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@germannp
Last active January 5, 2019 16:29
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chains\n",
"\n",
"Consider a chain of particles connected by springs with growing length `l`:"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def F(x, t):\n",
" l = 1 + t\n",
" r = np.diff(x)\n",
" F = np.zeros(len(x))\n",
" F[1:] += l - r\n",
" F[:-1] -= l - r\n",
" return F"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## $\\mu v = F$\n",
"\n",
"For masses $m$ that are small compared to the friction $\\mu$ Newtons equation of motion $m\\ddot x = F - \\mu \\dot x$ simplifies to $\\mu v = F$, which can be integrated to find the positions of the particles over time:"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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RwXZxcRGu6/quTBAR+ZHoiW2tZ599Fl/96lfx8MMPx30rRES3WVtbk6FUd2LbqIqgG2wb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\nYEp0FUFsd/Pud78bR48eBQC8733vw3v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C0ia2QKWOYOuQBmDvoAZx3ah7tkDlsAbWEYiS\ni8GWiCL13HPPAQByuVzkNQSgMumzeTADUJlM+qkhuK7rO9imUqmmRxGrn+Mn2IpFcSbC2PILqHzf\nrl27ZvW6Ok6fPi3rCOLnmIiShcGWiCKj7oZw5swZ49O5glpfX5dbctkMtuVyWV7Xz8Q2n8/LwGka\nbHWrHOLzdLb7Uu+jVCrJTrIJdWJr8217UUdYWVnB+vq6tevqyGQyOHPmDADghRdeYB2BKIEYbIko\nMlevXpU1hHvvvTfyxw+rX7uysiJDTtBTx8IOtqYTW2DvpDZTYWz5BVT/QhJ1zxao1Ge2trZYRyBK\nIAZbIoqMWE0edw0hl8thcHDQ2nXVt9uTGmzFdNxPsPXTs1Un1zYXkA0MDMg6QBzBlnUEomRjsCWi\nSJRKJVy4cAHA3qEMUdcQgOp+bbNeqgk1uEUVbEWlIIqJbZBDGgC7PdtUKiWn7XEsIMtkMtwdgSjB\nGGyJKBJx1xAKhQJmZmYA2F84JoJbd3d3oK2+AGjv1BBlFcFPsG1paQllyy+g8v27efOmr/5vUOph\nDVeuXIn88YnIG4MtEUVCvG0bx6EMwF4IEtO1sIKtn2ktUAmOjuOgtbVV62vCXjzW2toqp9p+t/wS\ndYSwdkYol8u4efOm1WvrYB2BKLkYbIkodLU1hKgPZQAq20M5joPR0VGr1xYTSb/BVizOamtr065I\niGCrW+kQr7nuW+epVEoeFhF0L1vbwXZsbEy+TnH0bNPptNzT9oUXXtCeghNR+BhsiSh0ly9fxs7O\nDoB4aghAJQANDw8jm81au26pVAq01RdQCY4mB0aEXUUAgh/SIF6P5eVlq+Evm81ieHgYQDzBFmAd\ngSipGGyJKHTi7dq2tjacOnUq8sd3XTe0gxmWl5flAQZ+g63oHusuHAP874qgW0VQ7ydosHVdV4Z/\nW8T38fr1674OkAhqYmJC1kZYRyBKDgZbIgpVsViUhzLEVUNYWFiQE+Pjx49bvba6MMpvsBVVBJNg\nKwKqaRXBZHIqJshBqwjA3vfAJhFst7e3rV9bh1pHuHDhgtEvDEQUHgZbIgrVSy+9hN3dXQDx1RDU\n41fDOkrXcRxfx+kCMD5OFwh/8RgA2bH1c0ADsHe8sOjC2u7Zqr+gxFVHED/Pu7u7uHz5ciz3QETV\nGGyJKFTibdr29vZYaghAJfj09vaiu7vb6rVFsO3t7fU9jfYzsQ37gAYg+MQ2k8mgt7cXgP0tv7q7\nu9HT0wMgvmB76tQp+T1jHYEoGRhsiSg0hUIBL774IgDg7NmzSKXi+SdHTGxt1xCAyiTSbw2hVCrJ\nmkRSF49tb2/7PohAvC62gy1Q+X6qE/kopVKpqt0R4thTl4iqMdgSUWguXbqEfD4PAHjZy14Wyz2s\nr69jeXkZgP0aAlAJbEEXjgHJ69iq96PepwnRsw0z2C4tLWFjY8P69XWIOkI+n8fk5GQs90BEFQy2\nRBQa8fZsZ2dnKNNSHerb1LbvIZ/PY319HUDwwxkAf1UE3Sm4n46tOkH227MVgX99fV3+kmOL+v2M\na2p74sQJdHZ2AmAdgSgJGGyJKBT5fB4XL14EsLfnZ9w1hNbWVgwMDFi9tjqFPHr0qK9rqIHRTxUh\nqolt0C2/APtT24GBAbnlVpx1BLGn7cWLF62HdyIyw2BLRKF48cUX5XQwrhoCUN2v1T3VS5fNrb4A\ns2ArXtsoFo8B/ie2auC3HWwdx6nazzYu4ue7UCjIX+aIKB4MtkQUCvG2bE9PD8bGxmK5h93dXdy6\ndQtAOP1asX9qJpPxvdtC0CqC6cTWzwENgP9g293dLe8xzJ7tzMxMbNPSsbExuUPD+fPnY7kHItrD\nYEtE1u3s7MiFNPfee6/1SamuGzduyFOpwt4Rwe9zFIExl8sZbRcWxcQ2k8kgl8sB8F9FcBwnkp0R\nXNfFjRs3rF9fh+M4chHZ5OSk3OWCiKLHYEtE1l24cEEGqCTUENLpNEZGRqxfX0xs/dYQgEpgNKkh\nANEc0ABUprZ+J7ZAuFt+jYyMyOcWV88WqPycl0oledIeEUWPwZaIrBNvxx45cgTDw8Ox3YcIOqOj\no9pv2etyXTfwVl9AJTD6DbZhLh5T78vvxBaovD4LCwtygm5LJpPB6OgogHiD7fDwsHyerCMQxYfB\nlois2tzcxJUrVwDsTbHiqiGUSiX51nQYNYSNjQ3Z6fS7IwLg7zjdcrksA6JpFcF1XaPDFkSwtTGx\nzefzoew3K76/N27cMA7utqh1hMuXLwd6vYjIPwZbIrLqueeek6ErzhrCzMyMfNv9xIkT1q8vaghA\n9BNbtU5gOrEF/G35FSSohbkzAlAJtoVCATMzM9avr0v8vLuui+effz62+yA6zBhsicgq8Tbs8PBw\noElmUFNTUwD2Jmlh7MpgY6svoBIY/eyIAJhPbAF/hzTYmNgC1b8Q2KLueBFnHWFgYABDQ0MAWEcg\niguDLRFZs7q6KvcTjXNaC1QCztDQkNzE3yYR0Do7O31fv1wuy6Nq/U5sTRePAf72st3e3jaqMKha\nW1vldcKY2La2tsout/iFJi7i5/7atWtYXV2N9V6IDiMGWyKyRp1SxRlsXdeVwTaMGgIAKwvH1AVZ\nfk4dA8KvIqj3FWQBmZjehzGxBSp1hGvXrllfoGZC/bnn1JYoegy2RGSN+B/y8fFxuWF9HObm5uRe\nomEsHAPsbPUV9DhdIPwqgo1jdYFwt/wCKr/A7OzsYG5uLpTH0NHb2yurEQy2RNFjsCUiK+bn5+Up\nX3HXENS3o8MItsViESsrKwCC7YigBluTjm2Ui8fUwB1kRwPxOq2srBjvpatD/T7H2bMFKj//t27d\nCm1CTUT1MdgSkRViOqVuexQXEWyOHj2Kzs5O69dXp462gq3JfcaxeAywU0VwXVee2GZTZ2ennArH\n3bO955575DZ3zz77bKz3QnTYMNgSUWCu68r/AZ+YmDA+bMD2vYhgE3YNATj4E1v1vmxt+RXWFFPU\nEaampmLt2XZ2dmJiYgLA3i98cd4L0WGT+GB74cIFvOMd78BrXvMaPPjgg/jgBz8Yym/7ROTfzZs3\nsby8DAC47777Yr2XpaUl+ZZ5WAvHRDDLZDKBusQiKLa1tSGV0v/nOMqJbTqdRltbG4Bgwbanp0fe\na9jBdmNjQ/48xkXUEZaWlmLdW5fosEl0sC2VSnjPe96D+++/H9/73vfwz//8z1haWsIf/dEfxX1r\nRKQQ09p0Oo2777471ntR34YOe0eE/v5+o0Bay+9xulFObIHK/QXp2KZSqaqjdcOgfr+vXr0aymPo\nOnv2rHzNf/SjH8V6L0SHSaKD7fz8PObn5/GGN7xBTkZ++qd/GhcuXIj71ojo/5TLZTz33HMAgDNn\nziCXy8V6PyLY9vb2hrYzgwhmAwMDga4jgq1pDzjKiS1QCbZBOrZA+Ft+9fT0yO953AvIcrkc7rrr\nLgB7p/H53QOYiMwkOtgODQ3hnnvuwdNPP42trS0sLi7i29/+Nv7f//t/cd8aEf2fq1evykle3DUE\noBJsw5rWuq5rZasvYP9NbINUEYDqYBtW71Tt2cZN/PdhY2Mj9gky0WGR6GDrOA4+85nP4F/+5V/w\nqle9Cg8++CBKpRLe//73x31rRPR/RA0hl8vhjjvuiPVeVlZW5GlPYQXbtbU1FAoFAMEWjgH+jtMF\n4pvY2gq2hUIB6+vrga7lRXzf1Z+FuNx5553yHQzujkAUjUQH23w+j4cffhive93r8D//8z/47ne/\ni87OTnzgAx8wus7c3Byee+65uv9XKBSMpxdEtKdYLMpq0D333KM9PQxLFP1aWzsiAPFNbP0G2yAd\nW6D69Zqfnw90LS9J6tlmMhmcPXsWwN5C6DD27yWiavH+r1AT3/ve9zA9PS0ntB0dHXjf+96HN73p\nTVhbW0N3d7fWdZ566ik88cQTnh/XvQ4RVbt48SJ2d3cBJKOGIIJMV1cX+vr6QnkMW8E2n8/Lya9p\nx1YNSH4mtn6rCIVCAfl8Htls1ujrBbW6sbCwgNOnT/u6TiP9/f3o7OzExsYGpqam8IpXvML6Y5i4\n77778L//+7/Y3d3FxYsXcc8998R6P0QHXaKDbblclv8nVh7n83m58bWuc+fO4aGHHqr7sYcffjjQ\nqmaiw0y8vdrV1RXahNSE2q81/XdCl5g09vT0oKWlxfd1/B6nC1SCaSqV0v73K5VKwXEcuK7re2IL\n7N2332CbzWbR09OD1dXV0BaQOY6DkydP4vz584no2Z48eVIG7WeffZbBlihkiU50999/P9rb2/HZ\nz34WOzs7WF5exuc//3m85jWvMZqyDg4O4t577637fy0tLdoTDyKq2N7exqVLlwDs7dkZ9y+Ia2tr\ncu/SMEO22OrL1o4IgP8qgum/XWJqazqxVSfKNheQhUV8/5eWlkLr8upKpVJyT9tLly5he3s71vsh\nOugSHWx7e3vxN3/zN/j+97+Pn/zJn8Qv/uIvoq2tDY899ljct0Z06F24cEEGpCTUENTp3MmTJ0N7\nHDGxDdqvVfuqfie2pp1mEYSDTmyDiDLYAvH3bAHg5S9/OYC97xu3qyQKV6KrCMDegpQnn3wy7tsg\nohpi0/mjR49ieHg45rupBJiOjo7A23B52d7elsHO1sIxwH/H1u/ENgnBdmNjAzs7O2htbQ10Pa/H\n6OjowObmJqampmL/xWt4eBhHjx7FwsICnn32Wbzyla+M9X6IDrJET2yJKJlWV1flhPTlL395aH1W\nE+J+Tp48Gdr9hLEjQktLi3FnVQRT04mt3ypCNpuVXxt0ZwS1whHWzgiO48ipbRImto7jyHB99epV\nrK2txXxHRAcXgy0RGTt//rz8c9zTMABYX1+X3dcw+7VqEAvasRUB0bSGAERfRXAcR06VbU1sgfCC\nLVCpoywuLsbeswWq/3vCPW2JwsNgS0TGRA3h+PHj6O3tjfluou/Xtre3Gx+qUMvvcbpAJdhGtXgM\nsHdIQ0dHB9ra2gBE17NNwu4IfX19GB8fB8BgSxQmBlsiMjI7O4u5uTkAyZjWApW3m9vb2wNXBBoR\nQczGY/g9nAEIXkXwc1CACOBBqwhAZdodZrAdGBiQv3wkoY4AVBaRzc7OYnZ2Nua7ITqYGGyJyIiY\n1qZSKdx7770x380eEVzC7NcClSAWtIYABKsi+A22YsIb58QWqPxiEGYVQexnCyRjYgvsLYYW2+KJ\n/x4RkV0MtkSkrVwuy7dR77zzTvmWcpzUfm2YNYR8Po+VlRUAdoJtkCpCHBNbW8fqApXXb2VlRZ6+\nFgZRR1hYWLBy30G1t7fjzjvvBLBXR3BdN+Y7Ijp4GGyJSNvU1JRciCPeVo1bVP1aEZ6B4FWEYrGI\nnZ0dAMEWj0W13RdQCeA7Ozu+vl6l/mIQZh3h1KlT8s9JqSOI+s76+npi7onoIGGwJSJt4u3TXC6H\nu+66K+a72XPlyhUAewExzH6tzR0RguxhC8Q7sQWC1xGi2PILqOxnCyQn2N51113I5XIAWEcgCgOD\nLRFpKRQKeP755wHsdQVNQ1VYoti/FqgEsFwuh66urkDXCnLqGBBPx9bmsbpdXV1y794wJ7ZJ288W\n2Nu3+OzZswCA559/PtQqBtFhxGBLRP+/vXuPirLO/wD+nkHuyB0UUBS0BUXBa6br/k6xtmZbFrat\nZbmtuWlptW1mpmtmpd3NMis7p0521Da11lu1rpVtq5t7Km+AdwRsuQnIHWRGmOf3B+f5zowCMsxz\nm+H9OmfPHrnMfJkH4s3n+Xw/3y45deoUrFYrAOO0IWjVXws4bxxzN0C7W7HVsxUBcL/P1mQyiaqt\nmhVbwHjzbAEgIyMDQFvf9qlTp3ReDZF3YbAloi6Rb5uGhYWpegiCK+Q2BED9YCsHMCXaHRyDoZat\nCN09oAFQthUBgGbB1oh9tgMGDEBYWBgAtiMQKY3BloiuqrGxEXl5eQDaNr8Y4QhdwB5UQkJCEBUV\npdrztLS0oKqqCoCyo7569erl8nG68noAbQ9o8Pf3V+xYXcD+OlZVVbm9Ga0zUVFR4o8Hxz+E9OR4\nxG5eXp4ifygQURsGWyK6KsfRREZpQwC0m1974cIF8fUrPeqrO+vu7pG67rQimEwmVUZ+SZLkNHFC\naY7zbI1SsQXsP0eSJDkdUU1E7mGwJaKrkm+XxsfHKxLslFBbW4vq6moA2rUhAPofzgDoMxUBsLdN\nKNmKAGjXZ1tdXY3a2lpVn6urYmJiEBcXB4DtCERKYrAlok5VVFSgtLQUgLGqtY63lR37KNUgHyHs\n5+cneiPd4c7hDIA+PbaAssfqhoWFwdfXF0DP7LMF7D9PJSUlqk6HIOpJGGyJqFNyNclkMmHYsGE6\nr8ZODiihoaGIiIhQ9bnk0BEdHa1Iy4M7FVtJktxuRWhtbe3WqVdKtiJoORkhIiICoaGhAIwVbB37\n1Y8eParzaoi8A4MtEXVIkiQRbAcPHtztW+dKkyRJBJSkpCTVN7PJFVul2jDkYOjOqC+g+5vHLn+c\nrlKyYgtoNxnBsc+2oKDAMEfZBgcHY/DgwQDa/oA0yrqIPBmDLRF1qLCwEHV1dQDsszeNwLFXUu3+\nWqUnIly6dAkWiwWAe6O+gO5XbC9/nK6S12uxWBQ5WEB+PS9cuKDqZATA3o5QW1uLmpoaVZ/LFXI7\nQl1dnaGqyUSeisGWiDok3x410hG6gLb9tY4TEWJjY91+PKVm2ALuBVu9Tx8DnCcjyH88qMXxDyCj\njP0CgJSUFB6xS6QgBlsiapfVasWJEycAAGlpaWKjjxHIla2IiAhFNnN1Rq2JCIDnVmwBZUd+AfZ2\nD7WEh4eLXmwjVUZ9fX0xdOhQAG1H7Mqn+xFR9zDYElG7Tp48abgjdIG26p5ccVO7DQGwBy5fX19F\nQrS7wdax0trdqQiAMYJteHi4ZpMRABiyzxZwPmL35MmTOq+GyLMx2BJRu+Q2hIiICCQmJuq8GruK\nigpxGzw5OVmT5wPaqotKTkQAPK9i67h50NMmIwD2tpWGhgZDjddKTExEeHg4ALYjELmLwZaIrlBX\nV4f8/HwAbdVaoxyhCzj3R2pZsVWivxawB0J/f/9utXfoGWz9/PzEEcBKT0ZQuxUBcO7HNlKfrclk\nElXb/Px8sWGTiFzHYEtEV3CsGhlpGgJgDyQxMTHdPuCgq1paWsTpZkYY9SWvSaZ1sAXUG/lVVVWl\n+mSEkJAQ8XxGCraA8xG7OTk5Oq+GyHMx2BKRE0mSRBtCYmKi6ocfuMJmsznNr1VbZWWl6MVUKtgq\ndeoY4N4c2+6GyN69ewNQLtjKlXBJkjRpD5Cr/IWFhbDZbKo/X1dFRkaif//+ANragIzUA0zkSRhs\niciJ4/GeRqvWlpaWihmwWgRbx9vjSrUi1NfXA2DFVub4umrRZyv3ZTc3N6OsrEz153OF/PPmeIw1\nEbmGwZaInMjV2l69eokxREYh3z52PElKTXKw9ff3F0eyusvTWxGUPFYXaDsSWe7b1aLPdsCAAaJn\nXO4jN4q0tDRxjY4cOaLzaog8E4MtEQktLS3Izc0FAKSmpiIgIEDnFTmTg21cXJwma5MriLGxsYps\noJMkyTDBtjsHNADOrQhK3C43mUyiaqtFxTYwMBBxcXEAjDXPFgACAgKQmpoKAMjNze32NSLqyRhs\niUg4c+YMLl68CMB4bQgtLS34+eefAWjThgDYK4hK9ddevHhR9HXqEWwde3K7eySuvO7W1lbxveIu\nLScjAPbvn3Pnzqm+Yc1V8s/dxYsXcfr0aZ1XQ+R5GGyJSJDbEEJCQjSZEeuKoqIiEUK0WJvVakVN\nTQ0A5SciAPbKp6uU2jzW3Wqg0oc0APY+2+rqak1O3pKDbUtLC4qKilR/PlckJyeL11j+eSSirmOw\nJSIAbbv1z5w5A6CtamQ2G+s/D3I/pI+Pj9g9ribH2+J9+vRR5DHdPZwBsAdbs9ns8jVy/Bx3pyIA\n6mwg02IyQmJiovijwGhjv8xmsxj9debMGTFFg4i6xli/uYhINzk5OeI2udHaEAB7AElMTOzWwQau\nUnMiAuB+xdbVNgSZ/HnuTkUA1Am258+fV+QxO+Pr6yv+ODLaBjIAGDFiBIC28XacaUvkGgZbIgJg\n34WdkJCg2K13pVgsFhQXFwPQvr82KCjI6ShZd8hB0Gw2IzAwsFuPoXewDQoKElVfx6DujuDgYAQF\nBQHQvs+2uLhYjJAzipiYGMTHxwNgOwKRqxhsiQhlZWWiUmbEam1hYaHYga91sFWqWgs4j/rq7pQF\npYJtdzePmUwmxUd+aT0ZAbD3aUuShHPnzmnynK6Qq7ZlZWWGm7dLZGQMtkQkqrU+Pj4YNmyYzqu5\nkny72N/fX1Sy1KZ2sO0upYKtO6OklD59DLC/zlpVbOPj4+Hv7w/AmO0Iw4YNE33AnGlL1HUMtkQ9\nXGtrq+jjS01N7fYtcjXJ/bVJSUmabGpramoSoU3JYCvfuu9ufy2gfysCoPzpY4D9da6vr1dsjFhn\nzGazOOTDiME2MDAQKSkpANr63znTlqhrGGyJergzZ86gqakJgDHbEOrr68Xtaa3bEAB1KrbuKczk\nEwAAH6hJREFU9OzKAccIwVapHlvA+XXWqmortyNUVFQoGtKVIrcjNDU1iYklRNQ5BluiHk6+zRkS\nEoJBgwbpvJorOVbTtJqtq1awZcW2Y1pPRgCcv5+MWLUdNGgQZ9oSuYjBlqgHc5xdm56ebrjZtYC9\nDSE0NBRRUVGaPKccrMLCwkQfprusVqs4fMDTg628fovFotiBCv7+/ggLCwOgXcU2KipKfC1GDLaO\nM21Pnz7NmbZEXWC832JEpJns7Gwxu3bkyJE6r+ZKkiSJwJGcnNztSQKukoOVUgczAM637ZXYPNbd\nWb5KBlvAszeQmUwmUbXNz88XkzeMxHGmbXZ2ts6rITI+BluiHkqSJNGG0K9fP0RHR+u8oitVVlaK\nQKhVf60kSapORADcq9jKY7qM0IoAqNNnW15erlnIlINtfX09Lly4oMlzuiImJgYJCQkA2tqGjBi+\niYyEwZaohyotLRUBzoibxgB9+mtra2vF7XU1+msBZSq28igoV7k7xxZwDuZKBlu5Qm6xWFBXV6fY\n43bG8Q+ms2fPavKcrpKrtuXl5SgtLdV5NUTGxmBL1EMdPnwYQFvQMeLsWsAebGNjY90Kg65Qe+MY\n4PlzbNU4VhfQZwNZ7969xfMasc8WaJtpK183zrQl6hyDLVEP1NLSgtzcXADAkCFDEBAQoPOKrtTa\n2orCwkIA2lVrAXugMpvNirZnOI76cmeTnhE2j5nNZjGyTMmKbXR0tHhttOqzBexV28LCQkPOiw0I\nCEBqaiqAtpm27lw7Im/HYEvUA508eRLNzc0A7Lc5jaa4uFi0BGgZbOVAFR0d3e3b/e2Rg607/bWA\nMTaPAeqcPubj4yMmX2gZbOUxd1arFcXFxZo9ryvkn9Pm5macOnVK59UQGReDLVEPJN/ODAsL02xT\nlqvkfkcfHx8MGDBAs+eVK7ZKtiEAysywBYzRYwuoc0gDYO+z1aoVAQAGDBggKsVGbUdISkpCaGgo\nALYjEHWGwZaoh6mtrRWhMSMjQ7MRWq6SA0b//v3h5+enyXO2traKnfFqBVt3e4WVqti6e8tdjYot\nYH/dKysrNWsL8PPzQ//+/QEYN9iazWZRtT179qxmm+uIPA2DLVEP43iCkVHbEJqbm8UtYS3bECor\nK8Vc3759+yr62EpUbCVJUqzH9tKlS26NjpK/DrUqtjabDZWVlYo+dmfk77OioiLRpmM08s+rJEk8\niYyoAwy2RD2I4+zagQMHIiIiQucVta+goECELj02jgHKHs5gtVphsVgAuBdsHSuY7gZbACLEd4dc\neW5ubna7rcGR4+uuZTuC3GcrSZLYtGg0ERERGDhwIIC2qSacaUt0JQZboh7k3LlzqK6uBmDMk8Zk\n8u3ggIAAxMXFafa8cpAKCAhwuxfWkVKHMzhu+OpusHVsYVDq9DElq7ahoaHiGGMtg21cXJyYDmLU\nebaAvWpbXV2Nn3/+WefVEBkPgy1RDyJXa/39/TFkyBCdV9Mxx2N03RmN5SrHE8eU7D1WeoYtoEzF\n1oiHNJhMJlG11XIygtlsdjpe16iGDh0qgr88i5qI7BhsiXoIi8WCY8eOAWgb+N7dzUdqq66uRlVV\nFQD77WGtyBVCJdsQAOfgJ+9