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@qpleple
Created May 9, 2018 22:11
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Parabola fitting and rotation of the space"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"from matplotlib.pyplot import *"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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/vnTypJScLE2ZImXM6OtUQHCjJAL8WMaMZgRRbKwZWdSjhzR5sq9TAQCA1Ei2\nkzUpepLuKXKPKuStkKJz5m2dp90nd+v1uq8rxOKRHelPTIwZQXTmjJSUJD35pHQfa7cDHscnDuDn\nGjUyH4oxMVLdulK3btK0ab5OBQAAUmr53uXae3pvqkcRVcpbSS3KtvBwOsD/HDhgRhCdOSNVqmR2\nMxs3ztepgPSBkggIAG+/bT4cM2UyC/V16SLNmOHrVAAAICUcTofyROTRo+UeTdHx87fN166TuxhF\nhHTp0CFTEJ06JQ0cKP30kzRsmFSwoK+TAelDmK8DALi5AgXMh2OvXtK8eWbrz06dpJAQqV07X6cD\nAADXc/DsQS3evVj9avdTxrCbL6by9yiiinkr6pFyj3ghIeA//vjDTDE7ccJsc9+2rVS5stnRDIB3\nUBIBAeL5583oob59peho6amnpA4dpNBQ6emnfZ0OAABcy5T1U2TbtrpFdkvR8Qu2LdDOEzu18PGF\njCJCunL4sBlBdOyYtGyZ9Pnn0sGD0ty5Uhj/agW8hk8eIECEhZlFrA8elN56S/riC/NB2q6dNGeO\nr9MBAID/LyEpQVPXT1XTUk1VLEexmx7/31FEKZ2aBgSDI0ekBg3Mn0uWSLfcYtYg6tBBqlPH1+mA\n9IWSCAggdepIHTuaNYr275cWL5buvdcMxZ03z9fpAADAf32x6wsduXAkxQtWL9y+UDtO7NBr977G\nKCKkG0ePmoLo0CHpm2+ku+6SnntOypZNGj3a1+mA9IdPHyDAjB5tvl3p0UPKnFn68kvp7rvNlLOF\nC32dDgAA/C3KGaWi2YuqacmmNz3271FE5fOUV8vyLb2QDvC9Y8ekhg3NbmZff22eaT/6SFq1Snrz\nTSlPHl8nBNIfSiIgwOTObYqiH36QZs6UsmSRvvrKfOvSurX0ySe+TggAAHaf3K2Vv69U1xpdFRoS\netPjP97+sbYf367B9w5mFBHShePHzQii/ftNQXTvvWZHs969pVq1zG6+ALyPTyAgAHXsaKae9e1r\ndn/ImtV8uNaqJbVqJX32ma8TAgCQvkU5oxQWEqZO1Trd9NhkO1nDfhjGKCKkGydOmBFE+/aZUfF1\n65rX+/c3RdGkSWYXXwDex396QAAKCTEfnmfPmqJIMvO2v/5auuMO6YknzMLWAADA+y4lXNLMjTP1\naLlHlS9rvpse//cootfufS1Fo46AQHbypCmI9uwx62vWr29eX71amjpV6tXLbHsPwDcoiYAAVaGC\nKYhmzjQTxB24AAAgAElEQVTztiWzVtE330g1akiPP24+eAEAgHfN3zZfp+NOp2jB6mQ7WcO+H6Zy\nucvp8fKPeyEd4DunTkmNGkm7dkmLFpmySJLi46Vu3aQiRaQhQ3waEUj3KImAADZokFS8uNS9u3T5\nsnkte3Zp6VKpalXpscfMekUAAMB7HE6HyuUup7pF69702IXbFmrb8W2MIkLQO33aFEQ7dpgR7/fd\n9+9748ZJ27dL779v1tsE4DuUREAAi4iQJk4038aMGfPv69mzS8uWmaG6jz5qRhcBAADPW39kvX75\n4xd1j+wuy7JueGxScpKGfD9EFfJU0JMVn/RSQsD7zpwxpdC2bWbtzMaN/31v3z5p2DDzzPrgg77L\nCMCgJAICXJMmZg2iESPM3O6/5chhiqIKFaRHHjGjiwAAgGc5fnUoIjxCz1R55qbHzts6TztP7NTQ\nekPZ0QxB6+xZ6f77pc2bzS68TZv++55tS889J4WFSf/7n+8yAvgXn0ZAEJgwQcqYUXr2WfNh+7dc\nuaQVK6Ry5aTmzaXly32XEQCAYHc27qzmbJ2j1hVbK0emHDc8NjE5UUO/H6oq+arokXKPeCkh4F3n\nzplRQxs3moLo/48UWrhQWrJEGj5cKlTINxkBXImSCAgCt90mjRxpCqG5c6987++iqEwZ6eGHpZUr\nfZMRAIBgN2vTLMUmxKZowerZm2drz6k9jCJC0Dp/3ox4j442ZdBDD135/tmzUs+eUvXq0vPP+yYj\ngKtZ9n+HHXhRZGSk7XQ6fXJvIBglJUl33SXFxEg7d0o5c175/vHjUoMG0t69ZjHrv7cbBQAAaWfb\ntipMrKCsGbLqly6/3PDYhKQElX2/rHJkyiFnF+dN1y4CAs3582Za2bp10oIFZr2h/+/55yWHQ/r5\nZyky0vsZgWBmWVa0bdsu/ZfF1xZAkAgNlSZNkk6ckF555er38+Qxo4hKlJAeeED6/nvvZwQAIFj9\nEPODdpzYkaJRRLM2zdK+0/s0rN4wCiIEnQsXpGbNTEE0b961C6JffjGbrzz3HAUR4G8oiYAgUq2a\nGbY7aZL0009Xv583rymKihUzH94//uj1iAAABCWH06EcmXLcdJey+KR4vfHDG6pZsKaalWrmpXSA\nd1y8aL6MXLtWmjNHatny6mMSEqSuXaX8+c1aRAD8CyUREGSGDZOKFJG6dJEuX776/Xz5pG+/Ncc0\nbSqtXu39jAAABJM/L/ypT3d8qvZV2isiPOKGx87YMEMxZ2MYRYSgExtrFqZevVr66COz++61jB8v\nbdokvfeedMst3s0I4OYoiYAgkzWrmd+9Y4c0evS1j8mf3xRFBQuaomjNGu9mBAAgmEzbME0JyQnq\nHtn9hsddTrys4T8OV+3CtXX/7fd7KR3gebGxZmHqH36QPvxQatXq2sft3Su9/rrUosW1p6EB8D1K\nIiAINWtmPpxHjDCLWF/LbbdJ331n/mzSxMwbBwAAqZOUnKTJ0ZPVoHgDlcld5obHTl0/VYfOHWIU\nEYLKpUtS8+bmufKDD6Snnrr2cbYtde8uhYebUUQA/BMlERCkJkyQsmQxc76Tk699TIEC5gM9b16p\ncWOziCAAAEi5Jb8tUczZmJsuWH0p4ZJGrh6pe4veqwbFG3gpHeBZcXFmVNDKldKMGdLTT1//2A8/\nlFaskEaNMqPZAfgnSiIgSOXLJ731llmcetq06x9XsKApinLnlu6/X3I6vZcRAIBA53A6lD9rfjUv\n0/yGx02OnqzD5w8zighBIy5OeuQRafly86zZrt31jz1+XHr5Zal2bTOaCID/oiQCgliHDlK9elLf\nvtKRI9c/rnBhUxTlyiXdd5+0fr3XIgIAELD2n9mvr/d8rc7VOis8NPy6x12Mv6iRq0eqfrH6qlus\nrhcTAp5x+bL02GPSkiXSlCnmmfNGXn5ZOndOmjxZCuFfoIBf4z9RIIhZlvkwjouTeva88bFFipii\nKHt2qVEjacMG72QEACBQTY6eLMuy1LVG1xse9+4v7+rYxWMa3oD9vhH4Ll82W9t//bU0aZLUqdON\nj1+2zOx2NmCAVKGCdzICcB0lERDkSpWSBg+WFi6UFi++8bFFi5qiKFs2UxRt2uSdjAAABJr4pHhN\n2zBND5Z+UIWzF77ucWfjzmrMT2PUrFQz1S5c24sJAfeLjzdb23/5pdlNt+uN+1FdvGiml5UpIw0c\n6J2MANKGkghIB/r0kSpWlJ59Vjp//sbHFi9uiqIsWaSGDaXNm72TEQCAQPLpjk917OKxmy5Y/fba\nt3U67rTeqP+Gl5IBnpGQYHbPXbTI7E6WkrWFhg6Vfv/djGzPlMnzGQGkHSURkA5kyGDmi//xh/Tq\nqzc/vkQJUxRlymSKoq1bPZ8RAIBA4nA6VCJnCd1/+/3XPeZE7Am9ve5tPVbuMVW/rboX0wHulZAg\ntW4tffaZ9M470nPP3fycDRukt9+WunSR7r3X8xkBuAclEZBO1KplPtDfe09at+7mx99+uymKMmSQ\nGjSQtm3zfEYAAALBtmPb9EPMD+pWo5tCrOs/To/5aYwuxl/UsPrDvJgOcK/ERKlNG+mTT6Tx46UX\nXkjZOV26mN1zR4/2fEYA7kNJBKQjI0eaLe87dzZzym+mVClTFIWFmaJoxw7PZwQAwN9FOaOUITSD\nOlS9/pZOR84f0Xu/vKenKz+t8nnKezEd4D6JidLTT5u1LceNk156KWXnTZggRUdL774r5czp2YwA\n3IuSCEhHsmWToqLMqKCRI1N2TunS0rffmp3S6teXdu70bEYAAPzZhfgLmrV5lh4v/7jyZMlz3eNG\n/DhCCckJer3u615MB7hPYqL0zDPS/PnSmDFmG/uU2LNHeu01qUULswsagMBCSQSkMw88YIYMjxwp\nbdmSsnPKljUjimzbjCjavduzGQEA8Fdzt8zVucvnbrhgdcyZGE2OnqyOVTvq9ly3ezEd4B5JSVL7\n9tLcudKoUVLfvik7LznZTDPLmFF6/33zJSOAwEJJBKRDEyZIOXJInTqZh4CUKFfOFEWJiWZE0Z49\nns0IAIC/sW1bDqdDlfJWuuF29sO+HybLsjTo3kFeTAe4R1KS1LGjNHu2NGKE1L9/ys+dMkX6/nsz\nNa1AAc9lBOA5lERAOpQ7t5kj/uuvpjBKqfLlzdSz+HhTFP32m+cyAgDgb3754xdtOLpBPSJ7yLrO\nEIndJ3frg00fqEdkDxXOXtjLCYG0SU42a1fOmiUNGyYNHJjycw8eNCOOGjY0JROAwERJBKRTTzwh\nPfywmTOemrKnYkVp5UopLs4URfv2eS4jAAD+xOF0KGuGrHq68tPXPWbIqiHKGJZRr9z9iheTAWn3\n91SxmTOlIUPMM2JK2bbUo4cZhTR5MtPMgEBGSQSkU5YlTZwohYebBwLbTvm5lSuboig21hRF+/d7\nLCYAAH7h1KVTmr9tvp6u9LSyZcx2zWO2/LlF87bO04s1X1S+rPm8nBBwXXKy1L27NH26KYdeT+V6\n63PnSl99ZaanlSjhmYwAvIOSCEjHChaU3npLWrXKzCFPjSpVpBUrpPPnpXr1pJgYTyQEAMA/fLDx\nA8UlxqnHHddfsPq1715TtozZ1LdOClf5BfxAcrL07LPmWXDgQGno0NSdf+yY9OKLUq1a0gsveCYj\nAO+hJALSuc6dzWigvn2lQ4dSd261atLy5dLZs6YoOnDAIxEBAPAp27YVFR2l2oVrq3K+ytc8Zt2h\ndfpi1xfqc1cf5cqcy8sJAdfYtvT889KkSdKAAdLw4amfKtazp/nScNo0KTTUMzkBeA8lEZDOWZb5\n5ighwcwlT820M0mqUcMURadPm7Lp4EHP5AQAwFe+/f1b7T65+7rb3tu2rVdWvqK8WfKq1129vJwO\ncI1tmxFADof5snDkyNQXRIsWSfPmSYMGmQ1OAAQ+SiIAuv12883Rl19K8+en/vzISGnZMunECVMU\n/fGH+zMCAOArDqdDt2a+VS3Lt7zm+8v3Ldeq/as06J5Bypohq5fTAaln21KvXtJ770kvvyyNHp36\ngujsWfMFY6VKUv/+nskJwPsoiQBIMkOFa9Y0c8mPH0/9+TVrSkuXmnnp9etLhw+7PyMAAN52+Pxh\nfb7zc3Wo2kGZwjJd9X6ynaxXVr6iotmLqmuNrj5ICKSObUu9e0v/+5/00ktmfUpXdiPr21c6etRM\nM8uQwf05AfgGJREASWYO+fTp0rlzZm66K2rVkpYskY4cMUXRkSPuzQgAgLdNXT9VSXaSukV2u+b7\nn2z/ROuPrNew+sOUMSyjl9MBqWPbUr9+0vjxZqrZ22+7VhAtW2aWK+jdW7rjDvfnBOA7lEQA/lGh\ngtnydMEC6eOPXbtG7drSN9+YKWcNGphvmAAACESJyYmaHD1Z999+v0rmKnnN9wd9N0gV8lRQm0pt\nfJAQSDnbNotTv/WW9Nxz0oQJrhVE585JXbpIZctKw4a5PycA36IkAnCFfv3MYtTPPmvWGHLF3Xeb\noujgQVMU/fmnezMCAOANX+7+Un+c/+O6C1bP3DhTu0/u1ogGIxQawrZO8F+2Lb36qjRmjFlH6N13\nXSuIJPOseOiQNGOGlOnqGZgAAhwlEYArhIWZD/0zZ1yfdiZJ99wjffWVFBMjNWxo1ioCACCQOJwO\nFbqlkB4s/eBV711KuKSh3w9VrUK19HCZh32QDkgZ25YGD5befFPq2tUsVu1qQbRihTRpklnsulYt\n9+YE4B8oiQBcpVIl8zAxf770ySeuX6duXbNj2r59UqNGri2IDQCAL/x26jct27tMXap3UVhI2FXv\nT/x1og6dO6Q3G74py9V/cQNeMHSo2cW2c2ez3X2Ii/8CPH/eXKN0aaaZAcGMkgjANfXvL1WvnrZp\nZ5JZwHrxYmnPHlMUpeVaAAB4yyTnJIVaoepcvfNV7527fE5vrn5T999+v+oVq+f9cEAKDRtmSqIO\nHcwIIFcLIsk8Gx44YEacZ87svowA/AslEYBrCg83DwGnT5vdL9KiYUNp0SJp1y7pvvukU6fckxEA\nAE+IS4zTjI0z1KJsCxXIVuCq98etGaeTl05qZIORPkgHpMyIEWZDknbtpKlT01YQffutGYX08stm\nkxIAwYuSCMB1Va4svfaaNHeu9NlnabvWffdJX3wh7dhhRhRRFAEA/NXCbQt18tLJay5YfeziMY1b\nO06Pl39cNQrU8EE64ObefFMaNEhq21aaNi1tBdGFC1KnTmaa2RtvuC8jAP9ESQTghgYMkKpWNTth\nnDyZtms1bmzKpm3bpPvvN6OUAADwNw6nQ6VvLa0GxRtc9d7IH0cqLjFOb9TnX8vwT2PGSAMHSk89\nZUaFh6Zx470BA8xGJNOnM80MSA9SVBJZltXEsqxdlmX9ZlnWgGu8X8SyrO8sy9pgWdZmy7KauT8q\nAF8ID5dmzjQFUc+eab9e06bSp59Kmzeb0ujMmbRfEwAAd9l0dJPWHlqr7jW6X7Ug9e+nf9fEXyeq\nY7WOKpO7jI8SAtc3bpxZO6hVK+mDD9JeEK1aJb3/vvTSS1KdOm6JCMDP3bQksiwrVNL7kppKKi+p\ntWVZ5f/fYYMkLbBtu5qkVpImujsoAN+pUsUMWZ4920wZS6sHHjC7pm3cKDVpIp09m/ZrAgDgDlHO\nKGUKy6R2Vdtd9d6g7wYpLCRMQ+oN8X4w4CbGj5f69JGeeEL68EMp7OpN+VLlwgWpY0epZEmzOxqA\n9CElI4lqSvrNtu19tm3HS5onqfn/O8aWdMtff88u6bD7IgLwB6+8Yqadde3qnh3KHnpIWrhQio42\nRdG5c2m/JgAAaXH+8nl9tOUjtarYSrky57rivQ1HNmjOljnqVavXNRezBnzpf/8zi0q3bCl99FHa\nCyJJ6tdP2r/fTDOLiEj79QAEhpSURAUlHfzP74f+eu2/hkh62rKsQ5K+lvTCtS5kWVZXy7KclmU5\njx8/7kJcAL6SIYMZtnz6tFmfyLbTfs3mzaUFCySn00xDO38+7dcEAMBVH23+SBfiL1xzweoBKwco\nV+Zc6lennw+SAdf33ntmOtijj0pz5pilAtJq2bJ/dzO75560Xw9A4HDXwtWtJc20bbuQpGaSPrQs\n66pr27Y92bbtSNu2I/PkyeOmWwPwlsqVpaFDpY8/lubPd881H3lEmjdP+vlnqVkzM7QZAABvs21b\nDqdD1fJX0x0F7rjivRX7VmjZ3mUadM8gZc+U3UcJgatNnCi98IL54m3uXPcURGfOmN3MypVjmhmQ\nHqWkJPpDUuH//F7or9f+q5OkBZJk2/ZaSZkk5XZHQAD+pW9fqVYt6dlnpSNH3HPNxx4zDzZr15r1\nii5edM91AQBIqTUH12jLsS3qEdnjigWrk+1k9V/RX0WzF9Wzdzzrw4TAlSZNkp57zkzhX7DAjPp2\nh5deMs94s2ZJmTK555oAAkdKSqJfJZWyLKu4ZVkZZBamXvT/jjkgqaEkWZZVTqYkYj4ZEITCwsy0\ns7g4qUsX90w7k6THHzcLY69eLT34oBQb657rAgCQEg6nQ7dkvEVPVXrqitfnb52v9UfWa3iD4coY\nltFH6YArTZkide9uvlxbuNB9BdEXX5jnvFdflSIj3XNNAIHlpiWRbduJkp6XtFTSDpldzLZZljXM\nsqyH/zqst6QulmVtkjRXUnvbdtc/HQH4m9KlpVGjpK++kmbMcN91n3zS7Mbxww/mWzGKIgCANxy/\neFwLty/UM5WfUZYMWf55PT4pXq9++6qq5KtyVXkE+Mr06WYjkaZNzW6xGd3UXR4/bq5brZopiQCk\nTyla99627a9lFqT+72uD//P37ZLquDcaAH/2/PPSZ5+ZIckNG0pFi7rnuk89JSUnS888Y+bXL1ok\nZc7snmsDAHAtMzbOUHxSvLpHdr/i9UnOSfr9zO9a0maJQq5ebhPwupkzpc6dpcaNpU8/dV9BZNtm\nY5IzZ6QVK9w3MglA4OHTDoBLQkLMKCLbljp2NMWOuzz9tHkIWrlSatHCTG0DAMATku1kTYqepHuL\n3qsKeSv88/q5y+c07IdhalC8ge6//X4fJgSMWbPMM1ejRtLnn7t3vaB588yopGHDpEqV3HddAIGH\nkgiAy4oVk8aPl779Vnr/ffde+5lnpGnTpOXLzQ5oFEUAAE9YtneZ9p3ed9W292+teUsnYk9odKPR\nVyxkDfjCRx9J7dtLDRqYdYPcWRAdPmwWwK5VS+rTx33XBRCYKIkApEmnTmZOfP/+0u7d7r12hw5m\nYcYlS8wOaJcvu/f6AAA4nA7lzZJXj5Z79J/Xjl44qnFrx+nJCk8qsgCr98K35syR2rWT6tVz/zR8\n2zbT1