{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be16a389",
   "metadata": {},
   "source": [
    "# Overleaf\n",
    "\n",
    "Reimplementation of diagrams from https://www.overleaf.com/learn/latex/Feynman_diagrams"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "873be78f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfeyn2.feynmandiagram import FeynmanDiagram, Leg, Propagator, Vertex\n",
    "from pyfeyn2.render.all import AllRender\n",
    "from pyfeyn2.auto.position import feynman_adjust_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0a179236",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 4242f76 'PDF' (315x157)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: fb52e06 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<wand.image.Image: 1da18da 'PDF' (171x83)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: c3c393c 'PDF' (494x251)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mpl:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ascii:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "*                                      *\n",
      " ->                                 >-- \n",
      "   -- e+                           -    \n",
      "     --                      +  ---     \n",
      "       >-                      >        \n",
      "         *~~~~~~~~~~~~~~~~~~~*-         \n",
      "       >-                      >        \n",
      "     --                         ----    \n",
      "e- --                              -    \n",
      " ->                                 >-- \n",
      "*                                      *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 8e11a76 'PDF' (332x332)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicode:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "*                                      *\n",
      " ↘↘                                 ↗↗↗ \n",
      "   ↘↘ e^                       +   ↗    \n",
      "     ↘↘ +                    μ^ ↗↗↗     \n",
      "       ↘↘                      ↗        \n",
      "         *~~~~~~~~~~~~~~~~~~~*↘         \n",
      "       ↗↗                      ↘        \n",
      "  -  ↗↗                         ↘↘↘μ^   \n",
      "e^ ↗↗                              ↘ -  \n",
      " ↗↗                                 ↘↘↘ \n",
      "*                                      *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: e118d56 'PDF' (477x176)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-1, 0)\n",
    "v2 = Vertex().with_xy(1, 0)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1, v2).with_type(\"photon\").put_style('opacity',0.2).put_style('color','red').with_momentum(\"$k$\"),\n",
    "    Leg().with_target(v1).with_xy(-2, 1).with_type(\"fermion\").with_incoming().with_label(\"$e^+$\").put_style('opacity',0.2),\n",
    "    Leg().with_target(v1).with_xy(-2, -1).with_type(\"fermion\").with_incoming().with_label(\"$e^-$\").put_style('opacity',0.2),\n",
    "    Leg().with_target(v2).with_xy(2, 1).with_type(\"fermion\").with_outgoing().with_label(\"$\\\\mu^+$\").put_style('opacity',0.2),\n",
    "    Leg().with_target(v2).with_xy(2, -1).with_type(\"fermion\").with_outgoing().with_label(\"$\\\\mu^-$\").put_style('opacity',0.9),\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6446cf50",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: a932de6 'PDF' (329x157)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": 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jqhjajdlQmQXP+J2XXkW853yqqMD8yff8yg8871TSVeTJrpj/qpMfH8Lxdbyq1Cf+78N8xcf8xDOviz/kgzd8+4rfeM4vvOhQ0rt8wl88irbvJnYjIqdl6xs5nPTRlhWNdy89IWKwGd/RCwJmFe4cvaYJD81YExhuDtbRlFhWAdfXzKilJjRDrRmyo7cMau00M0T2XA3M0TQMaAhuOTwuQHnKP7qjw2RQzapIkhiTUpAMKtoVRRLj0YkoPEO0LB6dgcmgY1sESYxFZXAy6FgXQRLjEBmkDDoWqktiHBoDlUHHRmVJjEFhsDIY08oYFAYsg46dqpKob/6gZdCxVFUStY0fvAw61ipKorbpCcigY6+aJOqanYQMxrFY1+wXJCGDjs1KkqiYMzQ/8pjv7EeRcnJSVmdsQT6XqLaAxnzDY+BTVa8owO6ZkjEBk5mZ4FsMFG9Am+oTeFlj+ZIWwc33GmZmrA+nScTPb2Dw2d2p2GomTTdHyzAL2z9zvhB6d4Gmm6OubRNjcLqSSuiuFBXDw5uk/kW8lZqSuDlZKi/0ZAZBR5+4OdF3w9k9147lhcz+SDFH33Nzqi36vqtF2rRciy5PtgFt0n1s94mrh+Vou+R9pw0n8EyD/2Fz7OprmSIlFTvnD/4+fEgwtDth818EJRDiyQ7BG97hCVP27G2SUngMu+f6cI8+kShOrgXcTTGSp/e0uwdZfYvlhUA5giYlkhvszOtnLF8MxtHp5AY7M8t4xcvQdJyUMUnlBjuzE8glSpmSWG6wM7/gXKKMGcnlBuMzlDHjQmXQ4RiYS5Qw4WJl0GEZuLwm3ICLlkGHaZAkhld/4TLocA2QxNCqL14GpdiGVj0CGXT4ektiWLWjkEGHsbckhlQ6Ghl0WHtKYkiVI5JBh7eXJPpXNyoZDGfuX93IZNDh7iGJvlWNTgYd9h6S6FfRKGXQ8UBnSfSrZqQy6PigoyT6VDFaGQzxgk8VI5ZBxw+dJPEftjMgtfmDOQEAAAAldEVYdGRhdGU6Y3JlYXRlADIwMjItMTItMTFUMTU6MjM6NDcrMDA6MDBoR6jEAAAAJXRFWHRkYXRlOm1vZGlmeQAyMDIyLTEyLTExVDE1OjIzOjQ3KzAwOjAwGRoQeAAAACh0RVh0ZGF0ZTp0aW1lc3RhbXAAMjAyMi0xMi0xMVQxNToyMzo0NyswMDowME4PMacAAAAtdEVYdGljYzpjb3B5cmlnaHQAQ29weXJpZ2h0IEFydGlmZXggU29mdHdhcmUgMjAxMQi6xbQAAAAxdEVYdGljYzpkZXNjcmlwdGlvbgBBcnRpZmV4IFNvZnR3YXJlIHNSR0IgSUNDIFByb2ZpbGUTDAGGAAAAE3RFWHRwZGY6VmVyc2lvbgBQREYtMS41UzZawQAAAEp0RVh0c2lnbmF0dXJlADlmOTc1NDY3YTg5ZWNlYTkzYzM4M2ZhMjE5N2M3ZGMyYWJhZDdmZDBjOTA3MjI0OTZmMjVmOTE4OGNhZWFlZmYnJEiAAAAAAElFTkSuQmCC",
      "text/plain": [
       "<wand.image.Image: 9f97546 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: ec64ccd 'PDF' (158x80)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 31f95cb 'PDF' (511x251)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mpl:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ascii:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "*                                      *\n",
      " ->                                 >-- \n",
      "   --                              -    \n",
      "     --                         ---     \n",
      "       >-                      >        \n",
      "         *->---->---->---->--*~         \n",
      "       ~~                      ~        \n",
      "     ~~                         ~~~     \n",
      "   ~~                              ~    \n",
      " ~~                                 ~~~ \n",
      "*                                      *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<wand.image.Image: 6192ee4 'PDF' (332x332)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicode:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "*                                      *\n",
      " ↘↘                                 ↗↗↗ \n",
      "   ↘↘                              ↗    \n",
      "     ↘↘                         ↗↗↗     \n",
      "       ↘↘                      ↗        \n",
      "         *→→→→→→→→→→→→→→→→→→→*~         \n",
      "       ~~                      ~        \n",
      "     ~~                         ~~~     \n",
      "   ~~                              ~    \n",
      " ~~                                 ~~~ \n",
      "*                                      *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 51e2446 'PDF' (477x176)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-1, 0)\n",
    "v2 = Vertex().with_xy(1, 0)\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1, v2).with_type(\"fermion\"),\n",
    "    Leg().with_target(v1).with_xy(-2, 1).with_type(\"fermion\").with_incoming(),\n",
    "    Leg().with_target(v1).with_xy(-2, -1).with_type(\"photon\").with_incoming(),\n",
    "    Leg().with_target(v2).with_xy(2, 1).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg().with_target(v2).with_xy(2, -1).with_type(\"photon\").with_outgoing(),\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ede56f63",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pyx:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 6787b02 'PDF' (315x359)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynmp:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 8ae13e6 'PDF' (180x111)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tikz:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 0f54c29 'PDF' (158x183)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dot:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: 98f5804 'PDF' (547x451)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "feynman:\n"
     ]
    },
    {
     "data": {
      "image/png": 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ggw6KPfbYI9q3bx8ff/xxzJkzJ3784x/H6tWrax+/9957x9KlSyvq3gQAkBI7+wDQRB588MGi4/322y/T0F+0aFHcfPPN8Ytf/CL++te/7vDxgwYNirPOOiu+9KUvxaGHHrrNl+V/8YtfjOOPPz6OP/742rXly5fH3LlzY9CgQSWbHwCoO7EPFW769Onx/PPPb7F+xRVXROfOnZt9HuB/PPHEE0XHJ598crPPUFNTEw8++GCMHz8+HnzwwdjRC/oOPvjgGDlyZHz1q1+N3r171/k6Q4cOjX79+sWiRYtq11588UWxDwAZEftQ4aZPnx6TJk3aYn306NFiHzKUz+fjqaeeKlobPHhws13//fffj9tuuy1uueWWWLx48XYf26VLlzj//PPjwgsvbNRH5/Xs2bMo9j/88MMGnwsAaByxDxVu4sSJMXHixKzHADazcOHCLWL36KOPbvLrPvPMMzF+/Pj4r//6r/jkk0+2+9iTTjopLrroohg+fHi0bdu20dfO5XJFx24LBADZEfsA0ASWLFlSdNylS5fYa6+9muRaa9asiTvvvDNuvvnmePbZZ7f72M6dO8eFF14Yl1xySQwYMKCkc6xatarouBT/gAAANIzYhwr2z//8z/H9738/Zs+eHccdd1zW4wCfsvnH2PXq1avk13j11VfjlltuiYkTJ24R2ps75JBDYty4cfH1r389dt5555LPUigUYsGCBUVrffv2Lfl14NPctwZg28Q+VLC5c+dGLpdr1Htsgaax+d3uu3fvXpLzrl+/Pn7zm9/EhAkT4g9/+MN2H7vTTjvF2WefHePGjYsjjzxyi5fZl9Jbb721xdsWsv6IQdLnvjUA2yb2oYLNnTs3+vXrF7vuumvWowCbad++fdHxunXrGnyuQqEQzz77bEyePDnuvPPOeO+997b7+J49e8Y3v/nN+MY3vlGyf2TYkc0/eaBjx47Rs2fPZrk2LZf71gBsm9iHCvXuu+/GsmXL4uyzz856FGArNv9HuGXLltX7HEuXLo0777wzJk+eHC+//PJ2H5vL5eLkk0+OsWPHximnnBKtWrWq9/Ua47HHHis6PuaYY5p9BgDgf1RlPQDQMHPnzo2IiEMPPTRmzZoVxx9/fOyyyy7RpUuXGD169BYvIQaa10EHHVR0vGjRopg9e/Z2v6empiaee+65+P73vx+HHnpo9OrVK/7xH/9xu6HfrVu3+O53vxsLFy6MmTNnxumnn55JZD/yyCNFx8cee2yzz0DLNH369Dj99NOje/fu0bZt2+jVq1ecd9558eKLL2Y9GkCm7OxDhdoU+3PmzIn//b//d3zlK1+JgQMHxv333x+TJk2Kt99+Ox588MGMp4SW65BDDokePXoU7egPHz48rrzyyjj66KOjQ4cOkc/nY8mSJbFo0aJ45pln4sknn6zzZ9Mfc8wxMWbMmPjqV7+a+V3v582bF6+++mrR2vHHH5/RNLQUGzdujJEjR8avf/3r6NmzZ3zlK1+JXXfdNebPnx9Tp06NUaNGxec+97msxwTIjNiHCvXcc89FRMTLL78cL774YvTu3TsiIq699tra3f4///nP8YUvfCHDKaHlatWqVVx99dVxxRVX1K6tXr06vv/97zf4nH369IlRo0bFyJEjY9999y3BlKUxY8aMouM99tgjDj/88IymoaW49NJL49e//nVceuml8eMf/zhat/6fX2uXLVsWnTp1ynA6gOx5GT9UqE07+7fffntt6EdEdOjQIS688MKIiHjppZeyGA34/8aNGxdf+tKXGnWO3XbbLf7+7/8+HnvssVi4cGH8y7/8S1mFfkTEtGnTio7PPPPMqKryKwZNZ86cOXHrrbfGySefHD/5yU+KQj8iokePHtGxY8eMpgMoD56JoQKtXr06Fi5cGEOGDIljjjlmi6/vscceERHxySefNPdowKe0bt067r333hg9enS9vq9fv35x+eWXxx/+8IdYsWJF/PznP48hQ4aUZUDPmzcvnn766aK1L3/5y9kMQ4MNHTq0ou5qf8MNN0RExA9/+MMm/UhJgErmZfxQgZ5//vkoFApxyimnbPXrS5cujYiIXr16NedYwFZ06NAhfvnLX8Zll10WkyZNijlz5sQbb7wRGzdujHw+H3vttVf07ds3+vfvH0cddVQMHjw49tprr6zHrrPJkycXHe++++5x4oknZjQNLcVDDz0UvXv3joMPPjjrUQDKltiHCrTpJfzbivkHHngg2rVrF0OGDGnOsYDtGDhwYAwcODDrMUoqn8/HlClTitbOP//8aNOmTUYTpeXtt9+OPffcM4488sh46qmntvj6T37yk7j88sujXbt2sXbt2i2+/sADD8Spp54aZ599dtx1113NMXKzWLlyZXz00UfuSQOwA+X3ekBghzbF/gcffLDF15588sl46qmnorq6OnbeeefmHg1oQWbPnh1vvPFG0Vp1dXVG06Snc+fOERFb/YSGmpqa2peyr1u3LtavX7/FY/7jP/4jIiKuvvrqJpsxC4VCISIiVqxYkfEkAOVN7EMF2nQn/ilTpsTGjRtr15cuXRoXXHBB7L777vHP//zPWY0HtBCTJk0qOv785z8fhxxySDbDJKhdu3bRtm3brcb+tGnTYvHixbHPPvtERMSqVauKvv7iiy/GI488EkOGDNnqJyP827/9W+yyyy61/zdnzpy45JJLitbK1W677RZ9+/aNV155JR555JEtvj5v3rwMpgIoP7nCpn8eBSrCJ598ErvsskscddRRsWjRoujevXucfPLJ8e6778bdd98d+Xw+7r///jj22GOzHhVI2AcffBB77713rFu3rnbtuuuui6uuuirDqdKzxx57xJo1a7YI/iOPPDIWLlwYV111Vfyv//W/YsGCBUWf0nDhhRfGxIkTY8aMGTF8+PAtzvvBBx8UvTrs/PPPjxEjRsRXvvKV2rVy+9SHT7vrrrvi3HPPjdatW8eZZ54Z/fr1ixUrVsSTTz4ZBx54YNx7771ZjwiQOe/Zhwrz0ksvxcaNG+Poo4+On//853HppZfGT37yk2jXrl2ccsop8a//+q+x3377ZT0mkLiJEycWhX6bNm1i5MiRGU6Ups6dO8eKFSsin8/XfhrD448/Hk8//XT80z/9U+2nr3x6Z/+dd96JO++8MwYMGBBnnHHGVs/bpUuX6NKlS+1x+/bto3v37mUd+J92zjnnRKdOneLf//3f4+GHH4777rsvunfvHocffnhcccUVWY8HUBbEPlSYQYMGxadfkPPQQw9lOA3QEuXz+bjllluK1kaMGBGf+cxnMpooXZ07d45CoRCrV6+OTp06RcTfXkHRrl27uPTSS+Oxxx6LiOLY/8///M/45JNP4tvf/nbSH0s3bNiwGDZsWNZjAJQt79kHAOrld7/7XSxYsKBobcyYMRlNk7bNb9K3YMGCuO+++6K6ujp233332n8A2BT7a9eujVtuuSV23313N0sEaOHs7AMA9XLzzTcXHR900EE+6rOJbIr9VatWxT777FN7h/1N90bYdddda78eETF58uR477334p//+Z+jXbt2db7O7NmzSzc0AGXBzj4AUGfLli2LGTNmFK2NGTMm6ZeLZ+nTO/vvvfdeTJo0Kc4888zo379/RETtzv7KlSujUCjEDTfcEO3bt49x48ZlNTIAZULsAwB19rOf/Szy+Xzt8c477xwXXHBBhhOl7dM7+xMmTIi1a9fGd77zndqvf3pn/4EHHohXX301Ro0aFbvvvnsW4wJQRsQ+AFAnGzZsiJ/97GdFayNHjqwNTkpvU+yvWLEixo8fH8ccc0wcddRRtV//dOz/x3/8R+Ryufj2t7+dxagAlBnv2QcA6mT69Onx1ltvFa25MV/T2hT748ePjxUrVsRPf/rToq/vvPPO0bp165gzZ078+c9/juHDh8eAAQMymBSAcmNnHwCok/HjxxcdH3PMMXHwwQdnNE3LsCn2n3nmmdhvv/1i+PDhWzymY8eO8ec//zkiIq6++urmHA+AMib2AYAdeumll+LRRx8tWnMTuKa3KfYjIr797W9v9UaIm27Sd/jhh/tUBABq5QqFQiHrIQCA8jZu3LiYMGFC7XH37t1j6dKl0bZt2wynAgC2xc4+ALBdH374YUyePLlo7aKLLhL6AFDGxD4AsF1TpkyJjz76qPa4qqoqLr744gwnAgB2ROwDANtUKBSKXr4fETF8+PDo2bNnRhMBAHUh9gGAbXr00Ufj5ZdfLlpzYz4AKH9iHwDYps0/bm/AgAFxwgknZDQNAFBXYh8A2KoVK1bE9OnTi9bGjh0bVVV+fQCAcufZGgDYqjvuuCM2btxYe9y+ffuorq7OcCIAoK7EPgCwhUKhEL/85S+L1kaMGBGdO3fOZiAAoF7EPgCwhblz58aLL75YtDZ69OhshgEA6k3sAwBbmDhxYtFxr1694vjjj89mGACg3lpnPQAAUF42bNgQd9xxR9FadXV1Rd2Y780334zZs2fHc889F6+88krMmzcvVq5cGRs2bIhWrVpFnz59YvDgwTF69OgYOHBg1uMCQMnlCoVCIeshAIDy8dBDD8WwYcOK1hYuXBj9+vXLaKId27hxYzz66KNx7733xsMPPxzz58+v8/eOHj06xo8fHx06dGjCCQGgednZBwCKTJ06tej4iCOOKMvQz+fzMXv27Lj99ttjxowZ8cEHHzToPBMnTozly5fHAw88EK1atSrxlACQDbEPANSqqamJ6dOnF62NGDEim2G2YdGiRTFp0qSYNGlSLF26tCTnfPjhh+M///M/4/LLLy/J+QAga17GDwDU+tOf/hRHHHFE0dqiRYuib9++GU30N2vXro277rorbrvttpgzZ06dvqdTp04xZMiQOPjgg+OAAw6IvfbaK9q2bRtr1qyJOXPmxI9//ONYvXp17eP33nvvWLp0aUXdmwAAtsXOPgBQ63e/+13R8QEHHJBp6C9atChuueWW+MUvflGnl+kPGjQozjrrrBg2bFgMHDhwmy/L/+IXvxjHH3980ScMLF++PObOnRuDBg0q2fwAkBWxDwDU+v3vf190fOKJJzb7DDU1NTFz5syYMGFCPPjggzt8/Gc/+9morq6Or371q9G7d+86X2fo0KHRr1+/WLRoUe3aiy++KPYBSILYBwAi4m83vHvqqaeK1k444YRmu/67774bt912W9xyyy3x+uuvb/exXbp0ifPPP7/2o/NyuVyDrtm7d++i2P/rX//aoPMAQLkR+wBAREQsXbo0Pv7446K1ww8/vEmvWSgU4qmnnooJEybE3XffHevXr9/u40866aT45je/Gaeffnq0bdu20dfP5/NFx+7GD0AqxD4AEBERL7/8ctFxp06dYq+99mqSa3300Ufxq1/9KiZMmBAvvPDCdh/buXPnuPDCC+OSSy6JAQMGlHyOT9tpp51Ken4AyIrYBwAiImLZsmVFxwMGDGjwy+O35dVXX42bb745Jk6cGB9++OF2H3vooYfGuHHj4mtf+1p06NChpHNE/O1VBfPnzy9a69OnT8mvAwBZEPsAQERErFu3rui4Y8eOJTnv+vXr4ze/+U3cfPPNW9wAcHNt27aNc889N8aNGxeHHXZYyf+x4dPefvvtWLVqVdHa/vvv32TXA4DmJPYBgIiILd4v35j3rxcKhXj22Wdj0qRJceedd8b777+/3cf36dMnxowZE3/3d38XXbt2bfB16+OJJ54oOt55551jn332aZZrA0BTE/sAQETEFpG9ePHiep/j9ddfj7vuuismTZoUf/nLX7b72FwuF6eddlqMHTs2hg0bFlVVVfW+XmPMnj276Hjw4MHNPgMANBWxDwBERMTnP//5ouOFCxfGo48+Gscdd9w2v6empiaef/75mDlzZkyfPj2ee+65HV6nW7du8fd///fxzW9+M9P3yG/+loKhQ4dmMwgANIFcoVAoZD0EAJC9mpqa6NWrVyxfvrx2bdddd43LL788hgwZEu3atYuampp44403Yv78+fHcc8/F448/vsMb7W0yePDguPjii+Pss8+Odu3aNdUfo04WLFiwxZ39n3rqqTjyyCMzmggASkvsAwC1brjhhrjyyitLdr7evXvHqFGjYtSoUdGvX7+SnbexfvSjH8V3v/vd2uM99tgjli9f7mX8ACTDy/gBgFqXXnppzJw5Mx5++OEGn6NLly7x5S9/OUaNGhVDhgwpy4CeNm1a0fGZZ55ZlnMCQEPZ2QcAiqxZsybGjRsXEydOrPP3DBgwIIYNGxZnnXVWDBkyJFq3Lt/9hK29hH/WrFnxpS99KaOJAKD0xD4AsFVz586NiRMnxuOPPx5LliyJfD4fuVwuunXrFvvtt18MGDAgDj/88Dj22GNjzz33zHrcOrvmmmvi2muvrT3u1q1bvPnmm9GmTZsMpwKA0hL7AECLkc/no3fv3vHGG2/Url1++eVxww03ZDcUADQBb04DAFqMP/zhD0WhHxExevTobIYBgCYk9gGAFmPSpElFx5///OfjkEMOyWYYAGhCYh8AaBH++te/xj333FO0ZlcfgFSJfQCgRZg4cWKsXbu29rh169Zx3nnnZTgRADQdsQ8AJC+fz8eECROK1kaMGBGf+cxnMpoIAJqW2AcAkvfII4/EwoULi9bGjh2b0TQA0PTEPgCQvPHjxxcdH3TQQTFkyJCMpgGApif2AYCkvf766/Hb3/62aG3cuHGRy+UymggAmp7YBwCS9tOf/jTy+XztcceOHWPkyJEZTgQATU/sAwDJ+uSTT+JnP/tZ0dqoUaOiY8eOGU0EAM1D7AMAyZo6dWq8++67RWtjxozJaBoAaD5iHwBI1uYft3fcccfFQQcdlNE0ANB8xD4AkKQXXnghnnjiiaK1cePGZTQNADQvsQ8AJOnmm28uOt5jjz3iy1/+cjbDAEAzE/sAQHJWrVoVt99+e9HaxRdfHG3atMloIgBoXmIfAEjOlClT4uOPP649btWqVVx00UUZTgQAzUvsAwBJKRQKW9yY78wzz4wePXpkNBEAND+xDwAk5dFHH41XXnmlaG3s2LEZTQMA2RD7AEBSNt/V32+//eKEE07IaBoAyIbYBwCS8c4778S9995btDZmzJjI5XIZTQQA2RD7AEAy7rjjjti4cWPtcfv27aO6ujrDiQAgG2IfAEhCoVCIiRMnFq2dffbZ0blz50zmAYAsiX0AIAnPP/98vPjii0VrdvUBaKnEPgCQhM139Xv27BlDhw7NZBYAyFrrrAcAAGis9evXx69+9auiterq6qiqqpx9jbfeeiseffTR+NOf/hTz58+P+fPnx7vvvhuFQiFatWoVvXv3jsGDB8fo0aNj4MCBWY8LQJnLFQqFQtZDAAA0xqxZs+Lkk08uWluwYEHsu+++GU20Yxs3bozHHnsspk+fHg8++GAsWLCgzt87evToGD9+fHTo0KEJJwSgktnZBwAq3rRp04qOjzjiiLIM/Xw+H4899lhMnjw5ZsyYER988EGDzjNx4sRYvnx5zJw5M1q39uscAFvy7AAAVLSampqYMWNG0dqIESMymmbrFi5cGJMnT47JkyfH66+/XpJzPvzwwzF+/Pi4/PLLS3I+ANLiZfwAQEX74x//GEcddVTRWjm8hH/dunVx1113xc9+9rN4/PHH6/Q9u+66awwZMiQOPfTQGDBgQOyzzz7RqlWrWLt2bTz++ONxww03xIcfflj7+B49esSSJUuiVatWTfXHAKBC2dkHACraH/7wh6LjAw44INPQX7RoUdx6663xi1/8It5///0dPn7QoEFx1llnxSmnnBIHH3zwNsP9pJNOiuOPPz6OP/742rVly5bFCy+8EIceemjJ5gcgDWIfAKhos2fPLjo+8cQTm32GmpqamDlzZkyYMCEefPDBHT7+s5/9bFRXV8c555wTPXv2rPN1hg4dGvvuu28sXLiwdk3sA7A1Yh8AqFj5fD6eeOKJorWhQ4c22/XfeeeduO222+LWW2+NpUuXbvexXbt2jfPPPz+qq6tj4MCBkcvlGnTNPn36FMV+XV49AEDLI/YBgIq1dOnS+Pjjj4vWjj766Ca9ZqFQiCeffDImTJgQd999d2zYsGG7j//iF78YY8aMidNPPz122mmnRl9/48aNRcdt27Zt9DkBSI/YBwAq1quvvlp03Llz59hjjz2a5Foff/xx3HHHHTFhwoR44YUXtvvYzp07x4UXXhiXXHJJDBgwoKRzfPTRR0XHYh+ArRH7AEDFWrx4cdFx//79G/zy+G2ZN29eTJgwISZOnFh0J/ytOfTQQ2PcuHHxta99LTp06FDSOSL+9qqCefPmFa316NGj5NcBoPKJfQCgYq1fv77ouGPHjiU57yeffBL33Xdf3HLLLfG73/1uu49t27ZtnHvuuTFu3Lg47LDDSv6PDZ/25ptvbvEPDgcddFCTXQ+AyiX2AYCKlc/ni44bE9qFQiGee+65mDhxYvzqV7+KDz74YLuP79u3b4wZMyYuvPDC6Nq1a4OvWx9PP/100fHOO+9cr7v5A9ByiH0AoGJ17ty56HjJkiX1PsfixYtj6tSpMWnSpHjppZe2+9hcLhennnpqjBs3LoYNGxZVVVX1vl5j/P73vy86Pvroo5v0lQQAVC6xDwBUrM9//vNFx4sWLYrZs2dv9+P3ampq4rnnnouHHnoopk6dGnPnzt3hdbp27Rrf+MY34pvf/Gb06dOnsWM32Oaxf8IJJ2Q0CQDlLlcoFApZDwEA0BD5fD569uwZy5cvr13r2LFjXHnllTFkyJBo3759rF+/PpYvXx6vvPJK/Pd//3fMmTMnVq1aVafzH3fccfF3f/d3cc4550S7du2a6o9RJ4sWLYp99923aO1Pf/pTHHbYYRlNBEA5E/sAQEW78cYb44orrijZ+Xr16hWjR4+OUaNGRd++fUt23sb60Y9+FN/97ndrj7t37x5vvvlmtGrVKsOpAChXXsYPAFS0Sy+9NO6///54+OGHG3yOrl27xplnnhkjR46M4447rtnfi18XU6dOLTo+66yzhD4A22RnHwCoeGvWrIlx48bFxIkT6/w9++23X5x00knxla98JYYMGRKtW5fvHsjWXsL/0EMPxUknnZTRRACUO7EPACRj7ty5MWnSpJgzZ04sWbIkampqok2bNtGpU6fYf//944ADDoiBAwfG0KFDY6+99sp63Dr7p3/6p/jBD35Qe9y1a9d46623ok2bNhlOBUA5E/sAAGUsn89Hnz59YunSpbVrl112Wdx4440ZTgVAuSu/N6QBAFDr97//fVHoR0SMHj06m2EAqBhiHwCgjG1+H4KDDz44Bg4cmM0wAFQMsQ8AUKZWrlwZ06ZNK1qzqw9AXYh9AIAyNXHixFi7dm3tcevWreP888/PcCIAKoXYBwAoQ/l8PiZMmFC0dtZZZ8Xuu++e0UQAVBKxDwBQhn73u9/FggULitbGjRuX0TQAVBqxDwBQhsaPH190fNBBB8Wxxx6b0TQAVBqxDwBQZpYuXRr33Xdf0drYsWMjl8tlNBEAlUbsAwCUmVtvvTXy+XztcceOHeOCCy7IcCIAKo3YBwAoI5988kn87Gc/K1obNWpUdOzYMaOJAKhEYh8AoIxMnTo13n333aK1MWPGZDQNAJVK7AMAlJHNb8w3dOjQOOiggzKaBoBKJfYBAMrECy+8EE8++WTRmo/bA6AhxD4AQJmYMGFC0fGee+4ZZ555ZkbTAFDJxD4AQBlYtWpV3HHHHUVrF198cbRp0yajiQCoZGIfAKAMTJkyJT7++OPa41atWsVFF12U4UQAVDKxDwCQsUKhEDfffHPR2plnnhl77713RhMBUOnEPgBAxh577LF4+eWXi9Z83B4AjSH2AQAytvmu/oABA+KEE07IaBoAUiD2AQAy9Pbbb8fUqVOL1i655JKoqvJrGgAN51kEACBDt99+e2zcuLH2uH379jF69OjsBgIgCWIfACAjhUIhJk2aVLR29tlnx2677ZbRRACkQuwDAGTk+eefj5deeqloza4+AKUg9gEAMrL5rn7Pnj3juOOOy2gaAFLSOusBAABaog0bNsSvfvWrorULLrigom7M9+abb8acOXPij3/8Y8yfPz9ee+21eOuttyKXy0WbNm1in332icGDB8fo0aNj4MCBWY8L0KLkCoVCIeshAABamgceeCBOPfXUorV58+bFgAEDMppoxzZs2BBz5syJGTNmxP333x+LFi2q8/eOHj06xo8fHx06dGjCCQHYxM4+AEAGpk+fXnR8xBFHlGXo5/P5ePzxx2Py5Mkxbdq0+Otf/9qg80ycODHefPPNuP/++6N1a7+CAjQ1/0sLANDM8vl8zJgxo2htxIgRGU2zdQsWLIgpU6bElClTYsmSJSU550MPPRTjx4+Pyy+/vCTnA2DbvIwfAKCZ/fGPf4yjjjqqaG3+/PnRv3//jCb6m3Xr1sXdd98dt956azzxxBN1+p5dd901jjnmmDjssMOiX79+0atXr2jVqlV8/PHH8eSTT8aPf/zjWL16de3je/ToEUuWLIlWrVo11R8DgLCzDwDQ7H7/+98XHR9wwAGZhv5rr70Wt9xyS/ziF7+I999/f4ePHzRoUJx55plx2mmnxcEHH7zNcB82bFgcf/zxcfzxx9euLVu2LJ5//vkYNGhQyeYHYEtiHwCgmT322GNFx1/84hebfYaampqYOXNmTJgwIWbNmhU7erHngQceGNXV1fH1r3899tlnnzpfZ+jQodGvX7+im/n95S9/EfsATUzsAwA0o5qami1eIn/sscc22/XfeeeduO222+LWW2+NpUuXbvex3bp1i/POOy+qq6tj4MCBkcvlGnTNvffeuyj2P/2yfgCahtgHAGhGr7/+enz00UdFa8ccc0yTXrNQKMTjjz8eEyZMiKlTp8aGDRu2+/gTTzwxxowZE8OHD482bdo0+vrt2rUrOl6zZk2jzwnA9ol9AIBmtGDBgqLjTp06xR577NEk1/rwww/j9ttvj5tvvjleeuml7T62U6dOceGFF8Yll1wS++23X0nnWLFiRdFxly5dSnp+ALYk9gEAmtFrr71WdLzvvvs2+OXx2/Liiy/GzTffHFOmTNniVQSbGzRoUIwdOza+9rWvRYcOHUo6xyabv12gZ8+eTXIdAP6H2AcAaEaffPJJ0XHnzp1Ldt5p06bFhAkT4vHHH9/uY9u1axdf//rXY8yYMXHYYYeV5PrbsmzZsvjggw+K1nr16tWk1wRA7AMANKvNd/F3dBf87SkUCvHss8/G7bffHr/61a/i3Xff3e7j99133xgzZkyMHj262V5K/9RTTxUdd+rUKfbdd99muTZASyb2AQCaUadOnYqOd3RH/K1ZsmRJ3HHHHXH77bfHq6++ut3HVlVVxfDhw2Ps2LFx4oknRlVVVb2v1xibf/LAUUcd1ewzALREYh8AoBl97nOfKzpeuHBhzJ49O4YOHbrN78nn8zF37tz47W9/G/fdd188++yzO7zOHnvsERdddFFcdNFFsc8++zR27AZ74IEHio6PPvrojCYBaFlyhca8dgwAgHrJ5/PRs2fPWL58ee1ax44d48orr4wjjjgiOnXqFOvXr49ly5bFwoUL4+mnn46nn346Vq5cWafzDx06NMaMGRNf/vKXY6eddmqiP0XdzJ8/f4s7+z/zzDPxhS98IaOJAFoOsQ8A0MxuvPHGuOKKK0p2vj59+sTIkSPj/PPPL/nH5jXG9ddfH1dffXXt8R577BHLly/3Mn6AZuBl/AAAzezSSy+N+++/Px5++OEGn2O33XaLc889N0aOHBlHH310yT++rxTuvPPOouPTTz9d6AM0Ezv7AAAZWLt2bYwdOzYmTpxY5+/p379/nHHGGXH66afH4MGDo02bNk03YCO98sorceCBBxatPfjggzFs2LCMJgJoWcQ+AECG5s6dG5MmTYo5c+bE22+/HatXr46qqqro0aNH9OjRIz772c/GUUcdFUceeWTsvffeWY9bZ9/73vfi3/7t32qP99hjj3jjjTeidWsvLAVoDv7XFgAgQwMHDoyBAwdmPUZJ5fP5uP3224vWvv71rwt9gGbkTVMAAJTUnDlzYunSpUVrF1xwQUbTALRMYh8AgJL6+c9/XnR80EEHxSGHHJLNMAAtlNgHAKBk3n333bjrrruK1qqrq8vy0wIAUib2AQAomV/84hexfv362uO2bdvGhRdemOFEAC2T2AcAoCRqamrilltuKVo755xzolu3bhlNBNByiX0AAEpi1qxZsWTJkqK1MWPGZDMMQAsn9gEAKIkJEyYUHR9yyCFx5JFHZjQNQMsm9gEAaLTFixfHzJkzi9bGjh3rxnwAGRH7AAA02q233hqFQqH2eNddd43zzjsvw4kAWjaxDwBAo6xbty5uu+22orXRo0fHzjvvnNFEAIh9AAAa5Z577on33nuvaM2N+QCyJfYBAGiUzW/Md8IJJ8T++++f0TQARIh9AAAa4fnnn4+nnnqqaG3s2LEZTQPAJmIfAIAG23xXf6+99orhw4dnNA0Am4h9AAAaZNWqVXHHHXcUrV100UXRpk2bjCYCYBOxDwBAg0yZMiXWrFlTe9yqVau46KKLMpwIgE3EPgAA9VYoFOLmm28uWhs+fHjsvffeGU0EwKeJfQAA6m3OnDnx8ssvF625MR9A+RD7AADU2+a7+v37948TTjgho2kody+88EL867/+6xb/QAQ0nVyhUChkPQQAAJXjnXfeiX322Sc2bNhQu3b99dfHt7/97QynopyNGDEipk2bFhER++23X3z961+Ps88+Ow488MCMJ4N0iX0AAOrl3//93+Mf/uEfao/btWsXy5cvjy5dumQ4FeXsz3/+cxx22GG1x61atYqamhrhD01I7AMAUGeFQiE+97nPxV/+8pfatVGjRsWkSZMynIpKcO6558a0adNi48aNRevCH5qG2AcAoM7mzp0bhx56aNHa7Nmz47jjjstoIirFwoULY//994+ampptPkb4Q+m4QR8AAHU2efLkouOePXvGkCFDMpqGSrLvvvvGJZdcEq1atdrmYzb9Q8C8efPiBz/4QRx00EGx//77u7kfNICdfQAA6mTjxo2x9957x4oVK2rXvve978W1116b4VRUknfeeSd69+4d69atq9f32fGH+hP7AADUyQMPPBCnnnpq0dqrr74a++23X0YTUYn+5V/+JX7wgx9EPp9v0PcLf6gbsQ8AQJ1cfPHF8bOf/az2+PDDD4+nn366Sa9ZKBTi/fffj48++ih22WWX6Nq1a+RyuSa9Jk1r9erV0bt37/jggw8afS7h3/T8DFYu79kHAGCH8vl83HfffUVr55xzTpNdb+XKlXHjjTdG//79Y/fdd48+ffrE7rvvHv37948bb7wxVq5c2WTXpml17Ngxvv/975fkXN7j33T8DFY+O/sAAOzQ008/HUceeWTR2vz586N///4lv9asWbNixIgRsWbNmoj4287iJpt2FDt06BBTp06NYcOGlfz6NL3169fHgAED4o033mjwy/m3x45/4/gZTIOdfQAAdujhhx8uOj7ggAOaLPRPO+20WLt2bRQKhdh8X2rT2tq1a+O0006LWbNmlXwGmt5OO+0U//f//t8mCf0IO/6N4WcwHXb2AQDYoZNPPrnol/rLLrssbrzxxpJeY+XKldGjR49Yu3ZtnSKwqqoq2rdvH8uWLYvOnTuXdBaaXj6fj0GDBsWLL75YG+dNzY7/9vkZTIvYBwBgu2pqamK33XaL1atX167dfffd8dWvfrWk17nxxhvjyiuv3GIncXtyuVxce+21cdFFF5V0FprHnDlzYsSIEZlcu6qqKvL5fPTr1y++8pWvxPDhw1v8J0v89Kc/jWuuuabeP4M33HBDXHbZZU04GQ0h9gEA2K6FCxdu8ZL9N998M/bcc8+SXaNQKET//v3jtddeq1doANnK5XLRt2/fWLBggbv0lxnv2QcAYLtee+21ouPddtutpKEfEfH+++/HokWLhD5UmEKhEIsWLSrJRylSWmIfAIDtWrx4cdFxnz59Sn6NuXPnlvycQPP59Nt8KA9iHwCA7fr444+Ljrt27VqS865fvz7uuuuuGDp0aHzpS18qyTmBbHTs2DHrEdhM66wHAACgvO20005Fxxs3bmzwuQqFQjz77LMxZcqUuPPOO+Pdd99t1Gy5XC569eoVTz/9tPcLV6DHHnus5Dd6rKtNd+bfd999a2/QN2DAgExmKQeFQiGOOOKIeP311+t9g76+fftGly5dmnA6GkLsAwCwXbvsskvR8RtvvFHvcyxdujTuuOOOmDx5crz66qulGi0KhUJceeWV0b1795Kdk+aRz+fjBz/4QW10N4dPf/TeeeedF2effXYccMABzXLtSnDFFVfElVdeWe/vu+yyy/xjWxkS+wAAbNfnPve5ouOFCxfGo48+Gscdd9w2v6empiZeeOGFuO++++I3v/lNPPfcczu8Trdu3WLVqlWxcePGeu0sfvjhh3V+LOXj7rvvjhdeeKHJryPw6666ujq+973vxdq1ayOfz+/w8VVVVdG+ffsYNWpUM0xHffnoPQAAtiufz0fPnj1j+fLltWsdO3aMK6+8Mo466qjYeeedo6amJl5//fV47bXX4umnn46nnnqqzhE+ZMiQGDt2bHzlK1+JP/zhD3HaaadFoVCoU2xsct1118VVV11V7z8b2Vi/fn0MGDAg3njjjXr9PdeVwG+4WbNm1elnsKqqKnK5XMycOdM9N8qU2AcAYIduvPHGuOKKK0p2vj59+sQFF1wQI0eOjP79+xd9bdasWTFixIhYs2ZNRETRLn8ul9vmrr/grxzjx4+PSy+9tKTnFPils6OfwYiIDh06xLRp04R+GRP7AADs0MaNG+PUU0+Nhx9+uMHn6Ny5c5xzzjlxwQUXxDHHHLPd9/iuXLkyJk+eHD/5yU9i0aJFtev9+vWLyy67LD788MO45pprtvg+wV/+Vq9eHb179y7J57IL/Kazo5/B6urq6NSpU4YTsiNiHwCAOlmzZk2MGzcuJk6cWOfv2XfffeOMM86I4cOHxzHHHBNt2rSp1zULhUJ88MEHsXr16ujYsWN06dKl9h8Jrr/++rj66qu3+B7BX97+5V/+JX7wgx80+OX7Ar95be9nkPIm9gEAqJfnnnsuJk2aFE888UQsW7YsPvnkk8jn89GjR4/o3bt3DBgwII4++ug45phjYq+99mrSWQR/ZXnnnXeid+/esW7dunp9n8CH+hP7AABUNMFfOS699NK45ZZb6vRRewIfGkfsAwBQ8QR/+Vu4cGHsv//+2w19gQ+l0zrrAQAAoLE2Bf3mwb/pWPBn73vf+95W3+st8KFp2NkHACAZdvjL0zPPPBOHH3547bHAh6ZnZx8AgGTY4S9PP/zhD2v/f4EPzcPOPgAAybHDX15eeOGFmDFjhsCHZiT2AQBIkuAHWrKqrAcAAICmcNVVV8V11123xfrVV18d119/fQYTATQfsQ8AQLIEP9BSiX0AAJIm+IGWSOwDAJA8wQ+0NGIfAIAWQfADLYnYBwCgxRD8QEsh9gEAaFEEP9ASiH0AAFocwQ+kTuwDANAiCX4gZWIfAIAWS/ADqRL7AAC0aIIfSJHYBwCgxRP8QGrEPgAAhOAH0iL2AQDg/xP8QCrEPgAAfIrgB1Ig9gEAYDOCH6h0Yh8AALZC8AOVTOwDAMA2CH6gUol9AADYDsEPVCKxDwAAOyD4gUoj9gEAoA4EP1BJxD4AANSR4AcqhdgHAIB6EPxAJRD7AABQT4IfKHdiHwAAGkDwA+VM7AMAQAMJfqBciX0AAGgEwQ+UI7EPAACNJPiBciP2AQCgBAQ/UE7EPgAAlIjgB8qF2AcAgBIS/EA5EPsAAFBigh/ImtgHAIAmIPiBLIl9AABoIoJ/+6ZPnx6nn356dO/ePdq2bRu9evWK8847L1588cWsR4OKlysUCoWshwAAgJRdf/31cfXVV2+xft1118VVV12VwUTZ2rhxY4wcOTJ+/etfR8+ePeOUU06JXXfdNebPnx8PPPBAzJgxI04++eSsx4SK1jrrAQAAIHWbgn7z4N903NKC/9JLL41f//rXcemll8aPf/zjaN36f7Jk2bJl0alTpwyngzTY2QcAgGZihz9izpw5ceyxx8bJJ58cM2fOjFwul/VIkCTv2QcAgGbiPfwRN9xwQ0RE/PCHPxT60ITs7AMAQDNryTv8HTt2jG7dusXixYuzHgWSZmcfAACaWUvd4V+5cmV89NFH0bt376xHgeSJfQAAyEBLDP5NLypesWJFxpNA+sQ+AABkpKUF/2677RZ9+/aNV155JR555JEtvj5v3rwMpoI0ec8+AABkrCW9h/+uu+6Kc889N1q3bh1nnnlm9OvXL1asWBFPPvlkHHjggXHvvfdmPSIkQewDAEAZaEnBP2vWrPj3f//3eOaZZ2LdunXRvXv3OPzww+OKK66IIUOGZD0eJEHsAwBAmWhJwQ80Le/ZBwCAMtHS3sMPNB2xDwAAZUTwA6Ug9gEAoMwIfqCxxD4AAJQhwQ80htgHAIAyJfiBhhL7AABQxgQ/0BBiHwAAypzgB+pL7AMAQAUQ/EB9iH0AAKgQgh+oK7EPAAAVRPADdSH2AQCgwgh+YEfEPgAAVCDBD2yP2AcAgAol+IFtEfsAAFDBBD+wNWIfAAAqnOAHNif2AQAgAYIf+DSxDwAAiRD8wCZiHwAAEiL4gQixDwAAyRH8gNgHAIAECX5o2cQ+AAAkSvBDyyX2AQAgYYIfWiaxDwAAiRP80PKIfQAAaAEEP7QsYh8AAFoIwQ8th9gHAIAWRPBDyyD2AQCghRH8kD6xDwAALZDgh7SJfQAAaKEEP6RL7AMAQAsm+CFNYh8AAFo4wQ/pEfsAAIDgh8SIfQAAICIEP6RE7AMAALUEP6RB7AMAAEUEP1Q+sQ8AAGxB8ENlE/sAAMBWCX6oXGIfAADYJsEPlUnsAwAA2yX4ofKIfQAAYIeaI/hramri7bffjnw+X5LzQUsm9gEAgDpp6uC/6aabYs8994x777230eeClk7sAwAAddaUwT9jxoyIiLjmmmvs7kMjiX0AAKBemiL4V61aFXPmzImIiFdeecXuPjSS2AcAAOqt1MH/0EMPRU1NTUREVFVV2d2HRhL7AABAg5Qy+H/7299G69atIyIin8/b3YdGyhUKhULWQwAAAJXr+uuvj6uvvnqL9euuuy6uuuqqHX5/TU1NdOvWLVauXFm7VlVVFfvtt1+89NJLUVVljxLqy08NAADQKI3d4X/66aeLQj/C7j40ltgHAAAarTHBf99999W+hP/TvHcfGk7sAwAAJdHQ4L/33ntj48aNW6zb3YeG8559AACgpOrzHv4lS5ZEnz59tnku792HhvHTAgAAlFR9dvh/+9vfRi6X2+a57O5Dw4h9AACg5Ooa/DNmzNhu7Ed47z40hJfxAwAATWZ7L+m/+OKLo0uXLlt9v/7W3HPPPTFixIhSjwhJEvsAAECT2lbwV1dXx6RJk+p0Du/dh/oR+wAAQJPbVvBXVVXV6+X5dvehbsQ+AADQLLYV/HVldx/qzk8IAADQLL75zW9GdXV1g7/fnfmh7uzsAwAATWbJkiXx29/+NmbMmBGzZ8+OjRs31vul+59mdx/qRuwDAAAlU1NTE08//XTcd999MX369Hj11Vcjl8tFLpcr6Ufnee8+bJ/YBwAAGmXVqlXx0EMPxX333Re/+c1vYtWqVdG6des6f6Refdndhx0T+wAAQL3V1NTETTfdFDNmzIg5c+ZETU1Nkwb+1tjdh20T+wAAQL29/fbbseeee2Z2fbv7sH1+KgAAgHrr3r173HPPPXHAAQdERDR7cLszP2yfnX0AAKDB8vl83HvvvXHNNdfEK6+80qg77deX3X3YNj8RAABAg1VVVcWIESPipZdeinvuuSf222+/2vWmZncfts3OPgAAUDLNvdNvdx+2zk8DAABQMs290293H7bOzj4AANBkmmOn3+4+bMlPAgAA0GSaY6ff7j5syc4+AADQbJpqp9/uPhTzUwAAADSbptrpt7sPxezsAwAAmSnlTr/dffgffgIAAIDMlHKn3+4+/A87+wAAQNlo7E6/3X34G//tBwAAykZjd/rt7sPf2NkHAADKVkN2+nO5XOy///5292nR/DcfAAAoWw3Z6S8UCnb3afHs7AMAABWjPjv93bt3j7feesvuPi2S2AcAgERMnz49nn/++S3Wr7jiiujcuXOzz9OUNo/+XC4XW0ubUaNGxaRJkzKYELIl9gEAIBGjR4/eatguXrw4evfu3fwDNYPNo39rfvSjH8V3vvOdZp4MsiX2AQCAircp+seOHRsrVqzY4uvXXXddXHXVVRlMBtkQ+wAAQDLy+XxceOGFMXny5C2+JvhpSdypAgAAEjFr1qw45ZRTomfPntG2bdv4zGc+E8cdd1yLes96VVVVTJo0KX70ox9t8bWrr746rr/++gymguYn9gEAIAHf+c534uSTT45FixbFGWecEVdeeWUMGzYsFi9eHHPnzs16vGb3ne98J6677rot1gU/LYWX8QMAQIV77bXXYt99940zzzwzpk6dWvRRc/l8PlauXBldunTJcMLsXH/99XH11Vdvse4l/aTOzj4AAFS4V155JQqFQhx44IFbfKZ8VVVViw39iIirrrrKDj8tkp19AACocMuXL48BAwbEunXr4mtf+1qce+658cUvfjE6dOiQ9Whlww4/LY2dfQAAqHB77713PPbYY3HqqafGPffcE2eeeWZ069Ytqqur46233sp6vLJgh5+Wxs4+AAAk5OOPP45HHnkkrr/++pgzZ06ceOKJ8cgjj2Q9Vtmww09LIfYBACBBNTU10a1bt2jfvn28+eabWY9TVgQ/LYGX8QMAQAV77rnnYsmSJVusP/bYY7Fy5co48sgjm3+oMucl/bQEdvYBAKCCjR49OiZPnhyDBw+OQYMGRdu2bePll1+OmTNnxmc+85mYM2dO9O3bN+sxy5IdflIm9gEAoIJNnz497r777vjTn/4Ub731VmzYsCF69+4dZ5xxRvzjP/5jdOvWLesRy5rgJ1ViHwAAaNEEPynynn0AAKBF8x5+UiT2AQCAFk/wkxqxDwAAEIKftIh9AACA/0/wkwqxDwAA8CmCnxSIfQAAgM0Ifiqd2AcAANgKwU8lE/sAAADbIPipVGIfAABgOwQ/lUjsAwAA7IDgp9KIfQAAgDoQ/FQSsQ8AAFBHgp9KIfYBAADqQfBTCcQ+AABAPQl+yp3YBwAAaADBTzkT+wAAAA0k+ClXYh8AAKARBD/lSOwDAAA0kuCn3Ih9AACAEhD8lBOxDwAAUCKCn3Ih9gEAAEpI8FMOxD4AAECJCX6yJvYBAACagOAnS2IfAACgiQh+siL2AQAAmpDgJwtiHwAAoIkJfpqb2AcAAGgGgp/mJPYBAACaieCnuYh9AACAZiT4aQ5iHwAAoJkJfpqa2AcAAMiA4KcpiX0AAICMCH6aitgHAADIkOCnKYh9AACAjAl+Sk3sAwAAlAHBTymJfQAAgDIh+CkVsQ8AAFBGBD+lIPYBAADKjOCnscQ+AABAGRL8NIbYBwAAKFOCn4YS+wAAAGVM8NMQYh8AAKDMCX7qS+wDAABUAMFPfYh9AACACiH4qSuxDwAAUEEEP3Uh9gEAACqM4GdHxD4AAEAFEvxsj9gHAACoUIKfbRH7AAAAFUzwszViHwAAoMIJfjYn9gEAABIg+Pk0sQ8AAJAIwc8mYh8AACAhgp8IsQ8AAJAcwY/YBwAASJDgb9nEPgAAQKIEf8sl9gEAABIm+FsmsQ8AAJA4wd/yiH0AAIAWQPC3LGIfAACghRD8LYfYBwAAaEEEf8vQOusBAAAAaF5XXXVVRPwt8D9t0/GmrxcKhXj//ffjo48+il122SW6du0auVyueYelQcQ+AABAC7S94F+7dm107Ngxbrrppli0aFHt1/r16xff+ta3orq6Ojp37tyc41JPuUKhUMh6CAAAALJx/fXXbxH8m+Ryufh0Mm7a1e/QoUNMnTo1hg0b1iwzUn9iHwAAoIXbXvBvTVVVVeRyubj//vsFf5kS+wAAAMS1114b11xzTZ0fX1VVFe3bt49ly5Z5SX8Zcjd+AAAAomPHjvV6fD6fjzVr1sTkyZObaCIaw84+AABAC1coFKJ///7x2muvRX0SMZfLRd++fWPBggXu0l9mxD4AAEAL995778Xuu+/eqO/v2rVrCSeisbyMHwAAoIX76KOPGvX9q1evLtEklIrYBwAAaOF22WWXRn1/fd/vT9MT+wAAAC1c165do1+/fvV+330ul4t+/fpFly5dmmgyGkrsAwAAtHC5XC6+9a1vNeh7L7vsMjfnK0Nu0AcAAECsXLkyevToEWvXro18Pr/Dx1dVVUX79u1j2bJl0blz56YfkHqxsw8AAEB07tw5pk6dGrlcLqqqtp+KVVVVkcvlYtq0aUK/TIl9AAAAIiJi2LBhcf/990f79u0jl8tt8fL8TWvt27ePmTNnxpe+9KWMJmVHxD4AAAC1hg0bFsuWLYsbbrgh+vbtW/S1vn37xg033BDLly8X+mXOe/YBAADYqkKhEB988EGsXr06OnbsGF26dHEzvgoh9gEAACAxXsYPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AAACJEfsAAACQGLEPAAAAiRH7AAAAkBixDwAAAIkR+wAAAJAYsQ8AdfDJJ5/E9773vZg1a1Zs2LAh63EAALYrVygUClkPAQDlbtq0aTFixIiIiNh1113jq1/9apxzzjlxwgknRJs2bTKeDgCgmNgHgDrYuHFjHHDAAbFo0aIoFArRunXr2Lhxo/AHAMqS2AeAOpo+fXqcddZZW6wLfwCg3Ih9AKijQqEQRx55ZDz77LNRU1Oz1ccIfwCgHIh9AKiHOXPmxLHHHlunxwp/ACArYh8A6un000+PWbNmxcaNG+v8PcIfAGhOYh8A6ukvf/lLfO5zn4uGPoUKfwCgqdU59pcsWRK77LJLdO3aNXK5XFPPBQBl7e/+7u9i8uTJ23zvfl0JfwDKWaFQiPfffz8++ugjPVhh6hz7m/5C+/XrF9/61reiuro6Onfu3JSzAUDZeuONN2LfffeN9evXl+ycwh+AcrFy5cqYNGlS3HTTTbFo0aLadT1YOeod+5v+s0OHDjF16tQYNmxY000HAGXsu9/9blx//fWN3t3fGuEPQFZmzZoVI0aMiDVr1kREFL1tTQ9WjnrH/iZVVVWRy+Xi/vvv9xcMQIv017/+NXr37h0ffvhhk15H+APQXGbNmhWnnXZaFAqFyOfz23ycHix/DY79iL/9Bbdv3z6WLVvmJRwAtEjXXXdd/MM//EODb9ZXX8IfgKaycuXK6NGjR6xdu3a7ob+JHixvjYr9TevXXnttXHTRRSUdDAAqwbp16+Kwww6LFStWNFvwb7Ip/Dt27BhnnHFGDB8+PIYMGSL8AWiQn/70p3HNNdfU6/ksl8vFDTfcEJdddlkTTkZDNDr2AQAAaJlyuVz07ds3FixYoBnLjNgHAACgUd57773o2rVr1mPwKa1LdaLFixdH7969S3U6AAAAmsmSJUuiT58+Df7+1atXi/0yU+edfQAAAKAyVGU9AAAAAFBaYh8AAAASI/YBAAAgMWIfAAAAEiP2AQAAIDFiHwAAABIj9gEAACAxYh8AAAAS8/8A6GuNgzXkSqUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mpl:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ascii:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "      _b                  _c            \n",
