IM 8.5.10 Lesson: Piecewise Linear Functions

What do you notice? What do you wonder?
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/5X0mcaIhptOpekfqPcg1nHjh0jsZs48Vd98EF/7bLLadp44y216aababPN9ta///2wnnxyioYOnaaJE6dpzJixRlF9q622WiEh2WKLLYxeGQ24/S9lm7aAqRukKEhT/vrXv+qxxx6LTA9ljU6KspcVdtQxyIKNk+uV9ohwaLizaE+IB20TZS+LtII1aaWcpA2PtCJVgAjSprtiZv0Rnh2A0B/Z92mupJXOPYvwqGP0U3TMacMjrfSvSLWywA4pCoMZ+m7u02CGX8Kg7SSdq5V8UNhRLKWAZkU+kJZAQJgPJjHMG7/77ruG5CAW5xlSQUEBxA4dOui2224zIEaRD9g74lfCI1zXk6kkGgn+SRxcw7H+kBbR+FCg7DvXK2ljGgoyg2TKNZygP0SHpJVwg+9d7sGOQkqDkUV4YEdnnAV2pIf8pPEhXJf0hf3Q+NBYZJFWwgA7OoMswkOsDKlkWjQc7yTPlDnCIk+feuopkxcWv+XLizVvXrG6dSvWmWcu1CGHjFajRo/rvvseVIsWHXXxxTN18MHLdf75xXrrrWL17j1VjRrdZfRCIBWcm222mZGAUOdsvCjbKLRDUqw7CAi6aDR+1p29ghedHg04ZdC+d7na9EKgqRsuYQT90LYRDu0TovfgN9d7iAd1Im1a+T9Y055QTtKGB3ZW3M8Ujmv6rD/Cs9P6dtrffnO9klbKUBbhUS/o3OmvWF7uGif8UU6YAoNAZ4Ed8WEwTniEnSZuNn4MtKhjhJfVUWbaJUryQSOGBAKRWhbkA+JBRwBZYPqFKyOr1157zSiVUiEAjyuFj8pGw/PGG2+YChxOOCQFBkphSDoFFA4LYBkBMJKigKY9SCfMmMYx7UHaiBNkgYYsi8MrnLqjCFFgGiGLckJ5Z4RBJ8x92oO6wzQFHV+ag/LBiAcyULFiRdMO0DHPnj1fM2ZIXbtKZ54p1axZqjffpLOYpz/+mKfZs4s0ZkyJ3nhDOucc6ZRTpIsumqXatVtoo40gFX8xEo2///3vql69eplBBXXm0ksv1XbbMY1TwZwosSL5ID7hA/xpP2gr0mJHHYNcUcei/hX+d3nPtJeEQ/tE5562feJ/dioti04ArGlfKSdpw7PYQVQhIWkPsCNelLe0cbNxIa3UM4hN2oM6xuDDDnrThEda6QsZ4GeBHYSBwRF9NvdpD8JgCvxPJx9Md5DhVGgrbqXxgb3TifIO9ghYLgeFFMUkpkpo2BiNWqkHc/JUUgoIcaDSstQWqYcd9YT/6clHGJH4zzSMNGY02mkbRhoI8g3xYRYdMg0j4visiBvlCike4WZxrA/kg5HdMcccY6Y9rKSiVq0z1bPnWL31lnTSSdK550o9ekjw4aBKGDO08PcffpAefhiCslj77DNIm29+nDbc8F/adNOdtN9+ldWmzSuaN2+ljhllEX2vqlWrapdddtHOO++sww47TAyMwnnHM9MutE10BBCQfGWPBp4ySkOar6zbDtSTj+Q1xGLnyUdy7Dz5kIyiFYbEmGZp0KCBOc8991wdfPDBZvmrfXfXXXfppZdeSo6yaKBKDVuEcNx0001mqoVltLBSRvR0EnSI6Hnccccdev31180UDBkUdXjyEYVKvHeefMTDKcrV+kA+WA6/4447rpj+gIBst93+OvHEDjrwQOmCC6QRI6TyJLGLF0tjx0qPPLJUBx00Qttsc6d23PFGPfBAR02fvlhFRSWy1Zv2AQICobjlllvUqFEjMzUQJh60B0gVkYrSPmF36J133jEEmDDsYcNDnM3Ull0pFtWe4NZLPixyya4WO08+kuGGa08+JDNP9Mgjj+jmm282lZ6KD0HgDL6jwrdq1So5yv/1AdiMUGhQOJm3RRRGAebknnecNERRDYX9uScfFonkV08+kmNmfawP5INVZv/+97/LkI9NN62svfb6XHfcIU2cKDFLFOjrLTxlrnxH0r1wYam+/365br75Nx100ExVrrxYjRuXasgQac4cGuGcN9oA6r1tH5BY8M4e3CPuxgDiP//5TyOZQSl1n332MRKSoPSDe3THbr31VtWqVcusrOvUqZMRbwfDJGyePfmwKCe7Wuw8+UiGG649+RCNw0IzMmBup9BJh4+OxdpwePLhnguefLhjtz6QD+aN69Y9Tzvs8C9VqLCVWcVy8MHXqWXL3/TrrzmJR4ATlAsmbpGSDBw4Tl26TNJNNxXrhBOkk0+WXnxRGjZMmjUrR1QKBUZjTft0/PHHr5gSQiqz5ZZbmmX6SDnswTTxDTfcoG222cYouOKGaRzmsMPz4bYD9dMuFr34V4udJx/xMbMuPfmwSKxjV08+3DPMkw937NZ18oHCHB0zSmloxvMc7owXLFiiTz75RjVrPqrNN79CVau20quv/qIZM5BSumNHBzV6NEvjl6tTJ+n666UTT5SuuEJ6+WXp++8ldGXz6XzT0TF9giQD42YQD5RTkYIwJRxU2kNvBf0RvuOOc4cddhDWmcOKh7YD9eQjed5a7Dz5SI6dJx/JMVsrfHjy4Z4Nnny4Y7eukg86CaYx0LFiOhVDXuydxDJE22lbCQXSjY4dS1W58hJVrDhdn366RPPnp2Ad/4WbDgrCk5tqldBd/+QTqU4d6eCDpbp1pS5dpHHjJASsSEvCZAfdMKaFWIXDstytt97akAwU1YMkCrsTrKhhWgYCsuGGG2rXXXfVww8/7MmHX+3i3AD41S7O0K3wWGap7Yq369CNJx/umeXJhzt26yr5gHgwZYHUgL1Y/vKXv5iOmU3hIAUc6GdMny49/rhUubJ0/vlL1Lp1T82bx3JRd8yszyD54B1hsiLwt99kJCFnnSVVrJgjI+++m3sfpdTKijtMtWMRGZ00VrxASoIHZfzBBx/U9ttvb9KJYTM2zcSGDCPO4GFH717yEUQl3r3Fzks+4uEVdOUlH0E01qF7Tz7cM8uTD3fs1lXygQImuhx77bWXIR5MQ0BA9thjj//uo1FsVrA0bCgde6zUqJH044+L1aXLp1q0qGzH7opemHzYcCAgLNmdOlV69dXcapoqVaRrr81JQjCXU1RkXUNYio1RJogES7wZjYYJBdIVpmhYnQdBYU8p7CmgzB48rEQIbFBIZToKN7x3PYgLdczb+UiOINh5Ox/JccMH9WKds/Nhk8roCKUtNMpprEgMIllMj2MKHQt7WRm6sv90vXry4YqcTMPo7Xy44beukg9WkWDMjI3f2AAO8sFUxL777qdu3YaoX78SXXaZVK2a1KyZ9PPPEILFZhVJuMN2Qw7bHyunXaLCQCCBnarvvpNYVPef/+ROCNFnn+VW2UBSICs2PYWMjNF+sXKG9ox2DD/hw65yufHGG3XiiSfq8ssvN8t9eR8mNGG/+Z49+ciHTPnvPfkoH6N8LtZp8kEFZe4UYz+Yj2VEgcEnRg6IZ9nrhee14fDkwz0XvOTDHbu1mXywEg3jfRh9Cx80TExXsJkj0g72UNlhh5116qn11LbtL0bfAokHkgcMikIEmMrAyNfqIh82zvwbm3A//STdc0/OqNlxx0lPPin16yexBdXs2Us1YcLPqSyc0tFhrAxjilhdRRKEIuvJJ59sjNwFl+7auMW5evIRB6VoN558ROMS5+06TT5otJo3b27MndO509Bi3rhevXpmn5UmTZoYOyBpRJKAiH97RoFa6Jt178mHRSL51ZOP5JhZH2sj+aC+0GgjBWBXWySUYRsZNv5Yjm3atKkuuuhSNWzYRE2bTtYxxyw3q07698/Z77Bu1xT5sP/nirCC8U6TJjIGztBFufdeaciQpRox4mdNnfqblixZVaIRDCPfPeSCjfgwqIZiKtIglFNZnsuuu1YRN5//fO89+ciHTPnvPfkoH6N8LtZp8oElQKyOYuHQzrudeeaZZktyGrYuXbqY3SgZYVFIXA4aRUZS1pCQnd6xYfGMyJPpnZxWfPTcqycfFrHkV08+kmNmfayN5IP6xJQGxreOO+44XX311YaEUI8gJsGD+jd79gJ9880fuvfe+TrssOW68spSY2sDnc2g87WBfBAfCAgmPL79Vrr7bql6daaHitWgwQx9+eVczZzJppLBVMa7p31hD6s999xTG2+8sSEfSD9QUmWaGfxcDk8+XFDL+fHkwx27dZp80KEzKmLNPNuaY+IcM+tMwUA42JflnHPOMeLbcKNWHmS4h1iweRsm1t9//31zYk4Z0sM3NndjH4727durXbt2RmELHRQaifDhyUcYkfjPnnzExyrscm0jH9Qr6sJFF11kRvDsGMvyU/ZmQVcrvAoEnQlMozduLB11lIzFUha7hPQwTbLXBvJh8YeEsPKFGaVevaQbbihRtWpLVKPGErVqVaJvvlk5XRQkUNZ/1BXsGGSxrQQWXcGN5bjnn3++aZMgai6HJx8uqOX8ePLhjt06TT4QM7KFLg0ZEhCUsNq2bWs6f0hAx44djUIWilsu5IPw2cWWTexatGhhzldffdWs/Ucp7K233tK1115rJC/PPvus+RebzkUpuXry4V5IPflwx251kg9L2Cnr2MdAYZR6QgNtDxocpB6YGN90001XTB2gw/Dhhx8avS3cIhnAdsbAgdKtt0roUDzyiPTLL2WnWmy4XNcm8hGMF5KQqVOL9fLLf+jss+fr2GOLdfXVUvv20ujRORKCmzgkhEEP01RMKaP7wb5SGCiLauOQhLDRJe7RFUF6G8wLG0dPPiwSya+efCTHzPpYp8kHkYdksI09Wt/NmjVbIeVAWe2DDz4wBn5sYpNcKVRIUCAVTz31lJmTDk6roG/CCITdbHFHJUcC8sADD5glc+F/BclHVAMQdl/omREOUhdWgIRHioX85ftGo8TmVyx7SkrSwmHaDggbBFEkLOw+znOW5INGen3d1TZt3lrsIBXchw/eUS5ffvllnXDCCbrggguMNBASb8s8dYg9TPbbbz9jv8Ma1EJvwZIPBIfsoTJ4sHTaaRLLWLEoyjRLgMeEf1+GfKRNK4GXt9pllQgUeAFpmDBhkn74Ybo6dFiqmjWlSpWkU06RunXLrdZh1oS0l0dCSBukDmkvtlDCB99pI5Daonx/0kknmQ0wx4wZE1knyRvq2Nq61JZ2BGNzSH1cpTsWI9IKKSNvXXVkbFhcCc9O+aeNG+GRd6SVfM0iPG9kLJhbbvd5jYyR+XSe6HjQKHKFlNDIUeE5XQ7CJSwsDHIygqRAMF9NAaGyPv7442YjKCo5RIA5bAhI1Nwr5IMpGxoN4kb4ridpYiRDISU+ruFYf1Ru7A8wQgI7+97lin8IEZYorT0Dl3CCfqjckBnCTRs/sCMfaYizwg77DWAXjLPLPWmjLDOvTxlyCSPsB4VNrGeS1rTYgT/YURe4D/+Lb08//bQwkIVOApINdnKl3Fv3xIH8vOqqq7TddtuZZbRIPY499lhDShYvXqLp00v1zjsobJaqdu0Sde5covnzS1RcXLjOgB0KrFzDcXN5xoYGpBxS5eI/6If0g9vUqdOMEbTp00v05pslJn0HHliiSy4pVceOOaNpS5fmFHKD/oP3YMi0Miv9wDL4jXv7L0gHe8SQF+QJFmKp5+FyQHuEjRHyCezC38Phx3mmbaJOUN/iuC/khrpA/ac9ThseaaVdIm8ZuBb6b5xvhEfbPnjw4NRx439gT9vJ1H4W5Y5ygmSMwXja8Egr/V5W2EGuKCMjR440RCsO3oXcEB4zIbRDWRA3yxsiyQcZBXulsWZahOkXq/NBwYIUUEFdDggGGcbuucypXnrppUa68vbbb5uOnwpBJlxxxRU6++yz1aBBA9WvX99UkKiEU3G6du1qDAfRCLFfhT0hTZz2ubwrEgoqN40FmVee+/K+IyKngNJJlec2znfixCiKhi6O+/LcUDgJj3SX57a874QBWWDUmBV2rDTICjvygnJCp1deWuJ8p/x/9tlnmaTVYkeYUXlBxUd3AyVIVmJw/uMf/zB1MlgWSBvljfqCSXGmDz76qKtGjhyjr776Vc89t1CHHVasGjVmq0OHyRo+fCCViEoAACAASURBVJImTlxZX/KlG+zee+89k9Yk9SlfeJQRrJFC4PK5ifsevMANvRbux4+fpBEjJql37591xx1TVKPGPB199HJde22J3nvvDw0YMFVjxtAmRLcLkOfu3bsbwhaOA/h269bN6IPYvMBWym677WaU8MPpoT1CGoUV1izqBPGhLFAnospJOL7lPZMe2jrMJmQRHmWxb9++ZgBS3r/L+w525Cl5Eca1PL/5vpNWBrNZhEc5Yfk5BuvShkdaaYvRc0RylC/+cd8THmWEvOA+rr987giDthPpa1Qf7MID8BNJPiAAZPz1119viAeNGWveYfFMhaCAet111xk2CZlIcuCeEQQFnsabAsE0Dv9o06aNEd1TwW6//XZjFvm+++4zBIQGK2q6AXbMqIxKTgXPNUA0QuNNoaBgxD2pjDRk/J+KFNdfPncUJOKNxnw+N3Hfkx7iBF62wMf1m88dZAHyQbpd8AqGSxiMokhvVthBPmwnFfxX0nvSRmNBOSFPkvqPck+esjwzi7Ra7BjlRYVHHmES3HZ4TKkg3WBQECwLpBOiQMMDme/du4++/XasunQZr6uvnqKqVYt0zTXF6tPnV40ePVHjx8erG2BHHeUahUXSdzSykCTimtRv2D14gRuDBnC030nb999PVLdus/Too8WqVatUxx8/X5ddNlmvvjpBvXtP0KhREzRu3EoMwI+BD3WMumHDslfKDuRj9913X2GgDfLBKhlLMKxbrrRHhMO3rLCjLFD2gmkN/jPJPWWH8OiQ04ZnsSNv6UiTxCPKLdgxyKWOZVFO+AdppY3KIjzKCf0X/Vja8MCOcLLEjnYTWz/gGIVvoXfEJ3gSBm0nKhB/OvmgQ3/++eeN0ieZBftkFAX5sAqnderUMdKRpOQjTFQsGaGxRLEV0oMBJFa58D/Y2IsvvmgICIkPH8SVQoUYLG1cABZ2R6FHDJn2QNRqK3XasEgbcSI/okiYS/hZ6nyA3fqq8+GCfdAP+YpIk7IeVe7Ip+eee0677LKL2UQNqcdRRx1lOsKoxgDxd58+ffXTT78b2xhXXpnT77jtNglVhoTjBTNYWBNGxoIY5btH5G2nhbkPH6SVlT0jR0o33ZQzGX/MMdKzz+aW7LKfDCt80HmhjtmpCDAPH7Z9YF+cnXbayRgkY4fcunXrmrwLtz+IsgmH9okBV/h7OPw4zxAFOoaofI/jP+iG9gnSxhRT2vAsdhC0tVHng3STVtoopjnSHl7nIy2CeSQf1s5Hq1atzHQH0y+QjSD5wO4HUhAqWNIDP7Yick9nijVVLKfSuTLdgiSDCgGpgAygZAfDDB+efIQRif/syUd8rMIuEUXa+ejwt6TP6I0QHkSV+/DBNCiNJqvAqBsoZLP6i87W1qOgHxrGbt36qWPH33XCCdJBB+UslrJ7rMtBx7mukg+bXkgIK2a//jq3yueAA6TDDpMeewwF2JwlVduB0gZFkQ8bFgMkVsMwIEMfLZ842pMPi1jyK9hBipBEpyVG9u+efFgkkl1pf3r27Ll6dD6oeGzExHJXlHQQfZ1xxhlGJwPm/cQTTxjFNhcGSaFilMfmTR06dDCNGltj33DDDUa0i3SDin333XebeVREluiHoJwa1SB48pGsIAVde/IRRCPZfRbkg86O8v7OO++YaUeMglEvIBrBA3fUNUgFDTKkH8IeRTzw9/PPi3XffSNVvfpCs/qje/eccS4XA1yE979APkgHBASBJkINbISwad7xx8tg1LIle8mUaurUBRo8uDD5QDqFgjt5gf4anWNUXnjyESzFye49+UiGV9A1ZAHpGFND3Kc9Viv5QByH+AzNebarZu175cqVja2Pxo0bG2VQ9CJcDiopFRdbIehzsMsky2iZ36cz5