SbVhKwtW9ffe8VKadK0OVuC3bWzyKm5LeddsWTeorWyY9IMtUFutdu5g+Rn533qkocdvLs2HmhU75br/MmWtD8zA3OP2t1ea636jEzqYxJZGAwFiDEd61oTsrRuW3/3pYNi3bS+Rd+GjOfVpAPNd6y64Gsz1GaZleWIPoYL/v9mTeQBENVEguiF1aC4YeXxFETw6QyPfn0m9g8IrMFAvKM1EI11DARnbqibHk/Iojy5rSdgCyZi06y8sS024PeuO4MfwQ5Y9yKRZCqyYaF30vzeHlmUprR21tR0t0yz8KZY66zWuGvxVQB/36kP+K38t2Hu6NQ9SFJfw0AdpqPEK2qTMpf2VCqJwqPoJezTL824b8akoL+x03nhh+oNo5e77psxg9Q5LzebIKD+fsY34f2MtB9fk9v5b8PT6tYrgv4kRPwd0q9z3gdJSJ0653KjCYPwCaR5aUY63eW48O/kdo33yxX9wCiMv2QTrk8eGSI6Ag6moG9t2P/F7GRNlDjl0gw7pJ5aOXXqyqn8SENnXBmbSwUYLyqJjv3UmY1nKr4t80no0faXsaIEiF/BRaIBnItSce4OUif7W6Vm9T9H1X9Vj71BEm+RdmIJQST/ZfVdudUvh9S/qqNvqT98g9SQ3lHibZY0mRVHooyDN/FHmTgzjdozKw28NwQ0hwN6BCoPKaEk3YtKwNhwRLXuk076CGoZNXDQcRwZvreTZY9EZi+d0s4+ztv8iei04JQl6ZbDD2eHV7X4uHuFVfPrOmcs6m6Kr7hssr+1VZFcEZ/PdJkn1hOs8SXS/NFFgqt94PIZzZ3tdaL6Q5vo6piSzdy737pwsX1VyxUrF15iJ4uNkq+rbyg1Z+O8VsNC1UmcvORPRfxtPrfRwL2p/oA1eZp6Z/aGffoewaXcA/xBlKlQLfhQL/oPgBGP3qsA7IQS8qDVNswHKRSheDUvA3Q7MZoRcJMxlEygujn1QdyzfPfq3dEp/bXh5e5YXW2Ngfvza0ZF6UgFL/E0fTq4LBlvTE2qb/KuuzYSXVnjTfM1osvqMHVbm9950quIZlbqaL6YP7jk3kUtA0GnX2nvq53f3WoSsvEdDRnULgo2fN7lNZJgI8/VWi33c3bBZnGY05+dm+3qc7fNmj4YGKLj2nfqFP+g7jdDlxEV5XsJQZP6hYrS1l0VQr4c69Xueixp90gnZPmE5OF22j+SYEWHlZ0K/Hgsh/Ztsbh6h2DNRlvv6jJh9XaJaHCZDiUDKNTMkvb8vsqCyf3ZNdSmO0fa0Y4baJTtpbKzuVzeeSI7fCKr2Z0WypapnXJ4gnoWy3PoUIlIQ1TXdqhQJIXp9Wx5fYdpeWh2TY5D+YVyKd0jw3iumwi/BC3cEy4o83QlZnW79MrCgCjbhWXBlRZVVZZv4rIKpXC01HFlHdHLoeWVl6UVc/J5uGm6CViW5mulYMk+HqNYr0AyUPivLg2oMs2MPqtuhHyRyiwvNJej1Br+fcLyoAyu8D9B7bgmzUqfFobF5nKnK4+t8MPJkI/xHUNWk117jugWF+xazTAALQn6+UE9lhoI5ApGA/iuJOsrlNP28SVVuBVajXmircLel46w2bJS1Q0Ft0KDuikDFL/3pYrid1Q4FvofwRIo4R9h2ftSwc6jHAMqLcCql8YPHtlzGoByNXYN6v8hXnRaOhUvx0sVLCexwupGDR4NOYC7PePa5keIPACnuAdD7dEadRuTIiS6Lb7uskb381My5yjzF8lGCjBRqdwrWJCagfB3yCy7XT1i92hbcZ5Ci1FJkgYMDf6n+jspIsHFjJrTOdzSMuOa9DbDcj/nH9N9bIoGVgzHPWIQuFuYtaMRaq8eCKI0gEF6lPOZjBz3EEvaaxwSUT9U/8JbJZPJJLBLolH1La/RbF9AbC8JJjv/mMnssKjLRBJyqj9QXxNko0Ux/X79epfiXkm6fmKwF/en1HLc6LxloXWKvGa5rVCVL83VuiPcDEX/K5pTXOxHfx6HHB0t2FI0qI2rCZFTrvPWU67zVuS/kTsLnc7IKhFg30e4FOkqNSfH5PtkmUy6Cpiv/36k2sbqCeCFNa+URpoY0sZoYmCgCr3qgZz6s8I0gP1bYiR+D79H56NOz0EVWCTy2/fffvSCCx59W7uRV9995eqrX8GLesOXNm360iZ+T/El3uZqL+FyzSZ8XxpTiI/G0nkT4zznFZ0t4ipMz5v4q9ssqbdKUZt6u82knPCrt6PZwsnn0XySVnyPR1ZXAn72yx48bWJsu7apnI3Hy8bygUK5Js32qcytapqgmn95uexccj205vGgJ+euOeG2SORmKZr/qKzcx9SFctMJdwMUFZDJITs7dnOp1EKZCxg304Cevyfya+vlKqv6aXK1qIj3imL+L6hL+yvUlFfE0VKZ7E8gBY3M/8VoJCFgizH1W6VyC76nH6b7jiibYVxUmVIEspry/LgZIlCeP11Z4zs/AwvVwtGFEut5S1JY4lfyT0N/evOLo+rUEgjcqc9IkGpQbv3iW7Co5b+KgjvpzYdH85PLcc4X21ouwEGl/S4qnUAvoSlXUUhR1eKr2VWFTB+GMl6FsiQsVD1R3urlAAIoSn7JQkmiVVCHSpCwDH/qPepXQ0Db77CJOAImohB+RPWr31ev5g/kE+zTa4lbvZo8xdWPffQu9yJTPCNB66s+zXoJt/0L6hSoCuBIoK8fnBGG87OoRckJpLqyWe4YbpGi50g0+3I3UD85Oa0fzubfoXxPLbW3