assets/notebooks/ls-ses22.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "83bfd58f-2159-4961-a21f-ec888ca91f8a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "51c22c4c-98c7-41c2-ac57-41f0127d6a4a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# import old work\n",
    "\n",
    "from session15 import get_session15_endomaps\n",
    "XG,YG = get_session15_endomaps()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b87a3822-a626-4cc8-bc1a-e6430eef6ca9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(XG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c240e98c-3c46-4dab-9ab2-0dd9b157d1f9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(YG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5b01b14c-66c5-4f07-9412-e82e46d523bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_cycle(n):\n",
    "    nodes = range(n)\n",
    "    edges = [(i,(i+1)%n) for i in nodes]\n",
    "    G = nx.DiGraph()\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(edges)\n",
    "    return G\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c0299b33-e930-4d22-8940-1ab78a4d352d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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P+zB3794tSWrcuLHHcUUdO3aUzWYzOTFgLgolUEk2bdqkvn37qkWLFlqxYgVPmwIB5tixY1q7dq17grlx40aVlZWpRo0aiomJcU8xo6OjVb16dbPjApWKQglUgg0bNqhfv35q27atli1bplq1apkdCUAFnTt3Ths3bnRPMdeuXauTJ0/KZrOpS5cu7ilmXFwcJzgg6FEoAR/LzMzUlVdeqQ4dOuiLL77gBn8gSDmdTn3zzTceh65/++23kqSmTZt6HFfUvn17Wa1WkxMD3kOhBHxozZo1GjBggLp27aolS5aoRo0aZkcCUIm+//57j9dGbtmyRYZhqGbNmoqNjXVPMHv27Klq1aqZHRf4wyiUgI+kp6dr0KBB6tmzpxYvXqyIiAizIwEwWVFRkTZs2OCeYmZmZur06dOy2+3q1q2bxxST48QQSCiUgA+sWrVKV111leLj4/XZZ58xeQDwi8rLy/X11197bJPv379fktSiRQuP44ratm3LNjn8FoUS8LLly5fr6quvVmJioj799FNVrVrV7EgAAsihQ4c8tsm3bt0qp9Op2rVru7fJ4+Pj1aNHD1WpUsXsuIAkCiXgVUuXLtXw4cPVp08fzZ8/nx/2ACrs7NmzWr9+vcc2+dmzZxUWFqbu3bu7p5ixsbG8KAGmoVACXrJ48WKNGDFCAwYM0Lx58xQWFmZ2JABByDAM7dixw2OKefDgQUlSmzZtPA5db9WqlSwWi8mJEQoolIAXLFiwQNddd52GDh2qOXPmyOFwmB0JQAjJycnxuA9z+/btcrlcuuSSSxQbG+ueYnbr1k3h4eFmx0UQolACFfTvf/9bo0eP1ogRIzRr1izKJADTnT59WuvWrXNPMNevX6+ioiKFh4erZ8+e7ilmbGysateubXZcBAEKJVABc+bM0bhx4zRy5Ei9//77stvtZkcCgJ8pKyvTtm3bPKaYR44ckSRdfvnlHscVNW/enG1yXDAKJfAHffjhh7rxxhs1btw4zZw5UzabzexIAHBeXC6X9u/f7y6Ya9asUXZ2tiSpfv36HscVde3alZ0X/C4KJfAH/Otf/9KECRM0fvx4vfPOO5wNByDgnTx5UpmZme6SuWHDBhUXF6tq1aqKjo52TzF79eqlmjVrmh0XfoZCCVygf/zjH7rttts0ceJEvfnmm5RJAEGptLRUW7Zs8ZhiHj9+XBaLRR06dPCYYjZp0oRt8hBHoQQuwFtvvaU777xTd911l1577TV+gAIIGS6XS3v37nWXy4yMDH3zzTeSpEsvvdTjuKJOnTpxT3mIoVAC5+m1117TPffco/vuu08vvfQSZRJAyDtx4oTWrl3rftAnKytLpaWlioiIUExMjHuKGRMToxo1apgdFz5EoQTOw0svvaQHH3xQDz/8sGbMmEGZBIBfUFxcrE2bNrmnmGvXrlVeXp6sVqs6d+7sMcW87LLLzI5bIYUlhvbnFarUcCrMblXTOhGKCA/dqSyFEvgdM2bM0OTJkzVlyhQ988wzlEkAOE8ul0u7du3yOK5oz549kqTIyEiP44o6dOjg96dl7DlaoNnrc5S265hy8ov00wJlkRRZu5qS2tTT9dGRalU/tCayFErgNzz77LN67LHHNHXqVE2bNo0yCQAVdPToUfc2+Zo1a7R582aVlZXpoosuUq9evdxTzOjoaEVERJgdV5KUm1+kKQt26Mu9J2SzWlTu/PXq9OPnV7Ssq+eGdVTj2tUqMal5KJTAL3C5XHrqqac0bdo0PfXUU3r88cfNjgQAQencuXPKysry2CY/deqUbDabunbt6jHFbNiwYaXn+zgrR08sypbhdP1mkfxfNqtFdqtFTw5pr1FRkT5M6B8olMD/cLlcevzxx/Xss8/qL3/5iyZPnmx2JAAIGU6nUzt37vQ4rmjfvn2SpGbNmnkcV3T55Zf79Oi219P26IUVuyu8zkP9WmtSUisvJPJfFErgJ1wulyZPnqznn39eL7zwgh588EGzIwFAyDty5Ij7Hsw1a9Zoy5YtKi8vV61atRQbG+ueYkZFRalq1apeuebHWTma/OkOr6wlSTOGd9TIIJ5UUiiB/3K5XHrooYf00ksv6ZVXXtG9995rdiQAwC8oLCzUhg0b3FPMtWvXqqCgQA6HQ926dfOYYtarV++C18/NL1Kfl9NVYji9ljncblXK/QlBe08lhRLQD2Xyvvvu06uvvqrXX39dd911l9mRAADnqby8XF999ZXHFDMnJ0eS1KpVK4/jitq0afO7D1iOm7lea7/Lu6B7Jn+PzWpRbPM6mjUh2mtr+hMKJUKe0+nUpEmT9NZbb+ntt9/WbbfdZnYkAEAFHTx40OOtPtu2bZPT6VSdOnUUGxvrnmL26NFD4eHh7t+352iB+r7yH5/lSrn//6llveA7UohCiZDmdDo1ceJEzZw5U//85z81fvx4syMBAHygoKBA69atc5fMdevWqbCwUGFhYYqKinJPMTOKG2n+tmNenU7+yGa1aFx0E00b0t7ra5uNQomQVV5erltuuUXvv/++3nvvPd1www1mRwIAVBLDMLR9+3aPp8kPHz6sRhP/IcfFvjueqEmdakp/KMln65uFQomQVF5erptvvlmzZ8/WrFmzNGbMGLMjAQBM5HK5tHPPdxr4r5364b03vmGR9NW0/kH3mkbfHd4E+CnDMDR27Fh99NFHmjNnDmUSACCLxSJX9bryZZmUJJek/XmFPr2GGYKrHgO/o6ysTGPGjNFnn32muXPn6pprrjE7EgDAT5R68Zggf7hOZaJQImSUlpZq1KhR+vzzzzV//nwNHTrU7EgAAD8SZq+cjdvKuk5lolAiJJSUlOjaa6/V8uXL9emnn2rw4MFmRwIA+JmmdSJk0Q/b0r5i+e91gk3wVWTgfxQXF2v48OFasWKFFi5cSJkEAPyiiHC7In38JpvIOtWC7oEciUKJIHfu3DkNHTpUaWlp+vzzz3XllVeaHQkA4MeS2tSTzeqbB3NsVouSWl/4qyADAYUSQauoqEiDBw/WmjVrtHTpUvXp08fsSAAAP3d9dKRPDjWXpHKnS2NjIn2yttkolAhKZ8+e1cCBA7V+/XotW7ZMiYmJZkcCAASAVvVr6IqWdb0+pbRZLbqiZd2gfO2iRKFEECooKNCAAQO0efNmrVixQldccYXZkQAAAeS5YR1l93KhtFstem5YR6+u6U8olAgqp0+fVr9+/bRjxw6tXLlSsbGxZkcCAASYxrWr6Ukvv2/7qSHt1djHD/yYiUKJoHHq1Cn17dtXu3btUkpKiqKjo82OBAAIUKOiIvVQv9ZeWevhfm00Mio47538Ee/yRlDIz89X3759tX//fqWkpKhr165mRwIABIGPs3L0xKJsGU7XBT2sY7NaZLda9NSQ9kFfJiUKJYLAiRMn1KdPHx06dEgpKSnq3Lmz2ZEAAEEkN79IUxbs0Jd7T8hmtfxmsfzx8yta1tVzwzoG9Tb3T1EoEdCOHTumPn366OjRo1q1apU6dOhgdiQAQJDac7RAs9fnKG33MeXkFXm8UceiHw4tT2pdT2NjIoP2ae5fQ6FEwPr+++/Vu3dv5efnKzU1Ve3atTM7EgAgRBSWGMrYvlsP/Wmy3nrjNXVpcWlQvgHnfPFQDgLS4cOHlZiYqFOnTik9PZ0yCQCoVBHhdr0zY6p2rF6suX9/MaTLpMSEEgHo4MGDSk5OVnFxsVJTU9WyZUuzIwEAQsyhQ4fUtGlTGYahiIgIHTp0SDVr1jQ7lmmYUCKgHDhwQAkJCSotLVV6ejplEgBgiunTp8vpdEqSzp07p1dffdXkROZiQomAsW/fPiUlJclmsyk1NVVNmjQxOxIAIAQdOnRIzZo1U1lZmftrNWrUUG5ubshOKZlQIiB8++23SkhIkMPh0OrVqymTAADTTJ8+XYZheHytoKAgpKeUTCjh93bv3q3k5GRFREQoNTVVl156qdmRAAAhrF69ejp+/PjPvt62bVvt3LnThETmC+1HkuD3vvnmGyUnJ6tWrVpKTU1VgwYNzI4EAAhx69atU25urnbs2KG7775b77//vpo0aaJmzZqZHc00FEr4rezsbPXu3VuXXHKJVq1apXr16pkdCQAANW/eXM2bN5fd/kON6tmzp9q2bWtyKnNxDyX80vbt25WUlKQGDRooLS2NMgkAgB+jUMLvbN26VcnJybrsssu0atUq1a1b1+xIAADgN1Ao4Vc2bdqk5ORkNW/eXKtWrVKdOnXMjgQAAH4HhRJ+Y8OGDerdu7fatGmjlStX6uKLLzY7EgAAOA8USviFzMxM9e3bVx06dNDy5ctD9mBYAAACEYUSpvvyyy/Vr18/denSRcuWLdNFF11kdiQAAHABKJQw1erVq3XllVeqZ8+eWrp0qapXr252JAAAcIEolDBNSkqKBg4cqLi4OC1evFgRERFmRwIAAH8AhRKmWL58ua666iolJCRo0aJFqlatmtmRAADAH0ShRKVbunSphgwZoj59+uizzz5TlSpVzI4EAAAqgEKJSrVo0SJdffXVGjhwoD755BOFh4ebHQkAAFQQhRKV5tNPP9U111yjoUOHat68eQoLCzM7EgAA8AIKJSrFv//9b1133XUaMWKE5syZI4fDYXYkAADgJRRK+NycOXM0evRojRo1SrNmzZLdbjc7EgAA8CIKJXxq1qxZGjt2rMaNG6f333+fMgkAQBCiUMJn3n33Xd14440aP368Zs6cKZvNZnYkAADgAxRK+MQ777yjCRMmaOLEiXr77bdltfKvGgAAwYo/5eF1b775piZOnKhJkybpzTffpEwCABDk+JMeXvXqq6/qrrvu0v33369XX31VFovF7EgAAMDHKJTwmhdffFH33nuv/vSnP+nFF1+kTAIAECIolPCKGTNm6KGHHtKUKVM0ffp0yiQAACGEQokKe+aZZzR58mQ98cQTeuaZZyiTAACEGA4FxB/mcrn05JNP6sknn9TTTz+txx57zOxIAADABBRK/CEul0uPPfaYnnvuOU2fPl2PPPKI2ZEAAIBJKJS4YC6XS5MnT9bzzz+vF154QQ8++KDZkQAAgIkolLggLpdLDz74oF5++WW98soruvfee82OBAAATEahxHlzuVy699579dprr+mNN97QnXfeaXYkAADgByiUOC9Op1N33XWX/v73v+vtt9/WbbfdZnYkAADgJyiU+F1Op1MTJ07UzJkzNXPmTI0fP97sSAAAwI9QKPGbysvLdcstt+iDDz7Qe++9pxtuuMHsSAAAwM9QKPGrDMPQzTffrI8++kizZs3SmDFjzI4EAAD8EIUSv8gwDI0bN07//ve/9fHHH+vaa681OxIAAPBTFEr8TFlZmcaMGaPPPvtM8+bN0/Dhw82OBAAA/BiFEh5KS0s1atQoff7555o/f76GDh1qdiQAAODnKJRwKykp0bXXXqvly5drwYIFGjRokNmRAABAAKBQQpJUXFys4cOHKy0tTYsWLVL//v3NjgQAAAIEhRIqKirS1VdfrTVr1mjx4sXq06eP2ZEAAEAAoVCGuMLCQg0ZMkTr1q3T0qVLlZiYaHYkAAAQYCiUIezs2bMaNGiQNm/erGXLlumKK64wOxIAAAhAFMoQdebMGQ0cOFDbt2/X8uXLFRsba3YkAAAQoCiUIej06dO68sortXPnTq1cuVLR0dFmRwIAAAGMQhliTp48qf79+2vv3r1KSUlRjx49zI4EAAACHIUyhOTl5alfv346cOCAVq1apa5du5odCQAABAEKZYg4fvy4+vbtq0OHDik1NVWdOnUyOxIAAAgSFMoQcOzYMfXu3VvHjh3T6tWr1b59e7MjAQCAIEKhDHLff/+9kpOTdfLkSa1evVrt2rUzOxIAAAgyFMogdvjwYSUnJ+vs2bNKT09X69atzY4EAACCEIUySOXm5io5OVklJSVKT09XixYtzI4EAACCFIUyCB04cEBJSUlyOp1KT09Xs2bNzI4EAACCmNXsAPCuffv2KSEhQRaLhTIJAAAqBYUyiOzdu1cJCQlyOBxKT09XkyZNzI4EAABCAIUySOzevVsJCQmqVq2a0tPTddlll5kdCQAAhAgKZRDYuXOnEhISVLNmTa1evVqNGjUyOxIAAAghFMoAl52drcTERNWtW1erV69WgwYNzI4EAABCDIUygG3fvl2JiYlq2LCh0tLSVK9ePbMjAQCAEEShDFBbtmxRUlKSIiMjlZqaqrp165odCQAAhCgKZQDauHGjkpOT1aJFC6WkpKh27dpmRwIAACGMQhlg1q9frz59+qht27ZauXKlLr74YrMjAQCAEEehDCBr165V37591aFDBy1fvlw1a9Y0OxIAAACFMlB8+eWX6t+/v7p166Zly5bpoosuMjsSAACAJAplQEhLS9OVV16pnj17asmSJapevbrZkQAAANwolH4uJSVFgwYNUlxcnBYvXqyIiAizIwEAAHigUPqxZcuWafDgwUpMTNSiRYtUrVo1syMBAAD8DIXSTy1ZskRDhw5Vv379tGDBAlWpUsXsSAAAAL+IQumHFi5cqGHDhmngwIGaP3++wsPDzY4EAADwqyiUfuaTTz7RiBEjNHToUM2bN09hYWFmRwIAAPhNFEo/Mm/ePI0cOVIjRozQnDlz5HA4zI4EAADwuyiUfuKjjz7S6NGjNXr0aM2aNUt2u93sSAAAAOeFQukHPvjgA40bN0433HCD3nvvPcokAAAIKBRKk7377ru66aabNH78eM2cOVM2m83sSAAAABeEQmmid955RxMmTNDtt9+ut99+W1Yr/zgAAEDgocGY5I033tDEiRN1991364033qBMAgCAgEWLMcHf/vY3TZo0Sffff7/+9re/yWKxmB0JAADgD6NQVrIXXnhB9913n/70pz/pxRdfpEwCAICAR6GsRNOnT9fDDz+sP//5z5o+fTplEgAABAUKZSV5+umn9eijj2ratGl6+umnKZMAACBocOChj7lcLk2bNk1PPfWUnn76aT322GNmRwIAAPAqCqUPuVwu/fnPf9Zf/vIXTZ8+XY888ojZkQAAALyOQukjLpdLjzzyiP7617/qxRdf1AMPPGB2JAAAAJ+gUPqAy+XSAw88oFdeeUV/+9vfdM8995gdCQAAwGcolF7mcrl0zz336PXXX9cbb7yhO++80+xIAAAAPkWh9CKn06k777xTb7/9tt5++23ddtttZkcCAADwOQqllzidTt12221699139e677+rmm282OxIAAECloFB6QXl5uSZMmKBZs2bp/fff17hx48yOBAAAUGkolH9AeXm5bDabJMkwDN10002aM2eOPvzwQ40ePdrkdAAAAJWLN+VcoHfeeUcNGzbUtm3bVFZWprFjx+rjjz/Wxx9/TJkEAAAhiQnlBXrzzTd1/PhxJSYmqkePHlq9erXmzZun4cOHmx0NAADAFBTKC7Bnzx5t27ZNknT69GmlpKTo9ddfp0wCAICQFvJb3oUlhrIPn9aWnJPKPnxahSXGr/7auXPnuu+ddLlcslqtmjZtmnbt2lVZcQEAAPxOSE4o9xwt0Oz1OUrbdUw5+UVy/eQzi6TI2tWU1Kaero+OVKv6NdyfffDBByovL3f/b6fTqRMnTuiBBx7QkiVLKu8bAAAA8CMhVShz84s0ZcEOfbn3hGxWi8qdrp/9GpekA/lFmrX+gN7L3K8rWtbVc8M66vtvs7Vnzx5JktVqldPpVMuWLTVq1CjOnAQAACEtZArlx1k5emJRtoz/lshfKpM/9ePna7/LU5+X09Xm7HZJUrNmzTRhwgQNHz5c7dq1821oAACAABAShfL1tD16YcXuP/R7y50ulTtd2l6lg56av16PX9PTy+kAAAACW9A/lPNxVs4fLpP/a+bG45qbleOVtQAAAIJFUBfK3PwiPbEo26trTl2Urdz8Iq+uCQAAEMiCulBOWbDDfc+ktxhOl6Ys2OHVNQEAAAJZ0BbKPUcL9OXeE7/78M2FKne69OXeE9p7rMCr6wIAAASqoC2Us9fnyGa1+GRtm9WiD9dxLyUAAIAUxIUybdcxr08nf1TudClt9zGfrA0AABBogrJQni0xlOPjB2dy8op+8zWNAAAAoSIoC+WBvEL5Zjb5f1yS9ucV+vgqAAAA/i8oC2Wp4Qyq6wAAAPizoCyUYfbK+bYq6zoAAAD+LCgbUdM6EfLN893/x/Lf6wAAAIS6oCyUEeF2Rdau5tNrRNappojwkHgVOgAAwG8KykIpSUlt6vn0HMqk1vV8sjYAAECgCdpCeX10pE/PoRwbE+mTtQEAAAJN0BbKVvVr6IqWdb0+pbRZLbqiZV21rFfDq+sCAAAEqqAtlJL03LCOsnu5UNqtFj03rKNX1wQAAAhkQV0oG9eupieHtPfqmk8Naa/GPn7gBwAAIJAEdaGUpFFRkXqoX2uvrFW4do7qF37nlbUAAACCRdAXSkmalNRK04d3VLjdesH3VNqsFoXbrXp6cBt1DT+mgQMHKiUlxUdJAQAAAk9IFErph0llyv0Jim1eR5J+t1j++Hls8zpKuT9B4+JaatGiRUpISNBVV12l5cuX+zwzAABAIAipk7kb166mWROitedogWavz1Ha7mPKySvSTw8XsuiHQ8uTWtfT2JhIj6e5q1Spos8++0wjRozQkCFD9Omnn2rQoEGV/n0AAAD4E4vL5fLNYY0BorDE0P68QpUaToXZrWpaJ+J334BTWlqqkSNHasmSJZo/f76GDBlSSWkBAIC/yMjIUHx8vHbu3Km2bduaHcdUIbPl/Wsiwu1q36imukZerPaNap7X6xTDwsI0b948DRkyRNdcc40+/fTTSkgKAADgn0K+UP5RDodDc+bM0TXXXKPrrrtO8+bNMzsSAACAKULqHkpvczgc+vDDD2W32zV69GgZhqExY8aYHQsAAKBSUSgryG636/3335fD4dC4ceNkGIZuuOEGs2MBAABUGgqlF9hsNs2cOVN2u1033XSTDMPQ+PHjzY4FAABQKSiUXmK1WvX222/LbrdrwoQJMgxDt912m9mxAAAAfI5C6UVWq1Vvvvmm7Ha7Jk6cqLKyMt11111mxwIAAPApCqWXWSwWvfrqq3I4HJo0aZIMw9C9995rdiwAAACfoVD6gMVi0Ysvvii73a777rtPhmHowQcfNDsWAACAT1AofcRisWjGjBlyOBx66KGHVFZWpsmTJ5sdCwAAwOsolD5ksVj0zDPPyOFw6NFHH1VZWZkef/xxs2MBAAB4FYXSxywWi6ZNmya73a7HH39chmFo2rRpslgsZkcDAADwCgplJXnsscdkt9v16KOPyjAMPfPMM5RKAAAQFCiUlWjy5Mke91TOmDGDUgkAAAIehbKSPfjgg+6nv8vKyvTSSy9RKgEAQECjUJrg3nvvlcPh0F133SXDMPTqq69SKgEAQMCiUJrkzjvvdL9RxzAMvfHGG7JarWbHAgAAuGAUShPddtttstvtuuWWW2QYht5++21KJQAACDgUSpONHz9edrtdN998s8rKyjRz5kzZbDazYwEAAJw3CqUfuOGGG2S32zVu3DgZhqH33ntPdjv/aAAAQGCgtfiJMWPGyOFwaPTo0SovL9esWbMolQAAICDQWPzItddeK5vNppEjR6qsrExz5syRw+EwOxYAAMBv4gkQPzN8+HDNnz9fixYt0nXXXafS0lKzIwEAAPwmCqUfGjp0qBYsWKClS5fqmmuuUUlJidmRAAAAfhWF0k8NGjRIixYtUkpKioYNG6bi4mKzIwEAAPwiCqUf69+/vxYvXqzVq1dryJAhKioqMjsSAADAz1Ao/VyfPn20dOlSZWRkaPDgwSosLDQ7EgAAgAcKZQBITEzUsmXLlJWVpYEDB6qgoMDsSAAAAG4UygBxxRVXaPny5dqyZYsGDBigM2fOmB0JAABAEoUyoMTGxmrlypX66