{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "458e426e-d9b8-449b-be2e-8de5c78c0852",
   "metadata": {},
   "source": [
    "# A test notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d5c4982-ad22-4339-8ec5-2866b62fe32d",
   "metadata": {},
   "source": [
    "Just a test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bacc4b48-257e-46f1-ad3e-b7fb889f2467",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-1/2, 1/2), (1/2, -1/2)]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x,y = var('x,y')\n",
    "eqs = [x^2-3*x*y==1, y^2-3*x*y==1]\n",
    "sols = solve(eqs, [x,y])\n",
    "sols = [tuple([s.rhs() for s in sol]) for sol in sols\n",
    "    if all(eq.rhs().is_real() for eq in sol)]\n",
    "sols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "557a044f-d442-45c8-8be8-985070cbf72d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cYjIh1mr/3/9Mjm4RCQvtkxaxsa+/NudmzSwI0JwIb9fOBGhWt5o4UQFaxKZcM9wt4hRcq8UCU3TvvRY0gJnEuPeL6T6nTTP7okXElhSkRcJs61Zgxw4gZUqgUSMLlpS/+qq55kru8uXD3AARSQwFaZEwmzkzpqBG+vRhfODdu4FHHjFd+WefBZ58MowPLiJJoSAtYlGQvv/+MD7omTPmAY8fB6pVA0aPDuODi0hSKUiLhLkzu2EDcMstYQzS7Dk/9RTwyy9AjhzA9OlmX7SI2J6CtEgYMT5S3bpA9uxhXCg2dapZRs6tVpalNxORxFKQFgkjxkji1uSwmD0b6NfPXI8ZY0pQiohjKEiLhHGom0m+ONQdliDN4e22bc11585Ax45heFARCSYFaZEwYWrswFB3zpwhfrCDB02+US4YY7Hqt98O8QOKSCgoSIuEyRdfmPPDD4f4gRiYW7QA9u8HSpQwY+wpUoT4QUUkFFwTpFVgQ+wsMhL4+Wezduuhh0L4QJcumSFuLiHPlg2YNw/InDmEDygioeSaIN25c2dERkZi3bp1VjdF5Cqff27OjRsDWbOGcKtV165msRi3WPFcpIjeDREHc02QFrEr1rOYMsVcB9ZxhcSbbwLjxpliGZMnA7VqhfDBRCQcFKRFQuyHH4C9e4EMGYD77gvRg0yaBPTpY665SKxVqxA9kIiEk4K0SIh9+qk5cy46TZoQPMDcuTF5uHv2BLp1C8GDiIgVFKRFQrzQOrD1qkOHEDzAihUm+nPB2GOPmSFvEXENBWmREKcBPX0auO024M47g/yfb9pk9kKfO2fOH31kMqWIiGvoN1okhCZOjOlFcz1XUPd03XMPEBUF1K5tuuvaCy3iOgrSIiGyYwewfLnp3AZ1qPu330wx6qNHgcqVga+/DtFkt4hYTUFaJEQ+/NCcmzYNYuGpPXtMmk+m/SxXDvj2WyBjxiD95yJiNwrSIiFw/jzw8cfm+umngxigmfh73z6T7nPRohBmRhERO1CQFgnRgjGORrMH3axZEAM0N1wXKwYsXhyGKh0iYjXXBGnl7hY7YeKvQC+a+bpvyu+/Xxmgly4F8uQJRjNFxOaS+XxM+OseUVFRyJgxI06ePIkMTPEkEmbcGVWxognOjKs3FU+3bo2Zgy5eHFiyRAFaxEOxyjU9aRG7GDvWnB988CbjKaN9nTomQJctCyxbpgAt4jEK0iJBxHnoQDGNLl1uMpMYh7iPHDHbrDjEnStXsJopIg6hIC0SRO+/bxKAVaoE3HFHEv+Tb74BGjYETp40/8n332sVt4hHKUiLBMmFCzFD3T16JDHDGKtZ3X+/ifRcFr5wofZBi3iYgrRIkHz+uZk+5jz0ww8n8pu5fnPIEKB9e1Mso107YOZMIG1avT8iHqYgLRIEjLHDh5trVopMmTIR33zxIvDcc8Arr5ive/UCPvlEubhFBDe7g1NEAMyfD2zZAqRLBzz7bCJeEs47t2kDLFhgxsfffRfo3FmvqYj4KUiLBMGwYebMAJ0pUyKyiLHEJKM7C2RwvJzz0SIi/1KQFrlJrHT1ww9miPvFFxP4TfyGBx4wW6xy5zaVrLjVSkQkFs1Ji9ykoUPN+YknEphrZMIEoH59E6ArVADWrlWAFpF4KUiL3IQ1a0y1yIgIs97rhqWxuECsY0fgn3+AVq1MjzpodSxFxG1cE6RVYEOsMGiQOT/+OFCkyHXuuH8/cNddJtsJF4ix+z11KnDrreFqqog4kApsiNxEL7pGDeCWW4Dt24GiRa9xRyYkadvW5AzNnBn47DOgSRO97iIeFqUCGyKhFdjWzPwj8QZo7n/u1w9o3NgEaJbG2rBBAVpEEkyru0WSgPUuvvvO5Bvp3/8aw9vsPbNQBnEe+u23zVYrEZEEUpAWSUJ2sT59zPUzzwCFCsW5w7Rp5h9OnADSpwc++ABo3Vqvs4gkmoK0SCLNng2sXm3SageGvP1Onwa6dwcmTjRfV61qEpRcc7JaRMQjq7tFwoHTzH37mmvGY+Yh8eNWqvLlTYDm6m12tX/8UQFaRG6KetIiifDhh8DWraa8s39f9N9/m0npESPMOHiBAsCnnwJ16+p1FZGbpiAtcg2XL1/GvHnz8NFHH2Hfvn3InLkg1q79DEBqDBgAZNz8A/Dkk8DOnTEpx0aNAjJk0GsqIs4Z7h