FDWzigmyJeM0tQkax7PqTy80+UxfUHPlBZIRVNQ+v0xRm8REKPoLmNr0+Uo48v9GFbXPKylqQ2IKm00QddgyWGMROCTxdLB9nCY8P7j2DjlsV/+mfr0C0r/NkeXbbpPlOTBBwT0mVz1zx9S/wJecBF9Wgv3p032iP2v4VSgfgW2G+HUEdEXU6iq4CtpLJfIN9XQG8dwa1VoO8XC2SrPDDyCOQptXgbcPvlAgBfxBoGwftQKeKFrNTASPt3pGGqDt/QRasn2kri+H6L80MJRsmVYJrAKyDItpJUy3/15WYIJqcJ9Q5N/LFJ4c3dc1URpWl9hW6mu50MUIelg4ucTPf15zs5DFo1c0VSp1tKB9jkwIyuM45kb+IP8gHed+6jO3v0KbIknzLy636E8KPTdCuUpB0wLo9JKnAO6pv0vS31EtBha/fJemkgLVVnd8KCk4qBTpQ5m7FbifBKrPJcq0pZAFVG/XbOFz+Tcq2MLrcmV28Nmi/OHskh82bau0k8eWCaPijQPWQ5lUvslwVCfHkXBMIehqUgtDNLeauH1huvZTbYmw+luPjyWoNGEuxRLR7LK5fSyXFUyK7PURQv2v8D3XOt2NJ6liBbmPGOsakw1kbeOs+31Wm5qpH+iJWSzqdPr2O7zc2TmtnrzCig6bBd/vgQmzOlz0STWIlmZEQfupogOZFHUZ7EkUnMn0RrpIMqAgHRJAOjIJ3yGw1I/MAp9q9S3Q/clADNm1wEeO+xbwg5OIYHZLY3ehG5lJk2xhco+6JWybpEVz2wrR6hZyD0QXZbeDVB+onmlimpkWprdAs4WEZDSQppsDlcdCBJJESIYFuAtUnC4GIF2C3Uu2Kv7L1bdz6FxtqxpG4TqQOqOUNAJ2HLvPWA2GgDy4O4vaDrtyl6P+1fAll+SyFcQ28GHqh7fvvf37udylf0fNwhzgz87Y+cf5x9GnF6ygHu18sAbipWeF0YPBgp2GaKeQduxxdEr3SgbH1kvH7tvqSLhedomOvZyts2dw8acu3dY/f+ucuMtCuP/e4zC4XnH3OLZ8ZuxTWxy8dJfU5dhDeKPSlJy5pn/+7u3XrJhmr9C5CuleGflGQocKnlAUaRKp0BAHV0ZwUt9VCqk6zYOgRIuMfePJzdmBdpPJ7/6B23+f+sp9NMDZevovvfYHG5dGPISQq1DojqNckchVrCcCYz/Q0hI0m3NKDRfkgsrnamo+p0CAq1FyvC3a3Nak/s5VX282x9Ufy3E39VAx6o7LpCvO2wK+ch9jNqpJCutcIOooKnYWtDK8gTRVYygRQfwgzKM5+jP2jOZdx3r32Py7rQUPOzAnoRs95NvRAR0qLGU11Taqu1bUYSzMcWjMEir067JQQHfIrLBHsrgv00/Wavd8HRLMEEYFSW3HCSNQehnrHztKqHcDyo4VfZ6gPKCR+gufwA8GegxUEo4A+gd0BASHiH6jYMLIsUdQJTs/C641KN4oCHWolCMLlMfIdtWKScjx7SM5LD9HnfmhrGI0S139UWfUnxgOXdJFW+AMcGjKr6eHAttHF5sUoeArYKDcxMSYcKA/xUDhPiEOEAPafSIUFArN0r24ynI91EPARDXvIDYyvqZaWeroBOUABQA/E+DXC7PWafDLQY2oiwpUEyj4RQtVlUp1GrM7In2p2A7VuiOW6otMiGOo5Mrp05ejVuTy6dNX/k/7mybZQ0nUmfrbx3U4KueDnlHm5wdh8FFeKnoaKKh/TK18StOPhwG9Xo5mqXAxvw/79YQwwDR+nAKQQ4izVXioB84qcppWB7IqjU45z4CE17OvF1Dw+oTFqxtz8dxwtogBnF9MjIl/in+K8s3hM9laIn0TiCbTAXL0T798bPXqx36p3chrv0O+GC9Xaj48Ecv8U8UEeBvUEsDlTepiU5OvlpeNGvpnKF0RvUooWhIjnx6GeBapXCQYTw9DNg6/OC3gZjp76oNTj9Kz6Jqobxb9NDqc08vcKReOpcsQV2K8InXFaXW3aI6Ofr1k48rp7CX7rx+v1UKPsfvzQU0Kc83i2VdILmd2/yX55zT9luN2+Cu4nKfwPcK/CvDVU+pHh8+LaldIf1fA5h3ndT6Fln9/W/9Ce1vndfvJtnPVO2xhm3qbafHVCN1X363UXHq9xuVD8OSD29Z8pZ5cZrern9cAdGW/uib/ud+VK0L9a42r6C90kL8KzxwLQw9NkIQJL0ASU8M+VG0KsUdgdvpgP/6NqqP0/gHZFUfGEijZLHpiIgvV5/Bltrj8Qd7XQd5p4P+7tJo30NMO6VGBwahSPMYiaaBYoLY6uEnciyhhh1Z/vvacG/rjpsvnpzs0B1Id6fmX8119l88XnOxe/uGrzzHcdu7UtY3+2vmXN5zUyj3ZcPl8p1sZSs6/nGXtwrV7Ka0XZdz83fwjjINpZWYw85lL8BRK4nGyIir2RiOsEyipuEcIakpGjWgBjLiHWOgj0Yi34gW1kKPxHt2Na5q+lwg1RdRSpFDNzosb44YJXnAfoEOpZW//6u1lhYA6leevezbI26zNHO811M2dc5HFxpk4i1jPC0s21/BWW5DnPQbn2X1WK43/aM2n18DfSoybbNHijFpamzXI31eRibGUOxSu/lT96YZlq1Yt20DaSBuG6knw2eusHs5EPBfNmVvHKdaQzcDfz9ZsXmLDWGXy2U5OsYSsIn8CS12jQIyD12KKqZrLPy7mSPdICmd6WGHG8NDZkkHuE4h9TU8FpmUO/VjC/EinToFyoNDz2p9XD6g78WgQdPG7Z3R0T/Z5dTM9lsL8Ktek7szl2L+gQwGgwkZHc2g5Su7NvVqwGy2Ua4KSXUwt1X4PaM5paaEu6jQ5zVFyNabxvUksVt2T/4VeamYPlLtffdQsk+2sUTY/zDXl/05W53/Bz9UK3p7LjapZ2ZxOm+UlZXrL3HHGqO8+wVroDaCTTnTxitMxmiAAYQzVJQH+nj3oIHnPaN6Zq6sNSLjBl8tKgVr2mj/9CWi9dnKca8rBQBsd5R1tzVlgrl5pbnPw6kZclCr2CHxMnHohLz+3KRQokzALyeIKFU1TNCiayJdoHvDYe7K6mZLm8S3uJ9dojuaJ62/qN/tjQxnSnhnKPw+LNrLi8ZKyJ3x1YhiI1aNAtP6NzCGzYv3DmaGh/LvQZnt0evgIhTFV0kE/PYxAnOHhCQUZdCWY5JWJwMzlAGl1mpNbDU7yyGnhRMILsYhH3VRAijrPcBU8/Cj1Y9NY6cnGVW0CjTLaz7E3epvaT/LtTV72Rs+0WVVmd0dz/MGTI5F0OsIviaqDlbbO5X6xT3PeXbXHRtf/z+fdka+eKPr8KF7IF4vBsT9MFPuPJMBTBMq9hQxXelQ+bewnf18ap4Ib+mSMrtDU5zqlD8QANa5MBGh/OwOvSDfcV2d66mfEWsbGWmIz6nsyZDWQSmqmxDneYyvjHPmRXHZxeueyRGLZzvRioKnGto9nIPkibAJA16adcOZRQr1iAP3bUyBR7T4RgAWTKxhkCYFwshq+7iV9r0whk50cmRcTg4fy5x4OmmNkHndIA2+YuMbmE9dwGYB4KFTsvnDE6Ah47r/fE3AYI+oXADpkdlENcZ8OZEEf8FFGZNxMs6ZLpG3SUFLL7Q2kcFU/A/Jsw+vWDa/7emewLaoeibaF1B9qUNnuqWK3+UfXYVL1v/omD15xxeDkPnXTOKSVcCbDGtOu0YQNpGAP7U1HU58UrqGu8xIbHtkQ3LVhb7Dx46ET3Ffcm1q0YcOizNmf3bC3VjWfAcpSv3MyTlgJ23FHQgmgvk+gk8pL0mcCDOn08MDAQlf+/SlTZ1z12fnqntOhbOTL9/ZdevbAPN+yby1f/uUtC/ixm8ZBo59LTXEW060hGrTDplNprWd58fwB/b/E27BdS/s7U+rGVCeQ46nzaw9QccnmZerGZZs3Yw9aVHt+Kh6HN4ti6lxIhT/wahnZtWwzlY9QHQ2c79C+dxzvVDKy8GqKWQERO9YAKbpsDUTLdWV5dE8PVPjvj9pqw7ah/PFVtkit7aj6G5xY9mfJrCz1j1e0BcnPol4UjtrCdbahIVtd2HaURujnFJR8CuOuUUfhrGhgKKgjCYNSvCc1WKlEp8wHUaAYynFNyzZn+2MnYv36dbMDBTonl/T/ma5IKAyEGz+4eRnVtaX6tss2o34u8mWorFtuFgm4A6qK/yp/gLEBVat5WnPDdKA574ubuFJ/IUfZ/Y2Nt6mN+ZNNTSTaeI56gKwkXerTe9DDHUw8/H35FY3nNN7GGuBKWhrV9ep+0k1WjNWVaHkW1yA+QHWNu8rtBw2a5YXuE40rs7/GA+j09V3hA98yRnFPOGr8ltGlsFdD/7tRce3LH6Trcneuiy7K7J3khKu+3qUaXPWaX7T6/Kfj9BX2eZq2XAcZT79u1ClJzUtHUqfqSMWBcZS43Ena0cUGLgpkKxB1QM+0Fxz10wgg6r5rltnFpH05pepUq3Y2HfYqeKRntmUFNz+XmcOs1H31U6cC6RTVLfCg7RNBF1UF2/wBgu0fFQtPEU1sSg3VcNsR7dWq3af87tUFn1l3ltXpaJxpNvtcZkH2WmMst3JqRpxUH+WC0E1qOGtP66s1MYv+VLu8/XFXvV/ZbunYYBeVN64ls0ur6NzpV9xzlmQwB5qC4Tq70WC0tk8dWJXeHvkD0h9zJOM0vD86/1NJMaIAolctvlByferCsqOKDKceOfUu1PsmoFCamV5mCrMUOCi6V6FJosMF22AcrKJgQDVhfYh6tepp/lYgvnCEAbJQ1L0rOpajEmRcasMiPfxhgGoVo4rwreQpV6fUJHH2e8fa1s2c13Apl1b89a58ozdoap2sjgLN9uISl7P1DrulyeIkt0zr6JjWocoPOZsaXPb6jtqBblsgsaRre2xHi4nELm0MhG1+x1SXwLpFi53b+aHRYo/IrbZtuWAKu5cSEXfybnnmUCaXGTpQr0xK2O2WWY76f+nAjNVf7nCZHU5XqIkTnpt6VtvsFlPXg1031g/VRdpkkyVpD7jnmax88QwDvg/66NnMRdRXTcGTmQc3cuINwN5IQqi0yzb+YFVHuVqI5s4ADfg5oE4ybDLd28mFSFmYvRoomsWXEdLU2Wl3GJy93ZNb/d5gqmNaqJZSO1l6PVRy0nZIj/45EetjLguh1rLqR+SK0hO6NrsqcNX8zoUdjQYDJ7tb4os6+i+Y0qpY2AWlnLRDWdGFTfGY1gV0zNAtJ7pdo24se0D88AwLY/gZmE9iuP4V5v7CSR/RThaHLh+UeBkXwU6BC7lGOevK65udTv+tS/PfW7qj3ljTcj3b9OkbV85t8xsMj7Ddj7DGpthZKwKPvso/c/1K9aLE12fMWLV1y1D9ua8lyJdWXr/bG+noCFutf/mLILe39ITUV4igr3876fpX5g2zeB52sWnIL4fXHlgeUzOx5QfIvJQyrKQE9wHUqVq+PEaOrz0wVvNbJZVSfsuMzxN4l9PkedFzw9V5Dj+nzpgoT4ZxCxJfC5RWLc74YVHxKlExCYt0JAOMatREhHBSCAtSfod6x6Ls8HCWECLwXZ9nd5Dz1T24JUdWs6fU3++fcnT49Qe+kBs+wdsMZgPXMp3U5S958snPP/EE7bvkOPCuTUDTUQ/UzirLhML9yPahoe1D5Fj5jWsaoveyP00PehdUAHk/seDVWsvDWXXXsyn/4wfpXc2V3/Qxli3jl/5hj/83avSCfpTNxOEKLmTjxOEKuxgNlsQn0xgct724mhynupNW1Ph6o3RYS3/+2TJrzLlkFz+ip3qCHKf6eqW02QJLjBYuuj4sobhCWqa/YHGEHpcnumuWSOhxeaL7sOakNR6vvmo+YcfFA8UFXEPZf9UjyudIOyNwx/i90DdsujS/FX2UAwvWSVK4NxaMhAGw3oowp/uc8CTi7D2rBgZWwb/60faR7SPsEbjkXy4G0XaqhXPwe2cePjxjxuHD6ssQuR1fq6PF0E+o2t1nePTn8TUmxz/A3crMoCc7egESuoTHYc7mYdg6etORoOhR7BBGD+qJopELrl4S6cJNRtEAsLP/OdvnJq0Wo0GolY2Et9VFB2Kf+4bZvVyxfOMz3WdFfSIryj6DwWghre7aQbdiDrkTL3A3vNDuDpk93HqXwam+bWmUJZfNn5ozKV5Pmmq8PF/jVY+2Tlk2M2RzSXKjmbQ4RZcQavEYrN/9rlXwtIQqzxQNMzPPfHYLvuPoO9TbT8bpGw5CQPGd+SyX/Cyf0Vxjd2R9NmsunnXYa8xGHzn+sSfM5J0y0DZEXWWxkXjcR75KBLNLHi7XvX2G8VOrf4Ykg0AMdBESIpo7MgAfyakA6rkqpI6UjNs0px7cMV+D5BF49Tez1VGnYmq0WIijp985m4Sn2gJR9b07riPPFo97OYbUZbxJCpot7H/lpZBicglCPN7WOfJkcHqc3ElWqvvz/1E6bIQrG+tz6WkM1SM9FBTR7FSs8KyBBytSmNEoquJNFN5EQyTiCrnKDx1h58yxCepPHU5nxGoxEQeeOZi2m80DxNxncVhr6BmEfUarxejw+WSiHhWk19bSY7aKR5MsteblJpfTLtjimBouXsm3d3djjYM+wEW0El9dM/ueVRWIsXwe43R7SgbVZqrnqoJ1X/kuF7pcgf8duv4q6vayV5U9zMV91GxO59UUjW8rHV6u799WzKMT7umRCXbYUKM+foaCcwgaoqZUtmodV3p+X7akb4dnU9B9La38RPFUG2SCC90tVA4XwEFhyOpZZrUCsgWYHsczLFBBVGNtstoN1bw0Z+O4fYIbvZVt4EUcJEKOhHeincWqONw+q6w5Go+WGOSR7LhKV+KBqbBPpfUvOf9QqkpDyVhBeyyZQGMsdA5FBUqvFMtUyGq9vjnsAJU4UcrxldP1CCaofyDkSAifoP5QwWx+SyUGxp75BzGAvtG7uQ38LehlyEQMeh0TeE6Bm7tYdXqdkt0uOb3kfYlNwmOdDyacOq/qlFo1v+PTmTi3E/glC9W11b34A22zmLzvb231Q0L2Bgg60OTW4YdstO+YOJnO38TtpH7zy9ymokWyA79qlVSn38HtpFlImFnhu3b4boNWXklOXV0Iwo7lQ1hrZyPFcwtjwFP7iEKSHSSJw509kh8kj6pr+H1jR7km9vcvqN9657vffefkv+fKxge1X+7RdjYUPIESN7gTvRkB/RMYtEkaVkdHApmdBPpnKmz0n1xSWFOyVIuLrinZwpoCRe6kyiVZoHX088F+UX4+WKS4iBTP0IWxGtZgOdMaV4KTayqHQF/VihBwTbgDXTCmKoOBJeNhwJMzEVjtjIFLuU38fPR7hqNG1JS7g/qRCuy3vmQ3W9Vu8qbVbP+SzazGRJH83MzP90Ck2m31mMjP8TiLn5uwD2Ugr2PFvPQjB5BnSJvQxGQZZEB+LopqzGzDbMmbkAPkZVJjeO5FzOSBKCgJze2ZS4Gemc9twrwY6u9H61iUQTcRvtdT9RW3tRxAWwFs2tcuJRnI6xjmBdWjbgFNRHMHiF1uHYBfUR/ut5Ug2jXAaT96+9RH/FToRwIzGbKmVJ1AZQnoabSB1yyIg7ByAridHApPMjyw0OiV6RjSbCuzwLAvFizBliWJua1tsuAgvNPbmljYbpt8lkWam7b3XZiOiKJskMOtmfScnsbPW208knwjuXrXK4Q1iKIgNyYXXDVT9C2Ye/78GQ5BEEXfFdde2RwauOysdJNL5AzCy84ard/nGAVN8alecnFdgu5Gbd5DJTL+hHZK0vApVy3OfU8XTSJg1TlssivsPYUlIqvn66PzrVTymCc4wgF6SDNR0pDf+9Gp+VnsUH5WtpHYsuhOaey8zdwLN47V8MTbm78g687+P3cx6tcAeNpjYGRgYGBk8s0/zBIfz2/zlUGeZQNQhOFCWfF0GP0/8P8c1jusIkAuBwMTSBQAYwQM6HjaY2BkYGAV+d8KJgP/XWG9wwAUQQGLAYqPBl942n1TvUoDQRCe1VM8kWARjNrZGIurBAsRBIuA2vkAFsJiKTYW4guIjT5ARMgTxCLoA1hcb5OgDyGHrY7f7M65e8fpLF++2W/nZ2eTmGfaIJi5I0qGDlZZcD51QzTTJirZPAI9JIwVA+wT8L5nOdMaV0AuMJ+icRHq8of6LSD18fzq8ds7xjpwBnQiSI9V5QVl6NwPvgM15NXn/AtWZyj3W0HjEXitOc/dIdbetPdFTZ+P6t+X7xU0/k6GJtOe1/B3arN0/pmz1