+LizILVoaHuuzaAwERJBCBNLEuaOtV8o9WunZSY6N7rd+okTZ4sff211LIlRREAwH0OnD2g\nL3d/qU7VOilD6L+LsAxdNVTxSfEa3mC4D9MB0vz5Utu20r33SosXSxER7r3+tGnSN99Io0ebjUkA\ngJIIQJoVKGCmm61bJ40Z4/7rd+kiORzSl19KTzwhxce7/x4AgPRnSvQU2batrjW6/vPajuM7NGX9\nFHWv0V0lc5X0YTqkdwsXSm3aSHXqmGegLFlufk5q7N1rNiBp0MBMNwMAiZIIgJu0amW2sH/9dSk6\n2v3X797dFFGLFpn7JCS4/x4AgPQjISlBUzdMVbNSzVQsR7F/Xu+/or+yZMiiwXUHX/9kwMM++URq\n3Vq66y4zmtrdBVFioln/MSzMbBYSwr8KAfyF/x0AcAvLkiZOlPLlM7uTXbrk/ns8+6z07rtmR49W\nrSiKAACu+3zn5zp64egVC1av2r9Ki3cv1it3v6I8WfL4MB3Ss88+M885d95pCqKsWd1/jzFjpDVr\nzLNb4cLuvz6AwEVJBMBtcuUy30bt3GkWsvaE55+XJkyQPv1UeuopiiIAgGuioqNUNHtRNSnZRJKU\nbCerz7I+KnxLYfW8s6eP0yG9+uILM7U+MtKsFZQtm/vvER1tRn4/+aQZrQQA/0VJBMCtGjWSevY0\nI36WLfPMPXr2lN5+W/r4YzNqyd2LZQMAgtuuE7v07e/fqluNbgoNMds5zds6T9FHojWiwQhlDnfj\n9lFACi1eLD3+uFS9utnZ9ZZb3H+PS5fMs1O+fGYUkWW5/x4AAluYrwMACD5vviktX262sN+yxYww\ncrdevaSkJKlvX7Nd66xZZl49AAA3E+WMUnhIuDpW6yhJikuM08CVA1UtfzW1qdzGx+mQHv29i2uV\nKtLSpVL27J65T//+ZsT38uWeeT4DEPgYSQTA7TJnlj76SDp+3Cw4bdueuU+fPtKoUdLcuVL79qY0\nAgDgRmITYjVz00w9Wu5R5cuaT5L07s/vKuZsjMbeN1YhFo/H8K4lS6RHHpEqVjSjsHPk8Mx9li0z\nI7179jQjvwHgWvgUBOAR1apJQ4ea7VvnzPHcffr3l0aOlGbPNiOXKIoAADcyf+t8nYk788+C1Sdj\nT2rEjyPUrFQzNSzR0MfpkN4sXSq1aCFVqGBG9+TM6Zn7nDplnpPKlTMjvgHgepicAcBj+vWTvvpK\neu456Z57pCJFPHOfV14x5dBrr5mpZ9OmsZUrAODaHE6Hyucpr3uL3itJGv7DcJ2PP68xjcb4OBnS\nmxUrTEFUtqxnp3/ZttSjh3TsmFn3KDNLbgG4Af4ZBcBj/l4rKClJatdOSk723L0GDZKGDDG7q3Xp\n4tl7AQACU/ThaP16+Fd1r9FdlmVp76m9ev/X99WxakdVyFvB1/GQjqxcKT30kFSqlCmLbr3Vc/ea\nM0dasEAaNswsig0AN0JJBMCjSpSQ/vc/adUqsyOZJ73+ujR4sDR9utStG0URAOBKDqdDEeEReqbK\nM5KkV1a+ovDQcA2rP8zHyZCefPedKYhKljRlUe7cnrvXgQNmRHedOmaENwDcDNPNAHhchw7Sl19K\nAwdKDRua9Yo8ZcgQM3JpxAgzkmniRKaeAQCkM3FnNGfLHLWp1EbZM2XXukPrtHD7Qr1e93Xdlu02\nX8dDOvH999KDD0rFi5uCKE8ez90rKclsd5+cbEZ2h4Z67l4AggclEQCPsyxpyhSpcmXpqaek6Ggp\nIsJz93rjDfNgNGqUKYjef9+8DgBIv2ZtmqVLiZfU444esm1bLy99Wfmz5lef2n18HQ3pxI8/Sg88\nIBUtKn37rZQ3r2fv9+ab5p6zZpmR3QCQEny/DsArbr3VPKTs2iW9/LJn72VZZsezfv0kh0N64QWz\naCMAIH2ybVtRzijVLFhT1W+rrgXbFmjtobUaXn+4smbI6ut4SAd++klq2lQqXNgURPnyefZ+P/9s\nRle3bm1GEwFASjGSCIDXNGwo9ekjjR0rNWlidvTwFMsyI4mSkqRx48wQ6wkTGFEEAOnR9zHfa8eJ\nHZrRfIbiEuPUf0V/VclXRe2rtvd1NKQDa9ea556CBU1BlD+/Z+93/rwZuV2okJl2z7MPgNSgJALg\nVcOHmzn4nTtLNWtKBQp47l6WZQqppCRTEIWEmMWzeVgCgPTF4XQoZ6acerLCk5qwboJizsZoevPp\nCg1hkRZ41rp1UuPGphj69lvpNi8sf/XCC9L+/Wb9oxw5PH8/AMGF6WYAvCpDBmn2bCk2VnrmGc/v\nQGZZphh68UVTFPXty9QzAEhPjl44qk93fKr2Vdvr3OVzGvnjSD1c5mE1KN7A19EQ5H75xRREefOa\nHc0KFvT8PefPlz74QHr1Venuuz1/PwDBh5IIgNeVLWsKm5UrTYHjaZZl7vf882bq2YABFEUAkF5M\nWz9NicmJ6h7ZXYO/G6xLiZc09r6xvo6FIOd0Svffb7a3/+47M/XL02JipG7dpFq1pMGDPX8/AMGJ\n6WYAfKJLF2nJEmngQLNWUbVqnr2fZUnvvGOmno0ZY6aejRzJ1DMACGZJyUmavH6yGhZvqMuJlzV1\nw1S9UPMFlb61tK+jIYitXy/dd5+UM6cpiAoX9vw9k5Kktm3NCO3Zs6Uw/pUHwEX87wOAT1iWNGWK\nVLmyWVwxOlqKiPD8Pd97zzxAjRplFrN+4w2KIgAIVt/89o0OnD2gcfeNU+9lvZU9Y3YNrssQC3jO\nhg1So0ZS9uymICpSxDv3Zbt7AO7CdDMAPnPrreZhZtcu6eWXvXPPkBCz00fnztKIEWZ7WABAcHI4\nHbot623KEJZBy/ct1+t1X1euzLl8HQtBatMmUxBly2YKomLFvHNftrsH4E6URAB8qmFDqU8fadIk\n6ZNPvHPPkBBzv44dpWHDpKFDvXNfAID3/H76d32z5xt1rNpR/Vf0V6lcpdTjjh6+joUgtXmzeaaJ\niDAFUfHi3rnv2bNsdw/AvZhuBsDnhg83D1SdO0uRkVLRop6/Z0iIme6WnGy+fQsNlQYN8vx9AQDe\nMTl6sizLUqbwTNp5Yqe+aPWFMoRm8HUsBKGtW01BlCmTeZ7x1nQv2zYLVcfESD/8wHb3ANyDkUQA\nfC5DBmnePLPo4lNPSYmJ3rlvSIg0dapZ6PG118x8fgBA4LuceFnTNkxT49sba8K6CapfrL4eKv2Q\nr2MhCG3fLjVoYJ5lvvtOKlnSe/eePt1seT9smFS7tvfuCyC4URIB8Au3326mgK1Z4911gkJDpRkz\npDZtzE5r/8fefYdHUXZ9HP9OGiX03gkIghRpCUV6780ACkhvCQFpIqDIIwqKhU4ISSjSe+81KEVK\ngNA7BCT0Tgqk7Lx/3I/vI1JDdncmyflc116rm92d3x86mZy573N++sl+xxZCCGEbK06v4E7kHVI5\npeJ+1H3G1R+HJvtwhJWdPq0KRI6OsGMHFC5s32P37atWMA0ZYr/jCiGSPtluJoQwjbZtYetWNZq+\nVi31sAdHR/jtN7X1bOhQ9e9ffGGfYwshhLA+v2A/8qbLy5pza+hWphulc5Q2OpJIYs6e/d91SlAQ\nFCliv2NHRcEnn0CaNDB3rrpuEUIIa5EikRDCVCZPVquJPvtMTQnJmtU+x3VyUpPWLBYYPFhdcA0Y\nYAEHeWMAACAASURBVJ9jCyGEsJ4Tt0+w6+ouimYuSmrn1IyqNcroSCKJOXcOatZU1ww7d0LRovY9\n/hdfwPHjsGED5Mxp32MLIZI+2W4mhDAVV1e1v/7+fejUSV2A2YuTE8ybB61awcCBMHGi/Y4thBDC\nOqYFT8PJwYkz984wotoIsqfJbnQkkYScP68KRLGxaovZBx/Y9/grVqgpZoMGQcOG9j22ECJ5kCKR\nEMJ0SpWCsWNh40aYMMG+x3ZyggUL4OOPoX9/tbJJCCFE4hAeHc7skNmkdk5N4UyF6Vuhr9GRRBJy\n8aIqEEVHw/btULy4fY9/5Qp066Ymwf7wg32PLYRIPqRIJIQwpd69oUUL1SMoONi+x3Z2VtPWWrSA\nzz9Xd+yEEEKY34LjCwiPCefxs8eMrz9eRt4Lq7l0SRWInj5VBaKSJe17/NhYNQE2Lk5do7jIf9pC\nCBuRIpEQwpQ0DWbMgBw54NNP4fFj+x7f2Vlte2vWDHx8YNo0+x5fCCFE/Oi6zuQDk3HQHKj/Xn0a\nFW5kdCSRRISGqgJRRARs2wYffmj/DN9+q3o2+vuribBCCGErUiQSQphWpkxq69fly+DlBbpu3+O7\nuMCSJdCkCXh7Q0CAfY8vhBDi7e0P28+J2ycAGF9/vIy8F1Zx5QrUqAFPnqgJrKUNGJS3fbvaXtal\ni5oEK4QQtiRFIiGEqVWpAt9/DwsXQmCg/Y+fIgUsWwaNGkGvXmp1kxBCCPMZvWs0AL3K9eKDrHbu\nJiySpKtX1QqiR49UgahsWftnuHFDbTMrWlT6JAoh7EOKREII0xs6FOrVU/2Bjh61//FTpIDly6FB\nA+jRA2bNsn8GIYQQr3Yv8h7rz60npVNKRtcabXQckQRcu6YKRPfvw5YtUK6c/TPExakC0ZMnsHSp\nmgArhBC2JkUiIYTpOTio0fSZM0Pr1vbvTwSQMiWsXAl166rJIrNn2z+DEEKIlxu0ZRA6Ol9U+oKM\nqTIaHUckcmFhaovZ3buweTN4eBiTY+RI2LlTDdCw9yQ1IUTyJUUiIUSikDWrmuZx8SL07Gn//kSg\nCkWrVkHt2qovwLx59s8ghBDieZExkcw/Pp/Uzqn5tsa3RscRidz162oF0e3bqkBUoYIxObZuhVGj\noHNn9RBCCHuRIpEQItGoWlVdMC1erKZ7GCFVKli9Wl1AduqkGmsLIYQwjs96H2ItsfSv0B9HB0ej\n44hE7MYNqFVLPW/aBBUrGpPj+nVo3x6KFQNfX2MyCCGSLykSCSESlSFDVG+g/v3hyBFjMqRODWvW\nQLVq0KGDWuEkhBDC/q4+usrcY3NxcXDhm+rfGB1HJGI3b6oC0bVrsHEjfPSRMTliY1UfoogINWE1\ndWpjcgghki8pEgkhEhUHB5gzB7JkgTZtjOlPBKp55Lp1avraZ5+phpJCCCHsy2e9D3F6HF3KdCGl\nU0qj44hE6vZttZX86lXYsEH9bjfKt9/C77+Dn59aSSSEEPYmRSIhRKLzd3+iy5fVtDEj+hOBKhSt\nXw+VKkHbtmoCmhBCCPvYcXkH686vA2DwR4MNTiMSqzt31Aqiy5fV7/Rq1YzLsnkz/PADdO0KHTsa\nl0MIkbxJkUgIkShVqQKjR6ul2NOmGZcjTRp117FCBfj0UzUBTQghhA3Nn4+ePz81CtYmdDyMvlGc\n9zK9Z3QqkQjdvatWEF26pFYH16hhXJawMLUyuXhxmDzZuBxCCCFFIiFEojV4MDRqpPoTBQcblyNt\nWtW/wMNDbYFbvdq4LEIIkaTNnw89e6JdvYoDkP8RfDn7gnpdiHi4d08ViM6fh7Vr1Woio8TEqBXJ\nUVFq+7r0IRJCGEmKREKIROvv/kQ5ckCrVnD/vnFZ0qVThaKyZaF1a3XBKYQQwsq+/hoiI597yenp\nM/W6EG/p/n2oUwfOnlU3dmrXNjbPsGGwaxcEBEDRosZmEUIIKRIJIRK1zJnVXbfr19UybYvFuCzp\n06t+AqVLg6en6m0ghBDCevQrV+L1uhD/9uCBKhCdPq0KRPXqGZtnxQoYOxZ8fNRUMyGEMJoUiYQQ\niV758jBxolrJ88MPxmbJkAG2bIEPP4SPP1aZhBBCWEec9orX5YpWvIWHD6FuXTh5UvUQrF/f2Dzn\nzkHnzqqv4dixxmYRQoi/ya9UIUSS4OWlVhKNGAFbtxqb5e9CUfHi0LKlWl0khBAiYeIscTi8Ypql\ng4GrSEXi8OiRWjV07JiaRtqwobF5IiLUqmMXF7UiOkUKY/MIIcTfpEgkhEgSNE1NOStWTDV/vHrV\n2DyZMsG2bfDBB9C8ufGFKyGESOxmHpnJ1fQv/9n1jI72DSMSlceP1aqhkBBVIGrSxNg8uq5ubp08\nCQsXQt68xuYRQoh/kiKRECLJcHVVF3/R0ap59LNnxub5u1BUpAg0awbbtxubRwghEqsHUQ/4asdX\nTG6egwjn538W4QyhX/Y0JpgwvSdPoEEDOHRIrdhp2tToRODvD/PmwciRavubEEKYiRSJhBBJSpEi\nMGsWHDgAgwYZnUY11t62DQoVUhemQUFGJxJCiMRn+I7h3I+6T/nBE+jRFK5mcMACXMvoyJHvvKky\ndKrREYUJPXmitpUdOACLF6uVvUY7cAD69VO5ZCifEMKMNF1/xeZuG3N3d9eDg4MNObYQIukbNAjG\njYP5880xLeT2bahVCy5fhg0boHp1oxMJIUTicOj6ITwCPehTvg/RcdHMOTqHsIFhZEyV0ehowsTC\nw6FRI9i7FxYtglatjE4E9+5B2bJqi/zhw2rFsRBC2IKmaYd0XXd/l8/KSiIhRJI0ZgxUqQI9esCJ\nE0angWzZ1Haz/PnVReuuXUYnEkII87PoFnpv6E0212wM/mgw847N49MSn0qBSLxWRAQ0bqwKRAsW\nmKNAZLGoARs3b8KyZVIgEkKYlxSJhBBJkrOzWlqeNq0aRf/okdGJIHt22LED8uVTy8z37DE6kRBC\nmNv0w9M5EHaAX+v9ytpza4mIicDb3dvoWMLEIiPV9u7du1XfnzZtjE6kfPstbNoEkyaB+zvd2xdC\nCPuQIpEQIsnKlQuWLFFbvDp0UHfxjJYjhyoU5c6tGmnu3Wt0IiGEMKe7kXcZtn0Y1fJXo12JdvgF\n+1E2Z1ncc8lf2OLl/i4Q/f47zJ0Ln35qdCJl9Wr4/nvo0gV6So91IYTJSZHIbObPBzc3cHBQz/Pn\nG51IiEStWjXVm2jtWhg1yug0Ss6cqoF1zpyqULRvn9GJhBDCfIZtG8ajp4/wbeTL3mt7OXH7BN7u\n3miaZnQ0YUJRUaoxdVAQzJ5tjn6EAGfOqBtV7u4wdarqRySEEGYmRSIzmT9f3V64cgV0XT337CmF\nIiESqE8fdYH2n//AunVGp1Fy5VIXstmyQf36atqJEEIIZd+1fUw/Mp3+FftTIlsJ/IL9SJ8iPW1L\ntDU6mjChp0+hRQvV+2/WLNX7xwweP4aWLSFlSlixQj0LIYTZSZHITL7+Wq2T/afISJmPKUQCaRr4\n+0OZMurC8fx5oxMpuXOrQlGWLFCvHsjARyGEgDhLHL3X9yZX2lz8p/p/uBNxh2WnltGxVEdcXVyN\njidM5ulTVYjZuhVmzIBOnYxOpFgs0LmzuuZYsgTy5jU6kRBCvB0pEpnJ1avxe10I8dZSpVJ38Zyc\n1N3G8HCjEyl586pCUaZMULeuGokrhBDJmV+wH0duHmF8/fGkTZGWmUdmEh0XjZe7l9HRhMk8ewae\nnqohdGCg6vljFmPGwMqV8MsvUKOG0WmEEOLtSZHITPLli9/rQoh4cXODRYtUf4AuXdSuTjPIl08V\nitKnhzp14MgRoxMJIYQxboXfYviO4dQpWIfWxVpj0S34H/Knev7qFMtazOh4wkSio6F1a9iwQa0W\n7tbN6ET/s3EjDB+u+iL17290GiGEiB8pEpnJ6NGQOvVzL0W5OGAZbZJuu0IkAXXqqLt7y5apu3tm\nkT+/KhSlTasyHj1qdCIhhLC/L7d9SWRMJFMaTkHTNDZf2Mzlh5dl7L14TnS0Gm2/di34+ZlrYtjF\ni6o49OGHanWTNKoWQiQ2UiQyk/btISAAUqQAIDxnZro1sTC9aOQbPiiEiI8vvlAXl8OGqR4GZlGg\ngCoUubpC7dpw7JjRiYQQwn7+uPIHc47OYfBHgymSpQigtp5ld81Oyw9aGpxOmEVMjBptv3o1TJkC\nXibahRgRofojaZra4v6ve79CCJEoSJHIbNq3h1On4OJFXMPucL1pdYZuG8rtiNtGJxMiydA01dyy\nWDF1oXn5stGJ/qdgQVUoSplSFYpOnDA6kRBC2F50XDRe67xwy+DG19XUwI6rj66y/vx6upXphouj\ni8EJhRnExEDbtqrXz6RJ4ONjdKL/0XW15e3ECVi4UP0+F0KIxEiKRGZUsCAULIimafg19iM8Opwv\nt35pdCohkpQ0adRFpsUCzZubp5E1wHvvqUKRiwvUqgUnTxqdSAghbOvXvb9y+u5pfBv5ktpZLb8I\nOBSAruv0LGeivUTCMLGx6l7q8uUwfjz07Wt0oueNGQOLF8MPP0D9+kanEUKId/dWRSJN0xpomnZW\n07QLmqYNfcV72miadkrTtJOapi2wbsxkZts29QA+yPoBX3z0BbOPzub30N8NDiZE0lKokLqgO3kS\nOnZUBSOzKFxYFYqcnFSh6PRpoxMJIYRtXHpwie//+J5WxVrRqHAjQK0smn54Oo3fb0z+DPkNTiiM\nFhsLn30GS5fC2LHmawa9di18/bVa5TRkiNFphBAiYd5YJNI0zRHwBRoCxYC2mqYV+9d7CgPDgMq6\nrhcHTHbqTmRGjVKP/xpebThuGdzwXu9NdFy0gcGESHrq1YNff1Wrir77zug0z3v/fdixQ22Pq1UL\nzp41OpEQQliXruv4bPDB2cGZCfUn/P/rq8+s5lbELWlYLYiLg06d1E2dn3+GgQONTvS8U6fUCqcy\nZWD6dGlULYRI/N5mJVF54IKu65d0XY8GFgHN//WeHoCvrusPAHRdlwY6CTF3rnr8V2rn1ExpOIXT\nd08z7s9xBgYTImnq319dgI4cqZaxm0nRompFkcUCNWvCuXNGJxJCCOtZemopmy5sYlStUeROl/v/\nX/cL9sMtgxv135N9O8lZXBx07gwLFqjtXIMHG53oeQ8eqC3rqVPDqlXSqFoIkTS8TZEoN/DXP/79\n2n9f+6f3gfc1Tdujado+TdMaWCtgspQ3r3r8Q+P3G9OyaEu++/07Qh+GGpNLiCRK02DaNKhYUW07\nM9tUsQ8+UIWi2FhVKDp/3uhEQgiRcI+ePqLfpn6UzVkWH4//dSA+c/cMQaFB