IM 8.8.7 Lesson: A Proof of the Pythagorean Theorem

What do you notice? What do you wonder?
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7ZwMYOdnw0849zgvdYTPimeCC8IRmJNHKjmUNaWdJR0F6Dy2AbU9G5kVjciw2sfbWIp8WSJ23RR7BakzYRbvDMiYsJx/fp1pnfSQuHAQ1oa/DWXAJeA3CVAkyj5jBsbG2Boa4DqE+UceCwAeEgACD1L3DBEShZeGMLM3oZm+ggND8W+/fuYr/3XXz9+Bh/UF/xQrgQkwGK65+mABgGMFy9eYGxsDBcvXkRfXx+zKpDFIjUtFcEhwfD09oS1nRV0RbrQN9eHka0IRvaGMHM3hVusCwLW+yIo2x+RpWFIb0tB7o5MFHXlovxQMWMTJlceccuwVPdLrXManwSE83dlw8zFBM0tTXj95jXTN2kpc+AhLQ3+mkuAS0DuEqAJlnZte/bugY6pNksZpclKegHlr+c22UvLi2RJfCDNZ+oZNXtq81rYBdtghc4KODo7oK29Fbdu32LuLk5KJnd1Z9YK0nkCEdMBCeoDibWCeFrIDUkBnFTBmLhbqJoxMdm2tLVgfeZ6+AX4wt7JHhbWFtDUW4OVOiugY6YNkb0hzD1N4RHvhqiiMMRXxiC5IYFxwpALZOPRMgbyyRpBcVUELCijjMAF6Yu0xYJ0aNMcAQfpIP2PahIRE6+zpzNz99Emg+5f+uDAQ1oa/DWXAJeA3CUgmYQHhwahbaiFvJ3Zi6JQnDQ4UORrWlRaztajaG8uM3//pPFP6OjrMNr6K1ev4O1bcSAqgUFaGKl/pi4UclcKFbqARD7SzxJQwYDFH+IATuYS+f3fKafSQZzkEnn+/BkL4Dxz9gwO9hxEe0c7CosKmbVCZCzCas3V+GXZT/jz3/4Lf/n5f7BE5xdoW2vC0s8coflBWFsXj/UdqSjcm8usFEQ8R2CCFv62C01ol4AJBYJ6crUQ94ytvzXWZ6QzF990usSBhwopPG8ql4C6SIAmo8uXL0FPpIuM9rTPvmFFLsiL5lpSpGQUC0I73+CcAKwUrcBqXQ2krEthpGRUG4ayYXgcyNejTAIyGLCY5LAgORGYIGsFWSmIv4JcIM+ePWPcFZRuSsDu9OBpdO3bi+bWZpRsKEFUbBTMrc2hY6jDSOF+XP4D/r78b1husIzxtFj6m8Mr2QNkqaLMpeKuPFSfrGCAgqwTkgezUhC4kACMyfgKsbWihWVAKVrHSb/IymLjYo3Dhw+z2JOvpQlw4DGdVPhnXAJcAnKVAE3kVIPEzMIUidVxYjOvAndmip6QhXQ9WpgoIFBCSqbvoIvV+hqfSclu3LjBFlBpN8x0u1a5KogcTy4BEfT8haVCKtVUQowlARZv3r5hMnny5Alzgdy+cxuXr1wGWSuIw2LHrh0seLOorAhpGWlw93GHkYUR9Ex1scZQA0u0fsZK0XLoO+rCwteUWZ6iyyOQ2bkO+buzWWxF41ANCxKeyfUhJB2ati2XWlHXXwnXaCdExUSyGBSS43QHBx7TSYV/xiXAJSB3CdDO0NHJEWF5wcwsTAvitBOajAIv+bml4kYkVpDRZpbOTAGGdqE20DbThKuPKyoqK3Dy5Ek8ePAAlApJbgNVBx8SwDHVakEWC7JWEKig+6U009HRURZbQS6Qnbt2oqmlCUUlhUjPSkfc2lh4BXjCzM4UxrZGMLYXQddaG9rWWjD3MQXV2PFO9UBUaRgDFkVdeSzNtK6/igGLz5aKi1JxFVOsFWwszCPGQpk6Tm4WCio1sNLH5i2bmeWMZD3dwYHHdFLhn3EJcAnIXQIfPrxHcHAQ3GKcxQFuFznwUMbCQYtcx8UWFh9ACwctmiauxnDwsEd6ZjoLAr5x84ZgSMkkAELaYkHAiMVUSFF4S1JNJcDi2bOnuP/gPqOZpzTTk70nWTbIps5NqG+sR35hHtamrUVMYjQCIwJg72EHC2czRopl6WkOYzcRbAIt4ZHkhoBMXwYsCLBRjEXZwSKWztw0LM4E+SLFdJJ5Vp2BNd0bxZYEZfrDydWJgTcCHTOBVQ485D698gtwCXAJTCcBWhjWrVsHC08z8U7wYjO3eCjZukMLCPnpKQsipjwS9qG2sHK1ZGRSRM1+9uxZvHr1iqVDz7Sbna6vZfWZBHRIWy1IjygbhOqDkMXiypUrGB4eZmybHR0d2Fi5kfGZEH9FcFgwvAO84OHvDjsPO5g6msDa2xJOoQ5wCLWDY6Q9/NZ7I7I0FAk1McjYlIZSxl1Rhpq+jaxyMMv+kAITJDPJg5hllQEelX1NsnZsPFYGA1t9lFeUswKG3+pzDjy+JR3+HZcAl4DcJPDbb7+ipqYG2uZaLOuCTNDKnkD59cULpwSAEClZWmsyI5OydLeAk7sjMrIycPzEcUZ7T9aE+QSjSgMIaRAhHVvxOc30w3u8ffeWxVg8evQIV69dxfCZYRw9dhRbt29l2TmUZhqfGI+g0EC4errAycsRjt4OsHKzhJWnBTxi3OAzSYoVnOOP+MpoRrZGwIJcISzV9GQF6gaqmC5+YbGQcoMsVmDxvXFBY5eAqqGpAS6MXmBBt9+aODjw+JZ0+HdcAlwCcpMALVj79u3DCp3ljGKZguq+N8Hx7xW/o6bdLAU+Fu3LY9TsFp6m0DXSQWBwILbv2M6sDAQSJHEg0ub1f0GcmisBGvRMQEMabJAe0P8pzoKovInpcmhoCD09Pdi6dSsKCwsRFR0FX39fOLo4wsjMCHrGuhBZGcLIzhBGjoawD7KB/zpflq0TURyC5MYEZG9bj8K9OSg9UChm2jxdDXKFEM08ASuuS7LRJeL7oFRebStNpK5LZRk+pAvfOqYFHqQc9EdSCP7gMlBnHaAdlmTC/NZA4d/JXgIk+9OnT2PZ6qUo2V8gZklUsquBL0bTL0a0UJOLgfhAiGl2XctaOEXYQ1O0hoGBpuZG3Lx1k7FUkhWEWSs+fvhMjEUWC3LRELCgjJCh4SEcPnIYm7duxobyMoRFhMHFzQVWtlbQNdTBijXLsdpAA/pWuqwInm2gNSsoGFsexSi817enomR/PioOlzAK79q+jWgcrGHAgtpI7qIZ00y5jskUdJFeZHSk4cclP6J/oB+/ffp+baBpgQdNxKQ4T58+xeMnT/GYnqUf9NmTJ1KPKd9L/5a//lJ2spCHRPaPH7OB/GhsDGPjExibeIzxx0/4Y1IGYxNPmEzoeTq5jD0W6/Cr16/ZDkz2Sys/47ckQMCDeA40tDSQ0ZmGtvPc4qEqwIcWGyKrKuwiUjIX/FPjR6zRWoP8/HxWeIyyQo4ePQIqk04ZMuGR4TC3NIeWjhaWrliKP//1z/jff/sT+98q4xUQOeuzomPRGyKQ2pzE+CvKD5UwS4uEYZPAhCTVlKww3GoxPUhUpA5RHxD7qYmHEXx8vRnjKlmzvndMCzyIVa2vvx8iM3OsNjSGprH5lIcZ1hgaY5WuATT0RdA0Npvy/dTf8/dfy3D+MlkjMsFqAxFWrtHC0mXLsGTpMixZtRqr9I2gITLFaiMz/jAywyoDYyzX1mPPq6fKRWQKDUMTrNYzQFJyMgPa3xss/HvZSoA2OA8fPoSegR4Sa2LZLlWRkya/1sIWLokVRFwhtxhucc74f/70f+PPf/4z/vsv/43/+sd/4ac1PzITvKmnMQMoROPNuCt2ibkrmikL5Py/SbEYOZaEFEtAxFhcV6bXFQKAebuy8Pelf2fBvGTtkna1zTRjTAs8iL1u34GD+NnICvZlHfBqO/TFw7P1INzq9kAnYh1ESQXwaj34xfdTf8/ffym/ecuj9SA8mw/AvW4PrLNr8JOJDQMetvYO+PsaPVhmVcOjqRterT28P9p64N64D0tdg2BX2v61TFp74NlyALoha+Hs4or37z/MNEb453KSAAEPmmts7W3hm+aFtpFGmZqA+WIx/WIhK7lIgAejY+/Kg0OoLTS0NWBmbob//dc/IbosggVtMgpvAhdUxVSqgim3WMi3f2TVzzOdh2I7CHQ6RzvAztEWz188Z9lO8wYer9+8wf6Dh7DSzgPBe88gcWjii0fC4BiiT9yCVX4jnKq2g95P/Q1//6XMFiyPwXHE9z9AxKErcKvaDl03f3j7B6C/v5+ljwVFxkAvJAkhXed4fzB9HUds713oRq5H0J5hJAyOf6GjpLPxAw9hlVkJZ1cOPOSELb55WjLJUipkQGAArPwtQCW2Z5rk+OfCW6QohqK+vwpJdfEwczOBq4cL9u/fzzgc3NzdIHIyQNnB4s+p0gQ05lN4jPe98Pqe+oSsHWUHCrHSYAUrYEfhGbNxs9CkMK3FgwGPnkNYZe/JFrKkM08g/aBFNObkHVgXNsO5eieb0KW/56+/lNeC5DH8GIlDYtARtm8ENllVMPUMQE5ePm7fucMQJrnGTvT2wc4nEJYZGxF9/CbvkzNPEHfqPnSjMhG89ywShx9/qcPDEwygWWVx4PFNdCDHL2mSojiPjMwMrDbTYAREfJER5iIj3S+04FC8xcajpQjK8oepgzFLZSWOD5qLqE+JStzMygyeSe6sgBnLWFqkHBfSslOn12ShDM4NgJWDFctEoiSE2Vg7OPCYAqgWBBDkcS4GOiYQ13cP3u1HYBSRAtfAUGzeupWR5dDETR1ND4oYb23vgLFHAJyrtrNFV3D3Iw8ZfeOcHHjIETXI4NSkt+RuaWpuwj9W/p1lJajTxKyO90JWCwId+buyYB9iCzMbU1RWVeLevXufzezUr7T73bFzB0RWIoQVBKNpqJYHg6pZNg1VoTV01EdZRRkLKqWxPNuDWzy+sXApc+Emq1LC6THEHL8J16rtWGnvCe/gMBw/cYLlu9Pglj7EgXqPkF1QBD2vUPhv7RW7XKbs9JV5T4q+Ngce0hoivNekwwSeew714L9++C+WFsn9/sK0eFC/kGuFgkFTGhKhZakJCxtz7Ny5E4+fPP4qJZ36lWrxFJUUQWRnwNItKfuBYjzUEZAttnuifoytiISprQmrvjsXNwvNRBx4CBF4DD9GwulHiDp6HRbrNmCNhR38AoNQWlqKu3fvTutHk+weL12+DO+gEIgi01g8CAEYRS/4QrkeBx7CAxvSLSKdpceZM2fw57//GcVd+eJdMTfJC2pxZqDjYjPqTlXCO8UDP6/+CX4Bfli7di2uXr3KLB3S/Sp5TX1LZGCR0RGw8rFA8b58ztWiBlYP0of609WwDrREYnIixsbH2JpE/T3bY0bgse9gD1bYuiFo9xDiTz/68tH/EFHHb7LgUh7jIdt4Dhb02P8A4ftHoO0XDUNLG2zdvgO3b99mLH67d+9mbpWpnUw7DPKxPXv+HBvKK/DTam1YZdcg7tS9r+IbhAIM5N2O2L57LLg0cNcQCySNH5DS44GHzB1lmVExmdXyfrZjhv9OhhIgPaYy7H/74W/I2pwuznrgrJKCAR60syXXCpF1WfiYsayV1rZWtgHq2teF5ubmz2Z26TmJXtOc9OLFCzQ1NTFCMC+peA9u2RKmZWs2lhuyfK3flAYzJ1Ps2r2L1cmR7vvZTA/TA4/Xb9DVfRA/iSxhW9IGj5aeKY+DcK3fC/3YbDjX7ELi8OLdVctq8aTgRxZEeuo+S0/+h4E57B2dcOHCKAMU5EqhAkgVFRWM7VESyCMZ4BTQRYRvHR2bUFJSiqycXPykbQjfzmPijI5F6HIhi8eaoKRJHT4IjxZ6TOoypSU3dUM3OBFOLi4sKG42A4b/RvYSmJiYwNLlS0EcDzSp8UVJ+YsS9QEFkbacawBVYF0pWgFLG0sMnB5gbKQ07xALaVtbGw4cOMA+I6BBn9OD5itKld6zZw/y8vKwfv166BhpI6EqlrlruMtF+X08G5Ax3W8oXscjyRVBYYEso5LWorke0wOPNwQ8DuAvK7Ww0jsC2hHrpjzSoB2eCoP4XATtPYOkRbioyQpwkOzIHUKpnZGHLsM+vw7L9E2QmZXNfKQ0gCWDmcDFuXPnsHHjRty6deszIKFI8ps3b6KhoQFUjZEmhBcvXyI5JRVLzB0R1n2BgQ+ZtVmI7qlp2kQxMjZFLdAOS4V2RNrkY1KXw1OhFZqCH0xsOfCY6wNWXFIAACAASURBVKwh49+/e/8ORsZG8E/3YaZ4DjyUuyiR/MnKUdNbgbD8YKzSW4nYuBjcuHkDv/7262dXL81N5GppbGzEyMgIS42mzyhFemxsjM1HtbW1IGBJj3Xp62Boa4C8HdmMs4WAzXQLG/9Muf3/LflTOjQV1TN3M0VdfS2zvlOfz/WYEXiIXS3ukxwIYyxQkdwA/36IeRE46Ji/q4VZOQbHWdZK0I5+GEevg5mjC7Zu28YK7RDgkD5oR0GDmgprEcggCwcVVhocHERVVRUrqvT27VsGVH777RPu3bsPe2dXaAXEsXiRxRbvIbYiUdrsuJTeinWYuQ/7H7D0Y04gJq1lin9NbIe+fr6sBDsteHxBUtLCc6mVubqI8IvibVyjnWFgaoCysjIGJGjjIz0n0Wv67MSJE2htbWWZLZRdd/78eRQXF6Orq4vNYzRv0eJE8R4eXh6wD7JF1fENHGSqWLwHA6QjjaxQoKO7AwaHBj9nMs111pgReDACMXsPBHeJORDYJE6788kHAxzc0jHvwE2SI+3IKYDUrXoHjPyjEBwZjb5Tp1gqmvQAl3QqfUYPAhv19fXo7OxkIKS6uprVR5C4X+j3f0xOCoNDQ9A1tYRlZiViTt5efPEepKNSeivRX3HW0CNOICZRLiU+U0R8ZlYm9O11Wd0HboZXPPCQuFYah2pZ1oqFhxkr/kauEgITBBxmmpPoe8pu2bx5M3uurKxk4INACYEOOui/9P7YsWMwsTCB/zofNJyuQQeruaL4+/3Wrp5/N31/0IZg47EyOITYIyUtBROPJ6bVidlMJTMDj28QiC02k71M75e5VsaRMPAQ4QcuwDa7GmZegcjOK8DVa9eY++R7HUeTwKNHj1BeXs5cK1TvQjLApf9Lg/39hw/Ysm07NK0d4VK1nbl0aPGV6T1N4+YQ+vkpLomsd5xATFpjlPOarHgtrS1YZbSCZU5QnAef/Kef/OUhF1pQiOCr8tgGhOQGwsBSDzFxMcySOpvaGzTP0HzU0tKC9vZ2Fos2HVCh39H5yDqioauBpNp4tJxtYHE98rgvfk7Z6hBZI9Oa18LG1RoUWEx9Od+DAw9FLpoMdEywbAri2TAMS4aDtz86NnVi4vHjacHDdB1LA5gelCf/7t27b6JOAiTPX7xATmERNF384LflJFtwhQ4M5N0+Djym0yzlfEZxA4cOH8IynSUoP1TMFyIFmuDJ0kFU9Xk7smDpZw6RuSEqNlYwt8l04GEmDaH5iDJYKN5MMj9N91v6jmp6rM9YDw3RKmRvzeBU+Qrs74WAsfqBKrjHuSA8KoyBS7JgzffgwEMRwGPS1E/cHLEn78C9Zic0HDwRGhOHkyd7WfQ3DUh5HHReUpBr168jImEt9EPWIqz7/CSl+uK1fHDgIQ9tm985yUVIdNsrdVYgf3c253pQwEJEgKN9tJmxxSZWx8LATg8ePh4sQ+XFyxfMtTK/3vz+v2gzREynPn4+MHYVoeJwqTjegwebCtbSR1axwr25MLTWR1t7GwsHmM7K/v3eF/+CAw8FAA8WzzE4johDl2GytggaptYoKduAO3fuyHWAS5SAwAf50ftO9cPWyx/m6RsQ03tn8cV7SPU1Bx4S7VD+MwFj4qlZo7eGpW6yuh4KWHwXsvtT6f9OBpFSgKdPmhdWG2pgbcpaXLx4kQWvK0IjaNE6N3IOxubGcI11Rt1AFateq9JyVVOdZUGl5xtZhpONvTWuXrvKrPML2Sxz4CG1GMnavC8BHFRVNmjHAHQCYmHu4IKu/d14+VIcsKWIQU7XoIH++vUbdHRuhqGrD1xrdrJqt7K+Z1U5HwceitK871+HTPovX76EsbkRi5jnwEO2vnnJYs4CSCddK8QiahNoBX0TPTQ01oPixMjytJBd7Pd7+stfUIzA7j27oWOsjYjiUDSfEVOqUzslbebP8tGFuciVrB21pyphYKvPKPDfvH3zTff+l708/TsOPOQEPFj2xGSqrGfTfiw1d4BvYDAuXbo0qwDS6btrYZ/SBE8cHxk5edB0C0TgztNil8siDDblwGNhuiTLf5NeUmyAk5sjfNI80Xa+iS88Mt4902JO2UKtI43I7FwHDZNVsLC2wOHDh/H23VuFAg6J7tCOmTL0ikuKoWG4ijHX8nRq5QONqaCEgr0Ta+OwRmcNzl84LxOrGAcecgAejBCs/4GYEKygAZqW9sjOzcP9Bw9mTEuTDEZ5PtNAp0mesmc8/QJhEpeNiMNXGWOqqlgqZNVODjzkqWlzOzftsskVGJsQCyt/c0ZeNXXy4+/nvyAR6CArUv1ANbMsrNBZjpCwEFy+cpktIiT/hZjN59bb//41XZOuffPWTdYeK18LlB4oRPv5Js5eK2PgOd/xQ7rTcraepbpTphPxRNEastCDAw9ZAo/JVFnmWtk5ANO4LJg7uqC1rY1FfCvSjPktxaD0xSNHjsLU0RV2hU2MwGyxpdhy4PEtDVHsdzQuyMyfX5gPAyc9NJ+p4xYPWSw8l1oZGRsRgpV2F8IlyhErNVcyCwMxiy4kK0GWGkJ939vbCztnW/ikeKK2r5JT58ui/2VwDrKS5Wxbj3/88necOHkCv336TSYglQMPGQEPSTwHlbH3bOyCoV8kfAKDcez48c+1DWQ5WBdyLpro371/j/rGJqy2sId3aw9LsV1M4IMDj4VokGz/SztfWgRb21uxxkwDNb0b+Y5XRosGWTlSm5IgcjSAuZU5qMgk7VppDlCGlWM6zaF2UJuIB8TM3hSJ1XEs24bIxea7U+f/m7+FTCI7ibXDNsQaru6uePL0CX7/Y+HWDtIBDjwWCDxYLMfQBBIGHiH8wChscmpg6OyFdRkZuDJZMlooA1wy6Kk9NPEQd0hyahpWOngheM+wuJ7LIon34MBDog3Kf5bo496uvdAwWoXyQyUceCwAeNCCQXEyG4+WITgnACJbQ0RERbAsErJ20tgX2kE6QFaYjMwMWLibM16RthFOny8BAcp4Jj2iFNpf1vyMnbt34v0HMUeLLHSHA4+FAo+hcUYI5rf5OPRDEmHn5YdNnZ2sjorQAMdUhaFdJhWXc/XygaZ/LCKPXFs0KbYceEzVBuW+p7FysvckNEVrULgnV1yv5dLCd23KmLCVeU1aLCiANHdHJqt9Y2FvwQjB7t+/r9T4stloFwEiKjrnG+A7Wc+lXMzpwvVAKZYfCvT1XOsGa3srRo9OLjFZrWkceMwTeIhrfYwh9sQtuFZth55nMCITktDXd+oze99sBpsyf0MDnZRp4PQgDCxtYZ5ejti+u4sCfHDgoUzN+/raNKFduHAB+qZ6WN+eyn38c7R4EOCg7IPGoRokNyTA1MUYXv5eICsSFZOkgEBZLRpf957sPqH5iOq5mFqZwm+dN5qG61g2Dt2fMgHdYrs2pdCWHy6BhvEq1NbX4uPHDzK1lHHgMR/gMVngLfzgJViur4CevSuKyzYwEiShBGzNdiqgyYhSGbft2ImVZrZwrtq+KCjVOfCYrYYo7ne3bt+CuZ054iqiGZkUX2xmb/Eh0EGU1kHZ/lhtoIGEtQmMDVZCYa64XlzYlWg+In4PKoD588qfWT0X2nnzwoGz1wVZgCTKgoooDoGJlTEuXZY9BQQHHnMAHiyeY3Ac8f33Ebr3DAzDU2Dp4o7tO3eq1K5i6tRAu6Fnz58jv6QUK+w8ELCjX+3BBwceU7VA+e+JxMo7wAsBGb5iCm2+y/3uLp8WZFqYq06UwzrAkrG/VlVXMUIwocZzfE/TCHxQxVuq57JE6xcU7s4Fi/fg+vBdfZAF6KBzVJ8oh6GTAQqKC/D8+XOZpNBK9zsHHrMEHv8GHQ/g13kMK2zd4e7tgzNnz7KIfFUwY0p3/NTXBD5u3ryFgPBIaAclIJL4PdQ40JQDj6kaoPz3ExMTiEmIgWuMEyscRuZeWU2kaneeyVRZAh052zKwVPcXaGpr4ujRo8xiIMQA0rloGLWfFjxHZ0fo2emg5uRG7n6bo/ttvjpPlsaEmljom+mi71TfguuyTNfvHHjMAngwQrCBh4g+eh1OZe1YYWSBtHXpSicEm65D5/sZAScicertOwVzFw9YZVYhtvfuZDG5J5AVcZdQzsOBx3w1RX7/o4WmoCif7dwbTleLA0wVNNnOd5JWxv9oYSBTeG3fRkQWh+Knlf+Ef6A/bt26Bar0S4u2qm+EqP20GRodHYWeSA9eSe7MlcTp9OXrciHdahysgV2wNaLiopjlTB7xQRx4fAN4iFNlxVkrwbtOwzg2E1oiEzQ2NTGqX1Uf3FOXELqfV69fo6mlFYauvnCr28MydpLU0PLBgcfU3lf+e6LPrm+sh5mHCXMdcL/+l4sMLQpkBSJCsJL9+XCJcoKOoTZKy0rx7NkztQAcU7WQNkPbtm2DrqkuYssj0Txcx2SwiWe6yMUaSLFC2dvWw8zZFFu2bmH8KvJY5zjwmAl4TAaQRh29Dve63dDzCoWHrz96+/rwkXLh5VTGfurAU/R7QrcPHz1CelYO9HzCEbD9lFrye3DgoWjN+v713r17xyY7ysgo6yniAYVTrD20KJAlKKUxEZae5nB2d2ZZK2/evFGZrJXva8GXv5C4XIjV1shehOwt6xnw4m64L0GprCxvTUO18E3zQkBYAC5euii3umIceEwFHoz2fALxAw8R3n0BNjnVMPEMQHpmNq5du6a2A1wy3AndUmbO+dFReAeHwiQuCxGHrqhdPRcOPCQ9LpxnymY4cKAbZk4mKNidzXz6sppQVfk8tMiSi4HK2IfmB8HU0QSx8bEYGhpiGWmqHs/xPQ2k+yN+j5DwEDiG2ovruVzg9VxkrdNkUSvelwcLDzNsrNool6BSSV9z4CENPCZBR9yp+yBCMOPodDj5h6B90yY8fkx0scJj/JN0pCyfCXzQInCwpwfmrp6wzqkVu1zOPFabWA8OPGSpMbI5F+OUGeiHpbM51rUlc+BxuZUxuFIAKTFIOkXYw9TGBBsqxKn7siR0kk0Pyu8s5HI5ceIEnDyc4JvqxeJbyALUyV0usnG5XGpl2VExGyJg72aHU/19zNohDzcLaQkHHpPA4zMh2Mk78KjbA33vUITFJeH4iRNqGc/xvSmCXC7kc29qbWP8Ht5th5BwekxtMl048PieBij+e9K5C6MXYO9hj7jK6EUNPGj3SQsrFcxLa0mGnq0u3LzdsGv3Ljx58kTtLa9TtY8WQHIptbS2wNzBDEk1cWgaruXuuCnuuPlaQUjfKCXbKdwBSclJGB8fl2vMEAceBDwm4zmowJtV5kZoWjkgv6gEN27ckJuPa+rAEuJ7GuxUzyUlbR1+sXBCyL4RtXG5cOAhPI0j4EFjzifIm9UYab/QLJvdnIwm5/lO6nP9HwVOUoG0+v4q+K7zws+rf0J0bDRGzo+wzDN57UKFpxFftojNRxMTyMzKhJGDCPk7szjfi4x0m1x56e0psHS2wM6dO5kL70vpy/bdIgcejxlRFpWxj+i+AG3/aOiaWWLr9h0sSpwmwsV+kDn33v37cHB1x2rfKMScuC1OsVXxTBcOPISn2eTLp5oi4THh8Ep2Z6bfuS7aqv57CSFYaXcBrPwtsFJrJRqaGjA+MQ4iBFusoEOirRJw6uHtAbtAG9SdqmQF8WjHrup9r8z2Uwqtd7InAkICcO/ePblvuBct8BCnyk6w2AVyI/wosoK1rS3OX7igFoRgkoG60Gea6Giwn78wiuVaerDIrGKBt6pOLsaBx0I1Q/b/J12juiLpWelwCLNF42Dt4vHhTxKCUapsRkcaVopWwNjMmMU1ULzVYgcc0tpG89GpU6ewWms1s4yRO4osRDzeY36ZLgTayg4WQc9Sl4FcRTDeLj7gQQGkw+KslchDl+FQ2ITlInOkpa9Xadpz6YEp69c06X2gfPodO/GLvgnj94gfeKTS8R4ceMhaSxZ+PtIzosouLCmEbaAVavsqWXClMneCCrk2C+xrQk3vRkQUhULDYBXCI8Nx+cplfPz1I37/g1tepbWL9IQWx7b2Nvxz2Y9Ia05mKbYs2FRGrgeF9LsA2kqgg9wsUcXhMLM0ZXVZCNjJG+guKuAhTQgWtHMAJrEZMHVwQXtHB5vw5C1s6cGjaq9JGZ+/eIHM3HxoOPkgUMXruXDgITwNpPH37v071NbVwtrHEhuPlqk98KBUWcpaKekugFucC/RM9FBQWIAHDx5wy+s3VJR05c3bN4hPiMdK/eUo2J2D1pFGtdcXWQMi0j8qLmjkJEJWdhZev3n9DanL7qtFAzwIdCQMjiH6+E241+2BUWAMq0tCWStUwVHdc+EXqjI00Inf49r16wiIjIFBRCrCDoyqrNWDA4+FaoR8/k872U2dm2DlaYmS/QVqm7VAO02a9CkzI61lLSy8zGHraIvtO7bjxYsXiy5rZT7aJIkJcnFzgYmbESoOl7JMIB7vMXuXC1mJkhsToWWghcGhQRa8PJ++mOt/1B94THJzJJx+BHKt2OfXw8QzEOlZ2bh06RIz2c1VaIv19wQ+CKQdOXoMNt4BsMquRvSJWypZz4UDD2FqMVnWuru7YeNujeyt69UypVZi3q4+WY6wgmDomusgPDKMxS2oWhl7ZWoRzUcEPvoH+mFsYQyfFE/UnqpEO/F7CMCNIfQ2kB42n6mHkYshc+29ePmCbS4V0adqDzxogYnrf4CgXachilwHWy9/tLS2YWxsTK55yoroPGVcg6jiX7x8icbmFhh7BsK1dvckuZhqFZLjwEMZ2vP9a9JC0tvbCydvR6Q2JU2mS85+B6cKkz0jBNuTC5sgKxiY6aOktAS379zmrpXvq8e0vyCw1tnZCZGVISJLwsT1XHiWy3fBF1nc8ndm44cl/8CBgwdYJouiLP9qCjwogPQxI7yiCqueDV1Yae8J//AoHDt+nBFjKUrA044UFf/w0++/s8q863PyoOcbgcCdA6yeiyplunDgIUwlpHF57tw5eAV4IrYiisU/qIPpnO6BzNrkWkluSIDI0RDO7k6s1gpV5f30+ydhdogKtIp05vHjx8jNz4WRvSGyN69H60gDr278DasP6SNlUDlG2MHByQETjycU6t5TS+AhCSKNPHIV5unlWG5shdyCQty8eVNhpiQVGK/zbiKL96CS1Rcvwt0/EMaxWYg6dkOlXC4ceMy7++X6xz/+9Qeu37iO0KjQz6mS6gA8KN2zprcCQdn+WC3SQFxCHM6NnFvUhGCyVCQCH1euXEFwWDBsA61RdrCQWcuEbgFTVvtoTFGF45/X/ISt27YyFzrN64o61Ap4iANIx0GEYCF7hqAXkggjW0eWBkruAUWkCSmq45R9HVJS4hc4euw4DKztYVfUwuSuKlYPDjyUrUHTX5/06uHDh0hITmA+e6rGqrLAg7g5LrWgbaSR8SQ4hNlBR6SNquoqRpSmCL6E6aWsnp9SPZfjx4/D1skG/ut8GPMrxXuorP58w2KxUMBC1jdixaXYGLJ2KLruj/oADwoiHRxn8QY+bYewzNoV7j6+GDl/ngeQymmeoV0GgY/G5mb8qGXIUmwTh8YZBX2SdPE9Ab7mwENOSrHA0xLwIBKxrJwsuMe6ouZkhcouHORDbz/fhLwdWdA0Xw0jEyPs378fb9++5Vl0C9ST6f5OukPgo7GxETrGWkhpTELL2XrucpkCYAiIUWDzStFyVNdW48PHDwrXR7UAHlTgjcrYRx25CqeSVmjZOCM9IxN37t7lAVvTjVAZfUYDncAHWZPiE5Ow1NpVnGI7OC74KrYceMhICWR8GtIpIhErKSuBc7gjNh4tVTngQRM7kTLVn65GTHkkVumtgJ+/H85fOM8WRiIEo/vkh+wlQHKleI+U1BQYO4pQsDtXHCdEzKZTFuDF+p50M7osHAam+qwoo6KtHdTrqg08WKrsOAMdIXuGYZFcwAjBGhobQQFbtCjyQ/4S+O3TJ9y5cwfWDo7QDUtGtArEe3DgIX+9mM8VaOGgXWtzSzPs/GxRvC9fdXask7TnEteKR6IblmksQ25eLnMfEQ8OBxzz0Yq5/Yfm/WvXrsHF1Rn2wbaoPlkxmR3FwQeBrdq+jTDzNEFGdsZntu65SXjhv1ZZ4MECSAfHEXPiFryauyEKjIFPYDCOHD36OVCGD/KFK8hszkADnSbV/tOnoWtuBevcOsScvCNocjEOPGbTs4r/DY1Z0iUq/27rZYPc7ZkqAzyowBvFpKxrTYaJixEsrC2wY8cOxgbJ48sUp0sSHTpy5AhEpiIErPcFFUEj19dir+dC1riUpkQY2Yhw7MQxvP+gHPJMlQMe4oyVCRAhWETPJdjm1UHfyQup6etZVDPfVShugEtfiQb7u/fv0b6pE5q2rnCt2QUh13PhwEO694T1mhbpY8ePwc7dFultKYJnL5W4ViqPb0BYfjCM7EQIiwjD0PAQiy/jllfF6xfNR8TvQfEeKzSXI7k+QVzP5eLiJRcjPW0cqoFzpAPCosJYFVplAWLVAx5D44wQzH9rL/TDkmHt4YO29g48efKEuVZI4fihHAmQEj95+hQZufnQdAuE/7Y+xu8hxEBTDjyUoyOzuSot1GfPnoWTpxMSa+IEnRZJkzkRglGtEKcIe1jYm6NsQynu8viy2XS1XH9Da8GzZ8+QmpaKNcYayN2Rxeq5LNbYDrLI5e7IhLmLKdraW5klTlnrpcoAD8lCEXvyNtxqd0HbIxhBUTEsnZN22soSoFxHjoqdnPqAApUuXr6MoOg46IenIvzARVYNWGjgQ6JPVlmVcHZ1xfv3H1RM2urbXAIexLnj5e+JiOJQRgYlNBM5AQ6ayJuG65DWkgwzdxO4+7hj566dLLhRWTtJ9dWK+d0Z9QPFn3n7erG4Bio8uFhTbJvP1CEg0xe+Ib4YGRlRaranagCPSRbSiEOXYZVVBU1rJ2TlFbCCZbTQ8UM4EiDwwfg9jh+HpbsPLDMrEdt3V3DxHhx4CEdnpraEdOjR2CMEhwUhKNMfNGHSQi+knSqBDoobCM0PgobhKsQlxGL4zDDevXvHN0FTO1SJ70mXCMieOXMGRuZG8Ex0Y3E4xGMhJH1SRFtKuwtg7mGKkg0lzBJEoExZh6CBhzieQ0wIFrbvHERR62Bs54SOzk6+q1CWxsziujTQX716jaaWVug5e8O9YS/LPBKS1YMDj1l0pJJ+QovFs+fPEBMXA78Ub3FgoECABwEOcq1QpoR9qA1Waq1AeUU5Hjx8wOM5lKQv37ss6RPFe2zbvg06Jtosxfkzv8cl9akDNCN4udTK3JXxVTGwdrbC8RPHla6rwgUek6myCQMPEbC1FyvsPGDv7ILTp08rnGXte4rNv/9aAoSmx8fHkbwuHWvcgxC8Z3jS6vFYEBwfHHh83WdC+oQsBxkZGXCLcmHpfywjQck8DJJ4DiIEI/KlZSuWseJaZOEjsM0P4UqAwMfLly+Rl5+LNSYajNSN+CyEZkmbETwsQPfpHqlqr2u0MwPzY+NjzCpHMlHWIUjgISYEe4Too9fhUrEZy40skJC0lhOCKUtL5nFdUmrKMLp0+TKcPb1hmpiLyKPXwZhNBcBkyoHHPDpVgX8h3SFLgr2/LcgvT5YGeUzKszknTdy0SBH/QXRpOJas+Rm+fr64fv36552jMidxBXaLyl6K+ofA4bVrVxEQHMD4PcoPFS8Kfg/S3awt6TBzMMWWLVuYK1zZ+ios4MGsHBOIP3UfwbsHYRqfAy0jU9TV1zM2Q2ULS2VHnRIbTmRQ3QcOQGTrBPuSNsHUc+HAQ4lKMYtLE/Do2NQBa3dLlB0oZJVdZwMSZPmbTZOEYFTFk/zjbrHO0DbUQn5BPnP10kLG56RZdKaAfkL1cY4dOwYbJ2vG71HfX8V0S50tH01DtfBb5w0ff28WtC2EuEjhAI/JAFKqcupRvxd63mFw9/XHyZO9jMmQmzIFNHrn0JTff/8Db9+9Q3VtHVaa2cKn4ygSBseUHmzKgcccOlEJP6Uy8QcOHICFozkKdmcrJaWWAhApgDS1OQmWXuZwcHHA9h3bmcme2sdBhxIUY4GXpD578+YNGhobYGpngrW1CWgarlUZkrq5AmsCVBt6imDsIEJ1TTWzdigzqFTSfcoHHpNWDkYIdvAibHPrIHL3R0r6emamJyHxAS7pLtV7pr4j0Dg2PoG4xCQst/dCcNfZSX4P5cV7cOAhbF2icT84OAhrRyusb09lFV7nOunO9/fMtTLazMrYhxeGwNjBiBGC9Z3q4wXehK02s2odzUlUAZn4PSw9CNjmoO18k9qBD4kex26IhKmlCUbOjwimQrtygYfEtdL/AAHb+mASmwF73yA0NrdgbHxcMEKalTbzH31TAlTP5dr167B3dYd2UCKiKN5jmAOPbwptEX9JwIPqbTi6OSKxOhYt5+oVEuNBk3XbhUaUdBfAOcoRRlYiFBUX4caNGyyeg2+C1EMpSb8uX74MTx9POITYseBLioUQGl/MfMEz/Y8CshsGaxjHTFp6Gl68eCGYTbzSgAcFkJLJPa7vLrybu6HnE47AqFgcOnyYmTL5AFePAS65C7J6kG+x71Q/dC1sYJlVhbi+e0oDH9ziIekZYT6Tvjx48ABevl6ILA5jXB4LmYS/918CHORaoTTLjI406NnqwN7FHlu3bcXExASvci1MNZl3q2h9ofno0KFDEJmJEJztj+bhOhbETLrwPX1Rhe9JnzM2pUHLUBOn+k+xkIV5C0zGf1QO8JiM5yAWUtu8emhY2CMzNw9Xr13juwoZd7CQTkeDndIkN23egpUW9qyeC4FPZfB7cOAhJM34ui0EPIjuOiQsBAHpvmgcqpXfYjAZRNpwugaBWX74RfNnhIaHMtp24n+gtvBD/SRA8xH1b3t7O35c9gNSG5MYR4sQUrdlAWwoKNrYXYSg0CC8ePmCgWeh9KKCgcdj5tuPH3iIyEOXoBeWDA1DY3R0bmbleSmSnR/qLQHq4ydPniIz0xBGkQAAIABJREFUvwArHLwQtGuQWb4UDT448BC2ntFiT/wYqWkpcA53QP1AtVyAh4QQbMOhYtiH2mLZ6qWorK5kzKmUAcEtr8LWk4W2jvqX+D1SUlOwQn8ZSvbli8GHils9CDwV78vHX/75P+g+0I1ff/tVUABaccCD4jmGJ1iBN7/Nx/GzuQNMLSxw7twIN2MudPSo2P8JfFy5ehVeQaHQDU1G5JFrCne5cOAhbKWhBYFM4SWlJbD0NEdtX6XMgQeZ1FtHGpCzLQNrzDSgZ6iLnp4etgvmgEPY+iHL1kmsazZ2NjB0NkDdqUqVdrlQGjjFq3gkusHc0hxPnz0VFOigvpM/8JgEHMzKcfgqnMvascLUBglrkxmz5SeetSLLMaQS55LsZo8eOw5TZ0/Y5NaJ67kMTSjM7cKBh7BVhRZ+Aqidmzuhb6WH6hPlsgMekxMzLTAxGyKxWqSBgCB/FvX/4eMHFtQubOnw1slSAqRrFGxKtXb0jHThn+7D6rm0jzbJTucWwDw6V7cLAWpKof1Z82dGEy9Ed6F8gYdU1goRgpkl5sHI3hn1DY14/vw5N2PKcvSo2LkIfJCJs7a+AQZufvBo3M/IxRTlcuHAQ9gKI1kMDvYchJaRJjYcLJIJvTWZoNsuNKHsYBG813pA11gXmVmZvIy9sNVBIa1j8R4d7dAz00VCVQwLNmWBpipWz4UAU3COP4zMRHj46CFzswjNgic34EGpkhQ4GHPiFjwaumAcHAff0HD0HDrMc+EVMoyEfRG2o/39d9y/fx/J6RnQ84tE4M4BULZTkgLSbDnwEL5+EDg9N3IOWgaazB2ykGwDCQspVbpNb0+BlY8FrO2s0dnZ+blSp9AmZ2H3kPq1jvTt8ePHyMrJgrGjCDlbM5grTpWCTWmMUAFDysoqKy+DUC14sgcek1aOhNNjiDpyFQ6FTTDyDETq+kxcuHCBZa2on8ryO5qPBBj4+PQJ50bOw90/CKYJuWJ+DwW4XDjwmE+PKfY/pB9UD0VPpIe05rWMl2A+4IP+Q7vAmt6NiCgOg7aZFoLDgnHy5EmWZUULDj+4BEgCpAujo6PwC/SDY6g9s4xRvMR89G6uLhJZ/J7aGlcZzfhnzp47K9iCqjIHHjShx/c/QMieYYii0mHt6Yem5hY8evSIE4Lxsf2VBGhxoeyF/d0HYOLoBtuCJlA8UNIZ+ZKLceDxVVcI7gPSDZo3zC3MEFcRPa+aGrRgUBn74q482IXYwNDcAIVFhbh16xaLIeGgQ3DdrvQG0XxE/B52Lrasxokk2FQVyMWoCq2FrxlS01OZ9YZiV4R4yAx4SFwrRArl1dwNDSc/+IaE48jRY3j1+rXgomqF2BmLtU00OF69eoXahkYsM7GGb+dxuddz4cBDNbSN9MLVzRX+63yY1WK2Zm8CHESgRK4VspYYu4gYC+qu3buYa4Wn7qtG/yujlQR4X79+jbr6OhjbGGFtfQLTo46LwiYWI51Pb0uBsZ0Reg73CNqaJxPgQaCDyp0TDTYxUq40s0NOQeHnSnjUkfzgEphJAqQf9BifmEBicgp+MndCaPcFplPyCjblwGOm3hDW51TdOCIiAo6hdixFkHg3ZmOSJoBSe2ojQvODsNpIA9Fx0Z8Jwfh8JKw+FmJrSEfGxsYYv4eRvSEK9+Yy/ROsy+VSKwNHLjGOCIkIxu07twVNU7Eg4CEBHGQaD+06C4OIVBhaO2DLtu0sa4V2snyQC3FYCbNNv/72G+7cvQtLOwdoBcYj5uQdcbCpHNwuHHgIUwemtopIvPLz8yFyMGCF4r4JPIiBdNK1UnG4BC7RjiwwdUN5GctaoXNx18pUCfP3M0mArGJXr12Fk4sT7INt0TBQLVjwQdaYgj05MHEyQmNTA169fiVoXV8A8BBbOeJO3YfvpqNYZusOO2dXDA0N8QDSmTSZf/5NCRBIJbB6bmQES7V0YJ1Xj/iBR3IhF+PA45tdIZgviUSsubkZGqJVYnP36MwWDwId7aPNKNybBx1rLUYItnvPbp5FJ5jeVL2G/PHH7zhx8gSWrVgKqlRMrrvZuvtmY5mT1W+IHj0kLxDufm44c+YMS6EVsrTnBTwo5ZGsHNFHr8GlvBOrrZ0Rn5jEqo/SRMGtHELucuG2jfSGdqQfPnxE55atWGpsBY+m/Yg//UjmKbYceAhXD6RbRvNJz6EeLF2zBBVHS9mOc+pkLQYcTYz0iSrZahisgpe3J0vFJVcNt7xKS5S/nosEaE4iHWpoaMAPS/6B9e2pLMWW4oem6qEy35cfLoG1nyUKiwtVovzI3ICHhBBs4CFC9p6BRUoRRLaO2FhZxSJouRlzLirNfzuTBGihePr0GdZl5WCNWyCCdg+xGj+yjPfgwGMm6QvrczJ3nzl7BktWLUHB7pyvgIfEtUJMjV5J7li6aikjBKPKtjyAVFh9qaqtIfBBwaZR0VFYY6yBor15zO1HuqdMsCG5NqWKJ9bGwdzBjIF0VXApzhp4iLNWxhkhmGdTN3R8IuDq7Yv93d2fTZnc0qGqQ0tY7SY9+u23T7h0+TL8IqJhFJOJ8IMXZepy4cBDWH0+U2sIPNy4cQOrNFdhXVsyS42VTLjk124crBFH8ruKYGppii1btrBFgls5ZpIo/3w+EiB9unfvHlzdXWDhbYaKw6XzSu+W6K6sngn81PVXwiPOFeFR4YyQkQwAQl+Lvws8grvOsuJuRAgWeegKbAsaoGXvDgMjYxzs6REsQcl8lIv/RzgSoIHz7t07HDx0GFZeAbDNb0Bs7x2ZgQ8OPITT199qCU344+Pj0BfpI6os7PNOk4iSiKGR/O4G1npYtWYVdu7ayThh6D/84BKQpQRoPiK96u3rhZG5EXxTvVDXX8XAh6xAxHzOQ9aOnO0ZsHS1QGtbK5szZXnf8jrX94HHnjOMECxwRz8Mo9Jh4e6N2vp6tHd0oKmpifEvCB1dyUt4/LzylQAhd6rpU1PfACOvIHG8R/8DmRSS48BDvn0nq7PTZP/27VvYOdjBLd4ZFETXfr6JEYK5RDvB1NYEuXk5qK6uRm1t7Wdrh6yuz8/DJSCRAK1zpIvt7e0QWRkiekOEONhUiS4XCnYNzPSFm5cbLl2+xAwBkvYK+XlG4LHvYA9W2LohYFsfPBr2QtszBP7hUazWChX3Ik77trY27Nu3j2exCLmHVbxtZGq/e+8eUtZnQs8vCsF7hmVSz4UDD9VQDAKf5LMOCQuByEUf9QPVWN+RCjMPEzi6O2LL1i2M