quv1L9/f50+fdrsSAAAABTKQBMdHa2UlBTt2rVLffr00cmTJ82OBAAAQhyFMgD16NFDq1at0r59+9S7d2/l5eWZHQkAAIQwCmWA6tq1q1JTU5Wbm6vk5GQdP37c7EgAACBEUSgDWKdOnbR69Wp9//33Sk5O1rFjx8yOBAAAQhCFMsC1b99eq1ev1okTJ5SYmKgjR46YHQkAAIQYCmUQaNeundLT03XmzBklJibq0KFDZkcCAAAhhEIZJFq3bq309HSdO3dOCQkJys3NNTsSAAAIERTKINKiRQulp6fLMAwlJCTowIEDZkcCAAAhgEIZZJo1a6b09HRZLBYlJCTou+++MzsSAAAIchTKINSkSROlp6fL4XAoISFBe/fuNTsSAAAIYhTKIHXZZZcpPT1dERERSkhI0O7du82OBAAAghSFMog1atRIq1evVs2aNZWQkKCdO3eaHQkAAAQhCmWQa9CggVavXq26desqMTFRX331ldmRAABAkKFQhoB69eopLS1NDRs2VFJSkrZt22Z2JAAAEEQolCGibt26Sk1NVWRkpJKTk7VlyxazIwEAgCBBoQwhtWvXVkpKilq0aKHk5GRt3LjR7EgAACAIUChDzMUXX6yVK1eqbdu26tOnj9avX292JAAAEOAolCGoZs2aWr58uTp06KC+ffsqIyPD7EgAACCAUShD1EUXXaRly5apW7du6t+/v/7zn/+YHQkAAAQoCmUIq169upYsWaLo6GgNGDBAaWlpZkcCAAABiEIZ4iIiIrR48WLFxcVp0KBBSklJMTsSAAAIMBRKqFq1alq0aJESExM1ePBgLVu2zOxIAAAggFAoIUmqUqWKFixYoH79+mno0KFasmSJ2ZEAAECAoFDCLTw8XPPnz9fAgQM1bNgwLVy40OxIAAAgAFAo4SEsLEzz5s3T0KFDNWLECH3yySdmRwIAAH6OQomfcTgcmjNnjkaMGKGRI0dq7ty5ZkcCAAB+zG52APgnu92uWbNmyW63a8yYMSovL9eYMWPMjgUAAPwQhRK/ym6367333pPdbte4ceNkGIZuuOEGs2MBAAA/Q6HEb7LZbJo5c6bsdrtuuukmGYah8ePHmx0LAAD4EQolfpfVatXbb78th8OhCRMmqKysTBMnTjQ7FgAA8BMUSpwXq9WqN954Q3a7XbfffrsMw9Bdd91ldiwAAOAHKJQ4bxaLRX/729/kcDg0adIkGYahe++91+xYAADAZBRKXBCLxaIXXnhBdrtd9913n8rKyvTQQw+ZHQsAAJiIQokLZrFYNH36dDkcDj388MMqKyvTo48+anYsAABgEgol/hCLxaKnn35aDodDU6ZMkWEYevzxx82OBQAATEChxB9msVj0xBNPyG6367HHHpNhGJo2bZosFovZ0QAAQCWiUKLC/vznP8tut2vy5MkqKyvTs88+S6kEACCEUCjhFY888ogcDocefPBBlZWV6fnnn6dUAgAQIiiU8JoHHnhAdrtd9957r8rKyvTyyy9TKgEACAEUSnjVPffcI4fDoTvvvFOGYei1116jVAIAEOQolPC6O+64Q3a7XbfddpsMw9Cbb74pq9VqdiwAAOAjFEr4xK233iq73a4JEybIMAy98847lEoAAIIUhRI+c/PNN8tut+umm25SWVmZ3n33XdlsNrNjAQAAL6NQwqfGjRsnu92ucePGyTAMvf/++7Lb+dcOAIBgwp/s8LnRo0fLbrdr9OjRKi8v16xZs+RwOMyOBQAAvIRCiUpx7bXXymazaeTIkTIMQx999JHCwsLMjgUAALyApyRQaYYPH65PPvlEixYt0nXXXaeSkhKzIwEAAC+gUKJSDRkyRJ999pmWLVuma665RsXFxWZHAgAAFUShRKUbOHCgFi5cqFWrVmnYsGE6d+6c2ZEAAEAFUChhiv79++vzzz9Xenq6hgwZoqKiIrMjAQCAP4hCCdP07t1bS5cuVWZmpgYPHqzCwkKzIwEAgD+AQglTJSYmatmyZcrKytKAAQNUUFBgdiQAAHCBKJQwXXx8vFasWKGtW7fqyiuv1JkzZ8yOBAAALgCFEn6hV69eSklJUXZ2tvr166dTp06ZHQkAAJwnCiX8Rs+ePbVq1Srt3r1bffv2VX5+vtmRAADAeaBQwq90795dqamp2rdvn/r06aO8vDyzIwEAgN9BoYTf6dKli9LS0nTw4EElJyfr+PHjZkcCAAC/gUIJv9SxY0elpaXp6NGjSkpK0tGjR82OBAAAfgWFEn6rffv2Wr16tfLz85WYmKgjR46YHQkAAPwCCiX8Wtu2bZWenq6CggIlJibq0KFDZkcCAAD/g0IJv9eqVSulp6fr3LlzSkhIUG5urtmRAADAT1AoERBatGih9PR0lZeXKyEhQfv37zc7EgAA+C8KJQJGs2bNlJ6eLovFooSEBH333XdmRwIAAKJQIsBERkYqPT1d4eHhSkhI0N69e82OBABAyKNQIuBcdtllWr16tSIiIpSQkKBdu3aZHQkAgJBGoURAatSokVavXq1atWopMTFRX3/9tdmRAAAIWRRKBKwGDRooLS1Nl1xyiRITE/XVV1+ZHQkAECIKSwydKK+i8EZtdOScTYUlhtmRTGVxuVwus0MAFXHixAn17dtXBw8eVEpKijp37mx2JABAENpztECz1+cobdcx5eQX6acFyiIpsnY1JbWpp+ujI9Wqfg2zYpqCQomgkJ+fr759+2r//v1auXKlunXrZnYkAECQyM0v0pQFO/Tl3hOyWS0qd/56dfrx8yta1tVzwzqqce1qlZjUPBRKBI2TJ0+qf//+2rNnj1asWKGoqCizIwEAAtzHWTl6YlG2DKfrN4vk/7JZLbJbLXpySHuNior0YUL/QKFEUDl9+rQGDBig7OxsLV++XDExMWZHAgAEqNfT9uiFFbsrvM5D/VprUlIrLyTyXzyUg6BSs2ZNLV++XJ06dVK/fv2UkZFhdiQAQAD6OCvHK2VSkl5YsVtzs3K8spa/olAi6NSoUUNffPGFunXrpv79++s///mP2ZEAAAEkN79ITyzK9uqaUxdlKze/yKtr+hMKJYJS9erVtWTJEkVHR2vAgAFKTU01OxIAIEBMWbBDxgXcL3k+DKdLUxbs8Oqa/oRCiaAVERGhzz//XPHx8Ro0aJBWrlxpdiQAgJ/bc7RAX+49cUEP4JyPcqdLX+49ob3HCry6rr+gUCKoVa1aVQsXLlRycrKuuuoqLVu2zOxIAAA/Nnt9jmxWi0/Wtlkt+nBdcN5LSaFE0KtSpYo+/fRT9e/fX0OHDtXnn39udiQAgJ9K23XM69PJH5U7XUrbfcwna5uNQomQEB4ern//+98aNGiQhg8frs8++8zsSAAAP3O2xFCOjx+cyckrCsrXNFIoETLCwsI0d+5cXX311br22ms1f/58syMBAPzIgbxC+fpwbpek/XmFPr5K5aNQIqQ4HA599NFHuvbaazVq1CjNnTvX7EgAgEqUm5urt956Sxs3bpRheE4KSw1npWSorOtUJrvZAYDKZrfbNWvWLNntdo0ZM0aGYej66683OxYAoBIsXLhQd999t6QfHtyMi4tTYmKi4uPjVSOyXaVkCLMH3zyPQomQZLPZ9K9//Ut2u13jxo2TYRi68cYbzY4FAPCx7t27u//7uXPnlJKSolWrVsnlcqlmnXq6+NZ3fbrtbZHUtE6ED69gDgolQpbNZtM///lP2e123XzzzTIMQxMmTDA7FgDAB86cOaN169YpPT1dFotFLtf/1UaXyyWbzaYpf3pQSyzVdMCHD+ZE1qmmiPDgq1/B9x0BF8Bqtervf/+77Ha7brnlFpWVlen22283OxYAoIJyc3OVkZGhNWvWKCMjQ9u3b5fT6VSdOnVUq1YtnTx5UtIPw4W6detq6dKl6tatm4oWZWvW+gM+OTrIZrUoqXU9r6/rDyiUCHlWq1VvvPGGHA6H7rjjDhmGoUmTJpkdCwBwnsrLy7Vjxw5lZGS4S2Rubq4kqVWrVoqPj9ekSZMUFxenNm3aaMqUKXr++eclSV26dNHixYvVsGFDSdL10ZF6L3O/b3I6XRobE+mTtc1GoQQkWSwWvfLKK7Lb7br77rtlGIbuu+8+s2MBAH5BYWGh1q9f754+ZmZmqqCgQA6HQ927d9d1112n+Ph4xcbGql69n08EExMTNX36dI0ZM0YzZ85UlSpV3J+1ql9DV7Ssq7Xf5Xl1SmmzWhTbvI5a1qvhtTX9icX105sIgBDncrn06KOPasaMGXr++ef18MMPmx0JAELe4cOHPaaPW7duVXl5uWrVqqW4uDj3f6KiolS1atXfXc/lcmn79u3q1KmTLJafv2YxN79IfV5OV4kXj/cJt1uVcn+CGteu5rU1/QkTSuAnLBaL/vKXv8jhcOhPf/qTysrKNGXKFLNjAUDIcDqd+vrrr93Tx4yMDO3bt0+S1Lx5c8XFxem2225TXFyc2rVrJ6v1wo/gsVgs6ty5869+3rh2NT05pL0mf7rjD38f/+upIe2DtkxKFErgZywWi55++mk5HA79+c9/lmEYmjp1qtmxACAoFRUVKSsryz19zMzM1KlTp2Sz2dStWzcNHTrUPYH88T7HyjAqKlInzpbohRW7K7zWw/3aaGRUcN47+SMKJfArpk6dKpvNpscee0yGYejJJ5/8xa0RAMD5O3r0qHvymJGRoU2bNskwDF100UXq1auXHnzwQcXFxalnz56KiDD3vMZJSa1Ut3q4nliULcPpuqB7Km1Wi+xWi54a0j7oy6TEPZTA73r++ef1yCOPaPLkyXruuecolQBwnlwul7755huP43v27t0rSWrSpIl78hgfH6/27dvLZrOZnPiX5eYXacqCHfpy7wnZrJbfLJY/fn5Fy7p6bljHoN7m/ikKJXAeXn75ZT3wwAN68MEH9de//pVSCQC/oLi4WBs3bvSYQObn58tqtapz586Kj493l8jLLrvM7LgXbM/RAs1en6O03ceUk1fk8UYdi344tDypdT2NjYkM2qe5fw2FEjhPr732mu655x7de++9evnllymVAELeiRMntHbtWvf0cePGjSotLVX16tUVExPjnj5GR0erRo3gKliFJYb25xWq1HAqzG5V0zoRQfkGnPMVut85cIHuvvtu2e123XnnnTIMQ6+++uoferoQAAKRy+XSnj17PI7v2bVrlyTp0ksvVXx8vEaNGqW4uDh16tRJdntwV4yIcLvaN6ppdgy/Edz/tAEvu+OOO2S32zVx4kSVlZXprbfeolQCCEqlpaXavHmzx/E9x48fl8ViUceOHZWcnKypU6cqLi5OkZGR7NqEOAolcIFuvfVWORwOjR8/XoZh6J133vHbG8kB4HydPHnSY/s6KytLxcXFqlq1qmJiYjRx4kTFxcWpV69eqlmTyRw8USiBP+Cmm26S3W7XjTfeKMMw9O6771IqAQQMl8ulffv2ucvjmjVr9PXXX0uSGjRooLi4OP3lL39RXFycunTpIofDYXJi+DsKJfAHjR07Vna7XWPHjpVhGHr//feD/p4hAIGprKxMW7du9di+/v777yVJ7du3V3x8