s7w6lg61SFVulN5DpMRkBsLe9VFVViTsbRuPr64u0tDQAwPHjx0WL\nCxG1YbAl6iFyc3NFkDFyG4LjbWAt+2ubmppEAFUr2JpMJnGwQXc4BlF3pyJc/niucqw8q7WBrL6+\nHk1NTYo+dmcc/5AyctVW/vm9dOmS+GOViNow2BL1EPJty5iYGMTHx+u8mo7JgSIqKgrh4eGaPa9a\nG8cAe/BT6tQxQP+KrVqnjwHOr7+W7Qjh4eGIjIwEYOxgm5CQgJiYGABsRyC6HIMtUQ9QXl4uxmeN\nHDnSsLNrbTYbCgoKAGhbrQWcg63SM2zlW/XuzrB17InVe/MYoN7IL8fXv6ysTNHHvhq5apufn+/W\n1Ag1mUwmUbUtKipCRUWFzisiMg4GW6IeQK7qmM1mpKen67yajhUXF4sZonr110ZGRip+IIQc/Nzp\nrwWMVbEF1Au2fn5+YhSdlhVbwP5919zcjJKSEk2f2xXp6emi+s+qLZEdgy2Rl2ttbUV2djYAICUl\nxa0eT7XJ/bVms1nM69SKWhvHAOWP0wX0n4oAqBdsAf02kA0cOFAERiOP/QoODkZKSgqAtkNXtDql\njcjoGGyJvNypU6fEBhwjbxoDnI/RlUcaacFms4nbuUq3IUiSJI4/VTLY6r15DNAm2JaXl2vaEuDv\n749+/foBMHawBew/z01NTTh9+rTOqyEyBgZbIi8n36YMDQ3V/Pa+K5qbm1FUVARA+zaEqqoqEfKU\nrtharVZRGTVCj60awdbxZDWlyNehpaVFjH/Tivz9Z+TjdYG2dcrXgO0IRG0YbIm8WF1dnag6ZWRk\naHrYgav0OkYXcN6g1LdvX0UfW6kZtoCxTh4D1DukAdDvaF3A+XhdeTOjEZnNZnESWV5enrgzQNST\nGfe3HBG57ciRIyIsGr0NIS8vDwAQGBio6TG6gD04+fn5KT5izDFseFuPrWNQVzrYRkREiE18Wk9G\niIuLQ2BgIADPaUeQJEmcLEjUkzHYEnkpSZLE7cmkpCSxy9yIJEkSAWLQoEGaV5YdN44pPQrNMfC5\nG2zlIGo2m7v9Gjl+rpErtiaTSfQ7az0ZwfF43bNnz4o/Do0oIiICSUlJANraEYy8ViItMNgSeamC\nggLU1NQAMH61tqqqCrW1tQC0768FtJmIYDabERQU5NZjyUG0u9Vamfz57lZsg4KCREhW4za4fD20\nrtgC9u/DmpoazXt8XSX/fNfU1Bi6dYJICwy2RF5KrtYGBARgyJAhOq+mc3IbAqB9f+3FixdFKFN7\n1Je71WA52HZ3IoJMDrbuVmxNJpOqkxHkfue6ujpcvHhR8cfvjOMfWEZvR0hNTUVAQAAAbiIjYrAl\n8kJNTU04ceIEgLZB7u5W+NQmB4fY2Fi3N1i5Ss2NY4ByM2wBe4VVqYqtu8EW0GbkF6D9BrLQ0FDR\nCmH0YOvr64vhw4cDAE6cOKH5HwFERsJgS+SFcnJyxMD2UaNG6byazrW0tKCwsBCAPm0IjsFW6Rm2\ngHKnjgHKtSLIFV9PCrZ6tiMUFBQY/gAE+efc8UAWop6IwZbIy0iShEOHDgEA4uPjVbm9rqT//e9/\nohI5ePBgzZ9fzaN0ASh2OANgvFYEQN1g6+fnh8jISADaV2wBe7C9dOkSfv75Z82f3xV9+/ZFfHw8\nAG4io56NwZbIy5SUlIhd5EbfNAbY+2t79eqFxMREzZ9fDkxqtCFIkoSGhgYAygZbo2weA5yDrRph\nSs8NZAMGDBCvlWMfuFHJP+/nz59HSUmJzqsh0geDLZGXOXjwIADnvjsjk/sXk5KSNO8Fbm1tFUfp\nqlHZbmxsFMfBGinYKtmKILdY2Gw2NDY2uv14l5P/4KioqNC8HaBXr14YOHAgAOP32QLA8OHDxbWV\n79oQ9TQMtkRexGKxIDc3FwCQlpYGf39/nVfUufr6elEx1aO/trKyUoQlNSq2jiOwlOixlSusRmxF\nANTts21tbUVlZaXij3818vfl+fPnVfn6lOTv74+0tDQAQG5uLqxWq84rItIegy2RFzl27JgIP0bf\nNAY4V8H06K/VaiICYKyKrZKtCI6BXY1Zto7XRY8+W8fvS0+o2so/91arFceOHdN5NUTaY7Al8iLy\n7ceYmBj069dP59Vcndy3GB4eLjYJaUkOSoGBgYoEz8spXbE1YiuC2hXb0NBQMaNVjz7bqKgoccyy\nJ/TZ9uvXD9HR0QDYjkA9E4MtkZc4f/48iouLAbRVbZQ+GlZpNptNVMAGDx6sy3rloNS3b19Vnl8O\negEBAW63DwDGnGPr5+cnWl7UqNiaTCZRtdWjYmsymUQ7Qn5+vuiZNiqTySSqtkVFRZofR0ykNwZb\nIi8hV2d8fHyQnp6u82qurqSkBM3NzQD0aUOQJEkEW7VGoil5OANgzFYEwF6NVqsHVQ62ZWVluoyx\nkr8/L1686BHTBjIyMuDj4wPAvpmUqKcwRLDdt28ffvnLX2LBggVXvO/AgQO48847MXr0aNx6663Y\ntWuXDiskMrZLly6JoexDhgxBUFCQziu6Ovm2rtlsFjvPtVRfXy9OaFKjvxawVzCVOk3NiHNsAXVn\n2QL269PU1CTGp2kpKSkJZnPbr0tPaEcICgpCamoqACA7O1ux60zkCXQPtu+//z5eeOGFdn+xVVRU\nYN68eZgxYwYOHDiAJUuW4Omnn2ZDPNFlTpw4IaqfnrBpDLAHhMTERF2mN6i9cQxQvmKrVCuCkj22\ngD24q9GKADhX1EtLS1V5js74+/uLGcueEGwB+38Hmpubcfz4cZ1XQ6Qd3YNtQEAAtm7d2u5g9l27\ndiEpKQlZWVnw8/PD+PHjkZmZia1bt+qwUiLjktsQIiIidKl+uqqpqUn0A+sx5guwB1sfHx+x2UZp\nSp46Bhi3FUHtim1MTIyomOrRZwvYv0+Li4vR1NSkyxpckZSUhIiICADcREY9i+7B9t5770VISEi7\n7zt27JiYyScbOnQocnJytFgakUeorKzEuXPnAHjGpjHAeWzSNddco8sa5GAbExMj+hGVZLVaYbFY\nACjTiiBJkiqtCEr0rMpfX3NzsyqzU318fBAbGwtAn8kIgOeN/XLcRHbu3DldZgAT6UH3YNuZmpqa\nK34hhIWFobq6WqcVERmPXI0xm80YMWKEzqvpGvl2bu/evUVg0ZrjRAQ1qDXqC1CuFQGAIqd5qT3y\nC3DeQKaHPn36iCKMJwRbABgxYoSodLNqSz2FSdJji2k7Fi9eDKvVilWrVom3zZ49GykpKXjyySfF\n27Zu3Yp3330Xe/fu7fJjl5eXi2MzLzd9+nTYbDbExcV1f/FEOqqtrYXNZoOfnx+Cg4P1Xk6XyGv2\n9/fXZaObJEmoqakB0LbRRo0e35aWFhHyQkND3a4KO645ODgYfn5+3X4sq9Uqjr8NDw93u8rf2trq\n1HahxtHIFotFtAAosebuaGpqgsVigdlsRlhYmObP3x2NjY2wWq0etWaijsTFxWHjxo2dfoy2B7O7\nKCIiQvyHXFZTU4OoqCiXHmfz5s1Yu3Zth+9X4zZkT9Xa2orGxkYEBwfzddWI0r+stLiGev+CNZlM\nov9QLb169VL0OVxZ89WuoZ+fn1vB+HI+Pj6qv57+/v66HxEdFBSkyR9iSv4MBgcHe8wfvN6Evwv1\nY+hgO2zYMGzbts3pbTk5OcjIyHDpcaZPn47MzMwO3x8TE6Pb7VBvc+zYMUybNg3r16+/oj+aPAOv\noefjNfRsvH6ej9dQP4YOtlOnTsXatWvx6aefYurUqThw4AD27duHLVu2uPQ4sbGxDK5EREREXk73\nYJueng6TySQ2Rnz11VcwmUw4evQoIiMjsW7dOqxYsQLPPfccEhIS8Oqrr+q2i5qIiIiIjEv3YCuf\nltSRMWPGYPv27RqthoiIiIg8laHHfRERERERdRWDLRERERF5BQZbIiIiIvIKPsuXL1+u9yLIuwQH\nB+Paa6/l7EQPxmvo+XgNPRuvn+fjNdSHYU4eIyIiIiJyB1sRiIiIiMgrMNgSERERkVdgsCUiIiIi\nr8BgS0RERERegcGWiIiIiLwCgy0REREReQUGWyIiIiLyCgy2REREROQVGGyJiIiIyCsw2JLiPvro\nI6SmpqKkpES87eTJk5g5cybGjBmDyZMn48MPP9RxhdSempoaLFq0CBMnTsR1112HRx55BGVlZeL9\nvIbGV1JSgrlz52LcuHHIzMzEa6+9pveS6CpKSkrw8MMPY9y4cZg4cSIWL16MhoYGAMCBAwdw5513\nYvTo0bj11luxa9cunVdLV/PCCy8gNTVV/JvXUHsMtqSo8vJyfPjhhzCZTOJtFosFc+fOxfjx47F/\n/36sXr0a7733Hr7++msdV0qXe+qpp1BVVYUvvvgCe/bswaVLl7B48WIAvIae4uGHH0bfvn2xd+9e\nrF+/Hl999RXWr1+v97KoEw8++CDCwsLw3Xff4bPPPsOZM2fw8ssvo6KiAvPmzcOMGTNw4MABLFmy\nBE8//TSOHTum95KpAydOnMCOHTvE77/y8nJeQx0w2JKiVq5cibvvvtvpbd9++y1aWlrw0EMPISAg\nAEOHDsWdd96JzZs367RKak9cXBwWLVqEsLAwhIaG4q677sKhQ4cA8Bp6gpycHJw+fRoLFy5EcHAw\nEhMTMWvWLGzZskXvpVEH6uvrMXz4cCxYsAABAQHo06cPsrKy8OOPP2LXrl1ISkpCVlYW/Pz8MH78\neGRmZmLr1q16L5vaIUkSli9fjvvvv1+8jddQHwy2pJjvvvsOp0+fxv333w9JksTbjx8/jpSUFKcq\n7tChQ5GTk6PHMqkDzzzzDAYPHiz+XVJSgpiYGAC8hp7g+PHjSEhIQEhIiHjb0KFDUVBQgKamJh1X\nRh3p3bs3Vq5cicjISPG20tJS9OnTB8eOHUNaWprTx/Nnzrj+9re/wd/fH7fccot42/Hjx3kNdcBg\nS4qwWCxYsWIFli1bBl9fX6f31dTUIDQ01Olt4eHhqK2t1XKJ5IKioiKsWbMG8+bNA8Br6Ak6ukYA\nUF1drceSyEU5OTnYtGkTHnzwwXavZ1hYGK+lAVVWVmLt2rVYvny509t5DfXRS+8FkGfYuXMnnnzy\nSaeKnSRJMJlMePHFF1FQUID09HSMHz++3c93rODKHB+L1He1a3j77bcDAM6ePYs//elPmDZtGqZN\nm+b0sZfjNTSW9q4ReYaDBw9i3rx5eOKJJzB+/Hi8//77vJ4e4qWXXsLvfvc7JCcno7i42Ol9vIba\nY7ClLpk6dSqmTp3a7vvy8/PxyiuvYMeOHe2+PyIiAufOnXN6W3V1tagmkTY6u4ay7OxszJkzB7Nn\nz8YDDzwg3s5raHyRkZGoqalxeltNTQ1MJpPTrW4ynr179+LJJ5/EsmXLxM9oREREu9czKipKjyVS\nBw4cOIDDhw9jxYoVAJyDLK+hPhhsyW1ffvklGhoaMHXqVKcf6qysLMyZMwfDhw/HJ598ApvNBrO5\nrfslJycH6enpei2Z2lFYWIi5c+fiqaeeEtVbGa+h8Q0bNgylpaWoqakRf3BkZ2dj0KBBCAwM1Hl1\n1JFDhw5h8eLFeOutt5zueA0bNgzbtm1z+ticnBxkZGRovUTqxM6dO1FVVYXrr78eQFuwlSQJ48eP\nx6xZs/D55587fTyvoQYkIjc1NDRIZWVlTv9LSUmRjh49KjU0NEgWi0XKzMyU3nrrLenixYvSkSNH\npLFjx0rfffed3ksnB7NmzZJef/31dt/Ha+gZpk+fLi1dulSqr6+X8vLypF//+tfSxx9/rPeyqAMt\nLS3SzTffLG3ZsuWK9124cEEaPXq0tHXrVslisUj/+te/pBEjRkinT5/WYaXUkbq6OqfffUeOHJFS\nUlKk8+fPSyUlJbyGOjBJEhtASHlDhgzBN998g/j4eABAXl4eli1bhtzcXERHR2Pu3LmYPn26zqsk\nWVlZGW644Qax8c9kMon+2w8++ABjxozhNfQA58+fx9NPP40ffvgBISEhuPvuuzF//ny9l0Ud+Omn\nnzBz5kz4+fmJnzf5/3fv3o3i4mKsWLEC+fn5SEhIwIIFCzBp0iS9l02dKC4uxqRJk3DixAkAbdeY\n11BbDLZERERE5BU47ouIiIiIvAKDLRERERF5BQZbIiIiIvIKDLZERERE5BUYbImIiIjIKzDYEhER\nEZFXYLAlIiIiIq/AYEtEREREXoHBloiIiIi8AoMtEZGK0tPT8emnn3bpY1NTU7F582aVV+S+m266\nCWvWrGn3fT/99BMyMjJw7tw5jVdFRAT00nsBRERamjlzJg4ePAhfX18AgCRJCAwMxIQJE/Doo48i\nKSnJrcffuXMnRo4cif79+wMAsrOz3V5zVz311FPYsWMH/Pz8ALR9bX5+fhg1ahQeeeQRDB8+XJHn\n2b17t9O/161bhzlz5sBsNmPMmDE4evSoIs9DROQqVmyJqMeZMmUKjh49iqNHjyI7Oxs7duxAS0sL\nZsyYgYaGhm4/riRJePHFF3WrVppMJmRkZDh9bXv27EF8fDzuvfdeFBUVKf6cp06dwhtvvIGWlhbF\nH5uIyFUMtkTU4/Xt2xd//etfUV1djcOHDwMALly4gAULFmDcuHEYOXIkbrnlFuzatUt8zrZt2zB2\n7Fhs3boV48aNw9tvv4309HTU1NTgoYcewsyZMwFc2V7w0UcfYfLkyRg5ciRuv/127Nmzp8N1bd68\nGbfddhtGjhyJiRMn4vnnn0dzc7NLX1tkZCSWLl0KSZKwf/9+AEBrayveffddTJkyBRkZGcjMzMSb\nb74Jm80GALBarXjuuefwf//3fxg5ciQmTZqE9957TzxmZmYmXn/9dXz77be44447YDKZMHbsWKxZ\nswY//PADUlNTUVBQAABobm7Giy++iBtvvBEjRozA5MmTsWHDBvFYa9euxbRp0/DNN9/gt7/9LUaM\nGIFp06YhNzdXfMyXX36J2267DaNGjcK4cePwyCOPoLy83KXXgYh6BgZbIiIAly5dAgDRovDXv/4V\nJSUl+Prrr3Ho0CHMnDkTixYtwtmzZ8XnWK1WHDp0CN9++y3mz5+P3bt3Q5IkrFu3zim8ybZu3Yp3\n3nkHr7zyCg4ePIg5c+bg8ccfb7dd4bPPPsOqVauwZMkSHD58GBs3bsSPP/6IZ555xuWvzWazwWaz\nia/t3XffxaZNm/Dyyy/j8OHDePXVV7Fp0yasW7cOALB+/XocPHgQ27dvx+HDh/Hmm29iw4YNIhjL\nbrjhBjz//PMA2nprH330UQBtlWPZs88+i3379uG9997DoUOHsGjRIrz88svYsWOH+JiioiLs3bsX\nmzdvxn/+8x8EBATg2WefBQCcP38eCxcuxMKFC3Ho0CHs2bMHJpMJr776qsuvAxF5PwZbIurxioqK\nsHLlSiQnJ2PUqFEAgDVr1uCDDz5A7969YTKZkJWVBZvNhpycHPF5VqsV9913H4KCgpweT5Kkdp/n\n448/xtSpU5GRkQGz2Yybb74Zq1evRlhY2BUfu3HjRtxxxx0YN24cAGDgwIGYN28evvjiCxHCu6Ki\nogLPPvssQkNDccMNN4jH/sMf/oD09HSYzWaMHj0aWVlZ2LZtGwCgvr4eZrNZ9OqmpaVh//79mDhx\nYofP097X3NDQgB07dmD+/PlITk6G2WxGZmYmrr/+evFc8sctXrwYISEhCA4OxqRJk3DmzBkAQGNj\nI2w2GwICAgAAYWFhWLNmDYMtEbWLm8eIqMf5xz/+ga+//lr8Ozo6Gtdeey2WL18uwlxeXh7eeOMN\nZGdno6mpCUBbJdJisTg9lrxJrCsKCwuRlZXl9LYbb7yx3Y/Nz8/HmTNnsGnTJqcKKACUlZV1+LxH\njx5FRkaG+Hd4eDgyMjKwYcMGREZGor6+HjU1NbjmmmucPm/w4MGiynzPPfdg3759+NWvfoWxY8di\nwoQJmDp1KiIjI7v8tQJtfzBIknTFcw0aNMiprSMiIgIhISHi30FBQeJ1Tk5OxsyZM3HffffhF7/4\nBa677jpMmTIF6enpLq2FiHoGBlsi6nGmTJmCVatWdfj+hoYGzJo1CxMmTMDOnTsRGxsLm82GoUOH\nXvGx8u39rvDx8RF9rFcTEBCABx98ELNmzery4wNARkYGPvnkkw7ff3kwlzmuq2/fvti+fTtyc3Px\n/fffY+fOnXj77bexfv16pKWldXktFoul3UquJElOYf3y4H65JUuW4IEHHsD+/fvx73//G/fccw9m\nz56Nxx57rMtrIaKega0IRESXOXv2LGpra3H//fcjNjYWAMSmMncMHDgQ+fn5Tm/btm0bjhw5csXH\nJiUlOW2gAoC6ujrU1dW5tYaoqCj07t0bp06dcnr76dOnMWDAAADAxYsXYbFYMGzYMMyZMwd///vf\nkZqaiu3bt7v0XImJiTCZTO0+V1fHqkmShNraWsTExCArKwurV6/GM888g40bN7q0FiLqGRhsiYgu\nk5CQgF69euGnn35Ca2srDh8+jPfffx9hYWEoKSnp8PMCAwMBtLUR1NfXX/H+GTNm4IsvvsD333+P\n1tZWfPPNN1i2bFm7Fcs//vGP+Oc//4mdO3fCarWirKwMf/7zn/H444+79bWZTCZMnz4dGzZsQE5O\nDmw2G/773/9i+/btuOuuuwAA8+fPx5IlS1BVVQWgrYWitLQUgwYN6vBrzsvLQ2NjIwB7v21ERARu\nuukmvPPOOygoKEBLSwt2796Nffv2iee6ms8//xy33HKL2GDX2NiI3NxcJCcnu/U6EJF3YisCEdFl\noqOj8cwzz2Dt2rV46623MGLECDz33HPYsmULPvroI5jNZiQmJl7xeZGRkbjtttvw2muv4dNPP8XO\nnTudQuu0adNgsViwdOlSVFdXo3///li1apXoiXX82JtuugnV1dV45513sHTpUgQFBeE3v/kNnnji\nCbe/vsceewwmkwkLFixAZWUlEhISsHDhQhE2X3rpJaxYsQJTpkyB1WpFTEwMbr/9dvF+x3VOmDAB\nQ4YMwfTp0/H73/8ekydPdnr/ypUr8dJLL2H27Nmoq6tDYmIiVq9ejUmTJnVprbfeeitKSkrwl7/8\nBRcuXEBQUBBGjx7daSsJEfVcJqmj7btERERERB6ErQhERERE5BUYbImIiIjIKzDYEhEREZFXYLAl\nIiIiIq/AYEtEREREXoHBloiIiIi8AoMtEREREXkFBlsiIiIi8goMtkRERETkFRhsiYiIiMgrMNgS\nERERkVdgsCUiIiIir/D/mw0FS1q83gkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f36c54dfe80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_particles = 10; n_steps = 100; dt = 0.1\n",
"\n",
"X = np.zeros([n_steps, n_particles])\n",
"X[0, :] = np.cumsum(np.ones(n_particles)) - 5.5\n",
"\n",
"for step in range(1, n_steps):\n",
" v = F(X[step-1, :], step*dt)\n",
" X[step, :] = X[step-1, :] + v*dt\n",
"\n",
"\n",
"def plot(X):\n",
" plt.plot(X, np.cumsum(np.ones(n_steps)*dt), '0.5')\n",
" plt.xlabel('Particle Positions')\n",
" rest_length = n_particles*(1 + n_steps*dt)\n",
" plt.xlim([-rest_length/2, rest_length/2])\n",
" plt.ylabel('Time')\n",
" plt.gca().invert_yaxis()\n",
" sns.despine()\n",
" plt.show()\n",
"\n",
"\n",
"plot(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## $\\mu (v - \\langle v \\rangle) = F$\n",
"\n",