J4UZc+D6ExwjD7vioeGd5HvhvU+R+DZcGZ6YBPNfAi0G97iBPwFXqph2cW8+D7kjMfwtinHb6kLb6Wygk3cZytSEoptGrlScdHtLPeri1JKueACMZfU1ViJG1Sq5E43dIt7SZZFl1zuRhb/GOs44xFVDbrJzB5tYs35OmaXTrEmkv0DajnMWQB42mNgYNCCwk0MLxheMPrhgUuY2JiUmOqY2pjWMD1hdmPOY+5hPsLCwWLEksSyiOUOawzrLrYiti/sCuxJ7Kc45DiSOPZxmnG2cG7jvMelweXDNYXrEbcBdxf3KR4OngheLd443g18fHwZfFv4NfiX8T8TEBIIEZggsEpQS7BMcJsQl5CFUI3QAWEp4RLhCyJaIldEbURXiJ4RYxEzE0sQ2yD2TzxIfJkEk4SeRJbENIkNEg8k/klqSGZITpE8InlL8p2UmVSG1A6pb9Jx0ltkjGSmyDySlZF1kc2RnSK7R/aZnJ5cmdwB+ST5SwpuCvsUjRTLFHcoOShNU9qhzKespGyhXKV8SPmBCpOKgUqcyjSVR6omqgmqe9RE1OrUnqkHqO9R/6FholGgsUZzgeYZLTUtL60WbS7tKh0OnQydXTpvdGV0O3S/6Gnopekt0ruhz6fvpl+nv0n/h4GdQYvBJUMhwwTDdYYvjFSM4oxmGd0zVjK2M84w3mYiYZJgssLkkqmO6TzTF2Z2ZjVmd8ylzP3MJ5lfsRCwcLJoszhhyWXpZdlhecZKxirHapbVPesF1ndsJGwCbBbZ/LA1sn1jZ2XXY3fFXsM+z36V/S8HD4cGh2OOTI51ThJOK5zeOUs4OzmXOS9wPuUi4JLgss7lm2uU6zY3NrcSty1u39zN3Mvct7l/8xDzMPLw88jyaPM44ynkaeEZ59niucqLyUvPKwgAn3OqOQAAAQAAARcApwARAAAAAAACAAAAAQABAAAAQAAuAAAAAHjarZK9TgJBEMf/d6CRaAyRhMLqCgsbL4ciglTGRPEjSiSKlnLycXJ86CEniU/hM9jYWPgIFkYfwd6nsDD+d1mBIIUx3mZnfzs3MzszuwDCeIYG8UUwQxmAFgxxPeeuyxrmcaNYxzTuFAewi0fFQSTxqXgM11pC8TgS2oPiCUS1d8Uh8ofiSczpYcVT5LjiCPlY8Qui+ncOr7D02y6/BTCrP/m+b5bdTrPi2I26Z9qNGtbRQBMdXMJBGRW0YOCecxEWYoiTCvxrYBunqHPdoX2bLOyrMKlZg8thDETw5K7Itci1TXlGy0124QRZZLDFU/exhxztMozlosTpMH6ZPge0L+OKGnFKjJ4WRwppHPL0PP3SI2P9jLQwFOu3GRhDfkeyDo//G7IHgzllZQxLdquvrdCyBVvat3seJlYo06gxapUxhU2JWnFygR03sSxnEkvcpf5Y5eibGq315TDp7fKWm8zbUVl71Aqq/ZtNnlkWmLnQtno9ycvXYbA6W2pF3aKfCayyC0Ja7Fr/PW70/HO4YM0OKxFvzf0C1MyPjwAAeNpt1VWUU2cYRuHsgxenQt1d8/3JOUnqAyR1d/cCLQVKO22pu7tQd3d3d3d3d3cXmGzumrWy3pWLs/NdPDMpZaWu1783l1Lpf14MnfzO6FbqVupfGkD30iR60JNe9KYP09CXfvRnAAMZxG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<div id="statistical-learning-with-math-and-r-springer" class="section level3">
<h3>Statistical Learning with Math and R, Springer</h3>
</div>
<div id="chapter-7-nonlinear-regression" class="section level1">
<h1>Chapter 7 NonLinear Regression</h1>
<div id="polynomial-regression" class="section level2">
<h2>7.1 Polynomial Regression</h2>
<pre class="r"><code>n=100; x=rnorm(n); y=sin(x)+rnorm(n) ## data generation
m=3;p.set=c(3,5,7); col.set=c("red","blue","green")
g=function(beta,u){S=beta[1]; for(j in 1:p)S=S+beta[j+1]*u^j; return(S)}
for(i in 1:m){
p=p.set[i]; X=rep(1,n);for(j in 1:p)X=cbind(X,x^j)
beta=drop(solve(t(X)%*%X)%*%t(X)%*%y); f=function(u)g(beta,u)
curve(f(x),-3,3, col=col.set[i],yaxt="n"); par(new=TRUE)
}
legend("topleft",lty=1,paste0("p=",p.set),col=col.set); points(x,y)</code></pre>
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" width="672" /></p>
<pre class="r"><code>## Data Generation Closed to Even Function
n=100; x=rnorm(n)*pi; y=ceiling(x)%%2*2-1+rnorm(n)*0.2