N+Ahh0QvkE8mHZBJB0lVvXkwyUXcn48+XDHLgvyAZlgGWzFihXNqglWUFDPsCAcNf1SXmxZMou9jubNl6tq1UWqU2ep+vbNTTs4CChX/O5/hXzYBEFCwIopqI8+kq64Qjr5ZOm880r14otFevNNFDDnOllLtf/g6slHEI1k9558JMMr6HqdJh9kPOJflAdvu+02/ec//1G1atV06qmnGpPNSCOixMNBAArdEz4NL50fUzlMrQRFa3xn3pDvjCz4V9TIgn948lEI6cLfPPkojE+hr1mQDyQcKHJbk96sYmF5LMrcSXSY6EyxZTF2bG7TtcqVl+mcc2apV68FsexbFEon3/7XyEcwvUzFTJ0qtWsnnXOOdPjhYDdbr79epB9/zEmMcAPGSQ7bxqFoypQyU9ngmK8dixu21/mIi9Sq7vy0y6qYxHmzWiUfNkJUIKQUaMYiCUGUg8IpkUlbiew/0l49+XBH0JMPd+yyIB9MubAHi93MDPKB9AO7EZDuOHWMThE1ESx6Mo2w227SXXctUIcOA/TbbzPcExjw+b9MPmwy0UH8/Xd0Y5arSpUi7bffMp17rtSnT85GSHmG2Gw49sqAiRUMt9xyi6pWrWoMxGFDKDjIsm6TXD35SIJWWbeefJTFI+7TaicfNHxIH1hmgwIWSlZUKBoiNMKzWnERF4B87jz5yIdM+e89+Sgfo3wusiAf1KcXXnjB7Cey4YYbGhLCFAx7HsXRp7LE49NPZTrKo4+WWreWJk2ar169+hqdhHzxT/J+fSAfYFlcjJHDherU6Ts1azZHZ54p7b+/VL++1LVrbj+ZuNNXLIc98cQTzXTaJptsYnbIZQoZCUiaw5MPd/Q8+XDDbrWSD9g5ylTMPderV89Mt2BkjNEYJ5vBYXp9bTg8+XDPBU8+3LHLgnwgWUT5mq0EWL552mmnmXvKdHkHUwEzZuQ6RVa0YFb8vfdy0wRz5sw3Boaow1kc6wP5ACcGXAysBg0apvHjZ5lpl0cflWrXlmrUyG2+hyRk8uSctKnQVMxjjz1mjI9hkwWJFjZaMI3P6o00hycf7uh58uGG3WolH8w3Y/AEI0bofKBkWrNmTaOfQYcF8YCU5Fvq55ZEN1+efLjhhi9PPtyxK498WL0l9DqYXkGKGCXNoGJT3zDMxJJy7vFb6GCaZdKk3AZqbCt/0UXSF1/k9D7whz4V1g09+SiE4qrfLPmwS23JhvnzpX79cpvvQfBq1cotz+3fX8LskLUREg4NKQfGyILkA705lmenOTz5cEfPkw837FYr+aDBbNq0qSEd6HkE7XzQOLIckDXurnY+3CCI9uXJRzQucd568hEHpWg3hcgHnRi6UVgZfPLJJ83O0Kzmor5QkcMHJJ46h7GsqBVd1j0jbZaKjhsnPfVUzn4HegkTJuRsWFh3nnxYJJJdw+Qj6BuF3u+/lzDYVrmyVK2a1KqVNGqUhP0U8iXIGbGEikl8dHjYi2fbbbc1m9FBRKMO/m3PqO/2nScfFonkV08+kmOGj9VKPpiXZBls8+bNzRxlkHzQgLLPA0bHaOSoMGvy8OTDHX1PPtyxK0Q+qKwQdDZ/o+PhxBIm9myirD/GJR/wlhEjpMsvlw4+WLIWS5mCCR6efATRiH9fiHzkdEJyxsiQetx+e85IGTsDP/lkjoRgSdUeTFWxHwbS48MPP1yPPvqoMbEepXCKpIsywBlFTm2YXD35CKKR7N6Tj2R4WderlXyg14HhI7TuP/30U2P865RTTjHa25gKxgAY0zFrmngAjicftogkv3rykRwz66MQ+aCDYZXDP//5TzPfj+idPUAw2hc18i2PfDCi/uMPacAA6fzzpZNOkp5/PrcKI2qreE8+bC4luxYiHzYkSAgrX1DL6dFDuuEG6bjjZJRTX301Jx1BSrJ8eakZnLHUlq0jkGxBSMJtJm0tU2SQE6ZqsPuCBCzszv7fkw+LRPKrJx/JMcPHaiUfVBKMemFc7JJLLjHsHeNHWB7F8Bh7sGD+fG04PPlwzwVPPtyxK498NGrUaAX5QOGQ1SzUHUxxh49C5ANywQKJzp2lM86QTj1V6tIlp2yaT+joyUcY4XjPcciHDcmSEIy6ffhhThoFKbzsMundd3Mm22fOLNH06fn3diHf0QFhVcw222xjzkqVKpl9rVB8jdL98eTD5kDyqycfyTHDx2olHyjGMWfNrodPP/20sWjKapeLL77YEBIU46KU5+ImjUoOwaGCIYbmxLIpI0bC5T0NqP3GPcsSo0SSnnzERX1Vd558rIpJeW8ou5RV6gC7WoIh5TI4UuWZKRY6EoyGMe+/88476/HHHzf1KvyPKPJB5wbxgKu8+abMHi0ol6JYihJkocOTj0Lo5P+WhHwEQ7EE8cUXcwSRPWMaNpQ+/rhEX389Sx991EsLFiD1CPqSad/YvZsyAkHlxOActl9YBRXVxnryURbDJE+efCRBa6Xb1Uo+6PTR84B8QBKoBNj1wORzsJFdGb1kd4SH4TK2/GUah5M9ZBBNIobEsirm23nP9tbco4FOoxo+PPkIIxL/2ZOP+FjhkrIPUWBlCivAzjvvPLNdOvUlSIxtJ8bU5UknnWQUD1l6idQjajQbRT7o0GbNyq2yQL+D6RYMiUVs3LpKIjz5WAWSWC9svtnVLrE8BRxZEgJZrFpVOvDAUp111kK1aDFMv/22zGxsFyQgGHBkT6vNN998Bflgeg4dEQyShckH8WOp7tixY53M7weiam4h0XTIrIqK0kUJuy/0bLHzu9oWQin6G20C/R79LW1J2oO2aJ3d22X69OlmDpJ5SCQgFCx7pgWGcGgcMTnM7pzs28LJ8l12reV/zJGysR3vmzVrpltvvdVIX6iQ4cOTjzAi8Z89+YiPFS4h4uw8i5h86623Ngak9thjD7Vo0cJIQIKh0aBQztk+gMadRoUGnvIfPsLkA8XF4cOlW26RUGi8+25p4sQc8YjwHg7O/NcvtV0FlnJfkDdIXV3JB3kDAUHnY8wY9tgpVe3ay3XAAYvUsGGJPv88p6djFzyR7yjvIyFjWo5zp512Mjp1wWkXyhLt4scff2xM77P7N7sas/IwSHrLTWDIgScfIUASPFK3Wc0GgQyTxATBGKeefAQQA1AMibGpHLodFFIKuT0Bi9PlwB8rZlq2bGmW8/IvTioblZGTSsU73PF/Ro0sWYQdhg9PPsKIxH/25CM+VrikXLLD8z/+8Q9jNAox+WabbaajjjoqUpcjbuhB8vHrr0s1cKB0ySW50XOLFrmpFzq1uIeXfMRFqqy7tOQjGBr5NXNmqb76ap4uueQnnXjicp1ySs5GCHZD2Li4qKjUKMxjZI79s2rXrq3777/fSDaCpIK2EYOPrJ6i7HEedthh5h3fXA9PPlyRy9nS8eTDHT98bhDlncaLOe3rr79ed955p1nxwrM9ETtHSSGiwgq/g3wwEoRQIFlBcY+waNjDoj8qB/9k1Q2KWTTS4QPy0b17dzPyZGRqCYzLlakl4oNoEwxcwgj6IU2I0qyYNPgt6T1TXsQJHBgFJfUf5R4JF2mlASP8KDdx34Ed0wrsSBwkknH9h92BHfPbSBrC35I+W+ywtUG4Sf1b95TbV199VVtttdUK41Eso2XkyjYE1l3S64IFCzVp0hR9/fXP6tRpiU4/fbmOPXapXnhhqSAjRUU5Uh43XEg6aWXJfFw/hdxR7hhpI70p5C7uNwYUiOep33H95HNHWQN7VhFRBvO5i/OecgJ2gwYNEnUjjp9CbmiPpk6drk6dvlDnzvPVsOFSVa26VLVqLVWzZiUaOrRUU6YUa8aMBaYNZJULkrIwLtQrVk+hD2KNlm2xxRY6++yzTbpd6y7tCO0J5SQL7Bgwsp8Ng8ZCuMT5lsNuqpEuhPGI4z/sBoxIK31NFuFRTqx0EX3E8P+SPJNW+rGssCM+9DmElzZupIP4of5AOQn30eH+OMlzJPmgENHIHnTQQdpzzz11wAEHmHnII444QpyYCWbnTZfDkg8UrQiHnXIhFyjvUWiDYmmUrj744ANDgqgcwW/23zQSn3zyiSENdA5UXteTsOg80UXh367hWH80iOiyQKDsO9craSNO6OLQGLmGE/RnDchlkVb0dVhWCJnhPvgfl3uwQ/fnu+++Sx0W/6fiUMYINyo+4Eu86QBY6QXGlIegWxou9JB23XVXY7uDzoDpF0aslJug2yT3kydP1+DB4/Tss5NVsWKRjjxygbp2Jc5M2SQvz6SBJfIQtyTxyOeW8oEkFAzzuUnynjKCrkEY3yRhWLfEjX2nKHtZlDvyGOIGobH/cL1SpphKxt4H2E2cOEO9e89Q7dqztdtui3XkkSVq165Y33+/UD//PFPTps2MzG/qAEYd2YDQkg8kbtWrVzcdDB2XSxypC7R1lJO02JFW6gzEzZIolzhZP4RHB0r8signhEtYDAazCI80IgVFd9EV/2BaKW9ZYUd8GLhRz9LGjTiSF7QnlJc/nXzAEimQjHZYd965c2cj4kP0x0lE+mNpx+GAQMCmkJ7ApuhMadiuuOIKs0IAlsUBSaGBQvJCocmXaAoS8STj6OSpqK4n/6PhoZNi3tc1HOuPzKezQmHWvktzJU7M+8Lg04Rj/cLcycss0gp25CXpzSI8sCMfssSOcky4Nv3BKyJUiO7ll19u9lnBjg3YBN1QvnCHLhKKpCw/R2+JRsg1zUOHfqcuXYbrkkt+1L77LtL55xepY8cJGjLEvRxTF6gT5G8w/q73EGh0E7i6hhH0B16UExrI4HuXe3CnzpJWyqBLGEE/YEe+W+Ib/Jb0nvLCBnOUq9wg5DuR3199NVzt2/+mq69eokMOWa7DD5+pa64Zo/ffH67+/VfNd9raBx54wFhJhYCgG7LjjjvqrrvuMu1w0nhZ99QF0poVdrRLSKGpI/YfrlewIw8ox1nkK/FgkEoblUV4pJW2mLxJW45tOckKO+LTs2dPYWWXsF3zwPojDPIBcpmvH3agAtHTLoilYHSwdaQgiF0RbyJ94AobYtQMgcAN7pMcloAgEsIvIiwUULGNgCiQ77zr0KGDGjRoYKZUICNRB8yOxgx2RliE6XqSTtJFA4R43jUc6w/swIhRmX3neiVtxIm4gY1rOEF/jBoJD3F68L3LPdgxGkCknkV4YEfHkgV2pAfsqJCEG04fcWf0jAQDewusPkC6QdmjfFHmrR9bXulUOnbsaKQkwe/WXZzrnDlFGjiwSNddt0j7779AN9ywWGPGLNPcuUy1uJdjdHkgbYxU0oRj/YIdgw7qpn2X5oo4mBGoK27Bf1PWGCghscii3IEdeUvdCP7H5Z6yQvsIiQ5it2jRYs2bt0yTJ5fos89KVa9esY48colq116sdu2KNGxYkWbMoG3MlQFwIj733HOPkXYgMX744YdNmim7LnHDD+0I9Z9ykiYcwiKtSK6pR/QPrnGy/giPeJEXaeNmw4QUIdXMotxRTiAy4fbB/ivJlbQieaKzzwI7+mmmNckL7pPEJcotYUCMKMt/OvmgULLipFWrVobFwqSo3PwYqQgNB0wcrWusnVKArcQiiiAE30EsCIMCwEnCyEDIB0bMaEAgGmQEzL5du3YFlVvxyyiKBpKw0xykD3YH0yOOaQ8KFQ0jRC7tYXGjQwazLA6vcJpDETwpf1gkZfdRFEnZBh0FP/IPSV34KGRkLOw2/MxqB1bUoVjK7GXVqst19910BNO1cGECzdJwwP99prFmNAshz+KgbjNqpGHK4qBhZDoi7SoB4kLeQHqRgEblU5L4Usdok6hj1I20B+0Y4dA+gWG4faK5AtLx4yWso7Kc+uSTpfr1pY4dpZ9+ylm2RXkVBVTaRggvgy3aPd6Fw0wSZ9onpACUk7SdisXOL7VNkgM5t5QT+lz6VfI47UG5WGeX2sLC2Fju5JNPNkwbETPEgI6Zgtq2bVtVqVJFzzzzjOrXr282TIKZxzkopDBkxFaIIhkFUZkYZdIBUAk4mYpB9A3bKnR48lEIncLfPPnI4QNxZbksxsAs+cDewt57720kOVHE2pV8sA8L9jvYmr1uXQnDYW3aLNX48dM0aVLhjeUK5+bKr558rMQiyZ3tQFcX+bBxg4RASGlC2ayOVTHYdmncWOrVK2fhlvEGbhgI0rHkIwt0ZJAKJC2clF3eRR2efEShEu8ddQxJCpLUtCTak48A5hAJVqOwKRJMG5ErG80hCYGd0VBfffXVBnQroUC0GOcAaERLzz33nC644AKj68GSXuanYH+wNkaiLD9jnqk8CYQnH3FQj3bjyUcOFxpy5pf322+/FUp9rGg544wzzMiVMhk+XMgHnQx7grz1lrTfflLt2rn9QebNi7erbTgO+Z49+ciHTOH3a4p82FhRPiCnCEqRhBx9dG7nYpZdszyXQfHQofnJB/GHbHz11VdmiuaJJ54witCQDL6FD08+wojEf/bkIz5W+VxGrnaBfDCt8sILLxhJB5IQlJNYoYKYjt1uWYZLgUbkidlozEnHPWjsYYyISjmtvoYVI3KFtVM58rF2+y9PPiwSya+efOQwoxxTHlFIZVUBc+psAofeBKOaqIY7KfmAv4wblxvZHn54bg8Qpl0w2rtkiScfyUtvzse6PO0SlWZLQObOzU27NG0qnX66VK2adN99lJ9RGjz4FxUVrTo9R3vJYBFF6O22286cRx99tJEyR03VevIRlQPx3nnyEQ+nQq4iyQcdOtMuSDggF+gs0BCzyRxzvxjCYboFYsB3GDYrANbE4cmHO+qefKzEDsLLfD8KwkwHUq4L6TjEJR9IvNHHHjVKatIkt0cLlkt//DE3309nQwcKweefafUWSJGXfKzM1yR3kMzVqfNRXtwgrKiesJsxxION644/fq7uvHOe+vdn0zqIK2b/cyExfYixMpSmWZLLyXJwpMhIm8OHJx9hROI/e/IRH6t8LiPJB1IHlhHVq1dPbdq0Ufv27c1KlLp165rpFzaY4xtzj4ir0cJmOdmaODz5cEfdkw937OKQDzqPOXOkYcOka6+Vjj0214lg3TJ4ePIRRCPZ/f+a5CMq9ZSjP/6QevaULrpono44YrHOOqtUL70kff+9hF4xFgrmzPlD1apVM0bwUJqGfLAsl0Ek7WT48OQjjEj8Z08+4mOVz2Uk+UDUjFIohZYdFjnZDhxlp9dff90omjIFg4iaeXFsI7Asak0cnny4o+7Jhzt25ZEPRqNMqfTtm5u7r1RJat9eitghwEs+3LPBYIfEaF1c7eKS7P79h+vtt3/RBRcs1557SkccIbVrl9v7Z+bMBbryyqvN/jAoTGMTBN0lbLQwoAwfnnyEEYn/7MlHfKzyuYwkH4gfISCI8eig6OC5R/mTuUPmx6nwLIPFEipLU7MQF+eLZKH3nnwUQqfwN08+CuNT6Gsh8gHxQMr99tvSqafmFEsZtTKPzyg2fHjJRxiR+M/rg+QjiMbXX3+r0aMnaNq0Zfrkk5xE7aijpPPOk1q2LNaAAdN1/fW3qUqVY3T88cebgSJtZJTStCcfQWST3XvykQyvKNeR5AOHdvkPRp7sklgqOifAIxmBkHDPuyilvKgfZv3Okw93RD35cMcuH/lA/P3zz9LTT+eUBFlOi74Heh95Vjya+uN1PtzyYn0jH3ap7ZIly4yNEDb6ZsabclatWqlOOWW5Wreepo8+Gqthw8ZqxoyZkctyaa8ZRGI9munzQvpNcXLG6st4Ox9x0Crrxva13s6HWO61zJALTO9i3rxOnTorlh1iBAXLbphdXxsOTz7cc8GTD3fswuQDaYfdSh3lwKpVpRtvlIYMyS2fLPQnOlBPPgohlP/b+ko+gnY+MFTG8lxshCBpO+EE6fbbZSQjEyfmlugGd0Wms2OFIfaV2LCO6XU6PgaSrocnH67IrRzoe/IhCus8Y7W0Ro0auuyyy/TII4+Y/S7QmOZEAfX888+PFOW5Z4GbT08+3HDDlycf7tgFyQcSDYxAjRghsZJl772lBx/MGYfKJ+0I/tmTjyAaye49+ViJFzZCMFT2+OM5qRt6Rg0a5Czpom+KVK64