"The global friction $\\mu v$ in above example allows only the outer springs to somewhat extend, while the springs in between remain compressed (think particles moving though honey). Friction with respect to the neighbors $\\mu (v - \\langle v \\rangle)$ allows all springs to extend equally (the first behaves odd because we calculate its velocity from the boundary condition, which is to not move the center of mass):"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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MobAlhBAbtLW14dixYwAMARq56Ssesm42MzNzVITBLB4jh8qAkPCM3DoGhDK20iNrxnx9\n5maFyLMit4ylpaWpITFxks3IprGGhoZR+d0VK1YAMFzgGzdujHouIYS4BYUtIYRYxOfz4a233oLf\n74fX68Xzzz9v6/kSQ1iwYMGonKxsHANGbx0bGRlR4lFaDqxifnxkM8LMmTOVyxsZN5DrBAxXNtLt\nFfE6MjIyalnD0qVLlRt8/vx5W9dLCCGpQGFLCCEW0HUdv//971U11rPPPhvVWY3F8PAwHjx4ACA8\noyqIsM3NzR0VKRgcHFQf29k6BoQL28gcraZpSkSbhbUgW8YGBgZGfX3+/Pnq7Mgsrdfrxfr16wEY\nw3KRbjAhhLgFhS0hhFjg4sWLalVsdXU1Nm7caOv59+7dU66nOKFmRDjK7X8zZqc1skkBCC1oiLZ5\nLJ6wBULusCyNMGMW4JENBx6PJ6zaS+IQwsaNG9V1nTt3btTZhBDiBhS2hBBigbNnzwIAioqKLG8Z\nMyO369PT00cNh+m6rtzcyBgCED7YFS2KIANa0a7J7PCanV9BhHRnZ+eoSrDc3FwUFRUBMIR5JFLt\nNTw8PGqILC8vTw2RXb58mUNkhJAxgcKWEEIS4Pf71XDXunXrorYPxEPXdXW7fsmSJWFNBYCx+Utc\nWdn4Ffl1IVorggyFRdt+Zh4oi9ZlK0saAKCvr2/U10WEi/A2s3DhQjWcFrleFzB+VnIuV+wSQsYC\nCltCCElAa2urchyjVXEloqWlBd3d3QCgbt+bkaEyIHpMQYRtfn5+1BYGcWKjCVvzkFo019TcjBBt\nA5nkiB8+fDiq/cDr9aKyshIARg2QAYaIl+jEpUuXRn2dEEKchsKWEEIS0NzcrD5ORtiKW+vxeLBs\n2bJRX5fb/Pn5+WEOqiDCNnLNriCbx6IJW03TlLiN5thaFba6ro/qswVCfbzt7e1KvAterxfV1dUA\njE5buU5CCHELCltCCInDyMgILly4AMCIAdhtJQCM4SoAqKysjCo+RdhGc2sB4NGjRwCg8q6RxNs8\nBoTiCJEDXoCRo5VsbqQwBYA5c+aoj82LKQTzBjX5Ps2sWbNGvfbly5ejXh8hhDgFhS0hhMRA13Uc\nOHBA5Us3b95s+4zu7m7VERvNrfX5fMqRjeYG67quhseiublAKGIQmd0VRIxH9tgChossgjlal212\ndrbaMiYLJswUFhYq8SutEWbKysrU10+fPs0hMkKIq1DYEkJIDC5cuICLFy8CMLKxjz32mO0zzNnT\nyDW6QPjGMbM7KgwNDSkxOHPmzKivEa3my4w0KUSr+wJCa4GjRQ2A0JaxO3fuRI0zrF69GoDh6Iq7\nLGiahm3btgEwnGduIiOEuAmFLSGEROH+/fv44IMPABgRgK997Wu2K76AkLAtLCyMGiUwtw2UlpaO\n+rq56iuWsBViXV8iYSuv297eHtVRFUHu8/mirteVHC0Q3bVdtWqVyvKeOnUq3rdACCEpQWFLCCFR\n+N3vfodAIIC0tDS88MILUbOxiQgEAqrmKppbC4SEbX5+ftT8rrmCS9bURuKUY+v3+0c5roBR6yUD\naNFqu/Ly8pSrW1tbO+p6vF4vtmzZAsBogDAP4xFCiJNQ2BJCSAQ9PT1qE9eePXuiOqlWaGhoUE0A\n0fK1ANRig1htC2ahGS1jq+u6quGKVgUGABkZGQAMxzUa5m1n0dbfZmRkqOuLNkAGhFzbjo6OqOt5\nN27cqK6Pm8gIIW5BYUsIIRGYxZt56t8uclt+xowZqu/VTE9PjxocE8czEhHYubm5UV1jn8+n4gPR\n1u0CoaGyaPlYIFwwR2tGAIDy8nIARkQjmkNsFu7R2hGysrKU+L1y5QqrvwghrkBhSwghEUj9VlZW\nVpibaQefz6cE3sqVK6M2FphbBqIJXwDK/Yy2ahcIX5Mbq4oskbDNyMhQz+3q6or6GNmINjQ0FDWu\nMHPmTMyfPx9AdGELAJs2bQJgVKix+osQ4gYUtoQQYkLXdSU4582bl9TAGGAsJJCIgHS5RiKvk5eX\nF7OjViq4UhG20mMbS9gCIdc2kWMLxI4jVFVVqa+bh96EsrIytfDh3LlzCbPBhBBiFwpbQggx8emn\nn6raq1jxACvU19cDMASjuJ2RiDNcUVERVUD7fD41PBZr65g5NytZ2kgk2+rz+WKKSRHWEo2IpKCg\nQLUy3LlzJ+pjVqxYoT6O1o4AhFzb9vZ23Lx5M+pjCCEkWShsCSHk/6e+vh6fffYZAMOhlEl+u/j9\nfty6dQuA0X8bTbSab+nHGhwzu56xljOYhao0F0QirQi6roc5vGZkQK6trS2qs6tpmsob37p1K6pA\nLioqUnGEmpqaqI9Zs2aNEsifffYZXVtCiKNQ2BJCCIws629/+1sAhhB84YUX1C18u9y+fVvFEOT2\nfCTmyivzbX4zPT096mPpgY3E3DsbKzZh7r8114eZEWEbCARiurYibPv6+sL6d82sX78egPHzjBZZ\nSEtLw/bt2wEYg2jRtpkRQkiyUNgSQqY9IyMj+NWvfgWfzwePx4MXXnghppC0ggxPZWVlYcGCBVEf\nI4sOPB5P1I1jgDVha3Y8Ey1oAGJ32ZqvIZZoraysVK8RK0awcuVKFX2oqamJ+piNGzeqBodjx45F\nfQwhhCQDhS0hZNpTX1+vXMpnnnkmphi1QiAQwLVr1wAAS5cujdqGAITytbNnz47pDEtDQVpaWszB\nMHNsIFYUwVwDNjAwEPUxeXl5qk4s1mrd7OxslReO5bRmZmZi1apVAIC6ujr4/f5Rj8nIyFDrie/c\nucOFDYQQx6CwJYRMe2RJQk5ODjZv3pzSWTdv3lTicfXq1VEf4/f71QBWrJovINRhO2vWrJhurJVW\nBPPihmhCEzDcXhkgi1X5BRhbyACj+SBWy4J838PDw1E3lQHGEJlc1+nTp2O+HiGE2IHClhAy7Wlq\nagJgiLZk670Euf2em5sbc41uU1OTyuDGegwQck5l5W00zMI21tpfs2scr/KroKAAQHxhK8Nhfr8/\nZmShoqJCucRXr16N+pjs7GysXbsWgLGwIVb2lxBC7EBhSwiZ1gwMDKiu2FQiCIAxVCXZ07Vr18aM\nBkhjQnp6eszXHBkZUa0J8YStuMPZ2dkxX88cdYjl2AIhYRttra4gwhYIxSki8Xg8WL58OQAjbxzr\nNbdu3QrAGIA7e/ZszNckhBCrUNgSQqY1J0+eVB+nKmxra2vVMNe6detiPk5uz1dUVMTM1z58+FCd\nJY0F0RDHNlYMATBiBuJExxO2hYWF6sxYK2+zs7PVsgiJcERj5cqVAIw4QqxBs5KSEuVYnzt3LqyT\nlxBCkoHClhAybbly5QpOnDgBwBC1sdoJrFJXVwfAqO+KtVBheHhYRQwqKipinmWOA8TaSgaEogXx\nqsk0TVPCN9bwGBDuDMeKGQChXHBDQ0NMobxo0SLk5uYCAM6fPx/zrB07dqjrYtaWEJIqFLaEkGlJ\nS0sL3n33XQBGHvZb3/pWSvna7u5u1dsqbmU0pOYLCL+tH4lZ2MarHpMe21gxBEG6bGPVfQHhznBL\nS0vMxy1btgyAEZeItYXM4/Fgw4YNAAwBHCveUFFRoQbSTp48GdMpJoQQK1DYEkKmHf39/XjzzTfh\n9/vh9Xqxf/9+5S4mi1R8AeGrZSORXKrX68XcuXNjPq67uxuAIbpjVYYB1oWtdNnGE7aZmZnKaY7n\n2C5cuBCZmZkAgBs3bsR83IYNG9SbhViuraZpePLJJwEY29jo2hJCUoHClhAy7fjwww+VcPzKV74S\nc/OXHWT6f+7cuSqrGg0RtnPnzo0bH5Drk4GuWNh1bBO1D4jYjufYer1elY29ceNGzLW4eXl5yt2t\nqamJ2ciwcOFCFW84deoUXVtCSNJQ2BJCphWBQEBtBlu3bp2qnEqFtrY2FUOorq6O+biRkRE1cJVo\nUE2aGuLlawEjswsYSw/iIQ5rogEtydl2dHSEreuNRNbrdnd3x60HkzjCwMBAzE5bAHjiiScAGN9P\nvEwuIYTEg8KWEDKtaG5uVh2y8bKwdhAh5vV64wrl27dvq2ErcTKj4fP51Ca0RANtMgxm3i4WDXGH\n47UiAKFmhGAwGLbSNxLz4Fu8doTFixerwbUrV67EfNz8+fOV2D99+nTC6ySEkGhQ2BJCphWyClbT\ntJTrvQDDhb106RIAI1srWdZoSB41Kysr7uCYeaVtvKovwLqwlZxuIsFodojj9dkWFBSoobZ4wtbr\n9aoVu9euXVNvKqKxfft2AEBvby9qa2vjXichhESDwpYQMm3QdV0tRygvL1e351Ph6tWrKg6wcePG\nuK8tfa5LliyJm4k1C1unHdt4m8cAhOWD4wlbTdNUm0E8YQuEVuyOjIyoGEg0li1bhpKSEgBGQ0Ks\n7C4hhMSCwpYQMm04fvy4Gt6Kt8rWDpcvXwYAFBcXK6EXjUePHqlb+5JPjYXka3Nzc+MuXtB1XWVm\nE4l0yeAODw/HFYzZ2dlKJLe1tcU9U+IInZ2dKjoRjfnz5yM/Px9A/E5bTdOUa/vw4UO6toQQ21DY\nEkKmBdevX8eRI0cAGLf3RUClQm9vr4o2rF69Om4PrtnVjLeYAQh12MZrVwAQNtwVrxIMCNV96bqu\ntpXFwkozAgAsXbpUfRzPidU0TbnZd+7ciSuY16xZo+IQn3zySUKHmRBCzFDYEkKmPK2trfjNb34D\nwLhl/+KLLyZsEbCCVHwBodvtsWhqagIA5OfnK/cyFhIBSCRszaIvkbCVui/AXuVXvGaE3NxczJs3\nDwBQX18f98wNGzaoazx79mzMx3m9XuzZsweAIfDZkEAIsQOFLSFkSjM4OIhf/epX8Pl88Hg82L9/\nf8JuWKvIlH9ZWVnCWi4RtvHiCoDhqIpja7XDFrDeYwskFrZlZWUAjExsvIgBAFRVVQEw+nnjnZuT\nk6Oq0C5duhS3q3blypVKXH/22WcJK8oIIUSgsCWETGkuXbqkhOLzzz/vSBMCYORPZT1uvO5awHAe\nxYVN9Pp9fX2qOSCRY2tuOLAaRQBCA2exMG9Ei7eBDACWL1+uPpbBvFhs3rwZgCGY4+VnNU3D3r17\nARib0s6dOxf3XEIIEShsCSFTGlkKUFpaivXr1zt2rtxO93q9WLNmTdzHmm/TJxocM+darVZ9AdZb\nEYDElV/5+fnq8Y8ePYr72OLiYlX7defOnbiPLS8vV9+TDN3ForKyUr0JOHXqFHttCSGWoLAlhExZ\nAoGAEluystUJhoaGVHftqlWr4nbXAqH+2jlz5iTM14qw9Xq9mDVrVtzHmoVtomuwI2w1TVPRikTC\nVtM0LFq0CIDREZyookveBHzxxRdxYw6apmHnzp0ADBe7pqYm7rmEEAJMAmHb3NyM73//+9i6dSt2\n7tyJH/3oRwnzYYQQAhjiSW7rOylsL126pM7dsmVL3McODg4qcS151HjIrf/S0tKE8YL+/n71sdUF\nDUBiYQvAsrAFQi0PPT09cbtvgfD2iESu7ZIlS1Qs4sSJE2xIIIQkZMIL27/8y79Efn4+jh49il//\n+te4efMm/vVf/3W8L4sQMsHRdR0nT54EYIg6p7K1uq6rSf2ysjKUl5fHfXxDQ4NyMc151FiIsE20\nmAGwF0XQNM3y9jEgJGwfPnyY0IU115dJ9CMWubm5qkP44sWLcVsXzK5td3c3Ll68mPC6CSHTmwkt\nbHt7e7F69Wr81V/9FbKyslBaWopvfOMbcatiCCEEAA4fPqwiAGvXrnWk3gswogKyQGHDhg0JHy89\ntzk5OQkzs36/Xw26JYohAFCusaZpYVGDWIj4TTQ8BoTyvUNDQ+qaYlFQUKA2hiWq/QKgss49PT0J\nH79ixQrMnj0bAPDpp5+yIYEQEpcJLWxzc3Pxj//4j2E1Os3NzQn/cSCETG8uXbqEEydOAADmzZuH\n5557ztGzAcMFXrVqVcLHSwyhoqIi7gIHAGECMlEjAhDqsU0UWRAkh2uOMMRCKr8A4+/dRKxYsQKA\nIeTjVXkBhnMtWePTp0/HfaymaXj66acBGFlbceEJISQaE1rYRlJbW4tf/vKXePnll8f7UgghE5R7\n9+7hvffeAwDk5eVh//79ltxMKwQCAdVdu3z5cmRlZcV9fE9Pj8qoJto2BoTnWRP14gKhHlurwla6\nbK3MKRRa/N4RAAAgAElEQVQXF6s1vVJrFg8RtsFgUDnlsfB4PKr6q6mpKaFwXrx4scpInzx5knMW\nhJCYTBphe/78eXzve9/DD37wAzz22GO2ntvW1oarV69G/W9kZIQDCYRMEfx+P9566y0EAgGkp6fj\npZdeCltMkCq3bt1St/ETVXwB4fVXVoStefDKyhIJu46tHWGraZpyba04tnPmzFHXfO3atYSP37Bh\nA9LT0wEAZ86cSXgtTz31FAAjfvHpp58mPJ8QMj1xxsZwmSNHjuBv/uZv8A//8A/46le/avv5b775\nJl577bWYX5cORkLI5KapqUmJtueff97SAJYdJN8/c+ZMNQAVD3Euc3NzUVxcnPDxra2tAAxRK6Iv\nHsPDwwBgOT8sDrM8LxFz5szB7du38fDhw4SP1TQNVVVVOH36NG7fvo1gMBh3G1p2djbWrFmD8+fP\n4+rVq3j22WfjOuBz587FmjVrcPnyZdTU1GDXrl0Jq9MIIdOPCS9sL1y4gB/96Ef4j//4D2zbti2p\nM/bv3692j0fy8ssvJ1xFSQiZHDQ0NAAA0tPTsXLlSkfPbm9vV+dv2rQpoUvq9/tx8+ZNAEZsIVG+\nFgg5o+bNX/GQrGyiDltBIhlWlx2IGO/v78fQ0FDC6EVlZSVOnz6N4eFhNDc3Y968eXEfv379epw/\nfx5+vx9Xr17Fxo0b4z5+9+7dqK2tRTAYxPHjx7Fv3z5L3wchZPowoYVtIBDA3//93+Ov//qvkxa1\nADB79mw1VRuJFVeEEDI5EOFZUVHhWK5WkCEnr9ebUIABRu2VTPBL/jQeIyMjqm3BPLgVD7eFrTnn\n29HRkbDabOHChdA0Dbquo7GxMaGwLSsrw6xZs9De3o6LFy8m/LkWFxdj9erVYa4t77gRQsxMaKuy\npqYGjY2N+MlPfoI1a9Zg7dq16v+a104SQkhXV5e6lW8lJmCHwcFB1YZQXV1tKbcrOdPs7GwsXLgw\n4eNbW1vVMJhdxzZRh62QrGMLWFvUkJmZqcSs1JzFQ9M0rFu3DoCxTMNK5GHXrl0ADOPj+PHjCR9P\nCJleTGhhu2nTJly7dg2XLl3C5cuXw/6v1b/4CSFTn5GREbz99tvqfy9ZssTR82tra5UY3Lp1a8LH\n67qOW7duAQCWLVtmKe7U1tamPrb695vUamVnZ1t6vGRxA4GAJXGbm5urniNvGhIh7QVNTU0YHBxM\n+Pg1a9aon0+iITIAKCkpQXV1NQBjqDjeWl5CyPRjQgtbQghJhK7r+L//+z+VT929e7elQS07yMar\nuXPnWhKdHR0daojN6ipfcUSzs7MtO7AiTq3GLsyRBStdtnabEYDQdrVgMIjr168nfPzMmTNVH/DF\nixctieEnn3wSXq8XwWAQhw4dsnRdhJDpAYUtIWRS88knn6Curg4AsGrVKjzxxBOOnt/a2qqiT2vX\nrrX0HPNa2UWLFll6jghbK/21QrJ1X4C1yi8glPe9f/9+wtW6gLGxTL4H+b0kQmYoRkZGcO7cuYSP\nLyoqwpYtWwAA169ftxR7IIRMDyhsCSGTltraWhw7dgyAIcC+9rWvWWofsIO4tV6vF6tXr7b0HOmv\nLSkpQW5urqXnTFRhKwNjPp/Pcu2XDMs1NDQk3EIGGE649PyeOXPGUrf47t27lbN98OBBlU8mhExv\nKGwJIZMSXddx+PBhAEYX9Ysvvuh4y8nIyIgaGquqqrIUEQgEAsqxterWBoNB28I2GAwqAWg1imAW\ntlaiCADCmhCsDu1K1VowGFRZ40SIa9vX12dpwUNWVpZy51tbW3H16lVLr0MImdpQ2BJCJiXt7e3o\n7u4GAOzZs8eyM2qHS5cuqcznpk2bLD2nsbFRLUBYtmyZpee0t7djZGQEACwvlTBnUa1mcs3CX14v\nEXl5eWqAzIpjCxgOrOR5pYItEUuXLlULF2pqaiw9Z+PGjeqNwNGjR+naEkIobAkhkxOzE+h0CwJg\nOMKff/45AENsWlmJC4RqvrKysiw7tubBrERdsYLZcbXaY6tpmootWK380jRNDeNZqfyS58jQXGNj\no6VsrqZpWL9+vXqOeb1wLDweDx5//HEAxsBebW2tpesjhExdKGwJIZMSEbZlZWWWhZ0dbt68qaqk\nHnvsMUvZ3UAggPr6egBGO4DV7Ov9+/cBGPVaVp3nZIQtYL/LFgj12Vp1bIFQl3BPT4/lSi7ptAVC\n2eZEVFdXq+s7evSopXwuIWTqQmFLCJl0fPHFF7h79y4Ad9xaILRpbObMmao3NRHm7lYr28YEya5a\n3TgGjI+w7ejosHy731xzZjVnm5+fr36fNTU1lkSqx+NRWdvOzk5cuHDB0msRQqYmFLaEkElFV1cX\n3njjDQSDQaSlpWHNmjWOv0ZnZ6caANu0aZNl51XypGlpaZb7a3VdV05orNXf0ZB1vUBo8YIVZJnD\nwMCA5eeUlpYCMMSwVdc2NzdX5YWtDIMJkmXu7e3FlStXLD1n5cqV6ho/+eQTS124hJCpCYUtIWTS\nMDQ0hNdff12Jsm9+85uOL2MAwm+Dm2+PJ0L6VBcuXGi5qaC/v1+JVDvfi9nNtPpaQKgZwWrdFwC1\nJhcw3HKryOKFpqYm9PT0WHrOsmXL1M/h5MmTlvK5Ho8HzzzzDABjqO7o0aOWr5EQMrWgsCWETAqC\nwSDeeecdtLe3AwCeeuopW7f77byOCNslS5aoSf1EDAwMqCEwq0NjAMLyp8kKWysre4VkhG1ubi7y\n8vIA2BO2UvsFWHdtNU1T1V9tbW1hyy7isWjRIvXn4ezZs7bywISQqQOFLSFkUnDs2DF1q3/9+vXY\nvn27K69z69Yt5S7KlL4VzNuvZHDKCskKW8nIer1eW0spJI9rR9gCobYGGXSzQlFRkVpBbKdndu3a\nteo6T548afl5Tz/9tFq1+9FHH1l+HiFk6kBhSwiZFEiV07x587Bv3z7HN4wJUvGVk5ODqqoqy8+T\nNoScnByV97TCgwcP1PMk/2oF6crNzMy0/BwglLG1shHMjAjUhw8f2uqLFRf1iy++sJx9TUtLU1nb\nxsZGyzVjhYWFyu29efMm7t27Z/k6CSFTAwpbQsiE59GjR8rZXLduneVhLru0tLQo53XLli2WX2dk\nZAQ3btwAYAg5O6JbHFCr/bWCOK52q85kSYOdVgTAWA8MGFENKx2zgrQc6Loe5monYsOGDernaKfp\nYMeOHcjKygIAHDlyxFJGlxAydaCwJYRMeG7evKk+Xrp0qWuvc+rUKQCG+LO6aQww2hBkAEwGpqzg\n9/uVY2tX2Erdl3lNrhVk0CwYDNpyXkXYAvb6bOfMmaM2o1mt/QKMjWeyue3ixYuW+2mzsrJUTOXO\nnTu2xDQhZPJDYUsImdDouo7r168DMGqnZIjJabq7u1W91Lp16yyvqQVC+dGcnBwsWLDA8vNaW1uV\nuExW2Np1bM0NCnZc28LCQuWgWl24ABjDYJI5bmhosOWgbtiwAYDxvcqfASts3bpV/f7o2hIyvaCw\nJYRMaD7//HPluomD5wbnz59XAkhymlYIBoPKiVy+fLmthgJxa4FQhtUqkle1I8CBUBQBCO/CTURa\nWhoKCwsBGILcDuYtZObvORFLlixRb2Qk+2yFjIwM7Ny5E4AR9bDah0sImfxQ2BJCJiz19fVqur2k\npMS1JgRzxdfSpUuVgLNCc3OzGsSyG5OQW/o5OTm2Baq4rXY6bIHw6MJYNCMAxhsSEfx2RKbH48HW\nrVsBAPfu3UNTU5Pl527evBlFRUUAgEOHDtkS8YSQyQuFLSFkQtLc3Izf/OY3AAxX8jvf+Y4aCnKa\nmzdvore3F0Do9rdVpILM4/GgoqLC1nNl2j+ZJRPmui87pCJsZVFDR0eHrc1l2dnZaoisrq7OVjRg\n48aNqvnBTvVXWlqaWtrQ29uLY8eOWX4uIWTyQmFLCJlw9Pb24o033sDIyAi8Xi9efPFFWy6qXWTq\nfubMmbZdVxG28+fPt129JY5tMsJWhqnG0rE1byCz69rKUF1XV5et52ZmZqpBvuvXr6sFHVZYtmyZ\n+n2eOnXKcm0YIWTyQmFLCJlwnDhxQomur3/965g/f75rr/Xo0SPVumC3SmxgYEBt4qqsrLT1uiMj\nI6o2y66w1XU96ShCVlaWigXYFbalpaXq9WTLmlWqqqrUc61uIRMee+wx9Xs5ffq0rec+88wz8Hg8\nCAQCOHz4sK3nEkImHxS2hJAJha7rqhN2+fLlqK6udvX1Tp06BV3X4fF4bFV8AYZAk9vqy5cvt/Xc\nBw8eqOfaHRwbGhpSbQp2s7mapiEjIwOAIa7t4PV6lQi3u7I2MzNTRTXE5bbKzJkz1Z+D2tpatZzC\nCsXFxdi8eTMAIwZhV5ATQiYXFLaEkAlFR0eHcjLdbEEAjBopGRqrrq5Gfn6+redLzdesWbMwe/Zs\nW88VpxcAysrKbD3X7LTarfsCQi6v3SUNQKjP1q6wBULLGlpbW1Wm2SobN24EYDQ52G052LVrlxLz\nR44csfVcQsjkgsKWEDKhELcWcHcZAwCcOXNGiTu7jQt9fX24c+cOAHtLGQTJmZaUlNgeipMOW8D+\nggbAGWHb0dFhux9War8A+67tvHnz1Kric+fO2XrtnJwcPPbYY+p15fdGCJl6UNgSQiYMQ0NDapCr\nrKwsKdFmlZGREZw9exaAIaBFNFmlvr5eiatkhK3cEjcPZFklVcc22bW6QEjYjoyMoLu729Zzi4uL\nUVBQACB8m5wVNE1Tru2DBw/CHG8rbN++HdnZ2QCM+i8ubSBkakJhSwiZEAQCAbz99ttqq5Xd2i27\n1NXVqSUHdhYyCLKUoaSkJGzdrBXMg2N2BTUQvlghmQo0EXh2KrsE8/XabUbQNE3FS27evGm7W3bN\nmjWqeeLEiRO2npuZmYndu3cDMN5U1NTU2Ho+IWRyQGFLCBl3dF3H+++/j8bGRgCGqHVb2J4/fx6A\n4SLa7Z8NBAJqG5r59rpVzCtp7YpiINxptdtjC4TiC3ZbEYDw6IRd1xSAGgIbGRkJi51YIZXqL8BY\n2jBr1iwAwOHDh9UbG0LI1IHClhAy7pw8eVI5aJWVlfjyl78MTdNce722tjbcu3cPgCGi7b7WvXv3\nlNsoA1F2SFXYSoetpmm2VvgKEl9IRthqmpb0BjLAiF7IkF4yq27N1V92XVuv14vnnnsOgOFWf/rp\np7ZfnxAysaGwJYSMK3fv3sXHH38MwGgX+Pa3v52UC2mHc+fOATCEzrp162w/X2IIaWlpWLhwoe3n\nS6NAWlqa7SYGIHzrWDJvAHJzcwEYwjaZrKnkgpubm5XItoqmaSqTfPPmTbWO2CozZ85Uv7Pa2lrb\nOd9Fixap1z979ixaW1ttPZ8QMrGhsCWEjCtSt5WVleXq2lxhYGBAucMrV6603QOr67paMFBRUaEG\nsezw4MEDAIZbm4wwFTFod9OZIBlbv99vW5gCUI5tIBAIc5+tIsIyGAzabkcAQg0WwWBQRUrs8PTT\nTyMtLQ26rrP+i5ApBoUtIWTc0HVdTccvX75cTcy7yenTp5Ou+AIMUSqrWVeuXGn7+bquq2xqMo0I\nQKjuK9nWCPO2slSaEQDYzrkCxkIKiUOI+22HoqIiFQGpqamxLc7z8/NV/deNGzfQ1NRk+xoIIRMT\nCltCyLjR3NysRJrbyxgAo03gzJkzAIxs7Jw5c2yfIblQj8eDFStW2H5+T0+PyraK82kXeX4yVV8A\nwlxmu9vHAEMYijhOZlGDpmlKmN66dSupOIQMkfX19eH69eu2n79jxw51d+Djjz9m/RchUwQKW0LI\nuFFfXw/AEImVlZWuv9758+fVbfwdO3bYfr6u62rb2NKlS5OKTZibBCarY+vxeJJerSuIsO3r60sq\n57p06VLk5eUBCGWm7ZCVlYWdO3cCMIYBkxHHhJCJB4UtIWRcuHPnDk6ePAnAGOhJNi9qFV3XlVtb\nXl6e1NDXgwcP1LBSMjEEAGhpaQFg5GNFHNpF+mft5oMFs2Nrt0tWkNqsZIevFi9erPLF8gbHDh6P\nRy1suH37tvq52mHLli1KHH/00UdJiXxCyMSCwpYQMuY8fPgQb775JoLBIDIyMvD000+7/poNDQ3o\n6uoCAGzdujWpoS3Jg2qalvS6X3E4Z82alXSlmQiwZAbXgHCnN5nKL8DYDAcYGVu7zQaAMcC2aNEi\nAEa8I9k4gvwM7FZ/AcbP76mnngIAdHZ2JnUGIWRiQWFLCBlT+vv78frrr2NoaAiapuHb3/52Utu3\n7CK3q2fMmJFUNhYICdt58+apZgG7iLBNpr9WEGFrjhTYwQlhO3/+fPVxMn22QGhZQ0dHh2qKsMOM\nGTPUIo+6urqkGhqqq6uVe3/8+HH15ocQMjmhsCWEjBl+vx+/+tWv1DrZL3/5y0ktOLBLT0+P2nK1\nfv36pATh0NCQWuqQzLYxwKjHku99PIVtdna2WuzQ29ub1Blz5sxRfcPyc7HLihUr1Bm1tbVJnbF9\n+3Z4PB7oup6U46ppmloI4vf7cfDgwaSugxAyMaCwJYSMGZcuXVLDU9u2bVOT7W5z5swZdatbcpl2\nMU/vJyvGHz16hGAwCCB5YRsMBtUZyQpbTdOUayuDaHZJS0vD3LlzARjtFsmQlZWlfpZ1dXVJxRHy\n8vKwZs0aAMDly5eT+n5mz56NrVu3AjDyvrIumRAy+aCwJYSMGTJ5XlxcPCa5WsBwWiWGUFVVhcLC\nwqTOkTaEvLw8lS+1i7kRQUShXczCLdnhMQDIyMgAkPzwGAAVIUmmy1ZYvnw5AKC7uzvphgXpIw4E\nAmr5hl2eeOIJ9fNk/RchkxcKW0LImODz+dDY2AjAEJjJDk7Z5ezZsxgeHgYAVe9kl6GhIbVIYtWq\nVUlfuwjbvLw8NY1vF3MmNtm6LyDk9iazeUwQ17mrqyupPlwg3P2Wn7FdZs2ahYqKCgBGllocbTtk\nZmZi9+7dAAwHuq6uLqlrIYSMLxS2hJAx4fbt20pEVVVVjclrjoyM4PPPPwdgrL9Ntje2vr5eXfvq\n1auTvp5UN44BzglbaRNIVpACocovIPk+25kzZyr3OpktZILEWrq7u5M+Z9OmTWr73eHDh1MS/YSQ\n8YHClhDiOsFgEKdPnwZgDC6lIuzscPHiRdX5mqxbC4RiCEVFRUltKwOA4eFhtLW1AXBO2Ca7eQwI\nObapdLemulpXkOq0u3fvJlUdBhiRBhH68mfNLl6vF3v27AFg1H+dPXs2qXMIIeMHhS0hxFV0XceB\nAwfUQM66devURL7bryvZ2jlz5iS92czn86lrX7lyZdIxBLOjmaw4lusRktl8FvlcEf7JkJeXp2rP\nkh0gA0IOfjAYTGpZA2CIUhkMbGxsTPp6qqurVYb6008/Tbo1ghAyPlDYEkJc5dSpUzh//jwAY8PY\n3r17x+R1m5qalEO6efPmpAXpnTt31C3pZJcyAOHC1nwL3y7isHq93pRyyuJuJttjCxjtCuI+mwfj\n7DJ37lwUFRUBMJY1JMuWLVtUxOL48eNJnSH1X4Dhsh86dCjp6yGEjD0UtoQQ16irq1PCoKSkBC+8\n8ILqLXUbcWszMzPVIoBkkIGmrKyslCIEcqs+KysrpQhBqh22Qm5uLgBD2KbSACA/k5aWlqTzupqm\nqd9RY2Nj0mJ7xowZKmt77dq1pOMR5eXlavFDbW0t7ty5k9Q5hJCxh8KWEOIKHR0d+O1vfwvAyIJ+\n97vfTenWuR36+vrUVPvatWtVtZVddF1Xg0iVlZUpRSjMG8dScVqdErbi2Pr9ftUakQyygSwYDKKl\npSXpc2QoT9d1lWlOhm3btqk3T6msyN27d6+KWRw4cCCppgVCyNhDYUsIcYVLly7B7/fD4/HgpZde\nUtPmY8Hnn3+uhMjmzZuTPqelpUWtWE0lhiBnAanFEACo4apkxbpg7sAdHBxM+hxzp28ya3GFkpIS\nlT2WLXHJkJubi3Xr1gEwYg3JLqCYMWMGnnrqKQCG255sPy4hZGyhsCWEuIKIk4qKCpSXl4/Z6w4O\nDqpp9uXLl6e0ulbynl6vVy0SSIaenh709PQASK0RAQgtaEil6gsId3xTaUbIzMxUnbypNCMA4e0I\nqSyO2LJlCwCjo/fChQtJn7Nu3TrMnj0bgDFIlso1EULGBgpbQojjdHV1obW1FcDYddYKZ8+eVQIk\nlYovXdeVsF26dGlKMQrzYFWqwlbyp04K21S6bIGQC51sl60gwjYQCKS01nb27NlqYcP58+eTjhF4\nPB7l2vb19eHUqVNJXxMhZGygsCWEOI6szgWAZcuWjdnr+nw+tZChsrIyJaf47t27quoplaUMQEjY\nZmZmphxFcErYSnsAkJpjC4T6bFN1bMvLy1WuNdktZIJEULq7u1OKNixZsgSLFi0CAJw8eTKlFglC\niPtQ2BJCHKWtrQ2ffPIJAKC0tHRMs7WXL19WedFU3FrAmKoHjCyrU/na8vLylFcJSxTBnJFNBrOw\nTfUWu4j1/v7+lISfx+NRK3br6+tTGtiqqqpSzQ+pOK2apinX1ufz4fDhw0mfRQhxHwpbQohj9Pb2\n4pe//CWGh4fh8XjwzDPPjNlr67qusrWlpaXqVnSySBvC4sWLw0RgMoiTKXnNVBB3NdXhMXPlWKou\npDlekUqfLWAswQAMkZxKzZbX68XWrVsBGJ3Gd+/eTfqssrIyNZB28eLFlM4ihLgLhS0hxBF8Ph/e\neOMNNST1la98Rd3CHQucWsgAGFVljx49AgDlICbL4OCgcllTGWQDjEotcTFTrfvKzs5WtVipCttZ\ns2YpoX3v3r2UzlqyZInKM9fW1qZ01qZNm9RZx44dS+msp556Sp114MABtbSDEDKxoLAlhKRMMBjE\nO++8o2657969WzlcY4V5IUOqmVhxa4HUha05d5pqvtachU1V2GqapnK6qa6N9Xg8Ks+cqmOblpaG\nFStWADAWfKQy2JaZmalc24aGBty/fz/ps3JyctTWvLa2Npw5cybpswgh7kFhSwhJmfr6ejXss2bN\nGjzxxBNj+vrd3d2OLGQQZPittLRUVVkli1nYpurYOilsgdAAWrJdr2ZkUUNzc3PKywzkjYnP50ND\nQ0NKZ23dulX9eTh58mRKZ23YsEEJ+E8//dSRnxshxFkobAkhKVNfXw/AKMf/yle+kvKAlF1OnjyJ\nYDAITdOUQ5csvb29KtuZSnetIA5mfn5+ygNfZiGV6lmA4WgCqQ+PAVDLFfx+Pzo7O1M6a+HCher7\nS6XRADAiF+vXrwdg/DmVqEwyeDwePPfccwCMn9nRo0dTujZCiPNQ2BJCUiIQCCi3dtmyZY44iXbo\n6+tTJfyrVq1CUVFRSuddvXoVuq4DSL3mCwgJ21T7a4HwLGyqdV9AyPVNte4LCHejU+2zNbcj3Lp1\nS/0+kkWqv4LBIM6fP5/SWeXl5aiurgZgdOR2dHSkdB4hxFkobAkhKdHU1KTWvI71MgbAqHISYbZr\n166Uz5OlDGVlZSguLk7prMHBQSXy5FZ9KpizsBNN2BYVFcHjMf5JSbXPFghlm3t7e9Wyj2QpLi7G\n4sWLAQAXLlxIefBrz5498Hg8CAaDrP8iZIJBYUsISRpd19UQTXp6+pi2IADA0NCQGhqrqqpKuU7r\n0aNHasDICbfWPKzkpGOraZojUQSpMUt18xhg1GvJGwGnhK1EWlKNIwChNbt9fX0qj50shYWF6rxr\n166x/ouQCQSFLSEkaY4cOaLytdXV1WMeQ7h06ZIj63MFs4CSPtVUEKdR0zSVQU2F4eFhAEY2VtzR\nVJCMrSy1SJXS0lIAxgBZqmRnZ2PBggUADBc91TjCkiVLUFhYCAA4fvx4yuft3r1b1X+9//77rP8i\nZIJAYUsISYrz58/j+PHjAIzb9s8+++yYvr55IUNZWZkjjqhkhefMmZNyGwIQypoWFRWpzthUkMhA\nqgsjBNnM1dfXl7LQA0Ku9MOHDzEwMJDyeeKat7e3pxxH8Hg86s1PW1tb2NrnZMjOzlYbydrb29Uq\nZ0LI+EJhSwixza1bt/D+++8DAAoKCvDSSy+lXLFll9u3b6vBHRkOSgWfz6duKafaXSvILflU+2sF\nEbZOOeOS0w0EAionnQrmHHGqfbaA4ZqLM53qsgbAqIKTNyzHjh1LWcxv2LBBifmjR4+iu7s75Wsk\nhKQGhS0hxBZdXV14++23oes6srKy8J3vfMeRQSa7SLY3OztbTamnQmNjo7qdvGzZspTP03VdObap\n9tcKbglbIPUlDYARRZBrS3UDGWD8bpcuXQrAmTiC1+vFjh07ABhxiVQ7cjVNw759+6BpGkZGRnDw\n4MGUziOEpA6FLSHEFpJr1TQN+/fvd8yNtEN7e7u6lbxhwwZHhJ4MFGVnZ6sS/lTo7OxUmdhUh9oE\nOc8pdzwnJ0d97ETO1uv1oqysDADw4MGDlM8DoN609PT0qM12qbB+/Xr1fZ8+fTrl8+bMmcNBMkIm\nEBS2hBBbiKBcuHAhKioqxuUaJNvr9XpTXsgAGDEEGYIz3/5OBbNj6UT+Fwi1IjjlkJvfEDhR+QWE\nYhdONCMARixEfh9OtCOkp6dj48aNAIxIzaNHj1I+8/HHH1eDZIcOHXIkr0wISQ4KW0KIZcyumRO3\n65Ph0aNHKm+5YcMGNQCVCtevX1eVV2vWrEn5PCCUMc3JyUFBQYEjZ04mYdvd3e3IRrOsrCzVjiDD\nfamyadMmJZZlADEVsrOz8fjjjwMwKt6uXr2a8pmEkOSgsCWEWMY8ST4eyxiAUFWTx+NReclUkaUM\n+fn5jixSAEKO7fz58x1bMey0sDW3KzjRZQuED8qluoFMkJxtc3Nz2Pa1ZMnNzVXrkmtqahwR4Js3\nb1Z1YocPH3bsjQIhxB4UtoQQSzx8+BBHjhwBYIiXVFfXJkN/fz8uX74MwHBW8/PzUz5zeHgYt27d\nAmDkOZ0QoX6/H21tbQCciyH4/X6VsTVnY1PBLGydEHdAuLBNtaJLEGELQEVGUkVyscPDw2olcyp4\nvU6OoCYAACAASURBVF7s3bsXgDFgefLkyZTPJITYh8KWEJKQ/v5+vP766xgaGoKmaXj66afH5TrM\n61C3bdvmyJmNjY0IBoMAoFy8VOno6FA5S1lakCpmB9CpHtuMjAwVR3DCCQUMN1QqtZxoRgCMVgkR\nzOKup8qCBQvUkODJkycdcVhXrlyJhQsXAjDqxDo7O1M+kxBiDwpbQkhcRkZG8MYbb6h/pJ977rkw\nB22sCAaDan1uRUWFY00DMpA0Y8YMR9oQgPDBKaeqvsxRAaeEraZpKtbglLAFQn22TnTZAsZ1yrKG\nu3fvOtIXq2kadu3aBcCoOrt48aIjZ+7btw8ejwd+vx8HDhzgIBkhYwyFLSEkJrqu4ze/+Q3u378P\nANi+fbsjyxCS4fr16+jp6QEQuo2cKrquqxjCkiVLHMvCirBNT093JC4BhDu2Tq4uNm8fcwqJX7S3\ntzu2rleELeDMsgbAGIAUR/3EiROOrMWdNWuWuptw69YtXLt2LeUzCSHWobAlhMTk2rVrKtO4atUq\ntUJ0PJCVpXl5eY4NrpmHkZx0oUXYlpSUOCaW3RK2bjq2ANSbolQpKChQ7QhOtQ5omobdu3cDMHKx\nTp37+OOPqyaMgwcPOjaYRwhJDIUtISQm4jbl5ubi61//umMizS53795FU1MTAMOtdaJnFgg5f2lp\naY4JW13X1S34uXPnOnImYOSchRkzZjh2bmZmJgDnhscAI1csf1ZkiM4JVq5cCcBY/iDufaqsWLFC\nDULKNrtUSU9PxzPPPAPAqMhzYhEEIcQaFLaEkKgEAgHVG1pVVeWoS2iXzz77DIDRF7pp0yZHzgwG\ng2oQadmyZUrgpUp3d7daT+tUdRgQ7qg6ucJYfq9O1lOlpaWp6iunFjUA4a66E8saAMO1lXjN/fv3\nHXOYq6qqwgbJzG9MCCHuQWFLCInK3bt3Vb3UeHXWAsYAUmNjIwBg69atjgnQ27dvK7Fhzm+minlg\nyi1h61TdFxAStk7fLpcWA6e6bAGgqKhIDeM5tawBANatW6cG8pxY2AAgrD3E5/Ph6NGjjpxLCInP\npBK2//RP/+RYHQ8hJDa6rqt/4DMyMsZtdS4QWp+bmZnpyPpcQdzarKwsLFmyxLFzpeIqOzvb0a5f\ncYFzcnIci2IA7ji2QPhqXSebAcS1bWxsdEyMZ2VlqY1zV65ccSxvXF5ejurqagDAuXPnHHWvCSHR\nmTTC9tq1a3j33XfHLeNHyHTik08+CRsaG68YQmdnp9p2tmnTJmRlZTlybjAYVOcuX77c0e9PlhKU\nlZU5+veVuOdO/QwEOW9oaMhRASptA8PDw+jo6HDsXLl74Pf7wzbhpYq8aQoEAjh16pRj5+7duxdp\naWnQdR3vv/8+678IcZlJIWx1XcePf/xj/Omf/ul4XwohU56amhocO3YMgDH89Oyzz47btYhrbM5B\nOsH9+/dVDdWyZcscOxcI3Xo3b+ByAnFUneqwFaTuKxgMYmBgwLFzzTEMpxY1AMZiBVkA4VTtF2D8\nvuSO4NmzZx37WRQUFKi+3Lt37+LSpUuOnEsIic6kELZvvPEGMjMz8fzzz4/3pRAypWloaMB7770H\nAMjPz8d3vvMdZGRkjMu1jIyMoKamBoDhqjrVBwuE8pkejweVlZWOnTswMKByu24JW6fdc/MgmpOV\nX/n5+Y5vIAPClzXcunXLUTEu1V8jIyOqXs4Jtm/frrLBH330kaPXTAgJZ8IL24cPH+K1117Dj3/8\n46TPaGtrw9WrV6P+NzIy4kgpNyGTnc7OTrz11lvQdR2ZmZn47ne/6+j0vV0uX76MoaEhAM4tZBBE\n2FZUVDg2jAaENwBMRmErOV6nENfWSWELhIb9gsGgY92zgHGHQjK8Z86cUX/+UiUtLQ379u0DAAwO\nDuLjjz925FxCyGjGr7/HIv/yL/+Cb33rW6isrEy6huXNN9/Ea6+9FvPr4ioQMp25cOECfD4fNE3D\n/v37HRdmdggGgzh58iQAQyBKbZITdHR04MGDBwCcjyHIuYDzwlYytk476OaGBaedxPLycly9ehUP\nHz6Ez+dz7NpLS0sxe/ZstLW1ob6+3tGYyu7du3Hz5k0MDw+jpqZGbRFLlYqKCqxduxaXLl1CTU0N\ntmzZgjlz5jhyNiEkxIQWtqdOnUJNTQ1+8pOfAEDSofv9+/djz549Ub/28ssvOzphTMhkRQZxKisr\nsWjRonG9lqtXr+LRo0cAgJ07dzo6hCW5TE3TVOG/U4gzWVJS4viQl7ipTrvo5syu080Is2fPVh93\ndHQ4urCiqqoKbW1tuHPnDoaHhx1z3ufNm4d58+bhiy++wNmzZ/HYY4859udv7969qKurw8jICA4d\nOoQ//MM/5EA0IQ4zoRXd7373Ozx69AhPPPEEHnvsMfzBH/wBdF3Htm3bcODAAcvnzJ49G6tWrYr6\nX3p6Orxer4vfBSETn0ePHqnb6OPZWQsYb2BleK2wsFDVJTl1tgjbRYsWqcEppxBh62R/rSD5V6eF\nrTna4FblF+DsogYg5LYHg0HVc+wUEn3p7Ox0tC83NzcX27dvB2DUlTU0NDh2NiHEYEIL27/927/F\nhx9+iHfffRfvvvsufvGLXwAA3n33Xezdu3ecr46QqYO5Nmm8he21a9eUCNq1a5ejd1Sam5uVE+zk\nUgbA2Dgma16dFrYjIyMqiuC0sPV4POpn7PSShtzcXOWkOi1sy8rK1Gphp7aQCStXrlQ/Z6fW7Arb\nt29XZ3/00UcIBoOOnk/IdGdCC9vc3FyUlpaq/0pKSqBpGmbPnu3owAch05n29na1srasrGzcM+eS\nrc3Pz1el+U4hg0ZpaWlYsWKFo2c3Nzerj+fNm+fo2eZ1rG4M9EkcwefzOXqupmnKtZV+X6fweDxq\n0OvGjRuODgF7vV5s3LgRgNEU4uS1Z2Rk4MknnwRg/P+eU5vOCCEGE1rYRlJeXo5r166N92UQMmXo\n6+vD66+/jqGhIWiaFjOLPlbcv39fDYlu3brV8ZiQ3FaurKx0/M1xW1sbAEMUFRcXO3q22Ul1o35N\nBsjMAtopysrKABirhp1eTiAZ6YGBAcfjCJs3b1YxDXnj5xTr1q1TeeMjR44op58QkjqTStgSQpzD\n5/PhjTfeQFdXFwBg3759WLx48bhek7hX6enpWL9+vaNnd3Z2quUJ4vQ5iZxdUlLi+ECqOfvqxhY4\ncYGd7LEVJJYxODjo6AYyAFi8eDGys7MBOLusATDE/qZNmwAAdXV1jkYpPB4Pnn/+eWiaBp/Ph4MH\nDzp2NiHTHQpbQqYhwWAQv/71r9Xt8507d6pbr+NFf38/rly5AgBYs2aN460C5hymG8JWhI8bNWlu\nC1sZonND2C5YsEB97HSfrdfrVcOF9fX1jkcptm/fru4ayECjU5SVlamasrq6OkeH1AiZzlDYEjIN\nuXz5shJ6q1evHvcIAmC4tZKTdHohAxAStqWlpY5uMQOAQCDg2ipdIDyK4KZj6/SCBsDoCXdjA5kg\nOeyRkZGwIUgnyM3NVXcOrly5ou5uOMWTTz6pfvYffPCB460UhExHKGwJmYbU1dUBMOq0vvrVr457\nl+bw8DBOnz4NwMi/mvtPnaC3txe3b98GYKzndZrW1lYlyt0o3TdnX6UJwEkkb+y04ylIntTpZgTA\nmL0Q4ex0OwIA7NixA5qmQdd1xwe9srKy8MwzzwAwojIcJCMkdShsCZlm+Hw+NWizYsUKVxxAu5w9\ne1atL929e7fj51+5ckUNLjld8wWEO5FudtgC4ZvCnEL+DLjlGIqL3d7e7vgAmaZpKlpy69Ytx+uz\nCgoKVAXehQsXHK9EW7VqFcrLywEYQ2qDg4OOnk/IdIPClpBpRkNDg3IX3XAv7eLz+XDq1CkAwMKF\nCx1dnyvIYFF5ebnjjQVA+MYxGWZyEhG2OTk5rmxKlLovv9/vuPAEQsJ2eHjYlbiDLGsYGhpyJe4g\n0ZihoSHHh9Q0TVOu7dDQkOMNDIRMNyhsCZlG6LqOCxcuADBEkjhF48mFCxcwMDAAwB239uHDh2hp\naQHgjlsLuLtxDAgJW6c3pQlubh8DwnPHUovmJIsWLVLfg9M5WwCoqKhQ8ZjTp087Lv7nz5+vqsvO\nnDnjeHsEIdMJCltCphEff/wxbt26BQCorq52xf2zQzAYVNna8vJyLFq0yPHXMAudVatWOX7+wMCA\n6iF1642CxDTccIMBhDVQyGs5yaxZs9SfNfMiC6dIT09HZWUlAGMJhxtxB3Ft29raXMny7t27F16v\nF8FgEO+//74rzjkh0wEKW0KmCWfOnFFbvebNmzch1lLfvHlTTZpv3brVlSE2ESHz5s1zZWuXtCEA\n7jQiACEX1a08tPnn4kZUIC0tTQ2QuREVAEJufE9PD5qamhw/f+3atWpI7ejRo44Lz6KiIuzcuRMA\ncPv2bccjD4RMFyhsCZkGXL9+HR9++CEAownhxRdfVLnK8eTMmTMADGElt2KdZHBwUAkpN7prgfBJ\nf7eErQwsjYWwdaPLFgjFNNzYQAYAVVVVaivb5cuXHT8/LS0N27dvBwC0tLSoOx9OsnPnThQVFQEA\nDh48yEEyQpKAwpaQKU5bWxveeecd6LqO7OxsfPe733Vlst4uDx8+VO0MmzZtcnx9LmBMyYuIkgEj\npxFhO3PmTNeiAuLYuvVmxJzddVvYDg0NuVL7lZ6ert4cXb161ZWs8IYNG9SbgM8++8xxgZ6WloZ9\n+/YBMCIuH3/8saPnEzIdoLAlZIpz9uxZ+P1+eL1evPTSS660AiTDiRMnABjrRd3aeiZ9vXl5eSgt\nLXXlNR48eADAPbcWMNoEAPeEbUZGhnpjIYN8TjNv3jz1sRs5WyAURxgeHsadO3ccPz89PV25tl98\n8QXu37/v+GtUVlaq7+PChQvqzxchxBoUtoRMYXRdV8NTy5cvd21q3y6dnZ24dOkSAGDdunWuZF8H\nBwfVmtJVq1a5kt8NBAJK3JiFm9OIi+rGzwkwhqNENDvd0yrk5uaqITU3HFvAqIuTZRNuDHgBhmsr\nkQeJ0jjN008/rX4fhw4d4iAZITagsCVkCtPS0qKGgSZCZ61w/Phx6LoOTdPUwIzT1NXVqb5eWbvq\nNA8ePFC3vN160+Dz+dRGMLeELRDeZesGmqYpV9s8cOckXq8XS5YsAWAIWzcEYWZmJtatWwfAiDy4\nMWyXm5urnOHGxkZX8ryETFUobAmZwtTX1wMwbvfLP/jjTXd3Ny5evAjAmDQvLCx05XVkqnzWrFmu\nxRDc3jgGhGde3eqxBUKDaW45tkAoruFGl60gQ4Ld3d2uvY5UfwWDQZw/f96V19i+fbt6I3Po0CHH\nN6oRMlWhsCVkivLgwQPVEVtRURHWVTqefP755wgGg9A0Dbt27XLlNXp7e3H37l0ARu7SjRgCABVD\nmDVrlms/3/7+fvWxm0N/bkcRgJCw7erqUrlhp1m6dKn6fV+7ds2V1yguLlZvFM+ePascdSfJyMjA\nnj17ABjRDbdiD4RMNShsCZmC9PT04PXXX4fP54PH48Hjjz8+3pcEwLitXlNTAwBYsWKFqjZyGsnW\nAnClRkyQrOicOXNcew2zaJL8qBuIaDYLaacxL7D44osvXHmNGTNmoKKiAoDh2ruVT922bRsAY9jO\nLdd27dq1KCsrAwB88sknahEIISQ2FLaETDGGhobwy1/+UmX/vva1r2HBggXjfFUGly9fVk6d3M51\nAxkcKi4udq0FIhgMqqxoSUmJK68BhGde3eqxBUL5XTcyo8LcuXNV+4JbixqAUKb60aNHrjUwLFq0\nSMVPTpw44YrT7fF48Pzzz0PTNPh8PnzwwQeOvwYhUw0KW0KmEIFAAG+//bbKFu7Zs8e1wSm76Lqu\nbqfOmTPHNbHt9/tVP65bSxkAo9lBhtNmz57t2uuMtbB1q8cWMK5fHEg3he2KFSvUz8qNZQ2AMQy3\ne/duAIbLfeHCBVdeZ+7cuepNYH19fdiKaELIaChsCZlCnDlzRom69evXu9Y4kAyNjY3q1v2WLVtc\ny73evn1buWduLWUAwgeg3OywNTuBbgpbGUzr7+93dVDJ7Q1kgBHZqKqqAgBcuXLFte9n8eLFSqif\nPHlSvdFxmieffFL9fj744APXmisImQpQ2BIyhZCFBHPmzMG+fftcE4920XUdn332GQAjy1ldXe3a\na0kbQnZ2tqsRDMmIZmRkuNbsAIQWJmia5uoAoOR3dV13dYBs7ty5AIzscHd3t2uvs2rVKgDGz8+N\nRQoAwgYge3p6VAuJ02RmZuLZZ58FYLQ9fP755668DiFTAQpbQqYIvb29SmxVV1e7sqI2We7evYum\npiYARo2RWxu0fD6fEherVq1y9WcgP+t58+bB43Hvr1LzcgY336iYfyduOoJmd9utRQ2AscFLfv9u\nLWsAjLsCBQUFANxb2AAY8Qp5o3bs2DFXh/wImcwk/bfxyMiIqxkpQog9zP94T6RlDABw9OhRAIaL\numnTJtdep76+XrmNbmaL/X7/mGwcA9zfOiaYYw5uOrbFxcVKoLvZZ5uZmanaEcwtGU7j8XiwefNm\nAEBTUxNaWlpceR1N0/ClL30JgPEG7tNPP3XldQiZ7NgWtkNDQ/jhD3+I9evX47nnngNg3IL53ve+\nxyoSQsaJYDCoVtSWlJS41gSQDPfu3cOdO3cAGBVJso7UDSSGUFhY6KrgfPDggcpTut04MR7C1k3H\nNi0tTdW8uenYAqHhwdbWVnR1dbn2OuvXr1c/P+mOdoPy8nKsXr0aAHD+/HlX3xgQMlmxLWz/7d/+\nDdeuXcMrr7wSdpsvEAjglVdecfTiCCGJ0XUd77//vrqD4mZ+NRkkD5iZmelqxdfw8LAanKuurnb1\ntv2DBw/UxzI85BaDg4MADLfbTcz53aGhIVdfSzbBuVXFJcgAGWCsv3WL7OxsrF27FoDx5qqzs9O1\n19q7dy/S0tKg6zp+//vfuzaAR8hkxbawPXjwIH7+85+rIDsA5OXl4Z//+Z/x0UcfOXpxhJDEnDhx\nQlUNLVq0aEI1IXR3d6vtTxs2bHB1wUBDQ4OafjcLGjcQpyw3N9d1wSnuqVu5ZMHsCLvZZQuEmhHa\n29uVcHeDgoIC9Vri5rvFjh07oGkagsEgjh8/7trr5Ofnq5qxe/fuqYUnhBAD28K2v79f5ZbMFBUV\nqeldQsjYUFtbi8OHDwMwhnJeeOGFCTU0du7cOeUoSQ7RLSRHmZOT47qLKosZ3Kz5EiTv6mbVFxAu\nbN3ssgVCwhZwbwOZIFnr1tZWtLa2uvY6hYWFyrW9ePGiq40P27dvV3/2Dh06xEEyQkzYFrYLFixQ\nGSLzLZAPP/zQ9X9MyP/H3pvGRpWl9//fW1XewTvYxsbY2OAdY7yAwTbdrM3S0zPTO2gyUaSMNC8m\nUmaURMok8yIjRRkp8yLRKBn9otFkkjBNd6d7lkDTDaYbr4CxjQ3Y4N3gtcBreber6v5f3P85dau7\n6XYV3HvOsc9HsmSlR7kPruV+73O+z/eRSDwMDQ3hD3/4AwBNlJw9e9bQOChfcTqdtJOckZFhaCSW\nqqpU2O7YscPwmDPSsTVD2JKOrdHCNiAggL5/jO7YxsfH03+P0UPI2dnZNLXCqGUNhLKyMtq1raur\nM+w6VqsVp0+fBqDZRuRpqUTiwWdhe+bMGfzgBz/Az372M7jdbvz617/Gj370I/zt3/4tvvvd7xpR\no0Qi+RJIIHxgYCDOnDmDiIgI1iV50dzcTE9xjPTWAlqcGOlaGbmUAdC6meRaRm4cAzTBTlYQGzl0\nRwgLCwMAw0/frFYrbYQY7bMNDQ2lQ2Tt7e2GelJjYmKox/327duG2iySk5NRUFAAQBPsRne+JRJR\n8FnYvvnmm/ibv/kb3LhxA1arFb/85S8xNDSEf/7nf8bbb79tRI0SieRzOJ1OdHd3AwB2795NQ+95\nwel00o7Vli1bkJqaauj1SCcuMDAQ6enphl6L5PECxkd9LS8v046t0akIgMfHa8ZmK/JQYHQyAuCJ\nv5uamqI2EqMoLS0FoP0Njfa/Hj58mPrWP/nkEzlIJpEA8Ots69VXX8Wrr776vGuRSCSrpK+vD8vL\nywD4y6wFNI8hif8rLy831BrgdDrpxrXs7GzDh6zI0XlQUJDhVgS9JcAMYUvsAWYKW4fDgaWlJUMH\nC/UPO52dnYa+bgkJCUhOTsajR4/Q0NCAffv2GbbAIywsDOXl5aisrMTg4CDa29vpxjWJZL3il7Dt\n6upCd3c3PSLT881vfvOZi5JIJF8N2a4VHBxseI6qr7hcLjoVHhcXZ3hCQWdnJ/0uMnIpA4Ec+W7d\nutVwL69+iMvMjq2RCxoIn99AZmT3e8OGDUhMTMTQ0BA6Oztx4MABw64FaNabR48eYXp6Gp2dnYY+\nfO7duxeNjY2YmppCZWUlMjIyDPdjSyQ84/O7/+c//zn+4z/+40v/m6IoUthKJAYzMDBAlzHs3LmT\nqxQEQMsLJRPhFRUVhos/kk+6ceNGbNu2zdBruVwu6gk12oYAwGva3cyOrdnC1m63G/733LlzJ4aG\nhjAwMIDZ2VlD/56ZmZkIDw+Hw+FAfX09MjIyDPsc2Gw2HD58GB988AGmpqZQX19P48AkkvWIz+cj\n7733Hn72s5+hpaUFDx488PoheZUSicQYxsfH8c4778DlcsFms1E/Hy+oqkpTU6Kjo5GVlWXo9Vwu\nF/UaZ2VlGXbkS5iYmKBZufHx8YZeCwC1mwAw9KieQIbHzIiPCgsLowOPZgw+kfeiqqqGLmsAtOG4\nvXv3AvDevGcUOTk59OSmuroaExMThl5PIuEZn+8CJGaEp1ghiWQ9MDc3h3PnzmFhYQGKouC1114z\nRVz5wtDQEO1olpSUGN6tffjwIRV/RqchAN6DTmZGfQHGx30Bnq6w0XFfBJJna3TkF6C9XmTI0ujY\nLwAoKipCaGgoAKCqqsrQaymKgtOnT8NiscDlcuHixYtykEyybvErFeH8+fNG1CKRSJ7CysoK3nnn\nHbqq86WXXjLcu+oPDQ0NALR0gt27dxt+vc7OTgCaN9RoGwLgEbY2mw2RkZGGX49YAhRFMcVyQoTt\nwsKCKQNkRNiOj4+bsuCHeLCHh4cNT0cIDAykJyoPHz40vGu7adMm6h3u7e3FvXv3DL2eRMIrPgvb\n1157Db/61a9w+PBhfOc738Gf/MmfeP1IJJLnT1VVFYaGhgBoW4eMzoX1B4fDQY948/PzDT86V1UV\nHR0dAIC0tDRTOppkMUNsbKzhtgfAvOUMhI0bN9Lfjd4+BnhvIDOja5ubm0tPEYxesQto2/bIyuWa\nmhrDr1deXk4XoXzyySdfOuAtkax1fP5m/uEPfwin04m8vDwkJSUhMTHR60cikTxf9J7A1NRUHDly\nhHFFX05tbS3cbjcURaH+QiMZGhrC1NQUAPMiz8jDhVkWENLFJOLIaPQWM72/1yji4uJoJ9rIdbeE\nDRs20JXwpNtvJEFBQfQhtLe31/DM3oCAAJw8eRKAZl0i6SQSyXrC5zbAgwcP8OmnnyImJsaIeiQS\nyeew2+1UwOXn5xvuW/WHmZkZuj43NzfXlO8H4pO02WymCFuHw0HTHsyKWCNdU30n1Uj0nWEzkhEs\nFgtiYmLw+PFjw60BhJ07d6Kvrw+jo6NwOBwIDw839HpFRUWoqamB2+1GQ0MDTp06Zej10tPTsWPH\nDnR1deHGjRsoKiribiuhRGIkPnds09LSTDmCk0gkGiSzVlEUUwak/KGurg4ulwuAdhxqNC6Xi3oI\ns7KyTEkM0G8c0x+hGwkRtmZEfQHwWm5hhscW8CxqIDYPo9F/hszo2m7YsIGu2W1tbcXi4qLh1zx6\n9CgURYHT6cTVq1cNv55EwhM+K9S//uu/xt/93d+hpqYGPT096Ovr8/qRSCTPD6fTSW0IKSkpph1J\n+8Lc3ByampoAaLFDZqQFdHd3Y2FhAQCQl5dn+PUAjwc0JCTEtBMrkk5glrDVd2zNEraxsbEAgLGx\nMRqlZiTR0dH0mmYIWwDUmrOyskJPNoxk06ZNKCwsBKB5ic2IU5NIeMFnK8Kf/umfAgCuXr3qdSSq\nqioURZFZthLJc0JVVfz+97+nR7S8rspsamqiIsiMbi3g6WKHhIQgLS3NlGuOjo4CABITE02zgxDx\nTmKjjEbf+TajswhoPltA68I/fvzYFP9yRkYGxsbG0NPTg4WFBcMfGLds2YKtW7diYGAA169fR0lJ\nieEDgS+88ALu3r2LpaUlXLhwAd/73vfkaatkXeDzJ+s3v/kNlx4/iWStUVlZSbu1mZmZKCgoYFzR\nF3G5XLh16xYAYPv27VSkGImqqujq6gKgHSubcbNWVZUO/pjRkSaYnYpAFjQA5mXZ6jeODQwMmCJs\n8/LyUFdXB7fbjba2NhQVFRl+zfLycvz2t7/F7OwsmpubDU82CQsLw6FDh3Dp0iXY7XbcuHED+/fv\nN/SaEgkP+Pxtaca0s0Sy3mloaEB9fT0A7cb/7W9/m8tuy/3796kP1KwIsuHhYboZyyzP8dzcHO2e\nEk+o0aiqSge49N5XI7FarQgNDcX8/LwpcV+AZrOIjo7GxMQEBgcHUVxcbPg14+LiEBcXB7vdjjt3\n7pgibNPT05GQkICRkRHU1dVhz549hj+wFBUV4c6dOxgaGsK1a9eQnZ1tSv6yRMKSVX2qvvOd7+C/\n//u/AQBvvfXWV/5v5fIGieTZ6O7uxscffwwAiIqKwltvvWWasPEVsj43KioKO3bsMOWaxBdpsVhM\nsyGYvXEMAB3GA8zr2AJaAoOZwhbQhvEmJia8BvSMJi8vD3a7HQMDA5icnKT5r0ahKAoOHjyI8+fP\nw+FwoKWlxXBBbbFYcPr0afy///f/sLKygkuXLuHtt9829JoSCWtW1QIiuX/k99TU1Kf+SCSSZ6O6\nuhqqqiIkJARnz571Oh7miYcPH9KhlOLiYtMsAcTHv23bNlPSEACPvxbwDDsZjT5HNjAw0JRrCJUu\nPwAAIABJREFUAh47AumKmwGxI0xNTZmygQzwHjpsb2835Zo7d+6kVovr16+bsvY2Pj4e+/btA6A9\nFHZ3dxt+TYmEJatqA/z0pz9Ffn4+Wltb8U//9E9G1ySRrFtmZ2fp9P3+/fu5zouurq4GoA1w7dmz\nx5Rrjo6O0u4piVAyA/KabN682TQxre+YmvlwQ04HzEpFAODlzX7y5Ikp65HDw8ORmJiIoaEhdHZ2\n0nW0RqIoCkpLS/G73/0OExMT6O7uNuWk4+DBg7hz5w7m5uZw+fJlbN++nUtrk0TyPFj1O9uMJ0uJ\nZL2jjx8ya5uWPwwMDKC3txcAsG/fPtPEHlnKYLVakZ2dbco1VVWlwlY/6GQ0emFr1oIGwCNszVjQ\nQNDbO8zKswU8Hu2BgQHqoTaa7Oxs+qBCrDxGExQUhEOHDgHQHhxu375tynUlEhasWtjKJASJxHhI\njFVMTIxpR97+QLq1+pWhRuN2u+lShp07d3qtfzWSqakpKjLN2jgGeKcSmJVjC3j8vGZ2bIODg6l4\nN3rtrB4ibFVVNe2I3mazUW9tT0+PaRvXdu/eTQcfP/vsMywtLZlyXYnEbFY9keByufDee+99ZedW\nURS88cYbz6UwiWS90dXVRW+uPHdrR0dHaZ379u0zTWA+fPiQCsxdu3aZck0AXuH2Zm0cAzweV4vF\nYlqOLeDp2Oo9vmawadMmzMzMmNqxjYuLQ3h4OBwOBx48eGDasg/9mt3r16/j5ZdfNvyaFosFx44d\nw//8z/9gbm4O165dw/Hjxw2/rkRiNqsWtk6nEz/5yU++8n8jha1E4h8jIyN4//33oaoqgoOD6dYg\nHiHHpzabzbRuLQB0dHQA0IRXenq6adclQiswMNDwyXk9RFgGBgaaemJGRLSZw2OAtsSgt7cXQ0ND\ncLlcsFqthl9TURRkZWXh5s2b6OjowOLioikPahs2bMCuXbvQ0tKClpYWVFRUICIiwvDrpqWlISMj\nAx0dHbh58yZ27dqFhIQEw68rkZjJqq0IQUFBePDgwVf+yK1jEonvTE1N4be//S1WVlZgtVrx1ltv\nmSqgfGFubg53794FoHVNzeokqqpK/cdpaWmmxl+Ro+JNmzaZKjDNXs5AILaH5eVlU7u2pBvudDq9\nUiiMhnT/XS6XaekIgLawQVEUuN1u1NbWmnbdEydOICAgAKqq4sKFC6asMZZIzESORUokDFlcXKTb\niADgm9/8pikT4f7S3NxM81XNXNYyPj6OyclJAOYtZSCQjq2ZG8cAz/CW2cJWP6hmdpYtgQzrmUFC\nQgL1s5OHNjOIjo6m1ofbt2/D4XCYct2IiAi8+OKLALRlJ42NjaZcVyIxC5mKIJEw5OOPP6bDMkeO\nHDE1wspXnE4nXZ+bmppq2gYuwGNDAGDaIghAE5dEUJstbEnH1uzlHPpBNbPW6gJabBwRmHpfs9Eo\nikIFZn9/v2kCE9C6toDWLSabBs1g7969NE/36tWrpj7ASCRGs2ph+8orrxhZh0Sy7nA6ndS+k5ub\ny/0e95aWFip0zF6tTTppSUlJpiYEjIyM0Id6IgTMgsRPmTWcR9Bfz+zJ+cTERACA3W439br6B0r9\nQ5TRxMbGIicnB4DWtTXr7002kgGa5eSzzz4z5boSiRmsWtj+9Kc/NbIOiWTd0dfXRz2Me/bs4TpS\nz+VyUR9gXFycqXYAu91OhY6ZaQiA50hcURRTM2wBT7fUTCEPeHeIzYz8Ajxd8fHxcVOvHR0dTa/d\n1dVl2nUBz0Pi8vIyWltbTbtuYmIi8vPzAWii2sw0ConESKTHViJhBMmsDQ4O5tpXCwCtra2Ynp4G\noG0xMlOEk26txWKh3S2zIMI2Li7O1LW2gMffaraw1Xt6zVzSAHiEraqqmJiYMPXaxOLS29tr6tBc\nUlIStmzZAkBLHDHT9nfo0CHYbDaoqorLly+bdl2JxEiksJVIGLC0tESPPDMyMrheb6mf2t68ebOp\nGbuqqlJhu2PHDlPzXPUbx8zMryXXJh1bM7eOAWw7tnrfttkdxIyMDADa6URfX59p11UUhcbmkTW7\nZhEeHk4tUD09PaZ3qyUSI+D3biqRrFHIshOSE2rWalh/6ejooANUJKLILIaHh+kwj9mDdQ6HA/Pz\n8wDMXaULaIKSpE+YKeYBrWNLHrQWFxdNvXZERATtjI+MjJh67aSkJPq3bmtrM/XaOTk5dM1uTU2N\nqV3bAwcO0FOBjz76yPQuvUTyvJHCViIxEZId2dvbC0Bbc2nmlL8/kIUM4eHhpotwkl1rsVhM/zvp\nV7uamQABeFsAzE5FUBSFiiyzp+X1XmYzI78Ab6vL/fv3TR2cs9lstHM6MDCA/v5+064dGBhIN5BN\nTU2hqqrKtGtLJEYgha1EYiJVVVVoaWkBoC0aOH36NNdDY6Ojo3j48CEAoLi42HTLBBG2KSkpCAoK\nMvXa5ChcURQaQ2UWeguA2Tm2gMf+wCIGitg+hoeHTbdCkOFEp9NJPfBmUVRURDvGZovLnJwcus3v\n+vXrpqdSSCTPEylsJRKTuHPnDr1hxcfH4/XXXzdlbeizoF+fu2fPHlOv7XA46AYqFl1t0rGNiooy\nXVyy7NgCnoE1M3NsCcnJyQA0y87w8LCp105MTER0dDQA7fNqJoGBgSgtLQUAPHz40NSuraIoOHny\nJGw2G9xuNy5cuCCz6yXCIoWtRGICqqri008/BaAd6Z85c8b0DqSvOBwOOriVl5dnutdTv6Lb7G1j\ngCdL1WwbAgCvqXwWwpZYEYgP3ExIli0ADA0NmXpt/bKGvr4+6rE2i+LiYoSEhADQOqdmEhUVhYMH\nDwLQFmSYuYVNInmeSGErkZjA6Ogojcs6fPiw6ZPu/lBXV0cHmFgsjyAds4SEBNpFM4vl5WXaLdYL\nLbPQWwCIyDQTMsDFYpAoKCgIUVFRALx9zmaRlZUFQHsYNTOhAND+7UVFRQA0G47ZkWelpaX0s3b1\n6lU5SCYREilsJRITIH49FkNQ/jAzM4OmpiYAWhqB2R7TsbExegxt9lIGQOsUkqNYs6O+AG9hy+Ih\niFgvzPa4EkiXnIWw3bx5MyIiIgB4PN5mUlRURH33DQ0Npl7barXi6NGjALQTG7O7xhLJ80AKW4nE\nBEhmbUpKCj1q5Jn6+nrarSX77M2EdGsVRTE95gsAHj16BEB7ECHh+WZCvK02m42JZYXYH1gJW/Ig\n9eTJE9O9noqi0IfP7u5u+jkwC336iJlrdgkZGRlISUkBANTW1jIZIJRIngUpbCUSg7lz5w71a5IQ\neJ5ZWFhAY2MjAC1j12yPqaqquHfvHgAtOcLszVuAx9uZkJDAxONKvK0bNmxgkppBOrYrKytMhojI\ne25paYnmGJsJ8XQvLS2ZOsRF0K/ZbW5uNvXaiqLg2LFjALTX/8qVK6ZeXyJ5VqSwlUgMpK+vD3/4\nwx8AaEfKLLqPvtLc3Ew7dWVlZaZff2xsjC6EYLW8gkR9JSQkMLk+GR5jNWBIBgXdbrfpSxoA77/7\n4OCg6ddPTU1FcHAwADAZokpKSqJ5vvX19aZ7XRMSElBQUABAezAnudsSiQhIYSuRGMTjx4/x7rvv\nwu12IzAwEGfOnDE9WcBX3G43bt26BUCLXWIh7PS+RhZ+5KWlJTrot2nTJtOvD3iGtlhk2ALevl4W\nR9GxsbHUskNsIWZis9noQ9X9+/e9UirMQFEUmlAwOztretcWAI4ePUq/ry5evMjMliKR+IoUthKJ\nAczMzODcuXNYWlqCxWLBG2+8gfj4eNZlfS0dHR1U1JHjULMhwjYxMZGJDWFsbIz+zkrYEhHBwgYB\nwOvvziLLVlEUOrTHomMLeIYWl5eXqUfeTNLS0qi/u66uznRhGRISQjeSTUxMoKamxtTrSyT+IoWt\nRGIAv//976k38PTp00hLS2Nc0eq4ceMGAG2AJTMz0/Trz8/P01WqLLJrAY8NAWCTYQuw79jqhS2r\n4SFyFD8yMmJ6xxTQTiwiIyMBsLEj6Lu2MzMzuH37tuk15OXlITU1FYA2SDY+Pm56DRKJr0hhK5E8\nZ2ZmZqgnbd++fdSrxjv9/f302LekpMT09bkA0NbWRoeVWAhrwDM4tmHDBmbWkYWFBQCgPk+z0Sd3\nsPDYAp78YFVVvbroZqEoCnJycgAAvb29TMT1jh076ElPQ0MDk4SIU6dOwWq1wu12o7Ky0tTrSyT+\nIIWtRPKc0R9bkrB1ESDrfkNCQlBcXMykBhLzFRcXx6xbSjrGW7duZZJIAHi6pCysGICWZ0r+7ayz\nbAHvLrqZkBQTl8uFnp4e06+vKAq1BI2NjTEZ4oqJiaE1PHjwAH19fabXIJH4ghS2Eslzhixj2LRp\nE2JiYhhXszr0u+lLS0vp5ikzmZiYoH5KFksZAK07SUQUi8UMgDbAx1rYAuyzbMPCwmjnmMWiBkDr\nGpOuPYtlDYC2IIXUcPPmTSY1lJeX09fi8uXLcLvdTOqQSFaDEML23//931FWVoaCggL82Z/9men7\nwyWS1TIzM0M7GiJk1hKqq6sBaEffJSUlTGog3VpA8/axQD+oxErYzs/P0yNnlquX9Vm2LFAUhQ7v\nsRK2+k2BXV1dTDJ9bTYbCgsLaQ0sfK7BwcF44YUXAGjrwVtbW02vQSJZLdwL23PnzuHChQs4d+4c\namtrkZaWhv/8z/9kXZZE8gWWl5fxzjvv0G4GqwxWX7Hb7fSIc+/evcyyU0mnOzU1lZmgI2t8rVYr\nswxb4q8FwDQejrwPzN58pYfYEUZGRpiISsAzxDg3N4eHDx8yqaGoqIh63mtra5nUUFhYSDfCXbly\nBfPz80zqkEi+Du6F7a9//Wv85V/+JbZt24awsDD8+Mc/xo9//GPWZUkkXrjdbnzwwQcYGRkBABw4\ncICZMPIVso/earUy89ZOT0/T7WyshsYAT9RXTEwMrFYrkxr0R/+s4r4Ajw2C5UpVkowwOzuLqakp\nJjXs2LGDinxWncrw8HDk5+cD0E42yAITM7FarTh58iQA7eFLbiST8ArXwtZut2NwcBBTU1M4deoU\n9u7di7/4i7/AxMQE69IkEoqqqrh06RL14OXl5eHw4cOMq1od8/Pz1AKQl5eHsLAwJnWwXspAIP5a\nVoNrgPfRPw/ClkWOLSE5OZn+zmJRA6C9BllZWQC0ZQ2srBnl5eVQFAVut5tZ1zY1NZUK7JaWFibr\nhiWSr4N7YQsAn3zyCX7zm9/gj3/8I+x2O37yk58wrkwi8XD9+nU0NjYCAFJSUvCNb3yD2TS9r9y+\nfZt2CFktZAA8wnbTpk2IiopiUoPb7aYdW3LkygJ9x5ZVji3AR8c2MjKS1kHSKlhAhhmXlpaYDZFF\nRUV5iUqySMVsjh07RgfJLly4IDeSSbiDa2FLPFV//ud/jtjYWMTFxeEHP/gBPv30U58yBR8/foy2\ntrYv/VlZWYHL5TLqnyBZ46ysrODatWsANFH2xhtvMBUjvuB0OumU9bZt25htRltYWKADd6yWMgDA\n+Pg4/S5g2bHVf7fx0LFlKWz1G8hYDg2npKQgPDwcgJa1zAp915YsUzGb0NBQHDt2DID2mSFWJomE\nF7i+A5OuiX6QJDExEaqqYmJiYtU34nfffRe/+MUvnvrfyReWROIrPT099Gjy5MmTXsH2vNPc3EyP\nmffv38+sjvb2diooSSA+C/QdQbIcgAV6IcnKGgKARr45nU6oqsrsFCIuLg7379/H2NgY3G43k8Uh\niqIgMzMTDQ0N6OnpgcvlYuLBjo6ORnZ2Ntra2nD79m28+OKLTKL58vPz0dTUhMHBQVRXVyM/P5/p\ne1Ui0cN1xzY+Ph4bNmzA/fv36f9tcHAQNpvNp47Km2++iQ8//PBLf+Li4uQHUuI3ZBlDaGiolx+Q\nd5xOJ+rq6gAACQkJTH2txOO7adMmZl1jwCNsIyIimD7sEmEbGBjIRLQQ9CcPLE+1SOSX0+lkNkAG\neE4TlpeXmXpLSRzf0tISs2E2RVFw/PhxWgdZ7iKR8ADXwtZqteK1117DL3/5Szx69Ajj4+P4t3/7\nN7zyyis+PbVv3rwZOTk5X/oTEBDAbPpZIjZut5sK2507dzLpJPlLS0sLHA4HAKCiooJZN25qaooO\nBe3atYupN1m/cYwlpIvOMsMW8LZBsBqYAjzCFmCXZwtodgTyoMHKZwto70+SuMJizS4hKSkJubm5\nAIDGxkamr41Eoof7O/EPf/hDlJeX4/XXX8exY8eQmpoq474kXHDjxg2aOcoyospX3G437dbGxcUx\nXSRx7949+jurpQyA5vMlwfeshe3c3BwAtlvHAO+OLUthGx0dTR8ayUAxC6xWK9LS0gBoJzWsBKWi\nKLRrOzY2hq6uLiZ1AMDhw4dhtVqhqio+/vhjZn8TiUQP98I2MDAQf//3f4+bN2+iqakJ//iP/yiU\nj1GyNmlvb6c5jrGxsfSGJwKdnZ30SLesrIxpl5R0vrZu3YqIiAhmdZCYLwDM84fJQgRWizII+uUQ\nLMP4rVYrtaiw3jpJYr+mp6eZpjTk5ubSB5/q6mpmgjIyMpL683t7e70eVCUSVnAvbCUS3nj06BE+\n/PBDANpwz5kzZ4RJQgA8++bDw8PpjZoFc3NzVBywTEMAvIWt/uibBSQ+iWUiAuDdMWaZZQt4FjUM\nDAww7QpmZmZSO4J+BbTZ2Gw2HDhwAIAm9nt6epjVUl5eTiP6PvnkE6/NeRIJC6SwlUh8YGxsDOfP\nn4fL5UJAQADOnDnDLHfVH+x2Ox18KSoqYuov7+7upr+zFrbEHxgeHo7g4GCmtRBhy/phSe/xZRn5\nBXgWNSwsLNCsYRbolzW0tbUxzXAtLCykg89VVVXMBH9AQABOnToFQHtYraysZFKHREKQwlYiWSWq\nquK9997DwsICFEXBa6+9hi1btrAuyydI9qXVakVhYSHTWsjgXWRkJPMuKRG2rOsAPH5W1sI2KCiI\n1sC6Y6v3PbO0AAAeL/ji4iJTf2tAQADt2g4ODjJNakhLS6N/l+bmZuavkWR9I4WtRLJKhoeHqQA6\ncuQI8y6jr0xNTdHj0127dnl5KM1GLwoyMjKY+nzdbjeGh4cBaMN0rCFHuaw7x4qi0HmGxcVFprWE\nh4fTDvLo6CjTWlJTU2mnlDycsaKwsJC+RqwWNhCOHz9O37OffPKJHCSTMEMKW4lklTx48AAAH91O\nf6itrYXb7YaiKCgrK2Nay/379+kxLss0BEDz15JtX6wTEVwuFx3UYp2KAHi6xjysTSXddNaxUhaL\nheY+d3V1we12M6slMDCQfhd1dnZiYmKCWS1hYWGoqKgAoPl+5SCZhBVS2Eokq4QI2+3btzOfWPeV\n6elp3L59G4DWrY2OjmZaD+kcx8TEMLdzkBxdgL2wJVFfAPscW8AzwMYy7ovAi7AFPJ7w+fl55kkN\nxcXF9MSD9XrbkpIS+t1y9epVLt43kvWHFLYSySqw2+10aIVl7qu/1NXV0W5teXk501qmp6epH5D1\nUgbA49mMjo5mvoVQ72WVHVtviLCdm5tjGj8GaJ5SMnjJclkDoNk0srOzAWiLV0hcHAusViuOHDkC\nQPucX79+nVktkvWLFLYSydcwPz+P9957D4B2DCmasF1YWKDd2tzcXMTExDCth3S+AfY2BAAYGRkB\nwL5bC3jnxbIW2YAnS5elWCLo/c/kNWNFYGAgUlNTAWjpCKz9pHv37gWgvU63bt1iWktmZia2bdsG\nAKipqcHk5CTTeiTrDylsJZKvYGVlBefPn6fetWPHjnHRSfOF5uZm2nErLS1lXI2nwxUXF8c8Ks3p\ndNLXdvPmzUxrAbw7o6xzbAGPuGYd9wUA8fHxtEvKw9Q9WSc7OTmJwcFBprVs3bqVisnr169TzzgL\nFEXBiRMnYLFY4HQ6cfHiRebCX7K+kMJWInkKqqrid7/7Hb2J7tu3j3ZGRMHtdtMOTnJyMhdbtYgN\ngYdUifHxcXrT5SnqC2Af9wV47BA8CFubzUb92DwI26ysLPrwwXJZA+HgwYMAtK5/Y2Mj01ri4uLo\nQ3RPTw/a2tqY1iNZX0hhK5E8hStXruD+/fsAtJvYsWPHGFfkOx0dHZiengYAul+eJT09PXSKnAdh\nqx9E4kHY8taxJQNss7OzTKf/CcQuMjg4yLyewMBAZGZmAtDsCC6Xi2k9KSkp9O9TX1/PfHDr4MGD\niIyMBAB8/PHHzCPjJOsHKWwlki9hamqKDj5s3boV3/rWt5gPOfmKqqqor68HwH59LoH4a8PCwpCY\nmMi4Gk8mamBgICIiIhhXw2/HVlVVLlalEuG2vLzMdAMZYdeuXQA0H3tvby/TWhRFoV3bubk5tLS0\nMK3n8xvJqqqqmNYjWT9IYSuRfAn64PVvfetbXHTPfKW3t5d6//bt2weLhe3HfXl5mQrbrKwsLh4U\nyN9ny5YtXNRDjvxDQkKYv16AJvgJrDuAgOazJTx+/JhhJRqpqal0wI51OgKgRRGSv1FDQwNzb2t6\nejp9oG5oaMD4+DjTeiTrA/bfnBIJhxABFh8fz3zAyR9UVaUdkrCwMBQVFTGuSFvKQMQR6XSxxOVy\n0QxSHhIRAI+w5SHDFvDuGvMQ+RUREUEfMnnIs7VarUhPTwegCVvWQlJRFDoHMDY2xryLDGhbGi0W\nC9xuNyorK1mXI1kHSGErkXyO+fl5PHz4EACoh040+vv76YDN/v37ueg4kwGbqKgoJCUlMa5GsyEQ\nscaLsCU5trwkb+jfNzx0bBVF4WpRA+DxijscDtjtdsbVaGkNZF32zZs3GVej5UMTsf3gwQM6PCqR\nGIUUthLJ56itraWdF1GFbU1NDQAgNDSUi27t7Ows+vr6APCxlAHwnqznRdiSji0vwlbfseVB2AKe\nWDYerAiAdtxO3s96CxMrbDYbXbPb1dXFxQNARUUFQkJCAGiDZKwH7SRrGylsJRIdDQ0NdGgsOTmZ\ni2xTX3n8+DEVkXv37vXySbKiq6uLPizk5OQwrkaDdNeio6MRHBzMuBoNkj/Ky8pmIkYAMN/2RSAe\n0vHxcS4G2kJDQ5GSkgIAuHv3LnM7AqCt2SWZv+QhlyXBwcF48cUXAWifOx46yZK1ixS2Esn/T0dH\nBz7++GMA2nH5G2+8wUVn0VfITcNqtdLODWvIYE1UVBRiY2MZV6NBOlk8xHwRSFeUB+sI4O315SHL\nFvDurvOQZwt4NuiNj49jeHiYcTXa67Znzx4AwL1797gY2iosLKRJKNeuXcPU1BTjiiRrFSlsJRIA\nQ0ND+N///V+oqoqQkBCcPXuWi5WmvjI/P0+9rHl5eVz8G5xOJ3p6egBofkQeHhZUVeVS2BLPLw9R\nX4AmsEn3mPh/WRMfH0+F/6NHjxhXo5GdnU1fMx6WNQDAgQMHYLFYoKoqF11bi8WC06dPQ1EUrKys\n4KOPPuKiuy1Ze0hhK1n3LC8v4/z583A6nbBarXj77bcRExPDuiy/0K/P5WVLWn9/P+1E8rCUAdAG\nfcixP0/ClreOLcDX9jFAE0hk+JCXjm1QUBAyMjIAaB1S1ssjAC1BoqCgAIAmticnJxlXpD2UkI1k\nXV1ddAGORPI8kcJWsu7p6uqiN+1XXnmFm0EiX1leXqb+4G3btnllfrLk3r17ADSfHdlnzxoS8wWA\nm7/TysoKHarhxWMLgE7Y87Q5ihxp2+12brp+xI4wPz/PjeAuKyuDoihQVZUbX+vBgwfpMpQrV65w\nESMnWVtIYStZ95DM2o0bNyI3N5dxNf7T1NREB3wqKioYV6OxvLyM9vZ2ANpxLRloYQ0RHkFBQdx0\nbPUdUV5ybAGPLYInAUJes6WlJTgcDsbVaGzfvp3+rXhY1gAAkZGRyM7OBgC0tLRgaWmJcUXa0o8j\nR44A0DY8NjQ0MK5IstaQwlayrnG5XOjq6gIAZGRkcOH/9IeVlRXU1dUBAJKSkpCamsq4Io2Ojg56\nvJ6fn8+4Gg9E2CYlJXHzmus9rLzEfQEeWwQvcV8AvNJKeIizArS/0/bt2wHwI2wBoKSkBID2ENDa\n2sq4Go2cnBxqJ6mursbc3BzjiiRrCSlsJeuanp4e2sUQNbMW0Lq15OZw8OBBbsQaGaSJjIzkxuKx\nsrKCkZERAPzk1wKyY+sLMTEx9D3Oi7AFPB7ysbExTExMMK5GY+vWrUhISADAx5pdQFu0cfz4cQCa\n4L527RrbgiRrCilsJeuWqakp/N///R8Azf9JsihFw+1248aNGwA072FaWhrjijQWFxfpSs+8vDxu\nxLbdbqfDPTwJW31OLA9pFgSSg8zDMTYhICAA0dHRAEAfUnhgx44d9Pe2tjaGlXjQr9kdHx/nZmAr\nKSmJWr8aGxu9fO8SybMgha1kXbKwsIBz587RLtmpU6e48X/6SkdHB6anpwEApaWl3AjI7u5uKiB5\n6obrO3xxcXEMK/GGHPUrisLVe5GIbF5SEQi8JSMAQHh4OB2QvHPnDhfdUUBbs0sGtqqrq7mp6+jR\no/TB6cKFC1ykSUjERwpbybrD6XTi3XffxdjYGADgyJEjQg+NkeGL8PBwZGVlMa7GA/Eub9y4kR6F\n8gARtqGhoVx1Romwtdls3DycAB5bxPz8PFerUImwnZqa4iZjF9BWRgOaHWF0dJRxNRpWqxVlZWUA\ntBMLHlb/Atp31qFDhwAAo6Oj3CQ3SMRGClvJukJVVfzxj3/Ew4cPAQBFRUXYv38/46r8x263o7+/\nH4C2RtNi4eMj7Xa7qbDdsWMHV0KNx8UMAH/LGQj6QTaeurbJycn0d566tvr0D16WNQDA7t27ER4e\nDgCoqqripmtbXFyMLVu2AAA+++wzuZFM8szwcReUSExiYGAAd+/eBaANepw4cYIr0eUr9fX1ADQx\nRFZo8sDDhw+xsLAAgJ+lDID2YGO32wHwJ2x5XM4A8CtsN23ahODgYADA4OAg42o8BAcH02UNbW1t\n3AhIm81Gu7ajo6PU/84ai8WCl19+mW4ku3LlCuuSJIIjha1kXUEGJ2w2G7797W9z0+ELXFymAAAg\nAElEQVT0h/HxcSrSd+/eTYP0eYB0qoKCgmgEEg9MT0/TY2sS8s8LJNWCJ3sE4BkeA/iK/FIUhXqk\neUpGAEAtQTMzM1wNtxUUFNDvCZ6O/ePj41FcXAwAaG9v52ZVskRMxL2rSyQ+oqoqXcaQnp7O1XYn\nf6ipqYGqqrBYLLQTwwMrKyteSxl46kDqj6x5SkQAPDm2PGXYAt4dZJ4ivwBP1503YZuenk4fmnnK\ntLXZbCgsLASgeeDHx8cZV+ThhRdeoB34y5cvc9PploiHFLaSdcPjx4+pf4unKX1/mJiYoF3RgoIC\nOvHMAx0dHVheXgbgGaThBdIJCg0NpXFRvECO+XkTtnrPL08dW8AjbKenp7mKIwsODqYeYJ6ELeDt\nxedp61dISAgOHjwIQFt5TU6jJBJfkcJWsi5QVRW1tbUAtCNMfd6kiNTV1XHZrQWAe/fuAQAiIiJo\n9BEvEC/m1q1bufNWE2HL03IGgO+OLY8byAjEWz4yMkLj+Hhg48aNXmt2iReeB4qLi+kDZ2VlJVcP\nKxJxkMJWsi64du0aFVw5OTlc+VF9ZX5+nnZrd+3ahcjISMYVeVhZWUFPTw8AzYbAk3h0u91U/JAp\nbF5QVZXexMlxLC/o69EvkeABfQ4xTwNkgPepEPnu4YV9+/YBAJaXl+lyFx6wWq04duwYAM2a89ln\nnzGuSCIiUthK1jzNzc2orq4GACQkJODll19mXNGz0dzcTDtnZKMQL/T19dHayGQ4L0xMTNAcVt4S\nEdxuN/UU8hb3ZbVa6YMgT3mxgHZ8TV5LniK/ACAqKor6uHmK/QK0wcn09HQA2hDZ4uIi44o8ZGRk\n0IeChoYGDA8PM65IIhpS2ErWNN3d3bhw4QIA7Wj87bff9pryFg23241bt24BALZt24b4+HjGFXlD\ngt+Dg4O5G87SH1Xrj7B5QO9d5WnYjkB8vzzFfRHI+2xgYIC7gSPiMX/8+DE3yxoIFRUVALRVyTwl\nJADASy+9hMDAQKiqKjeSSXxGClvJmsXhcOD999+HqqoIDg7G2bNnufMv+sqDBw/gcDgAACUlJYyr\n8UZVVa+lDLxFqRFha7VaERUVxbgab/TeVd46toDH98uzsJ2ZmeHKywpotifyOeCta7t161YaxXfj\nxg2u/KwRERF0I9nIyAhXQ24S/uHrziORPEfu3r1Lp/PffPNN7o6ffUVVVdTU1ADQvvh5S3Z49OgR\nParmaSkDgRxpbtq0iTvRrT8K5jGGjlgReBo0IpDVugC4yowFNKsEGVR98OABdx1l0rVdXFxEa2sr\n42q8KS4upqu4q6qquHzvSfiEr293ieQ5QjJrk5KSkJKSwraY50BnZyc9zjxw4AB34ozcGAMDA7nz\n16qqSj2YvFkkAG/vKm9xX4Cni8xb3BcAREdH0xW2vCUjAB6v+eTkJMbGxhhX401ycjIVjw0NDVwJ\nb4vFgpdeegmAJryvXbvGtiCJMPB1Z5RInhMzMzN0Spq3zqY/qKqKqqoqANqxcEFBAeOKvHE6ndwu\nZQC0wTEy0c+jsNUf8fNolyHClre4L0ATQLGxsQD4FLb6aEHeMm0VRaEDqOPj4zTRhBeSk5NpNFlj\nYyN3DwYSPpHCVrImId1aYG0I266uLnrMWlZWxp0Ps7Ozk3r08vLyGFfzRfQrOklwPk+Qjq2iKFxG\n0ZEHFR47tgC/G8gArQNP1jfzJmwBzQdM1jjzNkQGAEeOHIHVaoXb7caVK1dYlyMRAClsJWsOu92O\nyspKANoNLyYmhnFFz87169cBaDfJPXv2MK7mi5Bu7caNG7m0fRB/7caNG7na0kYg3eTQ0FDuLCYA\naJII8azzhl7Y8thVJp7zgYEB7iLT9Gt2u7u7ufMpR0VF0a5yZ2cnTV6RSJ4Gf9+gEskz4HA4cO7c\nOSwvL8NiseDEiROsS3pm7HY7+vv7AWi5tbx1a10uF7q7uwFofkIehRnp5OkD/XmCdEJ5s3AQSEdv\neXmZS3FLBsjcbjeXuac5OTkANEsRj6tiS0pK6HuPZH7zREVFBbXofPTRR1y+ByX8wN8dSCLxk8XF\nRZw7d452RL7xjW8gNTWVcVXPDjketNlsXHZrHz16RG0IvA2NEYiw5TUZg3QZeRW2et8vj5FfiYmJ\ndMud3nbCCzExMVR88yhsw8LCUFxcDECzcdntdsYVeRMUFESbFA6HQ24kk3wlUthK1gQulwvvv/8+\nHj9+DAB48cUXkZ+fz7iqZ2d+fp7eCPPy8rj0XxLfYEBAAJc2hLm5OXrUz7uw5a0bT9AnNfAobIOC\ngmg3nrfVugTiPR8dHaXfUzxRWlpK3388dm0zMzPpg/PNmze5s0xI+EEKW8maoK2tDb29vQCAgoIC\nlJeXM67o+dDQ0MDt+lxAO1olg3ppaWlcCjN994lXYcu7FYF3YQt4byDjkdzcXGrT4bFru2HDBhQV\nFQHQPPPj4+OMK/JGURScOHECAQEBUFUVH330EVfxZBJ+kMJWsia4f/8+ACAyMhKnTp2ix5Iis7i4\nSG0IaWlpXPpDBwYGMDU1BQDIyspiXM2XQ4SOxWLh8m8IeMQijx15wHtpBK/+RpLHOj8/j7m5OcbV\nfJHQ0FBqjSIb+nhj//79VHzzuO0rIiICL7zwAgCtM9/W1sa2IAmXSGErEZ6VlRU6vJSZmUnD2kWn\noaGBbqQ6ePAg42q+HLImNCAggNtYNSJst2zZwm1HlAhbHpczAN4WCR5TBwDvbjyPR/2AJx3BbrfT\nB0Ke2LhxI82NbWlp8dqIxwslJSV0JfbVq1e5fT9K2CGFrUR4ent76Zcbr+LKV5aWlmjEV2pqKpdL\nBZxOJ+2YZGVl0UgonnC73dRzqV+9yhOqqtKBRx6XMwDweljkPcsW4DPPFvBeNc1jpi3gsTwtLy+j\npaWFcTVfxGaz4ciRIwCAqakpLrN3JWyRwlYiNC6Xi36xhYaGcikA/aGxsZH7bm13dzetcdeuXYyr\n+XKePHlCExt4XMwAaAKCPJjx2rFVFIX7JQ1BQUEIDw8HwG/HNjIyEps3bwYAbvNYk5KS6EKJhoYG\nuN1uxhV9kaysLPp5rq6u5i4bWMIWKWwlwqKqKi5evIi+vj4AQH5+PpcZqr7idrupvy05ORnbtm1j\nXNGXQ27Meu8gb+gHx7Zs2cKwkqejP+4NCQlhWMlXExwcDABYWFhgXMnTIT7boaEhxpU8HXKq1NfX\nx+0g3r59+wAAk5OTXA66KYqCY8eOAdAeDD/++GPGFUl4QnwVIFm31NTU4Pbt2wCA7du34/Dhw4wr\nej48ePAADocDgOcGwxuqqtIBmJ07d3L7QEGOpPXdPN7QewR5TJUgEJsEr2IM8NhN7HY77dTzBon9\nUlUV9+7dY1zNl5OdnU03NlZXV3PZtU1MTKTZu+3t7dxaOyTmw+fdSCL5GlpbW2lI9+bNm/H666+v\nmaExYq2IiIjgduHB0NAQnTzfsWMH42qejn4xA69JGfqjfZ6FLbFJ8CxsyfG0qqrcdm1jY2Pp6QEZ\nvuQNi8WCiooKAMDExAS3AvzQoUNyI5nkC0hhKxGOkZER/PGPfwSgdZHOnj1Lj0lFZ2RkhG5OKi4u\n5rYTSrojFosFaWlpjKt5OkTYxsbGMq7k6eg7trymNgAeYcuzn3HLli30M8PjBjIC8aSPjIxwO+iW\nm5uL6OhoANrpGI+ZscHBwXjppZcAANPT07h27RrbgiRcwOddUyL5CpqamuB2uxEQEICzZ89ye8Ts\nDzU1NQA0gcPj+lxA64aRNITU1FSvjFOeWFhYwMTEBABwm18LeHtseUyWIJCMXZ49tjabjfpsR0dH\nGVfzdHJzc+kJAllwwhsWi4UuuhkbG6ORiryRlZVF0yZu3rxJP/OS9YsUthKhUFWVDi1lZmZyLVh8\nxW6300UTRUVF3A4SDQ0N0ZsH8QvyiH61Ks9pGfqjfV7jvgBPN5n33FAS+8VrJxQAwsLC6HuSZ29o\nbm4uwsLCAIDbWC1FUXD8+HFYLBa43W5UVlayLknCGClsJUIxNDREhQCv/lN/Id1am82G/fv3M67m\n6bS2tgLQ6uQ5N5gsZrDZbIiPj2dczdMhR/tWq5VrSw3x//Ia90UgcVqTk5Nc10q86YODg1xuSgO0\n15ys2e3p6cHY2Bjjir6c6OholJSUANC2UPb397MtSMIUKWwlQkE6mlarFenp6YyreX48efKEHu8X\nFhZym2fqcrm8ljLwakMAPMI2MTGR68FC/dYxXgfcAE/HVlVVuFwuxtU8HdKxVVUV4+PjjKt5OvoH\nc15X7ALa6RHxLfPatQWAiooKesp1+fJlLpMcJOYgha1EGPr7++kX6/bt27kWVb5SX18PQBPsBw4c\nYFzN0+nr66MeS55tCKqqYnh4GADfNgQAmJ+fB8DvcgaCfrCN5+lz0rEF+PbZxsbG0tWw7e3tjKt5\nOhs2bEBubi4Abc0ur6kYISEheOGFFwBoQ3lNTU1sC5IwQwpbiRA8efIE7777LlwuFwIDA3Ho0CHW\nJT035ubmaAj6rl27uPZZEj9gUFAQtm/fzriapzM9PU3FF+8+bHJcznMiAgDqtQT4jvzauHEj/QyR\nrj2PKIqCnJwcANoWP17tCACoNcrpdNKHcB4pLCykn/erV69yneAhMQ4pbCXcMzMzg3PnzmFxcRGK\nouD111/n2jPpK83NzfRol+xp5xFVVamwTUtL4/p4X79SlRxN84oowlb/wMWzYFAUhXbpeRa2gCf2\ni+dlDYD2cEj89I2NjdyKcKvVitOnTwMAlpaW5EaydYoUthKuWV5exm9/+1tMT08DAE6fPr2mvLUu\nlwu3bt0CAKSkpHDdXXzy5Al9HUi8Dq+QiXhFUegGJV4hKQM8L2cAvK0SPHdsAY/95MmTJ1zHk23a\ntInGk/G6rIFw8OBBANqD2PXr1xlX83SSkpLkRrJ1jhS2Eq65ceMG9clVVFRwm+3qL21tbbT7xXO3\nFvDO2+R52xjg6dhGR0dzLxhF6diGhYXR4TbehS3ZQAZ4x77xCOnaDg8Pc53BGh8fTwfebt265ZW/\nzBuHDh2iD2KXLl3iPqJO8nyRwlbCNSQFYevWrXQwYK3gdrtRXV0NQBNgPHdBVVWlHaWUlBQa1s8r\n5AiarC7lGXKsy2tuMUFRFLpAgufhMUAbICMiXG9L4ZHs7Gz6O+/dxbKyMgDa69/S0sK4mqcTHByM\n48ePAwCmpqbQ0NDAuCKJmUhhK+GWqakp2q3NycnhOgrJH9ra2mgcUUVFBbfrcwGtm0RqJR0mXpmd\nncXk5CQA/hMRVFWl3U+ehwYJpPvNewfMZrPRdbA8L2oAgPDwcGpH4F3YJiUlITExEQDQ0NDAdaRW\nTk4OkpKSAADV1dXc+oIlzx9+76SSdY/+6JvnRQD+oKoq7dZGRUVxHZ0FePx/NpvNq8PEI/qBId6F\n7fz8PBUHvMd9AR67BM+LDwgk9ot3YQt4rD0PHz7k+ogf8FimJicnuV2zC3g2kgHaIFlVVRXjiiRm\nIYWthEuWl5dx+/ZtAEBCQgIiIiIYV/R8uX//Pt3iU15eznW31u1204ntjIwM7vODibANCgryyjTl\nEVHW6RJE6dgCWk4soAlbVVUZV/PVEO+q2+3mWiwCmnWCPITxPEQGaB1mksHb2NgIu93OuCKJGfB7\nN5WsW9xuNz744APqjcvPz2dc0fOHLJqIiIjg/mh/cHCQLhEgNwmeITevhIQErh8YAHh153hep0sg\nPmCekwYIJBJwZWWFe59tQkICwsPDAYDr2C9Ai9QiqQP9/f149OgR44q+miNHjsBms0FVVVy4cIH7\nhxzJs8P3t75k3aGqKi5dukS9Zrm5uXQH+FphZGSE3gxKSkq4zoMFgI6ODgBaty4tLY1xNV8POXrm\nPb8W8O588p6KAHjsEjzn2BL0yQi859kqikIfGru6uuiDJK+UlJTQBzFiqeKViIgIGlU2ODgoN5Kt\nA6SwlXBFXV0dGhsbAQDbtm3DK6+8suaGxki3NiAgAAUFBYyr+XrIQ0Zqair34mtxcZGKLt5tCIC3\nV5X3WDLAI2x5j/sCtFrJylrehS3gOZlyu91oa2tjXM1XExwcTL22PT093EeqlZaW0u+DyspKIR7M\nJP4jha2EG7q6unD16lUAWrftzTffFOJm7wuzs7P0qHHXrl3cRzxNTExQLzDPcWQE/aCQ7Ng+f4gP\neGZmRogjXVE2kAHagxixT/C+rAHQhsiI3573ru3nN5JdvnyZcUUSI5HCVsINpJMZFhaGM2fOcC/6\n/OH69etCrM8l6DtHIgjb4eFh+rsIHdulpSX6O8mI5RmSX+xyuYRIRiBxT5OTk9ynDQCg6SiDg4Pc\ndxVDQkKoTayrq4v79ImtW7eisLAQgOZj5t0bLPEfKWwlXLC4uIi+vj4AQEFBASIjIxlX9PyZm5uj\n63MzMzO57yjqlzJs27aNDrfwDOnMxcbGCvFgRMRLYGCgEMJW31UWIRlB/3DDu/ACvGMNec+0BTSv\nLRnQFGEJwqFDh6g3+PLly0KcOkh8RwpbCRd0d3fTPM+1lllLuH79Ou1ykWEGnhkdHaU2BN6TGwhE\n2PKeX0sgXlURMmwBb2ErQsdW//DIezICoG0gjImJASCGsN2wYQMdemttbeU+LSM0NJR+9w4NDXGf\nQCHxD+6F7f379/Hd734XxcXFKCsrw1/91V9xvU9b4h9kGcPGjRuFWIPqK/Pz87Rbm5GRQb10PNPa\n2gpA86fxvpQBAKanp+FwOACIJ2xFyLAFvAfcROjYhoaGIiwsDIAYHVvAY/np7e0V4uGBWKpWVlZo\n9jjPFBcX0610lZWVQvyNJb7BtbB1uVz43ve+h4KCAly/fh0XL17ExMQE/uEf/oF1aZLnSFtbG/Vy\nZmRkrLkUBEALB19eXgagrc/lHVVV0d7eDkB7TUTIWB0aGqK/iyJsyZpPIr54R9+xJe9n3iF2BFHC\n+YmwdTqd3C9rAIAtW7bQz9vNmze5f+CxWq04evQoAMDhcHA/+CbxHa6F7ZMnT/DkyRN84xvfgM1m\nQ0REBI4ePYr79++zLk3ynHj06BF+97vfAdBu7gcOHGBc0fPH5XLRCLPU1FQhOtKjo6PU/5mVlcW4\nmtVBjpptNhvtyPAOEYci+GsBbwEuQuQXACQmJgLQHnzI4CbPJCcnU2uKCOkIAOj3tsPhQEtLC+Nq\nvp6MjAyayV1fXy+ETUWyergWtnFxccjOzsZ7772H+fl5jI+P4/Lly3jxxRdZlyZ5DoyNjeH8+fNw\nuVwICAjA22+/vSaHxu7fv09FoghJCIBnKYOiKEIsZQA8R82xsbHcbxwjkO6WKLF2esuEKMKWdBNX\nVlaE6NpaLBaajtDZ2cm9bxXQuszEXlVbW8v9A4SiKDh58iRsNhvcbrfcSLbG4PrbX1EU/Mu//Asq\nKytRWFiIsrIyuFwu/PCHP2RdmuQZmZubw7lz57CwsABFUfDqq6/Szspag8SYRUZGYseOHYyrWR1d\nXV0AtDQEEdIFAI+wFSHmi0D8fSJk2AJAUFAQFeG8x1ER9LYUEfJsAc+wpgjLGgDtXk0sVtPT00J0\nbaOjo2nNAwMDaG5uZlyR5HnBtbBdXl7G97//fZw8eRKNjY2orq7Ghg0b8KMf/cin/z+PHz+mPs7P\n/6ysrHD/dLkWuXr1KqampgAAJ06cQEZGBuOKjGFgYIBu5dFH4/DM9PQ0zYMVIbsW0Dqf4+PjALSO\nrSiI1rFVFEWo7WOAlrdK0hF435BFiI+Ppw9ookzuZ2Zm0prr6upoyg3P7N+/32sjGe+rjCWrg+tv\n0+vXr2NoaIh2aMPCwvCDH/wA3/zmN+FwOFadq/nuu+/iF7/4xVP/uwj5nGsJt9tNUxByc3NRXFzM\nuCLjIIMJQUFBQqzPBYC7d+/S30WJXhsZGaE3UhE8zIDmvSbHzGTxgQiQbVMiTZMnJCTgyZMnQlgR\nCDk5OXj8+DEePXqE+fl57t8jiqKgrKwMH374ISYnJ9HV1cV9w8JqteLUqVP49a9/jcXFRVRVVeHE\niROsy5I8I1wLW7fbTX9Ip2t5ednnqfk333wThw4d+tL/9v3vf1+ILtpa4tGjR/SGTrxka5GhoSE6\n1bx3714hkgX0SxmSk5MRFRXFuKLVQbYIKYpCt03xDklEAMSJ+wI8tgmRhC3p2I6Pj8PlcsFqtTKu\n6OvZuXMnPvvsM6iqiu7ubiGypLOzs3HlyhXMzMzg5s2b3AtbQPuey87ORnt7OxobG1FcXCzUqY/k\ni3Ct6AoKChAaGop//dd/xeLiIiYnJ/HLX/4SxcXFPnVZN2/ejJycnC/9CQgIEOJLbi1BurUBAQFI\nTU1lXI1xVFVVAdAm3vft28e4mtVht9upV1WEGymBeCc3b95MO4q8oz/KF2VBA+CxTfAe66SHCFu3\n2y1MDnpcXBy9z4mwrAHQOqBFRUUAgL6+PmHSBo4cOQKr1Qq3243KykrW5UieEa6FbWRkJH71q1+h\nubkZBw8exMsvv4yQkBD8/Oc/Z12axE/m5+fpMER6erowQzO+MjIyQgew9u7dK8wAFunWirKUAdC6\nzKJtHAO8h69EErYid2wBMTaQAdrpA/G4d3d3CzMLUlhYSJtFN27cYFzN6oiKiqKJNR0dHejp6WFc\nkeRZ4FrYAtrRxn/913/h5s2bqK2txc9//nOvLymJOKysrOCdd96hnar8/HzGFRkHSUIICAgQplur\nqirtpqenpwsjxmdnZ+nQh0jJGouLi/R3Uf7WgMdjK0IMFSEqKorWrV/kwTvE4760tEQflHknLCyM\nWsxaW1sxPT3NuKLVUV5eTnOaL168KNSDm8Qb7oWtZG3gdrvx4Ycf0qnk0tJSIfxX/jA7O0snmXft\n2sX90AdhfHwck5OTACDUa6NflSpS1Jf+KF+kkwvRUhEAb++1KJFfgLbQhYgt/VAn75SVlUFRFLjd\nbtTW1rIuZ1UEBwfj2LFjAIDJyUnU1NQwrkjiL1LYSkzh8uXLtBuYnZ1NVxquRZqamuixoSgLGQBv\nH58oebuA99GySEMf+o6QKHFfgGfQbXZ2VohIJwKxqYyMjAjjD9Yva+jo6PDq8vNMTEwMrfv27dtw\nOByMK1odeXl52L59OwAtskwU24rEGylsJYbT1NREj+a3bt2Kb33rWz4nW4iCfn3u9u3bhbLNEGGb\nmJgolOeTdGwjIyOFWU0LeDq2VqtVqM8DeW+oqipU7icRti6Xi+Y0iwAZ4nS5XEIsayCUl5dDURS4\nXC5huraKouDUqVNyI5ngSGErMRRVVVFfXw9A2/Ty1ltvCdWd8pXbt2/TI1qRurUzMzM0MkuUpQyE\nkZERAGLZEADNNwlAKDEOgB6NAxBK2Or91yIJ2/j4eHoSQU69RCA2Nha5ubkAgJaWFmE82Z/fSCbS\nw4REQwpbiaGMjY3ReJ0DBw4I4zf1B31nIi4uTqjj/Lt379LOBLkZicDy8jJGR0cBQJj8WgJ5ABIp\nwxbw9gOLcqQPaENvkZGRALx92byjKAodIuvr68Py8jLjilYPGZxdWVnB7du3GVezekpLS2mGd2Vl\npRwkEwwpbCWGou8wiNYJ9BX9BHBFRYVQx8sk5ispKQnR0dGMq1k9Q0NDVJAnJyczrsY3iLAVyfYB\nePuBRbvhk66+SMIW8Hx3ulwuoaKotmzZQi0gDQ0NwniybTYbnQOZnp6mVjqJGEhhKzEUImy3bt0q\n3A3cF1wuF52i3bx5M7KyshhXtHrsdjtdNSrSUgbAM+FusViEWaVLIDm2on0uRO3YAp482ydPngjl\nnUxMTKSnXaIsayAQS9b09LRQtWdmZtKH5ZqaGqFSQNY7UthKDKOhoYF62chR2lqlvb0dU1NTAMTr\n1hIPmcViQU5ODuNqfINkkiYkJAgVmQV4VuqKLGxFOhYHPMJ2cXFRmEl9QPtsEmtTR0eHMMsaAO27\nn2xQq6urE+aBQlEUHD9+HID2Pr9y5QrjiiSrRQpbiSE8ePAAly5dAqCFoxcUFDCuyFjIUVVUVJRQ\n3VrA0wFKTU0VzgNN4nji4uIYV+I75Bhf5OExIs5FQT9AJlKeLQD60LmwsCCUHcFqtVKv7eDgIHp7\nexlXtHq2bNlC71137twRqvb1jBS2kufO4OAgPvjgAwBAaGgozp49K9RmJV8ZHBykncOSkhJYLOJ8\nrKanp6kNQaRhN0DropAuuWiJCIBH2IqWEhIQEEC3eOnXAotATEwM/S4STdimpaXRB0/iiReFoqIi\n+kBUVVUlTNcWAI4ePUr/7hcvXhTOfrMeEecOLBGCiYkJvPPOO3A6nbDZbHjrrbcQExPDuixDaWho\nAKB13nbv3s24Gt/Qe95EG+4bGxujv4uUFwxom/jIII1oFgpAzO1jgHa8TIaZRBO2FouFJpY8ePBA\nmGUNgPYe379/PwDt797f38+2IB8ICQmhloSJiQlUV1czrkjydUhhK3muXLx4kWZbfvvb36Y3kbXK\n9PQ09ajm5+cjODiYcUW+0dHRAUAThiTeRhT0W4FEE7b6ro9oHVvAe/uYaJDvpNHRUeE8wvn5+QC0\nYVWRMm0BrWtLOp+irav9/Eay8fFxxhVJvgopbCXPjbm5OfT19QHQMmtF85r6Q21tLdxuNxRFEWoh\nA6CJEuIZE/G1Ih23DRs2CDeApfemiuZrBkCtCGTJhEiQ9AxVVb26/iKQkJBAH0DJQ6koBAYG0u/I\nvr4+aoESAUVRcPLkSVgsFrjdblRWVrIuSfIVSGEreW50dnZS75RosVH+4HA4aOh4Xl6ecJYL/VIG\nEV+vwcFBAFoHTqQUCsDbmyqaKAc8XWYR/Yb67r6+6y8CiqJQy1BPT49wf//CwkJYrVYAHguXKMTE\nxFBh/uDBA6HsFOsNKWwlzw3SQYiOjhbuaNgf6urqaOxOeXk542p8hwygJCYmCifKFxcXqSgR0e6i\nP8IXUdgSX7BoCxoA7e9NLEOiLWoAPF74lZUV4cRVWFgY8vLyAGjfPyKtZAa0KKceWyAAACAASURB\nVEcyfHj58mWhhuDWE1LYSp4Lk5OTNIImIyNDuA6ar8zOzqKpqQmAtoKW7HIXhSdPntBVtCJ3awHx\nNo4BsmPLEkVRhN1ABgDbtm2jEXEiLTwgkK6n0+mk36GiEBwcjBdeeAEAMDIygpaWFrYFSb4UKWwl\nz8zCwgLOnTtHb3LkiXwt09jYKHS3lgyeKIoi3FIGQLupANqkeHx8PONqfIdMtAcGBgo5PEY8tgsL\nC4wr8Q+Se6xfySwKVquVRvO1t7cLs6aWEB8fj23btgEAbty4IdwAX2FhIW1kXLlyRbgs5/WAFLaS\nZ8LpdOL8+fN0SvTo0aNISEhgXJWxOJ1ONDY2AtCyJUXMUCWdnqSkJK/AfVEgQz8xMTHUsycS5CFQ\nRFELeFIRFhYWhNqCRSD2lfn5eUxOTjKuxndI82Bubk6oZQ2EiooKANrfn3yXioLVasWpU6cAaO9/\nuZGMP6SwlfiNqqr4/e9/j0ePHgEAiouLUVpayrgq42lvb6dP6aIlIQDazZAc5YuWXUsg/loRHyoA\njzdVxAxbwNs+IXLkFwD6/SUS6enp1Osp2rIGQNtySF6D+vp64bzaKSkpNLO8tbVVbiTjDClsJX5z\n7do1muGakZGBl156ac17a1VVpetzo6OjkZ6ezrgi3+nq6qK/Z2RkMKzEP9xuN+3YijqkuFY6toCY\nwjYiIoL+G0Rb1ABoXUP9sgbRYtcURaFd27m5OeG8toDcSMYzUthK/MLpdOLGjRsAtKn6V199VahV\nsv7S19eH4eFhANr6XBGFfHt7OwAgKipKuKE3ABgfH6c3EVGFLfEVkiEg0dDbV0T0GCqKgqSkJACg\nn2fRIEOfTqcT3d3djKvxnbS0NCQmJgLQvLaieYVDQ0O9NpKRhoeEPWtfiUgMoa+vj96cDx06JOyR\nqi+oqoqqqioA2pdaQUEB44p8Z3Z2lt4Ec3NzhRTm+qNjEaO+AE+XU8REBMDbQiFqp4rYWMbGxoQT\nVYDWUCDvHxHTERRFoWt2p6enhVs4AWheZ/IdVFNTI+RD3lpECluJX5Cp+uDgYDrhutbp7++nomr/\n/v1Cdtvu3bsn9FIGwHN0HBkZ6XUkLhIk7mstCFvR/JEEImydTiempqYYV+M7+mUNXV1dQorzzMxM\nhIeHA4CQHU9FUWjXdmlpCdeuXWNbkASAFLYSP1BVlT5d79y5U8ipdH/Qd2uLi4sZV+Mfd+/eBaCt\nFRXRhgB4hK2o3VrAI2xFFeZ6b7CoHVu9jUXEPFvAM/y5sLAgpFfYYrHQ79KHDx/SbG2RSExMpCkV\nTU1Nwm2zW4tIYSvxmU8//ZQeuYg4fOQPg4ODePjwIQCgtLRUyG7txMQE9ROKmjU8Pz+PiYkJAKAe\nSdFwOp102EfUjq1e2IqWQ0qIjo6mcwEiCioA2L59O30t7t+/z7ga/9izZw/9N9TX1zOuxj8OHz4M\nm80GVVVx6dIl4bKR1xpS2Ep8oqmpCbW1tQCAhISEdSNsyTFZYGAgioqKGFfjH3ofXnZ2NsNK/Eff\nWRM1L1l/dC/iAxKgHcGSiXBRfYVWq5W+h/Sb7EQiICCALmu4d++ekHYE/bzCvXv3aCa6SERERODA\ngQMANMtaa2sr44rWN1LYSlZNV1cXLl68CEDzN545c2Zd2BBmZmZoksDu3bvpnnnRIMI2Pj6e+tpE\nQ3/MJ2oigl7Yihr3BXhsFCLGfRGInWVgYEDYLhvxys/NzQmbp1pWVgar1QpVVVFTU8O6HL8oKytD\nTEwMAODy5cuYn59nXNH6RQpbyaoYHh7G+++/D1VVERwcjLNnzwp7jOort27dop2QkpISxtX4x+Li\nIrVSiLqUAfB0bDdu3CjsA4bekypymgj5/K8FYbu0tCSsz3bHjh1CL2sAgPDwcLrw4M6dO9RuJBI2\nmw2nT58GoHmeL1++zLii9YsUtpKvRVVVfPDBB1hZWYHVasVbb70l7OCRrywvL9Pw8B07dtAnctHo\n7u6m4nwtCFtRN44Ba6djS4QtGYQTEf0AoojDV4BmqcjJyQGgpdWImlJRXl4Oi8UCVVWp3U00Pr+R\njDQTJOYiha3kaxkdHaVP0MePH1838V6A5ikmR0r79u1jXI3/kDSE8PBwbNmyhXE1/uF2uzE0NARA\ns1OIiv6IknTaRIR0zEUdHgO0zj+xVNjtdsbV+A/ZQraysiKsHSEiIoLaKu7evSvsUf7Ro0fp5/ry\n5cvCWlxERgpbyddCMmstFouw0/T+sLKygrq6OgBaZyc1NZVxRf4xNzdHlzLk5eUJuZQB0IQH6UaJ\nHPWlP7oXNe4L8HSbRe0QEkj3X1QrAqB9HsiDhojLGgikeeB0OtHc3My4Gv8IDQ3FwYMHAWgWPtJU\nkJiHFLaSr4UI25SUFGF9jf7Q1NREJ74rKiqEFYRtbW3UhpCfn8+4Gv9ZCxvHAM/RvT5ZQESIP1jU\nHFsCsVWJLGwtFgtNR+jq6hK2SxgXF4eUlBQA2myDy+ViW5CfFBUVUdva1atXhX/4Ew0pbCVfyfDw\nMJ1Ez8zMZFyNeTidTtqtTUxMRFpaGuOK/IcMlMTHxwubJAB4PJAxMTFCC0LSsQ0LC6M5qiKy1jq2\nc3Nzwh5/Ax7v/MzMDEZGRhhX4z9kQNfhcAibzWu1WnH06FEA2r+D3Esk5iDut6rEcKanp/HOO+8A\n0D6o60nYtrW1UQEicrd2ZmaG+lJFt5GQEH1RFzMQFhYWAEBocQ4AQUFBADTvs8g+27i4OPo7WWAi\nIunp6TR+8d69e4yr8Z+MjAxERkYCAGpra4XtPu/cuZPa12pra4XM5xUVKWwlX8ri4iLOnTtHxd0r\nr7witB/QF1RVpQsZYmJi6BGfiOj9diIv03A6nXSAUeSuM+A5uhc56gvw9geLHPkVHx9Pu896u4to\nBAcHC7+sAdBsFWVlZQA0Xz2xwomGoig4efIkrFYrXC4XLly4IKxIFw0pbCVfwOl04t1336Wes0OH\nDgnf7fOFgYEBepRXUlIibLcW8AjbmJgYYaPKAGB8fJzeFESO+gI8wlbkqC/Aex2wyMLWarUiMTER\ngLiRXwSSKjAzM4O+vj7G1fjP7t276RKZ6upqYQVhbGwsFen9/f3C5gyLhhS2ki9w8eJF9Pf3AwAK\nCwvpB3O9QLq1QUFBQg9b6aN/RM6uBbwHe0Tv2BJPqugdW72wFTnLFvAMIw4NDQnb6QS0rG0y4Cuy\niLJarfS+Mzo6KnTSg34j2SeffCK0j1sUpLCVeOFwONDS0gJA+5I8efKk0B1LXxkfH6cDC7t376Y+\nQhHp6uqi3UHRhS3poAcGBiIiIoJxNc8G8aOuJWEr+s2aCNuVlRWh0xFsNhuys7MBAB0dHcKmCgBA\nQUEBtbvU19czrsZ/Pr+R7Nq1a2wLWgdIYSvxQu9nOnHihNBT2/5QU1MDVVVhsVhQWlrKupxngnRs\nNm7ciOTkZMbVPBvkiDgxMVH4By19KoLIWK1W+lqslWQEQOzYLwDIysoCoK0JFtkzbLPZsHfvXgCa\n91nkpIeUlBS6RKOxsVH49xjvrC/VIvlaOjo6AGiTwlFRUYyrMZeJiQkqBgsKCoTuDM7Pz6OrqwuA\nloYg8gOK0+mk0+oi59cC2mAiObZfC8OYpOssurCNiIhAYGAgANB4Q1FJSUmhrwv5PheVPXv2UC96\nQ0MD42qejcOHD8NqtUJVVVy5coV1OWsace92kufOwsIC9daKPEHvL/purei+Yv1SBjJQIiojIyP0\nSFX0zvPS0hK1h+iP8kWFiA7RlzQoikK926J302w2G83d7uzsFHbw6v9r796joqzWP4B/Z0AYLoIg\n4IXyghCGyEU0BLGU9KClKHjMsjwd86Sl1emXmWmmVtrdLLOytWply8tJsRTUIlNLIam4iQNWAqJL\nRMQLw02uM+/vj3ftzUxCiUy8vHuez1pnnZgZhmd8Z+Z93r2f/WxA3nLafJtdtmGOGvXq1YvPAhYW\nFqK4uFjhiMRFiS0BII8kHThwgCdDttSzFpBri9lobWhoKO+jqFYFBQUA5JF38z6dalRaWsr/W+09\nbM1PzCIktmxkUM19bBmW2F68eFHhSDqP1dRXVlaqfgSalSMYjUbVj9rGxMTwEqTU1FTVXxB2V5TY\nEgDAkSNHLBaN9e3bV+GIulZWVhZP6tU+WltfX89r69hCEjVjJ2ZPT09VL+YDLBNAtb8WoLVOWO2L\nxwCgf//+AORkUM0jg4A848bKj9TcHQGQ65/9/f0ByB1rGhoaFI7o5jk6OuLuu+8GAFy+fJl2JPub\nUGJLkJubiyNHjgCQm5XPmDFD9Qt0OqKlpQXZ2dkA5JEOT09PhSPqHPO94tXeDQFonRpWe/9awHLK\nXu19bIHWUWe1t/sCLOu31d7P1tnZmSeDer1e1eUIAHDXXXcBkEt5fvrpJ4Wj6ZywsDAMHDgQgFz+\nRjuSWR8ltjauuLgY+/btAwC4ublh9uzZQowkdYRer+cjTmyfcjVjPR/d3NxUX4YgSRJPbL28vBSO\npvPMF1mpvd0X0JrYqnmDBsbHx4d/96m5mwBjvlkDWzuhVrfccguvG1b7qK1Go8GUKVOg1WphNBqx\nf/9+1V94dDeU2NqwpqYm7Nq1CyaTCY6OjnjwwQeFWKndEZIk8REALy8v+Pn5KRxR57S0tKCoqAiA\nPFqr9pH3qqoqPn1PI7bdD/u+EGHEVqvV8hpu87putQoMDOSJul6vVziazrvzzjsByNu9Z2ZmKhxN\n55jvSFZSUoL8/HyFIxILJbY2rKioiF/5JiYmCpE4dNTvv//OazhHjx6t+kSwsLAQjY2NAMRYAHj+\n/Hn+3yLUfZvXojo5OSkYiXWwXa6ampqEGHXq168fAHkBmdpfj729Pf8OUHt3BEDuiDJo0CAAQGZm\npqo3nwCAsWPH8rK3gwcPqr5lXndCia0NYz0OXVxcEBAQoHA0XU+SJF5b7ObmhrCwMIUj6jw2MuPq\n6orBgwcrHE3nsSlhnU4nRCkCG9m0s7PjSaGamZdTiLDCm13cNzU1obq6WuFoOo+1bayrq7O4SFQr\n1iGhpqaG7xCpVvb29pg4cSIAuSuP2muHuxNKbG2U0WjktZiBgYGqH6m8GadOnUJ5eTkAuROCnZ2d\nwhF1Tn19PT+mat+UgWFTwrfeeqsQ71FWi+rq6irE6zEvpxAhsWUtvwD1b9QAAH5+fvx7Te2bNQBy\neRVrxaj21l+AfO5lC8nS09OFqFXvDtR/5iM35dSpU7wMQYQp646SJAlHjx4FINcJhoeHKxxR5508\neZJPz6l9UwZAHjVj22iqfccxhp24RKllN09sRZhK9fLy4hccat+oAZDbS7Hpe3bRq2ZarZYv8D13\n7pzqR6E1Gg3i4uIAyN93hw4dUjgiMVBia4MqKiqQnJwMQK7zE2HKuqPOnTvHt2kdM2aMEAt52NSc\nt7e36rshAPL7lNUFqn1jBobV2IpQXwtY9uJV80p1xt7eHr179wYA/v2gdqwcoaKiQohkPTw8nG9/\nnJaWpnA0ndevXz+EhoYCAI4fPy5ERw6lUWJrY6qrq7Ft2zY0NjZCq9VixowZQiR1HfXzzz8DkE/M\nIozWNjU1WWyHLMI0t/lUsCgLG9l0vQitvgDL3dNEmUZlF1Fq72XLBAUFCbNZAyDX248aNQqAXF7B\nysnUbOLEibzmft++fapfGKc0SmxtSGNjI7Zv384XRUydOpX3BrQlVVVVfHTT/OpfzYqLi/mXoQib\nMgCtU8HOzs58hyu1Y9P1oiS25iUVoiS2AwYMACAPAlRVVSkcTee5uLgItVkDAERFRfHPECspUzMX\nFxe+kOzSpUu0I1knUWJrIyRJwq5du/g+6OPGjROiC8DNyMzM5F/uImzIALTWzzk7O8PX11fhaKxD\npB3HGDZiK8osibOzMx8NFKGXLSDWDmTM8OHDAcgX9WfPnlU4ms5zcXHByJEjAcglWOy8pmbh4eH8\nouro0aO0I1knUGJrI86dO8cb94eFhfFm17amoaEBWVlZAOQpew8PD4Uj6jyj0chXPAcEBAjRDUGS\nJD7FaL5SXe3YZhOijNhqNBo4OzsDkFtKiaB37968Blrti5OYwMBAPjNVUFCgcDTWER0dzS8QMzIy\nFI6m8/64I9l3332ndEiqpf4zILkhv/32GwB5pGjy5MlC1GDejJ9//plvYDBmzBiFo7GOoqIi1NfX\nAwCCg4MVjsY6KisreaIkysIxSZL4azKvTVU7ljCJ0O4LkBMMtvhShMVWgHwhxXqVFxYWClGO4Orq\nyhdd5efnC1EK4+3tjdGjRwOQ64dLSkoUjkidKLG1AZIk8cR2yJAhQtSU3oyGhgbeBNvPz0+YFlJs\nQYiLi4vqtwRmzKeARTlO165dg8lkAiBWYstGzURo98WwWQJRElugtfa+qqpKiB69QOuGDUajEdnZ\n2QpHYx1jx47lsyDffvst/84gN44SWxtw6dIlVFZWArDNnrXML7/8wlsS3XXXXQpHYx0NDQ28DCE4\nOFiIMgSgNbF1dXXlDdnVznxESZQ+tkBrWYUoI7ZAa2JbXV3NZ3jUzt/fn8/UidDTFpCPE7uYz8rK\nEqKbgE6nw7hx4wDIWzvn5eUpG5AKiXEWJO0ymUy8Vkej0QizYr6jmpub+Wjt4MGDeZG+2v32229C\nbcrAiLbjGGCZ2NKIbfdmXtctwsIkQF7ox2Y/2AyeCNiobW1trRDtzAAgIiKCvwcPHTrES83IjaHE\nVmCSJGH//v180Vh