43bhwKFy6M1KlTo3LlylgRWPEaj6VLlyJZsmRXHdu2bQtHU0X8zp07h2bNmqFFixaYOXMmNmzYgO++q46oqNTIlnIznvjpaZOchAGauUDnzAE++kgBWkScFaSnTp2K7t27o1+/fti4cSNq166NJk2a+Hsm17N9+3YcPHgw+ihWrFiomyoSrWfPnljA8pHR+PPXHfdhFjZeqIZbP55ohrfZe2YVqxYt9OqJiPMyjlWvXh2VKlXCe++9F31bqVKlcP/992NYoL5fnJ50vXr1cPz4cWRKcM2/xGdxEbmWEydOIG/evDh79mz0bQXxAUZjDu7F1/6vOcCd6qOPUIBBWkTEiRnHLly44B8mbNiw4RW38+uVK1de93srVqyI3Llzo0GDBliyZMk173f+/Hn/k419iNwMTscEAnQqAP1QHFvxvD9A/8OqVwBuBzBTP2siEmIhDdJHjx7FpUuXkDNnzitu59eHDh2K93sYmCdMmIDp06djxowZKFGihD9QL2fR3niwN85PI4Ejf/78IXku4h0Xuc8KwP0AIpEMg7EDaXAOS1AE5f1BGzgX634iIo5e3c2FX7FxhD3ubQEMyjwCatasif3792P48OG4iwt14ujTpw9eeOGF6K/Zk1aglptRK21afA+gvvlpxQHkRS+8jC/Q+4r71WB1DRERp/aks2XLhoiIiKt6zYcPH76qd309/GO4M7DNJY5UqVL5x/NjHyJJ8scf/i1VOZs08Qfoc0iG19EHJbAdX2ApgJg56goVKuCOO+7QCy0izg3SKVOm9G+5WrRo0RW38+tatWol+P/hqnAOg4uExPHjwMsvm+xgH3/sX7X99333o3zKOeiPoTjr71fPiL47P2B+znSfIiJOH+7mUHS7du1QpUoV/9A155u5/eq5556LHq7+448/MGnSJP/Xo0aNQqFChVCmTBn/wrMpU6b456d5iAQVc22PHg3897+mGAaxdzx8OD7ZWAM7ZvOD5nnkyPEGDh6MQPbs2f0/y926dfOv/hYRcXyQbt26NY4dO4ZBgwb59zuXLVvWn8WpYMGC/n/nbbH3TDMwc48qA3eaNGn8wXru3Llo2rRpqJsqXsGV2+PHA2+8ARw5Ym4rW5arEIFmzbBvfzL0usfc/N//pkLXrtffiSAi4th90uGmfdJyTWfOANyvz57z4cPmtttuAwYOBNq0ASIi/PlJGjcGFi4EOCPDTQUREXpNRcSaWKXc3eKNOeexY01e7WPHzG2FC5tyVu3bAylSRN+VRawYoFOnNlk+FaBFxEoK0uJeBw4A77wDvP8+cOpUTM+5Xz/gsceuCM60ezfQo4e5fv11bge0oM0iIrEoSIv7bNoEjBwJfPGFKQAdmHNmz7lVKyD51T/2ly6ZTjXXktWuHROsRUSspCAt7sAoO3cu8PbbTAAfc3udOqyWAXDh4S3X3nH41ltMBwqkS2fKQWuYW0TsQEFanI1zzJw8HjcO2LPH3MYI+9BDwIsvAlWr3vC/WLMGePVVc/3uu2a6WkTEDhSkxXm4BHvVKrON6quvWGXF3J4lC/D000CXLkACc7izRsajj5qOeOvWZshbRMQuXBOkx44d6z9Y0ENc3GueMgX48EPg119jbq9Y0QTmRx4B0qRJVKzv2BHYtQsoUMDE/GuklBcRsYT2SYu9ceEX08p+8gkwaxaz3ZjbGYy5t5lRtlq1JEXXCRPMt3MdGfdD16wZ/OaLiMRH+6TF2X75BZg8GfjsM6ali7m9QgXgmWfMGHWmTDe1ALxbN3M9dKgCtIjYk2uGu8UFuPDryy/N1ikG6YCsWYG2bYEnnjBBOgi5TR58EDh3ziz65voyERE7UpAW68tD/u9/wNSpwOrVMbcz0UiLFsDjjwNNmrDSRVAe7vJl819yHprp49lZv87OLBERSylIS/jt3QvMmAFMmwasjFW8gvPKdeuaoewHHjCrtYOMmcS++cak/WQTQvAQIiJBoyAtocdl1FyNzYVfPH766cp/ZyUL7n/i3uY8eULWjJkzgQEDzDXrbFSqFLKHEhEJCgVpCQ1O+C5bZrKAzZljes8BHF++806TorNlSyAMtZk3bwbatTPXXbsCHTqE/CFFRG6agrQED+uCz59vju++M6UhAzi+fPfdJihzrjl79rC98n/9ZR6SzalfHxg+PGwPLSIetHWrmUrLmfPm/y8FaUk6Rj1uMGZtRx6RkVf+e+7cQLNmwL33Ag0aAGnTWtKhv/9+05EvWtQkKItT/EpEJCi49vWNN4DZs82ukWB0CBSkJeH++QdYtw5YvBj4/nuz6CuQXCQwjM2MII0ameDMTGAWpvDiSm4Oa/MXJ3NmM/LO3VwiIsFccrNggQnO7LMQ/+wdPhyc/19BWq4flLnIi3PLrCzFn8DYQ9jEfJoMyg0bmt4yo6FNvPyy2dnFjGLTpwPFi1vdIhFxUzLEadNMcP75Z3MbR+m49uWll4CSJYPzOArSEuPsWWDtWlOzkQGZRSziBmV2RblNivPLDMocQ7ZhwuvRo2OGmlgkq149q1skIm5w/rwpZ8vytr//bm679VbguedMHfpgr4N1TZBWgY0kJhJhIOaw9Y8/ml4zPx7Gxp7xXXeZusxcdVWunO2zf/DTbffuMSk/A6u6RUSSiv0V5vvnh/8//zS3cXEYd4s8/3zoci6owIaXfsIYhNlTZgFlBucDB66+Hz8GcntU7domOJcpY/ugHBsXlTPVJ0fq+cmWZaZt2NEXEYc4cYKdQGDUKODo0Zg/k1wYxjIC6dIl7f9VgQ0v45Jmbgxev94cXOy1ZYtZSRUbg+/tt5tkIjzuuMPkynRoVOPT5EpuBmjmRRkzxrFPRUQsdvQo8Pbb5u8I685TkSJAnz4mtXCQMhV7Z7jbs06fNsUoNm40PWUezO4Vd9g68PGPZR151KgBVKmS9I+BNsOn3LixGTDgdDnLTkdEWN0qEXGaQ4fMkDazEnKZDnFAsW9f4OGHzULUcFKQdtI6fyYLYQ+ZSwkDx86d5t/i4gKvypWBqlXNwYAchsxeVtixwwTm//s/8/mDOblTpbK6VSLitCU6b71