{
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   "source": [
    "# Rigidity and Flexibility of Graphs in SageMath\n",
    "\n",
    "Jan Legerský\n",
    "\n",
    "2nd Software and Industrial Workshop in Cambridge\n",
    "\n",
    "[jan.legersky.cz](https://jan.legersky.cz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![S1](./animations/S_1.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tools\n",
    "\n",
    "- [SageMath](http://www.sagemath.org/)\n",
    "- [Binder](https://mybinder.org/)\n",
    "- [Documentation](https://jan.legersky.cz/public_files/documentation_rigidflexiblegraphs/) generated from docstrings  using [Sphinx](http://sphinx-doc.org/) (tests)\n",
    "- Animated SVG\n",
    "- [POV-Ray](http://www.povray.org/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic notions\n",
    "\n",
    "**Definition**\n",
    "\n",
    "Let $G=(V_G,E_G)$ be a graph with an edge labeling $\\lambda:E_G\\rightarrow \\mathbb{R}_+$.\n",
    "\n",
    "A realization $\\rho:V_G\\rightarrow\\mathbb{R}^2$ is called *compatible* with $\\lambda$ if\n",
    "$||\\rho(u)-\\rho(v)||=\\lambda(uv)$ for all $uv\\in E_G$.\n",
    "\n",
    "The labeling $\\lambda$ is called\n",
    "\n",
    "- *(proper) flexible* if the number of (injective) realizations of $G$ compatible with $\\lambda$ is infinite,\n",
    "- *rigid* if the number of realizations of $G$ compatible with $\\lambda$ is finite and positive,\n",
    "\n",
    "where the counting is up to direct Euclidean isometries.\n",
    "A graph is called *movable* iff it has a proper flexible labeling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
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oezjLspLjsWdVPKR3bxQUnTA4bci9/XBo7fJ6r8XPS0Gvrl3wyvin9H6iq6Co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\nfc9d6ty6xeV5XS6X+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      "text/plain": [
       "Graphics Array of size 4 x 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from rigid_and_flexible_graphs.graph_generator import GraphGenerator\n",
    "from rigid_and_flexible_graphs.rigid_flexible_graph import RigidFlexibleGraph\n",
    "C4 = RigidFlexibleGraph([[0,1],[1,2],[2,3],[0,3]], name='4-cycle', pos={0:(0,0),1:(1,0), 2:(0.8,0.8), 3:(0.3,0.6)})\n",
    "S = GraphGenerator.SmallestFlexibleLamanGraph()\n",
    "T = GraphGenerator.ThreePrismGraph()\n",
    "M = GraphGenerator.MaxEmbeddingsLamanGraph(7)\n",
    "K33 = RigidFlexibleGraph(graphs.CompleteBipartiteGraph(3,3))\n",
    "N = RigidFlexibleGraph(448412, pos={0 : (-0.5,-0.75), 1 : (0.5,0.5), 2 : (1.5,0.5), 3 : (2.5,-0.75),\n",
    "                                       4 : (0.5,1.5), 5 : (1.5,1.5), 6 : (1,-0.25)}, name='No NAC')\n",
    "Q1 = GraphGenerator.Q1Graph()\n",
    "examples = [C4, S, T, M, K33, N, Q1]\n",
    "# show(*[G.plot().show(figsize=[4,4], dpi=80) for G in examples])\n",
    "figs = graphics_array([[G.plot() for G in examples[:4]],\n",
    "                       [text(G.name(),(0,0)) for G in examples[:4]],\n",
    "                       [G.plot() for G in examples[4:]]+[plot(Graph([]))],\n",
    "                       [text(G.name(),(0,0)) for G in examples[4:]],\n",
    "                      ], ncols=4, nrows=4)\n",
    "figs.show(figsize=[10,5], axes=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Theorem** [Pollaczek-Geiringer, Laman]\n",
    "\n",
    "A graph is *generically rigid*, i.e., a generic realization defines a rigid labeling,\n",
    "if and only if the graph contains a *Laman* subgraph with the same set of vertices.\n",
    "\n",
    "A graph $G=(V_G,E_G)$ is called *Laman* if $|E_G| = 2|V_G|-3$, and $|E_H|\\leq 2|V_H|-3$ for all subgraphs $H$ of $G$.\n",
    "\n",
    "**Our main interest - non-generic (proper) flexible labelings of generically rigid graphs**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr class =\"row-a\">\n",
       "<td></td>\n",
       "<td>is Laman</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>4-cycle</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>SmallestFlexibleLamanGraph</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>3-prism</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>MaxEmbeddingsLamanGraph_7vert</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Complete bipartite graph</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>No NAC</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Q_1</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  is Laman\n",
       "  4-cycle                         False\n",
       "  SmallestFlexibleLamanGraph      True\n",
       "  3-prism                         True\n",
       "  MaxEmbeddingsLamanGraph_7vert   True\n",
       "  Complete bipartite graph        True\n",
       "  No NAC                          False\n",
       "  Q_1                             True"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table([['', 'is Laman']]+[[G.name(), str(G.is_Laman())] for G in examples])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rigid graphs - number of realizations\n",
    "\n",
    "Given a Laman graph $G$ and a rigid labeling $\\lambda$, how many compatible realizations are there?\n",
    "\n",
    "We fix an edge $\\bar{u}\\bar{v}$ to get a system of equations:\n",
    "\n",
    "$x_{\\bar{u}}=0, y_{\\bar{u}}=0, x_{\\bar{v}}=\\lambda_{\\bar{u}\\bar{v}}, y_{\\bar{v}}=0$,\n",
    "\n",
    "$(x_u-x_v)^2+(y_u-y_v)^2= \\lambda_{uv}^2$ for all $uv \\in E_G\\setminus\\{\\bar{u}\\bar{v}\\}$.\n",
    "\n",
    "- well-constrained\n",
    "- the number of complex solutions is the same for generic choices of $\\lambda$\n",
    "- solving using PHC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "s5 - 5.25000000000000*x5 - 2.90473750965556*y5 - 16.0000000000000\n",
      "-2*x1*x2 - 2*y1*y2 + s2 + 16.0000000000000\n",
      "-2*x1*x5 - 2*y1*y5 + s5 + 9.00000000000000\n",
      "s2 - 8.00000000000000*x2 - 9.00000000000000\n",
      "-2*x2*x5 - 2*y2*y5 + s2 + s5 - 4.00000000000000\n",
      "-x1^2 - y1^2 + 25.0000000000000\n",
      "-x2^2 - y2^2 + s2\n",
      "-x5^2 - y5^2 + s5\n"
     ]
    }
   ],
   "source": [
    "L = {\n",
    "    (0, 3): 2,\n",
    "    (0, 4): 3,\n",
    "    (0, 5): 5,\n",
    "    (1, 2): 3,\n",
    "    (1, 4): 5,\n",
    "    (1, 5): 4,\n",
    "    (2, 3): 5,\n",
    "    (2, 5): 2,\n",
    "    (3, 4): 4\n",
    "}\n",
    "for eq in T.system_of_equations(L, [4,3])[0]:\n",
    "    print eq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "PHCv2.4.46 released 2017-09-28 works!\n",
      "# real:  10\n",
      "# complex: 2\n",
      "{0: (2.62500000000000, 1.45236875482778), 1: (6.69301815045698 + 1.39680810523952*I, 2.00018903641813 - 4.67398922344618*I), 2: (-1.99354617629808 + 0.780433658070314*I, 1.34365493147118 + 3.48122502111472*I), 3: (4, 0), 4: (0, 0), 5: (-3.01751595497781 - 4.58646357544753*I, -4.37292058156694 + 4.44255940038919*I)}\n"
     ]
    },
    {
     "data": {
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Nzyhxey3t6hAqKSE+KbnI64nJn4vdVQCAlLR0qKmpVejawBfFiZQB8PUXptevX2P//v1Q\nVi6e30VGRqJly5bF3oSWlpa4ffu2QmWvDCNtRAQPDw9YWVmhS5cuha+npqYCALS1tcvtQyAQYMeO\nHRg1ahTGjh2Lc+fOSS1eRj5kZWVh/fr1aNy4Mfbu3Ytly5bh6dOnGD9+fIW+AHAchxkzZsDU1BRT\npkyRaKxNmjTBpUuXEBcXh/79+yM9PV2i/TPM98qkZUtExDwrcZuKsjIsmhnjyr0Hha8REa7cewBL\n0+KFASJinsP0PzM+5B1LEBTI9evXsWXLFqxcuRJNmzYtsU1UVFSxaUfA1wQhNTUVjx49knaYDKMw\nzp49i/Dw8MIqYAUKEoRq1YovjlYSoVCI/fv3o2/fvhg2bBiuX78u8VgZ/nEch8DAQDRr1gwLFiyA\nnZ0dYmNjsWDBAmhoaFS4X39/f9y6dQtbt24t8YefymrVqhXOnz+PiIgIDBkyBFlZoi3AxjA/MstO\nnXD5XgTy8vJL3D579DD4nDyHA2cv4/GL1/hl7VZkZGVjYv9eRdrl5eXjSlgEOlpaltiPvGIJgoJI\nS0uDg4MDunTpgpkzZ5bYhuM4REdHl5ggtGvXDkpKSmyaEcP8T8Hdg86dO8PKyqrINnETBABQUVHB\nkSNH0LlzZwwYMAB37tyRZLgMz65fv44OHTpg3LhxaN26NaKjo+Hl5QU9Pb1K9fvlyxf8+uuvGDVq\nFLp37y6haIvr0KEDTp8+jZCQEIwePRq5ublSG4thvgcDBgzA24REnA65VeL2kT27wXOGE373OQDz\nCdMR+SwO5zevhG6Noneeg0JC8TYhEQ4ODrIIW2JYgqAg3N3dER8fDz8/v1IX2Hnx4gUyMjJKTBC0\ntLTQqlUrliAwzP9cvnwZt2/fxuLFiyEQFH2orCIJAgCoq6vj5MmTMDU1RZ8+fRAZGSmxeBl+PH78\nGIMHD4aVlRUEAgGuX7+OkydPlnoXV1wrVqxASkoK1q9fL5H+ymJlZYWjR4/izJkzcHBwYFNOGaYE\n6enpWLZsGX7++Weoqapi7jYfpGeWfNdt2s8DEXfiADKuB+Gmz2a0bd6kaF+ZWXD32gtrKyuFW4OK\nJQgK4PLly9ixYwfWrl1b5urHJVUw+palpSVLEBgGX+8eLF++HO3atYOtrW2x7ampqRAIBOUualUS\nLS0tnD17FgYGBujVqxdiYmIkETIjYwkJCZg+fTpMTEwQERGBQ4cO4datW+jWrZvExnj69Ck2bdqE\nBQsWoEGDBhLrtyz9+/dHQEAADh06hGnTpoEthcQwX+Xn58PX1xfGxsZYtWoVnJ2d8c/Nm4hPTsG0\nddvETqg5joPzum14n5SM3T4+UopaeliCIOdSU1MxefJkWFtbY9q0aWW2jYqKgra2NurVq1fidktL\nSzx+/BhJSUnSCJVhFMb169cREhKCJUuWFLt7AHz9u6tatWqFK05oa2vj4sWLqFGjBnr27IlXr15V\nNmRGRjIyMrBq1SoYGRkhMDAQa9aswePHjzF69GiJVyCZPXs29PX1S6xIJ00jR46Ej48Pdu3aBXd3\nd5YkMD80IsL58+fRunVrODo6wsrKCk+ePMH69ethYWEBX19f+F+4CgePDaXeSfiv9MwsTPDwhP/5\nK1i5cmWZP+7KK5YgyLk5c+YgKSkJe/fuLffDqeAB5ZK+8AAosmAaw/zIPDw80KZNG/Tv37/E7amp\nqWJPL/ovXV1dXLp0CUpKSujZsyfi4+Mr1R8jXRzHYf/+/WjSpAmWLl2KyZMnIzY2Fm5ublBXV5f4\neGfOnMHZs2excePGSj3gXFGTJk3C5s2b4enpiRUrVsh8fIaRBw8ePICtrS369u2LmjVr4s6dOwgM\nDIShoWFhmzFjxsDf3x9Hr9+Emf00HA8OKfXB5by8fBwPDvlfu5uoW7cutmzZgtevX8voiCSIGLl1\n9uxZAkC7du0Sqb2pqSn98ssvpW7nOI5q1apFv/32m6RCZBiFExISQgDo2LFjpbaZNWsWtWjRQiLj\nPXv2jOrWrUumpqb06dMnifTJSNalS5eodevWBIBGjBhBsbGxUh0vKyuLjIyMqGfPnsRxnFTHKo+H\nhwcBoE2bNvEaB8PI0uvXr2nixIkkEAioadOmdPLkyXL/FmNiYsjayooAUO2a2jS+b0/aMGMK7Vk4\nmzbMmELj+/YkfT1dAkA9rK0pJiaGXr9+TQYGBtSkSROKj4+X0dFJBksQ5FRSUhLVq1ePevfuLdIH\nSE5ODqmoqND27dvLbDdo0CCysbGRVJgMo3B69+5NJiYmlJ+fX2qbSZMmUceOHSU2ZnR0NOno6FD7\n9u0pNTVVYv0ylRMZGUl9+/YlAGRpaUn//POPTMZds2YNCYVCio6Olsl4ZeE4jtzd3QkA7dmzh+9w\nGEaqUlNTadGiRaShoUG6urq0fft2ysnJEasPOzs7qlKlCrW1MCc1NTUCQGpqatTWwoJcXFwoLCys\nSPvY2FiqW7cumZmZUVJSkiQPR6pYgiCn7O3tqXr16vT69WuR2kdHRxMAun79epntVq9eTVpaWpSX\nlyeJMBlGody+fZsA0OHDh8tsN3z4cLK1tZXo2GFhYVStWjWysrKijIwMifbNiOfdu3fk6OhISkpK\n1LhxYzp69KjMfsl/+/YtaWlp0cyZM2Uynig4jqNffvmFBAJBuX8bDKOIcnNzydvbm/T09EhdXZ0W\nLlxIKSkpYvfDcRwZGRmRk5NT4Wtl/dhUICoqinR0dKhDhw4K8yMRSxDk0MmTJwkA+fn5ibzPkSNH\nCAB9/PixzHbBwcEEgCIiIioZJcMongEDBlDTpk3LTZBtbW1p+PDhEh8/JCSEqlSpQv369aPs7GyJ\n98+U7cuXL7R06VLS1NSkmjVr0pYtW2R+Huzt7alWrVqUnJws03HLk5+fT3Z2dqSsrEynT5/mOxyG\nkQiO4+jUqVPUrFkzEggENH78eHr16lWF+/v3338JQIX+Ru7du0dVq1Yla2tryszMrHAMssISBDnz\n8eNHql27Ng0YMECsX7QWL15MdevWLbddWloaCYVC2rlzZ2XCZBiFEx4eTgDo4MGD5bbt2LEjTZo0\nSSpxXLx4kVRVVWnEiBHsTp6M5OXlkY+PD9WpU4dUVVVp3rx5vHxB/+effwgA+fj4yHxsUeTm5tLQ\noUNJTU2Nrl69ync4DFMpd+/epe7duxMAsrGxofDw8Er3uXbtWqpSpUqF7wLfuHGDNDQ0aMCAAWJP\nbZI1VsVIzkyfPh05OTnYvXt3qdWISlJQwag8mpqaMDMzY+shMD+cFStWoHHjxhg9enS5bSVRxag0\nvXr1wpEjR3D8+HE4OTmxxaqkiIhw7tw5tG7dGk5OTujRoweePHmCdevWQVtbu/wOJCg/Px8zZsyA\nhYWF3K6oqqysjEOHDqF79+4YOHAgbt0qeQVZhpFnL1++hJ2dHdq1a4ePHz/i7NmzuHTpEtq0aVPp\nvk+dOgVbW9sKVx7r2rUrTpw4gYsXL8Le3h75+SVXQ5IHLEGQI3/++SeOHDkCLy8v1K1bV6x9IyMj\nRUoQALZgGvPjiYqKwvHjx7Fw4UIoKyuX216aCQIADBkyBPv27cO+ffswe/ZsVodeCgrKF/br1w81\na9bE3bt3ERAQUKR8oSz5+fkhLCwMW7duhVAo5CUGUaipqeH48eNo06YN+vbti4iICL5DYhiRfP78\nGb/++iuaNm2KK1euwMfHBw8ePEDfvn3F+sG1NAkJCQgNDcWgQYMq1U/v3r1x+PBhHD16FFOnTpXf\n6z/PdzCY/4mPj6datWrRsGHDxH5YLj09nQQCAfn6+orU3t/fX6TnFRjmezFq1CgyMDAQ+ZZutWrV\nyNPTU8pREe3YsYMAsNLDEvT69WuaMGFCYfnCU6dO8V5KNDk5mWrVqkX29va8xiGOz58/k7m5Oenq\n6tLjx4/5DodhSpWdnU1btmwhHR0dqlKlCv3+++/05csXiY+zd+9eEggEEitXeuDAAQJAs2bN4v0a\nVRKWIMgBjuNo6NChVKtWrQq98e7du0cA6Pbt2yK1f/bsGQGgv/76S+yxGEbR/PvvvyQQCER+7iY/\nP58EAgHt3r1bypF9tW7dOgJAa9eulcl436uUlBRatGgRqaurk66uLnl7e8vNHN9Zs2aRpqYmvX37\nlu9QxJKYmEgtWrSg+vXrU1xcHN/hMEwRHMfR0aNHycjIiJSUlMjR0VGqf2ODBw+mzp07S7TP7du3\nEwBasmSJRPuVBJYgyIGAgAACQH/++WeF9t+3bx8BEDlj5jiO9PT0aNGiRRUaj2EUib29PdWvX5+y\nsrJEap+amipSKVRJWrx4MQEodx0TpricnBzy9vYmXV3dSpUvlJbo6GgSCoW0Zs0avkOpkLdv31Kj\nRo2ocePG9O7dO77DYRgiIgoNDaVOnToRAOrbty9FRkZKdbyMjAzS0NCQyg85a9euJQC0fv16ifdd\nGSxB4Nnbt2+pRo0aNHr06Ar34ebmRg0bNhRrn8GDB1OPHj0qPCbDKIKYmBhSUlKirVu3irzPmzdv\nCACdPXtWipEVxXEczZw5kwDQgQMHym0vSt1tRVCZ4ygoX9i0aVMSCAQ0YcKESpUvlAaO48jGxoaM\njIxETlDl0fPnz0lfX59atmxJiYmJZbb9Xt6bjHyKjY2lESNGEAAyMzOjixcvymTc06dPEwD6999/\npdL/okWLCIBcVZhkCYKMlHTR5DiO+vfvT7Vr167U8wB9+vShgQMHirXPmjVrSEtLi3Jzcys8LsPI\nu0mTJlGdOnXEKkn36NEjAkAhISFSjKw4juNo8uTJJBQK6fjx40W2hYWFkYuLC1mYF12508LcvMSV\nO+WVpI7jzp071K1bt8Lyhffv35dy5BVz/Pjx72Y657///ku6urpkYWFR5A7N9/LeZOTbp0+faPbs\n2aSiokL6+vq0b98+mZaJdnJyImNjY6k9K8BxHM2YMYMEAgH5+/tLZQxxsQRBSkS5aPr5+REAOnXq\nVKXGql+/Pi1YsECsfa5fv04A5PaDlWEqKy4ujpSVlWnDhg1i7Xfr1i0CQA8fPpRSZKXLy8ujkSNH\nkoqKCp0/f55iYmLI2sqKAJC+ni5N6NeTNs6cSnsWzqaNM6fShH49SV9PlwCQtZUVxcTEyDxmUUjq\nOOLi4mjs2LEEgFq2bElnz56Vy4f7iL5OSTA0NKR+/frxHYrE3L9/n6pXr05du3alhw8ffhfvTUa+\nZWVlkaenJ2lra5OWlhatWLGC0tPTZRpDfn4+1alTh9zc3KQ+joODAwmFQjpx4oRUxxIFSxAkTJwP\nQlUVFRoyZEilxktOTiYAFBgYKNZ+6enppKysTN7e3pUan2Hk1dSpU6lWrVqUlpYm1n4XL14kAPTi\nxQspRVa27Oxs6t+/P6moqJC6mho10q9Hx1Yvppy/zxAXer7Yv5y/z9Cx1YupkX490tDQEPtaIG0B\nAQGkoaFRqeNITk6mefPmkZqaGtWpU4d8fHzk/u7n8uXLSUVFhZ48ecJ3KBJ18+ZNUlNTI2VlocK/\nNxn5xXEcHTp0iAwNDUkoFJKzszN9+PCBl1gKfjS6ceOG1MfKy8ujESNGkKqqqsymT5Wm/ILgjMgC\nAwPh6OiIujVr4NjqxRjYpSOUlYvXu87Ly8fpkFuYvWUXLpw/j0OHDmHMmDEVGjM6OhoARF4DoUCV\nKlXQunVrhIaGwtnZuUJjM4y8evPmDfz8/LB8+XJoamqKtW9qaioASHUdhLKoqqpi+PDhOHvmDEb2\n7oGdv86ApoZ6qe2VlYUYatUZth0sMG3dNowbNw5EhLFjx8ow6pIFBgbCzs4Odr17wNvdVezjyM3N\nRXJyMpYvX46srCwsWLAAc+fOhZaWlgyPQnyvX7/G6tWrMWvWLDRp0oTvcCQqLi4OOTk5GGtrrdDv\nTUZ+3bhxA25ubrh79y4GDRqEc+fOoVmzZrzFExQUBB0dHVhaWkp9LKFQCH9/fwwdOhRDhgzBxYsX\n0blzZ6mPWxIBkbyu0KBYxPkgLJCemYVp67bB/8JV+Pv7V+iiuWvXLri4uCA9PR2qqqpi7Ttjxgyc\nO3cOMTExYo/LMPJsxowZCAgIwIsXL1C1alWx9vXz88OkSZOQm5sr0qJqkhYTEwMzMzP83L0T9i2e\nCyUl0dc9o68HAAAgAElEQVSz5DgODh4bcPT6TTx8+BBGRkZSjLRsBccxvHsn+JVyHKv3H8Zvu/Zj\n5qgh2DhzauHrHMdhoscGHLp0DRxHmDx5MpYvXy72ApJ8GT16NK5fv44nT57wlmhKQ2nndOfxM9h5\n4i+8eB8PAGjZ0ACLJ41DH8u2hfvK03uTkU9Pnz7Fr7/+ipMnT8LCwgKenp6wsrLiOyyYmprC3Nwc\n+/fvl9mYmZmZ6Nu3L+7fv49r167B3NxcZmMXYCspS0BMTAwcHR1h17sH/BbPFSk5AABNDXX4LZ4L\nu9494OjoiNjYWLHHjoqKQpMmTcRODoCvKyrHxsYiMTFR7H0ZRl69f/8eu3fvxqxZs8RODoCvdxCq\nVKnCS3IAAFOnTEE9nRrY4e5a5Ev16v2H0WHSDFS3GYY6/UZj2K/L8fTVmyL7KikpwdvdFXVr1sAU\nJydZh15EwXF4/+c4Ctx99AR7gs7DzKhRsW1KSkrY4e6K+rq6aNe2LXx8fBQmObh+/TqOHDmCtWvX\nflfJAVD6OW1QuxbWTJuMe35euOfnBeu2Zhjy6zL8++JVYRt5em8y8iUxMREuLi5o2bIlwsPDERAQ\ngDt37shFcvD8+XNERUVh8ODBMh1XQ0MDp0+fRrNmzWBra4tHjx7JdHyAJQgSUdpFUxYf6FFRUWJP\nLypQcLvs1q1bFdqfYeSRp6cn1NTU4OrqWqH9U1NTeftiFxYWhmvBwVg3fXKxHxpCIqLhMmIQbvlu\nxqWtq5Gbl4feMxciMyu7SDtNDXWsc5mEa8HBCA8Pl2X4hco6DgBIy8iE/bJ18FkwC9pVS54Cpqmh\njg0znXDn7l3ejkNceXl5mDFjBjp27Ag7Ozu+w5Goss5p/84d0MeyLYwa1INRg3pYMXUitDTUcSvq\ncZF28vDeZCSH47hK7Z+ZmYnVq1ejcePG8Pf3x6pVq/DkyROMHTtWrDun0hQUFARVVVXY2trKfOyq\nVavi3LlzqFevHnr16oXnz5+Xu09lz8m35OMMKDA+P9CJCJGRkRVOEAwMDFCnTh2EhoZWaH+GkTeJ\niYnYuXMnZs6cCW1t7Qr1wWeCsG/fPtSvrYeBXToW23Zmowfs+/ZEc8OfYGrUEH6L5+JVfCLCnhSf\nIjioiyX09XTh5+cni7CLKes4AMDFczsGdO6IHm1bl9kP38chrt27dyMyMhJbt26Vmy84klLeOS3A\ncRwOXwpGRlY2LE2aF9uuaOeU+X/h4eFwdXVFWwsLqKurQygUQl1dHW0tLODq6iry9xeO43Dw4EE0\nbdoUS5YsgYODA2JjYzFv3jyoq4s2A0NWgoKCYGNjw9tzTzVr1sTFixehqamJnj174u3bt0W2S+qc\nlIQ9pFxJ5X2gf8tv8VzU7jcaYU9i0MWs6Jf6by+aos41i4+Px6dPnyqcIAgEAlhaWrIEgflubNy4\nEUpKSpg1a1aF++AzQQi9eRM2Fq1KLG7wX5+/pEMgEKBmteLTqJSVhbCxMMMtnv62yzqOw5eC8SDm\nGe76bSu3H76PQxyfPn3Cb7/9hkmTJqFdu3Z8hyNx5b03o569QKcps5GVnYOqVTRwfM0SNDNsUKyd\nIp1T5qvY2FhMcXLCteBg6OvpomdbM4zrOhHVNKsgNT0DETHPcOKPI/Dy8oK1lRV2+/iU+ozJ1atX\n4ebmhvv37+Pnn3/G6tWrYWxsLOMjEk1SUhJu3LiB7du38xpHnTp1cPnyZXTp0gU9e/bEjRs3kJKS\nIrFzUhqWIFQSnx/oUVFRAMSvYPQtS0tLLF26FHl5ebzNuWYYSfj06RO8vLwwffp01KxZs8L98Jkg\nREVHY1zXieW2IyLM3rwTXVq1RIuGBiW2MTNuhCNXZfdQ3bdKO443CYmYvXkXLm5ZBRURrzdmxo1w\n+Mo+uZ+SsmbNGuTk5GD06NFyH2tFREZFYVxXh1K3NzNogAcHvPE5LQ3Hrv2DCR7rcd3bs8Qkgc/3\nJiMecaszzvPyRatWreDr61ukOuOjR4/g7u6OM2fOoGPHjggJCeGtOo+ozp07h/z8fAwYMIDvUPDT\nTz/hypUr6Nq1K9q1a4eE+HjU1alZqXNSHvaNsJL4/ECPioqCuro6GjUq/pCfqCwtLZGRkYHIyEi0\nadOmwv0wDN+2bNkCjuMwZ86cSvWTkpLCS4LAcRyys7NRTbNKuW2nrffCoxevELJrQ6ltqmtpIjs7\nGxzHyXS6S1nHEfY4FomfU9DWwRUFBfTyOQ43HkRh+9HTyLpxGgKBoMg+1bU0kZOTAwsLC5nEX1m9\nevXiOwSpKeu9qawsRCP9rw+Smzc1xt1HT7Dlj5PY4V78WSC+3puMeCpbppiI0KNHD/z+++/Ys2cP\nDA0N8ccff2D48OHF/s7lUVBQENq2bQt9fX2+QwEAGBsbY9asWViwYAHG9emBne7SLTPMEoRK4PsD\nPSoqCi1atIBQWP7di9JYWFhAWVkZoaGhLEFgFNbnz5+xdetW/PLLL9DT06tUX6mpqWjcuLGEIhOd\nkpIS1NTUkJqeUWY7F8/tOBd6Fzd2eKJuLZ1S26WkpUNNTU3mX8DKOo6e7drgof+OIq85eGxAc8Of\n8Ov4kSV+aUhJ+1rCWV6nQhIRnJyckJycjCNHjny3d2ItLS3LfW9+i+MI2Tm5JW7j673JiO6/1RlF\nPVcF1RkJgMPEiRAqK0NdXR0bNmyAs7Mz1NTUpBu4hOTk5ODcuXOYN28e36EUiomJwfLly2HXx0as\nEtgF5wQAHB0d0b59e5GmG32fVzIZ4fsDvTIVjApoaGigTZs2CA0NxbRp0yrVF8PwZdu2bcjKyoKb\nm1ul++JzipFJy5aIiHlW6nYXz+0I+jsUwd7r8VOdshOhiJjnMK3k9aGiSjsOTQ31YndQNTXUUbN6\nVTQ3/KnEviJinqPV/+qQy6MjR47g/v37uHjxItq3b893OFJjamJS6ntz0c596GvZFg30dPElIxMB\nF67i+oOHuLB5VYnt+XxvMqIpr0wxUPo6JgVlim/cj4RATR33HzxAjRo1ZBW6RAQHB+PLly8yL29a\nltJKYIuyDklBxcx/Iv/FFCcnXL12rdzxWPpeSaJ+oF/1WivRD3SO4xAdHV3pBAH4+svQzZs3K90P\nw/Dhy5cv2Lx5M6ZMmSKRWvl8JgiWnTrh8r0I5OXlF9s2bb0XAi9eQ8Cy+dDUUEd8UjLik5KRlZ1T\nrG1eXj6uhEWgowxW/ixJWcfxX2VNNeD7OMqTnp4ONzc3DBky5LueWgSUfU7jk5IxYbknmo92Qq8Z\nCxD+JBYXNq8qsUqVvJ9TpvwyxUDZ65gAXxP/jbOm4OWrV4iLi5NmuFIRFBQEAwMDmJqa8h0KgLLP\niSjrkADiV8xkCUIl8fWB/urVK6SlpUnkzdupUyc8f/4cCQkJle6LYWTN29sbaWlpcHd3l0h/qamp\nqF69ukT6EpeDgwPeJiTidEjxtUl2nTiD1PQMWE93h/7AcYX//rhyo1jboJBQvE1IhIND6Q+VSlNZ\nx/FfV7zWFvn18Vt8H0d51qxZg8TERGzYUPrU0e9FWed0z8LZeHZsHzKuB+H9mUO4sKXk5ACQ/3PK\nlF/SVpR1TADFLWlLRAgKCsKgQYPk5lmJss6JqOuQAOKdE5YgVBJfH+iSqGBUoGDBNHmd48swpUlP\nT4enpyccHBxQv379SvdHRLzeQTA3N4e1lRXmefkiPTOryLb8m+eQ98/ZYv/G9+tZpF16ZhbcvfbC\n2sqKt2k5ZR2HqNIzszBn8y7U0tFBnTp1JBxh5cXFxWH9+vVwc3OrVKEIRSGpc8r3e5MpX3nVGUVd\nx0RRS9pGRETg9evXGDRoEN+hFBK1YmZ565CIc07YMwiV9O1F07aDRZFbP/k3z4nUR0UumlFRUahe\nvbpEnq5v0KAB6tWrh9DQULmab8cw5dm1axc+f/6M+fPnS6S/zMxM5Ofn85YgAMBuHx+0atUK09Zt\nE+vhQODrh8O0ddvwPikZF3x8pBhl+SRxHPGfvyZrpqam2LVrF4YPHy7FiMUzd+5c1KpVCwsWLOA7\nFJn5Xt6bTNnKqs4ozjomgOKUKf7Wrl27oKWlhWrVqslN3OWVGRZ1HRJA9IqZLEGQgMpeNJ0rcNEs\neEBZEre/2IJpjCLKzMzE+vXrMX78eBgaGkqkz9TUVADgNUEwMjKCr6/v15J0IOwop5RdgfTMLExb\ntw3+F64iICBA7EVxJO3b4wBQbpnEAv89DltbW/zyyy8YMWIExo8fj61bt/I2BazApUuXcOLECRw6\ndAiamqVPsfjeFH1vAjsqeE75fm8ypSurOmNF1jFRtDLF3+rQoQPfIRRRVsVMcdYhEbViJksQJKAy\nH4S/rN2KwAtXsf/AAbEumlFRUejYsewl78VhaWmJxYsXIzc3FyoqKhLrl2GkxdfXFwkJCRL9BVce\nEgQAGDNmDB49eoRVq1bixv0obJw1BYO6WJa6GE5QSCjcvfbifVIyAgICxFoMR5rGjBkDIoKjoyP+\nifwX61wmVeg4/vjjDxw8eBAuLi64fv06Dhw4gG7dusn6cAAAubm5mDlzJrp27YpRo0bxEgOfCs7p\nxIkTceN+pMK+N5mSlVWdsSLrmMh7meL/io+PR79+/bBy5Ur06dOH73AKlVdmWJx1SEStmMkSBAmp\n6Afh24+foCQU4tq1a7CzsxPpjkBubi7+/fdfODo6Six+S0tLZGZm4uHDhwqZ6TM/luzsbKxZswZj\nx46V6K+R8pIgZGdn488