9CrXC0cHRwMTCiPF\nxUHXrjBvHowebb5tXLGx8MkncOWKusH0r0t3IYRItKzVuNoJKAzUANoCgZqmZfj3mzRN66lpWrCm\nacF37tyx0qGToE2b1ONfJjaYiIPmQN+NfdF13YBgQiRdKVOqcbUZM6q7gnfvGp3oecWKqa1n0dGq\nUHTxotGJhBAiYYbvGM6t8Fv4N/F/rhg0LXgazg7OdC3T1cB0wkgWC3TvDnPmqK3gX31ldKIXffkl\nbN0Kfn5QubLRaYQQwnrepkgUBvyzNp7nv6/90zVgja7rMbquXwbOoYpGz9F1PUDXdXdd192zZs36\nrpmTvjFj1ONf8qbPy8gaI1l3bh0rTq8wIJgQSVvOnKo30Y0b0Lq1GrVrJiVKwPbt8PSpKhRdumR0\nIiGEeDcHww7ie9AXHw8f3HO5///rkTGRzD46G89inmRzzWZgQmEUiwV69oTffoNvv4VvvjE60Ytm\nz/7fhLVu3YxOI4QQ1vU2RaKDQGFN0wpomuYCfAqs+dd7VqFWEaFpWhbU9jP58+VdLVqkHi/Rr2I/\nyuQoQ9+NfXn09JGdgwmR9Hl4wIwZsHOn+aanAHz4oSoURUSoQlFoqNGJhBAifmItsfRa14scaXIw\nqtao53626MQiHj59KA2rkymLBby81O/hb76B//zH6EQv2rdPFbFq1VKT1oQQIql5Y5FI1/VYoA+w\nGTgNLNF1/aSmad9pmtbsv2/bDNzTNO0UEAQM1nX9nq1CJ3k5cqjHSzg5OBHQNIBbEbcYtn2YnYMJ\nkTy0b6+aY06dCv7+Rqd5UalSsG0bPHkCNWqofghCCJFYTDkwhSM3jzCxwUTSp0z/3M/8gv0onrU4\nVfNVNSidMIqug48PBAaq7WUjRxqd6EVhYdCyJeTJA0uWgLOz0YmEEML6NKN627i7u+vBwcGGHNv0\n1q5Vz02bvvIt/Tf1Z9L+SezpuodKeSvZKZgQyUdcHDRrBlu2qEfNmkYnetGhQ1CnjuqjtHMn5Mtn\ndCIhhHi9a4+v8YHvB1TJV4UN7Tag/WNeePD1YDwCPZjccDJ9yvcxMKWwN12HPn3UzZmhQ+GHH8w3\nSj4iAqpVU1NG//xTbQEXQgiz0jTtkK7r7m9+54us1bhaWNPYsW9cv/p9ze/Jky4PPdf1JCbOZI1T\nhEgCHB1h4UIoUgQ8Pc05er5cOdU08/59VcT66683f0YIIYyi6zo+G3yIs8Th28j3uQIRgN9BP1I7\np6bDhx0MSiiMoOvw+eeqQDR4sDkLRBaLmn4aEqI6QkiBSAiRlEmRyIyWLVOP10ibIi2+jXw5cfsE\nv+791U7BhEhe0qVTC/scHdXCvgcPjE70Ind3tdLp7l1VKAr791gBIYQwiRWnV7Dm7BpG1hhJwYwF\nn/vZg6gHLDyxkPYl27+wBU0kXboOAwbAlCkwcCD89JP5CkSg+iOtWAG//gqNGxudRgghbEuKRGaU\nJYt6vEHTIk3x/MCT7/74jov3ZR62ELZQoACsWqUaRLdqZb6JZwDly8PmzXD7tioUXb9udCIhhHje\nw6cP6buxL6VzlGZApQEv/HzO0TlExUZJw+pkRNdh0CCYOFENivj1V3MWiObOVaubevQw50ALIYSw\nNikSmdGKFerxFiY1nISLowte670wqr+UEEld5cowfTrs2KF6Jpjxf7WKFWHTJrhxQxWKbtwwOpEQ\nQvzP0G1DuRVxi+lNp+Pk4PTcz3RdZ9qhaVTIXYEyOcsYlFDYk67Dl1+qMfKffw7jxpmzQLRnD3Tv\nrn6v+vqaM6MQQlibFInMaNIk9XgLudLm4sfaP7Lt0jbmH59v42BCJF8dOsCwYRAQoO56mtFHH8HG\njWrLWa1acPOm0YmEEAJ2XdmF/yF/+lfoT7lc5V74+c7QnZy5e0ZWESUTuq5+n/76q5pmNmGCOYsv\nly9DixaQP7/qAiGTzIQQyYVMNzOjR4/Uc/q325Nv0S1UmVmF8/fPc8bnDJlTZ7ZhOCGSL4sFWrdW\n28/WroVGjYxO9HK7dkHDhurCdscOyJ7d6ERCiOTqWewzSvuXJiomipO9T+Lq4vrCe9osbcO2S9sI\nGxhGKudUBqQU9qLr8PXX8OOP4O1t3tU5jx+rGy9hYbB/P7z/vtGJhBAifmS6WVKTPv1bF4gAHDQH\nApoG8PDpQ77Y+oUNgwmRvDk4wJw5ULo0fPopnDhhdKKXq1oV1q9XfZRq11a9ioQQwgg/7v6RM3fP\nMK3JtJcWiG6G32TlmZV0Kd1FCkRJnK7DiBGqQNSzp2pWbcYCUWys+h1/5oxaQSQFIiFEciNFIjNa\nvFg94qFEthJ8+dGX/BbyG9subbNRMCGEqyusWQNp0kCTJnDrltGJXq56dVi3Di5dgjp11PQzIYSw\np1N3TvHDrh9oV7IdDQo1eOl7ZhyeQawlFi93LzunE/Y2ciSMGqV6/Pj5qRsvZvTFF2rr9tSp6kaL\nEEIkN7LdzIxq1FDPO3fG62NPY59SelppnsU944T3iZfesRNCWEdwMFSrBiVLQlAQpE5tdKKX275d\nFbPef19tPcssu1GFEHZg0S1Um1WN03dPc9rnNNlcs73wnjhLHAUnFeT9zO+ztcNWA1IKe/nuO/jP\nf6BLFzUIwqwFosmTVSPt/v1VU20hhEisZLtZUrNhg3rEU0qnlAQ2DST0YSjfBH1jg2BCiL+5u8PC\nhXDwIHz2GcTFGZ3o5WrXViufzp5VK4ru3zc6kRAiOQg4FMCev/Ywtt7YlxaIADac38DVR1fxKier\niJKy0aNVgahTJ3MXiNasUcWh5s1VU20hhEiuTHqaTuZSp37nZQlV81fF292bifsnsv/afisHE0L8\nU/Pm6k7jypVqlK9Z1a0Lq1fD6dOqUPTggdGJhBBJ2fUn1xmybQi1C9SmU6lOr3yfX7AfOdPkpFmR\nZnZMJ+xpzBgYPlxNCJ0xw7wFouBgaNsWypWD+fPB0dHoREIIYRyTnqqTuXnz1OMdjakzhlxpc9F9\nbXei46KtGEwI8W/9+qml6ePGqSacZlW/vipmnTypikYPHxqdSAiRFOm6jvd6b2LiYpjWZBraKzoT\nX35wmU0XNtGjbA+cHWW2eFL0889q1H27djBrlnkLL1euqG3Z2bKpyaWu0q1BCJHMSZHIjKZPV493\nlC5FOqY1nsaJ2ycYs3uMFYMJIV5m3Dho1kwVjNatMzrNqzVsCCtWwLFjUK+eFIqEENa3+ORi1pxd\nw/c1v6dQpkKvfJ//IX8cNAd6lOthx3TCXsaOhSFD1JSw2bPNWyB6+BAaNYKnT9VU0OzZjU4khBDG\nk8bVZhQTo56dE3Znrd3ydiw7tYwQrxCKZS1mhWBCiFeJiFATxU6fhj/+UEvWzWrtWvD0hLJlYcsW\nSJfO6ERCiKTgTsQdik0tRsGMBdnbdS+ODi+vDDyLfUae8Xmokq8KKz9ZaeeUwtbGj4eBA6FNG7V1\ny8nJ6EQvFx2tbp7s2gWbNkGtWkYnEkII65HG1UnI7jG9uZY9FRYXF65lcmL3mN7v/F0TG0wkXYp0\ndFvTjTiLSbvqCpFEuLqqVURZs6pl61evGp3o1Zo2haVL4dAhaNAAHj82OpEQIinot6kfj54+Ymaz\nma8sEAEsP72cu5F38Xb3tmM6YQ+TJqkCUatWqnOCWQtEug69eqmpn9OnS4FICCH+SYpEJrJ7TG/K\njPAjz4M4HIA8D+IoM8LvnQtFWV2zMqHBBPZd24fvQV/rhhVCvCBHDrVcPSpKLV9/9MjoRK/WvDks\nWaKmszVsCE+eGJ1ICJGYrT27loUnFjK82nCKZyv+2vf6BfvxXsb3qFOwjp3SCXuYMkVtu/74Y1iw\nIMEL4m1q1Cj47Tf49lvo2NHoNEIIYS5SJDIRt58DcI15/jXXGPX6u2pfsj0NCzVk2PZhhD4MTVhA\nIcQbFS8Oy5erkfOenmo5u1m1bAmLFsH+/aqoFR5udCIhRGL06OkjvNd7UzJbSYZWGfra9x6/dZzd\nV3fj5e6FgyaXoUmFnx/07atuQCxcaO4C0dy5MGKEKg6NGGF0GiGEMB/57WwiuR68fEtYrgdxzA6Z\nzdPYp/H+Tk3T8Gvsh4PmQM+1PTGqB5UQyUnt2mrU7/bt0KULWCxGJ3o1T091Qf/nn9C4seqtJIQQ\n8TF462BuhN9gRrMZuDi6vPa904KnkcIxBV1Kd7FTOmFr/v7Qu7fayrxkCbi8/j8BQ23eDF27qu1l\ngYHwiuF7QgiRrEmRyESuZ3z5/v2/0kPn1Z3JMy4PQ7cNjfeKoPwZ8vNTnZ/YemkrM4/MtEJSIcSb\ndOwIP/ygltwPGWJ0mtdr3Vo1F929W/VTiow0OpEQIrHYcXkHgYcDGVRpEB65PV773vDocOYem0ub\n4m3InDqznRIKWwoMBC8vdZNh6VJzF4gOHVI3RooXh5UrzZ1VCCGMJEUiEwn9sicR/1qeG+EMfw3x\nZnvH7VTLX41f9v5CwYkFabawGZsvbMaiv90SBS93L2q41WDgloFce3zNBumFEP82dCj4+MCvv8KE\nCUaneb1PPlFL8P/4Q90NlkKREOJNIqIj6L6mO4UzFWZkjZFvfP/8Y/N5Ev1EGlYnETNnQs+eqq/d\n8uWQIoXRiV7t0iW1rTpLFtiwQaZ6CiHE60iRyESqDJ3Kke+8uZbREQtwLaMjR77zpsqwqdQqUIsV\nn6wgtF8oX1X9iv1h+2kwvwFFpxRlwr4JPHz68LXf7aA5ML3pdGItsbLtTAg70TSYOFE18Rw4UC3D\nN7N27WD2bAgKUn0loqKMTiSEMLPhO4Zz+eFlpjebTirnVK99r67r+AX7USp7KSrmqWinhMJWfvsN\nuneH+vVhxQpzF4ju3FE5Y2PVqPtcuYxOJIQQ5qYZVSxwd3fXg4ODDTl2UvAs9hnLTy9nyoEp/Hnt\nT1I7p6Z9yfb4ePhQKkepV35u0v5J9NvUj1nNZ9G5dGf7BRYiGYuKgnr14MAB1Q+hRg2jE73enDnQ\nuTPUrQurV0PKlEYnEkKYzd6/9lJlZhW83b3xbfzmCar7ru2j0oxKTGs8jV7uveyQUNjK378j6tSB\nNWvM/TsiIkL1Hzp2TPUJ/OgjoxMJIYR9aJp2SNd193f6rBSJEr8jN47ge9CXBccXEBUbReW8lfHx\n8MGzmOcLDSQtuoUav9Xg2K1jnOx9ktzpchuUWojk5cEDqFIFwsJg1y4oWdLoRK83axZ066buvq5c\nae4/AoQQ9hUVE0Vp/9I8i33Gce/jpE2R9o2f6bSqEytPr+T6oOukcUljh5TCFubPhw4dVOFl7VpI\n9foFZIaKjYUWLWDjRrXaqXlzoxMJIYT9JKRIJNvNkoAyOcswvdl0wgaGMbbeWG6G36TdinbkG5+P\nEUEjCHsc9v/vddAcmNFsBtFx0fRa10u2nQlhJxkzqgvVNGmgQQO4etXoRK/XpYtqSLppk2r0+eyZ\n0YmEEGYxfMdwzt07x4xmM96qQHQv8h6LTyymw4cdpECUiC1cqIYy1KihVhCZuUCk66qh9vr1MHWq\nFIiEECI+pEiUhGRMlZGBlQZyru85NrbfiHsud0b9MYr8E/LTakkrgi4Hoes6hTMXZnSt0aw/v555\nx+YZHVuIZCNfPlUoCg9XjT7v3zc60et16wYBAarJZ6tWUigSQsCeq3sYv2883u7e1C5Y+60+c6vW\n8gAAIABJREFU81vIbzyLe4aXu5eN0wlbWbwYPvsMqlVTK4hSpzY60et9+y3MmAHDh0Mv2d0ohBDx\nItvNkrhLDy4xLXgaM47M4H7UfYplLYaPhw/tSrSj8cLGnL5zmpO9T5IzbU6jowqRbOzcqbZxlSsH\nW7eCq6vRiV5v2jTw9oZmzcw/4lgIYTuRMZGUmlaKWEssx72Pv9WqIItuociUImR3zc7urrvtkFJY\n29Kl0Lat6uezcaP5f2dNmQJ9+6oVsTNmqCESQgiR3Mh2M/FKBTMW5Oe6P3NtwDVmNZ9FKqdU+Gzw\nId+EfLildyMyJhLv9d6y7UwIO6pRAxYtgv371Qqd6GijE72elxf4+qrtBZ98AjExRicSQhjh6+1f\nc+H+BWY2m/nW28a2X9rOhfsXZOx9IrV8uSoQVaqkVpWavUC0YIEqEDVvrlbCSoFICCHiT4pEyUQq\n51R0Lt2Zgz0Osq/bPloUbcGy08t4FveM1WdXM2DzAGItsUbHFCLZaNnyfz1/OnUCi8XoRK/XuzdM\nngyrVsGnn0qhSIjkZteVXUzcP5He7r2pWaDmW3/OL9iPLKmz0KpYKxumE7awcqU631eooApEaUze\nTmrjRvX7tHp1dSPGycnoREIIkThJkSiZ0TSNCnkqMKflHK4NuMboWqNxcXRh4v6J5B2Xl1F/jOJW\n+C2jYwqRLHTtCj//rC5mP/9cNdo0sz59YMIENSWmfXs1OUYIkfRFREfQdU1X3DK48VPdn976c2GP\nw1hzdg1dS3clhVMKGyYU1rZmDbRpA+7uqviS9s39yQ21d68asvDhhyq7TOQUQoh3J0WiZCyra1a+\nqvoVR3oewcXRhVg9lm+CviHv+Ly0W96OPVf3yDY0IWxs8GD48ku1nWvkSKPTvFm/fjBunOpRUbUq\n5M8PDg7g5qZGIwshkp6vtn+ltpk1f/ttZgCBhwOx6BZ6uUvnYLObP1+dxx0cIFs2tdq1bFm12jVd\nOqPTvd7x49C4MeTJowpaZs8rhBBmJ0UiQbFsxfil7i/cjbzL6Fqj6e3Rmw3nN1BlVhXK+Jch8FAg\nEdERRscUIskaM0ZNEhs5Um3pMrsBA1SPin374OpVtQLqyhXo2VMKRUIkNX9c+YNJBybRx6MPNdxq\nvPXnYuJiCDwcSP1C9SmYsaDtAooEmz9fnb+vXFHn8zt31Ovdu0P69MZme5NLl9QgCFdXNQgiWzaj\nEwkhROIn080EoKaP1J5Tm0PXD3Hc+zhZUmdh/vH5+B705ditY2RImYEupbvg7e5N4cyFjY4rRJIT\nG6uW9q9cCfPmqe1cZubmpv6g+Lf8+SE01N5phBC2EB4dTulppdHROeZ1DFeXt+9avOL0CjyXeLL6\n09U0K9LMhilFQiXW8/nNm1ClCjx4ALt2QbFiRicSQgjzSMh0MykSif8X+jCUkn4lKZ+7PFs7bMVB\nc0DXdXZf3Y3vQV+Wn15OrCWW+u/Vx8fDh0aFG+Ho4Gh0bCGSjKdPoVEjdbG7erX6Z7NycFB3nIOo\nAUBNdgJqkozZm3ALId5O7/W9mRY8jaBOQVR3qx6vz9adW5ezd89yud9luVYwucR4Pn/4UE0KvXAB\ntm9XzbWFEEL8T0KKRLLdTPw/twxujK8/nh2Xd+B7wBdQja6r5q/KolaLuNr/KiNrjOT47eM0W9SM\nQpML8dPun7gbedfg5EIkDSlTqulhpUqpBpw7dxqd6NXy5VPPv9GZ3+j8/6/nzWtMHiGEdW2+sBm/\nYD8GVhoY7wLR+Xvn2XZpGz3L9ZQCUSKQNat6/vf5/O/zvNmEh6ubKKdOqUEKUiASQgjrkpVE4jm6\nrtN4QWN2hu4kxCuE9zO//8J7YuJiWH12Nb4HfdkZupMUjin4tMSn+Hj44JHbw4DUQiQtd++qEb5X\nrsC2bVCxotGJXvR3D4vIyOdfr14dduxQd6aFEInT/aj7lPQrSYaUGTjU8xApneI3KmrQ5kFMOjCJ\nvwb8RY40OWyUUljDjh2qp09c3PMTNlOnhoAA8219jopSTar/+AOWLIGPPzY6kRBCmJOsJBJWo2ka\n05tNJ6VTSjqt6kScJe6F9zg7OtOqWCuCOgVx3Ps4Xct0Zfnp5ZSfXp7ygeWZHTKbp7FPDUgvRNKQ\nJYsqDuXIAQ0bQkiI0Yle1L69+gPivXwxOBND/vxqGs7vv0OvXubdoiCEeLM+G/pwO+I2c1vOjXeB\nKComit+O/kbLoi2lQGRyO3dCkyZQtChMnfr8+dyMBaLoaGjdWuX+7TcpEAkhhK1IkUi8IFfaXPg2\n8mXftX38uvfX1763RLYSTG08lbCBYUxuOJkn0U/ovLozecblYei2oYQ+DLVPaCGSmJw5VZ+FtGmh\nXj04fdroRC9q3x4uFKhLdPW6hIbC8uXw9dcwfTr07i2FIiESo8UnFrPwxEJGVBtB2Zxl4/35paeW\ncj/qPt7u3jZIJ6zl99/VipwCBdTvGi+v58/nZisQxcXBZ5/B+vXg56f+WQghhG3IdjPxUrqu02ZZ\nG9acXUNwj2BKZi/51p8LCg3C96Avq86sQtd1mrzfBB8PH+q+VxcHTeqSQsTH+fNQtSo4OqqG1gXN\nNkl63jz1/N8rdl2Hr76CMWPA2xt8fVXzUyGE+V1/cp2SfiUplKkQe7ruwcnBKd7fUWlGJR5EPeC0\nz2k0+Z/flHbtUqtU8+WDoCDInv2/P/jX+dwsLBbo1k2tHho7FgYONDqREEKYn0w3EzZxJ+IOJfxK\nkDNNTvZ3308KpxTx+vxfj/7C/5A/gYcDuR1xm0KZCtHbvTedS3cmY6qMNkotRNJz4oTq9ZMunbq4\nz5PH6ESvp+swZAj88gv06QOTJkmhSAiz+7snYVBoECG9QiiSpUi8vyPkZghl/Mswvv54+lfsb4OU\nIqH27IEGDSB3brVtK4fJdwTqOvTtq244fPst/Oc/RicSQojEQXoSCZvI6pqVGc1mcPTWUUYEjYj3\n5/Omz8uoWqO42v8q8z+eTzbXbAzcMpDc43LTc21Pjt48aoPUQiQ9JUrA5s1w7x7Urg23bhmd6B8i\nI1/oXq1p8NNPMGgQTJkC/fs/3xBVCGE+gYcD2XhhIz/X+fmdCkQAfgf9SOWUik6lOlk5nbCGP/9U\nBaJcudQKohcKRC85nxtJ12HoUFUg+uILGBH/S1EhhBDvQFYSiTfqtbYXgYcDCeoUFO8xuP925MYR\nfA/6suD4AqJio6ictzI+Hj54FvPExdHFSomFSJp271b9iQoXVhf4mTIZnQioUUM979z5wo90XW0L\nmDABBgxQ2wRkRZEQ5nPpwSU+9PuQinkqsqXDlnfaGv742WNyjc1Fm+JtmNl8pg1SioTYvx/q1lVb\ny3buVCuJXvCa87kRRo2Cb75R/ZKmTpXfH0IIER+y3UzYVHh0OGX8yxAdF80xr2OkT5k+wd/5IOoB\ns0JmMfXgVC4+uEh21+z0KNuDXu69yJPO5HtphDDQ1q1qGk2JEmoCWkajd24uXqyeP/nkpT/WdbWS\naNIktbLol1/kQl8IM4mzxFFjdg2O3zrOce/j5E2f952+x/eAL3029uFA9wN45PawckqREAcOqAJR\n1qyq/vPKLctvOJ/b008/qVVEHTqoXkQOsvdBCCHiRYpEwub2X9tP5ZmVaVeyHXNazrHa91p0C1su\nbsH3oC/rz63HQXOgRdEW+Hj4UMOthjS9FOIlNmxQ4+ZLlYItWyBDBqMTvd4/e0p8+aVqai3/awth\nDj/u+pGvdnzFnBZz6FCqwzt9h67rlPQrSUqnlAT3lGs7MwkOhjp1IHNmVSDK+241QLv69VcYPBja\ntoW5c9XgBiGEEPEjPYmEzVXIU4Hh1YYz99hclp5carXvddAcaFCoAWvbruXi5xcZWGkgQaFB1JpT\nixJ+JfA94MuTZ0+sdjwhkoJGjWDZMggJUf0lHj82MMyjR+rxGpoGkyeraWc//wxffy09ioQwg+Dr\nwYzYOYI2xdvw2YfvPtFq99XdnLxzUsbem8zhw2oFUcaMaovyGwtEb3E+t7UJE1SBqE0bmDNHCkRC\nCGEEWUkk3lpMXAxVZlXh/L3zHPc+Tu50L9vQnnBRMVEsPrkY34O+BF8PJo1LGjp+2BGf8j4Uy1rM\nJscUIjFatQpat4by5WHTJkib1oAQ8ehhYbGoQlFAgCoUff+9rCgSwigR0RGUDShLZEwkx7yOJWjq\naLvl7dhwfgNhA8NwdXG1Ykrxro4cUYMO0qaF338HN7e3+JDBPYkmT4bPPwdPT1i4EJydDYkhhBBJ\ngqwkEnbh7OjMvJbzeBb3jC6ru2DRLTY5TirnVHQu3ZmDPQ6yv/t+Pv7gY6YfmU7xqcWpNbsWy08t\nJ9YSa5NjC5GYtGgBixaphqSNGkF4uAEhPv9cPd6CgwP4+UH37jB6tBpnLIQwxqAtgzh/7zxzWsxJ\nUIHodsRtlp1aRqdSnaRAZBJHj6otZmnSqHrPWxWIIF7nc2ubOlUdukULKRAJIYTRpEgk4qVw5sKM\nqzeOrZe2MuXAFJsfr3zu8sxuMZtrA67xY+0fufTgEq2WtsJtghvf//49N8Nv2jyDEGbm6QkLFsDe\nvaqhdUSEnQN8/LF6vCUHB/D3h65d4bvv1EMIYV9rzq7B/5A/X3z0BTUL1EzQd808MpMYSwxe7l5W\nSicS4vhxtYIodWpVICpQIB4fjuf53FoCAsDHB5o2Vb2zpUAkhBDGku1mIt50XafZomZsu7SNQz0P\n2XULWJwljvXn1+N70JctF7fg7OCMZzFPfDx8qJy3sjS6FsnWwoXw2Wdqt8DateoPBLu4e1c9Z8kS\nr49ZLKpQNHu22nY2fLgNsgkhXnAz/CYl/UqSJ10e9nXbRwqnFO/8XXGWOApNLoRbBjeCOgVZMaV4\nFydOQM2akCKFKhAVKhTPL3jH83lCzJihVpc2agQrVqjsQgghEk62mwm70jSN6U2nk9YlLe2Wt+Np\n7FO7HdvRwZFmRZqx+bPNnO1zFh8PHzae30jVWVUp41+GwEOBRETbeymFEMZr21YVXIKCoHlziIy0\n04FbtVKPeHJwUH8cdOgA33wDP/5og2xCiOfouk63Nd0Ijw5n/sfzE1QgAth8cTOhD0OlYbUJnDoF\ntWqpVThBQe9QIIJ3Pp+/q1mzoEcPNYBh+XIpEAkhhFlIkUi8k+xpsjOr+SyO3jrKsG3DDMnwfub3\nGd9gPGEDw/Bv4o+OTs91Pck9LjcDNg3g/L3zhuQSwiiffQa//Qbbt0PjxnbqUTRokHq8A0dH9UdC\n+/bw1Vdq8pkQwnamHpzKhvMb+KXuL1ZZBTwteBrZXbPTomgLK6QT7+rMGVUgcnRUBaLChd/xixJw\nPo+vgAC1mrRuXbWCKGVKuxxWCCHEW5DtZiJBPt/4OZMPTGZDuw00LNzQ0Cy6rrPnrz34HvRl2all\nxFpiqf9efXw8fGhUuBGODjJHVSQPCxaoFToffQQbNhg09SweYmNV3kWL4Jdf4IsvjE4kRNJz6s4p\nygWUo6ZbTda3W5/g7dlXH12lwMQCDKsyjFG1RlkppYivs2fVNmNdV1vMihY1OtGb+fpCnz7qZsay\nZVIgEkIIW5DtZsIwP9f9mRLZStB5dWduhd8yNIumaVTJV4WFngv5a8BffFfjO47fPk6zRc0oNLkQ\nP+3+ibuRdw3NKIQ9tGunehT9+SfUrw+PHtnwYDdvqkcCODnB3LnQpg0MHgzjx1spmxACgGexz2i/\noj1pXNIws/lMq/TvCzgUAEDPcj0T/F3i3Zw7p3oQWSywY4cVCkRWOJ+/yYQJqkDUvLnaYiYFIiGE\nMB8pEokESemUkoWeC3n87DGdV3fGoluMjgRAjjQ5+Kb6N4T2C2Vp66W4ZXBj6Pah5BmXh06rOnEg\n7IDREYWwqTZt1JSYgwehXj14+NBGB/r0U/VIICcnmD9ftcMYOBAmTrRCNiEEAMO2DyPkZggzm80k\nR5ocCf6+6Lhoph+eTqPCjciXPp8VEor4unBBFYhiY1WBqJg1ZohY6Xz+Kr/8AgMGqAFqS5ZIDyIh\nhDArKRKJBCuRrQRj641l04VNTN4/2eg4z3F2dKZVsVYEdQrihPcJupXpxorTK6gwvQLlA8szO2S2\nXRtvC2FPnp5qKf+RI2ok8v37NjjI0KHqYQVOTmqr3McfQ//+MGWKVb5WiGRtw/kNjN83nr7l+9K0\nSFOrfOeqM6u4FXFLGlYb5OJFVSCKjlY96IoXt9IXW/F8/m8//ABffqluYCxaBC4uNjmMEEIIK5Ce\nRMIqdF2n+aLmbL64mQPdD1AqRymjI73S42ePmXN0Dr4HfTlz9wyZU2WmW5lueHt445bBzeh4Qljd\nhg2q8FK0KGzdClmzGp3o9aKj4ZNPYNUq1buid2+jEwmRON14coNS00qRM21O9nffT0on6+ztqTm7\nJqEPQ7nQ94L0+7OzS5dUD6LISFUgKmXey63/99138J//qCEFv/2mbggIIYSwLelJJAynaRozm88k\nc6rMtF3elsgYe83fjr90KdLRp3wfTvU+xfaO26nuVp2xf46l4MSCNF3YlM0XNptm25wQ1tCoEaxZ\noxqc1qoFt6zZPuyvv9TDilxc1Fa5Zs3Axwf8/a369UIkCxbdQsdVHQmPDmeR5yKrFYhO3znNztCd\n9CrXSwpEdhYaqlYQRUTAtm02KBBZ+Xyu6zB8uCoQde4Ms2dLgUgIIRIDKRIJq8mSOgtzWs7hzN0z\nDNpsnxGqCaFpGrUK1GJ5m+WE9g/l66pfcyDsAA3mN6DIlCKM/3M8D6IeGB1TCKuoVw/WrVN3oatW\nhatXrfTFHTqoh5W5uKieFY0bg5cXBAZa/RBCJGm/7v2VbZe2ManhJD7I+oHVvnda8DScHZzpWqar\n1b5TvNmVK6pA9PixWhFaurQNDmLF87nFovoPjR4N3bvDjBngKDVFIYRIFGS7mbC6IVuH8PPen1nR\nZgUtP2hpdJx4eRb7jOWnl+N70Je9f+0llVMq2pdsj095H0rnsMUVmRD2tWePWlmUIYO6E124cAK/\ncNs29VynToKzvcyzZ2qr3IYN6o+MrvJ3qRBvdCDsAJVnVqZl0ZYsbrXYKtPMACKiI8g9LjeNCjdi\ngecCq3yneLOrV9UWswcP1Cm3XDkbHchK5/O4OOjZE2bOVP3lxo0DK/0nKIQQ4i0lZLuZFImE1UXH\nRVN5ZmUu3L9ASK8Q8mfIb3SkdxJyMwTfA77MPz6fqNgoPsr7EX08+uBZzBMXR+m4KBKvI0fUyiJH\nR3VHumRJoxO93tOn0LIlbN6s/ujo3NnoREKY1+NnjynjX4Y4SxwhXiFkSJnBat894/AMuq/tzh+d\n/6Bq/qpW+17xateuQfXqcO+eOl97eBid6PWio+Gzz2DpUhgxAr79VgpEQghhBOlJJEzFxdGFRZ6L\niLPE0XZ5W2LiYoyO9E5K5yhNYLNAwgaGMa7eOG6F36LdinbkG5+Pb3Z8w7XH14yOKMQ7KVMG/vhD\n9YaoXh0OHEjAl126pB42lDIlrFypbm537Qpz5tj0cEIkWrqu473emysPr7DAc4FVC0QAfsF+FM9a\nnCr5qlj1e8XLhYWpLWZ376oiuc0LRAk8n0dFQYsWqkD0yy8wcqQUiIQQIjGSIpGwifcyvcf0ZtP5\n89qfjAgaYXScBMmYKiMDKg3gXN9zbGy/EY/cHozeNRq3CW54LvEk6HIQRq3IE+JdffAB7NoFGTNC\n7dqwc+c7flHXrnbZA5YyJaxerbJ27gzz5tn8kEIkOnOPzWXB8QV8W+NbPsr7kVW/+2DYQQ7dOIS3\nu7fVtq+JV7t+XRWIbt2CTZugQgU7HDQB5/PHj6FhQ5XV3x+++MLK2YQQQtiNbDcTNtVrbS8CDgew\nqf0m6heqb3Qcq7n84DLTgqcx48gM7kXdo1jWYvR2702HUh1IlyKd0fGEeGvXr0Pduurm8fLlql9R\nvPz+u3quXt3q2V4mMhKaNlVFrblzoV07uxxWCNM7c/cM7gHuuOdyZ3vH7VafPNZ1dVeWnFzC9UHX\n5fecjd24oQpEYWFqBdFH1q33vdo7ns/v3VMFosOH1Xm5bVsbZBNCCBEv0pNImFZUTBTlp5fnVvgt\njnodJWfanEZHsqqomCiWnFzClINTCL4eTBqXNHT8sCM+5X0olrWY0fGEeCt370KDBnD0KMyfD23a\nGJ3o9SIioEkTtWVuwQL45BOjEwlhrKiYKCpMr8CN8BuE9Aohd7rcVv3+B1EPyD0uNx0+7IB/U3+r\nfrd43q1bqkn1X3+pVTlVTL6z7+ZNdaPh/Hk1kbJZM6MTCSGEAOlJJEwslXMqFrdaTERMBO1XtCfO\nEmd0JKtK5ZyKTqU7cbDHQfZ338/HH3zMjCMzKD61ODVn12T5qeXEWmKNjinEa2XJAtu3Q6VK8Omn\n4OcXjw+fPaseduTqCuvWqT+e2rdX/S+ESM76berH8dvHmdtyrtULRABzjs4hKjYKbw9vq3+3+J/b\nt6FWLTXNbMMGAwpE8TyfX7igVjldvgzr10uBSAghkgopEgmbK5a1GFMaTiEoNIgfdv1gdBybKZ+7\nPLNbzObawGuMqT2Gyw8u02ppK9wmuPH9799zM/ym0RGFeKX06dW2hiZNoHdvNZHmrRaa9uqlHnbm\n6qr+KKlUSW1tWL7c7hGEMIUFxxcQeDiQYVWG0aBQA6t/v67rTDs0jYp5KlI6R2mrf79Q7txRBaK/\nCy7VqhkQIh7n88OHVYHo8WPYsUP1ixNCCJE0yHYzYRe6rtNxVUcWHF/Ajo47qO5mn/4lRoqzxLH+\n/Hp8D/qy5eIWnB2c8SzmiY+HD5XzVpbGn8KUYmOhZ0+YNQu8vGDKFHB8XWuTvXvVs92aZjzvyRO1\nVe7AAbXVoWVLQ2IIYYizd8/iHuhO6RylCeoUhJODk9WPEXQ5iFpzajG7xWw6lupo9e8XastvrVpq\ny9b69eqfDfGW5/MdO9QUs4wZYcsWKFLEDtmEEELEi817Emma1gCYCDgC03VdH/OK93kCywAPXddf\nWwGSIlHy8+TZE8oFlCMiJoKQXiFkdc1qdCS7OXfvHH4H/ZgVMotHzx5RKnspfDx8aFeyHa4urkbH\nE+I5ug5ffQVjxoCnp5okljKl0ale7fFjqF8fgoNh2TJo3tzoRELYXlRMFBVnVCTscRghXiHkSZfH\nJsdps7QN2y9v59qAa6RyTmWTYyRn9+6potC5c7B2LdSpY3Si11u6FD77DN5/X/VMym393Y1CCCGs\nwKY9iTRNcwR8gYZAMaCtpmkvdOTVNC0t0A/Y/y5BRNKXNkValrRewr3Ie3RY2QGLbjE6kt28n/l9\nxjcYT9jAMAKaBKCj03NdT3KPy82ATQM4f++80RGF+H+aBj/+COPHq21cDRuqQsxLnTihHgZKl079\nsVK2LLRurf7QEiKpG7B5AMduHWNuy7k2KxDdeHKDlWdW0rlUZykQ2cD9+6oodPYsrF5tggLRG87n\nU6eqQQEeHmpwgBSIhBAiaXqbnkTlgQu6rl/SdT0aWAS87D7t98BPwFMr5hNJTOkcpZnYYCKbL25O\n0v2JXsXVxZUe5XoQ0iuEXV120bBwQ6YcnML7U96n/rz6rDm7Jsk19xaJV//+ahXR7t1q2s6tWy95\nU58+6mGwv3sqlSoFrVqppq9CJFWLTizC/5A/QyoPoWHhhjY7zowjM4i1xOLl7mWzYyRXDx6oqWCn\nTsGqVVCvntGJeOX5XNdVnzofH9W3bssWtdVMCCFE0vTG7WaaprUCGui63v2//94BqKDrep9/vKcs\n8LWu656apu0EvpDtZuJVdF2nw8oOLDyxkK0dtlKrgFGb783hZvhNAg8F4n/In7AnYeRPnx9vd2+6\nle1GltRZjI4nBJs2qW1nOXOqfy5U6B8/PHhQPXt4GJLt3/7+w+v4cXVnvoH1+/gKYajz985TNqAs\nH2b/kJ2dduLs6GyT48RZ4igwsQBFshRha4etNjlGcvXwoTpPHTsGK1dCo0ZGJ/qvl5zPY2Ohb1+Y\nNg26dIGAAHCyfusrIYQQVmbT7WZvcXAHYBww6C3e21PTtGBN04Lv3LmT0EOLRErTNKY1mUaRzEVo\nu7wt159cNzqSoXKkycE31b/hcr/LLGu9jAIZCzB0+1DyjMtDp1WdOBB2wOiIIplr0EA1Kn34UE0T\n27fvHz/08DBNgQj+10i1eHHVWHXzZqMTCWE9UTFRtF7aGhdHFxZ5LrJZgQhg/fn1/PX4L7zdZey9\nNT16pFYNHT2qtvOapkAEL5zPIyLUMIBp02DIEJgxQwpEQgiRHLxNkSgMyPuPf8/z39f+lhYoAezU\nNC0UqAis0TTthaqVrusBuq6767runjVr8mlaLF6UxiUNy9osIzw6nLbL2xJriTU6kuGcHdX0s6BO\nQZzwPkG3Mt1YcXoFFaZXwCPQg9khs3kaK7s5hTEqVIA//1TbumrWVHe/AQgJUQ8TyZQJtm6FokVV\noWjbNqMTCWEdfTb04eito8xtOZe86fO++QMJ4BfsR660uWhWpJlNj5OcPH6siu4hIarJfpMmRif6\nl3+cz2/eVNuMN2xQvYjGjFH96oQQQiR9b1MkOggU1jStgKZpLsCnwJq/f6jr+iNd17Pouu6m67ob\nsA9o9qbtZkIUy1qMgCYB/HHlD4bvGG50HFMpnq04vo19CRsYxpSGU4iIjqDz6s7kGZeHIVuHcPnB\nZaMjimSocGFVKCpVSm0/mzQJ1biof3+jo70gc2ZVHCpcGJo2he3bjU4kRMLMODyDmSEzGV51OI0K\n23b5yaUHl9h8YTM9yvbAyUGWjljDkyeqQBQcDEuWQDMz1t7+ez4/c0atGj11Sm3b9ZbFZEIIkay8\nsUik63os0AfYDJwGlui6flLTtO80TTPjrziRiLT/sD29yvXipz0/se7cOqPjmE66FOnwKe/Dyd4n\n2d5xO9XdqjP2z7G8N+k9mi5syqYLm5LVlDhhvKxZ1dazFi2gXz/4Nc8ELOMmGB3rpbKP/2RIAAAg\nAElEQVRkUcWhQoVUoSgoyOhEQrybIzeO4LPBhzoF6/BtjW9tfjz/YH8cNAd6lO1h82MlB0+eqCmR\nBw7A4sXq/GlKEyZwqMMEPvoIIiPh999NuNpJCCGEzb2xcbWtSONq8bensU+pPLMylx9c5nCvw7hl\ncDM6kqlde3wN/2B/Ag8HciviFoUyFaK3e286l+5MxlQybkTYR1wcDBoEEyeqVUVz50Iqk07Ivn1b\nbZELDVVbJ6pXNzqREG/vQdQD3APdiY6L5nDPw2R1te12/Wexz8gzPg9V81VlxScrbHqs5CA8XPUd\n2rsXFi1S0xfNatEi6NQJChZU58oCBYxOJIQQ4l0Z2rhaiIRK6ZSSpa2XYtEttF7ammexz4yOZGp5\n0uXh+1rfc3XAVRZ8vIDsrtkZuGUgucflpseaHoTcNFd/GJE0OTrChAkwfjysWAG1a8Pdu0anerls\n2dTqp/z5oXFj2LXL6ERCvB2LbqHTqk5cfXSVJa2W2LxABLDs1DLuRt6VhtVWEBGhVuLs2QPz55u3\nQKTr8PPP0Lat6j+3Z48UiIQQIjmTIpEwhYIZCzK7xWyCrwfTb1M/o+MkCi6OLrQt2ZbdXXdzpNcR\n2pdsz/zj8ynjX4bKMyuz4PgCouOijY4pkrj+/WHpUjhyBCpWhDNnjE70ctmzq0JR3rxq28eePUYn\nEuLNft7zM2vPrWVsvbFUylvJLsf0C/ajUKZC1C5Y2y7HS6oiI9U21127YN48+OQToxO9XEwMeHmp\n6WWffqqmQ2bKZHQqIYQQRpIikTCN5kWbM6TyEPwP+TPryCyj4yQqpXOUJrBZIGEDwxhXbxy3I27T\nfkV78o3Pxzc7vuHa42tGRxRJmKenKsA8eaIKRWadJpYjh8qZO7dqIPvnn0YnEuLVgi4H8fWOr/mk\n+Cf0Ld/XLsc8fus4e/7ag1c5Lxw0uUR8V1FRqjH177/DnDlqhY4Z3b+vzoUBATBsmFrtlDKl0amE\nEEIYTXoSCVOJtcTSYF4Ddl/dzZ6ueyiXq5zRkRIli25h68WtTDk4hfXn1uOgOdC8aHN8PHyo6VYT\nTebYChu4ckVtrTh9GiZPNu9EnLAwNdr51i1117xiRaMTCfG8sMdhlA0oS6ZUmTjY4yBpXNLY5bg+\n632YcWQGYQPDyJw6s12OmdRERUHz5qpYPns2dOhgdKKXO3dOna+vXIHAQOjY0ehEQgghrEl6Eokk\nw8nBiYWeC8nmmg3PJZ7ci7xndKREyUFzoH6h+qxtu5aLn19kUKVB/B76O7Xn1Kb41OJMOTCFx88e\nGx1TJDH586vmrA0aQO/e8PnnEBtrdKoX5c6tJp1lywb1/4+9+w6L6lrbOPwbioq9N7D3jiiW2GJX\nVKyo2As2sMeYZmJicmI8MZZELFixYBdFjdhQYouCLSp2RYXYFUVE6v7+WMlncmIShJnZA7z3dc21\nDcLez0nE4zyu9a626sQhISxFfFI8vTb1IiY+hs09N5utIHoR/4JVv6yiV/VeUhCl0qtX6uSyfftg\n+XLLLYiCglQ5/vSpOgFSCiIhhBB/JCWRsDiFchRic8/N3H1xF/fN7iQlJ+kdKV0rk68MM1rPIGJi\nBCs6ryBnlpyM2TUG+1n2eO30IuxhmN4RRQaSKxds2wYTJ6rVRB07wrNneqf6KwcHVRQVLAht2oAs\nbBWWYkLgBI7cOcIS1yVULVTVbM9d88saouOjZWB1KsXFQbduanXikiXqlDBL5OOjyvFixVRB3rix\n3omEEEJYGimJhEVytndmvst89t7Yy6cHPtU7ToaQzSYbAx0HcmLYCY57HKdblW4sPb2UavOr0dy3\nOZvCNpGQlKB3TJEBWFvDd9+pNyP798M778CNG3qn+qsSJVRRlC8ftG4Np07pnUhkdstPL2d+6Hwm\nNZxE7+q9zfZcTdNYELqAWkVqUd++vtmem1HExanZbLt2qa1bQ4boneivkpJgwgQYMQJatVKrPuUE\nMyGEEG8iJZGwWEOdhjLMaRjTD09n66WtesfJUOrZ18O3iy8REyP4puU33Hx6E7eNbpSeW5ovg7/k\n3ot7ekcUGcCwYepv1e/eVccqBwfrneivSpZURVGePOqN0+nTeicSmVXor6GM2jmKlmVaMr3VdLM+\n++eInzl7/yyj6o6SmXVvKT4e3Nxg505YtAg8PPRO9FdRUWqQ9pw5MG4cbN+ufs8TQggh3kQGVwuL\nFpcYR5PlTbj06BIhw0KoVLCS3pEypKTkJH68+iPeId7svr4bWytbulftjpezF41KNJI3DSJNrl5V\nR0Ffvw6zZ4OXF1jaL6mbN9Uw6xcv1LyOWrX0TiQykwcxD6jrUxcrgxWhw0MpmL2gWZ8/wH8AWy9t\n5df3fjXbDKSMID4eevZUW2znz7fMYf0XL6o5STduqC3AI0fqnUgIIYQ5yOBqkWFltcnK5p6byWqT\nlW4buhEdF613pAzJ2sqaTpU6EdgvkMujL+Pl7MWuq7tosrwJjosc8TnpQ0x8jN4xRTpVoQIcP64G\nWo8Zo/6m/dUrvVP9WZkyakVR9uzQsiWcO6d3IpFZJCYn0mtTLx6+fMiWXlvMXhA9fvmYDRc20L9m\nfymI3kJCAvTurQqiefMssyAKCFCrOKOiVPktBZEQQoiUkJJIWLwSeUqwvsd6Lj26xMCtA0nWkvWO\nlKFVLFCR2e1mEzkxEp+OPhgwMGLHCOxn2TMhcAJXH1/VO6JIh/LkUW+mPv0Uli1Tq3YiI/VO9Wdl\ny6qiKFs2aNECzp/XO5HIDCbvnczB8IP4dPTBqZiT2Z+//Mxy4pLiGOVsgS2HhUpIAHd38PeHuXPV\n6khLkpwM06ZB585QsaIazN+kid6phBBCpBdSEol0oUWZFsxsPRP/S/589dNXesfJFHJkycGwOsM4\nPeI0hwcfxqWCC94h3lScV5G2q9sScDlATp4Tb8XKSr1x2bxZFTB166rhqZakfHlVFGXJooqiMDn8\nT5iQ3zk/Zv88mzH1xtC/lvnPS0/WklkYupDGJRtTvXB1sz8/PUpMhL591e9js2fD2LF6J/qz6Gg1\nRHvqVOjfHw4dUkP6hRBCiJSSkkikG+MbjGdArQFMPThVBlmbkcFgoFHJRvh19+P2hNtMe3caFx5c\noPO6zpT7vhwzDs/g0ctHescU6Ui3bvDzz5Ajh1pRtHix3on+rEIFtTXD2loVRZcu6Z1IZERn7p3B\nI8CDJiWb8F2b73TJsO/GPq4/vS7H3qdQYqIqXjZuhJkzYfx4vRP92bVr0KCBGkw9Zw74+oKdnd6p\nhBBCpDcyuFqkK68SX9F0eVMuPrrIz0N/plrhanpHypQSkhIIuByAd4g3B8IPkNU6K72q98LL2Yt6\n9vX0jifSiadP1ZaN3bvVscxz50LWrHqneu3SJVViGQxw8CBUkrn5wkgexjzEebEzicmJnBx+kiI5\ni+iSo+v6rhy5fYQ7E+6Q1caCvvksUFISDBgAfn7w3//C++/rnejPfvxRrXCytob169VsNSGEEJmX\nDK4WmUY2m2z49/InZ5acdF7XmSexT/SOlCnZWqvTz4IGBnHB8wIeTh5subiF+kvq47zYmRVnVhCb\nEKt3TGHh8uVTx0Z/8IE6OrpxYwgP1zvVa5Urq61nycnQvDlcuaJ3IpERxCfF02NjD+69uId/L3/d\nCqKI5xEEXA5gSO0hUhD9i6QkGDRIFUTTp1tWQZSUBFOmQIcOUKoUhIRIQSSEECJtpCQS6Y59bnu2\n9NzCned36L2pN4nJiXpHytSqFqrKPJd5RE6MZF77ecTExzB422AcZjvwwd4PuPn0pt4RhQWztoZv\nvlEDYK9cAScn9TfilqJKFbX1LDFRFUXXrumdSKRnmqYx5scx/HTrJ5Z1XoazvbNuWRafXIymaYyo\nM0K3DOlBUhIMGQKrV8NXX8GHH+qd6LWHD6FtW/jPf1TGY8fUSY1CCCFEWkhJJNKlhiUaMt9lPntv\n7OXDfRb0J7ZMLHfW3HjV8+KC5wWCBgTRvHRzvjv2HeW+L0entZ0IvBYoJ9OJv9WlC5w8qQasdugA\nn32m3pxZgmrVYP9+iI9XRdH163onEunVgtAF+Jzy4cNGH9KnRh/dciQkJbD41GLalW9HmXzSKvyd\n5GTw8ICVK9XQ/U8+0TvRa0ePQu3acOQILF2qXjJ/SAghhDFISSTSraFOQxntPJrvjn3HqrOr9I4j\nfmMwGGhepjmbem4ifHw4nzT5hJDIENqvaU+leZWYdWwWT2Of6h1TWKDy5dVA68GD4csvoX179Tfl\nlqBGDVUUxcaqoujGDb0TifQm6GYQY3eNpWPFjnzVQt9TOrdf2c7dF3dlYPU/SE6G4cNhxQp1Utin\nn+qdSNE0Nb+tWTM1w+3YMbWKSAghhDAWGVwt0rWEpATarG7DsTvH+GnwTzI02ULFJ8WzOWwz3iHe\nHLlzBDsbO/rW6ItXPS8cizrqHU9YoKVLwcsLChWCDRugYUO9Eylnzqh5HzlzQnAwlC6tdyKRHlx/\ncp16S+pRNGdRjg09Ru6suXXN03pVa648vsKNsTewtrLWNYslSk6GkSPVyYtTpqhVRAaD3qnU8fYe\nHur3RFdXdXpZ3rx6pxJCCGGJZHC1yLRsrW3Z6LaR4rmK03ldZyKeR+gdSbxBFussuNdw5/CQw5we\ncZp+Nfvhd96P2otq02hZI/zO+RGfFK93TGFBhg5V2ylsbaFpU5g1S/0Nut4cHWHvXvVmrXlzuHVL\n70TC0j2Pe47rOlc0TSOgd4DuBdHVx1fZd2Mfw52GS0H0BpqmCurFi+Hjjy2nIDp7FpydYdOm13Pc\npCASQghhClISiXSvYPaCbHffTkx8DK5rXYmJj9E7kvgHjkUd8enkQ8SECGa1mcWDmAf03dKXErNL\nMCVoCnee3dE7orAQTk5qTlGHDvDee9Cpk2VsP3NyUkVRVJQqim7f1juRsFTJWjL9tvTj8qPLbHTb\nSLn85fSOxMLQhdhY2TDUaajeUSyOpsHo0bBwoTp18auv9C+INA28vaF+fXj+XG17/eADsJI/wQsh\nhDAR+b8YkSFUK1yN9T3Wc/b+Wfr595MByelAPrt8TGg4gcujLxPYN5D69vX5+tDXlJlbhu4buhN0\nMwi9tsMKy5Evn/ob8x9+UMWMoyMcPKh3KqhTB/bsgSdPVFEUIYsYxRtMCZrC9ivbmdNuDi3L6n8u\neWxCLMvPLKdr5a4UzVlU7zgWRdNg3DiYPx8mTVJH3etdED15At27q+KqRQu1mujdd/XNJIQQIuOT\nkkhkGO0rtGdWm1lsvbSVKUFT9I4jUsjKYEXb8m0JcA/gxrgbTHpnEsHhwbRc2ZJq86sx78Q8nsc9\n1zum0JHBoN4kHT+uZgG1aKEGySYm6pvL2Rl274ZHj1RRFBmpbx5hWVacWcH0w9MZ7jQcL2cvveMA\nsOHCBp6+eioDq/+HpsGECaqMnjgR/vtf/QuiI0fU6WU7dsB336lroUL6ZhJCCJE5yOBqkaFomsao\nnaNYdHIRvl18GVBrgN6RRCq8SnzF+vPr8Q7xJuTXEHJmycmAmgPwdPakWuFqescTOnrxQhVGvr7Q\npAn4+YGDg76Zfv4Z2rSBokXVKqfixfXNI/QXHB5M61WtaVqqKbv67sLW2lbvSAA0WNKAZ3HPCPMM\nw6B3C2IhNE2tHJo1S60kmj1b34IoKQlmzIDPPoNSpWDdOlVICyGEEG9DBlcL8RuDwcAP7X+gRZkW\nDNs+jMO3D+sdSaRCNptsDHQcyIlhJzjhcYLuVbqz9PRSqi+oTnPf5mwK20RCUoLeMYUOcuZUR1Kv\nWgWnTkGtWrBtm76ZGjSAwEC4e1etcrp7V988Ql9XH1+l24ZulMtfjo1uGy2mIDp99zTHI48zss5I\nKYh+o2kwebIqiMaM0b8gunsX2raFTz4BNzc4fVoKIiGEEOYnJZHIcH4/8axUnlJ0Xd+V8KhwvSOJ\nNHC2d2ZFlxVETIxgRqsZ3Hx6E7eNbpSeW5ppwdO49+Ke3hGFDvr1UyVRqVLQpQuMGKFWGenlnXdg\n1y41m6hFC7h/X78sQj9PYp/QcW1HDBjY4b6DfHb59I70/xaELsDOxo6BjgP1jmIRNA0++ghmzgRP\nT5g7V9+CaMsWqFFDneq4ZIlaJZlb34PwhBBCZFJSEokMKb9dfnb02UFiciId/TrKTJsMoGD2gkxu\nNJnrY68T0DuAGoVrMPXgVErMLoH7ZncO3z4sg64zmYoV4dgxtRJg8WI1v+P4cf3yNG4MP/6oTjtr\n0QIePNAvizC/+KR4emzoQXhUOFt7b7WIk8x+9+zVM9acW4N7dXfyZpNz0zUNpkxR27pGjoR58/Qr\niJ4/h8GD1YDq0qVV+T10qP4zkYQQQmReUhKJDKtigYpsctvE5ceXcdvoJtuTMghrK2s6VepEYL9A\nroy+wph6Ywi8FkiT5U1wXOSIz0kfYuJj9I4pzCRrVvVG78ABiI+HRo3g88/1G2rdtCns3Ak3b6qi\n6OFDfXII89I0Dc+dnhwIP8BS16U0LtlY70h/suqXVbxMeMkoZxlYrWlq3s/XX8OwYep4eb0KmSNH\n1ImNK1eq0urYMahcWZ8sQgghxO+kJBIZWsuyLVnUcRF7ru/Bc6enrDTJYCoUqMCstrOImBDB4k6L\nMWBgxI4R2M+yZ3zgeK48vqJ3RGEmzZrBL7+Auzt88YUqi65e1SfLu++qk4hu3ICWLdXpZyJj+/bo\ntyw9vZQpTabQr2Y/veP8iaZpLAhdQN3idalbPFXzKzOUL76Ar75Sq3UWLgQrHf4kHB+v5g41baoK\nqkOH4MsvwdYyxlcJIYTI5KQkEhnekNpDmNJkCktOL+Gbw9/oHUeYQI4sOfBw8uD0iNMcHnwYlwou\nzA+ZT6V5lWi7ui0BlwNISk7SO6YwsTx51EDr9etVQeToCD4+auWAubVoAdu3qxwtW8Ljx+bPIMzD\n/6I/H+77kJ7VevJF8y/0jvMXh24fIuxhmBx7jypivvhCbe/y8dGnILp4ERo2VCuZBg2CM2fUTDMh\nhBDCUhj0WllRt25dLTQ0VJdni8xH0zT6+ffD75wfft38cK/hrnckYWL3XtxjyaklLAxdSGR0JKXy\nlGJk3ZEMrT2UQjkK6R1PmFhkpHoDtm8ftG+v3hA6OJg/x5494OoKVarA/v2QP7/5MwjT+TniZ5r7\nNqdWkVocGHgAO1s7vSP9hftmdwKvBRI5MZLsttn1jqOb//xHbekaMACWLQNra/M+PylJDcf+5BPI\nkUMNp+7SxbwZhBBCZB4Gg+GkpmmpWkIsK4lEpmAwGFjmuoympZoyaNsgDt06pHckYWJFcxZlStMp\nhI8PZ5PbJsrmK8tH+z+ixOwSDPAfwInIE3pHFCZkbw+7d8P330NwMFSrpt4YmvvvRdq0gW3b1OqB\n1q3h6VPzPl+YzrUn1+i0thP2uezZ7r7dIguiBzEP2By2mYG1Bmbqguibb1RB1K+fPgXR5cvQpAm8\n9576PeHcOSmIhBBCWC4piUSmkdUmK/69/CmTtwxd1neReTWZhI2VDd2rdidoYBAXPC/g4eSB/yV/\n6i+pj/NiZ1acWUFsQqzeMYUJWFnBmDFqVlHt2moGiYsL3Llj3hxt24K/P5w/r4qiqCjzPl8Y38OY\nh7Rf0x5N09jVd5fFrk5cdnoZCckJjKw7Uu8ouvn2W3XUfZ8+sGKFeQuipCSYOVNtfb18Gdasga1b\noVgx82UQQggh3paURCJTyW+Xnx/7/oi1wRqXNS48jJGjhzKTqoWqMs9lHr9O/BVvF29i4mMYvG0w\nDrMdmLx3Mjef3tQ7ojCBcuUgKEgdc/3TT1C9Oixdat5VRe3bw+bNqrBq0waePTPfs4VxvUx4ies6\nVyKeR7DdfTsVClTQO9IbJSUnsejkIpqXbk7lgpnzyKzvvoPJk6F3b/D1NW9BdOkSNG4M778P7drB\nhQuqqJKj7YUQQlg6KYlEplM2X1kC3AOIjI6k87rOsookE8qVNReezp5c8LxA0IAgmpduzqxjsyj3\nfTk6+nUk8FogyVqy3jGFEVlZgZeX2ubh5AQeHuqN2+3b5svQsSNs2qQG1bZrB8+fm+/ZwjiSkpPo\nu6UvxyOO49fNj4YlGuod6W/tvr6b8KjwTDuwevZsmDQJ3NzUQHsbG/M8NylJrV5ydIQrV8DPD7Zs\ngaJFzfN8IYQQIq2kJBKZUgOHBqzptoafI37GfbM7icmJekcSOjAYDDQv05xNPTcRPj6cKU2nEPpr\nKO3XtKfSvErMOjaLp7EyRCYjKVtWDZD29oYjR9Sqoh9+UG/szMHVFTZsgNBQVRRFR5vnuSIN1qyB\n0qXRrKx4Viwfdhu2MqfdHLpW6ap3sn+0IHQBRXIUoXPlznpHMbvvv4eJE6F7d/Wfz1wF0enT0KCB\nWr3k4gJhYeDuLquHhBBCpC9SEolMq1uVbsxtN5dtl7fhtdMLvU76E5bBIbcD05pP4/aE2/h186NI\njiK8t+c97GfZ4xHgwem7p/WOKIzEygo8PdWqonfegbFj1fXsWfM8v0sXWL8eTpxQ29CkKLJga9bA\n8OFw6xYGTSP/g2hW7LRh7LUCeif7R7eibrHzyk48nDzIYp1F7zhm5e0N48ZB166wdi3Y2pr+mTEx\natWSs7OaebZundpeWqSI6Z8thBBCGJuURCJTG1N/DB81/gifUz58+dOXescRFiCLdRbca7hzeMhh\nzow4Q7+a/Vh7fi1OPk40WtYIv3N+xCfF6x1TGEGZMrBrl9oOcvMm1KkDH3wAL1+a/tnduqk3kj//\nDB06wIsXpn+mSIVPPvnLL4gscYnq4xbM56QPBoOB4XWG6x3FrBYsgNGjoXNn9f1ljoJo1y51euJ3\n36nh+BcvQq9esnpICCFE+mXQa/VE3bp1tdDQUF2eLcQfaZrG4G2D8T3ri09HH4bVGaZ3JGFhol5F\nseLMCuaHzOfqk6sUzlGYYU7DGFFnBCXylNA7njCCJ0/UFpGlS1V5tGCBOpXM1DZsUMNsGzeGnTsh\nRw7TP1O8BSurN084Nxgg2TLnlsUnxVNidgnq29cnwD1A7zhm4+MDI0ZAp05q9lcWEy+guncPxo9X\nqwKrVFHPb9zYtM8UQgghUspgMJzUNK1uar5WVhKJTM9gMLC402Lal2/PyJ0jCbicef5QLVImb7a8\njG8wnkujLxHYN5D69vX5+tDXlJlbhm7ru7H/xn7ZrpjO5c8PS5bAwYPqzWW7dqq8uXfPtM/t2RNW\nr4ZDh9SbW3OsYhIpF1f8b/YLlSxp3iBvwf+iPw9iHmSqgdVLlqiCqEMH2LjRtAVRcrIqhKpUAX9/\nmDZNzSKSgkgIIURGISWREICttS0b3TZSp1gdem3qxdE7R/WOJCyQlcGKtuXbEuAewI1xN5j0ziR+\nuvUTrVa1otr8asw7MY/ncerIqsPfeBKR34Zkg4GI/DYc/sZT5/QiJZo1U7OJpk5VM0UqVYI5cyAh\nwXTP7N0bVq6E4GA12DpWDly0CNeeXGNc0xhe2v7PvqHs2eE//9EnVAosCF1AmbxlaFveDEvhLMCy\nZTBsmCp2N22CrFlN96yQEDWYesQIqFULfvkFPv3UtM8UQgghzE1KIiF+kyNLDnb22YlDbgc6re3E\nxYcX9Y4kLFjpvKX5ptU3REyMwLeLLzmz5GTMrjHYz7Ln65HVqP3ZAhyeJmEFODxNovZnC6QoSiey\nZoXPP1eDrRs2hAkTwMlJrTIylb59YcUKCApS81SkKNLX3ei7tFnVhs21sxL1/X8hTx71E6VKqWUk\nffvqG/BvhD0MI/hWMCPqjMDKkPH/iOfrCx4e0KaNWtWTLZtpnvPokSqi6tdXg6lXrYIDB1SJLIQQ\nQmQ0MpNIiP9x4+kN3ln6DlltsnJkyBEccjvoHUmkEyGRIXiHePP5IF9KP/vrz0fks8bhSaL5g4lU\n0zTYtk3NHrl1S636mTkT7O1N8zxfXxg8GFq3Vs811Zte8feevXpGsxXNuPbkGgcGHsDZ3lnvSCk2\ndtdYFp1cRMSECArlKKR3HJNatQoGDoRWrdT3ip2d8Z+RlASLFsGUKeoUwnHj4LPPIHdu4z9LCCGE\nMCaZSSSEEZXNV5ZdfXfxNPYpbVa14dHLR3pHEumEs70zK7qsoOQbCiKA4k+TzBtIpJnBoI6sDwtT\nbw79/dXqgf/+F+JNcMjdwIFqvsqePeoEtLg44z9D/L1Xia/ovK4zYQ/D2NJrS7oqiGLiY/A960uP\nqj0yfEG0Zo36XmneHLZuNU1BdOQI1K0LXl5Qu7bahjpzphREQgghMj4piYR4g9rFarOjzw5uRt2k\n/Zr2/z9nRoiU+DWf9Rs/fjsP9N7Um0O3Dsmg63Qme3b44gtVFrVsCR98ADVqQEDAmw+/SoshQ2Dx\nYnW0dvfuUhSZS1JyEn239CX4VjC+XXxpU67N65/s3Vu9LNja82t5Hvc8ww+sXrsWBgyAd9+F7dvV\n96Yx3b4N/fqpQdSPHqkTCPftg6pVjfscIYQQwlJJSSTE32haqimb3DZx5t4ZOq/rzKvEV3pHEulE\n+OThxNj++WMxtrDevSa7r++m6YqmOC5yxOekDzHxMfqEFKlStqza2rJzp1pl1LkztGgBp04Z9zke\nHmqby86d4OZmmlVL4jVN0xi5YyRbLm5hbru5uNdw//MnODqql4XSNI0FoQuoXrg6jUo00juOyWzY\noAqcJk2MXxA9fw4ff6xWCm7erH586ZL6/jMY/v3rhRBCiIxCSiIh/kGHih3w7eJLcHgwvTb1IjFZ\n5smIf9f4w/mcnjaKyLzWJKNmEZ2eNooPFpwlYkIEizstxspgxYgdI7CfZc/4wPFceXxF79jiLbi4\nqMHW8+apa926MGgQREYa7xnDh8P8+erNcM+eUhSZiqZpTNoziSWnlzClyRTG1h/710/68EP1slCh\nv4Zy6u4pRtUdhSGDNhqbNkGfPtCoEezYATlyGOe+iYmqkK1QAaZPV6v3Ll9WBz0SOqMAACAASURB\nVNgZ6xlCCCFEeiKDq4VIAe8T3ozeNZr+NfuzosuKTHFqjDCCd99V1zcci6VpGkfvHMU7xJtNYZtI\nSE6gddnWjK43mg4VOmBt9eYta8LyREXB11/D3LlgbQ3vv69eOXMa5/7e3jB6NHTtCuvXg63tv3+N\nSLlpwdOYenAqY+uNZU67OemyZBmybQgbLmzg1/d+JXfWjDc0Z8sWVZQ2aKC2YebKZZz7BgbCpElw\n4YLaXjZrFjinnzFUQgghxN+SwdVCmJhXPS++bP4lq35ZxfjA8TJPRqSMh4d6vYHBYKBRyUb4dffj\nzoQ7fNn8S8IehtF5XWfKfV+Obw5/w8OYh2YOLFIjb141yPrSJXB1hWnToGJFtTohISHt9/fygu+/\nV0Oz3d2Nc0+hzD42m6kHpzLIcRCz283++4Koe3f1skBPY5+y7vw6+tXslyELoq1boVcvqFfPeAXR\nqVPQti20bw+vXqntZT/9JAWREEIIAVISCZFinzT5hAkNJvDDiR/4IvgLveOI9KBfP/X6F0VyFmFK\n0ymEjw9nc8/NlMtfjo/2f4TDbAcG+A/gROQJM4QVaVWmDKxbB0ePQunSMHKkGna7di0kJ6ft3mPG\nwOzZ6s1s375qi4xIm6WnljJxz0R6VO3x/1tA/1bDhuplgXzP+hKbGMvIuiP1jmJ0AQFqBVGdOmrV\nT1oLokuXXt8vNBS++04No+/WTeYOCSGEEL+T7WZCvAVN0xgaMJTlZ5bzbetvmfTOJL0jCUv28qW6\npmK6atjDMOaHzMf3rC8v4l9Qt3hdvJy96FWtF3a2JjjvWRiVpqmh0598Ar/8AjVrqhknHTqk7c3o\nrFnw3nvqoK1Vq8DGxniZM5P159fjvtmdtuXbsq33NrJYZ9E7UqpomkYV7yrks8vHsaHH9I5jVDt2\nqPKmdm3Yswfy5En9vW7fVqcTrlgBdnYwcaL6PkrLPYUQQghLJtvNhDATg8GATycfelbryft732fe\niXl6RxKWzMVFvVKhaqGqzHOZx68Tf8XbxZuXCS8ZvG0wDrMdmLx3Mjef3jRyWGFMBgN07AinT4Of\nn+oLO3VSc0+Cg1N/34kT1da2detg4EBISjJe5sxi55Wd9PPvR+OSjdncc3O6LYgADoQf4PLjyxnu\n2Psff1S7+2rVgt27U1/mPHgA48erodRr1sC4cXDjhtoSKgWREEII8WaykkiIVEhISsBtoxvbLm9j\ncafFeDi9ee6MyOTWr1fXXr3SfCtN0wi+Fcy8E/PYemkryVoyLhVc8HL2om35tjJM3cIlJMDy5erN\naWQktG4NU6eqk5pS45tv4KOP1G7GFSvUwGzx7w7cPICLnwvVClUjaGBQymf4uLqqa0CA6cKlgttG\nN4JuBhE5MZJsNtn0jmMUgYHQpQtUqwb79kG+fG9/j4cP1fbM779XM4cGD4bPPoMSJYyfVwghhLBE\naVlJJCWREKkUlxhHl/Vd2H1tNyu7rqRfzX+fPSOEMUQ8j8DnpA8+J324H3Of8vnLM6ruKAY7Diaf\nXSreUQmziY1Vx9rPmKHeyDZvrt68Nmv29tvQvv5abWcbMACWLZOi6N8cunWIdmvaUTpvaYIHBVMw\ne8GUf/Hcueo6bpxpwqXC3ei7lJxTknH1xzGzzUy94xjFnj2qj6tSBfbvh/z53+7r792DmTNhwQL1\nvdarl9pmVrGiafIKIYQQlkpKIiF0EpsQS8e1HTkYfpB13dfhVs1N70jCkjx7pq4m2tcQnxTPlotb\n8A7x5vDtw9jZ2NGnRh+8nL2oXay2SZ4pjCMmBnx81Naxe/fUNrTPPoNWrd6uLPryS/V1gwbB0qVg\nJQvK3ujonaO0Xd0W+1z2HBx0kKI5i+odKc2+DP6Szw5+xpXRV6hQoILecdJs3z61JbNSJVUQFSiQ\n8q+NjFTfSz4+EB8PffqoArVyZdPlFUIIISyZlERC6CgmPoZ2a9rxc8TPbO65GddKrnpHEpbi3XfV\n9eBBkz/q7L2zeId4s+bcGl4mvKShQ0NG1xtN9yrdyWqT1eTPF6kTG6vKnRkzICIC6teHTz9Vo6xS\nWhZ9/rlaLTF0qHqTLEXRn52IPEHrVa0pkqMIBwcdpHiu4npHSrPE5ETKzC1DlYJV2NN/j95x0iwo\nSM3wKl9e/bhgChd53b6ttl4uXapOEBwwQG3DLF/etHmFEEIISyeDq4XQUY4sOdjZZydOxZxw2+jG\n7mu79Y4kLMXYseplBrWK1sKnkw+REyOZ3XY2j14+ou+WvpScU5IpQVO48+yOWXKIt2NnB6NHw7Vr\nsHChWlXUsSM4OqrTyxIS/v0eU6eqYmnpUhg5Ur1ZFsqpu6dou7otBbMXJGhgUOoLovbt1ctC7Lyy\nk4jnERliYPXBg+rXfLlyagVRSgqis2ehf3/1NUuWqJlDV6+q7wEpiIQQQoi0kZVEQhjJ09intFjZ\ngkuPLhHQO4DW5VrrHUlkYslaMvtu7GPeiXnsuLIDK4MVrpVc8XL2okWZFhjScg67MJmEBHUK08yZ\ncOECODioMTjDh0Puf5ixrGkwZYqaUzRypJp7lNn/E5+9d5bmvs3JnTU3wYOCKZW3VOpvNn++unp6\nGidcGrVb3Y7zD84TPj4cGysbveOk2k8/qe6tdGk4cAAKF/77z9U0tSXt229h717IkQM8PNRR9jKQ\nWgghhPgz2W4mhIV49PIRrVa24vLjy2zrvY025droHUno6dEjdU3p3gkTCY8KZ2HoQpacWsLj2MdU\nLlgZL2cvBtQakPLTnYRZaRrs2qXKogMHVEE0fLgqjBwc/v5rPvpIbV3z9IR58zJvUXT+wXma+zbH\nzsaO4EHBlMlXRu9IRnP9yXXK/1Cez5t9ztR3p+odJ9UOH4Z27VTBc/AgFCny5s9LSFAHRc6cqVYQ\nFS2qvg9GjEjdyWdCCCFEZiDbzYSwEAWzF2T/gP1UKlAJ17Wu7Lme/mdFiDTo0UO9dFY6b2m+afUN\nERMj8O3iS+6suRmzawz2s+zx3OnJhQcX9I4o/ofBoOYSBQVBSIj68axZUKaM2mZz4sSbv2b6dHj/\nfbXwZdw4VRxlNmEPw2i5siVZrLMQNDAoQxVEAItOLsLaYI2Hk4feUVLtyBG1gsjBQf0af1NB9Pix\nGkZdtqz6NZ+QoE7xCw+HDz+UgkgIIYQwFVlJJIQJPH75mFarWnHx4UW29d5G2/Jt9Y4k9LB9u7p2\n6qRvjjcIiQzBO8SbdefXEZcUR7NSzfBy9qJL5S7YWtvqHU+8QXg4zJ6t3ii/eAHOzmqeUc+ekC3b\n68/TNJg0SZVK48apr8ksK4rOPzhPC98WWFtZc3DgQSoVrGScG7dqpa779hnnfqkUlxiH/Sx7mpVu\nxuaem3XNklo//wxt2qgVQQcPQvH/GRMVGgre3rB2LcTFQfPm6tdzu3YylF0IIYRIKdluJoQFevzy\nMa1XtSbsYRhbe2+lXfl2ekcS4i8evXzEstPLWBC6gPCocIrnKs6IOiMY5jSMYrmK6R1PvMHz52qo\n9bx5cOmS2s3o4aFmEZX6beyOpsGECTB3LkycqLbqZPSi6Oy9s7Rc2ZJsNtkIGhhExQIVjXfzxYvV\nddgw490zFdb8soZ+/v3Y238vrcq20jVLahw/rgqiwoVVQWRvrz4eFwcbNqhy6PhxNW9owAC1bbJ6\ndV0jCyGEEOmSlERCWKgnsU9otbIVFx5eYGuvrbSvYDmn4wgzuHdPXYsW1TdHCiQlJ/Hj1R/xDvFm\n9/Xd2FjZ0L1Kd7ycvWhcsrEMurZAmqa26nh7w7Zt6mOdOqlZLW3aqFUX48bBDz+oLWgzZmTcoujU\n3VO0XtWaHLY5ODDwAOXyl9M7kkk0XtaYBzEPuDT6ElaG9LWsJiRELcgqVEgVRA4OcP26OpFsyRJ4\n+BAqVQIvL1UQ5cmjd2IhhBAi/ZKSSAgL9iT2Ca1Xteb8g/P49/LHpYKL3pGEubz7rroePKhnird2\n9fFVFoQuYPmZ5US9iqJmkZp41vWkb82+5MySU+944g1u34ZFi9SCl4cP1QqNQYPUa84cVSR98IGa\nWZTRiqKQyBDarG5D3mx5CRqQ8WYQ/e7c/XPUXFiT79p8x8SGE/WO81ZOnlQFUb58EBioVgstW6Z+\na7SyAldXVQ61bJnxfn0KIYQQepCSSAgL93tRdO7+Odb3WE/XKl31jiTMITBQXdulz62GLxNe4nfO\nD+8Qb87cO0OerHkY5DgIT2dP427lEUYTH69GYS1bpn75JSerrtLKSq06+vhj+OqrjPNG/NidY7Rb\n046C2QsSNCAobcfc/xMLKHw9d3qy7PQyIidGUiB7Ad1yvK1Tp1T5Y2en5gvt2KG2TJYrB0OGwMCB\nr7edCSGEEMI4pCQSIh2IehVF+zXtCYkMYWXXlfSp0UfvSEKkiKZpHL1zFO8QbzaFbSIhOYHWZVvj\n5exFx4odsbay1juieIOICPD1VYXRjRtga6tOiBowAJYvT/9DgA/fPkz7Ne0pmrMoBwYewCG3g+ke\ntmKFug4aZLpn/IPouGiKzypOtyrd8O3iq0uG1Ni9G7p2hcRE9WvPzk4d+Dh0KDRtmnHKSiGEEMLS\nmLwkMhgM7YC5gDWwRNO0b/7n5ycCHkAi8BAYomnarX+6p5REIjOKjovGdZ0rweHB+HTySddHGIsU\nuHNHXUuU0DeHEd1/cZ/FpxazMHQhkdGRlMxTklF1RzG09lAK5SikdzzxBsnJ8NNPavbL2rWQlAS5\nc8Pw4dCnDzg6pr836wduHqDT2k445HYgaGAQxXMV//cvSscWhi5k1M5RHBt6jAYODfSO848eP4ZN\nm9Scod//mFerFowaBb17y6whIYQQwhxMWhIZDAZr4ArQGogAQgB3TdPC/vA5zYHjmqa9NBgMo4B3\nNU3r9U/3lZJIZFaxCbF029CNwGuBzG03l7H1x+odSZiKBWxRMZXE5EQCLgfgHeJN0M0gslhnoVe1\nXng5e1HPvp4MurZQz5+r4dY//aRWEiUnQ+XK4O6uXhUq6J3w322/vB23jW6Uz1+efQP2UTSnGQbD\nJySoq62t6Z/1PzRNw3GRI1YGK04NP2WR31svXkBAAPj5qdVDiYlgba1OKduyRW03E0IIIYT5pKUk\nSsli83rANU3TbmiaFg+sAzr/8RM0TTugadrL3/7xZ8CEa76FSN/sbO3Y2msrXSt3ZVzgOKYfmq53\nJGEqU6aoVwZkY2VDtyrd2D9gPxc8LzDMaRj+l/xpsLQBzoudWXFmBbEJsXrHFP8jd241m2jAAFUQ\nde4MRYrA1KlQsSLUrg3TpsG5c+r0NEvjd86Pruu7UqNIDYIHBZunIAJo3Vq9dHAs4hi/3P+FUXVH\nWVRB9OQJrFyptpMVLgx9+8LZs9CvH+TNqz528qQUREIIIUR6k5KSyB6484d/jvjtY39nKLArLaGE\nyOiy2mRlg9sG+tboy8dBH/PJ/k/Qaz6YMKFWrdQrg6taqCrzXObx68Rf8XbxJjYxlsHbBuMw24HJ\neydz8+lNvSOKP7C2VnOK+vWDbdvUXPU7d2DmTMieHT7/HGrWVKuKJk2CI0dUoaS3RaGL6LelH41L\nNmb/gP3mHd7s4aFeOlgQuoBcWXJZxBy7iAiYN08VP4ULq6HTJ07A4MEQHAy7dsGPP6rZQwcPQvny\neicWQgghxNtKyXazHkA7TdM8fvvn/kB9TdNGv+Fz+wGjgWaapsW94eeHA8MBSpYsWefWrX8cWyRE\nhpeUnMSonaNYfGox4+qPY1bbWVgZ0vk0WfHajRvqWrasvjnMTNM0gm8F4x3ijf9Ff5K1ZFwquODl\n7EXb8m3l17iFSEpSK4r8/OC//4X331cfv3dPbR3y94f9+9VOqyJF1DY1Fxdo0cL8c2W+PfItk/dN\npkOFDmx024idrZ15A+jk0ctH2M+yZ5jTMOa5zDP785OT1WqgwEB1al5IiPp45cpqBVGXLlC3rtq6\neOmS2mFrMKiCqFIls8cVQgghxG9MPZOoIfC5pmltf/vnjwA0TZv+P5/XCvgBVRA9+LcHy0wiIRRN\n05i4eyJzjs+hf83+LHVdiq21+edeCBPIwDOJUirieQQ+J33wOenD/Zj7lMtXDk9nTwY7DiafXT69\n42V6iYnQvz+sWwfffQcTJ/755589U6tD/P3VNTparUR65x21AqltW7VFzVQnpWmaxqcHPuU/h/5D\nr2q9WNl1JVmss5jmYf/k5W876rNnN+tjfy/Hzo86T7XC1czyzHv3YM8eVQzt3QuPHqnix9n5dTFU\nufKfv+byZfXbnabBgQNQpYpZogohhBDib5i6JLJBDa5uCUSiBlf30TTtwh8+pzawCbXi6GpKHiwl\nkRCvaZrGfw79h08PfEqHCh3Y4LaB7LbmfTMiTCA4WF2bNdM3hwWIT4pny8UteId4c/j2Yexs7OhT\now9ezl7ULlZb73iZWmKiOuVs40aYPRvGj3/z5yUkwLFjajBxYCCcOqU+XqiQKotatlTHmpcpY5zT\n0pK1ZMYHjueHEz/gUduDhR0XYm1lnfYbp4YOhW+ylkzFHypSPFdxfhr8k8meEx0NR4+q/2m7d8Pp\n0+rjhQur/67t2qlxTIX+5vDCq1fVb3GJieoeVauaLKoQQgghUsikJdFvD3AB5gDWwDJN0/5jMBim\nAaGapgUYDIZ9QA3g7m9fclvTNNd/uqeUREL81aLQRYzaOYqGJRqyw32HrLQQGdLZe2fxDvFmzbk1\nvEx4SUOHhng5e9Gjag+y2mTVO16mlJCgTjfbvBnmzoWxKTh08f59tdIkMFCtPHn4UH3cwUGVBk2b\nqmvFim9fGsUnxTN422D8zvnxXsP3+Lb1t/oObV6/Xl17/ePBrUa1+9pu2q1ph183P9xruBvtvk+f\nwuHD6oS74GBV9iUlgY0NNGr0uhiqVevfV4hdu6b6s7g4tYKoenWjxRRCCCFEGpi8JDIFKYmEeLNN\nYZvou6UvFQtUZHe/3RTPVVzvSCK1Ll9WVxnO8UZRr6JYcWYF80Pmc/XJVQrnKMwwp2GMqDOCEnlK\n6B0v00lIUB2Iv78aTuzllfKvTU6GsLDXxUNwsCqRQM0zatIE6teHevXAyQly5vz7e0XHRdN9Q3f2\n3tjL1y2+5sPGH1rUqV7m0nV9V47cPsKdCXdSXZ4mJ6vfhkJC1IDpw4fhl1/UtrAsWdR/k2bN1Kth\nQ3VkfUpdv64KothYVRDVqJGqiEIIIYQwASmJhMhg9t/YT5f1XSiYvSB7+u2hQoEKekcSqSEziVIk\nWUtm3419zDsxjx1XdmAwGOhcqTNezl60KNMiUxYEeomPh5491aln8+fDqFGpu4+mwZUrr0ujw4fh\n97MqrKygWjU146ZePfWqVk2VFg9iHuCyxoUz986wxHUJgxwHGe1/W5o8e6auZprYHfE8glJzSjH5\nnclMbzX9378A9e88MvJ1IXTiBISGwvPn6udz5lT/rn8vherVU6eQpcbNm+oeMTEQFKRWHQkhhBDC\nckhJJEQGFPprKO3XtMeAgcB+gTgVc9I7knhbR4+q6zvv6JsjHQmPCmdh6EKWnFrC49jHVC5YGc+6\nngx0HEjurLn1jpcpxMdDjx7qNKtFi2D4cOPc98GD1wXG79fHj9XP2dpCaafr3G3Zlrgsv/JR+Y0M\nbtSBUqWMM98ozcxc+E49MJUvf/qSG+NuUDpv6b/8/LNncP68ep079/r19Kn6eRsbVdz8XsI5O6th\n09ZGGOkUHq7+dTx/rgoiR8e031MIIYQQxiUlkRAZ1JXHV2i9qjVPYp+wyW0Tbcu31TuSEGbxKvEV\nGy5swDvEmxORJ8iZJSf9a/bHy9nLbKc8ZWZxcdC9O+zcCYsXg4eH8Z+haWpFyokTsPuXU/hZtScx\nKZHk1TshogEAuXKpVUYVKkD58q9f5cpB/vxmLJC2bFHXbt1M/qiEpARKzSlFrSK1mV13J9euqdk/\n16+ra1gY3L79+vNz5VJbvapXV1dnZ1UQZctm/Gy3bqmCKCoK9u9XWweFEEIIYXmkJBIiA/s1+lc6\n+HXg3P1zLOq4iKFOQ/WOJFLq/Hl1lWmuaRISGYJ3iDfrzq8jLimOZqWa4eXsRZfKXbC1ttU7Xob1\n6pXqRAIDYckSGDLENM/Zd2MfXdd3Jb9dfjWHLUvlP62QCQtT5cidO3/+urx5VWFUqhTY26tX8eKv\nf2xv/3YzdswpMVHNbIqM/PPr11/hZOxmLlTrAWsD4HKn//+a3LlVWVaxoiqDfn+VLGmesuzOHbXF\n7MkT2LcP6qbqj51CCCGEMAcpiYTI4KLjonHb6Mbu67v5