3ZTmo7q6OuzatYsFA/LNkGr0r6q1kvSRLHAZWRkwcjRE7rYMsRVOCeRi5GbZeLSMpdBSyvibN2+YVUYVZDoj8OjqPoCfRZYwiFqPNdZOSM/KwZUrV9gkQMKnaPObN2+ipqYGg4ODgvcpqUJn8DZ+LQFaQAh8jFy4ACcvXxjHZyP6xK1Jfo8n87Z+cODxtayF+AnNNdT/Obk5+OeaHxCcE4gVussRFhGKgYGBz/Fl9LuHDx8iMzOTzUdkKeHgQ4g9qvptIt26ePEiAoL94RBih/JDJV8FPc/HbTKn/1xqBXHaJNbEwdDUkAVgq5LOTw88Xr9G1759+F///Rdo6BmisbmFsUrSBECDmR400InTngY/7TQo8IY+4weXgKwlQPr2/sMHFlOkZWYFxw2dSFhgii0HHrLuJfmcTwI8Wlpa8H/+X/8HfvjlB+QV5DFCMEpzlJ5zaH66fPkysrOz2feqNBHLR3r8rPKSwMePH3D48CFYO1ohODsAjadrFBpsStaO5rP1MHUzRmx8LF68fKFSQHtG4LF3714sWbIE9fX1zMox3e6BBjbVUtizZw86OjrYa3l1ND/v4paABOhW1dTiL6u0EbxnaEEuFw48VEOfJMCjqqoK//mf/4mSkhJm5SCQMfWgOYo+P3z4MPsdpUBON29N/R9/zyUwVwmQXhHwra2tgZZIk2VWtZyrVxi5GFk78nZmYdnqJTjZexIfPn6Y6y0o9fczA4+uLvy/f/oTXNw9cO3atWlz4mlSIP8rWTtoYqAy0wRG+MElIGsJ0ED//Y8/8Oz5C4RGRGCJjZs4xXZwfF7uFg48ZN1D8jkfzSdPnz6FpZUl/r+//S/oGeixmis06U8FFfSe5qQnT54wKyxtnjihoXz6hZ8VTP8o3iM+IR6mriYo2V+gMEr1tpFGWPmbw8fPBxRz+dun31SqS2YEHl379+N/lmlghZktsnLzWECN9EBnC8Hvv7OAluHhYRQXF+PIkSMMiKiUBHhjVUoC4tiiWzCztoVeRBqij9+YV4otBx6q0e2//vYr9uzdg180fkFa61roWmsjOCQY9+7f+4qRlEAHAZLz58+joqICO3bs4IGmqtHNKttK0rnLVy7D3tEezpGOqO+vYlWUOy+1yo1cjNwsxfvy8T8//jd27NzBwDW1Q5WO6YHHmzfYd+Agllk6wjK9HCIXb7R3djKQIdlV0AIwMTGBnp4e5o7p7e3F+/fvVeneeVtVUAI0wEj3TvT2QdvUSszv0Xd3zuCDAw/hdz7NNZROHRAYAGt/SzQN1zLKal0LXZSUlTBLiCSOg/SCfnv06FFs3LgRx44dY5wG0psl4d8xb6GqSYD0i6wNBw8ehL6xPkJyA9E0VCt2ucgBfBDoIGuHV7I7jM2M8eDhg68AuCrIcGbgcbAHK+3cWQE487RSOPoGobe3jwX5iXedNxlLYGtrK65evcpcMXyQq0KXq34bSc/evn2HxpZWaNq5wa1+75yDTTnwELYeUB8TqOg71QcdIx2sa01hwXvEVEql7s3tzLB9+3a8fvOaWVlv377N5iOKSaPsO5qj+Hwk7D5Wl9aRntGmu6a2Bss0lyKlMUlcz+Wi7Ou5EPDYcKgYKwyWo7mlmYHrP/6lWtYO6vcZgcf+nkNYae/J6mSE7huBKDwZQRFRGL14EX19fSyN9sCBA7xGi7qMHhW7j0/EaDkxgdTMbGh5hCBwx8Cc6rlw4CHsDicLBgWHZmVnwtzDFNUnylnJeyrOVXWiHG6xznDxcMbxE8dx6tQpUNZLV1cXi++QWEGEfYe8deokAQIfFIuUtDYJWmZrULAr5wt6/zmlyl6e2U1D1ZeDcvxhYKLP3I0UY6mKAPubwGOVvSeC955h1UEDtp7Eakdv+AQEory8HENDQ9yUqU4jR8XuhQYb7WqJ38MvPBqGUesRcejyrF0uHHgIu8MJPIycH4Gdsx0ii8MYQySbvIm/YLSZFYwjQOLg7IDS0lKcPn2auYIJsKjiRCzs3uCtm40ESGfJ8ubh7QFLX3NUHd8g0xRbsnbU9m2Ero028gvzmJWFrqmKx3eBR0jXOVaSPK7vHlxrduIHLQOUV2zERxVFWqrYSbzN00uAFhiq53Kg5xDMXL1hnVuHuFP3ZgU+OPCYXqZC+ZTSA6trqmHpbiHOFhht+hyst+lSKzNlpzQmYoXuMlaNljJZVHUSForMeTsWJgGaj0gHB04PwNDUAD6pXizeg4CyLCwelEK7tj4eBub6GBoeUml34uyAx5knSBgcQ2zvXVhnVWG5pg7OjYyoZFDLwlSL/1tIEpAM9BcvX6K6rh46Tl7wbDmI+IFH302x5cBDSD35ZVvIanHnzh34BfrCL82bVaDdNIWSmt5TsGlglh/0TPVYOXDys3Nrx5ey5O8UKwHSP1bPpaMdemY6SKiORcu5BpkEm9afroaFnzkS1sazLNPpuGwUe7fzv9qsgUfS8GNG2ETpi5p+0bC2tWNZLXygz1/4/J+ykQDtMh6NjSE+KRmanqEI2Xfuu1YPDjxkI3tZn4XmE3Kh7d69G6Z2JkhrSWbm6ul2jAQ+6geqYBVgATMrMwZWuKtF1j3CzzdXCZAOUoZVRmYGNM3WoHBvLig2g1wl0+nxbD/L2pIOXQsd7O/eJw4qVbEUWmk5zh54nHnCJvOEgYeIPHQJSy0csS4jg5GXkKD5wSWgLAmwxerTJ5wfHYWdqzvMU4q+W8+FAw9l9da3r0t9SaRMaelpcA53QOXxDTNO2DSRkxm77GARVptqICYuBs+eP5uW7PDbV+XfcgnITgKkw7QmXrx0ET7+Pozfo+JIqbieyzxSbEnPW0ca4LnWDf6h/rh1+5bKZ5HOCXgkMfAxwVIXvVu6sdrcFu0dHQx9ya7b+Jm4BOYuARrsHz58xN69XdC3doBjeSfiBx6y+CTS26kPDjzmLmNF/IOsV8QJ5OjpgLiKKDbhfm+n2H6hCWkta/HPlT+iurqalW4gfeAHl4AyJUAZJwd7DsLSwZLVc2kYqGaF3eZKLkaWveL9+TBzNUF1bTVevnqp8i7FOQMPsctlHLG9d2CfXw8LZ3ccPXpM5RGYMhWUX1s2EqBF683btyivrMQKMzv4bT7OUmwThx9z4CEbEcv1LAQWqPbThooNMHMzRWl3gXii/kZ6IZmpaWKmOhlE3rRk5RLs7drLClhyS6xcu4uf/DsSIH6NV69fMTBs6mCC1Ka1LDuL9HW27hX6HcWIhBeFwNXHBf0D/TPWTvtOcwT19dyBh8TlMjiGiIMXYRy1DkGRMbh67RqPKhdU1y6+xkhMnBTvERUbh+UO3gjZP4LEoa/ruXCLh/D0g4LlqC6Ub5APfNK8xJP0LP3iZBWpH6iGdaAlrO2tMXxmWKWj/oXXO7xF85EAzUn3799H4tpEWHqYo2hv3pzruWw8Wgq7IBvk5OeofFCpRIbzAh5il8tjZsqmXaXILwK5BYVMKJIT82cuAWVIgAY6BSdeuXoVNk6u0AlLQdSxr+u5cOChjN759jUpNXr7ju0wcTRG1pb1MwaVzrRbpHiPDT1FMHExQkhYCO7evct87aQT/OASUJYEyBI7OjoKF3dnOITYMoBM7sHvuRBJz0mnKW3cwskc+7v3s9pD6mDJmzfwYOBjaBwxvXfgVr0dxm6+2LR5C0sl4gNdWSrOr0sSoIFJ/tXjJ3uha2kLq5xaxPU/+CLThQMPYekKzRljY2MIiwqDY7g9y1aZq0maJnKa0NNbU6BvqYfSslI8e/aMW2KF1dWLrjWSzVB3dze0DbVZvEfzmTrmRvwW+KDvGk5XwzvJA0Ghgbh957baUFgsCHh8TrE9dh0W68pg5+WH/oEBtuNcdNrFb1hQEqDBTvEeLe0dWGnpCLeGri8o1TnwEE53UV8RWKS6LNrG2iyFtn10djvCqdYPmqwbh2oQXhQKYytjZkH58OGDygfjCae3eEvmIwHSceL3qG+ox19/+otYx8nq8Y14D7J2FOzJgYWrGRoaG9RqU78w4MGyBR6zLJfwA6PQD05AYHgk82nRRELC5geXgLIkQDEDVM9lXVYOVjn7IWTv2c/xHhx4KKtXvr4uzRVUzn591noYOOqhrr9qVmboqaBD8p4m7OqT5XCNdoKzuzPOnj3D4z2+Fjv/RMESID1/8eIFYmJjsMJgGQuebjvfCGLileiu9HPL2XqE5gXCwdWBuWrIiqsuhwyAxyS/x+A4gnYO4GcTWxSVlrGJhAMPdVET1bwP0j8CH5cuXYZ7QBD0o9azeA9mqRueYGy8VlmVcHZ1xfv3H1TzJtWg1dRHVONitc5qRJaEov38v+nRpSfiubwmemkibtK300VCUgIePHjArCpqIC5+CyosAQIfRO9vbmUOIzcR6k6JQfZ04IPAs8jBANm52YyygmJF1OWQCfAQT+SPEd//AG41u7DUwAR7u/apRdqPunT0Yr0PGujkctnT1QVda0fY5Dcgtu8ec7tQGQAOPJSvGeQK2Vi5EStFK1B5TFxYay4gY7rfksuFSJeS6xOgY6aNuvo6RnaoTpO38nuOt2CuEqDNEAW/nzh5AsvXLINfug8aBmu+DKSmQogXm5HWvBZ6RnoYHBpkGyiay9TlkA3wmCRoShgkfo+7LN5DW2SKkfPneWCXumiKCt4HDXJaaMi82dNzCB7ePlhl4wqv1h4WbMqBh/I7lfro4aOH0NbVZnVX2mYZ7T8d2Jj6GYEPqufik+YJI0sRjhw5gg8feD0X5ff64m0B6TvFevT19cHF1QVrRKuRWBv3Reo46S3x0lj7WyI8Ipyx8dL/1OmQKfAgoiYCH1FHrkLTNwq+gcG4fecON3Gqk8aoyL3QQCUT/sOHD7F//37UNzRg3/79iE1Khn5gHIJ3D7F0cKtM7mpRVpdK+qhzcyf++vNfUHqgiAXb0cQ7FUTM9z3tHIl23SbQisV7XLp0SW0yA5TVb/y685MAbYIoc2vv3r0oKyvDvn37kJScBBMXY+TtyELbSCPTf9LZvJ1ZWKWzkqXQkkVQ3Q6ZAg9pfo/gPUNY7eCFzP+/vff+iirruoX/jDu++/3yvHeM9773fUIHn25ttdtMzjkVFDlHyVEQEyBZkuRozqgooGKWIGZtcxYTtjl133nHWmVpqahFKuoU+4xRo6DiqbnX2XvuFebKyOSSNl1jbLpmCLr0e8glSe7Ms2fPYsWKFdi4cSNrOrx89Qo9R3sh9wuCVUoOovZcgO2iUpHjMUaDTxPxgwcP4O7pDsdQe1Ay3VAJxpfeRySGqwO2ZGK29SzEJ8bj3r17TErH6GeLrx1nCNDaR4mhRHqbmprQ2NjIDQ0pobq3txe+gb6QR7uiuL2Ay8EpROgU7gAvXy+2VZrLdO0YceKh0Pe4y7tJr+qtMHT2QGNTk+jnomuWo4W/hy5wzul4+hStra2oq6vD3r17WYabHqfb8xcvsHXbNpg4y+GU18BhQTe5SC4di+GkCZXGiXZ2tMMjDY4vEYjhPE7kg3aTJMT0m/6vrO/x5OkTUXU3FoM+zr6T5qQnT56go6OD56O2tjb+n0g3z0fPn2Pnzp1wdHNA0CJ/VB0qQ0FLNnsA16xbw4SFXqdrx6gQDyYfXX2I2XuJ+7k4ePpg7959wsWpa9ajZb+HLlDaQa9evZp3FefOnfusuoou+D/++ANlFRWYZGKNOf7RcHWT48WLF1r2a3T7dGhCfvTHI8yNmsuxbBZUOlU/KsSDSMvK0w0cR6fyxKkzpnI/F9qF6uKkrtuWI51fRzbe39+PLVu2oKGhASdOnOD8DpqD6Dk66J76E1FzQ1N7E8yrToJnohz6hvq4fuO6zq6Zo0c8ON+D+rmcUvRziYzGxYsXxYUunetGcmdKF/SlS5eQnp6O06dPD6jdQBc6LTbUzyUqJhb/8fd/Qebqyp4Qyf1giZ6wcgy6e7phYGqA1Jqkb6o4DsfjoXwveT6qDy9nN7aljSWOHTvGNiJRGMVpazkCZOdXr15FWVkZe15pc0NzDz2uetD/t2/fRkJSAmaazcB3k/6FisoKJim6SoxHjXio5nsErt0PI59wZC7Nxv37Dz4DXnUQxN8CgaEiQBcpJWLRDoN2EBRDHegip8eoL8jpM2fwy+TJkMlkIhQ4VNCH8D4aJ5qEs3OyYSm3wPK9xcMSDFMSC3XuKZxTsqsApjJjBIcEc/Kx6g50CD9HvEUgMCACNM+QV41CKZRrRrlFA9kavY7mqq6uLsyYOR0TfpqAy5cv4+Ur3VXcHVXiocz3iD90Ex7lGzHHzgXrN2wQ+h4Dmql4cCQQoIuYytWys7M5f+DTC52ep4WPRHwyMjPxt//1vwTxGAngB/EZNCaU+Oskc8LcnDAOgahDGkbiNcpk0yVr0vGr3lQUFBbo9M5yEMMiXjpKCDx9+hTV1dU8H9Hc9KkXg+akvr4+LFq0CH/7j79hxswZnAdCOVD0nC4eo088eu6xTHXsvsuwSs2Hi28gurq7hYtTF61JS34TldHS7oJCLidPnuQKBrqAacEjMbGjx44hMCwCP5vaYaZnGFzd3ESOh4bGjsbh1etXqK2rhZWrJXKbs0YtqfRLRIXIR113JSJyQmFua4bm5mYef12d5DU0tOJrvoAAEQ0q6y8oKOA8DyIU9Bjdnj1/xp6OwOBAzDSdAXNPU0yfPR19d/t0eoM+6sSDvB50S+y8g/CWEzAMSUBUQhKuX7+us2zuC/YnHtYQAkqSQaQjJyeHewe9fvOGyciGTZth4+aJWb6RCN50BLYLiiGqWjQ0MO86B9+4eQOhEaHwm+fN3TeJCHyJJIzW46