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@dfm
Last active April 24, 2020 19:06
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The basic idea is that we have $u, v \\in \\mathbb{R}$ and we want to map those to $x, y$ with $x^2 + y^2 \\le 1$.\n",
"This is achieved using:\n",
"\n",
"$$\n",
"x = f(r)\\,u / r \\\\\n",
"y = f(r)\\,v / r\n",
"$$\n",
"\n",
"where $r = \\sqrt{u^2 + v^2}$ and $f(r)$ is some carefully chosen function.\n",
"\n",
"See below for demo:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log(sqrt(u**2 + v**2)*atan(sqrt(u**2 + v**2))/(u**4 + 2*u**2*v**2 + u**2 + v**4 + v**2)) - 2*log(pi) + 3*log(2)\n"
]
}
],
"source": [
"import sympy as sm\n",
"import theano.tensor as tt\n",
"\n",
"funcs = {\"log\": tt.log, \"Abs\": tt.abs_, \"tanh\": tt.tanh, \"sqrt\": tt.sqrt, \"cosh\": tt.cosh, \"sinh\": tt.sinh, \"atan\": tt.arctan, \"atan2\": tt.arctan2, \"exp\": tt.exp}\n",
"\n",
"u, v = sm.symbols(\"u, v\", real=True)\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = sm.tanh(norm)\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = sm.tanh(norm) / norm\n",
"\n",
"norm = sm.sqrt(u ** 2 + v ** 2)\n",
"radius = 2 * sm.atan(norm) / sm.pi\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = 1 - sm.exp(norm)\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = 2 / (1 + sm.exp(-norm)) - 1\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = norm / sm.sqrt(1 + norm ** 2)\n",
"\n",
"# norm = sm.sqrt(u ** 2 + v ** 2)\n",
"# radius = (sm.sqrt(4+norm**2) - 2) / norm\n",
"\n",
"factor = radius / norm\n",
"\n",
"x = factor * u\n",
"y = factor * v\n",
"r = x ** 2 + y ** 2\n",
"theta = sm.atan2(y, x)\n",
"\n",
"log_jac = sm.simplify(sm.log(sm.Abs(sm.Matrix([r, theta]).jacobian(sm.Matrix([u, v])).det())))\n",
"\n",
"np_transform = sm.lambdify([u, v], [r, theta], modules=\"numpy\")\n",
"tt_transform = sm.lambdify([u, v], [r, theta], modules=funcs)\n",
"\n",
"np_log_jac = sm.lambdify([u, v], log_jac, modules=\"numpy\")\n",
"tt_log_jac = sm.lambdify([u, v], log_jac, modules=funcs)\n",
"\n",
"print(log_jac)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
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CpuRzuG9UiM3fI6WznB3s8KdJ4Ug8W45dmTwIov9l394ThBBxrfy4TEq5EQB0R+JzdGW+XDe0QvSrt3ZmwclexXukdNFcdTDif8nB6zsycX1/P5tavo7a126JSykT2npMCBF91dF3GQDbWKacOiw5rxzbjhfiT5PC4evupHQci+Rgp8KTU/rjsc+PYfPRc4iNCVI6EpkRfYdTcnQzU5YAWA6AR+H0Kyklln2TDj8PJyy6jv++6+P2oYEYFuSFN3dkoq5Ro3QcMiP6ntiskFIulVK+LqVcdNVJTiJsTy1Ccl4F/jKlP9yc2v2lj65BpRJ4btogFFXV4797+DGj3/BiHzKKhmYN/vFdBiICPBAbE6x0HKswItQHtwwOwAe/ZONCdb3ScchMsMTJKFYfOIv8sjo8O3Ug7HgizmCevjUCjc1avL2TC0fQZSxxMrjymkb8+8dTuL6/H67rz2mlhhTq64Z5Y0LwxZE8ZBbx5ljEEicjePuHLFxqaMazUwcqHcUqPTYpHB7ODnj5mzReAEQscTKstPOVWHPwLOaNDuGtZo3E29URT07pj32nL+LbE0VKxyGFscTJYKSUePGrNHi7OuKJmwYoHceq3TOyNwb29MSyb9JR29isdBxSEEucDGbrsfM4kluOpbcMgJerg9JxrJq9nQqvzBiM85X1eO9nrgBky1jiZBDV9U14dXsGhgV5YQ6nFJqEOtQHdwzvhZW7z+BMaY3ScUghLHEyiBU/nUbppQa8PCOS9/YwoaenRsDRXoUXv+JJTlvFEie9ZRZV46O9ZzA3JhjDgrkuiCn5ezjj8cnh+CWrBDvTi5WOQwpgiZNetFqJpzcfh6eLA5beGqF0HJu0YGwo+vdwx0tfp6OmgSc5bQ1LnPTy2aGzOJpXgeenDYSPm6PScWySg50Kr84agnMVdfgnF1a2OSxx6rKiynos/y4TE8J9MTOql9JxbNqIUB/cN7o3Vu0/w4WVbQxLnLrsxa/S0KTRYtnMSAjBk5lKW3JLBPw8nLB003E0abRKxyETYYlTl+xIK8J3aUV4fHJ/hHTnwsfmwNPZAa/MiMTJomok7Obtam0FS5w6rbq+CS9sTUNEgAcenNBH6Th0lSmDAzB1SADe+fEU547bCJY4ddrft2fgQnU9/jF7KBzs+BYyNy/ePhhO9io8s/k4tFrOHbd2/ARSp+zKvIB1h/Px0HVhiOKccLPk7+mM524biIM5ZVhz6KzSccjIWOLUYZV1TXh6UyrC/d3x58n9lY5D1zBXHYzr+/vhte0nOaxi5Vji1GEvfZ2GkksNeGtuFJwd7JSOQ9cghMDy2UPhYCfwlw0p0HBYxWqxxKlDdqYXY3PyOSy+oS+GBHkpHYc6IMDLGa/MjETS2XLOVrFiLHFqV3lNI57ZnIqBPT3xyI3hSsehTpg+LBC3Rgbg7Z1ZOFlUpXQcMgKDlLgQIkwIEW+I1yLzIqXEX7ekorKuEf+cMwyO9vx335IIIbBsZiQ8XezxxBcpaGzmRUDWxlCfyKUGeh0yM+sT87E9tQhP3DQAgwI9lY5DXdDd3Ql/nzUE6YVVeGsn761ibfQucSHEEgDLr/F4nBAiUQiRWFJSou/myISySy7hxa/SMbZvdyy6LkzpOKSHKYMDcPfIYMTvzsbeU6VKxyED0qvEhRDRACqklG2eNZFSJkgp1VJKtZ+fnz6bIxNqaNbgT+uOwtlBhbfmRnGhByvwt2mD0dfPHX9efwwXLzUoHYcMpN0S1x1Jt/yK1T18J4C+QojlACbrjsrJCry5IxNp56uwfPZQBHg5Kx2HDMDF0Q7/vms4Kmub8NTG41wJyErYt/cEKWXCNR77dSxcCBEmpXzdUMFIObuzSrByzxncN7o3pgwOUDoOGdCgQE88OzUCL36djlX7c7FwHO99Y+k41YB+50JVPZ5Yn4Jwf3c8d9sgpeOQESwYG4pJEf54bftJpJ2vVDoO6clgJS6lnGOo1yJlNGu0eGTdUdQ0NOO9e6N5VaaVEkLgjTnD0M3NAY+sPYqq+ialI5EeeCROv/rnziwcPlOGV2dFon8PD6XjkBH5uDlixd3RyCurxVMbUjg+bsFY4gQA+DGjGB/sysbdI3vjjuggpeOQCYzs44Nnbo3AjrRirNzDy/ItFUuckF9WiyfWp2BwoCdeuJ3j4LbkgfF9cGtkAJZ/l4mDOReVjkNdwBK3cfVNGixemwytlHif4+A2RwiB12OHIsTHFY+sPYoLVfVKR6JOYonbMCklnttyAscLKvHmnGFcK9NGeTg74IP7YlDT0IxH1h7lIssWhiVuw1btz8XGpAL8aVI4buZ8cJs2IMADr90xBIdzy/D37RlKx6FOaPdiH7JO+06XYtm2DNw0qAcen8TbyxIwc3gvHC+oxEf7zmBggCfmjghWOhJ1AI/EbVDexVosXpuMvn5uePtO3heFfvPs1AhMCPfFX7ek4khumdJxqANY4jampqEZcasTISWwcr4a7k78ZYx+Y2+nwrt3RyO4myseXp2EgvJapSNRO1jiNkSrlXhyfQqyiqvx7j3DeSKTWuXl6oCVC9Ro1Gjx4CeJqGloVjoSXQNL3Ia8viMT36UV4dmpAzEhnLcFprb19XPHu/dEI6u4Gk+sPwYtF1o2WyxxG7HucB7+80s27h3VGw+M553rqH3X9/fDs1MHYkdaMd74PlPpONQGDojagF+ySvDclhO4vr8fXpo+GELwRCZ1zAPj+yCntAYf7MpGUDcX3DsqROlI1AJL3MqdLKrC4s+SEe7vjnfvGQ57O/7yRR0nhMDL0wejsKIOz285gUAvF0yM8Fc6Fl2Fn2grVlxVj/s/PgI3Jzt8vHAEPJwdlI5EFsjeToV374nGoEBPLF6bjNQC3oPcnLDErVR1fRPuX3UEFXVN+HDBCPT0clE6ElkwNyd7fPSHEejm6oiFq44gv4xTD80FS9wK1TdpEPdpEjKLqvHevdGI7OWldCSyAv4ezvjk/hFobNbgDx8fRkVto9KRCCxxq6PRSvz5i2M4kHMRb8wZiokDOH5JhtPP3wMJ89XIL6vDwlVHUNvIOeRKY4lbkSt3Jfz2RBGenzYIs4ZzcQcyvNFh3bHinuFIya/AotVJaGjWKB3JprHErchbO7Ow7nAe/nhDX84FJ6O6eXAA/jF7KPacKsUTX6RAw4uBFMMphlbi431nsOKn07hTHYynbh6gdByyAXPVwaiqa8KybRnwdLHH32cN4TUICmCJW4F1h/Pw0tfpmDKoB16dFckPEpnMgxPCUFHbhHd/Pg0vF0c8fWuE0pFsjl4lLoTwBrASwJVVVuOllFxx1YQ2JRXg2S9TcX1/P6zgxTykgCen9EdFXSP+80s2XBzs8Nhk3p/elAxxJJ4jpVxqgNehTvo65Tye2piCsX27I35eDJzsuT4mmd7lqzojUdeoxds/ZMHeTmDxxH5Kx7IZBhlOEULEAkjmUbjpfHeiCI9/cQzqEB+snK/mAsekKJXq8oLLGq0Wb+zIhL1KYNH1fZWOZRMMUeJhAOIBxAohkqWUP1z9oBAiDkAcAPTu3dsAm6OfT17Ao+uSMTTICx8tHAFXR57aIOXZqQTenDMMzVqJ1749CTuVwIMTwpSOZfXa/fTrSrilMinlRillBYA5up+9LoSIB/C7EpdSJgBIAAC1Ws15SHr6JasEi9YkYUCAB1YtHMmVecis2Nup8K87o6CVEsu2ZcDBToUFY0OVjmXV2m0AXQm3SggRdmUIRQgRBiDbgNmohR/Si/HHz5LRz98dq+8fBS8X3tCKzI+9nQrv3DUczZpkvPBVGlQCmDcmVOlYVkvfw7gy3dF3BQBvADzBaSTfphbi0XVHMTjQE5/ePwperixwMl8Oujsf/vGzZDy/NQ0NzVoOrRiJXiWuG05ZZKAs1Iatx87hifUpiAr2xscLR8CTt5QlC+Bor8L790bjz18cw7JtGahr1OCRG/vxOgYD44CqmduYVIAlG1MwItQHH/1hBNw4Bk4WxNFehXfuioKTvQr/3JmFuiYNnrp5AIvcgNgIZmzd4Tw8+2UqxvX1xcr5arg4chohWR57OxXenDMMzo52eH9XNuqaNPjbtEEscgNhiZshKSX+80sOln93EhMH+OGD+2I4D5wsmkol8OrMSDjZq/DxvlzUN2mxbGYk7FQscn2xxM2MVivx2rcZWLnnDGZEBeLNOcPgwEvpyQoIIfC3aYPg6miH937ORmVdI96+M4pXGuuJJW5GmjVaLN2Uik3JBVgwJgQv3D4YKh6pkBURQuCpmyPQzdURy7ZloLzmCOLnx/BkvR54iGcm6ps0eHhNEjYlF+DPk/vjxekscLJeD04Iw9t3DsOR3DLcFX8QF6rrlY5ksVjiZqCyrgnzPzqMH09ewCszI/HY5HCe9CGrN2t4EP67QI3cizWY/cF+5JbWKB3JIrHEFVZQXovYD/bjaF453rlrOOaNDlE6EpHJ3DDAH2sfGo1L9c2Y/cF+pBZUKh3J4rDEFXS8oAKz3t+P4qp6fHr/KEwfFqh0JCKTiwr2xsb/GwtnBzvclXAAP2deUDqSRWGJK+THjGLcGX8QjnYqbPq/sRjTt7vSkYgU09fPHZv/OBYh3d3wwKojWH0gV+lIFoMlroDVB3Lx0KeJ6Ofvji8Xj0V4Dw+lIxEproenMzY8PAYTB/jj+a1pePnrdC7A3AEscRPSaiX+vj0Dz29Nw40R/vhi0Wj4ezgrHYvIbLg52SNhvhp/GBuKj/adwaLVSahpaFY6llljiZvIpYZmLFqThITdOZg/JgTx89RczIGoFXYqgRenD8ZL0wfjp5PFmBt/AEWVnILYFpa4CeSX1WL2+/vx08kLeOH2QXhp+mBebkzUjgVjQy9PQSytwcz39uHEOc5caQ1L3MgOZF/E9Hf3orCyDp8sHImF4/pwDjhRB90Y0QMbHh4LlQBmf7AfW4+dUzqS2WGJG9Gag2cx78ND8HFzxNZHxmN8uK/SkYgszqBAT3z16HgMC/LGY58fw2vbM3jC8yoscSNo0mjx/JYTeG7LCUwI98WXi8ehj6+b0rGILJavuxPWPDgK943ujfjdObh/1RFU1jYpHcsssMQN7EJVPe5deQirD57FouvC8N8FXImHyBAc7VVYNnMIXrtjCPZnl2LGe3txqrha6ViKY4kb0OEzZbhtxV6knqvEO3dF4ZmpA3kCk8jA7h7ZG+seGo1LDRrMfG8fvjtRqHQkRbHEDUBKif/uycHdKw/C3ckeWxaPw4yoXkrHIrJa6lAffP3oOPTzd8fDa5Lx6rZ0NGm0SsdSBEtcTzUNzXhk3VEs25aBSRH+2PrIOAwI4BWYRMbW08sF6x8eg/ljQrByzxncnXDQJueTG6TEhRDeQohoQ7yWJTl94RJmvLcP36YWYuktEYifx5vbE5mSk70dXp4RiXfuikJ6YRWmrdiDfadLlY5lUnqXuBAiFkAcAB8hRJj+kSzD1mPnMOPdvSivacSaB0bh/27oy/nfRAqZEdULWxePg7erI+Z9eAjv/nQKWhuZhqjXdd9CCG8AYVLK1w2Ux+zVNjbjxa/SsD6xAOqQblhxz3D09HJROhaRzQvv4YGti8fhmc2pePP7LCSdLcc/50bBx81R6WhGpe+R+GQAEEIsEUJs0JW61coorMLtK/ZiQ1IBHr2xHz6PG80CJzIjbk72eOeuKLwyYzD2nb6IW/61G/utfHhF3xIPA1ChOxJfCuCZlk8QQsQJIRKFEIklJSV6bk4ZUkqsOXgWM97bh6r6Zqx5YBSenDIA9lyFnsjsCCEwb0wovlw8Fu7O9rj3w0N4Y8dJq529IqS89riRECKulR+XSSk36sbDK6SUP+ieu0FKOaet11Kr1TIxMVGvwKZWWdeEZzYfx/bUIkwI98Vbc6Pg5+GkdCwi6oDaxma89FU6vkjMR1SwN1bcPRzBPq5Kx+o0IUSSlFLd6mPtlXg7L+wNYLmUcpEQYjKA6GuNj1taiR/KuYgn1qeguKoef7l5AOImhHEFeiIL9HXKeTy7ORUAsGxWpMVdx3GtEtfrxKaUskIIkS2E2InLR+RtHoVbkoZmDd76PgsJe3LQ28cV6x8eg+je3ZSORURddPuwQEQFe+Oxz4/isc+PYXdWKV6cPuggzWgAAAgdSURBVAgeVjAlWK8j8c6yhCPxzKJqPP7FMWQUVuHukb3x3G0D4ebExRuIrEGzRot3fjyF934+jZ5eLnhzzjCLWN/2WkfiPDOno9VevnT+9hV7UVJdj//OV+O1O4awwImsiL2dCk9OGYAND4+Fg53A3SsP4pVv0lHfpFE6WpexoQCcr6jDXzakYH/2RUwe2AP/mD0Evu48eUlkrWJCumH7YxPw2vaT+HDvGezOKsFbc6MwJMhL6WidZtNH4lJKbEwqwM3/2o1j+RX4xx1DsHJ+DAucyAa4OtrjlZmR+OT+kaiqb8Ks9/fh3z+eQrOFTUW02RIvrKzDwlVH8JcNKYgI8MC3j03AXSN789J5IhtzfX8/fP/49bhtaE+8tTMLs/9zwKLuU25zJzallPjiSD5e3ZaBZq3EklsGYMGYUE4dJCJ8c/w8nt9yAjUNGjx6Yz88fENfOJjBRX1Gm2JoaQrKa/HM5lTsOVWK0WE+WD57KEK6c9k0Irps2tBAjA7rjhe/SsM/d2Zh+4kivBE7FJG9zHes3CaOxLVaibWH8/Da9gwAwNNTB+Lekb159E1EbdqRVoTntpxAWU0j4q4Lw2OTwuHsYKdIFps+Ej994RL++mUqDp0pw/h+vnjtjiEWedktEZnWzYMDMLpPdyzblo4PdmVjR1oRXp89FOpQH6Wj/Y7VHonXN2nw/q5sfLDrNFwd7fHs1AjMVQfzxCURddrurBI8szkV5yvrcN+oEDx1ywCTLgBjtHundJapSnx/dime+/IEckprMDMqEM9NG8Rpg0Skl5qGZryxIxOfHshFd3cn/G3aIEwb2tMkB4Y2U+JlNY14dVsGNiUXIKS7K5bNjMSEcD+jbY+IbE9qQSX+uiUVxwsqMSHcF6/MiESor3EnSFh9iUspsSn5HF7dlo7q+mYsuj4Mj96o3EkIIrJuGu3lNQbe2JGJRo0Wj07sh7jrw+Bkb5zOseoSzyiswgtb03A4twwxId3w91lDuNo8EZlEcVU9Xv4mHduOFyLMzw3LZkZibF9fg2/HKku8sq4Jb+/MwqcHcuHl4oAlt0TgTnUwpw0SkcntyryAv21NQ15ZLWZEBeLZqQPRw9PZYK9vVSWu1V6+38ny706ivLYR944KwZNT+sPb1boXQyUi81bfpMH7P5/Gf3bnwEEl8OikcNw/rg8c7fW/4tNqSvx4QQWe35qGlPwKxIR0w0vTB5v1lVREZHvyLtbi5W/S8UNGMcJ83fC32wfhhgH+er2mxZd4WU0j3thxEp8fyUd3Nyc8OzUCs4b34pxvIjJbuzIv4KWv03GmtAY3DeqB528bhN7du3ahocVfsfljRjHWJxbg/nF98NjkcJNOsici6oobBvhjTN/u+GhvLlb8dAprD+fh6VsjDL4dizgS12olci/WIMzP3QipiIiMq6iyHu7O9nDv4kphFn8krlIJFjgRWawAL8PNVGlJ+RvlEhFRl7HEiYgsGEuciMiC6TUmLoSIBXDTVT+qkFIu1S8SERF1lF4lLqXcCGAjAAghJgMoM0QoIiLqGEMOp0RLKZNb/lAIESeESBRCJJaUlBhwc0REZJASF0Isge6IvCUpZYKUUi2lVPv58d7eRESG1O7FPkKIuFZ+XKYbSrnynA1SyjntbkyIEgBnO53yMl8ApV38u8bEXJ1nrtmYq3OYq3P0yRUipWz1KLjdMXEpZcK1HhdCeAPI6UiKtkJ0hBAisa0rlpTEXJ1nrtmYq3OYq3OMlcsQwylhALIN8DpERNRJel92rzuZ+T8nNImIyPgs6WKfaw7rKIi5Os9cszFX5zBX5xgll0nvYkhERIZlSUfiRETUglmXuBBiuW72y5XvY4UQO3Xz0lt7/jUftwVCCG8hxAbdvlsuhAhr5Tk2vZ/4Puo4vp86RsmuMtsS1/2fm3zV92EA7pRS3qT7PrbF86/5uBHyxQoh4q/6Wt7i8Xbf/EaUI6Vcqvv63fRPU++nFttecmV/tfKYSfaXub2PWmxb8f3TBrN7P5nT50/xrpJSmu0XgHgA3ro/xwGYrPuzN4D4Fs+95uNGzjkZl287cPXPvAEsV2CfeQNYDiAWQFgrjyuyn3R5oq/aX0uU2F/m+j4yl/1jKe+nFhkU//wp2VVmeyTeil8vKpJSVgDw6eTjxtTqfWOAX48YTHnUBFyeu58MIFZ3Y7KrKbWffriyj6SUPwDo29qTTLC/zPV9ZC77pzXm+H66mrl9/kz6HlNsebaOXM7fQkWL71teJdre40ZxrfvG4PKbPx6X3/zJug+nIbbZ5r7TvSmu3ALhdd2v5ldvV5H9pMsF4Nf8/zNkACPtrxbM8n1kRvuntVxm9366QonPXweY9D2mWInLdi7nb0UiLv9HydGdQLjYycc7rYP/0IyQUr7e8kkdePN32bX2nRAiTOrGLXVHIC2vpjX4frpq2x25z04sLo+x/u7IyZj7qwWTv486wwz2T8s8ir2fOsjkn78OMO17zNTjV50YY1oCIAmXx+OujBXG4fKvInH4bfxpQ4uxpt89buSMbY674arxQ91/sCXGznNVpnjdfos3h/3UYrvRbTxmsv1lbu8jc9s/FvR+MovPn9JdZXEX+wghvOVVv3p29nEDZ4kGoJZXHRkL3R0ddf/CLsflX528ASw1Va6OMOV+0m0vFsAi/ParY5KUMkGp/WVO7yPd9sxq/3SWqfeXbptm/fkz1XvM4kqciIh+Y0mzU4iIqAWWOBGRBWOJExFZMJY4EZEFY4kTEVkwljgRkQVjiRMRWbD/B7r7xKZsYCKpAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ccn9c3VuZcVfMpty+B4DhUXmtOlS5qljKMLQHU1+vQaXBQI0GaagAbt4K2zYEKgjcnBVo+HxxT8Ky1CuYXVUTpB2w+wFK7XDBTFhgHoTVZR1MbhkzGcZLrgHJjiLZg8gqQHbdnig+dwuwDK5ZeSh1N3RMwZCwnDYfR6E4VlLLuDiLpEdg6Yaao9iKcoGi4WUTV4ngMEuv58urJdgYSVeWBrNp5ZwogETxlIN2P0AB4mGuodro4bAMk2KHYeI7s4dJB4zWhobJFAoXguSw27ON87q611jp5F37JxjY6KferyoSXXasPmBdIYrr1Nm34sJM4iFLLhBwDCrLMRUEZalXJXrZuErK9bnA7gcos5mwenlvFqxfXo2ZqPwKAq9idJlImQBjmMzAIGkbXQ6SPbdnApD3ISg7AkwEly6Owu0YakdXbA9dISjYEAUgIhuwHblAGipqgxdDBVAA2cnvlnfiKX75ArsPoASdwsRNNEx8vgBobzr9CCY76V6ZDEdxDoDkqCJZhowuEwDkF4mlKPfENK0g0C7ypmYiwPhh4brfMlO2ujsqH70rpMEydYPEhdnGLpCNqzQcodSvR13aGEFFtmnPXWmHBjEVKWPSJRA0iaf8Kp6H4gEBrAVhI/XgYaLy3ylMIMtRPYQwmSmYpfjJZtNuOpR8iSlImPZNmRgQBjAiYEfKZaRKQlCUPA2WoC0qG5q5QD6uUt2fEAZjqHTzUEr74VB0NEdFp0PtQxRPAeKR1AW7H6AAtvOvBmFdeuSedOAZxFRmMNFtHlYmA/fGp42CtB4KnWK5BCIaQhE8bgUUad9DxYFmNW7iwSJ1/ZwVrRVGw8ZdfKWomA4qGLhAXbvUjwAJkGpHVm4MWv0uZlKOReoMJ7758hKknc1P0W0ftDsBiurwgfsCYB6E1RAAwhGdUcxkqkxk3SuT2rbd5mEXh2w5ne7bsOsTiEzcIN+GtheFigQ8ddPG5Wn5fTp17lF9nkkpE7lDZoSIXZ4Z3SlteLUSlXUuUHSjYT8C5NwfHRsx52gQaxErSgVl36ZB2ryTMDNpZ/GUA3YnQCkWqouFICwwBEanQFT6rpuDG8FE1oOgqymn0mdDyvVeGretqOxuGvq8MD8y3fF3ynm3hwf5VqlEaWTjJuhVS+TuWHap9AKzZbWiXKBuIhxsnZxJFWwhVAIYGDdJpS8HaXU8JQrSSpseWgt2X0DxNgvCAjaeAsRBWGAcoNV1pJyGwR5MRvGSgYszUh/LMZRtpxyC9nfSunSXp41HF6BLjl463rk9DjIcpM/SQlgEYIlGcXQbw9jKDlQABBPhdLlJTAUYw2M0XD2qI/CA3Y6