Rendered UVA 823

uva823.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA3C8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 1:\n",
      "All three stoppers will fit in the triangular space\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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wvtFrfDWcIRYAxAmswcZe0cD1FACgBYH1lYEnRp2bIRYA1yCwAADCBNYnxldNGWIBcAEC62/qqgONBcDZCSwAgDCB9cT4qhtDLABOTWABAIQJrHfGV50ZYgFwXgLrdrupq0E0FgAnJbAAAMIElvHVUIZYAJyRwAIACLt8YI0eX40d35QYHhliAXA6lw+soSocmaywDQBwMtcOrNHjK94YYgFwLhcOrBp1NTAtarwB7zQWACdy4cB6WYelv39adHhFheoNAPq6amBVWv9HbUiZN+CdIRYAZ3HVwKqnZ1rIGABo6pKBtWt81TRKls3p0z3LszQdX+1/IYZYAJzCJQNruw5H0/o0Voe6WpQ7/ggAHV0vsCqdffVB68bqVleHGGIBML+LBVbhulq0a6w56mqhsQCY3MUC64Bui36LxupZV+UjFgCau1JgzbPyr411PLPWB5nkpb8zxAJgZlcKrKk8HoFR1ppWk9UVAEzuz+gN6CUxvlqmKj1j5UNjvfjUW38+KPn+9H+7ASDkGoE1+Tq944jhzC/3icYCYE7XCKycgSt+/czQQgCwuMA5WJb9qTnbHYAJXSCw0qz4X9KxALA6e2C1WfY11gdt68rbDcBszh5YAADdnTqwHLU6DUMsAKZy3sBqXFdW/FWnjvWOAzCP8wZWe1b8mykhAHzlpIHVa9m/eGP1rquLv90AzOOkgdXXNRf9a75qAHjFGQOr71zlygfIBrx2QywAZnC6wBpxTtAFF/2Rp15d8O0GYDanC6xBLrXoO7EdAH52rsAauvJfpLFK1NVF3msApnWuwBrt9Ot+iboCgPJOFFg1Fv8TN1aNN/jdid9oAOZ3osAq45RLf626AoDazhJYxdb/kzVWsXf33cneZQBO5BSBVXL9X1b/2QNgeQn13t13GguAkk4RWFUtXTJvACxbXreuAKCq+QOr9IDl9njMOmRZ3tfCb+27Sd9fAE5t/sCawXQNULtaAaC6P6M34Jh5QuC5scpucv0t/Nry5k620QCc2eSBNZU1AGrGQM2tAoAZzXyIcNoiqPYFw+pfFXzFdEdhATi1aSdYkxfB8xcMB76O4RuQ5EAhAGVMG1in8OE6Dt3aYNZzrQBgEnMG1rkGFc/nZn3+lylNH7wKQywAapgzsE7qubRSQ6ZLdBUAFDNhYF1gRPH8+g6eun32t+oTQywACpgtsK63dl7s5SZoLABGm/kyDQAAJU0VWMYSvMhlsQAYaqrAAgCYwTyBZXzFJoZYAIwzT2ABAExiksAyvmIHQywABpkhsNQVu2ksAEaYIbAAAKZSPrCMrzjIEAuA7soHFgDAbGrfKmfv+OrFgYXR2FW4eQ4AfdUOrJd9KKoXV9J9vwUA8LPCgfXbyOE5j/a10YffOv6A1GWIBUBHVQPrx7VwLaHscrk+2v3+9hSW41PRWAD0UjWwvtGne55Lq8PTAQAnUzKwvhozDGmd5elk1nkYYgHQRcnA+tvwvpFZAMAm9QLracBQqmlk1kkYYgHQXrELjVatq9VzZjEr13YHoLFigfWuZl0tNBYA8LNKgfU+vlr+WbOuFsvmaayJ2X8AtFTrHKzKg6vP1jV6lg0GAPooM8G63++3x222WHG4cGKGWAA0UyWwZqyrhcYCAD4oEVizH2jTWLMyxAKgjfHnYDWqq1/Xzfh9DJc7GM6biRflslgANDA+sG651nmOql8fc9MPv8I0BABYDA6syOxgzZpND/X8w/se4cvHNA2Zj90GQNrIwLrfb4/b/Xbbv7AFw2h5tOPHKy3WAMCwk9zf2uhAiawxlKqZ9aGOH+lzrHAyju8CEDVmgvXWRnvHV02/dXj8ps5OeAeAixs2wXrcdgZInxvpHLwZjrSajyEWADkDAuvt1KvtDdJ/LLTOonb/LjOxzwAIKXGh0VeMuhipi4gCAFv1Dqx946uxl3rf3VgGIvOxzwBImGCCVeFGOuZYAMDrugbW7rOvKpwzfuQbhczEPgPgsO4TrO0HByvU1cLKexX2NADH9Aus9+u2b/yVMnW12LHyWqwB4Gr6TrCq5RJ8RxcDcECnK7nvWKoKjq8W++42WPblnNWvHzm7A4B2+t0qZ9N6Vn92sCmYTEP6eH6Tf907v/+wG3cDsNeYexG+ovK6JphKWffFps/M8w/vewQA+E6Xc7A2xsgs7TLLdp7YeiOjg7enXH/9452RpDQAu7QPrPv9fntsXfzqDxJ2vCIrdVYkrZ49Z9Zf/9aeA2CjuocI4TtNL+7/3Fj1Qx+AmhpPsLafIzzRWcVGG0Msn5DWH5LlKd72rz0NwEYmWEyj/1RpLatJmh+AKlpOsCYaRlHeqGN2b0cMb4ZYAGzQ/CR3lbVyoGm3sWdE/ddYAPCaZoG1K6ymqzHN1EGF882/+HYhAHyvTWBNF0rUVuHT9LYNIguAF/S92TNsVKrVHw8HCgF4SYPAKrUkMrOCHyUHhQF4hQkWAEBY+jpYBWcOzOn4R+mHUdPBGxf6mAPws2hgWXYIOXgYbv31Lz+Pz7eIPvIUPuwAfMeV3ClqX768Uk7rf92dWc7EAuBnuXOw/EVPyO522RpMB69upbEA+I4JFhVtbfUjs6h9v26IBcAPQhMs4ytGO3je+k4iC4Cv1LpMw3RTAWEZt+MtjeyFHZ891x0F4DuJwPpxfZuumdpRYy1kP117Hs3nG4BPDgeWamC01Adw5+P4GwKAT2odIoRN4nkvlgCIOBZYDcZXE61whndx072lbx/XiT61AHRhgsWs2iWNWALgoAOB9fK0Ycef9/VXuB2vaK7ZzBRavKXOxALguIoTrFlCZJbtBAA62xtY7QcylccBlbeNYQyxAHi3K7B21dWmpaf+cGjTFlp2r0JjAXC73bodItx3k7iaS9W+4V39ZAQAUrYHlrO14Qdl/zIAoKN+J7nvvNdbsaVq1J3yAICJbAys7rFQqrGkUjUtPhuBxyz1qQVghC2Bdbgvdq87FVar3VuuyRpp98YGHlljAVxbxetgfbCsdmNXq+XZpVJr02WJgAbgSy8HVmgl2beCjm2s3XVl9W0tHmTJXTZdLQKQM8EEazGqscyu6kt9KuQQACmvBVZ0FLP7D/vHo/dQYHnd+1668VUf2Tc5vMsMsQCuatgEa/e6s6xZrZet5Sl2L7dW1d1GXc7DBTgACHohsBosIweP962jrEbf0j8yuLo5qjjIkQ9DwyA2xAK4pN8Cq9kf6ccfda204Ck4qTZSVwftGGLta+7dPb3hiTQWwPWMPMn9+LqzrosHM+s5rQ62kcNGx+1+A7dORg/2tB0NwHf+/PQf28fC0lgHn2T99eeV9dfH3PTDL1JXQUduqr3u3C8f4ef/+orNNR/5oAMwjx8Dq5fU0vP8IL8ugfHFzlGgoIPTzV/nmo4CA9DU94HV6w/u9dSZ0t+3/40T2+OOD30a7Y6dW2WIBXAlJS40WuFmOEeoKwDg2TeB1f1P7XkbS121U/Drd4f+zyj4egBo46vAGnQgY8bGUletlWqSwP8ZpV4PAM2UOES46n8znCMOXo+U11X4SFTYBgBm8SmwCpyH2+dmOEe0OCuf71QYbSZHlRP9DQHAXrUmWKsKa+p3HBbsb+znwR4HYKu/A6vSWKZmY1lrRxn1eWiyxw2xAM7u6TpYlepq8bymDt+0IptxZevnodteaPhcLosFcGolruT+s+GZJa1KWac/TfeInQ7AEe+BVf6P6SGZZZWtqemHod9ON8QCOK8JJljPXrmV73GtH5+I52+bRvaU/Q5Ayp/bbYLx1Qefb+WbXV9TD0hrHz4Ju/fasLQyxAI4qckmWM+eV6UPX8l6ccHa91tUs+64TYmspwFo537KleV+e+llPW6+Kn9av34GSu39///339GbAEDS/wDV1azjAyZMOgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 2:\n",
      "All three stoppers will fit in the triangular space\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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cixZX3XmysK4GSatra2RWe3XPtUImIrCAw8lXM6WzkwHT6lqeWaqIcxJYwFGs0FUfT/zKU348fI27ca70rTKvZ9b7Evi8sW4+lY5jMAILmNxqXfXx9K/X1UoZtPZ39r2SWTs0FoxEYAFzWrmrPjby+tOvVAObRcbizPq0Ml0YcSoCC5hHumj9ka29uJFJB1ff+jSRevaB7/+laiytxvgEFjC8TYZVuSPV1bvF90pYHGcwL4EFjGrXrkpuKHqkuvqwbEnZdWMZYnEGf+29AwB/en8ffn/zfP9nj114/ZZXh6yrdx8X+5591OXPVf+v78Yfz1M9LxRMsIABbLu46r41vgzndePU1bVnz1U+x4JhCSxgP+MtrkpmVyulwzAn6V/LDvb6CuPrJ0qoMSyBBWxuvK563apv8yM3xILEUUWcgcACtjJ8Vy1+17++MpinwxQtsrixpjg6WEBgAWsaaXHVfa/U1aqzq/EtvjCaNJZKY0wCC1jB8MOqT0auq0lO4dOhY8E7x+Y2DUBngDssbOnreCkPhelO4VMjt+ro/rs/gzs1MAwTLOBls82rPllWRWsPXWYc6iy4VqiIOCqBBSwyz+IqxucqIccjsIBnTD6s+iocX4WJMHVtLFuM9WJjSTRGI7CABxyuq17hjfxHcgcEFnDb0btq2Z0Fqqe6s4ljnO/HD6QcYi18NMQEFvDF0bvqRc7KI3ZbvW56xhgEFnC5XM64aH3xjTFXdaQ2eCp13NudgxFYcG5nHVZ5Fx+WxuIYBBac0lm76hXbjK8O5tlaklYchsCCM9FV6wiz4Mw/mdeXbVnnzjgEFhzd+RZX/WjM1VdHteCSn6uEHIDAgoMyrALYj8CCY9FVK9hmmnLgmc3jE6lmdmUCxgAEFhyCrnpY/s7rrXwolmExCIEF07K4ahP6KbH4CwphUgILZmNYBTA8gQWT0FWFZ4cihighQyxORWDB2HTVOSiJD7qKYxBYMB6Lq8bgbT63XTzJNPYmsGAYhlUARyGwYG+6aismGtMxh2JeAgt2oqvG5n19JZqJkxBYsCGLqwDOQWDB+gyrBmBqAmxJYMFqdBW8zCVFJiWwoKarYATSjF0JLIjoqgPxvrwq5cMZCCx4gUXrAHxHYMHzDKsAuEtgwcN0FQCPEVjwE101v/FX/FiW9OHreXBymJHAgu9YXHVi3ss3oJk4PIEFVwyr4Eh0HPsRWKCrAIgJLE5MVwGwDoHFyVhcxahczrpYAMeBCCzOwbCK1QijofhZMAiBxaHpKgD2ILA4Il3FtM48gLm+gJ8xYGQnAoujsLiK+b3HwJn53eUwBBaTM6xiAKYkg/BTYBwCiznpKg7qtK12zqPmwAQWU9FVAMxAYDE8i6s4mRMOsc52vJyBwGJUhlUATEtgMRhdxZzasdOphljVkd58nlOdTYYhsBiDrmIY3o434AxzeAKLXekqNrFNMxliLfDIMVZ/BrYksNicRevwsGN3w8nvqsqxCSy2YlgFT3ofYh21sd5fEg55aHARWKxOV3Em+XW9Y395TnWijtqgTE1gsQ5dxcyGWv801M4kdphdHe8kMjyBRcfiKljnrfx4eXCkY4FvCSxeZljFDA7QKLPv/7v8iucxTgvHI7BYSlfBho6x4H1BXc1+yJzWX3vvALN5f41/f817/wf400or099/2+Zd877G0iv5xbBMsHiAxVWcz5iXFOedY33U1Yw7DwsILG5zEZBj2fLdfb1tzdhYi2dX9w9zrpPA2QgsvtBVUFi1sS7z5MVK+/n005qesS2BxW+6Cv40+Dvyx0qvYffw6+6NfD6hJbDOzeIqWNPaiTby5cJV42/MQ4ZrAuuUDKs4q2eLZ/Ah1mXUxvq2rp7dydEOCp4isM5EV8HmNki069s37P7LvcFuCC+mILBOQFfBle2HWNuMwXbPrPubrs6AumIWAuu4dBWczy6ZNc0dRMe/4suBCKxjsWgdVjDLEOt6c5f1/5L1+PMbX3FCAusQDKtgeNvfVeEjs9pXiF3+HjfICjN4nMCama6CRRbMk5IR1ErfUfjjRj982vqDh7PsUdcPTx7idY65CKwJ6SqY1r6rgL7eN2HBo7bnyiAzEliTsLgK9la10TgrrTfYh9ePdJBzBc8SWGMzrIJ17D5J0g23XJ8ZZ4l5Cawh6SpY314rsc6jWn1V8iNkKwJrJLoKZnCwC4UreX05/7HPD4cnsPZmcRXsZ/EQK9z65bi/+ovHV8c+LZyEwNqJYRVMKxw+ffTEwV4JXjmi450NzklgbUtXwWCW1VJ7ge9glwuXHcv7o450Hjg5gbUJXQUDG+F9/fCXCx+x+08BQgJrNRZXwaHlSbTLfd5bi0/IpnE5QlBzAgKrZlgFp5En0QHe+hfv/NRHDV8JrIiugpktLps8iea9Vrh46dVlwoOFHwms1+