标签:
既然我们要学习赫夫曼树,那么我们首先就要知道什么叫赫夫曼树。
那么什么叫赫夫曼树呢?
一、什么叫赫夫曼树?
书上说:“赫夫曼(Huffman)树又称最优树,是一类带权路径长度最短的树,但是我们仅学习最优二叉树。”
看到这个还是不明白什么意思,因此在学习之前我们要结合这个图了解几个基本概念。
![技术分享](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASEAAADaCAIAAABmXWMiAAAgAElEQVR4nOy92ZccxbU+Wv8Bj37liSfeeq27zJnsezC6cLE4lnQukmwkdCQjDhhhLAFGxhiBjYwt9DNGso1sBmOQbQbbQhgzI0AgBgkkdXcNWZlZYw9Sd1flnFWVmRH7PsSQEZlZQ7cEnrrXXlqlrqErv/y+iB07duydA0ehZpfAKoJVxGYBHAXc8hAjbyFmFfl7uYFdGvoJyCpyw3aJWPyVXBVsHZkVbNWwVcVWBVsVZOrI1CNDC41yaCihoURmiVkhNPLEgvZk0J7otcd7rYlea7K7MNlrFXqtYtAuhYYSmWVi5BNCQ8G2Bo4umVsBr8qsAq4Otgq2MuiS2S/7WAFbhcjKR9ZkZE1E1gSyJ5GdR3YBO0XsFMm1UxDcMnga+BXoVKFbh24Dug3wa+DXwKuCVwe/Bn4VvDp4VXAr4FTp17Yr2NawrYNTBVcHpyI8qEgPLAXM5JcUL0e6KPG+LFNlMVTJ/a0D5+jYGgIcsoiVIrNALA1c0C6EBoUMWSqyNWqWSmwQcJTNfw2NdarQrWVprAF+A/w6eA3w6uDWwCH/VsGugVMBpwZuA7wauHXhQV16YKlgKf84GvtbpUpOvPj4mj9D4LLw4q/RwKmAXQW7ToAjqBHgIlMlAwy2icW3IR6lzMnAmAyNQmSWkFWm6LiVpIm/dHRw9PiVBLhOFbzKZ6oxwhtxHuvU6Y10q+BPgT8FfhO8KfCa4DXBmwK3AW4D3CbT1RR4DfoUfdCUHjg6OGosG5kDyMgjIy9d2jJVlkSVXHoMQ0ZeuowBNhg4RwFPHWRumaMW/0URWU8DtwpODZwGtmsEuMjQIkNDpo4sjY0rHLuSiF1kFiIrH5r5yCxiu4wdGQs6IVSpr8VQw7aGbY0MVzh+/WeqMcIncMrgauDp4Mtf2K2CPw3+NPhT7N8p8KfBmwJvCrxpqqv4BekHU+A3wa2Aq8UycBSRA1F7MmpPcpllTnfLVBmFKp+2xrRB5qrYVriBUwanDK4am6dT36Y/cNjWMoGj98MpIpvwVQVXHGzq0KlT+AiCDDhkqdwFR5YKjv7X0hi2FWyXsaNiV8fk60kamwF/GvxZ8GfAn+nzYFp+MCM8mAKvCp5OGPw3oLF/WKrkxGsm7gEy8lh0DPrZcODK4OmDzNWwXQZHlczVqHk6Xdx7jUzgsKWRaRpZZeJnZw119AG2y+Bo0sgkGg0b6NjWyOqWr3exTd5V+YzXY8gqIqvE1g9lugygg2gNPKYl7wz4s9A5A/5Z6JxhD2bBnwXvDPgz4IkPZoUH0+DXwK+Ar8UyYzQgAiMa407jMlWWRpU+GhtKl08DOAkyXQLObfYHTkOWEpmEjkVhMUNcCAXcMnbKyFKwreJkCEhwABydzPsENR5WYuPTX0FjkVmMzFJoFCNTiUdKtwJeHfxZ8M+Afwb8s+xfwTpnwT8D7ix4s+DOZj2YAW8KOnXoVKGjZ2osbE2MpLFlqgyjSi4dRxLpMiTKlBqxsFXkBk4ZXB1cjkKFmU5/72rYUcHRqMUvZq/0ayx0NoWdOnZq2K4iq4KsCrYqBDhsZwCH7RJ2FOwo2C1hV8E2mQ1UZGvYYX5XAkG3gh0dO3pka5GlhpYaWWrEg0iuDq4maSzzkhlifdhWxHYR2QVk55E9ySyP7AI1q8h9mMgsiBojywm6yCbzmHdGMkljc+CfpaJyZ8GZiY0rzZ8Grw6uIDC7JDqKCY2J8Y9lqiyKKjmOowRKarhKjlsjeeFlcITgjDwSxEHPxGWI83KnDp0G+M14me43wWuAWwenhm06nDCHSgrvUrML3OkSXWd5kVqjDrfof/Pf0C+sgaOCrYJTHnDJ2eE47k05JXBK4JawU8BOHjt5rrHIykdWnkeTiUVmEVkKtsvYJmsJThQdnClJM+6sJDOiMe8MFZg9DdYUWFNgT9O3+GegMwN2BUwlsb7ixhdj/L/LVFkaVT41jdkqRe1cgPMbNA7WmYHONHSmKHAUOz5rl4cBRyYEhW1EluNdDo5dxl9nv3R0cDSwy2AqYJWy5yh5LJc8pRirkTRGDFlFbCuY+kUMKIpbBewpcKbAIbKZBpeIh9gseDPgkolrCuwpsJrIrCOjgcwGsurIbCCriew6mCqYpb++xv7RqfIZaKwCbhXcKng1am6Vphrwp8QX+HXBPhXgsrEbAThslLCZ4RRJRpyf9KL/PGusCU4TnCbYU/SBMyX/Zgqcafpfu4mtGjLryKgjsxoZ1bBdCdsaNst/Yxr7x6TKII0loM9wsocDVwGb7Fqw9AK3Dk4N7Co18pT4AoILMb8JnWnozEB3Froz0GXYUTegykKoQ4CLzGJoFIN2iZuIXRK+7CCSii0FtYvIyCBTRpAtgQbdxlHAVYZqjAeU4/0xrxKP624F3Co4DWp2A+w62HWwG9iqY6tG/7Ub4E6By6To1LFdR1YtMithW+8tqN35EjKU86WxZaoMoEofjbEQUPZCNpNGnx5w3dkYuK4wRFHg6EKWJKElzcpHZiE0CkG70GsVuYnwUQTTo5SwE0KAGzqPCXLKMq8MXnlx8xgJpqXnMZrSUQenAQ6BlOc3VJFZwXYNXDKQs11pt0ni2sishm09aJWxeT40tkyVYVTpozGH7RumY2Wj7jme18Gpk0atzoEjwbfQKPJoQWzmJMv7lIDj8HF/APdfDBAfA1vK0PUYuGUapsu2keYxkkE3KOZhazRN0auB2wC3RlMc7ArYFWxVsa1jm8iMRLSbLObWALcKNpGiBufFV1ymyjCqLGtsMcBZ5XTsXrLzobGgPdlrTQRtnjtH96C5RZYKHlmE1JjSCJIVBjjZIdWwrWGngh0y0NbArYFLXqNjW4XzMo8tU2UYVUbSmGSfMXBSol12QDY0hgJXEJ3sbOASOaACcMhSkVXGVnlo7D4jFzYGpAR2EeziKBrrLoz3WhNBOx+0C3wPmh+viMwyJjk7PrnNFbpgo1tJFXA1ZJWDdiloF0NDiUxVUGmZmZRxf740tkyVNFUGasyRcxpG8a1F4GwdbHLUog5OnS0hGuDUwa5RI0+JL6BZ4U3wmuBPsTzXKZYzzlGrkiS0yCwz1PoCxzZzaaQosZxlGdly+Nit0K1Gm/wVBZkjzGNJEBJbrgVsFRY1j4VGkaSB0xmMf1tHw66KXZXueJLYI82B0MFVsV2OTIVceGSWMh/g86ixZar0p8qnrTGCTgOcxlKBa8bre+LtOFWwK9jSGWrKIOCMeGHDpwIBuFJkKmSWwLYq5RC4Org6djRsq8gqR6aCzBLzrArs34Lw3yJYBYYP+9cWsqjMAjbzssZIwkeGxoL25Mljz3/09h8/evtPx985dPydQ5XJt/lEFJn0EBSySuSkBouOkLlUBbeMXRU7Knbi41KhQSzPpFv4G9PYPyxV+mtMPPaTAC7tCA0anKrg1MFpLMIBIDsexAHwGuxZMXTDhyWCQqGPkeN3k5FZwDYN2goeeZHMEmTNE6fD8Vw4hx6FoAk4NEyUx2Y+9YBKiCZz2EXqGVo8yEaIO4nMPNNYATtFnkUVWfmG8tahpx++49ZvrPjSf46NjV27Ye11m6+5bvM1W7ds2Lplw5pVK8fGxtasumr3Pd9+88Wn2s0ToTkZmpM81i8l4DkK+Br0WC6io8QnOFiKFpL9unPS2DJVBlIl1hjf1hATyXganhSo7bfwEPPQTAUsFSwd7AqDpgpOBewKNlVkKFGrFLVKUVtBhoJMBZsKtsosVM02Xr0K+BUhh00HVye5Ktim64rI5CEBMlCVQqMUtItBuxi0S2FbCY0SshRyOAJZpcgshgalGrJ46i3PFSxFVpGaGRuyipFViMw8siaRNYks8iCP7SK28+AUwSmCw1J7nQK2i9gusFfmkTWJ7QIxcOkxCmQVIjMfmfmP3v7DdZuvWXnl5bvu/NbLz/96vvYhywkuBO18rzUZtCeDdj40CvrEW88e/PmOb17/xS/8+913frOhHEEW+VtF7JRYTKVMz1z5GklyxbbCvERyLXRyE1WR0BjPuydZi5kpwstUGZEqWRobkNwp+gDplb0EXAmsMlgakMISFDUNLBUbStQqBAuTwfxE2MpH7ULULtC/bhXAJnxljPFV8DXwVX6OiJwd4geBkKWQLAFsa5GphkY5NMpBWwnaStAuh20tNFRkqeBp2FGQTc+9CkhJvxHTBYW8wQKyyBm+iciaiKzJyKLpvMTrA7cIbhHcApugiAc4Kb6Yz13gKtgpkW/y4Vt/uG7z167b/LXj7/yR7Tsr/NhvaOR7rYnA1AJLD+1KaFex18BeFbtKZE0eevoXK6+8fPs3t1byr2OnCG4JPAW8MlUXy/QlSa5sDaaw1R2JeZR4fDlTY2FrIlgYD1sTxJapsjSqLEljo674VQYcS4exVTAVbJSidp7cP8H9oAbWJNh5sPPgFMApgKdARwW/zM/D8s/n2FHgLC0ytLCthm01aJXDthq2tbCth20NWeS9CnaKkZUPzcnIoidKiJ/Gf0MeJ0x4apycSWHHUoh48uAWiPFIBn+Z+HqyBgO3jB0F26WHH7rvus3XfPjWH8i94fcSvAp0Z3FgAQ4BAIceClwcEvMA9QAAUBf3Wsirv/nSU5s2rH35+cckjQlYEYiYwMps7a5EZonsQSfudcJd5AJbosaWqWJNSBpLWxI7Dl/CPch0DByNAsfNosAho0Dun/AnBOCIEfjcEvj0bE/Ks+cHivQEcMy0yKhEho5sjTpONtngzyNLPEgS/4b7b2xYytOn7AKy82mBMeVIxjUWmuPEJI156kLjo00b1h3YtzsxHCK3hkMPUACBif3pyConxki2+ipEdhl1pnFoAY6sVvOO227afc/tvfYE9RVdkWcqOCqylMiMc/BICBsZJWwUB2gGGXlRYMtUWRpVzkFjmSkzrjCODgMuMvI4/pwYOGxOxGYXwC3xM6pLAA6ZOrJ18HUBuDgnkB/WSlR3SNLaJsPYJDleeS4am9aObdq4bvzDP0vuh1MjM1Xk1MQvI5pYSom5IhPInsSdKUDBc888teOWG3rtyVhjvjZEY+0iaicP44i3FZuF86Oxf26q5NKnyvvBl7HJONj5Jg6AaGaZA4eMPCIFieLodh6bk9icQMY4sah9GlmT/IxwqnQEBS5OMmJHX5npyKxiq4KdCgeOwyQWz0j43AljIbv08crJhNj440yNITtvzn68aeO6auEt5siVkFXE3XmiLhLaEtcA/JLJK3k9wIQXiuw87ky98tILO2+/Jb4LdFUmaYwFo4tBuxC1ClEr3++wM1kvcXqItkyVRVEllwliZjmH4WkySbdbBVsXUFOxoWCjhI1SynGPgSN4Re3TYetU2DoVGRNk74hP2fGfozElLRM4ZNKKlmBXwa1CpwIe2S+Swtz8YL+II4dPSIFXwCmJ0fYBxj31wJggRjx1c+bEdVuuUU69xp0Z7GgQ+bg7z8XTa00QjWFxsGeCpDvU7YnITGoM2QXkKM8fenrX976DbQU7Ci3n5PCYcnIeG0VjieXZMlWWQJVcIlArOgYJ+CRfwiom1tYUOMkxKFPgTBVMFRtlDpzoSPCRCRmTyJhIABe2x9lGkDC6U/LRcg7YoSW4eEk9ZJJyllWw6+DUwCNV7zQ+PokRvEzgRBMnExadLyZEJZqoLlFm9+267Zmn9tOT7Y4CXgWiDvh17pbQOcosIKsYD/NUKjTSmNYYi1/RmgU7b//Wy385hG1+dTyuGGcq0ADjCL5iYppapsoSqPJ3oDE6D5xP4ErYVgTgFP4b8phshiB68py9+Nw0dvLYoWs3rI2sAqshUYaoA16VT1CixuRaLovT2Fz1gzWr/8tuz7DvnNQYy1pUkPGPprG/TarEGhOjtGkEk54AGWhHcwCwqWKjjNoKapdQu4iNEli0jopw/yYJcAQ1bmF7vNce77XHA0NYqIjA+ZV+wNHcHLcOfh26dfArpLyRtE9P3fS45hHfS2HnSshTUpwqowIm2zmJ4vLOk73WBDH37Mlrr1lb/Phl6lfYZRx62K0mPpC8F9mporkD12NcYzwh65kn99937504MJHFsxNLvLgVqdAEjgrWkNi9qBZRY8tUWRRVMjSW2Hbs523HAdm+G47aYOCwo0Tx0DgRtSei9riIGjLGw/Z4t3W61x4P2hMp4HTwK5nAYYslcZNzin4jAzhyxJglwnAcs4FzE/stJaFC23CN/eWPj96x4xv8Wdxr486suGAQP40upfgZGflZ+oeyNEZ3aYx8aORXfOk/52eryJsSUoEUlKydVOb17hMC4zd9sMaWqTIKVeKYh5g1MwC47FASRzANnK1jhh11AMjxNcIbAbiwNR622LxPVrFscAqMib6Dk1dhJYdSwPHByatDp0YaamBHpVXESPEwVweH1RVzNfIYOyq2VWyr2NEwf6WnxcBxkyc0/oBPOMTu2PGNl/70GH3WqeLIT8S+khrjiRpL1die3Xc++eiDOOqGpsJy7QSNOaw+maCx+J6mqmthubDpMlUWRZVcehcfm4Uoq7weH8kSY5j4RjmIpLE9e2HTwyqDVRZTeNhnjgcLp4OFU8HCSW5isCg082JQWwgWCSWRaYwodrJpsMipiscQsi1xWkGs1tCpQ6dGQrqDDUtVfqkk/LnTX/zCv3cXJrBdwrYCqAN+vd+siKwidsvQ0eV8qFJCukM1Vjjx0rqrVyF/FvcM8aAnC6yp2C7TGoDCXeAy4PdRnMGWqbI0qmRrTPQWRln1SpHf2Bk4D8CFxjiLg6f2jhw6ayOLxMpUGTUOHDkZMQy7NHAJ7PwKq66+OI0dffX3N92wmQqpMwORk56gpDCxpy5NY3w9RlBacdl/zlU/ABwiW+cFC1hFEFYD0C4P2ia2S0M1tkyVoVT5O9AYicv12hPs5CLHjp4yGAZcnYaMxOJhaetXYIzUGOvUwa+Cq0l9DFJGktx5xIkkYj/z5P77dt1OmyGENnRnPxuNrb96VemTV6DXxt057BBnhjOD17ItD0op/HvT2N8mVaQ9aBG4wSY65dnA2aXzAlzQPk2CRd3WODuBz7Gjh3nikHTayaZ10erS6aMRjZ9iIueUvGp8XqifsXCTUI9WeeiBex57eA9NSMUIfJ03+0ks5KhjQ9Kgyg9tGkv/7DhKKuoIGSRpjZEP3PHN64+8dBC8OqBuXKTRY70ePR0cFcjJzvTZEyG8nhDMMlUWSxUpl0rcGMmM5PLXiKCLT0lZM+cDuF7rVLd1uts63Vk43Zk/LWNXZCsNlS9k2bAkAEeP1taH2GAESa9KVnt9sMYSEae779z+/DO/AkcFfxoij85RQrZOaORjjbll8NRj9zBNXXzhBblcLnfBhRfHOvvKY29yjTGZcY3Fct115/bDz/4KXBVwBH6N1vygLk0VfFY1mic3ioGWeD8q2S1pmSqLpUofjdGDPX2As4rILHxmwHUWTnUWTnXmTxMTsPusgKPw1ZiX1d9Y0wMSayInte7b9e1nn/oFOBp05yA0h2qs+cRapqaLPpfL5b70g4pVRMVdV8Qqu/g/7nt5uMa+yzSGutBpyhqrQacaa8zXoKNLDuroGlumyjCq5PpetuAqiABlZrIl8gPYh6jnETh//pQ/d0oGTiopg22N4cWPptfj+hDeMMvEjn/aiBEn4Yg7t8cefmDf3u+Do0NgQG8hc6El+IrP3Bdr6aLP5Ta/4cxjAIDm79aLT1x6YPx0YJxmSpvgeR48v2Hrlg0n3nsePA0iF3pnaDNO2gahBp0qHWjJJCZqjKzErKJ4N0UVLVNlUVTJ0hgPqjKAxNELeLJWFmoSgucVuAGDU1zikwNHr5wUh2iyirmLAc6mtT5js0cTmBB6It/q5UO/2XnbNnArENrQPctWw/1i90/LGrv1CAAAQDR/9O7kE7ijMJlxjfGukMrKL18+rb4HngahDb25uOEt15jHNJbIdeKRRiu7ov0yVRZFlVzGuDICcGTnZIAhI4+t8nlYyLZOEye7uzBOTHCyS2x/nRUiT9ZXqVPU3KZUwyjTSBUkbnYNWzVsVbFVpdWtrawO3AlLdxtx9Gr+nTWrrgK3AqEF3Tlsl2lOsJCOyLMWQyP/7i7RVSQas5FZSGsMoIPsDI2Bo/Rak1/8wn/0WpPgqlTbnhhlJrUZK4letTg+/19Ia2yZKkujiqixIi3wYJdov92/XeDyvIbuyMBNDTG3GTdqcBpgk/4MNWzVzlFj4OhrVl1VLRyFoAWBQRulko1RWntD4xojOcFv3JyjP0RizccTMUY+wWE3W2OHn/3lrju30+3XyIfO9CCNpZJ0ZY2VwEoU+l+myiKokqOndIwSkMKLxGi2iIJNdhC1VUBGAZtFsMukGgmrml8UHyCjgNoF1C6idhFb/R0AVg1cPEweLIwHCwQ+amFrPGApf9yCdl6Y+sv84B0FLh1OdRvg8Qqy/S0LOGRWmVWwVZHqii1GYwf23X9g/4+gOwehExolZJUw6c7q69CpQKcKnopsJTQK3YWJ0CggqxSZUxiav4u1tfpfLsrU2ERoToamnNbgKNtu3Pzu68/QDDoUgFeLG1Pw2D2tMFMGp5Qd1aAao7dsmSpLo0oOmxo2NWzq2CKRFh1brHW0q4KtYauMzBIySOG4ErZIYFpBpkKbgptlbCnYUsBScdwDQUW2hliPUHASdNTBIcsSHTsqthVkFiOjQCxs58N2vtea6C1M9FqTQTvPrdea7LUKQbvIa0oiS6g/nrkt6Nbp4MQHqkzjQ5RLW5zI41OFRqJsnfQpjTf7Ew2ppCZG1KqFo2tWXQWdKUABcnXMK/uSZFO/Cp6GHVKTjOQWPvMDJqcr/uMCMqV9LltjMTihQauUzVU/XHHZf5IAGrZ1wAjbgubZHjR2y9gtYbeI7SKyCsSwVcAW68xEt9RJkEBbpsrSqJIjO9zYqjOrYasKbo3uqLgVoAVQVfZFec10VUiB43k6cUM6xPIvWb/3qtSsiRTE69JNcR7pJnXwQqPUaxU685O9VkGsg9drFRL1x0OzjEWip82tsR5CWcZ3HskAxrHLAg6ZGo6pIGgsTqKp9fsau+/d+dxvDwAKoDsDfhVcPYaLoOHq4GjIKkev3ZbYHbvsJ6915vNv3ZWpMYJJgfCJUGr7zde/8eJBCn7nLAS2kEUlaMwpCZXqaPUlWuTYVcEjB4fJ/Y2T+papsliq5Eh7ONnIpFkX2pZpPJmS7zDw2HTCL+IjEGaBteR4z4d5rwqdOuk+iAWUyd8K2qXuQiFol8R2Chn1xy11CHBelTQEEjbysxAcDpyWcdUja8w+O7lm1VULsxUITfBrsT8pe5jo9dvHJIX92y9OFroLehjBsayAI3alvgdBu/T6nw9uv/l6fqcg9LA/M0xjvFwk0RjrLejy21phAC5TZdFUybGdgaZgDdbeqi9wdLzpH7amYKUdKi9uC4/dCmFbfOKAfTOOXWgoYjuFRAdR0n8++fkpw44QV7XE3gWCJWqm03hRlcWL9HPUGHjVIy8/veOWbwAOBmgsDiqOjV30udxlD36AgP68d2+2xsSmj63Gx6u/svJs5SOKj10BHCX5PWAeo8s5oX8n96ziTaRlqiyOKjnwSG3+KdZwcRq8qZGASw82aeCyhwqKFP2QFHBAYLU1fm53AHB4NOD4WYb4TJ602BVqpguV1jnc50Vj4FUPPr5v7wP3Q9AaRWMXX3gB2x3rIevtp64ZojH37MR1m685eezPccfH0MX+7Agao0UTMjRGfTbeiGiZKoumSk5u3DQD/gz40+A1hwOXbjgtoEavJ92XmnhElko+igxU/L+xt8BeRnFkyPKqL/wapFMGfQzZethWeREi4eir0MNK7Fj1qWkMvOqBn+85cOAX4NUzNVZ/fO2Y8PMvd1UBoPHk+jH55+ILL/ifG8fGxjb9TlG4wLbffP07rz4T3yNvBoduhp82usb8CssLYfgsU2XxVMkJ2AlRy0UBxwcnIbmBDjz0DtVj/rFRhwww4ocnRxq3wplxXoAjFhnyHr84Mo0EHLW4O45XAb8KfhU6NfCrrONef+vU9/74Bzu232LPjmesx6xnvz2W9bPikgsvSv7uxv/J5XL/dmBc0caPXHvNuqOCwJCtA+ohuzJIY7aC7SJ2pM4vwzS2TJVFUyUnYMfhW6QDIE/9f5fAufURgFORFTcoiEupsFoR0KkKrUP6WYVAceS1w2tWrzpx9IWUxlRk7b/6YklLF30ul8vlcl/cdEXqd7e+XD70+1+uu3p14cSrwg3ScOgjt5kdb5A0VsJOunTZYI0tU2VxVMmlsCNWF+frbOASMSI5EbavAyB/GvenKRDyuM4/aoiTnfomyS9mSUVhec61tBE52Mm2NFIv7XxpDNzKwqy+9eubt27ZeOK9P4saw7aG7bd+dVlO/Ln15TKyVKw+fLnwuyMAs3++7Q8FAOgim5d20yB0sT8jBgYGaUw+JDqyxpapMipVcrRLWtJqg4EbxbCjUwhSjjgdbPgIR5zyxNqXbZsMCciKvUP7AScslJmRTU+dW3JBxb4nv3MMuJJU7kY8fMXz1vuaJmoMHB0C88RH7239+satWzYefvbRafV9iptbAecMZP6g9oKR/F27cIiiYdcg6pBg/UCNVcCtkKoe4onS5NjhidTP5MkyVYZTJZe9NB8GHI+WipbYEolvZ59gEeKeOl8BpxynBGTpHtihoYw0PkkQZN1m4q70BY4QsXRuGlPB00WNVfPvTFdOAwpOvP/qru/euvLKK9asWrn73p0H9v/ovTf+cOLoWzO+pKXC77etuOzS9TsPt+PfOe7UyZtu2HL3d7ZbczpEXew2xSs9V40NC+EsU2UoVUSNCetyeYXK4zkicHzTU2z5ngROvqkScLYWD079gLM1cof69ZkfcXDihybFFAHRIrOMXB17VUx2hGjWgk4KejHg0j6VIDOxs57YkSQ9lTGNvfL8k+vXrplWPwC/AVEHog50ZvTJt589+PCB/WhOSEEAACAASURBVD/aduPXt27ZSBrVXrd5wx23bnv4oR++fOiJuepx0cui6xP/zPOH/rhm9ap3X3uuH0UkscUaS1RGIM2Oh2psmSqLoEouXkKIZ+Y7Neg2KBsE55jf1NBQ+DWkLwaxnYohQ6mjI/JUYuoXhrHQLHfm8535fHehQKzXKop/BWicYLCVeS9JscOv2OQ3IL8xS8gq45hkDBlHxbYit0vM0FtylhMPsNDpTgev2jPKu+/dufO2m3tthV64X4PuGUAdQB3ozYNXT0slBpAT0Z/C3XlAIQQ2chvztY+33bh115077NlxZKlplymBGx+206uXWIpkkcltmSqLp0pOepoXpfAHz4Zq5pghDhhIDuwkEMQD1q8ycJGlDrg35B6g/tP66MCFRjFoF0KjiCwlCzjaPzZRQ0oqTC/UfsvWmKeCp02r72/dsvG5gw9LNOpMgd8Evwa9sxA6gEJAAe6ZuNtC7hRym8htYm8Ke9PYPwO9NoQO4AhQF/cM5NTobGbrOPQO/+mZNauueve1Z0XfLFtjnL6pKBybKCoZAlumyiKpkqPNcz2hqhk5dsEhY3ci7aLw+5cGLjE09kNwKHDY0cVPy6TCYoArhkZBNNYnuxQaBQZcCTtlmhQrdRYWygM7CmtwrsStK10FO+l5TAGXtJAtg6e+9+az69euHv/wJRFP6JwF1AOvQSY0TKJkbh135nC3hUMPhz4xiHwIHei1sT+L7Ip4F2J3yD+7MDe77cat3/vO9nbzk4Eao5XMsCXMJJZGk/Qljeng68tUWRpVchlFv2hdVSGLrE/4hV+SOFCJY2fiN2kEhwInBZfkd/EvM7IDkNEnm1dKE53AeHYS687T8EaZmqckzY1bddCGjtw8BTzlwP4fbrtxizVzkuSeI0tFloZ7JoQOOJV4jSFfcnqfh3h3afBjFdkVHHrP//HpNauueufVZ9LBBsa5Gg89Z5SjoOsuVlxaxGGZKouhSk4ozF2iZpd4Wdn0Qjl9MeloaTqOlEZtxMEp4X4gYT09NP4jojYUuEhoWR+XYUt4en5KY24Jc2MCS2vMPvPx1i3XHNi3GxyFl8WO7CoOfeSf5deSlln2eowN2OIMILpeFBn/7MLc7E03Xnf3d7YbUyflZ3VsV8BtsJPz5PC8UFaJLBE9XidQLkCyTJXFUIVorEQ6/7FWn6SZkvTlksDJgdp+wHGwsl3tEYFjnoAIXOYnf7rAEdSEWYtMXGIXMuwUmMZiG//whTWrVp54948EZ2QpkVlG7hSOushpZK2CqolIHbe0xtI4SGsYYULjmVZUY1YldR6Rlz0boLFlqiyaKjnejExuWlfk7aqk28/jqqkBgwOXuQeSvAfC3D3cAci6SaKdL+DEpqMo0cmSHstXwC2CWwC3kGivTro/YycvPoud/FOP7d265Wvz9WOk4Tq2i5FZwt0FHHqhqSaAouD4QqROBEGwzCvNnAmRpYoTGgv969iq0EpMUrEKdlYl3vJSeU+tZaosjSo5RPtDy80gTQm4hKOSGTvKXGtm4yXAMRJwA1EbDThSfb4wALhEz76kq93RwC9jQTyJ9urERI1Zs8d33vaNvfff2W2d4ocgkVPGoYe7rfT4GrOzU4deU9JYYpEjH/HIEJi8KRxPaH96es2qq55/+hFkadiqgFMHpwnulFDEYiqV40sSghRsl5apsjSq5NiAlI+sybji7GDg2Fo2DZyI16BhaUnAZc7+ozkAUvOubODsIrJF4ArYLoJTArcMPgNOkFamcY1V8q9v2rD25ecflQTpVQD1sNfMvARJY91GWicJxylN0EEaI6/xz9rmwq7v3n7TDVvmq5/Qc76SxhJ59JqssWWqLIUqOTYg8TYFE6E5GVlFVoYhYwZPLB/TXMFsv6+fe700ByAxeC9mIVtCVpE3axaN/JKUsiBeEB+haX0LT4GOCl0N+4qoJW5EVKIdfvbh9WtXVfKvc6AjawJ1ZnDoRjR3KcPNw6JCJJFwkPnAr0SpeDcSU9HlT5DiaXYFh967b7++ZtVVzz/9OLaFqYyWgmmQUtLY0YUskBjAZaosliq5yCyEpvBxxmTQnozMDOASJoa2+OMYFLcSsc3HcwrI8gfpuDCFVUdyn5SUlZAVI7Jk4KBTlnTlFan5JW49Y3z3vbft+u63uq1T8QzmFHFg4t5CaOYjqyB0nCA3lYBGujNWwOMjNx/4S2wBUwjapCBMIZErxLebBsxmEub+Wdts7brrjm03fH2hdlpalRGN0beURQyXqbI0quTYXls+NPKhSbfbkKWk/ZMBg1PGAOboiGWaJYBOvCwjDMWXy3RIroNXk0csnR6O9HTwNET6fZHa8VaBWT6y8rykmRj946iRdlWBMRGakwQmcTVPzSkipxg5ReQUWd2LPHYK2C1iEjn0FeiUoVOerh7btHHdcwf3g1skDlVoToS2gkMv8hqBMR4YE6GZJ43IWE014omptNCao2GnzM6AknqAKrIVZJeRXY6sUmQqoVEMjUJkZke6Y1TdSmo+FG+fDm4N9+x33zmyZtVVh599XKiDWwc3PlfC0vYU0k5tmSpLoEouNIqkVlbQ5mkjJWyrGYNBamNxsNE6J141EUtFossueNIZY49XBb9Oz+rExygqQjqPCm6ZQIbsAnNjTofm6dA8FZqnIms8ssYjazIBHGsGN95lxWXjngwpiMkrA9YKlQ9d8ejll4+8+tv161Yr46+RgH5k5QNjInSbOPJ7ZqmzcIq3A2fr5hJb55CDRuQclxKZJJ+gRCscxpubKttbK44ydWASn0xpTIQ3NNTImbKNhV133bHtxq8vNE+DVwevJsUk2WENklu0TJUlUCWXuQOYdqnTNhhZCkrWfoUEnABZ/LF8cBKrtfCzgDFwdNOGxLsIaoFxKjBOBsbJ0PwktD6J7JORdSqyJoYCJzoD4ov56/kL0hrb95N7d9xyvT1/imd7ILuIe23UMwKGOzFBY3HGo9hTQowLi2lZ5FkyjQTtfKbGpBvUZx4TeRmQHCtTxYH13tEja1Zfdfi5xxK+5eBI3TJVRqFKbvGxF3o7s2ft9AzOoMFZ4SOcCpolgfN4MaCaMPtrfNMGHAVZfCARgTsZmicj6xSyTyN7UjhRX4jMPFlL9FoTvdZ4rzXeXRgP2hOhMUmWTKSLF6+eG1mF0MxHZp4LgOtkvvbh1i3XPP7LPTQj0VXAUcDTIfJxZxbZxYj/OWOS/IkBCfuJiDB/Gf990CZfe5LHP6Q7kmDtCBojy7nILGN/lq7QbtwyXzvBWS7eu2WqLI0q56Cx9Loz0wYDlznmLQE4MwHcKeYAnEb2uAwc3V5kwE30WhOJ1qZ8GklvhogaO/X+C+vXrj5x9JCUxdeZBtQFr0Y2THA8BeXJ5w/VWNp4KJl/YTGcmKGx7PjkII0hS8VOBQL7vXfeJHto51Nj/9xUyWWCcn6AE8KpqTV331gqTkbGeBIdvwcaC81RakZmITT4nH661z4VGKcF4CZIBVzRH+PNy4X+A5Nyl+4MR06E9anHfrJpw9r52oeiTqDXgtDhDe3TfY+IxpK5+cInpP+0qLHMeSxJOCkGMJLGpN0qb9o2F+6+69s3/e/ms9Xj6X2nZaosliq5zOFhKHYjOQAjLIKHY8fbyDucKKpwdJdPEXzNc7rXPsWwOx1ZZGQqgJtkLacsgY8Dl55kOPvJC4ypE9u/uXXvD7+LWQ87bJewo+HQw905actfaJnJpZJ58EyczTKFJ4+OccwjY1CXliiL0Fg8Ndk67lnvvvPmmlVXHX7usT6RyWWqDKfKEI2dh4XsOQAnkUZ+bxo40V1mwNE+rpFFyriPBFwy0TMLuMKJl67dsPbNF5/iesB2Cbk1iDqRU5PSasTzDovVmPxL0b3EdinupZLpOI2sMTFvMO3+YW/aNlu7vrdz241fn1Y/GKCxZaoM0VjGtfUfV5ZoKU8A8eKvWbvy0hCVOvAnnlQlZ+mIl0ytdZpGyY248x22iwkIEt5XeupPoEbe9fRv9l17zVpt/HWaBkqe7Z6FyI+sctCeTL5dkBCXSsaz8svoU0LlgliW9JUq73gyCPNhGov65A3G06NXg8glIcfHD/yfZaqMThVZYxwmcQgcOrmPYFgs0yV+rJA7k17mptPwRFhZJpF0Dry7MNmZn6AWN1CcCI3JOGXTLdOOj06ZbKeKB12DdtzOlL6MNKdjZZs68xN3f+dbP7j7NvfsaXIYlhYhDB3ca5OP6rXykVkStpjTRgozport8LN98n1KxDDpVfAacn1yiDCLwg3VGEplMEkzg6ODV4VOHXpne11334M/3rRxfTX/zjJVBlOFvKXXygdt2g6uj8ZGsUTRyZSNCpxbSQCXSJReHHDz413a7o0MJGS3VwFXZcc01HTBhqBdkCqfkSINLOlJnzhy7Ya1h35/gAFXQpYCXoNUkuIFHpjGKNbC8FmSP3yIxtL+CRkRY435OnQyqluLQ/hIGhvqfXmsVkenAaEzfur4+rVrHj+wd5kq/ahCXh8aRZEquaQTzwwPxUgsnpxlmFdIzgKOuChi0BazAkniAb7ILIv7rZFVDk0lNEuhUeLXLAM30V2YJFco9SmlMVyVwMGOCfEPKdLzvKSKPe2/qmK7/OZffnvthrWFE68E7QL7TAV3zkLUAa8OtPklhTUyFQY0+ZLF0CyFZon8HhyarjFYY2QfjHs1fAFAHVSisa5ctlpQEXWuRtAYn/F4NhMrnyoE68T62J3ZXsfd9+CeTRvXV4vvLlMlQRVs82yYmCrIKss1TMULi6NMDHo+rTt6slda5sA20Fmn/gy/fwxNsawKW5EXKUddHXs6ZkX8QkPptYrdhbw/N+nPTXbm892FvNielFQLpHC4FZq65ujpGnpkzJPT2MuRqezZ/d3tN1/fanzca9G8IWzrENgQWOBVaYHBeAIhCwMNHHYSOX5AsuZ00l49M2qfXmcnjlSwAKaCnbLcQF2orevRbImMO5Ja6sRCIkdCyZka0kqv3z31ahCY46c+Xr/2v8kKbZkqvJ0naeEpUIUOatkai1ht12Q+C+eT0z9/TByKhi5wuw16VqovcEUy52K7TCuwe7S0ZcQaKPKqer1WsdcqBW0lNMqRqSJTw5aOLR3betwrXV4c82EvcTj3bOWja69Z95tf/YRXLAsN4h92oTuX5O6AtbtkOqsyL4kqU2Ppw7bCaxTW4TZr3hDvS6Y7R6YCh+WCkCOhxLjGxItKS6Iz0+s4+x7cs2nDem38rX9yqiRmVEoV4ZvLviL70JBVCxsEXOpLSN6I0IC0r/HByauKwImVHoJ2sdfKk1p2QofyKvfUY6BbpaCtBK1y0FLDNukJoMt95sk1kpmHGIdPI59D/uiHbx1ad/Xqk8deDI0ytbaCvBmIuuBPMcKxRt0JTovNvEVgbZ05OWQZnSkevk+aMYMJ8155JI25lSEv4I4coS8vcCCv7rJHDacCPWP81Il1a9c88vMf/9NShVlZpEpkquIIkhMREdeLiZOqqahovL7MzK8ZAlki9iWsZRML2aBd7C5M0vHJUSlwiRxtg5sWGXpkVASrRkYFWULTDaHUmdCVtBK0yr0FpbegPPKzPdf9z4Yz+nGpeUfXhNCLizeJHd/cevyxiYaL7G/RljkWGVALQZvmVSWqDnONpVN1cHL9lqWihDMmPisuq/iL+8iP34h+uVoxVdxm17cf+smPr92wTp94+5+NKkGrHLTKvCcga8CpYbkBZ06Eo19CWgI1/lQk1GZIH8sdbnIR88yvEbSLnfkJMj7R9SgnB3f6hQa+yJQsMqqRUUVWLS661Ae7oFVeqH3yrW3XP/jjewh8BDtk1SDq4m5L6o6TqTHx93LLHGTqkaFFphoaSnchOyuHyylTY1KMxJfDA1muIPUG3UHLtvQvcYq+IhP6UEXF3fbpUyfWr13z2MMP/JNQhWiMK41ShTRS4v3Kzl1jkVDHK90jYyTsxCyblLdAXjMIOOKqueLA08B2HVt1bNaRWUdmPTJqkVFDVh3c5mDg8h+9tu7/W/3a4YMicMiZhqgH3ow0ti1VY6FRDtqlzny8DZqZXZrpKy5WY1goloYTnh5fKngZuSBcYOn8jwFUQU6j59v7Hvzxpg3rKpNv/2NTpZ/Gkm3KRtFYWl0J1PgiT6ziL6bnDMVuSDTJ1kKj1F2gZ9pTwHGiT7E6gVPgNMFugjWFzSY2m8hoILOO7QY7RV+XJMHge+6pA9des66ef090A5C/gEMf2/XYA0w3LE30eiNPCbcnFlhbDY1y0C76c+Od+dOd+dOZGsveek44ip6GHWGZlApZYbbK5yLJdMDi92bVJBx5HuPP6mSFRia0f1SqgF0N2yrxEjM0lkWV7PVYpqPMNSZ4wEOAG2rx/c5YVevgqJGp9FpkUC+yLSa+zOBEJwWVpsCbBncKnCmwp8GaovBZDXCacfFAGbveQnnnbTfvvmdnZ65ElBC0ykFbQz0HddrS4MTV5aWaSopzV3oZZrLWjKYaGvE8lvYVMwOJWVlX8snFFG7Y1kIh37dfzTMxppd59xP/HYkq3lSvQyc0bfytfySqcI3xQZMoLWMek6kiaCyVD/YZaAwlEguEkZUAR7IoIrNADuePANw0ONPgzFCzp8GeAocUhGnS0tMuKT1dr+aPrV+75pVDB8GuYYvNOVYDR93ImRGAq4FTp28kH8K7IdOeyOyTnRrYxLjGKsisRIYeGXpkapFR7rXyvVacvp2hMboJpki71bKNojHxdmROFJkai2MMbHMp/s2oVNFxtz1+6sSaVVf9dM893tzkPwBVwKmzOxtTJWyrQUsNWupgqmTH7qUxQx66wlSR10wne0TgIjHgK8bBqOejkb1zZBVJvt8g4Pxp8KbBnQH3DLhnqTlnwJkFdwa8aaH0UhPc5iuHf7dpw1er+ffBaYDTALsOdh13WjjsRmY9aGlBSwvbOjKrrA5hM67f5E9DZ4aaP80/Ftt1bNW4JVbVyKwgUyNFbzJr99HEfJLM0a+HA92zzhrUJccp1li/ogCiJqXJiiPsVfuKeShV3CaOuo/+cv+6q1efPPbnv2uqgNukJBGpYtUioxK29aFUyd6D5nvbwBJG+D432cwmuSfC3naBGNk4Dw2Spzccu1CsWMa3RGPsdOyoyBITalnKuVeNnWw6n0yDPwPeDHiz4J2h5p4Bbxa8GVadswneVM/Q995/z87bvmnPFuJRymlC6EFgI7MatrWgpQYtLWxrkaFjqwZ2nY5PfB7rTFMT5jFkVZGpk7krYdiqYEvHlsr3x9JGD3E6Cm1+KxyNSe1Tl+MbRJISXF28U6FRkrOEWINMngHEkUxojPOSJVVkB1dGoYqpoM5CRSteu2H9T/fc481N/N1RBbwG7QQQ86ROW3DYVWRWRqGKMI/FWys6ZvlXPAEZk6JZFk3HCs0iKaNFUpKDdp64QEE7LzRrUljuSXZ7EcSOLcS1yng6D9+rcTSxU2h8bsoh+/E18PgoNRUj6M3ERucZGixaaIxv3bLx4GP7wa2DU6Wusz8NqAedebB5GFCNDB2ZGrJ07NTBrdEjgGRzOd6ArmG3ip0Kou1S1cgoI1OlZmmYmK1jp4IpD0piMdq0IT6PJTTGzS7RAmbkLFn8ewXbCim9FJqFoJ0PjHxoFiKriG2FJYmTibGMbQUcNTkd8RvBt9TYhJbc2u5Ple7C5JsvPvXwQ7t/cPft122+5oc/2DU7O73zjtv/e/VVv/jpfY/8/EeTH730d0EVVmqyLlElbig1KlWE82PxXkqFp65mJviERj6yiuT285PV/DC2cEq0RCp1RuIWe7vEU6R5fJmi1m3EGT2p3cZBboMv1CTKNLpyrZw4+sKaVVed/uAlsCusy1YduvOAuuBPg1MFRwe7CnYF2zrYDClS6sirSNnWQs4ozwTlDRezW5j7FfC0fkU74lBH5tEyyRReFXCA8cqbtH4WazTD+q0U+VnPDA6IaVY8wWogVayZj0n9hUsu+fz2m7c+/NB9zzy5/8O3/vDRO3888d7zU7W855p/eubXP91z97qrV33xC//+7R03vv7CE3+zVAGnAnYF25pEFdJtw60tiirC2RbqFeis32bcAifRSSA0JyO7QLq/kGdDocIZLfVIDwv07ZUoLQD4HeUZPSwFJrFh0Nc1l5KbUuZWwakc2Hf/1i0brJnTwhqjCqEFkQudBnYqJGVGWn7En1wlHj+dK+hcJHZbzGfmbcgp9hoZlQZb9vHNpMakXhaZFprjkTUhFA8vYIc3OihgR9aYOEeJ29aSP5ZNlYX6h3vvv3PllZfvvf/OUx8c7ksVT4fIR935wJxcaHzw4h8f+dbN1335yv/n0O8f/lujiji9p4aV2mKpImmMporbxJEoYbtIDNmkrpUAnFUgpc6YxvKBMdlrT/TaE6LGBvvZGQsAIWWObPKMBFzK3nvjDwf2/2jv/Xdv3bKR2NX//ZWVV16+b+/3D+y7//QHL4Gjg1uDqAO9FgNOlyLUiRUITeclPnNG45zRNKb+VTUm2mga65NBIlLl2ad+tvLKy5967CfWzMcpqhQir4678xCaEHkQeTjyMOph1I06ZyP/TGir9eKR733nljWrVp469ue/ClUyA7PDNLY4qsQaw/EePzms1recFaFR4sSueKaQJeMVQiM7asyXsHRk4sAx9xoLB4eGA+fo4Oi9Vum5gw9vu3HL2NjYthu3HNh3/8HHHjpx9AXRHj+w98C++zdtWPeNb9x49szs0Tde4H8dsfuUCKwxbmnMMywlyrDxzEMxP2PQHlfW2ZZFWmkUjYmWklkBO0VwyuDIg3FCafxYF3+BQBVj6uT2m7fet+v27sKERBVLQZ0zOPIBMA5s3J2H7hnsNbDXwF4dubXIqaHOHOrM46gDOMI9Syu8f93ma5589MHPhiojWnKZulSqxBoTvOF8aBT7xb7EBJ+EAnmVLCazYr907Bg44auLOQd8k2AU4KyZ0wf23b/yyit233PHu68/l4hQ89Eo/m+3hQLvndf+sOvOHSsuu/Tg4w/1jHIoRq74qpp8K0cn6y5sl8nis9eaILkaJF2Dn6HMRCmZNT9kjhpFhIvWmDihgVsAtwhuiWqs/4hOupinOYosVRt/a/VXVr72wm8kqlhl3G0BCnC3hZzqSFQxipHbxIHd7bgP/Oj7d9+5/VOlSiY3BlAlc1NusVSJYx7suxZZzDe5xkgTKPFA9KCSGhMGwmzgWKgK0wBdeUTgjrz0+5VXXnFg3/3ztRMZkPkz0GtDz4TIJ4ajHqAQd9vQa4M/tdD4ZO/9d6/88hXvvPoMrZgr+iRsLCeBDVKPPmhPdhfGucZ6rQleC6Df0S9JbMM0hrOq5STPv1ikCdggIz0NyONE2xFwS+AqUu2dLJdJ9MFE6jeVY9dtvqZeeEekCvJnMAqQPxvRqv2Lo0pkVXDPOvz8H3fddfunRJURNSYKLLltSDTG/tyIVElrrMROSg/RWBpBGbi86CgmNMaxSNxRLGeTDAauu1Dcfc8dO265gYQxBNNxZw5CDwAg9KDXxt157E0zm8LeFO4uQK8NURcAQ+QtzJZv+t/NP91zjwQcv5cp4MTyRmK9jc9WY0MsUYdd1hiZTrUlaMyeHV9/9epG8d2YKqaCAxt12yFbRyydKk794JO/3vvj+84vVT51jQ2kSjInmB/FIWechMVVErv0El8MBgTtQmTGgdeEA8AvQPxlYs0qJmWngZurHl+/dvVzBx+Wg11V6LUBhRBY4M+mP5x/lIBdBTpnIHQAR4/9cv9NN2zpLhTFEYG9ncfok8WZxUpg/Xa9RLENdQWHCmwUjfH+PYlGB7HGPBU8ndYsyFrxc9xE2nUXilu3bDj1/l/4DQotHUfdyKmfP6roe/fsPvibx84XVRa1HhtIFbouFX3FUaiSrMVNPpRUgOm18kGbGJnWisz5LrLtILqHSAr6YGlXusC6141U+5JfUiKzJjNYZEydvG7zhtInb0iL9c4ZwCEEBnh1cCvNJ9aPjY2NjY1teuIYzortJoCL7AruGu+9+/aOW77RWSgS+IRvqGK7nE6DSqy7Buwscxuqn6EbaKP8FWQVwZHDUcZkaOaRVcROCbwy+Br4FXogX5SZuNwn52IE8j328AMPPXBvTBWnhkMvMMpZVHnr4Iax5M+Gn9RHoEp3obhm9Vem69n8WRRVkhobZiNRRZQfB6o/VZIaI28QNFbgRXb4Bmvmlmui9hUBLj1xJTz7RPgonb2WBs6fy1+3ecOp9/8SA+fVILQh8sCvg/en++TbevGFF6zY/85Q4OhTlv7m6y/v+NbNMRp0UJCAi4To/IBSHH9tjSXLyJHADM2HpBrrW1GHDtJC0nBTObZm1crOfIH5/xVAvcjS0lSpPnY1Af+Kf70gl8vlchdceHF8R779+nCqvPvas9u+cT30zHOhSobGErsRKRtFY4kpbihVcuIb+FcJjCIpi8XhS2ssXTQrCZytpr1qyTkWhgQx1Th9ASJk22++/o0Xfxt/jlcH1IOgBX4N/KTAqMZ+dnQUT52/5qknfrl3z48iU/TFNWSXg3ZB9AxxVhHmTMaLU98oEjrvGhMLyAkaS+VJJcLWji7uPm//5v++8eJvGW46RD7402mqHL2bIn/R53K5XG7FQ6/3Wvkgv+ty4Z5c/eRwqmz/5v8eee1F6C4smSoZGkuXV5ANCxIahSpZL0hSJYfdCjVhezEySc1AXpakyP7lSdM0x4yJOK6PRepgBe0iPbuaSnLhukfCkjrT0qPUy4ee2HnbtriimF+HqAOdaWGI+t2tudznLpI0dvkjVQCAXoNO66lLhlTb700bv3r65IfI0pClhoYSGsVeu9Br5dO1zhOTWHrVkfYnM+cuSSHkeItbxp6KhQZL/I8m1nhpBYrrQxa7i0cHuifeqcXbuMKJlcyusPaZiRWXXdptKxS3Xgt6RpoqfAYjCvvW88WgXcERABwTh7+L8K0xqwAAIABJREFUL/ziryaHUOXoq8/cdMMWQD3s1pZAFe6UZRSfGzCViXGR0agiWiZVctLfljejxUlZLG1FcsmQvBpOBE6CdqmfxhIze2Kq7ed2I0s1p0+tWXXVQv1j4AJDHejOpteyzV+vzdJYM+kwCG9MAFf65I1NG7/W9doR3TMssHE62bMjHSsTFSW6iLwMcGLTDMs1FYnGWElgDTwVhJYUPDqX6azyj0poLPHFwC2Dp8Ua86qYF4cSC4G4vNhW5bnfHth9704GXQNQAE4lRZVnfjAmSOymJwK/B+Sn18Clb30xvie5yx+pYm8QVfy5/MorL59rTOLQWyxVkv4hn6kGhD3SUZ/RqCJ+h0yqDNEYt3S1k7QnKvrKo2us35CQ+NORWX5g911PPfrTGLvIg+5ZYJVeRGs8/rUMjQVTGWMYX+ymzvY+8MO7nnriAO4aLNBaEIET6S5v9ZxXjbH0q4RUFqWxSAipM42p4Onp1HXJZI1t3bLxxHt/pqBFHnTOZNzZ124TUM/teI3qC/uMKpO7V+TID7knPWQPosp9u779zJM/x6GLvZlFUSXpIgrLrbREeRwuKbaRqYIkPzZJlT7nxywdmZpkli4atnRyip7W4qHGCle01aBVRtZwjSWkO8Ais7ziskvnqscpKP4ZCB3uH4s6R5ZafzxrHgumBjsJ4to6Msva+FtrVq3EUQc5DVI5nTjZItETcfxEKH/pGiMhfpb2gVjGAMveyiNLTO3n54/itgYs1YCX3S+SJGZ2yEUFl63HMsvCCQMuebDisksXmiep+4Aj3kdPpMq7d4uoX0ZQh/CMTJWzIPzgTn0AVZ558uf37fo29qZx6C2KKlxjkn6yqJIwGuYZbCmqyJakygCNySqyq7E5NSxWnBOe4rUrwra6WI2J9SjTRrxz5mRXAAXg1vgCMjE+LUVjDDsRuHVXry6efBuiDrZVZCmDNUZKdHyqGuO73rLG4oM2QruthMYyj9ukitr3qWHaa5UuueTzFKXeAoR2JlVkjVHUwU9RxTWYxHrYHkSVN1787fabr0eWBigILX1EqvTVWBZVlqKxLKoIf7ScoEqWxtwKtivC7CRXAkmUXhJ/zysxWRVkkrLGwzWWWOnJ5ctj4O7+zvZDT/+KXkbPwN35GEG3Ig4Q4OiNzPVYOJ2RS96/gmdoKI/+Ys9DD9wLPRO685n7YyL1xbyq86Yx1udWTODqtSZIVXcmGOFoM81GJUbEJp5ZVGkPBGJ8muI4yAhE7NxxNf/OmlVXMUeRrYFTVHlvlxjV+NIjVQAIwF86VU4de/HaDeuQpeKeifwzI1IlHV0bQJWk9+hmlJ0chSqCd5raH8uWqcMqXWVWFBSLMaWroMVFczOSp9LrsVAu8yCezxNfv2nDulPv/4W8C3CEnaoUXxaPOXlVvgHNNPb+7zZJAf1NTxyTVsNiDxThC7/72rPbbthClvgEuHRQnqdWnUeNia8XNSbMY6lc1cTWllwDRyhJEK+4eCAh/hAhRZBwl3zC6Q9e2rRhPeUGjsBvZFLlmKAxJrIQOkmqNH/z1bGx9b9ThlOFuOvIUnFnDvfMEamSnJqEOGGaKtJC1GEt16RKIZVRqCIs/7QEVXKSQOO/mirZKVri6KhYBW2RGsuUWWbNvRWXXUqzfv0ZCD1phSqe2PNr4Neav1k/NvRnxQ+afF0rDlGCp1T65I31a9eAowPqYq+RLlUv7vAmupguWWN8G018C9/jCtqToVHAtgqJBbpAFK4xcSmSXhFI8TFbQ3JYmNwI8ux87cSKyy6lizHA/ajS/LUE+0X/9yNVCMBPUOXwfRu/uv7yf7kg94VH8kOo8tHbh67bvAFZKvZmcOiOSJVBwYwUVZI7hJ6c18/FOYwqAtQadlSRKgM0JhQJSWiMlrZKz2OL1pgc9CxmHDJ3dOzo3Vbpkks+T/coAhu6cxJw4snzTh069ZTGLr7wglS6wdjY2P/1P+8nYrsy4guNT1Zcdik4OvQWoNcWgUtvbZ2vuGKGxlhckcUGS+dLY+n7kljw8BH6kks+3zPK0JkGHPSlivJzGfeL/ucIQDArUqX5m6+OjY198d/+7fIv/ag6jCqHnv7V3d/ZjiwVuU2IOqNQJW5GlRmdT1Glr8YEiLK3AdJlTvpqLP1OvwYeEVLfwle0xhUx8WW0+FkVmTq2h2uMPyuOT3FSM7uwhebJFZddSq+E1N4QWZWex54Q7zXJN7j8EbWJ7Ub1u/8iseALP66K/JNx6BnlSy75PDg69qdx6LIAXUabbczqmpy7xqSEDCETX0gukc9WpsTDXb4McoiRrdSOS2b8gJBszaqrqoWj0JkB1B1AlWM7ku7Cje9anCrH7qFj24UX5C7f/x7uBQABdvpShayHkaUipw4oGIUqEunTlp7HEoAQd1GgpbTW6k8VLksSHhOp0l9jXoPOV6TwFZUWLx5YZf9WsV3Hdg3bNWzXkUlaYOhhW0XWsJiHsCsSyTky8SLBI1+mfskln+8ZGnh1wBF4TXBrsfkN6DSh0wS/AV4dXMlpufjCC3K5W48I8eJjN0oCvPWNtuR2C0G2af2jlV++Ahwdu02IuqR8H+toytufk9C5ih0lMkmSdIElSdNuwpEZV4YiZ8xJXizTmCKUBqHJtZFZwLb4+QpVl6uCJ1Rxc3XaatCrCJ3pEhqr0novxEjJF5v3/knKjN8g8ksyGu6+547nDj4MfgNwNJAqh24cG/Jz8YUX5HJf+OXEWRz1cNQeQJXrNm/46O1DyFKxNw1RZ0SqSFeasBRVwKlim0RudGRqyJaypRLVwpPNExPx2FicZZEqOSlhhFn8dUnhb6cKdp1W4bGq2Kpgu4JtHsGvsQBRJTS0sE3KFCtxQFY+MhAbn99TvUKo/Pw6+LRO3ZpV/1Utvg9eEwCzb8WMVvPitV3rCY2xKDIA9LBTDl69VRbZEUDtJHDdBnTqJ957ceuWjeBWsFsDHCFbZR36VOwo2C7T3zhl7KjYKfPjCCxcXmQ+Q1FI6SwLLdiJwMrkZaFRCmmNBvKWMnZUdlpZA1cl8UDsqnxPDFzSgl0DjwcMdXBp+1la9syrsYKBQlzKrrIqZRn4i0Ep8uD4O4e3btmA3QoAxm51IFUevvritLJEgeVWPHQ07PTY/lg2Veaqx1dcdin11jpnIbBHpIpwpY2hVAGyEWVXsVVFZgXbVXCr2JZalnExS41CZarEwUbyJQWqJPPu6SXxCCYdDCqsIBbZK9OxUwGvQev42FVsaZGphm01aCtBSwla5XjzPrVOEKNeiYVZHKJxdPBq0JmCDi3suu3G69578zB4M4Aj7pdSI4V7eW1Xb6r5xFezNOYyByBO+Rkbu/jCC249AgAd2afq1KFTf+WFgztvvxm8KrhVttbXwdGwrbF8VtofNTLJrkixu0BSaUiN3gIp0xkaxYjuTpJpgcTTVdYUXAmNIsv6K0SmwvwNIkjW0c+vgEtdEVLIjZqngCeUviJF5nzumzRofVxe+Ja59OCSO1hJuEaZ2Twk7DRXPQ6oh5z6MKocfeSLF2XLK5db8dBbEU2x6iGzL1Uee/iBfXu/TxeW3QXcbY9IlYwSv/2pklwKOUR4FdEvTeQfYyeDKpLHSBd1lCp9NCZFhMk166ybIHdbaaEsLvrQIKMLfSCFdFIx5czgR3/gZh7/5U/3/eSH4E0BYHCnJWg8UvZ1mlu2xoIp5mw8e99Y6vnwTDqEsOu7tx5+9lFwK+DVAYfg13gDaCKY0FDIGV5ibJ1Q4FnUjKzJTRsBBNLslO/wSOd5kaVim9eUpiVZsF3GTpHVcmPFOejRZlbL0aukNDbNGik0qcYcrooMjzGtMXJ4DPdM3JkbgSpn4MitucSP4FEAAO7U+lGlu1BceeUVc9Xj5Fvh0Educ0SqxEpziQ2iCgWEGtMYm94zI+HJLZNUzAnIuMOo0kdjfXK6pK0GYXnNb4/4hThwCXUl1mYjAjetn1z55f8XvGlAIXTOMvimwJ1ahMZccg7vD4LGLvocvfOO+G2RpXbmCysuu9SaOQ2ODv4MRB3R5xajcAmN8aAc3xvtt3uTiOaJzJZg5EMjX1XbBVIDB9mskJtDIijlOIdD0tjUuWusM1/YtGFd6fRRHPqjUaUBCPr94G5tAFUe+OFdTz36U8QO9QGORqcKNVFF/anSV2OUKnFqCEp0BZAPRsrh+4pIlWyNjaK6RGAqrfUB0sqMXIkRZwZcEzqke8Ms+DObNn5t/PibEHWh15JgSmA6WGNeVT7HedHnaESkB54knr/86dd33HoTxbRzFkI3HdVNB7775RyIFBkMS+IxFosf0b+uRlaeFZyidTtY1JG3U2DZGx7rlha7Rsx9cjM0lhGaEuzU+3/ZtGEd4AjZlVGp4jtJeUUtNJAqxU9eX3f1ao4D6syjTmtRVJFsIFVSGqvH/aDlFCieESJGlaSVYeKgGqPKSBpLT479jrKJUk67hZn5ZtK7Eidw/QYFzp8Bf+aVF57eefstENgQOkkcR9QYoZ32802ixFIaCw2l1yquu3pV4cSr9PLJppyIeGp8ybTBFBww+kjguFKBMexooTkRmuOhOc6L4bCdcZ6XyDzMuL1dSmYpjaW/Z/r7P/zQDw/8/EG+OjrvVDGmTl67YZ02foTiYCgYBYGpLYoqQ2ywxmxSpz6VMM00kwiGk10Evk2X3lDpq7EMz1DYGfjsNEa7bPDIx9b3jrwIODonjb21U1qG08C+C6ycQ2SWf/Orn+zZ/d3ILCOSgowj8OvJUS3lsmeK6tPR2CTVmDEZmfnIHFFjJJ52ThpDlvrQA99//NFfIbdx3qlCKrUUP36N44C67cg7uwSqnB+NJbaqXZZvJVAl3qxPX/4AjeFEnEfcQOvUoVPHXjVNi0jeDcQphyqtMWmLIwEciTSIA7A3Na1/smb1f/U6DnTnZUBHiCsSjXXqx74vTmJ8Ge4xButztRMrr7y8M19AJEm0OwcRcxT7ZyQlPJlMLWVcaZ9l6gBfEdtqaOZJzXNeCoplgfDSDyq7d7VU2wQWbZM1Fntfwlqg30hx93dve/zRX51fqsxVj990w5ajrz4TX75dw1F3aVRJ0qMPVVJxRaIxFponG9aJU3YshEg2SCgmhCriXj+zYbF7GS9uInB9Byd5UZgpNj7Jxg6GmPni18Cr0Y5PLBR7+Nkndt21EyI/iWYfjfEMcLoeO/JtKZTMd6ejeQJlzyhvu/HrJ46+EH8H1IPeLKV4wuTk65hwKSGJ3B0gM3ECibJiHtjWkFXmlfkSZ23IRhzVGIWU5XMnMrndejxYpJPu2B0cMCHve3DPpo3XTKkfnBeqvPv6c2tWXXX8nedjqlgajjqRXV0yVaRee32oImusThuyiONF+nAd3xPjMxv/DuJTi9aYbMQBSI++KBFgGThgh4bSXSiQ5O54hhW/tEc2BKssj4Smxj138Je77/s+dOboJqPYMJa12/uTlDl3xf4mQK8Z1yAg+VWX/YyFkgNy8L5nqjtuueG9I3+K82WCNoSWlNgmDtVy3k18+kiM5MogSOTIwgcL0dqEf8/8E4U1iynwPBLeSobsdAvNIqrg1cCvQ6cBnQb4dWpeLa0xibVeVbzLmXb64/fWr7v64K/390x1yVSZVt/fedu2bTdusWfHYyhsHYc+chvnSJW4c2x/qgipuTXaBol/rOz3SuOIyIHE7C1TZWSNyT7SojSWyaRRgXOqGSfZnNqB/Q/sfWBPr62DW0+O0CyV4cjNUvEc+rPiErITmvvmbyGEeBLza/ZcfuftNx9+7nEBrybgEPzUaYhPW2MJ3lMOVXjp6USZMH4Ek2eTSA1Z0st38XLOQWPIUu327N49u1d++YoDP/uxPZffddeto1Ol9Mkbu+7csfLKK155/kn+p/fe/z1rdhJCD/sz54Uq0sGRPlQRrJq8QQkfWARwgC1CY4mLyXJ+UJ/YfSK+lHgveRcvv9MPOGxXIkMTT2Tz9vIHn/jl+nVrlZNvsdh0FnC9IL0Rmrv0vqqt4Y7Ldmos6DbGP3pl/do1rxx+SnB4GhD50D0jaYZrjLeZTGgsgVvq2gfITwI/4QuxtR/xmvpLSzwWPUxjqW+SoNQoGsNuBUJzYW7mwM/2/Nu//utlX/rPxw/sVU6+0Y8q/lz+jRd/+8Duu9asWrn+6tXPP/1Igionjr267aabukbtPFIlltAAqqQ0Fi9QOYzEFfSEZA4/K89DpkpOQoGfC0itOgbIDA1Y9IvDjIALEjKak+8S3+LXwCEdlmkJA2K8/EFVObXp2g0H9u+xzxaT50f5iZtI3JrpgashS8U9Vi8pPDNX//iB+7+3acP6afV94AFDtwqRRwWWwEEwMb8uYsWZcWJwERBPsDYdaYhXX6I+5azOyCxjR6MWv5F/pkq7P9MefBq4Wvx6VycP6AZaelrm84+ji+uxpGASVOnMAOqtX3f1M0/+Yt//+f76tWvGxsZWXHbp1i0bRBsbG7vkks9vv/n6Jx99UJ94O0kVrw6hC5FPU9jOK1WS54wzqeI3wa3h9OqGuq8acnTED87EVEltpslUySU9hAFvWKTGkssJwbniEc+McTHxFrfKuu7SajxhWy2eeOP42y9gqwJOrefOHfjFvpVfvmLv/bsWmuMxWJ0pan4TvDoOIfmD2meUY/ft+vbKKy9/8tEHOQ6YBOtDB7pzkp/Q3wNME7EfntitZAb6pTcmxJn6K8hSaa9h+ZtISNoqeERjcU/d5HSXGInlCHXmpQ2gypFXntmx/Zu0HLpbhcBeqH98/J3DovWlituAwAYUkkJj4NcO/nr/3j0/BLd6jlThMkseNRallaBKn4BwOloTS11EI0WVYRrLcieWrrHUPJa+GImgzMkWS/G0G6fWXb26WXo/9rm7LdtcOPj4L1ZcdummjV89sH/P+PHX5QoINfELv/vasw89cO/6q1evvPLyZ578uT+Xl8Jc/hSgHr3Z6bEmaymV8eXTkLLJYckaE/6QRjuI93FHsa1hR8vUGJeZpDHR4VmqxjZtXD/+4cvg1aHXBowBR9BrYbfZnyoa9mehZwIKIOriztkEVfb+6N6DTz6OLG3JVJE0RqjCXUc+p4