//0Tt2nXwLiEBwxesgL6eLmwszGBm3AjVtTSRkpaOiJjnuBIWgbcJiehh\nbY0Lu3fL3a+zY8eORfv27THFyanCxyEQCDB+/Hh069YN48ePh5WVFebNm4fly5fLvK769u3b8eTJ\nEwQGBsrNA4yy1qpVK+Tn50NVq6pCvzeZkpVWnbEi65jIe5ni//L29oaysjKmTZsGbW1tvsMpVFaZ\n4ZKUtQ6JqBUzWYIgQaJ+EF64fQ/xSZ+/XjSDd+P27duws7NDgwYNsGzZsnLHiY2NRU5OjkQeUC5g\nbm4OFRUVhIaGsgSBkXv79u3Du3fvsGjRIon2Ky8Jwtq1axEbG4uqVatiytSpmDx5Mvz8/HArNBRH\nru5HdnY21NTUYGpigqEjR8HBwUGuP4CNjIxw9do1hIeHV+o4DA0Nce3aNWzYsAG//fYbLly4gICA\nALRs2VImx5GQkIDff/8dU6ZMQevWZT+g+b0iIsycORONGzdGZGQkoqOjFfq9yRRn2akTTvxxBHl5\n+UV+5BR3HZOC6oxDRyrOnbagoCB0795drpIDADC3sMBfJ44VOyeAeOuQiHNOWIIgYeV9EJq0bInP\n6ZmYNGkSfH19C/d58+YN5s+fj/r168PJyanMMQoqGEnyQ1FdXR3m5uYIDQ2Fi4uLxPplGEnLzc3F\n6tWrMXLkSDRr1kyifctDgvDkyROsXLkS3bt3x99//41ff/0VP/30U5EvWaKuti5vzM3NK30cQqEQ\n7u7usLW1hZ2dHSwsLLBmzRrMmDFD6v9PFi5cCKFQCA8PD6mOI89OnDiBq1ev4syZM1BTU5PIOWXk\ni4ODA7y8vHA65BaGWnUus21Zd9EUraRtamoqrl69Ck9PT75DKfTp0yds3rwZgYGBSE9PL/GcFKxD\n8v5jEqpraaKVUcNS1yER55wIqGAiGSNV3140nZyccOXKFTx79qzwj4uI4OLigl27duHUqVPo379/\nqX39/vvv2LVrFz58+CDRGGfPno1Tp07h+fPnEu2XYSRp7969mDx5Mh4+fCjxRWwOHDiACRMmICsr\nS+ZTV4Cv14EePXrg5cuXSE9Px6BBg+DDKr6UKisrCwsWLMDmzZthY2PztVa4BMrdluTevXto3749\ntm3bhunTp0tlDHmXmZmJ5s2bw8TEBH/99Rff4TBS1MPaGi9jniLioLdIz1T+V3pmFszsp8HAuIlI\nq/bKg6NHj2LEiBGIi4uTWOGLikpISMDGjRuxffv2r8VsnJ1xKzQU71++kNk5YWm+jHz7i8qYMWMQ\nFxeH27dvF74mEAiwdetWDBw4ECNHjsTdu3dL7auggpGkWVpaIi4uTuKJB8NISl5eHlatWoVhw4ZJ\nZYXL1NRUqKmp8ZIcAMD+/fsRHByMPn364NOnTz9UCc2KUFdXx6ZNm3D58mU8fvwYpqamOHz4sMTH\n4TgOM2bMgImJCaZOLXlRtx/B+vXr8e7dO2zatInvUBgp2+3jg/dJyZi2bhs4jhNr329L2u5WoB84\nTp06hVatWvGaHLx//x5z586FoaEhtm/fjunTpyMuLg6enp7Yt3+/TM8JSxB40L17d9StWxeHDh0q\n8rpQKERgYCDMzMzQv39/PHtW8gMp0kwQALZgGiO/Dh8+jGfPnuG3336TSv98LpKWmJiIuXPnYsyY\nMTh16hTs7Ox+iAW4JMHGxgaRkZHo06cPxowZg3HjxuHz588S6z8gIAChoaHYunUrlEUs7/i9efny\nJVavXo3Zs2fD2NiY73AYKSuozuh/4SomeHiKvDheemYWHDw2wP/CVfj6+irMg+l5eXk4c+YMb4uj\nvXnzBjNmzECjRo2wZ88ezJ07Fy9evMCaNWugp6cHoOg5cfDYIPVzwhIEHgiFQowaNQp//PEH8vPz\ni2zT0NBAUFAQtLW10adPHyQmJhbZnpmZidjYWKkkCA0aNED9+vVZgsDIpfz8fKxYsQIDBgxAmzZt\npDIGnwmCm5sbAKB169b48OEDFi5cyEsciqpGjRo4dOgQAgICcObMGZiamuLq1auV7vfLly9wd3fH\nyJEjYWVlVflAFdS8efOgra0tteSckT9jxozBsGHDcOjiNbSyd8bx4BDk5eWX2DYvLx/Hg0NgZj8N\nR6/fVLiStv/88w+Sk5NlniC8fPkSzs7OaNy4Mfz9/bFgwQK8fPkSHh4e0NHRKdZ+zJgx8Pf3x9Hr\nN2FmP02654QYXty+fZsA0OXLl0vc/uzZM9LT06MOHTpQenp64evh4eEEgG7duiWVuEaMGEFdunSR\nSt8MUxmHDx8mAHT79m2pjeHs7Ext2rSRWv+luXz5MgGgXbt2UYMGDWjs2LEyj+F78vLlS7K2tiYA\nNGfOHMrMzKxwX+7u7qShoUEvX76UYISK5erVqwSADhw4wHcojAw9fPiQVFRUyNnZmaytrAgA6evp\n0vi+PWnDjCm0Z+Fs2jBjCo3v25P09XQJAPWwtqaYmBi+QxfbnDlzqG7dupSfny+T8WJjY2ny5Mmk\nrKxMOjo6tGrVKkpJSRF5/5iYGKmfE5Yg8ITjOGrcuDFNnjy51DZ3794lTU1NGjRoEOXm5hIR0YED\nBwgApaamSiWujRs3krq6OmVnZ0ulf4apiPz8fDIxMaHevXtLdZxx48ZR9+7dpTrGf2VmZpKRkRF1\n69aNdu/eTQKBgKKjo2Uaw/coPz+fNmzYQKqqqmRiYkIRERFi9/HkyRNSUVGhZcuWSSFCxZCbm0sm\nJiZkaWkpsy9PDP9yc3Opbdu21KJFC8rKyiIiorCwMHJxcaG2FhakpqZGAEhNTY3aWliQi4sLhYWF\n8Rx1xRR8H5s6darUx3ry5AmNHz+ehEIh6enp0fr16+nLly8V7k+a54QlCDxatGgRaWtrF/7xleTs\n2bMkFArJ2dmZOI4jd3d3MjQ0lFpMoaGhBIDu3LkjtTEYRlzHjh0jABQSEiLVcQYOHEgDBw6U6hj/\n9dtvv5GKigo9fPiQGjZsSMOHD5fp+N+7hw8fkqmpKamqqtK6desoLy9P5H379+9PBgYGlJGRIcUI\n5ZuXlxcJBAK6e/cu36EwMrR27VpSUlIqc7bC95IwRkdHEwA6c+aMVMcYM2YMKSkpUd26dWnz5s1F\nZodIiiTPCUsQeBQVFUUA6OTJk2W28/X1JQC0atUq6tevHw0YMEBqMWVlZZGqqipt2bJFamMwjDg4\njqM2bdqQtbW11Mfq3r07jRs3TurjFIiOjiYVFRVasmQJ7du3jwDQgwcPZDb+jyIrK4vc3NxIIBBQ\n9+7d6cWLF+Xu89dffxEAOnbsmAwilE+JiYlUo0YNcnR05DsURoYeP35Mampq5ObmxncoMrF69Wqq\nUqVKpaYiliYiIoJGjBhBAoGAGjRoQNu3b5fKONLAEgSemZqa0qhRo8ptt3TpUgJAOjo6NH/+fKnG\nZGlpSaNHj5bqGAwjqtOnTxMAunbtmtTHatOmDTk7O0t9HKKvv/R06dKFmjRpQmlpadSkSRMaPHiw\nTMb+UV27do1++uknqlatGh08eJA4jiuxXVZWFhkbG5ONjU2pbX4Ev/zyC1WvXp3i4+P5DoWRkby8\nPOrUqRMZGxv/MHfOOnbsSEOHDpVon2FhYTRkyBACQIaGhrR7926Fm7rNqhjxbOzYsQgKCkJaWlqZ\n7ZYsWQJ7e3t8+vQJJOW17SwtLVklI0YuEBE8PDzQpUsXdO/eXerjybKK0d69exESEoKdO3ciKCgI\nT58+xeLFi2Uy9o/KysoKDx8+xKBBg2Bvb49Ro0YhKSmpWLstW7bg+fPn2LJlS5krxX7P7t+/j127\ndmHp0qWFZRaZ75+XlxdCQ0Ph6+sLDQ0NvsORug8fPuD27dsYPHiwRPq7ffs2BgwYAAsLC0RFRcHP\nzw9Pnz6Fk5MTVFVVJTKGzPCdofzo4uLiCAAFBASU2/b69esEgKpUqUL379+XWkx//vknAaB3795J\nbQyGEcX58+cJAF24cEEm4+nq6tLKlSulPs6HDx9IW1ubJk6cSPn5+dSiRQvq27ev1Mdl/t+RI0eo\nRo0aVK9ePbp48WLh62/fviUtLS2aMWMGj9Hxi+M46tKlCzVv3pxycnL4DoeRkdjYWNLQ0CBXV1e+\nQ5GZPXv2kJKSEiUkJFSqn5CQELK1tSUA1KxZMzp48GBhcRlFxe4g8MzQ0BCWlpbFFk0ryePHjyEU\nCtG0aVP069cPL1++lEpMbME0Rh7Q/+4edOjQAb169ZLJmLK6gzBnzhwIhUKsX78ex48fx6NHj9jd\nAxkbOXIkIiMj0bJlS9ja2mLmzJnIzMzE/Pnzoa6ujqVLl/IdIm8OHz6MkJAQbNmyBSoqKnyHw8gA\nx3FwcnJC7dq1sWrVKr7DkZmgoCB06tQJurq6Yu9LRAgODkaPHj3QpUsXvH37FocPH0ZUVBTs7OwU\nf1FFvjMUhmjr1q2krKxMHz9+LLOdq6srNWvWjD58+EANGzak5s2b06dPn6QSU4MGDX6YB5QY+VRQ\ne/2vv/6SyXhZWVkEgPbv3y/VcQruiuzfv584jiMzMzPq2bOnVMdkSpefn09btmwhdXV1MjAwIAC0\ne/duvsPiTVpaGunr60t8TjYj33bu3Fnm2kzfo/T0dNLQ0KD169eLtR/HcXTx4kXq2rUrASAzMzM6\nduzYd1PVqQC7gyAHRo4cCY7jcOzYsTLbRUVFwcTEBLVr18b58+eRkJCAIUOGICtLtOW2xcGeQ2D4\ntnz5cpibm6Nfv34yGe/Lly8AINU7CBkZGXB2dkaPHj1gb2+P06dPIyIigt094JGSkhJmzJiBu3fv\nIiEhAQCQkJBQbJX7H8Xq1avx8eNHbNiwge9QGBl59eoV5s2bBycnJ9jY2PAdjsxcvnwZmZmZIq+e\nTEQ4e/YsOnXqBFtbW2RmZiIoKAj379/HsGHDoKT0fX2l/r6ORkHVrl0bNjY25U4zKkgQAKBJkyY4\nffo07t69i/Hjx4PjOInGZGlpiXv37iEnJ0ei/TKMKEJCQhAcHIzffvtNZg+JpqamApBuguDh4YF3\n795hx44dAL4mQd27d0e3bt2kNiYjmtu3byMzMxP29vZYvHgxrKysEBcXx3dYMvXs2TOsX78e7u7u\naNiwId/hMDJARJgyZQqqV6+O9evX8x2OTAUFBaFp06Zo0qRJme2ICKdOnUK7du3Qv39/CAQCnDt3\nDnfu3MHAgQO/30IGPN/BYP5n7969JBAI6M2bNyVuj4+PJwB09OjRIq+fPHmSlJSUaNasWRKN5/bt\n2wSgzEVSGEZabG1tydTUVKa3bO/fv08ApLYg1MOHD0lZWZmWL19ORF8XQcQPdktfXiUnJ5Ouri7Z\n2dkREdHff/9NhoaGVLVqVfLz8/thSp0OHjyY6tevT2lpaXyHwsiIn5+f1BcJk0f5+fmkp6dH8+bN\nK7PNn3/+SWZmZgSAunXrRpcvX/5hrgcsQZATycnJpKqqShs3bixx+5UrVwgAPX78uNi27du3E4BS\n962I7OxsUldXp02bNkmsT4YRxa1btwgAHTlyRKbjFlQJe/LkicT7zs/Pp44dO1Lz5s0pKyuLOI6j\njh07kqWl5Q/zYSPPZs2aRZqamvT27dvC11JSUmjixIkEgIYOHUqJiYk8Rih9Bc/GHD58mO9QGBl5\n+/YtaWtr0/jx4/kOReZu3rxJACgkJKTYtry8PAoMDKSWLVsSALKxsaHg4GAeouQXSxDkyJAhQ6hd\nu3YlbtuyZQupqalRXl5eidvnz58v8S9VnTt3ppEjR0qsP4YRRf/+/alZs2alvtelpWBBtvfv30u8\nb29vbwJAN27cICKiS5cuEQA6d+6cxMdixBMdHU1CoZBWr15d4vZjx46Rjo4O1alTh86ePSvj6GQj\nJyeHmjVrRt26dWMJ6w+C4zgaNGgQ1a5dW2rFTuTZ/PnzqVatWkU+Z3Jzc+nAgQPUtGlTAkB9+vSh\nf/75h8co+cUSBDly5MgRAkBPnz4tts3JyYnatGlT6r4cx5GdnR2pqqpKLNN1c3OjBg0aSKQvhhFF\nWFgYASB/f3+Zjx0QEEAAKD09XaL9vnv3jqpVq0aOjo6Fr3Xr1o3atm3LvozxjOM46tmzJzVu3Jiy\nsrJKbffu3Tvq06cPAaBp06ZJ/D3Ct40bN5KSkhI9ePCA71AYGQkMDCQAdPz4cb5D4UWLFi1o4sSJ\nRPQ1Qfb19aXGjRsTABo4cCDdvn2b5wj5xxIEOZKenk5aWlqFc5S/ZWlpSfb29mXun52dTTY2NqSt\nrShfHe8AACAASURBVE1RUVGVjufYsWMEoNTnIhhG0oYMGUJGRka8LDCzY8cOEgqFEv/SPmLECNLT\n0yv8lS44OJgA0KlTpyQ6DiO+EydOEAA6ffp0uW05jqPt27eThoYGNWnShO7cuSODCKXvw4cPVK1a\nNZo2bRrfoTAyEh8fTzo6Oj/sDIGYmJjCGRc7d+4kQ0NDAkDDhg2j8PBwvsOTGyxBkDN2dnbUvHnz\nIl9SOI6jqlWr0tq1a8vd//Pnz9SqVStq0KBBpb/Yv3v3jgDQn3/+Wal+GEYUERERBID27t3Ly/hr\n166lGjVqSLTPv/76q9hK6TY2NmRmZsbuHvAsIyODDA0NqW/fvmKdi8ePH1Pbtm0LHzhX9NVSJ02a\nRDVr1ix3HR7m+zFy5EiqVatWpVcPVlRr1qwhZWVl0tfXJ4FAQKNGjaKHDx/yHZbcYQmCnDlz5gwB\nKHKr9+XLl2JVGXjz5g01aNCAWrVqRZ8/f65UPAYGBjRnzpxK9cEwohg5ciQZGhpSTk4OL+MvWrSI\nDAwMJNZfWloaGRgYkK2tbeEX0IIH4/5bjYyRPQ8PD1JRUSmx8EN5cnJyaPHixaSkpEQdO3akmJgY\nKUQofQXV6rZv3853KIyMFMwMOHToEN+hyFx6ejpt3LiRVFVVCQCNGzeOHj16xHdYcoslCHImJyeH\ndHR06Ndffy18reBXyJcvX4rcT1RUFGlra5ONjQ1lZ2dXOJ7Ro0eTpaVlhfdnGFE8evSIBAIB7dq1\ni7cYXF1dydTUVGL9ubm5kbq6OsXGxha+1rdvX2rZsuV3t+Kmonn16hVpaGhUerX4mzdvUuPGjUlT\nU5N2796tUHeF8vPzqUOHDtSqVSuFvwvCiObjx49Uu3ZtGjx4sEK9Vyvry5cvtG7dOtLT0yOhUEgC\ngaDEqdxMUSxBkENTp04lAwODwi8Ra9asoapVq4r9Bx0cHEyqqqo0bty4Cl8MtmzZQqqqqmU+wMcw\nlTVu3DiqX78+r++zCRMmUOfOnSXS1/3794tVxrl79y4BoMDAQImMwVTcqFGjqHbt2pSSklLpvr58\n+UKOjo4EgAYNGkTx8fESiFD69u3bRwB+yPKNPyp7e3vS1tamd+/e8R2KTKSkpNDKlStJR0eHVFRU\nyMnJiTw9PQnAD/P/oDJYgiCHCh5iLKjPa2dnV+Ff8QsqI82fP79C+9+5c4cAUGhoaIX2Z5jyPH36\nlJSUlGjbtm28xjF06FDq27dvpfvJy8ujdu3akYmJSZHpUoMGDaImTZrIvHwrU1TBehf79u2TaL+n\nTp0iXV1d0tXVpaCgIIn2LWkpKSlUp04dGjVqFN+hMDJSMBNB0u97eZSUlERLly4lbW1tUlVVpWnT\nphXOwBg+fDi1b9+e5wgVA0sQ5FB+fj7p6+vT9OnTiYiodevW5OTkVOH+NmzYUOF5pgULpklyETaG\n+ZaDgwPVrVuXMjMzeY3DxsZGIl+Ytm7dSgDo5s2bha89ePCAAND+/fsr3T9Tcbm5udSqVSvq0KGD\nVKZ5ffjwgQYMGEAAyMnJib58+SLxMSRh3rx5pKGhQa9eveI7FEYGPn/+TPr6+tSnT5/vemrRx48f\nadGiRVStWjVSV1enmTNnFinWkpWVRVpaWrRixQoeo1QcLEGQU3PnziU9PT3KzMwkNTU12rJlS6X6\nmzVrFgkEAjpx4oTY+3bp0oWGDx9eqfEZpiTPnz8noVAoFwlou3btKpWIExG9fv2aqlatSr/88kuR\n14cPH06NGjVic715VrBgnTRLlHIcR7t27aIqVaqQkZGR3N19ffz4MamoqJCHhwffoTAy4uTkRFWr\nVhXrOUZFEh8fT+7u7qSpqUlVqlQhNze3Ehe8LFgtnFUsEg1LEOTUvXv3CADt2bOHANCVK1cq1V9+\nfj6NGDGC1NXVi/yyKQp3d3fS19ev1PgMU5IpU6aQrq6uXCw81aRJE5o7d26l+hg6dCjVqVOHkpOT\nC1+Liooq/Ftm+PPx40eqWbMmTZo0SSbjPX36lDp06EBCoZCWLFnCW3Wub3EcR3369CFDQ0PKyMjg\nOxxGBgpWbd+5cyffoUjcu3fvaM6cOaShoUFaWlo0f/78Mku3Ojs7U8OGDb/ruyiSxBIEOcVxHBkb\nG5O1tTUBkMiDb5mZmdS1a1fS0dGhJ0+eiLxfwWJC7HY0I0mvXr0iFRUVkdb3kIU6derQsmXLKrz/\nyZMnCxff+daYMWPop59+qlQ1Mabypk2bRtWqVaP/Y+/M46Ha4z7+mRmMQWlDoboVpZCibntIi5bb\nqkWlEi2KSqVdm6J9I21XSqWN6qmodNsTFapLG5I2bYpsYZjv88d9eJLBYMYMzvv1mtfrNue3fM49\n5pzz/f2+y6dPn6psTj6fT2vWrCEOh0OdO3euUEpVcXLhwoVaXT23tpGenk7Nmzcnc3PzGpU57d27\nd+Tk5ERcLpdUVVXJ1dW1sBBlSQgEAtLS0qK5c+dWkcrqD2MgyDArV64kLpdLampqYhvz27dv1LZt\nW2rRooXQLThhfPr0SeiLDwNDZZg9ezY1aNCA0tLSpC2FiIiUlJRo+/btFeqblpZG2traNGjQoCKr\nUy9evCA2m03e3t7ikslQAR4/fkxsNpu2bt0qlfnv379Purq6xOPxyNvbWyormNnZ2dSqVSvq27cv\ns4JaS3B0dCQlJSV69eqVtKWIhcTERJo5cyYpKChQ/fr1ae3atUV2a0sjMjJSLN4YtQnGQJBhnj9/\nTgDIwMBArOMmJiZSkyZNyMTEROQguhYtWtC8efPEqoOh9pKUlERcLldm/KD5fD4BIB8fnwr1nzt3\nLikpKdHr16+LfD9p0iTS0tJi0gRLEYFAQKampqSnpyfVXZyMjAxycHAgADRw4ECRF2jExYYNG4jD\n4dDTp0+rdF4G6XD79m0CUOn4RVkgPj6e7OzsSE5Ojho1akQeHh7lTlG8cuVKqlevnky4+lUXGANB\nxuFyuaSjoyP2cR89ekR16tShgQMHivSDGT9+PHXp0kXsOhhqJ87OzqSqqlrpSt/i4vv37xWucPzw\n4UNis9m0efPmIt+/evWKOBxOjXhAV2cKUj1fuXJF2lKIiCgoKIg0NDSoYcOGVebq8+HDB1JWVmYW\neWoJmZmZpKOjQz169KjWrkUvXrygSZMmEYfDIQ0NDdqyZQtlZGRUaKwOHTrQ+PHjxaywZsMYCDLM\nz58/icVikby8vFgK+vxOSEgIycnJ0dSpU8vccvb09CR5eXmpp6JkqP58/vyZeDwerVy5UtpSCklM\nTCQAFBISUq5+fD6fOnbsSEZGRsUMbXt7e9LQ0GCCQaVIRkYGNW3alIYNGyZtKUX48uULDR8+nACQ\nra2txN3sJk6cSGpqaiK7YzBUbxYsWEBcLlfqMS8VJSYmhqytrYnNZpOmpibt3LmzUvfRN2/eEAA6\nceKEGFXWfBgDQYYpyJ0OgPz8/CQyh5+fHwGg1atXl9quIKtSaGioRHQw1B4WLVpEKioqZQaVVSX/\n/vsvAaDw8PBy9du2bRuxWCy6f/9+ke8TExNJTk6u2K4CQ9Xi6upKXC5XJn2wBQIBHTx4kFRUVKhF\nixZ0584dicxz9+5dAkAHDhyQyPgMskVYWBix2WyZSf5QHh4/fkxWVlbEYrGoadOm5O3tLZZFSS8v\nL5KXl5eZHevqAmMgyDBHjhwhANStWzexVHgtCXd39zLTMObm5hKPx6MtW7ZITAdDzSc5OZmUlZUr\nXNlbUhS8RD179kzkPm/evCFlZWVydHQsdszBwYEaNWoks4WyagMJCQnE5XJp2bJl0pZSKq9evaIe\nPXoQm82mpUuXijVOIi8vj4yNjcnExISp4F0LyM7OprZt21Lnzp2rVc2ViIgIGjZsGAGgFi1a0IED\nB8T6O+jXrx/169dPbOPVFhgDQYZZvHgxNWvWjHbv3k0cDqfU/L6VQSAQ0MyZM4nD4VBQUFCJ7Xr3\n7k2jRo2SiAaG2sGKFStISUlJYn/LFSU4OJgAFKm6WRoCgYCGDBlCmpqaxdz/3r9/TwoKCuTu7i4J\nqQwiMmLECNLS0qoWRlpeXh6tX7+e5OTkyNjYuFyGamns37+f2fmtRSxfvpzk5eUpOjpa2lJEIjw8\nnAYPHkwASFdXlw4dOiT2IOLU1FSSl5cnT09PsY5bG2AMBBlm8ODBNGjQIPry5QtxOByJpkrMy8uj\noUOHkpKSEj18+FBom8WLF5OmpiaTIo+hQqSkpFDdunUrXYxMEpw4cYIAiOwLHhAQQAAoMDCw2LG5\nc+dS/fr1JRI3xCAaBcWh/P39pS2lXERERJCenh4pKirSrl27KhVgmpKSQo0aNSIbGxsxKmSQVSIj\nI4nD4dDatWulLaVM7ty5Q/379ycApKenR0ePHpXYjkdBkoLExESJjF+TYQwEGaZ58+a0aNEiIiKy\ntLSkXr16SXS+zMxM6tKlC6mrqwv12S0oBFVTy7UzSJY1a9aQoqJilad3FIX9+/cTi8US6YUsNTWV\nmjRpQkOHDi1mLH/8+JEUFRUrVXCNoXLk5uZSu3btqGfPntVyMSMzM5OcnJwIAPXv31/kXa3fmTt3\nLqmoqNCHDx/ErJBB1sjJyaH27dsLTZYgKwgEArpx40Zh8VcDAwM6efKkxF3fJkyYQEZGRhKdo6bC\nBoNMkpaWhjdv3sDAwAAAYG1tjTt37uDdu3cSm1NJSQkXLlxA3bp1YWlpieTk5CLHu3XrBgC4d+8e\nAEAgEEhMC0PNIi0tDTt27MD06dPRuHFjacspRlpaGurUqQM2u+xb4vLly5GWlgZPT0+wWKwix7Zu\n3QoFBQXMmTNHUlIZysDb2xsvXrwQen2qA0pKSti1axcuX76M6OhoGBoa4vTp0+Ua4+nTp/Dy8oKr\nqys0NTUlpJRBVti4cSOePn2KgwcPQl5eXtpyikBEuHr1Knr37g1zc3OkpKTgzJkzePLkCcaMGQMO\nhyOxufl8PoKCgjBs2DCJzVGjkbaFwiCcsLAwAkBRUVFERPTjxw9SVFSskqwo8fHxpK6uTl27dqXM\nzMzC7yMjI6lu3brUWEODuFwuASAul0smxsbk6OhIkZGREtfGUD1xd3cnBQWFCq+GSpqVK1eStrZ2\nme3Cw8OJxWIJrbj85csXUlJSouXLl0tCIoMIfP78mVRVVWnmzJnSliIWkpOTycrKigDQxIkTRcrC\nIhAIyMLCgnR0dJgCfbWA6OhokpeXl7n7jkAgoKCgIOrSpQsBoM6dO9OFCxeqdFfv+vXrBIAiIiKq\nbM6aBGMgyCgHDhwgNptdJPfvqFGjyNjYuErmf/DgASkpKdGwYcPoxYsXZG5mRgCoccMGNHlQX9o2\ndwb9vcyZts2dQZMH9SUtdTUCQOZmZhQXF1clGhmqBxkZGdSoUSOZfmmbN28etWvXrtQ2ubm51L59\nezI2NhbqL7t06VJSVlam5ORkSclkKAN7e3uqV68eff36VdpSxIZAIKDDhw9TnTp1qFmzZnTz5s1S\n2wcGBhIAunjxYhUpZJAWfD6fOnfuTG3bthWLMSiOomoCgYDOnTtHJiYmBIC6d+9Oly9floq737x5\n85i4yUrAGAgyyty5c6lNmzZFvisIjKyq4icXL178v0JtctRSS5MCPVwp904QCcIuF/vk3gmiQA9X\naqmlSTwer9oFBzJIji1btpCcnJxMB4lNnTqVunbtWmqbjRs3EpvNFroa9e3bN6pTp05hzBBD1RMR\nEUEsFqvGZit5/fo19erVi1gsFrm4uAh9IczKyqLmzZvToEGDpKCQoaopuCeVt35LAZGRkeTo6Egm\nxsaV9grIz8+n06dPU/v27QkAmZqa0rVr16T2ci4QCKhFixYyvTAl6zAxCDJKTExMYfxBAYMGDULd\nunVx/PjxKtHw48cPAMCYPr3x5Ig3Rpj1gJyccH9BOTkORpj1wJMj3rAy7Y4JEybA39+/SnQyyC4/\nf/7E5s2bMXnyZDRv3lzackokLS0NdevWLfH469evsXr1asyZMwcmJibFju/atQt5eXlYsGCBJGUy\nlAARwcnJCfr6+pg5c6a05UiEP/74Azdu3MCGDRuwY8cOdOnSBTExMUXabNmyBUlJSdi+fbuUVDJU\nFS9fvsTKlSvh7OyMLl26lKtvfHw8+pibw8TEBGdPnYRB4wbwmDkFfy9zhsfMKTBo3ABnT52EiYkJ\n+pibIz4+vsSx8vPzcfz4cRgaGmL06NFQV1fHrVu3cPPmTfTp00dqcUBPnz7F69evmfiDyiBtC4VB\nOBoaGrRq1api30+ePJlat24tcas8NjaWeDwe2VhaUF5ocOFOwa09W+ivnl1Is1FDYrFYdG7TqmK7\nCXmhwWRjaUE8Ho9xN6rl7Ny5kzgcDsXHx0tbSqn079+frKyshB4TCARkaWlJTZs2FZpTPzU1lVRV\nVcnZ2VnSMhlKoKCo5PXr16UtpUp49OgR6evrk4KCAm3dupXy8/PpzZs3xOPxmF2sWkBeXh51796d\ndHR0isQJisKxY8eIx+NV2iuAz+fT4cOHqXXr1gSABg4cSPfu3RPnaVaK9evXk4qKChOHUwmYHQQZ\n5OvXr/j8+XOxHQTgv2xGsbGxePTokUQ1zJg+HZoN68N7kVORzC6ZP7NhpNsKXgtnl7gywGaz4b3I\nCU0a1Mf0adMkqpNBdsnJycGmTZswfvx4tGrVStpySqW0HYRTp07h8uXL8PLygoqKSrHjXl5eyM7O\nhouLi6RlMgghPT0dixYtwujRo2Fubi5tOVVChw4dEBERgdmzZ2PBggXo168fZs+eDVVVVaxYsULa\n8hgkzO7du3Hv3j0cPHgQSkpKIvfz9/fHxIkTYWXavcJeAXw+HwcPHkSbNm0wefJk6Onp4cGDBwgO\nDi7MdCgLnD9/HgMGDACXy5W2lGqLnLQFMBTn6dOnACDUQLCwsICamhqOHz8OY2NjicwfGRmJGzdv\nItDDFco8xSLHLLt1gmW3TgD+29YvCWWeIjY5ToXV0nWIioqSmFYG2cXX1xdJSUlYvny5tKWUSUkG\nQkpKCubOnYuRI0di6NChxY6np6dj27ZtsLe3R5MmTapCKsNvrF+/Hqmpqdi8ebO0pVQpioqK2LZt\nGwYPHoxx48YhOTkZM2fORJ06daQtjUGCJCQkYOnSpXB0dESvXr1E7hcXFwd7e3tMHNAHvq4LRErp\nDPz3LPd1XQACYGtrCxcXFyQlJWHUqFEIDAxEhw4dKngmkuPjx4+4f/8+Zs+eLW0p1RpmB0EGiY6O\nhoKCAnR0dIodk5OTw+jRo3HixAmJ1SE4dOgQtDXU8VfPrpUaZ2jPbtBSV4Ovr6+YlDFUF3Jzc+Hh\n4YGxY8eiTZs20pZTJiUZCEuXLkVWVhZ27doltN+ePXuQnp6OxYsXS1oigxDi4uKwbds2LF68WKZj\nXCSJqakp1NXV0bBhQ+zduxfW1tZISUmRtiwGCSAQCGBvbw81NTV4eHiUq68wrwCPwyfQZeocqFqM\nRONB4zBy8VrEvn1frC+bzcaeRU5oXF8Vgvx8REdHIyAgQCaNAwC4ePEi2Gw2Bg0aJG0p1RrGQJBB\nYmJi0LZtW8jJCd/gGT9+PN6/f4+7d+9KZP6we/dgYdK+xK1HUZGT48DCxAjhYWFiUsZQXThy5Aje\nvn1bLXYPgP8C8n83EEJDQ7Fv3z64u7tDS0urWJ+srCxs3boVtra2aNq0aVVJZfgFZ2dnaGpqYtGi\nRdKWIjX27duH58+f49KlSzh27BguXbqE9u3b49q1a9KWxiBmDhw4gBs3buDvv/8W6u5YEgVeAZtm\n2xXxCrj75CkcRw9FuM8OXN3lAX5eHgbMXYaf2TnFxlDmKWLbvBn49PkzcnNzxXI+kuL8+fPo2bMn\nGjZsKG0p1RrGQJBBhGUw+pVu3bqhWbNmEstmFPP0KYx0xeMzbqTbEtG/ZdpgqNnk5eXB3d0do0aN\nKvXvWJpERUXByckJnUxMoKioiPT0dCxduhSdTEzg5OSE+/fvY8aMGfjzzz/h4OAgdIz9+/fj27dv\nWLJkSRWrZwCA4OBgBAUFYevWreDxeNKWIxW+ffsGV1dXTJ06FZ07d8b48eMRHR0NXV1d9O3bF/Pn\nz0d2dra0ZTKIgbdv38LFxQX29vbo27dvufqW5BUQtM0NNgP7ou0fzWCo0wK+rgvw9vNXRL6MEzpO\ndfAKyMzMxD///CPUJZShfDAGgoxBRGUaCGw2G+PGjcPp06fB5/PFOr9AIEBOTg7qKose+FQaqirK\nyMnJkZg7FIPs4e/vj4SEBJkMliwtvd/GWVML0/t17doVL168wIoVK8DhFN9Jy87OxqZNm2BjY4MW\nLVpI4UxqN7m5uZg3bx769OmDkSNHSluO1HB1dUV+fj7c3d0Lv2vatCn++ecfbN26Fbt370anTp3w\n5MkTKapkqCxEhBkzZqBu3brYsmVLufuL6hWQmp4JFouFBnWFx7FUB6+Aq1evIjs7mzEQxABjIMgY\n79+/R1paWpkrr9bW1vj27Rv++ecfsc7PZrPB5XKRlpkllvF+ZGSCy+WKHBDFUL3Jz8/H+vXr8ddf\nf8mcf6q/vz/at2+PN3GxCPRwxevAQ/B1XYh540Zg6l8DMG/cCPi6LsTrwEMI9HBFU/VGGDt2rNCd\nOh8fH3z+/BnLli2Twpkw7Ny5EwkJCdi5c6fU8qxLm8ePH2Pfvn1Ys2YN1NXVixxjs9mYP38+IiIi\nwOFw0LlzZ2zatAn5+flSUstQGQ4fPozLly9j3759UFVVLXd/UbwCiAjOO/aiZ3t9tGtRcjyPrHsF\nnD9/Hm3btoWurq60pVR7mLc2GaOg8E1ZBoKRkRH09PQk4mZkoK+PJ3GvhB7L/JmNJ3EJeBz73/GE\nD5/wJC4B7z5/Fdr+SVwCDGXUzYRB/Jw+fRqxsbFwdXWVtpQiVCS9X/SxfUKL/uXm5mLjxo2wtrZm\nHkJS4OPHj1i7di1mz54tsy5skoaIMGfOHLRp06bUTC2GhoZ48OAB5s2bhyVLlqBPnz548+ZNFSpl\nqCxJSUlwdnaGjY0NBg8eXO7+onoFzNrshWeJb3HcrXSXSVn2CsjPz8fFixeZ3QMxwRgIMkZMTAxU\nVFTQrFmzUtuxWCyMHz8eZ8+eRVaWeFb7CzDp1AkhD6KQl1d8tSnieSyMJ89GJ1snsFgsLPQ8AJMp\njlh14Eixtnl5+bgW+QRdZSg3MoPkEAgEWLduHSwtLdG5c2dpyynk9/R+v6fuLYmC9H4TB/SBvb19\nYTXRw4cP4/3799UmALumsWTJEnC5XKxevVraUqTGyZMncefOHezcuRPy8vKltuVyudi0aRNu3LiB\nxMREtG/fHn5+fqWmqWaQDYgIDg4O4HK52LFjR4XGEMUrwHHLblwKe4gbuzehSaPSA3tl2SsgPDwc\nX79+ZQwEMSF7V7iWExMTA319fZF+fNbW1sjIyEBQUJBY5s7Pz4ePjw8CAgLwMfk7LtwNL9bG1Lg9\n8u9dQl5ocJHPwRXzi7U9fzcMH758ha2trVj0Mcg2Z8+exdOnT2Vu96Ckon93HsdgmMsqaP81AZzu\nA3H+TnG/2t+L/vH5fLi7u2P06NFo27ZtVZ4GA4CwsDD4+fnB3d0d9evXl7YcqZCZmYmFCxdi+PDh\n6Nevn8j9TE1N8e+//2LYsGGYPHkyxowZg2/fvklQKUNlOXnyJM6fPw9vb280aNCgwuOU5hXguGU3\nzt8Jw3WvjWjWWF1om1+RZa+A8+fPQ11dHV26dJG2lBoBYyDIGDExMTA0NBSprY6ODjp16iQWN6Ob\nN2+iU6dOsLe3x8CBA9G9Wze4ePkg82fFMmBk/szGIq+DMDczY4qk1QKICG5ubujTpw+6d+8ubTmF\nlJTeDxCtKjjw/0X/bty8ifXr1yMxMVEmA7BrOgKBAHPmzEHHjh1hZ2cnbTlSw8PDA8nJydi6dWu5\n+6qqqsLPzw+nTp3CtWvXYGhoiJCQEAmoZKgsX79+hZOTE8aMGVPpQPxu3bvjn4gnxbwCZm32gn/I\nDRxbswTKPEV8/p6Cz99TkJ0jPI2prHsFnD9/HkOGDBGaWIKh/DAGggyRn5+PZ8+elcuv1traGsHB\nwfjx40eF5nz16hVGjhwJc3NzcLlchIWF4ejRozjs54eP31Mwa5NnuX0NBQIBZm3yxMfvKdh/4ECF\ndDFULy5cuIAnT55g5cqV0pZShNKK/ll264S10ydhuGn3Mt0tCtL77dixA8OHDxfZiGcQH4cOHUJE\nRAQ8PT1r7QtAQkICtmzZAhcXF7Rs2bLC44wePRrR0dEwMDDAgAEDMGfOHPz8+VOMShkqi6OjI4gI\nnp6elR7L1tYWH758LeYVsO9sENIys2A+exG0/ppQ+Dl17bbQcWTZKyA2NhYvXrxg3IvECGMgyBAJ\nCQnIzs4ul4EwduxY5Obm4uzZs+Wa68ePH1i0aBHatWuHhw8f4tixYwgLC0PXrv+9SOno6MDHxwdH\nr1yHrdtWkXcSMn9mw9ZtK45euQ4fHx+h1aAZahYFuwe9evWCqamptOUUQdxF/zIy0mXOhao2kJqa\niiVLlmDChAno0aOHtOVIjQULFkBNTU0stTe0tLRw+fJl7Ny5EwcOHICxsTGioqLEoJKhspw5cwan\nTp2Cp6dnsQxVFcHY2BidO3eC8859RZ7lwtyF80KDMWlQ8ToLmT+zMX/nfhh37CiTXgHnz5+HoqJi\nudzuGEqHMRBkCFEzGP2KlpYWevfuLbKbUX5+Pvbv3w9dXV3s3r0by5cvx8uXLzF+/PhibhbW1tY4\nevQoAm7dg5HNLJy5eVdo4DLw39bjmZt3YWQzCwG37uHYsWOwtrYW+TwYqi9XrlxBRESETL44i7vo\nH8CSyYdjTWft2rXIysrCxo0bpS1FaoSEhODcuXPYvHkzlJWVxTImm83GnDlzEBkZCR6Phy5dusDd\n3Z1JhypFvn//jlmzZmHo0KEYN26cWMYMCQnBs2fPkfT1Gxwq6BXgsMkTSV+/IerRI8yfP1/muLFa\nJwAAIABJREFUdpzOnz+Pfv36QUlJPDWcGAA5aQtg+H9iYmLQqFGjcq8YjB8/Hg4ODvj8+TM0NDRK\nbHf9+nU4Ozvj33//xaRJk+Du7g4tLa0yx/7zzz8xfdo0WC1dBy11NViYGMFItyVUVZTxIyMTT+IS\ncC3yCT58+Yo+5ua4sn8/s3NQSyAirF27Fl27di13dU9JI4mif/n5+RAIBDKZwaOm8uzZM3h6emLt\n2rVl3q9qKnw+H3PnzkWvXr0wduxYsY/frl07hIeHY/Xq1XB1dUVQUBCOHDlSKTcmhorh7OyMnJwc\n7NmzRyw1Pg4ePIjp06djwIABsLKygp2dHVgAvBc5iZTRLfNnNmZt8sSxK9dx5MgRfPr0CcuXL8el\nS5fg5+cnExnrkpOTERoain379klbSo2CecrJEAU+oeW9KYwaNQpsNhunT58WejwuLg7Dhw+HhYUF\nVFRUcP/+fRw+fFjkh62Ojg6u37iByMhIjBgzFs++pGDZvsOwd9+OZfsO49mXFIwYMxaRkZG4dv06\nYxzUIq5fv46wsDC4urrKXMEqpuhf9YeIMHfuXDRv3hzOzs7SliM1vLy8EBsbi127dknsd6agoAB3\nd3fcunULSUlJMDIywsGDB5l0qFVIcHAw/Pz8sH37dmhqalZqLCLCqlWrYGdnBzs7O/zP//wPbG1t\nK+UVMGHCBCxYsABRUVFQVlZGt27d4Orqitxc4UHNVUVwcDCICEOGDJGqjpoGi5hfv8zQrl07WFhY\nVCgoaciQIUhJSUFoaGjhd6mpqXBzc4OnpyeaNGmCTZs2YcyYMWJ7wDArqbWP36+5mZkZMjIy8PDh\nQ5kzEADAxNgYhk0awtd1YantON0H4uzGlRjaq+TsHFPWbsGzLyl4GBEhbpkMJXDu3DmMGDEC58+f\nx19//SVtOVLh8+fPaN26NSZMmABvb+8qmTMtLQ3z5s2Dr68vhg8fjv3790NNTa1K5q6t/PjxA/r6\n+jAwMMClS5cqdT/Nzc3F9OnTcfjwYXh4eGDx4sVFxouPj8f0adNw4+ZNkbwC9gnxCuDz+fDw8ICb\nmxsMDQ3h5+cntcKFo0aNQlJSEsLCiqeqZqgExCATZGdnE4fDob1791ao/9GjRwkAJSYmEp/PJ29v\nb2rUqBEpKyvTunXrKCsrS8yKGWoDkZGR5OjoSCbGxsTlcgkAcblcMjE2phEjRhAAOnv2rLRlFuPd\nu3e0YsUK4vF4pNGgHuXeCSJB2OUin/Tr5+iRnzdFHd5NLBaLts2dQY/8vOnNuSPF2ubeCSItdTVy\ndHSU9qnVWPLz84v8++fPn9SiRQuytLQkgUAgJVXSx87OjurXr0/JyclVPndgYCA1bNiQNDQ0KCgo\nqNz9f7+mDCUzbdo0UlFRoTdv3lRqnNTUVOrbty/Jy8vTsWPHSm1bcH/vZGJS5P7eycSEHB0dKTIy\nssz5IiIiqF27dqSgoEAbN26kvLy8SukvLz9//iRlZWVyd3ev0nlrA4yBICM8efKEANDdu3cr1D89\nPZ14PB7Z2dmRvr4+AaApU6bQhw8fxKyUoTYQFxdH5mZmBIC01NVo8qC+tG3uDPp7mTNtmzuDJg/q\nS40b1icAZG5mRnFxcdKWTAKBgG7dukVWVlbE4XBIRUWFxowZQwAo0MO12Ev/jd2biMViEZvNLvKZ\nMrh/sbYBHisIgEgPTAbRKM34dHR0pFmzZpGcnBy9ePFC2lKlxoMHD4jFYtHu3bulpiEpKYkGDhxI\nAGjmzJmUkZFRYtuyrinz+xHO1atXCQDt2bOnUuO8e/eODA0NSVVVlW7cuFHu/hU16H7+/EkuLi7E\nYrGoe/fuVfo8CA4OJgAUExNTZXPWFhgXIxnB398fEyZMQEpKCurVq1fu/i9fvkSfPn2QlJSEnj17\nYseOHTAxMZGAUoaajr+/P+zt7dGkQX1sdrTDXz27Ck0TmpeXjwt3w+Hi5YOP31Pg4+MjlcxVmZmZ\nOHbsGLy8vBAdHY02bdrA0dERkyZNQt26ddHH3Bxv4mLx5Ii3SEF5xcb/mQ0jm1lortsa12/ckMAZ\n1C5+d2/o28kIRrqtUFdZCWmZWXgS9wr/RDzGhy/JaN6sGf65dq1WxjUJBAL06NEDWVlZiIyMhJyc\n9HKKEBH27NmDhQsXQltbG0ePHsWff/5ZeFy0a/qfy4q5mRn2HzhQK6+pMDIyMmBoaIgWLVrgn3/+\nqbDb7r///otBgwaBw+EgODgY+vr6YlZaNnfv3sXkyZPx6dMnbNq0CQ4ODhJ3Q3ZwcEBISAji4+Nl\n0s21WiNlA4Xh/1i6dClpa2uXu9+3b99o7ty5JCcnR+rq6owlzVApjh07RiwWi2wsLSj9+rliK+nC\nPunXz5GNpQWxWKwyt7TFSXx8PM2fP5/q1atHLBaLhg4dSlevXi3mjhIXF0c8Ho9sLC0oLzRYpHMq\n+OSFBtNESwvi8XgysUtS3Tl27BjxeDxqqaVJgR6uQl2/Cly6Aj1cqaVWE+LxeOTv7y9t6VXO4cOH\nCQDdvHlT2lIKefHiBXXq1Ik4HA6tWbOG+Hx+Ba6pZq29psJwdHQkJSUlio+Pr/AYISEhVKdOHerY\nsSMlJSWJUV35SU9PJwcHBwJAffv2pbdv30psrvz8fNLU1CRnZ2eJzVGbYSJMZQCBQICYmJhyBfjw\n+Xx4eXlBV1cXPj4+cHNzQ2xsLOrVq4cTJ05IUC1DTSUuLg729vaYOKAPfF0XiLzarsxThK/rAkwc\n0Af29vaIj4+XmEaBQIDLly9jyJAh0NXVha+vL6ZNm4aEhAT8z//8D/r27VtsFakyRf8mu23BMabo\nn1jw9/fHxIkTYWXaHU+OeGOEWY8SC9jJyXEwwqwHnhzZAyvT7pgwYQL8/f2rWLH0SEtLw+LFizFm\nzBiZKj7Ypk0b3Lt3D8uWLcOaNWugp6dXgWvqXSuvqTDu3LkDLy8vuLu7o1WritVrOXToEAYNGoSe\nPXvi9u3baNKkiZhVlg8VFRV4e3vjypUreP78eWEAM0nAWSUqKgpJSUlM9WRJIW0LpTYizE+TzWZT\nk8aNRfLTvHTpErVt25ZYLBbZ2dnRx48fC49NnTqVWrVqVauD+hgqhrmZGbXS1hS6c+C5YBb90USD\nFBUUqIu+Ht332Sl0J6GlliaZm5mJXVtqairt2LGDdHV1CQB16NCBfHx8KDMzU+Qxfl3pDPBYUepK\nZ4DHCmqmoUZcLpdZ6RQDsbGxQndxVtlPJBaLVeTT9o9mxXZxbGrZLo6LiwvxeLxKB6xKkpMnTxKH\nw6YJA/oU25m7tWcL/dWzC2k2akgsFovObVpV66/p72RmZpKOjg517969QoG9AoGAVq9eTQDI3t6e\n+Hy+BFRWju/fv5ONjQ0BoOHDh9OnT5/EOr6rqyvVr19fJs+9JsDEIFQhlfXTfP78ORYsWIBLly7B\n1NQU27dvR8eOHYvM8c8//6Bfv3548OCBTBQwYageREZGolOnTgj0cMUIsx5Fjp385xamuG3BvsVz\n8We7Nth+4gwCrt/By1M+aFRPtUjbMzfvwmrpOkRGRoql4vDTp0+xe/du+Pn5IScnB1ZWVnB0dET3\n7t0r5G9anvR+qnXr4mFEBHR1dSt9HrWdPubmeBsfi8d+ReNA1vgcxZkbd/GP5wYUPInkOBw0UK1T\npH9tigOJjY2FgYEBXF1dZbI6eQElXVMAuBwWgXvRz2DcRgdWy9bhzAbXYimEa9M1FYaLiws8PT3x\n+PFj6Onplasvn8/HjBkz4Ovri/Xr12Pp0qUy7X9/5swZzJw5E0SEvXv3YtSoUWIZ18jICO3bt8eR\nI0fEMh5DUZhKylXEr4GfgR6uIgV+tm/fHj4+Pujfvz/WrFkDb29vNGvWDIGBgRgxYoTQG4K5uTk0\nNDRw/PhxxkBgEJlDhw5BW0Mdf/XsWuzYjhNnMX34IEwa9F+l5L2L5yD43kMcvBiCRRNHF2k7tGc3\naKmrwdfXt8IGQl5eHi5cuAAvLy9cv34djRs3xsKFCzF9+vRKFw8qKPoXFRUFX19fhIeF4eT1w8jJ\nyQGXy4WhgQG69uqNwMBAHPT1ZYwDMRAZGYkbN28i0MNVqNuaHIcDtfqlJ2ZQ5ilik+NUWC1dh6io\nKLEYn7KKs7MztLS0sHBh6bU7pElZ19SyWydYdusEACW6ltSma/o79+/fx7Zt2+Dh4VFu4yAtLQ1W\nVla4efMmjhw5gokTJ0pIpfgYOXIkevbsiRkzZsDKygoTJkyAp6cn6tevX+6xCmrxJCYm4t9//8WK\nFSskoJgBYCopVwkV8731xqj/89Ns3rw5Dh06BA8PDzx//hwjR44scbWAw+Fg7NixOHHiBPLzhVdI\nZGD4nbB792Bh0r7Y3yU/Lw+RL+Jg0alD4XcsFgt9O3dAePTzYuPIyXFgYWKE8AoUrElOTsaGDRvQ\nqlUrjBw5EtnZ2fD398ebN2+wevXqShsHv2JsbAxPT088jIhAdnY28vPzkZ2djYcREcjIyICBgQGG\nDx8utvlqM6UZnwAQ9z4J2n9NgI6VLWxWb8S7z1+FtvvV+KypBAUFITg4GNu2bQOPx5O2nBIp65qK\nSm24pr+Tk5ODqVOnwtjYGPPnzy9X3w8fPqBXr1548OABrly5Ui2MgwLU1dVx5swZ+Pn54eLFizAw\nMMCVK1fK7BcVFQUnJyd0MjGBoqIiOBwOFBUVYWZqCjabDQ0NjSpQXzthDAQJU5nAz0OuCzC+vzly\nc3IQEhICFxcXcLncMvtaW1vj48ePuH37dmXlM9QSYp4+hZFu8SC55NQfyBcIoNGg6EqPeoP6+PT9\nu9CxjHRbIjomRuS5IyMjYWtrC21tbaxevRoWFhaIjIxEaGgorK2toaCgUL6TqQAFqfgKHrwrVqxg\nqoSLiZKMTwDoqq8H3xULcHnHeuxZ5ITXSZ9h6rBQaCB5ZYzP6kBOTg7mzZsHCwsLmTdOS7um5aGm\nX1NhuLm5IS4uDgcPHixX6tro6Gh07doVKSkpuHv3LszNzSWoUjKwWCzY2NggJiYG+vr6sLS0xMyZ\nM5GRkVGsbXx8PPqYm8PExARnT52EQeMG8Jg5BX8vc4bHzCkwM2gN9fqqMDU1RR9zc4kmx6itMC5G\nEmbG9OnQbFgf3ouchL5w7A44j63+gfj0LQVGui2xa74DOrdrA+C/l5a9i+cgLOYFli1dKrKfZpcu\nXdCiRQscP368Wt5EGKoWgUCAnJwc1FVWErkPEYEF4btYqirKyMnJKdwKFkZubi4CAgLg6emJ8PBw\nNGvWDGvWrIGdnR0aNWpUofMQB+vWrUObNm1gZWUlNQ01jZinTzGh1xShxwZ07VT43wat/sCf7drg\njxGTcOrabdgO6V+svZFuS5y4dghRUVGSkis1Dh06hNevX8Pd3R2PHj2StpxSiY6JwYRetmIZy0i3\nJU5ePyyWsWSdR48eYcOGDVi5ciUMDQ1F7nft2jWMHDkSLVu2RFBQkFh3U6WBtrY2rly5gr1792Lh\nwoW4evUqDh06hF69egGonEu2NGrx1FQYA0GClOWnefKfW1joeaBI8KflvOVFgj8r4qfJYrEwbtw4\n7N27F15eXlWyAstQfWGz2eByuUjLzCp2rFE9VXDYbHz+nlLk+68pqcV2FQr4kZEJLpcr1DhISkrC\n3r17sX//fnz+/BkWFhY4d+4chgwZAg6ncquRleXRo0e4cOEC/Pz8pK6lplBe41NVRRmtm2oh/n1S\nicdzc3NrdBHIMWPGSFuCSJRnQaE0RFlQqAnw+XzY2tpCX18fS5YsEbmfn58f7OzsYGFhgdOnT6NO\nnTpld6oGsFgsODg4oF+/fpgyZQpMTU0xf/58GBgYYOrUqZg4oA+8FzmV6nVR4JLdv4sJZm3yxIQJ\nE0BEGD9+fBWeSc2FMRAkSFl+mqIGf1Yk8NPa2hoeHh4ICQnBkCFDKn8yDDUaA319PIl7Vex7eTk5\nmOjp4lrE48IsJESEaxGP4TR6mNCxnsQlwPCXmh5EhNDQUHh6euLMmTPgcrmYPHkyZs+ejXbt2knm\nhCrAunXr0KpVK2YFSoyUZnwKIyPrJ159+Aibhg2EHv+RkQkFBQWE1TCXlJUrVyI0NBTnzp2rFi+A\n3bp1E/malkVpCwo1iY0bNyImJgYPHjwQadGOiLB+/Xq4urrCzs4Oe/bsgby8fBUorVp0dHRw69Yt\nbNu2DcuXL4dAIMCE/3PJFvVvoqAWDwDY29vjzz//ZOrWiAHGQJAgpflpFgR/Lp08tvC7koI/K+Kn\naWhoCAMDAxw/fpwxEBjKpFv37jh76iTy8vKL/b06jxuJKW5bYNJGt3CnKys7B1MG9ys2Tl5ePq5F\nPsGIMWORlZUFf39/eHl54cmTJ2jdujW2bduGSZMmQVVVtVhfaRITE4MzZ87Ax8enXH7BDGVTkvEJ\nAC6eB/BXz65o3lgdH75+w+q/j0COw4F1fzOh7Z/EJaC9oWGNynhz7949BAUF4cCBAzJVFK00DA0M\nSrymwH8pTOPfJxVmMEr48AlP4hLQoG4dNNVQK9L29wWFmkhMTAzWrl2LxYsXi/S3y+fz4eDgUFgE\ndfny5TKdxrSycDgcuLi4IDDgND6/e4s9v7lkr/E5irU+x4r00WveFE+P7y/8N5vNhvciJ4RGP8f0\nadNqZepcccM8CSVIab63pQV/vnz7vlj7ivhpWltbY/369cjMzISysnK5+jLUHogIf/zxBz58+YoL\nd8OL1UEY07c3kn/8wKoDfvj8PRUdWrfE5R3rhaamPH83DB++fMWPHz+gra2N1NRUDBkyBJs2bULf\nvn1ldpVw/fr1aN68OWxsbKQtpcZRmvH54WsyJqzaiG8/0qBWXxU92+sj7O8daKhat9g4vxqfNYX8\n/HzMmTMHJiYmsLUVj09/VdC1WzecPXVC6DUFgIjnsejjuBgsFgssFgsLPQ8AACYN7IuDK/4/c09N\nvKa/k5eXh6lTp0JHR0ekuhbp6ekYPXo0rl27hsOHD2PSpElVoFL6REZG4v6DhyW6ZBu0bF6sXsrv\n1ObUuZKAMRAkREUCP4GSgz8r4qc5btw4LF++HBcuXMC4cePKpYOhdnD//n0sXLgQd+/eRaOGDbHQ\n62/072JS7AY9a9RfmDXqr1LHyvyZjQW7DoDDZuPixYuws7ODg4MDWrZsKclTqDQvXrzAyZMna+wW\nvrSxtbWFl5eXUOPTf+1SkccpMD6r04t0Wfj6+hZm7KoucS/3799HaGgokr5+E3pNAcDUuD3y710q\nc6yaeE1/Z/v27YiIiMC9e/egqFh6FsOkpCQMHjwYCQkJuHz5MiwsLKpIpfQpyyVblHopgHhq8TD8\nh2wu59UAyvK9LW/wZ0X8NFu2bIkuXbrg+PHj5RPPUON5/fo1rK2t0bVrV/z48QOXL19GWHg4Pn1P\nxaxNnhAIBOUaTyAQYObGXXj/JRlr3dzw/v17bN68WeaNAwBwd3eHlpYWpkyZIm0pNRJjY2OYm5nB\nxctHaPpSUcj8mY1FXgdhbmZWYx76qampWLp0KSZOnIju3btLW06ZJCQkYNy4cejatSsEAgE6GBkx\n17QMXr58CVdXVzg7O6Nr19JrRjx9+hRdu3ZFcnIy7t69W6uMA6Ds1Lmi1kupjalzJQVjIEiQ0nxv\nfw3+LKAg+LObYdti7Svqp2ltbY1Lly4hJSWl7MYMNZ6UlBQsXLgQenp6uH37Nnx8fPDo0SMMGDAA\nOjo68PHxwdEr12HrtlXkB3/mz2xMXrsF/iE34Ofnh2XLlkFJSTwZTiRNfHw8/P39sWjRIpFqjDBU\njP0HDuDj95QKG58Omzzx8XsK9h84ICGFVc/q1avx8+dPbNy4UdpSSuX79+9YsGAB9PT0cOfOHRw8\neBBRUVE4HRBQqWs6qwZe018RCASws7ND06ZN4ebmVmrb69evo0ePHqhfvz7Cw8PLlQK1plBSLR6g\nfPVSgPLX4mEQDmMgSIgnT57g0+fPuBwegbw84RWNnceNxIFzl+AX/A9eJL7DzI27hAZ/Fvhpdu3W\nrdw6xowZg/z8fJw5c6ZC58FQM8jJycH27dvRqlUr7N27FytWrEBsbCymTp1axLXB2toaR48eRcCt\nezCymYUzN++W+Pebl5ePMzfvwsjGAaeu/VeUr7q56Hh4eEBNTQ329vbSllKjqYzxOcVtK45evobB\ngwfXmMwkz549g5eXF1xdXWU2p31OTg62bdsGHR0d7Nu3D66uroiNjYWtrS04HE6lrqmt21YcvXId\nPj4+Neaa/o6XlxdCQ0Ph4+NT6oLJ0aNHYWlpiS5duuDOnTvQ0tKqQpWyQVku2QO6dsIo854waPUH\n+v1pjKBtbkhJzyh87vzOry7ZDBWHiUEQM58/f4arqysOHDgARUVFZGdnl+inKWrwZ2X8NJs0aQJz\nc3P4+/vDzs6uwufFUD0hIgQEBGDJkiVITEzEtGnTsHr1ajRu3LjEPuPHj8eff/6J6dOmwWrpOmip\nN4KFSQcY6baEqooyfmRk4klcAq5FPsGHL1/Rx9wcl67fxNq1azFhwgQoKytj0KBBVXiWFSMxMRF+\nfn7YuHEjeDyetOXUeKytrUFEsLe3R2j0c2xynIqhPbuVWADp/N0wLPI6iI/fUzBmzBicOnUKO3bs\nwLx586SgXnwQEebMmYMWLVrI5LkQEU6fPo0lS5bgzZs3pd4zKnNNjx07VmNTCickJGDp0qWYPXs2\nevfuLbQNEcHd3R0rVqyAra0t9u3bV+0WWMTFjx8/oCAvL3Lq3LLqpdSW1LmShkUFecgYKkV2djZ2\n7twJNzc38Pl85ObmQk9PD1wFBaR/S8aTI96lFvwoicyf2TCymYXmuq0rnLbLx8cH06ZNw4cPH9Ck\nSZMKjcFQ/QgNDcXChQsRHh6OIUOGYOPGjeWqO/Do0SOsWrUKwcHBYLNYICLk5eeDy+XC0MAAXbt1\ng62tbaH/MJ/Px+jRo3HlyhVcunQJZmZmEjoz8eDg4ICAgAAkJiYyWb6qkPj4eEyfNg03bt6Elroa\nLEyMSjU+9+3fj1atWmHp0qXYuHEj/v7772q92HH27FmMHDkSFy9exODBg6Utpwh3797FwoULcf/+\n/XLdMypyTWvqzgERwcLCAgkJCYiOjhZa1yIvLw+zZs3CgQMHsGbNGri6utboNKa/kpeXh+joaNy/\nfx/h4eEIDw/Hy5cvIcfhYMIAc/i6LixzjIysn/hjxCSstreB4+ihxY5PWbsFz76k4GFEhCROofZA\nDJVCIBBQQEAANW/enFgsFnE4HFJXV6e9e/cSn8+nuLg44vF4ZGNpQXmhwSQIuyzyJy80mCZY9iEe\nj0dxcXEV1vj9+3eSl5enHTt2iPHMGWSV2NhYGjlyJAGgjh070rVr10Tum5OTQ8ePH6fu3bsTAGra\ntCl5eHjQly9fiIgoPz+/1P7Z2dnUr18/UlFRofv371fqPCTJu3fvSEFBgTw8PKQtpdYSGRlJjo6O\n1MnEhLhcLgEgLpdLnUxMyNHRkSIjI4u0FwgENGvWLGKxWHTixAkpqa4cWVlZ9Mcff9DAgQOlLaUI\nv94zjI2N6fr16xUap7zXtCayb98+AkAhISFCj6elpdHAgQNJTk6ODh06VMXqqp73799TYGAgubi4\nUO/evUlJSYkAkJycHJmYmNDs2bPJz8+PJk6cSFrqapR7J6jYu9CC8aPopvdmen3mMN3dt436du5I\n6vXr0dfLp4q1zb0TRFrqauTo6CjtU6/2MAZCJYiMjKSePXsSAFJQUCBFRUVydXWltLS0Iu38/f2J\nxWKRjaUFpV8/J5JxkH79HE20tCAA1KNHjzJfzMpi6NCh1KVLl0qNwSDbfP36lebMmUNycnLUtGlT\nOnLkiMh/N0lJSbRq1Spq3LgxASBzc3M6c+YM8fn8cuvIyMig7t27U/369enff/8td/+qwMnJiRo0\naFDst8ogPUT5W83PzycbGxuSk5OjCxcuVIEq8bJ27VqSl5enFy9eSFsKEf13z3BycqrQPUMUxDlW\ndeDNmzdUp04dsre3F3o8KSmJOnbsSHXq1KGrV69WsTrJk5mZSXfu3KHNmzeTlZUVaWtrE4DCxabR\no0fTli1b6O7du5SVlVWkb2RkJAGgQA/XYu9D4/qZkpZaI1JUUKCmGmpk3c+MXgUeEvruFOCxggDU\nCmNU0jAGQgVISkoiW1vbQsOAxWLR1KlT6f379yX2OXbsGPF4PGqppUkBHiuEWskF1m+AxwpqqaVJ\nPB6P5syZQ2w2m2bOnEkCgaDCmo8fP04A6NWrVxUeg0E2+fnzJ23cuJFUVVWpbt265OHhUezmKwyB\nQEB3796lcePGkZycHCkrK5ODgwPFxMRUWlNKSgp17NiRNDQ06OXLl5UeT5x8/PiRFBUVae3atdKW\nwlAB+Hw+jRw5krhcbrl2x6TNmzdviMfjkYuLi7SlUFZWFm3YsIHq1q1LdevWpQ0bNoh0z2AoGYFA\nQJaWlqSlpUWpqanFjj99+pSaNWtGWlpa9OTJEykoFC8CgYBevnxJfn5+NGvWLDI2NiY5OTkCQEpK\nStS7d29atGgRnTlzhj58+CDSmOZmZtRSS1PkhVRhC6sttTTJ3MxMwmdfO2AMhHLw8+dPcnd3Jx6P\nV/hD6N+/v8g/9ri4ODI3MyMApKWuRpMG9qWtc6bT38ucaeuc6TRpYF/SUlcjANTH3LzQrejgwYME\ngFxcXCpsJGRkZJCysjKtX7++Qv0ZZI/8/Hw6evQoNWvWjOTk5MjR0bHQFag0srKyyMfHhzp27EgA\nSFdXl3bs2EEpKSli1fflyxdq27YtNW3alN68eSPWsSvDggULqG7dumI/X4aqIzs7mwYMGEDKysoU\nFhYmbTkiMXbsWGrcuDH9+PFDahp+v2c4OTmJdM9gKJtDhw4RAKE7Wzdu3CBVVVUyNDSkd+/eSUFd\n5fn+/TtdvnyZVq9eTZaWltSgQYPC3QE9PT2aMmUK7dmzhx49elShnWciqrRLto2lRaW/QlC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IC+vj4sLS2RkpLCU6autps8eTKePn2KtWvXNkPtqZZMSkoK3t7ecHFxgZOTE44fP97oY759+xYb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\ntGgR/Pz8ZD7zj5OTE37++WdcuXIFX375pdTPp6GhgdmzZ8PNzQ1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yXuYiOu56rW2iWZh6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\nGgUEQgghhBBCSDUKCIQQQgghhJBq/wd7YZXsQbi+qgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics Array of size 3 x 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_RR, res_CC = T.realizations(L,[4,3])\n",
    "print '# real: ', len(res_RR)\n",
    "print '# complex:', len(res_CC)\n",
    "print res_CC[0]\n",
    "show(*[T.plot(pos=rho) for rho in res_RR])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Flexible labelings\n",
    "\n",
    "**Definition**\n",
    "\n",
    "Let $G$ be a graph. A coloring of edges $\\delta\\colon  E_G\\rightarrow \\{\\text{blue, red}\\}$ \n",
    "is called a *NAC-coloring*, if it is surjective and for every cycle $C$ in $G$,\n",
    "either all edges of $C$ have the same color, or\n",
    "$C$ contains at least 2 edges in each color.\n",
    "\n",
    "**Theorem** [Grasegger, L., Schicho]\n",
    "\n",
    "A graph $G$ has a flexible labeling if and only if it has a NAC-coloring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr class =\"row-a\">\n",
       "<td></td>\n",
       "<td>has NAC-coloring</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>4-cycle</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>SmallestFlexibleLamanGraph</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>3-prism</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>MaxEmbeddingsLamanGraph_7vert</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Complete bipartite graph</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>No NAC</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Q_1</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  has NAC-coloring\n",
       "  4-cycle                         True\n",
       "  SmallestFlexibleLamanGraph      True\n",
       "  3-prism                         True\n",
       "  MaxEmbeddingsLamanGraph_7vert   True\n",
       "  Complete bipartite graph        True\n",
       "  No NAC                          False\n",
       "  Q_1                             True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table([['', 'has NAC-coloring']]+[[G.name(), str(G.has_NAC_coloring())] for G in examples])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4-cycle\n"
     ]
    },
    {
     "data": {
      "image/png": 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SsroU05zDFGRwLSaqYfKymtVANqQzdOvOYUqythTTnMMUZXAtJqpharKW1UB2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\nA2drxUu0vd3fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "Graphics Array of size 1 x 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SmallestFlexibleLamanGraph\n"
     ]
    },
    {
     "data": {
      "image/png": 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NAAAABRHdAAAAUBDRDQAAAAUR3QAAAFAQ0Q0AAAAFEd0AAABQENENAAAABRHd\nAAAAUBDRDQAAAAUR3QAAAFAQ0Q0AAAAFEd0AAABQENENAAAABRHdAAAAUBDRDQAAAAUR3QAAAFAQ\n0Q0AAAAF+f/nmHntximCyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics Array of size 1 x 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3-prism\n"
     ]
    },
    {
     "data": {
      "image/png": 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r82T3ngHfP/M3/0se3HDdAa+1XH5VXn/Sq/In731Pvydr736qO4cdVpv2duE3tJrMnz/4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\nAAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "Graphics Array of size 1 x 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for G in [C4, S, T]:\n",
    "    print G.name()\n",
    "    graphics_array([col.plot() for col in G.NAC_colorings()], ncols=4).show(\n",
    "        figsize=[10,3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construction of a motion from a NAC-coloring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: (0, 0),\n",
       " 1: (sin(alpha) + 1, cos(alpha)),\n",
       " 2: (2*sin(alpha) + 1, 2*cos(alpha)),\n",
       " 3: (2*sin(alpha), 2*cos(alpha)),\n",
       " 4: (sin(alpha), cos(alpha)),\n",
       " 5: (1, 0)}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from rigid_and_flexible_graphs.graph_motion import GraphMotion\n",
    "delta = T.NAC_colorings()[0]\n",
    "motion_T = GraphMotion.GridConstruction(T, delta); motion_T.parametrization()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg baseProfile=\"full\" height=\"500\" version=\"1.1\" width=\"500\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "  <defs>\n",
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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_f01ad0_1-5\" repeatCount=\"indefinite\" values=\"M 365 210 L 293 252;M 366 212 L 293 252;M 367 213 L 293 252;M 367 215 L 293 252;M 368 216 L 293 252;M 369 218 L 293 252;M 370 220 L 293 252;M 370 221 L 293 252;M 371 223 L 293 252;M 371 224 L 293 252;M 372 226 L 293 252;M 373 228 L 293 252;M 373 229 L 293 252;M 373 231 L 293 252;M 374 233 L 293 252;M 374 234 L 293 252;M 375 236 L 293 252;M 375 238 L 293 252;M 375 240 L 293 252;M 375 241 L 293 252;M 376 243 L 293 252;M 376 245 L 293 252;M 376 246 L 293 252;M 376 248 L 293 252;M 376 250 L 293 252;M 376 252 L 293 252;M 376 253 L 293 252;M 376 255 L 293 252;M 376 257 L 293 252;M 376 259 L 293 252;M 376 260 L 293 252;M 375 262 L 293 252;M 375 264 L 293 252;M 375 265 L 293 252;M 375 267 L 293 252;M 374 269 L 293 252;M 374 271 L 293 252;M 373 272 L 293 252;M 373 274 L 293 252;M 373 276 L 293 252;M 372 277 L 293 252;M 371 279 L 293 252;M 371 280 L 293 252;M 370 282 L 293 252;M 370 284 L 293 252;M 369 285 L 293 252;M 368 287 L 293 252;M 367 288 L 293 252;M 367 290 L 293 252;M 366 291 L 293 252;M 365 293 L 293 252;M 364 294 L 293 252;M 363 296 L 293 252;M 362 297 L 293 252;M 361 299 L 293 252;M 360 300 L 293 252;M 359 302 L 293 252;M 358 303 L 293 252;M 357 304 L 293 252;M 356 306 L 293 252;M 355 307 L 293 252;M 354 308 L 293 252;M 352 309 L 293 252;M 351 311 L 293 252;M 350 312 L 293 252;M 349 313 L 293 252;M 347 314 L 293 252;M 346 315 L 293 252;M 345 316 L 293 252;M 343 317 L 293 252;M 342 319 L 293 252;M 341 320 L 293 252;M 339 320 L 293 252;M 338 321 L 293 252;M 336 322 L 293 252;M 335 323 L 293 252;M 333 324 L 293 252;M 332 325 L 293 252;M 330 326 L 293 252;M 329 326 L 293 252;M 327 327 L 293 252;M 325 328 L 293 252;M 324 328 L 293 252;M 322 329 L 293 252;M 321 330 L 293 252;M 319 330 L 293 252;M 317 331 L 293 252;M 316 331 L 293 252;M 314 332 L 293 252;M 312 332 L 293 252;M 311 332 L 293 252;M 309 333 L 293 252;M 307 333 L 293 252;M 305 333 L 293 252;M 304 334 L 293 252;M 302 334 L 293 252;M 300 334 L 293 252;M 299 334 L 293 252;M 297 334 L 293 252;M 295 334 L 293 252;M 293 334 L 293 252;M 293 334 L 293 252;M 292 334 L 293 252;M 290 334 L 293 252;M 288 334 L 293 252;M 286 334 L 293 252;M 285 334 L 293 252;M 283 334 L 293 252;M 281 333 L 293 252;M 280 333 L 293 252;M 278 333 L 293 252;M 276 332 L 293 252;M 275 332 L 293 252;M 273 332 L 293 252;M 271 331 L 293 252;M 270 331 L 293 252;M 268 330 L 293 252;M 266 330 L 293 252;M 265 329 L 293 252;M 263 328 L 293 252;M 261 328 L 293 252;M 260 327 L 293 252;M 258 326 L 293 252;M 257 326 L 293 252;M 255 325 L 293 252;M 254 324 L 293 252;M 252 323 L 293 252;M 251 322 L 293 252;M 249 321 L 293 252;M 248 320 L 293 252;M 246 320 L 293 252;M 245 319 L 293 252;M 243 317 L 293 252;M 242 316 L 293 252;M 