vB555BHFx8erWbNmbF/jgvGnH1ABo0aNks1m05gxY2QYhj788EP+Jg/AdKdPn1ZmZqa7PK5fv15FRUWqUqWKoqKidPPNN7u3r2vXrm12XAQBjg0CvGDBggUaOXKkrrrqKs2ZM0dhYWFmRwIQIlwul3Jycjymjzt27JDL5dIll1zicXh4t27d+PkEn6BQAl6yePFijRgxQldeeaXmzZun8PBwsyMBCEKGYWj79u0eb585dOiQJKlNmzYeh4e3atWK7WtUCgol4EVLly7V8OHD1adPH82fP19VqlQxOxKAAFdQUKB169a5p4/r1q3T2bNnFRYWph49erinj7Gxsapbt67ZcRGiKJSAl61YsUJDhw5VQkKCFixYoKpVq5odCUAAOXjwoMf0cdu2bXI6napdu7Z78hgXF6cePXrwl1b4DQol4AOrVq3SVVddpbi4OC1cuFDVqlUzOxIAP1ReXq7s7GyP43tycnIkSS1btnRPH+Pi4tSmTRtepAC/RaEEfCQ9PV2DBg1SVFSUPv/8c0VERJgdCYDJCgsLtWHDBneBzMzM1JkzZ2S329W9e3ePCWT9+vXNjgucNwol4ENr1qzRgAED1LVrVy1ZskQ1atQwOxKASnTkyBGPd19v2bJF5eXlqlmzpmJjY93Tx6ioKHYyENAolICPZWZm6sorr1SHDh30xRdf6KKLLjI7EgAfcDqd2rlzp8fxPd99950kqVmzZh7H91x++eVsXyOoUCiBSrBhwwb1799frVu31vLly1WrVi2zIwGooHPnzikrK8s9fczMzNTJkydls9nUpUsXj+N7GjVqZHZcwKcolEAl2bx5s/r06aPmzZtrxYoVvJ0CCDDHjh1zTx4zMjK0adMmlZWVqUaNGurVq5d7+tizZ09Vr17d7LhApaJQApVo69at6tOnjxo3bqyUlBTVqVPH7EgAfoHL5dKuXbs8ju/Zs2ePJKlx48Ye08eOHTvKZrOZnBgwF4USqGQ7duxQ79691aBBA61atUqXXHKJ2ZGAkFdSUqKNGzd6TCDz8vJktVrVqVMnj+N7GjdubHZcwO9QKAETfP3110pOTlbdunW1atUqjgcBKlleXp7Wrl3rnj5u3LhRJSUlioiIUExMjHv6GBMTw4N0wHmgUAIm+eabb5ScnKyaNWsqNTVVDRs2NDsSEJRcLpf27t3rcXzPN998I0lq1KiRx/Sxc+fOstvtJicGAg+FEjDRnj17lJSUpIiICKWmpurSSy81OxIQ8EpLS7V582aP7etjx47JYrGoQ4cOHsf3NGnSRBaLxezIQMCjUAIm+/bbb5WcnCyHw6HU1FRFRkaaHQkIKCdPnlRmZqZ7+rhhwwYVFxeratWq6tmzp3v62KtXL47sAnyEQgn4gf379yspKUmSlJaWpqZNm5obCPBTLpdL+/bt85g+fvXVV5Kk+vXre0wfu3TporCwMJMTA6GBQgn4iZycHCUnJ6usrExpaWlq3ry52ZEA0xmGoa1bt3oc33PkyBFJUrt27TyO72nRogXb14BJKJSAHzl06JCSkpJ07tw5paamqlWrVmZHAirVmTNn3NvXGRkZWrdunYqKihQeHq6oqCj39LFXr16c4wr4EQol4GeOHDmi5ORknT59WmlpaWrTpo3ZkQCfycnJ8Xj39fbt2+VyuVSnTh2P6WP37t0VHh5udlwAv4JCCfiho0ePKjk5WXl5eUpNTdXll19udiSgwsrLy7V9+3aP7euDBw9Kklq3bu1xfE/r1q3ZvgYCCIUS8FPHjx9X79699f333ys1NVUdOnQwOxJwQc6ePat169Z5bF8XFBTI4XCoR48e7uljbGys6tWrZ3ZcABVAoQT82IkTJ9S3b1/l5uZq1apV6ty5s9mRgF916NAhj+njtm3bVF5erosvvlixsbHu6WOPHj1UtWpVs+MC8CIKJeDn8vPz1a9fP+3bt08rV65Ut27dzI4EqLy8XNnZ2R5vnzlw4IAkqUWLFh7H97Rt21ZWq9XkxAB8iUIJBIBTp06pf//+2r17t1asWKGoqCizIyHEFBUVacOGDe7pY2Zmpk6fPi273a6uXbt6PEDToEEDs+MCqGQUSiBAnD59WgMGDFB2draWLVumXr16mR0JQez777/3mD5u2bJFhmGoZs2a6tWrl3v62LNnT1WrVs3suABMRqEEAkhBQYEGDRqkLVu26IsvvlB8fLzZkRAEnE6nvvnmG4/je7799ltJUpMmTTymj+3bt5fNZjM5MQB/Q6EEAkxhYaEGDx6srKwsLVmyRAkJCWZHQoApLi5WVlaWe/q4du1anTx5UlarVV26dPE4vufSSy81Oy6AAEChBAJQUVGRhgwZorVr1+rzzz9XcnKy2ZHgx44fP+7x7uuNGzeqrKxM1atXd29fx8XFKTo6WjVq1DA7LoAARKEEAtS5c+c0bNgwpaena+HCherXr5/ZkeAHXC6Xdu/e7XF8z+7duyVJl112mcf0sWPHjrLb7SYnBhAMKJRAACsuLtaIESOUkpKiBQsWaMCAAWZHQiUrKSnRpk2bPCaQJ06ckMViUadOnTyO74mMjDQ7LoAgRaEEAlxJSYmuu+46LVu2TPPnz9dVV11ldiT4UH5+vtauXeuePmZlZamkpETVqlVTdHS0e/oYExOjmjVrmh0XQIigUAJBoLS0VKNHj9bixYs1d+5cDRs2zOxI8AKXy6Vvv/3W4/ienTt3SpIaNmzoMX3s3LmzHA6HyYkBhCoKJRAkysrKdP3112vBggWaM2eORowYYXYkXKCysjJt2bLF4/ieo0ePSpLat2/vnj7Gx8eradOmslgsJicGgB9QKIEgYhiGbrzxRs2dO1cffvihRo0aZXYk/IZTp04pMzPTPX3csGGDzp07pypVqqhnz57u8tirVy9dfPHFZscFgF/F431AELHb7frggw9ks9l0/fXXyzAMjR071uxY0A/b1wcOHPCYPn711VdyuVy65JJLFB8fr6efflrx8fHq2rWrwsLCzI4MAOeNQgkEGZvNpn/961+y2+264YYbZBiGbrrpJrNjhRzDMLRt2zaP43sOHz4sSWrbtq3i4uL0wAMPKC4uTi1btmT7GkBAo1ACQchms+mf//ynHA6Hxo8fL8MwdMstt5gdK6idOXNG69atcxfI9evXq7CwUGFhYYqKitLYsWMVFxen2NhY1a1b1+y4AOBVFEogSFmtVr311luy2+269dZbZRiGbr/9drNjBY3c3FyP6eP27dvldDpVp04dxcbGaurUqYqLi1P37t1VpUoVs+MCgE9RKIEgZrVa9frrr8vhcOiOO+6QYRiaNGmSDMPQ1KlTlZiYyBt2zkN5ebl27NjhcXxPbm6uJKlVq1aKi4vTXXfdpfj4eLVp04btawAhh0IJBDmLxaKXX35Zdrtdd999t0pKSrR582Z99NFHWrFiBYXyF5w9e1br1693F8jMzEwVFBTI4XCoW7duuu6669zb1/Xr1zc7LgCYjmODgBDhcrn06KOPasaMGR5f/+6779SsWTOTUvmHw4cPe2xfb926VeXl5apVq5ZiY2Pd5z9GRUWpatWqZscFAL/DhBIIES6XS8ePH/f4mtVq1bx58/TII4/85u8tLDG0P69QpYZTYXarmtaJUER4YP74cDqdys7O9ti+3r9/vySpWbNmio+P16233qr4+Hi1a9dOVqvV3MAAEACYUAIh4tlnn9Vjjz32s6936NBBO3bs+NnX9xwt0Oz1OUrbdUw5+UX66Q8Ki6TI2tWU1Kaero+OVKv6NXwXvIKKioqUlZXlnj5mZmbq1KlTstls6tq1q3v6GBcXp4YNG5odFwACEoUSCBELFy7UI488ol27dslqtcrpdLo/+/rrr9WuXTtJUm5+kaYs2KEv956QzWpRufPXf0T8+PkVLevquWEd1bh2NZ9/H7/n6NGjHtPHzZs3yzAM1ahRQ7Gxse63z/Ts2VMRERFmxwWAoEChBELMrl279Omnn2ru3Lnatm2bJOm6667T3Llz9XFWjp5YlC3D6frNIvm/bFaL7FaLnhzSXqOiIn0V/WecTqd27drl8faZvXv3SpIiIyM9po8dOnSQzWartGwAEEoolEAIO3DggKZPn64hQ4bo2yot9cKK3RVe86F+rTUpqZUX0v1ccXGxNm7c6J4+rl27Vvn5+bJarercubN7+hgXF6fLLrvMJxkAAD9HoQSgj7NyNPnTn99H+UfNGN5RI70wqTxx4oR78piRkaGNGzeqtLRUERERiomJcZfHmJgY1ajhv/dxAkCwo1ACIS43v0h9Xk5XieH8/V98nsLtVqXcn3BB91S6XC7t2bPH4/ieXbt2SZIaNWrkLo/x8fHq1KmT7PbAfMocAIIRhRIIceNmrtfa7/Iu6J7J32OzWhTbvI5mTYj+1V9TWlqqTZs2eUwgjx8/LovFog4dOnjc/9ikSRPePgMAfoy/4gMhbM/RAn2594TX1y13uvTl3hPae6xALev9sBWdn5+vzMxM9/QxKytLxcXFqlq1qqKjozVx4kT39nWtWrW8ngkA4DtMKIEQNm1RtmatP+DV6eSPbBapR61zqvXtSq1Zs0Zff/21JKlBgwbuyWN8fLy6dOkih8Ph9esDACoPhRIIYQl/TdOB/CKfrV+Wf1i11rzisX3dvHlztq8BIMiw5Q2EqLMlhnJ8WCYlKax2I23YvC1gX9MIADg/vKQWCFEH8grl6+0Jl6T9eYU+vgoAwGwUSiBElXrxmCB/uA4AwDwUSiBEhdkr5//+lXUdAIB5+EkPhKimdSLk60djLP+9DgAguFEogRAVEW5X5AW8yeaPiKxTjQdyACAEUCiBEJbUpp5sVt/MKW1Wi5Ja1/PJ2gAA/0KhBELY9dGRPjnUXPrhbTljYyJ9sjYAwL9QKIEQ1qp+DV3Rsq7Xp5Q2q0VXtKzrfu0iACC4USiBEPfcsI6ye7lQ2q0WPTeso1fXBAD4LwolEOIa166mJ4e09+qaTw1pr8Y+fuAHAOA/KJQANCoqUg/1a+2VtR7u10Yjo7h3EgBCicXlcvn67WsAAsTHWTl6YlG2DKfrgh7WsVktslstempIe8okAIQgCiUAD7n5RZqyYIe+3HtCNqvlN4vlj59f0bKunhvWkW1uAAhRFEoAv2jP0QLNXp+jtN3HlJNXpJ/+oLDoh0PLk1rX09iYSJ7mBoAQR6EE8LsKSwztzytUqeFUmN2qpnUieAMOAMCNQgkAAIAK4SlvAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVAiFEgAAABVCoQQAAECFUCgBAABQIRRKAAAAVMj/B7MygAKIlp2zAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(make_cycle(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "e292bae9-ba0c-4aae-9f88-ad5bbd75421b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_tail(n):\n",