mTWIoqmSvJ5F1Oz0kyVQZqrM+dHl1jSZkJGiOvz1yTiMMDtnVkaZGpUjN4LW4N2zppdI0tDTt1iLoQGOPHXzvwsx9v2rh+bGzsi1/4D96rlvgql1zy+bGxsZtu2PLYww8UP3mdfAdj6uQdO27qzBewU4XABNQFv5lcv/YfaKSRlYUrklIU/L0laCw1tOnM4ZFPSTmsF7ijg6szjZGycIoQeFTo6TXuLqYvdpEaU069uX7tmvgLoy7uzkPPANQFAMARbf4WUiPrYAhd3J3Hbr0fVXbe/q2X//L8kqkSGeXIVJNUIf/l4VYxyupWeDPohGsgbjtlO2j9qfJX1Zilir/MoGzq85989MEHdt8Vbxx5TfBn2OiiQ2AADiG0oNMEv2afnTzxrtSrttcqZQL35KMP7f3xbkAhdBekCME5a2zwiHgOGiPbPuygFF++uzyiVRE0lijlTaxEe/ydD43tuOWGIy/9nv6mcwZCV55Uq7z5G3KbyG2OSJVeq7TtG9cff/+tJVAlwUnyteOJKCGPPk5KpsbiqWw0qvTRWNZtTiOyCI2JH86/va2J3yyxrOcU5P89dezF6zZvIH1DMFk1oS52azTphuxOejXotQBHgLoQGOBPUXLIV0Gxc6dQp4WjLkbB9ltuevPF32GeVCHu7vdxEfnnxF6ErLF+0lqcxjLc9YqcNzQlhKR52LAKPpGZKmmMJBDbpLwc61XbZ+09ksbcSnISi7rYmzpfVLFmTm/9+ubSxIeLoor4S1HtElVSS5gBVInkJBXEcwNGoMpAjfVZdSwRuDRNHX0wcJFZJm0HIrNkTn+y/urVTeXdeNUeOtifwXaZHJckRxvjImf+FPTaEHUAADCCqMPMh8gHwACA///23vVLiipLG6//wI9+9ZOf/MZa8+t+Z0adsfXFoWveQaYpaxq0BClbW0QptZtGpbRb0G7KGzqKg2C30Cpoi9gqtAheAJWbUJWXiMh7VmUVVZWZcY+M2zn79+GcE3EiMjKr0AJnzZpce7GSzKyqjB3Pcy577/Ns1/CtGU8tuU2hOX522dJ/nZ2qgM4dceUyYO2zd/sIh7njCPy1dK/Eny/Hwqmj3FYfxGhmVVkFUAVahGZ5ouaNtGzQVpMYOaUbmTq+E8foJEZ+xBgHZC8sVCakE4NrVtfKqXlCpT2fEVgyVIwC6HkuHhufDHxO3YCXHqBT2VxQ+eE4RoKe8+JY1leE9evuOvLhntBx9gw4cuA4Ynx2iGz3MVHPNYrQmqRmTWKzhtR8u+NOfr5/8M47wFU6jXBzcgxxp5v4dxeMY5QJiRyb+EE4Vq+e7f3pzU5DoK97BramFhwqwrmjg2vu1Gbz84FKd47NARU9f3EcmwdUOnCs88IUcXV03R3XbpFfa7DpoivHPFlwm5k3djy7dfMjoZS0NQ6+RRoWBg5NTsUGEhccetodF2g2vPLClu0vv4itKf7bJq55EinUvhrk2fXdORZPZFXAZGcuzeiisTXOylgrYJcZx0TSt5ZxjDRlJ6L5Usc/Oj+OjTz12J6dL9AXzfgktoBQOf7Z+0Pr73fUcneo8A3xeInyBYcK2ZXFvm0iVLpxrMuwPX/HtY9nkYGz8yab/Tnx7PEDa1atsGbGwtOHyAazHDiOKUvnAnl36mIjD1YRWiVoRRKsMcfFVJ3XrFp56uTXvlqItCRts0QW8ecJ2tXY57sfSwoqRCMTFXY+ZZyepSeVr8E8RrVcytAqgVUAU2K9oVO+Sg6ejXlKyleyQSPmxFXMnByrV8/2LrmZRJKwlo9NYgsOlUMfvLnh1w8HKax2qAQci0xTXCeAhYVKeFu7QqWHLkwDITG2PCUr1KBzX2zMmNtxagGr8f4vWC1grQA6F8uKjhntN1We+PbW5Uur2S/DNbRvQOsCW0DnfFXCTPkMaaRelowxOTAK0CqDXQGbzJb0Y+SKPFlkLQszdj1NGhc6jcxU4Ztb+5bNXhh3m0TuhghshIZVCSsSUkRfFhH5QFPwSQ/ERsZtZJxGxm1kvEbGbWbJW54sIFlARDNHFskT1iQx4sxkjsWzWBXQq6BVQauCzheYV+fkGDvZOeYpKU/OeLIQOpYHALdFicvlc58ceeqxPTufp1DRi4Dc2AC04FDZ9erz2154FuvFdqj4iuQ0spErilzIwkPFZY0vu0OlJ7Js1XM4qQOIrxBZGNGPgCOH1BxWieNySMkhlVSdFLBWoNKLahEpxWj/l2LUceWwyw7PMS2H9TzWC+vX/eLwB3tIogNrebDr4KqcMGDeV/PYJL+HlMzmPJnFZ/UiWOSsQZU5rhA4jlSvs25RKaeRIW2jnEb266PvrrnzDtSaZR3lJaSKSBORJiFVxKqAZQHJWV/OIrIykbOI9BCop916ym2kvXrab6Q9OYOaWdTM+nIWywJSBKQIWBZQUCyvCEgRkSJhNceBuBPHWO18q8qdyCAEYyJnZgWsMqYxZbYf68YxMuqLoZJcYGHmWuDbxARQsRtE7+Rb8jHsNHFr5jJAheSmiVITDxWk5tymGEKFBGAvMVRIRz+3me0ClR5e/5nvWxdTcm/vv05XpbIUyaOHjTmqmGoGl5FSIkb+G/lkkNWhHMuxEoQCWMU9f3xx5KlNYTG1UQOvRQUe+QprJunMp/kj38pkOxMzx2LZJC2bZcKGaaeRsutEsz7tNjMvP//k9pdfxGYVayIQkUNDAisPmoDltF8f8xpjqJkGlaj2iqCJoGZRM+U3xvxmCjXTWM6AmgUlC0qWPlGzoGZBzmA5jeS030z5zZTfTKNmFssCZusWpFH1eawXsVHGRDmwVQV7HJwJcCbAqUGL13IL26BgleYeuVoqiZMiTntKihzudJqjnhxpVthFwDimE05+6o3Xntm6ZSN9VxUxcl3aJO2SQ2Xo/nuPHv6Yhwq0ymCUY8Bot0sBFSKnyXq7JUClx1czgSEti7Qs1rJIzfgquR8Bx1JEv5adqmDRFSXX5jUypo5jrYrVClYrTFq4zBzX1iZHL7EZTKKDpZ4b/ebjwdW3Oc0c6ERBaRyQA2YtIsTPm0Y0wIu+XPDlAlKKWC2xv1UCsxC0pSTSvAxAYV8I1kEv5TbT5sy5NatXjp47g3UKU9BFMCVQs1hOo8YYaqawnAbSxEgTQBVAyaDGmF8fRY0xTN5VMgkmp3EzhSjBUn4zheQMVrKY6ZwSjmG9gIwSMss4mL7scXBq4NTAIQHSGlgTDHlMllSjiyhaS0XyYySuqGaRmiE0I0yjIgVqOhDewXqWGFVu1AWsZQkqeJz4aqZVH+1dsni2/DWBCrLrvjV12aDSms2s/eVdp746SqBCdbhopUsHeFwyqATNCZhMehwqPSzrn8VaFusCMRKAinIs+I3UcWyHl8fB2YHQceNRx1V4D4JW6c4xpIpK7Wx/3y0TuRNglMCogDEOvgWtevyIKz02H3Nc0ZeLnOPISYSY4xLaQXCXmfLk9Lj4RX/fv2vyNC9tD2oWKxlCMKxkgAz5mhA41G+MdeSYnCbWxrE0VjLz5thkR44RT9LcY5Rj/CWrQQS/bXiNccwQAkhEcKJld+98duSpRxhUMoA9V8leTqgotW8Hbl9RFM6wQTkfQqWLXRqocBxLgEpP5FVmvppho10Cx3xFCOJRWCtEZnNOUwHrEceBVuWaUSQ7junmZtffN/jph7t9RaKCxI4MnhbXpQiMm/1jhtUikK2zkQ/aUvKFRbFVcXB6nyyfjny0e+iBteDUqWc0gaz3sJIBNQuBTzUBKxm/jTZ0cch+hNicHCO7i2SO2TWw2TzWmoRWLTwNZUS03Gi9IuMYuXB67Vo2KPXgCqwiTaUTUcFb75LFtdwxAhXUmkJ2/fJDpSp8ObhmdTV3hmwCmXZDkI0mAAAgAElEQVR1V7tkUIm7joNKyDHexcHC3WmGnY6J41iOTwq3lfESZip3HDgujIAFfV507mAct8IhacQ//dczf9i80W1m3GYWaXmwLwBqgcWdk48a1otk94zUfMyYtjEpP4/0WAm8FttvBK8Qx41seWTPG7vAqoAmYI4zlGCGRF5HctprjEU5k4kRDMlpNI95jHAMjCI2oxxrVcGeoDSzpxjN+EIqUiVMBuMi5RjdWkghbnSBzldt/drb92OJxDvy0e6hdXcFjWkwcl01+4NAJX360OCa1c3JNIVKB4RcHqiEXopCJcKxsG/dXBzDmsRiX6WLcFxkyg68FnHctyc+WLNqhTF93mmk7XrK13KAHLCqYXeSNguqYPiwaRBxppLxujQfx/GvEMfZ9bHB1StHz50BXYpPX/yS4AfnWFCvGNQEk1xQsOwJjOjjmyLW5+YYHw4JLrm/75bs2UPEgWwS+wGgQjp4fP63vUPr79dnMr4qdgHJZYBKhGMcVHpivepoCyyZEGyU9xppKTK341i8C2sVpJSp40i2NBQDqhLHsYAPjYbJE2dvXb60kvmcEKw1O4ZdDVqTfD6x3Uh2IZbF5xMPrB1R6LJ2x/HhtdjyaUL6ctkt/88x69RxQTd0Mokx8hC2BASLcYx+oJmak2PAynmwWcZWJTBoVXFrglhkrRjjGI10F1n5ghQlWA4siZrRcSnYpaPakY92r183GEAFI9dTxcsPlYBjTiP94V9e//WvHvLVfHecXAaoUAt2E7oIhhRyLLKfa45Sa3McS5LkEhxH1RGokhZWmeP0cSaDHIj905UxWw3TtNj6dXd9+uHuwHeeMYXsBn8xiRYoNMXaW5JYEGsI1s1fsaGo3d7f++rwY7+B1jRoAkUqWXdx27BEdgUco5+ZD8fYsS5sRTiGrQpujVOOheplsS0H5Rg2CiyjxQbXkGYBxyR+DdnOMV/J8A14yYuDq1ec/Pxd2otQryBX/UGgQhpKBVDZ8fLWbc8/gzTpB4cKdTiZxAwJzFwP1iVipM2c20x/F47xxhoCzsdxTOQkj9Tc7p3Pj2x5lAwnnpz1tBJyDVcmF5buYp6cInK5bY7LkHfJW9/TccMb1x/Y/w5YVdryy5CwJvpyxm2kPJLmUrLEsJLFqsBZFikZrznveWw+HAtjZZVkjun5oAdauNJL4FiQcZZ4I4c4fSXrNFIMlALWJeHbT/r7bgmggv2Wq0qXHyoklRpAhdDsD08N7/7Tzu5ouTxQwZoAJK1v5MDM97BSyDzJ1nsyicCO2o3zduO8XR+166PcYBasZ/hUeqRBO2a9NsPZ35gAaxJabAth1YjjsFpkp8Hz57/+eHD1SqeRJV/DVyXstzwlR1pLkiBnJyNJVU9J8RkeLv0w5smpRGfx1mmjH5hdT/X3LSsVciScQHr+us2MXU85jbQnZ/kSuNgKhPb+a6T8xti8OGaVEzmGrHFinOxmVKaCndFEWo6Jw3GwIDQLOBb0KyPZaiNcawWFPm4zwxf1Dd3/i6Mfv0nvkTGBXO3yQ4X9NorY0L1yZv399xw5/OEPDhWajKZNqgo9YBWpGfnggI3TSNn10UTHceXMeRqQDRS2aFSUpup9uYSUcsRxZKcedZzXzCkT5/v7bqnlvqKRUz0Hno7NGsn6+UrkREa7zek4Vw71dGO71XbHJQZaCUBLmc/7b/2ZYzXALCBN8uQs2TQ6jbSvCDHZjHaOOY2020xjJYPl9NwcY/pzCRwzx7nuwaUocGn9p69KpN4itqECXQRDBJNszAr0HGdnjpGxgxBMHD3S37csgAr2TF+vXGaocByjUGFMy/pKxpo5f+8v7zr11ac/OFQowawimIUe7gxsEYwC1nNIkzw54zYjMQ/OdzQgy6pXo4MTFWqtYK2CtSqm+9dafAFgVsGoYL3syXlfzq+/7xdHPvwzvRN6jpwNQ6pI9txukw4/nSwYpcJGQdxBKU9JeUqys7oPTvE1g5pFuvT+vh3Dj23E9rRPCr1l0shP8FUJaTlfZbWwamieIrqy4NAq0jRNkfHRERqAknDQno9WmnMRxVYVWlXCMZ/2EyOFVHzMrcSyqKXYWjESGGQNAbGRw0wWDmk5xGJuvJH6WqIVt+Hh+w4d2E2hYo0Dsi8/VPxwrZjHkcJaCpXG+DcDt63IZ0/+4FBBeg7peaTneY6FMV+f1bbRMGNEWj3rK4KviqxoNTaOMs1xvRq6LLTITh0bFU/Ov7Hj+a2bHwsW2diskrNhgeMi+8Mk4xcDHae77+S44F1PTntK1tckX5U2bRx6f/9ffL3iq7mYeYpELPaiK4tOU+A5BnySmm6O2fEKK5DIrLDU8zjY4xGO2cFSqpLAMasMRoHV73Jhj5BjAqvEy7WXw8cq5bGWx3qBnsWUJYoTIj55eaES5VjsYFgIlXLmyMDtKy9Uzv3gUCEASOYY1kVMqgG4nR9jqsiKxOZynDnR1pYmOE1IY83nvjq4ZtXK1qzARqYCIBvpRW6VlZlzHiNjUqK/mEMv2nGxLS85oE5KdZXJ8/19y2rjJaQVyCuBEUYF7CKvBDRzm1mvmeE5FgYhSQtMIw9mARsFlh+L78d8s+qbVd+oYjKPmeNxmdtAM8cosIWfFF/PhAnouTkW3JeRpzbt2bWN/vJWDZBzmaGCSHGGGhxrjKzMY1BJn/locM3q5tQPDBViPWCwvvRURYzQLAeGiA0B62JQ6kaf0xOjgcpsOR4sYkVoYNWgNRW1yTBz2prQZoT+vmUT0jfkFAM95GfW+G0MjXnIqS6GtCzWSYlQFqkZpGZ8mkYnib5Up4U1b7FgUVtwKeurItLyvl7w9cK5bz5ec+cdtlEn/w3M0/Kumve0AjFfp09cNe8okiMLrkxq8GnpfZhPU7OYtIPQc7F6Rd48o+IZFU8vY+rkatz5ZtDQgOWgjXjdHdd3M0eObyEl78s5YuHxLWagFevls71LbnaaOYoT3wR79nJCBaxxrJGWEcExqFxsxxuDyhd/e2to/f1WPfPDQsXXCz3xlAUdCPM0WWlyyRMS6qUVOsXv77ih++85+vHeQBWQKPK1OS4b9CjpZOT4E9bFQEWQ5Do8OUN6CC2A49TQcZ5e9PTiGztf2PqHp5A9Q/5LzNUKrlbgXwlet5WcI4uuLLRzjCWvM0xtQqRzoF70jRJvrl529bKrlRCtl61GsrpB7J7XfkvkmErG4xzWCvwpj0AvPtacYWTLpj07X2TyujXAHhjVywkVsIIZu9SZY3Go7H97x/Bjj3qq9MNCpSchiWmWwCqAxTkuNHZcx+K1JWK/geXvE3oZhguAPa+/NPL04yGxrRr4FtbyQQScSQgJcxobL/kok8BOLtFo3jwd1yl36WsC0iSsF5AR4n79/fccOfKJb44HrxCfxohBXnfUvKtInizyHCNxRa8x5jXG3EaKRQIFsuD02