241 315 L 293 252;M 239 314 L 293 252;M 238 313 L 293 252;M 237 312 L 293 252;M 236 311 L 293 252;M 234 309 L 293 252;M 233 308 L 293 252;M 232 307 L 293 252;M 231 306 L 293 252;M 230 304 L 293 252;M 229 303 L 293 252;M 228 302 L 293 252;M 227 300 L 293 252;M 226 299 L 293 252;M 225 297 L 293 252;M 224 296 L 293 252;M 223 294 L 293 252;M 222 293 L 293 252;M 221 291 L 293 252;M 220 290 L 293 252;M 219 288 L 293 252;M 219 287 L 293 252;M 218 285 L 293 252;M 217 284 L 293 252;M 217 282 L 293 252;M 216 280 L 293 252;M 215 279 L 293 252;M 215 277 L 293 252;M 214 276 L 293 252;M 214 274 L 293 252;M 213 272 L 293 252;M 213 271 L 293 252;M 213 269 L 293 252;M 212 267 L 293 252;M 212 265 L 293 252;M 212 264 L 293 252;M 211 262 L 293 252;M 211 260 L 293 252;M 211 259 L 293 252;M 211 257 L 293 252;M 211 255 L 293 252;M 211 253 L 293 252;M 211 252 L 293 252;M 211 250 L 293 252;M 211 248 L 293 252;M 211 246 L 293 252;M 211 245 L 293 252;M 211 243 L 293 252;M 211 241 L 293 252;M 212 240 L 293 252;M 212 238 L 293 252;M 212 236 L 293 252;M 213 234 L 293 252;M 213 233 L 293 252;M 213 231 L 293 252;M 214 229 L 293 252;M 214 228 L 293 252;M 215 226 L 293 252;M 215 224 L 293 252;M 216 223 L 293 252;M 217 221 L 293 252;M 217 220 L 293 252;M 218 218 L 293 252;M 219 216 L 293 252;M 219 215 L 293 252;M 220 213 L 293 252;M 221 212 L 293 252;M 222 210 L 293 252;M 223 209 L 293 252;M 224 207 L 293 252;M 225 206 L 293 252;M 226 204 L 293 252;M 227 203 L 293 252;M 228 202 L 293 252;M 229 200 L 293 252;M 230 199 L 293 252;M 231 198 L 293 252;M 232 196 L 293 252;M 233 195 L 293 252;M 234 194 L 293 252;M 236 193 L 293 252;M 237 191 L 293 252;M 238 190 L 293 252;M 239 189 L 293 252;M 241 188 L 293 252;M 242 187 L 293 252;M 243 186 L 293 252;M 245 185 L 293 252;M 246 184 L 293 252;M 248 183 L 293 252;M 249 182 L 293 252;M 251 181 L 293 252;M 252 180 L 293 252;M 254 179 L 293 252;M 255 178 L 293 252;M 257 178 L 293 252;M 258 177 L 293 252;M 260 176 L 293 252;M 261 175 L 293 252;M 263 175 L 293 252;M 265 174 L 293 252;M 266 174 L 293 252;M 268 173 L 293 252;M 270 173 L 293 252;M 271 172 L 293 252;M 273 172 L 293 252;M 275 171 L 293 252;M 276 171 L 293 252;M 278 170 L 293 252;M 280 170 L 293 252;M 281 170 L 293 252;M 283 170 L 293 252;M 285 169 L 293 252;M 286 169 L 293 252;M 288 169 L 293 252;M 290 169 L 293 252;M 292 169 L 293 252;M 293 169 L 293 252;M 295 169 L 293 252;M 297 169 L 293 252;M 299 169 L 293 252;M 300 169 L 293 252;M 302 169 L 293 252;M 304 170 L 293 252;M 305 170 L 293 252;M 307 170 L 293 252;M 309 170 L 293 252;M 311 171 L 293 252;M 312 171 L 293 252;M 314 172 L 293 252;M 316 172 L 293 252;M 317 173 L 293 252;M 319 173 L 293 252;M 321 174 L 293 252;M 322 174 L 293 252;M 324 175 L 293 252;M 325 175 L 293 252;M 327 176 L 293 252;M 329 177 L 293 252;M 330 178 L 293 252;M 332 178 L 293 252;M 333 179 L 293 252;M 335 180 L 293 252;M 336 181 L 293 252;M 338 182 L 293 252;M 339 183 L 293 252;M 341 184 L 293 252;M 342 185 L 293 252;M 343 186 L 293 252;M 345 187 L 293 252;M 346 188 L 293 252;M 347 189 L 293 252;M 349 190 L 293 252;M 350 191 L 293 252;M 351 193 L 293 252;M 352 194 L 293 252;M 354 195 L 293 252;M 355 196 L 293 252;M 356 198 L 293 252;M 357 199 L 293 252;M 358 200 L 293 252;M 359 202 L 293 252;M 360 203 L 293 252;M 361 204 L 293 252;M 362 206 L 293 252;M 363 207 L 293 252;M 364 209 L 293 252;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_f01ad0_0-4\" repeatCount=\"indefinite\" values=\"M 211 252 L 282 210;M 211 252 L 283 212;M 211 252 L 284 213;M 211 252 L 285 215;M 211 252 L 286 216;M 211 252 L 286 218;M 211 252 L 287 220;M 211 252 L 288 221;M 211 252 L 288 223;M 211 252 L 289 224;M 211 252 L 289 226;M 211 252 L 290 228;M 211 252 L 290 229;M 211 252 L 291 231;M 211 252 L 291 233;M 211 252 L 292 234;M 211 252 L 292 236;M 211 252 L 292 238;M 211 252 L 293 240;M 211 252 L 293 241;M 211 252 L 293 243;M 211 252 L 293 245;M 211 252 L 293 246;M 211 252 L 293 248;M 211 252 L 293 250;M 211 252 L 293 252;M 211 252 L 293 253;M 211 252 L 293 255;M 211 252 L 293 257;M 211 252 L 293 259;M 211 252 L 293 260;M 211 252 L 293 262;M 211 252 L 293 264;M 211 252 L 292 265;M 211 252 L 292 267;M 211 252 L 292 269;M 211 252 L 291 271;M 211 252 L 291 272;M 211 252 L 290 274;M 211 252 L 290 276;M 211 252 L 289 277;M 211 252 L 289 279;M 211 252 L 288 280;M 211 252 L 288 282;M 211 252 L 287 284;M 211 252 L 286 285;M 211 252 L 286 287;M 211 252 L 285 288;M 211 252 L 284 290;M 211 252 L 283 291;M 211 252 L 282 293;M 211 252 L 281 294;M 211 252 L 281 296;M 211 252 L 280 297;M 211 252 L 279 299;M 211 252 L 278 300;M 211 252 L 277 302;M 211 252 L 276 303;M 211 252 L 274 304;M 211 252 L 273 306;M 211 252 L 272 307;M 211 252 L 271 308;M 211 252 L 270 309;M 211 252 L 269 311;M 211 252 L 267 312;M 211 252 L 266 313;M 211 252 L 265 314;M 211 252 L 263 315;M 211 252 L 262 316;M 211 252 L 261 317;M 211 252 L 259 319;M 211 252 L 258 320;M 211 252 L 256 320;M 211 252 L 255 321;M 211 252 L 254 322;M 211 252 L 252 323;M 211 252 L 251 324;M 211 252 L 249 325;M 211 252 L 247 326;M 211 252 L 246 326;M 211 252 L 244 327;M 211 252 L 243 328;M 211 252 L 241 328;M 211 252 L 240 329;M 211 252 L 238 330;M 211 252 L 236 330;M 211 252 L 235 331;M 211 252 L 233 331;M 211 252 L 231 332;M 211 252 L 230 332;M 211 252 L 228 332;M 211 252 L 226 333;M 211 252 L 225 333;M 211 252 L 223 333;M 211 252 L 221 334;M 211 252 L 219 334;M 211 252 L 218 334;M 211 252 L 216 334;M 211 252 L 214 334;M 211 252 L 212 334;M 211 252 L 211 334;M 211 252 L 211 334;M 211 252 L 209 334;M 211 252 L 207 334;M 211 252 L 206 334;M 211 252 L 204 334;M 211 252 L 202 334;M 211 252 L 200 334;M 211 252 L 199 333;M 211 252 L 197 333;M 211 252 L 195 333;M 211 252 L 194 332;M 211 252 L 192 332;M 211 252 L 190 332;M 211 252 L 189 331;M 211 252 L 187 331;M 211 252 L 185 330;M 211 252 L 184 330;M 211 252 L 182 329;M 211 252 L 180 328;M 211 252 L 179 328;M 211 252 L 177 327;M 211 252 L 176 326;M 211 252 L 174 326;M 211 252 L 172 325;M 211 252 L 171 324;M 211 252 L 169 323;M 211 252 L 168 322;M 211 252 L 166 321;M 211 252 L 165 320;M 211 252 L 164 320;M 211 252 L 162 319;M 211 252 L 161 317;M 211 252 L 159 316;M 211 252 L 158 315;M 211 252 L 157 314;M 211 252 L 155 313;M 211 252 L 154 312;M 211 252 L 153 311;M 211 252 L 152 309;M 211 252 L 150 308;M 211 252 L 149 307;M 211 252 L 148 306;M 211 252 L 147 304;M 211 252 L 146 303;M 211 252 L 145 302;M 211 252 L 144 300;M 211 252 L 143 299;M 211 252 L 142 297;M 211 252 L 141 296;M 211 252 L 140 294;M 211 252 L 139 293;M 211 252 L 138 291;M 211 252 L 138 290;M 211 252 L 137 288;M 211 252 L 136 287;M 211 252 L 135 285;M 211 252 L 135 284;M 211 252 L 134 282;M 211 252 L 133 280;M 211 252 L 133 279;M 211 252 L 132 277;M 211 252 L 132 276;M 211 252 L 131 274;M 211 252 L 131 272;M 211 252 L 130 271;M 211 252 L 130 269;M 211 252 L 130 267;M 211 252 L 129 265;M 211 252 L 129 264;M 211 252 L 129 262;M 211 252 L 129 260;M 211 252 L 128 259;M 211 252 L 128 257;M 211 252 L 128 255;M 211 252 L 128 253;M 211 252 L 128 252;M 211 252 L 128 250;M 211 252 L 128 248;M 211 252 L 128 246;M 211 252 L 128 245;M 211 252 L 129 243;M 211 252 L 129 241;M 211 252 L 129 240;M 211 252 L 129 238;M 211 252 L 130 236;M 211 252 L 130 234;M 211 252 L 130 233;M 211 252 L 131 231;M 211 252 L 131 229;M 211 252 L 132 228;M 211 252 L 132 226;M 211 252 L 133 224;M 211 252 L 133 223;M 211 252 L 134 221;M 211 252 L 135 220;M 211 252 L 135 218;M 211 252 L 136 216;M 211 252 L 137 215;M 211 252 L 138 213;M 211 252 L 138 212;M 211 252 L 139 210;M 211 252 L 140 209;M 211 252 L 141 207;M 211 252 L 142 206;M 211 252 L 143 204;M 211 252 L 144 203;M 211 252 L 145 202;M 211 252 L 146 200;M 211 252 L 147 199;M 211 252 L 148 198;M 211 252 L 149 196;M 211 252 L 150 195;M 211 252 L 152 194;M 211 252 L 153 193;M 211 252 L 154 191;M 211 252 L 155 190;M 211 252 L 157 189;M 211 252 L 158 188;M 211 252 L 159 187;M 211 252 L 161 186;M 211 252 L 162 185;M 211 252 L 164 184;M 211 252 L 165 183;M 211 252 L 166 182;M 211 252 L 168 181;M 211 252 L 169 180;M 211 252 L 171 179;M 211 252 L 172 178;M 211 252 L 174 178;M 211 252 L 176 177;M 211 252 L 177 176;M 211 252 L 179 175;M 211 252 L 180 175;M 211 252 L 182 174;M 211 252 L 184 174;M 211 252 L 185 173;M 211 252 L 187 173;M 211 252 L 189 172;M 211 252 L 190 172;M 211 252 L 192 171;M 211 252 L 194 171;M 211 252 L 195 170;M 211 252 L 197 170;M 211 252 L 199 170;M 211 252 L 200 170;M 211 252 L 202 169;M 211 252 L 204 169;M 211 252 L 206 169;M 211 252 L 207 169;M 211 252 L 209 169;M 211 252 L 211 169;M 211 252 L 212 169;M 211 252 L 214 169;M 211 252 L 216 169;M 211 252 L 218 169;M 211 252 L 219 169;M 211 252 L 221 170;M 211 252 L 223 170;M 211 252 L 225 170;M 211 252 L 226 170;M 211 252 L 228 171;M 211 252 L 230 171;M 211 252 L 231 172;M 211 252 L 233 172;M 211 252 L 235 173;M 211 252 L 236 173;M 211 252 L 238 174;M 211 252 L 240 174;M 211 252 L 241 175;M 211 252 L 243 175;M 211 252 L 244 176;M 211 252 L 246 177;M 211 252 L 247 178;M 211 252 L 249 178;M 211 252 L 251 179;M 211 252 L 252 180;M 211 252 L 254 181;M 211 252 L 255 182;M 211 252 L 256 183;M 211 252 L 258 184;M 211 252 L 259 185;M 211 252 L 261 186;M 211 252 L 262 187;M 211 252 L 263 188;M 211 252 L 265 189;M 211 252 L 266 190;M 211 252 L 267 191;M 211 252 L 269 193;M 211 252 L 270 194;M 211 252 L 271 195;M 211 252 L 272 196;M 211 252 L 273 198;M 211 252 L 274 199;M 211 252 L 276 200;M 211 252 L 277 202;M 211 252 L 278 203;M 211 252 L 279 204;M 211 252 L 280 206;M 211 252 L 281 207;M 211 252 L 281 209;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_f01ad0_0-3\" repeatCount=\"indefinite\" values=\"M 211 252 L 354 169;M 211 252 L 356 172;M 211 252 L 357 175;M 211 252 L 359 178;M 211 252 L 360 181;M 211 252 L 362 184;M 211 252 L 363 188;M 211 252 L 364 191;M 211 252 L 366 194;M 211 252 L 367 197;M 211 252 L 368 201;M 211 252 L 369 204;M 211 252 L 370 207;M 211 252 L 371 211;M 211 252 L 372 214;M 211 252 L 372 217;M 211 252 L 373 221;M 211 252 L 374 224;M 211 252 L 374 228;M 211 252 L 375 231;M 211 252 L 375 234;M 211 252 L 375 238;M 211 252 L 376 241;M 211 252 L 376 245;M 211 252 L 376 248;M 211 252 L 376 252;M 211 252 L 376 255;M 211 252 L 376 259;M 211 252 L 376 262;M 211 252 L 375 265;M 211 252 L 375 269;M 211 252 L 375 272;M 211 252 L 374 276;M 211 252 L 374 279;M 211 252 L 373 283;M 211 252 L 372 286;M 211 252 L 372 289;M 211 252 L 371 293;M 211 252 L 370 296;M 211 252 L 369 299;M 211 252 L 368 303;M 211 252 L 367 306;M 211 252 L 366 309;M 211 252 L 364 312;M 211 252 L 363 316;M 211 252 L 362 319;M 211 252 L 360 322;M 211 252 L 359 325;M 211 252 L 357 328;M 211 252 L 356 331;M 211 252 L 354 334;M 211 252 L 352 337;M 211 252 L 350 340;M 211 252 L 348 343;M 211 252 L 346 346;M 211 252 L 344 349;M 211 252 L 342 352;M 211 252 L 340 354;M 211 252 L 338 357;M 211 252 L 336 360;M 211 252 L 334 362;M 211 252 L 331 365;M 211 252 L 329 367;M 211 252 L 326 370;M 211 252 L 324 372;M 211 252 L 321 374;M 211 252 L 319 377;M 211 252 L 316 379;M 211 252 L 313 381;M 211 252 L 311 383;M 211 252 L 308 385;M 211 252 L 305 387;M 211 252 L 302 389;M 211 252 L 299 391;M 211 252 L 296 393;M 211 252 L 293 395;M 211 252 L 290 396;M 211 252 L 287 398;M 211 252 L 284 400;M 211 252 L 281 401;M 211 252 L 278 403;M 211 252 L 275 404;M 211 252 L 272 405;M 211 252 L 268 407;M 211 252 L 265 408;M 211 252 L 262 409;M 211 252 L 259 410;M 211 252 L 255 411;M 211 252 L 252 412;M 211 252 L 248 413;M 211 252 L 245 413;M 211 252 L 242 414;M 211 252 L 238 415;M 211 252 L 235 415;M 211 252 L 231 416;M 211 252 L 228 416;M 211 252 L 225 416;M 211 252 L 221 417;M 211 252 L 218 417;M 211 252 L 214 417;M 211 252 L 211 417;M 211 252 L 211 417;M 211 252 L 207 417;M 211 252 L 204 417;M 211 252 L 200 417;M 211 252 L 197 416;M 211 252 L 193 416;M 211 252 L 190 416;M 211 252 L 187 415;M 211 252 L 183 415;M 211 252 L 180 414;M 211 252 L 176 413;M 211 252 L 173 413;M 211 252 L 170 412;M 211 252 L 166 411;M 211 252 L 163 410;M 211 252 L 160 409;M 211 252 L 156 408;M 211 252 L 153 407;M 211 252 L 150 405;M 211 252 L 147 404;M 211 252 L 144 403;M 211 252 L 140 401;M 211 252 L 137 400;M 211 252 L 134 398;M 211 252 L 131 396;M 211 252 L 128 395;M 211 252 L 125 393;M 211 252 L 122 391;M 211 252 L 119 389;M 211 252 L 116 387;M 211 252 L 114 385;M 211 252 L 111 383;M 211 252 L 108 381;M 211 252 L 105 379;M 211 252 L 103 377;M 211 252 L 100 374;M 211 252 L 98 372;M 211 252 L 95 370;M 211 252 L 93 367;M 211 252 L 90 365;M 211 252 L 88 362;M 211 252 L 86 360;M 211 252 L 83 357;M 211 252 L 81 354;M 211 252 L 79 352;M 211 252 L 77 349;M 211 252 L 75 346;M 211 252 L 73 343;M 211 252 L 71 340;M 211 252 L 69 337;M 211 252 L 68 334;M 211 252 L 66 331;M 211 252 L 64 328;M 211 252 L 63 325;M 211 252 L 61 322;M 211 252 L 60 319;M 211 252 L 58 316;M 211 252 L 57 312;M 211 252 L 56 309;M 211 252 L 55 306;M 211 252 L 54 303;M 211 252 L 53 299;M 211 252 L 52 296;M 211 252 L 51 293;M 211 252 L 50 289;M 211 252 L 49 286;M 211 252 L 48 283;M 211 252 L 48 279;M 211 252 L 47 276;M 211 252 L 47 272;M 211 252 L 46 269;M 211 252 L 46 265;M 211 252 L 46 262;M 211 252 L 46 259;M 211 252 L 45 255;M 211 252 L 45 252;M 211 252 L 45 248;M 211 252 L 46 245;M 211 252 L 46 241;M 211 252 L 46 238;M 211 252 L 46 234;M 211 252 L 47 231;M 211 252 L 47 228;M 211 252 L 48 224;M 211 252 L 48 221;M 211 252 L 49 217;M 211 252 L 50 214;M 211 252 L 51 211;M 211 252 L 52 207;M 211 252 L 53 204;M 211 252 L 54 201;M 211 252 L 55 197;M 211 252 L 56 194;M 211 252 L 57 191;M 211 252 L 58 188;M 211 252 L 60 184;M 211 252 L 61 181;M 211 252 L 63 178;M 211 252 L 64 175;M 211 252 L 66 172;M 211 252 L 68 169;M 211 252 L 69 166;M 211 252 L 71 163;M 211 252 L 73 160;M 211 252 L 75 157;M 211 252 L 77 154;M 211 252 L 79 152;M 211 252 L 81 149;M 211 252 L 83 146;M 211 252 L 86 144;M 211 252 L 88 141;M 211 252 L 90 139;M 211 252 L 93 136;M 211 252 L 95 134;M 211 252 L 98 131;M 211 252 L 100 129;M 211 252 L 103 127;M 211 252 L 105 124;M 211 252 L 108 122;M 211 252 L 111 120;M 211 252 L 114 118;M 211 252 L 116 116;M 211 252 L 119 114;M 211 252 L 122 112;M 211 252 L 125 110;M 211 252 L 128 109;M 211 252 L 131 107;M 211 252 L 134 105;M 211 252 L 137 104;M 211 252 L 140 102;M 211 252 L 144 101;M 211 252 L 147 99;M 211 252 L 150 98;M 211 252 L 153 97;M 211 252 L 156 96;M 211 252 L 160 94;M 211 252 L 163 93;M 211 252 L 166 92;M 211 252 L 170 92;M 211 252 L 173 91;M 211 252 L 176 90;M 211 252 L 180 89;M 211 252 L 183 89;M 211 252 L 187 88;M 211 252 L 190 88;M 211 252 L 193 87;M 211 252 L 197 87;M 211 252 L 200 87;M 211 252 L 204 87;M 211 252 L 207 86;M 211 252 L 211 86;M 211 252 L 214 86;M 211 252 L 218 87;M 211 252 L 221 87;M 211 252 L 225 87;M 211 252 L 228 87;M 211 252 L 231 88;M 211 252 L 235 88;M 211 252 L 238 89;M 211 252 L 242 89;M 211 252 L 245 90;M 211 252 L 248 91;M 211 252 L 252 92;M 211 252 L 255 92;M 211 252 L 259 93;M 211 252 L 262 94;M 211 252 L 265 96;M 211 252 L 268 97;M 211 252 L 272 98;M 211 252 L 275 99;M 211 252 L 278 101;M 211 252 L 281 102;M 211 252 L 284 104;M 211 252 L 287 105;M 211 252 L 290 107;M 211 252 L 293 109;M 211 252 L 296 110;M 211 252 L 299 112;M 211 252 L 302 114;M 211 252 L 305 116;M 211 252 L 308 118;M 211 252 L 311 120;M 211 252 L 313 122;M 211 252 L 316 124;M 211 252 L 319 127;M 211 252 L 321 129;M 211 252 L 324 131;M 211 252 L 326 134;M 211 252 L 329 136;M 211 252 L 331 139;M 211 252 L 334 141;M 211 252 L 336 144;M 211 252 L 338 146;M 211 252 L 340 149;M 211 252 L 342 152;M 211 252 L 344 154;M 211 252 L 346 157;M 211 252 L 348 160;M 211 252 L 350 163;M 211 252 L 352 166;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_f01ad0_0-5\" repeatCount=\"indefinite\" values=\"M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "motion_T.animation_SVG(edge_partition=[delta.red_edges(), delta.blue_edges()], colors=['red', 'blue'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: (0, 0),\n",
       " 1: (3/4*cos(alpha) + 1/2*sin(alpha) + 1, 1/2*cos(alpha) - 3/4*sin(alpha)),\n",
       " 2: (2*cos(alpha) + 1, -2*sin(alpha)),\n",
       " 3: (2*cos(alpha), -2*sin(alpha)),\n",
       " 4: (3/4*cos(alpha) + 1/2*sin(alpha), 1/2*cos(alpha) - 3/4*sin(alpha)),\n",
       " 5: (1, 0)}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "motion_T = GraphMotion.GridConstruction(T, delta, zigzag=[[[0,0], [3/4,1/2], [2,0]], [[0,0], [1,0]]]); motion_T.parametrization()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<path d=\"M 211 252 L 293 395\" fill=\"transparent\" id=\"edge_000d8b_0-3\" marker-end=\"url(#vertex_000d8b_3)\" marker-start=\"url(#vertex_000d8b_0)\" stroke=\"Orange\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 360 285 L 293 252\" fill=\"transparent\" id=\"edge_000d8b_1-5\" marker-end=\"url(#vertex_000d8b_5)\" marker-start=\"url(#vertex_000d8b_1)\" stroke=\"Turquoise\" stroke-width=\"5px\"/>\n",
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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_000d8b_0-5\" repeatCount=\"indefinite\" values=\"M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 L 293 252;M 211 252 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_000d8b_3-4\" repeatCount=\"indefinite\" values=\"M 293 395 L 278 285;M 290 396 L 277 286;M 287 398 L 276 287;M 284 400 L 275 289;M 281 401 L 275 290;M 278 403 L 274 291;M 275 404 L 273 293;M 272 405 L 272 294;M 268 407 L 271 295;M 265 408 L 270 297;M 262 409 L 269 298;M 259 410 L 268 299;M 255 411 L 267 300;M 252 412 L 266 301;M 248 413 L 265 303;M 245 413 L 264 304;M 242 414 L 263 305;M 238 415 L 262 306;M 235 415 L 261 307;M 231 416 L 260 308;M 228 416 L 258 309;M 225 416 L 257 310;M 221 417 L 256 311;M 218 417 L 255 312;M 214 417 L 253 313;M 211 417 L 252 314;M 207 417 L 251 314;M 204 417 L 249 315;M 200 417 L 248 316;M 197 416 L 247 317;M 193 416 L 245 318;M 190 416 L 244 318;M 187 415 L 243 319;M 183 415 L 241 320;M 180 414 L 240 320;M 176 413 L 238 321;M 173 413 L 237 321;M 170 412 L 235 322;M 166 411 L 234 322;M 163 410 L 232 323;M 160 409 L 231 323;M 156 408 L 229 324;M 153 407 L 228 324;M 150 405 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252 L 299 391;M 211 252 L 296 393;\"/>\n",