4eDif4rA1er2efznExMQoHI31sJEXDw8P9OvXT+ForMNkMuHy5csAIMxrAloX\njgGWGxuonWiLxwD5fccuqNhFlghuv/12APLmE+wzpnYBAQHw8vICIG9LK8LUvVar5TuS1dXV4eDB\ngwpHpC6U2AosPT0dOTk5AORRynvuuUfhiJQhSRLfV9zb21uYndZaWlpQXFwMQK6fE2Vk8+rVq3wU\nWqSOCOYjmqK0+wJaR59FWLzDODo68jZzorT8AuRyJfY9Icropkaj4V1+rl69ivz8fIUjso4hQ4bw\nNm05OTm0I1kHUGIrqBMnTuDw4cMA5D6g9913H+zs7BSOShlnz57l04mRkZHCJIBnzpzho4AilZiY\nL2wRKbE1r0EVpd0X0FovXFNTI8Rqe4ZN2587d06Y1+Xq6so35RFlswYAGDZsGN8K+ejRo0KM2gJA\nXFwc7Uh2EyixFZDBYEBKSgoA+aQze/Zs/uGwRay2VqfTCVWHyhaNOTo6YuDAgQpHYz1sJbqdnZ0Q\nfYYZ0UdsjUYjX5wpApbY1tXV8cW3ImDfgQaDQZjRaK1Wi7FjxwIArly5gpMnTyockXX8cUcyEfr1\ndgVKbAV08uRJfmX3wAMPwN3dXeGIlFNeXs4TwIiICGFGyoxGI//yDggIEGo0njXF79OnjzBdHgDw\nGm8HBwehXhfbzACAMB0EAFjs4CfKAjJA3qyBXVix70YRDB8+nHdQ+fnnnxWOxnrCw8P5RVZaWppQ\nJT9/F3G+XQnHVrz6+voKtfjmZrB9xHv06IGoqCiFo7Ge4uJiXLt2DUDrdpkikCSJjyKJ0r+WYSck\nkVp9AZajzyK1/PLw8OAXjKL0fQXkCyvWIkuUtl+APGrLtkgvLS0VZtc4jUaDSZMmAZAXoP7www/K\nBqQClNgKpra2licGttyzFpBHWX799VcAwMiRI+Hi4qJwRNbDFn44OzvzmjkRXL58mU9ni5rYitTq\nC7CsFxap5ZdWq+Wr7UXaqAEA34Xs8uXLuHr1qsLRWE94eDh/P4o0atu/f39eQpKTkyPUhdbfgRJb\nwZivCLX1xDYtLQ2APKIUHR2tcDTW09jYaLEpg0hlCOYrf0XpNczU1NQAEC+xFXXEFgDvjCBaYmu+\n2FSkcgSdToewsDAAQEFBAf/MiSA2Nhb29vaQJAnffvutMAv//g6U2Ark7NmzvN+dj48PH22wRQaD\ngdegRkRECJVMFBYW8gRCpMVwAHDhwgUAgJubm3BT9qzGVrRe0uY9eUVaPAZYJrbmfYjVzs3NjZep\nFRQUKByNdbFyBJPJhGPHjikcjfW4u7vzAZrTp08Ld9ysiRJbQVy6dAlffPEFjEYjevTogenTpysd\nkqIyMzMhSRI0Gg1Gjx6tdDhWVVhYCECu1ezfv7/C0VgXGxnr06ePwpFYH5umF2UBI2N+0SjawhZW\nDiNJkjA1mwyrzT9//jyuXLmicDTW4+XlhaCgIADyNrsivSdjYmL4ArnU1FTakawdlNgKoLa2Ftu2\nbUNDQwM0Gg1mzpxp04vGmpqa+MYUgYGB/ItABCaTiSe2AQEBwvTkBeTkgSW2IvWvZdgou2iJraOj\nIy9HEGnqF5BrG1kHC1FaYzEibtbAsA0bWlpahGqR1aNHD9x7770A5DZ0hw4dUjii7okSW5VraWnB\n9u3bUVVVBQC49957+cIAW6XX6/mUKNtHXBSlpaX8Kl2kTRkA+YuavTYRE1s2YitSD1tAXrUt4u5j\ngJxIsEEC0RLbnj178u4IIm3WAMgzPmz74MzMTKG2e/b390dwcDAAIDs7m3YkawMltipXUFDA6xLH\njh2LiIgIhSNSlnldVZ8+fYTauAAArxu2t7fnJyVRmPcKFS2xNRqNvLe0aCO2QGs5gkgJBHPLLbcA\nkKfsRUr+gNYa/crKSn4eEQUbtW1ubkZmZqbC0ViX+Y5kqampwr0vO4sSW5VjK1p79eqF8ePHKxyN\n8vLz83n7mujoaKGm6k0mE+96cdtttwmXILGRBzs7O+FqbM0TPpEWMjLsvShSuy+mb9++AOTFf6Il\n7rfddhsvtRCppy0gHzfWCjErK0uo7WhdXV35+f7ChQvIy8tTOKLuhRJbFWtubkZRUREAuZZUpCTu\nZphMJr4hQ+/evfl0jSiKi4v5iVW0bghA61Svr6+vcNP15lP0lNiqi/nsgWhtv3Q6HZ/VEi2xBVpL\n0erq6oTrIhAREcE7Hx0+fFiorh2d1S0S27S0NIwZMwaLFy++7r6MjAzMnDkTERERmDp1Kvbu3atA\nhN3T6dOn+YnE1nvWAnJZBlvdO3bsWKG2LQVaF3g4OTnB399f4Wisy2QyobS0FIB4GzMAlouqRExs\n2YWIaH1sAcvEVsTG+KxW/8KFC6iurlY4Guvy9/eHp6cnAHnDBpGm7O3s7DBx4kQA8veLSK3NOkvx\nM/8nn3yCV199FYMGDbruvkuXLmHhwoWYPXs2MjIysHz5crz44ovCXXndjKamJj466eTkJFwz+46S\nJAnp6ekA5K0wRdpmFpBHwthWyaJtygDICQO7SBMxsTUfsRWtPy8g9oitg4MD76wicmILiLVZAyAv\nbGR9bcvKyoRbaBUQEMDXWvz444+orKxUOKLuQfHEVqfTISkpqc3EbO/evRg8eDASEhLg4OCAqKgo\nxMbGIikpSYFIuw+TyYSvvvoKZWVlAOTpFtFGJzvqzJkz/KQzZswY4f49SkpK+GjYsGHDFI7G+swX\njonYqs58mlC02mhAvrgGxFw8BrS+J9msgkg8PT15Tbter1c4GusLCwvj788jR44oHI11aTQaxMXF\nQavVoqWlBV9//bVQo9I3S/Gz/0MPPdTu1FxBQcF1J/GgoCAhP3w3SpIkfPPNNxZbqrLVn7aM7Qvu\n5OQkZP0pO946nU7IEU1Wu+jo6CjkiKb55gwi1sKzY1ZXVweTyaRwNNbHPnMVFRXC7a4GtG7WcO7c\nOb74VhSOjo58k56SkhLhRm19fHwQFRUFACgqKuKdc2yZ4ontnzEYDHBzc7O4zd3d3aaH248dO4as\nrCwAwMCBAzFt2jQhT5QdUVlZyRO/ESNGCDciJkmSxaYMoo1GA62JrY+Pj5DvZzbaLtqiOIYNTkiS\nhGvXrikcjfWZX0yK1s8WgEXplogDR3fccQdvj8VK+ERy1113WexIJuLFV0dopG4ybr1s2TI0NTVh\n3bp1/LZ58+YhMDAQzz33HL8tKSkJH330EQ4fPnzDz11RUdHuatZZs2bBZDKpYvrTaDTy4n47Ozv0\n7NlTyCSgoxoaGlBfXw+NRgM3NzfhEj/z4+7i4gIHBweFI7K+6upqGI1GODo6wtnZWelwrK6+vh4N\nDQ3QarVwd3dXOhyra2lp4Qvk3NzchKsBB+SBFkmS4OTkxJMkkdTW1qK5uRl2dnbXDSiJgJ0nADHf\no83NzbyWX9T3KCCXBW3duvVPH9Othw88PDxgMBgsbjMYDOjdu3eHnmfHjh3YuHFju/er5Q1uZ2cH\nDw8PpcP4U0ajEXV1dXBxcemyf1edTifshxjo+uOuxDEU8URqzsnJidf5dYWuPob29vbd/rups7py\na24lPoMidusw19Xnia4+hj169BD+M3ijunViGxwcjN27d1vcptfrERoa2qHnmTVrFmJjY9u939vb\nGz4+PjcVI7FUUFCAxMREbN68WchFTraAjqH60TFUNzp+6kfHUDndOrGNj4/Hxo0bsWvXLsTHxyMj\nIwNpaWnYuXNnh57Hx8eHEldCCCGEEMEpntiGhIRAo9HwxRXfffcdNBoN8vLy4OnpiU2bNmHNmjV4\n+eWX4evri7feegsBAQEKR00IIYQQQrobxRNbtptSe0aOHIk9e/Z0UTSEEEIIIUStxFo+TgghhBBC\nbBYltoQQQgghRAiU2BJCCCGEECHYrV69erXSQRCxuLi44I477oCLi4vSoZCbRMdQ/egYqhsdP/Wj\nY6iMbrPzGCGEEEIIIZ1BpQiEEEIIIUQIlNgSQgghhBAhUGJLCCGEEEKEQIktIYQQQggRAiW2hBBC\nCCFECJTYEkIIIYQQIVBiSwghhBBChECJLSGEEEIIEQIltoQQQgghRAiU2BKr+/zzzzF06FCUlZXx\n23777TfMmTMHI0eORFxcHD777DMFIyRtMRgMWLp0KWJiYjB69Gg8+eSTKC8v5/fTMez+ysrKsGDB\nAkRGRiI2NhZvv/220iGRv1BWVoYnnngCkZGRiImJwbJly1BbWwsAyMjIRtCgjgAADodJREFUwMyZ\nMxEREYGpU6di7969CkdL/sqrr76KoUOH8p/pGHY9SmyJVVVUVOCzzz6DRqPhtzU2NmLBggWIiopC\neno61q9fj48//hgHDx5UMFLyR88//zyuXr2K/fv348CBA2hubsayZcsA0DFUiyeeeAJ9+/bF4cOH\nsXnzZnz33XfYvHmz0mGRP/HYY4/B3d0dR44cwZdffonCwkK88cYbuHTpEhYuXIjZs2cjIyMDy5cv\nx4svvoiCggKlQybt+PXXX5GcnMzPfxUVFXQMFUCJLbGqtWvX4oEHHrC47fvvv0dLSwsef/xx6HQ6\nBAUFYebMmdixY4dCUZK29OvXD0uXLoW7uzvc3Nxw//33IycnBwAdQzXQ6/U4deoUlixZAhcXFwwY\nMABz587Fzp07lQ6NtKOmpgbDhw/H4sWLodPp0KdPHyQkJCAzMxN79+7F4MGDkZCQAAcHB0RFRSE2\nNhZJSUlKh03aIEkSVq9ejUceeYTfRsdQGZTYEqs5cuQITp06hUceeQSSJPHbT548icDAQItR3KCg\nIOj1eiXCJO1YtWoV/P39+c9lZWXw9vYGQMdQDU6ePAlfX1+4urry24KCglBSUoJr164pGBlpT8+e\nPbF27Vp4enry2y5cuIA+ffqgoKAAw4YNs3g8fea6r//9739wdHTElClT+G0nT56kY6gASmyJVTQ2\nNmLNmjVYuXIlevToYXGfwWCAm5ubxW29evVCVVVVV4ZIOqC0tBQbNmzAwoULAdAxVIP2jhEAVFZW\nKhES6SC9Xo9t27bhsccea/N4uru707Hshi5fvoyNGzdi9erVFrfTMVSGvdIBEHVISUnBc889ZzFi\nJ0kSNBoNXnvtNZSUlCAkJARRUVFt/r75CC5j/lzk7/dXx3D69OkAgOLiYvznP/9BYmIiEhMTLR77\nR3QMu5e2jhFRh+zsbCxcuBDPPvssoqKi8Mknn9DxVInXX38d//znP+Hn54fz589b3EfHsOtRYktu\nSHx8POLj49u87/Tp03jzzTeRnJzc5v0eHh44e/asxW2VlZV8NIl0jT87hsyJEycwf/58zJs3D48+\n+ii/nY5h9+fp6QmDwWBxm8FggEajsZjqJt3P4cOH8dxzz2HlypX8M+rh4dHm8ezdu7cSIZJ2ZGRk\nIDc3F2vWrAFgmcjSMVQGJbak077++mvU1tYiPj7e4kOdkJCA+fPnY/jw4fjiiy9gMpmg1crVL3q9\nHiEhIUqFTNpw5swZLFiwAM8//zwfvWXoGHZ/wcHBuHDhAgwGA7/gOHHiBIYMGQInJyeFoyPtycnJ\nwbJly/D+++9bzHgFBwdj9+7dFo/V6/UIDQ3t6hDJn0hJScHVq1cxbtw4AHJiK0kSoqKiMHfuXOzb\nt8/i8XQMu4BESCfV1tZK5eXlFv8LDAyU8vLypNraWqmxsVGKjY2V3n//fam+vl46fvy4NGrUKOnI\nkSNKh07MzJ07V3rnnXfavI+OoTrMmjVLWrFihVRTUyMVFRVJd999t7R9+3alwyLtaGlpke655x5p\n586d19135coVKSIiQkpKSpIaGxulH374QQoLC5NOnTqlQKSkPdXV1RbnvuPHj0uBgYHSxYsXpbKy\nMjqGCtBIEhWAEOu7/fbbcejQIfTv3x8AUFRUhJUrVyI/Px9eXl5YsGABZs2apXCUhCkvL8f48eP5\nwj+NRsPrbz/99FOMHDmSjqEKXLx4ES+++CJ++eUXuLq64oEHHsCiRYuUDou0IysrC3PmzIGDgwP/\nvLH/T01Nxfnz57FmzRqcPn0avr6+WLx4MSZMmKB02ORPnD9/HhMmTMCvv/4KQD7GdAy7FiW2hBBC\nCCFECNTuixBCCCGECIESW0IIIYQQIgRKbAkhhBBCiBAosSWEEEIIIUKgxJYQQgghhAiBEltCCCGE\nECIESmwJIYQQQogQKLElhBBCCCFCoMSWEEIIIYQIgRJbQgj5G4WEhGDXrl039NihQ4dix44df3NE\nnTdp0iRs2LChzfuysrIQGhqKs2fPdnFUhBAC2CsdACGEdKU5c+YgOzsbPXr0AABIkgQnJydER0fj\nqaeewuDBgzv1/CkpKQgPD8ett94KADhx4kSnY75Rzz//PJKTk+Hg4ABAfm0ODg4YMWIEnnzySQwf\nPtwqfyc1NdXi502bNmH+/PnQarUYOXIk8vLyrPJ3CCGko2jElhBicyZPnoy8vDzk5eXhxIkTSE5O\nRktLC2bPno3a2tqbfl5JkvDaa68pNlqp0WgQGhpq8doOHDiA/v3746GHHkJpaanV/+bvv/+Od999\nFy0tLVZ/bkII6ShKbAkhNq9v37544YUXUFlZidzcXADAlStXsHjxYkRGRiI8PBxTpkzB3r17+e/s\n3r0bo0aNQlJSEiIjI/HBBx8gJCQEBoMBjz/+OObMmQPg+vKCzz//HHFxcQgPD8f06dNx4MCBduPa\nsWMHpk2bhvDwcMTExOCVV15BQ0NDh16bp6cnVqxYAUmSkJ6eDgAwGo346KOPMHnyZISGhiI2Nhbv\nvfceTCYTAKCpqQkvv/wy7rzzToSHh2PChAn4+OOP+XPGxsbinXfewffff48ZM2ZAo9Fg1KhR2LBh\nA3755RcMHToUJSUlAICGhga89tprmDhxIsLCwhAXF4ctW7bw59q4cSMSExNx6NAh3HvvvQgLC0Ni\nYiLy8/P5Y77++mtMmzYNI0aMQGRkJJ588klUVFR06N+BEGIbKLElhBAAzc3NAMBLFF544QWUlZXh\n4MGDyMnJwZw5c7B06VIUFxfz32lqakJOTg6+//57LFq0CKmpqZAkCZs2bbJI3pikpCR8+OGHePPN\nN5GdnY358+fjmWeeabNc4csvv8S6deuwfPly5ObmYuvWrcjMzMSqVas6/NpMJhNMJhN/bR999BG2\nbduGN954A7m5uXjrrbewbds2bNq0CQCwefNmZGdnY8+ePcjNzcV7772HLVu28MSYGT9+PF555RUA\ncm3tU089BUAeOWZeeuklpKWl4eOPP0ZOTg6WLl2KN954A8nJyfwxpaWlOHz4MHbs2IEff/wROp0O\nL730EgDg4sWLWLJkCZYsWYKcnBwcOHAAGo0Gb731Vof/HQgh4qPElhBi80pLS7F27Vr4+flhxIgR\nAIANGzbg008/Rc+ePaHRaJCQkACTyQS9Xs9/r6mpCQ8//DCcnZ0tnk+SpDb/zvbt2xEfH4/Q0FBo\ntVrcc889WL9+Pdzd3a977NatWzFjxgxERkYCAAYNGoSFCxdi//79PAm/EZcuXcJLL70ENzc3jB8/\nnj/3v/71L4SEhECr1SIiIgIJCQnYvXs3AKCmpgZarZbX6g4bNgzp6emIiYlp9++09Zpra2uRnJyM\nRYsWwc/PD1qtFrGxsRg3bhz/W+xxy5Ytg6urK1xcXDBhwgQUFhYCAOrq6mAymaDT6QAA7u7u2LBh\nAyW2hJA20eIxQojN+eabb3Dw4EH+s5eXF+644w6sXr2aJ3NFRUV49913ceLECVy7dg2APBLZ2Nho\n8VxskdiNOHPmDBISEixumzhxYpuPPX36NAoLC7Ft2zaLEVAAKC8vb/fv5uXlITQ0lP/cq1cvhIaG\nYsuWLfD09ERNTQ0MBgMCAgIsfs/f35+PMj/44INIS0vD2LFjMWrUKERHRyM+Ph6enp43/FoB+YJB\nkqTr/taQIUMsyjo8PDzg6urKf3Z2dub/zn5+fpgzZw4efvhh3HbbbRg9ejQmT56MkJCQDsVCCLEN\nlNgSQmzO5MmTsW7dunbvr62txdy5cxEdHY2UlBT4+PjAZDIhKCjousey6f0bYWdnx+tY/4pOp8Nj\njz2GuXPn3vDzA0BoaCi++OKLdu//Y2LOmMfVt29f7NmzB/n5+Th27BhSUlLwwQcfYPPmzRg2bNgN\nx9LY2NjmSK4kSRbJ+h8T9z9avnw5Hn30UaSnp+Po0aN48MEHMW/ePDz99NM3HAshxDZQKQIhhPxB\ncXExqqqq8Mgjj8DHxwcA+KKyzhg0aBBOnz5tcdvu3btx/Pjx6x47ePBgiwVUAFBdXY3q6upOxdC7\nd2/07NkTv//+u8Xtp06dwsCBAwEA9fX1aGxsRHBwMObPn4+vvvoKQ4cOxZ49ezr0twYMGACNRtPm\n37rRtmqSJKGqqgre3t5ISEjA+vXrsWrVKmzdurVDsRBCbAMltoQQ8ge+vr6wt7dHVlYWjEYjcnNz\n8cknn8Dd3R1lZWXt/p6TkxMAuYygpqbmuvtnz56N/fv349ixYzAajTh06BBWrlzZ5ojlv//9b3z7\n7bdISUlBU1MTysvL8d///hfPPPNMp16bRqPBrFmzsGXLFuj1ephMJvz000/Ys2cP7r//fgDAokWL\nsHz5cly9ehWAXEJx4cIFDBkypN3XXFRUhLq6OgCt9bYeHh6YNGkSPvzwQ5SUlKClpQWpqalIS0vj\nf+uv7Nu3D1OmTOEL7Orq6pCfnw8/P79O/TsQQsREpQiEEPIHXl5eWLVqFTZu3Ij3338fYWFhePnl\nl7Fz5058/vnn0Gq1GDBgwHW/5+npiWnTpuHtt9/Grl27kJKSYpG0JiYmorGxEStWrEBlZSVuvfVW\nrFu3jtfEmj920qRJqKysxIcffogVK1bA2dkZ//jHP/Dss892+vU9/fTT0Gg0WLx4MS5fvgxfX18s\nWbKEJ5uvv/461qxZg8mTJ6OpqQne3t6YPn06v988zujoaNx+++2YNWsW7rvvPsTFxVncv3btWrz+\n+uuYN28eqqurMWDAAKxfvx4TJky4oVinTp2KsrIy/N///R+uXLkCZ2dnRERE/GkpCSHEdmmk9pbv\nEkIIIYQQoiJUikAIIYQQQoRAiS0hhBBCCBECJbaEEEIIIUQIlNgSQgghhBAhUGJLCCGEEEKEQIkt\nIYQQQggRAiW2hBBCCCFECJTYEkIIIYQQIVBiSwghhBBChECJLSGEEEIIEQIltoQQQgghRAiU2BJC\nCCGEECH8PwvUGerNlCZHAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f36cc0b7198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.zeros([n_steps, n_particles])\n",
"X[0, :] = np.cumsum(np.ones(n_particles)) - 5.5\n",
"\n",
"C = np.eye(n_particles - 1) \\\n",
" - np.diag(np.ones(n_particles - 2), 1)/2 \\\n",
" - np.diag(np.ones(n_particles - 2), -1)/2\n",
"C[-1, -2] = -1\n",
"\n",
"for step in range(1, n_steps):\n",
" v = np.zeros(n_particles)\n",
" v[1:] = np.linalg.inv(C).dot(F(X[step-1, :], step*dt)[1:])\n",
" v[0] = - np.sum(v)\n",
" X[step, :] = X[step-1, :] + v*dt\n",
"\n",
"plot(X)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## $\\mu v = F + \\mu \\langle v \\rangle_{prev}/s$\n",
"\n",
"Integrating the chain with local friction involves inverting a matrix, which can be computationally expensive. However, at least in this toy example, approximating the term from the previous velocities leads to good results:"
]
},
{
"cell_type": "code",
"execution_count": 101,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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IFRUVRX0cWBxsJfBGe8zt5DE9GEcGWCfBdnx8POx+hB7kZTkGEdFSYrAlIvKRbJzKz89f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\nJSIiIiK98H81QkTwdsqlEwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f36cc023240>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.zeros([n_steps, n_particles])\n",
"X[0, :] = np.cumsum(np.ones(n_particles)) - 5.5\n",
"\n",
"K = np.zeros([n_particles, n_particles]) \\\n",
" + np.diag(np.ones(n_particles - 1), 1)/2 \\\n",
" + np.diag(np.ones(n_particles - 1), -1)/2\n",
"K[0, 1] = 1; K[-1, -2] = 1\n",
"\n",
"v = F(X[step-1, :], 0); smoothing = 1.2\n",
"\n",
"for step in range(1, n_steps):\n",
" v = F(X[step-1, :], step*dt) + K.dot(v)/smoothing\n",
" X[step, :] = X[step-1, :] + v*dt\n",
"\n",
"plot(X)"
]
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [conda root]",
"language": "python",
"name": "conda-root-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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