gqOIoXG+uSXiu8TLUgaY4rg7AtgfU8i6vgoF5vrHxnLpO8zCy45dWyB8IsBNbDvB4At62xfGqKu24+e9TXhzP7on64Q2D9RFfBmbzSSSvNnIa9YrjgYNf4Iuc7lTbaGeNUBNYNugrOKmms3JhXDB/fmU87n9TV/dfpt7fbZ+wAH9dkeALrT7oKGHKOdRnpiuHj+/Dta+rrbfPIDlzH3I9/GHICy6J14BsvNtZltYt6n1Yvbf+i9eBx3cqaberq2vuP0sSKjZ04sAyrgDWtelHv03hmpa188sjhrLo/i8/nOMM/zuN8gaWrgMe8vlBng9nJZhfCfnz+B/PrxT18/ccB2zhNYOkq4HlJY102mZ18e+OD8GN6317se2pbL57JpFOtbmczhw4si6uAlyVvyRtn1ocXXwW/7vDiJ3y9rkJvbxdvCaztiIFlWAWkqrHH9iuBbrXRU17/u2p49l7374VCsyxWdqDA0lXAasK3470WXD+4rXzHko8N/rj261u3HvXvT/OlnYIfzB9YugrYRDvyGPBzbWvszNpDojv77NYM7GvOwLK4CthDfllpkMxaaQfa27Xf+lf3x1R39kF9saqpAsuwCtjbGne32uveoettsT1FtwZUP27iTmO5ZQNrmyGwdBUwkpVu1P713qGf/vfXrffMn7ay/RL+O39GSLGLgQNLVwEDW+9TaHdutfD13963TVF92uJMr9mT7S4zGSywLK4C5rHNJ/3v99ZTj12bXIEPYwSWYRUwp1W/cPDWFge0+zp9GM2ugaWrgPmttCRrImc+drhlj8DSVcDhnPbG4Oc8avjRVoFlcRVwdNtfLtzRln9TXqPhfLSQta0cWIZVwJkMcuPQtW05tbpzn4VHduOHL9KRWaxmncDSVcCJHTizxjmoH2/Ufnlkb097ZZf1pYGlqwB+O1hm7XggtyrofmPd/5rCA/xEGFwRWLoK4IZjfMZwhP2/31jfuhNesLalgWXROsDDrhcSTfSSOc4+31mJtWDfdj8czuDJwBrntw1gKl+/anDM19Fh//qcLJcaYRTHSTwWWIO/HgDMY9jSmmK52CuF5OIgW7obWKP99gMcyNfSumz+cjvsvOpbiz83cO8hPkjIOr4E1ly/bQDzu36t3eAvtrO/zD9yg4ZrU0zmOJ7fgWVYBTCAb8daX//t474+zwFe5q9HWZcbR+RtjX29+T8ewCzeLk+/Zv86+t3K75yTx4/9///5p9kb+O1/qDW5ft9XJeYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA3C8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA3C8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA3C8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 3:\n",
      "Stoppers will not fit in the triangular space\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA3C8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026E5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026EA320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xqXwH/f9yzSIWAIcjsBaw/IU0twoSJwoB4BUCq7bWZcrXvxb6sq+osQA4EIGVWus+g1vdaUYFAcArBFbHLfZmkm8AHIXAirxWV/MbbIQCSY7h7zWlsQA4BIFVWHftattlssVfXWMBsH8CazZnBnMaC4CdE1jzqCsA4AuBNYO6Wo5FLAD2TGBNpa6WprEA2C2BNYm6WofGAmCfBNb71BUA8C2B9Y7rVV2tzSIWADsksF52Syt1tT6NBcDeCKzXWLjalsYCYFcE1gvU1Qg0FgD7IbB+oq4AgDcJrG/VdWUV5m7K0Bo+AHZCYD036trVto2xceFoLAD24J+tD2BUL9TVixN9G2kjBMbr7+j7Q73/1/eG6DYEQ7YvANwIrL95Mn9/yoUXp/jNe2hNrw/R4xhPG1gAGJbA+uLPunqc+6dN/J/+6nax0plPuNUKzl9fd4kh+uEJLWIBMDaB9aeHaXtmBj1zb4N7aU17/vUD4+tS3OQh+v7gH1e2ng6RxgJgYALrwe8Je073vO7TCbK3Xm6rnVhzjrl/OY0FwKgE1m/X6+XjY51u+OT2chNees26uPfcvoYIADYhsC6Xy+VyvV4vH5d1e+XTa73bEPeTjCsc82NdzX+5yWtvfxkii1gADElg3SbsjzXn6G9O8L2VWes01hJ70eY81ech0lgAjOfsFxod86zTY0NUj5xmoZ3+8/3xxke4OBgAPDh1YG1YVz8mwQiNtURdhYtNGguAYZ03sG4z/WgLM49uh7dVY93r8xhDBABrOmNgrbY3/Huvx9PjtUm/edjl8tIjfzTzAl3fP/MSw/5riC5SC4BRnC6wxtx09b0XF6juq01zMmPYTVff+/XGNRYAYzhXYI1WV6+f3nprS9Z90ev12Pj0+CWGaOlVQ40FwDhOdJmG0erqXW9dlGHCGcN77e1+iHb8DgA4iLME1nKbir734rWsXjywdy989e514d/9k7eefJ3qWfP6qwDwzFkC69Klw2NU/ficLz743cZayHJ1taZfQySyANjOKQKrvcHLu3dl/vEZJqxL5fGwXI1sde/C6/XjQ2MBsJHjb3KfP8k+XrZg5j1enm2Nevdp23Wsdbafr+zj43K9qCsAtnHwwEouCnVJr7f57GIKE5opaaxFz99tvoTkB4UAbOLIgTXz5NT9tN1C18b8egXRtxoruXr7MTa2P7P0jRoB4JmDBtbvcplTVyvcJeavd3p5t7HmH8MSBsmaX+9ukKMB4DSOGFjX6+Xj43r5mJYO6//I/3Ep691FlzmbsQ62sf2ZX5uxNBYAKzpcYM2rhq3K4LGr9n5ia6i6AoBNHCuwftfVtMratgwmN9a0RayFlq/GrCuLWACs7ECBtc+1q0d7X8caYQy/s+hFWgHgwVEC66GuJofWCGXweAx/3QL/7K/eKocllq/W+VnAZL+GSGMBsIpDBNbsXtj8ggKPPjXA16s5jMa9/wDgk/0H1p9z+4SZfsA4+NpYl59OF76+NNO+39FPCz6wiAXAanYeWAPG0TLG3JK1o7r6g8YCYGF7vtnzl7oa58d08329o/PXLfBf/fh2qq54K62+edH1B//XEC1xx2wA+G23gfVkdnxrxhx/FePru/wms17fET/zkF5/kvvx/PXxny6vuoI/hkhjAbCYfQZWNy+OPL1+E0yvrGblJqTV9w++/9e9nmoEgCd2GFhRXY2/fHXzzdv9tDFr6bsKvv787wbT/ZeSazeWRSwAlrG3wHo+HU6YKMefWF8563fPrNsjvxmHt4bo688YX/+rCQO72prc56bSWAAsYFeBZSJ87vF026cmm7YVffJIz/mItvl5n8YCoLafwEqnwB3NpxNm/08PfkyWRX/Ql4yq2gHgAHYSWKbcGR4Xt5YbxXblae0PXNYBkNrDhUbNfDtRfUrbfNquPgpAZ/jAeq2uNNjds05YevmqffJFa+fpk2ssACJjB9YyUbC7GjPvA8C+DBxYu+ugs1ou/jb7RSEAzDNqYKmrXVnis9rs89dYAMw2ZGCpK7alsQCYZ7zAUleMQGMBMMNggaWuAID9Gymw1BVDsYgFwFTDBJa6YkAaC4BJxggsdcWwNBYA79s6sK5XdXUASxSIqgFgvzYNrFtaqaudW+4DHOWrYRELgDdtF1jbLVztbrq0xre93X1pANjURoFVJ4Pp7+7Z0G5z++SpRrw1tS8ZAC/bIrAsyBxUlR8yBoC9Wz2w1NVBtZ/qoN8Ri1gAvGbdwBqmrnY0UQ4zZj9LRnX097ujrw4A21kxsEafOWnMyY99pIvGAuAnawXW8nU1YdYbf5ac8I6+GeYVwuB22Y3b1c3ecr8g2tIR3nwTNRYA31olsIZcuxrviP5uL8f56HbMrxfI7ZF7fKcA8Ff/LP4KQ9bV3chHt+slkk+N9ddB/v6/ju62iLXLQwdgcQsH1uoz0FsvOP55nrcG78X3suZncs+sZ8e2cp/EH7fGAuCJJQNr9blnQjANO0VOO6of/2STphxqeOODGfYLBMCmFtuDZdYBAM5qmcDa1X0GBzxROGH8Xv+TAd/vOpb6Vp52QAF4boHA2uHa1VBT5A7H7/SG+gIBMIA6sAaog8mT3QhT5OQjf2vUT9gDi38xTzimADyXBtYAdTXZu5duWoLLQQHAMXSBNVJdTVtN2LaxJtfV5N8bnmfBZaXv5qnGFIBvRYE1Ul3NsVVjWbs6CI0FwOVyaQJryLqaPNPd76a3mjn34Jsz9ieJgbW/nicZVgC+NTuwhqyru8kz3bQ7Fr/rfofjyX+eHMOBbfPuNBbA6c0LrLHraub5vvtS1hJz5T2tZtbVzOEfYWv/cpx4BWArMwJr7Lq6mX+AP95N7133p6qObYQnGdZm784iFsC5TQ2sPdTVzfyZ7r7ONDOzHtNq5uC1w3/IGNj+G3rIYQXgNZNu9rz93PWe5Ia89z9/nDR/fM63HvyiJYb/YPcsHuW9HGxYAXjZ+4G12wmjOvDHJ/lxhSIfqkXXRHb72f7BshEAm3snsPa8Z/i+Xb09/JUHY9FPYKEhWtlwX1KLWACn9PIerJm/eRvA3n8xt0I6GKJF2IwFcD6vBdZR/hd8vwGxWjoYokVoLICTeSGwjlJXN3sMiJXTwRAtQmMBnMlPe7COVVc394DYxTvb5DgNEQDM8W1gHXriui8oDPsWNz88QxSz4R3gNJ6fIjzBTDDyubBB0sEQxZwoBDiHJ4F1grq6GTMghkoHQxTTWAAn8LdThKepq5vHgNj8fQ9yGJ8YIgB4y5fAOlld3W3eEON3gyHK2IwFcHR/Btbp/9HfpCH21Q2GqKGxAA7tIbD8c//bp11HC43K0s+/KEMU0FgAx/U7sPxD/8W9Idpp/nF/896H3BABwF/9c7moq+88Dsyn3369OGbT/mpHDNF0FrEADurqn/bJrpeXBu/jct7f5BuiF/3/v/9ufQgAlP4LnRbH3kkru+wAAAAASUVORK5CYII=\n",
      "text/plain": [
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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72027192B0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 4:\n",
      "All three stoppers will fit in the triangular space\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026E5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72027192B0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026E5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Kv3FUkEpV1VWvoJT+/IrGAuDSBNYhKowjAGA3Amt/b3VVMLupttDKRlGGWABcm8Da2UQZraql+jtk1Rn+fe4aC4CLElh7ys2d6hxf9Tadm8YC4IoE1m5CddVKfrRyngBwAIG1j+m6KuiumsdXvYJn9DfIDLEAuByBtYNqd6RXS2MBcC0CKy1aVw2l2tZG0lgAXIjAimooiACA3QisHHW1kSEWAFchsEKW1ZUGG3yuKY0FwCUIrIR9uqm5GsvUkcYCoH0Ca7PmOqh+GguAxgmsbdQVAPBGYG2grvZjiAVAywRWKXW1N40FQLMEVhF1dQyNBUCbBNZ66goAmCWw1ng81NXRDLEAaJDAWqxPK3V1PI0FQGsE1jIGV+fSWAA0RWAtoK5qoLEAaIfA+ua8umquKIQoAPQE1qx0MjTXTPspWVrLB0AjBNY0A5kKaSwAWvDr7BOo1YK6Wnihv3OkzS/R8F/XLVHfWHdeVgCqJ7A+mbh+v+TCwkv8loFLQy3Rn+fyJRo/r7KFBYBqCaw3/xbN+NpfduF/+a3+ZqVbDlib4ekUt+D7Ek39p7//ayvhCcAtCax/jS7bO2XQ0AZDaX09frUtUTx5mn9G48nW5BJpLAAqJrBGfi7YC7tno5c3yKYers5d3S/nvFPqfFkijQVArQTWj8ejez6PSasX/cPNP3Q9IfF+ngf035IlAoB6CKyu67ru8Xh0z+7AiHkPppmGqGSINdM3q9at+Ll8WCJDLACqJLD6C/bzyGv0TDBNZda5ITGTVmVnteWJvC6RxgKgPne/0Wid7zqNG+J0DSxRJSM+APhx6wlWWToUXMrfH+Lr2GX4mOHwM6dMauI7w4JP4Z8lMscCoCb3DaxVl+ONd8Mq+/VhSHNWY80/Vg09875EAFCDOwbW8sHV9ruMvvzuy11Gl5TB8PbX3vdEGPu6RGXvyO13N4c/G+mkFgB1uN0erLV19Xz++b+I8dGWN8r7zvdddxwtrKuqSubPsnQ2YwFQhXsF1vI7p/ejkP0aYm1mHdZY+9XV3tMljQVAPW4UWEvK4IC0GhtSaUkSHNBYLc6uxv42FgCc6i57sJZvKjr+Nu79Qy9pl/Hn5uL7u5cs0cYN/h+LMLvg75++BIDj3SWwuuoHMwvL4OWWT+9b4Deew0drH2LVGaY+SfD6iCILgPPcIrAqv93AS1otbKzxvRu6zY049aCrDvtxCvj1CO8/vPwRZ475ePhQIQCnuf4erMrrqjc+hyW3JX//mVXbuV58XIThUAs/cTn+0OX72S40futz4w6z59NmLABOc/HAmrlI17ZTZ9xMw0xr3ntjFdTJ+0/O19LUET7+cNkKF9zJYv7cAOBgV36LcNWbUzUYv/f3dY41tWdrfD/S9//xxbBEZRuh4l+kM7b9rU8b3gE4y0UD6/HzJcD7XPt39dJY84E4E2Ef9zbNP+IqX997jdj4YUkb3gE4xRUD6/HoZvc313y1fRm6LGysr09nagN72Tocf7usLR+WtOEdgONdbg/Wt+to/dfZl+1HS/a8H+msm5HudG9VANjDtQLrp57mbzpQv/eYmH8rMPXJwSW/1Z13R7HixvrzicJW/vwAtO9CgbUsGSofXw0id7fKquGLdDbNsWobBgJwXVcJrFFdtT6+GvR3KxhOOzjE2rJnfP6YB7Tgpt3uGguAQ1wisBb3QiWjoFUqSYL5Dw0cvLOtkjUBgCntB9a/1/aZ8VWLddX7eGur959Z2BwFSzFfV90Z5VrQWIZYABym8cBqupvWqPNZVrVFbAWNBcDOWg6st7qaumheI8OGLVnz3/8zL/tNhcdsuppS/PHJ8l8GgGWaDayJaPqYAtfzMbMWts6qJJr6psJz02ps1d/3n3PWWADsps07ua8cSVWSAhHjW7cf8w7dyw6wqhZTIwFQpwYD6xpv+CW83/M9qz/yfsdPKX9FLPymIQBYqbW3CKcvh1NbhS5p/LyGd+teeujjby1viY8PUaG1J/Y69DIEA2AHTU2wioYN1ZZBsY9JMH4j7+W/LlyB99+6y3DnRk8VgIO0E1gugYu9rNPy7zR8+a1W1lsgAVCbRgLL9XOD8XDLKn6m0QCIamEPVumV78JXTBuH8qwpADnVB9aySrpwS6011QmWaDCZUhoLgJC6A0sUnKS5hZdGAFSl4sBq7iLPBSg1ABJqDSx1xVk0FgCbVRlY6opzaSwAtqkvsNQVNdBYAGxQWWCpKwCgfTUFlrqiKoZYAJSqJrDUFRXSWAAUqSOw1BXV0lgArHf2dxH2ly51BQBcyKkTrH5wpa6onCEWACudF1jeFqxYc0Wx+6upuRUB4FQnBVb6eujyN5haWks0KHz1WUEAFjsjsMyuAIBLOzyw1BXtMsQCYJljA+vYurrw1fCAhWxo9Q59WTW0LgCc58DAMrviGjQWAN8cFVj715WrXvdtmQuWqP4lLXhGgVeiVxsAsw4JrFNnV9e7Dh72jFoZOLZyngDcx/6BdWpdXfXSe+TzqrlQzzw3QywApu0cWIfX1Z0veQuf+6olqr9QV51h+OWhsQCYsGdgHV5XU492pYvg/HP5ut4Ff5BqK6Ls9RV+SVa7OgCcarfAquYzg3WcRdL1nhEAXMw+gXVeXX0cKFxmyjCzrsuXvGA1KlzAgpfYXq/KClcHgLPtEFjVzK4IqqoiqnuJVbU6AFQgHVgVXPquOsSKjK96xatRwxoWn/m+L8wLvMIAyIkGVgV1Na/dK2ANZ97/bc89k/7R636VAUAwsGqqq6khVtNS46vhaAWpdG5jFdfVQa9NQywAfoQCq6a6mtfiFbCqcz6rsdqYXWksALquywRWlXV1sSFWdnw1HLMsBp7Po0Oif5plz/Tol6fGAiAQWFXW1eACu93n97ZHjl+mX8m9F7N/iOKX2Dl/6+ZeZACkbQusuutq6s2shi5/X+tq4/JvfL9vGGXtsZ5DWm2sq4pfoQBc1obAqruuelMn2ERjfV3gyPJvP8hQaaklHQ6VOrcTNPEKA2A3pYHVQl31Zq50NV8B588tu/zbY2CYM23MrHFabXyC579CNRbAjf0q+aXzr13r9Fe6l1MegqDCpzJ/Vnuc88clKjhIb9wVX4+56ocXquXPGllWABq0PrCavWB8PPEKr4Bf6+qsh15ufJCvJxxffGMjAE63JrBa3jM87MWeaqyugmf29TR2Pc+ZJdp42CNV8qf8q8KEB2B/i/dgbfxAVwVmPjEX36a91pJt3QekQw1fhrNFdXXVsxkL4H6WBdZV/l/w+cY6/R7l59ZVr93GqrSuehoL4GYWBNZV6qo3HxC73tjp3cJbPR2cDi02VtV11dNYAHfybQ/Wteqq9/Xzg+PC2OnZLz/4KX+Bmj9i+a6V8wTgPmYD69IXrq97219GWZGVKLh/wYl/gXq2/0+p/PRe2fAOcBvTgXWDK8HXz82Nb+y0pbQKbvVUSTrs9NHCiEqWaB2NBXAPE4F1m2vAwoBYdWOn+V9foqp0qLOxqlqidTQWwA18Cqyb/eu/dsfVrmtTZzccsCltuUpOAwBmvAXWzepqcHpD1N8NlijGEAvg6v4NrNv/o39KQ7TVDZYoQ2MBXNoosPxz/+PlRlC73qlhv+PvyhIFaCyA6/oJLP/Qv3n//pzj79RQOUsEAB/96jp1NWfm84Orbriw9rcaYonKGWIBXNTDP+3FHt2ixXt29/2CFEu00P///n32KQCQ9D8doYfNiwoA6QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72027192B0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026E5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72027192B0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 5:\n",
      "Stoppers will not fit in the triangular space\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x800 at 0x7F72026E5208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Triangle number 6:\n",
      "All three stoppers will fit in the triangular space\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "import sys\n",
    "import PIL\n",
    "import collections\n",
    "from PIL import Image, ImageDraw\n",
    "\n",
    "EPSILON = 0.0\n",
    "PI = 3.14159265358979\n",
    "\n",
    "class GridPoint:\n",
