{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleContexts #-}

import Control.CP.FD.Example

model :: ExampleMinModel ()
model () = do
  let c = board
  let numNodes = c!0
      numEdges = c!1
      edgePos  = slice c ((cte 2) @.. (1+numEdges))
      edge i   = slice c ((2+numEdges+((i@=0) @? (cte 0,edgePos!(i-1)))) @.. (1+numEdges+(edgePos!i)))
  exists $ \numColors -> do
    exists $ \colors -> do
      numColors @: (cte 0,numNodes)
      size colors @= numNodes
      colors `allin` (cte 0,numColors)
      loopall (0,(size (edge 0)-1)) $ \i -> colors!((edge 0)!i) @= (size (edge 0)-1-i)
      loopall (1,numEdges-1) $ allDiffD . slice colors . edge
      return (numColors,colors)

main = example_min_main_void model

{-

  [numNodes,numEdges,[cumul. clique sizes],[clique elems]]

  0--1
  |  |
  2--3

  4,4,2,4,6,8,0,1,1,3,3,2,2,0

     0-1
    /   \
   4-----2
    \   /
     \3/

  5,6,2,4,6,8,10,12,0,1,1,2,2,3,3,4,4,0,2,4
-}

board = list $
 [
  200,367,
  30,60,85,110,135,160,185,210,235,260,285,305,325,345,365,385,405,425,445,465,485,505,525,545,565,585,600,615,630,645,660,675,690,705,720,735,750,765,780,795,810,825,840,855,870,885,900,910,920,930,940,950,955,960,965,970,975,980,985,990,995,1000,1005,1010,1015,1020,1025,1027,1029,1031,1033,1035,1037,1039,1041,1043,1045,1047,1049,1051,1053,1055,1057,1059,1061,1063,1065,1067,1069,1071,1073,1075,1077,1079,1081,1083,1085,1087,1089,1091,1093,1095,1097,1099,1101,1103,1105,1107,1109,1111,1113,1115,1117,1119,1121,1123,1125,1127,1129,1131,1133,1135,1137,1139,1141,1143,1145,1147,1149,1151,1153,1155,1157,1159,1161,1163,1165,1167,1169,1171,1173,1175,1177,1179,1181,1183,1185,1187,1189,1191,1193,1195,1197,1199,1201,1203,1205,1207,1209,1211,1213,1215,1217,1219,1221,1223,1225,1227,1229,1231,1233,1235,1237,1239,1241,1243,1245,1247,1249,1251,1253,1255,1257,1259,1261,1263,1265,1267,1269,1271,1273,1275,1277,1279,1281,1283,1285,1287,1289,1291,1293,1295,1297,1299,1301,1303,1305,1307,1309,1311,1313,1315,1317,1319,1321,1323,1325,1327,1329,1331,1333,1335,1337,1339,1341,1343,1345,1347,1349,1351,1353,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405,1407,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427,1429,1431,1433,1435,1437,1439,1441,1443,1445,1447,1449,1451,1453,1455,1457,1459,1461,1463,1465,1467,1469,1471,1473,1475,1477,1479,1481,1483,1485,1487,1489,1491,1493,1495,1497,1499,1501,1503,1505,1507,1509,1511,1513,1515,1517,1519,1521,1523,1525,1527,1529,1531,1533,1535,1537,1539,1541,1543,1545,1547,1549,1551,1553,1555,1557,1559,1561,1563,1565,1567,1569,1571,1573,1575,1577,1579,1581,1583,1585,1587,1589,1591,1593,1595,1597,1599,1601,1603,1605,1607,1609,1611,1613,1615,1617,1619,1621,1623,1625,
  6,11,14,25,40,42,48,53,61,76,80,87,89,92,108,115,120,131,132,137,145,159,162,163,164,168,172,173,176,182,
  3,15,16,31,34,35,37,38,49,58,67,78,86,91,100,110,114,123,129,132,133,140,143,154,167,168,174,175,193,197,
  3,10,33,38,43,45,48,51,65,66,82,88,90,93,94,103,107,128,131,141,152,155,168,185,199,
  0,4,7,26,28,33,36,58,61,72,79,81,90,99,105,114,115,124,135,152,159,161,173,181,192,
  12,15,28,39,43,44,45,66,83,84,85,99,102,108,112,115,120,126,131,152,157,163,171,182,183,
