Emaranhamento desbloqueia o dimensionamento para aprendizado de ma¡quina qua¢ntico
O novo teorema de Los Alamos No-Free-Lunch mostra que, no regime qua¢ntico, o emaranhamento também éuma moeda e que pode ser trocada por dados para reduzir os requisitos de dados.
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JjDHFRmMeCjJtOxfQEPt0IgAss3H+PQfM8S+dB5h6FPmHdWtHnxMTaZolJhqbcq2LMFoNHvOp078vkWCfTuZpdOVJqdrfp3zTpsG5XeUI6nkLufcAaGeLppsUQNLd8IYxajMbZVmPX5nHfExKR93Uj7mDKqSWITO+HJh8tGJiMO3A9hwQctGOT6Cw9CIFFj7j/JoPmeIj/7tpm0wUPYvIefTvPpmn00+nWcmqcuiJ9OrXjTYLafZzdPPqKJ9VVNPq6+ZdqlS360T62V6zL2arY41iNOY5lt3LVdUd1NrPH1HdC7cM4m4GNdgm3A5858SwOA85onMEDrlioLPXnfVM0ysITYKd2aZivGyucpIKVzbWDOQIaIdPPpWg0hUHTPPp3lWlZjerFuWZsM2mYmJjiIe3QqhBY+4/y6D5musVdXzxPqDF1dimzUM85rTmNN5m4zMzwqO5V718azh9YPucNKM3XH/wCg++jU73u3umnRpy8KK0SNeoj2kAsTFbBGHDAqx4VeU2dxMTEPdWBJ5eJuVZWxNl/7AMknzQGVxjkmFjGsYBHaNqHJ57wXOTZqjWn1DT6gz6ic5ZzK5uqn2ZsqgoUz6VVDaczkNOS0FXKDlmOP5tB8zxL53EHEYdanB/6MMNwHvd5qeGiH3WBawaZ2NdS1VqK8xrgsLrZBTgvndFGSzZiuHBQrMbJuya2hG0zEXGHc54U/sv8A2L2EB4DtX7xuwYw+YueNY5aMdx68xWKw2sZzWi2vFv5Svqt53oZ9ozloZyIaDDUZsMx/BoFxqfEvndCmMuOurzLaO/EebSctjE0jtNNQtUa6pJXe1pt3W2Kq1Kb8mLFdlnNVoagYwKKDP8q4UOmeHfONy7gIbDKm72jD8KP2Xfsfh7RDk3HA3QtC2Y3kHCpN7XvuPoAYhPAAk9qgzZ45m4zeYLmgvM5qmfaM5aGGiGlhNhmPRAzOyTRPu13iPzszMzMzMru7NlTum6bpum4SuxVa3lMh5UFdbRNCrSrT1JXupUPZY0pR+VyLJpaTWnZBbYzlIBkkwnySvywX5mxLI4KCVMY9SxnwEsIa0YmYpwL+NAPMZDzOWxnKacoyinzWjL4WbUM2VVgiqYqgWomw01V+SeSeSYSYWbVm0QV5nI2Aq02mJWzliKgTn0szcYLCILzBcpn2mnJUw0GGsiY6FTMZwoZszw353iXzupSGDDaegAmaOhnr+mqrh1NVcfVu00lhNh7MZSrHS018uZll7budEsQktVAtJLIhIpzHqeClzDkSsvMU5cERH2lqwy7DE7qwVSWQDcpr5onOMptLPdaynmmb5uETC0naZsi1ER9xPCpeWjtubr/CFiZmVhmLanYrPuPaYm2Y9TMDmLeRBeDPttDSDDp2nJ2Sx4Tw8N+d4l87rB3gjBxE07vBpq0hvprn1tm7VHMPDTnFt6/eo0xeWMKKdPuaai7JM94i4GIm3O5ZvKrXzXn3jNyrDdXN9EF1c3K0C2COhceZWccxGlByG7GaX87Tmzgoy2pOFirGbJ3tOZKkSw34clGHUBmZ28a68yyzt0ZmZ2M2+tmJun1QrDagWQqrQ0woRPDvneJfO60rZomlWxC9NJfVu0LE8dOebTwqUl3rrWW6ksWrNiXMK6/LN3lG4hEsJ5U21qiGqKS0fU4jWs8zwB4ZldrCJqNw7OquFa5K91SgPdSd21hKO0s/Phpl81zbnVcxzxC7jYRVXAzCbwZywYVI4BYW4pX2ssz6IMxmY9MDMChI9sJ4BjBaYLFM0QX6vxL53QFJiaZjPsVxtS0zYSVNg6Kn5dmpTzUadrZmvTC+wWUUhnfEvXdZ9oRHXLXtA7E5mxjPt1LbaznhjM7zMMzFPcHB3lDXYtsercndWuJ2Ja2abd7Oai2xDOS0ClKsFmY46Kxy0dtzdC2GctYxOeCoKxZYWPpCN6S1xrAsZyevw/5niPziOCUs05VaQ3qsa1mirmBYFmxhHQWBlxwVS0FXfTUfavdoRXKSraer7a3vsr9+DHbG96kJIKK2Y7ljmAZgXiRwzFPc+6GL5ZRfmX7Zs3UN5Bpo35SskS2xlBuUD7TTlQ1sJTVk32bj0BSZkJMnIIsnLbd5aQ7lj6Yn+vWqEzK1x7CZn0PD/m+IKTr66sRvpgHvYzPBRkiCIszH7M1XNXlESmkMd1OlX66w26pe80Kba6mNuq1r+fM/EKrNMoq7yzUpg3PuaD3Bm7gDEXdHXaT7xvyzPerMotFi0o1dj2Bmpr7N+Q7mkbrb3w3DMrZy1t4RTymnKzDWwmIK4xPFELHcu1s59RRGPUqkzaqR7YT6Xh/zdfbt1ZcnhmEcF9hFiztG9t7A/SC2W6hawWLGUnm06ajzDUZv09e1r2zdWhckopdyYImEOSK+GJ7TMzwrOJc26e4xHHebtsbsVbBrs3Jqq9r6ZiF5ivOVgKORQTk8V+1Wx3HhWbCQ6LGCPDUY6RKsyywABsNcPUAnt0hSYECxrYWz6nh/zfEvncQcRU5k2FIMQNAYph7wVrWLdW4Nihxw0Snm659qU/tMKqGts4e8H24PPbce8UTbHXhmCAwmVCbJYJ7xz5l8yp70XYsvI2qm2sDcyuUa90YNURxoSXWb24BMQHtiYneJ2mouRpszCpEf9PpBYTjoAJgrAjWgRnJ9bw/5niXzujMR/Lt4CVqXLMlIdyxf3rcoXQEVoXZ2GmqqPOTSafY5fNP4jPAfbjHdF7LafuCLwtcCe8xMQNiEyv8AGWe3+x9wcG32iHnaXTtiqxOSun8z3NudLGWfbsi0NuvfAiqTMqkJJiwCbJsCyxsy33gciWFeXszCpHXiYAhbiATBViGwLGcn+DQfM8R+dxSvMcrAcEHEBDRNMcWXgAtmMcDhU5VhWtFTA2Gm0I9526ajvo3bJg+2GOZX71n7j/kIpjPtX3IirNkdYPdTMx27QxYhzPY6F8O6rXWt+WZOVRwHci3kV7VuLV8uM5PGs9qwSchYfZzGOTK13NactA5EypmyEY4Ym3E3cQpMFQENgWM5P8Wg+Z4l87gFCB3LcUzEVaw2qczs0Y7YTnjpNPmNq9tlw3TTpvsewOaU2aY++NgJyY/ZUPls95uMZs8FicHHY+4Y43mMZ/j/ACeDeZdOeXZZ5qgv3LLtssrxwpXYrZY8zbBdmGsHjVWTDeqzfGt7O+eP606VJgrpw4xxCkwVhYbQIzk/yaD5niXzoAKgxLHhXWXOUoDuWPAPNoMwc6bThm1eo3cKrNhprFddbecH7Vq8qwkkxIT3/wBMZBxwPvFimZjNGi+0xlbBiDtxrO2DyS58aZEDR23NXZtiaXJvuUEkniCRAy2T6XYLbc9SrsDHceO0zyiFuAJiJzD9NWge3ELE/wA2g+Z4l86sbVZtx4VU7o9oUZz0gSpxYdQOTVwAyWt5Nd6SptlOvGLeD9p7xpmHg/AQGboW4L7SjBN9eHb3ntFG5n8yv5vD6SF05U7q1G5tTsFiY6FBYgLUDqXz5bIVK9AUJGYsYFJm0CbgISTxWomfbSNcZuMzMTH8ug+ZrV3eIXHvwSoKLbt095tm3gBmdhPeKBp6uY27crxkImkTdZa+W0z8s6wlZqRzdLE7QxPzP5f68MZHsZumeA78BKziWtmP7+0943kWs96VzVqcLZa3OQfZrJya3xLE28K6y5LLUGYseAshSBST2rmGabQJuAhYniATBVN6JGtJmenM2/yaD5ms7avMXzEJRUtjFyB3AmJibYe3DT1gC6w2PwVysqCfTWKQQdz327H0+Pp7q9lj8Kvyn+OGcQ95g8cdC+zQnBieVfeAYlT+S/8AdosLNQTzeFbz6bbHt7Z6UrKzdSwfyEsT0KjNOWqw2gRnJ9EGdjCP4tB8zxD9yIWJZagTngnsBAmYa8QiOJRXzH1FuehBua7yLzmlSJY+uBF3h9u17aw9R4L+K9+g8Fiy5crxEXaqM2OFa7ixyd0Hc3tyw9RNttmYfPXAMxUWsHUlg67TACZtgQTmhYWJ4K+IVBmDFpM+2ka4wkn1QYV/h0HzNSm/VO+3or9kHbbNpjQ7WNoSmoqejQVbn1NnMslP7dRcTbp1Bu5v0+q1mn2mf6A4inPE+8WKZmMMHgvuXhOZt7u20cNMu67WefU6psaaVthuS27K1AlmOJW9WG7NtM3hYST0KjNFQJDqKsWM38KmMv8ABoPma60rrrl6EOIhgaD2sMHkVjk5m8zKxEV2deToyCOGn/df+2s7DqLdy0MLab6cRvaL77zN8zngIDN0LTMBJJfhmfgnHSDE1H2mqzZVtOaqBLdRUaS8yYEZptRYLchs54YzFpJn20jXmFieAabc/wAI7qfX0HzPEvnVvLK8dCviCyG2V+c3Wb24iVLvs1dmbQ7Cb5pOWbrVU2NWwjAnS1WGqx7hnUaYPDP8n3g45meGCYcKpbtEEJLHExFUE1LVXNVdzLdMzlrEWs2WFpWGy1YU71WF2bivnHKfPLVYbVWNYW6szs0Ix66Rvf1tB8zxL50R9sKB4QR0IpZrmCr0e00o2VnueGl/b/nJmnufZvmlaqyAmi56xcradhGGDw9pnhidoSzTGYcStQS75m6E8NDVuey7fetZdqfstZ5jvUQ2MZ+ScApMFMzXXH1JtUk+kGhX1RPxB9UIZsE0W36rxL53AHEFmZyw0KkcB9ms9HtB3Oo+3Tx0v5N24UHFtgw6dms+9Ujsh32Gc/eDQGnKSclMciZrSc0xrGaEwQAsWOOOCYlDsbNtOn0taS3UGbiSTixxteJnc2mcHbWkN2IXJ4/kPSBxOzemFnZYTn0gpnLmFE5iiG6FyZ4cf/u8R+d0i1hKuWZYOYxrYTHAcNKm63UtvtxMGbTNFWYw74EXaDqeXuBXFF4ra8bWW50LHmpkgghoQohLZDFYbCSGUDsZy/KKyq8oT7Ym8Ccx2lFZzqSqOtrEHg3dOWXrFSicxUj6hra89IOIe49POYRjqxNs7CFpnqxAhnLmEE5iiG6GwmZPR4b87xE//dmZnadp2lShn1FiTIgcic4wOhhaozCygtXSwtJxZMNO8pOKuLd6P9Yh5lZRsqrCMDYOU8FZnk27K59ucwTmtCxRcwGZmZpKlVTqaURm3NWiGhKGeDR4gVF0y2M0OeCnBYYPSDiEeosOnfGyYE7TIm6Z6MGBGnKM5aiZrE5oENxhsJmfQ8N+d4l87p/WnUg3NqDhcmb2nMeCx5Xa3L5pnNM5pldhKcw45jxLyjOxab2m5oPuw9uJftjMVdsZtzcAMzT6dUF+oa5rUMFMzTXpjeYzkytjgNhrezZmYbN9eZkTInadp2lbIDYqA9p2nadp2mRMiZm6bpuMW11h83HaZy2nJM5Qm2sTdWJzhDcYbGmT6vhvzvEvndFS4DNuPH246ZfNc25+I9q/0caMLZbhW4VnMYZmJmflCMT/ABEWGwmdjMYldReU1d78sdOKUN2pLMXJjfr4J+R9281XBT3YYPUphGOrBm0zltOU05JnKEUVqc6ZgXQTnTnGcxpuP8fhvztfUW1nJactptMrqZmtPoV+TTnoMT4+J2mYPfU/nwE9haO/BSGh7FEzHbdwStmNGl5cFmmY6m/lKXZiTtq4We3Ae7/lV3HE91mJgzaZy2nKaclpXp98bT7Ty0mK5mub0nOE585zTmtN5mTx9/5/DfneIORrec057QXz6hKqzahm6qfai11GGpDPpxPpoNKxOp07CvkPOS05TRaHmzEG/wClwZtMwZgxgWqxMGYxFPfG2MhU4MMrQtHosaLpTFpXJuFId7bW2mpMNnT08yy/Tsz8hxFpYm7TsG5DTkGciW6cCV1qrvWgbbXPtSp6QWesNzVnOnPM5zTmtOY03mFy3/ieG/O8S+dwrEZtx45mTNxm8zTMxtv1LtZznn1DCfWNDq2x9TBqh9NzxOes5yQW15pvqI5lWTdVOZXOZXBbVbSr1tMARUqh1OnWL4iI20LZrhOfmJeKkfVFpzzE1LV1/UvkayyV2FrdTY/N5jTeZuMZiUzLug/+Z4b87xL50Rdxtb0MTS7UQt34Dj/w4r71HbZb+cCkxaGMpWutrnqWc1rhZYTEQtPJVDe5mMytMB33GKMmw8U/MnvMcP8ASHvRxH/meG/O8S+dP1pxAmJidpngfLpOKLmBZiFfssMcVEWt2NulAX7Sw34jWsYD3TzBicioMHtnvwoHfUWC4z/FfYHinRmVBGWJ3r6D/wCX4b87xL51NRMclm47u3QoydR+HAdyBMTEK/ZNTMF0phFKQXKsN7Gcxnp4qnbDWFmqFJsbcRzBETcXeYMxmbTLOw4r+HQnvKfy6B/5fhvztf38QstIT0ave78eFS5dKyYKZsQRnUUvYY9jMYOFXufeJXthEe0lQ2CwgJBClmPsEmJiU7TLV83H/jMEzYYQRF9z71fsf8uhh6Xv6w/i8N+dr/Lq/SFbCl6mKckCfaWJeqwXMYrZ4W9qrDgcBwHYupL10hA9oEJJg4L3gU7j5IogE2TbLPKsZccW/Ui5mJiYjLG96/2Wfs6N4ar/AMnw353iR/8At4jhtMFTGcibKxA9YOo1Xax2anJ41vA0FuJbblLH3dNVLWE8qvT23NYege77a9KncoMwDE/wv5Wncxje3vweKJiYmIRHlf52/s6BD/5PhvzvEvnYMFbGCgzlVKu6oTnw3MZuPCsZZzlk81PDHAMROY0Yk1cUUtFoWsWagtA2V6PeKBUC5LIJp8Qju0byqYY3tKhzHuXZesCzZCsaWSv9lv7Ok+3pe/8Ad4b87Xsg1nOhtYzcYT1J2SUth7F2sO0J6P8Alwr05M5yVKzFzFOC4w3GsBFZieFJiNtIsg7l2yTwf2lP7HcsyHMRsQSzstjYH+tP5t+XSPTGI1QZMf2eG/O8S+dxPU3avgpFqspXpxmqvTs03U0yy1rOHtxbuvBFChm3MfeDtFbcuYTtQniTkys8FbbFsBnMj3R33EfjV2TrPpq2IeGevP8AH4b87xL53oVrua/G/gO0FuRsRpyZyhFrSHl1aay5n4jt0L3WIvZ33HoVipTzR2yYTGbMRN0IIg/DqQZlvlTr/wAf+P4b87xL53T241e57npAJgrCxrYSTV1p+XK2l