    "    def __init__(self, x, y):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "\n",
    "stopper_list = [[0.0,0.0],[0.0,0.0],[0.0,0.0]]\n",
    "triangle = [0,0,0]\n",
    "vertices = [GridPoint(x=0.0, y=0.0),GridPoint(x=0.0, y=0.0),GridPoint(x=0.0, y=0.0)]\n",
    "angles = [0.0, 0.0, 0.0]\n",
    "\n",
    "possibilities = [ [0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]]\n",
    "\n",
    "count = 1\n",
    "\n",
    "with open('uva823.in', 'r') as infile:\n",
    "    while True:\n",
    "        nums = list(map(float, infile.readline().split()))\n",
    "        if nums[0] == 0:\n",
    "            break\n",
    "        triangle[0] = nums[0]\n",
    "        triangle[1] = nums[1]\n",
    "        triangle[2] = nums[2]\n",
    "        stopper_list[0][0] = nums[3]\n",
    "        stopper_list[0][1] = nums[4]\n",
    "        stopper_list[1][0] = nums[5]\n",
    "        stopper_list[1][1] = nums[6]\n",
    "        stopper_list[2][0] = nums[7]\n",
    "        stopper_list[2][1] = nums[8]\n",
    "\n",
    "        if count != 1: \n",
    "            print()\n",
    "        triangle.sort()\n",
    "        if triangle[0] == triangle[1] and triangle[1] == triangle[2]:\n",
    "            angles[0] = angles[1] = angles[2] = 60.0\n",
    "        else:\n",
    "            angles[0] = math.acos(((triangle[0] * triangle[0]) + triangle[1] * triangle[1] - triangle[2] * triangle[2])/(2.0 * triangle[0] * triangle[1]))\n",
    "            angles[1] = math.asin(triangle[0] / triangle[2] * math.sin(angles[0])) * (180.0 / PI)\n",
    "            angles[0] = angles[0] * (180.0 / PI)\n",
    "            angles[2] = 180.0 - (angles[0] + angles[1])\n",
    "            angles.sort()\n",
    "        ##vertices 0x and 0y are default 0\n",
    "        vertices[1].x = triangle[2]\n",
    "        ##vertices 1y is default 0\n",
    "        vertices[2].x = math.cos(angles[0] * PI/180.0) * triangle[1]\n",
    "        vertices[2].y = math.sin(angles[0] * PI/180.0) * triangle[1]\n",
    "        \n",
    "        index = 0\n",
    "        if stopper_list[0][1] == stopper_list[1][1] and stopper_list[1][1] == stopper_list[2][1]:\n",
    "            vals = [stopper_list[0][0],stopper_list[1][0],stopper_list[2][0]]\n",
    "            index = vals.index(min(vals))\n",
    "        else:\n",
    "            vals = [stopper_list[0][0],stopper_list[1][0],stopper_list[2][0]]\n",
    "            index = vals.index(max(vals))\n",
    "            \n",
    "        stopper_list[index], stopper_list[0] = stopper_list[0], stopper_list[index]\n",
    "        \n",
    "        possible = True\n",
    "        good = False;\n",
    "        \n",
    "        tri_perim = (triangle[0] + triangle[1] + triangle[2])\n",
    "        tri_perim_over_2 = tri_perim / 2.0\n",
    "        tri_area = math.sqrt(tri_perim_over_2 * (tri_perim_over_2 - triangle[0]) * (tri_perim_over_2 - triangle[1]) * (tri_perim_over_2 - triangle[2]))\n",
    "        max_rad = (2.0 * tri_area) / tri_perim\n",
    "        \n",
    "        for j in range(3):\n",
    "            if stopper_list[j][1]/2.0 > max_rad:\n",
    "                possible = false\n",
    "                break\n",
    "        if possible:\n",
    "            for i in range(6):\n",
    "                a = GridPoint(0.0,0.0)\n",
    "                b = GridPoint(0.0,0.0)\n",
    "                c = GridPoint(0.0,0.0)\n",
    "                \n",