SVQJLU1AnXw9cDvcd6dXqi19wIi28aCAEiGT09PUw+SL6fQjCUCL9h4wY4yBxgLjfFwpVpmN+YgikzJ+P3338fMFQ80GdL8TGNEY+k7rtI6LyNwLX7MFPmg8LiEnYn/aWjriQpGoMunTORD7q4qVyzqroahw8fQXZBIUzkPrBOL8LcnadZvdRO6HhobNiVY9KyowX2HnZIq09WeDu+0CRrtEgHfS6RHeqAm705A9Zelpg3f55OtR3X2KCKL1ILAaXtk3hYaWkpeo72YGnOUpjZm8I9zg3Lduaxjg31F5o0cxI6uzo5X43ep4uHxogHez567iH+4HW4la6Dnp0LNm/ZInYZumhVWvCb6IIll+bNW7eQvmAh7GRy6HsEwaVoFZd5k1y6kEzX7EDRmNy9exdLMhdDFu6Mkt0FGksqHYjEEPkgaerkyniYOhhzJQGVWtPuVBwCgZFEgGz/z7/+xIOHDxAeEc75TfrWepibG4bl+4uZgK863YCyjmX4RW8SK5ZSArYgHu9CJsrQyVDvuZ/L/iuwWVAEExs79Bw9Ki70kbRw8Vl8sdLi0d//CCtWroKlzB2z/GPgt2oP4g/dAHnf6CaIh2aNhXJsjnQegYe/O2KWRfIObyzCLKokhCb7ms5yBC7wg6WDBdra23inqVlkxLfpOgI0Hz18+JCVS/UM58DUzQQLmtJQ11PFyrp0HdCttrsC0y2moaKqgivtBPEYIeJB/VySuvoQ2XYG+sHx8A0I5HwPscvQ9Utv9H8fXaRkR+TpuHHjJhZnZsHASQ6b9CKEbTvGeUZkf0Sak3oE8Rj9EfnwDTQ2lN1fXlkOGy9rFLTksHaHKgkYq78p36N0TyHLtrt6uOL8+fMDlj1++DXiL4GAegiQ3VOyO+kLLVq8CMYFaFfEAAAgAElEQVRWRvBO8kDhjhzunky2p7R7Ih5NJ2ph4maEtPQ0na620myo5R15ock/4cgthG09ipnO3uwKp0lJV9mdeiYqXjVcBIh0UF4HVU25e/tgmoMHPKqaObRCHo7kd6RDEI/hIj3495O348qVKwgMD4TvPK+PunEqJ96xuqcJn/I98rcvxSyLGYiKjmI1STpncQgEhooArWc0H1EnWl8/XxjZGSChLAZVh5crQiuUVK2a33Smke3QLcYFHp7uTNR1dUM+JsSDJ/7uPiQcvgnfxlbMsnLAqtWrOYt3qIMs3jd+EVDuKh4/eYK169fDyNIGhmHJCNvaywmkTDo+8dgJj4dm7YXi1dtbtsPCxRwZ6xaye3msiMZA36vcbc5vmIcJU35E2fKy9yW2YkOkWVuR+reRvRBhoHyhtevWwtTCFDY+VtyBtq6n8n1oZSA7pIaGoZlBMDIx5JYCgnh8MnEPNcdD9X1J3X2I3X8Fztk1sHBw5soDcZFL/bLT7PkrSQe1m16ak4uJsw1hs7CU7YrsS9XeVP8WxEOz40S6KnGJsXAKc0BtVwW3/x5o4h3Lxyjfg1zdYUuD8fd//R0dezvea8BoFi3xbVJGgDxlZO85uTmYOHUi3GNdUbK78IOX42zj+/DKp/ZONpjeMA8/T/r5fZWVlLH40rmPmceDFgEKuSR23kZk62mYzk1FSGQ0Ll26zPHVL52weFwgQAgQ4aALnATBenqPYW5cAn6zl0NevhFxB66yaJ0yn0OVcCj/FsRDM3ak3P1RXxZDS0VfFgprkIfh00l3rP+nc6KJn8TFHIJtYeto+8WeP5pBT3yLlBAg7wS1bDh16hTCIsIwzfg3RBfO5eTlphN13KjwWzZONpi1YTG+n/AdTp85pbO5RmNKPHgReJfv4bdyD4x9wpBbUIh79++LfA8pXXEaPlcl6Xj4sB9btm6Fk7c/ZvrMhf/qvawV8zXCIYiHZgeLJmOKc+fm58DQUR8VB0q1knSoLggrTtVzPxdjJyNEx0Th5q2b7DonuxOHQGAgBMjO+x/1o6WlBTYONtCzm42FK+dz5RaFT1Tt62t/E/EoasvHf//wf3Dg4AGd9biNPfEgz0d3H+IOXoN72TpYevpj3YaNOl1KNJDhisfUQ4AucKpauXzlCgqLS2Hi6g2L5BxWxSV1XHVIB5EP4fFQD+/hvooy+qlDp6mVCcKzgzmU8VFC3Vfczl+boEfzOZr8KeSS3jgPxnZGKC0r5VJIsj1xCARUESAySvPRhYsXkJefhzmmc+AWLcOy1jw0Ha8dUtflqkNl+OfEv2Pzls382bpod1pBPKjagBIAo3efh+W8XMgDw9DZ2QmSuRaHQIAQULrsKUnx0OHDHFqZJfOFc0HTh6qVQeQhCeKhGbuirpvU4nu6yW8oassDeRNGkzSM5GeTvgcl+tnJbLGleYvYDGnGZCTxLTQf0e3582dctRIZEwkTB2NE5IaCiAN5OYjADsUeibBMmvMzSkpL2FsoiMcgJnalS1vt+3f5HmHbemESloSI2HjRz0USl6BmTvLtn39yR9mVq1bD3sMHBiGJitDK4ZtMWlVLZdWxOUE8Rn/caGKmrptm5mbwS/Nm3QLKoRjKZDwW76HFg5Qk5VEyePl54ejRo7wQ0O8Sx/hGgMgAdbhuamqCi7sLHAPtsWjVh9DKUEkH2fmKk3UwcNZDSmoyV3rqYlm3dng83hEa8nqQvkfgmr2Y6eyF/GVFeK7DsrHj+9L99q+nCZ4ucPJ8Xbx0GRlZ2TBx9YLtolKE7zjJyqPqhlY+JSOCeHwb/+G8gsaOJsyNmzbi+0nfoWB7NiduDmdC1jT5oHOlRYCS/aw8LJA6fx5vhuh3CfIxHOuQ7ntp3JWCYBmZGbBwMIdvshcL4jX0Vo+IKB4RXpdIJ/j4+XBJN32frh1aRTw45PKun4u8bD2mm1tjS3MzaLcrjvGHAJGOFy9fcmglIDQceh5B8Kjc/K5U9mNBsE+Jxbf+F8RjdO2JFuf+/n54eHnALsgG9UerPxZL0sLcjoGIDZEP6ueSUp0AA2t9VFZXKppbinyP0TUgLf10SpTu7u6GX4AfDGz0EVccjYoDJWqVyg5kXwM9RsQjIicU1rZWuP/gPud5aCkcQz4t7SIe7zwf1EMjbv9V2C8uxXQ9fZw+fUZny4qGPHI6/EbqWEws/4/Hj7FpSzMsnV1hFJaMoPWHFL1WSIFURYX0WyRjoOcF8RhdA6KEu7379mLqrKnI3LgYVE440CQrhccoPFTbXYmAdF8YWRhi3759Ot2yfHQtQ3qfrvTeUaks5foYGBvA0tOChfCo9Hqky8OJeKTWJUHfWB9Xr13l8J70UPv6GWsl8VAkm/YhpuMiZvlGwlXujrv37gn35tfHUmeeJdLx4MEDFBQVYeIcI1ikFSBqz4Uh5XIMRDroMUE8Rtdcnj1/hpjYGFh7Wyp6UkgoqXQgMkQ9NSoPlsHS2xx2jna4cfOGKLEdXRPSmk8nz+ujR4+QmZmJf3z3dzhHOKKcOspSAuko5CyRrWVtWowZ+tNx4uQJQTy+NImPxuMUu6d8j7k7T2GqjQsWZ2Ry/wQRW9Wa63HET4Tc85TTc/bc7wiPicMvFo6QL9/ApdbU1Xi4Xg5VOxXEY8SHjz9QuTvsPdYLQ1NDJFcmDCvDfyASMBaPcb4H93PJxjSTX5GYnMiLkS7G30fHMqT3qRzqffECvb298A/0x0+/TkB8aQwr75IHj/OVVHutjFD4kIhHcXsBfp0zFfv379fJViLa6fFQJptSB9Ejt+BVvRVz7FywZu06TraRngmLM/4aArRY0UX+4OFDbG9pgaWTDL/JgxC47sBHHWVVicNw/xbE42sjMvTnaCyp5LmouAjmMlOU7i7EqlGYnMeCfNB3kr5HcnUCfvr136iuruZ8D7EZGrq9aOs7eT568ACbN29mQTAjJ0NkrlvE+T6j4eVQtWcO7XVVYIbJdKxZuwYvXr7QVpiGfF5aTTw45NLVh9h9l+GYWQEnLz/sP6C7am5DHkUJv5EmbdJ6OH/hAgqKS2Hg5A7zpKWIbD/3jnTc/WK/leGQD0E8RsdoyGv1+++/w9PHE2FZIaCmWKqTqtT/pt1ofW81QpYEYPrsadixcwfbLy1U4tANBHg+On8eefm5XLXiHuuG4rZ8hSDYMPQ51LV98qQQwTVyNGAC//zFc90AVuVXaDfxeN/P5Q7m7jgB88g0RMYn4uLFS5xsqvI7xJ8SQ0Dp5Xj27BkOHjqE6MQU6HsEwaVoNeIOXFMokA4zgfRrxEQQj9ExGJq0SdvAxs0aSzmptFaniActHrQwUGtz2wBruLi54PjxY1x5IDwfo2NTmvpUIo/krSOp8ui4aFjIzLm6pHz/yFatfIuAcFjvZB0cguyQnJLMwnWawkBT36P1xIMWD1okEg7fhP+qPTALiERe4TLu/qcpkMT3jCwCNEHTzpgEeFatWQvXgBCYRabBf1XHF9vYf41EDOU5QTxGdkzp02jivn37NqJio+AV76FQcByF5LtvTdyaeJ4qGQpacmDhZoao6CjW96DfL8jHyNuVJj6Rxo3a2K9ctZIFwez9bbGwKY3zOajKhPM5RiiH41v2Sd9F3+mT7Mm5JY/+eKQJCDT6HZIgHkw+uvtYv0FeuhaWHv5Yv3ETs1NxoWvUXob9ZTQ5U6nltevXuSGgmdwHtguKQIq1lEycfPTeqIRWPiUngngMeyg/+gC6Dmlcd+3eBUcPB6RUJXAJrSYn7G9N6CP5PP0ucoen1SXDyMaQ5a2p8oHsWxzSQYDsljZBd+7cQWZWJoytjOCd5IncrVnc4I3yLTRtw0w8TtcjKj8cjs6OTOZ1bZ2TDPFQlNjeRfSe87CalwcX30Ac7e1lvQfpmPn4PlO6eEiA5/iJEwgKj8BsV1+4L9/AZdPUKHCoKqSfkgp1/hfEY2RtkcaWSqCzsrPgHOzIHTZHOwlvJInEUD6LFgjq5xKWFQxLe0s0NzdzW3RdWyRG1lK059NonKgqiapWPDzcMdtsJuKKo7iDMinWjqX90ndTRZi5lRkuXrrInjRdsivpEA+udLmHxM7biGg5AYPAGETFJ6Dv7l3h3tSea3nAM1Fe4FQqu7OtHYYWVpjjF4Wgje8EwbpHJ4H0awREEI8Bh2rID9JOn0poPQM8MTc3jBMwNb1THAp5GO57yCVe1lEEWYQTPHw8cPzEcZHvMWQr0twbyctB+WUk6W9gZAAzmTFyt2ShrqeKVUjHuoMyXTvU+0XfVJ9tStfCeBIjHh+En4LWH8BEUxuUlpeLC11z1+ugv4lIB100VCqbl1+A//73RJjPy+NKJerNM5LaHF8jGp8+J4jHoIfyi2+gMaakvLr6WljKLZC/PXtEelYMlxRo5P1nGvm3Lt20BAZ2ekhNS8Wt27dEyOWL1jL2T5C93r17F3l5efh58s+Qx7qi6mAZVoyiNsdgbZGIR87mDMw2mYU9e/fonHK35IgHh1w42fQG3ErWYqqROdra27mRGBmUOLQDARoLxa7iOYdWImLiMMnMHp6VmxWy590jKwj2KbH41v+CeIycndA4X716FaFzQ+ARL+dd43jwdigXE/qtDcdqkFgeCz2LOairr8PjJ4/Z/kcOZfFJw0WA5qTnz59zaGVu1FzMNJmB6IK5qD5Szl4OKpVWjqk23JfuKWR7Wrt+LYeEdCl/SHrE430/lz7EHbgKy5Qcdt2fOnVK7DKGe2WO4PtpMaKY/5atW+Ho6YNZ3uEIXHcQCZ23NZZA+jXyIYjHyA029bDYuXMnzBzNkN44j6WktWHi1uQ5EPmo7a6Ad7IHzGzMsG+/op/LyKEsPmk4CNCiTcm/lIcjk7vAVGaMtPpk1B+tYo+VNorcURmviZMxllcs59w4QTzeLf5fm9hH+znlwhG96xxm+c5FyNxIXLt2XeR7DOfqHIH30q6CtBwuXrqEZaXLYe7uB8uUXM7LofwcGrfRtg11Pl9pP3ZLyuDm7o4XL16OwK8fnx9x7/49pKQmwyHYDpWHyrBSR0tov0VkaMdMu1S7AGt4+nri/IXzOucil5qF03xECaRXrlxB4bJCWNibQxbpzOHAxmM1Wi3nT1oxDgG2WJyxmJOWaTOnK4dkPR60uCj7uYRu6cIcVz8szcllVkvGJg7NIkCYEyOnNvadXV2In5cGA48gOOU3IpobvPVpBeFQkhJBPIZvHzTmdOvq7oKhhQESlseOaHvwby302vY8eT0o2TR7cwZmWc5k8Sfy+unSgjF8q9HcJ5Bt0iaoq6sL0TFRMLQ14Aqk0o5lkrDT2q4KeMbLEZcQxxojutQXSNLEg8lHdx/rP3hVbYGpmzfWrF3LiW6aM2/xTUrS8fjxY6xbvwEyvyCYhCXBt6mdG7yNZRKpkmh8ei+Ix/DtlogmTYY5eTnQs53N1R1jWYKoDUSEyEfj8RqkVCdyk6+ysjI8ffZUeGKHb26D+gSyzf7+fqxevRr2jnaw8bZCelMqqI09C4JJwCtHYaCQJYEICg1inRFBPLQg1PJhIbmHpK4+xHRcgFNmBWS+ATh48JBwcQ7qMh3aixWE4//izdu3uHXrNrJycmDoIIN1WgFCtx7l0mdNanN8sIn73/SuCOIxtDFXfRdNhKRUamZthuCMAF5wtWHxH+tzoJAL9agJzQjifi6U/0LiaroUo1e1A236m+YkZbJzVlYWTG1M4JXowSqzRAi1LYH0a7ZKCcvRhRHw9PPApUuX2Ia0CevhnIvkPR602NDilthJ/VxOwjwqDXNj4zimJy704ZjGt99L+JIgWM/RXvj4B2CavRzulZsRs/cSSBBsrEpl1SEggnh8e3y/9YrXr1+hvr4OU/WnoHBn7rhMKh1w4TjTyOJTFKN3