plot(x,y,xaxt="n",yaxt="n",ann=FALSE, main="Follow Random Numbers via sin and cos")
## The function f below chooses 1, cos x, cos 2x, cos 3x as the basis
X=cbind(1,cos(x),cos(2*x),cos(3*x)); beta=solve(t(X)%*%X)%*%t(X)%*%y
f=function(x)beta[1]+beta[2]*cos(x)+beta[3]*cos(2*x)+beta[4]*cos(3*x)
par(new=TRUE);
curve(f(x),-5,5, col="red",yaxt="n",ann=FALSE)
## The function g below chooses 1, sin x, sin 2x, sin 3x as the basis
X=cbind(1,sin(x),sin(2*x),sin(3*x)); beta=solve(t(X)%*%X)%*%t(X)%*%y
g=function(x)beta[1]+beta[2]*sin(x)+beta[3]*sin(2*x)+beta[4]*sin(3*x)
par(new=TRUE);
curve(g(x),-5,5,col="blue",yaxt="n",ann=FALSE)</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="spline-regression" class="section level2">
<h2>7.2 Spline Regression</h2>
<pre class="r"><code>n=100; x=rnorm(n)*2*pi; y=sin(x)+0.2*rnorm(n) ## Data Generation via Random Numbers
col.set=c("red","green","blue"); K.set=c(5,7,9) ## Knots
for(k in 1:3){
K=K.set[k]; knots=seq(-2*pi,2*pi,length=K)
X=matrix(nrow=n,ncol=K+4)
for(i in 1:n){
X[i,1]= 1; X[i,2]= x[i]; X[i,3]= x[i]^2; X[i,4]= x[i]^3
for(j in 1:K)X[i,j+4]=max((x[i]-knots[j])^3,0)
}
beta=solve(t(X)%*%X)%*%t(X)%*%y ## beta estimation
f=function(x){S=beta[1]+beta[2]*x+beta[3]*x^2+beta[4]*x^3;
for(j in 1:K)S=S+beta[j+4]*max((x-knots[j])^3,0)
return(S)
} ## obtaining Function f
u.seq=seq(-5,5,0.02); v.seq=NULL; for(u in u.seq)v.seq=c(v.seq,f(u))
plot(u.seq,v.seq,type="l",col=col.set[k], yaxt="n", xlab="x", ylab="f(x)")
par(new=TRUE)
}
legend(-2.2,1,paste0("K=",K.set), lty=1, col=col.set);
points(x,y)</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="regression-to-natural-spline-curves" class="section level2">
<h2>7.3 Regression to Natural Spline Curves</h2>
<pre class="r"><code>d=function(j,x,knots){
K=length(knots);
(max((x-knots[j])^3,0)-max((x-knots[K])^3,0))/(knots[K]-knots[j])
}
h=function(j,x,knots){
K=length(knots);
if(j==1) return(1)
else if(j==2)return(x)
else return(d(j-2,x,knots)-d(K-1,x,knots))
}
n=100; x=rnorm(n)*2*pi; y=sin(x)+0.2*rnorm(n); ## Data Generation
K=11; knots=seq(-5,5,length=K); X=matrix(nrow=n,ncol=K+4)
for(i in 1:n){
X[i,1]= 1; X[i,2]= x[i]; X[i,3]= x[i]^2; X[i,4]= x[i]^3
for(j in 1:K)X[i,j+4]=max((x[i]-knots[j])^3,0)
}
beta=solve(t(X)%*%X)%*%t(X)%*%y
f=function(x){ ## Spline Function
S=beta[1]+beta[2]*x+beta[3]*x^2+beta[4]*x^3;
for(j in 1:K)S=S+beta[j+4]*max((x-knots[j])^3,0)
return(S)
}
X=matrix(nrow=n,ncol=K); X[,1]=1; for(j in 2:K)for(i in 1:n)X[i,j]=h(j,x[i],knots)
gamma=solve(t(X)%*%X)%*%t(X)%*%y
g=function(x){ ## Natural Spline Function
S=gamma[1]; for(j in 2:K)S=S+gamma[j]*h(j,x,knots); return(S)
}
u.seq=seq(-6,6,0.02); ## Draw the Functions as a Graph
v.seq=NULL; for(u in u.seq)v.seq=c(v.seq,f(u))
plot(u.seq,v.seq,type="l",col="blue", yaxt="n", xlab="x",ylab="f(x),g(x)"); par(new=TRUE);