OGcL5KWXXtL+++8vNqhjOwGWliO1iJqeWfmH/HeefOTHprwvXvIRQIhRGLY7MCyGeWmW2SL9gHgw1dKpUyejbMrUC8CtycOTD3f0Pflwx86Sj8WLl5hGHRt7iL5RAHzvvdzqhCj9jqg/evIRhUq8d558rMQJ6RtlDknI6NHSs8/mlJ0PO0y66SaJvUDnzCnWlCm/mo0R//a3v61YksvWAi+//LKz9MOTj5X5kPTOk48AYpAPjIw1a9bMmFRnmsWSD8R177zzjnmGiFDoXA4Ah2Xbk+dwWHyjcSlkItiTDxf0c348+XDHDvLRv/9gTZmyRO++mxN1n3aa9M47+RVL8/3Nk498yJT/3pOPVTGiSWY7Isz4sxT33ntzSs9MBT70ULE6dpyivfc+Uhtu+FezjxHLcv/+97/r3nvvXWVvEdpkpniYkmHBQb7Bpicfq+ZD3DeefASQwsz5u+++a6Zc2PYeq3mnnHKK2YeFDauQiLDviquIjsLM7oLsocBKGU4kLCwHoxCz0oY9XZgDY1dDlKLoKKP+58lHIOMS3nrykRCwgPOxY3/W++8P0yuvLDX2Oy6+WPryyxzxCDiLdevJRyyYIh158hEJi3lpJSEYKqNsMiVYvXqJTjlltrbf/mL95S/bq0IFluRubLYWYDuL4D5GtMO2fX3yySfNFhiQ7qAb+3dPPiwSya+efAQwg+Gyi+0NN9xgJBwoJR111FFGMQkrp9j1gDC4HLaQvvHGGzr33HPNzrXsXouUBeuSEBM6RXbVxYQ7u+YyBcT2wFSG8GErRxopjA2Tf/tdbS0aya5gh8Rs7Nix5e7HEydklgGy6WAWOwJTbiC2KNih4R9VjuLECTc06Ii1v/rqN1133TgdckixLr9cGjs2Z20ybjhBd558BNFIdu/JRzy8mI7B4F337tKlly7Xfvt9qq22OkubbLKvtt32UN1331OaMGGKSkpWSrKpK5hS2HfffbX11ltrt912MxJxzCyED9uu+9UuYWTKf/bkI4QRgGA4rKLygAAAIABJREFUjJ1mzz77bLOLLQqo7OtCh8B3lwN/6IqwSd3TTz9tJB0UXHtAItik7sorrzRSDzqK4Hfrzl49+bBIJL+uD5IPyhuNKFI2tgFgbyKeXQ+U+phPr1OHBny5brqJJYvR9jvi/sOTj7hIrerOk49VMSn0hqaWZd89exbrrLOmaaedvtPOO49V27ZF+uUXpM4rfaPrd8QRRxi9EKZmOPfcc0+9xc6IocOTjxAgCR5po5ht8KtdAqBRsRkx0sGz2RwjW1bCMMp1PQCa8Ng1lxOCQydo5xP5B5IWpB2waFg2ZCVqyoU4ePLhmhPrx2oXpu+effZZ7b777tp222211157mX2Lova6KIQkjTZGItkMjo2+Dj98rho3nqopU5aZBjvAnwsFE/nNk49IWGK99OQjFkxlHDFuXLSoVBMmLFKzZuNVp84sVa68TPXqSa+/nrOWysqYjh076eCDDy5DPnbZZRez5UaZAI1EMLcvjpd8hJEp/3m9Jh8kHsulMC8MirGDbaGTKRCmZVwO/gXZYHO6Cy64wGxQB9no1auXITcYvDnzzDONhOXhhx82e8o0btzYSFui5hoxq8xmd+iQEC5ExZ6wySQnyrRUHhRsCTeJ3yi3EClG2uBFnKLcxH2Hf+LEdtkQwbj+Crlj/pbwIHBp4wd2P/30k5EwEF6h/8b5Bnb9+/c32MVxn89Nt27ddOihh5o9Lhi5YXb6oIMOMiu28vkJv58xY7Z+/HGBOnVapurVi1Wlynw988yP6tixr6ZNS48deKHzxLRjFthB6En3uHHjUucDWFDu2LuJPElbTgjP6npBAMNYJ30GrxEjRpiylxY70gZ26JhRN5LGJeye9ggpMftkgWEW2KFzR3tCfQv/L+nzlCnT9NlnfdWjx0Q1b/67atSYq2OPLdJll5WoW7ditW/fX4ceepz+9rfN9Je//MVsUkfdef/991f5N2mD6NNvgGHSuITdgx3ll7Y4i7QSP8JiWjiLckca0YdkcJw2PNJKeQM7pv3DWCR9JrzvvvvO1DPuk/gHp/BJ+rD5RZrTCB7CfMFYOGVqA1E0+hVsGgcpOOecc8xyrFNPPdVMu9h3PNsN5sKBxXlGPAfR6dmzp9kJlzlFjNxgTwT7ITQktWrVMqSDSktD0KRJE6OJTeMSPqjUbIVOJzpo0CCzffTgwYNNRtLIJTnx98UXXxigCSuJ3yi3KMuiZ9C9e/fUYUEKiRNKYXTKUf9L+g5swTiLtIIdeUpaswgP7CjwabFDl2jnnXdeodXPZlt77LGHUZouD6+hQ4dp0KBh6tTpa91xx3gdd9xCHX/8UrVpM1adOvVQ585dMkkreEG+EXNngR2bPVInCLO8NMb5PnDgQKOAzjWO+/LcQIyoF5SZ8tyW9x28qLOkNSvsqBN0VOX9u7zv1FnapQ4dOmQSN/7XtWtXUyeywI46ZtvY3r0Hq0OHEbrzzumqXn2Zjj56uerW/VFnnvmM/v3v4/Wvf+2vypWPNH1EVJ0krbRLTJlT/srDprzvhEf7RDnOIq0WO9qoLMIjrbTFlBNIQ3npKfSdtEIqqRdcC7mN843wIEbkrUvcwCd4Uq/IB4hR5uQDaQTTHgQO2xw1apSpNA0bNjSWTSEIKP+RcQ0aNNCFF15oAAoTAZdnyAgSDXRLUHAFOJb1Uml5zxIvCAnkB9YaPiAkNGSwY9yTDtcTUgQDBXiml1zDsf7QXwFLq4Rp37tcLRYUBIiiSxhhP4xkSSsYp8WOrciRhjF6t8vywv9L8sx0H1KjtNjRKaEszSZb7PC5ySab6MgjjzQNZKH4YL9j/vwlmjJlse66a6kOPLBYZ59dqnHjirVw4VIjqaAByiKtYGfrXhbhMXKhrjISLZTGuN+oC126dFmxv1Ncf/ncUZ+RslLf8rmJ+x68kLiBHzjG9RfljjrAKBGSRd2IcpPkHSbLkVLSIdMWpK1j/JvOhC0v0qaVsKhj1H/KiQ1vwYKlmjy5RHfdJR12WKn22KNIl146XV26TNDw4VP0++9zVFS0ahtrsaOfYLSdBKcot2BHvMiLLMoJ/6DtRFKRRXjUMSs1Rjk+Kg1x35FWBtFItLLAjvhQRsgLwo4bj3zuCAMyQ35kTj7o0CEBBGznn1lt0qhRI9PIWnCJBJX8tddeM3oZkBaXg3/ZgzAIF9shN998s+m8WE2DmJcKQaVlPwMID41M+IB8AAwVCb0QwnY9STsdKP+jMrmGY/1RyOk8mUoinfa9yxX/xAnmCy4uYYT9IE6jg6fQpY0f2NHQUuizwo7KCHbheCd5plywq2eVKlX0r3/9y+zQzIaI5WG4cGGpRowo1bXXlurww0v16KPS+PE5+wmsCECcTmNGWtNiB/50djSM3CdJX5RbyIJtGKO+J31H/WQURTuQ1G+Ue4gH00y0N1Hfk7wDL6ZcabzTYkc+QmYYAFE3ksQjyi3tEeEgmQHDtOWEf9i9XahvUf9M8o72ifpPG2rDo2yj0sdWAV9/LT35ZImOOWa5KlVaqttvX6YBA4o1e3apWRUT/BdpBTsGW9S54DeXe8IjXpAtGzeXcKwfsKftpI3KotxRx5AcQVbThkdaITNgR39n4+x6ZSbDChHsgg3XsPBHGEhlLXbhPtj1OXJjORpCa2QsvDIA0BGHs0zWFrIkP6cQwO7IOBpImDc6GxAPpl2QYNBZYO6XEQMj15YtW5r4UJHDBwWUym0zLfw9yTOFCHLFMmIasrQHjTWNbBbLRSkExIkKRKORxUE+0JjZyp0mTLCj3FhJRZqw8At2WSy1pWLTQCCRQYJHx8cz5TDfgXGmPn2kSy6RqlSRXnghZ7Y6qGdtJWRZlBPwt+SD+7QHnQDiW+pSFgcEizpKB5rFgV4VAwkatbQHeEHaIB9psaOOQUqpY9SNtIdt62ifLCFPG6YlH9S3tAd1DPJBOYkKjyaQIoSS9Q03SDVrSiedJD3zjDR4cG7nZqKBX9physhTTz1lpg9oRwvVsfLijl/iBfmIilt5/qO+k1bqWRbljjqGVIb+MW14pJU2ibaJ/jXtQZvHoA0yw33agzCQpK4W8kFBwqgMhIDOBEDo8ACcRCH5YG8XO3pMkjiAhkS0bt3aTOHcc889uvHGG41dDwosDQgNyeuvv67bb7/dbGz34IMPGkXQqIbek48k6Jd1uz6QD1JMp0LjD9mlwc130BfCbzt3ZimtdPLJUvv2OUuRYa7iyUc+FMt/78lH+Rjlc7E6yQdxQEgNwYCEdO2aM9N+/PHSeedJrVtLw4eX6ocfZujxx5/UAQccoB133NGskHnuuedSdcyefOQrAeW/X6fJB1IEJA61a9c2S14RuVilGEaPTIugyEej7nIADowR7VkIB2QkPGqB6EBCYKrcUxijDk8+olCJ986TjxxOFGMEDugzd+iQ25+F5bSff557H1XMPfmIV8aiXHnyEYVKvHerm3wEY0UTPHu21KVLjpwffLB05pnL1bTpUO2++77aaKOcuXZWlLGknZG3q7TMk48g8snu12nyQeTp8NFwxcBY5cqVdeyxxxrFvRNPPFGW1SaDpKxriAsFzJ5lv+ZGq/ZbIZLjyUcYufjPnnzksELiMWmS9PDD0v77S9dcI40alRvx5UPTk498yJT/3pOP8jHK52JNkg/iZCUhkJAePdhMsUj/+ldbbbTRdqpQYUOzqowVZdtvv72ZDqcfcTk8+XBBLednnSQfdPL2tNIJFDCZi2J+izkznq1yJ0m17t2hSufTkw93/Dz5yJlER7GuUaOcxOOOO3JEBCNLhQ5PPgqhU/ibJx+F8Sn0dU2TDxs3pCAopf7883I1bz5MBxxQWRtvvKkhHxtttKkqVqyssWMnqKho1YoUp8+w5AOdQK/zYVGPd10nyQdTHOh00CmhRGMLCYmhAFAgeMeVuXMUUFCmRFlmTR2efLgjvz6TD/SwGJQNGpSbv65eXXrqKQnbeXF0jT35cC93nny4Y7e2kA+bguLiUv3++2y1avWCWcK+2277aPvtj9LRR7dV167oCBYbksIqGvoUlmsyiEUhGsV++o4wueAZJWIWHLRp02aFO/qdNIdXOHVDj/7/T1c4ZY6OTd5QKKVgUFAoHIjOUDhF8RT9DAoG31955RXdcccdZn2yW7LS+/Lkwx3D9ZV8oEDHYoaePaVzz5VOPFF6800JRfO47ZsnH+7lzpMPd+zWNvJBSiAF9A/YvWnS5CnVrz9ENWr8oSpVSvXII1LfvtKUKcWaPHmG7ruviVFIZbuD6tWrG6Np6P8xqLUHg2B2Td97772NAmu1atVM5xeewsEPhAa9EgbDkJZgODY8e/XkwyKR7LpayAeFgOVSxx9/vA455BBj4ZT9V6zCKUqoPJ988slmwyH0P1hBwKqXNXV48uGO/PpKPtDcf+cdad99pWrVpKFDc4qlSZD05CMJWmXdevJRFo8kT2sj+SD+dPr0A+TtjBnzNHGi9NBDUsWKufPOOxfp+ee7afvtd12x1cHGG29s9AkxOkcHZ8Np2rSpsUJsN7NDh4QdzsN2niAe9Fkso2dZPn1B1IpIi68nHxaJZNfVQj7ITKQbSDY6depk1mxfffXVwqQ6LLVmzZq66qqrzEoXbHGwUsUaz0mWnOxce/LhjuX6Rj769PlKo0YtUtOmOf2Oyy/P2SuAOwcGXrEA9eQjFkyRjjz5iIQl1st1gXzMnTvPrB6bO1caMEB68EFI/gLtvvs72mQTFFMrGN0QrA7vu+++ZWx5QGKuuOIK7bDDDiu2RICEMNBlvxJ70CFij4XtQHbddVezhQK2p9BNDE/jWD+efFgkkl1XC/mwUbIkhKWuGMnC0iSFniuNLlMviLkKibhsWH/21ZMPd4TXF/LBfPOcOUvVvv0Q3XXXEqHfcfvtOYul2M1KSjxA3JMP93LnyYc7dusC+QgaykJ/avp0aciQxbrwwu7aZZd9zBYHG2xQQZtsspkOP7yaRowYXUby8cQTT2i//fYzm0BCVNgSga0+qHP2QMqCjSj2bWLTO9xtvfXWxjYVqgJR+iGefFj0kl1XK/lIFrU169qTD3f81wfygTQXfej+/Zfr7LN/MxtmPfmkNHWqG+mwaHvyYZFIfvXkIzlm1se6Rj5svJcsweT3NN1008069NDK2nXXfbXddtVUp867GjiQnVRzZt1xj0T9pptuMkbL0A3BzANWYoM6HxAMpB6bb775CgkJkpSTTjrJLITw5GMdtXBqC8yfeaVwIGGxJ+zKSlIKfQvHyZOPMCLxn9d18kF5odzYMmTLj0UA5VFEv716STVqlGqffRarTZsSYT497eHJhzuCnny4Y7eukg9STP3EgOWYMT+qbduhqlnzZ+21V5Hq1i1Rt265AQFL3JcvL9WsWbPN1htsOIp5h7CxMiQfjRs3NtMzbBjJueWWWxoDmEjmPfnw5COyllEw2EgH3RKW9nKi4YzGNJ0JYjsKHO9ZyltIt8STj0iIY71c18kHDRBlg86M6UFGRpQfDojHH3/kFEuZZqlefamaN/9Wv/++RP91EgujfI48+ciHTPnvPfkoH6N8LtZl8kGaaPvRyVi0aKmmTFmuDz4o1dlns4Nuzmrqhx9K06axt9NyI8FgD7CofXEIByVTdju3Oh/nnXee2ezR63ysw3u7UEhgqbBNWCT2POiobMGhMHC6HISLvggKq6eccopq1aplziuvvNJsc06Hwuqa//znP0bBlSv7yLDOOKpQefLhkgs5P+sq+bBl6KOPPjJlhD0lKlWqpEcffdSY7Kdo/vyz9PTT0rHHskFcqYYNW6zPP++nBQuy2RzNkw/3cufJhzt26zr5CKacQQC2dtgt+vnnc/Z22Mjxttukjz4q0dChM9Sv31AtWxa9ASH9CFt0sEKze/fuZrAa3mCUtoK+il1en376ab377rtmoMJ2HnxzPRjo+I3lXNHL+Yvc1dZKH9hR8OGHHzbKPvfee6+RSJC5vXv3NmTA5ddkOBZSMdF+6aWX6p133jHn559/bkaxzOWxuy3zeewjQ2Hp0qWLKWSI18OHJx9hROI/r6vkg3JAo8OS7//7v/8zc74onUFAPv98gEaMKDYWS1lGy26c331Xqvnzy99YLj5yXuE0CVZht558hBGJ//y/RD5squ306DffSC1a5HbPrVWLVS8L9fLLYzVpUrHYyDvKBg/9CYNSyASD4/AB8cAmFRIS7IZUrFjRrNikDIb3Ewv7LfTsyUchdOJ9iyQfTH8g0qpXr57OOOMMnXnmmWapLVsc09ljhIwluFbEHe9XOVcUEKQpzZs3V4sWLQwrpYDQoVCQ+Ma2zGxcx/9Yt03hysdSiU+PHj1WmHwnfNeTfzHdg1a0XULsGhb+wJFdgWHdacLBL1iDExv8UfDThod/sCathJs2PLBDQjZmzJhMwgM7Vlcx9RaOG//i2z777LNi2R7L8bbZZkfdcENrXXXVEu2/f4keeqhEkyeXaOnSEpOfffr0MXkSDs/lmenAQYMGZZJW8Ae7SZMmZRIeAwTs71A3XNIW9kNd+Pjjj43EMvzN5ZntGpgmsx2GSxjWD9ghhWLalnJh37tc7aCLOkbdcAkj6Ic2jXBonxilB7+53lNfaU/SppX/I2VmuSrlJG14YEe7RN5S/lzSV1xcosWLSzRmTIluv71Ehx++VJUqLdRTT5Vo8ODczrpINbGqGjd8ygXKq5tuuumKVTHbbbedsVcVFU/6GrDgJP/y/QfVAKaEGCzjJ5+7OO/5DwNBjHxGxSlOGEE3xIcygv2TQmkI+il0TxjMRtBGEXZWRyT5YIntM888Y7a8xwAMUx516tQxFQlwsAHCc74lTYUiRyIpEEhSHnzwQUNyAAkdEBJGRWAJ1X333Wcadxgq7gEg6sA9Zni5UsFpKF1PKg+dHZ0K6XQNx/qzBnBIg33neiVtxAlRH1i5hhP0hwVbm9a02Fn7MJSXrLCjYYTMBOPMPf+ioh544IErDBZBPv76139r2217qGLFJercuUjTpy8y0yykDWkb5Zg8CYfn8gypxER0Fmm12NEhc+8Sn6AfOjwaC6srFfzmcg92bDKZFXYQR/KPzs8lPkE/4E9eoD+WFjvKCZ0AnQoNbfA/LvcQaOoY7RMYuoQR9sNeJ7QntFXhb0mfab9pTygnWWBHu0TeUv6SxiXofuHCIs2cuUhffvmbzj13jPbYY7EOPrhEjRuXauTIEs2du1iLFsVr5yGSTO9bg2VckZZiE4R0k0f23+Q/+QW+dN6UheB3644r3xjM0FemLcf8g/KGHZO02BE34gMJJC/yxT+YlvLuCYNpLbD508kHQND5s94a8TYgW/JBA9SxY0edddZZpkLlk0hEEQXe4R5waMyYenn55ZcNCUHng4pAJWAO78UXX1Tr1q31+OOPmymYfv36GXIRDpfMJyxGelRMporsSeeV5MQ/S7r4P51yEr9RbkkPmcbIJ+p70nfEiSkoGsekfqPck6+MaEl31Pck7wiDzp30ZoXdp59+GokdDQodP2WjcuUjtc02u6lChb205ZZ36IgjftATT4xVr17DNGTIyvwnTpRb8iRJuvK5JZ3kRRZpBTusB0MYssgL6gp1gunRfPFP8p40Mv2ZFXbdunUT06zU0yTxiHILXtRZ8MsCO0yEd+3a1bR5Uf9L8o5ySrvUoUOHTMoJ/yZulL0ssKMdITzKSVbYQbQof0lwinI7ZMhQde/+lV57rateeOF7XXbZb6padalq1Fiqhg2n6fXXR+jLL7/R0KFfF/wXbXndunWNrRBsgXBus802uuaaa8rkMflOX4R177322svYGalfv75pH6PKPe7ROSN/0+aFbc+oF1lgR3i2H+M+Ct9C72z/aa+UjQ8//NDMCvzp5AP2Red/3XXXGWDpoFD8xLwtc45PPvmkmTdD1JaUfEAekGJAMmCPSCwYuaAM1KRJEzOS5BssmmkXRkgUikaNGhl2GEU+6KQQWRNvwrQnYcDu4578D9ZLgYLUxPWXzx0kDrxgoEnjEg4T/8SJuMFAw99dnhFX04mTB2njB3aM3CnUhOcSn6AfsKNxZPov+N7eE98xYyaoQ4ehuvzyXtphh6909tmT1bv3XP3yy9wyfix2dHiEa8NIc0XCQ4dHnqTFDrzADglgFtgxYKATYPSWJo3WL2mEuCGBTJtWwqRBZB6e+mr/4XoFL/KCtiktdqTNDrbshpmu8cIf7RCSVNrPLMoJYVJfaU+ob2nihl/qAu0J5SRteGBHu0SHhUQhbdzAjnj17t1HU6fO1I8/LtQXXyzX5ZeX6phjlqpq1Xl67rnZ6tNntsaPn202t2N5bvi/pBGyhoXu3XbbzZhtRxJCh2rLC3HnX1jwhpigP7bRRhtp22231QcffLBi89Rg2JQTOngkbmnLMWmlLc4KO+KDFIV6RtjBeJd3Dxb4CZ6ERx9Lmv908oGYhUYfvQ46fTaPO+aYY/TSSy+Z6RIURclQ18POL0FcOJm3ZfULc3OAEyQ1gEAjjwIqDUL4oABRCBC/uhChYHgAS8WhYWTOL+2BGI9OJSreScMmbcSJzp38yeIAW8hRWs1v4gJ2dE4QyaywowxGYYeSOpZJx46VMZV+1FFSw4bSiBG592FsbBmjoSVPsjj8ahd3FCH4kIV8U6lJQqbs0gHQuadRIOSflBOkstQx6kbag3aOcGifaOPStk/E539R4TQKZ7CDENEh2w5v6dKc3gf7Ml1wgcTKmGuuyS2np2vApk9YJQHMmVaAoN55551GnYDyF2zzcMPg9eCDD16hwM70DJZVX3jhBVO2wnFk2guJCDMBacsxaaXfY6qEgXfag/4T0svAnfu0B2Eg1YbI2bxIGyb+I3U+yAwqC8wJpVMyhfl1NptjaSyiLNdI2MJAJ0ABoKOCQLRq1UqPPPKIIREQCb7xD8hAu3btTMGhgQkfnnyEEYn/vC6SD4gHvHDMGJbQSgcdJN18M3YBorXhQcOWZ08+4peNoEvaAuo8jXgWhycf7iiuz+QjiNqcOdL770vHHy/tuqt06qlS797SjBkopFLng65z9/nMq9M+QHSYcvn73/9upmaQfqAbgpEzRv7hw5OPMCLJnyPJBx0/gNM5kSmIW1D8YxSKWIZGiAxzOWB5jBqZr3/ggQfMVAuSlRtvvNGwesgEK11Y4otCKsqnbGaHNIJ4hQ9PPsKIxH9eF8mH3azqpJOk446TWrXKNTgRq+xWAOHJxwoonG48+XCCzayA8JIPd+zCko9gSBAMBMDY82nXTqpdW0ICevXV2AjJSUjCUpB85INwGQwzxYKEf6eddjKGy5C2IxGJkuR68hHMDbf7SPJBhXn22WeNHgZiIAgDoiWurqTDRg//ZBxLWpGsMKUCm0dkz3QChYAMh2ygEIkIFLEqBSDq3558WGSTX9dG8oGID8kXilctW7bU66+/bvK/qGipsXyIGeaqVaX//Efq0iXXyJQnWfTkI3nZCPrw5COIRvx72ktPPuLjFXQJdoXIh3XLIkgGJD/+KDVvLp11FjvoSrfemttWYfLknKQU94XIB+0OfR1TH6gXMFXG1CD9UVS/48mHzQH3ayT5YHqjadOmRteD+yjw3X+Z82kJDdIM7oMH/4PsMO1S3pyVJx9B5JLdr23kg3xnzh3NarbQZsdKNM/r179OAwb8ohdeWGZGOLVqSQMH5qwjxhHAES4dqJ92SVY+rGtPPiwSya6efCTDK+g6LvmwfmgHICHYA3nkkZxl49NPlx54gB11cybb+/X7WlOm5DfbQFj8l4EuZb7Q4clHIXTifYskH4w8kUhcdtllRrEUZRjAticSiihRVLxfZuvKkw93PNc28gHRZIoPbXS7WyUbRv3f//1dlSq10X77zTeKZiiX5TH7EgmGJx+RsMR+6clHbKjKOPTkowwciR6Skg8bOCQE1aSRI3PWjQ8/XDr00Jz59jff/E4//DBdRUUYtLQ+kl9pT+gjWXmEeoKr/qP9M2n1Cqf/RYPRJ1Mi6GGwnTFWTrm/5ZZbzIkNEJa/rg2HJx/uubC2kQ8qMauDjjjiCGORMGcYqII23HAT7bHH03rssT+UlHiAjicf7mUEn558uOHnyYcbbvhyJR/4hVgwOGHhCBJSFNL331+qVGme7r9/sX74AUuq0UqpcWJMO4XaAPZbWB7PoJz4uh6efASQo7FhHfRDDz1kFD7vv/9+c48SKCtSUAhlBcracHjy4Z4Laxv5oBIyzYdRILTOIR9//etftd122+vxx9/W5MkLFaFzXC4AnnyUC1FBB558FIQn70fKM3XML7XNC1HeD2AXR+cjbwD/3dmaVXDsktujh1Sv3iwdfXSRTj65RM89J40enZuqicsbaEdQB8BeEHav2Cvm6KOPNnuRYeOE7y6HJx8B1AAYNkfFoQCET1a8IB1ZGw5PPtxzYW0jH6Rk7tyFevfdntptt5racstK2nffw3Tttdfql18wcBNtYr88BDz5KA+hwt89+SiMT76vnnzkQ6b891mQD/sXOAGDlk8+GaFXXpmp004rNkt0zztPeu896YcfJJbu5luia8NhWhiSwV5nGCCzxsgwQ4F1YuqJy+HJRwA1QIZc0DkxpxU+PfkIgFXgFk1pb2SsAECBTzQQ2O/49ddSvfjiEh144EQde+xHeumlL818KITY9fDkwxW5nD9PPtzw8+TDDTd8ZUk+bCxY7TJp0jT98styvfqqVKeOVLlybnlu587SlCk5JfZ8TQ3TLVgOPeigg4wF1Ny08AZGSosxMlcDYZ582BySzJ4trDjAvgZGxsInZtcxsb42HF7y4Z4La5Pkg1EHy+JatpR22UW68MIidew4UuPGTXRP4H99evKRDkJPPtzw8+TDDTd8/Vnk49dfpxkJKu3N7NnS22/nLKXuvrvEKrq+faVZs6L1QRgAsRQXnTSsn1rygRTk/fffd7ae7MlHoJxgRAw7G6+++qratGljTvZ6Qd+DuS4UUL1K0sihAAAgAElEQVTORwCwPLde8pEHmMBrK/H4+mupQQMJ7fQHH8R0epGGDIk2rx7wHuvWk49YMOV15MlHXmgKfvDkoyA8BT/+WeQjuEO6VUrFRgjrJ848UzryyFw79PnnOeOFQSkI7QgrPR999FFVqlRJ//jHP7T99tvr5ptvNnvDEGeXw5OPAGpMuwAyduuZYuFk6gVT52z2heLpM88846xgE/hV6lsv+XCHcE1LPhh9zJ8v9euXG3XUqJHbqwUr+nPnFpn9haL2dkmaYk8+kiJW1r0nH2XxiPvkyUdcpFZ1tzrIh/0rBAOdDxRQ779/ZVt0773SgAHS1Kms+Mq5pi1BKZ69zZgBYE8yjJHRX7oennzERO6PP/4wWwlfdNFFRsGGzEh6QG7o+DCzzm6CnGxaE85AxFzMo5HZGCOL+pcnH0nRX+l+TZIPTB///ntuP4bTTpNOPFF6662cKJQihdQo38ZyK1MQ786Tj3g45XPlyUc+ZAq/9+SjMD6Fvq5O8hGMB8tz+/eXHnpIOuaYHBF54gnp++9z7RV6aQg4GJhjC4vFGPnsfNDu0NdRf+jLovov/u3JRzAH/gsIwIVPjKt07dpV55xzjpGIAFySgwygY2HDniOPPNIo76DAw1QOS9KCB4ZXYJgsvWS3VOISPjz5CCMS/3lNkA/yf/nyYk2fXqI33yzVgQdKJ58sffvtytEFKfDkI34+hl2yUg0DSDSMWRyefLih6MmHG274WlPkg3/nBj/S8OHonuU2r0Qx9cUXpfHjc3vK/PHHfA0YkH9XW9o5u0catkCYOaAeRREQTz4C5QQmx1QLe6ognQiemKhu1KiRsX7qsgIB8CEwrVu31jXXXKOOHTuaE+LBMiZ7EAf2dUHCUq1aNWPMJep/nnxYxJJfVzf5IP8YMYwc+YtuuWWqjjxyntmZlkrOevygEM2Tj+T5aX148mGRSHalbWKVH+0OdSPt4cmHO4JrknwQa8bULM9lOqZPH+mOO6TDDpOqV89tZvnNN/PVs2d+8oHe5Mcff2yW5e6///4666yzzLYRtH/hw5OPACJMdTCXhTQCU9fBs2bNmrr66qvNPhkBL7FvbYV86qmn9MQTTxgiAhlhysWKr3DDPFrz5s1155136vTTT/fko7TUmLSnYQxPT8UGP+RwdZIPWD/SK4jrQQcdrh13PEpVqz6kAQN+04IFq5o79uQjlFkJHj35SABWwKknHwEwEt5a7H744QfnJafBX65p8mHjYqUgLMNlOe5VV0nopp1++hLdccdYffPNIs2dW2JshFg/XEeNGqVatWpp66231sYbb6wttthCp512miG2QXfce/IRQATy0b9/f2O5jRUvr7322ooTk7Ksl0b3w+WwhYqVM5ALdrBF5wMJBmyR0TFhIxFhczumXZjiITPzST4+++wzoxdCp0yn5XqSbuIycOBAEwfXcKw/po1GjBghKqR953olbeBC3JBKuYYT9IekifAs+Qt+S3oPduQlehrEM+h/4cIiTZgwWS1bvmDWxLNfy4Ybbqzdd99bzzzzrGbNml3GPX7BDhP/WWBHeIw4MAREuMG4ud5DpJjaCKfVJTzwBztswnDvEkbQDyJeJIkoiAffu96DXefOnQ2GrmEE/X3//femPkOSgu9d7sGLvEBKmxY76hjYoVRP3XCJT9APUhT2KqJ9AsPgN9f7QYMGmTpBfXMNw/qjHaH+U07Shgd2DGawg8F0n/2H65XwMGFOP5Q2bjYOpBUpvkt4CxfShizSDz8sUtu2i3TSSQt0yCHzdeGFi9WtG4NlrNkuE20d/2vbtq0qVqy4Yjkuy3L32GMPU49sfOyVckJ5Y4VpFtgRHkuCyQvu7X9cr4RBP0wcrYDApe8P+4ncWA4SMGbMGNMR8zNYrT0gACiHUgmidDCsu3xXwqIDYOluw4YNjWSjfv36atCggemoaUAw7X7TTTeZKxkC+WDeLCrhKKN+9NFHpqOio8ed60lmMa1EY8F/XcOx/r755hv17NlTvXv3Nmmz712upI04ffrpp4b8uYQR9kNl7NatmymkWWDXr18/k15w5F8jRozU8OEj1b//aD3/fC/ts08NbbBBhRUVcquttlL16tVNAxiOG9hR4MEu/C3ps8WODpRwk/qPco+yGWJV8iQL7GhkKXsWu6h/xn0HaaNO0InG9VPIHWlEEppFneA/PXr0MOUEElLov3G+gVefPn1MJ5UWO/IRySJ1jPYtzv8LuSE8wvnggw8yKSf8i/pK2UubVsJiEEl4lJO04ZFWwoPgU/4K4RLnG+HRPlHHsignhEe+0kalDe+bb0bqo4+G66qrRuvAA3/XgQcuV/36RWrffrp69fpBQ4eOVPPmTwvLpxtttJFp77CGus8++xizFeH0Ezf6POpFFtgxAKTdpP3kPvy/pM+EQXsCSY3qg/P19eW9jyQfSCGeffZZYbWN0UnwgD0B0gUXXGBIBJKMpAd+2BUXkgPDZdSClOOee+4xDTlLmEgs8aAxYL6Mhi9qJ13IxyeffGKIEmu4eXY9GaXYjIN1u4Zj/ZGuIUOGmEqZNm74J/MpVIyS7T/SXBkxEh7hpo0f2CGdohIRHvH69dfp+umn6WrZcob22ut7bbHFBWXIB+vkzz//fJN34XSAHZIFGrTwt6TPpI3waHy4JvUf5Z7yaKULabEDL7AjTItd1D/jvmN5MmlFahTXTyF31AU60Kywo0OmkaXMFPpvnG/gBW6M9NJiRz4yMqZzp27E+X8hN4RHOLRlYJe2nPAviBZ1IgvsaEeo/ww004ZnsYMwUP4K4RLnGwNcyi+Dt7Rx43/Ej3yl400b3rRp043xw48//kKDBk1V69ZLVaVKifbcs0gnnjhDH388XX37jtZVV12r7bbbThUqVDDTLtdff70heeH0k1aknlliR79JeIQd/l/SZ8KgjwW3P418QAoQScHEmjRpIjaUo/LwU04qt7XzwQoUiENQKpKEhOCPk39CaBhZXX755SaRNWrU0L333muMmmHA5dBDDzXPNFjhqRcICgwPESLkBHBcT+JB48N/EDW5hmP9gSWNIgULzWf73uWKf+IEmUE65BJG2A+FkPDIx7TxAzvKCJ0o4c2fv0zjxi3To48u01FHLdcll8xWq1bdVLFiJW2zzTbGOM9JJ51kGlLch+MGdkgpwC78LekzaYNE0/gQblL/Ue6ZnqMukCdpsSP9YDd+/HiDXdT/krxDxE+nQqORxF8+t2BHB8o1bVr5B+0LHR6Dj3z/jPse7MgL8IsqR3HDwR1pAzsINHUjid8ot7RHhEP7lBV2tE3UCepb1D+TvKMdof5TTtKGR1qZgiRvkWwniUeUW8IjXnSgaeNG+OQtaYVIZ1HuKCd9+/bTb7/N0u+/Lzer9R57rES1ay/XkUcuU4MGi/Tii+P14IMvqXHje9S6dRtTTqP6FdJKP5YVdla/joE091H4JnlHGAgc/tRpF6ZRYIY33HCD2a0P5VIkHJACzssuu0znnnuuGa2iB+JCPPBDRWR+kPlVTpgy0zD33XefITs0nBQ6GndIyXHHHWdGXlTk8FQPmcYIlIrkEp8gYSJD7EiKApH2oNLQUGRlKIs4rQsKpzNnLtGoUdItt+RMF193nTRyJNN1s8zIDX2fxx57zKQFjKKkZ7yn8mSFHRWIaQ3CzeKApNJJZVFOaBgZmTE65j7tQf3yS22To0j7QedAHfOrXZLhZ7FDWgHBT3vQJqD/AGGgXc7iQGJEPQsPYF3Cpo7RR0FCCI8oskAKkwEYJ8Nu0QknLNc99yzQp5/+rjFj5mrevOi6TVohbAxUs8COPpKBDAPBcH/pklbCQAJlBzMuYUT5KTPtwk8AAXbduHFjQzxQCm3ZsuWKE0UavgO+ywHQjFII5/XXX9cbb7yhFi1amGW3zHvznYLMSaYieWGPGa5RhcaTD5dcyPnJerUL0yxff/2jBg1aqvr1c0vTHn44t2cLVgTJU/KXCgYJKFQxPPlwz1dPPtywsx2oJx/J8bPYra/kwyKGFgLcq0cP6dZbc+baTz1VatFCGjEit28M44uAGqVpE9d78mEBZPSFRAL2lMVIzIbLlUJK4wiZQNkJyQajNDrCMMPFLaJURGWMMHkOH558hBGJ/5wl+Vi6dJl++WW6XnvtJ/1/e/cBLVtR5Q1cMGJijHymGQcxixLkESQjgkTJUQSVKEFABBEJSkbAB4hkEJSMZAQcQAElCIogKjnoYERmHEQkvP2tX13rcV7Tffv06eZ230fVWmed7nPqVPhX2P/atatqypR/ptMiLU2z63ADs6BETormo35ZVn0W8lFFo/7vLEAL+aiPWfaZsXu+k4+Mh7u+D+FYa62IueaKWGCBiFNOGTs9t0pAiuajgpqKhHRgY1QthH/18oy6qakz4qUGp+LUURrl0mq0IxcKBilp9078hXw0LQVqwj8nuwpl3QnfOqH7/sEH/xQHH3x9vP/9P4wll/xTXHTRk+nclibEQ5xF81EH+fZ+Cvloj0u3p9pAmXbphlL79xm7Qj6ewUff99hjZFTEhRdGbLfd2DT0iiuOnd59550IypisNT3PJo2cbR2EPxNivV/k66SbdslZI0wQjJNOOilNvTjJ1kZjVp24s/tgkDoKrpCP5qUwCPLxz38+Gb/61W9ip512jbe97UMx22zzxZQp68Y119za1pajbmoL+aiL1LP9FfLxbEzqPMkCtGg+6qA1o5+MXSEfM+LiH4U9Lch990Wcf37E+uuP7ZS64YYRp576SJx00sWx7LLLxQILLBCf+9znkp1LPwPCSU0+WC1bX7388ssn24/tt98+FlxwwbQpmL05EBCbgI2CK+SjeSn0Qz4yq2dItd12B8Qb3zhHWs9uWdlb3vKW2GGHHZL2QqfUxBXy0QS1sW8K+WiGXRaghXz0jl/GrpCPztjpCmlC7ror4rjjIlZd9amYZ56fxpxzLhWzzfaKsPmilYAbbLBBMrZtpwGBc7c+dVKTD1oPmo099tgjqYFY9TqHxVQJdc7RRx8de+65Z1cQOhfD4N4U8tEcy6bkA/GwaMR85hZbPBhzzLF2zDLLrNM3D5ttttkScWWtriE0cYV8NEFt7JtCPpphlwVoIR+945exK+SjHna6xfvu+0dsueXh8cpXzjG9/zR4e9vb/j2uv/6mtFtqDg2+tCGM9Zk86B87mSpMevKBeBxyyCHJpsJypw033DDZZ8g8Q1GbQw1ieWsGt+m9kI+myDW3+bCz/jXXRCyxRMSHPvSneP/7PxcIhy2EXXYutTSbEGSz08QV8tEEtbFvCvlohl0WoIV89I5fxq6Qj/rY/f3v/4xjjz0x3vzmt4QdUMf6z1ljjjnmigsuuD3+9Kd/pDNjYKs/zGYQK6ywQtoZ3CZxFAKtblKTDyPiU089NU252PfC3h/2+7DtuMp14oknxmqrrVbIR2upt/xXYWamfT7wiIceijjjjDHi8YlPRJx55uNx2WU3pvowxxxzxJvf/OY0LWeHzU7MvAWmtn8L+WgLS62HhXzUgulZnrIALeTjWdB0fZCxK+SjK1TTPRiY2WzPQF7f6fC5OeZ4e7znPXvGRz7y19h33yfjqqsi7r/f+TGXp8027Zg6++yzx1vf+tZEQMxStA7wJjX50PHbNdA+HJbc2tnMXh9A2mijjdL9S1/6UlKpq3TDdEXz0Rz9utMuitjSMAZTxx8f8bGPRSAeN9wwtqb9r3/9n7TF9bHHHhuHHnpoMpiiFevHFfLRHL1CPpphlwVoIR+945exK+SjN+xsJWFLARsvWshx1FEnxrnn/ip22OGpWGKJabHyyhG77/6/sdlmB8WrX/266RqSl770pbHIIoskZUDr/leTmnwwdDGvZIrF70xGTMXYn/7AAw9MO4H2BvNz47uQj+a41iEf2Ujq/vsjdt014sMfjth004i7744ZjpHOK6Qw+UHs+lnIR/NyLeSjGXZZgBby0Tt+GbtCPnrHDlmgwWDewE7uySenpY3KLrssYrPNIt7//v+Nf//3g+OlL31DzDLLC9P0zMte9rJYYoklkuak1TB1UpMPQumwww6Lww8/PM3bq1h5vw1Cph91eu9FM/4XhXyMj894b+uQDxqPX/0qwtr0d787Yo89In73u2dvHKYB2LrY5nGFfIyH+rPfaVNle/Vn41LnCezygXd+9+OyAC3ko3cUM3aFfPSOHdnqbLLq9uoGfYxSKZBvuOGfscYa18cb3/ihePGLX5m0H69//evTzuDICuyrblKTD2eoOGXWihegDNoBm1YFcdDpumxoxngGkMiNeKWDgMzP26WjkI92qNR71o182Cb4iisiNtooYqGFIk44Yczmo10fX8hHPczb+Srkox0q9Z4V8lEPp3a+aBedd0KAtY6e2/kf71khH+OhM/478rDT9uoIyKOPPh0PPvhYfOc7V8Taax8Q//mfe8X73ved+NrXfhe//vXjaeVhNYZJTT5MuTAutWLhmmuuSUQAWaDOtQOgeaqmo1uV1LeXXnppbLLJJtOvL37xi9NPkzUHRutiT5HPf/7zcdppp6VpIKC2ukI+WhGp/78T+XBI0p/+FHHOOWMaD2cTUAE+/HCEM1rauUI+2qFS71khH/VwauerkI92qNR7VshHPZza+SILqwfLtfNT99l45COH8fTTdt/9R9x111/i5JP/GKus8tdYbLGnYqONpsX3vz82DZ6PspjU5EOldLzvTjvtFJ/+9KfTklurX84888x0nXfeeel00gxML3fkgzGiaR07ptKwuI4//vhkPIMB2kfkW9/6Vnz3u9+No446Km26cs4556SjkFvjKuSjFZH6/9uRD4f5mlY58siIxRePWGONiIsuirCiq0W7N0NEhXzMAEdPfwr56AmuGTwX8jEDHD39KeSjJ7hm8DzR5CNHrg+2x9Idd4wdVuf03KWWivjCFyJ+8IOI//5viwCeijvumGSn2uYMIgeIxkorrRSLLrpofOQjH4mllloqlllmmXQhDV+Q2wYOyyP0rIpw+Y+QuDj/H3vssekraSz1nTp1atpdtd15MoV8NCiEf33SSj5oNaxomTo14q1vjfjMZyJ++ctIx0V3i6WQj24IdX5fyEdnbLq9KeSjG0Kd3xfy0Rmbbm+GRT6q6bL1wQMPROyzz9i0+Jxzjp2k+5OfPBU/+9ndceutv2y8yWM1HpqUK664IhnF9js9Vw33BdU/+bfITLOwwCX8Xb/97W+nX2w02hGB/P14d+SCLQd7EhoPG6U4TEdhihcJYfOBAImHaov25YwzzkirblrDLuSjFZH6/zP5ePzxf8Y//zktfv7ziK22inQi7QEHRNx7b3eNR46tkI+MRO/3Qj56xyx/UchHRqL3eyEfvWOWvxgF8iEtpsht+njLLRGHHhrxkY9ELLro47H++nfFWWfdFH/969/jqaeabfSY8zqh5EOkSAJDT9MgDJKQDaRAY/e8H5sPZ8fYE8JeIfvtt1/azIzNB0tpcQjf2THbbLNNrLzyyrHFFlskktIuTkTGOTS+ZfVePX2319/33ntvOuUVy7ONfK/ft/q/8847E3m6/vrr+w5L3qTpv/7rv9LGZa1xNflv87jLL78ibrnlvjjnnL/F6qs/FYss8vfYdtvfxQ03PBh33TXjacbjxXHPPffELbfcEj/+8Y/D7/H81nlnn5mrrroqBoGd+GB30UUXhTKpE383P5bFXXbZZQOpJ/D6+c9/HlZZDAI7K47kle1Ut3zUeQ87mlBlUsd/Nz/syK677rrQ3rr57fYeXjfeeGOqe4PC7gc/+EHaWLFb3N3ea7PamGnqQfQn4tM3aRODwE5b0J+oJ/2GJ682VFS2ltt3w6bbe+FJ1+WXX9532nJc8qqd9ZtX4Wlj7CKtUMkD6BxPr3d5/eUvf9kYu/vvfyDuvPOB+OlP74/jjvtlzDffifGGN6wT73vfSvHVrx4fl1zy8/j5z++Ne+55pj+XZnm4+eabk9Ex+dkJF37JWAqI51zzgXgwKmX3cfDBByfbD3t8ZKNT2ghXUycDNBYyq0MTlvAPOOCApN1AMjw7/fTTk/2HvUXsqir+VpfJh0au8xFm00taCACdj4bUNJz8ncLVGOUlP2t6lzedhcaocTcNp/rdzTffGqeeekUce+w9scgif4sll3wyjjrqb3HTTQ/0HD7sfvazn6X8Smc1nia/YeeI6SykmoRR/UZ5akDCrT5v+psA0PkMop7ASycgzEFgp0O84IILpne0TfOYv5NHmsdB5FWYV199dSKp6kyOo+kdXnAjVPrFThvTCSOVWSA3TZfvhCecc889d2DY6Zv0J4PATj+iP4Fdv+Fl7H70ox8lgdwPbhk76VIW/aYtp0Vere4ZRHjamF2cyR3EMsfR5A47srZf7O6886444ICDY6655okXvWj2eOELXx6vec2/x3zzHRY77nhzXHjhvXHTTffGr399T1x//Q1p0P/xj388bNd+5JFHpjbZLi+e6U/MgDzn5IPNhYppN1Mn20qgDU1oQJAGRGDzzTdvPJ9UtfHwmzYF0dh6662TpiXbf7gjF0YOVt5gYK1OmjRI2pQ8bZPD7/UuHVgrQZCX9/YaRtU/tSZhp/AQuuq7Xn9nTRRyZMVRr9+3+n/iiWnx618/Ervuekd88INPxEorTUvntfzf/zEsHbPB6eUOO9N08os89vJtO7/IL02KhtnufS/PYKdOa9zKpJdvO/mVLkJPPem3bOFlilH9HgR2SLq8aqud0t/Lc9ghboPCTseNyOjIeklHO7/wgpt+ol/slCPs8j4f7eLr5Zn+yA7R+icY9vJtJ7/6Jv2J9tbJT93n2hhhrJ70Gx7sTEUoW1PmddPQyR/s9O00jP2mTRzSp1zt1j2IeqeeIIFmBPoNT15tLUH70Q92+qI111wzbdWez9lyn332DeI//uP2WGGFafGd70yLu+/+Z+y776Hx3ve+L170ohelfUPmmmuuOOuss9rWU7MRtEb69+ecfCj0b37zm4lgKHwjvFVXXTU1JELeypPVV189Aa9Qe3Uqk0z4FvAK0OqW3XbbLf3WUL1TaXTKVL6bbbZZIgatcWk4GrdCa5KWanjShN1l8lF91+S3zlonmwVokzDyN7DQuWpAOo1+HNtehkpf+MJTMffcT8Saa05Lxzw77nm8FS3jxQk7ZZXJx3h+67yDnVEj7Pp1sNMwM/noNzzfG+EgH1ng9ROm9gA76le/+3WEAO2CdjwIBzvTONrlIBztAi2FTq1fBy+4IR/9YqeewC6Tj37Tpj9iV6V/gqHw+3WZfAxCCGTyoZ70G568GRQp23Ya6l7zDbtMPvpNm7ilD9EiQAdR70bF5qOKq76IXHb+S5V8rLLKBnHEEbfHaqtFvOtd02LhhR+Od7xj/Xj5y2ef7s+OqRQK2lFrPSWjJ8zgVAEhAgxCCeMf/vCH6eAwLB5RYI9hxYvfrQmtgtHut0pl7shyWnYfxx13XJraQS6wKx2JVTCW3p5wwglppYv9QGg/VO5WVyUfvaalNSyVXH5NHyjIfl2VfPQblrz1Sz70fXiLFSxbbhmxwAKPxZZb/iXuuIOdTXPiIW+we76Sj37LtpCP5ggOmnzoY54v5EP/VDYZa1b3RpF8IFW0F1OmTIlXvvKV8ZKXvCTe9ra3xQknfDvuuouZQ8TJJ0dsvPEjMeecG8RLXzoj+WDegPC1ytEJJR8SYB8OBp/m3S655JK07NZozxzX17/+9TQNIrOtCe1WlMgHI1YqdYTCXh7mk4yEPKd+MqL0zN4i5kt1BgobCK2ukI9WRNr/p6CySdj110ess07EYotZJ/5IXHTRrfHYY2Mq3PZf1ntayEc9nNr5KuSjHSr1nhXyUQ+ndr4K+WiHSr1no0g+yGIylAkDU4nFFlssTjrppOnTuWO7pdoj5PHYZZdD4r3v/WDMPvu/xUteMnvMPvu74ogjzoo//MGU/owYTCj5ACyBT+Ngo7Evf/nLKSNOud1zzz1jww03TORgxiT29g9xoYrUAKokBoAyS8Xr0rmMR3AK+eiOO+Lx5z9HnHfe2KZhU6ZEnHZaxK9//ef46U9v7oixclAXkFHqOJquTtMMhXx0L4dOPgr56IRM9+eFfHTHqJOPQj46IdP9+SiSj5zqPJ1mxsIUWLtBu9kNpg6f/OQm8cEPbhpzzfXd2GqrB+Laa59Ou1ubYc1j/QklH7QTBL9543XWWSc+8IEPxLvf/e744Ac/GMstt1yy+UAcRsEV8jF+KSAeZqucyzLffBF2xLvxxgiVK+/z0YngqbjUeDaam3feeeOzn/1sshRvV5kL+Ri/HMZ7W8jHeOiM/66Qj/HxGe9tIR/joTP+u1EmH/pnRskMWNv11Tln3j366D/i7rv/Hrvs8kTMN9+0mGuuiB13HNs3JFs58DdhNh8Sh4AQPqyDWTDntfTsNcyLej8KrpCPzqXAbIVh6Z57Riy8cMR220X89Kdj2/OOaUP+nIxr25EP2iaGxfPNN1+8+tWvTnOIDJm22mqrZHjcGmshH62I1P9fyEd9rFp9FvLRikj9/4V81Meq1efMQD7kyZkxjz/OMHpampI/8MCxKfkllojYdden48or/xiHHjo11lxzrWATYvFJXpHTikmv/9vucCoQwgf5YIthvwU2GKy2rd5APsabCuk1Ef34L+SjPXp/+1ukHUt32WVs692ddjLNMrZjaf6ik+ZD2WK7X/va1+INb3jDdIvoWWedNW2vb0qu1RXy0YpI/f+FfNTHqtVnIR+tiNT/X8hHfaxafc4s5CPni52HyYzf/z7ihz+M2GyziGWXfSTmn/+AmGuu98TrXve6tIrGESumc/T3/bq25IPgwW6QDafKrrbaavGxj30sGZ1iP4xELbkdBVfIx4ylQKOBeNx0U8SnPx2x4IIR++8f8dvfPvuMlm7kg2Hxm970pphlllnS9eIXvzjVA3vAtLpCPloRqf+/kI/6WFSduHgAACAASURBVLX6LOSjFZH6/wv5qI9Vq8+ZjXxU80eG/OEPEUcddVu8850rxgte8MJ4wQtmSYNQg9EDDzxwIMvu25IPmg3TLIssskisu+66ccoppyT7j/PPPz/tt2HLc1a0o+AK+XimFFQaS2mvuCJiySXH1GeKKR+1/IzPsV+dyEf2d+211yYbn1e84hUx22yzxVvf+ta0Cy2NWKsr5KMVkfr/C/moj1Wrz0I+WhGp/7+Qj/pYtfqcmclHzqtl2B/96EfTwDPvG/Ka17wm7UY+iNmPtuTDygZnrtByGOWynmWA6s6QxTH36623Xno27OmXQj7GqgrLZHtKffvbY9qOFVYYIyG0IEhJO9eNfKhgllqffPLJccwxx8Sll16ajFTb2fsU8tEO4XrPCvmoh1M7X4V8tEOl3rNCPurh1M7X84F82PbC+WumXF74whemy6ITJhjaXb+uLfmwDMdZKwiIdcNVZzpG5LZxHZThSTX8Xn8X8jE2nXLXXfbtGDMsNd1i2oWConXNdhXfbuQDydBBqQP8IiOWRbdzhXy0Q6Xes0I+6uHUzlchH+1QqfeskI96OLXz9XwgH/p0e3vZXmPFFVdMW2ycdtppaTPJdgPQdjiN96wt+SBovvOd78SOO+6YllYSOiqqu8TYedSOpArAc3s/sBMZhns+kw8aDUZCv/qVrdIjFl88Ypttxv7//e/dS6Mb+egewjM+Cvl4BotefxXy0Stiz/gv5OMZLHr9VchHr4g94//5QD7kVr9OTrDzNA1jl/NBEA9htyUfSIYzBOzrsPfee6ddRm19zuaDEeIGG2yQ5v6dleFiH2IJbi8OWZExnYfLiDpnyt0zpKYbsXm+kg/EwzrsW24Zs0y2lHaffcYMherywEI+eqmxM/qtnu0y45ve/6nr5WyX3nHzBewGebaLvq9sr957WZh+h92onu0iR4SndtZJe9tLrp8v5AMmZPWE7fNhJYvdTD/84Q+nDcbmmWee9PtDH/pQvPe9703PvFtooYXS5ZwXzKiuQy4IPh24pbwuUz0qr4y6O/bYJme2Wuc3E5PWOJ6v5ON//ifSKbRWs9ix9IwzIixA6mTf0Yqb/4V8tEOl3rNCPurh1M7XKB8sV8hHuxLr/qyQj+4YdfJBtpnatp9WO2P+Tt91ek6G1tlkrNP3rc8nlHwYTTA6daooDYiD1hgeuuf/zmbJl70/GKfUcSopw1VzR6ZuGK+6nOPiBFN2JAwczTPZ/vWggw6KTTfdNKWFpqTVPR/Jx913PxpWsdit9BOfiDj//LHt0+tqPDKGhXxkJHq/F/LRO2b5i0I+MhK93wd5qm2Zdukd//xF0XxkJJrf2067IAjYmCkPIDvTA7nIl/9GCNRXLszIN3Ucf1iek2sZtTpF1mUuSWNATBxeh4g88MADSQXK9sQpt961uucL+bAT3f/93z/jggt+EUcc8Vh89KMR664bcd11Y4alvWg8MoaFfGQker8X8tE7ZvmLQj4yEr3fC/noHbP8RZl2yUj0dp9QzQfiYWntfffdl465Z3x69NFHT7/s8WHFSxMnbAeV7bvvvsluxG+kRnzecZnIuEsDknLssccmwtMaJ/Jx+eWXJ0JDM5IJUZO7NJg/NueL6DQJo/oN4mapsmml6vNefz/xhAPeno4773wyNtvsDzHPPP+Irbd+Mm699cl4/PExAthrmLRbts7/yU9+kgjmILATHsGCRPaanlb/sKNp6xe7HK7yvOqqq1Je87N+7qYFYTeIvKp3sENo/O4nXb41bWoXwjy/3W94sNPeqwOOfsJ05sRvfvObdLBkP+H4Fv4GKqZtB4XdDTfcEPqVftOmjQnnsssuGxh2+iZtwtla/aaPip+9nnrSL3b6D1prA0eD037TJjzpuu666waSV+nJtomDwE4bsw+SAZxBej/5VU8MvgeFnfSYjbj11lun21P2mz4bjmpjymVQrq3mQ0UkNNlysO1YeOGFY8EFF5x+LbvssrHttts2SgOCoVLZOdVWrfYL2XrrrVNBts53yaipnzXWWCPtttruMDuN++KLL04dkKkiZKbpBVwFpuNmQNs0nPwdjY4Kb7Qinfl5r/ff/e7Pce21j8aaaz4db33rY7HZZn+Jm2/+Y/zhD83yKi06bNvms+0xIiD8+kkj7MxZ6riF1WseW/3TemncCEjru17/y5eycC6BcHv9vp1/6WKErZ70g5uw4QU705iDwA6JkVdtuF3ae30mj2effXbCsNdv2/lnx0WIqjPt3vfyDF6mhJHefrFTjgY7SKrOu5d0tPOrPxIO4jaIeiIOBv76k0FgZ6Alr+pJv+HBTnjKVv1rh0cvz4SHoOqj+k2beIWnX0d8BxGeemLQy7aCPOslb61+1RODGURrENhJjzoivH5lorQK45JLLkl1+DknHyKcOnVqWtdrYylMGzj5ygA1YR+0GUYrBB7SgFGdccYZyf6DrQcWyFH1iJfNxwEHHJBYddaMVONVqS688MJEGqRPZXARrtLZyyU+ZIFQUfF7+badX42aADVCbpKee+65N37xi3vihBMeiKWXfiTmm++J2HnnX8bVV98Vv/lNb3nL6dMZ6iCsWJpzzjnjzW9+czIg3n///ZPwy/56vcNOmV5zzTWpw+31+1b/sNPxwK71Xa//Ya881RPh9vp9O//SpW3As0nZVsMUBuwQN7+r75r81sFedNFFibg1+b71G9g53XgQbULYBKh2ob22xtXr/1yfdbb9YqcckUB9EiLYa1pa/euHhHPuuecm7PqtJ8LXN6l72ltrfL3+R9jkNWsYe/2+6l/ehGeRgPpXfdfkN+yQSlqjQeRV+pCFrDlqkqbqN+oJgm9w3G89llfhaBe0H9V4mvwWnjqCbPndaxiw8l2+5E/fiUA/5+QDM/zKV74Se+21V2KMVDbIQPVqRwSqpGC8375FQKjpqK/EZwS+ww47JGtf8elIDj/88LTRGUbtWTuHfBAC7tTDwnXR3vR6UfUDHGOUrl6/b/VP/agyaZSt77r9/9//fSweeOCxOO64x2KZZf4RK630RJx//uNx2WU/jT/+8a89h5fjo95D+myV/qIXvShtnWv79KWWWiphnv31eqe1Uk4akXLt9ftW/7DTUSALre96/a8+KE8dt3B7/b6df4IY0RpEXjN2Olm/28XXyzNlLK+0Pb1818kv7M4777yBYUcgE1CmcTrFWfc5/PUVNFr9YqeeUKP/+Mc/Tn1S3TR08qc/oo0hpAbRn4jHwEF/oq/qFG/d52zvCCn1pN/wYGf6XNmqf3XT0Mkf7KRLWfSbthyHvBLEgwhPPSHcaQX6rcfySgYiW4PATnqQI+EJO+e/l7vyzJfwkEB1+TknHwA47rjjYtddd00CRSJMeeQrz3G1IwN1niESwnDRdOhA2JVsv/32qTAJMTYh9hghzGSe33aEB+nA3oWRbUXqpKGdH8Cq8EYC4uvXwU3HiEn24mwc9sADEYceOrZx2BprRFx55bR45JHH48Ybx+xRegmv6lcniOi9/vWvn35a7Ute8pKwbS7h19TBjrqPUB4Udsq+V+zapV+9UHeNLJTJIJxOjCAYRF61Adip91nz108ada5GoDSYg3Cwo0nReQ3CEZ7qWqcBRS9xwAtuhEC/2Kkn+hqkl3Dp1+mvhKN/gmG//ZP00PAYIA1CCGgLNG7qSb/hZeyULRLYr4OddNEG9pu2nBZ51c4GUe+0MWQm27fkOJrc5bUstf0XctiSkck222wTRxxxRBpFqQQapQujIlSbOJWUADS9IRwqHeow58g4P0RHwsDUdq7+Y1w2OFFx2gmOmY18sOfBVfbeO+Id74jYYouI226zmdK0JOjgr3yaOo3GPO9//Md/hFNq7dlP8+HUYvOYTV0hH02RG9soq5CPZvgV8tEMN18V8tEcu0I+mmOXv+xocGoEu9JKK8X73//+mDJlSiyxxBKx5JJLpsvz7bbbLofR0x3LQxgOOeSQFP5qq62Wzok555xzkloHGVlrrbWSoatNzBZddNE0JYCcUPu0upmFfFipbGbpF7+I+MxnIuabL+KQQyJsHEsJY6mtUXa/5APrpx6lVXrnO9+ZbD7mnXfeNLLVoJq6Qj6aIlfIR3Pkyg6n/WBXyEdz9Ar5aI5d/rIt+aAqNO2y8sorp+W15t2omGk/XKYlmqrDaT6oIM1x0Z7kaQnaEMKV2hMBMddPhedChBAP37W6mYF8WGFsx9KLLopYZ52I5ZaL+Na3In7/e53r2OFwcBsE+RAOomB6iV2AjdxolUxb9aOOLOSjtWbW/2/0XjQf9fGq+iyajyoavf0u5KM3vKq+C/mootHsd1vykQ1OGZ36TbAQTNWLBqNfRxC6+nGTnXzQdiAZP/jB2I6lyy4bcdZZEX/604yo1CEf/DAKRuCy8V2ncuIXdsjkIOajC/mYsbx6+VfIRy9ozei3kI8Z8ejlXyEfvaA1o99CPmbEo8m/tuSDUDrssMPiq1/9ajLkaiUfBFwnodYkEf18M5nJB/uOhx6KOO64CAfDrbIKw9KxHUtbMalDPnTE8Dj99NPjyCOPTHszmGLpVFY0XAzYfCf8flwhH83RK+SjP+yKwWkz/Ar5aIabrwr5aI5d/rIt+QCsqRWn2n7ve99L1tWmPWhBXAQcK99RcJOVfFAcsef4ylci5pknYq21Iu69N8LMUjse0I18eK+MNt9883jjG98Yr3zlK9M+Hs7FoQlpRy4K+Wheg8tql+bYldUuzbErq12aY1dWuzTDjrJhwk61Nf/PAHS55ZaLRRZZJFZYYYVYZ511Yt111007kn7mM59JWpFmWRnsV5ORfFis8stfRnz60xGLLhqx115jK1wYlrYjHhDrRj6MYqwM+s///M+wdHbWWWeNl7/85WkDMTY77ZaEFvLRvC4W8tEcu0I+mmNXyEdz7Ar5aIbdhJIP6/kZfNqZz+6jdjekAfHfZatVqy5GwU0m8kHb8fDDET/6UcTaa0csvXTEN785tqdHhz3UpkPcjXzQbtgC+3Wve11aPvuCF7wgLaV9+9vfPn2fgemB/etHIR+tiNT/X8hHfaxafRby0YpI/f+FfNTHqtVnIR+tiNT7P6Hkg6Azh0+g2XDMVItNfPIOaUbZ7Vae1MvKYH1NBvJx9933hOPuGZGee27E6quP2XicffbYszq2u93Ih/Kwd8p8880Xr3rVq+KlL31pvPa1r02aK6uF2BW0ukI+WhGp/7+Qj/pYtfos5KMVkfr/C/moj1Wrz0I+WhGp93/CyYeVLQy5GC/uvPPOaetz0zEIiK2MLYcdBTcZyMedd94TttA45piIhRaK+PjHI37ykzH7jroYdiMfwmFcSkO19NJLp/1ZLJU2fdbJoLSQj7roP9tfIR/PxqTuk0I+6iL1bH+FfDwbk7pPCvmoi9SM/iaUfBhF28fjk5/8ZLL7+NSnPpXsPmhBCCxbodv9lEActht18nHbbXfElVfeEzvvHDFlSsTWW0fcckuEnarraDwyvnXIB8Joia2yczqvHUs7GZsKt5CPjG7v90I+escsf1HIR0ai93shH71jlr8o5CMj0dt9QsmHEfSJJ54Ym2yySToU6cwzz0wbjiEf9qBnA+KYe4Ju2ARklMnHX/7yeJx77m9j443/lDQeu+8e8atf2da4t8Lnuw75yP6QENoO9/FcIR/joTP+u0I+xsdnvLeFfIyHzvjvCvkYH5/x3hbyMR46nd9NKPlg47H77rvHgQcemHbCdHqfbdCRD0tsqfI/8YlPpJFzpz0kOmcl0kZYDg0yMs8XEsGWhCNojdizrQkh2onkjCL5oNGwY+kNNzwV6633eHz4w49P3yq9jenFeFBNf1eXfEz/oMaPQj5qgNTBSyEfHYCp8biQjxogdfBSyEcHYGo8LuSjBkhtvEwo+WBceuihh8aXvvSltOrFNtyrrrpqIgPIwtSpU9OUTCdbgjbpn/6IEEUyTN3Qnuywww7p2n///dMJtsiMZaEqilNunelCSHYiOaNGPhiWOtTx4outZnk6Fl747zF16v+G5bW9TLNMB+xfPwr5aEWk/n/YmUosp9rWx6zqE3blVNsqIvV+67P0XeVU23p4VX3BrpxqW0Wk/m9kwcnHDof1u183oeTDJmOE//LLL5+E/9FHH50OlKMBseW6g+Us62ziCALak8MPPzz23XffNI1jKkecyAyDVufIbLjhhon8sDdBhiYD+UAunGJ+5pkR739/xBJL/CNOPFEluK8v4gHnQj6a1Laxbwr5aI6dLwv5aIZfIR/NcPNVIR/NsZvU5MM0B4LgqPsvfvGLafXE3HPPHcsuu2x8+tOfDjYg7EKauFypEA/aDlM5VtFkLYolvrQZP/nJT+Lkk09OdieTgXwwr7AAaN99x1a0bLllxLXXPhY33XRnWGrbr4MbIYCYmZIahCvTLs1RLNMuzbEr0y7NsSvTLs2xK9MuzbCbUM0HQUcDQe1l1QSNx8UXX5zUhzoOz71v4oSNcNCgbLzxxrHnnnvGAQcckDYtQ3i8R0BMzZx33nmJ7HQjHzY9s/wXIaJFaXrJl/xdffXVSdtSJ5y//OWv8dBDj8SNNz4e2277VCy88OOx0UaPxA03/DXuvvuhuPnmn6XppDphdfIDL2o05bDPPvskUug0YM87fVPnuVUx8ors1fE/nh/YSZMGPojwnPKKgP7iF7/oO23SrQ7ZAVa44+Wj7jvt4sorrxxIXjN2t912W2pbddPQyd9vf/vbuPTSS9Ny+E5+enkOO3Zeg8LOBoWOb+i3/sqDuga3O++8c2DYmZ7TNnrBqJ1f/ZFwTFnBsJ2fXp9dc801ccsttwwkr2zqtH/bJqiDvaal6l9eHe9gryEnZlffNfktPOnS5w2inkiDvNrzaBDhaWPMEWxH0W948mowMyjsDCrVEeH53QT/6jfC+P73vx/yTDYPyrU92wWxwLCNskVGbZ0vWhF2H/aTaDKfJByrZBAGUy+mdBi2OkdGB5dXaNCEXHDBBV3Jh0aNpDidlUDQETW9FJiOR9p0jt3CueWW2+LHP74tTjnl9lhxxYdjgQWeiC9/+a/xgx/cHt7B0J74V111VdewxotLmpC0973vfTHHHHPEu9/97thoo41SYxrvu27vCHek8uc///lAsLv22mtTgxRet7i7vYcdAUrAd/Pb7b16oTzVWeF281/nvXSpn4PIqzBgp5wHEZ5Ox07EttWvk5dufmB32mmnDQw7GlXtQnvrFne39/AioOS1X+zUE8QIWbjuuuv6ThviLByrA+v0J93y6r2+Sd0bBHYGCto/7PoND3bCY9+i/tXJy3h+hKd/uvDCC/tOW45HuWbylp81vasn2j8ZqZybhuM7eRWOdjEI7KRHHTHY6jdt0icMMhapfM7Jh9EEg1PkgC1G1dFIyJSzXrAjmoomDgnxLbKBjJx00knx+c9/Pk3BCK8u+ZBW6cHOfCO8phfShVipAI8++mjXcB5++Mm4+OInY4EFnowFF5wWZ5zBnoXmZiwNsKNJoRFQaE3TpRFOmTIlZplllunXe97znjjhhBP6Chd28qpM+0mffMEOM7799ttrYdcNC9jpsI1ou/nt9l7eTFUhgcLt5r/Oe6MynbZ60i928IedUbLfdeIfzw8Norwa2Y7nr+472Olo3fvNqzh1aI5vUGfqpqGTP3jRChp194udvMGOINA2OsVZ97n+KGvcBoUdoac/GQR2+l2DNvWk3/Dk1fS5soVhXYw6+RMeTRvy1m/axKFslSsN+SDCk0dEhtwxHd4pH3WeyyvNExJCptb5Zjw/FmyoI8Lzezy/dd4JA6nUxuA4KDeD5gMZUIEwHUttd9tttyQ8FZiLiskIzSqYtdZaK4GORPTjfK/wTj311EQ+HnnkkRScAqmj+dBJYIy+k37hNb3EKZ9Gx9I0Xji///20OPbYabHkktNixRWnxQ9+YIfRiCeffCZ+gomaT+c4Xljd3hEk73jHO8J5Lfmac845k81MP3mmLjRaUbn6CUf6c2chv8Lrlqdu7wkSo7F+sROPvOlwaBaE2y3uOu8RBR1jt3pSJyx46Wi1r0FgR6jk6bQ68XfzAzsj0EFhh6AilTqybnF3ew8vAwZCvl/s1BPkFCEnVLrF3e09zbA2puOGYTf/dd7rm7QJ7a2O//H86J/yNGm/4cEOwVK2ZMh48dZ5Bzt9O3I0iHoiTsQN0RpEeNqYwUcmC3Xy1MmPvJp6sTplENghFAZHwvO7U7x1n0ufKaaMXT/yvvrtDORDJEbqjEwXWmihZGiKZFh54tpggw1izTXXTFMktl2X+F6db7BGDdwFIBmzrPaYY45JnbkwNYa65EPjzoXWa3qq/lVKqiUjbh1Zq5Nd+3Tcd1/EYYdFLLvs2Mm0P/7x2PLaViWQzhoDJaj6cYSwFUYvfvGLk+bDuS0LLLBAIl1NyiCnRQerM8sdT37e5A47AjSTjyZhVL+BHRLcL3bChBGSkMlHNZ6mv4vBaVPkbLT3q+kareahjH2p7iJtyIff/Tj1hAAlpLSNfh2BLBz9Uyap/YaZyYf21q/TxpAPo+5+w8vYKVuCuV8HO+nK5KPf8Hwvr/ooArlfh6TSSGctTz/hySsSg7gNAjtyHEGdVEttgYCpY3RsDBiEnnLKKelkW6fbus4///wknAn7Jk4cOoojjjgiNt9889h2223TipZvfetbSdBkYaoxmMvdcccdUwP2XTuHHU8E+UA8LDK5++6IXXeNWGSRiJ12irjtNtoOAu7ZqRsU+dAIzeE7NO7Nb35zfOADH0jTYthyP66Qj+boFfLRHLtCPppjV8hHc+wK+WiGHTLDRus51XzkpGHp5neM2vsdTeQwq3dhYqCYntGtjpwKsEowkBAEJ6u1qt9Xf08E+UAs/vGPiJ/+NGLjjSPe9a6Ir30t4oEH2pOOnL665ENe85W/rd69w4jhddRRRyWNUVPyVw23kI8qGr39LuSjN7yqvgv5qKLR2+9CPnrDq+q7kI8qGvV/Tyj5IOyopkTq96BdDt/UhouWo0o8cnzi75aG55p8yL5d36+6KmLFFSM+/OGI006L+MMfIrppPuuQD/k2H0x9R+Urv+2c51R9bG747eSv3bednhXy0QmZ7s8L+eiOUScfhXx0Qqb780I+umPUyUchH52QGf85WTNhmo/xkzJab59L8oFcmPo9+eSIFVaIWHvtiAsuiHj44bGplm5IdCMfCB4bCZutWT1kAzdLmtppNRA2RM18NC3RIFwhH81