    "                a.x = (stopper_list[possibilities[i][0]][1]/2.0)/math.tan((angles[0]/2.0) * PI / 180.0)\n",
    "                a.y = (stopper_list[possibilities[i][0]][1]/2.0)\n",
    "                b.x = triangle[2] - ((stopper_list[possibilities[i][1]][1]/2.0)/math.tan((angles[1]/2.0) * PI / 180.0))\n",
    "                b.y = (stopper_list[possibilities[i][1]][1]/2.0)\n",
    "                tmp_cx = (stopper_list[possibilities[i][2]][1]/2.0)/math.tan((angles[2]/2.0) * PI / 180.0)\n",
    "                tmp_cy = (stopper_list[possibilities[i][2]][1]/2.0)\n",
    "                rotation_angle = 180.0 + (90.0 - (math.acos(vertices[2].y/triangle[1]) * 180.0/PI))\n",
    "                c.x = ((tmp_cx) * math.cos((rotation_angle) * PI / 180.0)) - ((tmp_cy) * math.sin((rotation_angle) * PI/180.0)) + vertices[2].x\n",
    "                c.y = ((tmp_cy) * math.cos((rotation_angle) * PI / 180.0)) + ((tmp_cx) * math.sin((rotation_angle) * PI/180.0)) + vertices[2].y\n",
    "            \n",
    "                base = Image.new('RGB',(800, 800),(255,255,255))\n",
    "                draw = ImageDraw.Draw(base)\n",
    "                draw.line([(0,0), (799, 0)], fill=(128,128,128))\n",
    "                draw.line([(0,0), (0, 799)], fill=(128,128,128))\n",
    "                \n",
    "                draw.polygon([(30.0 * vertices[0].x, 30.0 * vertices[0].y), (30.0 * vertices[1].x, 30.0 * vertices[1].y), (30.0 * vertices[2].x, 30.0 * vertices[2].y)], outline=255)\n",
    "                draw.ellipse((30.0 * (a.x-(stopper_list[possibilities[i][0]][1]/2.0)), 30.0 * (a.y-(stopper_list[possibilities[i][0]][1]/2.0)), 30.0 * (a.x +(stopper_list[possibilities[i][0]][1]/2.0)), 30.0 * (a.y+(stopper_list[possibilities[i][0]][1]/2.0))), outline=(0,0,255))\n",
    "                draw.ellipse((30.0 * (b.x-(stopper_list[possibilities[i][1]][1]/2.0)), 30.0 * (b.y-(stopper_list[possibilities[i][1]][1]/2.0)), 30.0 * (b.x +(stopper_list[possibilities[i][1]][1]/2.0)), 30.0 * (b.y+(stopper_list[possibilities[i][1]][1]/2.0))), outline=(0,0,255))\n",
    "                draw.ellipse((30.0 * (c.x-(stopper_list[possibilities[i][2]][1]/2.0)), 30.0 * (c.y-(stopper_list[possibilities[i][2]][1]/2.0)), 30.0 * (c.x +(stopper_list[possibilities[i][2]][1]/2.0)), 30.0 * (c.y+(stopper_list[possibilities[i][2]][1]/2.0))), outline=(0,0,255))\n",
    "                \n",
    "                draw.ellipse((30.0 * (a.x-(stopper_list[possibilities[i][0]][0]/2.0)), 30.0 * (a.y-(stopper_list[possibilities[i][0]][0]/2.0)), 30.0 * (a.x +(stopper_list[possibilities[i][0]][0]/2.0)), 30.0 * (a.y+(stopper_list[possibilities[i][0]][0]/2.0))), outline=(0,0,255))\n",
    "                draw.ellipse((30.0 * (b.x-(stopper_list[possibilities[i][1]][0]/2.0)), 30.0 * (b.y-(stopper_list[possibilities[i][1]][0]/2.0)), 30.0 * (b.x +(stopper_list[possibilities[i][1]][0]/2.0)), 30.0 * (b.y+(stopper_list[possibilities[i][1]][0]/2.0))), outline=(0,0,255))\n",
    "                draw.ellipse((30.0 * (c.x-(stopper_list[possibilities[i][2]][0]/2.0)), 30.0 * (c.y-(stopper_list[possibilities[i][2]][0]/2.0)), 30.0 * (c.x +(stopper_list[possibilities[i][2]][0]/2.0)), 30.0 * (c.y+(stopper_list[possibilities[i][2]][0]/2.0))), outline=(0,0,255))\n",
    "                base = base.transpose(PIL.Image.FLIP_TOP_BOTTOM)\n",
    "                \n",
    "                display(base)\n",