DLWHvaM9KPldl3as37KNsXieSAcRPAqtBAUHwcjOEPElMSzdrxQEI4/UgGOmITn0wXw3d0KuioeLpzNOnjrJc+1Y4Doa36kTxENJPkhy2391B4y8Q1FQuAwP+/uFi3MUrIYu8Ld//omnT59h85ZmmNnawyAoDqFbujXWa0UdcvG11wjiMTzDIBt48OA+TExNuISWdmfjNan0S4sJLXbLWnNh6mLM/Vzu9N0Rntjhmd2A7yZbpE3Q06dPsXXrVljbWcHay5Lb2NcqQysSIhxKe6J+QIvXpMNeboe9e/fi1etXA/5+KT6oM8SDyUd3H2tEUD8XAwdXNG/dKsTFRtgqmXS8fcsxx4JlyzBZ3wRWaYWI6bjEIS9t9nKoEhFBPIZuGGQD5M5ubWvFf/7zP5G/bem7kkTp7CaVk/to3tPumsjHgqZUTDechrLlZayWKTyxQ7e9gd5JeFISb2FhISb9OhGuUc4o2VXAvXQ45+hMo2S8HKr2SGEh6hlj526LzZs3c6LsQL9fio/pFvGgkEtXH2I7LsIiaSnc/INx7JiiZbUUB0ebzlm52JDM8LHjJxCTlMKhFdeStdy8L1HDvVZUScRQ/hbEY+jWRaSDEokDAgNg5mGChqPVGm+kpTpBa/PfRD5quioQvCQAVg6W2LGjBS9evhCe2KGb3/t3EuEgDZkzZ8+ABMGmGf6G8OxQVB9ezqRDSvkcA9kwkaaitjw4+TmgqrqKf+v7Hy/xP3SKeCgXINKLCNvaC/2AaMQmpeDmrVviQh+modJFTgI8W7dvh8w3EDO9wuC7cjcLgmlrAqnSHga6F8Rj6AZBuQoHDx7EdL3pWLgyjSf5gSZO8Zhip00LYOmeZXAKcYBvgA9OnjwpPLFDNz9+J22EaD7avn07bB1tMdtmJtIbU7mjLFWt6ILtEWldvrcIrmEuyMnNwbPnz4aJmva8XSeJB5VvJhy5Df+VuzHd0R1FpQoXJxmrOAaHABEOSti6cvUqisvKYerqBfPEpQjbdkyrq1YGIhuqjwniMTg7UL6ariGKpafNT4OVpwWUMXRdmOhH6zcoQy6Z6xfD0t0CCxYvwPUb1zlcpcRV3KuHANkfzUcXL15EQWEB9Ez1IJvrzMnNjcdrtVoQbLD2RXZDCcreCR5ISU3Bw/6HOrOB1kniQQsM7cLjDlyDbNlKzLFxxLZt27mfi3rmLV5FF/hf75p/HensQlR8ImbJfOCU14DojotgbQ6tKqv+dgmtIB7Ds2u2ib/+womTJ2BubYb44midmugHuzAM5vW0iDT0VnM/FzMHU9TW1eLJkyeixHYQJkn2R71WDh06hMjoSBg7GCE0KwiVB0t10g7JZqgsOzDdD3Oj5+L2nduCeKhO4tr6d2LXHe6CSroSpjZ2ONrbKy50NS90iuM/fPgQa9atg7O3PwxDEuC/ag/iD99QkI6ee9/UytBWu6DzEh4PNQ1B5WU08VNMnZIkzVxMsWxnniK3Q6LJe4MhDiPxWorZU0OygHRfWDtaoaOjgxMGCVdxfB0B8rzSfESCYK4eMtj723LSLi3MXCorwaoVdWyKZN3DsoLhH+KPK1ev8PqlC/aisx4PxeKiEBeLbD0NvYAYBASH4MaNG7yT/7qZj99nObTy9i33vcnNL4CpzBM26csQ3nIcROSkmM8xEAESxGPwNk5klHpe+AX6IWihPydNqjN5itd8qKqgfI+S3YWwD7SF3FOOy1cuixLbr5giLbJv/3yL69evIy8/j3uteCV4IG/rUtT3VktKEGwo1wGRqpiiSLj7ynH6zGmdsRWdJh5K8kH6HuHNPZjl7IXFSzLw9NkznXFZfeWaHfRTvKN99Yo9Q+HRsdCT+8N9+QaFIFhXn86QDuHxGLRp8Bsotr527VpYy6yQsW6hSCodguiUMt8jtzkL00x+Q1x8HIdciNSJ43MEyOYoGTckLAT6VnqIKYxE+b4SNJ2oY5G21TrubSN7mVebBCcPRxw+cohF6ITHQyIxflLRTDh8Ez412zDH2hHrN2zQKRW4zy/XwT1ChkwT35OnT7GjtRV2bu4wCIpFwNp9iD90XUE4JB5a+dTrITweg7eRe/fuccMq92g3VBwo1fnd5lB2qOq8hxaTpuO1SK1Nxnc/f4fqmur3Jba6sKgMzrI+fzVhQJ5XavDW1t4GE3MTbmO/eFU691rR5dDKQPazeHU67D3ssLNVd6T3dd7jwQtOjyLkErv3EuwXl8HWxQ3d3d3C6/Humn/79k8uTSuvrGJBMNPELETuOsey57oSWhHE4/MJXt1HlMT0wMEDcJQ7cILkeJv8B1oQhvMY5XsQ+aAmYBN++hH79+/Xmd2sunb1pdcR6fjjjz+wbNky/POHf7LsPJWVks2xOq6Oezk+taucLZmw9bTG2vVrecNM+Ej9GB/E430/l9uYu+METMOTuUrj6rVr47qkjbwcL168wO/nLyAuOQWTzGy5Cihu/1UWYpOKCumnpEKd/4XHQ/2pi4hH/6N+FBTmw97fjksXWRFyCKGGTyfV8fo/eT0o34Nan1v7WsJJ5oRz585xqaj6I6Nbr6QFleYjCq1EREZg0oyJiC6ci5rOCoUK6ZmGcSlUV9SaBwd/OxYRIwFHXQjLjRviofR8UL4HtWs39g5FUUkpS+3q1uWr3q/hxaS/Hy07dsJe7okpzj7wW90hWUEwdciG6msE8VDPTuhVtCAcP34cPkE+CMkIZHc3LZzjlTSM5O+mXXzBjhwYORgiPjGeu/3StTneDuV8tG37Nji7OsHI0QALV87nEmQmuePMy6FqY+X7iiELd0Jufi5X9gjiIZEcj48WnO4+0I7etWglrDz9sWnLFmbZ4+Vip9/56tVrbrNcsrwcxi4eMIvPwNzWU9zhlxZkVbx09W9BPNRb2shenr94jqYVTbCWW2LppiWg5lW6ntSnOvGP5t+0qFK79tSaJJjYGaGyqgL9/f3jquyfOlxfvnwZxaXFsHaygjxahsIdOYwLqZCOd5JLImLyWFcWnrtz545OdDkeXx4PIkqU79F9F1G7fud+Lh4h4ejt7dWJwfzaUkILCO1cnz9/gSOdnYhLSYWBewALgsXuu8y6FrocWvmUQAni8TVr+fAc7a6oBH1uTATcomVcQjveF4IRJyJnGlmhMnChHxzdHNDS0jIuNkOKTdArbmOfmJwAc2czBC8JRFnHsvehlRHHWoLhQdIq8Un1QkJKPK5evaoTa9X4Ix4q+R6hzT0wDklATGKyTrs46QKnBeTBw4dYv3ET3IPCOM/Ft6kNcQevv1MhlbYg2KfE4lv/C+LxgVx87S8SDGvf1Q4LJzOk1iZxgp9YDD7ocowUFuRFKt5VAFm4M/yC/HDixAnO96BrVxcP+l2k3Lph4wbIveSw9bbmKh8SWOPE5dMilKe0LZKCD1sajNCoENbyoBJjqR/jknjQoqTo53ILAav2YIajO4pLy3RSRZC8HNTU69at2ygoKoa5mzds0vIRsqUbCYdvsQfoW4u0Lj4viId6Uxe5/dMXpcPO3wbl+0tECe0o7ZjJi0QLbsbahTB3M8OCRQtw69Yt3jDoEvlQboL6+vqQnZMNQ3NDeMbJkb05A/VHq1ibQ3jUPia2FG6KL4uGV5AnOrs6dSIBedwSDw659NxF/MFrcCtZi+mmVmhtbdWJjGHlkkIX+evXb3D27DmERUZjlrMn/9boPRe4akVXS2XVIUqCeCit5Mv3ZD+08zaxMkZCWYxwf48S6VDubGnBVfZzMbDUQ31DPZ4+e6oz+R5kT7QJIpvy8fXBDKPpiMqPeC8INh5LZZVj/7V7qn5a0JQKZ29H7Nq9Syc0qMYv8XiXGJvYeQex+6/AZn4hZhkY4uy5c5K/0PkC//NP7quxe08HjCysMNMjBIHrDiD+0LteKxJMDFaHUKj7GkE8vkw46Bmlp4wS/mZaTOf23OO9uuBri8NIPacssfWZ5wkjc0McPnKYFxq6pqV8KPLLnmPr1q0wNjOGiYsRcjZnqgiCfbzLHyk8deFz6LqjpG47T1tsad6Cl69eStkU+NzHPfGgXX9SVx9i9lzAdPcQ+Pj7c4mtVC90Om/K56CGSsWlpfjXpCkgQbCYvdRRVrdkz9UlGQO9ThCPr89df/75lm2IutD6p/uw2JUuTOJS+A1EPioOlMBMbsL6HlTJQAu3VOckOvf79+9jWdEy/PLrL3CNcuGwXdOJWhFaUcOLRp4wyv+x87ZBXX0de8GkagvKWWfcEw9alIh8kL5HxPZjmGYrQ15BASc+SWlw6VyVu4qTp05xwuxkC3vIy9YrZM+7+sZtPocgHsrLXf37V69fYf369Zg8+xfWmeASWjUmSSks7Np+jsp8j7zmLEzRn4x5qfNYWVhq+g00JykFweIT4zDbbBbm5oah6lAZ91ohgqXtY6EN50f2UH6ghPOsisuKWdVVSmvTQLOOIB7vQg6UbJp45BY3RTN0kGHzli0cqhgING18jEgHJQJua9kBmY8/ZnmFKQTBjozfBNKBCIfyMeHx+LoVP3jwAHb2tpBFOqPhWI1CqloQD40ulOQRSCyPxYTJP6C2rhZPnj75+qBp0bO0MFLVyo4dO+Du7c6hlXk1iaDSUCIcq8axINhgyQxhRQq3jiH2yFiagfsP7ks+HUAQDyXxUIZcOi7AfmEx3PyCcPjwEa2vmaYL/BUJ8Fy5gtKKKlh7BcAiMQvh23oVKqTd40MQTEko1L0XxGPgVYrsiXbWVEL7/c/fYenGJRAiTmOTf0ALdH1PFfzTfTHbYBba2tq0vleH0n6uXb+GsuVlsHG2hizCGdSNlxJnhS0NzZZIZM4tRoak1CTcvnNb0qE3mnkE8VBJsqSQS2LnbV60zSJSEJs8D1euXNFadkleDurg2N3Tg4TU+TD0CIRjbh2idp9HYnffuFAgVZdofPo6QTwGJh5kU0+ePEZkVCRM5cac/CdUSoe2WAx2ZzvQ68nNXnmoDDZ+VpB7ynHq1Emt3QzxJujVK/T09CAmNprb2FMTvNI9hYo29kJmf8geM7IDyrUKigjkNYk2B4S3VA9BPFSIR/JRhappwuGb8NHQNboAACAASURBVGtqg3nAXBSVlmldPxcyOFogHj95go2bN8PVLxDGoQnwadiJuAPXWKNkPJfKfkoyBvpfEI+Bpywqd+zs7MRsw9lIrUvmEtqBFkTxmIbIyJlG1vfI3ZoFS7k5EhITcPPmTa3b8dJ89OjRI6xdtxaOLo6w8rRAWl0KhwiEINjI2EpkfjhcfWQ4e+4sk09BPD5avO9LfqdNVS6x+65AXrIa1p7+aN66jfM9xnqg6fvpRosDZbrn5OVD39YZlvPyENLcw94aQTjUsz9BPAYmHs+fP8fiJYth4WbGMt7kGhckY2QWjqHiSLtdcrXPq06Eia0xKior8PjxY63wxNJ8RLvv69evIzs7G6bWJvCMd0f+9mxFbpCwnxG7flKqE2Ats8Kx48ckr2orPB4DkCZavLnEdvd5WCVnQx4QjFOnTo25i5N2FSSXe/zESQSFhmOanSvk5RsR3XFR59vYD+S1GM5jgnh8TjzIvn4//zusbC0RXTBXSFdrUTItkY/qI8u5l4mtkw127Nwx5krLRDpoPjp69CjCwkNhYKWH6MJIVBwoxYoTdaJUdoTtJ3P9Ipg5maJjXwdvhOl6leohiMcAxIMXNMr3OHIb4duPQ99vLuKSknH/wYMxiaspdxXPnj1Dy86dsHJwxhy/SIRs7hSCYF8av288LojHx1OWchGpqa2BkZ0hCnfmcVdQUX0wtt4OVS8JlTRTvoRTiAN8/H1w5uyZMXG5k63QokfzEREgG3sbmLmaYtGqdG4iSOdJREn13MXfw7cj6thr6myM5m3NjL0gHt+Y5IezMx3L93KJbecdBK7dj5+NrFBVUzsmFzqFVu7du4flFRWYZmwOi5QcRQJplxAEG6p9COLxMfGgSYxyBwKCA+CX6o2aznKxcIzwjnW4iy8t5hT6ylq/GPq2czgkRj1PNL0A0ff98ccfHPKZMn0KnEIdsKw1j/OBFKWygnQMd6wHen/Z3iKYuhqjYUWD1oTaPp5F1P9PeDy+Rpoo5NJ9FwmHbkC2bCV+MzJDR0eHRuJryl0FCfCcPnsW8xYuxgx7NzgXNCJm76Vx32tlqIRD+T5BPD6eJMhl3tzcDFs3GyxenS6SSrWMdCgXIiIfVJYaVxINA0t9rFy9Ek+faqafCxEOqqK7cPECEpISMM3gNwQvDkDlQRIEqxUNBEfZZqoOL4e5pylKykvQ/6hf0n3FBPH4GvF491xi1x3E7b8C84RMmFnb4szZs6O+yyDiQQI8be3t8AoOxwz3YHg3tLLCqkggVS+BVEkyBroXxOMD8SBbI0nr5JQkuIa7oHxfsVhERnkRURKJodwT+ajpqoBHvBss7S0U/VzevP4woKPwF9kIJbSSloizqxNmWExHam0Sd5QVCcjDD6OoYweNx2rgFO6AtAWp7AGXmpKtqlkK4qEG8eCQS9cdRLWdYUXQuTGxuH7jxlfzPehCJcOgHQKFStQ9aFdBr6fPr6yugaW7D0xjFyN0Sw8SjtxmeXcq+x1oMRWPqU9IBPFQWCTZKdkbNSOTeckQWxTFFRQiRq+ZxUSdBeez15xpZGJI/TusvC3gG+CjlrYDjfXLly8HFS5W2sflK5dRWlbKVSsUWqGqFVoIhSCY5uyEcmd8Ur0QHBGM27dv4+2f6q8r6q4/mnqdIB5qEA9a0MnLQPoewRsOYY7MB7n5+V/UzKeLlVzXFy9eREtLC86fP/9NDwlJwfDE8