    "    nodes = range(n+1)\n",
    "    edges = [(i+1,i) for i in range(n)]\n",
    "    G = nx.DiGraph()\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(edges)\n",
    "    return G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e1a9a033-7411-4f7b-b143-78b9f28b2528",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(make_tail(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "7869c562-46b9-4a5f-a3ec-f2562574b558",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_shell(make_tail(0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f519e2db-af00-464d-a092-c0d47e2e9589",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 elements: {'X0': 0, 'X1': 1, 'X2': 2, 'X3': 3, 'X4': 4, 'X5': 5, 'X6': 6, 'X7': 7, 'X8': 8}\n"
     ]
    }
   ],
   "source": [
    "# so, here's my idea\n",
    "# instead of looking at points of x as single values, look at them as triples (s,r,t)\n",
    "XN = list(XG.nodes)\n",
    "XL = len(XN)\n",
    "XR = {j:i for i,j in enumerate(XN)}\n",
    "print(f\"{XL} elements: {XR}\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "41b2401f-91da-459f-bd13-74f24add6887",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9 arrows [{'s': 0, 't': 4}, {'s': 1, 't': 5}, {'s': 2, 't': 6}, {'s': 3, 't': 8}, {'s': 4, 't': 5}, {'s': 5, 't': 6}, {'s': 6, 't': 7}, {'s': 7, 't': 5}, {'s': 8, 't': 3}]\n"
     ]
    }
   ],
   "source": [
    "XRE = [{\"s\":XR[j[0]],\"t\":XR[j[1]]} for j in list(XG.edges)]\n",
    "print(f\"{len(XRE)} arrows {XRE}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "34545ae1-273b-4e2a-ba7c-34d7bef09013",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0), (0, 1), (1, 0), (0, 2)]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from session15 import zig_zag, reverse_zig_zag\n",
    "list(zig_zag(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "8ecf8eb4-5072-4427-9b37-d60968453d13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reverse_zig_zag((0,4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f56a22c5-1306-44e2-8eae-6da0a71c1746",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[10, 22, 38, 69, 49, 71, 97, 85, 74]\n"
     ]
    }
   ],
   "source": [
    "arrow_space = [reverse_zig_zag((a[\"s\"],a[\"t\"])) for a in XRE]\n",
    "print(arrow_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d26a736a-562a-4624-a7ba-02139091bf24",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[14, 26, 42, 74, 50, 72, 98, 83, 69]\n"
     ]
    }
   ],
   "source": [
    "arrow_retractions = [reverse_zig_zag((a[\"t\"],a[\"s\"])) for a in XRE]\n",
    "print(arrow_retractions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ad74964c-e8bf-45bc-b6de-df45659003d1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Arrows of A->B {10: 14, 22: 26, 38: 42, 69: 74, 49: 50, 71: 72, 97: 98, 85: 83, 74: 69}\n",
      "Arrows of B->A {14: 10, 26: 22, 42: 38, 74: 69, 50: 49, 72: 71, 98: 97, 83: 85, 69: 74}\n"
     ]
    }
   ],
   "source": [
    "f_1 = {arrow_space[i]:arrow_retractions[i] for i in range(XL)}\n",
    "f_2 = {arrow_retractions[i]:arrow_space[i] for i in range(XL)}\n",
    "print(f\"Arrows of A->B {f_1}\\nArrows of B->A {f_2}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "41a83846-0996-497a-856b-fb2f1c748bc9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compose_maps(f,g):\n",
    "    return {\n",
    "        k:g[v] for k,v in zip(f.keys(),f.values())\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "9ef6f8c5-c29a-49a3-819e-4ef30837beac",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{10: 10, 22: 22, 38: 38, 69: 69, 49: 49, 71: 71, 97: 97, 85: 85, 74: 74}\n",
      "{14: 14, 26: 26, 42: 42, 74: 74, 50: 50, 72: 72, 98: 98, 83: 83, 69: 69}\n"
     ]
    }
   ],
   "source": [
    "print(compose_maps(f_1,f_2))\n",
    "print(compose_maps(f_2,f_1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "45d687d6-c7ec-4afa-9b3b-ccc3745fd50d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 4, 12, 24, 40, 60, 84, 112, 144, 180]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# theoretically, we should be able to enumerate possible fixed points this way\n",
    "[reverse_zig_zag((i,i)) for i in range(10)]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "71b1643c-159f-4bd3-981c-6060113702ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# so there should be a unique composition where these maps are align\n",
    "# map the points to (s,s) pairs, then send those to (f_1,f_2) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "516d7f0b-bc56-47a4-94f5-01869eb7e548",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{'s': 0, 't': 310}, {'s': 4, 't': 1198}, {'s': 12, 't': 3278}, {'s': 24, 't': 10365}, {'s': 40, 't': 4999}, {'s': 60, 't': 10367}, {'s': 84, 't': 19207}, {'s': 112, 't': 14281}, {'s': 144, 't': 10370}]\n"
     ]
    }
   ],
   "source": [
    "X_normalized = [\n",
    "    {\n",
    "        \"s\":reverse_zig_zag((i,i)),\n",
    "        \"t\":reverse_zig_zag((arrow_space[i],arrow_retractions[i]))\n",
    "    } for i in range(XL)\n",
    "]\n",
    "print(X_normalized)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "df052e06-c169-4106-811a-8ecf6e5e06bd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('X0', 1), ('X1', 1), ('X2', 1), ('X3', 2), ('X4', 2), ('X5', 4), ('X6', 3), ('X7', 2), ('X8', 2)]\n"
     ]
    }
   ],
   "source": [
    "# let's see if we can use nx to find my \"inoming arrow count\"\n",
    "incidence_degree = [(XG.degree(i)) for i in XN]\n",