    "                tmp_lhs = tmp_rhs = 0.0\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 1\n",
    "                if possibilities[i][0] == 0:\n",
    "                    tmp_index_1 = 0\n",
    "                elif possibilities[i][1] == 0:\n",
    "                    tmp_index_2 = 0\n",
    "                tmp_lhs = math.sqrt(math.pow(b.x - a.x,2.0) + math.pow(b.y - a.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][0]][tmp_index_1]/2.0 + stopper_list[possibilities[i][1]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 1\n",
    "                if possibilities[i][1] == 0:\n",
    "                    tmp_index_1 = 0\n",
    "                elif possibilities[i][2] == 0:\n",
    "                    tmp_index_2 = 0\n",
    "                tmp_lhs = math.sqrt(math.pow(c.x - b.x,2.0) + math.pow(c.y - b.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][1]][tmp_index_1]/2.0 + stopper_list[possibilities[i][2]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 1\n",
    "                if possibilities[i][2] == 0:\n",
    "                    tmp_index_1 = 0\n",
    "                elif possibilities[i][0] == 0:\n",
    "                    tmp_index_2 = 0\n",
    "                tmp_lhs = math.sqrt(math.pow(a.x - c.x,2.0) + math.pow(a.y - c.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][2]][tmp_index_1]/2.0 + stopper_list[possibilities[i][0]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 0\n",
    "                if possibilities[i][0] == 0:\n",
    "                    tmp_index_1 = 1\n",
    "                elif possibilities[i][1] == 0:\n",
    "                    tmp_index_2 = 1\n",
    "                tmp_lhs = math.sqrt(math.pow(b.x - a.x,2.0) + math.pow(b.y - a.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][0]][tmp_index_1]/2.0 + stopper_list[possibilities[i][1]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 0\n",
    "                if possibilities[i][1] == 0:\n",
    "                    tmp_index_1 = 1\n",
    "                elif possibilities[i][2] == 0:\n",
    "                    tmp_index_2 = 1\n",
    "                tmp_lhs = math.sqrt(math.pow(c.x - b.x,2.0) + math.pow(c.y - b.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][1]][tmp_index_1]/2.0 + stopper_list[possibilities[i][2]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "\n",
    "                tmp_index_1 = tmp_index_2 = 0\n",
    "                if possibilities[i][2] == 0:\n",
    "                    tmp_index_1 = 1\n",
    "                elif possibilities[i][0] == 0:\n",
    "                    tmp_index_2 = 1\n",
    "                tmp_lhs = math.sqrt(math.pow(a.x - c.x,2.0) + math.pow(a.y - c.y,2.0))\n",
    "                tmp_rhs = stopper_list[possibilities[i][2]][tmp_index_1]/2.0 + stopper_list[possibilities[i][0]][tmp_index_2]/2.0\n",
    "                if tmp_lhs <= (tmp_rhs + EPSILON):\n",
    "                    continue;\n",
    "                good = True\n",
    "\n",
    "                break\n",
    "        print('Triangle number %d:' % (count))\n",
    "        count+=1\n",
    "        if good: \n",
    "            print('All three stoppers will fit in the triangular space')\n",
    "        else:\n",
    "            print('Stoppers will not fit in the triangular space')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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