ujqaCVHKzlq0VdKtCw9kJVuMa2B4Kh8oP0Wqx+nuaA0UqX5cMypS71Lbq5Xz9P762ngyJcTKpyILy16xnohyI91h8rO7c9se/4ZX5V+QKj0ROSIw4GwAKYEpkjKbcjUz+8Z5jU4mR03sqMnPxlcfbsjF0JRf+Rgs8I7jtW2zN39FYwCCYoG+gjs7Krg0bhfNkwDdHZcN9PIyofWEBJTptP9ff8+US0is0JeIT6NLfDI665W8NScr0gxjnmNMbc+6tZHnfoYSbW5zawri54iuWqenxVdrWCrRVst2krhsnEMtNKenS+OPLWJ/qHWJGCPnqm5LFCJtIAgf7SNY92hsvmJjfv27kFq/oeCSieO5WnxqBHu7ULHzXORbUy02TgY49oFob9vWS13CswqRYZvQetCu+OwRqR/Ct2NNVgoAVdV7Ss5X855MtG0IaPa93acGeEYMsvnTv5t8M5Vtjk7P47lkbowHENqGZP8WMCxQF9xQTlGJ7HKOfqHPB1c+bJBhRayUHrTng+JHOsOlaH77z16+KMfCio9kaLS4CYZORLkJaXZQYKFnabOQShD1zlYFLay5ntaV4fWsW2YUYHWBLgyeBrTAJKCOglaHasX+cRlsvEpF7XInw7yZSKALs7puEQPhmtuXURGHlsJtRfbX/r99ldews4MtuhsFi+AsirILHt60dcKSMt1Xys6jbQ7j7Ui1oKod1It1ULtx2KTmDUB2IPW5GWDCi1kCaAScOwioeLUpcE7V42eOfGDQKUHrBq0mFE1zCqYBTBCxyUUiYSdryJrd6wWsVpiZ8UrbVbe/dqLI1s2BbcQWhfAt8GoMGETiQv45sEsssGv2s20oOghOKxe4qyI1Nycjms/ERQ4DnQRGxI2C9Cq4FYVt8ZjNnjn7adPfY3tKWRVkZXwAWRVPaPs6SVfz7dzLBD2oNVPqsRiHgV+d+fpRRrz0MvYGF+A2L1K9GrKSCmRE8G+XOTlNLBWWbb0X0uZr+hyzlXAMy4bVJgxqNCwXPm7QUW7kB24fWVJOHf5oUI4NhmWhxG52UvjuPNf/W1w1W32bI5+Uq8AcsGaTHacWYBWGczK3AfIEzjGWwmp+QVyXDWoyuVttpbqv/Vn9ZlJZE0gK+EDyBr3jEoXjkXiivPhWFgyewk5duSjvUPr7mFbphpgH+wLlwcqF8ex+UGlljszcPtt9QnxMkOlB6wJNo9xes7RjSxnZCObx0aObTHzKKqMh5QCUoiOV4k3ZSLVv3zZuPA1Uoo0CeMZ0JoBgxwgJ7tPiVXHMcdZJHfHN8mOGybCRpyRcj723zJW8z4raZv/MiCAS+g4m1RdTESsNQGtidMnDg6uWQWeiq1xTCIQ9gTYIcd8s+IbZaQXQBVAyWI5gzjDShYHxcRMl4rE7vlNnaeXPb3sG2VMTmpa48R7oBVBL1EzimCV5lXnoeYJ0JFS9JUCMXLvyLje37dM/PZzOhU4Mnj65YEKUkrsdQoVpBZY/6fvBRXh2y8G19ypTucvJ1R6oFWkZhXBKoBVADNPF9kdTQJNBFWAYHerS6AKWMn6zTRBDKgCjja8Glp315GP9pC8hK9kUWsa2w2kiYhrjcUtcAWkCb4uYbMErfFwNduqtc8SVOLCrkFrgkAcmeO+WfWNiqeXfb2EjCIYeWAqCyia/yXVTLSUUxdj8hthKYaWA6LOFzPWs/SVbU9tf/klbNZY+2CiiMgaDhi0MxiTBkq0brLvEPYxC3QEiJQAZxaxQnDCDTQhbkEKiz/PojFjrxz9+M9D6+6iB3nMPGAX7PHLA5XACFSoFuUCQeX4538dWv+Ao41fNqj0sLvCqT4Eoh/djde0YEfuebkYxBF992vPbt2yMczT6UXsGd5cI4SnCsgo8Od/KaNiRqSanEmwa9y8UfXNKlmhIZ0pDUYdF6kY5LQDOjhOjChjB8apr65ZtfLUya+QVsSxDldMbxy4DsudrAvHOBVhKW5EUyCwgGDkcpjRiw3ktDrb2rtXHT+8l/7y1iT4xuWBSiyl270E/rtB5cB7u4c3PYbtqcsDlZ7wrgTOCm7D93Yc8c65EwfWrFrRmh2ljlNF7Lc8RXSbc5zVYY6rcPGDYJHWzrHaD86x6eLJZUv/n9qcCTnG90O5pBxrNz2ijsRdyNwcE88e6u+7hVVsSIBsaFUvA1RiTPM5HaiFhcquHS9ue+E5bE9eFo4FoxEn7RL7sUSb03GkDrpRPXnr8qXV7GeBO7Cr+XolWqCdbK6S9fUcMotBQJxTjwlEc5mx4nRy5irYwyC9iKOO63YtHCgj9YRKBqtCQquHqIq4r0iH/7pn6IG12G7EqBKvsp1ny5Jk42RVeWtDNn8VscvpTo+hdXcd/Wg39UmrBp4embguDVR4NbUguhATWltAqGz+3aPv7H0TW9VLDZUeGnHidF2IvlL7vYnZnI7z5bTbTK2/b/DTD98Iwy+taWw35r8A8DUJ6YVg6x8V9JwAZwLcGn/6I8YxZJaxUcR6HvQcaCIPvrjvmOMC9MRxqQrJPR+iHPNkcevmR3e/8XrQS/JibV4c05JmoeiyMLihMYsPzG0mnj3Uv3xpOGx7BljjYXDykkGl0zx26aAy9MDao59+fKmh0gPMa0HNgTN7PpAx62TzdNyf/mvkD5s3hrEXswK+SdTD52O+JvqahLT/RhwLadCZY9ZMes2qlaPnziDtIqav786xNn2ewGJpbp4SXTg2vPGBA29vp/81SoDs4G9dOqgEHOtScbvgUHHUwuCaVefPnrikUOkJJrvAa/bMuQVx3LkTB9as+rk1c554DYwcIBvMEq+CFM2oxI0eJtXyQZoo9B2/AOBOCrcXWGCjRLQf2of8yJqHXA73SmzgR0q205aJ5xixqnC8v+/f1cbUxe2y5msJHON5xVf0B+ziaRbewTarl77uXbLYmR2lr3gamBO8uy4FVMh+LCBYuA+89FBRZzL9t/ZNVNKXDio9wb1Z2MFJq53pX760Knwees3XwZ6MS2p2C/uK2MhhPU8GJ95xuO2AcCLB6CfNMtYLSOVAqUdGKeKjYFwP0Bm7Xl/O8I2zEvdafOjiyId/HnrgPtyaRbEmegtDs7aYXlQpladZ4jzWaSs1snnj7teeof/Vi+C3gn3IJYIKsLhihGB8gPQSQ2WicGrg9ttmp8RLBJWQY/yw191r83Hc0LrBI2wbhjUB7BlwZeo1K5/gwWQjUhMFZJSIYbOEzTI22VkJi/W8I0rLVrndFtBxkZ72neIZXPvJJ4d/tW/vm8gYj4QZF4RjseDhAnFstvhV75LF9sx5yitHwVatnWMLC5VuHLtcUBFGPx8YuM1Rq5cCKj3tvvPnsYvFXYNFu197ZmTLRj9QRDLK4Ju0L1Msk9N1cCIVpZjf/CR2Se5uTNAz9FowA7Q5LsBoDJd+M+U3M0FvUsQ3U+U4Ricr9kprNtPft6xUEMHgms0mXku0SezclpQHi3GM/y+PgMTpi9i2rcM7X36a/leVALmI/YZEmn1/qAT7seS14mWEyvGj7w2tf8CW8wsOlZ727XL32xDu/Do47tyJ9wdXrXBmR2lAVs5iv4X0fKSch9lce1kBGxKYyY5jRQ+FTtRiVgIjh5Vs/AszxxEfzek4r5nme9onc4zcTtYUHGv5Yurz/r6fOZYcdppdEI7F0sFtoeR2SsTmrvbdvD1zvnfJ4tniV/QDdgNbU36HGMmCQCX4tXzsPqTZZYfKgXf/OLzpUazmFhYq34VjkcGJyxVgJaOMn+pfvnRC+DxwHHI136jGgkXxDWtQ/xGrAdNFbOTA4h0XNiwmomU41sU4aCBglZgVwcjh4KtG87PB4JQ48EeH5Gw3VZnYPMYR7/19rw0/thHs2Ug+ujO7sJaPcTg+GBvF+DyWxLHYLZuTY7tfe2Zk80Z+EsNKFimZSI3IwkEl+NlEjv1QUNn+0h+2v/ISaOICQqUnMTDVPmjFlvioQ1RqaN3g0Q93k+eenPbNSWTXg2UAn/cgr5DLwJzafuBo0MWIkC0vtRlV24z0DQg+wP+UmQ8X7h3WV+2eijkBVDExthEr0Ui04Y1DB97/CzYqWC+EZygDskX3dSQBQGdLQjAy1rb46seEmEcM/e2X03ZFoTmzo71LFtdLX9NX7DrYM/H10oJChTeeY5cTKuK5T3dt3zr8yNDg6pWDq1def921N914Q/+tfc89+8zvN2/cs+v5Uuaz7w+VBI6134nYWIiCFpJR27Pz2ZEtjwT/9fUicg2XW2rHfEe8g6MtY9rW5blOLuMVbYl1Zlo+vkVuG5zmdBxWhfmXQdVyX53+8oM9O1/Yvu2p7due+s/nNt+8+Kbz586cPfFhrXAyYUJrywHQ38YXPYbkLPIJnHbc8/ieJ8f2vPbsyJaNpbFPT3/xlz2vPbv9lZe3b9uyfdvm7ds2v7PnpdNf7q9JXy4gVGLWhWOXAiqnvti/4aG11193bX/fLdue+e2BfTtOHztw+vgH2vRoffz06WP771x9+3vvvjXy1KPLlvbedOM/D298QDx76DtDpSc5ldlhdAzcxztu9Ou/nv7ivSMf7u7vu0WfOstWBUSwXuST9+2JxU6pxvCwgCHR4u5Y9wNNDE0VQBUirwTl5OEPXnKOtWYzB99/Y/MTG3p/enPvT28eXH3byFObtr/4NLHNT2xYueI/jh/7gry7+YkNhw684TTF2FTGrxUhmMTinCyQVhW4A7U6XU4ix5zZ0UP7d/3z9dcu/r8/Wba0d3DVipGnf7v9P5/b/sKThGObH//V4OoVvUsWL1vau/nxh49+tPs7Q6WT+UomVudxiaBy9MPdAyv7BlevOLT/dW3ybCeoOM10fSoPbgMMqV45eWDvq/3Llw6uWnHqs3cvE8dOffbutq3DAyv7Fi1atGjRIvKlif34xz9atGjRsqW9YjY1evqzRvXkPB3XycLVXSxPwt+k2HfmVzhz1csuCMdas5ndrz3fu2TxhofWvrPnlVru6447Lk8HZ7aW/+adP2/f8NB9vT+9ec+uF7QLY+2ZgORtGCVkHitzsGs+HNNqZ3a98vveJYtX3/4fP791WU38AtQsqAIgFzRu388cXkodeWf3S0Pr7updsnjPa8/SPPVl59h3g0q9/M3g6hVD6wZHv/ogASpmGZxZ8FTwLfAtwAiwD9gD5IKrgD0NeuHU5++uWfXze39xh1w9+V051sXULKjZ2eJXI5s3/vjHP1qz6uc7X376/IkDnXa69UlRyp5bf9/g9df94/r7BrNnDrb7KOa7hKyiJiA1i2M8iW0PuIVy8hjRKdQbJRhf/dDFcTExXWL7dr/cu+TmkS2PzZZPh8QIo8ZVaE2CUwdXBlcGVwHsgytDaxLMar16duSpTYRp4YSWGG6OFG1JWMm2U6u9nqMLx/a89mzvksXbtg7XS1/3L18qnj1E32pNg9MAvQBmBexpcOqhtS6AWQWjUJO+HNnySO+SxQf2vpoIlXaadbcutVQLApXjh99etrT39Bd/iUPFrICnAUaAbHAaYE9RqRIjB0YBrHHwW+A0wWkAcgB52JG//Nu+Zf/203PH988fKsk912NQrpe/GdmykYxeQYIyGkhJIzmN9CImUhN+Cyk06fHph2/0L196792rzn/9V94p8UFIj5fPRF5PolZg7TcygWyxe/MdOKbQaGzgO6V27tcPrt38+K/rlTORAKBRAnsaPA2wB9gDvwWuyjgmg6sC8sBv0Xc9TZstjDy1aej+u7ULYxF28dswowjsXIyviN+HY1rtzNq7V41s2ajVzpBLY2EqAawaG78d8ExwGhGOuQr4JiAXkAOuUq+lhjeu3/DQvdrU2S7Rl2SoRM2Pbtp5In1/qGx/4cm1d68iFxu6whwH3wLPBKsGmtQZKhLoeQoVVUTGBPZbsxeqAyv733/rlXlCZW6OHT/8dn/fLcHaIBJT0su4NQueBeThWdgziAHGAIB9GztNbE4cO7x3YGXfru1/uHQc42l2GTiWPXu4f/ktB/f/MVqMXwK7DsgDTwd7FsxKhyoNbpazZ8EzAHtHPznQ37dMPHfkknLs9Bd/Wba09/gnb0WnfQnsGUAu+BagFkFVtxWBWQL7Ang6IPfQX/cNrLy1ljv235Nju175/batwxGoqCL2DHA1rJe+G1SQVsKeMfTAuiMf7r5IjrXNs04jtW3k8bX3rKqXv4nAWsuB3QCMsWfg1jTSi50c52t5ZE1hMh17+rZnfrf2nlVk2Os07889r7YFstq3H3OQrc1rbn00EZTtjiOWPfPJmlUrx8UTEYLZs4A8cBSsl+ZbVh+SrQKuWpuoDt55h3j+aEKetG2t+B32Y8KZg4OrVoQB+mBxiFyw66DlwG+BUZp71R0mQkrgNkuF3OCdA7XcsXAQjN6gi+JYOyq+M1QOvL19eOMDkW+il8G3kVb6/lCxm/mh9Q8cO/xud6gwjrXXrRgSGNLQuruCmYc5Og9OA5ALrWn+Nica+uRBEhRZNLwXawK0aoDs418eGbzzdrq60EX+1HrCQEVzWdHlvpKJmJxGjTG/MYYaY6iZwsTkNOmNEn7se3MMKVmSvK9mj61ZtWJcPBFG/8wyeAZ4GtZL84nvJxyQoRNXpVYVB9esruVPdtqSgV7AWg7UuaeL2OUURw8PrOwL1od0+vIMcBp0saRm+RL7BI6Jzw0sij4e3weGBGahVhEHbl9Zr57qvmjsCJVoqKN9pvoOUDn+yVtr774jApXWDHZ1v5npAJW3nlzU9lj53HhnqLRmU/239hWz33SCCrGOHBt+ZP2Bfa9GJhBrHJANrWl6gzvGSD5/c2X0i159Zc99f6J/qDUhZscG77xDmzoLhsRXA2FOAZN+HysPpgR6dO7i2EUMNcb8+mhHmhGmzc2xlN8kcAx26sEfFUAVkJJ1m9kLxW9uX9FXzR4jEjdYy4M5DsgBexqMAtLC4y2JxjfRA77sgKs5qJXODwzcXp9IdePYRebHZoonBlb2kfobRqcKIAfMapxUyRxj93T5wE96eq646hru7v7Lm6IEuiiOHR+4/TZHTlrPd4QKtSAJ1pFjFwkVZ3Z02dLemvB5CJXWNLRmO0HlxCZ2NddcdUVPT/wSucftOw7zUDn12buDa1bjcGwKoUL0vTtwzMpve+aJXdv/wI0iEjgN8IxwpU6uLcG+fPO2tu/Fc8yQwJCOf35waP39jpyFVh4s0r88bJRGY0RmDlqFUD2CJMHULChZULJYyYCcATmDlYzfSPn1Ma8xihpjfnMMNcdwM4XkFJZTIKexwpfziKCSejkBy1kkp/1G2qun3Pqo10j7zQyS06iZRc0MkjNYFkDJgiqAIoIiIllwm5nHfvPAe29u92QqsI6NcfAtIl4LRt5XJU8mPQoE9kTkn/iKkJwxD6oTrCIYhQPv7Bre9ChYE51i94lnW3iyxTi2/r7BIx++EQ63Rgk8kwbo5+YYI9jfXXVFT0/PT54smbn3+rn7e82PRzIS6OKeXdtGtj4NRiHylTpCJTSkCXNz7GKgsm3r47te+X0IFbMGjp+97eQAACAASURBVNIJKsdiBLvhdyVNAG3v2r/jLpFQr6enp6fnpuc+4aGy6TcPHHhvHxjVGFTcZsZtZj1Z7GmflI9+tHto3V0RN3ka2DNx1+ti+4CE1SxWD//XDdFx4Oorex48CgDg1ai4nyHs+eNLI1ufRrqENNKQNxP0DmWNegUwJKSJviIhJYcVCVQJazlQc1iVfEVEzazXSDuNlDs75syMOrPnvfqoS7b7jTGPbkhSvpz2mmm3kWbXLPhy1ldEXxF9JevJgtfMes2M2yTzexYpIlIkrIpYDSoDckiVsCqd+mL/4KoVWBWxKlHNBs/Eeh4rAlZETKirCNEnYvhEFTCRm1czvppBaoY2wtKChl1hV6HB1bedPnkcG2WkSZhUlJOSVlLlbOZj9YqRWj7W0tJrprxm6vAHf1x/3yB57slpX8tjz/IUoVuYh6Pu+K7l4X38yZMlQwKzDjD+xPXhyz03bS2pWVCz/X23iNnRCHu7QYVVQmpZrAugCwE8YhY2DZsHVCaE48uW9tr1DIEKMiawa3SEysH1ESLd8ES+MY5JDO/Er3iS3fDCp4lQmS2d7F1ys9PSsFEOoEIQQqAS5ZgmOPWxSN2amgVXAWsyYXjrvvIONmMdOAaG0N+3TMic8zWBNDJsc1wWdBGpoifnfLmAlTyoeawVQC1g0gegKbiNjF1PO7Mpe3bMro+5pOc3kY9vprxmypdTnpx2m2nSrsFpZIh3GMfIollgXhM9WWCLwEjxIVIlezbd33dLKXWUToZaHnwLtAJWMljOYjmLlQwoAihksk16omaxmmWNG1O+mkJamrXb4zcYOTDzpfTn/X3LHEvFegEHpzZo4WKZKiiaQTWDGCg4+ErWk9Os41banDn30yWLLxRP0PojVcSe5auSJ6djx6I7cOyzcOV/9ZU9694CBAAAqA7apztupEP7g0cBwAE9K5491N+3DHwr3DHOCRUlA1q2E7sYx7J8z8vuUNn58tZtW3/LoFIA5PhKoRNUSq/9jMfpTa+UaJDcn/Wae3/Hk+wnO9h7AAC4VQqgsuGhtQcPvMWae0lYlYCu50VQxWjsXhNGtjyy57VnQ484DVob2m5zcOxXc3JM+PZQf98y7GlJI1PgOMlr5n2ZiNcWgz4Avpz3mqLbFJxGlrRicBppvuc3NXnMbaacRqo1O2bX03Y94zQi+1G3KZBfEgRbO6gJ5I4d3rv27tXhRogNPcl5uWTLYDXDCDbmq2NIozQL9LH5ZdLae1Yf/+xDcFUwOIKR4mCryKayAqEZ1iTWtE5kup+ir2Q/fm/Xrx+811doey7sasic8BXBV7KJh8riHMs+OxCi7IqeoaOMYOy+exzuUB00YWBl3+iZz8FpzhcqF8mxOaEysLL//FcHKVpsGbXqXaDyxWMJOAV/1qlnnMbbEY5dsXhHCbBVbIfK8cPvrr1nNbga2DOkiS5we+YenmBa7cxNN/6zMztK/UJEv7pH0i92HovGZNffN3jkb/ux0+Bz+dxncljN+3IBKSWeYJRjskRIwnooZnmpMLeZcptjTnPUaYzZ9bHW7FhrNuRYzJxGNlY131axURjeOHRg7w7qOLMKnpmAlQXhGNuBHDrwpw0PrwXfAnuKUavMWRGsApglMApMVj5Y2ZJuJjmsiRseuvfg/j9iTcSahK1J8PRQozspxBf/zocfjKOM3MdwRVOiMxsAtETQxXf2vLT58V8BssEszwsqgQpNZ8NswxarVGyHSmH02LKl/0qholUAub5S6AIVnmPXXHUFwSk283Y94zQ+272CB/HiHSUAfxYnQeX6667VpjOAPbph7sSxd3a/uHn4Yaxk6IoFu2B2lsv8Lhybiv2Gg/t3/frBX4LfQkYpsl6iOMuBVkBKkfXXSOAYCT8wCyuyeY45jZRdTzmNcBILAn3BhJagacPFGxxZvOnGG7TJc3QBgGzQC5eIY0H1nSNnb7rxBm1WBOyAPQ52lau+r7CNWYWFHJmKgVbEWh5rBdBLTlO4/rprnYYERgH0EiAPzDLoRdCLYBRAFUGJf8k46z7pxjEGlQgw6tWTN914A1gVQPa8oEI41j0uEj2j2QUqxz55b+3dd9IRudXAtjwHVP421L4eRDqBCrdWvPpKuiIGB4wEqAzc1j968hD4Bokwd+TY4KoVpKYLdBFcGZyZ7pf9/TnWmh296cZ/Vi6kwG8lO04nzT66cYz1BQ7bbbRzjPaAZeeywrbzXXSjwrRVWRw92t+3jDrOGgfPSMbKgnIMzPzgnbed/upDQC1wZ6Icq4JVZd1fK2CUQa+w/hKERWUwqqePfzi4+jYwqmCWwZ4Fzwwb7ZllUHMkynrRHHNKXTgGhrRsaW8p8xmgFljVy8cxvYDV4r7dr24e3kCbgPo20ifmhMoXazio/tOOEgA2BE8W/U8e4pfJbB2ZzLGh++8+evBtcKbBt8CMcYxdvDM7+uMf/4hes5ED7CccCenAsRPDi7o9OnMMqdkND917cP8u2hMkCNRSCxq3VWh7qHhHNslXgvNj4W0IRymFNKvP0FB7wiIwWonLHeUCLsxw9G9vD91/N3Wcq0Br6mI49nZCcnP4z3NwTBfByG14+L5Df90N7iwgE1oVFsQvgcU6p5AuZKSxMu21NU7bcJkTB955ffiRh2jHV98Eu8G6MI+DWQW9AHouGGEJAciFVHcub//Kkcemt+glJ3Fs7T2rj3+6F+xp8JQF5FgSteJQ2Tby5M5XnsFqEWlVQO78oHJk+LpwJFm+D7BTxocfjhCsZzGLeBiJUBl5atOeXdvAKgNGYJWjHGPXXBr7dNnSXpJawa0L4Crdl8jUceF6/eorSYzpyqu7cSya6caaMLLlkd07n8VWDTwtfsPMPGu+WMVame/4iJQC6fCLVP6YpsD7zlcyvpr2lLSvZLEmYT1Cm4TzyJF6pRwRmSKf3/P6tpGnN4GWA00C7IEuzZNjbPS57Q7inGhu88nDyRxjmw1p2zO/3fXqCFhlwD60qhzHgi57Nca3oIdyjVLOqm1/aev2l7bSD2ME1iT3I+MkpxfJ3HDptcLzfx+7m3yOqKenp2ft60hOJ1Y5DW9cf2Dfq2AUAHvz2o+RHFcXM6R4yWIHqGx+/Df7dr+K1SI2prBrzhsqL/280/TQ09PT809hSNGbToTKtpHf7tr+DJglQDa0askcI7UnxL/gm4H8chcLMyfU/auOEK/96afXxL4o5diFSCMfI4c1cecrf9g28jjWJMA+663KzCzQtU1njmEtn+g4ej/0LNIIXnOR6FxwaJ8vumV1t3xxPclKbX/p6e0vPg1aDowy1c2dm2Ms6n0ddc5RslZM3fN/ON8sebYjx7Ambt+2Zfu2LdgogN+C1mSUY6TR3hRYk2BNJj4ZfvThA+/8CawpsOuAHPYjk5RsZgnMAp9k4zlGQ47cdoVbKxaDjyVyjBzuBF0E5IBZmh/H8t3MyPE9k9pOVYZQ2bX9uW0jv8NqEVuz2FbnBRWB1Ij9y/LoGEIf978NrskY5oKVDJVNG9cf2PcamCXwTbAvJHPs/bdf2fSb+5GcRkoGACfH63kLq9euueqKnp4bfldSs9iF9vRdlGMRxQWsSQf27RjeuB70HHg6tKaiMgFkT19N5BhWaVSHtFREqpg01AksMCXRxsQRyap4YXsgpxGERsiB/z27Xhh5+jHQcmDVwNPnw7FgALr6SuocUCeoc/i14zVX3f1hwloRqVmkCi9sfXznK39AqoRdHVsX2HxbBpNxybwA1hS0LoA1Da0L7MkUWFNgXtj27JZdr74A5gVwZPAsMMmPTIE5BVaNBSc5cau2Q6v4s98mcIx/eLV2bGx+/OF3dr8EGqeVPwfHpKj+SpsZ+bgaR1xRgkLl0Pt/3vDQfUHUfm6oCAzG11x1Rc+1O4rBhTlglcAqg8MRrNURKmtWrTz1xQEwiuCp4NSTOXbwvZ2/HvolktNIywNy5ti+80WJ11x1Rc8/7BA09lW0zjGPrhxzFXBmo3I3jGPGeGeO5Ul/e6SGS/ZwIWGKYEhYl2gsu/30frSqHak54rUgAkmmsqMH3xq6/xeg5cCeoZmfOTgW7MGuvrKn58G/BnkkDanpyq4w70mDWa0EjvlK9tcP3vvRe7t8RcR2E9t1ttatgDUF1gWwLoA1zf7lrDUN1gUwpt75887NTzwCxhS4Org6GFNgToExBcYkmBPQqkCrRKuQ2jhGK18T5zG70KlymlgonUT2rgvOsQRlJAqV0W8OD6zsx2oROyqyZuaEyvjrc+082ePJo92gcsu/9RbGPge9AK4MbiPCseA6z584MLCyDysZbFTB05OjTIFDBa4E++ore25k6XE0SwtkDidybBrMIpiB/lYe6zmiKkMr+l0ZTL5AtsxCZxNYr2C9jLUSUouI5sqCIoy443BQnWQI2CA1ECIJJ2K9gGPV7oxmRILP1/K+mvPUnK/mfBZvFM992t93C2g5elqRG7MjNUHBoWz+8ud6XH0lSW7Sgg9uk5Bds2rFN5/9xVdEbDew3aCbbDKPmRciFuHYDFjTYEwd//Sva+8ZBH0SXAtsGfRJMKYo06wamBUwIh03+YVid461Q4J/pX/5UuHMQVCzYM+CU49wLNFvusRqowsRAEShAnqeWvjhBKjcdOMNs5Vz2G5iW54TKtVd8+XYokWLrn/0q0So5Mc+X7a0l8bJPA3s6QjHgjqa2eJXN934z6BmoTUFrhIMaTEjPh3nvtk1V10RhjVNtij/9KHwq4Ucm+Hrx8movPmJDe/seQWMIjiz4OmRJVyrAq0qWOPhNt0aB7NKGo1jLVC9DmKybdKWGklcCkiNHGHm4xlherddYo3Rz2lkaX7MngG32TFVyjwWxuXigYLkx4NHAdAsYtFkYtbM6E03/rM6+S3WcuDI2K4zoBRAnwB9MuSMMRWhGeGYeaFezdx0409Aq4Gtga2CVqM/Yl2A1iRoRVAijeraj8Ykx+7tAlvOJPTgas2cu/66f2zNnMNKBhwZWhfmDp6R48aJEibtZ+24nEoiVDY/sfGdN/8LnAb45nygUvwVV/w7x+Oaa5863g6V7S/9fvuLT9Mv7FtgTYAWdrvv4WvVrr/uH7XaGbBq4KrdOcYH60PXo3rotTD0OQfHBlffdvrYB8kcs6o0DtaaZK2+x1l/+wrowawtzcWxrB89NhcXfgro1L5PM0luNz+8cf2Bt18FcwI8rdMSOhjIOf+QWQoAdGBlr1jPYD2N9TR2bG5nY2M9Is15cP/rGx5aC0YejAJ4BlFuAb0AehG0CdAnQJ8ArQZ6DQxCHmJTYE6CMQn6JOgTg6tvP/3Fx9hqYFtHShWpFaRUkTqOtAooOVpLuaAcO/jea2TTgZUMeBpYE3NFp3OUYN+HYxxUTp84NHjn7WBP08M7c0KFLDq6joZBePXqKxfvyMX/eu9Pb67lv6FQQS4YZVDEoGIzwjHaeMqsgG915dhn/AmxSPp/Do7Ngkm6jxeJ1avf3nTjDWCUwCiBq4CrBKr/YFUuEceSaTYXx44f3rv2F6uwXgpamSSbmsWRMSgo0Jn7gc0Ix4bW3XXk4z9TjpG4YsixcdDHQR8HbYI+0Seir0yAXgN9/J3dOzY/vhGb09hrIbmClJIvl7xm0WvmsSJdCo7d+4s7jv3tTQoVcrB6vhwrUiSE/exDqNC3+A90hsrAbf8xeuowYB+s2hxQoav6n1zJ58ASHvScAcWyOxGA5NAHezY8fB+DUBWQC5qEZSE4xBzh2PFP3lp79yrQ84C9dtdzi+8Ix8KR2inNzTGjAnoZtBKxXduf3TbyO9DLoJfB01mSlJlF2tRPgj0F9iTYjGZ0xRioXMzBMV/JenKkTDFBtj5xdAz3uDl7NtW7ZPFM8WtAHlKExDPztDNVdCdNC3RQAwwRDJGfxyq7frZo0fI/Cxla8Mp1kZyQvly2tNdpZumGHvtgBVr5JdCr1LQqaBXQKqBVsVrBapn+q1XBmABjvF4Z611ys9MsAfaRWvaVotcsOPWcPSsgWVwojgW/YaZ4Iuj8AqoA2Ke61nNzrAhaiSKBVKJEoULf4j/QGSri2LGB2/7DMZvgNrtChYamrrnqip6eVZ9aWgeCAcD4mwOLuI2RS6KO2kx62S3/Wp84R6HiNMFpYFVEzWxw2DfCMSrIXP4GMCJp1uSYR7yw4+oraSXXRXOsv2+Z+O1n1HF+C1rTCY6zp0KO2dxsRh1HN7KkCC1uatpXMp6ccZsZp5ENjGdaXPU6YBqXNMNaDqvikb/uHrpvkO8YFHdOEM88wm1HF11z7UgJQAdTAlPiOPbmk4sWLVr0d1f2/P2rqZBjxO69e9Wxw3tpMM2eBs/gFk5FVtJRAb0KOnFpUApTQkoRa2UwyJw/sWfXf448/Tj4NljTWCsjpeQ1C25DwspCcCxaIDLEDoNiJQOkrmCuet+F5BgHlW3Pbdm140VAdheoBKczr7nqipu2feKbGgCAP+u2QyXz3O2LyClVNtk5JTBLm5/Y8M6br4ZQQR42ylgVO85joGapzIirgj3FrwTCiCJxGR/SWLTomqvuOXrxHDuwd+fwxgeZ18YB+x0Hp1Y7wSqB43wlqKdu68atpFiJcIRjgfuCpSPuvBlgh4JEUMShdXcdPbiPr1eMmBHIaO6L1k/9n0dLDliReez4MHNOz6rD3DzmyemP/vLar4d+6StZpIpYk8AzsDUVHmbT8rRM0SyDUQWjTKthtCJoRayWsFbAGqFZCcyKIxcHbusXU6fA08EogUaomIcFWSsGZRxcGQN91zPm3owt+DzGoOKopaH77zl+7HOwLnSAypvc0ZWrr//PFAAAqF4CVMghl59ce0VPzw1Pl8g5A7t44J2dw488GEKlNQ2eHkAleT9GXhpcveL08YPgG904pn/x5r/GQdRxPxZsSTiO1cvf9vctq1fOUa85Mrjqf3eOqVK9fHJg5a218Qro+YS8fMgxafyP/7Io+li6+yvGsUCe5Zqrrujpue915NhBzKOSOXr7iuVTheO0zFIvAnKCaiCk5nw1BybZhJQZ0wgEiwypJENKeg4WsV4ePXlocPXtjm3SHY5WwFoOFmQeYxwjnVMnhM/ZYicHyA01ES47