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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_000d8b_0-4\" repeatCount=\"indefinite\" values=\"M 211 252 L 278 285;M 211 252 L 277 286;M 211 252 L 276 287;M 211 252 L 275 289;M 211 252 L 275 290;M 211 252 L 274 291;M 211 252 L 273 293;M 211 252 L 272 294;M 211 252 L 271 295;M 211 252 L 270 297;M 211 252 L 269 298;M 211 252 L 268 299;M 211 252 L 267 300;M 211 252 L 266 301;M 211 252 L 265 303;M 211 252 L 264 304;M 211 252 L 263 305;M 211 252 L 262 306;M 211 252 L 261 307;M 211 252 L 260 308;M 211 252 L 258 309;M 211 252 L 257 310;M 211 252 L 256 311;M 211 252 L 255 312;M 211 252 L 253 313;M 211 252 L 252 314;M 211 252 L 251 314;M 211 252 L 249 315;M 211 252 L 248 316;M 211 252 L 247 317;M 211 252 L 245 318;M 211 252 L 244 318;M 211 252 L 243 319;M 211 252 L 241 320;M 211 252 L 240 320;M 211 252 L 238 321;M 211 252 L 237 321;M 211 252 L 235 322;M 211 252 L 234 322;M 211 252 L 232 323;M 211 252 L 231 323;M 211 252 L 229 324;M 211 252 L 228 324;M 211 252 L 226 324;M 211 252 L 225 325;M 211 252 L 223 325;M 211 252 L 222 325;M 211 252 L 220 326;M 211 252 L 219 326;M 211 252 L 217 326;M 211 252 L 216 326;M 211 252 L 214 326;M 211 252 L 212 326;M 211 252 L 211 326;M 211 252 L 209 326;M 211 252 L 208 326;M 211 252 L 206 326;M 211 252 L 205 326;M 211 252 L 203 326;M 211 252 L 202 326;M 211 252 L 200 325;M 211 252 L 198 325;M 211 252 L 197 325;M 211 252 L 195 325;M 211 252 L 194 324;M 211 252 L 192 324;M 211 252 L 191 323;M 211 252 L 189 323;M 211 252 L 188 323;M 211 252 L 186 322;M 211 252 L 185 322;M 211 252 L 183 321;M 211 252 L 182 320;M 211 252 L 181 320;M 211 252 L 179 319;M 211 252 L 178 318;M 211 252 L 176 318;M 211 252 L 175 317;M 211 252 L 174 316;M 211 252 L 172 315;M 211 252 L 171 315;M 211 252 L 170 314;M 211 252 L 168 313;M 211 252 L 167 312;M 211 252 L 166 311;M 211 252 L 165 310;M 211 252 L 163 309;M 211 252 L 162 308;M 211 252 L 161 307;M 211 252 L 160 306;M 211 252 L 159 305;M 211 252 L 158 304;M 211 252 L 157 303;M 211 252 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "motion_T.animation_SVG()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "Graphics object consisting of 13 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/svg+xml": [
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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_d2baa5_0-3\" repeatCount=\"indefinite\" values=\"M 342 200 L 252 252;M 343 202 L 252 252;M 344 204 L 252 252;M 345 206 L 252 252;M 346 208 L 252 252;M 346 210 L 252 252;M 347 212 L 252 252;M 348 214 L 252 252;M 349 216 L 252 252;M 350 218 L 252 252;M 350 220 L 252 252;M 351 222 L 252 252;M 352 224 L 252 252;M 352 226 L 252 252;M 353 228 L 252 252;M 353 231 L 252 252;M 354 233 L 252 252;M 354 235 L 252 252;M 354 237 L 252 252;M 355 239 L 252 252;M 355 241 L 252 252;M 355 243 L 252 252;M 355 246 L 252 252;M 355 248 L 252 252;M 355 250 L 252 252;M 355 252 L 252 252;M 355 254 L 252 252;M 355 256 L 252 252;M 355 259 L 252 252;M 355 261 L 252 252;M 355 263 L 252 252;M 355 265 L 252 252;M 354 267 L 252 252;M 354 269 L 252 252;M 354 271 L 252 252;M 353 274 L 252 252;M 353 276 L 252 252;M 352 278 L 252 252;M 352 280 L 252 252;M 351 282 L 252 252;M 350 284 L 252 252;M 350 286 L 252 252;M 349 288 L 252 252;M 348 290 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_d2baa5_0-1\" repeatCount=\"indefinite\" values=\"M 342 200 L 431 149;M 343 202 L 433 153;M 344 204 L 435 156;M 345 206 L 437 160;M 346 208 L 439 164;M 346 210 L 441 168;M 347 212 L 443 172;M 348 214 L 444 176;M 349 216 L 446 180;M 350 218 L 447 184;M 350 220 L 449 188;M 351 222 L 450 192;M 352 224 L 451 197;M 352 226 L 452 201;M 353 228 L 453 205;M 353 231 L 454 209;M 354 233 L 455 213;M 354 235 L 456 218;M 354 237 L 456 222;M 355 239 L 457 226;M 355 241 L 458 230;M 355 243 L 458 235;M 355 246 L 458 239;M 355 248 L 458 243;M 355 250 L 459 248;M 355 252 L 459 252;M 355 254 L 459 256;M 355 256 L 458 261;M 355 259 L 458 265;M 355 261 L 458 269;M 355 263 L 458 274;M 355 265 L 457 278;M 354 267 L 456 282;M 354 269 L 456 287;M 354 271 L 455 291;M 353 274 L 454 295;M 353 276 L 453 299;M 352 278 L 452 303;M 352 280 L 451 308;M 351 282 L 450 312;M 350 284 L 449 316;M 350 286 L 447 320;M 349 288 L 446 324;M 348 290 L 444 328;M 347 292 L 443 332;M 346 294 L 441 336;M 346 296 L 439 340;M 345 298 L 437 344;M 344 300 L 435 348;M 343 302 L 433 352;M 342 304 L 431 355;M 340 306 L 429 359;M 339 307 L 427 363;M 338 309 L 424 366;M 337 311 L 422 370;M 336 313 L 419 374;M 334 315 L 417 377;M 333 316 L 414 380;M 332 318 L 411 384;M 330 320 L 408 387;M 329 321 L 406 390;M 327 323 L 403 394;M 326 324 L 400 397;M 324 326 L 397 400;M 323 327 L 394 403;M 321 329 L 390 406;M 320 330 L 387 408;M 318 332 L 384 411;M 316 333 L 380 414;M 315 334 L 377 417;M 313 336 L 374 419;M 311 337 L 370 422;M 309 338 L 366 424;M 307 339 L 363 427;M 306 340 L 359 429;M 304 342 L 355 431;M 302 343 L 352 433;M 300 344 L 348 435;M 298 345 L 344 437;M 296 346 L 340 439;M 294 346 L 336 441;M 292 347 L 332 443;M 290 348 L 328 444;M 288 349 L 324 446;M 286 350 L 320 447;M 284 350 L 316 449;M 282 351 L 312 450;M 280 352 L 308 451;M 278 352 L 303 452;M 276 353 L 299 453;M 274 353 L 295 454;M 271 354 L 291 455;M 269 354 L 287 456;M 267 354 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429 145;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_d2baa5_2-4\" repeatCount=\"indefinite\" values=\"M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_d2baa5_3-4\" repeatCount=\"indefinite\" values=\"M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 L 355 252;M 252 252 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta = S.NAC_colorings()[0]\n",
    "delta.plot().show(figsize=[4,4])\n",
    "motion_S = GraphMotion.GridConstruction(S, delta, check=False)\n",
    "motion_S.animation_SVG(edge_partition=[delta.red_edges(), delta.blue_edges()], colors=['red', 'blue'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr class =\"row-a\">\n",
       "<td></td>\n",
       "<td>NAC-coloring</td>\n",
       "<td>injective grid</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>4-cycle</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>SmallestFlexibleLamanGraph</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>3-prism</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>MaxEmbeddingsLamanGraph_7vert</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Complete bipartite graph</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>No NAC</td>\n",
       "<td>False</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Q_1</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  NAC-coloring   injective grid\n",
       "  4-cycle                         True           True\n",
       "  SmallestFlexibleLamanGraph      True           False\n",
       "  3-prism                         True           True\n",
       "  MaxEmbeddingsLamanGraph_7vert   True           False\n",
       "  Complete bipartite graph        True           False\n",
       "  No NAC                          False          False\n",
       "  Q_1                             True           False"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table([['', 'NAC-coloring', 'injective grid']\n",
    "      ]+[[G.name(), str(G.has_NAC_coloring()), str(G.has_injective_grid_construction())] for G in examples])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Movable graphs\n",
    "\n",
    "Recall - we look for a **proper** flexible labeling, i.e., infinitely many **injective** realizations\n",
    "\n",
    "**Definition**\n",
    "$\\DeclareMathOperator{\\CDC}{CDC} \\newcommand{\\cdc}[1]{\\CDC(#1)}$\n",
    "$\\DeclareMathOperator{\\Upairs}{U} \\newcommand{\\upairs}[1]{\\Upairs(#1)}$\n",
    "\n",
    "Let $\\upairs{G}$ denote the set of all pairs $\\{u,v\\}\\subset V_G$ such that $uv\\notin E_G$ and \n",
    "there exists a path from $u$ to $v$ which is unicolor for all NAC-colorings $\\delta$ of $G$.\t\n",
    "If there exists a sequence of graphs $G=G_0, \\dots, G_n$ such that\n",
    "$G_i=(V_{G_{i-1}},E_{G_{i-1}} \\cup \\upairs{G_{i-1}})$ for $i\\in\\{1,\\dots,n\\}$\n",
    "and $\\upairs{G_n}=\\emptyset$,\n",
    "then the graph $G_n$ is called *the constant distance closure* of $G$, denoted by $\\cdc{G}$.\n",
    "\n",
    "**Theorem** [Grasegger, L., Schicho]\n",
    "\n",
    "A graph $G$ is movable if and only $\\cdc{G}$ is movable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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Zsyfy8vLwxhtvoE2bNtBqtbhy5Qqio6MtLuxtWX2qbdu2+PTTT3HixAl07drVtN3Pzw9+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\n",
      "text/plain": [
       "Graphics Array of size 1 x 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0Q5UK4Vi+fLk1yyEiIiIi8kglnXe3a9YYbw/pjy7PNYexi4tscd5tVQFxYP9+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\nRK5CYII=\n",
      "text/plain": [
       "Graphics object consisting of 29 graphics primitives"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CDC = M.constant_distance_closure()\n",
    "show(graphics_array([col.plot() for col in M.NAC_colorings()]))\n",
    "CDC.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Corollary**\n",
    "\n",
    "If $G$ is movable, then $\\cdc{G}$ is not complete."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr class =\"row-a\">\n",
       "<td></td>\n",
       "<td>NAC-coloring</td>\n",
       "<td>injective grid</td>\n",
       "<td>CDC non-complete</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>4-cycle</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>SmallestFlexibleLamanGraph</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>3-prism</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>MaxEmbeddingsLamanGraph_7vert</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Complete bipartite graph</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>No NAC</td>\n",
       "<td>False</td>\n",
       "<td>False</td>\n",
       "<td>False</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Q_1</td>\n",
       "<td>True</td>\n",
       "<td>False</td>\n",
       "<td>True</td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  NAC-coloring   injective grid   CDC non-complete\n",
       "  4-cycle                         True           True             True\n",
       "  SmallestFlexibleLamanGraph      True           False            False\n",
       "  3-prism                         True           True             True\n",
       "  MaxEmbeddingsLamanGraph_7vert   True           False            False\n",
       "  Complete bipartite graph        True           False            True\n",
       "  No NAC                          False          False            False\n",
       "  Q_1                             True           False            True"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table([['', 'NAC-coloring', 'injective grid', 'CDC non-complete']]+\n",
    "      [[G.name(), str(G.has_NAC_coloring()), str(G.has_injective_grid_construction()), str(not G.cdc_is_complete())] for G in examples])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Lemma** [Grasegger, L., Schicho]\n",
    "\n",
    "Let $G=(V,E)$ be a graph with an injective embedding $\\omega:V\\rightarrow\\mathbb{R}^3$ such that for every edge \n",
    "$uv\\in E$, the vector $\\omega(u)-\\omega(v)$ is parallel to one of the four vectors $(1,0,0)$, $(0,1,0)$, $(0,0,1)$, $(-1,-1,-1)$, and all four directions are present.\n",
    "Then $G$ is movable.\n",
    "\n",
    "Moreover, there exist two NAC-colorings such that two edges are parallel in the embedding $\\omega$ if and only if they\n",
    "receive the same pair of colors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "True\n"
     ]
    },
    {
     "data": {
      "image/png": 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9aSV0UsiXz9xbqIhcvSrSqhUvyYsviuzYYUyKS7B9u0j58rxerVvz+pni0SOR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\nZ8xgLYQjR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      "text/plain": [
       "Graphics Array of size 1 x 2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res, NACs = Q1.has_injective_spatial_embedding(certificate=True)\n",
    "print res\n",
    "graphics_array([col.plot() for col in NACs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<svg baseProfile=\"full\" height=\"500\" version=\"1.1\" width=\"500\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_0\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">0</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_1\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">1</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_2\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">2</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_3\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">3</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_4\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">4</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_5\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">5</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_8b610a_6\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">6</text>\n",
       "</marker>\n",
       "</defs>\n",
       "<path d=\"M 200 252 L 252 252\" fill=\"transparent\" id=\"edge_8b610a_0-1\" marker-end=\"url(#vertex_8b610a_1)\" marker-start=\"url(#vertex_8b610a_0)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 252 252 L 304 252\" fill=\"transparent\" id=\"edge_8b610a_1-2\" marker-end=\"url(#vertex_8b610a_2)\" marker-start=\"url(#vertex_8b610a_1)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 381 117 L 383 169\" fill=\"transparent\" id=\"edge_8b610a_3-4\" marker-end=\"url(#vertex_8b610a_4)\" marker-start=\"url(#vertex_8b610a_3)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 381 117 L 330 117\" fill=\"transparent\" id=\"edge_8b610a_3-5\" marker-end=\"url(#vertex_8b610a_5)\" marker-start=\"url(#vertex_8b610a_3)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 383 169 L 332 169\" fill=\"transparent\" id=\"edge_8b610a_4-6\" marker-end=\"url(#vertex_8b610a_6)\" marker-start=\"url(#vertex_8b610a_4)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 330 117 L 332 169\" fill=\"transparent\" id=\"edge_8b610a_5-6\" marker-end=\"url(#vertex_8b610a_6)\" marker-start=\"url(#vertex_8b610a_5)\" stroke=\"LimeGreen\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 200 252 L 304 252\" fill=\"transparent\" id=\"edge_8b610a_0-2\" marker-end=\"url(#vertex_8b610a_2)\" marker-start=\"url(#vertex_8b610a_0)\" stroke=\"Orchid\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 200 252 L 332 169\" fill=\"transparent\" id=\"edge_8b610a_0-6\" marker-end=\"url(#vertex_8b610a_6)\" marker-start=\"url(#vertex_8b610a_0)\" stroke=\"Orange\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 252 252 L 383 169\" fill=\"transparent\" id=\"edge_8b610a_1-4\" marker-end=\"url(#vertex_8b610a_4)\" marker-start=\"url(#vertex_8b610a_1)\" stroke=\"Orange\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 252 252 L 330 117\" fill=\"transparent\" id=\"edge_8b610a_1-5\" marker-end=\"url(#vertex_8b610a_5)\" marker-start=\"url(#vertex_8b610a_1)\" stroke=\"Orange\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 304 252 L 381 117\" fill=\"transparent\" id=\"edge_8b610a_2-3\" marker-end=\"url(#vertex_8b610a_3)\" marker-start=\"url(#vertex_8b610a_2)\" stroke=\"Orange\" stroke-width=\"5px\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_0-1\" repeatCount=\"indefinite\" values=\"M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 L 252 252;M 200 252 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_1-2\" repeatCount=\"indefinite\" values=\"M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 L 304 252;M 252 252 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_3-4\" repeatCount=\"indefinite\" values=\"M 381 117 L 383 169;M 378 116 L 382 167;M 376 114 L 381 166;M 373 113 L 380 164;M 370 111 L 379 162;M 367 110 L 377 161;M 364 109 L 376 159;M 361 107 L 375 157;M 358 106 L 374 155;M 355 105 L 372 154;M 352 104 L 371 152;M 349 103 L 369 150;M 345 102 L 368 149;M 342 101 L 367 147;M 339 101 L 365 145;M 336 100 L 363 144;M 333 99 L 362 142;M 330 99 L 360 140;M 326 98 L 358 139;M 323 98 L 357 137;M 320 97 L 355 136;M 317 97 L 353 134;M 313 97 L 351 132;M 310 97 L 349 131;M 307 97 L 347 129;M 304 97 L 345 128;M 300 97 L 343 126;M 297 97 L 341 124;M 294 97 L 339 123;M 291 97 L 336 121;M 288 97 L 334 120;M 284 98 L 332 119;M 281 98 L 329 117;M 278 99 L 327 116;M 275 99 L 324 114;M 272 100 L 321 113;M 268 101 L 319 112;M 265 101 L 316 110;M 262 102 L 313 109;M 259 103 L 310 108;M 256 104 L 307 107;M 253 105 L 304 106;M 250 106 L 301 105;M 247 107 L 298 104;M 244 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376 344;M 367 393 L 377 343;M 370 392 L 379 341;M 373 390 L 380 339;M 376 389 L 381 338;M 378 387 L 382 336;M 381 386 L 383 334;M 384 384 L 384 332;M 387 382 L 385 331;M 389 381 L 386 329;M 392 379 L 387 327;M 395 377 L 388 326;M 397 375 L 389 324;M 400 373 L 390 322;M 402 371 L 391 321;M 405 369 L 392 319;M 407 367 L 392 317;M 410 365 L 393 316;M 412 362 L 394 314;M 414 360 L 395 312;M 417 358 L 395 311;M 419 355 L 396 309;M 421 353 L 397 307;M 423 350 L 397 306;M 425 348 L 398 304;M 427 345 L 398 302;M 429 343 L 399 301;M 431 340 L 400 299;M 433 337 L 400 297;M 435 335 L 401 296;M 436 332 L 401 294;M 438 329 L 402 292;M 440 326 L 402 291;M 441 323 L 402 289;M 443 320 L 403 287;M 444 318 L 403 286;M 445 315 L 404 284;M 447 312 L 404 282;M 448 309 L 404 281;M 449 306 L 405 279;M 450 303 L 405 278;M 451 299 L 405 276;M 452 296 L 405 274;M 453 293 L 406 273;M 454 290 L 406 271;M 455 287 L 406 269;M 455 284 L 406 268;M 456 281 L 406 266;M 457 277 L 406 265;M 457 274 L 407 263;M 457 271 L 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389 179;M 395 126 L 388 177;M 392 124 L 387 176;M 389 122 L 386 174;M 387 121 L 385 172;M 384 119 L 384 171;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_3-5\" repeatCount=\"indefinite\" values=\"M 381 117 L 330 117;M 378 116 L 327 116;M 376 114 L 324 114;M 373 113 L 321 113;M 370 111 L 318 111;M 367 110 L 315 110;M 364 109 L 312 109;M 361 107 L 309 107;M 358 106 L 306 106;M 355 105 L 303 105;M 352 104 L 300 104;M 349 103 L 297 103;M 345 102 L 294 102;M 342 101 L 291 101;M 339 101 L 287 101;M 336 100 L 284 100;M 333 99 L 281 99;M 330 99 L 278 99;M 326 98 L 275 98;M 323 98 L 271 98;M 320 97 L 268 97;M 317 97 L 265 97;M 313 97 L 262 97;M 310 97 L 259 97;M 307 97 L 255 97;M 304 97 L 252 97;M 300 97 L 249 97;M 297 97 L 246 97;M 294 97 L 242 97;M 291 97 L 239 97;M 288 97 L 236 97;M 284 98 L 233 98;M 281 98 L 229 98;M 278 99 L 226 99;M 275 99 L 223 99;M 272 100 L 220 100;M 268 101 L 217 101;M 265 101 L 214 101;M 262 102 L 210 102;M 259 103 L 207 103;M 256 104 L 204 104;M 253 105 L 201 105;M 250 106 L 198 106;M 247 107 L 195 107;M 244 109 L 192 109;M 241 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L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;M 200 252 L 304 252;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_0-6\" repeatCount=\"indefinite\" values=\"M 200 252 L 332 169;M 200 252 L 330 167;M 200 252 L 329 166;M 200 252 L 328 164;M 200 252 L 327 162;M 200 252 L 326 161;M 200 252 L 325 159;M 200 252 L 323 157;M 200 252 L 322 155;M 200 252 L 321 154;M 200 252 L 319 152;M 200 252 L 318 150;M 200 252 L 316 149;M 200 252 L 315 147;M 200 252 L 313 145;M 200 252 L 312 144;M 200 252 L 310 142;M 200 252 L 308 140;M 200 252 L 307 139;M 200 252 L 305 137;M 200 252 L 303 136;M 200 252 L 301 134;M 200 252 L 299 132;M 200 252 L 297 131;M 200 252 L 295 129;M 200 252 L 293 128;M 200 252 L 291 126;M 200 252 L 289 124;M 200 252 L 287 123;M 200 252 L 285 121;M 200 252 L 282 120;M 200 252 L 280 119;M 200 252 L 278 117;M 200 252 L 275 116;M 200 252 L 272 114;M 200 252 L 270 113;M 200 252 L 267 112;M 200 252 L 264 110;M 200 252 L 262 109;M 200 252 L 259 108;M 200 252 L 256 107;M 200 252 L 253 106;M 200 252 L 250 105;M 200 252 L 247 104;M 200 252 L 243 103;M 200 252 L 240 102;M 200 252 L 237 101;M 200 252 L 233 100;M 200 252 L 230 99;M 200 252 L 226 99;M 200 252 L 223 98;M 200 252 L 219 98;M 200 252 L 215 97;M 200 252 L 211 97;M 200 252 L 207 97;M 200 252 L 203 97;M 200 252 L 199 97;M 200 252 L 195 97;M 200 252 L 191 97;M 200 252 L 187 97;M 200 252 L 183 98;M 200 252 L 178 98;M 200 252 L 174 99;M 200 252 L 169 100;M 200 252 L 165 101;M 200 252 L 160 102;M 200 252 L 156 103;M 200 252 L 151 105;M 200 252 L 147 106;M 200 252 L 142 108;M 200 252 L 137 110;M 200 252 L 133 112;M 200 252 L 128 114;M 200 252 L 124 117;M 200 252 L 119 120;M 200 252 L 115 123;M 200 252 L 110 126;M 200 252 L 106 129;M 200 252 L 101 132;M 200 252 L 97 136;M 200 252 L 93 140;M 200 252 L 89 144;M 200 252 L 85 148;M 200 252 L 81 153;M 200 252 L 77 157;M 200 252 L 74 162;M 200 252 L 70 167;M 200 252 L 67 173;M 200 252 L 64 178;M 200 252 L 61 183;M 200 252 L 59 189;M 200 252 L 56 195;M 200 252 L 54 201;M 200 252 L 52 207;M 200 252 L 50 213;M 200 252 L 49 219;M 200 252 L 48 226;M 200 252 L 47 232;M 200 252 L 46 239;M 200 252 L 46 245;M 200 252 L 45 252;M 200 252 L 45 252;M 200 252 L 46 258;M 200 252 L 46 265;M 200 252 L 47 271;M 200 252 L 48 277;M 200 252 L 49 284;M 200 252 L 50 290;M 200 252 L 52 296;M 200 252 L 54 302;M 200 252 L 56 308;M 200 252 L 59 314;M 200 252 L 61 320;M 200 252 L 64 325;M 200 252 L 67 331;M 200 252 L 70 336;M 200 252 L 74 341;M 200 252 L 77 346;M 200 252 L 81 350;M 200 252 L 85 355;M 200 252 L 89 359;M 200 252 L 93 363;M 200 252 L 97 367;M 200 252 L 101 371;M 200 252 L 106 374;M 200 252 L 110 377;M 200 252 L 115 381;M 200 252 L 119 383;M 200 252 L 124 386;M 200 252 L 128 389;M 200 252 L 133 391;M 200 252 L 137 393;M 200 252 L 142 395;M 200 252 L 147 397;M 200 252 L 151 399;M 200 252 L 156 400;M 200 252 L 160 401;M 200 252 L 165 402;M 200 252 L 169 403;M 200 252 L 174 404;M 200 252 L 178 405;M 200 252 L 183 405;M 200 252 L 187 406;M 200 252 L 191 406;M 200 252 L 195 406;M 200 252 L 199 407;M 200 252 L 203 406;M 200 252 L 207 406;M 200 252 L 211 406;M 200 252 L 215 406;M 200 252 L 219 405;M 200 252 L 223 405;M 200 252 L 226 404;M 200 252 L 230 404;M 200 252 L 233 403;M 200 252 L 237 402;M 200 252 L 240 401;M 200 252 L 243 400;M 200 252 L 247 399;M 200 252 L 250 398;M 200 252 L 253 397;M 200 252 L 256 396;M 200 252 L 259 395;M 200 252 L 262 394;M 200 252 L 264 393;M 200 252 L 267 391;M 200 252 L 270 390;M 200 252 L 272 389;M 200 252 L 275 387;M 200 252 L 278 386;M 200 252 L 280 385;M 200 252 L 282 383;M 200 252 L 285 382;M 200 252 L 287 380;M 200 252 L 289 379;M 200 252 L 291 377;M 200 252 L 293 376;M 200 252 L 295 374;M 200 252 L 297 372;M 200 252 L 299 371;M 200 252 L 301 369;M 200 252 L 303 368;M 200 252 L 305 366;M 200 252 L 307 364;M 200 252 L 308 363;M 200 252 L 310 361;M 200 252 L 312 359;M 200 252 L 313 358;M 200 252 L 315 356;M 200 252 L 316 354;M 200 252 L 318 353;M 200 252 L 319 351;M 200 252 L 321 349;M 200 252 L 322 348;M 200 252 L 323 346;M 200 252 L 325 344;M 200 252 L 326 343;M 200 252 L 327 341;M 200 252 L 328 339;M 200 252 L 329 338;M 200 252 L 330 336;M 200 252 L 332 334;M 200 252 L 333 332;M 200 252 L 334 331;M 200 252 L 335 329;M 200 252 L 336 327;M 200 252 L 336 326;M 200 252 L 337 324;M 200 252 L 338 322;M 200 252 L 339 321;M 200 252 L 340 319;M 200 252 L 341 317;M 200 252 L 342 316;M 200 252 L 342 314;M 200 252 L 343 312;M 200 252 L 344 311;M 200 252 L 344 309;M 200 252 L 345 307;M 200 252 L 346 306;M 200 252 L 346 304;M 200 252 L 347 302;M 200 252 L 347 301;M 200 252 L 348 299;M 200 252 L 348 297;M 200 252 L 349 296;M 200 252 L 349 294;M 200 252 L 350 292;M 200 252 L 350 291;M 200 252 L 351 289;M 200 252 L 351 287;M 200 252 L 352 286;M 200 252 L 352 284;M 200 252 L 352 282;M 200 252 L 353 281;M 200 252 L 353 279;M 200 252 L 353 278;M 200 252 L 353 276;M 200 252 L 354 274;M 200 252 L 354 273;M 200 252 L 354 271;M 200 252 L 354 269;M 200 252 L 355 268;M 200 252 L 355 266;M 200 252 L 355 265;M 200 252 L 355 263;M 200 252 L 355 261;M 200 252 L 355 260;M 200 252 L 355 258;M 200 252 L 355 256;M 200 252 L 355 255;M 200 252 L 355 253;M 200 252 L 355 252;M 200 252 L 355 250;M 200 252 L 355 248;M 200 252 L 355 247;M 200 252 L 355 245;M 200 252 L 355 243;M 200 252 L 355 242;M 200 252 L 355 240;M 200 252 L 355 239;M 200 252 L 355 237;M 200 252 L 355 235;M 200 252 L 354 234;M 200 252 L 354 232;M 200 252 L 354 230;M 200 252 L 354 229;M 200 252 L 353 227;M 200 252 L 353 226;M 200 252 L 353 224;M 200 252 L 353 222;M 200 252 L 352 221;M 200 252 L 352 219;M 200 252 L 352 217;M 200 252 L 351 216;M 200 252 L 351 214;M 200 252 L 350 212;M 200 252 L 350 211;M 200 252 L 349 209;M 200 252 L 349 207;M 200 252 L 348 206;M 200 252 L 348 204;M 200 252 L 347 202;M 200 252 L 347 201;M 200 252 L 346 199;M 200 252 L 346 198;M 200 252 L 345 196;M 200 252 L 344 194;M 200 252 L 344 193;M 200 252 L 343 191;M 200 252 L 342 189;M 200 252 L 342 187;M 200 252 L 341 186;M 200 252 L 340 184;M 200 252 L 339 182;M 200 252 L 338 181;M 200 252 L 337 179;M 200 252 L 336 177;M 200 252 L 336 176;M 200 252 L 335 174;M 200 252 L 334 172;M 200 252 L 333 171;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_1-4\" repeatCount=\"indefinite\" values=\"M 252 252 L 383 169;M 252 252 L 382 167;M 252 252 L 381 166;M 252 252 L 380 164;M 252 252 L 379 162;M 252 252 L 377 161;M 252 252 L 376 159;M 252 252 L 375 157;M 252 252 L 374 155;M 252 252 L 372 154;M 252 252 L 371 152;M 252 252 L 369 150;M 252 252 L 368 149;M 252 252 L 367 147;M 252 252 L 365 145;M 252 252 L 363 144;M 252 252 L 362 142;M 252 252 L 360 140;M 252 252 L 358 139;M 252 252 L 357 137;M 252 252 L 355 136;M 252 252 L 353 134;M 252 252 L 351 132;M 252 252 L 349 131;M 252 252 L 347 129;M 252 252 L 345 128;M 252 252 L 343 126;M 252 252 L 341 124;M 252 252 L 339 123;M 252 252 L 336 121;M 252 252 L 334 120;M 252 252 L 332 119;M 252 252 L 329 117;M 252 252 L 327 116;M 252 252 L 324 114;M 252 252 L 321 113;M 252 252 L 319 112;M 252 252 L 316 110;M 252 252 L 313 109;M 252 252 L 310 108;M 252 252 L 307 107;M 252 252 L 304 106;M 252 252 L 301 105;M 252 252 L 298 104;M 252 252 L 295 103;M 252 252 L 292 102;M 252 252 L 288 101;M 252 252 L 285 100;M 252 252 L 281 99;M 252 252 L 278 99;M 252 252 L 274 98;M 252 252 L 270 98;M 252 252 L 267 97;M 252 252 L 263 97;M 252 252 L 259 97;M 252 252 L 255 97;M 252 252 L 251 97;M 252 252 L 247 97;M 252 252 L 243 97;M 252 252 L 238 97;M 252 252 L 234 98;M 252 252 L 230 98;M 252 252 L 225 99;M 252 252 L 221 100;M 252 252 L 217 101;M 252 252 L 212 102;M 252 252 L 207 103;M 252 252 L 203 105;M 252 252 L 198 106;M 252 252 L 194 108;M 252 252 L 189 110;M 252 252 L 185 112;M 252 252 L 180 114;M 252 252 L 175 117;M 252 252 L 171 120;M 252 252 L 166 123;M 252 252 L 162 126;M 252 252 L 157 129;M 252 252 L 153 132;M 252 252 L 149 136;M 252 252 L 145 140;M 252 252 L 140 144;M 252 252 L 136 148;M 252 252 L 133 153;M 252 252 L 129 157;M 252 252 L 125 162;M 252 252 L 122 167;M 252 252 L 119 173;M 252 252 L 116 178;M 252 252 L 113 183;M 252 252 L 110 189;M 252 252 L 108 195;M 252 252 L 106 201;M 252 252 L 104 207;M 252 252 L 102 213;M 252 252 L 100 219;M 252 252 L 99 226;M 252 252 L 98 232;M 252 252 L 98 239;M 252 252 L 97 245;M 252 252 L 97 252;M 252 252 L 97 252;M 252 252 L 97 258;M 252 252 L 98 265;M 252 252 L 98 271;M 252 252 L 99 277;M 252 252 L 100 284;M 252 252 L 102 290;M 252 252 L 104 296;M 252 252 L 106 302;M 252 252 L 108 308;M 252 252 L 110 314;M 252 252 L 113 320;M 252 252 L 116 325;M 252 252 L 119 331;M 252 252 L 122 336;M 252 252 L 125 341;M 252 252 L 129 346;M 252 252 L 133 350;M 252 252 L 136 355;M 252 252 L 140 359;M 252 252 L 145 363;M 252 252 L 149 367;M 252 252 L 153 371;M 252 252 L 157 374;M 252 252 L 162 377;M 252 252 L 166 381;M 252 252 L 171 383;M 252 252 L 175 386;M 252 252 L 180 389;M 252 252 L 185 391;M 252 252 L 189 393;M 252 252 L 194 395;M 252 252 L 198 397;M 252 252 L 203 399;M 252 252 L 207 400;M 252 252 L 212 401;M 252 252 L 217 402;M 252 252 L 221 403;M 252 252 L 225 404;M 252 252 L 230 405;M 252 252 L 234 405;M 252 252 L 238 406;M 252 252 L 243 406;M 252 252 L 247 406;M 252 252 L 251 407;M 252 252 L 255 406;M 252 252 L 259 406;M 252 252 L 263 406;M 252 252 L 267 406;M 252 252 L 270 405;M 252 252 L 274 405;M 252 252 L 278 404;M 252 252 L 281 404;M 252 252 L 285 403;M 252 252 L 288 402;M 252 252 L 292 401;M 252 252 L 295 400;M 252 252 L 298 399;M 252 252 L 301 398;M 252 252 L 304 397;M 252 252 L 307 396;M 252 252 L 310 395;M 252 252 L 313 394;M 252 252 L 316 393;M 252 252 L 319 391;M 252 252 L 321 390;M 252 252 L 324 389;M 252 252 L 327 387;M 252 252 L 329 386;M 252 252 L 332 385;M 252 252 L 334 383;M 252 252 L 336 382;M 252 252 L 339 380;M 252 252 L 341 379;M 252 252 L 343 377;M 252 252 L 345 376;M 252 252 L 347 374;M 252 252 L 349 372;M 252 252 L 351 371;M 252 252 L 353 369;M 252 252 L 355 368;M 252 252 L 357 366;M 252 252 L 358 364;M 252 252 L 360 363;M 252 252 L 362 361;M 252 252 L 363 359;M 252 252 L 365 358;M 252 252 L 367 356;M 252 252 L 368 354;M 252 252 L 369 353;M 252 252 L 371 351;M 252 252 L 372 349;M 252 252 L 374 348;M 252 252 L 375 346;M 252 252 L 376 344;M 252 252 L 377 343;M 252 252 L 379 341;M 252 252 L 380 339;M 252 252 L 381 338;M 252 252 L 382 336;M 252 252 L 383 334;M 252 252 L 384 332;M 252 252 L 385 331;M 252 252 L 386 329;M 252 252 L 387 327;M 252 252 L 388 326;M 252 252 L 389 324;M 252 252 L 390 322;M 252 252 L 391 321;M 252 252 L 392 319;M 252 252 L 392 317;M 252 252 L 393 316;M 252 252 L 394 314;M 252 252 L 395 312;M 252 252 L 395 311;M 252 252 L 396 309;M 252 252 L 397 307;M 252 252 L 397 306;M 252 252 L 398 304;M 252 252 L 398 302;M 252 252 L 399 301;M 252 252 L 400 299;M 252 252 L 400 297;M 252 252 L 401 296;M 252 252 L 401 294;M 252 252 L 402 292;M 252 252 L 402 291;M 252 252 L 402 289;M 252 252 L 403 287;M 252 252 L 403 286;M 252 252 L 404 284;M 252 252 L 404 282;M 252 252 L 404 281;M 252 252 L 405 279;M 252 252 L 405 278;M 252 252 L 405 276;M 252 252 L 405 274;M 252 252 L 406 273;M 252 252 L 406 271;M 252 252 L 406 269;M 252 252 L 406 268;M 252 252 L 406 266;M 252 252 L 406 265;M 252 252 L 407 263;M 252 252 L 407 261;M 252 252 L 407 260;M 252 252 L 407 258;M 252 252 L 407 256;M 252 252 L 407 255;M 252 252 L 407 253;M 252 252 L 407 252;M 252 252 L 407 250;M 252 252 L 407 248;M 252 252 L 407 247;M 252 252 L 407 245;M 252 252 L 407 243;M 252 252 L 407 242;M 252 252 L 407 240;M 252 252 L 406 239;M 252 252 L 406 237;M 252 252 L 406 235;M 252 252 L 406 234;M 252 252 L 406 232;M 252 252 L 406 230;M 252 252 L 405 229;M 252 252 L 405 227;M 252 252 L 405 226;M 252 252 L 405 224;M 252 252 L 404 222;M 252 252 L 404 221;M 252 252 L 404 219;M 252 252 L 403 217;M 252 252 L 403 216;M 252 252 L 402 214;M 252 252 L 402 212;M 252 252 L 402 211;M 252 252 L 401 209;M 252 252 L 401 207;M 252 252 L 400 206;M 252 252 L 400 204;M 252 252 L 399 202;M 252 252 L 398 201;M 252 252 L 398 199;M 252 252 L 397 198;M 252 252 L 397 196;M 252 252 L 396 194;M 252 252 L 395 193;M 252 252 L 395 191;M 252 252 L 394 189;M 252 252 L 393 187;M 252 252 L 392 186;M 252 252 L 392 184;M 252 252 L 391 182;M 252 252 L 390 181;M 252 252 L 389 179;M 252 252 L 388 177;M 252 252 L 387 176;M 252 252 L 386 174;M 252 252 L 385 172;M 252 252 L 384 171;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_8b610a_1-5\" repeatCount=\"indefinite\" values=\"M 252 252 L 330 117;M 252 252 L 327 116;M 252 252 L 324 114;M 252 252 L 321 113;M 252 252 L 318 111;M 252 252 L 315 110;M 252 252 L 312 109;M 252 252 L 309 107;M 252 252 L 306 106;M 252 252 L 303 105;M 252 252 L 300 104;M 252 252 L 297 103;M 252 252 L 294 102;M 252 252 L 291 101;M 252 252 L 287 101;M 252 252 L 284 100;M 252 252 L 281 99;M 252 252 L 278 99;M 252 252 L 275 98;M 252 252 L 271 98;M 252 252 L 268 97;M 252 252 L 265 97;M 252 252 L 262 97;M 252 252 L 259 97;M 252 252 L 255 97;M 252 252 L 252 97;M 252 252 L 249 97;M 252 252 L 246 97;M 252 252 L 242 97;M 252 252 L 239 97;M 252 252 L 236 97;M 252 252 L 233 98;M 252 252 L 229 98;M 252 252 L 226 99;M 252 252 L 223 99;M 252 252 L 220 100;M 252 252 L 217 101;M 252 252 L 214 101;M 252 252 L 210 102;M 252 252 L 207 103;M 252 252 L 204 104;M 252 252 L 201 105;M 252 252 L 198 106;M 252 252 L 195 107;M 252 252 L 192 109;M 252 252 L 189 110;M 252 252 L 186 111;M 252 252 L 183 113;M 252 252 L 180 114;M 252 252 L 177 116;M 252 252 L 175 117;M 252 252 L 172 119;M 252 252 L 169 121;M 252 252 L 166 122;M 252 252 L 164 124;M 252 252 L 161 126;M 252 252 L 158 128;M 252 252 L 156 130;M 252 252 L 153 132;M 252 252 L 151 134;M 252 252 L 148 136;M 252 252 L 146 139;M 252 252 L 144 141;M 252 252 L 141 143;M 252 252 L 139 145;M 252 252 L 137 148;M 252 252 L 135 150;M 252 252 L 133 153;M 252 252 L 131 155;M 252 252 L 129 158;M 252 252 L 127 160;M 252 252 L 125 163;M 252 252 L 123 166;M 252 252 L 121 169;M 252 252 L 120 171;M 252 252 L 118 174;M 252 252 L 116 177;M 252 252 L 115 180;M 252 252 L 113 183;M 252 252 L 112 186;M 252 252 L 111 189;M 252 252 L 109 192;M 252 252 L 108 195;M 252 252 L 107 198;M 252 252 L 106 201;M 252 252 L 105 204;M 252 252 L 104 207;M 252 252 L 103 210;M 252 252 L 102 213;M 252 252 L 101 216;M 252 252 L 100 219;M 252 252 L 100 223;M 252 252 L 99 226;M 252 252 L 99 229;M 252 252 L 98 232;M 252 252 L 98 235;M 252 252 L 98 239;M 252 252 L 97 242;M 252 252 L 97 245;M 252 252 L 97 248;M 252 252 L 97 252;M 252 252 L 97 252;M 252 252 L 97 255;M 252 252 L 97 258;M 252 252 L 97 261;M 252 252 L 98 265;M 252 252 L 98 268;M 252 252 L 98 271;M 252 252 L 99 274;M 252 252 L 99 277;M 252 252 L 100 281;M 252 252 L 100 284;M 252 252 L 101 287;M 252 252 L 102 290;M 252 252 L 103 293;M 252 252 L 104 296;M 252 252 L 105 299;M 252 252 L 106 303;M 252 252 L 107 306;M 252 252 L 108 309;M 252 252 L 109 312;M 252 252 L 111 315;M 252 252 L 112 318;M 252 252 L 113 320;M 252 252 L 115 323;M 252 252 L 116 326;M 252 252 L 118 329;M 252 252 L 120 332;M 252 252 L 121 335;M 252 252 L 123 337;M 252 252 L 125 340;M 252 252 L 127 343;M 252 252 L 129 345;M 252 252 L 131 348;M 252 252 L 133 350;M 252 252 L 135 353;M 252 252 L 137 355;M 252 252 L 139 358;M 252 252 L 141 360;M 252 252 L 144 362;M 252 252 L 146 365;M 252 252 L 148 367;M 252 252 L 151 369;M 252 252 L 153 371;M 252 252 L 156 373;M 252 252 L 158 375;M 252 252 L 161 377;M 252 252 L 164 379;M 252 252 L 166 381;M 252 252 L 169 382;M 252 252 L 172 384;M 252 252 L 175 386;M 252 252 L 177 387;M 252 252 L 180 389;M 252 252 L 183 390;M 252 252 L 186 392;M 252 252 L 189 393;M 252 252 L 192 394;M 252 252 L 195 396;M 252 252 L 198 397;M 252 252 L 201 398;M 252 252 L 204 399;M 252 252 L 207 400;M 252 252 L 210 401;M 252 252 L 214 402;M 252 252 L 217 402;M 252 252 L 220 403;M 252 252 L 223 404;M 252 252 L 226 404;M 252 252 L 229 405;M 252 252 L 233 405;M 252 252 L 236 406;M 252 252 L 239 406;M 252 252 L 242 406;M 252 252 L 246 406;M 252 252 L 249 406;M 252 252 L 252 407;M 252 252 L 255 406;M 252 252 L 259 406;M 252 252 L 262 406;M 252 252 L 265 406;M 252 252 L 268 406;M 252 252 L 271 405;M 252 252 L 275 405;M 252 252 L 278 404;M 252 252 L 281 404;M 252 252 L 284 403;M 252 252 L 287 402;M 252 252 L 291 402;M 252 252 L 294 401;M 252 252 L 297 400;M 252 252 L 300 399;M 252 252 L 303 398;M 252 252 L 306 397;M 252 252 L 309 396;M 252 252 L 312 394;M 252 252 L 315 393;M 252 252 L 318 392;M 252 252 L 321 390;M 252 252 L 324 389;M 252 252 L 327 387;M 252 252 L 330 386;M 252 252 L 332 384;M 252 252 L 335 382;M 252 252 L 338 381;M 252 252 L 341 379;M 252 252 L 343 377;M 252 252 L 346 375;M 252 252 L 348 373;M 252 252 L 351 371;M 252 252 L 353 369;M 252 252 L 356 367;M 252 252 L 358 365;M 252 252 L 360 362;M 252 252 L 363 360;M 252 252 L 365 358;M 252 252 L 367 355;M 252 252 L 369 353;M 252 252 L 371 350;M 252 252 L 374 348;M 252 252 L 375 345;M 252 252 L 377 343;M 252 252 L 379 340;M 252 252 L 381 337;M 252 252 L 383 335;M 252 252 L 385 332;M 252 252 L 386 329;M 252 252 L 388 326;M 252 252 L 389 323;M 252 252 L 391 320;M 252 252 L 392 318;M 252 252 L 394 315;M 252 252 L 395 312;M 252 252 L 396 309;M 252 252 L 397 306;M 252 252 L 398 303;M 252 252 L 399 299;M 252 252 L 400 296;M 252 252 L 401 293;M 252 252 L 402 290;M 252 252 L 403 287;M 252 252 L 404 284;M 252 252 L 404 281;M 252 252 L 405 277;M 252 252 L 405 274;M 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       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "motion_Q1 = GraphMotion.SpatialEmbeddingConstruction(Q1,NACs)\n",
    "motion_Q1.fix_edge([0,1])\n",
    "motion_Q1.animation_SVG()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div class=\"notruncate\">\n",