33ddVgro7g5PQLMw1goQR04lS7Ix3N1j3P/AI/hvzvEvnegO1fRiLViGwLCSeH/AC66k76u3mdaDJc5b3TpY4gtmKmnJnJaCmZSuLm2xxtb0D7emP6/DfneJfO9B+y8UqjOiKzFugD7XVWmZY+YO69WNlfA9A93/LjuaZJ4KcNa29/QHq+4/p8N+d4l87rUZaw+aLWTMokZyeoN9npRMx34V/k4w3RWMtY+5uAh4p+R9Bvf0T6gh/p8N+d4l87rqECFj5EjWFvQH4dFKbjaw6G79P4p0Divt6Del/r6n+P6PDfneJfO6lQtFWujTvaT6S/jxRcx3megdxxQZLnJ6ffh/wA/QP4+ivqiH+jw353iXzulfc/hd+v0l/Hj/wAulPfin4dQ9z7n8PQP4dJ9uhvf1P8AH8/hvzv/xAArEQACAgAFAwMEAwEBAAAAAAAAAQIRAxASITETIEEiMlEEFDBhQEJScSP/2gAIAQMBAT8ByWVlZR57ZFZaWe1ZVZdbIjbZJ6VlJbISS5NQ90KLfAsPTuS+o8ROe3DX9mSlqd5oQuyUunD9jd9yH2Lkea5HzlFEXbJerLhCVs9io5QkS2WSRGFLceIltEb9LffivStHauyC/szFxNbv8isazjmxbIWxW5yJpLKI3RK6I4LfJ6YcGp1vlNbJGlItFJjWUFXqZJ2776ZGDbMef9UV+BdrziqKvgRy8/AkMoX6FA4JSby07ETEe+cCXIlZi37EL6ebF9LLyfbxXLOnhLyf+SNcDqRFiWYmKoSPuv0fcL/J1of5NeE/BowWT+nhpbT7XkuxF5LfJkd82UJZMookQ5yUWxYMhYekrDRKUVG0P6qXgePN+TVJ9qJS6S/Y3eS7Je1l51muyI0X2cPJlfJDdZ+clE0iStouCHi/A5yZJ+CMbZiy1MorutYSt8kpOTt5IQs5e191FZRVmnsus0hOtjnZCjQucrRfqpFDWUiihI2JPQizUJocezbDWqRObk7eaF2T9r/DwWX2cC3LNBGSrc1rwScrs6V+5iilwf2ybHIvNkVW7JPU77I8DyVYa1SJzc3bzQhdk/aymdOR0J/B9vM+2kdB/IsNcnTQ4qikaV4Ey74y35NT8EXLwisSRTjvQ8WXhDk64IYz+Dqv4Ot6+B4z+DUjWro2Ir9iS8DiYkZPZHTkaWUUPbbLbCVy5Jzc3b7EIXZP2sX1E0qQ8ebOrP5OpL5NTL7Fnyblf6IqiUbFKuR+pC22NRgt3SNN8kVWIcskjzZAjxlPjc6jOszrHWXwOSP/ADkVGMiWApu9R9pI+3mjRJFd7i3F9tFZRexYmhyRaORbFWaa4FKvcUsQUtGzJRclZHDTViWmeWpLEFKKJzjVkIrSbLJsluUUUJFNjawl+xtvd5Kcl5FjzF9R8nUgzRB8DwUdJlNZKHmRjfUX6Y8dyi2dP5Noss8jKKRRRua2bs1NKmiM62s0aXzsTw/TYsKIsOPUNESatqJVeSpDdcl50cCTZiSUdkajY0o09iFJoU/kTsXu3MfCxJbocHHnNJsWA/I9EeDqtljFuPYsvJXkofIqQsp4MZEsLSv0YfrjVmG56SDam7R1ImE9U3IW++T9TGjT8H/clGyeJW0e1Ma7EKNbyMT6jxEtshiSjwyWPqi1JEMOUhQhH3Dx69qJTb5zTKZwxrNZIvKyLsQzFwdL1xMNu6W6MNqU2YuyMLBTjuaGuGTlP2ipKs2Vp3JzvZFdsR5xw2yWNDD9pLElPnKih8DxZNVnWajW5qskrPGSzciM87pEMQW4n4Eng4mxFRk3InqbSZFp8E5aVZCNbvkZPcsUibsXakcZRw3IcsPD/bJ40p5UUJFEva87yUbNo52eRZLKRCPkc6I4lk2JEWX5MXeNrwYfqblEw2pNyHFcik27lwXfGUzURGLgoooobI4cpDeHh/snjyllRRRRRRL2vshh3uyc1xHNDXke6IvukRFwRoRZe1GC9CEtPA56vSsv+DmlyS35NBRzlWej5HLDw/2TxpSzooooorKfteagobzJzc8qIxsbEPnY832PJoSLIiZdF+SNP0iYqXBeTefJWW7On8jxYQ9pLFlIv5NJWdFds/ayKcnsOsP/AKXre4omk070SdbLKtspR2IO+1zojK8oidbnIqIIezydocsrOcqbKjHkeN/klJvnsRyafwT9rOooKo5Q5GJk/SX2UPbcTsorKSIoSytIshuOklQrFiUhzFI/6IUH5NUInU+B/hrvn7Xl/wByWI0Re2pkpaneUUMWaVcClnQol0MRsRVii+WSxX7UJ3lGEmNJcjxq9o5t853+BD7kmyeG1B32Qi5MxJ3sskLjJD7KzvLyWYcNTs0r5JTtji3LYWDp3kzqRh4JY8pFnPbZz2UcGovJRbFhS8n/AJx5Y/qcOPtRL6ub4JTlLksvKXoVeS8tye2xbIZI3yvLkayRCLe5VoWHLmQ3hx4JYzrYcrFvtmjkorPYs4LfgWHiPwfbz8nTguZGvAj+z7qK9sSX1WIxzk+X29GdXR05fBCGlamNt5wVsk7eUcrJZcFnGSTexGCQ8aK8GJi6faKTabeX9clsNFMUJfBHCxPg6E7Pt5eWdFeZGjCXMi8BHVwVxEf1C8If1U/A8fEfkcm/xLFmuGYeNiN8j+oaex9z8o68P8nUwvgvD5RWCacI0w8HSw/k6MPk6abOlH5HhR+RfTp+SWEkyKS5Rqi9memL3Yo4fhj6Tdn/AJI1YHwdTC8I60L9p9wv8n3D8I+6xD7jE+Tqzfk1y/iP0RrznRsSdbZwyim2dNtUdKMfczXhrhEsST2iKFb4hPGb4IrT6mSbbtnth/3J+3JD/k4aSWpknbvJvKCtknbErOnIUaLw4n3HhI6spPcZDDcjVGG0Sdt7kYr3S4JYupkfUTdvKfjJcj/OvxSlaSzWHJ8IX00vJHDjDexTwo+D7h+EOcmLJEU29iox3ZPFcsoK92YuJqeS2jYmUYnOcv4D/CsKFXKReCv2PHr2oePNjbZLaKWXjKHnKOHW8h4le0b1K8sKGpmJieIkvkStk2IhzRPnOX50h/jeSVsxOcrLMODNUYe0tt75R+CEHJkp/wBYjyS0q84Pfsl+Oyyyy/yWWYfN5xwpSP8Azw/2zqSlz2Qi29icqWlZpW6JU9s1w8rLK27X/IW0WRg5cGmGH7tzExXLKGai5PYlJRWmJ4vOFKOrs/r2Lj8a/gqLlwaYRj6iWM3stsrLIc5Ri5OkOSitKyW+2SVuib8dkvHYuO1fx/peGfUe7thzlgec485YfPZ4J9i7n3L8v//EACgRAAICAQMEAgMAAwEAAAAAAAABAhEQEiExAyBBUTAyIkBhE0JxUP/aAAgBAgEBPwHD7ZdsfYnn7SwtnhuhLU7eI8vssnNvZCh77pehKvhX5PvYux8dj4IfUfvE3SIqlh+yz7u/GVznV6FC+Tz3x33+F+iKr46sdIjO0bFHU+ueGfaX/Mvgi31M1Yq1EuokW5cmleMR5b7pevhbogvPwvPCxHjM3e2ZuonS2VPLet0iP4uscEp0JuUthRSzLbchx3R9mpGs1suR+RTNLNJGFmg0mllMuQpPtWHiKw0N3JYaJflKiQpWicrelC2VD9l0Od7IUPLF982T4SxZqQpH5Glt0aEaUV3Javmlhc4kPeYpeyUtKsitrxOVPYiqQic9qI3LkWxZ/vnWjU20fkaSlhuiKr4Pscd67WhMeHsy8L7PE34Eycq4KIuuTXeIunjUavyPyYkUiLvfKWF+T7K7PtshKvgXdwzxiZeIjZHfcboh7GbsvOrbbC+xYkS4FGl2SfgSrsWftshKvhWLLLLGxS2LHuiyzatiW+xskVFsUIrkagvJLQthU/JGC5HGxwVGkXT8kY7iHviRwWQ9ssvt+3AlXxIooorK2eVwT4FwPk/Cty/CJOxC32EtPJFlElSLPJwRYsS5wt3mihbY5E6NRZfzs53LxKxr1isUcvY+pWovSf5STvCjbGmK0Rlsam8P0JVmiqx9s0UV8EY99lM0nkm7LlinRRpXBpRSw9jUSmzUzUzUxsW5sbEYvns4GxW/jspEdi+zUU2ac2NNko+hLNDfo0tji0UJnk/6KmPkorc4xyJmr2ab4xYl5famNV3KOKKGy2aSMTg5HEtIr2TexuyirEiR0une7KJJeTqdOuChb4WxW5xuLZYZpxXssvUJd8s2U2JV21lZm74Iqh8FXuyCbZwURRHpD6Qv6SQoWqJ9EcdI0N7keSXrKEhbYaEqJc93GLN2KNfEmXRySePuzqbcESsQII6ktOyF07H0q4OluUdcRIjtuLd4qyq5GyOJCJPfsoss3Yo/AscYchf01Ya8HB9pEOcwjsJnMiCKOJjZ1OcUWIouuC8I1Y4zwasbsUfiXIveLvgSrFDlXBFDdIjGkf0oSt5e0iMifUIK3ZI6i/HH8Em9i67qKor2bFllNiXyLkk6RvIVZbF7x9nQ2V+JHgXOZbsXSHD3iR1ntQsJ/wCzEt7ykUafZqrgvNfOuStXbepmxQkMjuqP7iM6P8sRPciSo1rgl1V4OXbGdR1EgrQxK+SsX2V8K3+BcidFXmT8CVY4Exy2E6QqFhidEeoNtj24KbHjqO3SHxSNPlmyLLxRXxxH3rN+x0KL5xxiimNFG1FpGpGxqQ5X5KbKZROSiiP1ELgsSbNPzX3aTSUWWWLd2WamaxMs8Y2KNjUf0crP+ZlOir5JPwjcjGmVXzWXimaTSV22WN3t2rDKNht5vNlii3uRj5GseR4WLLRZZZublMo0lL46HsKJWWUKhvNGyxWaOR2I3s3KZWxpNJpKKRX6nL+BrCG88cjfoSG72xy8ecMX7L9ZvD47GNYaw2ojTYhvwhdOiSpCVYWGR/ZSzZqG29iSYkLDymJYbo6caLOWSWIFFCHzh/rWz8ho0rC5Hxl9nnDdCXsjxhDHwQzHkf7sRM0+jSyTS7GN0JeXhOjVZY9yWLLI+/3ZZbo3ZVdjexDfd9kVW+bKNLNI5b1+75G6Lb4Kw83Qle77Hu67PPZ5/csUnJ7Cj2PNXv2rsX/gdQ6fHa8Sy8S47V+7/8QANBAAAQIEBAUDBAICAQUAAAAAAQARAhAhMQMSIIEiMEFRsTJAYRNQcZEjQlJioTNTYHLw/9oACAEBAAY/AsTbxpfvOqpqi5JPdfOsBCAWEyO2p+iyQWnHyyey4i6YUHMf2jcjD38LE28afxyovxyYBLMN9RxDtyvpwaIvxyaJ8Q7Lgo/Ob2b8nD38LE28afzrpzIR2E3FtACGHD00wxDebBZINzpi/CpqoE+IWTYYaUI5rmw97h7+FibeNQi766yHICM8sVk0ziHon0xQ7yYLLD6uuogdtTxUCbDuqyHOy+zblYe/hYm3jURyPhCtUQVdcMStpOj/AGEmQwx0vqCYL/c6azsuKKVlSsSu+gntzcx6ezfry8PfwsTbxza2TQJ+qGa7XndcQYpxUSjPxpcLPDujiHoidVEI24mTnQ5tJ4qLhDq6onxL9k0NBN4bzJ783KPZZjzMPfwsTbxrB0ssonAfhfCeGdF/jEo31N0KhhhsdDTzx3UcJ209oVw1KqgiYywTYYVdHwnHVVUMEPMznk2VpXXqXqV1eT9Ew03V1fTh7+FibeNeXvpfsnnD8Sou0SYzhEVQU8NRpzmwRgi2THT9TEkEZUVf1P4TCpR1VX4QR5bLKOkrSqQqxSpCqASurq+rKObAyxNvHIfvoiOgjQ0ScVEoB8KieGh7aBD1ik/9hozx2CYWnDHLLh/uRZPiJoaBBHRVHLKIKKLtybKyqQnJqVZUAlfnML86DfwsTbxyG7ciIfGr+P8ASy9hOtIkU5sEZOs8Nivys0Vl9OH06IoYlkEnjoERhqsoVFOkhP8AOmyqQqxJoQqBXVbey+efBv4WJt45kPKhZEGkSrPLH+18xaPpxWKb+oX08O2h4r9kDFcoruV8IzhRXFrEI6BWXFEF3XDDK+nL16+xc39hBv4WJt45P4nDoCKqqJhMlZcSoTw1EoQvpmwsmM3RghPEqyC7xLMVnxCgYFXSEct9BLS4okW6I5Qr8nOfY5ovYwb+FibeOS0VHTAvr/IVtEZ+J9ws2H+lmN5NFJgsg9RWZfUhkYR6k8Vk0Cqooe2l4/0oWsjRWXEV3TQwyusSPlMsgNvYZovZQb+FiH8eOUI/3KLoqF9EEWnEOgZVkB4gmMsh2VfUiTLIbFNCN1xXWSGk27oyDKgcp4ihWqpDVUV9MOHqqVlhDq0vk+wzRezg38LE28L45JhPVMohLuuy4aoOLHT+dBxCiVlxL95Zor9Ec20mCqiILri9WgFOniKaEKiugjMlVkJ1KsqSeeY2HsM0XtIN/CxNvCY8oRyOiKGLiX+JVKieGFSTKDCE/wCSyzQ1hQVV8yzrPCguIruuEJzdVQmEZgTMRKoOQyyDfn5ovawb+FibeJN15Jg7r8aYoW6I0VHXHhuuA/tQAVZWVlmiCzEKyeJMLL4TpoAnN1WTMqTpdEHSEZVsq1XCJfnU085v05+aL20G/hYm3ibgVVlaXqC9YXrXrTuhid0Cy9K9C9CbKzojKvSF6UAyysqhlwMUO5l8JoVWVVRM0rK0qhUVlZVCsrKyoFxKi9V1dXV0zq6urycysqiitRW5uaL28G/hRgw1p4XpCsqLMFdX1HD/AEooe2gIRdxMIyfsmMLhZqrKJU0VuqzcpxoEuIqgQR0vounJorq6ZZRedgvSvSrSuqRK9ZWVk8Qr7iDfwsTbxpcW1uhELRJtEB0GTLhmxonuqzp0TRJuirLKdLCkwin5DBZRaf1Dsn5Lq6vLirEqhWldUPtICVibeNXxrMG4Qi76PwVQKyd6rhCDLLDYSIEq2RK4wuApptFOiqqaym0CGbBMLz+EwsOTWdF/tyaiVCqc35WHv4WJt41ZIgGXRWCsF6QvSF6AgcizCGl1YqmZeohGF3TQGFUiCjc1K9Krcp18TYWQEsy4g64CqfuTXCzLhDSzC0xFoJZWm72XrC9a9afNVXKuUwdZBddV1VyrlXXqXqVCE5InQJhfn1EqHkUlh7+FibeNeWLZMdNEYYlxxL+OFXTE3RkW6qsVZMLKsIXoTMVcqkYTZgmAorJoaKtQvlUt8KxTwhekLKWVSEE7L0hWCZNKysjFWq9SpEE5VRPPEn5HzP4WWBV9nUSoVQJ4lSeHv4WJt45GU36JpWX8kS/jhTqHFFophFcVlRZ4llCeXyqxBPWi9KoKldVSgXFECVVOyoqEK7p+sswvIw6DNkIJObSuqgFWZNDFZW10m5sssNvcMq6MPfwsTbxyKBfyFokwhcqlFUziwj+QmMgyGJGssFAsP/lZQWXUqkKcy4ogFWJ3XpssxAhhXCqmbTuqqjFZYoWXZUiThWTIzzIyYWmyyC8rriC4Cqyc2TCeaOyYW9vxKmmqgI+fCxNvGp4qL/IpoAydP/bSIlnhtFKjOoYroCGFpcUYXUphAqUCqZAWXdV1PoeEpohVNKGIK6LhWZUiVEZZRozm6fSxqnH6VZ5o79vbvEmh5GHv4WID8eJ2XHEv44WVSqzdP1nQKp2CaOH8OsoIhC4o3KIhhsg7OUZ5RvLsEwqUcXE2Cc620ZSimiXEE0JdMjN0IQmyrsuGIKyc2CYW1UunTG6Zd4vb9zysPfwsRvjwnjoF/H6k1tbJwnhH5XEQEwcqkIzIOaLP3k56r8LL2lm7y/yIlmi/XJbS/WX040R0REYRMJefwEe+hgsrLsuGIFWk8VEwDCdFlHq7qvtaqnLw9/CjA+PCrKvIsqFfVsOqyYSrLIbp47BCEelRFRL4VayZAxX7Ik3i5wmHun6FRLjG6eCqJ/sdOY3OihVYQSrsqVVqpzQLLAnT+z4k0PNw9/CxNvGml1xaWCzYn6XDQdl9SDcT+E0FuqCouKsSyCk3N05Tc/L16Jz0VbFB7FREWlRZYrpxUTzRWGh4kwpofEWVmVC8hzKaXiXDz4N/CxNvGpoqp4Z0VKxKs88FkwWQeo3WU9VmxP6oxBZuvSbm6dAdUdHzoryA3WTdQohEnFXTmfYr4WSGdKlV0OdIBC4Tya6XiXD7GDfwsTbxoeKgTQiVFVZovSsuHbV9YdVmjLBNB+1m6m6M3N06c2Cc84ydGE9ZZe6iiXHYoxQ9dDXK4LrjXxp+U55FQuEvoqqaOIrh9nBv4WJt4m8d+2nNiX7L47LsdP1I/SF/ks8NQgF9PpZGCTm88o3RQPPaWb9oHqooSsqGGbLND6ZZ4k8VFwUTR1T4Zeb9FlhldUn/ALHV3XFExXDbRxFcPtYN/CxNvEnPqTmbBUrGnM2NQuD9SeNfTgpCJfCixobMjGTRQlEm/SebtIKvOebHqjEb9FBGF9ZEpj6Vm/omg6Ks6JoxXus8VkwtqzRbJ9PfRUbp8zpoae3g38LE28LPFsnm5oFlw/3qdCDLusuEX76IMHvdDJ6Vh5k/eeWQCHMrJpfMsw6KFZIv7Jl3K+n0Tix0UTxXV6KlCq6Hiv2VZ1KoNPdUlVU9tBv4UY/HhN0E82JZMKDkZj6zZO64qHuvhObBRYn6Tx1B6KCOH0oRjpLNrZNy/mWXr1TGxQw0z26IRQj8p/7GTH0pxabQ3VZtFUJ4KqipWKVSqDTxFlQa6qntIN/Cxovx4lZPEePsr6appfUjsE86JxwxRJ4vSLfKCEJsyLVhTLL29pnO0uJQnoyi/KMUdkZ5TYrNEeFZYLas0RZMTl/CoN9XEVwj30G/hYv/AN0k0N+/J+Fkg9I0AL8UTGo7IZCx7KqMBsUcSHpM6W0OOmmt5/C+FSWHB3CfomhsE/UTeO/ZZIvToqU5X8Y3VTJjUJ4P1KtF3VOdX2UG/hYr2p4WSDkgMsmHHxG+kxm0KPYWlCiIqhA4Z2X0z6SvqQek8ylteSHecKyjooW3l8JlSsUqlZcRymhC44mXAN1XS8RTZWPf7HBv4UY6U8LMNd5fUN+iedQmzN+Vlg/sqiUKiWbsoDGHcLLCXbos0NkOYyaFcRVE/wDY6M2yJ/sVHCmWbEiYJsMWnZcUT/hZbKuitF3VKaOH7DBv4WJt4WWKycW1XTn0hfGkQBZRaGiuqgIO4RyxJroU9JQiChjIeCJfUwC47cy6pLPFbRdQ/CJZZYTdZov1Ky4olww/tVM8pv0VlxFcI5Fb/YIN/CxNvEq2TwKuhgvpw76o8U7aSZRwP0VYQvoxuHsjljWYAH8J4a8iqoGhErr4VBQaM8XphVLSoN1ECXq64Yf2qlfI0cVFSpTWPLYpx72qgAWJt4nRNGFwFVEn/sdcGGNB/CaQRCdfUHqHqTwlZ8In5CH1cJ/lk8I/5VcRl/1oV8L0OVYAdpNJlkh3nQKyGGDU3ZGMj9poOEKpQi0fCqXXCG0fPMpf3FZUnh7+FibeNXdZ44WZOI1aby/COiOLoArhXV0IoXqEaL0hinDMVwlZhfqJfyftfx1nVVhnRnKrF+l1K4YBID+xValRfiYKB7LiK4QmPTW45lfZ1Mqa8PfwsTbxK2hmWSCGgnUAquGuypGESGdOrFWMo/xoB7TynomZWK4YMpVV6guOIE91SIlekqkAVGCeI16afqYsIUUUMNU6iOaqoy4ooRujlGZkYe/Lccxk8NQqq8rcmplQcvD38LE28av9jrAQhV16irq6jKsFYKwUQYKwXRPdcNOyuVcr/ZNNiqLNFsnOj6mNYdEwt2QhXEWXclcNFdRDunX5mOEOJW08TsuEltdlbRdONVSryoPYYe/hYm3jTnKfW6OmPQMxomAnl/SzDeVFW+jNFZV0cIf5TOwWY1ZUpIaQe3LY8y6uvlUCoPbYe/hRkfHhWVp5RYch9UWkHuNAxP2E49Jm0X7k59K+JUCzYxAHZZYaLJhN+Qqpu84dMUPIsrTYxMmJV1eVlZW99h7+FiN8eFeVk2UZiqwq0vUqRr1BXEoQFZWVk7SiYddL9tFbFZYvSdHF6VSHh6LiorOmgFVV1/sZNEEfp1CrCrJp3QOYWQ4kaq8miFCqQr0q2i6uq/ZMPfwsTbxPMeSKq9FdXVAFVWCPCLr0hekL0L0KKHKvSmEC9K9KbLWFZTD+F6Kp4mTCB02Si+qfSmghACssxhD9EZE9SrqtUGLIuVdXkJCLvof7Zh7+FibeJ5RYcnExD0GvfSCbItbQ8USz4cNJNYS7xJnoqLNFobtyh8fcMPfwsTbxL5PK/wDY699NlDHFEF3XCAFeTRehNDQBZo6HyssNBPObBcIb4mYtD6YgSxaUQ0v9rw9/CxNvCzGw0tqhGvdWXEWCu64YZMTbQ8Vl2hXDWMJ3WaG/UTyw2lW6ZCHQdZHx9ww9/CxNvC+mLcp+yh01lSGV9Dd5vFfoE+J+kwoJUsqSyw6P5LBE6N9YR+34e/hYkX48ct2uoVxRBd1SEcunVZo1w/vRlMsovpEMqTh0uJBHS0QqOv2rD38KMfjxrsqllUqkKEENGUJfQ03Or4TipGsf9zqn0kzpIDWEft+Hv4WJt4lZVVYlQKgCvpI03kH0UWbGOyyw0hRg1Obp+UIbLKdYR+34e/hRuK08Kg5JM/jk5o+EIw4Qr3VdeaK/RPLKeSFXRXQdTczPAfz73D38LE28coCbG6rp3VaBcPFEqnSDPNFr/Oo6amRRi+4Ye/hYm3jkgJh00NGqFepViXdPR1fWRLNFbVRP01VR1shCPuGHv4WJt45L9uQ8ZTQ0C35Lx2XxrihP99TRh1wFV1PEn+4Ye/hYm3jknU8dE0HLeKyhy25LddQZcQdXZUMqlUuh4RB+4Ye/hYm3jkgaHNAuAV7qug63NkwsiNfyZvyfUVeTqvJb7Ph7+FibeOZSp1kaq2TQ2m3/AINh7+FibeOQTLueSdNbLLBbQ+n5Olpk8kfcMPfwsTbxyHiqTyzpyw20ke2H3DD38LE28ciHlnnHkjkj7hh7+F//xAApEAACAQMDBAMBAQEBAQEAAAAAAREhMUEQUWEgcYHwMJGhQLHB0fHh/9oACAEBAAE/IfW4dDQxZaXDVYB5VdVaPh5kx9f962LMilhuvNKlpkYxIxsjJlla3e+tlwO4kbpQQGk7DWsEeaIOTkbIc19IMfxyzWRMP+KkCoPkaX1+tyPW4dKrrLdCbViblGMXRaB9aud+1GciuK+ndC0fEYOa3nWImzoyfTwNrGlbLH3zsu1sxUygcidHF0fwkiy42CnpKkD2l/IqjwZurH/Eql+Phj1uR63Dpgi7UEwumHlEP+JGl1bpjv1rKDRoTtDuidca2iDCNBlivfPQlaHBWO7VYQZLgwWutc2LJNrqKKRiikbFIRuVk5PBZ+WURIP+K8WRJRW+H1uR63DpVGVQYdcKPuNXYeASH64jydh6razLcDJw6KNEdrO45zZElStVcyznKoHcU0GfS4ZtLEY6Z3Y2MbdIx2G/pxcUnuJc06QbkmfkSlwNAl3V/wATIEJg3yNL+H1uR63Dq54qr4LSvI5tWkUDXsyG2fZg74L/AC7dEyPao8jnoW9OzTk3h60yKx5ofA1DJmPLJVjJIqu6DpFX8Bkz1smewm7H+bLFBcisBCRlssFO7FdV3CVKg2JQp1WGcBpECcQjpfUSptB73/FCZdYf8V63I9bh1QGxNrqnTYOysiCzdVx6JDIHX6buWzqfqJCPyS0p2Id+hqpkMT9M2EYFf0a1zoipSfc9EtJUbfCHFkt9E+MZIhfQ8pIiwpEXHxUVwR5GyeEgh8AhtsbLK2P/AKOavjL4OZKW1pELBOiISFIxX+WCCGSJDlBotNQyGQyOv1uR63Dr5aqPpchMiU6aKgrR12CUurbbV/V4Fl/4MalzoNdGCIUatBo3Ax9FTWGlxjQjw2oYzyGocay1dkKFsMsl5GPqpHKIu5BT25HMtqo74uWJQJTq8EJoSUsnr39Eh4CTfRBITCZgYyGchEnygsiEVxGYRzD+VhHxjM86I3HMTiXA2kHsgewNGBuMY9VHrcOt5lg1D6JmCV1MiZQJzUlShYf+TIQw9FQoFIL7/wCI8losoVsJbbqS1vfsPSLapw7smoyfT5Dm8YJlixHsOq0jIRSveA4TRbESVBqNw6NZySa6T0upKw1avwW+hiXJPvgXavUhasBOwZAbISKy0xOJsxAihPDA2huyJcjkOQ5iZEEVHGt3JZLJZLJbnILcFuiTkTZE26GbIr/jPW4dbQ0xapbVdHfmqUuDs5yLTZdQspWeUO+wodz7GJkxC+6jgrsXt7CUEUDvMUpyrio/PyNQygD2R63F9sWxAqMg/aGUhRbn3y3Dq6kQCbUvbRcdt73F+/ooTShQCRNJHUr4YvAivqJEy4E9RtOQ2xWvKWamNVsMZGshuyTJfxOiR5RGTPl9bketw+CuyqXRQvL1WVE5QLVKBSNVlCl7pqXKbAtE2nKcMpkMD3GuRGDuQMl2FYgalPIqF/5wk7zQSbCkh0YQNVIIIFUukMlQ3GsJEqnBTddybPp+gT7tHWE7x7jbapQjS6uCnWX1gYsjPBqtBneF6aY0jPBpDUVZdVME/OjaEeV/BrfN6XIcvZYSsrRwGmuiLZI7Y6s8KRQ3QqroLQZJN6dQaskPCqJ7kMXVaszoJpaUaI//AAssfkLDEuyhGQd5AguYBuwlLYo5Ru4qlAv7wP0EEH7BftFU/QdQqLbRZRDS+jYEQ0YbKFZQ88djoz0di7MO25Y5vRKXCGSVuD+dKWJkWw2b5/S5HrcOiW5B3RDWZPvo7+dX7ui83ko55JQotCP9FoSS2qP3YgFsPYcl5ytNprsadmbbo2cSipnVDk+RAyPexCPRDuNv/o4ouB2BeRmS0kCVfcggc+E7iPTkxy76QIC1EYGCoqGlXC4xB99BO4ZPRY6pdbVu41rekEfIqmUmEO/gPe5HrcOuWieajVOlEjWoLiBsrodV4fQ0LW4tO6QyQ4taWjtFip3pQLt0z787CRRDqETMj90bDIGLCBP5QqZUWrbvwxsCVRb53bFqeTYqiTaHksJuNSIHBA1+yoSAWyRKyIpy01XFo70JiUstrgurFfZoh1fVkdkSYTsCWlN2LEnAjd0SNFmPg+hiG/wnvciiO76fCmU9dUCzV7kAaoc0K7QbXKNFc7TwUKPULytOhydkm0uEiRA8iaqid2wvZNcKrTJ5Jg3qlsGwSvBcgqi1BGOSBKJkYnmRMUXcuADYkMbEL+wxSHkiy0ggDNX0Q2LZjuRST4FthstnFESZGzybGl9MiYnPwH0hQ3+I97kcLu+hDVXW+FDdkXPbBXu1onR0cm+m/FiarJeOigJwKG2Y6bf0L7DRIWslgOBhUSsMoJ2iTtDdAxoZCARI0bsTdUIZS1X4JVyQJ3ZEQIirdxPDgUpSGLYLmxJz7iBBB9SoWYosiAEWLag76UoxNdibTPuPYLsNndl48Dq9Fs5YY5/CYfSjE4W43g/j97ketwERiY5ofwNDlCQ+aPuNCc0EgbPVmnKcCzUiWTEb5LCae4Q2V0WCRsjys0YlMisQqy+JS6COVuEiQ7YgWivPcQIVWRLel5siciy/RiLIRGaKqgw0G9oyZssFWBKJwQQL9ogQQbm3YneBurouSWZCFtmtDF2SONZRI6WWjVpkWjH8RSHqjAnCGfyHvcj1uGlwssNQ/gqHs7iVnViOe6JE9jgZuwC6JXH1oVF3iFIcHAcV0cCYvLxPJj8sN7FxtB/4Y4ghSGvvTG1nV8Fi/OhDdDWSiiFJxdIaOwu0jDsU6JCM8gemhDcCY32GC4prIXmsJuLO2lwUWUNeYsSyGGKzRKWW2+dUPuAyR/Cg8vo+gKG/ynvchzpekOAU9mWV1+SvDcTgs0fYt/2kVziupFcKnK4GYErYTnPBHYwWENlHEVLEkA9Ho0Ng6I1JlJQinOfcmTF4GSkTcGhm21QQR5K4kIwNbglqp0RrqVc6gwQqrBM3RSNlotkCxUkv+lzCWuK49SNRSXNwmPAHUoIKCg9gJ2D2rDYaMnsEiwwSWguQJNCiOUcJxE9iRIjRJY0IHolJnLhDf5j3uQiw/wDwEFg2E+idOVsjdDfmNmRynIT3JEsk53r3E2V6uiT8lAYnrAeSR/MCQyGK7SuJCG2IhIcMhZUK5ceSiVixuy5MdMmVhUsNDEiqs9Fq8ISKwJaizNimEJKkIeVcsn56agFirKgpHbi14EzUklcVyOAn2g2s0C4juKzuRM6m8kQyU90JriUw26JrFvQK3FiTSo0iVwmPC4icMkR/L73I9bh0TDuDratLocKzceSS2a0IeBazK9h9pO4luITJAd7sVgksVClzLK0tx8BpBmd6qoAyD3HEqsRqreENpWXgoIhO8FYpknaIbbu+jBJPqZkmQh67yKGI13oK/vhfC/dVsuh7W65YmLiqPqsJGQ04TYmaAW6M4+AxlGjsGxEcDRgmR8yU2MqK/wCM9bh0wUdmMrys+tt8/Qm2AgoU2IoauU2ZpL1BciVsjgN3C2KJYU1LrZCu33Y60YG23LItbQgl4SFQ+dFVW+CilXciYk6ELTpf+DklOVhlmTCwoboZZoMITNE5rZKu8UJLjRORBJEYYRJZHu7Jl1jLLLvWuOy54UPhQkiR6RpDvv8AA55b1kJGRLyIZMqorZJwwYiN2MwA1YJoj4HvCIXLqHpeqh8XpDsOxHYjsR2r6G1q/FiktcKHoR70e1EdNMPXJWDwMlxjz/gV1ocojXV3Lki3KVB4ZKqBSo57mMEQc+BVcrYXPtpU+wEJnNR0YzRztYZQpBVkD2KLS8idxd0AxKPwiEQJm3I7cibyVLkWUjK0h7ERQdloQ2pkcZvtfZc1CmMHtB3gUiqWoMOWTEU2TZWZK45sxvEE/wDgHP8Ao9COIMaGPI3qphSOOw0YZCGFxebHtL+JMJGTLC96lgzwDtIXsjBDdYI1ZU6Ig33GuepyPW4df3mbDW9I0okRTCxJh0rBSE9y1wXAzMUNE+My6VkXU5YfCZ7JHGrcInEqBzfgYk1tgTmJvAhJK02m0meSkog6q6Qq7TctGXIN1bQQUMG0mdz6jSO6u4snZkK+kXKfgpaSQ1WLa+skhKOxGY23SHO4bcvsswCsu8lV0Ib2wkxg9EMvYHObrSbYn6WGEttkty4HuZTtcsqCFRB2ZIkR8aZCeTJFgmeMskSYkKX4jbUIY76etyPW4fArG7hkhVEzsi3PAtlfZCWEt7sSVRwthkxQr3ErpP8AkiWssrVG8TF2oWTPYqDRD1SZFw+hzGrl9EUCFpNArU+xYxBkNEslSKLLIJSHFXYbroooeO5DomSMRYI4TS4MqU0KTaXKWlsiYsoSVaJLvZEw51gkyQVhaTbAfQcJEAkzJi3RDQtGBvjt1Pag0SL9x102auRKsf8AQ3PQmFvI4BiPlTInrMIUQqy3SzMdgwArXsuPW4daQ2rMWI0/o7QncpVDgf1HrmMNm8Wkfcj1msWEjwAnHa4iIlREruEbCg9QNYW41tp2I/8AWJdskwSpTtbh/FmWhdDT/hd3RJ9wkTbknAVgtDqphfNCEm3ITGtkmmUx3jCz3NVP0aySYJkSeCXYDGOShnCuOpZB/wB+h1fhY5ojSfBuKVlaoVhs3H4iYH8EJBaDh8b3hIRS1dh7pQhr0QyKXLCMov8A0PU4dNgQgoLyRdJiiXguBz3KTU/o004fQxFhio72VaIW44V+VjAzFxsKJJ2FBJCmNBLBzjT1GWx1xFGyK5bEmyJaRkdPElvllVIWESJt2JJyRs0PMbtVq6EkpmQ6SUvCWrDVdKgaYOxepJFEA1SzGJ+R7B9hiRiDEC0w6PRL7qw5zdFiwYDimqXIURjRJtwjwQDgXxvDElSP4EpsUJIQj/UYX63cU+mGX2DwGrsJNljCqVN7ISwjkO6jGVhSJBUBMhBU3Qx9MtC6K/cFNWoQJSuuRtyziJP/ACIIRYUiYTV0Q21rcq3BAyZGRZJe+4xQTWuyakUKVhyL4oFrF6okRVJt3WihGrEvYdhmzZRQOruJBOjuhpaSwjlqG7l/aPUSXBV0RVGcVJpRvLRGRhq7jTjI+A2kdLmg6KvcRQOoisnAkVEf4Eib+Uw+vjUQqA1uNn8HsciJHpCamrKmNLWdjL0hshs7vS8WQopnEqqSFxo1lfgTI8oTwmvFEXUGXQzsihWxUt0GsXUSZ2EiLgUM8uwqmN2Onr8Ql8vwIdcigbFhWKiTUQFQ2QMQ0D5XgVqwTaaGqEG/2hQPqAdwdHlpoQlhGhWmkSgiGSFSS1SVmJDGUZt5GbWXGoi9uSmIHpWWxE8A1x5yNTtoDs+XyyMxLqa0QkpeXsNdKENfxehyHq6Ty8B3UyRI6fchqqrRYXnRcTXA6JmR1UkFPOFAlsCHsck6bRb7ChK1K+WepSCT1VsknJKIouxou7YQ3huFsh5fIWrWAbHV4XYSgjS0wpCC4J0i2TF9Wm+4LMXaxUW3Z1QxbQhvuDoKBzp2Q3ogewk29tBMITDet3Ai7RD2t6S1YjDIyJI3AMJm3Jdx7BvAOxUspW45P2K6XPyTMbSwhvoc0Qml/AtKCEOy+T0OR63DoZYTIpDUSpcDJZSMxTTwmEJu1wEmQsBPo0uOrF1yJuMCb75KyYHWdSyGRZK8ElsZIIq+KJpZR1ZOqWQiUtIiWmQGKBgZNM76I47DVmSo4oPO1lRcsaICCFnMS8llQdChZnWyQk09x9yCHQkTUh3BqhJYWxZsBaCSWko0mtmUU68DwYuCZWzt8c3YSkBvVpRC2WBDCwMav5vW5HrcNIZCyyUrIluT2BEGpJWwmMU4ITHcH5sPMdiUq2UeZ5bCAi5jrVbE/UdHklWRdAu14E5HuFVxzJBFWxQ5udzmp17EndHHExXF9hVqiExz5IU7WFhETQRMovWOQ1dFDran3E4ckmO+tWFMrPyLJiqSrLK6EpNtVHcJxS0sttx/sg1lixC2JnZCRgljnqWdMlK5KAVrELF8MuC60zO5bDn21aUQpJYF0L5GtX/B73IX0bCUrIbejEm5dx6IaWd9IfUxTaXuhOWlvIFRuGXMqg3L0QoqndDemWlFsMveAhqhOgklVuRf+Sp4xpC4tZbDGk5khLkiVrA9Y5AVTOBtsbq2JJIWEA0VaKmtG3cXFNdkfTLuNNieCdwQ331HMVWLYQwSi3L0VoSIN6mBzTRtZ3fYoFti1lhsUgQ4TDtuFwm3pArCqym7aZKhsx8DlYDLlomYkujhSgb0Y0QpmIXQvka1ZP8AD73I9bhr49gxrbbWpCUiczgaUnBN10+9YnQ1UY0vWM1RuiGRRathqTS/gznB6nSGsr1L6El7eyHsbdSakFXLiKfwVbhCbQlDHXAtRCmKQtQKaxR4G47y4eEkwJwUi3sEMrrIScVdh0MpExExqb0bOifokVvgYPJkckMRbSNsjTTh6Np0QQfqV1kZQ6C3s+DJG6NQ5GZcEYvuQ50f0RVvELYWBjV/ye9yPW4CLh2stuhBBQcFHe2JMSyXuSx6UPcGrLTyuWEVFmyqtH1lLRsDq90M6lqOBlEWDXy6iclUE4bqNiRLWDGzyJTJlyQTkkbS0viG0EaQ0s/2FpWLwUPwSIU309iT1MoDroEMbRXuTIb7a6HrV7pLgtw1lp1ey0MhOwBVDJbhhsl79CsngNkawJ1bLk8oa6Ki4JEnRjooA5EvEsCBfH/N63I9bgJKMa2rMRu2W/rOTGzV6XKpwPDdjcRfm5XHV10iUsjkCmFBArq37ikr2rD5eAy7hDwSYv3LoKWjCE6Ti1pbRIaYh9BiYbKAhIFjFRKzGjg0WbDq1rtjLeUMTsC2h2i7xqhtE+0ha4TCHBMnm0+iEIXcbR38A1+TwxxCR0KfGEw0WBH/ABSH/smXR6JN2Ks6Lki7WPUoXA3u5XuGrDh/L6XIXPcvoMcfg0SbsWr4LLGYDZISbEye401cY1Dysq52lLYyKRWbiFXvuR30WSJeYPkRMl40C/5llBviw0uWLKFbMw7mCNi+DTkXQmIOWiS41QG9hqVNkRVfljUNwj4gxrm0DLtLaGQlFERCR/4DZGbva6JEkvZ6UJbcv13kgbWlH/yFtSQ2yiLIT+y2JMuWYn2R/wBWy6PWyIjUqQeVPdmbGz6ExKw8qiP4/S5CewsJTMkoKiaD/AZXUNcCG2vBraPYotHD/wB4aG8avqqbE3g5GDEDJG4+pIpRIh/+A5q2dh4hLBmXZCMxMTKQkq33IOdKCnegoSoSJl0dsVyDuQzGBLetWxLVeBCiwDNy7jcjSo5PvTWCjJT8JYtWAbPoSbsi3CXOv0KqHGGqXZ9FkQquvshbCkXdjfwMRu0Y1fxelyPxL/BCki4HMPeW9J1Cngnwn9jsZ7D8kUMaheTFQpfr0PSZY6WrJIC/YRcIriNpgfUCrFXl2lzm4yhoyGHo9x5YWhVsQqqhVXQkNiwqQ3LLlZcrbolkUbClW4vvoSrR1LZMVK0PFx320c8I8Cgarj8GbidnpZEU2ELqyuR0qUHcub0angGJZJ/RM4gZrS5PPHqULguj+RE6iwiqrEfwelyIHRk8BaNELL3G51siGgthtDtXh9xWVlLwQebguYnsRGuAdJKltaJ0NxZ6U8lXTNxNgWYa/bR0Tlk4Sui2LhfU2le8Wk6UU1HuJ2q3EbTcOtdItiRn2giLvWzEl6uox2qm447vCZOWU2EKRkOz2J+I5KMxdjnG4ey09FgQ0UOMIbpOANuroNt/OjG7EXb+D1uRMGir6FXE79CnhmQQ7kZOwTLgh4lGvZ1YmVmLJXuTf8RAQD0sTezJdBaLPeGnvD4d7BalS5kYUXS4ktD3LYoRxozVJBepPZFSRD6DgTEkRskX7KyKrkKbDM4OCRMyYircB12W4J5TeSORQyHB4Rpcb3jG7JDddloo3ZuBsFwUlwxUfPVNYipUDzyBFLguD0cqOq2GiT9P4EWQkP5/W5HrcBKQGZgSkmLaZwmLlAVFCo2M4FEuhJZvkdStOIWRiu+HiwQOuXkiVVGw1m0g+Owsh5pIJZ8kI04agQuaNTsJicFo5aKwE3B4II0SJ1FpOwstx5byJtiYhJ/QUo57tyNkSThDs5QZBv8AQ1vTYiWmayU/9kcq36GDfcAqRuhVnjKB5y7Mbb6UydCdluHtX5kZ/wAB73I9bho9Ir2iqVdhhCR0LWQSrKu3fQlJZCubElHcPI3r+CekqTJeQnJSNG678EkCH8GUi4dUznEZ1RShr+jqia0VGXCCYpVQklZRwJOwENmq0Kjhygy+F2JeNiEydKDJJO4gxm32GeENE1Tlh1K/AYnO4vIe7jWwIddknInJoCm8NoyPOvxULiKFxfKks+0b5Em7DIlXDJeK/wCM9TgWuNyMaWhiUqOR1XhZfwSlkNl04Q0uehU8iNCV2Mu6n0XXPWccdDj5jOBdCwbQJ2EJCoqwN1FeIxNDjgOeEPyS0saJRKTe43DmdB5toIZ3psh8VFxEV2LXArtydM0fZCmqO7KevlCvqErsTmtcKHKMZt01UmFi6GOiQio1DWYsycCKFC/skThjvKy/PxvahGw2DUfCkOZKN3pp+FvAmyM9jsA7BlBz9lxT6LOlOLF4o5ES4D9CGJPhm7Ow2V01okKQ3LI5tUDWMWJbHEzgHGyOSSu39xwSBbejwi9CsLXPkiDdSYyNwqE0ah0hSCpjaZsnhcYS0eblMbZVG5exMlT8Dg7nJFqRNJqfogL5TbsJDo+EkYjxB3qWE/Reh/gjBDZDHmgvkQj8MNNqtDENPsc73YqMqWzv0saUKvul8acCVY+4/pQJmLdQnmGj6iZ2Q3gW0RmuR2Y2TLDdno9bkRUPSENiAnYTsJ2CEzRkhqFmm5wFkb+xf6AVZXga2fiTf6UVlzI0NXyMh5fpPIcvvUO+vdWBaFNuhJ5HHBWaq2RON95HgJeRJ2fJNLYrBLUWh3o3Y5f11P8AyCFGQ9mw2bluRk3J7iZuxSZYk2WCRbmbqUhaKQNIcMrMQGs8mM0lBp1kc/BGPaRUYvjqM7lKKTA2Ww3hTyRWDckTqnWQ1gWZwID3I7YGrGSG7z8Hrcj1uHSlLHb/APxQ66pSN4WnKhHfcis32JP/AKCK8/8AwMUVEf8AxT/4Z/8ADMa+VQa0/wADsPAmfQSraTrDKFK0yrf9hbZjlkrtBOpVOhYyfOSN3wR4+zcYzJoh7QkWPfYLZVsgjCnRSR1QLFWFvQ4Km2ZVF0D1bGM6LpUTF2kSe6xghtoOAnaSfMpMzXJo49jzPM8yeZO1nDoI7DsRI5i2PGx3jYckPYTcCZgWUSrJkDEQ0WBuwxkbsk/J63I9bh0oZZVuRzW6LI1mfaTJWsuiie5/h1SbGvUo4HodA23fSBVDu3IimhqinKwyTSxRgxjQxUnnRUWl/Rq2iaslsRYcEsB9RUFqEhX2CzMUaN/HJqkGVWO49XoEhjk9D1iqsUDro4CZ1cAm4EzAnCzNEd1JQw6CoL0XtBvG7I25Je/8Xrci3M/+A0hqDXgQklpJGqop6KrNjS9VVl0bGLujlQlLVG7GhBKGyHq0OUN2GtApuM1rDCQV1Soppka1KJZDVEiHOZ50LJEPwsYhZCuDIrKsuhXKFca0KxKju1Sui6yiGS2OLTJgT8CCBGbBQ3JBcxiHBHYw2UbYQZNmRtycxL3JZOX8/rchPNT/AMBLCJzdUZE0QN5CXIh8tD+XBDagbJSx9gipRUR0PcD3ZyiK3dJbja5NkSIEHtnAcQplQWYXwT2E7B9o6jkCZ4fS5GX4YnYEdkWlRkRJPjgTVQLewjDNVGkb6lD6L5SQTMZaLFCyLZiE1IKzLC0ORC4BbeAwICeZhFA/yaA5IIrIRwpsJDJvyNmhXNUl/Lca/l9bketw1Wk7aHNb6GyomcxzHOxbyhDlDQsLdCuJENh4GVUGSz9RWElGvNxiNoHPWqkk2RNfa13fW2wkIXOhRQolcS2YmKHsHdUpEEoc1pWgbBuzSqcSFE2EXlDLJ0nIlKt5EU5NQucll2oS3KntOipL4TrX5lUf8nrcj1uGjEpCKdCWWsExK00ETNCglvSpjqyH1YrIQ0KSJUKlmTLkoXJA0+EI0o2/0ddlNbZHcZRgb0RKKR+SFE3bYHe+ojFq3I57ZggUVktqNJFoaHt3JKd0cCBVbh6VTd0bd/hTgayvmuP+P1uR63AVRDNy9ZCTIK7JTBIuUaz0DEnAhWWhDrDX0SbIXaWXQEEEqp330WXFhjuFkZCD6qdgiw5uhRhCW1R3KOhcEy1D0JO4sNLnWlvYhuXqo3qXVEQ1B+26f2+FPcaj5rr+P1uR6nAkVE4NkFCmw4QDb6IFDwvZapAiFJIWm2FBGEw7VG8xFCZtyahtkz0dhsGHORvVCs/9EVCgJtGjbGKqRWEhZDuA9JUU8pE1o7hoaZDRuL9FDuteoyGqwRrUmviVVHzIdf4vW5CtBeoCg2i/I3qt+pa3wkaffbVyKDew/JIznIjJVxNXjhFWNBLZlo3jQJENICXLApObspZQYQ6Ujc3LE6aGISRRh5e5xG3QlrQoxyQqui3foVojsF0RQpSyHBIVySTopTkgfD+Kzn5zX8PrciGadH0G5c9D26UmyuSspqKyB3hUVuTIEarqKuCCIWScetj0eBlFZuRO5eR489w9lvU6TcsPQgZJl3ejslo0i1RYC92Th1RMmzWlHkunYWnQRfpp/t6anA4640KEfAnA1lfM7fw+tyHPZf8ADoQq2JmDPBMrXkbt7CtU7joVIhKRRjdd6OyRHUKVx7EPQUkiFbVWelMKNxFw07ZUDorLVDuK3QK4UTQrWMIjHISZOyOVNFMkQuTYyfnMItN6dYaP19QeGJDjSShHUmNR8qt/D63I9TgJ2CyDMJFTnfBkr7jhbeNKNmSSJJNnM1orjkyUrFmHMSAz0URGzwYLcUQ8SHyVHUfQlQIN7ZbDy7mSCqsxWTm5IHwhqOWNov6JaOTdx+yMvFOxLYp2EKvv4KKkfTJQhEaqiPlx/D63IqKf+AaK2jLE+Rz6vyYyhbltVVUOmm5I+h299Em7CaTlY++EktZtsdFBEskNUNvZB62zpVeSwwNwbtk2xhs/TRKm1SdvIpEywY82ZmhDGNzPkWZbIeXc9X7fDJPBU2Ic3sGyI+CCIG/4fW5HrcNVfrd9VILGE4a/66ZIhSKt3zINPM7DbFsLJZzr+Q1+ky3GyM2tGlKETK6uI9w0DY9IkgT8DuPalhZR+BQszmRnEWHwORv3+Nj0ZcS9ErYoUKFCVon+L1uR63DodV0t3Rkb1VQTozaU4YqEHjfk4/giF90ksvBpWKNZsTo8Hv0foNFrBfo7g0xrMAttcuDs42IV2dghk0mp23HsJBQ7fomcj0czS7Qy+ASq62+RVUf2etyPW4dCZK0UJP8AUHkfQ7LR/CkR/SKMPYKpeqwr9DQhNlJP0c0KiWWjEPVCf/geQPceqcEai75FFzZgawjXQnuSdqiFzQPY3wNASH8jrX+v1uR63D4a9v0zcQiFJAWQxzkaVen/AFpbRXHfVDsluLVqEURpZa30j9i3WwSto6UOeRppDYhamDLyN3baOZDf/A57gRaYeA1Khp/DUj+RhqH/AFetyPW4fD4nqlNhjq8jF5Tbg0luhz7hboemyEuzYaHaleqJL/8A+J3JqVKHQsqhpbVNqzP/ALA7xn50YpLpko79xqPgrnd8v4f1etyPW4fBEIkfSuui3INHIN6suuhIgX36bomzQl2TYk0szbJNpjpgNh/AratDEjtqt2xU31q+knBE2604YtZ3+RoYn9Prcj1uHwMnYWrG7VqmUZBRDfV9hZM2wv7okTFigvi401DUPSnjfDm41mbjUdV+z5VWH9Prcj1uHW+hIa4MMoKotkT8ra/BArCHIoN6ftOi62R2fqt5Wlu5/LE4ITt03RuOj+RoYtf6PW5HrcOupSKDO58f5dUOi9a7/E7Rf/gosdCuXfldn9Hrcj//2gAMAwEAAgADAAAAEFPB5PntLnOFrobZp1GAvABbu2mHUkpOnRavXRKL0stQPwJ9fPKFPP8Azw2Lb+haYcMU5dtqgKQl8ZWNsfNg7MXzJxZnYoaleG/zzyhTywvzwZ3hPlrhkBvZJE1F0dJQcIFMvs43z3eWbYjFZp/l3nDCxTzxhzwSI3n8r14oGWhJS/cesoPv5g3CgsewHXF+rDLEYV/Ga3xzzyzjgkTe8E1RNItqLlQaeSb4fYyNjXcoIDaGqipNT2fHMI6TW0CjhmAtQ1a7UGMKi7EvOPowg7Za9OqkyR0SnNxbK2UI/vLI2V/XzxjC2lfoPr41sIr0Gw11CeQ9h9jb2cu7J77oJ8cKFqU1ziSELrzywHr4e7x3ZM+xcbhgdnBqCArwWZUIJjG15H7sSBozEI5ul8GtKkpu0TG0PJJ403ZF4ScDynys4/ba6tUIIgjTZQBpkb/KVh/4Au3f6raMMczL7g6sfAc5rF7uUEejIyuBgS1Qq1/ALZaIzEqr7s208CInRakh5ihTB/8A7ElXt4sD86+iyspqoSlu+OhoA4hFpWOCOv08oG5igosmkipdY3Ez4EZWRSTpZhvaqkmiRYQpVRK1b/iOZG9Wc8ydqX2fbC6ELxDOhCYkTPAlT1dmepT4Nj4n+sPfxjnWNSi2/iqLL4k/9R3WQlqOLgJenzyseP6zNNHXjDA9n5kNNmSWXfA1gctVM5IWK9MK6refBAeBIs/2jbfZ75VEV9/heraN3KtaibtjJ+B8pEvjbNHIT4m5eusm7JSNeQQlCLxT6iXxGhplBBkaupUbGUC6B8ptwLqMrV54pmpofOaoSOzqlCCLKgw8OXdVNQYAUkJAg1XUC/C9GG8xcjA7nQVvZcLtsbR6g2gH6C8Rta5PjInrK8gZG4tUbcWrFlmp261fMrt/olmwEoNlIF1m/wBRTRpPoCtYz3bvILzPX1h5ZezZZvKVdZtwnRNabeKoIkudgbbqMe0Z6o7suDJBpkbAUsgmExqdV1E+tsan44+eAznO3P3IeB6G4IwgdaC1WiMRjS8YOARigaKxy2WmcEZIoBQuQeA3N+oj+N1/7jrmYxCFWlVWfchzjng88s6DfWml0dQuZ1jDv7aS1i+v9NFfSp+lOADCS6js+3Zlfjxy2xo//wCrpaQD0zzyhT4HqXz9z+xec50xeUvuY0W5nFNJ29Km9fiSMPxU29zzzzzzzyg5DkYJaii83ZwiKZBSpTZ9G1nhfFeHI2kZxxzzxnzzzzzzzzzyhRRi86auxvk8vIh/cTzwDBxJC0dSl3zzzzzzzzzxlDzzzzzzzygOpATxVuT/AISZ5idLyRkl44/sy93Bu0888i088888918888888oL8YcMJEyrbM8yun7s0Zq1G/leYds9URx04288888sq8888888oKWCebVJkv1xFlF8eiW6GQn5zvif8s68dNFHX48841K8888888o0Z583fmL4clBsBA7YJcsnnl38zU88e8888sCE84t888888888oU8Mcz14KwCBEUWQ15j5k8Qvzou8889/8888sa888888888888oU888Sp5rQClsIincsmmu8x8cc2S088q88888ad88888888888oU88ztoMRV88jJTx0mE85jp888AMCR8Oc88888j88888888888oc88DB888898dhc/wDQnPPPofPPAPPA3PX/ADzzzx9zzzzzzzzzzyD/xAAnEQEBAQACAgEDBQADAQAAAAABABEhMRBBUSBhcTCBkaGxQMHw0f/aAAgBAwEBPxDxyM8cu5+HmfBBehOGCGJOH22Tx5OEHAXWe/DOHhRSaEzgs++5unCVWsER4AXoJlXgIeQjwW3tItfqWMMfA5cNxF28EZzmbZcs32LHI9QWcHuXAnMHccuyLPgPCPB4ibhLs9wQWWeA1yzR+/gIIPAiIAekkf8AQPJvnckpe7GGPM8tkcMh+dnrbjr1cq2R3crrDRIBhacS5tYT0d7dXJckdpgfUA4sHwQeo/2VlEEEEEDHxWCnX1lqx+v4ee2LtINkJsDYOZI1eGCTcWEOYi3ibcxj5OL8LZcsxOvdpkssu3gVYR4D1eqvaZFE7EGA+j+r4oFgNstV+LL2YfsQ3cOxfw4/Rhfp+X0FiGty2BHSYt9xDeSxygfDDmG2HXPg6RqAXwhjfieXbpCR3xCuZ5zzEuL/ALk9M8Ee42rERDXCP7r+pHrBCCCC/oMK0+LBtRyZ9D1BdrRjDjB7h+fG8x7iWMjInkgsnHF+JFnbywGdXpkvpe0kzlcVcadEKIEERE+xnXgAEIQggj/AyZ5LVsRMuhY+YEb2yCYwuL1GJCnD3YHMiuq/tihxl1yyXbG8G8QvxC98yvqD4bbF1kTzFke7PxH2SOyFNLM8EfLPR4EBBCEEEF/QYd4ZM+gjuyNHED3EOefB1Y8zqyN9znj3KTXu5ZZbdFjjGQmO3+XXr/rZfHEGyNtPVit8SAeomRWWR4O0Q9o9HgAEEIQgg8f0GG6LQ3IWHxR7GyIrNWfuOsYc5kDVKHJJh0OiE8glneF0uS7Ev3OjCUPKTna+Z2eWurJwiffv8TiEa9wJ0kHIseV4hAOJD1JepRGmeMXcH7SHgAEEEIQgjx/QYVhxH4sscRXtW/ba+ZXId8dJeIOLCC3CB+UY4tPHcyzg/wC3ODq3zzju0AhdsGJ8Xd9vGDqaYJytTgkYQNn6L7Fv2Wnc3j1+0LZ7jnwD82aakOkn0p7hCIIII8s50D/lhYRh7s3yZhd7LfxA0ZJg3FHodQBxHstclIeH72D7Wu88MyJT8S2loO+ozljvVgQev+reOrNDIamtXAGksuOc/wCJ2BTq66G7dnekds8MDpseuZ7h4AN8LG8P0B8dQQDlW4TplytFhfEGF6W08qTp6YG3E/HgGy1wlC9kJyvEk3JjM4CC6Ixffcow7GcaJL32ySWmcjuEP3Mp7tfZbdSiyCDw65lel1T/AOy6AJ/TS4oZ5UwLLrws2LWehKe4aTxsxDMBcvRDHdx1uxPMPASItHjmR15/sR1POBvhyeuT7R7HIEXg4ivX7SS/Af2xPc4mpFM4lpCk2yyOLbhvfBEQ2E6YQhajXwQuocMLwcfMNq1+IBmV361YUjYSVyPdqa2G8eEdQPuOczg4hYxzZvAY/Zvij3GfyE5n2kLsARkWDuDVkDGTj1OXK9zqxejwyyyyHM+M8FzLwXAcmY1QRCHn+IJvgtbB6nVgQbwXbd+DFxbsHIK6xxdWFq5EWdrVyQebYVCfR8bu0Q8/fCCgbJA9yQWe18Bn3M/eTj6jxJJJZKygl26o48Kd88QRDwCD+BsuPJFPSdxq62O6QAsT7GHqLh3JxC1deAKy4MnHSYCcQ/NcpPWN5PmFvXRMccN6vun/ALjPZkUlEllht80hlWmyct8NyAcXYcrjzgs2IQhCEP8AA+O/GLpJHFxGe4inNyY7s1ycwRadTl0cXOCMt5S5ExeLnYE/dor7f7v+8hX8twmWZ8LAOMSErrAOp556ktNmdw8ylOm33Bcf0WbZEIQhCBD+JkXiBeCO93xJfaRO41D36l6uUe0OII6tuXJHVpZzjiesg5H7kNZyF87MmvcP/fmKMT97ZQ5uevUAJQvQRg14XADWa5Y1xHfJcLIIhAgggv6zZjtY83f8WtYOWctOUQ8R2Q53A6LF4O71bhe0WPSLvto+U6sJ6yPVPdhMYVcLgo/++0jxGyeiT2beIo8xxnAk9VllkkjO04gggggjx/Wb5Be2Xe7hpunEzxYO7y3Lxsdz6EnIIhpcmEMmcXJOPEr1YmBYMOWOGRV+IpLkinYuQxgXW1eLl7XLgsG8J6nLGNOEXt+nPBHJOGIiPGz/AImTY4m7EZOrpk0eMmesNcnS5935CN7nuTS+6SMOCTvcTdW0QDHiwPAerFjIMYwupJUHsPAXdrbYzIPJ9RcCcMMMNt0hMCzh/wAuruz4sBkK9RbDObinxxebk3qejJB5uPJxA7m35gPudXdjXVr4l0cBInyZuW3w7vQVm403Bbha7tzvu2222MdWn5Tp3bcsNgI/DwG6ou1wn/5d7AuG4XaNtWoVcJZnt34Hzb8rQB4N7rK7N6yfTJ05tOMic7b7QvBdGSxuXdQUzd+CK9c97XYsGA8rYGLD5gPmGOjILi/K/Kw+bD5vykvBKekL0ujUewH73r37T8iPRLpHLvT6RwODJ9qZj66mFYNlsG0Hxxcn7wBtbFwMYXu45E7uSWDZnU38QPPD0TL0cngi7/CJa2YeIXol9K1cKUwEeoP3s+nxj5S3zD83C4b4oLuVdk/pG4lj+k5zxaeluTmb902ww92vyQjo3y9tqem72uZGdAZyuImKFf4n/wCHnY6wfa1Z/wCvxYV2fvPQduLjU/uz9/A46DZdCN1DZ9CfxLx7yvmZX6hyT2fpl1vbvwDm33eGQHjol344RGo42LfV2sL0RDb9oDBhGMvxKuyej3/jwsFu9wCGeBxkx+g+JM+ockz9L4RWsoZXxgloMiwLR6j7vdi+WEcIjAVrebljg+ZzdvzLQuYx6H9zbMxcl+N8cAfbw+Fo0tGyevp7PrXqTP0cx6D+/AOeLOzguTa+Yjjb95wQAuxbnueO3gB/xdxfR8R1HjpJsjgLJb+zbcM4b1+B5uzHXg+85ZY+Xnn6/n+jldj1HTGDxG9/l2jfknMd5YHKXbp+EC8F8YhGDCbR4TJ6ic6iHOLiC0cOiFpIuTfPyjry/PjbbiCz4s+hWe8H6R3HnfDgFnj8Tz1OO7EkVMGeJyfmNJS7ctmCIg9B/ctdu+G1176s5jiy1bzt345B9Bzx9Q7xateG5T+oPrwTzepdd8I8HF8P/RbXXqC3mYmQ8nPnwczkLYj15OIW2LPX0hxDn6nk3/hc188TeGOctfBBYcHg8q/EvjMT+dTJpXlKXb1L8Tzz46/J+jss3r6Oz6l6kx/4DGDZCPX1EdL7eDBjfYS3yAa/59tgdsuXgxCBcdHgckuAPo7PG73Jn6J5N/5AT/Ce/HRPfjfodvo6vk68Hd2+ro/q/wD/xAAkEQEBAQACAgMAAwEAAwAAAAABABEhMRBBIFFhQHGBMJGhsf/aAAgBAgEBPxDxwR8Z9W+OnxOj+rQ8bHb6P/vhaF3ENb6q8KNtv2QcsDj3e/nZnxXp7sGeWfD5H9JBnyGmS089XNR15eJhguDiXerk/dxXh5kQGsDo8u/ws70iLXthkPXnfgdb+DPwb07hOf8AA4U8iWEQ47sjS1dk/SWKDDPA/wBE/wCP/wBTbYVsRj0f+7q7hdIha3DhzHS8fUY+PPwNsHqPC3h7gww+LbaQjbHl3b/w+3k7fvwdxYkPsgyvudO5iRbXsPGk3qjuIp6fGHaAc8S/oZdTbCnMzUGHfJ34UDWz39yUn1adFt6uV+9+ko5WTm39rf3fpY+7C1A/H6eOoeMFLLLkgBD6bDrqePqcsF5OyLYl/wDMxMkVQepI4tU7Ousun5b4dT37nEcSCStOS1TrGCgvVg+LIvyDPDPk7Pi8O+O3heC2H+BcmTUVl+ttw3vBkR3l6jMLDy4IAw8D2/LbSQnCHW2Ltg+2CszizbZOe7bflisOoAYeGZ89i34aGTJPrw0W22z1Jx7tObxY8lk/cD3dTrK5nUHOtslsghci+yx7YL1EJvj2NxZ09Fttp7J4afB1eiAYeWZfPYn7+L/5J5HjgDYmXb+2Bt2P3enLNcg5OpVjRhawa6wBEGVJ98MWRiTxasvqR4dsAw+HRjwqvRAMPLPh89i0sFmz47Foi1NwbSSgjHJIGmUWyAisFzuA6QHF1o80w8NicGx9ybyIOzvhyBKS5l9pIbf6GxYt8PBnhVZ0gGHwfD8OxZswCxYWX+VkziTTJxY5ALQlkQol6S3Z6uJrLstH2tnmNxYNg6LV5RxLYuatxIdS663pdFlnkweuZU5tTw2DDwzYbfD8RBPOENxcR04lhBGmkMcz5naDDHu08S5wRpk4I8uO4Y32QV9xwmRtk0oepHYcp/oTzb6PNmwssYVrky5ywK/IAMPCLPqVZ+W/tzb92+N9Fjy/BPChc+oThgEmXoEE4MjJTictwY7grE4z/bvpjgQuPqA8X7wJu+BE5kLMl6kmNGFy8bHNv+rHljyvVtpZvTOnfwZC1LHstDhkQD15UJHrwuHflB3Mi8ERhMDq3DVnEj3+rGdvNuwJiAHqDcPc87iPAQHg27Tn6nhhF2/JDqNdI7IucE4t34nobZ8G3eC9rYEhjlCd2nUa7jsBIRN4ngds89mXCRsWNSppwXLghgZsHC070Z4Qx+kbAH7CFHBicvdo9lh4IwcWMZ5mvV6Pdny9/INcnrnlBHch6W+Fh5gjvgNjk4l1MYIs623umCznAtLtuRNiaT9drQ8IFOpnaunu6FpRYMHdkuEPbI9X1Sb3bdXdvd8QXq0GHfhBBIeG2yyx2WXFjm+JI5ueb1B0WwP5EP8ASKasas3ggZ4HXstusw2fZ3OO4G8XTPuGFo67uQtsa6WIVkZZtgMtLhAzix8cO59CQQQB4222W227HjDtLvdhwdze46sdtGhjCDb6LSxn6swnNMnq1RYJ+9rwSpyxeLPLITYeKxwlPfVkZOXcn1NLcq9xx334Beozs2Pq36sgDztttstvjohhqX2y1kPwNc2PIQftsM36vcGZDTYJZhkl3o8sCRHHSfK92ZYEUf1JGHcD7s8Bl3aj+xldq0dS2/EdyAtv6t8b4bfh0QBb2dQHBZvVgd3uYq68YhQzizmXS4hhHk8DjmemxeVmSzmxHtDDZw5mz7JOX345erCG2DlQBglPjl6j7wB8dHudO/8Ah0Wxr68FtqT/AEDwN9N3JdGEN4BHJs/F68BKfF45k2A45y0JW0Gyj1HDmXsgdBJnfE/Wf22Bb9f8eDGeOPn0SLSRyJtkeEAw8LjPch1MoYOU7uR5h9WMOZOVjdTIHDWUY2OriT6iT92N43c6aSpBa+ofuAf8x7uT8xyeecyNGNy7svt7neC19Tl1Izh7uA5vsSHq+2XrDJOJwlFkYX7b7Q2uh3DDJnF9TswLsIBZdec+eLYHcp4LPHHgFhQPcA6tWvBP1IR1HstPdqrYfbOctsPuz7XPMk6rZDCwJ7RLnE1Dnu2AykUcAuUSbOmTw75SDLLLLLLi4tyRYtXotLXuBAPjixbMwAYeGXBYYZ4+tv3xOOp3cNhmvcpszmOOWfvO+pzVoqg0PLkDJpLi0sTAbNv6t+nj+kXHiw/5YsjbI578ejL/AC5YRMXWP1xcfcAvdlU2ToeY73bLzvFxutovLOudgFx1MGQwydZsrocw3tf2s7Ys+LH8Q7vR4xsuIffjLq8DnmEcLWBWMGdJlmPcixABhf8Ao8HgsNufHk/jPeEAGHhT34eJkziO7Se5l7Gx3WDIuw7+pHWYGepF9lkuWLJ497IcXYkx8e/42Cr5QSfU4Akvdi7ASeElr4bi4hOffjqHuMa9zE4Pq9hbDTwZ63d4G/xnbAsVrAQBcm3INxls3Txu2Rx4ZL39rni67hhO7rgA+N4hs5L5PkO/w1whxZWHleJgFuWA8faIbJ+njRZeExawhxnjZOrivwP8npkceB7X+ZJxnwI5QR7fK4bf6Hl0g2Hp8Gu3iBw+J8j+E8gg5N+EQN3x6+UDWRQcOedeAfXwb4Q5fH38n+CgNZwniA5eX4dPCgawlq2eOfC4bHDXyXZfg9nxfn7/AIHp8vr49fPT5Hu6/B7PPvydfJ/6/wD/xAAqEAEAAgICAQMDBQEBAQEAAAABABEhMUFRYRBxgSCRoTCxwdHw4UDxUP/aAAgBAQABPxD6N6FOGcBrPn0GClFnfJMNlPySvp9rUx39ZEgNDB9o5r1/ZERp+ipUEO1VL1aTXLz6nv34uYmahBwS/BqWijHTV2TrMQ5RbbfQX4F/M2RHUTeEPcgvEEuKvUTxCW7OfMPkL/8AaVxOiFbX9Igt37FQ5foIQhCEIfWgA3BbZqHdf1d93zFo9mPqpaqfuYaZtTHZ9GXdTNvU+jKOpNnDD0HErB7HDKr0C4jLQANIZOWMlarfU/6rGKeoX4lrRr0IWKh7ATXWFDyxK79KhvtTbCTH2xVuWgzLUqYCsOpT1AIXgkN/iK3Ufot/qBQG2ARiYrb+ghCEIQhD6TLHe+EbP62+5cMWjK7GvouJg5NjEtrPbcUNPo/aL8Q0z1PoqXbKB0J6Nal4uwgEu2v4nMvy6lGCHlaBGIKGByxKc+rJ5R0Y3cOnquBvb1HDF9HLFbLKH6raUUqzSxe4q7+i1kAZB0QOLZ2YkF9wy3MnuPxN3u/qimgtjIdx9T1IQhCEPpyWGRYS1jARbbf1t93QnEBxGT3+oUbGoY5TwP5mZ2tJqe4mpU+l+vyyZ4gqPVO3aeUXjSMVQmVhu4FX5hY7VcD0AIc7wR2WQ+zuCkRGirHTieHjxFCWs2Ibt2SpYaxzGMQVXxN3vKlSoqAWUznI7MqOipWLT5i3HFNwNHQ0fHrUqVK+piBlhaRf8Ytt/QQhCEPQhD6CQblkTsiuv/g33/2W5ifWxRduEajoN6fbuMNC5IcNPyf9R3I4sL/c3IO8pr1BLRfsnlNepGSq8uvUCIwSA5aqI6vJTl9LLWmXBN3rlmv0alr7NexhmrwDYx4MLLLx1VtX0IbWAmo/mLiYGiZM7/alq5DeEHvxhj94vVn5ZkFOYITCfgj7xo8JYr45joJuvXhU78xHe2CYjidkOwnjKIlfTQHFfuxWu36D1IQhD0PoBWiDg5h1FCv/AId9747Yfadajj6SbO/eeoZxBgnj2/uA+oHLML04qbxzGsLHSaZqUYMPC/5Ne68x/vvLgi5MkqG95z7x23t9SNmtwwKW8Fy7lLN4vnhFRtVypgwVn2Y6PK+3owRTioWZqs8MREi1ZUqBLNqoe8YhxoErA253M9ZZ+0vUFsYwMkYILxCUyD1gjlrcMle8/tCVdTJ+x8xJUOq0nwSg2wnFXFOsSzzBxhmI0P0IStWOtpdOWLbfqeh6HoQGA9QXUF1PFDoh1RE4zA8xRup4meKeCW6lPUp/U33Gmf6hcfTsYVEYelMvR/30wSe/qPxHFY21HbUb5QiOfS2VjtZH4gwATmBT0oHuOMr0C2YeEjFrflEsLLU7+g24VvxLJxcIhayioozR9jir2jKuGVKllWtzKxMwLENHkleH6HBC9Xf7SkY0+WJiHTXLGaVe/SpcCLkclf2iA5Djvn+/mGixvSCaH0dsUuX6SPibPoIpkx5sdBtX1CC6gnDE8M5pNB9j0AZsD3Zxz8wMppMN4sNwwLizDUyXOqmMRYxT7l/KXc/tOJ+E40ldiW7L5ho5hD8MQRg/Q+4HUGPfiMg7PovTQ/LF4Jce3obiiMqnqBNlAMAnJBcjyf4I3SHDAzMJLuC1jsPENylvuAT0Kl5iteYC+O1+IeJk2cupUEVXoEZxjP8AEYUXuSpAAW3LEg0cCXfs29mUsZPgZUJFffiEiq0fuy71KUNQSoI2dyUpFFT0l0dEBMu5UqVGlyhYuc3TcW02Rrxj9n8Re3ylDauj29KlepBHa9KgW3bGsfEVy8sSwprPsRW6e7P3qIao+xDXh5i946S+J0z2Jyibb70d77kV2vvLuXpPLC6Ncs1TDacy7Kh2Q7GHYw7mHagXKB5QHKc4nXM0PE8Vr/Qt1McjcN1J93P0eSpD9v59UAbWoaXijBqPj6XXfCFUt2v5JrI/D2fMwzdnD7y6IHK8+SPboNriCugWKYWrEYOHwxhag2MqDjx6dxEEpJT8OZf0xoPEAhYvPM6+kHoFCbG4WeJb9pVsHb0RGfv7XiJZSrtYTO5IIKOZMRrwVEcVYqPzlSoC6lIb3tsO5uZbYlWs92NPswm9OHuxWLyypXpUqIuowqrWpkw+JTWg8wKeyXGogUVBs8uWYX4SaantNr9ybZRXll3Mt79SEPUhg7WXMLGD9o6K+hAhCECBAh6pruANn6Hyv+A5jv1WP/pf69cw4zOd8kbk9FRqZVzQltLpIZenkbPaB6jUfEIbUDYnEpqyVoPGPtZFOoZHzngjGbqHiEas+HZEh3la5dT2lHtE7QqwMIKK5lKH1EUvlmCBK4Bx4hFSvUYCBnMMTSiGzW5UMlAecqJ4YNroiCgd7R7S8pVnw235lT2R/lBxFv4I5YEG6IrkZX18xDLN8sGhPoYYdhLTR+Cbf4pdvtHxETamB0RTz+gfQeogLWLw0odq+pCEIQIQh9BBDeOM7tPxKXKS7sPszaCfR0pefaU42z7PQmJnf9+otdOJUdgiWxdOoPxUxaMzQXFdu5UyAcnvPZnM+6N2nTw+hiJbxJ/P9zWmkTqUqrt9FTZFaL5cMZfT4SdwlVgBzG8oMBUMZEGoBa6gUhfi95nq8ADKFQxtqpacHrpjAtxBA3vI9Q1IqYWrgt+eDv56gFAOh6efGXQ1olQKFqfyS5UEYOZlLjtxCb8IMrsCYzySTHFXQjdo92XQwZjNX0cwtZ3gqP2itt/XagMsxpQwePMTJW/QhCEIQIEP0SN7gfh5nCfcxOo+GI5CnZmUjqY3hvt65f7c+o1DoeAHzKLR0gBWyUo0Q0pZy/iaZSswX7Itlm8F8J5Ys1vEKppj1H8CVlHvNFAez3KlR2BrV8wrgY9tbg5bLNwhCN9E4AU+JU5Di+UPkQ2RdrjRHaE9+ijzmMMVnq4qGGbNv8RKqVZUG6JrAAxzE7au2GU3i5lK3vSUIwcUlgLDoxHsr8xTtfSoFswuTl9KgOdN5hyrVlepUqV+iFUblbC5mjVXfqQIQgQIEIQ/T43uCLFINgnuJfEW+wQbgcls9ojSD5md8P5/79DrkQOJTP8AYCNG33hVX7Hpj70sPN7yWBHr/ATLd392MQx37ikblbgHWYOX/EWH7PCReDbKhaLRxCZTe3zAHOOQCXlAxWLf4IYstvkQqFqHqI111cujMSx6PooPn+MEqC2AXrkG2V9LDRFpm+ko2weYB7GuGwgQ13LqWxQ8Ry2fMs4pP8X8x2LKlSpUqZEuSNLU0ifiAkDk4Ik8OmnbO6Kj2wm/mJdMQ2RpK+oFaJSPPJzEquPUhCEIEIQhD6eLm7qg6/REESf4vtMCVQ9G42ou0OIo2X0NP2j1MvJ6aJ8vXxLHErxRQWZJgHzOMqA+ZzAlS4gaXAU2RbA+InWjuVrxpJXB91+Ew4Tv2IjC248EqVUTUnXmPnLvXjxDiRqhl8KXKNq1tjAHobRGyBuiMfylZRGTmYPaUh23aYK34ruFQG2uZfGHxHH86MlW3MPwgSoJQrccQFTvlSpUNQWILaO1UQBW6FwKgyzmNP2qOPb4iW4PHYRylrLfW4KKcw8GVZIn0gricBvuR5nHB1HfoQhCBCEIQ9D6eEuZVR2Tui3kX6Lh46zw8QwaVU+UJ/vmCjY0wC06jcv5ZZQ/McZ+0tyDzHD6EVYZWD7kELgz3iBAgW1AU0Ze5YMJtwLVp/uhTOaMjBo4LTcXmKt68RCdJC6lYZ7Xl+IKVxohYrgeEqb3ejZktjsbj34kMphuId2jGJYAHwVE386JBL5T73GGMH5r5GWPI8QOgRaOy7ZhrGJJsvt1U/ETJnMntShQHwqN5H3YLt2oai+mMDL5eJYTGg6JUr0qV6EWZnf6YW0TV6A8zWgHEW/SoQIQIQgQhD9DhdS8M9PcR8H6DmlI2QxOvsiU3qx5RD1FKRyMt8iDaXvbWUUqO5uN0g+YLDzKbWXWCm79kCC5aqiI8Ke5m/ljgbSl6meufhchHA9Fg4gIY1Pk8yq4ozGAL1kOedMGoqMkKgMU3DqLxEOwR2P0ojqWWj+Yiso0cT2lDD6Cfcoxm1MdaQdwmA0HdhLJXi1Ldw7S2b/TqZ021KlTY4DK9ExWGAJUBG1VEr7I5Y5b/QFpFQReoVon9jxGmaDQaIt+pA9CBCBCEP0uN0H5j34iIJk+oJTFwc34iAFRkHtGQGCRh0MF5faC6+1LuVMZPE0JkagxPsQv4SpjkluqmJ1FT5THBfaUaDkdxY44nllWA2+I4zyw4ODUD36Acw+NvwIijO3hc/GQgBaHDfMIRxczOzoIF4Qah3rbCdRPesDA176jidg9Sw9DzLGsOpVlsBHr9CNYcxDBzBlK/E29MsMnR1pGmvI1mO5mce7fUrvFkiRAAyxnOMv+IyrhE46D+8RJasqVKlSpXoEy26JeR9AVo3OB/wByPrccBxFt9ahCEIQIQhD9DhhEzi6crk+1H6HWrTuVUN6Sb6nuxex94U1INafMP2nhzH2i7QrgpGy9o9IDH/fEOa/E4L9p/QEtejBLtrRdblGvsTq+zDINqwQzzNb7hlwdBJTo9932g2VWuCUym+ITY2NTP1m2pTB8xBTyh2EjJJHBFe2/MrLPB1LuxAdZoIIGosypEGsPcs2ZWALcyqNcoBBr3L57mDTkyLBoV9gzHI+6hbS8nUHYEt1IGEzDagFUsfr70Vr70cV9yPMI1IXr15iU5XB8pfeZ1UakYQOIjv7ES5/aIbUT5RLhnglupTFoqFT3zFb6IqC1gQb27YuVxwdTL9JAgQgQIQhD9DgwCyWDrb4ier7CB6tcUSsf1uGbb7s2X3Ipt/eKcp5U8jPNH1EyQNlVT/e35lvcv0cFqgwHVfMVCEw9wmeMQ8AMNgFcEHspGyMoCsBmBHkk5lArcsMV28QOwFddRVXbhVBcdTHCeYlQo78kOmfV6IFhxXcuX7SXhPZMMw623aZnqvUApvXMwl6AglXo1LuTmMA5ZjNgpH2YjCpkpaFy4X3DZvqONOMVtS4XvfPiWiwNHUD5x+aqoEZZb6jeIfiHI/iC7XxCR8dJz0ezOzDpvvCxlRsbhjOolKPYznEAUl6ItudosLIi5GWOJXiVKlQ9CBCBCEP1eF1vMjhOyCBn/B4+tnaSyEq2njp946XL1VjpnbXG/JK9Me4KxA5XxLgwDbHBxEKjeZq4qUAESv7CF9IZwwSR5KgCI3BiCcGV6mYaGH/Ycr4EMw4aThcQsvODqGrsLi4yLXEV6gN4HbKKpGUhgAOo7aLEg+5M/flzbCvdFfJdwCZi2QX3St6FrY8SxYB1GV1KB7v27iSoJOZQY9Nq3ElSvTPct7nmlnCwAa6ERqvmaD7kFqLKVIMCalotPaGvHtK7Yf3EmUT8were02bmwUR2MucQIEPQh+gjoWy3laT6pe2je4lNRclGGUymUypXperjl6EqIozeH/ftABbL6QbZi3L/ACpUoORUplu7CYDqNcEyxvcCgdKdREYYkauXUrrJtmJErMUJb5gW48kEVAOlCqNyDqPbcuVG94mAdOGLrq3PLGtwwsWf4JbQ4RlB6qDiFjqZ7i3ITliAupYjsqUftv0YImgcwjijPvEj2GuoCrK6gsOybBG72NtnGOIza8/8UYkelrOoejxAiSpUqVK9AWcjuCNc+hpisWqU3ML0NzMFOYByzQKaxTmf3moT3EwE5u2R1x7xWV7E5z9pu1HaJY4lfWFCGFeiXhwwEChnp1n+RP8AQl/+EEQWuiim13C6icoNJB/8ctCDlIOX7DDn+BYzDleHCO+4Gh5/mUjc6YWAb90MIBPXJGpioPrli0tvDBIG6UdkXzTszFKrg6gPA5WssQNA4hOvnGo0GV6IbMGjz5iD+TqWqYoEGi9syCXjJDfIlxDI9NUftFrdrg1JNnUuEQLckpaFVfMAODu2MCcscJUYS5TD1yGepZpS0WoJfCRTG4lWadgPdI8T+EpuplQxDUXqCM/CMapW+Al1SWHCP1l8Qf8AXFSErUsTXyNy8b/CP/BI/wDJJbIrr5pt0flS3XzjBaRiywzCIwVvtNl9qFXjlrBGlNPs+0bItypUqV6B6EFOYDTNYpXU/vKgVPMwKfiAHdhtumYsPE3j+02yijj1+/qxVXfMPG2K/wBD+9667eX9QYKT6AleVeIg6u3ABuLpAllNIl0J1YRjwzj4hCvKwNFa6RAMYZ4gCY+1CNANsMotWS7heMMjVbQLywoyMXSR7QrAPErgZpNJvodFO/MrIDaynpyJywjfu9pUjcgcXMbPHCpiBOxQFaXNmper3FBV+AbqKRHokOVHOKQdoXTFq+ZHiEVQUcUiBTeZtBOE/DNt8cWZwy3MXoS9In7AcRMZTQdxx9p1A3mJBqyMWLLasfR+itBcAWNybLHtgel94eohscBD12UpuIhrd1PEnph4MxLiWlep6kIQU5mmWalSiFp5hVfAQS1dh9siLD2R7RFZKjgiNr9JfcaYWQAy8+GPlAaSN0jGyouXBCByckUEXBKQe6aqPpNbwhC2x9Mt8IhZqwhNDutDFP5e4C98kZs6ynMe00iQ545Eo0U5vSOtPbM3zR1RHIuXlQHdD0aIcnCw/EoyaVuWYHl1xt8HRqAC2VcqoPQmFV8kwHfMM9hOD7TCQhzCCwUYoISbZURThlzpGyMt2jGLuyh6jmIwLY8j5maWAA1DTb75jjAeSbB1UcQBp4Uy6h3lEiSpUSUoRpm5f1iVbKiC7mKVRrxjcIrX0zBSA5luAM90jBZkiyV6noQhCEIYjWFjQSHllSTmWMNGepnSzDW5k3ylpn6H3R0QHZeCN4vikseZantL2gip1ioiUHtl3v0BHZMnZxAcAVXsxEaYWovSYYQj2SHhS0ECI0LOoOQj2CKlX7Igjqr5LcxsQdJtD+rW8GpTln5Qw4RZ6hmUrVxNptkJ4uILGYKwIehE0GBirytwklU4/dMWuoLSioeq0xhltJHom5I4yOrNSxqysLIVW6cLG7IMTGC+Il4SxCv3EuLAQcaR7TF4jWuDlYNMejz6BC7tWEkKMyNVu5W3V05Jpm/cgNFhVn6PDKjGyragYX7r7xzKVol+6MnKPGeBErbKlSpUr0Go3KNpg9RlK9SHoQhCWRMpmYA6jgiOWC9xGxTH5EAoopUp9IvC9R8HXwQQnZdQBkh1qBvVJzEyva7Ysyp5rj/cRAibH6Hj1L5OYIWwrXcVEx2zFTBL7zV8SsERVgsuyjKaHvG4wKmOlha2pW53gojEOzJuopTCBRG9m1z4jQWrNRDZcS2UCGQ8PBMvh04A9KGC+0ywAdl7iXb2gh6SYRoZ94RgHZUcE0/eIUM5/ULyBDLs7tQGFFDvro08wltybzMTaF2EyPTYx1U9YRSDF5Vyx0SjH5ggW3lnCRt7j6EvBth5lGLFhW2MYkFViickQZdjWYvjF2f9UaC8VKqMNBa9QLS7QfK0NBxHMqVKlfSRcEETzBXqQ9SIqFx/uHFIBCJU3FWBAgQITOimB4lcRsnkTK0kUoGKZq7cEOojzxh58yy8fOTObXXcAAAImhKQZM2EZlC97yStOTv0bRAbdB8xoK9W0tKOybSX7fTgMdcyh38xpjQhnfmMdWKqVHFoeyIrWc72QAAbcEE0wz5Oo/ANw3VQ3gNS7V+AfEurIa12/wBRvsaOCa1kTsE6nMQIg8o0fvEHMSvcIhFC3zKQ8wFTtdMslQ1BdGcH9pnEfvEWZFfb2l8WVCz9OWe7LGmBUdlPmIAKMy5YLOtHKHveSG34G6ZvWnZEispWZ+rCEYxJUrRxyuiAYefie0L0naU+AMJ/H9RoBq6TSTK2P2hi5WMqV6VK+km0xNzf6jLiL3XYsdI7I64dRDL6BAgQIECCQHVb4k3+cYT2i4pc+L8RNC9gI/aPpnIACXpBQwuFsJdkHiNgTpPyRboPeX2lDfwfyR1PuW0ikuM4gItyud8MIC1yt5oOyOb71DqpfzFj7wQI5IJW6j15iqsbuIgapFW6Sw+roGiVNJS37sy4uMTLQxuCGcy1iYKWnuLzEsJWzQ/iMRpMqIaVOSOSJTK/OzyR6mjXmdx0I0kVqKlJiMtQpxBzWNGJIm8oBuFpRuMW5YQe8fvEBFbTjxFttZcMpCNvCw26amYzFzafJDL8ItM4ydhZB6EvVS03TyYvFPHL3jGEaoPsgFEM/wAodNo5uMqVKlSvqCIEDwEX6CU5qlCXWhvxBEVWb9AgQIECBA9MAYnKuWD5VfbLXdsFovobIgs8p6feD03pRGZaDyw4CXiOyDtzARVOQ0y9MK1/ciMdMPNixavbEpiMWFL4TUUvdzZZm5UdTGUkHsjN9wl5IzpqY6vgEcUxrAS56a+YKNrm/djNPgggabhbi42NJEMPxKnSRDGzqMXL4ng0IGw3Ba8v8S1XUBIwofxFaGYN2w9jNssrPEcNEeI0A0PbE6tgk5SiRGaAvi2PMeZqTg9oqK1ZcuFgC1j+irB4jhXbGDLSezATh5ZCdkLBVTI4cZEFkDymSqLxue/oWKypwjbHStX8iAGdGJK+ivpCLUEvPnll79FAZh499IiF4ouqpawJUqBAgQIEqBD9IN0LXx3EpTqdPzFGCGBub4XmdEPGIjtmG2oEWlZUA7QKsxVNJFGVe4oSwU7h8Hk8FcxVhai7zH7VMqeY2/MyO2Dfuwoo0mNsYtoa68wlQmevywPywbolCKDB1M30AWFK1NW6ggNmYC2MU8ozeh1KVGFDEAkUOoxuzEsI1+xLRcp34hHsJiVvJSQ5Rq8PMc8ywgHuy9E2CfACMM0CjQwq04MkSqcPo4DyZ5imnHAegK0FsM9a5MtAl4NvvMU9sQzD4l8K9BbNMnh1hZ+KWn8xujfEF1sF+KiSv0AuJk4G1n3BvcVc+poZggY65icvlzECjFuVKgQIECBAgQIED6GNxtEq/gn9wnWj2laVis7PZh5JXIlTnEp1ColcrojlKXwjp1ZWDhAedYTSTfF++4jxVUu+OAb8I+JC3gafmUPP3MdGraZsKqB/eOh35gwGb1Adi56/LFLbV8GYZqPguJiWihM0KFU5nDA4942HlwS3iVZLIbC8/ZF7dqDzQZlELAPtAA6M/aWJ23NxZZKGK+F6RwDSS/GwxMixcOrgp7I9IuVmZYtlzFNvIdMMxTfZmVi2moVWsKnLFtiNihtaIBROV6PaXELKvtkAKjYWXPC0ka2waJ+FLTTBq9pkQV9NLx46jlfADH85E+mo7QXAlq+iYEx0It+hoZlGZ65i4p5bjRRirv0qVKlQIECBAlQIEr04K9Z/7BFbZuYXPNt+yUYfNe6Z7hwxAYdJFg7cH80KABdXZFIiw8mMKjBZb4O4iK2vodZOl0kcGMqbstvDd7PtGVNst3xMSAjsjzOKs+JZjBwOiWrRuEogs/5RqqzcADsLHcZVaFvxxEL9vp40BDnQeY4ai1eZcnWnii8YRug5lVUwVppgUL5Zp+qI85VPhTt4hpWM08QQVKpiNZ0IoDCx6maa7RxwAnBFRdsuX92s0hOVwRhe980F2b4mG1otQWXABOcIADZ3MQnlGgK7gZXiVprR6WMfsBLYOMfnmWkArLo5J+Z39ZtgdaYtTD5lMQoIBdHg3DFNO+Yi59CA7coGHXMp3PLcSKNxS5fWpUqVAgQIECBAgelfQRuCoBawSVr/ACy3uhoaPW0uC6INaxfN8xHrgNVMEF4WURldOpYi30C2oxNlDgLKxi5Gk8EtH2zv1BOYcpVIhfw8M8wt9oK0UahcDI6/LGTKgsDN8RofQ89SoqroXTLUGu/eagnAEMEqmopuSlSqRhDYQ4AoxqHCj4jPPKxjD5S2ozbDRY28sRCYTIypfoHcEe3DovlhbQbPLuJQYVZiWwGVBN0HEG8RKGfvMurq4vb7EaKfLmmVb5dkVg2L0jIEThm4TTnL1LDBWFcyy5J+4NFtccnuMq3BKGv2ev8A5FVb+gQ4YqeJC5cj0WyWWp95cac+hodgdYem5Vr5cxIoxV9KlSoEqVAgQIECBAgQJX0EbhUAtYbMF/h3FKWv49Ry1fxFuIZ3PbEa07gGkfMs2rCBOvh7MVea0P7g1L8KzGA4zweWIyrHMA+lWNV9JLaiV5TMuC2XlWbMKDz4h4ikr+7FV5QHcEZ4Y8vEdK2bnGSnugf5X3irVUQuYF7ftFNErJSbg3LlixF4GYWCtMCAYFPiZvxjJtilmThbS4WXCpyO+48mVK9wIJS56h3G2NYdVOITW+zglUg4C0RyhS5cFvDkmNR4C/ePSSyVzBaa8ARFtgRhHzFXavrVavk+/vHvLo6PRlnUMseTCVuXwYIFh6oUu5n1CFO7GJdKBdXMyxhjG4iqMVd+lSvWpUqECBAgQIECBD6aF3gZrD+f6jY70dHoCtEsnPCUVnxwGCl+gldQnMAvwqmlxbax7xqNr9G3JVAQmx+bgbvaZTlcdHSFvwsG2USMUBPYwX+M0cwWPZqU1IyIziyUJ2Q3KV0lRenQbjhuLo+gKTnfpcmMEGY5ZjWMMuNyh2cDqZxo5XBAlmQHrhjINslq8jLiK52VNpR4D5lUHsFO6mD9mXLlwQxWG2OPpEX3uSplGPzfsMavXn1BUAteCBa37L3itvY6lLNu13Nkb9yYAz5GKWjGIUFYXR58JQtU/aBPs2EtF794az7uZlVfjmJsSpUqVKlQJUqBAgQIECBKh9HDuoZ+0mWHg6XKjtCGm5oodZhaUwQVhXlCPGGO0EZQBA6PxkvNVWVHKKTY7jbF1tbg1F0uH3ITiNrOQDLkvaLtxF/MMztV+9jBkAIcDDwVWpyRQB3r5MVEtcsq/mP3qA+woOD1hlLtbiHwLp6YyGsDKmyUEeFj5dNwm0MdpEtSymPaC78og2/8QQmVMeYQvyM/aHxz/RBwtX/M4FSJ+7xL/Tv3hmma8HSMmVYNj1ejySg2ucuYAobWiKqubrFCFe5cFNS4+6N+xiPu/wDAl6qm10e8p1Xk4Qqkjy6JtE+Rjpi+7+JilrowRWMXpn4ih1AwmiKD9YnRGMr6V6IOGA0b88y4spFkqVKlSpUCVAgQPQPr4BUy0PYf/e0b9lrbCR5XjcBvIsWReY8aeKePaYETuEAFHoehHiXDuIkPY5hlg1VnB5dRE8aHR6alWsW1kYulw3ScwW80mlykQugDgIemOXWplo9HIdkGi3t9jDu8GfLzFFV2kfxO8Eo6SBdPMoaf/kba74lwq1HAEeIPeJ7r9o2WD8zACgh6K70JbEfJiM9NK9onZgUIrDcvcVVKLXuAVDOm4WKRG9t6zFJKv7kKtAaHJhosHsVLgzc2MnXklYBbPYR0NWLNsZtZcuXFQRXQEoFFoulh740490oavcExC10air6UuopnruBUmBcd75ilqxHfrXpUqERw1BGqdncdySq9Kh6VAgQhA/Q44kQuquXqK2K66PaJVKvMFNMeZm3mFW19phEL7Io0H3kS40Z8wqacjLaCJcBFcu/oEK0CXD0L3ykxaRKMwHiUOKOt9mJGFAHhxEUs8u5ioink8fEb5jPoVTvAfeGD3KQ/FxczJO0pE6MRI1CKV9owyH4hAHKBxAWkdy0maTPg/kRmtW/iIq7WdIyrx1DsaldZGij7uZd/KgglaqF+0qbQM9oPCgDnzORfleDGDRVeoAcdodUMB+ZMldgNJC2bZYD7OG38TI3vxv4hSw7GZ7riZfmVYF3/ABRX5xaf3CgO/aA2HbCh0/aB4+vCOWjFv9NJBo7/AGTvC0xp6HoQ9T0Pr4R8A2XTOvhY5PdEVrb6ofAy6MMtNCUZw9mIoaOkdgVW5ghdvB9ri1wO1cUqRPUBFXi98RMZRDx38+myI1lRNlbHszUKLxsRm3ZvSvP8Qq/YByjMF2P2jeLmIKbsYvZEI/IitoNPP7xVUqKYDkJDfMt9Io5JSFQhecSw+Q2zCboiAc6hBeK1jteo3ZcGX2YFfYh21AUcSrxxN3UbNspthp7GWQd8nBO5UM5OJE2Y5YHL5C4w0GMXgWXLmFkl1J5Vr8Rw7/cstTXmXLm9RQHh9VlZmVrU45veOblaRwxTL+uqgd6lmzbUT1IQhD9GjCBUB5S5gZOF+/qCtEUPa6JbQc9Qg0YW0gMxFzmNwWrG75Y+JS1idoPhmmw+Fzqvl1KkV2jB9pqhYrI7iX3AjK7N/wDOFXRPugomWCgm8zOqRvSLmIz7c9h2+8YKUkLgCkoRLopVWdVFCcm+ZQRRhj4jmKcMNbLLoI5QKKwysKqNOJwUeeYNWrw6dy13c4HTHFJm6N/LEkX9kjETYXdMWaQ021Kc+ymSwW5hws7j5PYE2B94VbfAIZNT/q//AJMB7renv4gYlPK3LlxqkYBh7HEoMtP2jKR0Q7aMt7gtQu1GzWcrZERz+sR0yqrZqXnqQhCH6VC+47wLx/yIuVzZxFXiJFffLzcdA33itP3glNPeZTR2ufERpjAuD6FIIvBcXjmWSKQx63MBS6W4H73qn8SwLLRGyZS5rWVhA5XeYPPQycMbEKydnJB5KWDJ2MIMZjYqlIwjHQfMNB6J7oByR0JDYfJHhZcgUNvULlOnuvMSuAre4zl1C4/KJkXfw8ROlDmQ92ZzihhcEBJw8lLc4YLUIXwPg7MkEZTs6eUprQaGiJbnCcCe8XUByZVJwl90xjLXRglwYIaOP4GZeRuyH0r6ZYPSHtlj2WKZWX9BJSJK1U+0feUYfqk3msVt7x9T9C/qI3+SE2e0qPdv/Yl6KOz6AetVRAusgtvqiojXMNsAZl/fR1Fq36jB7X4nN0KnvKkEPvFPtIZZI99yD+Ee3QK7IBI2QaWTUbZh/wBIcjOwMPclFcq6Sox5IqtaYfcO7uUdpz4h2cPuiY68fu8y2g92GSgViN1aStiiFa2Av7wQg9hLbLLPMNwobmZHR2pLIm216gLB4TVe0qUqpuF6JwWPIxLS6MQcH/SHDCNgzK55oQ4O5bqCSNxwdRBdvzLX6bly5dTWfH17Tcf3z3iJ+mEcAllN5SxuL9d/RoCzhaJnTlNtsZCfAN7dRFmD0ByQeM9DMGpvmi+Ed7PvGAJklHundFdNr6mYMrvrxM7CURiKU+f6BjcfsQW7bfQLLkt7Msgqwhp6yj0wyuMI58w+g5Lwynd3KvJ4iR6qrBca3qlPhlsHbDdfaLTxICY+YY13cCOBXdx+EDn2IWEL6gKCYY0MudsV2eMwWNp9oFfoOUy3K6YUrvyMqiu9VRbqhC2DoZ6ZT8Sl6OArYLQXyzoBPsTMrLZ+BnYjAiOE7JYN6TVQC6TiD6Z3zHLV+Yt2xbBzKNqsP3Rw0/o3LUohunJwfaO0Sk/RRiODHcNsRVWsYv6SXAVwLNC5vAENLX3h9BF4wm+UsVnYvbOqufoRWkeyYJHRG6trOXUfJOuD/e06a7VxumPJXof2giWMzCZmAa6NPYgul9oL/VO2kVkrWxEtoqtWle/iGKrEGFlBAlozGq6qhdI4JNLbiIhsyBiAWp1Ab73JvyS7eOMSCg/w8zS35R+ycEei5RtDSyRMzfA/aAgUUVSvMvXv8XEh5tFsi8sNZTonUtqB2XeWifnPk/MBVZ0CpSjt7ktsFqzB7xTPQBoitdoswfC1dv8Ae8XTupZjPTLF1BTyTqAlckebMuXL9CKUkRBSauPPpf13LiLE0YeP7xHJZwnP0iZrBihbB5h5eKKMHREWX6HoTdDOTkcLgGcahWFjaIe05pHMqKvP0b0OjP4s8Kf6s/1Z5f3jSCdHRFvvkjuZLv8AeaPnWRKdCeEapQ2qv6liOAGhP2cE/mYTcggLvUJgS2oIPfx5gdL3UTmfZC8o3+y4m2fQaZ50j9nJMV5YWMINQw+O4TXLYoa1EEEgIQmF/fFr8gYGt/hwKsWKLR/