ZSStB2hvY/QBlCAnqy7j0pSCsy1uZZ9Ly9H56gGjItLoVBD7wikG5KF3ajdybPZAM1v2+9MokgMbBH7LaRhg3YVVOlVkGiV8PhnwVWAyAOqURgEnSVYyCg/rmYU6rUPHzVCJ4AMeDtJI3m58CxHGXg3Y/QAHiUR3AqgoXYxk9ZiB0abRbM4HJIWUiINHlS1nv4kyDrgcUyVGIxFDR51qnI7aj118QN+k2YGInbQi3i6eUtPH6YMasB4uOi0iZenjUpfu4SuxCRfNVdLkgpjKCij5PPmYCQLs+ps5ejKQbSlZtHbT7AcreqI7kRct6feLSAL4j9QrmapjIegSTug+tXASTXUUSgGLN5SGzPipn7LIfsl5KRKukFAiRAgWbsrWp0h9902SWg06vJp6NwRCpkNJm+WX38Gnxl6YWqlKZxVRUfqc6AAxjJvUksh0VAo4NJfvlA3Y/QAEcCEaAaOudPN+Jm3jF4u/NeVGYeGj4ulJ2EHDdhUcAGXOOIohMYHKzoKyCRq0TxU5Mc22fjXJx1c3maaA4pI5TK6PYyq4LpFylDioH3Z/uhsKBIhm6N5InZb2L41VKNOpz0O4DKObCnozqzJ5tohTKTWCi9o0rDDRg2v6F8RLT2RcA492bA4okhMgMIHtw0ekzWwFKlK+veQ0XtvnEvXIxcReGygvAErk4Ra00tWMB0qkQtakoruKHla+FSqdIIpfIQaiHii+H8ajPQbsPoAA9LUcuzCQ2MmxDzE8OJARtq7oKJojiGbAdXq+P1EsIGK9KJopkFySDvD2I7Lo+vow2f9q9m+PBQ1CuTkv3zfcuDpVyyiUawMSAwENjELSNXCD9dPwuWFsg4YO1ZNRG+U/PrhWoSBasAhkFaaV+LjRQNgMlM5xFe9DuBygA4J9xGblAdd3XlV90iqfVj4KwkA5tweJhsuzmrMJE0raVOnvLZNOh9muQPgJIB43j11wPENVWBJIKAklT5UzZCoweLBYEpukxNPRNfcoF0vtY4x+loZH7Aw8EozZkb1XbG3KQ1rsuI0UymmGrt7k36gNYlXKB3Q9Qont1APhRHVvHrs9iKqN1fROdiZuIbXG7R2AyhMUiTHp3yR2vKzOCRhyo7dO6ZWcjpdLdsxOAJQIJbFK4DpXeyjSweIB4wAxjH9oFgoOOr6PbHMVUaj0HFXX80yAt0AdcZ8rDl/cxElOO4gDtAXuJNwfuvhmwvJPnTwD+efTentD8nBMPFsQKZOYG6fJLQVjdWaMZsLrTR9PofWwkShu5OBE89LLeNwedqE7N93mwdcT23J7dUAmF1brKs7jJ3iexrVMVC8HGWFR8RZar25LabFsC6p3NNWAriCIoFyoI4A5iKvUcMNQ0+4Y5PZzcxVOkbp3eD2j3ZjbqY+DlR31qObL3+hy0y24p3LcfmPkv5c/D5FMAf2Tm35f1z/ebm4BkdOOflNUWDRFHcRNgPKKj6kUzYKcxkwMwYRq0aeraZVbuGmswlWV2y3Vbm20PLr1ri2yfZLc/sz/Wf64Nv6/TferOU39eavla1p6f/vy170yf+5quFePedymfVT2760muI6D7YTLXk7lVxF3jtZ69zndHN+t2d/rLBfZSQAERfV7g4e0zAF+X5W9g34M8tp05JxeP6ugy6kvvtgH0X2hNg7lQZH87VYHZxYupi8Ouju9M7YbFoFNNlpuaavswBEjUyTe7Ld2J/V8HGFffQIbc/lDfxgiKEeDscVNw/kbnSgHBf0cTqNQfJkI/G9p8r/311AHCx/AwWFfXeQWHvpa3nfpm/TI0vORrNL5GfjPg98z8rcqr7+xh5h+J6Le7rfmOLrYYiJ3ep+MugPqroAFRL0D/hcUXUQeTwYVn3JQtyJN06Dx9Ybr9kH3oyqjtqOUorXob+tTqclE+gvzAahwj8o0Clyd04amVpUKf6sbIp3aDWswztyfxU8r0yq8ilTRVn9WmSEjXRoGi2bVtN8YxFZb9JlJ1JkHasuPtFR3rQ8ntnFE7maHro062ibEch8pLvCz9R7S3AX5V3sGjgfKjqzJ6IdiXAL4EgI8f/ntL2pE60fk6RiLpso+O1lEZ2579JYlgUjvTijKZAqN3m8Jf0G4/+rLddkv+Ekg8RPyx+PIHrNbXwCD0IzySpiDCkq7Kmee9ql1yVeE3WzvzIGir24KHgIwASdylBl8dVCS4iwAq6thDqKiArg26AitDySbGAliw7K1fOA/l5i6PdnMGbwb8DlnBSAD336J2zKtIT7+RBluBPXWCSE72676MUSdBDCa6Oa65Dc7tqdtACJMeApNRHPMZxwJ8Wat60NwanQf5pcXQ7dHr1e0I3J2RqzN0fbzLE7g3nQsW7HcXR/HxIn8egvM5PeeA+s7ItA2V3tcProfo+9amrzH/w+lcn+rWjJS5Xl+Ns8xiLAv2Ei5P+GZAeXMgM39fXoT+CYA/IMdR1o3IDBNH8ZHQrdGKZTaq479ManX2RnR6GAxgImUiNycECOy+6M4h7WBcp2sDrW6oVtRyV8aldcsLxt2CXe5cnuAzdItI5RGci4NGIV2/phM6F0i1aV2hXqmIKsm7F7s/VaUA5oZC4/roEZlSoikdGfkprVVZRfujPlIO6OeyVBeHcMlQsbaXcnm6NwPKmwPL8jdE9Akzr8NkJSiltxeQe3jrvcCklmt53bR6yY9ck0H+xTCJ9kXDZAAFn1/TzTH7tm1bHUT8p87TtgcXDwA0AEj+yOWpLg7scs2XPuHyZJ6Wata6Mya9uUCk9mfo0sBBpXT8NiEtgIrvsz6e4js1KaioNEFXVL6b1AZYWGyIbx4ctLFqv9jEtgKeY7Yo28KYiphXJ65+FDMYTatv+XEQdlR+FSYWCj1M4riKy0ff3hAkOxAJzw0G52Rk+qvRKgGYQqSmw6YNA68KoLSh/qCbqho8pskeKnp/WtoYKqYc0DooKaUSxVNQAKAfI6mOW99vZM8rxYokCtACCnhBnEXWoz6yY/czU1YsegqbB4ikKxvOORn4q10dfW4jVwe2Y/Gg/BQmUs+1twKTEBrSqQLgDEGyA5ERVIZpkUUgKfXDKfYOLlEQtoOD1G9N1U2R3eQg30LFK5a2b009ePfHqxIBghx7haArb1RcPa8CJKEm8OIq5QK7H6DsuTRB4EnShnNOBBx1KFjq2Pab2yP10cHEtGc69SJMwk8HEsAEAiMXpwOJOj5fVrcRAWPJ3VmFSGRaYbNKYpXPtmw4E9aXF+ioMIP07FpelltWCJW8wGqYuAGtQazENvag4qHh3lbYxVMmQ8nmBkIoYOwNI+u+IM9NOaMD0N25PBdZFHV2IOmm3te6QRpQA7Ej2R7ON+n2oVcYSzDx5c26hZPu1F2nH8HEQypI79pBn1fT1Hp/nuL0kZm4ia7vlIl0/qpeoPIRr5O0xypduUE9OMZQyYokb6Ctu22qZaBA5SwHOoaKdn36E1QK+HkjNX8QoK3ns68zukHQpEdPyj9gdwIUdWCT+MdK2vKck9Uh4hFMdFlTVx+LzW+dnWy+ai/q+EaBmHbs5wwkkRrZjZn407N6/TEsQKS66tGd2+NcHgMMDRrzLBMHiSugAtpbd+pD8kfQoXYcJp4C5UKpjq6fn9IFaGub9o7kdmJpPtltlnbQ7gQoiOedjNyggWIxHRVOnYgb5K12uv6mP9vpKF7XMRg/0hN06OV4iU/DuHy4jD5d9ilUDu7Txoj60+YVy8rs2M7dUZ1O0qYujlTz6oaDuuTS9F8qh6TbSGoCHLUyFkST4WQdkFXr9Xg3As7qQUvO9YELwtZyI5USTWwbTXYL7nr+dbg8UcA1ip2U9OEwMWCGibX5OSdRwLVb9y5Ttz6o73dvBoxbwoTc9v263z8Hoeh87KmTrrySAhE0pLPV/i+QUCDQzdT0rUGA3KZW1YpRF/ocQI26UN/uHlSmro9uJDI3NyXs7HUfsaY+Rml6XspBuw+gmAtdrkJ7sOEoDhAPE6s2loKLWtkEQ8S3DMJGHfUwTHzgVmaOYtxOO48tz6wD/blSsuOiGEqp6OMnWqVE7o4Hi5nApnZv5toAY6iAVFntsqBBpWvPQMZ1VLJtDddh25jOTZF9YgFXAIco4DoKwgJh3OWo3QdQgJiWwzjI4OoeXfRumLi74W5Wd2YLcDBBWN1hS96lymSqSg6AxECk9IDheVk9R0aRtAs4w4NM/MS4NNIH9LraLJNWBK28faL9PlQi9WHrU322SuUfGb62PD1nhFz8w69Phm1lbkqGgT64ARjKwRlIREFYqX+jIeT7AQoG6kTUx2TeSTdsHNyvM1Q4WjUcVSew6XswMWpiBIJtDpJOGUEpFgcSsxwOLXNXbqhWMFj3xvFyi6E0Pyerj/L9KLWiYyH6aWom/iJ/Ki+KlxCjvTccDQLw5TyUNjLT9HsIXej6RAFadWwhDFZGfOQkalP1h0/JP2h3BRQA9r4dbxoOLg00qCN5xfwwcQSTVha240Ydmvp62sI7hk2+7Hte3oXJQl7UrgeJVSaujjtnR1wfE5ytJ85Cwdynw+qOXTkBGgabqlPOvZ9rgraZQG24fqUPLVActW7XaTVMBlA5u/JHBAABZm5KAceonb0Rn3Ao2quUC+xugHJ4qHgUdJ3dTTwyVyysOwwMY72jD/Jn6yswMXfFAg54Os0pEgVLDRYDnJ1zZU+cA07Zno6niJKXnmljJDmxdlpyyiFygwBgQ6cwzLKcgwKVpgYiSLTjHMVTIuC0Ohk0ftRnV6XswWdHpUiZFZUyLLtgdwMUAKE6GU5kK+X8rNi+TGsjVNudl30AACAASURBVCeEiwOxezBhvQ0HgFnMZAgM2W7g4iwpkgheUPnqnOVz3/J9Xmj++lQKJX+2AjWe0rkxrJY1JcufDOeWfiUuDZSS8XEVkxeUNe1CwQxjqISwWBlKlrbLMHI+GYMZtBWwk3kp+u7lURDWBW3D59Iu2n0BBWgHeYU6qWWPny/bnqsfPR7Q7p+FSeuwrpP7bUxgcomKsc/x4C52AyBLZX2Met/k6lV5+hinZlwe1h8Ak5sByxUssi9WaTB4o6Je0NwX2UVZ3jIoDBAi1VJdK9cOVFt+OyidvOusentxp/fuSnWr/DZXhYLIK/nU/pwpg94VQlD2Ars/oCiLZ7JOgFPLuPKjeSeEfhKbj4nMYiQTUJiOPkp3MInA4d2Xbn0InIkqcTEULmnQ+wH96QAzMwMUsmnMRRHk76JNtW9g4U49lFmlZcJWF0OBggrDjAJ5qEAxXt0+U/N9ZzfpHjgjl2dwV/IKOAyAnJLwNyh2dkSlXGH3A5SRW+MeoKRNuzvdg35nF79rq7ovQbm4I++P6iy5OmpEx7QflfOQQV82rw9Asg0gokGDlhbFQpYVH9tP0uvcLuw2IlN6KyuwCDAEHkKfJGXRRnDQQySEisDKQ8a5R2ZoupZzjzzwgEHv+kTqYRZLaS6SHulR51NbUSnDiW7lWOD3Q+pdOCflfoAiNplnsqxOoqFisnmiTkZqJAJMqGDMvivImTownTlan6mOPZi0mErg3uj0EUhkHS5fna684i5A0+P8iQI4dHm4lWcqF7xSLmW9giXZzVhXBNbdKXDooEJuV/VXpFSE7FfnmpQ6uqNblydWILnM4LEFESg8gGSSWskb3Ylst0nq2Pz3VdovoAkHQnbs/oBSbHiweu6JdIJBTGXUVqhGwnow6qEzB4GV58CaT90GbJ1hO0Dn9sTQkH1vv3QGFptahi1HUk72SX/m0t15sAsZGrUTKcAIOKj2QFLNcZn/IeemdCBRJAntMQLiAkFBRrsYusMrCNVzIeVRf7RbuhyCA4+v2xk5lXK22QYw0r57EJMJBsskNYmXzKwMFw+HhX91Ls/I3Rnl+Xp6TgkW6Bu8B8h2yKD+QMFMYyV6eQSTqz+5c5m6OMnmVEl1jfJFRmpYuZbJR9fSANA0EMB1opo+ZxUw1Z1haEXv3Z52g5vsUwGSVh76GasCRQwg4vPJNGse1lSPWANJ6gCiEQx8NITssUve4tDwUSuQmLovo8cjXGj3AxQAxlWJ0qKZsVEbkj0bKgZCONi2nBpAUI9c+aDDd0oDbp3Q3BQdE9nUJ1S+cWm4e9q8USUCEqVIJNZilMgGaHiQcXucWkHP2waI9mua4ZLX66Q12aRyL3RMBCn3dn0XsImtlPo53KAAVupX90cHbwE74iPnlGFch1DF6DqSb5RE+8wQUi6ONw8YqT9TKVAqBYHbUzdeTN/Lo7+