      "                                        \n",
      "                                        \n",
      "*->---->---->---->-*->---->---->---->--*\n",
      "                    ~~~                 \n",
      "                       ~        c       \n",
      "                      + ~~~             \n",
      "                       W   ~            \n",
      "                            ~*->---->--*\n",
      "                               >        \n",
      "                                ---_s   \n",
      "                                   -    \n",
      "                                    >-- \n",
      "                                       *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "             d                          \n",
      "                                        \n",
      "                                        \n",
      "*->---->---->---->---->---->---->---->-*\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<wand.image.Image: ffbc5f8 'PDF' (332x498)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "unicode:\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "      b̅                  c̅            \n",
      "                                        \n",
      "                                        \n",
      "*→→→→→→→→→→→→→→→→→→*→→→→→→→→→→→→→→→→→→→*\n",
      "                    ~~~                 \n",
      "                       ~        c       \n",
      "                     +^ ~~~             \n",
      "                       W   ~            \n",
      "                            ~*↘→→→→→→→→*\n",
      "                               ↘        \n",
      "                                ↘↘↘s̅   \n",
      "                                   ↘    \n",
      "                                    ↘↘↘ \n",
      "                                       *\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "             d                          \n",
      "                                        \n",
      "                                        \n",
      "*→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→→*\n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "                                        \n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<wand.image.Image: e008ed3 'PDF' (477x393)>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = Vertex().with_xy(-2, -2)\n",
    "v2 = Vertex().with_xy(2, -2)\n",
    "\n",
    "i1 = Vertex().with_xy(-2, 2)\n",
    "o1 = Vertex().with_xy(2,  2)\n",
    "o2 = Vertex().with_xy(2,  1)\n",
    "o3 = Vertex().with_xy(2,  0)\n",
    "\n",
    "p1 = Vertex().with_xy(0,  2)\n",
    "p2 = Vertex().with_xy(1,  1)\n",
    "\n",
    "\n",
    "fd = FeynmanDiagram().add(\n",
    "    v1,\n",
    "    v2,\n",
    "    Propagator().connect(v1,v2).with_type(\"fermion\").with_label(\"$d$\").with_tension(0),\n",
    "    Leg().with_target(v1).with_point(v1).with_type(\"phantom\").with_incoming(),\n",
    "    Leg().with_target(v2).with_point(v2).with_type(\"phantom\").with_outgoing(),\n",
    "    \n",
    "    i1,p1,p2,o1,o2,o3,\n",
    "    Propagator().connect(p2,p1).with_type(\"boson\").with_label(\"$W^+$\"),\n",
    "    Leg(label=r\"$\\bar{b}$\").with_target(p1).with_point(i1).with_type(\"fermion\").with_incoming(),\n",
    "    Leg(label=r\"$\\bar{c}$\").with_target(p1).with_point(o1).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg(label=\"$c$\").with_target(p2).with_point(o2).with_type(\"fermion\").with_outgoing(),\n",
    "    Leg(label=r\"$\\bar{s}$\").with_target(p2).with_point(o3).with_type(\"fermion\").with_outgoing()\n",
    ")\n",
    "ar = AllRender(fd)\n",
    "ar.render()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52d52beb",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b8e1fd4d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "09790aa7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}