       "<table  class=\"table_form\">\n",
       "<tbody>\n",
       "<tr class =\"row-a\">\n",
       "<td></td>\n",
       "<td>movable</td>\n",
       "<td>reason</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>4-cycle</td>\n",
       "<td>yes</td>\n",
       "<td>bipartite</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>SmallestFlexibleLamanGraph</td>\n",
       "<td>no</td>\n",
       "<td>CDC is complete</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>3-prism</td>\n",
       "<td>yes</td>\n",
       "<td>grid construction</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>MaxEmbeddingsLamanGraph_7vert</td>\n",
       "<td>no</td>\n",
       "<td>CDC is complete</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Complete bipartite graph</td>\n",
       "<td>yes</td>\n",
       "<td>bipartite</td>\n",
       "</tr>\n",
       "<tr class =\"row-a\">\n",
       "<td>No NAC</td>\n",
       "<td>no</td>\n",
       "<td>no NAC-coloring</td>\n",
       "</tr>\n",
       "<tr class =\"row-b\">\n",
       "<td>Q_1</td>\n",
       "<td>yes</td>\n",
       "<td>spatial embedding</td>\n",
       "</tr>\n",
       "</tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  movable   reason\n",
       "  4-cycle                         yes       bipartite\n",
       "  SmallestFlexibleLamanGraph      no        CDC is complete\n",
       "  3-prism                         yes       grid construction\n",
       "  MaxEmbeddingsLamanGraph_7vert   no        CDC is complete\n",
       "  Complete bipartite graph        yes       bipartite\n",
       "  No NAC                          no        no NAC-coloring\n",
       "  Q_1                             yes       spatial embedding"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table([['', 'movable', 'reason']]+\n",
    "      [[G.name()]+list(G.is_movable()) for G in examples])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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O0qsHJQcDETejbcGh8CcOBPM4EBpHqdWD0oOBiJvR1uBQIA4ES3Ag2I8SqwdHCAYibkZb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\n",
      "text/plain": [
       "Graphics object consisting of 23 graphics primitives"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "('cannot decide', '')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S1 = GraphGenerator.S1Graph()\n",
    "show(S1)\n",
    "S1.is_movable()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![S1](./animations/S_1.svg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collision-free models\n",
    "\n",
    "Can a movable graph be modelled by a planar linkage in 3D that is collision-free?\n",
    "\n",
    "$\\implies$ Place edges into different layers and avoid collision with the axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"100%\" controls> <source src=\"https://jan.legersky.cz/img/collidingK33.mp4\" type=\"video/mp4\"> </video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<video width=\"100%\" controls> <source src=\"https://jan.legersky.cz/img/collidingK33.mp4\" type=\"video/mp4\"> </video>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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y8vJw4cIFcByn9OocdevWlSofgDLLWJbix148XdEyW8OGDZP4rq2srBAREYG8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\nIjg4WA0bN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      "text/plain": [
       "RigidFlexibleGraph with the vertices [1, 2, 3, 4, 5, 6] and edges [(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edges = [(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 5), (3, 6), (3, 4)]\n",
    "K33 = RigidFlexibleGraph(edges); K33"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: (sin(t), 0),\n",
       " 2: (sqrt(sin(t)^2 + 1), 0),\n",
       " 3: (-sqrt(sin(t)^2 + 2), 0),\n",
       " 4: (0, cos(t)),\n",
       " 5: (0, sqrt(cos(t)^2 + 1)),\n",
       " 6: (0, -sqrt(cos(t)^2 + 2))}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = var('t')\n",
    "P = {\n",
    "    1: vector([sin(t),0]),\n",
    "    2: vector([sqrt(1+sin(t)^2),0]),\n",
    "    3: vector([-sqrt(2+sin(t)^2),0]),\n",
    "    4: vector([0,cos(t)]),\n",
    "    5: vector([0,sqrt(1+cos(t)*cos(t))]),\n",
    "    6: vector([0,-sqrt(2+cos(t)^2)]),\n",
    "}; P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "  <defs>\n",
       "<marker id=\"vertex_b4b9aa_1\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">1</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
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       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">2</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
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       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">3</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_b4b9aa_4\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">4</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
       "<marker id=\"vertex_b4b9aa_5\" markerHeight=\"5\" markerWidth=\"5\" refX=\"15\" refY=\"15\" viewBox=\"0 0 30 30\">\n",
       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">5</text>\n",
       "</marker>\n",
       "</defs>\n",
       "  <defs>\n",
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       "  <circle cx=\"15\" cy=\"15\" fill=\"grey\" r=\"15\"/>\n",
       "<text fill=\"white\" font-size=\"22.5\" text-anchor=\"middle\" x=\"15\" y=\"22\">6</text>\n",
       "</marker>\n",
       "</defs>\n",
       "<path d=\"M 387 231 L 273 166\" fill=\"transparent\" id=\"edge_b4b9aa_1-4\" marker-end=\"url(#vertex_b4b9aa_4)\" marker-start=\"url(#vertex_b4b9aa_1)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
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       "<path d=\"M 447 231 L 273 166\" fill=\"transparent\" id=\"edge_b4b9aa_2-4\" marker-end=\"url(#vertex_b4b9aa_4)\" marker-start=\"url(#vertex_b4b9aa_2)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 447 231 L 273 84\" fill=\"transparent\" id=\"edge_b4b9aa_2-5\" marker-end=\"url(#vertex_b4b9aa_5)\" marker-start=\"url(#vertex_b4b9aa_2)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 447 231 L 273 428\" fill=\"transparent\" id=\"edge_b4b9aa_2-6\" marker-end=\"url(#vertex_b4b9aa_6)\" marker-start=\"url(#vertex_b4b9aa_2)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 55 231 L 273 166\" fill=\"transparent\" id=\"edge_b4b9aa_3-4\" marker-end=\"url(#vertex_b4b9aa_4)\" marker-start=\"url(#vertex_b4b9aa_3)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 55 231 L 273 84\" fill=\"transparent\" id=\"edge_b4b9aa_3-5\" marker-end=\"url(#vertex_b4b9aa_5)\" marker-start=\"url(#vertex_b4b9aa_3)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<path d=\"M 55 231 L 273 428\" fill=\"transparent\" id=\"edge_b4b9aa_3-6\" marker-end=\"url(#vertex_b4b9aa_6)\" marker-start=\"url(#vertex_b4b9aa_3)\" stroke=\"LightGray\" stroke-width=\"5px\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_1-4\" repeatCount=\"indefinite\" values=\"M 387 231 L 273 166;M 388 231 L 273 168;M 389 231 L 273 170;M 391 231 L 273 173;M 392 231 L 273 175;M 393 231 L 273 178;M 394 231 L 273 180;M 395 231 L 273 183;M 396 231 L 273 185;M 397 231 L 273 188;M 398 231 L 273 191;M 399 231 L 273 193;M 399 231 L 273 196;M 400 231 L 273 199;M 401 231 L 273 201;M 401 231 L 273 204;M 402 231 L 273 207;M 402 231 L 273 209;M 403 231 L 273 212;M 403 231 L 273 215;M 404 231 L 273 217;M 404 231 L 273 220;M 404 231 L 273 223;M 404 231 L 273 226;M 404 231 L 273 228;M 404 231 L 273 231;M 404 231 L 273 234;M 404 231 L 273 237;M 404 231 L 273 239;M 404 231 L 273 242;M 404 231 L 273 245;M 403 231 L 273 248;M 403 231 L 273 250;M 402 231 L 273 253;M 402 231 L 273 256;M 401 231 L 273 259;M 401 231 L 273 261;M 400 231 L 273 264;M 399 231 L 273 267;M 399 231 L 273 269;M 398 231 L 273 272;M 397 231 L 273 274;M 396 231 L 273 277;M 395 231 L 273 280;M 394 231 L 273 282;M 393 231 L 273 285;M 392 231 L 273 287;M 391 231 L 273 290;M 389 231 L 273 292;M 388 231 L 273 294;M 387 231 L 273 297;M 385 231 L 273 299;M 384 231 L 273 302;M 382 231 L 273 304;M 381 231 L 273 306;M 379 231 L 273 308;M 378 231 L 273 311;M 376 231 L 273 313;M 374 231 L 273 315;M 372 231 L 273 317;M 371 231 L 273 319;M 369 231 L 273 321;M 367 231 L 273 323;M 365 231 L 273 325;M 363 231 L 273 327;M 361 231 L 273 329;M 359 231 L 273 331;M 357 231 L 273 332;M 355 231 L 273 334;M 352 231 L 273 336;M 350 231 L 273 337;M 348 231 L 273 339;M 346 231 L 273 341;M 343 231 L 273 342;M 341 231 L 273 344;M 339 231 L 273 345;M 336 231 L 273 346;M 334 231 L 273 348;M 331 231 L 273 349;M 329 231 L 273 350;M 326 231 L 273 351;M 324 231 L 273 352;M 321 231 L 273 353;M 319 231 L 273 354;M 316 231 L 273 355;M 314 231 L 273 356;M 311 231 L 273 357;M 308 231 L 273 358;M 306 231 L 273 358;M 303 231 L 273 359;M 300 231 L 273 360;M 298 231 L 273 360;M 295 231 L 273 361;M 292 231 L 273 361;M 289 231 L 273 361;M 287 231 L 273 362;M 284 231 L 273 362;M 281 231 L 273 362;M 278 231 L 273 362;M 276 231 L 273 363;M 273 231 L 273 363;M 273 231 L 273 363;M 270 231 L 273 363;M 267 231 L 273 362;M 265 231 L 273 362;M 262 231 L 273 362;M 259 231 L 273 362;M 256 231 L 273 361;M 254 231 L 273 361;M 251 231 L 273 361;M 248 231 L 273 360;M 246 231 L 273 360;M 243 231 L 273 359;M 240 231 L 273 358;M 238 231 L 273 358;M 235 231 L 273 357;M 232 231 L 273 356;M 230 231 L 273 355;M 227 231 L 273 354;M 225 231 L 273 353;M 222 231 L 273 352;M 220 231 L 273 351;M 217 231 L 273 350;M 215 231 L 273 349;M 212 231 L 273 348;M 210 231 L 273 346;M 207 231 L 273 345;M 205 231 L 273 344;M 203 231 L 273 342;M 200 231 L 273 341;M 198 231 L 273 339;M 196 231 L 273 337;M 194 231 L 273 336;M 191 231 L 273 334;M 189 231 L 273 332;M 187 231 L 273 331;M 185 231 L 273 329;M 183 231 L 273 327;M 181 231 L 273 325;M 179 231 L 273 323;M 177 231 L 273 321;M 175 231 L 273 319;M 174 231 L 273 317;M 172 231 L 273 315;M 170 231 L 273 313;M 168 231 L 273 311;M 167 231 L 273 308;M 165 231 L 273 306;M 164 231 L 273 304;M 162 231 L 273 302;M 161 231 L 273 299;M 159 231 L 273 297;M 158 231 L 273 294;M 157 231 L 273 292;M 155 231 L 273 290;M 154 231 L 273 287;M 153 231 L 273 285;M 152 231 L 273 282;M 151 231 L 273 280;M 150 231 L 273 277;M 149 231 L 273 274;M 148 231 L 273 272;M 147 231 L 273 269;M 146 231 L 273 267;M 146 231 L 273 264;M 145 231 L 273 261;M 144 231 L 273 259;M 144 231 L 273 256;M 143 231 L 273 253;M 143 231 L 273 250;M 143 231 L 273 248;M 142 231 L 273 245;M 142 231 L 273 242;M 142 231 L 273 239;M 142 231 L 273 237;M 142 231 L 273 234;M 142 231 L 273 231;M 142 231 L 273 228;M 142 231 L 273 226;M 142 231 L 273 223;M 142 231 L 273 220;M 142 231 L 273 217;M 143 231 L 273 215;M 143 231 L 273 212;M 143 231 L 273 209;M 144 231 L 273 207;M 144 231 L 273 204;M 145 231 L 273 201;M 146 231 L 273 199;M 146 231 L 273 196;M 147 231 L 273 193;M 148 231 L 273 191;M 149 231 L 273 188;M 150 231 L 273 185;M 151 231 L 273 183;M 152 231 L 273 180;M 153 231 L 273 178;M 154 231 L 273 175;M 155 231 L 273 173;M 157 231 L 273 170;M 158 231 L 273 168;M 159 231 L 273 166;M 161 231 L 273 163;M 162 231 L 273 161;M 164 231 L 273 159;M 165 231 L 273 156;M 167 231 L 273 154;M 168 231 L 273 152;M 170 231 L 273 150;M 172 231 L 273 147;M 174 231 L 273 145;M 175 231 L 273 143;M 177 231 L 273 141;M 179 231 L 273 139;M 181 231 L 273 137;M 183 231 L 273 135;M 185 231 L 273 134;M 187 231 L 273 132;M 189 231 L 273 130;M 191 231 L 273 128;M 194 231 L 273 127;M 196 231 L 273 125;M 198 231 L 273 123;M 200 231 L 273 122;M 203 231 L 273 120;M 205 231 L 273 119;M 207 231 L 273 117;M 210 231 L 273 116;M 212 231 L 273 115;M 215 231 L 273 114;M 217 231 L 273 112;M 220 231 L 273 111;M 222 231 L 273 110;M 225 231 L 273 109;M 227 231 L 273 108;M 230 231 L 273 107;M 232 231 L 273 106;M 235 231 L 273 105;M 238 231 L 273 105;M 240 231 L 273 104;M 243 231 L 273 103;M 246 231 L 273 103;M 248 231 L 273 102;M 251 231 L 273 102;M 254 231 L 273 101;M 256 231 L 273 101;M 259 231 L 273 101;M 262 231 L 273 100;M 265 231 L 273 100;M 267 231 L 273 100;M 270 231 L 273 100;M 273 231 L 273 100;M 276 231 L 273 100;M 278 231 L 273 100;M 281 231 L 273 100;M 284 231 L 273 100;M 287 231 L 273 101;M 289 231 L 273 101;M 292 231 L 273 101;M 295 231 L 273 102;M 298 231 L 273 102;M 300 231 L 273 103;M 303 231 L 273 103;M 306 231 L 273 104;M 308 231 L 273 105;M 311 231 L 273 105;M 314 231 L 273 106;M 316 231 L 273 107;M 319 231 L 273 108;M 321 231 L 273 109;M 324 231 L 273 110;M 326 231 L 273 111;M 329 231 L 273 112;M 331 231 L 273 114;M 334 231 L 273 115;M 336 231 L 273 116;M 339 231 L 273 117;M 341 231 L 273 119;M 343 231 L 273 120;M 346 231 L 273 122;M 348 231 L 273 123;M 350 231 L 273 125;M 352 231 L 273 127;M 355 231 L 273 128;M 357 231 L 273 130;M 359 231 L 273 132;M 361 231 L 273 134;M 363 231 L 273 135;M 365 231 L 273 137;M 367 231 L 273 139;M 369 231 L 273 141;M 371 231 L 273 143;M 372 231 L 273 145;M 374 231 L 273 147;M 376 231 L 273 150;M 378 231 L 273 152;M 379 231 L 273 154;M 381 231 L 273 156;M 382 231 L 273 159;M 384 231 L 273 161;M 385 231 L 273 163;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_1-5\" repeatCount=\"indefinite\" values=\"M 387 231 L 273 84;M 388 231 L 273 85;M 389 231 L 273 86;M 391 231 L 273 87;M 392 231 L 273 88;M 393 231 L 273 89;M 394 231 L 273 90;M 395 231 L 273 91;M 396 231 L 273 92;M 397 231 L 273 93;M 398 231 L 273 94;M 399 231 L 273 94;M 399 231 L 273 95;M 400 231 L 273 96;M 401 231 L 273 96;M 401 231 L 273 97;M 402 231 L 273 98;M 402 231 L 273 98;M 403 231 L 273 98;M 403 231 L 273 99;M 404 231 L 273 99;M 404 231 L 273 99;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 100;M 404 231 L 273 99;M 404 231 L 273 99;M 403 231 L 273 99;M 403 231 L 273 98;M 402 231 L 273 98;M 402 231 L 273 98;M 401 231 L 273 97;M 401 231 L 273 96;M 400 231 L 273 96;M 399 231 L 273 95;M 399 231 L 273 94;M 398 231 L 273 94;M 397 231 L 273 93;M 396 231 L 273 92;M 395 231 L 273 91;M 394 231 L 273 90;M 393 231 L 273 89;M 392 231 L 273 88;M 391 231 L 273 87;M 389 231 L 273 86;M 388 231 L 273 85;M 387 231 L 273 84;M 385 231 L 273 83;M 384 231 L 273 82;M 382 231 L 273 81;M 381 231 L 273 80;M 379 231 L 273 79;M 378 231 L 273 78;M 376 231 L 273 77;M 374 231 L 273 75;M 372 231 L 273 74;M 371 231 L 273 73;M 369 231 L 273 72;M 367 231 L 273 71;M 365 231 L 273 70;M 363 231 L 273 69;M 361 231 L 273 68;M 359 231 L 273 66;M 357 231 L 273 65;M 355 231 L 273 64;M 352 231 L 273 63;M 350 231 L 273 62;M 348 231 L 273 61;M 346 231 L 273 60;M 343 231 L 273 59;M 341 231 L 273 58;M 339 231 L 273 57;M 336 231 L 273 57;M 334 231 L 273 56;M 331 231 L 273 55;M 329 231 L 273 54;M 326 231 L 273 53;M 324 231 L 273 53;M 321 231 L 273 52;M 319 231 L 273 51;M 316 231 L 273 51;M 314 231 L 273 50;M 311 231 L 273 49;M 308 231 L 273 49;M 306 231 L 273 48;M 303 231 L 273 48;M 300 231 L 273 47;M 298 231 L 273 47;M 295 231 L 273 47;M 292 231 L 273 46;M 289 231 L 273 46;M 287 231 L 273 46;M 284 231 L 273 46;M 281 231 L 273 46;M 278 231 L 273 46;M 276 231 L 273 45;M 273 231 L 273 45;M 273 231 L 273 45;M 270 231 L 273 45;M 267 231 L 273 46;M 265 231 L 273 46;M 262 231 L 273 46;M 259 231 L 273 46;M 256 231 L 273 46;M 254 231 L 273 46;M 251 231 L 273 47;M 248 231 L 273 47;M 246 231 L 273 47;M 243 231 L 273 48;M 240 231 L 273 48;M 238 231 L 273 49;M 235 231 L 273 49;M 232 231 L 273 50;M 230 231 L 273 51;M 227 231 L 273 51;M 225 231 L 273 52;M 222 231 L 273 53;M 220 231 L 273 53;M 217 231 L 273 54;M 215 231 L 273 55;M 212 231 L 273 56;M 210 231 L 273 57;M 207 231 L 273 57;M 205 231 L 273 58;M 203 231 L 273 59;M 200 231 L 273 60;M 198 231 L 273 61;M 196 231 L 273 62;M 194 231 L 273 63;M 191 231 L 273 64;M 189 231 L 273 65;M 187 231 L 273 66;M 185 231 L 273 68;M 183 231 L 273 69;M 181 231 L 273 70;M 179 231 L 273 71;M 177 231 L 273 72;M 175 231 L 273 73;M 174 231 L 273 74;M 172 231 L 273 75;M 170 231 L 273 77;M 168 231 L 273 78;M 167 231 L 273 79;M 165 231 L 273 80;M 164 231 L 273 81;M 162 231 L 273 82;M 161 231 L 273 83;M 159 231 L 273 84;M 158 231 L 273 85;M 157 231 L 273 86;M 155 231 L 273 87;M 154 231 L 273 88;M 153 231 L 273 89;M 152 231 L 273 90;M 151 231 L 273 91;M 150 231 L 273 92;M 149 231 L 273 93;M 148 231 L 273 94;M 147 231 L 273 94;M 146 231 L 273 95;M 146 231 L 273 96;M 145 231 L 273 96;M 144 231 L 273 97;M 144 231 L 273 98;M 143 231 L 273 98;M 143 231 L 273 98;M 143 231 L 273 99;M 142 231 L 273 99;M 142 231 L 273 99;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 100;M 142 231 L 273 99;M 142 231 L 273 99;M 143 231 L 273 99;M 143 231 L 273 98;M 143 231 L 273 98;M 144 231 L 273 98;M 144 231 L 273 97;M 145 231 L 273 96;M 146 231 L 273 96;M 146 231 L 273 95;M 147 231 L 273 94;M 148 231 L 273 94;M 149 231 L 273 93;M 150 231 L 273 92;M 151 231 L 273 91;M 152 231 L 273 90;M 153 231 L 273 89;M 154 231 L 273 88;M 155 231 L 273 87;M 157 231 L 273 86;M 158 231 L 273 85;M 159 231 L 273 84;M 161 231 L 273 83;M 162 231 L 273 82;M 164 231 L 273 81;M 165 231 L 273 80;M 167 231 L 273 79;M 168 231 L 273 78;M 170 231 L 273 77;M 172 231 L 273 75;M 174 231 L 273 74;M 175 231 L 273 73;M 177 231 L 273 72;M 179 231 L 273 71;M 181 231 L 273 70;M 183 231 L 273 69;M 185 231 L 273 68;M 187 231 L 273 66;M 189 231 L 273 65;M 191 231 L 273 64;M 194 231 L 273 63;M 196 231 L 273 62;M 198 231 L 273 61;M 200 231 L 273 60;M 203 231 L 273 59;M 205 231 L 273 58;M 207 231 L 273 57;M 210 231 L 273 57;M 212 231 L 273 56;M 215 231 L 273 55;M 217 231 L 273 54;M 220 231 L 273 53;M 222 231 L 273 53;M 225 231 L 273 52;M 227 231 L 273 51;M 230 231 L 273 51;M 232 231 L 273 50;M 235 231 L 273 49;M 238 231 L 273 49;M 240 231 L 273 48;M 243 231 L 273 48;M 246 231 L 273 47;M 248 231 L 273 47;M 251 231 L 273 47;M 254 231 L 273 46;M 256 231 L 273 46;M 259 231 L 273 46;M 262 231 L 273 46;M 265 231 L 273 46;M 267 231 L 273 46;M 270 231 L 273 45;M 273 231 L 273 45;M 276 231 L 273 45;M 278 231 L 273 46;M 281 231 L 273 46;M 284 231 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_1-6\" repeatCount=\"indefinite\" values=\"M 387 231 L 273 428;M 388 231 L 273 427;M 389 231 L 273 427;M 391 231 L 273 426;M 392 231 L 273 425;M 393 231 L 273 424;M 394 231 L 273 424;M 395 231 L 273 423;M 396 231 L 273 422;M 397 231 L 273 422;M 398 231 L 273 421;M 399 231 L 273 421;M 399 231 