  13,14,15,38,55,66,76,78,87,91,95,99,109,110,125,130,134,137,148,153,159,169,181,185,195,
  3,4,31,35,41,42,57,60,65,66,72,74,84,86,90,91,94,96,110,139,140,141,165,179,199,
  0,4,5,9,28,31,42,49,54,63,65,72,74,75,76,82,91,99,107,109,140,147,154,169,182,
  4,5,10,17,41,43,48,58,65,85,92,97,107,112,114,129,131,146,150,153,158,169,176,184,191,
  4,8,15,16,20,21,37,55,68,84,87,104,109,112,117,119,122,123,126,133,142,164,167,180,195,
  5,6,10,11,28,30,43,46,53,60,66,79,82,105,114,116,119,124,127,147,157,171,184,195,196,
  15,16,30,35,36,56,66,78,81,84,99,126,128,129,138,151,152,153,166,190,
  5,21,23,29,39,40,49,69,88,114,122,127,128,142,148,155,161,171,188,190,
  0,3,15,23,31,41,57,60,69,76,89,107,109,128,153,155,161,169,174,183,
  9,33,43,61,64,69,85,98,100,101,114,120,138,144,172,182,184,187,188,198,
  4,6,8,10,23,27,45,57,66,68,71,93,110,122,139,146,150,155,156,188,
  4,14,18,22,63,77,78,83,94,98,104,114,150,166,172,177,183,186,196,199,
  22,35,46,47,63,64,70,78,87,99,102,112,116,119,125,131,152,165,174,186,
  1,3,13,15,19,26,46,51,65,73,76,110,114,149,152,163,166,170,178,186,
  9,29,33,40,50,54,102,105,111,112,119,120,124,128,136,138,144,175,190,199,
  39,75,79,102,106,112,123,125,138,145,154,155,159,162,165,168,175,181,189,196,
  0,11,12,23,42,63,68,71,79,83,89,98,113,117,121,141,156,176,177,193,
  10,17,31,56,77,89,102,115,116,117,118,120,136,157,163,168,172,182,193,196,
  9,34,35,43,44,57,60,64,79,87,88,94,103,133,156,157,166,171,174,189,
  13,21,22,31,41,45,66,67,79,86,112,116,119,146,160,171,175,181,192,195,
  11,24,26,45,57,91,99,102,122,123,135,141,144,146,154,156,167,191,194,199,
  17,44,53,61,82,90,95,103,107,122,124,145,169,186,190,
  2,14,26,37,58,61,75,95,103,109,115,116,141,154,199,
  5,13,21,28,61,64,65,73,105,115,119,132,148,154,185,
  10,20,38,45,61,75,109,111,115,143,150,157,163,179,186,
  9,45,48,49,51,52,57,64,70,128,158,163,182,183,192,
  47,55,57,64,79,80,105,131,152,163,172,180,186,190,197,
  16,36,69,84,99,113,118,121,126,137,160,162,165,177,196,
  16,44,50,53,54,65,69,80,96,112,125,139,150,153,193,
  6,54,72,76,86,95,96,144,145,148,151,164,168,180,183,
  10,18,19,37,65,85,90,104,112,128,147,158,164,192,198,
  20,21,36,50,53,74,90,96,99,124,129,140,163,171,183,
  13,20,27,53,65,77,86,98,110,125,133,139,147,188,196,
  23,41,43,49,58,74,77,86,111,126,150,168,173,185,189,
  11,35,62,89,125,132,134,141,149,163,166,167,171,194,196,
  14,28,30,52,114,115,122,125,132,135,172,177,179,181,195,
  0,8,9,20,23,53,77,93,121,136,141,147,150,191,199,
  3,21,47,49,91,102,106,113,124,136,140,143,177,178,194,
  44,46,52,53,68,82,89,90,120,128,144,147,175,178,192,
  8,16,19,21,67,72,79,82,86,90,115,116,149,152,199,
  12,30,78,80,97,120,122,123,143,146,151,165,173,177,178,
  9,19,39,46,91,109,128,130,131,146,148,150,178,185,198,
  29,44,69,74,96,115,122,126,189,199,
  22,42,52,53,97,113,146,151,160,195,
  19,20,32,77,81,133,134,138,147,177,
  0,4,56,59,107,109,144,149,158,167,
  6,69,99,104,110,114,118,134,152,172,
  25,76,126,140,143,
  4,54,67,116,142,
  47,52,124,151,192,
  32,55,61,64,73,
  11,65,128,134,190,
  45,48,63,131,139,
  34,55,82,108,151,