l5p05GElMHfzqqybVg1WzfgrSdnTkiBmeZveQBwMzz4Exl7iY75olHPkTxb3JDM7cGuWBsd7du80ic2YV40vA/Yrp01vdKhFxiv37gWHDgIkTY9I+cKCRwZkF+Kz+M6ogbRX2fg8eNPnjAgczdjE4M0jHh+Ms3HxXvnzMwciUIwe8Wn6aW6u4/q1UKZP0zEbbtEXExvbtM8GZWzQDwZnrZfv3Nx/8rQ7OAQrSocZJDQ5Jc0yWx/btwLZt5jh1Kv7v4U9H4cJmIoQHtz3xKFEifKsVHBCguV2b6T6LFTOrusOYDlxEHB6cJ040i0yJf0tee82c7UZBOliBeNcu4LffTEAOnBmUOdFxLVzZdNttpndcurQ52CXkwd3xcs0hbvagAwGaydBCWOFSRFzgwAGTN+HDD2OCM1M/MDhzt6ldKUgndGiaS/4YHRiMeWaqGV7zHNjZfi0cg2UvmAdzUzIo85rZurTCKVH4uYe/WPzsowAtIjfCWUWm7nz/fZMtzCnBOUBBmrh/mEGYXTMeHEsNnANHYLnftWTKZHrFjBw8GIAZkHmtqg5BwbVzXMXNRWIcbGCNDxbaEhGJiwUuuFqbCY3+/tvcxqA8aJBJoOgU3gzSTIH5wQdmcoIHl/fFruYUH66/z5fP7GbnwTljBuXAoUAcUkyUxpWW3GbFtXJcJKY5aBGJL0MY9zkzQ1ig9ACL873+uulB22VBWEJ5M0hzrJQZ0uMGYe4jLlTIZN3iwUDMr3nOn1+FiC3CRWHMJMZfOO6D5jYrreIWkbh5nVhY57//NYGamB6CPWcmOnJacPZ2gQ2+c1xBwL3EDL4MyAzQ4U4lIzfEEpOPPmoGOjjUzUQl2gctIgGcZ+Z885AhMTWcuSmGPWd+uHdqcA5QgQ2xLc4lsboMlwwwFzdTfWqdnYgQ+2OTJ5sFYJy1JM5Esufcpo390wIntMCGc8obiacW0zNPbufOJkCz0syXXypAi4j5+zBnjsnl9MQTJkBzCyZ700w/0bat/QN0Ymh8V2yFw9rPPhuzZGDgQJOez+lDViJy8374AXj5ZWDlSvM116b07m1G3NKkcecrrCAttnH8OPDgg8CSJeaTMD8ZP/WU1a0SEatt22aC8ezZ5msG5G7dTMDm7lc3U5AWW2BemGbNzC8jq2d+9ZXZciUi3nXoEDBggMkSxjlofnh/8klzm1eyDCpIiy2GsFq2NEXWuRX9m2/MfJOIeBO3W44YYZKRBPY633efybnNREZeoiAtlmKS+06dTC5dVtjkghCvfEIWkSuxtzxpEvDKKzHZlqtVM3ufnZDCMxS0ulsscfEi0L078PTTJkC3agUsW6YALeJVXIvCFBYczmaAZg6pqVOB1au9G6BJPWkJOw5rcx8jc28T55dYw1UruEW8h0UDX3oJmDXLfJ0xo+lJc8V2qlRWt856CtISVj/9BDzwgKlfwmqcHNri1yLiLSdPAoMHA++8Y0bTuCiMU19MTpItm9Wtsw8FaQkbBuSOHU1BMdYk4SfnsmX1Boh4bd75449NwqIjR8xtjRoBI0cCpUtb3Tr7cc2cNPN2ly5dGlWrVrW6KRIHgzI/Ibdvb6651Wr9egVoEa/h/HL16iaLIAM0q/lyN8f8+QrQ16Lc3RLy/c9cFMZhbs45c+6ZB4uOiYh39jszGUkgkyBTVXNYu0sXIGVKeFJUAnN3a7hbQobZgdh75twTy21/9pkZ1hIR7+ziGDPGBOSoKHMb821zv3POnFa3zhkUpCUkpeOYro8LQqhGDZNBjFVBRcQbfvzRTHNt3my+5vYqBmwOd0vCadBRgr6d4o47YgJ0jx5m/7MCtIg3cK6Ze53vvNMEaI6iffABsGaNAnRSqCctQcPhbH5yPnUKyJLFzD81b64XWMQLWFb2o4+AXr1MsRxisqI33jCBWpJGQVpuGuecWfuZQZpq1zbX6j2LeMOWLWZ7JYe4ibn333sPqFnT6pY5n4a75aaLY/AXkkGZyQhY/3nxYgVoES/4+2+gXz+gQgUToJmgiIUxuMVSATo41JOWJLlwwQRkDmVxmIt5dhmo9Ysp4g1Ll5r9zlyHQvfeC7z7LlCggNUtc5ew9KTHjRuHwoULI3Xq1KhcuTJWrFhx3fsvW7bMfz/ev0iRIhg/fnw4mikJ9OuvZgHI0KEmQD/+OLBpkwK0iFemtzi0Xa+eCdCsWjdjhtlyqQDtwCA9depUdO/eHf369cPGjRtRu3ZtNGnSBPv27Yv3/rt370bTpk399+P9+/bti65du2L69OmhbqokIJ0fh7JYUpJBmYtBpk0zC8SusxdfRFyCpWSZunPCBPM1g3VkpKkHLw7NOFa9enVUqlQJ73EVwb9KlSqF+++/H8O4oz2Ol19+GXPmzMHWrVujb3vuuefw888/Y9WqVUHL4iKJs3OnSUIQWBjStKmpBZ0rl15JEbc7dsxUpfriC/N1sWJmW1WdOla3zLkSGqtC2pO+cOECNmzYgIYNG15xO79euXJlvN/DQBz3/o0aNcL69evxD0ulxHH+/Hn/k419SHB7z6NGmcVhDNDp0plP0cy3qwAt4n4zZ5reMwM00/lyi9XPPytAh0tIg/TRo0dx6dIl5IyT/41fH2Iy13jw9vjuf/HiRf//Fxd74/w0Ejjya99P0OzYYX4RmZCEqzgbNDDz0VwsotrPIu72f/8HtG1rSskePmwCNQcz33wTSJPG6tZ5R1gWjiWL8xedI+xxb7vR/eO7nfr06eMfLggc+/fvD1q7vYoDFly1ffvtMb1nrt1btAgoWNDq1olIqC1YYKrUff656T336QNs2ABUq6bX3lVbsLJly4aIiIires2HDx++qrcckCtXrnjvnzx5cmSNJ21NqlSp/IcEx8aNwFNPmTNx5oHD2wrOIu535gzQs6f5UE4lSpg68ArOLu1Jp0yZ0r+VahG7YLHw61q1asX7PTVr1rzq/gsXLkSVKlWQIkWKUDbX086eNUUxWI6bATpzZrNqm5+oFaBF3G/tWpOUJBCgu3Y1fwsUoC3mC7Evv/zSlyJFCt/EiRN9kZGRvu7du/tuvfVW3549e/z/3rt3b1+7du2i779r1y5f2rRpfT169PDfn9/H7582bVqCHu/kyZMcG/efJWEWLPD5ChfmnII5WrXy+Q4d0qsn4gUXL/p8r7/u80VEmN//fPl8vkWLrG6V+51MYKwKecax1q1b49ixYxg0aBAOHjyIsmXLYt68eSj4b/eMt8XeM82kJ/z3Hj16YOzYsciTJw9Gjx6NBx98MNRN9ZyDB82isKlTzddcczd2LNCihdUtE5Fw2LMHaNfOpPelNm1Mzu1MmfT6e2afdLhpn3TCtlW9/z7Qt6/JHsSFIRzaGjQISJ8+DG+SiFiONd6ffdb8DeDv/bhxZjW3dm7YK1Ypd7fHMPH9c8+ZlZqBQuwM2JUqWd0yEQkHbqfs3j0ma1iNGmYVN/Pvi/2oCpZHsL4raz1zEQgDdMaMZmh79WoFaBGvYCJH5t1ngGaPmVurli9XgLYz9aQ9MLTNQuwc2g7kgnnsMWD4cCaJsbp1IhIurFLH4W3u5MiRA5gyBbjnHr3+dqcg7WLsJXfpEjO0XaaM6T0r366Id5w7Z4a3Oa1F9eubgK20vs6g4W4XYi4YFsNgbWcGaK5JePtts+dRAVrEW6u377jDBGgOb/fvz7wTCtBOop60i5w/D7zzDvD668Dp0+Y2BmsWG9PQtoi3MBg/8ojJwc1kjew9N2pkdavEsz1p7qkuXbo0qjJllsdwE12gUg2zhjFAc4EYk+FzPloBWsRbfw/4wbxxYxOg+Sfxp58UoJ1K+6QdbtMm4IUXgCVLzNe5c5tfUCYo4P5nEfEOfkDv0AGYPt18/fTTwLvvAqlTW90yiUv7pD2QLeyVV4CPPzafnPlLyMT47EmzapWIeG/++b77gF9+AVjmgMG5Y0erWyU3S3PSDqxSw+1Tb71ltlIQ553Ye1YhDBFvWrHC1H3mNktOb82YAVyjhpE4jIK0Q1y8CHzyCfDaa8Cff5rbuHp75EiTMUhEvInV6p55xtSBr1gRmD3b5OEXd9Cspc1xKHvuXFNCjr+IDNBM38e8uz/+qAAt4lWXLwP9+pk5aAboVq1Mj1oB2l3Uk7axdeuAXr2ApUvN16zxzHnozp2BVKmsbp2IWJmghME5UMGOwZoFcrRY1H0UpG1o+3YTjKdNM18zILNKFfPsMlCLiHcdO2YWiHEkjQvEPvgAaN/e6lZJqChI28gffwADB5q9zcy5zQxB3ErF5CQFCljdOhGx2t69Zv/ztm2mSA7zI9SrZ3WrJJQUpG2ACQe4WpvZwjiMRS1aAEOGAOXKWd06EbGDn38GmjQx2y/z5QPmzwfKlrW6VRJqCtIWOnUKGDXKbKmKijK3Mc/uG28Ad95pZctExE5YTpIf3Pl3goGZAZqBWtxPQdqiouvvvWf2NgfKR95+u+k5N2tmhrlFROjrr4GHHzajbLVrA3PmAJky6bWxLX6S4rwE5yOCME+pIB1GFy6Y+ebBg838MxUrZlZl8pdQKzNFJDYWxeCiMK5RYU+aq7nTpNFrZOme2CNHTHo3HgzGPO/bZ655PnnS3LdvX9PzuknJ3VRgg8cl/jTbDPcwTppkFoDxfSTuZWRiEv4CJnfNuyAiwcJV20zrybjABaQTJ5rV3BKGtI67dl157N5tDgbkQKrH68mSJWjNUYGNEOLnBX4SZk/5999jCmBwK9Wzz2qvs4jEb/RooFs3c/2f/5g83BppCyL2dnfuNMdvv5mDf6R5/uuv638v5yPz5DF5mAsVMufAweFtHgkooKACGxYH5y+/ND1n7nmm7NmB3r2BTp00XCUi18aFpC+9ZK5ZNIc7P7ROJQnOnzdBl3+Ed+yIOTMwc8j6epiQokgR4LbbTIpHXjMg85pBOIzZpDTQGuLgzFEP/sJ16aLqVCKS8AD96qsmb4ICdAJ6xVu3XnlwIzmHqZk79Vpy5QKKFjULg3hmQA4cNsoapSAdpOIXgeDMD2qB4Pzii8DzzwPp0wfjUUTEKwGa61UGDLC6RTacK96yBfj1V3PwmkdgFW58MmQASpQwR/HiJiDzzKDMf3MABembXBDGOeehQ80ISiA4c4iKPWcFZxFJCCYyUoD+F3u/7AUze8vPPwObN5uDt3EVXXw4R1yqFFC6tDkzKPPM3rLDhyIUpJO4lYrl4bjPmQv+KGtW03NWcBaRxK7i7t7dXPfv77EeNOeN2RveuDHmYGBmrzk+OXMCZcqYjC48eM3A7OKN4wrSicBkAtznzIxg+/eb23LkMMGZKzATsKBPRCTalClmmxWxJ+3qAM3eDYep1683x4YNpofMIcm4Uqc2Qfj2283B/Mg8uALXYxSkE+D0aWD8eGDECODQoZitVCwjya1UadOG+F0SEVdmEmO5SY7gsvzsm286fmQ2Bp8UV1avWQOsXWuOTZtMzzkuLtKqVAmoWNEcFSqYeWMlkPBTkL6O48eBMWNMfm0WwSCuvmdwfuop82FPRCQpubiZZZA7Qh5/3OyLdnSAZk+GgXjVKmDlShOcWVMzLg5LV6kSc1SubPYXO/rJh5aCdDzYW2ZgHjfOFMEgLgrkPufHHgNSpgzxuyIirsUpV6b45PRZ8+bAhx86MFEJE36sWAH88IM52EuOm+2Re4nZQ65eHahWDaha1WxvUkBOFAXpWLh4kNsgOO8cGJXhNAhTsLZqBUREJO7FFRGJjamdmzY1NRhY6e6rrxyS6vPAAWDpUmDZMnMEtrPExlzHLONXs6Y5ypdXjyYIFKRh1i5wMRiT1wc+DNaoYdJ38hOvPviJSDCmz1gP+s8/zaJkzknbtlgGM3ItXhxzcH45Nv5RZA+GnzRYmotn1c4MCc8W2OC6Bo7ScLHG3LkxtzdsaIJznToKziISvIXNLVsCkZFmSy/rQdtq1xDH3vkH8dtvge++M8PXsXE8nvPH/MPIgz1mG2XlcjNPFthYtMhsdeD6hsCHwoceAl5+2fwciogEC//CPvGEya3ABEeMhdxVZHmjOGS9YIH5xMChbAbq2NjI+vWBBg1Mb5n1kSVoVGDjOvghkQGaC8BYKpL7E7kwTEQk2DiVxgDNzijnoC0L0OzOc7HXN