L 273 420;M 400 231 L 273 420;M 401 231 L 273 419;M 401 231 L 273 419;M 402 231 L 273 419;M 402 231 L 273 418;M 403 231 L 273 418;M 403 231 L 273 418;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 404 231 L 273 417;M 403 231 L 273 418;M 403 231 L 273 418;M 402 231 L 273 418;M 402 231 L 273 419;M 401 231 L 273 419;M 401 231 L 273 419;M 400 231 L 273 420;M 399 231 L 273 420;M 399 231 L 273 421;M 398 231 L 273 421;M 397 231 L 273 422;M 396 231 L 273 422;M 395 231 L 273 423;M 394 231 L 273 424;M 393 231 L 273 424;M 392 231 L 273 425;M 391 231 L 273 426;M 389 231 L 273 427;M 388 231 L 273 427;M 387 231 L 273 428;M 385 231 L 273 429;M 384 231 L 273 430;M 382 231 L 273 431;M 381 231 L 273 431;M 379 231 L 273 432;M 378 231 L 273 433;M 376 231 L 273 434;M 374 231 L 273 435;M 372 231 L 273 436;M 371 231 L 273 437;M 369 231 L 273 438;M 367 231 L 273 438;M 365 231 L 273 439;M 363 231 L 273 440;M 361 231 L 273 441;M 359 231 L 273 442;M 357 231 L 273 443;M 355 231 L 273 444;M 352 231 L 273 444;M 350 231 L 273 445;M 348 231 L 273 446;M 346 231 L 273 447;M 343 231 L 273 448;M 341 231 L 273 448;M 339 231 L 273 449;M 336 231 L 273 450;M 334 231 L 273 450;M 331 231 L 273 451;M 329 231 L 273 452;M 326 231 L 273 452;M 324 231 L 273 453;M 321 231 L 273 453;M 319 231 L 273 454;M 316 231 L 273 455;M 314 231 L 273 455;M 311 231 L 273 455;M 308 231 L 273 456;M 306 231 L 273 456;M 303 231 L 273 457;M 300 231 L 273 457;M 298 231 L 273 457;M 295 231 L 273 458;M 292 231 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L 273 422;M 151 231 L 273 423;M 152 231 L 273 424;M 153 231 L 273 424;M 154 231 L 273 425;M 155 231 L 273 426;M 157 231 L 273 427;M 158 231 L 273 427;M 159 231 L 273 428;M 161 231 L 273 429;M 162 231 L 273 430;M 164 231 L 273 431;M 165 231 L 273 431;M 167 231 L 273 432;M 168 231 L 273 433;M 170 231 L 273 434;M 172 231 L 273 435;M 174 231 L 273 436;M 175 231 L 273 437;M 177 231 L 273 438;M 179 231 L 273 438;M 181 231 L 273 439;M 183 231 L 273 440;M 185 231 L 273 441;M 187 231 L 273 442;M 189 231 L 273 443;M 191 231 L 273 444;M 194 231 L 273 444;M 196 231 L 273 445;M 198 231 L 273 446;M 200 231 L 273 447;M 203 231 L 273 448;M 205 231 L 273 448;M 207 231 L 273 449;M 210 231 L 273 450;M 212 231 L 273 450;M 215 231 L 273 451;M 217 231 L 273 452;M 220 231 L 273 452;M 222 231 L 273 453;M 225 231 L 273 453;M 227 231 L 273 454;M 230 231 L 273 455;M 232 231 L 273 455;M 235 231 L 273 455;M 238 231 L 273 456;M 240 231 L 273 456;M 243 231 L 273 457;M 246 231 L 273 457;M 248 231 L 273 457;M 251 231 L 273 458;M 254 231 L 273 458;M 256 231 L 273 458;M 259 231 L 273 458;M 262 231 L 273 458;M 265 231 L 273 459;M 267 231 L 273 459;M 270 231 L 273 459;M 273 231 L 273 459;M 276 231 L 273 459;M 278 231 L 273 459;M 281 231 L 273 459;M 284 231 L 273 458;M 287 231 L 273 458;M 289 231 L 273 458;M 292 231 L 273 458;M 295 231 L 273 458;M 298 231 L 273 457;M 300 231 L 273 457;M 303 231 L 273 457;M 306 231 L 273 456;M 308 231 L 273 456;M 311 231 L 273 455;M 314 231 L 273 455;M 316 231 L 273 455;M 319 231 L 273 454;M 321 231 L 273 453;M 324 231 L 273 453;M 326 231 L 273 452;M 329 231 L 273 452;M 331 231 L 273 451;M 334 231 L 273 450;M 336 231 L 273 450;M 339 231 L 273 449;M 341 231 L 273 448;M 343 231 L 273 448;M 346 231 L 273 447;M 348 231 L 273 446;M 350 231 L 273 445;M 352 231 L 273 444;M 355 231 L 273 444;M 357 231 L 273 443;M 359 231 L 273 442;M 361 231 L 273 441;M 363 231 L 273 440;M 365 231 L 273 439;M 367 231 L 273 438;M 369 231 L 273 438;M 371 231 L 273 437;M 372 231 L 273 436;M 374 231 L 273 435;M 376 231 L 273 434;M 378 231 L 273 433;M 379 231 L 273 432;M 381 231 L 273 431;M 382 231 L 273 431;M 384 231 L 273 430;M 385 231 L 273 429;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_2-4\" repeatCount=\"indefinite\" values=\"M 447 231 L 273 166;M 448 231 L 273 168;M 448 231 L 273 170;M 449 231 L 273 173;M 450 231 L 273 175;M 451 231 L 273 178;M 452 231 L 273 180;M 452 231 L 273 183;M 453 231 L 273 185;M 454 231 L 273 188;M 454 231 L 273 191;M 455 231 L 273 193;M 455 231 L 273 196;M 456 231 L 273 199;M 456 231 L 273 201;M 457 231 L 273 204;M 457 231 L 273 207;M 457 231 L 273 209;M 458 231 L 273 212;M 458 231 L 273 215;M 458 231 L 273 217;M 458 231 L 273 220;M 458 231 L 273 223;M 459 231 L 273 226;M 459 231 L 273 228;M 459 231 L 273 231;M 459 231 L 273 234;M 459 231 L 273 237;M 458 231 L 273 239;M 458 231 L 273 242;M 458 231 L 273 245;M 458 231 L 273 248;M 458 231 L 273 250;M 457 231 L 273 253;M 457 231 L 273 256;M 457 231 L 273 259;M 456 231 L 273 261;M 456 231 L 273 264;M 455 231 L 273 267;M 455 231 L 273 269;M 454 231 L 273 272;M 454 231 L 273 274;M 453 231 L 273 277;M 452 231 L 273 280;M 452 231 L 273 282;M 451 231 L 273 285;M 450 231 L 273 287;M 449 231 L 273 290;M 448 231 L 273 292;M 448 231 L 273 294;M 447 231 L 273 297;M 446 231 L 273 299;M 445 231 L 273 302;M 444 231 L 273 304;M 443 231 L 273 306;M 442 231 L 273 308;M 441 231 L 273 311;M 440 231 L 273 313;M 439 231 L 273 315;M 438 231 L 273 317;M 437 231 L 273 319;M 435 231 L 273 321;M 434 231 L 273 323;M 433 231 L 273 325;M 432 231 L 273 327;M 431 231 L 273 329;M 430 231 L 273 331;M 429 231 L 273 332;M 428 231 L 273 334;M 426 231 L 273 336;M 425 231 L 273 337;M 424 231 L 273 339;M 423 231 L 273 341;M 422 231 L 273 342;M 421 231 L 273 344;M 420 231 L 273 345;M 419 231 L 273 346;M 418 231 L 273 348;M 417 231 L 273 349;M 416 231 L 273 350;M 415 231 L 273 351;M 414 231 L 273 352;M 413 231 L 273 353;M 412 231 L 273 354;M 411 231 L 273 355;M 410 231 L 273 356;M 410 231 L 273 357;M 409 231 L 273 358;M 408 231 L 273 358;M 408 231 L 273 359;M 407 231 L 273 360;M 407 231 L 273 360;M 406 231 L 273 361;M 406 231 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L 273 185;M 452 231 L 273 183;M 452 231 L 273 180;M 451 231 L 273 178;M 450 231 L 273 175;M 449 231 L 273 173;M 448 231 L 273 170;M 448 231 L 273 168;M 447 231 L 273 166;M 446 231 L 273 163;M 445 231 L 273 161;M 444 231 L 273 159;M 443 231 L 273 156;M 442 231 L 273 154;M 441 231 L 273 152;M 440 231 L 273 150;M 439 231 L 273 147;M 438 231 L 273 145;M 437 231 L 273 143;M 435 231 L 273 141;M 434 231 L 273 139;M 433 231 L 273 137;M 432 231 L 273 135;M 431 231 L 273 134;M 430 231 L 273 132;M 429 231 L 273 130;M 428 231 L 273 128;M 426 231 L 273 127;M 425 231 L 273 125;M 424 231 L 273 123;M 423 231 L 273 122;M 422 231 L 273 120;M 421 231 L 273 119;M 420 231 L 273 117;M 419 231 L 273 116;M 418 231 L 273 115;M 417 231 L 273 114;M 416 231 L 273 112;M 415 231 L 273 111;M 414 231 L 273 110;M 413 231 L 273 109;M 412 231 L 273 108;M 411 231 L 273 107;M 410 231 L 273 106;M 410 231 L 273 105;M 409 231 L 273 105;M 408 231 L 273 104;M 408 231 L 273 103;M 407 231 L 273 103;M 407 231 L 273 102;M 406 231 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L 273 147;M 440 231 L 273 150;M 441 231 L 273 152;M 442 231 L 273 154;M 443 231 L 273 156;M 444 231 L 273 159;M 445 231 L 273 161;M 446 231 L 273 163;\"/>\n",
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83;M 445 231 L 273 82;M 444 231 L 273 81;M 443 231 L 273 80;M 442 231 L 273 79;M 441 231 L 273 78;M 440 231 L 273 77;M 439 231 L 273 75;M 438 231 L 273 74;M 437 231 L 273 73;M 435 231 L 273 72;M 434 231 L 273 71;M 433 231 L 273 70;M 432 231 L 273 69;M 431 231 L 273 68;M 430 231 L 273 66;M 429 231 L 273 65;M 428 231 L 273 64;M 426 231 L 273 63;M 425 231 L 273 62;M 424 231 L 273 61;M 423 231 L 273 60;M 422 231 L 273 59;M 421 231 L 273 58;M 420 231 L 273 57;M 419 231 L 273 57;M 418 231 L 273 56;M 417 231 L 273 55;M 416 231 L 273 54;M 415 231 L 273 53;M 414 231 L 273 53;M 413 231 L 273 52;M 412 231 L 273 51;M 411 231 L 273 51;M 410 231 L 273 50;M 410 231 L 273 49;M 409 231 L 273 49;M 408 231 L 273 48;M 408 231 L 273 48;M 407 231 L 273 47;M 407 231 L 273 47;M 406 231 L 273 47;M 406 231 L 273 46;M 405 231 L 273 46;M 405 231 L 273 46;M 405 231 L 273 46;M 405 231 L 273 46;M 404 231 L 273 46;M 404 231 L 273 45;M 404 231 L 273 45;M 404 231 L 273 45;M 404 231 L 273 46;M 405 231 L 273 46;M 405 231 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_2-6\" repeatCount=\"indefinite\" values=\"M 447 231 L 273 428;M 448 231 L 273 427;M 448 231 L 273 427;M 449 231 L 273 426;M 450 231 L 273 425;M 451 231 L 273 424;M 452 231 L 273 424;M 452 231 L 273 423;M 453 231 L 273 422;M 454 231 L 273 422;M 454 231 L 273 421;M 455 231 L 273 421;M 455 231 L 273 420;M 456 231 L 273 420;M 456 231 L 273 419;M 457 231 L 273 419;M 457 231 L 273 419;M 457 231 L 273 418;M 458 231 L 273 418;M 458 231 L 273 418;M 458 231 L 273 417;M 458 231 L 273 417;M 458 231 L 273 417;M 459 231 L 273 417;M 459 231 L 273 417;M 459 231 L 273 417;M 459 231 L 273 417;M 459 231 L 273 417;M 458 231 L 273 417;M 458 231 L 273 417;M 458 231 L 273 417;M 458 231 L 273 418;M 458 231 L 273 418;M 457 231 L 273 418;M 457 231 L 273 419;M 457 231 L 273 419;M 456 231 L 273 419;M 456 231 L 273 420;M 455 231 L 273 420;M 455 231 L 273 421;M 454 231 L 273 421;M 454 231 L 273 422;M 453 231 L 273 422;M 452 231 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       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_3-4\" repeatCount=\"indefinite\" values=\"M 55 231 L 273 166;M 54 231 L 273 168;M 54 231 L 273 170;M 53 231 L 273 173;M 52 231 L 273 175;M 52 231 L 273 178;M 51 231 L 273 180;M 51 231 L 273 183;M 50 231 L 273 185;M 50 231 L 273 188;M 49 231 L 273 191;M 49 231 L 273 193;M 48 231 L 273 196;M 48 231 L 273 199;M 47 231 L 273 201;M 47 231 L 273 204;M 47 231 L 273 207;M 47 231 L 273 209;M 46 231 L 273 212;M 46 231 L 273 215;M 46 231 L 273 217;M 46 231 L 273 220;M 46 231 L 273 223;M 46 231 L 273 226;M 45 231 L 273 228;M 45 231 L 273 231;M 45 231 L 273 234;M 46 231 L 273 237;M 46 231 L 273 239;M 46 231 L 273 242;M 46 231 L 273 245;M 46 231 L 273 248;M 46 231 L 273 250;M 47 231 L 273 253;M 47 231 L 273 256;M 47 231 L 273 259;M 47 231 L 273 261;M 48 231 L 273 264;M 48 231 L 273 267;M 49 231 L 273 269;M 49 231 L 273 272;M 50 231 L 273 274;M 50 231 L 273 277;M 51 231 L 273 280;M 51 231 L 273 282;M 52 231 L 273 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L 273 101;M 86 231 L 273 101;M 86 231 L 273 101;M 86 231 L 273 102;M 86 231 L 273 102;M 85 231 L 273 103;M 85 231 L 273 103;M 84 231 L 273 104;M 84 231 L 273 105;M 83 231 L 273 105;M 83 231 L 273 106;M 82 231 L 273 107;M 82 231 L 273 108;M 81 231 L 273 109;M 80 231 L 273 110;M 80 231 L 273 111;M 79 231 L 273 112;M 78 231 L 273 114;M 77 231 L 273 115;M 77 231 L 273 116;M 76 231 L 273 117;M 75 231 L 273 119;M 74 231 L 273 120;M 73 231 L 273 122;M 73 231 L 273 123;M 72 231 L 273 125;M 71 231 L 273 127;M 70 231 L 273 128;M 69 231 L 273 130;M 68 231 L 273 132;M 67 231 L 273 134;M 67 231 L 273 135;M 66 231 L 273 137;M 65 231 L 273 139;M 64 231 L 273 141;M 63 231 L 273 143;M 62 231 L 273 145;M 61 231 L 273 147;M 61 231 L 273 150;M 60 231 L 273 152;M 59 231 L 273 154;M 58 231 L 273 156;M 57 231 L 273 159;M 57 231 L 273 161;M 56 231 L 273 163;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_3-5\" repeatCount=\"indefinite\" values=\"M 55 231 L 273 84;M 54 231 L 273 85;M 54 231 L 273 86;M 53 231 L 273 87;M 52 231 L 273 88;M 52 231 L 273 89;M 51 231 L 273 90;M 51 231 L 273 91;M 50 231 L 273 92;M 50 231 L 273 93;M 49 231 L 273 94;M 49 231 L 273 94;M 48 231 L 273 95;M 48 231 L 273 96;M 47 231 L 273 96;M 47 231 L 273 97;M 47 231 L 273 98;M 47 231 L 273 98;M 46 231 L 273 98;M 46 231 L 273 99;M 46 231 L 273 99;M 46 231 L 273 99;M 46 231 L 273 100;M 46 231 L 273 100;M 45 231 L 273 100;M 45 231 L 273 100;M 45 231 L 273 100;M 46 231 L 273 100;M 46 231 L 273 100;M 46 231 L 273 99;M 46 231 L 273 99;M 46 231 L 273 99;M 46 231 L 273 98;M 47 231 L 273 98;M 47 231 L 273 98;M 47 231 L 273 97;M 47 231 L 273 96;M 48 231 L 273 96;M 48 231 L 273 95;M 49 231 L 273 94;M 49 231 L 273 94;M 50 231 L 273 93;M 50 231 L 273 92;M 51 231 L 273 91;M 51 231 L 273 90;M 52 231 L 273 89;M 52 231 L 273 88;M 53 231 L 273 87;M 54 231 L 273 86;M 54 231 L 273 85;M 55 231 L 273 84;M 56 231 L 273 83;M 57 231 L 273 82;M 57 231 L 273 81;M 58 231 L 273 80;M 59 231 L 273 79;M 60 231 L 273 78;M 61 231 L 273 77;M 61 231 L 273 75;M 62 231 L 273 74;M 63 231 L 273 73;M 64 231 L 273 72;M 65 231 L 273 71;M 66 231 L 273 70;M 67 231 L 273 69;M 67 231 L 273 68;M 68 231 L 273 66;M 69 231 L 273 65;M 70 231 L 273 64;M 71 231 L 273 63;M 72 231 L 273 62;M 73 231 L 273 61;M 73 231 L 273 60;M 74 231 L 273 59;M 75 231 L 273 58;M 76 231 L 273 57;M 77 231 L 273 57;M 77 231 L 273 56;M 78 231 L 273 55;M 79 231 L 273 54;M 80 231 L 273 53;M 80 231 L 273 53;M 81 231 L 273 52;M 82 231 L 273 51;M 82 231 L 273 51;M 83 231 L 273 50;M 83 231 L 273 49;M 84 231 L 273 49;M 84 231 L 273 48;M 85 231 L 273 48;M 85 231 L 273 47;M 86 231 L 273 47;M 86 231 L 273 47;M 86 231 L 273 46;M 86 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 45;M 87 231 L 273 45;M 87 231 L 273 45;M 87 231 L 273 45;M 87 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 46;M 87 231 L 273 46;M 86 231 L 273 46;M 86 231 L 273 46;M 86 231 L 273 47;M 86 231 L 273 47;M 85 231 L 273 47;M 85 231 L 273 48;M 84 231 L 273 48;M 84 231 L 273 49;M 83 231 L 273 49;M 83 231 L 273 50;M 82 231 L 273 51;M 82 231 L 273 51;M 81 231 L 273 52;M 80 231 L 273 53;M 80 231 L 273 53;M 79 231 L 273 54;M 78 231 L 273 55;M 77 231 L 273 56;M 77 231 L 273 57;M 76 231 L 273 57;M 75 231 L 273 58;M 74 231 L 273 59;M 73 231 L 273 60;M 73 231 L 273 61;M 72 231 L 273 62;M 71 231 L 273 63;M 70 231 L 273 64;M 69 231 L 273 65;M 68 231 L 273 66;M 67 231 L 273 68;M 67 231 L 273 69;M 66 231 L 273 70;M 65 231 L 273 71;M 64 231 L 273 72;M 63 231 L 273 73;M 62 231 L 273 74;M 61 231 L 273 75;M 61 231 L 273 77;M 60 231 L 273 78;M 59 231 L 273 79;M 58 231 L 273 80;M 57 231 L 273 81;M 57 231 L 273 82;M 56 231 L 273 83;M 55 231 L 273 84;M 54 231 L 273 85;M 54 231 L 273 86;M 53 231 L 273 87;M 52 231 L 273 88;M 52 231 L 273 89;M 51 231 L 273 90;M 51 231 L 273 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231 L 273 52;M 80 231 L 273 53;M 80 231 L 273 53;M 79 231 L 273 54;M 78 231 L 273 55;M 77 231 L 273 56;M 77 231 L 273 57;M 76 231 L 273 57;M 75 231 L 273 58;M 74 231 L 273 59;M 73 231 L 273 60;M 73 231 L 273 61;M 72 231 L 273 62;M 71 231 L 273 63;M 70 231 L 273 64;M 69 231 L 273 65;M 68 231 L 273 66;M 67 231 L 273 68;M 67 231 L 273 69;M 66 231 L 273 70;M 65 231 L 273 71;M 64 231 L 273 72;M 63 231 L 273 73;M 62 231 L 273 74;M 61 231 L 273 75;M 61 231 L 273 77;M 60 231 L 273 78;M 59 231 L 273 79;M 58 231 L 273 80;M 57 231 L 273 81;M 57 231 L 273 82;M 56 231 L 273 83;\"/>\n",
       "<animate attributeName=\"d\" calcMode=\"linear\" dur=\"12s\" href=\"#edge_b4b9aa_3-6\" repeatCount=\"indefinite\" values=\"M 55 231 L 273 428;M 54 231 L 273 427;M 54 231 L 273 427;M 53 231 L 273 426;M 52 231 L 273 425;M 52 231 L 273 424;M 51 231 L 273 424;M 51 231 L 273 423;M 50 231 L 273 422;M 50 231 L 273 422;M 49 231 L 273 421;M 49 231 L 273 421;M 48 231 L 273 420;M 48 231 L 273 420;M 47 231 L 273 419;M 47 231 L 273 419;M 47 231 L 273 419;M 47 231 L 273 418;M 46 231 L 273 418;M 46 231 L 273 418;M 46 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 417;M 45 231 L 273 417;M 45 231 L 273 417;M 45 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 417;M 46 231 L 273 418;M 46 231 L 273 418;M 47 231 L 273 418;M 47 231 L 273 419;M 47 231 L 273 419;M 47 231 L 273 419;M 48 231 L 273 420;M 48 231 L 273 420;M 49 231 L 273 421;M 49 231 L 273 421;M 50 231 L 273 422;M 50 231 L 273 422;M 51 231 L 273 423;M 51 231 L 273 424;M 52 231 L 273 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L 273 458;M 86 231 L 273 458;M 86 231 L 273 458;M 86 231 L 273 458;M 86 231 L 273 457;M 85 231 L 273 457;M 85 231 L 273 457;M 84 231 L 273 456;M 84 231 L 273 456;M 83 231 L 273 455;M 83 231 L 273 455;M 82 231 L 273 455;M 82 231 L 273 454;M 81 231 L 273 453;M 80 231 L 273 453;M 80 231 L 273 452;M 79 231 L 273 452;M 78 231 L 273 451;M 77 231 L 273 450;M 77 231 L 273 450;M 76 231 L 273 449;M 75 231 L 273 448;M 74 231 L 273 448;M 73 231 L 273 447;M 73 231 L 273 446;M 72 231 L 273 445;M 71 231 L 273 444;M 70 231 L 273 444;M 69 231 L 273 443;M 68 231 L 273 442;M 67 231 L 273 441;M 67 231 L 273 440;M 66 231 L 273 439;M 65 231 L 273 438;M 64 231 L 273 438;M 63 231 L 273 437;M 62 231 L 273 436;M 61 231 L 273 435;M 61 231 L 273 434;M 60 231 L 273 433;M 59 231 L 273 432;M 58 231 L 273 431;M 57 231 L 273 431;M 57 231 L 273 430;M 56 231 L 273 429;\"/>\n",
       "</svg>"
      ],
      "text/plain": [
       "<IPython.core.display.SVG object>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = GraphMotion.ParametrizedMotion(K33, P, 'symbolic')\n",
    "M.animation_SVG('animations/K33', edge_partition=[])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "collisions = {\n",
    "    1: [[4,2],[4,3]],\n",
    "    4: [[1,6], [1,5]]\n",
    "}\n",
    "h_fun = M.height_function(collisions); h_fun\n",
    "name = 'K33'\n",
    "M.generate_POVray(name, h_fun, antialias=False, frames=100, width=320, height=240)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import subprocess\n",
    "subprocess.call(['mkdir', 'img_'+name])\n",
    "subprocess.call(['povray', name+'.ini']) # not installed in Binder "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "subprocess.call(['ffmpeg', '-y', '-framerate', '24', '-i', \n",
    "                 'img_'+name+'/'+name+'%03d.png', '-vb', '2M', name+'.mp4'])  # not installed in Binder "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"100%\" controls> <source src=\"K33.mp4\" type=\"video/mp4\"> </video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<video width=\"100%\" controls> <source src=\"K33.mp4\" type=\"video/mp4\"> </video>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=\"100%\" controls> <source src=\"https://jan.legersky.cz/img/K33.mp4\" type=\"video/mp4\"> </video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<video width=\"100%\" controls> <source src=\"https://jan.legersky.cz/img/K33.mp4\" type=\"video/mp4\"> </video>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# from IPython.core.display import display, HTML\n",
    "# display(HTML(\"<style>.rendered_html { font-size: 25px; }</style>\"))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 7.5.1",
   "language": "",
   "name": "sagemath"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}