{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来，我们从一元拓展到二元的场景。假设某个贷款产品根据客户的工资和房屋面积来决定可贷款额度，并存在下面几个样例数据：\n",
    "\n",
    "|工资（元）|房屋面积（平米）|可贷款金额（元）|\n",
    "|--------|-------------|----- ---------|\n",
    "|6000    |60           |340000         |\n",
    "|6000    |80           |350000         |\n",
    "|8000    |70           |400000         |\n",
    "|8000    |100          |450000         |\n",
    "|10000   |90           |500000         |\n",
    "\n",
    "很显然，这里工资和房屋面积为自变量，可贷款金额为因变量。这些散点分布在一个三维空间中，如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0CXq9HpOTk6r2Qe4EjUQiGBoagt/vh16vx6ZNm3KezGoGKWKxGI4cOYLS0lJcc801KC8vp1ItjuNgMpkyEn/J/kajUTidTvh8PgwPD1PTcLEFq7mQAM2m9wJBrkj6YDAIr9eLYDCIo0ePZlR/am/Fi0WWxSLvXNsRGxMHLn4OUhkTMibj7B6PJ0NlIrxrAECtNuczNNJVCKmEBjEISTcajcJut8Ptdmf1UwmUVjpk28LbrVAohKGhIYRCIXR0dKCvrw8ffvih4gUy4Sy9cN9mZmZgtVoRj8fR39+vyh2LLFhVV1eD53l0dnYCyOyRBoNBmvpLeqQs+UjZRS5EsGRMquPe3l5Rk6B4PE4d24RkzGK+Vbr5bkev12eR8YULF9DQ0ACj0YhQKASv14uxsTF611BWVgaz2Yzjx4/D6/WqVvrMNTTSlQE70GCxWNDY2IiqqqqcJz8hxnA4DJvNBr/fj7a2NvT09Mh6Kig5SIVVaTAYxNDQECKRCDo6OtDQ0JCX25TYLTcrXSsrK8Pq1aupG1a+YN9HKtuMvS33er0Zt55EFE+qnnx64MVuLxQCliylqj92kWpmZkZUvhUOhwtefAWKtyCXTCaL1qZIJpMwmUyoqKiQvGuYnp7Ghx9+iNOnT+POO+9EaWkpPvOZz2D//v2orKykQxXHjh2D2+3GnXfeCbvdjra2NvzsZz9DbW0teJ7HfffdhzfeeANlZWXYu3cv+vv7AQD79u3D448/DgB4+OGHsX37dgDA8ePH8ZWvfAWRSARbtmzBM888QwqyOgAHALQBsAO4g+d5D6CRrijEBhoSiQSSyaSikywajSIQCODjjz+mVWeu21CllQEh3UAgAKvVikQigY6ODtTV1eVNAEIiZyvb8vLygqRrLJTun9RteTKZhMPhgN/vz9COkqkqthLMtfAyX7wXlBC3VF+UNQkKBAJwu92YmJhQPPIrhnwX0oQoZm9YjsDZY+Xpp5/G5s2b8eGHH1Kjpv379+N///d/MySBu3fvxuc+9zns2rULu3fvxu7du/Hkk0/izTffxODgIAYHB3H48GHs3LkThw8fhtvtxmOPPYZjx46B4zisW7cOW7duRW1tLXbu3IkXX3wRAwMD2LJlC9566y3cfPPNALALwLs8z+/mOG7Xpf9/ENBINwNE9kUSF1iNrcFgyKlI8Pv9sFqtVD61ceNGxS0DpT3VdDqNTz75BBzHobOzUzK5Vw0I6fI8j+npaQwNDaGiogJr1qwpCtkSFKpeMBgMNJusvb2dPi7lxEV8GAgZz1V6gxoU0hZgtbSJRAJlZWVoamqSHPkVOpOJXZzEWlf5oFjbUbutVCpF9fFtbW2izzl48CDef/99AMD27duxefNmPPnkkzh48CDuuececByHgYEBeL1eOJ1OvP/++7jxxhvpOsWNN96It956C5s3b4bf78emTZsAAPfccw9ef/11Qrq3ANh86S33AXgfGulehphpuLBnazAYJMXwHo8HQ0NDAIDOzk7U1NTggw8+UFwFKfFJ8Hq9sFqtCAaDWLFiBZYsWaLw0ylDMBjE4cOHZ4VsCYohGRP7TsVGXIWG4WyUjtFoRCKRwNTUlOS02VxhNsaApb4PVlkiZRIUiUSK1qYoZqWrhHSlzJj+/M//HBzH4e/+7u/wt3/7t5icnKTpK83NzZiamgJw0bx96dKl9LWtra0YGxuTfby1tTXr8UtYxPO889J+OTmOayL/8KkmXamEBjHo9foM0iWyqaGhIZhMJnR3d+c97y0nMXO73bBarTAYDOju7sbo6KgqQpQ7qUlle/78eXAch/7+/lkh2ysBdvRX6MMwMzND9dHstJlw8U5sdbzYmKsxYDllCWsS5PP54PV6MTw8XFDOW7GlZ0oHTYTP/cMf/oAlS5ZgamoKN954I1auXJnz9cL3Vft4LnwqSZdUQS6Xi/ZCc1U6BoOBWhuyEearVq0qOOdKSLpk6MBqtcJkMmV4L6iRd5EDQ8zNaXp6GlarFVVVVeju7obb7S6IcJUcbPNhIo0lY7ZFkU6nRTW1QhlXRUWFpNdAPijmUEO+vhSsSVA0GsWiRYtQVVUleafAkjEZbhB+hmKTrhJEo9GsY5jcETY1NeHWW2/FkSNHsGjRIjidTjQ3N8PpdKKp6WIR2tramuEX7XA4sGTJErS2ttJ2BHl88+bNaG1thcPhyHr+JUxyHNd8qcptBjBF/uFTRbrsQEM8HofNZstosMtBr9fTuJqampqMuBopKO3XEdIVGt309fVlCe7VWDYSgib7QC4YQ0NDqKqqwrXXXovS0lL4fL45IcP5QLqAePXPDjgsWrSIPs7qRlkZl8FgQDQaxdjYmOrFKhbFnEgr1gIYsUyUulNgTYJcLhcikQjS6XSG5jocDs959p3X68242yS2npWVlQiFQvjtb3+LRx55BFu3bsW+ffuwa9cu7Nu3D7fccgsAYOvWrXjuueewbds2HD58GNXV1WhubsZNN92Ef/qnf4LH4wEA/Pa3v8UTTzyBuro6VFZW4tChQ9i4cSP+67/+C9/61rfI2/8SwHYAuy/9fZD8w6eCdMUGGkwmkyLDEhJhbrPZYDAYsG7duqwIczGQhTclpKvT6eg4LQl7lKo61ZqTkwUyQrbV1dWUbAkKsWwkCRMOhwNms5kSl5i2diGOAYvpRoGLyoFjx44BQNZiFduiyGWiPh+9F+T2V6lJ0MzMDJLJJJxOZ4ZJkNoeupqLknAabXJyErfeeiuAi33hu+66C1/4whdw/fXX44477sCePXuwbNkyvPLKKwCALVu24I033kBXVxfKysrw4x//GABQV1eHf/7nf8b1118PAHjkkUdoi+YHP/gBlYzdfPPNZBENuEi2P+M47l4AIwD+mvzDVU26cgMNuQiAyJPGxsawaNEirFq1Ck6nUxHhAperV7nqh7iKkWpJSfWca8SYBcdxmJychMPhQHV1taSRjpqWBUE6nYbT6cTw8DDNTUsmkwgGg1ljnYSE8nkfsc80H2A0GmEwGNDS0kIfE8boCE3UxXx758pPd7a3IzQJIp62dXV1ko5tSkyC1PousLK6jo4OnDx5Mut59fX1ePfdd0U/w/PPPy+67R07dmDHjh1Zj69fvx6nTp3KepzneReAz4lt66ojXamEBqUHNokwn5iYwJIlS6ipNwlKVAo5cmTDHmtra9Ha2oqSkpKchAsoI0hC5l6vFyaTKadrmRrLRp7nMT4+Drvdjvr6eqxfvx5GoxHxeJwSCwtCxKQv6PF4cOTIkSw5FyHluUCxiE4Itj8qNgYt9O0lIK8pZAz6Sk2kcWNj4KamkO7qAhhdNdmO1AAM20OXMwkiwzBK4PV65/0IMHAVkW6uhIZciMVisNvtmJmZwdKlSzEwMJBx8CnR6bIQI12xsEez2QyHw6G6TysG1o+3uroa9fX16OjoyCkBUtJe4HmeZm75/f6MNgshbDEyMxgMVEtaU1MDjuPQ19dHV8yDwSDcbjdCoRB4nqcnHGlTzIWCYLYhdUueTqdhs9loeoeQeNjFu1weDFei0jX9v/8H07PPAiYToNMh/PrrSK9bByA3eUuZBBEyDgaD8Pl88Pl8CAaDOHbsWM7R8IVgdgNcBaTLDjScOHECa9asUUW24XAYdrsdXq8Xy5cvR3d3t+hBJ6fTFQNLunJhj+S5wggSue2y+VFAJtnW1NTQyvbUqVOK3cOUEHlNTQ3KysqyHMvI962kWibELBarw3oxBAIBOJ3ODFeuiooK+ltfDSABjGKLd4R4pFo1rJICmHvS1R86BNPzz4OLxYBLx2Pptm0IDQ7Sz5DPwp6QjD0eD2ZmZtDR0SH5nZSVleGDDz6A1WrFkiVLMi7+qVQK69evR0tLC371q1/h3XffxQMPPIB0Oo2Kigrs3bsXXV1diMViuOeee3D8+HHU19fjwIEDdLjiiSeewJ49e6DX6/Hss8/ipptuAgC89dZbuO+++5BKpfC1r30Nu3btAgDYbDZ0dHQcBlAH4I8A7uZ5np7gC5Z0xTS2sVgM6XRaUQ8oFArRZN329nb09vYqGtVVCkKkucIe1W6bJUhSfdpsNlHzc6VKB7H2gnDxjWz7ww8/zPv2XInbGSEUIuMBLisIyAlH/jYajRnVYK5FK/azzZfqWWxf5MagyfcgHIMOh8OYnJxEZWUlysrKCpoGU2SSdP589uumpi4SsNlc9Kgeue8kHA5Dp9Ph3Llz+P3vf48DBw6gsrISb775Jl588UX09vbC7/cDAHbu3ImDBw+it7cX3//+9/H4449j79692LNnD2pra2GxWLB//348+OCDOHDgAM6cOYP9+/fj9OnTGB8fx+c//3lcuHABAPCNb3wDb7/9NlpbW3H99ddj69at6Ovrw4MPPggAT/M8v5/juP8PwL0AfkD2ecGRrtxAA5k0kjvgiGcB6UGuXbtWkT5VzUlKbhedTieWLVsmG/YIqFMkkCENp9NJyba/v1+0haBUlcA+T6jhFSodhDI0NchXvcAqCEwmE3w+Hzo7O2WTf1kVxZWcOMsFNd+llAdDPB7H8ePHafuKTJop0dPmvd89PVmP8Y2NwKWWU7EMb3ItpBGToK9+9asYGhrCTTfdhJtvvhl+vx8ejwe//vWv8dBDD+E//uM/AFw8BgkB+3w+qqs9ePAgHn30UQDA7bffjm9+85vgeR4HDx7Etm3bYDab0d7ejq6uLhw5cgQA0NXVhY6ODgDAtm3bKJm/9957APDqpV3cB+BRLGTSTaVSSCQSogMNci0Ar9eLoaEhpNNpahDz8ccfF/VWlQ17LC0tRWdnZ8b4oBSUVqQ8z8Pj8WBsbAw8z+eUryklc/L+hGwrKiqyyJagENlXsceA5bx7Sb+YXS1nF3TYpI8riWLsg8lkgsFgyDjW2DFo0jcXhm4SMs5n8S61aRPiX/86TN//PmA0AhyHyP/8z+V/vwIWkWxPt6qqCjt27MC///u/IxAI0Oe89NJL2LJlC0pLS1FVVYVDhw4ByBwBJhc3l8uFsbExDAwM0Nezo77C0eDDhw/D5XKhpqYGMzMzhIgcAC5LXLAASVduNZNUugRksouNMGerBLV9WimIhT2Oj48rJphc7QWe5+F0OmG326kkR26ckUCp0sHlciEUCmFiYiKn78J8GXCQArtoJcw3YzWkfr8fR48epfaIbJsi3zn/HC8AUilAsO1iDkewkBtuYD2MhRelWCyGmZkZVFRU5PQwjj/6KBI7dlxUL/T0AAItc7EsIpVOSrKk+6tf/QpNTU1Yt25dxjTZ008/jTfeeAMbN27EU089hfvvvx8vvfSS6lFfsfNK5tzIeHDBka4cCImSW2SbzYbS0lL09vZmrZKyz1cDtjKRC3sUW/CSghTpsmRbV1eHdevWIRaLYXh4WNF2c5Guy+WCxWKhJLV69eqCtymHK0nYOp2O9gTJIl53dze1RwwGg5icnITVas1yKBO7NVdToepOnoTh5z8HF4shtWoVkrffDlwikmINRyiFUE9LQC5KXq83awya1dISJQUBv2wZ+GXLst6nWL+zGp2u3++nJj9/+MMf8Mtf/hJvvPEGotEo/H4/vvjFL+LcuXPYuHEjAODOO+/EF77wBQCXR4BbW1uRTCbh8/lQV1cnORoMQPTxhoYGeL1ecBxn4Hk+CaAVwDi7n1cV6er1euoDW1VVldMHNl9FQiqVyhn2aDAYEAqFVG2XgB08YKVlADL0x7kgRZBk+s1sNtPInQ8++EDRNq90e6EYYAlTLGpceGvucrky4oXILTnRhMuRLzc2BsN//zf4pibwZjN0p0/DYDYjeeedWftSCArdBpvAQJI9gMsLVeR7GB4epusmwkXMYlk5slBj68hWuk888QSeeOIJAMD777+P733ve3j99dexePFiXLhwAT09PXj77bfR29sLAHQ0eNOmTXj11Vfx2c9+FhzHYevWrbjrrrtw//33Y3x8HIODg9iwYQN4nsfg4CBsNhtaWlqwf/9+vPzyy+A4Dp/5zGfw6quv3g5gPwQjwMACJF2xg4vVv5aVlSmOMFdLuhzH4ezZswgEAmjLEfaoRpFAeq9CshVLB85X6QBclN9YLBYYjUZRXwel2xQSJ0nIICvMUiL/hTIGLHVrTiRtwWAS1rp8AAAgAElEQVQQgUAAkUgkK9uMEBD53Tin8+KLLx2P/OLF0J09m7HN+bLIJ9Y/lUqzYG0iJyYmEAwG6R1CWVkZEokEAoFAwR7GahbkEomE7BqHwWDAD3/4Q9x2223Q6XSora3Fj370IwDAvffei7vvvhtdXV2oq6vD/v37AQCrVq3CHXfcgb6+PhgMBjz//PN0f5577jncdNNNSKVS2LFjB1atWgUAePLJJ/Hqq6/ez3Hc4wA+ArAnYz/UfgnzCSTC3OFwoKmpiertlPqBEuewXCBhj4FAAIsWLcI111yTs7JQO64biURw6NAhSbIlUHN7TxbIvF4vLBYL9Hp9hmNZPmD7WZFIhHr8Llu2DOl0mmadEZE/e4uudIQ61/tfKbCStvr6evj9fvT392dI2oRSroaZGTQHAuCiUZjNZugCAfCChb9CP1OxLkJqFq2MRiNqa2uzPHvj8TgCgQCmpqaofSZrhsMu3im52BTipUuwefNmbN68GQBw6623Uj8GFiUlJdSDQYiHHnoIDz30UNbjW7ZswZYtW7Ie7+joAM/zG6T2Z8GRLsdxGRHm7Kiuy+VCMBhUvK1cLQBh2GM6naZTVbmghHRJhT48PIxkMomBgYGczkxqyJwk8JaXl6Onpydvv18WRA89OjoKr9eLzs5OrFq1ik4CSulrp6enEQgEEAgEcOLECUrExZYyKUGxiI5sQ8oUJx6PI7h0KcIXLkB/8iT86TRSBgNcf/InMF5K5yApysXal0JQaNVNhl5I35jcurOKErKQSdo17Miv2ASimp4u2Yf5jgVHujzP46OPPkJTUxONMCdQ2y6Qer5U2KPL5VK8/VzeC4RsGxsbcf311+PYsWOKrPCUVLp+vx8WiwXRaBR1dXX0tqdQxONx+P1++Hw+dHd3Y+XKlTkHSlgySqVS+Oijj9Db20slXWy/VDj6Op8TgJUQnclkQl1DA/DNb4IbHgYXjyO1aBHKTCZ6MQqFQjh16pSob6/S+PX5mATMEqWcooRt1wjvkMrLyxGPx5FIJKjdpBSil+4kFgIWHOlyHEct1oQolHRzhT2q8V8Q2xcxslXrOSrXFw0EArBYLEin07TV4vP5VG1fDIlEAna7HVNTUzQlo5BsNqkRYHbmfmxsDLFYLGvBZr6MAKuqLnU68O3t4AFwAMoAqh7w+/1YuXIlDAZDxpjr6Ogo9e3NtWB1pR3GhFATsiqXBk1Mps6fP0+PBbYqZj2MhQ5j8xkLjnQBaeIR6nRzgRCjz+eD1WpFOp2WDXtUQ+pC74WxsTGMjIygqakpL7IlEDvRCdmmUil0dXXRFdyZmRlV8i4hkbDDHkQSd+7cubz2W2rfCaQMUIS5Xj6fD/F4HOFwOKNFoUbgX+z2QjG2IzXmykrahAtWLPEUY1+uxECDGNjvwuFwYO3atQAy04+npqYoKf/ud7/DmTNnEAqFcPToUfT19aG8vDzLd4HneTz88MN45ZVXoNfrsXPnTnz7298Gzxcvep3Eu7/zzjuDEESvE1xVpKu20iV2g4RsczkUqVUOpFIpjI6OUrKV8l7IF8FgEBaLBYlEAl1dXVkXi3yjfch+OxwOOuxBTqK5lowJF2zcbjd1gmOnzsj8vXDQYbbSC+aqjyonaSMXo6mpKfh8Phw9ejTDpU1tztt8a1MIjxWp72LZsmV47bXX8Mtf/hIvvvgiTp8+jX/913+lrSwy9rt3716Mjo7i3Llz0Ol0NJCymNHrJN797bff7uYE0esEC5J0paDUF5bkj+n1epjNZqy7ZEeXC0rVDqSyDYVCiEajislW6YmcSqVw8uRJxGIxKnERQz5KB+KG1tzcjIGBgaxb2UKHIwoFcTQT6xGyC3esppREj5OquFAjdaD4la4asJK2hoYGBINBjIyMYOXKlbRHKjXgQL4DseNxvlS6BEouAhzHYfHixejq6sLAwAC+973vAbg4rPD4449n+C784Ac/wMsvv0y3SRZ9ixm9zsa7QxC9TrAgSTefg52Mu5L0XiKdUjoUAGQnAgvBWjguWrQI5eXl6O7uVrztXELwcDhMF8j6+vqyes5CKCXIdDqNeDyOw4cPY/HixbIGPfNlwEEMsiqCS1Xx6OgofD4f7Ruy2lo1VWExK91Ct0PIie2RslaRxJ0sFAplSNrYi1F5eTkSiUTRTGrmwuyGhdBL9zvf+U6W74LVasWBAwfw2muvobGxEc8++yy6u7uLGr3Oxrvzguh1ggVJumqgJOxRKaQW0oRkSypbcvuiBHLmNOFwGFarFeFwGJ2dnQgEAhmLUFLIRbqsNWQ6nca6detyfjdy8+jzFUJjHCJfW7RokWhVyBKxlBdDMc1yikW6UpBzJyMXo7GxMXg8HupXwlbFag1x1EyRyUEN6bKpEVK+C0TDf+zYMfziF7/Ajh078Pvf/16170Khx/+CJN1c1R0J6SNR6bnCHpVC2DNmyXbx4sWibQSlJ6dYv5gdPujs7KTStcHBQUW3XlKky3rl1tTUYN26dTh9+rSiA7wYOWfzARzHSVaFpFfKejEQm0RCRMWq9otB3vn2YoUXI7vdjtLSUpqeyxriEO2tEklbrmxApVDru9DV1QVA3Hfhy1/+MlpbW3HbbbcBuDgk8dWvfhVAcaPX2Xh3ThC9TrAgSVcOer2eptNWV1crCntUS4zsJJzc7TghKKXyGUK60WgUVqsVfr+fDh+w+6fU01ZIkKTqt1qtqKyszBiXVuO9KyScZDIJu92OVCqFysrKWdfYFkp4cr83Gy/EPp/NOJuenkYwGEQikcCZM2cyVBRzHTsOFFcyRvTCQkMcYZqFnKTtSts6ivku/PSnP8WuXbvw3nvvYceOHfjd736HnkuewMWMXmfj3SHiuwBcRaRLwh79fj/MZrNq/wUlV2aO4xAIBHDo0KGcvU/gMkkrOXD0ej0ikQhGRkbg8/nQ0dGBvr4+UXJQ0v8FMkmXOIqVlZWJ2jcqrWBZ0k2lUhmTgcRgXKixZW/XC8WVaGOwC3ck48zv99PennDhTk2ixXyYJCOQO1blJG2spC8UCiEcDsPtdsPn8xVkoK620s2lPtq1axe+9KUv4emnn0ZFRQVeeuklAMWNXt+1axfuuOMOfPe73x2EIHqdYEGSLnugCsMeGxsbsWzZMlX+C7lIl5VQJZNJ3HDDDYoOBqUSMzLE4PF40N3dnTM6SClBksigo0ePwmg0YtWqVZI9W6XKD6EUjqgceJ5HMpnMOLHICUl6hmQx59SpUws+fJJYMooRkVSihVjoZjFQ7EpXDcQ8GM6ePUtbYWJTh0olbYXErxOwvgs1NTX49a9/nfUcjite9DoT7y65gr4gSReQDns8f/58XgMSYiDkMjY2hubmZmzcuJEaXytBLtKNx+MYGhqC2+1GaWkpWltbM7wL8t0ucPHKPzg4iEgkgjVr1uQ0uVHSXuB5Hn6/Hy6XCy0tLRk9bLHvUOyEPHLkCDo6OujoJwmfZBewyJ9i3KJKfY7ZHI6QSrRgI8fJ5w6Hwzh37lzG3YDafmgxK91ibYeQqzD9mHwHYpI29u7AaDQqvgMFLpJuIVOSc4kFSbqxWAwffvihaNgj+bGUQox0xcg2n9VYKUKPx+Ow2WxwuVzUInJoaEhxr1Ku0g0GgxgcHEQqlUJ3dzdOnz6tyFUsVyIwifIxGAxYtmwZzYZSC9ZEm73AsJNXTqcTwWCQulOxRDxf5GpqiZtduGM/9+HDh9Hc3EwXrciUFTtxluv2fL4NNUi1vtipQzFJG+mXk1j6VCpFW1LkO5DaP410Zxlms1mSCAvxX2DJlnUvyxfCipQkTczMzGTFvSvNSRPbLnBxus5qtSIajebljSBneD44OIjy8nJce+21cLvdqu4klEJq2og1RCE9Q5JvxlaHan6n+TQGzHFclpyLnTiTMgViF+6UJmDnwpUibzFJG8/zOH/+PEpLS5FIJLJsItkWTWlpKWKxWM4F8/mCBUm6HMdJHmRGo5FmPimBwWCglafQKrJQEHJkDWOWL1+OgYGBrIM7X3NyIisLhUJ0Oi0fMhCqEnw+HwYHB2EwGDJ6wXOp0xWrisltKdHYskQsrIpns1c8m4kPwokzAtYUiFUQJJNJlJeXI51Oq4qiF2I+TaSR44woBQjYC3EwGMQf/vAHPPbYY/D7/dixYwdWr16Nz372s1i9enWG7wLBt771Lfz4xz+mFrCxWAz33HMPjh8/jvr6ehw4cABtbW0ALqog9uzZA71ej2effRY33XQTAOCtt97Cfffdh1Qqha997WtEqQCbzYZt27aRZJYDAO7meT4u/GwLlnSloKbSTSaTNBOqra1NMdmqOeFIxIcwQ00IvV6vuILU6XSIxWI4c+YMjSNvbGwsiAQIkZP2RDqdFvXgVbrgNpvQ6XQ5q2JiEyjsFRdDQUHeb67Nx6VMgQYHB2E0GpFKpTIW7shFSGnqbzFTLIpxQRKbbGMvxADQ3t6OW265BTfccAO+9a1v4ZNPPsHExATee++9DN8FADh27Bi8Xm/G9vbs2YPa2lpYLBbs378fDz74IA4cOIAzZ85g//79OH36NMbHx/H5z38eFy5cAAB84xvfwNtvv43W1lZcf/312Lp1K/r6+vDggw/iH/7hH7Bt2zZwHOcBcC+Y6HWCBUm6gLzTWC7STSaTGB0dxfj4OCoqKrBs2TK0t7crel8lci3izuVwOFBfXy9Ltux2o9FozvePx+Nwu91wOp1YsWJFTqWDUqRSKdjtdgCQ9XNQqueda0j1itl+IXHpikaj9OKc79RVMVCsJGCO41BVVZW1cMem/k5OToqmebA+DHMdkpkLSifbSExPf38/+vv74XA48NRTT2X4LqRSKTzwwAN4+eWX8dprr9HXHjx4EI8++igA4Pbbb8c3v/lN8DyPgwcPYtu2bTCbzWhvb0dXVxeOHDkC4OL5QdY0tm3bhoMHD6K3txfvvfceXn75ZbLpfQAexdVEulIwGAySFSNJnHA6nWhpacHAwABcLpcqz1lysoodDOz2W1tb0dnZqbh6kBsDBi572k5PT6O8vBxLly7F4sWLFe+3FGKxGKxWK6amptDc3Iyenh5ZIpjP3gtiEOsXklXzysrKDEJiV9HJH6mTvliV7mz54LIXISlTIHbRymQyIRqNYmJi4oqkeYhBqWTM5/Nl3JGJ+S4899xz2Lp1K/VFIGD9Fcix4nK5MDY2hoGBAfo81l9B6Mdw+PBhuFwu1NTUsPvrANAitr8LlnTV2DuKkS25bck3EZgFOyTAbn9iYkJxIrDUQprQ03ZgYAAOh6Mgn1zgIonbbDbMzMygvb0dpaWlipIKFhrpioHjOBiNRjQ2NmYQElsVC0eAhd6982kxTk1bQMwUiGSb/fGPf0QsFpPU1SqZNCzmsaH0osROo4n5LoyPj+OVV17JGOmV21+5dQux807mnBB9cMGSrhRYI3OWsIRkS1BMtYNw+2oTgdnnEiInV2K2RaFG6cD65AKZ3wm7qDcyMqKIyMVUDqQ1EQqF6LBAvos5Sj9PIZAiO6lVdJLvxVbF5NaXHYO9UvraYmWbGQwGLF++PGO7UmkeLBGz6pErkW7MDkaI+S6sWrUKZrOZejOEw2F0dXXBYrFQ34XW1lYaaFBXVyfpxwBA9PGGhgZ4vV62Om8FMC62vwuWdKWutoSQrFYrJiYmsky4hcin0k0kErRnK6fjzYd02aGPJUuWZOXAkc+oZtGNkOTo6Cg9wITfST5jwOy+Njc3o6mpCeFwOGsKi5yclZWVC65KlvLuHR8fRzAYBMdxGfpatiouLy9HWVmZ5LE6XwIlpSCX5sFqqol6hMi3SAtD7rMXE6zDmJjvAqteAC5qfi0WC4DLXgmbNm3Cq6++is9+9rPgOA5bt27FXXfdhfvvv58uhm/YsAE8z2NwcBA2mw0tLS3Yv38/Xn75ZXAch8985jN49dVXsW3bNkDCdwFYwKQrBlLFhUIhGAwGWbIlUEO66XSaOvW3trYq9l5QAp1Oh2AwiA8//DCnr4PaePexsTFqziNmTE6ep5R00+k0nE4nbDYbGhsbsXHjRnAch0QikbGYwwYPkkopHA7jo48+ylIUXOn+oVoQMm5pudy2ExrjiCVasItX86XSJdtQSpBSmupoNAq32w2XywWbzVZQmoeai3MhgxH33nsv7r77brp4vH//fgDAqlWrcMcdd6Cvrw8GgwHPP/885ZLnnnsON910E1KpFHbs2EGDX5988kls27YNDz/8MADUA9gj9p5XBekmEgmMjIxgYmICS5cuRXl5ecZtkhyUkC6bcWYymdDR0ZHRTJdCLtNz4OLB5XQ6MTQ0hHQ6jU2bNuW8TVVSlfI8j8nJSfj9fpSXl+fMZVNa6fr9fkxOTtL4EpLAKvZaMVNtkmFFiGl0dJT2vYXENJ+jdsS2IWaMA0gvXpFF38nJSbp4lc9+FYt0C21RlJaWorq6Gj6fD319fQAuf/ZQKCRqCkT+CKfN1JrdCKWNQKbvAgui0QWAkpISvPLKK6Lbfeihh/DQQw9lPb5lyxZs2bIl6/GOjg6qcICI0Q3BgiVdUlkNDw9jcnIyo+85Njam+CCS052y6b0k48zpdCreR7n0YEKKQ0NDqKurQ39/P06dOqWoLyhX6ZKEDIvFgqqqKtTU1KC9vT0ngeXS3/p8Ply4cAEcx6G2tpaeVPnAZDLBbDZnVcViUTtkHJYdA54PLQo1xC21eOVyuTAyMoJIJILp6WnqWysl6ZJCMUh3tgYjlKZ5hMPhjHYUK2PL9T37fD4sW7as4H2fKyxY0p2ZmcHp06ezFpmAy9VrvpUSuX0eHh5GQ0NDRpWoNCcNECdH4mlrsVhQXV2N/v5+lJSUIJ1O5zWRxsLj8WBwcBAlJSXUvvHkyZOq2gZChEIhXLhwAel0GitWrADHcbDZbIr2U+p9xE4kMccu4Tgs62PLmsTISbtmC4XKvTiOg8lkQllZGZ2AAqSrYuHFp7S0lL7/fCJdpVE9YqZAbDvK4/EgHA7j6NGjdMCFvRixv7fX68WaNWsK3ve5woIl3draWsmhg3xJl9zq2+121NfXU+cyFoUoElhP27Vr12Z42qqZ9BJuNxAI0Cq0t7c3g7iUtg2Ez4tGo7BYLAiFQuju7qYnB1kgyxdq1Adi47CBQIBaSgqlXUrHgIuhj50tna5UVSy8+LBVcSwWg9frRWVlZd6JDcX0Xcj3Asi2o8xmM3Q6HXp6emSlfAcOHIDD4cCaNWtoS0IYvf6lL30Jx44dg9FoxIYNG/DCCy/AaDTOSvS63W5HW1sb3nnnnVph9DrBgiVdg8EgefKysjEl4Hke4+PjsNvtqKury+hVir2v0oU3QqQejwcWiwUmkwnXXHNNwaOohCBDoRAsFgvi8Ti6u7tFTZzVkm4ikcDQ0BBcLpdoakWhkq1iSL50Op2otEtojkNsA0maRTHHgIsBpYtXUl4MJM3B4/FktWTYqlDJoMN88l0AMnu6UlK+SCSCtWvX4sSJE/if//kfPPPMM1i+fDluuOGGjBHgL33pS/jpT38KALjrrrvw0ksvYefOnbMSvb5r1y7s3r0b77zzTlb0OsGCJV05KCVG0lclB64c2RKoqXR9Ph/C4TDsdjtNHy4GiGfEJ598gu7ubtmQSjWJwD6fD0eOHMHy5cslJ9Pmg/eCGOQsI4VG6rFYDCaTCfF4nBKyksEQFsXKNitkG+SCYjQaaeo0GXQQcyiTW6icb/aQudoU5Pe+44478Morr+DFF1/E0qVLMTw8jB07dmSMALOLXhs2bKD5ZrMVvb59+3Z897vf/UtcbaQrd7Dm8l9ggxmrq6tRU1ODjo6OnIQLKCP0QCAAi8WCdDpNo4OKAWJ67nK5YDQaqVRLDrlIlygzbDYbjEZjTpldod4Lcz3RJmakTgZBSkpKMty62BX1yspK2QpxPo0BsyCDDmazOeNiLLVQaTKZ6AIl0YkXsk/FCqVU06bw+/309/3Hf/zHrBFggkQigZ/85Cd45plnAGDWotcv/S2ZRrBgSVcOUv4LrBl3dXU1zVH7+OOPFbcM5EiXvd3v6upCbW0tPvjgg4I+C3A5+HFychLt7e3o7OzEH//4R0UnvVwiMFFPNDY2YvXq1RgdHc1ZpciRptJb5WJMlBUCQkxC7wq2QhweHhatEEllOZ/GgJVAaqGSfGYysn78+HEA+cv3ilnpKo0zCofDKC0tlYxeJ/j7v/97/Nmf/Rn+9E//FID6EeBiWZouWNLNZe/Iki6bgltRUYFrr702w/BYTZ9WrL0QDodhtVrpeKHwdl/pyUWqSFJpsJ4OrEqDVCVK91dIui6XC4ODg6iqqqItlWAwqDgjTfi8eDwOi8UCr9eL8vLyjB6qsFoplGRmk6SkVtTZCtFut9NUA1Ih5quxvRIjsyzYqjgej6OqqgpLly7NWRXL9Ypno6crB3Is6nQ6yej1n/70p3jssccwPT2NF154gb52tqLXL8lKs6LXCRYs6QLy9o7hcJhqIa1WK8rLy0VTcAH1pEueG41GMTQ0BJ/Ph66uLhrGJ3y+0lslliDJMIaYp4Oak5utdInW1mQyZX0XasaAyfOI58LExATa2tqwfPlyRCIRBAKBLFUBIWJyC3sloabClKoQicE70diS6Sthzpvc734lPHmlwJJlrsDNYDCIkZEROtRSVlZG/TaIN0Mx90cJOI6TjF5/6aWX8Jvf/AbvvvtuxkVitqLX9+3bB0iMAAMLnHSlYDAYEAwGceTIEZSWlmL16tWiZMs+X40iIZ1O49y5c3C73ejo6JD1tCUSFiUHok6nw/j4OBwOBxobG7Py3/KBTqdDOBzGiRMnkEwmsWLFCtHpHbWkS9KAW1pa6MJCIpEQlTuxo8ChUAgnTpyA2WzOqIjng5WgUnAcB71ej+rq6oy7mlQqlWGMk0vKVoxKt5j+DbmOUak7ATbNwuv1IhgMZumK1Y56K610leiCv/71r2P58uX0OP2rv/orPPLII7MSvb5nzx4yqLFban+uOtJ1u904f/484vE41q9fr0gipJR0iR1iOBxGVVUVHRaQA6mM5RbpSK/Z6/XCbDYrUlEoQTQapdKpa665JqfKIVfVRPYzGAwiEolkXBTk+rysqoC0YPR6PZV3kRV2ojuVa0/MF4iRHSFiJVI28rnMZjOqqqrydmW70qoDoSlOKBTCypUrwXFcxsQZWxULe8Vi55BS0lUyAix1bnPcrESvE7il9nl+HtEKwbYXiBaWyGdGRkYUazJzTZkJ7RDLy8tpLycXcknMyMBEeXk56uvr0dbWVjDhslrb2tpaNDY2yhIukFuV4PF4cOHCBeqc1dPTU9A+ilVNZBpLrD1BFrGUVuRymMtFMDkp29DQEBKJBJWy8TyfRUq5joVimuYUU6drMBhyVsViqhFy16PGwFxMnz6fsaBJF7g4AmixWGAwGKgWNplMYmhoSPE2DAaDqNm41ELWyMiI4pNOinTFgh9Pnz6teIFMDOz+krThqakpRUbqUmRGMtN4nqf7WYgiQ069IDWNxbYnfD4fgsEgdSojVfFCak8AF9cdiEEMUVHIkZJUK6aYle5sV8xSVpFiPgzBYBDnzp3L+NxiVTHrpbtQsKBJ12KxwOfzYcWKFRlNfyXuXiyE7QXSsySrk1Lm5EoXx1gilQt+VDN4AVyutlgXNOH+qplIY8kwGo3CarUiGAxmjAEXCrWSMWGlGAqFYLfb0d3dnSXvUtqemC8aWyFhypFSIBDIGHYg34vZbEYymaTOXfmiWKoDQL3CROyu58iRI2hvb0cgEIDX64XD4aCLdGTRLhwOY3JyUiPduURnZ2dRtHOEdFnykvO0zYd0w+EwLBYLotEouru7Rf0/c+WksSBkOj09jaGhITQ0NIguvKk1J08mk7DZbJienkZHRwf6+vqKKtMq1nCEXHtCaiGLkHEx3r9Y21Dy3ZpMJtTX12ct2oXDYczMzCAej+OTTz7JMMYhn1Vp4OaVlq8JQS6gwhYhO2H48ssv4+DBg/T3Xrt2LXbu3InKysoM7wU2Gr2/vx8/+clPYDKZZi1+vb+/Hz/72c9MYvHrwAInXbUVrdx2AoEAPvzwQ2rhKFc1EJJW2nsdGRlBMpmUlJURqInhSaVSOHLkCKqqqqhTmdQ2lY4Bx+NxHD58GEuXLqUxPgsJStoTY2NjCAQCMBqN8Pl8iqbPxHClhyPICDAxw1m5cmWGMQ7piwsDN0mVKCwYilnpzibYCcNHHnkEbW1tiEQi+OIXv4iPP/4YRqMRzzzzTIb3AhuN/vWvfx179uzBzp07Zy1+/etf/zogEb8OLHDSzYVcBzWZyrJarUgkEviTP/kTRZM3SsieKB3Gx8fR0NCQZRwjtd1cpOv3+3HhwgXE43GsXbs2521/LtLleR4TExOw2WzgeT5nGkahmOsxYLGFLJvNhpKSEjoUImxPsJXibKYBF9t8XMoYRyyGXihlSyQSRZGvFQNqPCm8Xi9aWlrQ29uL3t5eOBwO/PrXv6beCzzPZ0Sjb9++HY8++ih27tw5a/Hr27dvxwsvvPCX+LSRrlwLQDgO3N/fjxMnTigedZQzJxcqHbq7uxGPxwtadAMuSnEGBweRTCbR3d2NoaEhRWOScqQrnEw7fvx43oRLqqxcabHzwaUMgOjqOtuemJqakmxPmM3mK17pEighbjmXLlIVh0IhfPTRR1lKAjVStmK1KNSmRpC4HCA7fl0Yjc76JcxW/PolfwbR+HVggZNuLtObRCKR8eMJJ9TYcWA1J7KYrpddfCMDAzqdjt7iKYFer8+SrsViMVgsFgQCgQxHsXx9coHL/rt6vR6rV68u2O7Q6/Xi/PnztCdMFjvElAVz5TWQD3K1J/x+P03Ejccvtutqa2vzak8AVzZmR3gH4HK5sH79eiSTySxXNqVStrkeAQYuki65mIh5L8it+aj1WChG/DqwwElXDkJiZFMVCvW0ZStSnucxNjaG4eFh0eyuBLIAACAASURBVMU3tabn5Icl7YmZmRnRBS2l22VJNxKJYHBwELFYDD09PQWv+obDYVy4cAGpVAp9fX1U0kMkQMLBh4qKCqrDna2IdiVQU2FK6Ww//vhj1NbW0sgoYo7DElNlZeWsjwEXcwGM4zhRVzYpKZvQi0Gn0825Jy+r0xXzXvjOd76TEY3O+iXMVvz6JX8G0fh1YIGTrpJKl+hh9Xp9VqpCviCGOhMTExgaGkJ9fb1k8KNcK0IIEq1OesHLli2TXNBSU+kmk0mcP38ebrc752KeEqTTaZw9exY+n49W38SxCpBWFgSDQVitVrhcLjidzowKivW1XQjgOA41NTUZxklSUTts77SyspK2YOZDoKQSSEnZ2DQLl8uFQCCARCKBs2fPqsp4E0JNpcsmAYt5L/z3f/83/vqv/5pGo+/btw+33HILgNmLX/9Uei8AF0+A8+fPw2QyZelhpaCk8uB5nuoDGxsbZZUDgHKFRTqdhtvtxtjYGDo6OnL62iqpdFOpFBwOB7xeL5YsWSJpTK4UZPgiHA6jvb2djnsqARmRraysRENDA2prazMqKNbNqqSkJIOIpWJ3riSkxoDF2hPRaBSBQCBrDDgej2NmZgYA8h7uuJJSL6Fvr9frpb6ywgsP+U3ZjDep3zRf0pUCG41+3XXX4d577wUwe/Hrl/yzRePXgauQdIPBICwWC/x+P5qbm6mjfi4oMaYhLQoAaGpqQm9vb87t5iJHYqhutVpRWVmJxsZGtLe359yuXKXLxg8tWrQIlZWVaGmR7OtnvVZ4MpDsOJvNhubmZlRUVKC5ublgImQrKDKVRUhKzKugsrISJpMJiUSiILIplkmM0jFgEssuHAP++OOP6YWMTA2qaU8A80tfS84fqQsPawZEpGzCRTvSFlRKusFgMKsCBzK9FwTR6BSzGL8OAJK+AguadNmDXuhpG4lEVE13kZaB2I/t9/sxODgInU6H3t5exONxTE9PK9quHOm63W4MDg6ioqIC/f39SCaTsFqtirYrRrps0nBtbS2uv/56GAwGxftKFgXY75UoHKqrq2kLZXp6WvRkVzK/n0t9wJJUY2MjfTyRSCAQCNCU2OPHj9M+MVsVz1WfuFDiNhqNMBqNaGlpoXdKZOAhEAhkVYnslB1b+StxB1PyWYoBqV6s1G9KpGzk4hoKhei5UlJSQtsyUooY1kt3IWFBky5weVw1EAigs7OT9isnJiYUR6UD4ooENgmCXXjyer15JwIDl7W2BoMhY1EvEokonkgTbpd45ZrN5iyTdqUnFSFynU6HYDCI8+fPQ6/XZ3nvComT53mk02nwPJ9hHq/T6cBxXMZJka/ky2g0oq6uDqWlpQiHw1i9enWGlaLT6UQwGEQ6nab+rrPZJ56NiTQy8CD07pVqT1RWViIajaKqqqqgivdKOZVJSdkGBwfBcRwdZiHjv+wFtry8nH538631lAsLnnQtFgsaGxuzVvfVJgKzpMvGj4slQeSbNBEOhzE4OJhF4mLPzQVCkERBIOeVqxQ6nQ6RSATDw8MIhULo6ekR7ZcR4iRkSy4UJMaGEDD5b1bpwb6m0BNdzEoxnU5TI3VhQi4hYTXHhRTmSnkg154IBoOw2+1wu92YmroYVCD0nlCyiDWfkoDJRVq4EMuO/46OjuL//u//8MILLyAWi+Gpp55Cb28v/uVf/gXJZBLJZBK33347HnvsMbz77rt44IEHkE6nUVFRgb1796Krq2tWR4DJmLEUFjzprlmzRrQ6VEOM5PnRaBTnzp2Dx+NBZ2cnGhsbRU8sNeRIVqnPnDkDv98vm96rZgyY9FnHxsZyJgIrQTKZRCQSwcmTJ9HV1SU7QUcUEcQkh+O4rIqNgPw2yWQSY2NjcLlcaGxsRCqVop+VvF5YFecDnU5HZ/bZPnEsFqOmMR6PB263O+O2Xa3W9koPRxBpl8vlogRFYnbUtCeA4g41yIUFqNmOsGUilLL19fXhL//yL/E3f/M3aG5uxvvvv49HHnkEt9xyCxKJBG644QbcfPPNdPKst7cX3//+9/H4449j7969szoCTMaMpbDgSVcKuRKBWZBIc6fTie7u7pzm5GpMz+12O+0zyyVMAMrInIRUOhwO1NbWYs2aNQWd/DzPw+FwYGRkBDqdDtddd52khpncUhsMBpw9exbV1dWoqqqiC1xi4DiO5tORNAyDwUCrYfZvALNCxOx4LCF8Er1CiFjMqUzKp4B8F/NBY8v20aWiheQWJkkffCHFrxOEw2EsXrwYX/7yl/HlL3+ZPp5IJJBIJOjxQzwYfD4f1dvO5ggwGTOWwoInXbmYnFy3kaz/LFlBV2JOnksGxm532bJlGVWXHORO4nQ6DYfDQcXcK1euRCAQyPvEJ4tug4ODqK+vx4YNG3D69GnZ55O2QG9vL5V6zczMwGazIZFI0Cw0QsQksNJkMuHaa6/NkNaRk1xYFbPvI0bE5DmFgBAm6RNLGalPTEwgEAhk9IlJVXylK112f+UIU25hkhDx1NQU/H4/jh49mld7gt2XYrUp8jEwT6VSWLduHSwWC77xjW9g48aNeOmll7BlyxaUlpaiqqoKhw4dAjC7I8Dk+VJY8KQrBblqVMx/dnJyUvHCm9RBzk6nNTc3U63t6Oho3icYKylrbGykE28zMzN5Jyiwi27XXXcdXXQTi+wR9m1J5UkqqubmZvo8MgXkcrlw9uxZJJNJehJ7vV56Cy/XtgCkiTgWi8Fut9P0WrIdsmDHbiNfSGltiarA4/FgZGQEwWAQn3zyCSXhysrKvPTExaiW89kGe7teVVWFqakpdHV1iQ53KNVNz/UYsNDAXK/X48SJE/B6vbj11ltx6tQpPP3003jjjTewceNGPPXUU7j//vvx0ksvzeoIcK7f46olXSkCcTqdsNvtWcGPUukRSsASI6ka2QpBTIqlBGxEjnAIQ433LgE7Biy26MYeXGJkm8vIxmQyIRwOw+v1YuXKlWhsbEQ8Hoff76dWg+FwmGo52Vt4KbIkC4ZjY2OYmJhAe3s7VaikUqmMxTkA9DGdTke3WYz2hNDb9ciRI+jp6cmoisltO0tQcp+tWAqIQj8fIUu5i6lYe0L4OYtZ6Sr5TFJRPTU1Ndi8eTPefPNNnDx5Ehs3bgQA3HnnnfjCF74AYHZHgHPdLS940lVCZKyrWE1NDdavX5/Vg1S78EZAtLZixCjctlLpUjAYpM17EpEjhJpFNwB0gVBuDJhskyWzXGQLXLaHtNvtWLJkCTZs2EBPGrPZjMbGRlHNrd/vh91uRygUooMShIzJLD8xaV+0aBGuv/76jJOaPTEJ6ZILBc/z9HOw0iJyYSm0wmRv21kbRfa2nQQysn3iYgduFiPbTK63nKs9wQZPEv+J6urqvEeA2ffNBdbsZnp6GkajETU1NYhEInjnnXfw4IMP0ru6np4evP3223SgaTZHgMmYsRQWPOnmAhv8KNSvslDjkQBcvBofP34cOp1OkhgJlKodotEoIpEITp8+LSnXIlDivZBOp+m0U0tLi+wCISGnYDCIsrIyxYsrXq8Xg4ODqKysxLp16xRdWKR6qUSL6nA44PP5EI1GYTKZ0NzcjOrqalmCkapqhQt2oVAIPp8PTU1NGYstxViwI59NaBgjFbgZjUZht9tpdZmPnrgY2Wb5VKhin/P48eNobW1FJBLJqz2hFl6vl14InE4ntm/fjlQqhXQ6jTvuuAN/8Rd/gR/+8Ie47bbboNPpUFtbix/96EcAZncEmIwZS2HBk67Uj+fz+RAOhzEyMqLIVUzJwhtwWWsbi8XQ19enSKqVi3RZRzGTyYT169fnPAnktknM2YeGhtDU1ITq6mrZsV1CSk1NTbTXzXEcJYOqqqqsaS/yPfA8j76+voLtIfV6PWpqalBWVoZAIACTyYS+vj7o9Xr4/X7avmH7xGTf5MiKEBLP8xgeHobb7UZPTw9qampkF+yKScRSfeLDhw+jpKSE9omJnlhN3M58Ms1Jp9Oorq5GTU2NaHuCDLGw7Ql22IGVICqB3+9HV1cXgIvS0Y8++ijrObfeeituvfXWrMdneQRYFguedIVggx8rKyvR19enKFYnV3shFovBarXSHzqRSMhWtyykCJJUomNjY9RR7Pjx44puGaUqXdIHrqiowLp162A2m+k2hRD2bWtqamjlQqa9iIdsIBCgrmDxeBzxeBzd3d0Zt5yK4XaD83rBL1kCXGrHkO+C9G1ZeZ1QAhUOh+H3++F2uzE8PIx4PI6SkpKMPjGpptjWB9FXku1KLdiJSdjId16s6SeO46DX6zNULURPLIzbkesTF6NVolQtoATCfVHTngCA0tJSJBIJeDyenO0JJWY38xFXDemKBT+ePHmSVg+5IEW6bFAjSwYOh0NxTpqQdFkDGaEHL3lurl6YcCEtFArhwoUL4Hk+q90hJGgli2TCaS8iWRsZGUFtbS3Ky8ths9moITwrFZPbd/2ePTD++78DOh34qirE9u7FVH29ZN9WCHZRS1hNkfbE2NgYotEodDodYrEYysvL0dfXh6qqKtXKCQBZC3axWAzJZBLxeLygBTvhQhqrJ87VJwYumuOQhcpC+sSpVEpx3l+xIOXb6/V6EQqFqBRRrj0htZA237HgSTeVStFpL9Z7AVC3OCZUO7BVqFhQo5qpNHY/xAxkhPuh1Jw8lUpRLazf70dPT49oZhohXeGIrtJFMna4YWBgIOPkJqPIfr+fLlaSySRCwqQFwH3yyUXCNZsBgwFwu5G8+25M79uH6667Lu8TXzgqS76TUCiEjo6ODKNx1t+gqqoqp3KC/TudTsNut2Nqago9PT10yIP8XrPVnpDrE7vd7ow+sdCfWMl3Ol+cynQ6HW2vEHdAsfZEKBTCrl27oNPp8M477yAej+Pb3/424vF4xggwz/N4+OGH8corr0Cv12Pnzp349re/DZ7ncd999+GNN95AWVkZ9u7di/7+fgDAvn378PjjjwMAHn74YWzfvh3AxX71V77yFUQiEWzZsgXPPPMMOI6D2+3GnXfeCbvdjra2NvzsZz/LWX0veNLV6XRoaGgQnfZS678AZNoiLl68WNLXVq3/QjAYxMjICIxGY5aBjPC5OUl3ehpwuZAeHcXRZBLtHR2y025CVYJSMggEAhgcHBQdbmC3LTS4FupaSQug5dAhdCSTgMmEVDSKtF6P8pkZrOrqukjEBYJEJjmdzqwWBQFRTgQCAQwPDyMYDFK3MrY9IfzNiXvb4sWLM9QZ7HtLtSeIrIsl4kIHI0if2GQyYcWKFQAuf+/ChIdcfeJiSL2K5VQm1OhKtSd+/vOf4+6770Y6ncaLL76IgYEB/Od//mfGCPDZs2cxOjqKc+fOQafTUX+KN998E4ODgxgcHMThw4exc+dOHD58GG63G4899hiOHTsGjuOwbt06bN26FbW1tdi5cyd9ny1btuCtt97CzTffjN27d+Nzn/scdu3ahd27d2P37t148sknZT/jgiddvV6fYQTCQg0xEoesQ4cOoa6uTjIJgn1fJRVpJBLBxMQEUqkU1qxZkzMiJ+d2z52D/+BBuNxuNCUS6LztNnAyukCe52EwGGC1WqkQXoxUWJBctkgkotgAngXbAmD9D+I8D/4//xOJaBScwQBdLIZIVRWsIyN0v3ItHEmBqFQaGxtlWxRSygly+z4+Pk7dysrLy+lCF3Fvk4u6B5RP2JHjMpVKFa0iZr/3RYsWAbj0vcfj9ELDetkSEo5GowW/dzH9G5RcABoaGhAOh/HAAw9kkDQ7AvyDH/wAL7/8Mt0vwhMHDx7EPffcA47jMDAwQC0A3n//fdx444302Ljxxhvx1ltvYfPmzfD7/di0aRMA4J577sHrr7+Om2++GQcPHqR5bNu3b8fmzZuvftIFpCdDlJIuWXxKJpPYsGGDpKxMzbbj8TiGhobg8XhQW1uL0tJSRZlkckMPMxMTCPzXf6FkyRIsW7kSlvPnoT91CuneXkDQVmBP9o6ODkoqY2NjCAaDAJBV3QHA8PAwpqam0NHRIWn4oxa0RaHToe/OO9H0858DOh1QXY3gCy+gpqaGCu8jkQiMRmNGa0Juio24rOl0Oqxdu1ZRQrIQYm5liUQCFosFExMTqKqqQjwex0cffZRhG1lVVSV7+y5GxKlUimqPly5dKurEptfrizZhx3EcTXgQ6xOT44J8h6wyRE2fuFiLcWq2wy44i40AW61WHDhwAK+99hoaGxvx7LPPoru7O2MEGLg8uiv3+KWE34zHAdCkDABobm6m1bQcrgrSlYLRaJRN4mUPtlWrVuHMmTOKxdxSpJtKpTA8PAyn04m2tjasWLGCTmIpgVilS/bTkExiVUsLTJcs6KDTARwHMC0UsUUyg8GAmpqajEWHdDpNq5/x8XG43W7EYjGaCmE0GotyIpFBD9qiGBhA7O/+DpzLhXRnJww1NWgEMm4dSWVG+sRsL5aQsdlsxvDwMDweD104LQbYQRqibWZlZ5FIBH6/H16vF6OjozR2nr1ISOlQw+Ewzp8/D6PRSJUlgPSCHftYMSfsgMw+sc/nQ0dHB8xmM20LsX1i4qnBZrwJobRCzQWlI8DCIktsBDgWi6GkpATHjh3DL37xC+zYsQO///3vVY8A5zPqK4ergnTVVrpE6RCLxdDd3U3JSE1UiF6vz+gXs74LxM+BHIRKc9LIcwnpEl/fcDh8UVtaXQ1uZgaYmAAaGmAIBMA3NwM1NaoXyXQ6HR04GB8fR2NjI9ra2uhq+MTEBJXelZeXZ5CKku8nHo/DarUiGAxmeQfzbW3gyYVDBCaTCfX19RkaaHaK7ezZswgEAjCbzairq8uYaCvkxA+FQjh//jzMZrPooAfHXU4GFrON9Pv9GdU6u1g3NTUFl8slOvQiN9jBtiiEC3bk/Qu9tf//2/vy8CartP07bbqv6b6kdEubtlCWtiCMOh+CoOIMcrlgZxxhkHFBBdyQbVRQfyw66IdQRxQF5BtFHRX8RkAdZxDnoxQoiyzd09p9S7O2zX5+f5RzfJO+SZM2pVByX1cvJU3TkzR53uc8517oTNeeiTr1J1apVGhsbGRJwNxC7M6i64xIhH7ebd/jVAJ8+PBhiMVi3HPPPQD6+LqLFi0CALtSX7FYzEYF9Pbp06dDLBbThF+r+wNAbGwsWlpaEB8fj5aWFrujTi5GRdG1B1t7R1oIlEol86Dl/tGoQMKZLapQKERvb69VZxQREdHPdwFw3ZzcYDCgqqoKHR0dSE9PR0xMDFsnmTEDOHYMgoYGmIKDQebMAfH1dfmQjCtuGDt2LBM3ULNvmqnG9WilAgV6Sk4J/1yaGD3Mam5udjm80hF8fHzg7e2Njo4OhIaGYtKkSfDy8rJSsXHHJtyueKBiQGmBCoUCUqnUpWh6W9tICtqtt7a2ory8HN7e3vD390drayu6u7uZ4MTR34rb3VLQIkwvyKGhoVaHpLYHds7A0UEa90LDNyfWarVob2+HVquF2WxmHPGBPDXsgaYnDwStVssuDvYkwPPmzcO//vUvPPTQQ/jhhx+QmZkJoE8CvH37dhQWFqKkpISJh2677TasWbMGCoUCAPDtt99i48aNzAb0+PHjuOGGG/Dhhx9i6dKl7LH27NmDVatWOSUBBkZ50aVFlHrQtre3OywErjISuru7cfLkSQQEBDiUGDtbdC0WC1QqFeRyOdLT0/nj1wMCQGbOBAEgP3YMppAQkMtrdoYCRtVvSqWSSSAdgWuCQq/uVE5LzbJlMhmMRiO8vb3R29uLyMhITJo0aVDzVT7Qi5BOp0N2drYVU4JvbEJFHS0tLaisrOzXrdOLBFc4kZSUBIlE4jbxA01iFggEmDZtGvz9/WEymdhFoqGhod9Fgn452kkIBAI0NTWhsbGRXZBdEXbwFUFXO2W+ObFcLkdXVxeioqL6CR64vhMDPT9XbB3pAa89CfBNN92EBx54AG+++SaCg4Oxc+dOAH3KsoMHD0IikSAwMBC7du0CAEREROCFF17A5MmTAQAvvvgi+3z89a9/ZZSxO+64A3fccQcAYNWqVZg/fz7ef/99jBkzxq7Kzer1G4Dq4R4eyDDDZDLxFjUaYOjl5YWkpCSIxWKHb67KykqIRKIBVVbd3d24ePEienp6kJ+fb7Ud44NWq0VNTQ0mTJjA+33aLVdXVzNlFZU32ru/xWJBZWUl5HI5+xn6xTdzo+KGpqYmJCcnuyXNl/v8aJ5aREQEs3g0Go3s4ImuzRV/AS4FbCgHe1wuMR0DGAwG5gGckpICkUjkliw1i8WCn3/+GW1tbU4lenAvErQgU/9e7kXC19cXGo0G5eXlCA8PR1pamsMOno+Xzf2scw/sTp06hSlTpgzpebe3t6OnpwcpNmMj7k6JHtrxzYl9fX0hEAhQVlYGsVg84GfqwoUL2LZtGzMPvwph9406KjtdyrWtra2F2WzGtGnTnLp6DmR6w5UCi8ViyOXyAd8cgONOV6VSoaKiAgEBAcjLy4NarWZO93zPi3tIlpGRgYyMDFbkuIc7XFmsyWRCfX09s7N0V2IuZWhoNBrezDfuwROXr2trds7XEVNebExMzIAqtYHA5RIbjUYrOTchxGpWabs2e0m0fOjq6kJlZSViY2N5ubz21mbry0AvEhqNBp2dnZDJZKxrjI2NRXh4OIxGo0NZsiOFHXdWrFAoYDab2fkEtxt2pfu1N9O1l2Zhb07c29vLZvOO6INKpfKaVKMBo6TosnknZ75KI8hLS0udPoF3JAWm44m0y0IEnU7nFD2EPq5t0aUzVaPRiOzsbPampLMxLgY6JKPkce7Mja6voqKCdTXUStFRsXMG3K6ZMjT4Phz2Dp7oRUKlUlldJGiRa29vh4+Pj0NerKugF+L6+nokJydbrXmgtQ3ETtDpdEyCPWHCBKdmko5ALxJBQUHw9vZGV1cXJBIJRCIRtFptv7VxKWyOChW3mFJKnE6nw6RJkyAUCtn7azAKO1eYLnxzYqCvqTl37hw7e6F8