9+YI+4Qdt68Zijx7rtNYGbiELGca4a7E4PJA5iTndnBmDVORCQUZs40C0+J26waNw7z63ziBDBvHjB7tuk1c8VaAFessYfMiXIezNylBTi248kgzVHwwYOtboWIuH1Bart25podAiYsCdv2qFmzgOnTgSVLTAWgAPaOubyce7/uuUcFBhzAk0FaRCSUmPzo/vtNCmpO644cGYbAzKDM8XQOaccu0cgeMhtz771mr7LjNmV7m4K0iEgQcYPJo4+avAuFC4dwLzT3dDEwf/652bscOzAzGD/4oFlSzhSb4lgK0iIiQTRwoNnJxD3QnJNmhbygYZYl7hmdNMnMNccuTsGsXsw1yq0qTLUprqAgLSISJIybr79urt9/3yTdCsp2KVaN+vhj4MsvTQ86gAlF2G1v3dp028V1FKRFRIKA5WsDC8U6dYq5vqmsX5MnAxMnmiwosbdKsYgAD5ZzFFdTkBYRuUkcdX7kEbNgjAmR3n77JnrNTCzC2rgcKw8MZ7PkHueYmdiBK9FUSMAzFKRFRG4SMxj++KPZ3skaACwAlej9zJ98Arz3HrBjR8ztLOfIurj8BKCMX57k2dzdIiLBwI7vsGHm+oMPTDXGBNuyBXj3XTOsffasuS1dOjOUzaxLFSroTfI4T+buFhEJBg5vM83nH3+YDi9rQ98Q/+Ry+TfHxBcujLmd88vMeNK2rZKMeEBUAmOVa3rSIiLhxFjLzi4DNLcijxqVgO1TX3xhitazB01MLMJEI127AnfdpbScchUFaRGRJGAOkWnTgOTJzTVHqeN1+jQwYQIwYoQpJk2889NPm+CsrVNyHQrSIiKJdOBATC7u/v2vUeKWi8E438wuNsfFicWku3UDnn3WZgWlxa4UpEVEEjnMzU4wK+kxyVefPnHuwGQj77xjgjPvRFxN1ru32Tyd6KXf4mUK0iIiicDa0Fz3xVjLaw53+506ZYIz55wDwblMGaBfP6BVq1h3FEk4/dSIiCTQwYNAjx4xObpLlgRw7pzZ3zx0KHD0aMxK7ddeAx54QFWn5KYoSIuIXMOvv/6KCRMm4Pfff/dvl9m7dzhOnMjjzzHyYvdLwKdTzKT0vn3mG4oVM9GbubRVElKCIKSFRY8fP4527dr5f7h58PoEF1NcR4cOHZAsWbIrjho1aoSymSIiV+nRowfKlSuHd999F/PmzcMXX5zGypV5AFzEB4/MRvIaVfgHywRo5tNmJhPm2GZ2MAVocUJP+tFHH8WBAwewYMEC/9fPPvusP1B//fXX1/2+xo0b42NWfPlXypQpQ9lMEZErvPPOOxh1xcbnW5nXELfhN4zAvajw4lZzM1N19u0LPP+8qU0p4pQgvXXrVn9wXr16NapXr+6/7YMPPkDNmjWxfft2lChR4prfmypVKuTKlStUTRMRuSamFh7BPc2xpMPL6Iex6IG3kQoXcBHAsYcfRs6xY4Fs2fRqivOGu1etWuUf4g4EaOKwNW9buXLldb936dKlyJEjB4oXL45nnnkGhw8fvuZ9z58/70+vFvsQEUmqTZs2YT/rTv7rYeTDNoxHb7zpD9Dfsowz+9XsaChAi1OD9KFDh/yBNi7exn+7liZNmuCzzz7D4sWL/Z9m161bh/r16/uDcXyGDRsWPefNI3/+/EF9HiLiLee4WhtAUQDMrD0VB5AXf+I35EILTscB2BbrfiK2CtIDBgy4amFX3GP9+vX++/I6LtbziO/2gNatW6NZs2YoW7YsWrRogfnz52PHjh2YO3duvPfv06ePP0F54Ij9CVhEJLFK3XYbXo2IwGYA9zAYIxVeQz+URQp8E+t+FVShSuw4J92lSxe0adPmuvcpVKgQfvnlF/z1119X/duRI0eQM2fOBD9e7ty5UbBgQezcufOa89c8RERu2rp1yPLkkxj0b8nbhaiNTvgYuzAZQEwHIHv27HjooYf0gov9gnS2bNn8x41wgRh7tmvXrkU15s4DsGbNGv9ttWrVSvDjHTt2zN87ZrAWEQmJv/82yUe4YOzyZVzOmhWdzzfG+NOB4PxW9F3ZKZg8ebJ2nYiz56RLlSrl30rFhV9c4c2D182bN79iZXfJkiUxc+ZM//Xp06fRs2dP/6KzPXv2+BeQccibHwpatmwZqqaKiJetWwdUqgT897/+AM19zoeXbsNkHwN0MqRP/zqjOFKkSIFWrVr5F742atTI6laLR4R0nzQXgHXt2hUNGzb0f33vvfdizJgxV9yH27HYu6YIzgNt3oxJkyb5k56w91yvXj1MnToV6dOnD2VTRcRr/vkHGDwYGDKE+644twaMH88/VHjlaeDMGe5IAVasGI+oqDdx6623ampNwi6Zjyu5XIRbsLjKm4E/Q4YMVjdHROzot9+Ybcn0oolZwtiByJLFnzSsXDnTqf7xRyARs3MiQY9VIU0LKiJiK+yTsHRVxYomQGfODHz5JfD55/4ATSxaxQDNGTYFaLGaCmyIiDewlGSnTpyHM1/XqQNMngzEyq2wejUwa5ZJvc1RcBGrqSctIu63aRP8pasYoCMizFz0999fEaADvWhq356LX61pqkhs6kmLiLtNnAh07swcwkC+fGZ4+447rrrb4sXmSJHC7MYSsQP1pEXEnZi28+mnzcEA3ayZ6VHHE6A5Vf3qq+a6Y0egYMHwN1ckPgrSIuI+TA98552mFx2YYJ4zB8iaNd67swfNuj9MXtinT9hbK+L+4e6xY8f6D5aZExEP++EH4MEHAVbPY1D+4gvgHmbhvrZBg8z52WeBPHnC00yRhNA+aRFxjw8/BP7zH5OopHx5s1S7UKHrfsvy5Wahd8qUwK5dQN68YWuteFiU9kmLiGdwBK1nT+CZZ0yAbtXKZCK5QYCmwFarJ59UgBb70Zy0iDgb83dyeJvFMWjAAGDqVODWW2/4rayqu3Ch2ZX10kuhb6qIZ+ekRcSDWA63eXMTbbnq65NPgBuU0o3trX+LW/FbihQJXTNFkkpBWkScaccOoEkTM5HMBWJcvZ2IPJ78tunTzXWvXqFrpsjNUJAWEedZuxZo2pQF500XeP58oHjxRP0Xo0aZHN2sOnn77SFrqchN0Zy0iDjLokVA/fomQDPVJzc4JzJAHz9utlAT15uJ2JWCtIg4x//+ZzKHcbHY3XebLCQ5cyb6v/ngA+DsWVOSskGDkLRUJCgUpEXEGQKLwgJbrL75BkifPtH/zcWLpnQ09egBJEsW/KaKBIuCtIjY37hxwBNPmElk7oVmFjGu5k4Cri9j1tBs2YBHHgl6S0WCSkFaROxt5EhTxYq6dwfef99sbE6iQC+aKUBTpw5SG0VCREFaROxr+HDgxRdjij0zYN/E+HRkJLBkiam5wWpXInbnmiDN4hqlS5dG1apVrW6KiAQrQAfSgLHA8+DBNz2BzE443XsvUKBAENooEmIqsCEi9sMec6AHzQDNVJ83iau5WeHq5ElgwQKzP1rEKiqwISLOXSQW5AAd2L3FAM3cJzeoXCliG64Z7hYRl2yzCiwS69MnaAE6sDeann7azEmLOIF+VEXEHqZNA556KmYVd6CGZBBs3WoqV3JReIcOQftvRUJOQVpE7JHq89FHY/ZB3+Qq7vg66MRkZblzB+2/FQk5BWkRsdaaNUDLljGZxN57L6gBmhnGJk0y18yHIuIkCtIiYp1t20w1K+bi5mquyZNvKlFJfBYuBA4dMhnG+FAiTqIgLSLWOHgQaNwY+L//A6pVA2bMSHKqz+sJ9KI5mp4yZdD/e5GQUpAWkfCLijLd2r17gaJFTbGMdOmC/jDccjV7trl+/PGg//ciIacgLSLhxbnnhx8GNm0CcuQwmUWyZw/JQ02fDpw7B5QuDVSqFJKHEAkpBWkRCR+fD3j+eeDbb4G0aYG5c4HbbgvZw33+uTm3bauSlOJMCtIiEj4jRpgE2ly9zXKTVaqEdMp78WJzrZKU4lSuCdIqsCFic5wc7tXLXHMfNKtchBDTgLLjXr06ULhwSB9KJGRcE6Q7d+6MyMhIrFu3zuqmiEhcv/xixpwZNTt1Arp1C/lr9NVX5tymjd4OcS7XBGkRsakjR0yvmXuhGzQARo8O+QTxgQMmDSgxP4qIUylIi0joXLgAPPRQzFYrdm+TJw/5K84t13THHUDevCF/OJGQUZAWkdB54QVg+XIgfXpgzhwgS5aw1eog9aLF6RSkRSQ0Pv2UKzrN9WefAaVKheWVZgrQH34w1w88EJaHFAkZBWkRCb6ffgI6djTXrAndokVYF5FzfRozjebPH7aHFQkJBWkRCa5jx0wX9vx5oHlz4NVXw/oKz5plziysJeJ0CtIiEjysB92unVkoxkxirGp1yy1hTQn+/ffm+v77w/awIiGjIC0iwfPGG8D8+UDq1CZxdqZMYX11WZaSqcGLFwdKlgzrQ4uEhIK0iATHkiUxQ9tcMFa+fNhfWS4gpxAnMxMJGwVpEbl5f/1lCjZzuLtDB+DJJ8P+ql66BMybZ645FS7iBq4J0srdLWLxPDT3PpUpE7PtKszWrDFr1jjCziQmIm7gmiCt3N0iFnnzTWDRIiBNGpNRjCUoLfDNN+bcuHFYkpqJhIVrgrSIWGDVqph56DFjgNKlLXsbuF6Nmja1rAkiQacgLSJJc/KkmYfmZDALNj/xhGWvJGtHb9pk6nawJy3iFgrSIpI0XboAe/aYYs3vvRfyylbX8+235lylCpA9u2XNEAk6BWkRSbzPPwemTAEiIkxe7owZLX0VuT+aGjWytBkiQacgLSKJw2xinTqZa85H16xp+eJyrlsjBWlxGwVpEUlcROTcM/Nv1qgB9Otn+avHueijR001zOrVrW6NSHApSItIwr3zjsksxm1WzMttg71O331nzvXqASlSWN0aEQcF6SFDhqBWrVpImzYtMiUwh6/P58OAAQOQJ08epEmTBnXr1sWWLVtC2UwRSYjISKBPH3M9ciRQtKgtXrdAkG7QwOqWiDgsSF+4cAGtWrVCp8D8VQK89dZbGDlyJMaMGYN169YhV65cuOeee3Dq1KlQNlVErodVKx5/3JSfbNIEePZZW7xebM4PP5hrBWlxo5AG6YEDB6JHjx4oV65cgnvRo0aNQr9+/fDAAw+gbNmy+PTTT3H27Fl8ztWkImJddasNG4DMmYEPP7R0u1Vsq1cDf/8N5MxpaR4VEW/MSe/evRuHDh1Cw4YNo29LlSoV6tSpg5UrV8b7PefPn0dUVNQVh4gE0c8/A4MGxWQVy5PHNi/v4sXmXL++bT43iLg3SDNAU05+LI6FXwf+La5hw4YhY8aM0Uf+/PnD0lYRT+AwN1dzX7wI3H+/ySxmI0uXxiwaE3GjRAdpLupKlizZdY/169ffVKP4f8QdBo97W0CfPn1w8uTJ6GP//v039dgiEqd4xsaNQJYslmcVi4vD3Bzuprp1rW6NSGgkev9Ely5d0KZNm+vep1ChQklqDBeJEXvNuXPnjr798OHDV/WuYw+H8xCREKzmfv11cz16NH9BbfUSszTlhQsA/1TYZKG5iPVBOlu2bP4jFAoXLuwP1IsWLULFihWjV4gvW7YMb/ITvYiEB4tmPPWUiYLNm5tCGjazfLk533WXrTr4Is6Zk963bx82bdrkP1+6dMl/zeP06dPR9ylZsiRmzpzpv+aQdvfu3TF06FD/bb/++is6dOjg32f9qA3/SIi41tixZiyZabxsNswdsGJFTJAWcauQpgvq37+/fwtVQKB3vGTJEn+SEtq+fbt/LjmgV69e+Pvvv/Gf//wHx48fR/Xq1bFw4UKk5x8LEQk9Vrbq29dcv/UWkC+f7V51rmNjKWuqXdvq1oiETjIfV2W5CLdgcZU3A3+GDBmsbo6Is/DPQdOmwIIFpovKFKC32GoTiB+3bLMsJRMZHjtmyyaKBCVW6UdbRGJMnWoCdMqUwIQJto1+gSxjtWrZtokiQaEfbxExTpwAunc316xuVaKEbV+ZH3805zvusLolIqGlIC0iBotn/PWXCc4vv2zrEXkFafEKBWkRMSu533/fvBLjxzMBgW1fFeYr+vNPICICqFrV6taIhJaCtIjXcak0K9Wxi9q+ve3TdwVWdVeoYMpai7iZgrSI140bB2zaZCpc/fe/sLtAKtCaNa1uiUjouSZIjx07FqVLl0ZVjX+JJNzBg8Arr8SUo8ye3TFBukYNq1siEnraJy3iZczk98UXQLVqZhzZ5vuZmKWUW0rPnwd27ACKFbO6RSJJo33SInLjOo8M0AzMTP1p8wBNmzebAM2ReRXVEC+w/2+liIRmsdjzz5vrjh2BSpUc8SqvXWvOnNWyYTpxkaBTkBbx6mKxX38FsmYFBg+GUwRK1WvpiXiFgrSI1xw+zOo35nrIECBLFjjFunXmrCAtXqEgLeI1rHDFynMc4n76aTjF2bNAZKS5rlzZ6taIhIeCtIiXsHzURx+Z63ffNWm7HOLnn4FLl4BcuYC8ea1ujUh4KEiLeAUzinXrZs5t25oSUg77fBHoRWvRmHiFgrSIV3z1lalMwVyaTFziMD/9ZM4OWYguEhQK0iJe8PffQK9e5rp3byBfPjg1SGs+WrxEQVrEC0aMAPbtA/LnB158EU7DBCZbtpjrihWtbo1I+ChIi3ghP3dgeJtnB5aOYoBm/hXuFuPnDBGvcE2QVoENkWt49VXgzBlTkeKRRxz5MrFIV6AXrUVj4iWuCdKdO3dGZGQk1gWyHYiI2bcU2HI1cqRjI1wgSJcvb3VLRMLLNUFaROLgVquePc354YcdXYA5EKQrVLC6JSLhpSAt4lbffgt89x2QMqUjt1wF8DPGL7+Ya/WkxWsUpEXciKm5XnrJXLPaVeHCcCouSmcW0+TJgZIlrW6NSHgpSIu40aRJpspVpkwmV7eDsYY0MUBzUEDESxSkRdyGlSi4opteecVRVa6uF6TLlbO6JSLhpyAt4jbvvAP88QdQsCC3PcDpFKTFyxSkRdzk2LGYRWKsFZ06NZyOo/ZUtqzVLREJPwVpETcZOhSIijJ7lRyauCS2f/4Btm0z1xruFi9SkBZxCy6DHjPGXA8bBtzi/F/v334zgTpdOjN6L+I1zv8tFhHjtdeACxeAunWBRo1c8aoEimqULu3YZGkiN0VBWsQt0Yzbrohz0i6JaLGDtIgXuSZIq8CGeBq3XF2+DLRsCVSvDreIjDTnMmWsbomINZL5fEy65x5RUVHImDEjTp48iQwZMljdHJHQY1GZatXMHDSXQpcq5ZpX/fbbzRasuXOBpk2tbo1I+GOVa3rSIp7Vr585t2vnqgDN+tHbt5trFz0tkURRkBZxsqVLgUWLgBQpzMIxF9m926yDS5NGK7vFuxSkRZyKM1WBXvQzzzi6iEZ8AvujS5RwxW4ykSTRj76IU82fD6xcabqagWDt0iAt4lUK0iJO7UUHimh06QLkyQO3BmnNR4uXKUiLONGsWcBPP5lUXL16wY0Ci8bUkxYvU5AWcRruh+7f31x36wZkywY3UpAWUZAWcZ7//c/sh+beyhdfhBv93/8BR4+a62LFrG6NiHXUkxZxkkuXgAEDzPULLwCZM8ONduwwZ061c0RfxKsUpEWcZOpUs6KKwbl7d7jVzp3mXLy41S0RsZZrgrRyd4snetGDBplrDnNnzAi3B2kNdYvXuSZId+7cGZGRkVjHPMYibvTll2Y1VZYswPPPw80Cw93qSYvXuSZIi7i+F/366zG9aJcXj1FPWsRQkBZxylx0oBfN5CUuz9Py22/mWsPd4nUK0iJO6kVzRbfLe9HcehUVBSRLBhQpYnVrRKylIC3ihH3RgRXdLp+LpkAvOl8+IHVqq1sjYi0FaRG7ZxcbPNhc9+jh+l40/f67Od92m9UtEbGegrSInc2cCWzZYrZbeaAXHTtIFy1qdUtErKcgLWLnFVSBueiuXYFMmeClIK35aJEQB+khQ4agVq1aSJs2LTIl8A9Mhw4dkCxZsiuOGjVq6L0S7/n6a+Dnn01eTBdnF4tLQVokTEH6woULaNWqFTp16pSo72vcuDEOHjwYfcybNy9kbRSxbS86MBfNLVfceuURu3ebs+akRYDkoXwRBg4c6D9/8sknifq+VKlSIVeuXCFqlYgDLFoEMHtemjRm25VHnD0LHDxorjXcLWLTOemlS5ciR44cKF68OJ555hkcPnz4mvc9f/48oqKirjhEHC/Qi+7YEcieHV6xZ485cxG7Swt8iTg7SDdp0gSfffYZFi9ejBEjRvhzcdevX98fjOMzbNgwZMyYMfrInz9/2NssElQrVpgjZUqgZ09PvbiBoe7ChU0yExGvS3SQHjBgwFULu+Ie69evT3KDWrdujWbNmqFs2bJo0aIF5s+fjx07dmDu3Lnx3r9Pnz44efJk9LF///4kP7aILQwZYs4dOgB588JLAj1pBmkRScKcdJcuXdCmTZvr3qdQoUJBe21z586NggULYmcg434889c8RFxhwwbg22+BiAjg5ZfhNYGedBD/hIh4K0hny5bNf4TLsWPH/L1jBmsR1xs2zJwfecSTK6fUkxYJ45z0vn37sGnTJv/50qVL/msep0+fjr5PyZIlMZNZlQD/7T179sSqVauwZ88e/wIyDnnzQ0HLli1D2VQR6zE/94wZ5rp3b3hRIEgXLGh1S0Q8sAWrf//++PTTT6O/rlixov+8ZMkS1K1b13+9fft2/1wyRUREYPPmzZg0aRJOnDjh7z3Xq1cPU6dORfr06UPZVBHrvfmm2R99331AmTLwcpDWcLeIkczn418F9+AWLK7yZuDP4IFiBOIS+/aZ7B0XLwKrVwPVq8NrzpwxydXo+HHPZEEVj4pKYKyy3RYsEU8aMcIE6Hr1PBmgae9ec+bfKwVoEUNBWsRqR48CH3zg6bno2EFaQ90iMRSkRaz27rvA338DlSoB99wDL4/4kxaNicRQkBaxEnc6MEgHetEeTrMVCNIFCljdEhH7UJAWsdLEiWaVVNGiwAMPePq9CAx3qyctEkNBWsRK33xjzi+9ZLKMediBA+as9PsiYdonHU5jx471H0yaIuIYCxYAc+awsgy87vvvgT//BDJmtLolIvahfdIiIiJhpn3SIiIiDqc5aREREZtSkBYREbEpBWkRERGbUpAWERGxKddswQoIFPXiyjkRERE7CsSoGxWidF2QPnXqlP+cXxkRRETEATGLJSs9s0/68uXL+PPPP5E+fXoku04