    "print(list(zip(XN,incidence_degree)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1723a563-1556-4b2c-a70e-c302b2757f8f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Yp': 1,\n",
       " 'Yq': 1,\n",
       " 'Yr': 3,\n",
       " 'Ys': 2,\n",
       " 'Yt': 3,\n",
       " 'Yv': 2,\n",
       " 'Yu': 2,\n",
       " 'Ym': 2,\n",
       " 'Yl': 2,\n",
       " 'Yw': 2,\n",
       " 'Yx': 2,\n",
       " 'Yy': 3,\n",
       " 'Yz': 1}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# oooooh that's interesting\n",
    "# networkx starts counting at 1 rather than 0 like I have been\n",
    "# old C++ habits die hard i guess\n",
    "#lets check y also\n",
    "{j:YG.degree(j) for j in YG.nodes}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7aa1b732-e2d4-49c1-b976-cd3a99d5150b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 10, 1: 22, 2: 38, 3: 69, 4: 49, 5: 71, 6: 97, 7: 85, 8: 74}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144}\n",
      "{'X0': 0, 'X1': 4, 'X2': 12, 'X3': 24, 'X4': 40, 'X5': 60, 'X6': 84, 'X7': 112, 'X8': 144}\n",
      "[{'s': 0, 't': 1225}, {'s': 4, 't': 2854}, {'s': 12, 't': 6007}, {'s': 24, 't': 4875}, {'s': 40, 't': 6256}, {'s': 60, 't': 12463}, {'s': 84, 't': 14449}, {'s': 112, 't': 16948}, {'s': 144, 't': 22935}]\n"
     ]
    }
   ],
   "source": [
    "# let's try to abstract the process\n",
    "def translate_to_arrow_space(G):\n",
    "    nodes = list(G.nodes)\n",
    "    size = len(nodes)\n",
    "    retract_node = {j:i for i,j in enumerate(nodes)}\n",
    "    arrows = [{\n",
    "            \"s\":retract_node[j[0]],\n",
    "            \"t\":retract_node[j[1]]\n",
    "    } for j in list(G.edges)]\n",
    "    G_alpha = {\n",
    "        i:reverse_zig_zag((a[\"s\"],a[\"t\"])) for i,a in enumerate(arrows)\n",
    "    }\n",
    "    print(G_alpha)\n",
    "    points = {\n",
    "        i:reverse_zig_zag((retract_node[a],retract_node[a])) for i,a in enumerate(nodes)\n",
    "    }\n",
    "    print(points)\n",
    "    print(compose_maps(retract_node,points))\n",
    "    G_s_t = [\n",
    "        {\n",
    "            \"s\":points[a[\"s\"]],\n",
    "            \"t\":reverse_zig_zag((points[a[\"s\"]],G_alpha[a[\"t\"]]))\n",
    "        } for a in arrows\n",
    "    ]\n",
    "    return G_s_t\n",
    "\n",
    "XG_A = translate_to_arrow_space(XG)\n",
    "print(XG_A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "7ae2191f-b897-452d-9b67-fc3a0601c914",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 3, 1: 7, 2: 23, 3: 31, 4: 49, 5: 71, 6: 51, 7: 127, 8: 128, 9: 199, 10: 241, 11: 221, 12: 288}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144, 9: 180, 10: 220, 11: 264, 12: 312}\n",
      "{'Yp': 0, 'Yq': 4, 'Yr': 12, 'Ys': 24, 'Yt': 40, 'Yv': 60, 'Yu': 84, 'Ym': 112, 'Yl': 144, 'Yw': 180, 'Yx': 220, 'Yy': 264, 'Yz': 312}\n",
      "[{'s': 0, 't': 276}, {'s': 4, 't': 382}, {'s': 12, 't': 1903}, {'s': 24, 't': 2725}, {'s': 40, 't': 6256}, {'s': 60, 't': 6276}, {'s': 84, 't': 6754}, {'s': 112, 't': 29032}, {'s': 144, 't': 37000}, {'s': 180, 't': 89011}, {'s': 220, 't': 97681}, {'s': 264, 't': 107680}, {'s': 312, 't': 142623}]\n"
     ]
    }
   ],
   "source": [
    "# lets see Y also\n",
    "YG_A = translate_to_arrow_space(YG)\n",
    "print(YG_A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6625dce6-0a4d-4b90-b124-437891805d52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "750925"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def map_N_x_N_to_N(a):\n",
    "    return reverse_zig_zag((a[\"s\"],a[\"t\"]))\n",
    "map_N_x_N_to_N(XG_A[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "047d53ef-5f76-4acf-9086-50b8fd102528",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[750925, 4085515, 18117202, 12002574, 19822996, 78419086, 105611395, 145530442, 266331804]\n"
     ]
    }
   ],
   "source": [
    "XG_A1 = list(map(map_N_x_N_to_N,XG_A))\n",
    "print(XG_A1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "8ea3b3da-5ab1-4ed2-a2a0-08baa0c6cb7b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[38226, 74695, 1834582, 3779899, 19822996, 20075676, 23382625, 424701052, 689857084, 3977562016, 4792352071, 5826007804, 10215278892]\n"
     ]
    }
   ],
   "source": [
    "YG_A1 = list(map(map_N_x_N_to_N,YG_A))\n",
    "print(YG_A1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7ccf8b5d-8b05-484d-8d9c-d43f40263ed4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[19822996]\n"
     ]
    }
   ],
   "source": [
    "# do these have any points in common?\n",
    "intersection = list(set(XG_A1)&set(YG_A1))\n",
    "print(intersection)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "c45f0d83-d234-47b2-8281-692fcbad48ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x_i:4. y_i:4\n"
     ]
    }
   ],
   "source": [
    "# yes! exactly one\n",
    "X_I = XG_A1.index(intersection[0])\n",
    "Y_I = YG_A1.index(intersection[0])\n",
    "print(f\"x_i:{X_I}. y_i:{Y_I}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "1d06f6d6-7f9c-4475-b289-448f2bf7c42d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'s': 40, 't': 6256}\n",
      "{'s': 40, 't': 6256}\n"
     ]
    }
   ],
   "source": [
    "print(XG_A[X_I])\n",
    "print(YG_A[Y_I])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "b8825f24-15dc-4c43-87d8-4daed6ccfb84",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "# the points that match are \"X4\" and \"Yt\"\n",
    "print(XG.degree(XN[X_I]))\n",