Yq6wg87Br1UJMDBKii7Qx7WtqqoacL7qCEKh0Co9ghuRYysFdnX+S+9LOy1KdeJyJ+l9bU+nXT0kox2oTqfDhAkTEBoaauVPYFvsuAVloM6OXtQG2zVzFUbci0R3dzdqamrQ3NwMf39/GAwGXLp0yWo0MVhLQOqpGhoaioKCAru0QHtr42Mn+Pr6Mu8DjUYzePMfO+jt7UV5eTl8fX2tmBRc4QPQV6hcMYmnDnS1tbVISUlBXFwc72vqqsLOHf4Nfn5+8PLyQmpqKluvyWTqxzHfuXMnmpqaEBYWhm+//RarV6/ulwJMsXTpUuzatYvNz0cyBZhiVBTdjo4O1NXVIScnx2nnLz7Q9AiuNSI3IoeLwcSl19XVDdgd0sd1xpTGFpQjzCdusPUnAKyNYtRqNRobG626Tu6MmBrqOJIEDwbU/Ofnn39GUlKSVdAmLSi2xY57kXDU2VEPht7e3n4HcM7CHjuhvb0dVVVV8Pf3R1BQEGpqaqx2EVTU4erpPZ0Jt7e3IyMjY8CDTldM4gMCAqDRaBAYGDjgQedACjtuITaZTOjp6UFAQMCQFXa2h3p8HPPc3Fy89tpraG9vx//+7/8iMDAQ33//PQQCAZMAT506FadOnYJSqbR6/JFMAWbPaVCvzFWG6Ohou+R4gUDg9OmsUCiEVqvFiRMnrKwR+cAXB8QHekLe3d0Ns9ls18uB+7jUzNzHx8dpUxpauBITE52eJ9orxNxi19DQwGwdY2Ji2Id7qN4BwMAdKF9BoTxitVrNOjtbBVtAQAA74U9NTUVsbKzbDg0NBgMqKythNBoxadIkKw8Nrq9DbW0tK3a2vsT2/jZUGUnn2IMtXLZSZ3rBb2lpQVRUFEwmE86dOwdCSD96naMRAV8hpoIPoVAIkUg07Ao7oM8L18/PD3feeSfmz59vtRYqATabzVixYgU++ugjfPnll+w+I5kCTDEqiq6jD5SzUTnU3EWn06GgoGDIptzALwcrtOtJT0+3e1/6ZvXx8UFQUBB++uknh3xYCjpWCQsLc7h1dha0s/P19YVOp4PBYGCEftuOmM46uR2xM8WNejvo9XqXO1BfX19ERUVZjWW4CrampiaoVCr4+PggOjqanZ4HBQUNqfAS0hdVT6lafEwKPl8Huj2mFzA+Cbafnx9kMhkMBgPGjx8/5JkwF/SgNjIyEtOmTesXcdTd3c0uYNXV1ew9N5BJPBUDNTY29mNp8B3YudsonjvT5ZMAb926FXPnzmUSXYqRTAGmuO6Lrk6nQ1VVFXp7e5GcnIzW1tYhF1wqfRUIBMjNzUVQUBCOHTvGe1/bQzJvb28r1yj6oeAKE6gRi1KphFAotBI3uAOUOWA7t3XUEVMPW0eFmGtU7k5vBzpfbWlpgbe3N6ZOncooVmq1GjKZjFdK7Cx5nxYukUjk8hybb3vMNYivrq6GSqWCn58fwsLC0N7ebsUlHixMJhOqq6uh1Wrtvj/sMQsGMomnBkqhoaG8zBJno5P4+MTO7kzVajV7TW0lwEePHsVnn31mpS7jPj9bOJL68vmgDFUaPCqKriPYs3c0Go2QyWSQy+WQSCSIjo6G0Wi0kgc6A+42m3ZwGo0GUqm038jDdks+0CEZtRwMDg5mwgSDwYCKigq0tbUhJCQEBoPBKgrcmW2iPdC5rVAoHHBuy511OlOIhUIhVCoVYmNjUVBQ4NZgRsrltfVT5us6aSGmto6Otv/cmbA7L2xUckv/hhMnToSXl5dd5R/37+rMQQ39+TFjxjjMxeMD16nM1iRerVajvr4eGo0GPj4+jH9O1+bImAhwPCemzU9YWBhT2NH18HXEfKkRVAL873//G9XV1Yzr3tPTA4lEgurq6hFNAaYYFUXXmU6XgmtOnpycjMzMTPbzriYCcxMZ6urqWAeXk5PTb030gIxSc1w9JLMVN4wbN86qg6QdMdczgW5hB5LD0guQWq228qJw1wor6gAAIABJREFUFXyFWKvVory8HHq9HjExMUzFx+2IufE6roAmMQ9k50hB547cDyt3+19fX8/8db28vNDb2wuxWMwMy90Bs9kMmUwGpVIJqVRqxc/lU/7RrlMul6O2tpYJOmwZJ0Dfrq2iogJeXl5Oh4Q6A4FAAIPBgLq6OsTExCAvL4/J1SlzgoojXDGJp4/d3t6O2tpalxR2bW1tCA8PtysBbm1tZfcNDg5GdXU1gJFNAaYYFUXXEaj/Aj1sqq2tRXx8PO+BlrOHYxTe3t5oaGhAU1MTEhMT+83MbO9rMpmstizOHpJRqW1MTAzv9pbbrdl6JqhUKis5rO32urW1FY2NjUhJSbG6AA0VXD8DGgTJBe2cuPE6zrp1cXmxQ52B2m7/1Wo1ysvL2YVDq9WitLQUQH8rTFfpclz3soKCggFfa3tdJxUWcMUw1A9aLBYjISFhyLN9CrPZzHZvtgGvfPN1eybxXJkzfe30ej3Kysrg4+NjdR7hSNih0+nwxhtvoKGhAX5+fqirq+OVANvDSKYAU4wKGTDQtxXkey40poUqWNLT0x12AMeOHcOvfvWrAX9fR0cHzp07h7i4OEilUodvckIIzpw5w5yznO3q1Go1oyWlp6cPmabFlZy2t7dDoVCww5+wsDDe1F9XYUsBS0xMdLqQc+lrarW6XyEODg5GW1sb2tvbIZFI+nGchwLKn9ZqtcjKyup3uMc1Oler1czonLubsOc/y+1AMzMz3ZpHptFoUFZWhpCQEIhEIrbjofH13IvEQNt/W9BoKbFY7NLf0RZ8rx3NmYuNjUVcXJxTM+yzZ89i+fLlmDt3LlatWuW2C8swwe6LNaqLrkqlwvnz5+Hl5YWJEyfajcjhYqCiq1arUVlZCR8fH1gsFqSnp9tNVuB6o9JCp9FooNfr2RaRz5NAp9OhpqYGOp0OmZmZTkmNnQV3biuRSODr68sKMf1AALDi6Q7khkXBpYClpaW55UNBZ8Stra3o6OhgCiXuazdY0QRgfZFw1ZOCXsRoMaG+CdRcJzg4GCqVinFuB/JhcAXcMUVWVhbve4SKOuj6bIUT9rjERqMRFRUVMJlMyMrKchsnG+gTfZSVlcHf3x8JCQlM7qxWq1m2Hrcj9vf3h16vx2uvvYYjR45gx44dGD9+vNvWM4wY/UXXaDSyLQhXYhsVFQWj0ciC7gbCsWPHMG3atH4fPC7Lgdr/lZWVITY2lpfAbntIZnuAptPpoFKpWLGjszqz2Yze3l6kp6fbVQsNBnRuq1KpeLf7XHBP12khpod6fIWYSwHLzMwckkDFFr29vcxMJyMjg30I6dpsuzpXCjGdNwcHByM9Pd0tFwk61mlra0NjYyO8vLwYDdAR9c8VUHZJYmIixGKxS+8RrnBCo9H04xIbjUZ2KMm1FB0qKOWuqanJboAq16tDo9GgpKQEGzduZLTFxx57DNOnT7dS5F3FuD6KLu0QqV9uVFQUS0vNzs526nFOnDiBvLw8tk00mUyQyWTo7OxkLAf6RuRzJRvMIRn1Bairq0NYWBiEQiFzY7L9sLp6oGOxWBifcijuYmaz2WrrTwuxQCCAXq/HmDFjIBaL3WamYzabUVdXh87OTqeUWa4UYvo3ValU/Q6zhgqj0cj43lKpFEFBQVbUP25XZxtdP9DBF2WuWCwWSKVSt3WgJpMJcrkcNTU1sFgsEAqFVnPYoY6denp6UFZWhuDgYEgkEqceR6/XY9OmTfjxxx+xfv166HQ6nD59GjfeeCNuvfXWQa3jCmP0F93a2lrU1tYiNTXVqrBQdZCzW5LTp08jJycHvr6+aGhoQENDA5KTk5GYmNhvGyaTyRAQEID4+PhBFVug7wS+uroaYWFh/bbk3A8r/XKFlUDDGiMjI5GSkuK2E3gAzIoyLCwMgYGBLG+L65o1GCks9+CQuvkPVsXELcQajYZFN1EmRUpKyqCDMPnWTb15nVHBcZkJtBDbs8LkmvXQDtRd4Hag3BHIQDNsZ7x/CSGor69HS0sLsrKynGbFlJaW4qmnnsJ9992H5557zq3v2yuI0V90VSoVfH19+31A6QyJ5toPhHPnziE8PBxNTU2Ijo5Gamqq3T/6zz//DC8vLyQkJLhcbLu7u1FVVQWBQICMjAyn5s2A9WEY/cAC1jNYgUCAmpoaeHl5ISMjw60KJzoT9vHxgUQi6ddtcbmwarUa3d3dVqIESiPie424cTkSicStB070sX18fBAVFcW2sVw/B1pMXC3E3d3dKC8vR1BQ0JDGFLbba9qx09FTcnIyRCKR216X7u5ulJWVITQ0FOnp6QN2oFxqIp0Vc1WT9G9MObxlZWUQiURITU11qrvV6XTYuHEjiouLsWPHDsYSuEYx+v10g4KCeA1obCN7HEGpVKKrqwtmsxl5eXkOt29UPdbZ2cm6E2feWNzZ6mACFfn8V2lXolAocOHCBeh0Ovj7+0MkEqGrq8spvuRAoFtypVLpcCbMx4XlzhG56jBuN9zW1jbgYw8GZrMZtbW16OrqshvFw3XqcsVYx5nHdgVcy8OYmBjU1tay8QohhIWI2jMlcuUAkI5usrKynB6v2FOwUVEH9f7t6emBxWJBXFwcwsPDncpPO3nyJJ555hncf//9OHLkyLXa3TqFUdPpms1m3uJKCEFxcbFDRgKN8ab2dLGxsQ5t+ughmdFoRGtrK7vq0zdlaGgowsLCrDo6Ww9adx6S8c1tadovPaxzpeO0fa70dH/MmDFISEhwy7qNRiPUajWam5vR2dnJTKttRxNDYSXQMcVgDpy4xjq2HXFISAjMZjPq6+vZY7vDyIVCoVCgoqICcXFxGDNmTL/HtlX+aTQap3nOKpUK5eXliImJQXJyslvXTelrkZGRiI2NteqKbW1Eg4OD2aHohg0bcPLkSezYscPps5drAKN/vGCv6AL2aWDcoMrMzExERkZCJpNZmW5zMdDclru1VqlUrKPz8fGBRqNBTEwM0tPT3XoVd2Vuy+04aSGmDl30i9vRDQcFjIJG/FAjIF9fX1aI6RfXQYxvffbAjTrPyMhw23bcYDCgs7MTdXV1TP5JTcRdWZ89GI1GVFZWwmAwICsry+WxEJfnTGfY9EIRFBSErq4uljPnTq8Oi8UCmUwGhUJh18CIe6HQaDQ4duwYNm/ezNbz8MMPY/r06byfu2sUo3+84MobnXYpfIm1fFJgZw/JbLfWarUaFRUVMJvNiIuLYxJYX19fJkZwdWtIQbtzLy8vp1VZfC5YXIcurgk2tcij9B53U9fUanU/5oCPj0+/6HW+9dljJXAZD3xR50MBPShrbm5GZmYmE2Y4spp0thC7eghnD3y+v3q9Ho2NjaiqqoKfnx8IIWyOy+XqDvbvSzvn2NhY5Ofn2+2cuRLxkJAQlJeXIykpCa+++ipT/UVFRY2momsXo6bTtVgsvMY2wC/cWwBWUuDk5OR+s6bm5mYYDAakpKQMmpFA47Epb9WWuE6v+HTrT7de3EJsjz7ETfMdzEzYEagvRXNzM+No2irD6Bpd7R6HIkKwBd/Wn1LXIiMjkZqaOqRCYgsqDY6IiHDqUIjrScDXsXPVYT09PUx2nJGR4dbdBPX+NZvNVhQz7oVMo9FYzdi5ngmOXj+z2cyy5lzpnIuLi7FixQo8+OCDWLZsmdsohlchRv94gRACg8HA+70TJ04gJSUFMpkMYWFh9qXAhKC9owMqlQrp6enMcMPZYks7rY6Ojn6OVwOtnZvNRelDthzdtrY2NDQ0uHW2SkF9AWJjY/vN+mxniPRC4UhVxwXt+IdjTNHb28t8JWJjY9np/0A2k86ASoO7u7shlUqHJPrgK8R0JCYWixEfH++2CwW3c05LS3NKTGA7enJkhUlnzq7Mynt6evDyyy/jp59+wrvvvovMzMwhP8+rHNdv0aVJEKGhofavyEolvP/yF3idOQNdcDAq581D3O23Oy1/5XZxVKc+1AMKWy/drq4ueHt7QyQSITw8fECOrrMYiALmaH30QkEvFpRnyt1WU++LoRYtWzgTdc7n5WCbCcf3fLk5Yu6Oqwd+2ZJHREQgPDycUQD5UjBcLcQ0W83Pz2/InbPJZLK6UGi1WhgMBggEAiQlJSEyMnLAzwg9yF6xYgUWLVqEJ554YjR3t1xcf0VXr9ejqqqKndpLpVK7Hgbeq1dDcPYsSFwcLBoN9EolKletgiogAN7e3lbbftv5HBU3hIeHIzU11a1dHJUzA2BGKY44upQx4UzBd5YC5gq4hP/m5mYolUo2v6av4WC9frngRp27cgJvr2OnhZhyTGUy2bBs96mxeHd3N7KysngbAO7Wn1uIuYd1fIWYEIKGhgY2cx5Iwecq5HI5KisrIRaLERwcbFWIaXoxVzRB/YHXr1+PS5cu4d1332X+ttcJRn/RBcCci7hx6bGxsSgvL0dcXBzv/JMYjfD5zW9gSUgABAJAIICguRmm1athufFGdqJOt/29vb3w8/NDQEAA1Go1fH19IZVKnRY3OANuQaQWdPbAJ8/lbgupYox+SLnqpuEYUyiVSiaPpvPPoajquOBaOmZmZrpF9MH1waB5cDSJwpnRibOgxuKD6ZwHKsRCoRC1tbUQiURIS0tzaydJZc00WolvZ0Dfg3SNX3zxBT7//HP09PTgV7/6FZ566qkBee+u4qGHHsI//vEPxMTE4MKFCwD6Lsb3338/6urqkJKSgk8//ZTlti1fvhwHDx5EYGAgdu/e7bRYaggY/UWXEAKZTMa2+ElJSawDoo70XPkkOyQzm+FfWAji5wdBYCBgsQAtLTBu2AAyYUK/30M7aJVKhdDQUBgMBhgMBgQGBlp1xIPp5mju1FDntnRbaEsN8/Pzg1qthkgkYg5j7gI1vaHmJI4OVrhev9yO3bYQ078fNx3C3ZaOwC+dM+XFCgQCq9GJWq1mf2Nbie5A0Ol0KC8vh1AoRGZmpttec4PBAJVKhfr6enbxt6WvDXVGTKXervDKtVotXnrpJVRWVuLxxx9HZ2cnSktL8fDDD2Py5MmDXostjh49iuDgYCxYsIAV3eeffx4RERFYtWoVNm3aBIVCgc2bN+PgwYPYtm0bDh48iJKSEixfvhwlJSVuW4sdjP6iC4AdBNluCevq6uDr64uEhAQru0V6SOZ9/DiEGzYAhABmMyw33wzTqlWATYgf3b7Zvgm522paSGg3x91WO9oG0zEF7RDdyeWlfq46nQ5hYWHo7e1lB0221DVXQUUfzc3NQ8o9s+dsRrPOIiMjh+1032QyQSqVOuycuRJdeqGghZjbEdP1cbf77rZ1BPp2FBUVFYiNjWUCCi7PmTqIUStHVwoxNdYhhEAqlTr1viCE4Mcff8SqVavwyCOP4LHHHnOr8IIPdXV1+M1vfsOKrlQqxZEjRxAfH4+WlhZMnz4dFRUVePTRRzF9+nT87ne/63e/YcTo5+kCwJgxY3iD5Cjv1F4mmWXaNBi3bYOgpgYIC4MlL48VXK6yKTY2lje5gc/hn+uR0NjYaKVYo4UuKCgIvb29bG47btw4t44puIdNtmwK7nxTqVSivr7eYRHhA43LiYqKciouxxHo7JxKaQ0GA8rLy6HT6RAfHw+dTofS0tJBqepswd1ROGsgw5XoUi4pvdhqNBoWp2MymeDj44Oenh6EhYUNmDXnKrhz4dzcXKv3Cx/PmVuIOzo6+kmwKSuBvoZtbW2QyWROsx6APiXaiy++CJlMhv379yMlJcVtz9cVtLW1sc9ffHw82tvbAVgnAAO/JPcOc9G1i1FVdO1BKBSyLaKXlxcvBYykpIDYvFnU6j7D8sDAQEyaNMmlTpDrkSAWiwH8olhTqVSoqamBQqGAxWJBVFQUI8TbhlcOBoQQdHZ2oqamBnFxcZgyZQpv6CVfsGRvby9UKhXT0dvaS4aGhjLllMVicXtk+EBR59zRiUwms+rm6MXMkRhBo9GgvLwcYWFhmDx58pB2FNyLbVxcHIu2USgUEIvFLDSUawozlPET9dFNSkpyOnDSUSHWaDSsEAsEAhiNRvj6+iI7O9spHwlCCH744QesXr0aS5YswV//+tdh724Hg6Ek9w4HRnXRpWOEkJAQtLe3o7S0FAKBgL3xbQ+ZKKi4wWAwOGQ9uAqax9XT08MSSqOjo1khbm5utqI10TW6Mgekblq+vr4uXyi43Rw3k4ubtXb+/HkYjUaEh4cjJiYGBoMBfn5+bvmwORN1LhQK+6nquN2cPdWaUChkSjh7SQtDQWdnJ4u2sc2as6X/0aRfZ72SuT66rv5N+cAtxJTTW1tbi4SEBHh5eaG+vn5AwYRGo8Gf//xn1NfX46uvvkJycvKQ1uQOxMbGoqWlhY0XaDPhKOl3JDCqZromk4mND+wpycxms9Xstbu7m31AabyKUql0SdzgLBQKBaqqqhzObe3xX+kHNCwsjPcD6koyxGBAu6zY2FgkJSVZMRIGMvsZCNyoc3tUKlfBpYZ1dnZCq9UiICAAMTExVvJhd/we7vzTFZ6z7WtoNpv7Ua86OjpQV1fndh9doK+5KCsrs8vp5RNMFBUVwWAw4Ny5c1i8eDHWrFkzrFllW7duxXvvvQdCCB5++GE89dRTWLduHd577z2EhYWhtrYWn3/+OebMmYMVK1YgMjKSHaR1dXXhtddew9dff43t27ezg7Rly5bhxIkTw7bmy7g+DtKMRiNMJpPLSjK9Xo/a2lq0trbC19eXdXzcLetQtqFUNQXAJe9cCntm5rTI6fV6tLe3Izk52e0UMBqXQ0MV7RUVejGz9dHlduy2237ubHUongOO1l5eXs6Mbwghg1bV2YK7drpjGSq4frUKhQIdHR0QCARMROEuQQxde2Njo0uHfGq1GqtXr0ZzczMKCgogk8kgk8lw7NixYRE8XLhwAYWFhThx4gR8fX1x++23469//Sv+9re/4cCBA2htbUVnZydiY2Oxfv16zJs3D/Pnz2d0yM8++wwREREghODJJ5/E4cOHERgYiF27dqGgoMDt67XB9VF0V6xYgeDgYBQUFCA/Px8hISEDfoi5rIGUlBT4+PhYzTbpB5R2Ic6yEYBfYsi7urqcipxxBRaLBS0tLZDJZPD29u5jYdgUuaFQhlyNy+EDn2sYFUv4+PigtbUVYWFhkEgkbmVrcA8QHQkFbHcVXGqYo8NEmq0WEhLidtc4W5FDeHg4G+9QLiwhpF9enbNFr7e3F5cuXXIpOocQgn/9619Yu3Ytli9fjkWLFl2R2e1nn32Gb775Bjt37gQAvPLKK/Dz80NPTw+Cg4Px3HPPDfsahoDro+hWVFTg+PHjKCkpwenTp2EwGDBu3Djk5+dj8uTJGDt2LPsAKRQK1NXVscDDgQ6DuGwElUrFKE3cbpgWOa4AwdUYcmdAZ85Go9GKE8vHz+XONsPCwgb0H3BnXA4ftFotqqqqoNVq4e/vD5PJ5LTZjzNQKBSorKwctF8sl/7HveBSjm53dze6u7uRnZ1t5ZDmDtC0hfDwcIciB9v0EK1W268Q2zYF3GLuSnSOSqXCmjVr0N7ejnfeeceKBTDcKCsrw1133YXi4mIEBARg5syZKCgoQGRkJHbv3o3Q0FAUFBRgy5YtbjV+chOuj6JrC51Oh7Nnz+L48eM4efIkLl68CB8fHyYUeP3115GVlTXoosItctQ/18vLC3q9HqGhocjIyHCrbym1pKQUMGe2tJREb+s/wFfkhjMuh2vCwlVl2es2bRkTA3WTBoMBVVVV7PDTndQ7ehGl8mB6ZjAYVR0fLBYLamtrIZfLkZ2dPahDPmpab8tzDg4Ohp+fHzo6OhAREeFULA/Q95y/++47vPjii3jmmWewYMGCEWEmvP/++ygqKkJwcDBycnIQEBCAVatWsfOWF154AS0tLfjggw+u+NoGwPVZdG3x+eefY926dZgzZw78/f1x6tQppmCbPHky8vPzUVBQAJFI5HJnSvm2RqMRMTEx0Ov1UKlUblGrcbtPe2kCrjwWX/w75TCnpKQgISHBrTM6aljubIYY7Ta5ijXuIRO3yHF3FWlpaW6NDQesiznXWNxWVedMt8kHPpGDu0Bd0jo6OhAcHMzMauga7Xl1KJVKrF69Gl1dXXjnnXeQmJjotjUNBWvWrIFYLMbjjz/ObrMVSFxF8BRdoI8kHRERYTVKoHlRJSUlKCkpwalTp6DRaJCdnc2K8IQJE+weIFGvB7lcDolE0u9Qwp5ajSuScOTUpNVqUVlZOWzdJyXDx8bGwt/fnxU5WkCcWaM9uDPqnE86TCOTgoODkZaWhrCwMLcVrcEYi/Op6gD0E8R4eXlZiRyys7Pd2pkD1tE5qamp7HXh8+qg5jTnzp2Dv78/du3ahRUrVuAPf/jDsHa3fMwEW/+EoqIiZGZmor6+HrNnz0ZxcTETzADAm2++iZKSEuzbt2/Y1jlIeIquKzAajTh//jwrxD/99BOEQiHy8vKQl5eHgoICpKWl4csvv8SYMWOQlJTEOI7OgLsVpPNh20MwamKiVquRmZk55NBDW9DuMyAggNeHgRYQbidH1WC2M2xbcK0Rh2OmbTabIZPJ0NXVBbFYzJgTA5n9OAt3GovzFTmLxQKDwYDo6GiMGTMGwcHBbs3Lc3VUYTabcfbsWWzYsAE1NTUs3WHp0qUoLCx0y7psYY+Z8N5771n5JxQVFSEkJAQ+Pj544403MHPmTDz44IM4e/YsBAIBUlJSsGPHjhFTlzmAp+gOBTSJ9dSpUygpKcGhQ4dw/vx5ZGVl4de//jXriIdCeaKcSJVKhba2NnR3dyMwMBDR0dFMHusOsxRHcTmurJHLRuAeJprNZlRUVMDf39/tpjrAL2br9gy07Zn9cMc7fIGNwC+sh/b2dkilUrdznanIwWw2Iz4+nnk5DNYjwRZqtRplZWUuHSISQnDo0CGsX78eK1euxO9//3t4eXmxRAlnpcCuwh4z4f333+f1T7gG4Sm67kJxcTE2btyI119/HcHBwawbPnHiBKNXUcpaXl6eSx8eW1tEWkBokaMHTNwC4uzs1Z1xOVxw/Rva2trYIWJkZCRbpzvI89S0h/KFXRmzcON9VCoVr9kP5SNHR0cjJSXFrdtq7mtvT+Rgj17HLcT2Lha081cqlcjJyXH68LarqwsrV65Eb28vioqKrmi3aI+ZsHfvXiiVSnY/kUgEhUJxxdblRniKrrvgyBvBbDajrKwMJSUlOHnyJE6fPg2z2Yzx48ejoKAABQUFyM7O7neQptPpUFVVBZPJ5NAWkSuSoLxNQsiAJuZq9fDF5dhGnScmJvaLHqKSVy7H2dmLBdfW0V1uXVyzH4VCgba2NphMJoSFhSEiIsIpsx9n0dvbi7KyMjbGceUx6cWCvo58EUTUOjIhIQFJSUlOx0N9/fXXeOWVV7BmzRoUFhaOiBcBHzNh165dnqLr/rVcP6Aii9LSUpw4cQIlJSXMbCU/Px8TJkzA8ePHMW7cOMydO3dQqiZ7s1dagLu6uqDX65GVleXWuBzA+ahzrtKKXiyAgRMvqBcDjZd3J6OCEIL29nbIZDIkJycjLi7O7sWCW+Rc2VnU19ejpaUFUqnUbTxS7hpbW1thNBoRGhoKkUjklFeHXC7HihUrYDKZUFRUNGzjA1dBmQlbt271jBfcv5brG7QzfOutt7Bz506kpaVBo9EgOTmZdcN5eXkICwsbUlquTCZDW1sbi92mJjq02xzKrNUdUefcAyaVSmUlGw4KCoJCoWBpBe7kOgPOG4tzzX4oY4Irv7ZHC6NOZtz0DHeCmq6LxWIkJCT0iyCyVdXRi/BXX32FDRs2YO3atbj//vtH1GkL6EvTiImJsWImbNiwgdc/4RqEp+heTSCEYMOGDVi8eDHi4uJgsVhQXV3NZsOlpaXo6enB2LFjWSEeN26cU3NM27mwUChk22laPFQqFUwmUz8THWeKAzW+iY+Pt0rncAcMBgN+/vlnNDc3s4sFdztNFXWDhTuMxe2JEEJCQlh2mFarHbTIwRFMJhMqKysdRucA/VV1TzzxBOrr6+Hl5YWHHnoIt9xyC/7rv/7LrWuzxZtvvomdO3dCIBAgNzcXu3btwmOPPYYffviBMXG8vLyg0+msmAlyuZzXP+EahKfoXmswGAw4e/YsK8QXLlyAv78/Jk2axApxWloaK3o6nQ41NTXQ6/WQSqUDdod8XRzQf8tPuyFq2iMQCBwa3wwW3d3dKC8vR2BgoNXs09ZxzVWjdQq1Ws0SeN3dfZrNZjQ1NbGEEgADmv24Cmod6cohKCEE+/fvx6ZNm7B27VqMHz8epaWlkMlkeOmllwa9loHQ1NSEm266CZcuXUJAQADmz5+POXPm4MiRI/jNb36De++9d9h+91WE6yM5YjTB19cXU6ZMwZQpUwD0fYCUSiVOnjyJkpIS7N+/HzKZDPHx8fD390dLSwt27tyJ7Oxsp7pPqkwKDg5miiO65VepVKitrWVbfqCv+EkkEqezspwFHVXI5XJIpdJ+fGQ+o3XaxXGN1u1Jcs1mM2pqaqBSqZCTk+P2ubbJZEJVVRV6e3sxefJkJrzhshHa29utzH7oOgfywaCPQ2lmeXl5Tnf67e3tePbZZ+Hj44N//etf7LwgJydnaE/YSZhMJvT29rIUjZH0r73a4Ol0r2GcO3cOCxcuhEQigVgsxunTp6FUKiGVSpnJz4QJEwbdZXV1daGiogIhISHw9/eHRqOBTqdjdohDpYTJ5XJUVVUN2VjHXtClr68vtFot4uLikJ6e7nZ1FQ1udLb75M5eVSoVi3+3Z/ZDDc9dkTcTQvDFF1/gtddew7p163D33XePyOx269atWLt2LQICAjB79mz87W9/wx//+EcUFxfDz88PM2fOxKZNm9yqsLzK4BkvjEa0tLSgt7cXaWlp7DaTyYSLFy8ykx+q3Jk4cSITcUilUofbaxp1brFY+gU22no3qFQqq06TzocdFbjBGn87C71ej/LychiNRohEIvSsqLzCAAAZsklEQVT09LCunVvgBnsxousHgKysrEEfStoz+wkICGBdYk5OjtMS4ba2Njz77LMICAjA1q1b3Z6a7CwUCgXuuecefPLJJwgPD8d9992He++9FzNnzkRcXBwMBgMeeeQRpKen48UXXxyRNV4BeIru9QpCCLRaLUpLSxl/uLKyEpGRkcjPz0d+fj6mTJmCuLg4GI1GnDt3Dmaz2WkXM4C/0+SLRQL6olKamppcenxXnqsjY3G65afr7O3tdSkRmStycJdxOd/j19bWIioqiikhHY1PgL7X//PPP8df/vIXvPzyy5g3b96IMhM+++wzHD58GO+//z4A4MMPP8Tx48fx9ttvs/scOXIEf/nLX/CPf/xjpJY53BgdRVepVOJPf/oTLly4AIFAgA8++ABSqdTKIOPTTz+FSCQCIQTLly/HwYMHERgYiN27dyMvLw8AsGfPHrz66qsAgD//+c9YuHDhSD6tKw5q5nLixAnWEdfU1MBkMmHGjBkoLCxEXl7ekDwBbGORNBoN9Ho9goODMWbMGISHh7u1wx2MsThXJMFV/fG5wlE/BnrQ507jcuAXGpuPjw8yMzOtRjb2xif//Oc/AfSpJOPj4/HWW2+5PeqdD3zMhJaWFhQWFqKrqwvJyclobm7GqVOnEBAQgD/+8Y8oKCjAvffei/j4eBBC8PTTT8Pf3x+bNm0a9vWOEEZH0V24cCFuvvlm/OlPf4LBYEBPTw82bNhgZZChUCiwefNmHDx4ENu2bWO5SMuXL0dJSQm6urpQUFCAU6dOQSAQID8/H6WlpVejCfIVw6ZNm3D06FEsW7YMLS0tOHHiBM6cOQODwYDc3Fw2H87JyXF5fkvtBbVaLdLT062kzXq9fsixSGazmaVzZGVlDdlYnM8VTqfTwWw2IyEhAXFxcU5ZNrry+6g1ZWZmptNF02g04q233sLBgwcREBAAlUoFf39/fPnll27PUuPCHjPh4MGDuPvuu1FYWIjHHnsMDQ0NqKmpgVAoxKRJk7Bz507ccccd6OjoACEEEydOxDvvvOP2g82rCNd+0VWr1ZgwYQJkMplV9yWVSnkVLI8++iimT5+O3/3ud1b3o187duwAgH73ux6hUqkQGhrKm4p85swZKxP44OBgNhsuKCiw6wHLdRqzd9A01FgkKhIYDs4w8Is9YkREBKKiopjyjxvEybVsHIwHc1lZmcvdc2trK5YvX46IiAi8+eabjMeqVqsHZcHpCpqamjB16lScO3cOoaGhmDdvHpYuXYoHHngAra2tEAqFKC4uxrp16/DNN98M2zquAVz7lDGZTIbo6GgsWrQI586dQ35+PrZu3Yq2tjZm1BEfH4/29nYAfW8ObrSIWCxGU1MTqqur8Z///AdZWVkQCAS46aabsGvXLjz33HNsRrdhwwbMmTMHALBx40a8//778Pb2xltvvYXbbrsNAHD48GEsX74cZrMZf/rTn7Bq1aor+XK4FfZsI/39/TFt2jRMmzYNQF+RlMvlOHnyJI4fP459+/YxEjs1+cnPz0dzczPKy8uRk5OD/Px8uwdNfJHv3CiaxsZGVuBsu+Hq6moYDAbGznAnaPesUCisaGbh4eEQi8UA+g4sKb1OJpMxNzPuOu0Z1BBC2GzbFYmwxWLBvn378NZbb2HDhg248847rR7f3fFBfEhMTMRzzz2HMWPGMGZCfn4+wsPD2UWDftY84Mc1U3RNJhNOnz6Nbdu24YYbbsDy5csdzoP4OniBQIADBw4gIyMD+/fvh8FgwLp16/Dzzz/j6aef7hd0d+nSJezbtw8XL15Ec3Mzbr31Vpbq+8QTT+C7775jqRNz5869YhzIkYJAIEBUVBTuuOMO3HHHHQB+8W8tKSnBt99+i2XLlsFgMODmm29Ge3s7tFotxo8f7/T8lhbY0NBQqwJHt/v19fXQarXM9pKacLuLeqRQKFBRUYGEhAQUFBTY7V6FQiFEIpFVweQa1DQ3N7NoJO6BotFoRFlZGUJDQzF58mSnRRotLS1Yvnw5oqOj8cMPP4zYOEyhUODAgQOora1lzIRDhw71u99IS4yvZlwzRVcsFkMsFuOGG24AANx7773YtGkTYmNj0dLSwsYLdJ4lFovR0NDAfr6xsREhISGor69nB2q+vr6Qy+V25ZoHDhxAYWEh/Pz8kJqaColEghMnTgAAJBIJo2oVFhbiwIEDo77o8sHLywvp6elIT0/Hf/7zHzz55JN4/PHHUV5ejpKSEuzatQvnz5+Hj48PJk2axObDEonE6W2wUCiEv78/6urqEBoairy8PFgsFlbgGhoa2Hx4sLFIRqMRVVVV0Ol0g+6efX19ERUVxahaXEoYLeZ6vR7h4eHw9fVlYx1H67RYLPjoo4+wfft2bNy4EXPmzBnRgvbPf/4TqampbFd4991349ixY1AqlTCZTBAKhWhsbPSIIRzgmim6cXFxSEpKQkVFBaRSKb7//nvk5OQgJycHe/bswapVq7Bnzx7cddddAIC5c+di+/btKCwsRElJCcLCwtDT0wOxWIyPPvoIx48fx4QJE3D06FEUFhZi+/bt+PDDD63SRen8ioK7bbIdXZSUlFzZF+QqRFFRESsIdNTw+OOPgxACtVrNTODXrVuHmpoaxMbGWs2H+QQAjozFo6Oj2YefewDW3t6O6upqp2ORqAghJSXFrYo7gUCAgIAAFigaFxeH1NRUZl5uu06u/Nrb2xvNzc1YtmwZ4uPjcfToUbebqnNRUVGB+++/n/1bJpPh5ZdfhlKpxHvvvcde5wULFuD48ePo6elBQEAAvv/+exQUFOCWW27B3//+dxQWFlp9Dj3oj2vmIA0Azp49y5gLaWlp2LVrFywWC69BBiEETz75JA4fPozAwEDs2rULADB16lSsWrUK+/btQ2dnJ26++Wbs3LmTN130iSeewLRp0/CHP/wBALB48WLMmTMHjY2NePnll1nhraioQEFBAQ4cOOChrzkJyqktKSlhB3VyuRyZmZlsPqxSqVBZWYl58+YNKk59oFikgIAA1NXVwdvbG1Kp1O0pFzR/r7Oz06EBjq2JzsaNG3Hx4kUolUo8+OCDWLx4MaRS6RVL4zWbzUhMTGQ7leDgYKvR20svvYRPPvnEipnQ1NTEKGOTJk3C//zP/4xmtZkzuPbZC+5Aa2srpk6dirq6OgDAjz/+iE2bNuHrr79m9+Gmi27cuBEAsHr1agDAbbfdhnXr1gEAO501m80IDw/HkiVLAMBDXxsCzGYzLl26hH//+9945513oNFoMGbMGEilUtYNZ2VlDYkjSwUSjY2NkMvl8PHxsTJYd1csEjXYiY6OdumC0djYiGXLliEhIQH33HMPLl26hJMnT+K1115DSkrKkNflDL799lusX78e//d//4d169b1K7oeOIVrn73gDtgbUdCZMAB8+eWXGDduHIC+EcXvf/97PPPMM2hubkZVVRWmTJkCQgiqqqpQW1uLS5cuwWKxYOHChbj77rtx5MgRAH2c4unTp2Pz5s04cOAAFixYAIFAgKlTp0KpVKKlpQVHjhzBrFmzGOVn1qxZOHz48HVLX/P29kZubi6+/vprrFmzBr///e+tTOBff/11VFRUQCQSsfHF5MmTXQq+NBqNqKurQ1BQEH79619DKBSyuatSqUR9ff2QYpEsFgtkMlk/5oMzP/fhhx9ix44deP311zFr1iwIBALceeedTv28O7Fv3z6r9yDf6M2DweO6KroAsG3bNjzwwANWI4ply5b1SxcFgLFjx2L+/PnIycmBUChEUVER+/Bt374dt912G1paWjBjxgyMHTvWZfqavduvd3Dpd7Q4/vrXvwbwiwk8zabbs2cPmpubkZqaamUCb8s7tlgsqK+vR1tbW7/ZsD0nM5rOUFVV5VQsklKpRHl5OeLj4x0yH2zR0NCApUuXIi0tDT/++OMVoX7Zg8FgwFdffcV2eUuWLMELL7zARm/PPvssPvjggxFb32jAdTVecDcMBgMSEhJw8eJFxMbGIjw8nDff6c4778Tq1atx0003AQBmzpyJxx9/HEuXLgUhBLGxsZDJZLjxxhthNptx8eLF65YzPBhQE/jjx48zE3idTsdM4IODg3HkyBGsXLkSqampg5qNOopFCg4OhkKhQG9vr0sGNRaLBbt378Z7772HLVu2YObMmSNOtTpw4ACKiorw7bff9vsed/TmwYDwjBeGA4cOHUJeXh7LmXKFvvarX/0KW7ZswZEjR/D2228jMTERIpEIer3ewxl2ETQhODMzEwsWLADQ5wR2/PhxvPrqq7h06RKSk5PxyCOPIC8vj3XErhRgWmC5QhKj0YimpiZUVVWxOTANAB0oFqm+vh5PPvkkMjMz8X//939XjRz2448/thot2Bu9eTB4eIruEGD7Bp07d67T9LX4+HjcdtttWLNmDfbv34/k5GQUFxdj/vz5vL/Lwxl2DX5+fhAKhZg7dy4OHz4MLy8vKJVKFhD6xRdfoLa2FomJiawI5+fnIzIy0qlu02Qyobq6Gr29vZgyZQoCAgKsYpEUCgXq6uqsYpHa2tqQlZWFTz75BLt27cKWLVswY8aMYe9u7dHBFixYYMW22b17N7777js2XgOA559/nnf05sHg4RkvDBI9PT1ISkqCTCZj3Y+9fCc++lpBQQEA4IMPPsBTTz0FPz8/vPbaa/j555+xe/duhIaGWh1cPPnkk5g6daoVfY2qwg4fPoydO3cCAPbu3YuSkhJs3759BF6Vawt0zkvHEidPnoRKpUJWVlY/E3guXInO4cYivfDCCyguLoZOp8Nvf/tb3HjjjXjggQfcTlVzBC4drKioiJdt44Fb4KGMXa2wnQu3tbW5xBm2WCzYsmUL87ANCQnBxIkT8fzzzzPeZF5eHvbu3QtfX1/o9XosWLAApaWliIyMxCeffMKoSPZmxtcTjEZjPxN4Ly8vTJo0CVlZWfjuu++wYMEC3HbbbU5Lm81mM95//33s3r0b//3f/43Jkyfj3LlzOHXqFJ588skrxr8FrOlg9syiPHALHF+JHXx5MMzYv38/mTVrFu/3amtrydixYwkhhGzYsIFs2LCBfW/27Nnk2LFj5MCBA8Tf35/09PQQQggZN24cueeee8h9991HPv74Y0IIIY8++ih5++23CSGEFBUVkUcffZQQQsjHH39M5s+fTwgh5OLFi2T8+PFEp9MRmUxG0tLSiMlkGp4nfQ3BYrEQtVpNXn31VRIXF0dmz55Nxo4dS2655Rby3HPPkX379pGamhqi1WpJd3d3v68LFy6QW265hSxbtoxotdqRfjpk0aJFZNu2bYQQQsLCwqy+Fx4ePhJLGq2wW1c9RXeEcf/995MPPviA/bu5uZn9/xtvvEHuv/9+QgghFy5csCqKqampxGQykbq6OuLt7U1Onz5Nuru7SUhICNmxYweJjIwkRqOREELIsWPHyOzZswkhvxRrQggxGo0kMjKSWCwWu0XdA8Jen/b2dvbvpqYm8uWXX5KVK1eSGTNmkHHjxpF58+aRV155hRw6dIg0NzeTLVu2kIkTJ5IffviBWCyWEX4WhOj1ehIZGUlaW1sJIZ6iO8zwFN2rEd3d3SQiIoIolUp22x/+8Acybtw4kpubS377299aFeFXX32VpKWlkczMTHLw4EF2+yOPPEIEAgHx8vIi48ePJx0dHSQ9PZ19v76+nnXMY8eOJQ0NDex7aWlppKOjgzzxxBNk79697PaHHnqIfPbZZ8PyvEcjTCYTuXjxIvnggw/Io48+SpKTk8l9991Huru7R3ppDLa7qszMTPb+am5uJpmZmSO1tNEIu3X1yg2TPOiHwMBAyOVyKxrS3r17cf78efz000/46quvGF0HANauXYuamhpUVFSwQzSFQoGqqiq0tbVBp9MhNTXVodUesWN5SQjBoUOHMHbsWIwbNw7//ve/YTQa8cc//hGpqamYOHEiJk6ciLNnz7LHWbZsGSQSCcaPH4/Tp0+zx9uzZw8yMjKQkZGBPXv2uOfFusrh7e2NnJwcLFq0CO+88w5qa2vx6aefOs3ZvRKwx7YB4DGpuZJwVJGv/MXBA1fx6aefkoceeoj9e8+ePeSxxx5zebywcuVKIhKJ2Gw4NjaWrF27lixcuJC34/3666/J7bffTiwWCykuLiZTpkwhhBAil8tJamoqkcvlpKuri6SmppKurq5hfQ2uZygUCnLPPfcQqVRKsrKyyLFjx8hLL71EEhISyIQJE8iECRPI119/zbur6uzsJDNmzCASiYTMmDGDyOXyEXwmow6eTne0YsyYMcxqjxDC/CSo1R6Afpxh2t38/e9/ZzzR2bNnQ6vVQqlUoqqqCmq1GjfeeKPd32vPT+Kbb75hfhIikYj5SXgwPFi+fDluv/12lJeX49y5c8jOzgYAPP300zh79izOnj2LOXPm8O6qIiMj8f3336Oqqgrff/898wDxYHjhKbrXOG644Qbce++9yMvLQ25uLiwWCx555BFs3rwZb7zxBiQSCeRyORYvXgygj2oml8shkUjwxhtvsPSNGTNmYNasWUhMTER2djZuuOEGNsJYu3Ytxo8fj6effhp6vR6AYz+JxsZGjBs3DmPHjkV9fT2amprQ1dWFWbNmISMjA7NmzYJCoQDgGVMMBWq1GkePHmV/W19f32H13PXATXDUBo9AS+7BCKGrq4vccsstpL29nRgMBnLXXXeRvXv3kubmZmKxWIhOpyMLFiwg69evJ4QQMmfOHPLjjz+yn58xYwY5deoUeeaZZ0hMTAzp7u4mRqORpKWlkZUrV5IVK1aQjRs3EkII2bhxI3n++ecJIZ4xxVBw5swZMnnyZLJw4UIyceJEsnjxYqLVaslLL71EkpOTSW5uLlm0aJHndRsZeMYLHjgGN4bFx8eHxbBQxZWfnx8WLVrEpMd8fhIJCQkwmUwQiUQIDAyEUChEREQE6uvrceDAAWbQvnDhQuzfvx+AZ0wxFNDcwCVLluDMmTMICgrCpk2bsGTJEtTU1ODs2bOIj4/Hs88+O9JL9YADT9H1AAD/bDg7OxstLS0A+nZE+/fvt/Ia/vDDD0EIwfHjx5