x6A1oc0Ig3cOiNkxMMqJUPlyU+wWPXm8lY9BhR1++ZefXdHT0/MPr46VAQGAM/7Nu0P33+3IEpvESoBcrJcCqCTE7gMWlVJH+vtucVpGRGcvzD4zt4qP3xz9gtc/wWqskvN6A2+WQo4Nb3zwwN6dodeQA9ZUguNofV232D0TzOjCsQy/H0vmWLtQFOMYUnPh4VZdKqWPDtz2H1pzKgEukUrWL1+8KckN3OOaq67o6fn7V1MTGABARUpGnjh9+4o+8dtDTmPMbabdZga7BjIm+JM4viJhk7V9MkssR1RiqaQiGHmkSm5TIHoSvpJDqnTsk31rf3kXdmSkSmRb0h4RbedYpDg42Hi3ccypjw2s7AvFhtXsvCKKC8uxJKhoFzIDt6889tnBTlB5e1kHcRz+cS0JOf7D9lHR1xsAANq5Z++/m7YrIFBxVbBnY1BJiN0Hjjt+eO/QA790jNlIbl4T4mvrIwP/39xfkINTzz/tyFRBr2zf9vvt234PWhn0CugVsOvgGnSPQavCx8EcB2uC1blO0FLxkGAlMrT7isQfvEvkGDkFHDv7HDtIFm/2ZbDecLSRioiUcHASzx4aXLO6PpGKz2Nx9ER0VxI9ctOLn2BSAuKNTxe/WrNqRfrUR6yJScY3a9jVyJl2vjoO63ls5DCRjKZFDwVWA1EAI4c1iR2IFuipZ0XY//arw5sebTUk8gqem2NHohJjbOMd5Zg2dXZo3V3HD78dQoUc/5kPwQjHtAJopRAPdLdZBb0CWpkaeYv/wPygMls+t/bee0aefsKaSSdCJf/CdQmF7OyKafD+hicLiuQrUy4AwMyxF4echhBCxZ4BV0uESvI8Rhx39OM9Q+vvB7PajWO6COmn/impzp5PKLAcw+IdRRWM6p6dL45s2RQ6zpgA5IAx0cFx4+H+3iizI1JFrBYYwcRuHJMpx4IcdJRjAhP2kKgYW7QNHNbzRAXFV0QUKHOoGVCzp7/Yv2zZLccPv0P+S1+n/mH/allQD++4oV1HjDrlphe/pvIsYFe/evPW5UuzZw4GnbV8LY99C2kFdrqZmOQr9BAUUgV6olkjBZlkLs2BIWEjh/Uc1sPjUkThY/++1wbXrM6PHvGVTDeO8ScXEx59b2YpJMRv/zaw8tbjh/eGw7EmAbLBKFwkxwgeqqBXvyvHOkNFK+x+4/Vb+5Yd/uvuRKj4LsDRB5NTY/f+iUAF0VrcSfHQjghUWlPgG1gvdIJKR46BIR14Z+fAwG016VicY/xpCF0Es97+9R78MAcfruGqGPjHLNl50wWAq4NdjywASMaDLADMKlse8FG+YAYjhMl0MHqe3FcyWKNBW25FnvVkOszT0EKsFo51rKIFODRMRMXksJJWJ8+vvfeezcMPs/6uadAESi2NEIzEGwtQ2LE4qbQjeDS/efneu++YLn4V1Hn4qgi+hfRS8MWwJmGNcF7w5IynpDwlxZ/AjxRDW3lwSoEiGuJ6T5775pOB2297/+3tc6wVP7ija2nKP+xIZffsfHZg5a1hIzxNAFUA3wKjlAyVOeaxEugV0KsXsVacP1SUXDGfXb/unlv+rfe9N19ph4rXsmHOx+yRC+KxCFTsafCNQOghESohx4IMGF9Idv7kJ/239h14+9VIoDa+8SBiYPN8yKDnkCz6DcFvCLhVx606UkSsiFhlqoNGji5+zCJYRa6GrQBGAXSKfrKv8BWRLaUkJmZIdKayblPwmkRqSiSHI5Aq+ErWkwnaSI0VkZcJagUFX81SU0JDRLNNSSM1hdQUUsmTNDZK7+zd0/vTxSNPbaxXvmISLhmsZbGWYZ9MIzUfil60PWrvrd35ytPkDA4mNcF6Hnsm0otuM+00iDZJ2pMzSJWwLmFd9JW0r475agqp5G8R/TMSt2RSmUSNUJewJrLlIrkWUZ3JDz/2m/6+Ww7t35XIMV5D32+m/GYe+fxXVk+//UrvksUjWzbas6MhYDQJPI2ufTpBJYhDBiWLighqDtQCaEXGIhKYKWIlhIrfFJEsfi+oqAXsmUVpdNPG9T/+0Y/W33fXGzuezZ3/NAIVS0++ScLb4+IXEahoEnYV7Cq+KnSHShLHoqZOC8OPbexfvvToR7sjy8WY13QxIlFEHlYeLIM+P/tSKfU5qDksi34j49ZTvjGJWg2/mSGKkFjJYDUDWhb0LASIsXJg5cHKBeeIyNmh4CAQUkVSJYC1vK/kPFnyZMltim5TdJuS18x7cg6pOTDzWBeRRo9Ic6SKvMKXC0abNZLjnmME2b6aIkeYsZ7BVtlp6Xv++FLvTxdveOiX+/a8OJH7DGlppKX4D2M9g83ZNgedPLZjpDl+KiIC05oAZCOjRLpL2vVRmwiVNVNIJY2PRaZWwL6DngVDAFMEMxDNDSR1RS4pRKVXkSpha0rMnN/w0H29SxbveuX3wpmD7RzzGmOurnYdMR3QGVT0IvgWFR6ObVDboRLhmACqBGoetALoJUawPA8Vd3aMiMwuAFTsOiC7JVcO//XPf9j86C3/1rto0aIf/+hHa1atJDa4mu5Bb12+9Pk/bPryb2+1QwVbk9hvIbM2H6jMzTGsZMCaFLOjQ/f/or/vlgN7X6VtS9stugbQJs8d/fDNoXW/6O9bdmDfa6AXQcuBImJZ8OUMshvIbnIrVWqgpkBLg5YGPQN6BkwRWjmwpJhkJ+giJ7ibB72A1bwv571mzmvm3IbkNXNeM+81C14zj1TysyKREPOUFJEQwzrRxAxfIc9jxr01SnQ4mEwAIU8aTBF83TGnDx54ffPjD/UuWdy75P+uWfXzrVt+88oLv6W27XcjT20cXL2i96eLe5cs3vz4wwf377Jmzgf3xlcySJPAaYBvgFEgd9RtpgI1u7AfuS74Svg1sJ7GeibCMc5XxEWMYBIL84i+ImC9Ar41UTi7betw//Kl11/3jxse/OUrz/9u58tPn/rs3VOfvXvy6DvfHN338nO/ffm5365fu+bHP/rRwIq+nS8/PVM8EQdJ6wJRF4znpjtZ+3KRcoxVTgVQaaaJWPpCQkWvYNfAvoOMaQIVczr7zdEPvjl64NQX758+/n5nqGSQNQnIxa7i69I8oRLhWGJ1IqWZUQa/JY4eH974AG1bOvzw7teePfXFX05/8Zea9KU2eeb0l/tPH9t/YN9/bXvmiYHbbr3+umuH1v3i6EdvgVagpuZAEbFWAr+FzEmvMcb9Cc5xxIj7DAEsegysbWUfHCgqxDjGLO/LRV8uIC2UcfYVMo/zB0nCV8hzXwmGpTR9S8sgLd1OMAbxNNbT2J4E5ILbQLpQFY+e/GLfG69tffmF377MOLZ758ipL9+t5U8w9HPdjVUR2Q1ALrZnuPNjmdgYyXZfGU+JfZM0ncqMqLK6QV2EVNFXRK5iU/DkLJIFrEjYkcFvYXNCnTh98L2d2194ctvW4cFVKwZXrViz6udr7vg54dinH/zRmv42ASFmDZCL7UZQ1hBJ82hUuTU4+5O8htTzlGMxqMgCkjO0I9FCQ8VXK8hRAWPsGsic9bXxjlAxStiewZ4BgLHTRHruoqAyb46ReJGrALLBmiiNfbrvjRdHNm8kN6N3yeLrr7t2cPWKwdUrhx9Zv+vVraMnP0pwnFEFRwXfRlreb6Z8Oc11NA4dh5Wx0LQMFbJM2C7Pi2NIKSCtAFaBc1zY5yo4rBUTAonDmqpAp8giLZljehrrGWxPkXEOtWq+JnjKKBnSwgmHb4yg55E1hR0VIxdZU54iJDYdjyiUkO82H45Z+Tk4RpX900grgKsCcnFrGuvF4I5jJcN3M4tARS/i1ixpLYlUKQ6VGMeihXghx4Ipdy6OXUKoyHlfn0S2Aj6JG2JAFvgW+Cb22AlooanEJgAABWhJREFUvwVOA5vV7waVnsReVYlMY+VCJfA08FtgTdIkdafFN1kAqHnQimBOgWeAb4M1RRyHiKhBWFRKfJfCyhiSR4n5zfNITQXn8NukI4KAGysyYqekmTHxU70YcCxwEy+eEduexYyF7LJkiOIJFiNbgHhkVbHTwMjByMGegZ06dmawM4OdWXAb4MrgW4BcQC52ZGROeKFeXbxlK1vtCEjNBtKRwTAZiFuFyu/BXaC7sgjHWN4i6zYzfiPjN7jWE6oEdh38FmAfXBWcOrZnkFYKDLdmcGsGuxpgDJ6FW9NIFbtBJbGAoTtUAlOkgGOXFyolsCehNY7NKjYrCwKVkGOJljyhEaa5atC2FOwZVoFRAF2iGcDWNDgy+C3ACDwDzEksi1gWsCxE8gRhmDuNlRTxl9887zXOeY1zvjxGFZjV8Gq5RFAejHyi45BCxU9BK4FRglYRTJIvioS5g4UZ78fAfZFQhE4UeDJzWrCpc+UxTxU9vYhaU9iewc4s5ZgzA61xMIvBXw/I4zTG6K6aH+zZvEd3aM2xYD/GC8ghLUODk5pAu5nQuKKUOI/FORbkbzQJrBo4dbDrQWNU7BmEY0iv+F37CcahklgTHN+h5UArcATL/U+CSk8sUMsvDGLui+xx1Syd5VsVsKfBbYJv0mbB2AfPBM8EVwW7AcYEKDlQcliWAsfxC4lgZEJyCsljMcd5zVGWCOJGdwo+KueAdSrBFagvIoUon5ZAq4BeBrMMrRKYYWedEMERrbXQcbzxk0kgsB4jFW+EXTEjG2JfzYQtWsIducBLr5LLDId5ShWRULGdYyx+xWjGN+aKxBXDohYaYAzWiknhLkg6QPi9oMLHIeJrSIly7H8iVL43xy694yhAF9JxAtZEznFi8Ap5TvJmiIoUsA8vFMfahDjbORaV/fmuHNPFRI6RXCJSRST/T+PYf0+ohByLdeyOebA9Tz3/BQBWcliWUFNETQE1s1gWQKW9PLj7lyKOI14LzGuOOs1RpznqytxGhXecVezkOFqbY1TAqoBdAatI5I0ieXpWQhFoHgW5FFL8wd6KxKnaFDAzQeaEUwJP8X1kgnfb1hXhLyQ/i7Q20dyu+7GAY/xBz+CvcArv/OnvPOg5UEVQhBi1OgW9Ynmz/4XK/KGSwDHS8XYOx3HlIJ0TjvnujsO6yK3sx/zmmN8c5b2G5FGvOWo3zjvNUbc51ua4AljFRMdhlRVxk3OKVjXBcUQ5jNVMBX5MdpwRy7cIfIT9ojjGhzRiv5D8NrqVamt/zAeyEjlGszTRWD9XNSZy8goFMPKgSYHefWKdx5wc+1+ozAcqYcwjcFP3wSk56hh4sN1xWgEz39EFADm+RnDDOc5rjHoNNu+TXSwbnFx5rOPgZBaZ5FCb44LByaxAqwxmEYwC1nNURYyIhxkF0JmuGOkwpOewTls2Yz2Pg0+a+dBxgUUntOBJMOHEQoVIzXpKhqwGu3EsKNT4fhwLzvWQeSzSOsPIg5bjORbeUyVhARlbKP4vVOYPlR7eR4EjAj+2uynwbDCGRaqKI0GkPMvZc0kPVQJVCo6IBjfPa4y69fNu/Zxb/zYwPljkKen4DMBq1cJDHzRGFC6yabBIL/EnVpItdrCFF/ZoVWjrytgSrs1wROU368dDuqwhSzRJys+KSM1iQ4JWob3FOE/d+XCMTWVZpigY6pdE+tBxdyGgQXAf+Rnsf6Hy3aCSzDF+tTCfXW808hssBhbAcZ48yuLgbbkjnc7aSCWxslzUa4HjyMmIuXzX7riY76wiU1f/HhxjIfXYBBUJE5MO4hfPsWA/Fi0KEdhKhu//lAc9R1tkdEkTa8KcHPtfqMwJlf8fSk2wCcrR0W8AAAAASUVORK5CYII=)
路 径:由一结点到另一结点间的分支所构成。如:a->b a->b->e
路径长度:路径上的分支数目,如:a→e的路径长度=2 a->c的路径长度=1
树的路径长度:从树根到每一结点的路径长度之和。如:树的路径长度=10=2+2+2+2+1+1
带权路径长度:树中所有叶子结点的带权路径长度之和。
树的带权路径长度:树中所有叶子结点的带权路径长度之和。
赫 夫 曼 树:带权路径长度最小的二叉树。
了解这些基本概念后,可能还不是很理解什么是赫夫曼树,那么我们再看这样一个例子。
已经a的权值为7,b的权值为5,c的权值为2,d的权值为4,判断下列哪一个是赫夫曼树?
如图所示,
赫 夫 曼 树:带权路径长度最小的二叉树。
树的带权路径长度如何计算?
(a)计算方法:WPL=7*2+5*2+2*2+4*2=36
(b)计算方法:WPL=4*2+7*3+5*3+2*1=46
(c)计算方法:WPL=7*1+5*2+2*3+4*3=35
赫夫曼树则是:WPL 最小的二叉树。
第三个带权路径长度最短,因此第三个就是赫夫曼树,即最优的二叉树。
二、如何构造一个赫夫曼树?
知道什么是赫夫曼树后,那么如何才能够构造一个赫夫曼树呢?
书上给出了如下方法:
(1)由给定的n 个权值{w1, w2, …, wn}构成n棵二叉树的集合(即森林)F = { T1, T2, …, Tn },其中每棵二叉树Ti 中只有一个带权为wi 的根结点,其左右子树均空。
(2)在F 中选取两棵根结点的权值最小的树作为左右子树构造一棵新的二叉树,且置新的二叉树的根结点的权值为其左右子树上根结点的权值之和。
(3)在F 中删去这两棵树,同时将新得到的二叉树加入F中。
(4)重复(2)和(3), 直到F 只含一棵树为止。这棵树便是赫夫曼树。
看到这个方法后,可能还是看不懂,所以我们再看一个例子。
例1: 已知权值 W={ 5, 6, 2, 9, 7 },求构造赫夫曼树,并求其赫夫曼编码。
2.在该集合中选取根两个最小的
和
作为左右子树构造一棵新的二叉树,且置新的二叉树的根节点的权值为其左右子树上根节点的权值之和。
3.在该结果中删去这两棵树,同时将新得到的二叉树加入F中。
然后现在集合中最小的两个为
和
或
,因此这时候便会出现两种形态的赫夫曼树。
或者
重复(2)和(3), 直到F 只含一棵树为止。这棵树便是赫夫曼树。
4.因此根据左0右1的规则,最终结果也将有两种,这两种都是赫夫曼树,都是最优二叉树。
其一:
WPL=6*2+7*2+2*3+5*3+9*2=65
6的编码为:00
7的编码:01
2的编码:100
5的编码:101
9的编码:11
或者
其二:
WPL=2*3+5*3+6*2+9*2+7*2=65
6的编码为:01
7的编码:000
2的编码:000
5的编码:001
9的编码:10
********************例子一结束**********************************
做完这个例子后,应该差不多明白如何构造一个赫夫曼树了,那么我们再看一个下面例子练练手:
操作要点1:对权值的合并、删除与替换
——在权值集合{7,5,2,4}中,总是合并当前值最小的两个权值
注:方框表示外结点(叶子,字符对应的权值),圆框表示内结点(合并后的权值)。
操作要点2:按左0右1对Huffman树的所有分支编号!
Huffman编码结果:
d=0, i=10, a=110, n=111
WPL=1bit×7+2bit×5+3bit(2+4)=35
哈夫曼树学习笔记
标签:
原文地址:http://www.cnblogs.com/xingyunblog/p/4196619.html