Yug8lfaZmJnZfQAHUAe/kk16eAGbRvDoZx1D0vuh6NhCry5j6aGUMbLr21Kfbv12Y1DIWJqygQgUqtYdEEJFyQAXPSKEQYNWJCr4KMADUB0qLdKDSO0W1UC1Pxc/XHbZ0Jg2NJB2udXzvvsj50rCQ/arts4KGpA9+1FcDmuG8lD2L4iirHX9PsURtH7QXAQoR/RnA3wMAM//J5e2+TL1vcLih3X3pHu8oJupEtTVUJ6Mg8Gjeiero0TEM1Qnaj8kozjKECsGAQ7s5XplUmGy+LDfXRgGHuk8YgDRu+187ORiYBVEmXJVJ+aXl3IaoFWZk19MoEDUbdGvtkIzuUE43UAGbYWUA9de7QsYBphvSJTSgBVDS35+sdy5PTZvMSwHGgKnkXLMapyHAjAyZNss5vHBUx9vNgVJefv4tM39FRJ8R0Z+Z+StX7Adm/svBhofpwxv7wvIeJEHnDx816dRJtDuuLa1OJN8DKwJGCA4ZsfHwgF3PioRtGTVULO6McXG2AUg27iAiADGQ0buyEwioMFHL4vIIYKrLUuIl+h4eAoFLtDS7IwU+xNn9kVEgtGAtOB8LMzWQ1KFbu65dHn/ncj0GKQPVx0kVYYTB0hrElTS/nRlgxO0hBSQUUEQzZwVIs2CrG9W5hb2EQvlWXpHBzN8S0RdRoQKe70fqxLyK9PHvJDF/HnF3EABjxTxAFsp0sROBSZSnLArEhuU9dOC3BQUFn97DRLs4nXuzcQFKLrMpuADAZhSKLNs8b0kpE0Ag0h5XQAA4IQ8n15NQgFNVCeooDm9quDVRBieojfakdr1kxcL1+yAESkQ6fO3FZT9Lmhn1ke8kOFTtDhkomLSgo/t5KNcLht72FEmVYhMQTeylXvQFoELh66DYpxi/TF3a+QblrYL/4Tf/cxPNO26OeSGXBk83/8Ovo3SsCUBqW67tg7YStJV1DYVh3MRPXpP9U4CpMClpIxeHyAOlKBJZRoMIUQyWvO6OuXCsPY6AyuM2muvDTEgqWJrnqWztwuYMBpCKrYgLtHEN2JpgB/L3WZMUvH0gVUO9y5PvQ/bDwQhhW/6xiqotKNiIWhrBSZrU9/ccNb0/A0Vyi1mzLxaULQrkB2b+XqcvvEx9dQMXlfPu0SxGYuuhUyuRC+Q7/VSd6LxuW/F6BBwdhPXrFUR1NCeASV23QNGqZKsQySA5bckoEw2W6XksJyYxYdMgKQAhpqxkOO9aksgrUE9SvoGP6mMKqxrZCmTKujgA5seEWpC2A4TahlEgGkLckiLA1LrarUFrO1IsQ4s6dm3PP5wJZvi3qiA5/j1ARJB5Xya2FWXynYdJyftU3JzBy9SjFkcbaoAIhpKvsd14Sbg/vg1q6V5BaGC4Mj0oBAptG2bImGDjJmqeSV53bk5RHxpC2yk1ZSIuTnEpti3htFmgCGA29EpFTNKSOlgNFGYgQYBS1tNmlnOfYCQqsRQ5H+WuYCIAqUx6L/GX7CWV3pvyMbGitgRp6zR6owJKMT27Vn0a0EOpFKVwTD24Tq77NVko+PjIUgCWnBKSnZRtju7tARpY8xezsLF9e6mg7BcA/pFyh/qX8i7jv5b3G4cvU19oeLfI1N3p2gvWg4co6TaigOhMkXhwtP1s+XD1OndGt4dRHtv2SN+vE7k5ysXZRJHk9U0DpUDjtDG2LRmQnIgbVBRMovjJSS2nokhOAM5pwwmMxIRzSSdKWV0wAUhA2sAk7lKBk8yj4fyrnI+DwEnkvPT+omCgLoFyzsSlEffGRljVskCirFdQsAOMlIv6pc5T0OmCs7OZs2oXrzH9SINbBWK1vUQM5W8A/hakf1E+w5epL7W9Mq9EZ2kXhcbuzm7MZLgtW3HWzggMVZ3IJwXrdf/dMtnl0ScMQKCWm3tTYVKBkoxrc9oYJ2pQkXQBSFYqMVDEEhNOlFVKAtUhYmLCVlTKmQkbEc6JQER4BmpsJbtBzQUSmIj7QxvVoWd5YVVTDzaeUnu3OldVbWjYAM3VcushRBSAltwabRpoO+XE7Rne2wN17IAiouxcvKFr4yj3N7FtZbr9ji3d9KQViYbAZGasXh5OZEOQNmhPQ6hTRzVNxU2C2a5QLhGJ+yPxEjVcfDqlHDcpquPhZEEiLs9pSxkolD/NX+kNs1GeVA48MeG5ujc5PTHhnLasXAg48wYiRkobzlW1bODUbpJNQIuplBsLmwuQOxGDigtTQMPiCqhRH60cvOrQ35eGjlIpw9gIlf0pw1hGCDkFIt/9dCq+e3h05FoZt6fGmMKvxLWN/u7jg3Z/QFG2pFhWLXgToN0WOjBEQdZ4P2Eh4NKkbhdwhSrjgNOpkAKXLghL3M0zIRdDEWVS3ZkSkD1tCRsKVLak1jNMHsq6hko+lROg6KAscU0TmNTbJ5iAlIBNrvIN55TblmIpIR8XClRAZQ5JmZchIz6kXJ86ZNrAYM6viomY2IhOk+8lcInMdwaVdokpJbIaVzk6QW2qSN6XoOw7teD+nW5IdwiIG4BoZB4Mk/0ZqROjehBBiE1Zdun2j9v9OCWtjuR0MMnwkDjJaUt43M5ZuQhMSEGlqJMGlPjnMPHWgALClhpQnnnL9c/AduIMF2wdVCSuUqEiPV36w4Ycg6kwaeemg0g5V1WlOIgYYECl6e9RrXdBVygAcZDv60+Gj1/EbqBIvN0NUNbcFDRIdEO81E+3R6w8dHoHHpcWuydUy+r2vALR8ZNInYxUjCgQr04A6xLlIeKiRiQgq9wdDZOqSDYBSKqq5EQJD1v5UyDJyxYoG2UQRXZmqlBJIDzTqS0X92cjxnPacKKE87bh6XwCJYCIcCbAQ4X0Q2CBNvpjftWpKLV+pmyoUpTq6IKp6nsjFZLwAIICSd4FUQIKUFXxxKM9USdnQnezYMuT2bIDW4yjXGN3A5SLbWWEZ6mdNeUj1qmKIK/LH0FF1wkAY10f5eqYjjKDSTIwORF3MHmznY06edjOFS4CkYcyTCFK5VQu7nPZ4SRAQQm+gmvsZMMJz+UEC1QyN8rBpg3YUukDDSrYylyVApV6A6K4OUaRKBeIVZ76HloQEwYSZlmXmSiO+h2hVy43Mxq4QyKpguHjW923E9l9AeUGAdmRDRXJJeagsJvmljkqC7V/8CDivl6Bivn1lU4jSqX+YQoT86dg8ridizJJeFRqBUCnUs4mfrLhiTeciHFmwnM6YTsxtlQGmIUPKLEU+d7TVm5wTEh8qjESIlQXJ48cwaWjSosKDgMLFRyhwD3yABkBBkGMRX+/Di6Ri6TNBHoxCdRqcxPc8rYPqBEZKfrVjPJUV+P2UDli41Gefr86QJC91iJIhHU0QAKVUsuTm4cCCw8i9K5OcVsimLzZzkWhNFXy0faMh+2MEzh/EmNDGQEqExzMxDYCzhB3Z8MDE55TqmB5SidsWwvqbknVVYA5cx5OPm05kZnztJMCjQ60Ko5i1YUEIi04KhD896Mh44CgXSBfLwSABotfvnEcZQ9adr8yRK5RMPcHFG1BQBZApzBGLwmrF9/K3cUuLbeLfcXhmmZfxpWzcZE4bRi4VcPEVZ1sMEPEtCU1A7bFTR5UzORxO+PNKcOjfT7jgVIFySOd8bglPNAZJzS1cipK5eR6xBnZ3TkXl+cpnfBEJzzwCYmf8bSd8FwUysYbNpwqkJ6JQQUwj8VVesIJQCojxVtxghKouE0ylFwhsCk5wW2yW3OJ3JR8rUT09yUdXzqqVzAAOmXi0yJzimAXRjJ8fC143NyVbp8O2n0DRdus4wJhQPaIHbkZsIt74Bh8wrhJLaulLKxa8duSsmo9K5QcN2kjO6mO5tSgK1kX5832jMey/EhnfLQ9F6jk9ez2ZMUiozyiVM6F/E98ylAB4ZHO+Ck9YmPGM5+qCvkIZFyfB0o5TsKEB0o401YVCvNWJ9qdi4tD6pywGgHSX0aDAZsfB+0GGbdHg8MDpEZYW3oXj6lpi89//SXsRkHa+weKGYGZK5WcFsDmBjaMewRp8rUxxfDRdXR+r5R0+RaMNbETaFenzWaV9dPWXJ0KFfNX4iUFJgKSBpTnCpJHeq4uz8kNHZ95wyOdkZjwxA84l+/mxAlPKWHbTtiYy9R61M8HtsHZU3mkG583nDZGkmeEmONXPby4PK2Mv0ZgIBG5PPq70OEWneaXa72gj4bqJjJajJvo/T6ihG7g4ni7f6A4OzIS48t1Ls5Oeb88jZ/4eiOFQkEZleaHkitour/cwcx9O2W9qhI1C9aP6EjM5E2ByH93eovHLeEjesLjdsZvtrcZKFSAQjnvZGIo+TOVL+Utn5Cw4YlPFTBPfMLP9IgnPuGpKJOfU4bcz+mh1hU7p1SeaEBASjhvhMSnOuGNyh3I9c2HyQZtNXREpGi3x4z+WC9pX6n4ZcxdFxOzUcvdfT0km+xVxGiIOXzA0zsY6fnggPIi5hUGxctdHQeNi5RRBJ66zu2zdIhumBQw6oTUulYqG9jMMxG357GAReIlj9sZH21PRaU84U0BisAlq5McoNX7nbDhkZ/xxA8VJEjFLdqArSiPRz4jlTlDCXnCW2JCouzyPG8JqcyCpeLmbHLc7OCBcg7UD4WoFOP2lBOrh5Hr+kRxGHWivx6nekIIOVtVN0s2ehTB3svBbmD3A5QrHmh0sUVqxU1yi+vttas+nRoZxl9U3WUFpdoXyHQgoTYbtoJEXJ3tnCFC+fPjAhKBycf0hEd6xhulVN7Qcw3Oajvzhic64ZEzTE546C78RMUt2oqbQ4QND3jYzm2+CrVJdFz2N1W4NPeOQd052D1XHK93bpCH/ECddNt4B7GTSHkcGum50u4HKO/Yok57aexltd6sXOQ6jV2ddvVQjanoRzW2m/nIwUTSH6hNvd+IO5AITD7enipQPqanHJQtMRQ9se2MDW9wxluccl5+GIqFypYDt+e04UxU4HZGSmTuGZJ9TtwgslGeJGcB2m67m7o9K1/OyPWZWNSRX3JSWWgvNCN2ZPcFlBvOQdFDxodjJpP8YcxEtou+XFjHKZe8zNj9xVXuTvQgaT2h7bSx+cWvIztbdm3ebM/4qPx9vD01mGzlj95m1YJzSc8uz2Md5WlAAYCf+AEfM+Etn/ATHqursyHhZ34EEvC0nczhPKcTEiWkolIeUkLaCHxuauW0cX7aWz22di8PkdyrEwRk1TkzcRQEcZTRuZ4EaXWZYb2Dfb3GWYDrHgk5snLQv553G7+HNh3hWbU9SHRp3LYtv8YDmGl3R4ZW5VED+hfe3JMDxglcg6wyt0SUysdUgrIFJm/ojI/puZThcB7KCU94Ur5rfpTBGyTakLDhLC4PbXjCqSgkmYG7dSqlvsKD27HJMbWDt6dEx5hGHXo3Pfw+cMilOaJ07snuFyhHYiq/QPxlqjp8+mD9otiJ25btZDCPGQhBUpdLRy6T1mrQtcw3yVB5MjB5g4RHYjwScHIHdq69JgF4BgA84YwznnGm7BI90anOY3nczng6n/BICc9+/9yfAGQj9WQz5dLU4eMF8/GSi+IPEcRW2lid3PYe2/0CRdvCtXLrqforqmQ6AjTJPxRL0W2qX2lAuTruMy+jB0lVBCVusmV4bEqZfFQDsTkY+/H2XGHym43xCMIjbSFQTkh4i4SfyzbP5TUXZ9pwxjM+IsJP9IgzCE/Io0E/Ux5deqJTf2dzwYU819afXznmLo4SfWkC4ZG74vK6iW+w3tERGMznsrzQe49fyF7kt5uIPieify5vEDycv9P4bpGXmLj2TizY7/BYRK2Izx/1D3cFkkqPnkzfPYIATdHkAGsJtBYXyAwTFzdHYPKIDY+04SN6yOs1jfCGqLpEj2U7b/RwM4mrlYya0jcejo4zekdQeF5rLEp9rtoV19Z7f13e4Ef35kApT7L/IzP/vqx/fiT/Re2Iy/AutnOr7XWmOsigs+g4hO+oNXZRICIT1DZw7fgnNCiImyPgOBHhASdsyJ8POOFEhMdyz00uW2IzKE+BK+sSr8mPRGg3GZ6oAc66Ou146iHL8jU/67f+Tt71NXWNXUGFl1Aon6G93OsbAL8/mP+itvcrcZMRn2vLO7vVL9veD5B2I2QdQIlrtBv/NgGBAssJlP8KTE604ZEe8EgPONFWASPukNR7U2bZbrAQEYUk8AJg9k3v49IP6y+hDo5sc6aoit3k2n1hewmgfILyIvTyhPvfHsx/tVvbwoU2e1r9yE7w0zFRNEj71MunRUkdtftq92EvAZQf3bp/d/FePgCAiL4kou+I6Lu3z//tZjv3arezc3D5pAKDpKAgy+d3OaHr1X4RewmgfIf87mIQ0ScA/u1gPgCAmb9h5t8x8+/ePPzmBXbzV2QL/Tgt6mW5WS+VS+e8I3+SUxspmJ/i2/agmm1jdb9/EfsV8vPmQCmvH/20wOIPKC88J6K/zvLfle0p+yXlv1fG5195YR33RuLJLF4gtPcK5zLywGj9MOlzeX5JWy6T0NBef/HEhLfMeELCEyc844wnPuOJn8vnOach4cycyzLhLfJdx0/lLuQzygOYyjbPvOFc9u3M7d098tdevN4flz/2X7xzH7lmBmVvcu2+sL3IPJTy6tFPmPkblfbFLP+WJvMD+h3DWqBs+QaPG9ml22OUA92/knyJxNS9IjS5nRAVkipIMmzOBS5vy1PVHpHwBOCJGflR8mVEiKi6OQmMJ054AuMJ1IBUQVLarbDa2n4tqJBpmej0yLkbnboX6JxXdfh3CYsrQlgvNrGtBFwvzp9UvGi8nMqDZG5ut4SPGu2U/uHhSFxOgU5ndHBhjl+pIKpErm751ReTJ9Ofq1Khphp4y9Pi+QFPOOENygOTyh1+b+sT2s44UX69aN4G48ycYcLAExOeeMNbPuEti0p5yGNHrB4VWZXT1l6/oZUK2lsHzbFhcj8cB1OOZ2Dp6o+zbnEZRNB5Z8rjV/3ENvXg4t1OrcveyIYqSOXDd3qoZZlpeXSbO2UENqAi/bm8WoJR3Bt5YXn+JLZuRO64Cc/pVJ9bsjHjiU/4iR9xKjfzPfEDfqoAIXxcp9PnYd6NGady7GfOX0F2c/IT73/iB/zEj/XvLZ/yQ5b4oXy2v+bqbG5fGwzri9TVuWbW7s9Cf2HXeSduyHSqi2vnKlflzgLZ9wuU98j24FItAp+k+U84gBxVQnqaeJkQykrByK87SrqJTyD/PfEJj0glTpKfZfKWH7CB8VN6DCF9LjNn82MMsiXO0HkqbtITN5XTIPKAtwUmok5EscziJ7L/9VhUWrNj2mEXBjfo47VdAy2Oy9yR3RdQLnR33pnNgOFsF0K6nm9D3Bvi6gKB8+3m5poUV0i1weqXunZMgoHJczrhvD1nkKQN29aCpxvn2axvyzLwBkAbiTmX2a4nWDl1LoB6y6cKkp/SY6hI6l/a8Mz5afjP6VRBlxQItTIRRaJVSTt+asqh/OlO7TtvpFS6Dq7T32Es5kWtXBy/qtdo3CIeUn/9E4NWnomypxC0GzNzhdBfY/omM/bbMsvU5IbfdudSUQFN63gMrh3unDZs2xnntOVno6StvQ9ny88hOVF2XZCAR/WQ00Rt6PiJzjhTfor9E53qA6sB1MdASnBXYCJw+n/TR9l14kf8nB4rZH5OD/g5PdTnzD7zlv/SVl9Z+sxbfhATb2AGzmlTrl0+VxUuEQiiL8mnXxDPODJKeIkCEXgRI0u/3W29W6LdJVDehVHpgFoRXeraTEedou1Sn6bjMSYw69uTDqQvJCZwiaXkrLyeUN5bo1yJ5wKWZ96wpVN9gJHEUiQeJc+EPVN+utqb8ujGt5zqzYTazshuzpmpuDcn/MyPeMsPBiY1bsJbViUqdiIw0cPddvjYKpd2ThpkPHhDdbHi5oQuiy0Sq5x3L1nepet0P0B5gcDqivWdVkFmUbXIcoVFpEBGEIrcnU6hiC8TPGVL4CPL1IKxGTBcO+Vz2rCd8nuF07bhmTm/dIs3PKh35yDlu3/PaMPJCVkxPNJzfdWF3NAnc0me+KGApXd5BCbi4jyV15VqdSLujjy4Wty3psAKVCpU7XkgBZXIfRkFZLt4x14HHblARzr2hRAggf4LtL1i9wOU98gqZGYuzkHYGF8ohIbLl84R/Py0kR4qy9x+tVUnzM9kze7P87aBOMNk27JCyQ+kz3f6/lxcIYHKz+kxP2mNNiSiolTyQ5K2ckeyiaEUZZLKhDUZNcpuTYbKz+kBT0lA0mIn1c2pLk7e5zpsrFSL8LTFUoJhYnOyaB8k/nvw+Tz/qlcAZALBN7iVqf9heTcy5YMDCiWAZcYWl54ZuBDdNcbSpxmExefMurrg8jAfrzSAMCaiXZlOkXBrtx6GL68ku8DCwKZcRPkdNpkFJ2KklMlA8q7SLeGcrPzbzlxfriXzPBIT0tZGX9pbAx/qA5j8e43FElN5t/FWA7QCElEmT2nD/3d+k0eD0gOe0wlvC1Dk8yx/BSrMhJRKoJYBTlt+Dak6F8bd8SrFQDrDpU9HS4fN70aEZm6PL+dB0qkqtjGTAAqSvjIapUGlgXNLN+z+gWJckLYcxyL6Dv8SNoqDaL7NvkITpCWb1gVmlbvTPpEf2lxUSvMHmpsjv/JE5xakJcaZt/J60KJQKEvop/JKUCQgcQJOORD6hFN+XCMe8Lg9t1eRcv+Q6gqTlJXKU2ojOtrNEZjUQKy6DSAx4ZyaGmnLLc2qE4zdHTUadEilBOX89zds5yWFwkrbJrZ2+525b6CMJre54WViBicax2ASo87CGhgl5LcSrgRby/7s5Ucuz26cRdd3akdUih5K1hPbwJxfkrVJcDarFaJUR0qA7OY8Exfxkj/flgDpeSOk8lN33ggnYpzThhMSEqg+syR6L4+4O6JWRJVooEQwMcpExVJSUShczkdKWoXIn4updCpArQ+UR1fmknzcSAkI/FZGeFZMvqZo334VT70vsNBDxxcNI3NxbYBYsXDsAsnoT02TclEAFS6/1odxa6DbgU2rdSSfWxvdaE9VKYCM7Gh5XdMTIXs9KigCADhDU1dGUR5SQjrlN/c98IZnKvBI+SVcJzzkB0uzPNmtf1xjvW+njs60WMmZqUIkA6XB5O05DzNrV+f5vCGlDefi6nCiAhPq1ElzC6kev5xT48pM3B1f3qfp71rbbH5K7+po5bCjjAbbu9qunIMC3CNQXshqJ0UGxuEJdKXy0K3yigLtejBKprbjIKXTqz8Ec1GFk9xqbKHtSH4jH8AnhkzH3zirCKQMGCquDgCjVPIb/YqSIa6qZKOEJ+bm8gQmLo8GSqqjOKcaeDXKRMMkqbiJwKPARGInXMCC1I5d/xl3Z0ed+M8RPAgOABFIAghFQBoGZEdxEm+u/rscMgbuDSjyY/q+z5iFUxWjYV8OwAGb1sHG1esB41RKKo9IVBPdch1WSkUgkYAtQ4VoM2/124iRzjko+7AlIGVVUl8PKm8aLDvpoZKKywOgPh5BYiMyC1aCr3VEJzmY8IZUoCKBWB87sUpMzodSJ0plaLgMh4Z3YBKqEgzSDnbuM2x1kQAAIABJREFUbj8jC0BD8v3rMqsjRzMXaMHuBijLbo1EPvW6j6dcEpjlFkfRLk7nzgzcJ606hiM/7JY1eEpSXVajOD1g0FRKDUy2sm0mKTJMNpRXWjSokFInqbzu4qG8qFxGezbakIIXcYkJVPSjCIB2h7MGicwvEYXSArANJmcPk0RGhdWTas5BO6+hOtlRDPpzmj9SJYv98molwYGrMlh/ycl1dwOUoSWgPtjDdEIf57CBWRMLCZrddYHcBDcLGdWRgd6FkTRpprTBaECoaartOkQs21TLSATaOK+nRiTaGJwAQj52TvWg8jyULRWM5P8Tn8DFP5JArbxH+JwSiMrL1DnFL9+qCsWeVf28FX2Tn6gUPc+kgaQND3fKpLg66bwVNwf5U9yeVGBS0igF6oR1DKVP7/LRp3W/HzrfpPkhYL1cOnrq07zVgKzfxqrV4+Cr1Uhkdw2UUWC2jsgcbk9BZEHBTEdxonIKeF1dp0iGiqV8iqtDhTAZLDlDj/ggZXLVAC2KKyCuY9ryYxoJQLmvR2IoiU44bUXCAGAinLYEPpNydfo3D4rJsn4inHz6u4dl9KaO5DDtwoTTVs9RjZ1ot6aO+ii4K3Wig7XD2MYoTfXBoWtyaaf39XVw/cZW1cqNoHLXQKl2i5hKYmAbt1Fh44ePufXzqQukQeBjIlB5Chy63S7uUutTUWOIR3zQ2uWiYmoHBHI0tsQbkoRNSkxF4MKlVzDlafqn4vrkN/b1KmV8inuFoh+dIDBhRnuEgYKJCcJK3CS5UZ0gGGuCq0YhaNC4nZ2oE/WVdfW0+hjaAD6X2Er85GL70IeN23wSuUL2IaI7sNSnzcZjQqWhhpUjxTJVJ1zcHmoXbHVhlNtD5T+GhQSpa8KDLHSTBHLyq3zi8iTGQimiegyVTeL+lIs/399TJq+J0iPGiRmpgETezSOT4AQmFSplr6M3E+ZTat0ePVoj9+ZIrESCrc/nNqoDBs7nrQKQEyllUoApqqS4OqFiSc6lMa5Gv2wA4SDTQUrSTB53cGv5KqjKQZq3yN2RbejAq2ojHx+bvLht2dfLIXRXQFmy0mNyJ8udyUxRVeXG8RH0znGkgtxcls5lCttRysMrFa96yC53cRjJK2qkwYfAm6yX4xeQJhW8kX1PyI0X94cISCQ3EDK2LfdCJiDRqYKFiKp60W8gnAEF8DBpD3sSRaKX9fCwKBKBh74RUOImFSacT1pTGQ0spPJGKqYuqzTT8fX3FtQNlYs5GeEp6uvM3J2jHV8X372B8DKo3A9QBm5NHcmQZQHIJfNIdp6NMnR7oDq7bk9BRtKM2pELVakUUR3V7ZF1DxHYtsWt8a4PAS1mknyQNoBKdXE20FZcqXPuzKctqxENFqrKhOopH7k9+kFIeZMWLHILADPyLFg0cCSnRDqYOHBErk3n6gS/9KE60d+fWh8CxJRpX1IPJhWoXRjWvSoeo/fHL7/vQdnyEvS/BwBm/pPL+wTAf0Z7wdfXzBy+7KvZ4IAFHAm5c6xCRI8MDSx3yPlsWlPGxz1Iwc7HVAZQkEPVbk04CiSgSoBMH2Gi4maVfVWjPpSoKLG8Y1WZcYmpyByVTZ3S4gIRUYYINqSE+j5kIvt+ZACHgaKfayJAqc83kXWZAZtQlYoGAp/zOol7k9BGeKTzJvdZOnCU5qFiXKMINC4vUjpSzl873nYVidqeXWc1YqPaQODudO1Vut/Ebg6U8vLzb5n5KyL6jIj+zMxfuWI/MPNfLmq/zq1YBEg3vJtVjLTTuT0DleIBY+5qLm2PFEuFhnNhTPuyqwo6pl0FGKN+WOeVvRMFpYeSpdEybEyJWkyFYIeUq57PaoWoDAoVNhJTVSqiTLS741/HYb8O7fa09frwJx1wrQDpVQnUHJQ5TNy6cYNiEHTKwwMEATDQlxd10sdI2rYMyPqT5Y6F+zxl03koE6Ys1V+0l1Ao38orMpj5WyL6IipUwPP9SJ0Q0ZcAvgSAjx//LicaRRJvXLs9OZbQYDADkOn02vR8lh2LYig1OAtY6ChARDEVo2B0GUYPKG55kFGfmpbJk900gUomg8RUJN4iO8BA+cUq56y8XyerkQwTKoQhNIhkpVLcT3e+bEzQQUQpkgoZNYoDlSaBVhZYaJh0oGhKBuF6+966dNdW6N6wrTtzSZbcFQ+QGxutqJErg7Iv8ebA+r6dAoWvg2KfAvgewOdE9NmgneOvIlWzQa+2lS+1XlBBVJ6Dcuh/EXU50mVd/e5XLVgPf3VlUhfQOp+0pyZ/1aCmdNik/4pCkLkgakJZHdZlGd4tN+6d7V/SdwuzGgpOapJavSfHjuL4+3PYKJEGExsrIefOUHye1PndjY+w+r3xZV07Rp1E392FnTZUJW50Z2qrs2XfZVC2gMLbvzPz31SZz5Fdm+91oQIcUS1fEdHXAL6dblC+gMHPXg48UojH6IFLMms2uwNtSLX+qkePM2ARBM7tGcxJMXEP2JmzRm3IocFco61+iZPo7ZlPsut5My2eUgO+4iNJp9xkoyWYyrktFEUn7aAoLHFxiFDWZUfLd+DiKCPT8ZO80J6yJq5NzVeQMKqkfKIAU4/Y1GFjbq5EhUkUN9EQSLaeAVDqgR+pk+jHYOYe6SFrX65zd+p56uMsffCXW/xkxAZRIzJcfAO7CCh7rxAtwPnOw6TkfSpuDhF9CuBfD24ce25PV3bFbXHAMu4LbJ63oUtVyaLKResKNBIeMvU1qOT60HDybZSOWYOyBUzYCmiAGkMBsRsBykPBtFG+iEk6eGm8cSBDRI5ZysmBRaYOvsaCoOABAYpyEWusJNc3KiupNNmsh4lan6k7o0YCYEjeKPZiysHl+bTZPBO0Mre0JWDcYJsvFZT9AsA/5kcM4l/Ku4z/Wt5v/O9FlfwI4BMAh4OzwxsFy2hP7l9kOvPUXMePt2kBEwHKlskLLa2f6CZgMDEUtS9y0crXLGpmOBzt1wUSdR0AKdDIeaqPJqAKCQFkPc0F3vVlYarfi/hq80/mJ9O+zU/BQxoq8IDss54zkmwZAxOlRNovu3vOSQCOCBDdujmAQZm6zrXcLCaye+9OPQaV59WJUxdTN12rkRca+bk5UIrb87cg/Yvy+SOAP/n8hYbz5+AmvSFk6k+rUhLe7SGqeXWYWEZ7oFQAoDov1wu6zmDV9Q1MAnjIXukyMgysyxQlZmAhozHiCqk2TONbgQqau1JdIlEnlM8pS0NEdd9B9rjr6Vft6KDCLsTNNUw2rQBCq5F6/EFwtQu+du4M1XxKKr222ep3blAwcxZBubgMr6kTjtNmMbkwfqLPrZpXot2doTqJ4ilXDiPfz8S2yPRNbiFMkDuHnjV7qQVuU+3IKxPdUJSVitnIPvp16ZeVhQpEWplU2Kg4iyaWialQOQd6f6FcIEYGC9WV/K9Ap8Y2CnR8DMW8WkT2w5y/YN3NSzGwkHWvSNSvs1ElHjAFDAYCdRutrBmyHYCinhJ1DH3n7o+vd4sumMjmHvU4hcrMRuXSTv5Buz+g7CmSMmlt+vwUDaCEWKUot6N21B3rVI4GARxgfMdTYKmgIpiArUAmdG98Od18BV9uXAd0BQ5cbho0blDJr2ABKnTYg8QuTs0ABO3EtE6s4JRamQgavXKgPn6ithcFVH26h8kQNF0bPN+eM+/qdAqmnjBXVrblJrPZkxvYHjzexxjKi5oKssb31WA+9V6rDEaLawCtJ9ayMHcge1h4F6eb6FbrqA4u2xSVMigDvQ637vK9SoqgosEGECixKQso2CBQKwKWsmETjIXq/1MH3hWW7ahjMq6NpEeqRMPEwKOHiW4rDKhGkFHnbFSuA4s5xhlAnCoCeoBcaNalK9+2g8TudHsFqktGfu4HKMGojrn7eHqfT5vkNmz7JHUyKOp4q585yzZOYqx23L2grYKK6uxaTdTmqX33UX43rExqvZSvhSX2UdRYgwWKy0Ztm3qyG0G5QjBw0auowZeJ6ZPSAaXlTyHiO7OPl7iO3sVMfBk/AjQZIh4rG7Yg6eoE52UUO6n7wYM8jtVJ137bThgTmQRof1UvSweAkQrZg0wDQu5yfip+7SSMzkXxbkvn4uhyyA14xVBVgXJ1oNMVYGp7Cio+P3R3UqlT4joVNAKVGuTVw8ho4EBTLLKLolqgzwGpna8nZeL3+Gu0HlMPkbZOVjWojiQxlKizj2ImMQzcJxbKB8cWKZgOBmnSxkHrRnd0MHZWfgC3W9j9AWU22hOkR1Px96yDiZ/oNpjX4p8U17kzBkbW9anZrk4XT/Ftqu128BJIbK0eVHpVK0V9mJEg5ebUfHVcmq7mPMx6CvvvRtKjNOv+zFSJ+fTA2YHHHmx854/bDB7vGJgPxB5WJ3DqZGY8UB+zURzvJn3ILk/4si6Jm0SzZMucFDVV1NRrP/v9zFn52Z8+6wRQaqGfPdull/Kmw6OHilYgXm0QtXXjwuhZsz6P2j7XfQjLqaFk2DxA5dc83cvMNxV8e7EZeECdBN2JfaeW2whGHX8lLbzvB/Xch/UHw8Xdw5O6TxdkVemRYuvg5fJbnmyXW3tQn9oGM2ErcHTelaM+dwOUzgaBWUA60MDd0TcMjq59BSDzy26A0Ado6y96MIws7Q5dn3Ab/X5o90e7SWYdbjtyoWrAyP4EYMlM5Qqf6gnKuuxI2ZC58C+JoehjCDsfufWBgrgAMB4mkUoZuzg8zJ+6OkZx2HUA82n2k2nyVp0FZQQeE3Vyrd0fULTy6NKD8qJiVHzE58OrFDWErB9rMHvmLKDgYyDgwWM/MXB9Wn6Q7qASlTHlZYjYtx2VreChBgviVl+rFDgok08IzPzKBummo1EHmhA4cHkeBiluI4LJMK7i2vY3/y25PBys+zjIxKKJbL4NYwUeQ3Xi7cLJbNruCijd3JJIkeh5Kp2LlP+rj0gM4iDDeSlAP3s2UCkrro/+zBdzKcGoMRgNA+O+yAiOhoovEywP88s+1GXn6tREk5Y3XOtAl12wIVQcQOT8aNg4RaB/lfdUSYWBm8xGMxgpKMXqafTZq5NcL7qxT63vjOx0D6HW56FCLigwiqe49OoGXfju5PsBindxIpcnmjm7M9GtKhG0EZ/cPoYdxCgRP4ys1/02uoAxqrpoo02xUuHWvFEqrb4D1WDZpJUEAwaBC7XCGjxAg7c5HL3jKxa4PgYc6vxImlc0kdsTwcIrFKNKELQTgckcav/ckj2Y9IAI1t0DqKeKRamTcNbtSJ2MXKYbqBPgXoBiaO6Uh1YkkxEeDyNRKeEwp8xLqZ3XqhQz2U1V79ZdLCWMj2hAYO7+sDoXWlkANk3f+2NUjzSkFIpOr/ESVm2TqgfUmbx6J3nF1Qkscnk8VKYgceuhKoHLlzq+rRlMTFoATt++tB2N6kzWbZtycps6MedlUP6wOjH7M9uhNbsPoIiNVEqgSCIFM3oNaQUBa6UwmbqvJrvFcZLjrs8QKnUbCiJ638t/zLYhoz78HBO49lR6BxINDUmrhRVgzAmNT1v/Sx/kjX6d90AidXcgcQuYhGXrfnIPFoYDRLDuXJ34fEm6e2Zsdw45VhwTJWPX23aO2v0AxQdFfRBWgq8aMGZYWQGG839GpdQ6pVP7BzDBuTbyrJCXhkqBQc1z8RL4NG7rDKVQ5PAFMlXvqz/0eR422m4RQwFieJi8ACImL1g35ZQbRLKOvuzFMFEguNjVceehuT1sYycmMKs6Prs0qTuKkeypkw972NiexAqOsg6gUyOjYWVT16S3Z4CEmyddDkY5RB3JuD/lAuPTCD4LSmVSNsrTAIECTN1dtX9dLEXy9OlQcJH1GQgOm4aCbitIn0JmNLEtaPOdwgRtfXb8USDWm1UxDhbAMXUyW7/A7gQoxVZVShBj0WV3Z89Kz/QjPuTKoEElVDECIHLtwub52Mo1UNELemi5blqOw8MDDiyqcZOvG4Q7J277nQXX65LbYzpkS1t2gdCnR4C6GUyAHh5qsVMnHibdOeL+nMDDk4M63APHqxMfpE0q/4N2eSoYOD/3FOiHkPW6mq9SARLNnlUBWq1SdJ3I9QEAFql6dChZOi64PorxqFKphdRfBYXMmvWnxrk5Zm6JdnlUmbZB9QlYV8jlLZm7VjtlImkrUNHLen2UPoCDVjnDp67twSSCQ1RWwcQomFqe+2FiHUNRw8TtnHIPCCBOi9bdk+EusfsBCtBDA+gnukUukQ+yqniJ7wjikkDwEgz1mruRo47E+1CpbU0VyhgqmJSXtsXNqXNWSlotryr5ER2GKu8aN4FYrb70KQjOa2geIL4tDtIjkEg+q68kgsUEJiZugbhcCBPABEdHQVkDtu486G2y3Q/o+n0Dw3t2ooCrtmiafdTWAXuJZ8ruvhmwPHf2TwD+OXgJ2JpF8ZBQpbj0kuYBMxpGNi9Yr36CarP80oSPi6xtDKBCbt9Ux70YKgIE6vNB7Vox4FDl9D4b2Ch4klrWlfwQ+simsZcZYAK4dMCIymlwAM4t6fN34QN0CsTsn1ci0fHvjepMHk8wfN7J4HEE3SMew7hLsKPvkcszfDNgedL9H5n590T0ZyL6XL9+Y2hq5CZDIV+9ozcJRrNqPYDCYWQdoHV5/hGOJq4ymUULVbaqkWDkJ2+/deAZVEpRALYcXB0wzHNqu7oKLCOIRArFbFy3dcRc+dV4iodF3Y0RZFznHsGmKQO3Lf/py8xGdBCkLYzq+PNT2x4NE3vbc3H23KALVcrNX/QlRkSfF3h4+wzt5V/fAPj9cqOjE6ClmyJw/XI8kT3h/Zelg1Jsv2QbpOP5xevzy755n5sYoBIMo4T+lQ+lbP7jUlbq5eOXfJ2un6mKoF350/WHf2fVztmmm/XVP19n1H7wV8vp40jozwe7euqc9+eD7XcSfQf1OuH6ne4ND4/iJuH14K8z6DZdZ6/73PpAF3T1imXkBvnYyUy17NhLAWX2ZsBPUNyh8gT830YNENGXRPQdEX339vzfAsL2xDU28il3yhg5XNPdL0dJq3VkWf/y+ItMtxlAReePfhW7X1NXbrRMOt11tihfdyjzdDPdiVV6rZda/fAvKKPBN9xecvuG/WObnoNumbuyUX0/CjOCibZImUTfdb5+JE2+22h73G1jaZh45gYF+e/0Xp7ZmwMX3gz4o6v3AwIrLxP7BgD+w0f/E6sM2Ym63gVhVX40VZ8Ak9Y9rS3BzBnxcZluKJmVe+OGtqUNE6R1daKYSnWN0D4Bn8YljayLUwKsXLYvMZUofurbrS6PSiS3A90wsm7Ib2BkQZkuJqGWya/rskHnDJfd+iz4asvBdm4FuRA0E8CM63D77Or09+v4OSfTYWLVjm93un6B3fzNgQtvBvwOWcH8UAK4/3ZgwwYkXSzFzz/JO5E/E9SQ8XwGrb6V1z8uEqWeHkrOteK7knMbPVR8nXrBbACoPD1Nl+cGhR4UQh+qIBmBpe6QHLLAQefpT3c6a5bLj+oMLbpuffsuvYPNCkSkHNv1bl5Hl+/T+nkmkTIZxkyA4V3EeR84HCLu4iba1ZF1qa+/IB8fmblBMu9Et1mn3kfSZ24vEZQN3wwobw5k5u+LO/MJgD+gqJBdk1/+DhRcOmEADiBWMMF8lVqm9EY94a0qFR2kFaXSBW5hoWICrNFMWzcZDoPymKuVnD8I2gp8VDsaULosdJmgnFEqrs6SMhltJ2hjpFh6dzReNmm68w4AUrd5FCYYlB/AxBy/d6VNGx4KDiYROHx8xIHGmHdrTFvHYQK8zJsDwzcDypsDy/I3RPTJ3juSVe384WfKOjiEz0sZuT5B+W49oR9K5tJxu7QCHa12/BPzyz6ZxxuM3B8HFWnSD7D0gJEn/Vtw5OPDGCyq8b1h4m5SW7eyYAF8PCh8OQ+LJZDUZbbpQ4DYjj+MdUUuTQQYNxPWbpPDuIk5J6lP21ufuTphnoHOBb8Kyn6xiW0FPAcqJNTxz9wA7DAyYB+spPKBXsEgLl/jKQUOApXm+gCQteL6AKjd3gNAoAJGez+w1hEJpZMrqJxL2iad3rlACgzG9ZGOT5VGOdYDWa6HJYfRPj2p9CdgoBjehH0DoITwUOkzoMhnX4Zt+clypDIA2HiJyx+mVbcBPWQmMDHtaZhInZHrMlIsvryYnmIvZety6qG1aPc1UxawLo53X/T6zPW5BCoSpDVuSVM9Zo5KoFQgUEGsZkI1ImoFg/y2K1M3yIBF5aGWQahkwjRXtp37qNFJvi7q8yKwzNJCSPQdenc5UiWz/Blgum04MNRj4f7cjGAido2ro2MkvuyV6gS4N6CYt4k7mKgYSxczAWBcn9ns2tE6C2wsDGJXSikO6d2zmIpLM6M8gQsENLWSl9Et9+7NBCylrIZGrTcACekNRrZybQZlQrdHp0cQMevc5y8tB6M4sjyCyQgw7h4dCxzpvA4mUdzEnYM9cITujB8F0nnadCD2CsDcD1Bqx05A2losRQNj4W7kkVtEQAODrEvAle3UfB+kjabnH4UKoNWFhYZc3NUFGtQLl2dgCQCCWk6ft4FScRVXH9rWKZKgrRFYLgZJyYuX4yHh1k58o5/ezi5MtO3AxM838TBYGtVR1rk6g3ImEPtBP1NWnfjh6I7k+buRtXsjNnCLvNoI56esQgUxMGpMBROAVAiUuqVDd2BRsZVaRurqZdVmK1eJZs+JnE4NB2lLrXdfkS+zY2FZnxYBZgCQWmYIHL/MffpRF0eX9TGTqP1BnEOfCx+EPRQ32ctLo3IOMle4PvcBFMCqD+/6AIhiKuEdxmV55BatBmkNyBR09MS3vA9AGFMBzL0/OWvgAqHBBoQwtiJlZBORYqkwceu5Lpektt/DmIlpFK18XUFss+vUM5/jvFCJ7K13eWP3ptXZgYkuGwRg+237Du7344IgrLa9mMrucjBM7LexYPcDFLFOpQTAUOvhhLfJLNphGwFUWufPPawOJ7s5Ktr9AVDBYCbADcpl8KFAUMVNBm4Q6p6UcqUhf/cxdL5Kq8oFDS45XRV2bXZ24DrcUyr21zyotwAWHxidqpJSburi6H24RJlcABNjM8gM1c0AJIkbTGYxlkW7H6AIdb1K8aM+QCtn4INwKHkaTwEQzqQFoB/KlFMbVFDq08ao8YpaxnZ4PazcZsLacs1dKZ2dBm5QKccoF6suV9tAA4NxeaI03XtUOtBiMDew7r4S2G1FamVl9GcECOAASEbpCiR1W1053/Fdez5m4uvpuqXekmKJhoh9/cjVkbIjFbRg9wMUMQOQwaiPho92b4Kh5ClUVJ26rjrkSkylG1JWagMo11hRWnVkpxxqpGradpwS2VEstQ3TfrNZmmTY551wUOgCC67ZYUBW53lolDS7zq1MAJKWp8rpdkK1MdheBBM9woKgnN4fXU/23cNEbBSEjVyd6An23tXZUzEH7L6A4qGx5/qYd+hwGDMZqpigjoEKBvuiYiojqOTaug66uAoQq5WaHoEJ6OIrcG2YsopeUVoPEZWHuMwRWwnMjmMpNs27Nb5MCJJSPo67DGASxUtWYMK+3P49Ou24J8AI6gyHiCPV4td93YN2P0AZAmSiUtSoj39imymjYSHpgFMvCKFS7/mRGIeKqXio5LZhlMYwriIhG1h46PRcr4eFVivSbFS2bleV0WlAAJEAIBQ1MrLJtdoBZgSXECw8LuOHgX35VcjMYFLLuY4tbTiYtGNke5wLLs0QGCNXR5cxqmXnfp0P1+VxJ9WDQs9NGakPbiHG6t6I+SAtMJhJ69opGoJKnSimAgB1mj64vNVP0l0nl86aSoltIYZS8mo7nPOZUKfw533THT8v2GfDUpDmTj+Z6ur82XLLFpRfhwoHaWW9cyNsnV1F4vNWVQkwvDeni5nI/ui6XtmspEcw8a5OpFB0IHav7AG7E6AgVh9+OXJ95MsIg7SqbaDBY0GpRI88CGMqpfN3I0A1vSkQPUNWq5W6mSCGInm1T09coXoqnXLJ5SyQpPKuy6M2cvXENr3DUdkJRIDeranlfD0NC9VuGJBdgEm1YCTHH8MyTPQxj2CitmvLTwCxMqpTyx6/4/h+gCK25/qM7vWZTc0fBmkxhUoUUzkClVyrj6tUqKj91mmRCzPLK3tXzbtEup6uq+urzCE4TOcPYi17FsdUAoio9rwa6ctxV29JsQxGcdqypEvn24EJT+7PCd0kjtN1+RFsXJsGJlFaCKnjMAHuBSiMfIDb1kABWNcHQOmp8VCynpovMPDujdgKVEo97/4AaNP0IZ29dXc9rAygm1kLVrNfpcUzo4RkqhtUyyMDYDxMzL1rI2XOriHAuUYwF9nQ5ZF2te0BZCCpd12eACCmXqAKLlUkvs6Si9OVlWuiLV/k5kjazM2R/Q9dIknbGdVhbjC5wO25D6BoG7k7NX8lSKtiJn44eebm6PRI1Uiv5z5YC8gvf4ur5N21j0AIh4aFVZEbVFscq5LQtQkCs0DsGtW8tvu9FXDt2e7clRlAXP5KPCUqNxwhGrg3tUwtH3XoVn42kmPqL7gzI8USzoQdqg0Fky5tUOcCmAD3BhRRKUADhHwpXYyEx0FapWDC6fmrUBnFVAKodGDTnbPEc9qMXKc+vNuihph1+pK748rocl1ZFdSt+ZPHml/r8gBzgHTbmKgRk34AJDV9WGcAk5GLo7Zv6kcKRJfduUen1ttVGw4mJi3absKlMAHuCSgVBs71iaAiZ3w28uOh4uGwBxWgc5us+1OW9AgQ5/aMC8ScGzojzz7VagXODar1izmwTN0dCsqglQN8ugJkyQOUm6RtQZmENrhuL4mlmPSJYukgUvL24RMAQMPD13cuTq03c1f2FMsIQkdGdGpaUEfHTX4VCiX8pVdpWpWsKBXVzlhxTPI5fmhTTWNArqahC6TUio7PhG4Q+fpoxwi04G0L5xxTJPpUu95uoORNtnnA5iM9wbbd9sK8iWIxaZM4SV3XEACGE9XC+gsw8fu8q1iGKifo5b+ZAAAOlklEQVQCiGyHe5jsBWGvUCfAPQHFqJGiUiLADEd+AhA5V2nk3qxAJW+u5RmoDFwgHStBVSQ6rjN2g/L63BXSeSNYrMAlqudtCpyuoflFuzwXxbU1BYlTJCbvqHsT1glcHA5UyEiZ1GOYqI3RVPxQbQwAE9XxMInKL9pLvNv4c9i3Af6oX0u68u7j3oID01DJDQ8UTBCk3VU16Nwb2UY3+a1rD7tQAWBHgcTtUMPLQAOUXERareT1OVgAdHEW4DhconqRzYBT29grEuT3gJlDxKRfCRKzruHh27gGJqPRHFe3Hcee2pC0YERn5BZ5e18esFTeU/w3AChvDfz3oNjw3cdDM8PDgImn5A1b5QH0M2klrWsbZjgZwH5Mxbk5AGxdYBhXATCZXdtaInCNrQAwdy+b7UmbohIYzQVxQ86yC/GzYgu4yHVUF08RG07BP2jDepe4PgFATP7ULZqAxENsApJaN2pvAIrlmEnk5kTKZDSiU49Zyqdgn8p1cMGrNF7s3cbF/oGZv48yJu8+lvz2KtL0U19gdkJCOSiB2igv+JKABib/xTF3F5/+Uk2eLx/9stUy6mJlNhenDwq2qd1o9RC0Jdvkcuzlj3Q990fuTx+3PQd92cN/KW47an+2n/XY9PEiOAb058Wc39SfX11vCBPf1iJMuvK3hMlu+TEwLoEJ8IJAIaI/oyiVwGbvPgYAMPM3zPw7Zv7dG/o4J0Ynp1Xo07ryCio75X0njr7wIVQGecML1W3DwgH2Vy/hIrCYDinHGsBlBTB7oDnyN4PNLujUMQxBMzkPuyDx34mGUtLHr74fqdO16a6fWSxFXZO7MROxCCbT8uO4yaUwAV7g3cZq/T8y81e+0MK7j0NjTiAdYGVWLo4L0poTB1d+EFPR5YF+SBnoZ9QCsYsU5an61g0qaee8vRpb4bIuVyu3/dHDzADqiJC4Q96Nse6NjD6hc4vMfpsXqqlFXa4/HVdb2Kb3593qbpCWddnWobu0CCJ6febe6PQZLPZcnFGZ0Y+pUSGDmElXfiEI+y5jKHtv/CuB1zDQuvDu48l2B1ABYqiMJr75u5N9+WjIWI28DMtUcKB9SZP6egSnD9qWdYmvuMBtrpIX9HZNABet6XoOV4OwgwtKjyC9iEXbnQEEiCHi6tl5Gy5tBBKdtgKTblLeBBQrZY7CpB7fvvIZwYQ5XQwT4OWGjTtQyLuNMXj38a4ViIRQyRsYQ0XVn6ZNIBRCQba7Vwaw81WAwZwVAChtyY+IGg3KuXq70vYYLLlOg1YdIRJA1f2zoBheUldcbEsWNB+qlgshYtIdSExbF6iSMD1SLZK+ApwlOOzETMw2FoOwuv0D9iJAKYHY713aF+UzfPfxko2gkhseQwWAvzmwfnt7oz8qb+TCaJuVMUpBjwQpyDEEUKVOMMwsx9vcj+L6BO4QYF0iAPZ5sMEIT25LH9S++3OpHZngFpY/AhBdfgUiutwVIBnm75WJYn2dalmImWiY+DIeJnqbF9j9TWwLoQKrMFYmvmn3Z+RGDep09/+ILaqVXTfIKxb0YIGCwky1AApegHWLzHZgFEyt65QMTPEbuT+TC3h/kptL2AOJ2p4HCbCgSHTeDBahIlpQJdfAZFpHlZ3BRNsH+zwUfXLUr2WFis6LoAK4vAWo7NSZxUzqBQv0bs5ePpRocJPigAAsmLtDOT+GCzmFxQEgRsiYgeaozVVKVD5WIl1eABGzvRlIVP2bqpKVcqOpDTovgsmwTqBiRjCJ1MwBuw+gABYQEt+oeR4QDipAkLcDlYU6eyoEzBYOeiLcMB99+9KsCsyahyTV8iUNfj9afRNbSRYXHWC8gtFl4+TLbbSdCFqrEAFuAxKd/5Iw8VA4CpOwzmBER9sIJhf8YNwPUIAeKgB4mwwne6hoE0AAdkatdqPCfUCrAxczGUClKwd08ZcuH9zcEx1fQdmGxDrKcDPA7dGOjFoHrGItOh0q5iLmYy+6d/rzEVxr5iX0AwsBEdngB7KrvwIQnz6BiNnGqPPrvFurksg9MvmLQ8MAukcRqHq7yuRC9Xk/QBkBIvE6VHQ60DqXicMMYioraiVygWQ7M1UTgSdQPp0rJImdO2S3b4eH/YXiVEpACuOWjWw7AAtgvz0M2psAJNeJ88JAq2pvpkZMfvRLH43gRJ9HYFLb1u0ehIm2C2DCH2wMRUz9WptlANOJb7NALdC3eQ1URrBwUAECtTItgz5vByyAg4se3QH6OMjAxYkgY76WFeAEtgugKDuoM4IIsA8Ssx8rIAnKDcvsQWfk4vh8P3N1FSYjcEV2A5gAdwQUTglU3Z1ysKJUSkxFyEujSWs+UAu0fOfKLA0rq2JHhpbrphfKjlwhwLpDMku2rkj96hLldPNgatZ5aBeT91wqtGKX5pAyWbFBe3vzUYCDAPFlVlybqNwIKDMw7ULBweQaN2c1AHslTIA7AgqgoBKZDqbq9RX35+gI0FG1AnQjPIcUCwJXCAhn5AKwozVOhZALxLKHmFMxtZxXMy9sy3cg+2vf7+O1INHLK8BZKftLwiQ6PrXOv44YSnDwERxms2lfGipAG30aQSAARbURhFz5I2DJZ24MFz1aBKCLvdh965Mjm012O3zvT+TeRD+eAyWStxl3nPF8lTFITNmZOrkkVtK5QA4Ol8ZM4GDiJ65Fz5C94ofjToCC2nmN6/O+QAVo7kAdOdqJrUgd184sKBuVA2CHf90bEWeT2Ppf+5gGnYqJrBz/MjQWLtoQHlHdVYgAtwOJXl4pvzKFHkAXL1mpu3rn8M7Etc7VueA2i/sAihyXkmWkYyE+NjKLqYgJVAB07/sRW42rLNTtYyE4Fl+ZlB/CZRRvKVndMC8zEDDFxmFGdvmvWt/UpK0j8AC6YPFufETVWXJt9sqvPHLjGhcnTC/95GjMxG/3ArsPoABdjKSLpwTDyWFMBYjBInUvVSvadmIrwI4C2VMiI9fElx+5RWVbvjPOJrLdFBgrNthcPJR8AUT88p5yOapgZjNXwzIXujhHYeL3aWYXPBflfoACdJ3zIvcHsKDpfrn5OFSkzVldwCia2bBw5OKEMRZdb1C+HpZ3ZwZvS/TW7lnqsnrbEzG10cVyWAQIMIeIr3OpCzRTJTMYRG2MhoSj+pfCJDoWFzMZqpMLH7J0P0AZxDCW3B8AvBX3x8+ErcPGyv3xHVts5ALN1Mq0fuDa7MQrvOsydIlcua6vu1mxtZe7QbTaYXZdntbE1bZyDpXtuj0TBbPkAq0oEuCYewMcd3GA27s5khbsF3+oMZR6WHtQARoc/D08R4K1QIur6DZmagVQsZVB0LZTLIErtHPD4UiFLCsXsZHLE/0wTVysF7XBj+SSalmFiC87gsqKIonqh8AJhmaPqhKT937ABLgToAD5AGkbj7aEMRUgjKvsQqVuNIBBBJVaxrtBiOtLWtDGtWABIrj0MFkBTNjWyEYT/0a2qKiHk+ZWoHJJLEWv7ymZCCR6+Ygqiep5IIT7eAwmYRtu3y6FCXAvQKmdLIAKUO/DEfKSDrD6gKt8AZuPq7htHnGBTH3nBkVt77YxGOVRozYGfjvuzW78JGijtrXq8kSvKL3GZoooyjsSQ/HrRikM2pipidHyLUFy1MXR9b0y6Vysth0O0o7YfQAFqBDpoFLzgwtfuzH+Ph60L2PZBZL2I0UzcoNmz1nRFrlCWBy1idrTTXenMoDDZFJbrrT4q7UHnqOu06j8LWIpl4JEp+9CJ4DCUtD2AhdH2wVDw9fCBDguVEMjon8qD6aW9c+J6J/LqzSi8tP8oXlJNnjXDqcUnMDxCR1SnnlcPywTpOm29y4k3U7QFrF7PUeCLRO1FeRLO2F7ul1fN/rzdqT8XtnRvql4Rncc0baicxOcx7Cdyfcx7OyJ8/euVQlzfA1E7V0Kk0H9KUwGfYoTX+T6XA2UAoXP1PqnAP7IzL8v65+78tP8XVuBSi26AJUV6RjVjzqxa9NAJWp/dFFdAhYPF7+fwDBtCTCXAmcVLgvb2gXIKG0GKH8+V0Hil03ZFLcV1TVtpPiHaw8mpswOTLRNYHKpXe3yMPNXRPT3KukzAF+X5W8A/BPsC7/28uPtlIPU7s40pgL0w8ojF0YFawHkmbWune4Lm8VWorknuXL5UIkrSN+Js4gN4y1A21fspKEfmg6txExWHqo0suW7lGflfF5U9kh8ZS/QOio/emL88gjQbVVJ3qXjMZP3MYZS38nDzD8S0W8P5gMAysvE5IViP3+b/sv/CSD0ne/c/gcA//WX3okXtNfju2/7X44U3gXK4lsCtf3o1n84mA8AKC8T+6bsw3fM/Lu9fb1H+5CPDXg9vns3IvruSPldoOy9JTCw75Bf9PVDCdT+28H8V3u1V7tTu1VQ9ncA/hMR/UN5ydenBRZ/QFMZfwWAUf6rvdqr3b8RrwbGjjZM9El5S+BF+a7slxcopbuwD/nYgNfju3c7enwvBpRXe7VX+/XZTSa2vdqrvdqrAa9AebUXtItnRL/aL2ZHZ717uwugXHuQr/bu7eoZ0e+xEdEnRPTXcl3+UznWu7ejs94je++BcouDvAf7AC9SPyP697/gvryE/cDMfyl/4VyqezNm/gp5WofY4e/wvQfKLQ7yjuxDukjNjGgA4Yzoe7ailO8d/DM7/B2+90AJ7IO+UD+gi3RpRvQd26cAvgfwORF9tlf4Tu3wd/iLPw/lBab237N9iqy+Piei75n52196h66wD3ZGdPkh+6KsfkVEXwO45+9qZIe/w18cKC8wtf+9tRk8P7SLlJm/J6IvP8QZ0UT0qbikRU3+6y+8SzcxN+v9/7jkO3zvJ7aVg/zj/9+uHZwADINQGH4jdLjukhm6SqbswRByaKEBD2r/bwNBHyEqG65ZpKQuK7J/vbiN7KFJz/F/lNrORXQWY8Au2Wv5kNSq1bjaumqPHihvqjXq35oUNaUNFADxZNzyAAiKQAHghkAB4IZAAeCGQAHghkAB4OYG4YOe5OgUAPsAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 288x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"u0 = np.linspace(-10, 10, 500)\n",