MbKLoKYfOTFNYA1A0gOqokY9rryY+WltVhLCMQF2h4o/EVALfGKLFiHKzMKry3EOrgJ1ESQ8rUG9kUWU+ktYxRDUAqki0ZjDMmbiCphwnZEcrDkeyZ+kmPt3HDb2dPX0X9OZTAh1LXjqZSrybPeJ1ReWUaPieZjiHzmJMNHjEW2xUuAuibBfiaVk4lGiJwC0xhJ1SbJTZKLfP6u+7EHMZX0ZglK7fVlRC8B6IDyz7S9Ncq+39w0n7KaT5LQGn8hBJROcIxr0hjzG9tPeO9/TfMgK3YgwCq6gQtpi0pXaKGB0axKOj3I8Ca1dQIOc84ugBaqj/AKmMKTCyrKGCnxFoRu3+yb2Xthh8K28o8Nv4ROTU3faB1KxwoCxbUImurUl3yhe7EoI8sGaHI9kyKOrGLWh7YAlGUHrMJ17o/WqpO/MURr7IetnWixmyZ4E/zZ5n3ngfvLhTMbAgbOVJrxPf6K5eGP8A6k8n7zr/ACnXCvH2p1AfE6UfMUq+2mxjG4llih5gulNA5z+N2CaAfMOaR0VmvXxMBh7TaubRxTtf/FvuGPWeXUfm1fULY6G3frdZg0e84UH4D6BdywJi3dPzHb6aQZdAYDK7xGNPhnLFcl9H1y+F0+YaXl4L3DJcBEMYBLdg/L4Y7FEiLHtm24Jrwzt1KxxsaHiPOnTFVKqJV6GV0Q3yEGPZBQu278xDcHDEdOGsEuSvzBKdq+hnEoJ04lQ6Z2Rf9fj1KrZh9pZ/ZL9Lly5cC27+HuNS5OHuXLl+lLwwTSmkc5LNsVOBvmH8rQZbp4lmozWhigHDzBND4mqxOZ/ebRxbaiv/AItz+vA+AnPJsl9ptHES1y9RxCdR5e5bplegzTPEbW/UXWBU93/fiWL6mgOY8BrCBay2UuZYPM463bMVdHRGQObgP7g6s+qGlI4gGuWvz5gCV5acePQwwMrDHI8TqjjpICTsvbxDYNc+P+xqBvMAMHoigMC9v2RVcUlClOfQ5jGCpXljWFZntxFsmQi8Lf7+huKg7uVV6W4rb+UP8RM+huBEnC+3E8DBeUH04PpTRKdBnKol0SGa89QmHHmGsznpnDTOOMf4WnAnxEaanJZsn94ttxbagDhnAs9xEc/+fd+oMCHNIPbfxB58NFES040RKG3pnNL59OFFMy2Rc0eBim78xXei4JatziaW1B/1Qe/sR/5UpxfYqKNh4I7b5tDLFOVPInmTcm5f8rt8Op5UUoVxQ1f7YRCuD+0s3eXroRsSjkOSKUKDonG4YiGV6+0o3S6MJ2+ZlkOb3EvF8uCXc+wYJm8rBAtW94QGlaIFN8GiOA1gwgeIqUVckXJa1NMAvxDmr7w5w+YrVnnuX3grzzEjspz3Bomb+85zZXcx0AbLxMUgULjFEtH4jwj4idNTkM2SmW7X7wgVSVd7I8yxXuX+mIKfvKH/ANO+559Z29Rq9vpcLWiCXKIFygOn94Br70zcC3MUTJQHidePLHC/wIHrzOTM8RlxBNiBkrQrxL3P2ZfuVm4vs2we6wHdS4xLZVjYWdrbFcp+8Bbp94GCuxykNB8nh6haNcGeDuKM/lcLiGl4IMoa1wlGPWDvPEA9Eaywb118S1YOj8y4v8J0h8SkoS2uOZai+wlk6zGfvLdIatjfcSk1QRsqK7X3i+195ic5ailxmFo2xEkODv3/AMy3uXLqPvNP6A02QUpvk/WQKYEf/PvuBW2AFcHu9/Qb+XUc+gnRDko94zKqA5XH8y4FZ947j6CkjsngYYX+aly5c0Rp02BtJiMFQ6gLVxCkfEEvzWEJJA7JySzfwiluuHAHXvKRp1ba9sp6PbwR1Qc/4uX/AAWvUItz3yIlKtR5dRoMcHRDeISZWFd4PQdonWNxoJt5nSHsjbYZY2TAdD6dga/99yPqrt6/dEpr9BFcq6H9YQU7gpr/AMu+4UBuUs4ceCIi8+qLWCK7rE4D8TgJ946ig8S1ZbnXLL7f4+hQ8aX3BdHmXhcNLue0pbkdPfohQLGZMDXUFJ9iVAXA9k9sfBAFAdhbF8r5h+1XMVPZYvfiMQXFu+4VoNY7HYSp0bFG33mxRWmKIWxffiOQA1TT5IEaY/ugANK90R1z6tMdv7SwfQsjBAW7iA9hyKRU6fJPaZT/AHxH1Gm4Loe73/Rqxoy54/VJjzRK/wDHuFxzgMg2tb8TQBwdTzSUNsEOLRa0Ly4itr9DG8sFZkr7H/fVweWoQ7ATBL9RaCq3HiKEOTHMArbaypdbHM2U8smYgY6wmBaC3hiLllwLZcyvjldS8cANB5YaE4UcdwzgWxj0gDF+5Nry4nUxlXQQwLQ4x+Uyw/aNdTw7e8ZAN8kBBpfu+gex162+i07Eio7goFjEAVsjUUcevmuyP6LLPwxKaf1VTBSz/wAe4RXbPUrHTlEcrL9Oa4i239Jmgb+kZbyP7eir1A4TQsx158QRZHvDZn4IzI4ZIo+DBGA4OC47izT2+hKWm/pGZGRgK0FrDdtB2zbuewhgzBMECXvs7IRZsv8ASE6xLglXLGX2GvlCNfKArtxFDNPt9DI8RWL1R+isn+A9NxPmf5MyiV2RWemHwjKvIJ+J4GcEcyjs+0odMowaiG1QWfokdhpvz+suJU/+Le5eN+8jsnfqTEB61KilAxudAY4JlmUN3jgmQ8INyuxPglraMWykyJU6MR/yCX3+cRlC7MBd0Rbb9PwvRxNjcM30lHmU0E50HxKyW8Oz46ihTcys79FaY2PDHV1jqWGvTceIAEdKEGWRmKgeIIINLCzYznR5PHoT3CsaH4Hcx4KI+MXBqqq0/mHN7zFXwIa9z+PoVWM9l0RTzEWn7xZx+gishVwP6o0wXb/xbqZxg+gsb6iaE0amh+xDL9+g219CGW/yhQcbo5jhsAc9j/U2BLYq+ZHYudDDBVPRLVhDiMwAX7R+Nv3+jBbAjUbeiBV7D1NQNRoi+ipGClDQMzEn3kHcvmLqIgEG9MxKbpAEud9p0KsHUMT0DEt4coDAgurgH3gAAwYmLU9sx6mJxPhVT8PP2/7H00N6cMR4FNMy2DMvEvxTETZ9NWHTuXP1l3/4dwtZPoHN0RCfOsQwrxnHdHtQMfbY5ME37inazMtGX4jp8sHN2J+/9x3BYIiLgIlo/M2x7MVKp9oqK5/sepLN46Ahcw7ValGxYOrzD5h/JIKU+hcB4hhiVtw7YnKzN8kK2VLJjn0iImiZ5GHmvtMkePRijZBlDAtPvEw0mHkhE3r0xihxuBDBlEJwiG/A3Ffu/wAfSTy0w/RcHLWz7SzTL8UxE2enuJqJT+mFzUO//Dv2T62GA+ChlXDxFOXBgVj9Jut1T5ituUCaMfniOn7W+PiXRkRGV+j83+x6O0LYbAOXCp4ILNpTmX2jznoseJvlngRlQNXj29RaBuEgKLfl7YyNr9CuMZLpmDNJCRtlgWLhlfE6i0epKqDt6O6F/wAMxQhDhdkEjhniEFnPxDmC3RGC6iOsuf3nhSMrrlfUrtcPzEpr67rUvKO4VKrAlMGVpIsiS3X6A2A2l/8A5t9zf6QtnkuSCdQpXdviKXro37kfAw6Gn6QSytgL4Jp4d8MaoT9ox6r0GAl0HKRrFt+IsNwdvVvj0C2iUBwbOUtxi9dEYrhx6KLZGGmxYRtDMKv9cwe/prCrQblo8GCeRKJxT/qK0y/5LZOYfK3Eq0stLuGi8yyOBomfWpgu+sfH/Y5fqVNkIodC/wBOzJThOyXLDh1KuZ5B6C+vr3PURXEU/wDm33NwZCJ60yxAUFsTlUL+0W+glQaSVwo81Y+5MkSeC34Yjhr/ADub5h7B/MAiTxn9pZicRw1HbI4jAfEUtrfoCEtGIttvr5uYSm6mvWg7dSxaGANBDBfcc+z1Ft7nDL4o3XHaXqaYDxHWjiaePHMTEPBESwLE5i1tfvH5oHqKNmJc0offECNPoDd0iI1vft/9/Q84yP1Hm74iU/8A4G+9Mt3K7Szoj1AiRNwGFUbt+jD0AFq4MyOuV/qMInVs/MpCIfw9cC3cVw+ufaWmBYXYX9k6yANBAtitipgp9AtloRFX07hUWKeGK396X6IhFE5INO+yf3DdlVLZLgTyfRhrI/aXCrbVR85dFdeDzN4q4Oj9CoeOZdn6Y03DSvz/APi77+QuiO/UlMJAEvW7fiLA8e6OllfQ3/3XpRtuLcWE2ehADWbX8QVvvoen3H1MK5IyvOBleiXmgwOiUiOYezqO/oyYEgLI0kd5Yaf6nK14w/5+YNfbqv8AaZf5WbVZ4QE2OpWvzojpezwfHmP4SEf0fLTD+pU06ZiP/wAPfcLQioOLPz6oqFypFAIIBkM/EWpb8/RQhgNxrzY+hOL36WVdpINA4RHcZcEDl4i2+o5hbjcUCK0xVNwIsOYD7wdfR5oZiehr1QtB8MB0Pzn5qk+jioBEjjxT7ovkd/oYk4Y94lP6n3P/AMNvv5iZgmjBAVoJwQ7WCNQXc0SxJXUtrWOPXkcEMrsqx+g4dkduYJxDFXCO/L6MDVJr2Qk2Fh7+nLMDK+IyTRQ6Iq+m+LHCS9jKyPrirWUVrt+vROfsH8RfI6iMt+on1MCcMIq1l+pkJU2adf8A4W+7gmHYrao5WUeaD7RCrrgGot79KmJCptl6MsRczMPJ9OWQeU4IRo4H8mbiPoH2yU+59AZj/h1L+ghwOnpiIOz09oUj9fMyOz0DUBjv3F8jv6vvP8R/UyuRqJ/799wgteYg+GBG2njwEUtr9Ny/XM/B+/0Xtwcq8Qf7UTKLi3XpkmzCPrVaZF8SxTTAePq/zbPQ/wBXH6Oa+E+hfI6mzi9RE39CM2hUFg8fqUDKLGn/AN++5EWTy9usXEGpw8+f0/8AV59dpqMW5qP06Zs9/QmC80fvHf1fkT8ifvo/ofkP0m5uc/Rq95+R+of+r7//2Q==)
Pixabay
O campo de aprendizado de ma¡quina em computadores qua¢nticos recebeu um impulso de novas pesquisas, removendo um potencial obsta¡culo a implementação prática de redes neurais qua¢nticas. Enquanto os teóricos acreditavam anteriormente que um conjunto de treinamento exponencialmente grande seria necessa¡rio para treinar uma rede neural qua¢ntica, o teorema qua¢ntico de No-Free-Lunch desenvolvido pelo Laborata³rio Nacional de Los Alamos mostra que o emaranhamento qua¢ntico elimina essa sobrecarga exponencial.
"Nosso trabalho prova que tanto o big data quanto o big emaranhamento são valiosos no aprendizado de ma¡quina qua¢ntica. Melhor ainda, o emaranhamento leva a escalabilidade, que resolve o obsta¡culo de aumentar exponencialmente o tamanho dos dados para aprendaª-lo", disse Andrew Sornborger, um cientista da computação em Los Alamos e coautor do artigo publicado em 18 de fevereiro na Physical Review Letters. “O teorema nos da¡ esperana§a de que as redes neurais qua¢nticas estãono caminho certo para o objetivo da aceleração qua¢ntica, onde eventualmente superara£o suas contrapartes em computadores cla¡ssicosâ€.
O teorema cla¡ssico do No-Free-Lunch afirma que qualquer algoritmo de aprendizado de ma¡quina étão bom quanto, mas não melhor do que qualquer outro, quando seu desempenho écalculado em todas as funções possaveis que conectam os dados aos seus ra³tulos. Uma consequaªncia direta desse teorema que mostra o poder dos dados no aprendizado de ma¡quina cla¡ssico éque quanto mais dados se tiver, melhor seráo desempenho manãdio. Assim, os dados são a moeda do aprendizado de ma¡quina que, em última análise, limita o desempenho.
O novo teorema de Los Alamos No-Free-Lunch mostra que, no regime qua¢ntico, o emaranhamento também éuma moeda e que pode ser trocada por dados para reduzir os requisitos de dados.
Usando um computador qua¢ntico Rigetti, a equipe emaranhou o conjunto de dados qua¢nticos com um sistema de referaªncia para verificar o novo teorema.
“Demonstramos em hardware qua¢ntico que poderaamos efetivamente violar o teorema padrãoNo-Free-Lunch usando emaranhamento, enquanto nossa nova formulação do teorema resistiu ao teste experimentalâ€, disse Kunal Sharma, o primeiro autor do artigo.
“Nosso teorema sugere que o emaranhamento deve ser considerado um recurso valioso no aprendizado de ma¡quina qua¢ntica, juntamente com big dataâ€, disse Patrick Coles, fasico de Los Alamos e autor saªnior do artigo. "As redes neurais cla¡ssicas dependem apenas de big data."