OoVjh7tRULKPMxy9oJDdg3ncxD5EcRCfWLxLawE8fhAPCheT4uKg58d8rYt5WqEzxY7LfYAjMdzJWJI+hhZGxZjptl0pM1P5ZYJA+2CaV6hDQ2VvG7cuBFn33ls6fGvHTwfvXyJru4uxCXEwczRBCQIVrG/RBCOMbgeiOSRloej3BGkDDuYDe3XxnksnhPEQ03iweSjq4/Jh3vZepi5emH9hg2f9XOhC5x2FUeOHEF1dTXf1qxZw7ob9NyXDpowqNfKxk2b4eYXCMOgePg2tSP+0HXuKpvcI7wc3yITg3leEA+FJZJNnj59GgGh/gha5M+CT8Lbobld7HBIE40TeR2SKuIxddYUnmuo0kSVUNDf5HUlUbjy8nI0NDSgqqoKN27c+GqOANkFCYIRUfHw8YC9n+3HgmBUtSL6rWg0AZsSd0nUz9TW5L2I2JfWE21//IvEY3trO6Y5eyF0ay9okh74Ns4Ww3f6HlG7f4fD4lK4BwTjSGcnX8B0odKN8jLWrVvHkwDVt1+9ehWbNm3iZkn03KfHX38pXN03btxEYVExzN28YJ2ah9CtR5HYeeddaGXkdvqDWZwl/1oaL759br+JXX0suGa3uAxucne8ePHy06HR+f+VO9o1a9fAytUSpBNAu2ixoEiDeBBpocWorruSkzznGM7Grt278ObtG56LaD4ib9bmzZt5Puru7uYN0Pbt27Fq1aoBPbZkE7QJIld+UXERrBwt4RknR86WTEU+B3WUFYRDo4RDSU5XnW5A9uYMzDGfzaFR8qpL9fgy8djZiklmdnAqWAHvxvZPbm3wbmyD3+p9iNl3ZVy1W6eFjPq5RGw/BurnEpOYhGvXrnFohUhGcXExyMNx69YtbuhExkEuztraWtCFT/8rdyTK3cjx4ycQFZfAIRy3krWI3nMBlNAqkkiHR7iIXARv6X5nu2SzH+zYq6EVnvU7YRCWDFcmHi+keg0P+bxpYaKGU7GJMZDNdeISWuHtkA7poAWJxovIB1U8OITYQebmwqEU8nLQvFNTU4PVq1fzHPX69Wt2z5PqMRGPXbt2fSZCRu7733//HXMjI6BnPgeRueFYvrf4fdWKsI+xsw/Cvrg9HzPNZrB+yus3r9+vJUOeBMbojV8kHtt27MQEPRMYx2fBJrPyo5t1RgUsF5ZidmgKPGq2jbsFkrw/3M9lRTsMPAKQX1iI9vZ2ZGZmYv/+/SzuQrsGIhZ0owv+2LFj7OqkyYCeo9uz58+xe08H7N3cMcc3Av6rOhB/8Dp7l0RoZXikg7w1NEZzwlNhkpQDslmbjA92bL2kHFaLl+NX1wC4yuWgsuXxdpBdkr2a2ZsipSpB4e0Yg9i1ckcn7oe+qJGnqqAlG8aORoiOiebuwsuWLUNraysePnzIGx4imnTQ5ufcuXOoq6vDiRMnmIzQfPTq9Svs27cPZhamMLDTw4Km1A+9VoQg2Jh4OVSvCSIepAo73fw3rFm3hsdLuYmV2tz1ReKxvbUNvzl6KnqAdN3hHTjtwulG1RUxey/DLqcObuWbWOtC8m75QeR60G9N6u5jkiAraMLPc4wQEBjIsupKj4aqQdAFT5M8JZrSxU6xU3KB1tbXY6qBCYyiF2Fu6xmhzTHIMfiWzcUfugGD6EXs9UjovM2hK1Ubjj98E7aLSt+FWsYf8Xj0xyNkZGXAzN0U5ZQwSG50QTwkiQEtSqSlkVqThAlTfoSbmyuTCCLUNP+ozkf0N81TpElEOR8kHEfkpKysDN/9+B1s/K1RuruQZc/JJoSXY+iEcKSvp/qjVdB31ENRyTL2VinJpA4Rj3ZMc6Icj6OKbqfdd9/f0+Qds+8y7Mcz8aCQS1cfonefh1H0Arj6BuLY8eN4PUDcjS502lFQHXxJaSkaGhuRmJqGicZWcMqrR+y+y0zohJdj+F4OVTISd1BBPEKajypI3Uc23McEejzmeJA90o1c6ua2ZoguiOBFSyww2rPADGXBovGjfi7+871hZW/JGx1q+jfQ4kTjT5ufFStWMOEIiwjDpOkTEZ4diuoj5Qp7ON0gSIeWEXGqbLH0MUfSvEQuYqB1RYrHFz0eLW3tmO7sjbBtxz4r46TSztj9V2GfWz9uPR7KBY7yPUK2dGOOTziSUufjTl/fgHZAF/qDBw/QtGIFJs+cg0n27vBpaheCYCPs5VCOC92Tx8MwZvG7BOmPE6HHc1UL2SJNWFXVVZhhPg0luwpECa2WLTBDIR70HlqYinflwz7QFgHB/jh95vSAuh1kA+TlIOKhZ6SHmZYfBMEoiVGQUO0koTQ28jgZfAK8OTxMOTk0llI7BPEY5sJHIZeEw7fg39SOGQ5yLK+oBO0ylMZA9xRmuXLlCsoqKmEq84Bx9AKEtxwHuf+FPsfIejkE8fj2FESkg5RKHVzs4Z3swSWZYqHRzoVmsASExpHyPZasToe5zBQZWUs40Z3GXDknUZiFEuFLl5fCxtkGsggn5G7NYil20eBNu+2AiEdYVhAsbS3w5OmTj4oVvn3la88rBPEYJvGg8AhVn8QduAbn/Abo2TigpWXH+2Qu0vTo6TmKpLR0GHkEsCAYtbFnwiG0OT7zpqkSh+H9fY89HgbC4/HZbENEeEvzFvyqPxU5WzJEUqmOeDuUJIXIB+UCxBZHwdTOBI1Nje+7mRLp6O3tRUpqCsydzBC40J873lJ+iCCf2k06aHyJeKRUJ2CW4SyuSKNrWUkoP7vQtfiBLxMP1vHwRui2XkW5LC2S726J3X2I3X+FczxcyzeC/lc+N97uFToRihLbmI6LsErJgYWdA0jD48HDh9i8pRleIeEwCU2Ad10L40Y5MgpdFAVpGW+YaeL3Mhk8eJ2TS0Ob3+UpqdgwET/SSeEcD/fxo+NBk9TD/oeQu8vhEu74QZtBxxZf5SI8Xu+VJbY+KV6wcrDi6iXK6aBGgCQIZuNtjXk1SVyGSx4SWtDGK1ZS+t1EDklvhwTjzp07+1k5tBZzjY9ObUDiQd0OW1rbMNVGBu/6nRwWoNCA8kZ5H0EbD8M8NR92WVWcB6J8btzebz+GsK1H4dvYiil2crh7eCAjMxP6FtaY4x8FecUmhGzuRPj2DziOW6xUbGk0MSC8ZwbGwatuB8K3H3tvv/SdYe/Gixr/uRHxeKn7AmJEOijRcO++vfjh5++RsXahkL6WKuE6o9DwoIWIb5SXcZo0PRS6HpTrQV6Mwp25MJebQuYmw8KFC2FgagB5lIyl1ut7qriSSXg6tN/ToSRHNFYFO3IwaeZEHD5yiBNMdcbj8ezZc7S2t+OHX6bi+1lG+Leh5Ue3CYYW+EHPFP/nl9/wj6mzQP9/+prx9v8EQ0tMMLDAj3NM8F8//YK//cd/4H//13/hb//7v/CPKTPwo54ZP8+v+wTP8YaVJn4v4fyjvhn+c8JEtuFPcSebpfH61+Rp8PP3/0z6/iN6riP/EOmg8sr4hDgYOhugtrtSuNclRDxUSQZ5NFacqucwWePxGi6HpgWJerek1iUhcJEfHMPsYCI3wg9Tv8f/+P/+B/7n//8/OYk0c90iEOlgT4fQ55CUp4dsYPneIkyc/TNadrTw9awzxIPiRnfv3UP7rt1oaW3Fjrb2z27kEWnZ2YodrW2fPTfQ68fLY4RJy44daG7eym7N7S07FDgNgOF4wWTMfue3bLS1DTvb2nDi5ElJN1xSlxdRBvzJkycx22AWkqsSeEes3EmJe83uet+TCPJYKL0Up+vZA0XeCkryJGLAtxN1qDtaBepGS5LZC1emIbowAvJYGcw9TTHLZgYmzvoJP075AVNmTMYsg5kwsTCBl68X5i+Yj5LSEs7zmJc6D5N/m4xJsyfCN82LvSHvO8yKShZJEBCyG8rfmWE5HcWlxR8VMqg7D2jD6wYMtdDOiLKg37x9y0mSb97QvertzbvHVe9Vnx/Pf6tiovr3eMZkrH771/BXPEeLsWrGvzZclKN1DiSjnZ2TDSN7A0Vs/5QQDNMk4WKyQSTjnaeCQiENx2p4IanuLMeytjxkrF+ItPoUxBTNVRALD1NMM/sNP8/4N/4x4e/4/qfvMeW3KdAzmAN7R3skJCUwsdi4aSP2H9jPcX/qs0KaQS9evsDLVy85D4DGnrxdVF1XXlEOEzNj/PTrBDiF2SNj3UKFQumpOuEB03IPGNkQkVEzDxMkJSe9TxoerTljtD53QOJBX0buG3ETGIwXGxitC0xbPpc2E5cuX4Kdgy333+AqBpFQOORd7irVHAulx+JdXkVDbzXqeip5MSeJ67KOIhS3F3DJ6oKmNO4mG7ssCv5pPrAPsIWZqykMrPUw02gGZhrMgKmlCeyd7OHp7Yno2GiULS/F6rWrsadjD44d68WVq1dw7/49bkhJ3Wifv3iuIBkvFSSDPNZUvaIk1TT27zeTb97wLvn6jetYu24NfP19MMdkNhwC7Vg2v3TPMj7392W1oiHckG1kNEgt2R2NjUeCG1xcXbiklsZWascXiYfUfog4X4GAQGBgBIg80mK0YuUKGNsaIm9rltjZDnFnS7kVlFNBxIK8FOX7i7GsNRc5zZlYsnYBkqviEZkfjtDMIATO94NjkD0s5OYwczSBsY0RjCwMYW1nBVe5K/wD/REXH4fikmKsX78eu/fsRu+xXly+fBn37t3j3Sx5KmjslCTiz7/+fC+B/ummYODR//xReh8tVkROSM+lra0VMXExMLYwgrmrGZ/70k1LWAWVvDOjsYCKzxx6aI/GJDw7BPqG+iwCJ4jH5zYuHhEICATGGAGamKhbcvjccHglenCYRUz8H1eFEKFQ5laQx6L68HJO2CRVVyIVi1bNR2ptEuJKorgFvV+qN3yTveAe6QYHHzs4ettD5uMMV28ZPP08EB4ZzmGQxRmLUVpWik2bN6Fj7x70HjuKi5cu4k7fHe7ZxN6KFy84uVlJMogQDOSxUCUaI2FSZBdEaOh7+x/1o6u7C3n5efDwcYedhw28kzwxrzqRlW0pJEQYkatf2M7QScNIYEfjML8hBRMnT8TlK5c5VDwS9qDJzxAeD02iLb5LIDAGCNAiRhnw9nI7nrAooXAkJkCt/gzVUIiy5PTdPRGM2u4KVBwsZfEsUu2kTqyJ5bHsrfBP94EsyhkuEU5wDnGErZc1bOTWkPm4wNPfA37BvoiIiuDEzaXZS1Fevhzr1q/jUAjp95w/fx6UZ9Hf3895FaoeC1rs6UYkQpsOOh/KdaI8kDNnzqC+oR4RUeGwk9vBIcgOc/PCkN+SzTkpnKsiQjBjdg0R/pRk/N2/v8PxE8clmaMmiIc2Xf3iXAQCI4wALSjUkyN9QTpkYc6gGL7OuM9VyAXrV3A1iEK/oqazHKUdy7hygybpeTWJTCoCFvhyfNw2wBpWXuaw9baCrYc1bFyt4ObnitDoEMSnxCFtYRpyC3JRVVOF1WtWY/uO7Th0+BBOnDyBS5cu4eatm0wsSLaa1ImV3orXbz7kVyjDI6pkQ+m1GOFhHpGPU5IPIqrU9uHatavY2boTWTlZ8PB3h6WbOTwT5FiyZgEIX7Ij4QHRvPeDMC9uz8fff/xv7Nu/j71WNHZSOgTxkNJoiXMVCAwSAdrFdvd0w83bFVH54e93rFrprVAhEopdtaLUdKByU3L9U+JmUVs+J22mN6Zibm4YfFO94BzhyGWmenazYWCnDxNHY5g5mMLG2RoBYQFISInH4szFKCwuRGNTAzZv2Yz2Xe040nmEm6pRjgWFpqip45MnTyTjtRikaXz15bSQEWEiQnX37l10dXVxU0HfIF/oW+rBNsCKS7IrD5Zhxcl6LgkWJERDJORMI3cQ/m7yv7B2/VoOy9FYSekQxENKoyXOVSAwCARo8aCFs7KqEvY+tshtzuQ4vTaRjvcE48wHxU0qF2w6Xsu5KFRimr15CRaumo+I3BC4x7nCxt8SBo56+NV4CqbqT8FMkxkwMNeHua0ZPHw9MC99HnLyc1BTV6PIrdjXwUmb534/h6vXrnKPCyIVf/zxiBM4yWOhWglCnoq3fyrKrIm4ScVjMQjTUOulSvJBGJAX5PGTx9xcbsfOHYhPiudqGD37OZzoSBojNGYsvS7CMKMehqGqtMkGk1BYVMi2K4iHWiYtXiQQEAiMNgI0GVG+QUhEMPzSvFHTVT66rvFPPRYqZabklqfbe1Gsk3XcDbWsYxnyti5l931SRTx3y6UwiJ7DbEzWn4QJU3/ApOkTMW3ONBiaGsBR5oj4pDj2VqxYtQK0CHZ2d+LsubO4cfMGJ20SqXj06BEvlFRu+imxUJIJWljpJg71ECCsiJRRHgiV85InLSMrAwYm+vjVcArbGEm0EwHhMIwQJRs1AkLXkancGPGJ8eyVIpuW0iE8HlIaLXGuAgE1EaBF4tXrVyBhKQtnMyxZvYDr/1ePwm6UvBaUaU8S3k0n60DJq/XvtCyW7yvG0s0ZWLAiFYkVsQhI94G1nyXm2M7CL3Mm4p8//QP/mvAPTP71F8ycPRNWNlYIDg1Gbn4u51bs2r2L8ypId+LRH4940VPNqaCd+Ju3HzQraAJWEgulp4LulSRDea8mjOJlnyBA+BGeVNZLuNNYUGUFedXMLc0xYcqPcAi2YyG02p5KJpoiBDPyIRgidm4xMtZ6IaE4IoRSOgTxkNJoiXMVCKiJAC0OFJtPSUuGY4gdhy3YDf41/QpVj4WKt4J2V0qFzdquClQdKgMRipLdhVjWmsf6FZS8mVAag4iloZBHy2DtZQkTRyPMNp+F3/R+g76JPqztrFm/IjQ8FFnZWZxfQcmLnV2duHDxAu7cucOKmyyK9fz