rOlnfP7u5zKnJT2QmURG9ejlI5adXsaC\n0AWER4VTPFdxRtQZwTCnYRTLVUzveBnSq1fQpYs6vWz5chg40Lj3X/3LaoZsG0KlgpUI7BuIfW77\nv/3c2Fi18uj3FTW/v27fVgVLdPRfvyZ3bihQQK06yp8f8uV7/eP8+dUqHDu7N7+yZXt9upfVk0cA\nJOcvCKhVUAkJKtObXjExauvXkyevr398PXqkhkr/kY2NKrmedW5FYu6rvGd7gwrlrP9/9VSBAvpt\nvYuIUL+dPXyoCiJnZ31yCCGEECJlpCQSIhNISEpg5I6RLDuzjIG1BuLTyYcs1ln0jiX+SUiIuso7\nKqNKSk5i17VdeId4E3gtEBsrG7pX6Y6XsxeNSzaWAtXIYmOhc2dVDvj6Qv/+ab+npmlMC57G58Gf\n07x0c7b02kLebHnTdM/oaLUS548rc+7e/WtB8/vrf0uaf3KAdwFozsG3ypQr159Lqd9fhQr9ecWT\nvb362LWnV6g0rxJfNf+KT5p+8lbPMpXISFUQ3b8Pe/eqE9GEEEIIYdnSUhLZGDuMEMI0bK1tWeK6\nhFJ5SzH14FQioyPZ3HOzDPO1ZFIOmYS1lTUdK3akY8WOXH18lQWhC1h+ZjnrL6ynZpGaeNb1pG/N\nvuTM8g/nrIsUs7ODrVvB1RUGDVKra/r2Tf394pPiGbZ9GCvPrjRq4Z0rF1SqpF7/JjlZlUrR0X+/\nGujVq9efX3BjEwDWuL3+mK3t369Cyp5dbYezfcvdkAtDF2JjZWMx24rv3oUWLeDePbWaTAoiIYQQ\nIuOTlURCpEO+Z3zx2O5B1UJV2dlnJw65HfSOJN7kzBl1leN/TO5lwkv8zvnhHeLNmXtnyJ01N4Md\nB+Pp7EnFAhX1jpchvHwJHTuqI+1XrwZ397e/x9PYp3Tb0I2D4QeZ9u40pjSdIiu/fhObEIv9LHta\nl2vN+h7r9Y7DvXtqBVFEBOzeDY0a6Z1ICCGEECkl282EyIT2Xt9L9w3dyZU1FwG9A6hTvI7ekcT/\nkplEZqdpGkfvHMU7xJtNYZtISE6gddnWeDl70bFiR6ytjHAGeCYWEwMdOsChQ7B2LfTsmfKvvfH0\nBi5rXLgZdZNlrsvoWzMNy5HM7Zdf1LVmTZM9YsWZFQzeNpgDAw/wbul3TfaclLh/X/32decO7NoF\nTZroGkcIIYQQb0lKIiEyqXP3z9FpbScexDxgZdeV9KjaQ+9I4o9kJZGu7r+4z+JTi1l0chERzyMo\nmackI+uMxMPJg0I5CukdL9168QJcXODoUVi3Dnqk4LednyN+xnWtK0laEv69/GlaqqnpgxpT3t/m\nJUVFmewR9ZfUJzoumgueF3RdXfXgATRvDuHh8OOP6kQzIYQQQqQvaSmJrIwdRghhPjWK1ODEsBM4\nFnXEbaMbX/30FXoVv+INHB2lINJRkZxFmNJ0CjfH3WRzz82Uz1+ej4M+xmG2AwP8B3A84rh8v6RC\nzpyqPGjQAHr3hi1b/vnz155bS3Pf5uTOmptjQ4+lv4IIYNIk9TKRU3dPcSLyBCPrjtS1IHr4EFq2\nVKfI7dwpBZEQQgiRGclKIiEygFeJrxi2fRirf1lNnxp9WOq6lGw22fSOJeR0M4sT9jCM+SHzWXl2\nJdHx0dQpVgcvZy96V++Nna2d3vHSlehoaNtW/TLfuBG6dPnzzydryXwa9ClfH/6aJiWbsLnnZlnB\n9TeGBQzD77wfkRMj03zKW2o9eqSGVF+9Cjt2qLJICCGEEOmTbDcTQqBpGtMPT+eToE+ob1+frb23\nUjRnUb1jZW4yk8hiRcdFs+qXVXiHeBP2MIz8dvkZ4jiEUc6jKJuvrN7x0o3nz1VRdPIkbNqkTkAD\n9e+3n38/Ai4HMMxpGPNc5hnlBDPdHD+uriY43uvZq2cUn1Uc9+ruLHFdYvT7p8Tjx6oUunwZtm+H\nVq10iSGEEEIII5GSSAjx/7Zc3EJ///4UsCtAgHsAjkVlu5Nuzp9X1+rV9c0h/pamaQTfCsY7xBv/\ni/4ka8m4VHDBy9mLtuXbYmWQXdn/5tkzaNMGTp9WW8+qNrqB61pXLj26xOy2sxldb3T6P8HMhDOJ\nfjj+A2MDxxI6LFSXAwiePFGlUFgYBASo/5ZCCCGESN+kJBJC/Mmpu6dwXevKk9gnLOu8jN7Ve+sd\nSQiLF/E8Ap+TPvic9OF+zH3K5SvHqLqjGFx7MPnt8usdz6JFRUHr1nAm6iDZB/XA2iaZDW4baFU2\ngyxJ+e9/1XXyZKPeVtM0qi+oTg7bHJwYdsKo906Jp09VQXT+PGzbBu3amT2CEEIIIUxABlcLIf7E\nqZgTocNDcSrmhPtmd97f8z6JyYl6x8p8jh5VL5EuOOR2YFrzadyecJu13ddSLFcxJu2dhMMsBzwC\nPDh997TeES1W3rzQe+YCEvu0JvpeIWZWOp5xCiJQ5ZCRCyKAQ7cPEfYwjFF1Rxn93v8mKkqtGjp/\nHvz9pSASQgghhCIriYTIwOKT4pkQOIH5ofNpVbYV67qvo0D2AnrHyjxkJlG6d/beWeaHzGf1udW8\nTHhJQ4eGeDl70aNqD7LaZNU7nkV4lfiK0T+OZunppbQu5cI9bz+unMuTsbYu/f49/Pv3tJG4b3Yn\n8FogkRMjyW6b3aj3/if/u0WwY0ezPVoIIYQQZiDbzYQQ/2jZ6WWM2jmKgWzE/AAAIABJREFU4rmK\n49/LX+YUmcvly+paqZK+OUSaRb2KYsWZFcwPmc/VJ1cpnKMww5yGMaLOCErkKaF3PN2ER4XTY0MP\nTt49ySdNPuGLd78g6ql1xhuCbIKZRPdf3KfE7BJ4Onsyp90co9333/w+bDw0VA0b79zZbI8WQggh\nhJlISSSE+FcnIk/QbX03nsQ+YYnrEvrU6KN3JCHSnWQtmX039uEd4s2OKzsA6FypM17OXrQo0yL9\nD2h+C3uu78F9szuJyYms6roK10qu//9zvx+nfu2aOk69RQsdgxrD3LnqOm6c0W45/dB0Pg76mIte\nF6lcsLLR7vtPoqPVtrITJ2DDBuja1SyPFUIIIYSZSUkkhEiR+y/u47bRjUO3DzG+/nhmtJ6Rvo+l\ntnTBwerarJm+OYRJhEeFszB0IUtOLeFx7GMqF6yMZ11PBjoOJHfW3HrHM5lkLZnph6bz6YFPqVa4\nGlt6bqFCgQp/+byHD1U5dP06/Pij0XdqpWtJyUmU+74cZfOVJWhgkFmeGR0N7dvDzz/D+vXQvbtZ\nHiuEEEIIHUhJJIRIsYSkBCbtmcT3J76ngUMD1vdYT8k8JfWOlTHJTKJM4VXiKzZc2IB3iDcnIk+Q\nwzYHA2oNwMvZi2qFq+kdz6ievXrGwK0D2XZ5G+7V3VncaTE5suT4289/8ACaN4fwcNi1C5o2NV9W\no9q1S13btzfK7XZe2UnHtR3Z0GMDbtXcjHLPf/LiBbi4qDn6a9eCm+kfKYQQQggdSUkkhHhrGy9s\nZGjAUGytbVnVdRUuFVz0jpTx3LihrmXL6ptDmE1IZAjeId6sO7+OuKQ4mpVqhpezF10qd8HW2lbv\neGly5t4Zem7syc2om3zX5jvG1BuTou119++rouj2bQgMhMaNzRDW2Iw8k6ijX0dO3j3J7fG3Tf7r\nIiYGOnSAQ4fAzw969TLp44QQQghhAdJSElkZO4wQIn1wq+bGyeEnKZG7BB38OvDx/o9JTE7UO1bG\nUrasFESZjLO9Myu6rCBiYgQzWs3g1rNb9NzUk9JzS/PFwS+4G31X74hvTdM05ofMp8GSBsQkxHBg\n4AHG1h+b4vlLRYpAUBA4OKiFOEePmjiwKcyYoV5GEB4Vzo9Xf8SjtofJC6KXL6FTJ1UQrV4tBZEQ\nQggh/p2sJBIik4tNiGXsrrEsOb2EpqWasrb7WornKq53rIxh3z51zRDHO4nUSEpOYte1XXiHeBN4\nLRAbKxu6V+mOl7MXjUs2tvhB189ePcNjuwebwjbRvnx7fLv4UihHoVTd69df1Q7Me/dgzx5o0MC4\nWdOLj/d/zIwjMwgfF27Sk/FiY1VBFBQEK1dCv34me5QQQgghLIxsNxNCpNnKsysZtXMUObPkZE23\nNbQqK8VGmslMIvEH155cY0HIApadWUbUqyhqFK6Bl7MXfWv2JWeWnHrH+4uQyBB6berF7We3md5y\nOu+98x5WhrQtQI6MVN8WDx7A3r1Qr55xspqcv7+6pvE4sPikeErMLkEDhwZs673NCMHeLDZWHW2/\nbx+sWAEDBpjsUUIIIYSwQFISCSGMIuxhGD029ODio4u8/877fNXiKzn9LC3u3FHXEqZbLSDSn5cJ\nL/E754d3iDdn7p0hd9bcDKo1CE9nTyoVrKR3PDRNY+7xuUzeO5liuYqxrvs6GpZoaLT7R0SooujR\nI1UUOTsb7damY6SZROvOr8N9szu7+u6iXfl2Rgj2V69eQZcuarXWsmUwaJBJHiOEEEIICyYlkRDC\naF4mvGTi7oksOrmIOsXq4Nfdj4oFKuodS4gMR9M0jkUcwzvEm40XNpKQnEDrsq3xcvaiY8WOWFtZ\nmz3To5ePGBowlIDLAbhWcmV55+Xkt8tv9OfcuQPNmsHTp2q1S506Rn+Ecfn6quvAgWm6TbMVzYh4\nHsHVMVfTvCrrTeLi1GKnXbtg6VIYMsTojxBCCCFEOiAlkRDC6LZe2srQgKG8SnzFD+1/YLDjYIuf\nn2JxAgPVtZ1pVgyIjOP+i/ssPrWYRScXEfE8gpJ5SjKyzkg8nDxSPQPobQVeC2TwtsE8iX3CjFYz\nGFd/nEm/52/dUiuKnj2D/fuhdm2TPcoiXHhwgeoLqjOj1QwmN5ps9PvHxUH37rBzJ/j4wLBhRn+E\nEEIIIdIJKYmEECYR+TyS/v79ORB+ALeqbizquIh8dvn0jpV+yEwi8ZYSkxMJuByAd4g3QTeDyGKd\nhV7VeuHl7EU9+3omKW1iE2L5YN8H/HDiB6oVqsaabmuoVbSW0Z/zJuHhakXRixeqKHJ0NMtj3976\n9eqahuPBxu4aq0rACRFGL/7i46FHD9i+HRYuhBEjjHp7IYQQQqQzUhIJIUwmKTmJmUdnMuXAFIrl\nLMaqrqtoVrqZ3rHSh3v31LVoUX1ziHQp7GEY80Pms/LsSqLjo6lTrA5ezl70rt4bO1s7ozzjzL0z\n9Nnch4uPLjKu/ji+afUN2WyyGeXeKXXzpiqKXr5UJ3HVrGnWx6dMGmcSxcTHUHxWcTpV7MTqbquN\nGEwVRD17wrZt4O0Nnp5Gvb0QQggh0qG0lETG3xAvhMhQrK2s+aDxBxwdcpSsNll51/ddJgROIDYh\nVu9olq9oUSmIRKpVLVSVeS7ziJwYibeLN7GJsQwJGILDbAfe3/M+N57eSPW9k7Vkvj3yLfUW1yPq\nVRS7++1mTrs5Zi+IAMqUgQMHwM4OWraE8+fNHuHfLVqkXqm09vxansc9Z1TdUUYMBQkJ0Lu3Koh+\n+EEKIiGEEEKknawkEkKkWEx8DB/s+wDvEG8qFaiEbxdf6jvU1zuW5dq+XV07ddI3h8gQNE0j+FYw\n3iHe+F/0J1lLxqWCC17OXrQt3zbFg5BvPr3JkIAh/9fencfZXP7/H39cZsxgMGLs21CWsg6GRFJZ\nIiEtCJEQhvxSNy361Cc++VY+LdLYkj0+lQhlyRKVxAyNPbsMIoaxzYxZzvX74z00lWVmnDlnzDzv\nt9u5XWfOuc77/Rq3y9t4znVdb1YfXE2n2zsxqd0kihUolsXVX9/evc6MoqQkJzSqUcPbFbmHtZYG\nHzcgKSWJzf03u23JYFISPPEEzJ0LH3wAQ4a45bAiIiKSA2gmkYh4RIBfAB+1/YgVPVYQlxTHXVPu\nYvjK4VxMvujt0rKnd991HiJuYIyheXBzvnjsCw7+v4O82uxVIo9G0nZ2W6qOrcq7P73LqfhTV/28\ny7oI3xBOrfG12Hh0I5+0/4S5j83NFgERwG23Odt3+frCfffBjh3eriiN6dP/vMNZBkUcjWDT75vo\n36C/2wKi5GTo3t0JiN57TwGRiIiIuI9mEolIppxJOMPQZUOZEjWF2iVrM6PjDI9tdnvTOHnSaYOC\nvFuH5FiJKYnM2zmP8Ihwfjz0I/l989O1ZlfCGoZRr3S9y/32n95P7wW9WfPbGlrf2pqPH/qY8oHl\nvVj51e3a5ez5bq0TGlWv7u2KuKE9iZ5a8BRfbP+Co88fpbB/4RsuJTkZevSA//0PRo+GF1644UOK\niIhIDqONq0XEa77e/TV9F/UlJi6G4XcP56WmL+Hv6+/tskRync3HNjMuYhyzts4iLimOxuUaM6DB\nAOfv5nfD8c3jy/ut3+epuk9l6a3t3WHnTrj3XjDGCYqqVfNyQfPnO+3DD2foY6fiT1H2vbL0rNOT\nCe0m3HAZKSnw5JMweza8/TYMG3bDhxQREZEcSCGRiHhVTFwMzy59ltlbZ3NH8TuY/NBkGpdv7O2y\nvG/ePKft1Mm7dUiuEpsQy7SoaXzw8wf8duY3ACrfUpk5nebQsFxDL1eXfjt2OEGRjw+sWQNVqni7\noox7f937DP12KFHPRN3wTMuUFHjqKZg5E0aNgpdfdlORIiIikuNoTyIR8apiBYrxaadPWfzEYs4n\nnqfJlCYMWjyIsxfPers07/rwQ+ch4kEBeQNISE7g+IXjBOQNoG6puhw4fYDGUxrz8GcPs3L/Srz1\nC6KMuOMOWLnS2aD53nudja29JhN3N7PWMmHjBBqXa+yWgOjpp52AaORIBUQiIiKSdTSTSETc6nzi\neV5d9Sofrv+QsoXLMv7B8bSr2s7bZXnHmTNOGxjo3Tok11gXvY5+X/dj2x/b6HR7Jz58wPl7eDD2\nIBMjJ/Lxpo+JiY+helB1BjYYSM+6Pd2yT05W2rrVCYny53eWnt16qxeKyMSeRCv3r6TFzBbM6DiD\nHnV6ZPrULhf06QNTp8Ibb8Brr2X6UCIiIpJLaLmZiGQ76w+vp8+iPmz7YxuP13icMQ+MoVTBUt4u\nSyRHik2I5eUVLzNh4wTKFy7PR20/on219v/ol5CcwOfbPyc8IpwNRzYQkDeAHrV7ENYwjJolanqh\n8vTZvNm541lAgLP0rFIlDxewZInTtmmT7o88+vmjrD64msNDD5PPN1+mTutywTPPwOTJTjj0xhuZ\nOoyIiIjkMgqJRCRbSkxJZPTa0Yz4fgT5fPMxovkIwhqG4ZvH19ulecZnnzlt587erUNyLGstn2//\nnCFLh3Ai7gRDGg1hxL0jKOhX8LqfjTwaSXhEOHO2zuFiykXuqXgPYaFhdKzekbw+eT1QfcZERTlB\nUeHCzoyi4GBvV3R1R88dpcL7FXjuzucY3Wp0po7hcsGAATBpEgwf7iwzy+b7jYuIiEg2oZBIRLK1\nPTF7eHbpsyzdu5RaJWoR3jacuyve7e2ysl7z5k67erU3q5Ac6teTvzJk6RC+3fct9UvXZ9JDk/5y\n2/v0Ohl3kim/TGF85HgOxh6kTKEy9KvXj371+1G6UOksqDzzNm2C++93Vn+tWQMVKnjoxGPGOO2Q\nIenqPmLNCF5f/Tp7Bu/htqK3Zfh01kJYGIwf7+w/9OabCohEREQk/RQSiUi2Z61lwa4FDFk6hENn\nDtG9dndGtxyds5egxcU5bYEC3q1DcpSzF88yYs0IxqwfQ4G8BRh570jCQsPwyeNzQ8dNcaWwZO8S\nwiPCWbp3Kb55fHnk9kcICw2jaYWmmGySUmzc6ARFRYs6QVH58h44aQb2JEp2JRP8QTA1StRgWfdl\nGT6VtTB4MISHO7e4f+stBUQiIiKSMQqJROSmEZcUx6gfRjH6p9G5cwmaSCa5rIsZm2fw0oqX+OPC\nH/QO6c2o+0dRIqCE28+199RexkeMZ0rUFGITYqlVohZhoWF0q90tXUvZslpEBLRoAcWLOxP1ypXL\n4hNemg14aXbgNSz4dQEdP+vI/M7z6Vi9Y4ZOY60zWWnsWHj+eRg9WgGRiIiIZJxCIhG56eyJ2cPg\nJYNZtm8ZtwfdzuiWo2lbpW22ma3gFrNmOW337t6tQ256G45sYPCSwWw4soHG5RrzYZsPaVAmU//u\nZ0hcUhyzt84mPCKcqGNRFPYvTK86vRgYOpBqQdWy/PzXsn49tGwJpUo5GU6ZMl4t57IHZj3A9hPb\nOTDkQIbCb2th6FD44AN47jl4910FRCIiIpI5NxIS5XF3MSIi6VGlWBWWdFvCV52/ItmVTLs57Wg1\nqxWbj232dmnuM3my8xDJpOgz0fT6qheNJjfi0JlDzOg4gx97/+iRgAigQN4C9KnXh039NrG291ra\nVW3H+MjxVA+vTquZrVjw6wJSXCkeqeXvGjWCZcvg99/h3nudNsu8847zuI59p/axbN8y+tbrm+GA\n6IUXnIBoyBAFRCIiIuI9mkkkIl6XmJLIhMgJvLHmDU7Hn6Z3SG9G3jsy222am2FJSU6bN/vdKUqy\nt9iEWN768S3GrB+DtZYhjYbwarNXKeRfyNulcfz8cSZvmsyEjRM4fPYwFQIr0L9+f/rU60PxgOIe\nr2ftWmjd2llytnq1M7PI7dK5J9Gw5cN4b917HHruEGUKpW9qk7Xw4ovO0rJBg+DDDxUQiYiIyI3R\ncjMRyRFOx5/mP9//h7EbxuLn48eLTV5kaOOhBPgFeLs0EY+4mHyR8ZHjGfn9SE7Hn6Z77e6MvHck\nFYtU9HZp/5DsSmbhroWER4Sz6sAq/Hz8eLzG4wwKHUTDsg09unT0hx+gTRvnbmfffQclS7r5BOvX\nO22jRlftkpCcQLn3ynFP8D18+fiX6TqstfDKK87m1AMGOJtVKyASERGRG6WQSERylL2n9vLiiheZ\nt3MeJQNK8srdr/BM/Wfw9/X3dmkZM22a0/bq5c0q5Cbgsi4+2/YZw1cN50DsAVpWbsk7Ld+hbqm6\n3i4tXXae2Mm4iHFM3zydc4nnqF+6PmGhYXSp2YX8efN7pIbvv3eCokqVYNUqKOH+/byvadaWWfSY\n34PlPZbTonKL6/a3Fl59FUaNgmeegXHjII82ARARERE3UEgkIjnST9E/MXzVcFYfXE35wuV5/Z7X\n6Vm3581zJ7RLd0K6dGckkb+x1vL17q95ffXr/HLsF+qUrMM7Ld+h1a2tvF1appy7eI6ZW2YSHhHO\njhM7KJq/KL3r9mZA6AAq31I5y8+/ejW0bQu33uoERcXdtfrtP/9x2ldfvWqXJlOacOLCCX4d9Ct5\nzPXTntdeg5EjoU8fmDhRAZGIiIi4j0IiEcmxrLWsPLCS4auGs+HIBqoUrcIbzd+gc83O6fqPmEh2\nZK1lyd4lvL76dSKPRlL5lsq8fs/rdKvVDZ88Pt4u74ZZa1nz2xrCI8KZv3M+LuuiTZU2DAodROvb\nWmfp391Vq+DBB6FqVVi5EoKC3HDQ6+xJtOX4FupMqMO7rd5laOOh1z3cG2/Av/8NvXvDxx8rIBIR\nERH3UkgkIjmetZZFuxcxfNVwtv2xjVolavGvZv+i0+2dcsR/qiV3sNayfP9yXvvuNdYfWU9wkWD+\n1exf9Kjdg7w+OXOD88NnDzNp4yQmbZzE8QvHufWWWxnQYABPhTxF0fxFs+ScK1bAQw9B9erO82LF\nbvCAW7Y4be3aV3x7wNcDmLZ5GkeGHrnu9zRypDOLqFcv+OQTBUQiIiLifgqJRCTXuLR3y7/X/Jvd\nMbupHlSdl5u+TNeaXbPff7I//thp+/b1bh3iddZaVuxfwRtr3mBt9FoqBFbg1btfpWfdnvj5+Hm7\nPI9ITElk3s55hEeE8+OhH8nnm48naj5BWMMw6pWu5/bzffsttG8Pd9zhBEVFsyaP4tzFc5R5rwyP\n3P4I0zpOu2bfUaNg+HDo0QOmTgUf5dsiIiKSBRQSiUiuk+JKYe6OuYz6cRRbjm+hUpFKvNjkRXrV\n7ZV9Nrhukbp57YoV3q1DvCbFlcKXO7/k7bVvs+n3TZQtVJbhdw+nd0jv7DNOvWDzsc2MixjHrK2z\niEuKo3G5xoSFhvHoHY+69c9l6VLo0AFq1YLly+GWWzJ5oH/9y2lHjvzHW+MjxjNw8UB+fvpnGpW7\n+t3P3n4bXnoJunWD6dMVEImIiEjWUUgkIrnWpY1/3/zhTdYfWU+ZQmV4ofEL9KnXh0L+hbxdnuRS\nCckJTI+azn/X/Ze9p/ZStVhVht01jO61u+fqcOjvYhNimRY1jXER49hzag/FCxSnb72+9G/Qn/KB\n5d1yjsWL4eGHoU4dZ3bRpe2FMuQqexJZa6kzoQ6+eXzZ2G8j5ir3rx89GoYNg65dYeZMBUQiIiKS\ntRQSiUiud2mD6zd/eJPVB1cT6B9In3p9GNxwMBWLVPR2eZJLxCbEMjFyIu///D7HLxwntEwoLzV9\niQ7VOmjvrGtwWRcr9q8gPCKcr3d/DUD7au0ZFDqI+yrdd9XwJb2+/ho6dYKQECcoCgzM4AF27XLa\natX+8vLaQ2tpOrUpk9pNom/9Ky8rfe89eP556NwZZs0C35vk5owiIiJy81JIJCKSxoYjG3j/5/f5\nYvsXADxyxyM8d+dz3FnuTs8WMm6c0w4c6NnzisftOLGDjzZ8xIzNM7iQdIFWt7bipSYv0Ty4+Q0H\nHLnNwdiDTIycyMebPiYmPobqQdUZ2GAgT9Z5ksB8GU13/rRwITz6KNSvD8uWQeHCN15r93ndWbR7\nEUeHHiXAL+Af73/wATz3HDz2GMyerYBIREREPEMhkYjIFRw6c4iPNnzEpI2TOHPxDHeWu5Pn7nyO\nh6s/7JlNrtu0cdolS7L+XOJxKa4UvtnzDWM3jGXF/hX4+/jTtVZXnm34LCGlQ7xd3k0vITmBz7d/\nTnhEOBuObCAgbwA9avcgrGEYNUvUzNQxv/rKCWwaNnT2KyqU3hWpw4Y57TvvXH7pxIUTlHu/HP3q\n9WNs27H/+MjYsfDss/DIIzBnDuTNZvvqi4iISM6lkEhE5BrOJ55n6i9TGbN+DPtO76NkQEl6h/Sm\nb72+VLqlkrfLk5vMqfhTTIuaxkcbPuJA7AHKFirLwNCB9K3Xl+IBxb1dXo4UeTSS8Ihw5mydw8WU\nizSr2IxBoYPoWL1jhgPfL790ln41buzktwULpuNDV9iTaPTa0QxbMYxtA7ZRo0SNv3QPD4dBg6Bj\nR/j8cwVEIiIi4lkKiURE0iHFlcLSvUuZuHEi3+z5BmstrW5txTP1n+Ghag/hm0drQeTKXNbFdwe+\n45NfPmHeznlcTLnI3RXuZnDDwZkKKiRzTsadZMovUxgfOZ6DsQcpU6gM/er1o1/9fpQuVDrdx/ni\nC2cT6SZNnI2tA/65UuyvDh1y2goVAGc8VB1blbKFy7Km15q/dJ0wAQYMgPbtnfP4+WXkOxQRERG5\ncQqJREQyKPpMNJ/88gmTN03myLkjlC5YmqdDnubJOk9SpVgV95xkzBinHTLEPccTjzt89jBTf5nK\n1KipHIg9QJF8RehWqxt96vWhbqm63i4v10pxpbBk7xLCI8JZuncpvnl86XR7J8JCw7i7wt3p2gfq\ns8/giSegWTNnY+vrBkVpLNu7jAc+fYA5j8yhS80ul1+fNAmeeQbatXNmLCkgEhEREW9QSCQikknJ\nrmQW71nMxI0TWbJnCRZLo7KN6FG7B51rdiaoQFDmD96+vdMuXOieYsUjLiReYNHuRczYPINl+5bh\nsi7uq3QfT4c8zcPVHyZ/3vzeLlHS2HtqL+MjxjMlagqxCbHUKlGLsNAwutXuRkG/a68lmzMHuneH\ne+5xgqICBa7S8VLQmxr8dvxfR36K/ono56Lx9/UHYPJk6NsX2raFefPA399d36GIiIhIxigkEhFx\ngyNnjzB762xmbpnJ1j+24pvHl7ZV2tKjdg/aVW1HPt983i5RskhiSiLf7vuWOdvmsODXBVxIukDZ\nQmXpVbcXvUN6U/mWyt4uUa4jLimO2VtnEx4RTtSxKAr7F6ZXnV4MDB1ItaBqV/3cp5/Ck0/Cffc5\neW7+K2WAafYkij4TTfCYYIbdNYz/a/F/AEydCk8/Da1bw/z5kE+XChEREfEihUQiIm62+dhmZm6Z\nyeyts/n9/O8U9i/MQ1Uf4pHbH6H1ba0pkPdqUw7kZpHiSuGHQz8wZ+sc5u6cy6n4UxTNX5RHb3+U\nrrW6cneFu/HJ4+PtMiWDrLWsO7yO8Ihwvtj+BUmuJFpUbkFYaBjtqra74t5jM2dCz57QogUsWHCF\noOjkSacNCuK1717jP9//h/1D9hNcJJjp0+Gpp6BlS+ezCohERETE2xQSiYhkkRRXCqsOrOJ/2/7H\ngl0LiImPoUDeArSt0pZO1TvxYNUHKexf+Mof/u9/nfaFFzxXsFxTXFIcK/avYMGvC1i0exEn4k4Q\nkDeADtU78ETNJ2h5a0v8fLSRTE5x/PxxJm+azISNEzh89jAVAivQv35/+tTr84870U2bBr17Q6tW\n8NVXVw57klKSqPhBRUJKh/DNE99cDpfuv/8as5BEREREPEwhkYiIByS7kllzcA1f7vyS+b/O59j5\nY/j5+NGyckva3NaGNlXa/Lks6dNPnQ1K4uOhYkV4803o1s2730AudeLCCb7e/TULdi3g233fEp8c\nT6B/IG2rtKVj9Y48WOVBAvwysGux3HSSXcks3LWQ8IhwVh1YhZ+PH4/XeJyw0DAalW10eaPrKVOc\nZWP/2FdowAAA5g6+n8e+eIxFXRdxNrIdPXpA8+awaNE19jMSERER8TCFRCIiHuayLtZFr+PLnV+y\ncNdC9p3eB0DVYlUZfqgST4xdjW/CxT8/UKCAc+sjBUVZLjElkXXR61i+fznL9y8n8mgkLuuifOHy\ndKjWgQ7VO9CsYjPNGMqldp7YybiIcUzfPJ1zieeoX7o+YaFhdKnZhfx581/egPrBB507lPn7c3lP\novs/rM++U/sYVXIfPbr70KwZfPONAiIRERHJXhQSiYh42Z6YPSzdu5Qle5cwPmwJFc/8s4+tUAHz\n22+eLy6Hs9ay/cR2lu9zQqE1v60hLikOH+NDo3KNaFm5Je2rtSekVEi6bo0uucO5i+eYtWUWH0V8\nxI4TOyiavyi96/ZmQOgAln9emf794aGHYO5c8EuOY1fMLqpPqUeX4m/y+eBXaNoUFi+GAE1CExER\nkWwmy0MiY8wDwBjAB5hsrX3rb+/7AzOA+kAM0Nlae/Bax1RIJCI5lc2TB3OFa6sLaDn9PppVaMY9\nwffQqGwj3U49E+KT4ok4GsFP0T+xNnotP0X/xKn4U4Azk6tl5Za0rNyS5sHNCcwX6OVqJbuz1rLm\ntzWER4Qzf+d8XNZFmyptqHg8jPHPP8CzdQcxdN8kyp9N4VAgvFK0J9Flp7FkCRQs6O3qRURERP4p\nS0MiY4wPsBtoCRwGIoCu1todafoMBGpba/sbY7oAD1trO1/ruAqJRCTHCg6GK8wYOlWiEC1G3EbU\nsSgsFt88vtQsUZMGpRvQoEwDQsuGUrNETS2DSiPFlcKumF388vsvbPp9E2uj17Lp900kuZIAqFas\nGk3KN6FJhSbcX+l+Khap6OWK5WZ25OwRJm2cxMSNEzl+4ThPRhVi3DfnCEj6s88FX5jddQB9Z4zz\nXqEiIiIi15DVIVFj4N/W2tapX78MYK39vzR9lqX2WWeM8QWOAcXtNQ6ukEhEcqxPP4V+/SAu7s/X\n0uxJFJsQy9pDa1l3eB2RRyOJOBpxeSaMn48fdUrWIaRUCDVK1OC5lB71AAAJkUlEQVSO4ndQo3gN\nShUsleOXSp1JOMOvJ38l6lgUvxz7hahjUWw5voX45HgA/H38CS0bSpPyTbir/F3cVf4uggoEeblq\nyYkSUxKZt3MedzbtSvAVlo7+VtiHimeSPV+YiIiISDpkdUj0KPCAtbZP6tc9gEbW2kFp+mxL7XM4\n9et9qX1O/u1Y/YB+ABUqVKj/m/bmEJGc6tNPYfhwOHQIKlS45t3NrLUcjD1IxNGIy6HR5mObOZ1w\n+nKfIvmKXA6MqharSnCRYCoVqURwkWCK5i960wRIFxIvEH02mj0xe9gVs4tdJ3ex+9Rudp3cxfEL\nxy/3C/QPpG6puoSUCiGkdAghpUKoHlSdvD55vVi95DYuY8hzpdeBPF7a01FERETkem6akCgtzSQS\nEbk6ay3HLxxnx4kd7Dixg+1/bGfHSaeNiY/5S9+CfgUvh0ZlC5WlRECJy4+SBUtefh7oH4hPHh+3\n15qUksSp+FOXHzHxMcTExXDk3BEOnz1M9Nlopz0T/ZfgCyCoQBDVilWjWrFqVC1WlWpB1ahTsg7B\nRYJvmuBLcq7fAn2peDbln69rJpGIiIhkYzcSEvmmo88RoHyar8ulvnalPodTl5sF4mxgLSIimWCM\noVTBUpQqWIr7Kt33l/diE2I5GHvw8uPA6QMcPOO06w6vIyYuBsuVfwGQ3zc/Bf0KXn4E+AVQ0K8g\nfj5+5DF5MBjymDx/eSSmJJKQnHD5EZ8c77RJ8cQmxHIu8dxVv4+gAkGUL1yeioEVaVq+KeUKl6N8\nYHluK3obVYtVpWj+om79cxNxp5Wd+tF51ngC0uRBF3yd13t7rywRERGRLJOekCgCqGKMqYQTBnUB\nnvhbn4VAT2Ad8Ciw6lr7EYmISOYVyVeEuqXqUrdU3Su+n+xKJiYuhj8u/HH5cfzCcc5ePMv5xPNX\nfMS6YnFZFy7rwlp7+bnLusjrk5d8vvnI75ufIvmKUMq3FPl885HPNx9F8hWhaP6iFMtfzGkLOG3R\n/EUpXbC07t4mN7XeU8cxBbh/nnN3s+jCPk5ANFWbVouIiEjOdN3lZgDGmLbAB4APMMVa+6YxZgQQ\naa1daIzJB8wEQoBTQBdr7f5rHVPLzURERERERERE3Curl5thrV0MLP7ba6+leZ4APJaZAkRERERE\nRERExPuudNMOERERERERERHJZRQSiYiIiIiIiIiIQiIREREREREREVFIJCIiIiIiIiIiKCQSERER\nEREREREUEomIiIiIiIiICAqJREREREREREQEhUQiIiIiIiIiIoJCIhERERERERERQSGRiIiIiIiI\niIigkEhERERERERERFBIJCIiIiIiIiIiKCQSEREREREREREUEomIiIiIiIiICAqJREREREREREQE\nhUQiIiIiIiIiIoJCIhERERERERERQSGRiIiIiIiIiIigkEhERERERERERFBIJCIiIiIiIiIiKCQS\nEREREREREREUEomIiIiIiIiICGCstd45sTHngF1eObmI5wQBJ71dhEgW0ziX3EDjXHIDjXPJDTTO\nJTeoZq0tlJkP+rq7kgzYZa1t4MXzi2Q5Y0ykxrnkdBrnkhtonEtuoHEuuYHGueQGxpjIzH5Wy81E\nREREREREREQhkYiIiIiIiIiIeDckmuTFc4t4isa55AYa55IbaJxLbqBxLrmBxrnkBpke517buFpE\nRERERERERLIPLTcTERERERERERHPhUTGmMeMMduNMS5jzFV3kzfGHDTGbDXGRN3Ijtwi3pCBcf6A\nMWaXMWavMeYlT9YocqOMMUWNMcuNMXtS21uu0i8l9VoeZYxZ6Ok6RTLjetdnY4y/Meaz1PfXG2OC\nPV+lyI1JxzjvZYw5keYa3scbdYpkljFmijHmD2PMtqu8b4wxH6b+HdhijKnn6RpFblQ6xnlzY8yZ\nNNfy19JzXE/OJNoGdAK+T0ffe621dXVrQrkJXXecG2N8gHCgDXAH0NUYc4dnyhNxi5eAldbaKsDK\n1K+vJD71Wl7XWtvec+WJZE46r89PA6ettbcB7wNve7ZKkRuTgZ9DPktzDZ/s0SJFbtw04IFrvN8G\nqJL66AeM90BNIu42jWuPc4Af0lzLR6TnoB4Liay1O621uzx1PhFvSOc4bwjstdbut9YmAv8DOmR9\ndSJu0wGYnvp8OtDRi7WIuFN6rs9px/9c4H5jjPFgjSI3Sj+HSI5nrf0eOHWNLh2AGdbxM1DEGFPa\nM9WJuEc6xnmmZMc9iSzwrTFmozGmn7eLEckCZYHoNF8fTn1N5GZR0lr7e+rzY0DJq/TLZ4yJNMb8\nbIxRkCQ3g/Rcny/3sdYmA2eAYh6pTsQ90vtzyCOpy3DmGmPKe6Y0EY/Rz+OSWzQ2xmw2xiwxxtRI\nzwd83Xl2Y8wKoNQV3hpurV2QzsM0tdYeMcaUAJYbY35NTchEsgU3jXORbO1a4zztF9Zaa4y52m0y\nK6ZezysDq4wxW621+9xdq4iIuN0iYI619qIx5hmc2XP3ebkmERHJmE04P4+fN8a0Bb7CWWJ5TW4N\niay1LdxwjCOp7R/GmPk4U2IVEkm24YZxfgRI+xu5cqmviWQb1xrnxpjjxpjS1trfU6dm/3GVY1y6\nnu83xqwGQgCFRJKdpef6fKnPYWOMLxAIxHimPBG3uO44t9amHdOTgXc8UJeIJ+nnccnxrLVn0zxf\nbIwZZ4wJstaevNbnstVyM2NMgDGm0KXnQCucjYBFcpIIoIoxppIxxg/oAujOT3IzWQj0TH3eE/jH\nDDpjzC3GGP/U50FAE2CHxyoUyZz0XJ/Tjv9HgVXW2qvNphPJjq47zv+2N0t7YKcH6xPxhIXAk6l3\nObsTOJNmKb1IjmCMKXVp30RjTEOc/Oe6v9hy60yiazHGPAyMBYoD3xhjoqy1rY0xZYDJ1tq2OPta\nzE/9PnyB2dbapZ6qUeRGpWecW2uTjTGDgGWADzDFWrvdi2WLZNRbwOfGmKeB34DHAYwxDYD+1to+\nwO3ARGOMC+cfpLestQqJJFu72vXZGDMCiLTWLgQ+AWYaY/bibBbZxXsVi2RcOsf5s8aY9kAyzjjv\n5bWCRTLBGDMHaA4EGWMOA68DeQGstROAxUBbYC8QBzzlnUpFMi8d4/xRYIAxJhmIB7qk5xdbRr/8\nEhERERERERGRbLXcTEREREREREREvEMhkYiIiIiIiIiIKCQSERERERERERGFRCIiIiIiIiIigkIi\nERERERERERFBIZGIiIiIiIiIiKCQSEREREREREREUEgkIiIiIiIiIiLA/wcs+p045WhIagAAAABJ\nRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x106973190>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figure(figsize=(20, 10))\n",
"\n",
"X = np.array([[-1, 1], [-0.5, 0.5], [0, 0], [0.5, 0.5], [1, 1]])\n",
"plot(X[:,0], X[:,1], 'bo-')\n",
"\n",
"p2 = np.poly1d(np.polyfit(X[:,0], X[:,1], 2))\n",
"x = np.linspace(X[:,0].min(), X[:,0].max(), 100)\n",
"plot(x, p2(x), 'b')\n",
"\n",
"for u, v in X:\n",
" plot([u, u], [v, p2(u)], 'r:')\n",
"\n",
"theta = np.pi / 8\n",
"R = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])\n",
"XX = np.dot(R, X.T).T\n",
"plot(XX[:,0], XX[:,1], 'go-')\n",
"\n",
"p2 = np.poly1d(np.polyfit(XX[:,0], XX[:,1], 2))\n",
"x = np.linspace(XX[:,0].min(), XX[:,0].max(), 100)\n",
"plot(x, p2(x), 'g')\n",
"\n",
"for u, v in XX:\n",
" plot([u, u], [v, p2(u)], 'r:o')\n",
" \n",
"xlim(-1.5, 1.5)\n",
"show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.13"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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