w.seq=NULL; for(u in u.seq)w.seq=c(w.seq,g(u))
plot(u.seq,w.seq,type="l",col="red", yaxt="n", xlab="",ylab=""); par(new=TRUE)
legend(-3.7,1.1,c("スプライン","自然なスプライン"), lty=1, col=c("blue","red"))
points(x,y); abline(v=knots,lty=3); abline(v=c(-5,5),lwd=2); title("K=11")</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="smoothing-spline" class="section level2">
<h2>7.4 Smoothing Spline</h2>
<pre class="r"><code>G=function(x){ ## The values of x is assumed to be in the ascending ordere
n=length(x); g=matrix(0, nrow=n,ncol=n)
for(i in 3:n)for(j in i:n){
g[i,j]=12*(x[n]-x[n-1])*(x[n-1]-x[j-2])*(x[n-1]-x[i-2])/(x[n]-x[i-2])/(x[n]-x[j-2])+
(12*x[n-1]+6*x[j-2]-18*x[i-2])*(x[n-1]-x[j-2])^2/(x[n]-x[i-2])/(x[n]-x[j-2])
g[j,i]=g[i,j]
}
return(g)
}
n=100; x=runif(n,-5,5); y=x+sin(x)*2+rnorm(n) ## Data Generation
index=order(x); x=x[index];y=y[index]
X=matrix(nrow=n,ncol=n); X[,1]=1
for(j in 2:n)for(i in 1:n)X[i,j]=h(j,x[i],x) ## Generation of Matrix X
GG=G(x); ## Generation of Matrix G
lambda.set=c(1,30,80); col.set=c("red","blue","green")
for(i in 1:3){
lambda=lambda.set[i]
gamma=solve(t(X)%*%X+lambda*GG)%*%t(X)%*%y
g=function(u){S=gamma[1]; for(j in 2:n)S=S+gamma[j]*h(j,u,x); return(S)}
u.seq=seq(-8,8,0.02); v.seq=NULL; for(u in u.seq)v.seq=c(v.seq,g(u))
plot(u.seq,v.seq,type="l",yaxt="n", xlab="x",ylab="g(x)",ylim=c(-8,8), col=col.set[i])
par(new=TRUE)
}
points(x,y); legend("topleft", paste0("lambda=",lambda.set), col=col.set, lty=1)
title("Smoothing Spline (n=100)")</code></pre>
<p><img 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" width="672" /></p>
<pre class="r"><code>cv.ss.fast=function(X,y,lambda, G, k){
n=length(y); m=n/k;
H=X%*%solve(t(X)%*%X+lambda*G)%*%t(X); df=sum(diag(H))
I=diag(rep(1,n)); e=(I-H)%*%y; I=diag(rep(1,m))
S=0
for(j in 1:k){
test=((j-1)*m+1):(j*m);
S=S+norm(solve(I-H[test,test])%*%e[test],"2")^2
}
return(list(score=S/n,df=df))
}
## Data Generation
n=100; x=runif(n,-5,5); y=x-0.02*sin(x)-0.1*rnorm(n)
index=order(x); x=x[index];y=y[index]
X=matrix(nrow=n,ncol=n); X[,1]=1; for(j in 2:n)for(i in 1:n)X[i,j]=h(j,x[i], x)
GG=G(x)
## Plot the Efficient Degree and Prediction Error for each lambda
u=seq(1,50); v=NULL; w=NULL
for(lambda in u){
result=cv.ss.fast(X,y,lambda,GG,n); v=c(v,result$df); w=c(w,result$score)
}
plot(v,w,type="l",col="red",xlab="Efficient Degree",ylab="Prediction Error via CV")
title("The efficient degree and Predition Error via CV")</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="local-regression" class="section level2">
<h2>7.5 Local Regression</h2>
<pre class="r"><code>n=250; x=2*rnorm(n); y=sin(2*pi*x)+rnorm(n)/4 ## Data Generation
D=function(t) max(0.75*(1-t^2),0) ## Function Definition D