5gCTjSwmbasIiXjaCCChJCJE/8oJQwu2GjRvg7euNaXrTYONjhcTlcShqL0BdtwoJGQXyq03hQ02cCxGPyPwwWNlaseYLjYGUDkE8pDRa4lwFAmoiQDkLlCxp5WSJ+NJo3nl+aUKkHSnFjKkHBIVjKg+Voqg9H3nbliJzwyKkNaQgqjCChaUC5vtBFuEMSw8LmDqZwMTOGIaWBjCxNIGDiwMvOhFzI7B4yWLU19dj2/Zt6OzsxLlz53Dnzm1Qa/YvhT4G8kwID4WaAz7GL1OSECKGFOaiaovEpESY25jDwtWMtU8y1y9E1eEy3amq+hqJH+XniHjMb0yBvrEeLl++xHkeY2wCg/p6QTwGBZd4sUBAGgj88fgPDleYu5ly5QeTis5yVBwoAeVV5G/P5ryKtPpkJCyPRdjSEJbw9k3xhnecBxz97WHvZQcXH2fIvFwg93aDf5AfouOikZaexp/dtKKRcywOHznM1SDXrl/D/Qf3Wcb5xYvnTDCUvUJUkzdVwyFKYkH34pA2Aqrkg8J8RDJ7jvagqKQIPoE+sPewhWe8nKthSJiNQnLkhROhmMGHYii0SeqyM/Sns5YHXV9SOgTxkNJoiXMVCKiBAC0AlFRqYm4CY5khwrODEbjQD/JYV8ginCALc4K9ry2sXC3h7OXIGg2+QT4IiwxDSmoKMrMyFB1NGxvR1taGw4cVxOLq1avs1qVKGSqzJPeuauhDSSLUOEXxknGCAJFMCp1R8m9jUyMiYyJh62oDO39rhC8NZgJcf7RaQT5ECEbtZFQiHiW7CzDN4Dd07O3g61FKJiWIh5RGS5yrQEANBIgAHDp0CDNmzoC5rTn8QnwRlRCJlPkpWJq7FOWV5aCKkOatzewSP3b8GM6f/x03btzg3h3c2fTFC57MaOeq9FaoEg3VBE5BONQYlHH6ErINCqGR7ZAoGSUJk2bK0pwsuPvJuTeMe7wbJx9TGIbyiYQH5NseEPIUkfou5VCtWr2KvYtSMjFBPKQ0WuJcBQJqIECTfV9fH3btasfBgwdx/PhxXLhwgYkFNR9TEgsiFKoeC2WOhRpfIV4iEBgSAmRjZHdkhxSGqamtQVB4IIxsDUBl1EkVcSwMxwREhGG+6AEhckbNCk1djFFQWMDJvUMakDF6kyAeYwS8+FqBwGgiQB6JTz0VSpIxkLdCeC1GczTEZysRUHpAyAbJC0KS81euXmFp9qTUJBaCI8XZsKXB3JxOEJCBvR+cEH6yDs6hjkhITGBvkhJjKdwL4iGFURLnKBAQCAgEdBABIiJEiKkclxKTSZQsc2km5hjOxs8z/g3vFE/ut9MoRMk+8n4Q8Vhxqg7+ab7wD/RnjRspmYcgHlIaLXGuAgGBgEBAxxBQ9YIQCaHEZcoFoTCMsakxfvjle9gF2rBsfnVnucgDOdvIeTCUYBpbFA0HJwfcvHlTUiq8gnjo2EUsfo5AQCAgEJAqAkoSQmEY8oKQqNymzRvhF+CH2cazYOdnw+XfRW15ClGycdwhlxJM59UkwdLWkgX4CDu6SeEQxEMKoyTOUSAgEBAIjCMElIsoV8S8fYOHDx9iz549XO5taWcJCzdzBC3yR+b6RaykS4JaXxLI09XHKdyyZM0CGFkYchNEKSWHC+Ixji5m8VMFAgIBgYCUEFASEA7BvH6F/kf9H0TJAnxg42YFzzg5kivjUdyez40HKQRBi7KuEg7l76LfSEKABpb6oJ5GlLArPB5Ssm5xrgIBgYBAQCCg9QjQwko7e9IEoRLxFSuaEBUTCTtXW9j52yA0Kwi5zVks/8+9iXRclIxUiI3sDLFm7RpO0iVspHAIj4cURkmco0BAICAQEAgwAkQ+lOW41JmVmtPt3rMbOfk58ArwhKWbORSiZGmoPrKce8Poqgek4kAprDwsUVJWwuXJgniIi0QgIBAQCAgEBAKjjAAttpSMyqJkPT2ora9FYFggDG0MYO1niaTKeFQeLFUQEB0TJas+vJy1PBYtWcTJuETIpHAIj4cURkmco0BAICAQEAgMiIAyD4QW3ddvXoN6CV29dhWt7a3cJoCqYWZYTEPwkgBumNhEmiCn67FaB8Iwdd2V8Ev1RlRMFCfgUi6MFA5BPKQwSuIcBQICAYGAQEAtBJShGCrH7e/v5+6teQV5MDDRxy9zJsEjUY78bdlo7K2RvBeEuk6HZQYjMCQQt27dwpu3b9TCaKxfJIjHWI+A+H6BgEBAICAQGFEElEmonAvy9g03UaNcEOqQa+dgi4nTJsI+yBaLVs1HjYRFyRqP1SC2OAoevu7ckZpCTlI4BPGQwiiJcxQICAQEAgKBISHAHpC/FL1hyAty6/Yt7swcHBoMPVM92PvbIqkiHsW7ClDbXflBGVUCoZimE7WYV5MIF09n9Pb2cn+mIYGk4TcJ4qFhwMXXCQQEAgIBgYDmEVDmgnAyXtBUzAAABqRJREFU6ts3HIY5cPAA5qfPZ/VPc1czBC30x5K1C1B5qJQJiFIzQ1vvSTiNRNQcPOzR1tbGcvOaR3bw3yiIx+AxE+8QCAgEBAICAQkjQOSDk1FfK5JRT546ibLyMvgH+8HByx4ecXIklsdhWWueVouSUZJs3ralfM6k5fHy1UtJjIogHpIYJnGSAgGBgEBAIDAaCCjzQV6+fImLly5i7dq1iE2IhaOHA2x9rRG8JBA5WzKZgGibHgiJpBW158M50BFly8tAuiZSOATxkMIoiXMUCAgEBAICgVFDQDUP5PmL59ztdU/HHuQX5rMombnMDG7RLkhvnIfKQ2VakwdCRKh8fwncI92wJGMJHj95PGoYjeQHC+IxkmiKzxIICAQEAgIBSSOgzAV5/fo1Hjx4wA3YGhrrERIRDH1LPVh4mSG+NBrl+4sVBGQMRcmIeFBVjm+yFxKTEnD/wX1J9GsRxEPSl4g4eYGAQEAgIBAYDQSUeSBUovrk6RPcuHGDpdkXLE6HiZUxZlvPRNAiPxTuzEXj8RoWJdN0KGbVmUbuS0NJseGRYeypIeKk7YcgHto+QuL8BAICAYGAQGBMEeBQzJ9/sh7Iw4cPceLkCRQsK4CJpQkmzZ4IjwQ3FLRkg8pbqdKEci80RUKI9IQtDYZvkC8uXbrETfS0nXwI4jGm5iy+XCAgEBAICASkgAAt5qpeEEpGvX7jOouS2djZYMLkH2EbYPVelIxIiCbIBxGduJJoyDxdOCxE1TqCeEjBosQ5CgQEAgIBgYBAQE0ElCSEwjAvX77A7Tu30bytGQFBAZhlOBM23laIL43hctza7opRT0ZNq0uGg9we+/bvA/VrEcRDzYEULxMICAQEAgIBgYCUEKAF/j0JefuGq0pIlCw1LRXWDtawcDVD4AJfLF6djoqDoydKtmTNAtjKrbFt+zbu1EueGW0+RKhFm0dHnJtAQCAgEBAISAIBWuzJ2/Dq1Ss8+uMRhz1Ky0oREOIPe087uMe6IWF5LHfIbeitHtFk1NzmLNh4WmPlqpWchyKIhyRMRpykQEAgIBAQCAgERg4ByrWg3jAXLlwAqYrGJcTCztUW1t6WCFrsj+zNGajrqRyRPJDi9nw4+NuibHkpHj9+zKqsI/dLRv6ThMdj5DEVnygQEAgIBAQC4xyB9yGYN2+YgFB33I69HShcVgDfYB+Yy0zhFuWC1NokVBxQhGGGmoxavq8YzmEOWJqTxdojRHq0+RDEQ5tHR5ybQEAgIBAQCOgEAhT+oGTU/v6HOHHiOBqaGhAeFQYjGwNYepkjtiQKy/cVY8WpukGX41YfWQ55jAxpC9Nw+/ZtDvloM2iCeGjz6IhzEwgIBAQCAgGdQEDpASFvhFKUjMpxd3fsRvqi+TC2NMJMyxkIWODLeSBcjqumHkhdTxV807wQmxSDy5cvC+KhExYjfoRAQCAgEBAICARGEAEiIkRCSA+kv78f1CG3sKgQhiYG+HHq93CNdgYljTYcq/mmKNmKk3WIyA1FQJg/Tp48ycRmBE91xD9KeDxGHFLxgQIBgYBAQCAgEPg2Ap96QV69eok7d+5g/cb1cHBywL+nTICVjwXmN6Rwc7oviZKRiFh8WQzc/eU40nkEr9+8/vaXj+ErBPEYQ/DFVwsEBAICAYGAQIAQUJIQpSjZvXv30LJjOyIiI2Bgps+iZLFFkdwbprbrnSjZ6QasPtPIpbkLV6bB0cseu3btAjW40+ZDEA9tHh1xbgIBgYBAQCAwrhAgAqIMwxAJefToEQ4eOogFixbAxtEG5jIz+KX5sDR7+f4SVkVdeboeOVsyYOdpg02bN+HFyxdajZkgHlo9POLkBAICAYGAQGA8IqAkICRKRh4MEiU7fuI4KirLERgSAFtXa7hFyRBbFIX87dnI3ZYFa08r1NbVcjdder+2HoJ4aOvIiPMSCAgEBAICAYHAOwSISFBJLiWjXr16FZs2bUJiciIc3Oxh7WnJyajTjH9FQWEB+h/1a3W/FkE8hFkLBAQCAgGBgEBAAggoyQfngbxLRN1/YD+KS4vgE+iDnyb9G5lZmXj48KEgHhIYT3GKAgGBgEBAICAQkBQCH0TJ+rmMlqTZDx48iGfPngniIamRFCcrEBAICAQEAgIBCSCgzANRipIR4Xj+/Lno1SKBsROnKBAQCAgEBAICAckjoCQi2v5DRI6Hto+QOD+BgEBAICAQEAjoEAKCeOjQYIqfIhAQCAgEBAICAW1HQBAPbR8hcX4CAYGAQEAgIBDQIQT+H3J8lJrpsXylAAAAAElFTkSuQmCC[/img]
[size=150]Both figures shown here are squares with a side length of [math]a+b[/math]. Notice that the first figure is divided into two squares and two rectangles. The second figure is divided into a square and four right triangles with legs of lengths [math]a[/math] and [math]b[/math]. Let’s call the hypotenuse of these triangles [math]c[/math].[br][img]data:image/png;base64,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[/img][br][br][size=100]What is the total area of each figure?[/size][/size]
[size=100]Find the area of each of the 9 smaller regions shown the figures and label them.[/size]
[size=100]Add up the area of the four regions in Figure F and set this expression equal to the sum of the areas of the five regions in Figure G. If you rewrite this equation using as few terms as possible, what do you have?[/size]
[size=150]Take a 3-4-5 right triangle, add on the squares of the side lengths, and form a hexagon by connecting vertices of the squares as in the image. 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[/img][br]What is the area of this hexagon?
Find the unknown side lengths in these right triangles.
Use the applet to explore the relationship between areas. Follow the directions below.
[list][*]Consider Squares A and B.[/*][*]Check the box to see the area divided into five pieces with a pair of segments.[/*][*]Check the box to see the pieces.[/*][*]Arrange the five pieces to fit inside Square C.[/*][*]Check the box to see the right triangle.[/*][*]Arrange the figures so the squares are adjacent to the sides of the triangle.[/*][/list][list=1][*]If the right triangle has legs a and b and hypotenuse c, what have you just demonstrated?[/*][/list]
Try it again with different squares. Estimate the areas of the new Squares, A, B, and C.
Explain what you observe.
Estimate the areas of these new Squares, A, B, and C.
Explain what you observe as you complete the activity.
What do you think we may be able to conclude?
Close

Information: IM 8.8.7 Lesson: A Proof of the Pythagorean Theorem