e5KpVq2LdunUJ/sTDoL9///5E1ahOzGPY/XuS8hrY9bkk5Xv0/PX+6+c/9H8D3fT7f6PHYehlgM6TJw9uueUW7/Sk+WTz5ct3w/tFREQk6sUm3j8x35OUx7Dz9yT2NbDzc9Hz1/uvn//Q/v4n5ffMTb//CXmc6/Wg4fWFY507d7blY9j5e8LxGHb+nnA8hp2/JxyPYefvCcdj2Pl7kiKxj+P15++J4W4r07e5mddfAz1/vf/6+dfv/0kL/v55tiedGKlSpcJrr73mP3uV118DPX+9//r51+9/Kgv+/qknLSIiYlPqSYuIiNiUgrSIiIhNKUiLiIjYlIK0iIiITSlIX8OQIUNQq1YtpE2bFpkyZUrQi9mhQwd/lrPYR40aNeCV58/dfAMGDPBn0EmTJg3q1q2LLVu2wImOHz+Odu3a+bfd8OD1iRMnXPv+jxs3DoULF0bq1KlRuXJlrFix4rr3X7Zsmf9+vH+RIkUwfvx4OFlinv/SpUuvep95bNu2DU60fPlytGjRwv97y+cxa9asG36Pm97/5Yl8/uF+/xWkr+HChQto1aoVOnXqlKgXtHHjxjh48GD0MW/ePHjl+b/11lsYOXIkxowZ40+FlytXLtxzzz3R+dSd5NFHH8WmTZuwYMEC/8FrBmo3vv9Tp05F9+7d0a9fP2zcuBG1a9dGkyZNsG/fvnjvv3v3bjRt2tR/P96/b9++6Nq1K6ZPnw4nSuzzD9i+ffsV73WxYsXgRGfOnEH58uX9v7cJ4bb3/0win3/Y338mM5Fr+/jjj30ZM2ZM0EvUvn1733333efJ53/58mVfrly5fG+88Ub0befOnfN/7/jx431OEhkZyQQ/vtWrV0fftmrVKv9t27Ztc937X61aNd9zzz13xW0lS5b09e7dO9779+rVy//vsXXs2NFXo0YNnxMl9vkvWbLE/7Nw/Phxn9vwec2cOfO693Hb+5/Y5x/u91896SDjUEiOHDlQvHhxPPPMMzh8+DC8gJ+uDx06hIYNG0bfxo3/derUwcqVK+Ekq1at8g9xV69ePfo2Dlvzths9F6e9/xwx2bBhwxXvG/Hraz1Xvj5x79+oUSOsX78e//zzD5wkKc8/oGLFisidOzcaNGiAJUuWwCvc9P7fjHC9/wrSQcQhss8++wyLFy/GiBEj/EO+9evXx/nz5+F2DNCUM2fOK27n14F/cwq2l4E2Lt52vefixPf/6NGjuHTpUqLeN94e3/0vXrzo//+cJCnPn3+YJ0yY4B/enTFjBkqUKOH/Q825TS9w0/ufFOF+/11XBet6uKhp4MCB170P/7BWqVIlSf9/69ato6/Lli3r/38KFiyIuXPn4oEHHoDbnz/FLQ/KEaTrlQy14/On+Np8o+di9/c/mO9bfPeP73anSMzz5x9lHgE1a9b0lzAcPnw47rrrLniB297/xAj3+++pIN2lSxe0adPmuvcpVKhQUD9x8Y/0zp074fbnz0VigU/ZfN4BHO6N+6nb7s//l19+wV9//XXVvx05ciRRz8Vu7398smXL5i+nF7fXeL33je91fPdPnjw5smbNCidJyvOPD6dDpkyZAi9w0/sfLKF8/z0VpPkLySNcjh075v+EFTtoufX5c/sKf3kXLVrkn6sJzPdxq8abb74JJz1/fjJmtZu1a9eiWrVq/tvWrFnjv43b0pz6/scnZcqU/q00fN9atmwZfTu/vu+++675+nz99ddX3LZw4UL/yEGKFCngJEl5/vHhKmc7v8/B5Kb3P1hC+v6HZXmaA+3du9e3ceNG38CBA33p0qXzX/M4depU9H1KlCjhmzFjhv+at7/44ou+lStX+nbv3u1fAVizZk1f3rx5fVFRUT63P3/iym6u5uZtmzdv9j3yyCO+3LlzO/L5N27c2Hf77bf7V3XzKFeunK958+ZX3Mct7/+XX37pS5EihW/ixIn+le3du3f33Xrrrb49e/b4/52rnNu1axd9/127dvnSpk3r69Gjh//+/D5+/7Rp03xOlNjn//bbb/tXAO/YscP366+/+v+df0qnT5/ucyL+7AZ+v/k8Ro4c6b/m3wAvvP+nEvn8w/3+K0hfZzsNX/i4B//4Rr94gH+LEp09e9bXsGFDX/bs2f0/sAUKFPD/H/v27fN54fkHtmG99tpr/q1YqVKl8t11113+YO1Ex44d87Vt29aXPn16/8HruFsu3PT+jx071lewYEFfypQpfZUqVfItW7Ys+t/4POrUqXPF/ZcuXeqrWLGi//6FChXyvffeez4nS8zzf/PNN3233XabL3Xq1L7MmTP77rzzTt/cuXN9ThXYUhT34PP2wvu/JJHPP9zvv0pVioiI2JS2YImIiNiUgrSIiIhNKUiLiIjYlIK0iIiITSlIi4iI2JSCtIiIiE0pSIuIiNiUgrSIiIhNKUiLiIjYlIK0iIiITSlIi4iI2JSCtIiICOzp/wGp3LxV1aU2TAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Graphics object consisting of 3 graphics primitives"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p1 = implicit_plot(eqs[0], (-1.6,1.6), (-1.6,1.6))\n",
    "p2 = implicit_plot(eqs[1], (-1.6,1.6), (-1.6,1.6), color='red')\n",
    "p1+p2 + point(sols, size=50, color='black')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0beabbfc-ca03-44b1-ab31-699a2ebde9b1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "SageMath 10.8",
   "language": "sage",
   "name": "sagemath-10.8"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