mfRGFhIWpqalBTU4OmpiacP38eQUFBHtvLYQBfbuDp06cRGxsLb29veHl54eGHH2YXSg+uDniKrgcA7M+GH3jgAeTm5iI3NxednZ3485//DACYM2cO0tLSIJFI8PDDD+Ptt98GACZVzsnJgUQiwbRp0xw6aBEHFLbi4mI2Gz527BgEAgHWrVuHxMRERmE7ePAg+7mNGzdCIpFAKpXim2++YbcfPnwYUqkUEonEYYL0tQauKT8AK1N+Co8z2FUIR7OHKz0E8WD0YfXq1aSoqMguEf+RRx4hH330Ebs/vd/mzZuJSCRis+HExESyZcsW8tJLL5HXX3+93++xJ2M2mUwkLS2N1NTUEL1eT8aPH08uXrx4ZZ78EMBHBZPL5eTWW28lEomE3HrrraSrq4ucOXOG5Ofnk9zcXHLXXXeRrq4uhwIbD64Y7NZVj7WjB25He3s7YmJiUF9fjy+++ALFxcWora11yfYyOjoaRqMRer0eer0e3d3dUKvVdn/naLO+pFSwv//97zAYDOjp6cGGDRswc+ZM5gq2adMmbN68GadOnbL62b17947Qqj1wBp7xggduxz333IOcnBz89re/RVFREUQiEVatWoXvvvsOGRkZ+O6771i6hb0xxdSpUxEUFIS8vDzmcyuXywH0RSWNHz8eDz30EKOejabZsD0qmL3DSA+uMThqg0ekKffAg8vYuXMnmTRpErn55pvJo48+Sp566inS2tpKTCYTMZvNZM2aNWTRokWEEEIef/xxK++IjIwMEhoaSpKSksjixYsJIX00tLFjx5KwsDC2PSekz8Bm6dKlJD09neTm5pLS0lL2OLt37yYSiYRIJBKye/dudvupU6fIuHHjSHp6Olm6dKlbDW3sUcE8BjXXFDyUMQ+uPSxevBinT5/G0aNHERERgYyMDLsn87YUtrCwMGzduhVCoZDdvmnTJojFYqxcuRIzZ85kh2qHDh1CVVUVqqqq8O6772LJkiUAgK6uLqxfvx4lJSU4ceIE1q9fzzrrJUuW4N1332U/5046mz0qmAejBI4qsufL8zWSXwBiLv93DIByACIA8ZzvPw1g3+X/HwvgHAA/AKkAZADSAFy4/P+pACoAXLx833gAFZd/dgeA33Eet+Ly938HYAfn9h2Xb4sHUM653ep+bnjecQDqOP++GcDXdF2Xb2Pr93xdW1+egzQPrmZ8LhAIIgEYATxBCFEIBIK9AoFgIvpSTeoAPAoAhJCLAoHgUwCXAJgAPAHAcvlxngTwDYB0AC8SQi4CgEAgiLn8/UQAv7TJQOPl2xzd3shzu1tACGkVCAQNAoFASgipADDz8vO6BGAhgE2X/3vAXb/TgysHT9H14KoFIeRmntsedHD//wfg/9F/CwSClMu3HwRwUCAQKC/fxxZ80SpkELe7E0sB/E0gEPiir1NfhL6D708FAsFiAPUA7nPz7/TgCsBTdD24ntAmEAjiCSEtAoEgHkD75dsbASRx7icG0Hz59uk2tx+5fLuY5/5uAyHkLIACnm/NdOfv8eDKw3OQ5sH1hK/Qty0HrLfnXwFYIOjDVAAqQkgL+kYSswUCgUggEIgAzAbwzeXvaQQCwVRBnzv8Ani2+h44CU+n68GohEAg+Bh9XWqUQCBoBPAS+mahfNvzgwDmAKgG0IO+rTwIIV0CgeAVACcv3+9lQkjX5f9fAmA3gAAAhy5/eeDBgBgogt0DDzzwwAM34v8D3sffRuukcPAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1,projection='3d')\n",
    "X = np.array([6000, 6000, 8000, 8000, 10000])\n",
    "Y = np.array([60, 80, 70, 100, 90])\n",
    "Z = np.array([340000, 350000, 400000, 450000, 500000])\n",
    "ax.scatter(X, Y, Z, c='red', marker='o')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "现在我们不能用一条直线去拟合它了，而是要用一个平面去拟合它，如下所示："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import numpy as np\n",
    "from matplotlib import cm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(1,1,1,projection='3d')\n",
    "X = np.array([6000, 6000, 8000, 8000, 10000])\n",
    "Y = np.array([60, 80, 70, 100, 90])\n",
    "Z = np.array([340000, 350000, 400000, 450000, 500000])\n",
    "ax.scatter(X, Y, Z, c='red', marker='o')\n",
    "\n",
    "X, Y = np.meshgrid(X, Y)\n",
    "Z = 30*X + 1000*Y + 100000\n",
    "ax.plot_surface(X, Y, Z, linewidth=0, antialiased=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "和求解一元线性回归一样，我们将回归平面的函数记为：\n",
    "\n",
    "$$\n",
    "\\hat{y} = a_0 + a_1x_1 + a_2x_2\n",
    "$$\n",
    "\n",
    "平方损失函数：$$ loss = (y - \\hat{y})^2 $$\n",
    "\n",
    "要想让拟合的平面最接近样例数据，就得让平方损失尽可能的小。\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "loss &= (y - \\hat{y})^2 \\\\\n",
    "&= (y - (a_0 + a_1x_1 + a_2x_2))^2 \\\\\n",
    "&= \\sum_{i=1}^{n}(y^{(i)} - (a_0 + a_1x_1^{(i)} + a_2x_2^{(i)}))^2\\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "将其完全展开可得：\n",
    "\n",
    "$$\n",
    "F(a_0,a_1,a_2) = a_1^2\\bar{x_1^2} + a_2^2\\bar{x_2^2} + a_0^2 + \\bar{y^2} + 2a_1a_2\\bar{x_1x_2} + 2a_0a_1\\bar{x_1} - 2a_1\\bar{x_1y} + 2a_0a_2\\bar{x_2} - 2a_2\\bar{x_2y} - 2a_0\\bar{y}\n",
    "$$\n",
    "\n",
    "分别对 $a_0$、$a_1$、$a_2$ 求偏导，并令其等于 0：\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial}{\\partial a_0} F(a_0, a_1, a_2) &=& 2a_0 + 2a_1\\bar{x_1} + 2a_2\\bar{x_2} - 2\\bar{y} &=& 0 \\\\\n",
    "\\frac{\\partial}{\\partial a_1} F(a_0, a_1, a_2) &=& 2a_1\\bar{x_1^2} + 2a_2\\bar{x_1x_2} + 2a_0\\bar{x_1} - 2\\bar{x_1y} &=& 0 \\\\\n",
    "\\frac{\\partial}{\\partial a_2} F(a_0, a_1, a_2) &=& 2a_2\\bar{x_2^2} + 2a_1\\bar{x_1x_2} + 2a_0\\bar{x_2} - 2\\bar{x_2y} &=& 0 \\\\\n",
    "\\end{aligned}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "求解这个线性方程组，可得：\n",
    "\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{aligned}\n",
    "a_0 &=& \\bar{y} - a_1\\bar{x_1} - a_2\\bar{x_2} \\\\\n",
    "a_1 &=& \\frac{(\\bar{x_1y}-\\bar{x_1}\\bar{y})(\\bar{x_2^2}-(\\bar{x_2})^2) - (\\bar{x_2y}-\\bar{x_2}\\bar{y})(\\bar{x_1x_2}-\\bar{x_1}\\bar{x_2})}{(\\bar{x_1^2}-(\\bar{x_1})^2)(\\bar{x_2^2}-(\\bar{x_2})^2) - (\\bar{x_1x_2}-\\bar{x_1}\\bar{x_2})^2} \\\\\n",
    "a_2 &=& \\frac{(\\bar{x_1y}-\\bar{x_1}\\bar{y})(\\bar{x_1x_2}-\\bar{x_1}\\bar{x_2}) - (\\bar{x_2y}-\\bar{x_2}\\bar{y})(\\bar{x_1^2} - (\\bar{x_1})^2)}{(\\bar{x_1x_2}-\\bar{x_1}\\bar{x_2})^2 - (\\bar{x_2^2}-(\\bar{x_2})^2)(\\bar{x_1^2}-(\\bar{x_1})^2)}\n",
    "\\end{aligned}\n",
    "\\right.\n",
    "$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "bar_x1 = 7600.0\n",
      "bar_x2 = 80.0\n",
      "bar_y = 408000.0\n",
      "bar_x1y = 3188000000.0\n",
      "bar_x2y = 33280000.0\n",
      "bar_x1x1 = 60000000.0\n",
      "bar_x1x2 = 620000.0\n",
      "bar_x2x2 = 6600.0\n",
      "a1 = 32.10526315789474\n",
      "a2 = 1273.6842105263158\n",
      "a0 = 62105.263157894704\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "X1 = np.array([6000, 6000, 8000, 8000, 10000])\n",
    "X2 = np.array([60, 80, 70, 100, 90])\n",
    "Y = np.array([340000, 350000, 400000, 450000, 500000])\n",
    "\n",
    "x1 = np.sum(X1) / X1.size\n",
    "x2 = np.sum(X2) / X2.size\n",
    "y = np.sum(Y) / Y.size\n",
    "print(\"bar_x1 = {0}\".format(x1))\n",
    "print(\"bar_x2 = {0}\".format(x2))\n",
    "print(\"bar_y = {0}\".format(y))\n",
    "\n",
    "x1y = np.sum(np.multiply(X1, Y)) / Y.size\n",
    "x2y = np.sum(np.multiply(X2, Y)) / Y.size\n",
    "x1x1 = np.sum(np.multiply(X1, X1)) / Y.size\n",
    "x1x2 = np.sum(np.multiply(X1, X2)) / Y.size\n",
    "x2x2 = np.sum(np.multiply(X2, X2)) / Y.size\n",
    "print(\"bar_x1y = {0}\".format(x1y))\n",
    "print(\"bar_x2y = {0}\".format(x2y))\n",
    "print(\"bar_x1x1 = {0}\".format(x1x1))\n",
    "print(\"bar_x1x2 = {0}\".format(x1x2))\n",
    "print(\"bar_x2x2 = {0}\".format(x2x2))\n",
    "\n",
    "a1 = ((x1y-x1*y)*(x2x2-x2**2) - (x2y-x2*y)*(x1x2-x1*x2)) / ((x1x1-x1**2)*(x2x2-x2**2) - (x1x2-x1*x2)**2)\n",
    "a2 = ((x1y-x1*y)*(x1x2-x1*x2) - (x2y-x2*y)*(x1x1-x1**2)) / ((x1x2-x1*x2)**2 - (x2x2-x2**2)*(x1x1-x1**2))\n",
    "a0 = y - a1*x1 - a2*x2\n",
    "print(\"a1 = {0}\".format(a1))\n",
    "print(\"a2 = {0}\".format(a2))\n",
    "print(\"a0 = {0}\".format(a0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "得到二元线性回归的解为：\n",
    "\n",
    "$$\n",
    "y = 32.1x_1 + 1273.7x_2 + 62105.3\n",
    "$$"
   ]
  }
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