  24,34,54,112,156,
  12,47,72,148,163,
  74,126,145,162,170,
  73,78,104,175,192,
  19,83,127,130,166,
  20,90,98,137,165,
  22,24,29,49,132,
  82,92,116,134,184,
  160,184,
  192,199,
  0,129,
  20,80,
  8,29,
  93,171,
  101,165,
  124,193,
  2,100,
  66,173,
  151,191,
  164,187,
  3,130,
  118,176,
  121,184,
  25,106,
  159,193,
  121,123,
  5,62,
  97,101,
  6,143,
  123,163,
  19,125,
  17,108,
  122,168,
  181,184,
  25,41,
  62,70,
  29,103,
  48,67,
  46,160,
  79,170,
  143,152,
  38,184,
  2,40,
  191,195,
  7,196,
  62,199,
  76,141,
  82,166,
  36,80,
  51,189,
  13,97,
  3,192,
  90,180,
  47,176,
  13,172,
  92,121,
  50,64,
  65,113,
  108,123,
  26,106,
  34,153,
  90,123,
  34,39,
  116,178,
  22,179,
  50,61,
  84,105,
  84,93,
  19,108,
  29,59,
  63,185,
  119,129,
  50,177,
  80,194,
  13,36,
  46,56,
  38,144,
  82,193,
  72,93,
  49,95,
  42,155,
  117,140,
  109,189,
  19,35,
  31,125,
  118,191,
  163,169,
  40,167,
  91,127,
  3,121,
  124,149,
  40,174,
  30,175,
  19,132,
  18,165,
  34,93,
  37,63,
  10,55,
  88,95,
  76,122,
  7,91,
  25,141,
  29,173,
  139,173,
  8,130,
  110,158,
  81,174,
  113,114,
  95,182,
  136,149,
  5,199,
  56,106,
  36,120,
  133,187,
  111,172,
  19,34,
  96,197,
  32,108,
  27,63,
  50,188,
  20,116,
  50,118,
  10,50,
  24,172,
  86,138,
  35,50,
  141,153,
  98,132,
  70,143,
  1,97,
  8,160,
  37,170,
  4,73,
  1,94,
  88,146,
  59,61,
  104,156,
  62,172,
  117,139,
  66,189,
  33,134,
  122,169,
  95,163,
  95,152,
  83,140,
  110,189,
  147,159,
  22,147,
  59,173,
  30,41,
  33,183,
  181,187,
  88,105,
  93,151,
  6,130,
  24,30,
  84,130,
  72,120,
  118,159,
  147,189,
  122,149,
  24,175,
  39,169,
  164,186,
  93,187,
  13,156,
  119,176,
  73,91,
  174,178,
  71,198,
  10,134,
  30,101,
  79,93,
  180,187,
  1,50,
  51,59,
  18,169,
  73,153,
  1,198,
  137,154,
  61,106,
  80,113,
  48,142,
  100,111,
  97,133,
  82,97,
  136,170,
  53,134,
  65,177,
  7,80,
  73,137,
  6,70,
  115,166,
  72,196,
  40,109,
  91,101,
  2,177,
  120,185,
  55,65,
  72,166,
  104,165,
  173,187,
  54,71,
  3,61,
  52,56,
  120,149,
  64,72,
  42,43,
  75,185,
  62,68,
  108,147,
  30,111,
  25,58,
  39,93,
  75,117,
  61,194,
  140,153,
  80,121,
  93,102,
  9,177,
  7,163,
  17,70,
  5,168,
  63,178,
  74,160,
  148,158,
  9,84,
  30,76,
  63,80,
  68,99,
  20,152,
  7,182,
  7,22,
  71,134,
  32,100,
  107,164,
  23,62,
  5,98,
  130,192,
  65,144,
  139,161,
  24,124,
  31,47,
  29,140,
  61,153,
  53,109,
  20,26,
  143,160,
  47,195,
  171,172,
  185,193,
  128,173,
  38,96,
  14,171,
  176,199,
  111,139,
  21,54,
  80,171,
  116,185,
  184,199,
  37,88,
  62,133,
  3,150,
  48,109,
  46,176,
  24,178,
  59,172,
  180,198,
  64,109,
  110,111,
  101,146,
  66,164,
  5,117,
  144,179,
  71,126,
  166,169,
  107,151,
  46,85,
  106,139,
  27,153,
  97,148,
  68,185,
  17,179,
  10,142,
  168,169,
  4,46,
  113,152,
  52,176,
  6,38,
  22,48,
  20,120,
  2,84,
  71,85,
  91,116,
  0,189,
  116,197,
  142,147,
  33,165,
  86,198,
  146,149,
  152,187,
  44,62,
  48,175,
  56,150,
  63,161,
  71,164,
  17,171,
  19,66
 ]