    "print(YG.degree(list(YG.nodes)[Y_I]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "11171b96-417c-42c8-9f3b-a18898078c1b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'generators': ['X0', 'X1', 'X2', 'X3'], 'relations': [(('X0', 5), ('X0', 2)), (('X1', 1), ('X0', 2)), (('X2', 1), ('X0', 3)), (('X3', 2), ('X3', 0))]}\n",
      "{'generators': ['Yp', 'Yq', 'Yz', 'Ym'], 'relations': [(('Yp', 6), ('Yp', 2)), (('Yq', 1), ('Yp', 1)), (('Yz', 4), ('Yz', 1)), (('Ym', 2), ('Ym', 0))]}\n"
     ]
    }
   ],
   "source": [
    "# these don't seem to have any special qualities in common\n",
    "# unless we consider that they both have 4 generators?\n",
    "from session15 import make_presentation\n",
    "X_pres = make_presentation(XG)\n",
    "print(X_pres)\n",
    "Y_pres = make_presentation(YG)\n",
    "print(Y_pres)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "4e119971-0a72-427b-be6b-892d576caf41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'generator_count': 4, 'generators': ['X0', 'X1', 'X2', 'X3'], 'substitutions': {15: 3, 4: 3, 8: 6, 18: 9}, 'relation_pairs': {15: ('X0', 5), 3: ('X0', 2), 4: ('X1', 1), 8: ('X2', 1), 6: ('X0', 3), 18: ('X3', 2), 9: ('X3', 0)}, 'max_depth': 5, 'max_steps': 18}\n",
      "{'generator_count': 4, 'generators': ['Yp', 'Yq', 'Yz', 'Ym'], 'substitutions': {21: 3, 4: 1, 23: 8, 18: 9}, 'relation_pairs': {21: ('Yp', 6), 3: ('Yp', 2), 4: ('Yq', 1), 1: ('Yp', 1), 23: ('Yz', 4), 8: ('Yz', 1), 18: ('Ym', 2), 9: ('Ym', 0)}, 'max_depth': 6, 'max_steps': 23}\n"
     ]
    }
   ],
   "source": [
    "# I wonder if there's a connection here with my \"standardized presentation\"?\n",
    "from session15 import standardize_presentation\n",
    "X_pres_std = standardize_presentation(X_pres)\n",
    "print(X_pres_std)\n",
    "Y_pres_std = standardize_presentation(Y_pres)\n",
    "print(Y_pres_std)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "0cf1bf4e-1606-4d0e-8929-8c2e6039dcb5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{}\n",
      "{0: 0}\n",
      "{0: 0}\n",
      "A_0:\tDiGraph with 1 nodes and 0 edges\n",
      "\t\t[]\n",
      "\t[]\n",
      "[]\n",
      "{0: 2}\n",
      "{0: 0, 1: 4}\n",
      "{0: 0, 1: 4}\n",
      "A_1:\tDiGraph with 2 nodes and 1 edges\n",
      "\t\t[(1, 0)]\n",
      "\t[{'s': 4, 't': 25}]\n",
      "[439]\n",
      "{0: 2, 1: 8}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "A_2:\tDiGraph with 3 nodes and 2 edges\n",
      "\t\t[(1, 0), (2, 1)]\n",
      "\t[{'s': 4, 't': 25}, {'s': 12, 't': 222}]\n",
      "[439, 27507]\n",
      "{0: 2, 1: 8, 2: 18}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "A_3:\tDiGraph with 4 nodes and 3 edges\n",
      "\t\t[(1, 0), (2, 1), (3, 2)]\n",
      "\t[{'s': 4, 't': 25}, {'s': 12, 't': 222}, {'s': 24, 't': 927}]\n",
      "[439, 27507, 452700]\n",
      "{0: 2, 1: 8, 2: 18, 3: 32}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40}\n",
      "A_4:\tDiGraph with 5 nodes and 4 edges\n",
      "\t\t[(1, 0), (2, 1), (3, 2), (4, 3)]\n",
      "\t[{'s': 4, 't': 25}, {'s': 12, 't': 222}, {'s': 24, 't': 927}, {'s': 40, 't': 2668}]\n",
      "[439, 27507, 452700, 3668026]\n",
      "{}\n",
      "{}\n",
      "{}\n",
      "C_0:\tDiGraph with 0 nodes and 0 edges\n",
      "\t\t[]\n",
      "\t []\n",
      "[]\n",
      "{0: 0}\n",
      "{0: 0}\n",
      "{0: 0}\n",
      "C_1:\tDiGraph with 1 nodes and 1 edges\n",
      "\t\t[(0, 0)]\n",
      "\t [{'s': 0, 't': 0}]\n",
      "[0]\n",
      "{0: 1, 1: 2}\n",
      "{0: 0, 1: 4}\n",
      "{0: 0, 1: 4}\n",
      "C_2:\tDiGraph with 2 nodes and 2 edges\n",
      "\t\t[(0, 1), (1, 0)]\n",
      "\t [{'s': 0, 't': 3}, {'s': 4, 't': 19}]\n",
      "[6, 280]\n",
      "{0: 1, 1: 7, 2: 5}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "C_3:\tDiGraph with 3 nodes and 3 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 0)]\n",
      "\t [{'s': 0, 't': 28}, {'s': 4, 't': 49}, {'s': 12, 't': 103}]\n",
      "[406, 1435, 6682]\n",
      "{0: 1, 1: 7, 2: 17, 3: 9}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "C_4:\tDiGraph with 4 nodes and 4 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 0)]\n",
      "\t [{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 243}, {'s': 24, 't': 349}]\n",
      "[406, 28684, 32652, 69775]\n"
     ]
    }
   ],
   "source": [
    "# the authors mention a sense in which the presentation was minimal,\n",
    "# but it's hard to tell if if I have it it here\n",
    "# let's go back to these arrow maps and see what else we can work with\n",
    "\n",
    "for i in range(5):\n",
    "    A_i = make_tail(i)\n",
    "    A_s_t = translate_to_arrow_space(A_i)\n",
    "    print(f\"A_{i}:\\t{A_i}\\n\\t\\t{list(A_i.edges)}\\n\\t{A_s_t}\")\n",
    "    print(list(map(map_N_x_N_to_N,A_s_t)))\n",
    "\n",
    "for i in range(5):\n",
    "    C_i = make_cycle(i)\n",
    "    C_s_t = translate_to_arrow_space(C_i)\n",
    "    print(f\"C_{i}:\\t{C_i}\\n\\t\\t{list(C_i.edges)}\\n\\t {C_s_t}\")\n",
    "    print(list(map(map_N_x_N_to_N,C_s_t)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "577bb178-5326-4d4c-b447-49dfe8ffa2fb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 0}\n",
      "{0: 0}\n",
      "{0: 0}\n",
      "A_0:\tDiGraph with 1 nodes and 1 edges\n",
      "\t\t[(0, 0)]\n",
      "\t[{'s': 0, 't': 0}]\n",
      "[0]\n",
      "{0: 1, 1: 4}\n",
      "{0: 0, 1: 4}\n",
      "{0: 0, 1: 4}\n",
      "A_1:\tDiGraph with 2 nodes and 2 edges\n",
      "\t\t[(0, 1), (1, 1)]\n",
      "\t[{'s': 0, 't': 10}, {'s': 4, 't': 40}]\n",
      "[55, 994]\n",
      "{0: 1, 1: 7, 2: 12}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "{0: 0, 1: 4, 2: 12}\n",