RLOSjOXaFfDTHrpCP5tgV8tEMu0I+OuD2XJAPG4M98sjjcf/9EYcfPmbfscYaEQxL2X3UVQaZKrHcSWfbqtnxn80Gm5a3v/3t8apXvSpe85rXxEc/+tFkgNvqv5CPDhWgxmPYFYPTGkB18AK7crZLB3DGeawNI/jF4HQckDq8gl0xOO0ATpfHyMKkMzjtkqeRfP1ckI/rrrPB2OOxxx4RH/hAxFZbRdx669hKlzogZGHHZsYKnuOPP/5Zxjq0Huxd5p9//ph11lmnL6FlUGrr+VZbm0I+6iDf3k8uj7LapT0+3Z4W8tENofbvC/loj0udp4V81EGpvZ9CPtrjMvCngyYf99//2/j2t2+Jddd9POadN2LvvZ+x76ir8UAcLMNadNFF401velPSbFiybA8RjYpDPizptYLF5mF5/443vvGNsd9++01fcpwBK+QjI9H7vZCP3jGrflHIRxWN+r8L+aiPVavPQj5aEan/v5CP+lj15XNQ5AMnePjhp+O00/4WSy/9SCyzzFNx0kkRDz00Zlhal3hoNFbobLPNNmkrdHtzvOxlL0sk5KCDDkpGpTLMn2XNX/3qVwPheNGLXpT8LbnkkmmDKO+rrpCPKhq9/S7koze8Wn0X8tGKSL3/2nCZdqmHVasv2JVpl1ZU6v0v5KMeTn37GgT5sE/Hf/93xPe+Ny0WX/zx+NjHHo+zzkIO6tt35IwoeGlabbXV4hWveEXSaNBsICE77bRT2omVXwKRhsTy2alTp6YdYzfZZJO0LTby0uoK+WhFpP7/Qj7qY9XOZyEf7VDp/qyQj+4YdfJRyEcnZLo/L+SjO0YD8dEP+aDNsKIF8TjqqIhFF306llrqf+KEE+6Kv/yl2S54ucPZYost4rWvfW288IUvTMSDMenBBx/8rB3sTL9Y3WIDF0zfihbCstU938iH5cdlh9PWWlDvvyXZtldXnwbhCvlohmLuC4rBae/4FfLRO2b5i0I+MhLP8b0f8mFLjQcfjPjKVyLZd6y//hPxox/9Nq6/vv326nWzorO2ZfzSSy8d//Zv/5amX9Zee+20gyuy0cQ9V+TD8jMamHaEp5d02qtlkNurIx+2lS/bq/dSCmN+C/noHTNfaANle/X+sLOybxBbhBfy0awcfFXIxzjYqVg2ynKSp3MZXEZp9sXQARDQSIVlqk5JzIfGtQuyKfmwVcbtt0est17EwgtH7LNPxF13PRF33/1g3HRTZ/JByIrTYW8OtGO3IT9V578G6Ijvb3/72+k4cnlESpoKed8Nep8PabdvyCiSD3WBQa4lY/062MG+rHZphmTRfDTDTT9QbD6aY1dsPpphV8hHB9wIAqNam2ltttlmsc8++6TLWS/5mG0H4uy1116xxx57xNe+9rXYdddd0xbs7bQGiMBll12Wpi5aSUA1CeJVKE8/PS2dPnv55RFrrjl2ONyRR0bce+/T8cgj/5cIz5VXXtmW8Ei30zg/+9nPxrzzzpuWyTpwzwidAK868SFYBCgCJW7PmjrfFvLRDD3YFfLRDDtfFfLRDLtCPprh5ivYFfLRDL9CPjrgRhDQZBx66KHJANO8fj7fhe2DkQLCscMOO6QTDS1ZRUQcPFdV5+WGbdrgG9/4Rgqj3fbkSIERvp1Er732x3HHHb+Ls89+NFZccVostljEeedF/PGP0+LPf344HZH+qU99Ku02igz5rkoYEB3PZ599cHHtTAAAIABJREFU9mTLwZ7jbW97WzoFuJq2nPVuO5xmf3Xuk4F8sFsZ5Km2RfNRp2Y820+Zdnk2JnWeaGNl2qUOUs/2k7Er0y7PxqbbE7LseX+qbTeQBvEe0IT6gQcemFZ5GM0jCNgazcZ9990X7CMuueSSpCGxC6h95WlJ7JPBCYNgd8jaggsumPbRWGyxxeK73/1uIigaQr6coMvQc5555ok555wz5p13lXjvey+OVVb5Z1xzDS2MUfHjyUaDNsOqFEfWv+9970vLYKVPfMKj9VhllVXSsti8L8erX/3qWGaZZRJLz3HmeyYfpg7ys6Z3aTACNU2ig2waTvU7I4sbb7wxaVRyHqvve/mtDB1GSHsFs16+befXFvKZfLR738szeaO1ckqyMunl205+2aJcd911qUw6+an7HF7sZUzNDQI7RJjBKbJcNw3j+YPdhRdemDAcz1/dd1Z4aUumMOt+08kfvPQZ2nm/2KkniJs2YRDUKc66z/Vp+joGpzCs+914/vL26trbeP7qvNPGDN7Uk37Dg51+SdkaRNaJfzw/sKtqPsbzW/edvjOfzFr3m07+tDGnv9Nuk1ud/NV5Lq/k3KCwk5677rorzCD0mzbpFwYbxozdIHiAMF4wqIDqhqOS6ihsK77eeuvFnnvumTQXOiMFalfQNdZYI21JLtOe0YzYpMs7TkO+4YYb4j3veU/MNttsiTDYntweGZ4TMC6N4YILLoh3v/vdiVCMEYtXx7zzrhxXXHF3PPzw3+PRR/8eDz74YJrisTTWslgX7YatzqVLh5SJBC2McDL5sIplo402SoI3x5vv2GzeXl1Dz8+b3H1PY0QTpGNsEkbrN2xuNCCdRb/pE4bzTpSVdLbG1et/jZFw1yB7/bbVv7wpCw1IuK3vm/xHsgh4eR0EdgSo+g3HJumpfqPTJvCQ9erzpr91sOeee27qaJuGUf2OLZSpSG27+rzJb/jTtiFu/WKnHJEFbQKRbpKe6jf6H23s+9//fsKu33oibG0iaxeqcTX5rR/Rn6gng8BOeMpW/WuSnuo3sJMuB2kOop7AXl71UYMITx7Z/Rk0ZPlQTX8vv+VVfTPYGgR20qPfVBb9pk0+pI9pgzQaMAzKTTj5wKQAonM84YQT4swzz0wajK222irOOeecxNbWXHPN1KFghDKOwSEfOnzOMyMxW5Hn3UFNgcw111xpeuaaa65JgkHlsNmXJa+ZLMwyy6wx99zzx8EHHx5XX31N8IugONTtJS95yXR/L3/5y5NWRZoYKvKnE6FtWXzxxdOmYW95y1vSLqaHH354yg8/1Uv8Cs1Vfd7kN0Fn5O6MDeE2CaP1G2Vw8cUXp/wJv/V9L/9hxABXXqWzl2/b+ZVH2q9LL72077Aydsp5UNhJl7IYRF5hpyxcua61w6TuMzZL0ia8ut+M508e2WgNIq/i0Y7gN4i8SpN6Nwjs1BPYqXeI6niY1HknPFrbjF2/bUyc2qs2NgjschsbJHbKFYZ18BnPT8ZOPz+IvGbsBpFXYcmjslC+/aYv1zvtQnjj4VLnnfSoI9I3iDonDOVKaUAhMCg34eRDwpEKTNsog8qPiujYY4+N7bffPrE/RANzk1FExWiaNiRrPrAxhfCud70rTYEgIKZKpkyZkjoNILkwte985ztpWsb5KfzRlCy11FJJtZr9YcNnnHFG0qQgHTQgpmgQFyMq7JZfaifqdmz89NNPT9M8119/fWLo2U8OM9897/Qu++nlLg2DCm/QaRv18GDXC9bj+R31vA46fc8X7DJu7uOVf913whnVNvtc5DWHWRef8fxl7Mbz08u7QaZNvKMc3qCxI6dpj8xcDMoNhXzIAAKSL9Mop512Wnzuc59L5OOTn/xk0kYgGVR5Rjaf+cxn0tyujOflrrYmf+c73xmvf/3rE1lgeAqkqqM1sbPo//t//y9e97rXxdxzzx0nn3xyIjXZH20M9eipp54aG2ywQay88spxwAEHTCc72V++8y8NyJHfxRUECgIFgYJAQaAgUB+BCScfhLVpE3PcRgTm4Gk2aD2QB5oGp7p+6UtfSnOblrFa+WJqw9xzdgiM72lAzj777KCBoCVBaKqOIRWbDipG2grhmfNrJQ3CQ4LMuSE8g2Z51TSV3wWBgkBBoCBQEHg+IzDh5IOQp7Ky1JadxZZbbpnuhx12WNpQCjFhQOa9/TRcu+22WyIriETV+Y9wZKO/VuLBL5LBCh7hQF4QjHb+sl/aDJd0FlcQKAgUBAoCBYGCwOARmHDygQwgDOw8LGljvW35mDkqS0mzBsIqE+8tBWOTkZfRVSFAErI1bl4qVn0/7N/Sh+zQooyag5d0uUYNO+RQuaon7qNKBDP5zUtGh13GcEPereyhvXNnW9WJbA8rvfDK7XYUsFO/9D20sC7YZfy0j1HAT78JK+lRxu36w2GVp3hzvy1tuR8fZnrErdxgph+uOmmFn/5lvMFo9ZtB/5Y2bcDVTgsvfbDUxwzDdcLOc5jBTjn739RNOPnICQW4S0VoBT/78c7V6vhXqdhpWAJ4zDHHJOtehdUPGK3xNP0vfSqPaSFTPUceeWTHPDaNo+l38IGTJcAnnXRSMvRlHT0KnWzGzRI7KwSUq71b/B+1zlZ6GB9/+ctfTkRafRy2U4Y0iKYspcsydv8RkE5tbCLTrC3rtNhhnXLKKan+mX5tFQ4TmSZxKTurA3bfffd0feUrX0m7Kn/xi19Mq/EIiGE6uEmDwZg2e/zxx6dpZhrfUejvCEiDR0b7Fg5YUWL6WtqGUe/ESTBaHWmVBkKZnboGNyvfjj766LSyiZ3gRLVfaYOXPu3rX/96Wv5bjVv6aOitArU/FRI8kU5dg53l3EwVqqYOntuzStvVN1vxo5yr6e8lrUMjH70kstWvzJq6YSey6aabpmkZx9Efd9xxaXql1f9E/1eBVHx7may22mppH5B2JGqi0yU+Akql2nzzzRNuprQY+Oo4vBumU65sftj46PjtqfKFL3whYagxDFtIVbHReVgNtcQSS6SldsPGTtqQ3fnnnz+23nrrJKDOOuusZKxN4A+7/ul0CVDL6xmPK1u/2XshcsN0OlWr6wwUGL677Ki8+uqrJ/I70QKgFQvpI9BXXXXV2G+//dJxFOuuu24SAKNQ7wjvnXfeOdU7BM5UunQa5Ayj3hHulmCb1rdjtf0uskNEpI28cHyHPZosXJCHiSBK0mYvKuYEDh5Vz5RhjtuA2gacK664Yiy//PJpkJjTPhF3bRERJxP0I/bjyY5dpYGNsjawsSqVeQQC0sRNSvKhM2VkSoAyIFVgNpBBRHQiw3a58uv8s23LMBphOxwIeOp4IxVLnU1pWV+uEVqaPEwHIx0tIarD11HQ0NhXBdvWmQ3b6SSoHe3/sssuu6ROxDr4URACCPkiiyyS2oby1U4I/FGoe8pVp7vSSiulXXp1WNI3Chot+Giz0pNtw2gZCHjL+5X3MB3N1YknnpgIJU0RA3qjdps0asNZcA0jjcqPFkFfzFaPELdZlpWLptMnWmtE24JsbLfddmmRgnSZus/O/i1WNNL2SivyaxBhb5eJaCfqkrgslEDClWuVfEgPrS9ibnsJWsKJcrBDMJylpn4ZPFeJm/YBM1fetNFAsYpvL2mdlORDxqlG99577ySkdGwa5ec///m0qcpEVKLxQFaIBKdRPG0MBj7sNOX06qgQEFoEvwl5qknEbdjkQxrhpEPTaSlnAot2AUGa6I4sY5bv8CKkdGA0MgiwOqcjGSXyQZ2L+EoXDNXHYTuq7qxK1lnpZJFMdXGYwrMdLjDbf//90xTMKExt6PRhp40abBFI+j9aBukbJn7qvdG74y8QIXVNP+J8LlsaVNX27bAe9DP9h34CaYTZtttum8hujsc0rrZr0KUPRIJh+c1vfnNC6qI4lRmM9B1OPa+SD7+9s0kg8juR5AN24kciYYeEIJLZKVvtNcsy0y401M8r8qHCUFtNnTo1jVQUqIpvJAo0AI2C04mpXKNEPqq4wIndgukrDFx6h+1yAyDY84on5Uq7NexyRTwITPvG0LRpdH6PCvlQftSl2oaRn7uOVdvQRobpaGJ0Zjp5oyXp03EZWQ1bs1DFhSA3+jNiNjpW5sN2yLh2uvHGG6fpAv2JKQPamWETcmVnF1JpM9VsVIwgUdkfcsghE26zkMtKP2J/KHXNmS7ZGQya8stEiaZLP2PqxSB2IoicOGhx1f9W8iGd0mGn0/XXX39CyUfGCHYGpMhtlXxU30u/vsUWGOpmEzcpNR/Ihzm7TD4wMh2vuSjztRrrKLhRJh8qmAaoMVKRjoJwV2aEJG2M04MJKyMXc8hGysMWoMpTYzvooINSgzPFZ/RCEzIKRp0EpVETexQdAtueddZZJ83hGtEM0xlp6kwRInPKBDzVsrlt0wjq4yg4GCJINhnUz4xCuqTJFAYBT5giH6ZJlS9BNUwHH+WHhGsL7CnYkal32vAw7WXakQ8GsciHdJEbhCg5gnwgchNR3qNOPtSnbIDdSj6kHeE0OCRvDcKaDh4mJfkgNI3WCQGdvhGxjkLlB9qwhVTuDEaVfKhAGh+LZeybYICh56PgdAoqtLKlPpVGFv5GKcNy0mRE5/BCQnSLLbZIWoaFFloonEVkmqNpIxxUnpSfdKr/LjYgDImHof5uzZMpSOc3me/Wfg0QkCRGd5bbj8KAgeAxfUu4U3uPSj9Ca2T1klGy9MFSmbJdQDaV+TAdcqT/pYlxKB8bKJotGhFTDMNy7cgHDBElGhq4SR8ywshTHZyIPlAco6z5UF6dyId0s3fT/ylvMq4pZpOSfKgw+SwYrBtjpfLTGKnCm4Ix6EYyiuRDh8oexTyteVkaBUJzFDCThiw8/SYMaGR0vAyghtmRSYsOlvBkf6JxMoJde+21k9qWFkQnPCwnfUbBMNIeaDrslcOojSAdJnGDCcJB06Ec4YjsWrbHnodF/TCxy2UmTZY3qm/5HKn8bph3OJlOo4pnQ6F82QJY/aKMh42dtgo7dUw5Syf7FH3yMAl5O/KhLdAaMWSHm/6FdhWZmyiyCa/JSD6k2WDGdAySqaz7wWxSkg8VmtCkgjRtQP2IuVoGhIyMiiMITAMZ8alwo+B0EOw7VllllbT/iNEJ/KjPpHeY6dQZGNnZu8VomLEp9Z7lyjqNYU4d5A6W8R+cXAiHUZRpF/8RgGE5pI2QYihJyNsPQifBkt8UzLA1C8rOSEnH/73vfS+NjtkE0DLQ0AwTO2UGP50psoZY0rqNiqPdcOQEOw92KNqGaSFlSyvSjwAYRB7VLSSI/Q7saKDVQURpmGlDgmhNq1MH+hfTBUimA0Id6cGPQetE1UF9ifbAZsLy7tbBHzyVs7rI+HMYTp9mKoqczc6qJlN/ntN+IHfs3RC4JnJjUpIPlQQLs/bdHCODRIAQBsNk2rmQ8l0FM0Ih3JsUTg5nkHfTLToubB95yxtSEVqmXyaqAbbLk7Iz4pQ+o0+NU7k68I9gICBGycHSCEDjG/boEzZUyQT7UUcdlewWjFJoFSbKkG68slGvCPTzzz8/lWkWAIwBh0kqc5oJSXVMB2s6aJjtIKcp37UL+9xoFwildmHzOB0/LciwnQGN08P32WefdBk8IMLDxpB2w+DPbtrZaQv6ZFpffYz+Rf+sbk5kH62/QCJN5fpdjZsWCeEk3xi4D8MhHfqSqjGpqWVEDeklc8kO+LHfUtbVPNRJ86QkHzljGCJ2TQggI6MmnKRTgfRaKDl/z8VdJ6uhmRIy/eLy28h92AIUTjl9VPOEqXR5NkoY5nLJZTsqaZMObUDn5fJ7VNKW24J05TZLaA1bQOWyzOlr0olWw3iufitLJA1BcsFuVMo3t1ntVdmOAtlVDvozaWnt16SXvNDH6F+GpRXM/Ue7OpPfDav9tsMOCYZXlhvuyrvp4GFSkw8FoyLljrZdIZZnMyIAM50W3FqvYVX0agpz+rIAlcZRSFc1jaP+G16jipl0lTbbrAYhRrldaMOj4pSp9Eibsh0VQild7chkfp7T639xMyKQMapiA8tWmeF/07o4qcnHjHCVfwWBgkBBoCBQECgITAYECvmYDKVU0lgQKAgUBAoCBYGZCIFCPmaiwixZKQgUBAoCBYGCwGRAoJCPyVBKJY0FgYJAQaAgUBCYiRAo5GMmKsySlYJAQaAgUBAoCEwGBAr5mAylVNJYECgIFAQKAgWBmQiBQj5mosIsWSkIFAQKAgWBgsBkQKCQj8lQSiWNBYGCQEGgIFAQmIkQKORjJirMkpX+ELChjo2H7OTXuitifyHX/7q6iY+daG0/blfBmc3lwyBty+0cCTsljqpTH1zjbabkzBDnI/WyTbfw7MAp7LrOtte2Wu9lV071OteruvEUfwWB5xqBQj6ea4RL+COJQCYaSEYWKjpo50AcdNBBE36gk/QQRASYMx1sWex8jB133HGkTlgdRGHK55VXXpkOznI+hHM2nGWB+BGqsBgVZ1dHh2gdc8wx4VDBTs55Jptvvnkqs7rpdyyEw/VgUdc5g8m5LuMRUvVZvc4EGq7icA4R0lc3fXXTVPwVBJogUMhHE9TKN5MeAR2zQ5scdEbQ65A9M7Lca6+90oFPMpk7andX69bR+Vn21wpMt/fZP4GB+Dg1krAzgnZK6AYbbJC0H3XC4Uc47dLiWevz1mfV/363bk3tf75yuse7twuDf2dCOLHTibbyaCSPfCgLh4ERlr6tuk5h8ZP9Zj+tZZTDaecvP+Mn5636DJ5OCEY+pLvqcnzuxx57bDopWn6E41kOp+qv+r3657Rah9lVXfZfDSeH5cRYB8s5lyT7y+9yGM4toVFSn7xD6M4777xUtxyqBt/iCgLDRqCQj2GXQIl/KAhQ8zv226ibhsGIUGfv7uCuTEj811kTQg7zMlqlIeH4NxrmP48yWzOj4ycouh2iRhtAC7DZZpulUzf9d+Il8uEo+hxOTldrPDktjqdvN7qVB2FWBVXOb34mX6YA/PdOXsWXnbzmw7jyN/ld6933+fCu1vQ4BXj99ddPJyvzI21Oz3TKqBOMxduqARGG5/xXnXTwy7kjCJ00FPIvXcpS+fPrP+eeD1vM5Zte/Iss8Vt9zj+CqOw9byUf6kOOL5edtOf4hM2PPFWnnORHGcBZ+PKiDHIeM/lQzsJrV/ccIb/lllsmwsGP9P3617+OLbbYInbdddeO+OT8lntBYCIQKORjIlAucYwUAjpko9m555475p9//lhuueXSMdEEwW9+85t0bDQNCNX2pptuGt/4xjfSUeaf+MQnYsUVVwwC4Oabb07H1nu2wgorpJG8UWUWUITFDTfckEabK620Uqy88spx+OGHJ6HSCoZvjIKF9c1vfjMJxUw+Vltttfj617+etATCEJZwqqNwgkgaV1lllfR+jTXWSPkj1Agzwt1I2PHXSFAmDnfeeWfKn+/5ufbaa1M+TP189rOfjbXXXjsco+20Uup+4UrD6quvnjDyXVWY5nwhF4TcqquumtKzzjrrJEFIiDqu/nOf+1x86EMfirnmmiuFedxxxyWSNc8888QCCyyQ8nHkkUemtPpGGpAweV9rrbWC/0zmCOnddtstbrrppiRw11xzzTj++ONzUqbfCXrk5uSTT44ddtghpe3jH/940jwoJ9ou6VWWO+200wxTXSeeeGIceOCBiQwIEEkxXcK/ixZnq622SvUoaz6+/e1vxxe+8IWkMZF/uClLJCXbhQjHEeU0PpwypwWRVxgrT3XTb0RZPdluu+1SmcHXc5jQlikzBI3tiXLLWCoz03g0S3CTDmXQiSxPB6z8KAg8xwgU8vEcA1yCHz0EjCyvv/76WGqppWLDDTeMM888MxEFwtqo0XQAQUy4Lr300kkAsAMhJE477bQkcHT8e+65ZxKq5vsJoG222SYRFgL5Rz/6UWy00UZJuF144YVJ6G2yySZJ+BASVec/obXwwgsnLUceNdN8LLroorHeeuulNF588cWJZCAp0iIeRIpglGaE6pJLLomjjz46aRa++93vphGz/B588MFJOBspZ/JB6C6//PJJ64AsycdHPvKR5I9dQZ4G8VzaCO7vf//7Kc8IgbhzWNX8IFLS8r3vfS8uuuii2GOPPRJpQHYQPGlccskl07PLLrssTbUQyvLKL7yM1BGsK664IpAEeRKWO4JAoIqf1gohhDVSZnpBGbY6GMCRYBeGOMQp/4gW8gZfJI1WRljKRf6Qv5133jkRRwTAO/XGVIz0n3LKKbHsssvGEksskcpRuagv6s7WW2+dptGk3RSLeiNuZO+hhx5KcWeypM4hu9LHPuPss89O6fMdYktjI7yPfvSjsffeeyc85HfbbbdN+br33nsTvojiYostFvvtt19KH7JBg5LrGCNm2BVXEBgmAoV8DBP9EvdQECAc7r///jBKNmo2WiR8jTxNcRA+V111VRotGokbSeqwjVgJjHXXXTeWWWaZuPzyy9Mzz42ckQKj/jzK9h2BQhibf6d5IHyM1quOYEBWCHhChsuaj4UWWiiN/H1DYNx2220p3UcddVQaCRMsBB+hiSwRmJ4RaNKTpyr22WefQH74yYThmmuuicUXXzyN8uX/9NNPTxoJo2uCjOYHWTHyp6UgEH2PpHlHGLZz8iPP/LoIUSNweMmXsGEjHukVN5IhvcgdjQDhDEsGtzQVBKfRuzsBTWPg/+233x7zzTdfTJ06NWmtlIU4Wh0NCtJC60KrxZ80fupTn0rkEhGTbjgjajQsND7qCkFP2yU+z6QTuUB8hKtOsMNAqKTPN6bzkBHYyY+w8zQajYg0Cu+Tn/xk0nYpE2VkagQx9h528r7LLrskzPmhYRG/shMmDRBSSANC+wFLZEg9o0WBLyylSR1EiJAfaSquIDBMBAr5GCb6Je6hIaDjRyKQBp08hzS0Ix9GnoQOpzMnsAhAwjE7o01CAakhkPihZqeVMJJ1Ub8bpT/44IP5s3QnQKxGoHUgTDnCh7CidkdMOMKHoDOfLzyChhASD01AdvxdeumlSdAQOARtXfKBjFx33XVJYAlPfv0ntGh3CDr2GbAST6sj5Hwj7TQmhC9hS91P6PkO9jQQiEV2V199dSJVtCW0FByiJT1G9oceemjKM2IAW6N/2hFkbcEFF0zEiDDu5DL5gEMuS+nffvvtU1qqZUIjAnckCcHK5EPZShOtAo2HvGSHDCIAVfKhfiGt2YkX+VF3YNRKPkzlwNg3yh9BQDYQK2RPev1HUKrpVdbq1g9/+MNUbgic/55XnXKTRu+R0uIKAsNEoJCPYaJf4h4aAnXJx5QpU9L8fraxyOQDAcikRSYy+aBFIewJHpoVwo5QITT9NndfNTD0LfKBPLQjH4SIkTBH+IiTAKLyJ6AIQYKchqXqPEcYTHX0Qj4Idd9k2xVkgsaFoM8EigbhiCOOSOF6X3UEJnU/QrT77rundLqbOumVfCAwbHIQBGHC0RSI36Y+lKGVMrRQ/CqbTg75YJ8h3bks+aVZgF9VmCMfH/vYxxLJaiUf4kE+kMWMkXB8w0ajSj5MBWVNFj/jkQ/vEUXaKVoXZItmiD0H8pfjQsTYrlTrnrJW37qRD2QKCTQdR6NVXEFgmAgU8jFM9EvcQ0OA4GIDQPNBm8C103wgHwRBVlNn8oEAVAVAJh9Z88GOgEqd/YFpkHwZcVZHzOJFPkzzLLLIItOFVdZ8mAKijeFayYdwCENkwCjXe47AZJuBfBjt0gjQ3hBs8sqfi7aBIL3jjjuSFsW0Sxa6WdgJL2szTFNYCkubwV6Gmj9rKVLEEYkMEZ5IFiIGZ9MuyMh45IMGx3eWGecwaYFoIBif0jhkDBEF2POHfCBM0jUe+fCOZkpYuSylGflgv1GHfIhffKZX2FooIw6WwqXVqpIPGhr+s+tGPkz5mL5h8EprxAZF+aozuWwRkrzUNofbiXyoA1WnLsATxkXzUUWm/B4GAoV8DAP1EufQESAITAdQgxNyRsaEWeu0S6/kg4BCCtgE0HwwNDTKpO0wTUPImYOvOuSAPYXpA8KGsM/kw6g8q+4JoKrmA0Eg3AlP5AfxoeWwYgc5YgBLoJmesdKBcJQ/KnxpOeCAA4JNyXjkQxw0BfIlD+KnpZl33nnTzqRwqzqCzeia3YF4kB0reBh2jkc+rB6iKaDZEIf8i9O0FXJl9A/HalqkjXBn84KcdCMfCNC3vvWtxuQD1tKAVLABoQ2SR+mENRJUJR+0Fr2QD4QABqZ52MfQZMgXspTta/JSW+WaXSv5QETVPStu1Afln7Fi1EtrI93FFQSGiUAhH8NEv8Q9NAR0yoSo6QBqfdMYnhGCNARG4oSgUS5Vfe6sERRz7oRAVQBYLWGKhHYAeaBut3KD4R81uZUxbByE1SqwhYkAEV6ENsFLYBA8eSMuQCEf4pReq0n89y07CVoDo2JTE2wKqOEJJUKHP1uYE0gEIgGPeNGqEOwMJ8UnHMQBicnCTvjCETbtCcJiLxLhmybwXdXJhzjk21STJaEIHoJEKCJecJUvuGSHlMHLFEpeyYHs0GggDb5neGnUL/+0NtJmikiaCXn/OznvaLqQsFyW/EqftCi37AhtUygZB0SSgSvslS2tBCzh4F2eulGXlBk/SJP30pcd4iLtpk6kBzFj4yFNyoimyGoWBAHppDkTRiZk/Fh1A5+q5oKxLkJk6k1503D4Dm6+ZWCL4FqhRBsmja11MKex3AsCE4VAIR8ThXSJZ6QQ0EkTQgQJoYd86NBpBIw6CR7TITa9MprNgo3wpM5mBFpdrmhk7jkCw/EnDAJd+IQXo0RCslXzQVhJCyGI1BCE0kdIS0sWjISPOI2IaUg4z8QpjQwTCSdTAEblVQHDDw0KYcmPqRPTJkiJfIsPcbC81khbmjhaHMKM9oLgz3tlICyt00f8I07yaKmuTdNMvxB+7FZ8g9RkGxf5yE5YbBLE4zuEh8AUnucIgefiJ6wUqlegAAADNklEQVRhi/gQ6MoQMWjFNYft7h0tFDKTy9JzaYBxLjfPYFvFQdqRnVze7rA0HQcTS7UJfmlWZsrENxnbnA7fCYc/6YED4mCPEmlCUJFCxFL8pnaQSVNh8ISd9Kpr1bKFT66z/MAF+fUtcoVQ82M6h2aF1i+Ty5y2ci8ITDQChXxMNOIlvpFAgIAgcAlaAoM6nwDUcevY3b03+iYAc2edhT0Vf34mQwSL73zD8ec73yMPWWXvO+9anfgIECNqJEY40pPTkv2L07PqFINn4ieAq/FkAuHb7IfgkR6Eg8D1HUEoTcIk8PN/3wlDPoTtO6N1WBGW7fLBv/QhBTkecQjD5Rt540dc2Xnuff6OYOYvxy9O4bn44dc7GPFbTXMOs3oXPn++G6/cfFPFwf+Md/4uYwkTeKhDwuZPevI3/ktXdr4TNr8ZB/8RT1ok2hbaIWGqN8JF3GiZkBxhwdI3OS3CrtZZ4br4qWKpTtGOITTSxU9xBYFhIlDIxzDRL3EXBP6FAEGKBJ1xxhlJ25KFWAFo5kcAyUIakQx7wdCO0FawA6K9MF3ElqZKOHpBBWkx5UKLZ3pLfMUVBIaNQCEfwy6BEn9B4F8IICBG065CPp4/1UK5016YjmHzgYSwm2Hnwp6EbRJy0lRbgXzQgpTpludPnZoMOS3kYzKUUkljQaAgMNMjgICYcmGXYsdVtjP+m0IpriAwsyFQyMfMVqIlPwWBgsCkRIBmg5aCXQrC4e4/zUhxBYGZDYFCPma2Ei35KQgUBAoCBYGCwIgjUMjHiBdQSV5BoCBQECgIFARmNgQK+ZjZSrTkpyBQECgIFAQKAiOOQCEfI15AJXkFgYJAQaAgUBCY2RAo5GNmK9GSn4JAQaAgUBAoCIw4AoV8jHgBleQVBAoCBYGCQEFgZkOgkI+ZrURLfgoCBYGCQEGgIDDiCBTyMeIFVJJXECgIFAQKAgWBmQ2BQj5mthIt+SkIFAQKAgWBgsCII1DIx4gXUEleQaAgUBAoCBQEZjYECvmY2Uq05KcgUBAoCBQECgIjjkAhHyNeQCV5BYGCQEGgIFAQmNkQKORjZivRkp+CQEGgIFAQKAiMOAL/H9OXp7bx/qetAAAAAElFTkSuQmCC[/img]
Approximate the percentage recycled each year with a piecewise linear function by drawing between three and five line segments to approximate the graph.
Find the slope for each piece. What do these slopes tell you?
Elena filled up the tub and gave her dog a bath. Then she let the water out of the tub. The graph shows the amount of water in the tub, in gallons, as a function of time, in minutes. Add labels to the graph to show this.
[size=100]When did she turn off the water faucet?[/size]
How much water was in the tub when she bathed her dog?
How long did it take for the tub to drain completely?
At what rate did the faucet fill the tub?
At what rate did the water drain from the tub?
The graph shows the speed of a car as a function of time.
Describe what a person watching the car would see.[br]
The graph models the speed of a car over a function of time during a 3-hour trip.
How far did the car go over the course of the trip?
There is a nice way to visualize this quantity in terms of the graph. Can you find it?

IM 8.5.10 Practice: Piecewise Linear Functions

The graph shows the distance of a car from home as a function of time.
Describe what a person watching the car may be seeing.
The equation and the graph represent two functions. Use the equation y = 4 and the graph to answer the questions.
When [math]x[/math] is 4, is the output of the equation or the graph greater?
What value for [math]x[/math] produces the same output in both the graph and the equation?
This graph shows a trip on a bike trail. The trail has markers every 0.5 km showing the distance from the beginning of the trail.
When was the bike rider going the fastest?
When was the bike rider going the slowest?
During what times was the rider going away from the beginning of the trail?
During what times was the rider going back towards the beginning of the trail?
During what times did the rider stop?
[size=150]The expression [math]-25+1250[/math] represents the volume of liquid of a container after [math]t[/math] seconds. The expression [math]50t+250[/math] represents the volume of liquid of another container after [math]t[/math] seconds. What does the equation [math]-25+1250=50t+250[/math] mean in this situation?[/size]

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