"y0 = np_log_jac(u0, 0.0)\n",
"U, V = np.meshgrid(u0, u0, indexing=\"ij\")\n",
"\n",
"plt.plot(u0, y0)\n",
"\n",
"plt.figure()\n",
"plt.plot(u0[1:-1], (y0[2:] - y0[:-2]) / (u0[2] - u0[0]))\n",
"\n",
"plt.figure(figsize=(4, 4))\n",
"plt.pcolor(u0, u0, np_log_jac(U, V));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These samples are non-uniform in $x, y$, but we can use the Jacobian to correct for that (note that the distribution is uniform in $x^2 + y^2$ not $\\sqrt{x^2 + y^2}$):"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"u, v = np.random.uniform(-10, 10, (2, 500000))\n",
"r, theta = np_transform(u, v)\n",
"log_jac = np_log_jac(u, v)\n",
"\n",
"plt.plot(r, theta, \".\")\n",
"\n",
"plt.figure()\n",
"plt.hist(r, 50, histtype=\"step\", weights=np.exp(log_jac), density=True)\n",
"plt.ylabel(\"p(e)\")\n",
"plt.xlabel(\"e\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now here's how you might implement this in PyMC3:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"INFO:pymc3:Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"INFO:pymc3:Initializing NUTS using jitter+adapt_diag...\n",
"Multiprocess sampling (2 chains in 2 jobs)\n",
"INFO:pymc3:Multiprocess sampling (2 chains in 2 jobs)\n",
"NUTS: [v, u]\n",
"INFO:pymc3:NUTS: [v, u]\n",
"Sampling 2 chains, 0 divergences: 100%|██████████| 120000/120000 [01:29<00:00, 1347.92draws/s]\n",
"The acceptance probability does not match the target. It is 0.6450403441286882, but should be close to 0.8. Try to increase the number of tuning steps.\n",
"WARNING:pymc3:The acceptance probability does not match the target. It is 0.6450403441286882, but should be close to 0.8. Try to increase the number of tuning steps.\n"
]
}
],
"source": [
"import pymc3 as pm\n",
"\n",
"with pm.Model():\n",
" \n",
" u = pm.Flat(\"u\", testval=0.01)\n",
" v = pm.Flat(\"v\", testval=0.01)\n",
"\n",
" r, theta = tt_transform(u, v)\n",
" pm.Deterministic(\"r\", r)\n",
" pm.Deterministic(\"theta\", theta)\n",
" \n",
" pm.Potential(\"jac\", tt_log_jac(u, v))\n",
" \n",
" trace = pm.sample(tune=10000, draws=50000)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>mean</th>\n",
" <th>sd</th>\n",
" <th>hpd_3%</th>\n",
" <th>hpd_97%</th>\n",
" <th>mcse_mean</th>\n",
" <th>mcse_sd</th>\n",
" <th>ess_mean</th>\n",
" <th>ess_sd</th>\n",
" <th>ess_bulk</th>\n",
" <th>ess_tail</th>\n",
" <th>r_hat</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>u</th>\n",
" <td>-0.516</td>\n",
" <td>90.479</td>\n",
" <td>-14.099</td>\n",
" <td>13.812</td>\n",
" <td>0.932</td>\n",
" <td>0.659</td>\n",
" <td>9429.0</td>\n",
" <td>9429.0</td>\n",
" <td>59617.0</td>\n",
" <td>13161.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>v</th>\n",
" <td>0.495</td>\n",
" <td>75.024</td>\n",
" <td>-13.304</td>\n",
" <td>14.513</td>\n",
" <td>0.817</td>\n",
" <td>0.641</td>\n",
" <td>8439.0</td>\n",
" <td>6852.0</td>\n",
" <td>43720.0</td>\n",
" <td>12517.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>r</th>\n",
" <td>0.507</td>\n",
" <td>0.290</td>\n",
" <td>0.057</td>\n",
" <td>0.995</td>\n",
" <td>0.003</td>\n",
" <td>0.002</td>\n",
" <td>8515.0</td>\n",
" <td>6942.0</td>\n",
" <td>7152.0</td>\n",
" <td>5531.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>theta</th>\n",
" <td>-0.008</td>\n",
" <td>1.812</td>\n",
" <td>-3.052</td>\n",
" <td>2.839</td>\n",
" <td>0.008</td>\n",
" <td>0.006</td>\n",
" <td>47475.0</td>\n",
" <td>47475.0</td>\n",
" <td>49760.0</td>\n",
" <td>55024.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" mean sd hpd_3% hpd_97% mcse_mean mcse_sd ess_mean ess_sd \\\n",
"u -0.516 90.479 -14.099 13.812 0.932 0.659 9429.0 9429.0 \n",
"v 0.495 75.024 -13.304 14.513 0.817 0.641 8439.0 6852.0 \n",
"r 0.507 0.290 0.057 0.995 0.003 0.002 8515.0 6942.0 \n",
"theta -0.008 1.812 -3.052 2.839 0.008 0.006 47475.0 47475.0 \n",
"\n",
" ess_bulk ess_tail r_hat \n",
"u 59617.0 13161.0 1.0 \n",
"v 43720.0 12517.0 1.0 \n",
"r 7152.0 5531.0 1.0 \n",
"theta 49760.0 55024.0 1.0 "
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm.summary(trace)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That gives us what we want, I think:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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jtVeK2eZpVv3zaFz4AwBma8ywDwBgfoQ/AARE+ANAQIQ/AARE+ANAQIQ/sKR0p8XTtLgKqBXCH1hCWojTTndMvR1kpSkahPAHljO6h9Bo1XQT7qmDQJp0YzegSh9L6jXkZnkIiBW+wBLSMM+7Gt4mu63h305owp1iEQThDzyDNNnbJ/hRN4Q/AATEhC8ABET4A0BAhD8ABET4A0BAhD8ABET4A0BAhD8ABPR/CKDtYMLz304AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.hist(trace[\"r\"], 50, histtype=\"step\", density=True)\n",
"\n",
"plt.ylabel(\"p(e)\")\n",
"plt.xlabel(\"e\")\n",
"plt.axhline(1.0, color=\"k\", lw=0.5);"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.hist(trace[\"theta\"], 50, histtype=\"step\", density=True)\n",
"plt.ylabel(\"p($\\omega$)\")\n",
"plt.xlabel(\"$\\omega$\")\n",
"plt.axhline(1.0 / (2 * np.pi), color=\"k\", lw=0.5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And this is the distribution in $u$ and $v$:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 396x396 with 4 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import corner\n",
"corner.corner(np.vstack((trace[\"u\"], trace[\"v\"])).T, labels=[\"u\", \"v\"], range=[(-20, 20), (-20, 20)]);"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 1000)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(trace[\"r\"])\n",
"plt.xlim(0, 1000)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.7"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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