      "A_2:\tDiGraph with 3 nodes and 3 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 2)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 140}, {'s': 12, 't': 312}]\n",
      "[406, 10444, 52662]\n",
      "{0: 1, 1: 7, 2: 17, 3: 24}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24}\n",
      "A_3:\tDiGraph with 4 nodes and 4 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 3)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 678}, {'s': 24, 't': 1200}]\n",
      "[406, 28684, 238407, 749724]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 40}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40}\n",
      "A_4:\tDiGraph with 5 nodes and 5 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 4)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2104}, {'s': 40, 't': 3280}]\n",
      "[406, 28684, 470947, 2265280, 5512900]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 49, 5: 60}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60}\n",
      "A_5:\tDiGraph with 6 nodes and 6 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 5)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2725}, {'s': 40, 't': 5090}, {'s': 60, 't': 7320}]\n",
      "[406, 28684, 470947, 3779899, 13161055, 27235950]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 49, 5: 71, 6: 84}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84}\n",
      "A_6:\tDiGraph with 7 nodes and 7 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 6)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2725}, {'s': 40, 't': 6256}, {'s': 60, 't': 10500}, {'s': 84, 't': 14280}]\n",
      "[406, 28684, 470947, 3779899, 19822996, 55762140, 103169514]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 49, 5: 71, 6: 97, 7: 112}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112}\n",
      "A_7:\tDiGraph with 8 nodes and 8 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 7)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2725}, {'s': 40, 't': 6256}, {'s': 60, 't': 12463}, {'s': 84, 't': 19390}, {'s': 112, 't': 25312}]\n",
      "[406, 28684, 470947, 3779899, 19822996, 78419086, 189628159, 323202712]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 49, 5: 71, 6: 97, 7: 127, 8: 144}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144}\n",
      "A_8:\tDiGraph with 9 nodes and 9 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 8)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2725}, {'s': 40, 't': 6256}, {'s': 60, 't': 12463}, {'s': 84, 't': 22450}, {'s': 112, 't': 33008}, {'s': 144, 't': 41760}]\n",
      "[406, 28684, 470947, 3779899, 19822996, 78419086, 253901929, 548483872, 877993704]\n",
      "{0: 1, 1: 7, 2: 17, 3: 31, 4: 49, 5: 71, 6: 97, 7: 127, 8: 161, 9: 180}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144, 9: 180}\n",
      "{0: 0, 1: 4, 2: 12, 3: 24, 4: 40, 5: 60, 6: 84, 7: 112, 8: 144, 9: 180}\n",
      "A_9:\tDiGraph with 10 nodes and 10 edges\n",
      "\t\t[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7), (7, 8), (8, 9), (9, 9)]\n",
      "\t[{'s': 0, 't': 28}, {'s': 4, 't': 235}, {'s': 12, 't': 958}, {'s': 24, 't': 2725}, {'s': 40, 't': 6256}, {'s': 60, 't': 12463}, {'s': 84, 't': 22450}, {'s': 112, 't': 37513}, {'s': 144, 't': 52794}, {'s': 180, 't': 65160}]\n",
      "[406, 28684, 470947, 3779899, 19822996, 78419086, 253901929, 707839237, 1401242535, 2134690650]\n"
     ]
    }
   ],
   "source": [
    "# C_0 here doesn't seem correct either\n",
    "# it should really be \\mathbb{N}\n",
    "# this map is unique composition I-> N -> C_n -> T\n",
    "# maybe I can define N=C_0 with a lambda function somehow?\n",
    "\n",
    "# I think that in order to treat N as an object\n",
    "# I'll need to step out from the graph to presentation\n",
    "# let's put that aside for now\n",
    "\n",
    "# A_0 feels like it's missing an identity map\n",
    "# something identifying that unique node such that s=t=0\n",
    "# i'm also wondering if i should reverse the direction\n",
    "def make_tail(n):\n",
    "    nodes = range(n+1)\n",
    "    edges = [(i,min(n,i+1)) for i in nodes]\n",
    "    G = nx.DiGraph()\n",
    "    G.add_nodes_from(nodes)\n",
    "    G.add_edges_from(edges)\n",
    "    return G\n",
    "    \n",
    "for i in range(10):\n",
    "    A_i = make_tail(i)\n",
    "    A_s_t = translate_to_arrow_space(A_i)\n",
    "    print(f\"A_{i}:\\t{A_i}\\n\\t\\t{list(A_i.edges)}\\n\\t{A_s_t}\")\n",
    "    print(list(map(map_N_x_N_to_N,A_s_t)))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "483f41dc-8c3c-477b-9957-89295a09f554",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "12\n",
      "24\n",
      "40\n",
      "60\n",
      "112\n",
      "144\n",
      "180\n"
     ]
    }
   ],
   "source": [
    "#  the sequence of sources seems intriguing\n",
    "print(2*2) # 2^2 3^0 5^0 7^0\n",
    "print(2*2*3) # 2^2 3^1 5^0 7^0\n",
    "print(2*2*3*2)  # 2^3 3^0 5^0 7^0\n",
    "print(2*2*2*5) # 2^2 3^0 5^1 7^0\n",
    "print(2*2*3*5) # 2^2 3^1 5^1 7^0\n",
    "print(2*2*2*2*7) # 2^4 3^0 5^0 7^1\n",
    "print(2*2*2*2*3*3) # 2^4 3^2 5^0 7^0\n",
    "print(2*2*3*3*5) # 2^2 3^2 5^1 7^0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2fcac26a-d851-48fa-94b0-e1eebb1c2b98",
   "metadata": {},
   "outputs": [],
   "source": [
    "# maybe i was onto something with prime factors\n",
    "# Given any C_n, there's a unique map\n",
    "# from C_n -> C_p1^q1 x C_p2^q2 x ... C_pn^qn -> T\n",
    "# determined by the unique factorization"
   ]
  }
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