K=function(x,y,lambda) D(abs(x-y)/lambda) ## Function Definition K
f=function(z,lambda){ ## Function Definition f
S=0; T=0;
for(i in 1:n){S=S+K(x[i],z,lambda)*y[i]; T=T+K(x[i],z,lambda)}
return(S/T)
}
plot(seq(-3,3,length=10),seq(-2,3,length=10),type="n",xlab="x", ylab="y"); points(x,y)
xx=seq(-3,3,0.1)
yy=NULL;for(zz in xx)yy=c(yy,f(zz,0.05)); lines(xx,yy,col="green")
yy=NULL;for(zz in xx)yy=c(yy,f(zz,0.25)); lines(xx,yy,col="blue")
## The curves for lambda=0.05, 0.25 have been drawn
m=n/10
lambda.seq=seq(0.05,1,0.01); SS.min=Inf
for(lambda in lambda.seq){
SS=0
for(k in 1:10){
test=((k-1)*m+1):(k*m); train=setdiff(1:n,test)
for(j in test){u=0; v=0;
for(i in train){
kk=K(x[i],x[j],lambda); u=u+kk*y[i]; v=v+kk
}
if(v==0){
d.min=Inf;
for(i in train){d=abs(x[j]-x[i]); if(d<d.min){d.min=d; index=i}};
z=y[index]
}
else z=u/v
SS=SS+(y[j]-z)^2
}
}
if(SS<SS.min){SS.min=SS;lambda.best=lambda}
}
## The optimum lambda has been computed
yy=NULL;for(zz in xx)yy=c(yy,f(zz,lambda.best)); lines(xx,yy,col="red")
title("Nadaraya-Watson Estimator")
legend("topleft",legend=paste0("lambda=",c(0.05, 0.25, "lambda.best")),
lwd=1,col=c("green","blue","red"))</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<pre class="r"><code>local=function(x,y,z=x){
X=cbind(rep(1,n),x); yy=NULL; beta.hat=array(dim=2)
for(u in z){
w=array(dim=n); for(i in 1:n)w[i]=K(x[i],u,lambda=1); W=diag(w)
beta.hat= solve(t(X)%*%W%*%X)%*%t(X)%*%W%*%y; yy=c(yy,beta.hat[1]+beta.hat[2]*u)
}
return(yy)
}
n=30; x=runif(n)*2*pi-pi;
y=sin(x)+rnorm(n);
plot(x,y) ## Data Generaion
m=200; U=seq(-pi,pi,pi/m); V=local(x,y,U)
lines(U,V,col="red",type="l");
title("Local Linear Regression (p=1, N=30)")</code></pre>
<p><img 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" width="672" /></p>
</div>
<div id="generalized-additive-model" class="section level2">
<h2>7.6 Generalized Additive Model</h2>
<pre class="r"><code>poly=function(x,y,z=x){
n=length(x);m=length(z); X=cbind(rep(1,n),x,x^2,x^3); yy=array(dim=n);
beta.hat=array(dim=4); beta.hat= solve(t(X)%*%X)%*%t(X)%*%y;
X=cbind(rep(1,m),z,z^2,z^3); yy= X%*% beta.hat
return(yy)
}
## The same function local is used as in the previous section.
n=30; x=runif(n)*2*pi-pi; y=sin(x)+rnorm(n); plot(x,y) ## Data Generation</code></pre>
<p><img src="data:image/png;base64,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" width="672" /></p>
<pre class="r"><code>y.1=0; y.2=0; for(k in 1:10){y.1=poly(x,y-y.2); y.2= local(x,y-y.1)}
z=seq(-2,2,0.1); par(mfrow=c(1,2))
plot(z,poly(x,y.1,z),type="l", xlab="x", ylab="f(x)", main="Polynomial Regression （Order 3）", col="green")
plot(z,local(x,y.2,z),type="l", xlab="x", ylab="f(x)", main="Local Linear Regression",col="green")</code></pre>
<p><img 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