#include <knotkit.h>

bool verbose = 0;

static const struct {
  const char *name;
  int crossing_ar[3][4];
} rolfsen3[] = {
  { "3_{1}", { { 1, 5, 2, 4 }, { 3, 1, 4, 6 }, { 5, 3, 6, 2 } } }
};

static const struct {
  const char *name;
  int crossing_ar[4][4];
} rolfsen4[] = {
  { "4_{1}", { { 4, 2, 5, 1 }, { 8, 6, 1, 5 }, { 6, 3, 7, 4 }, { 2, 7, 3, 8 } } }
};

static const struct {
  const char *name;
  int crossing_ar[5][4];
} rolfsen5[] = {
  { "5_{1}", { { 2, 8, 3, 7 }, { 4, 10, 5, 9 }, { 6, 2, 7, 1 }, { 8, 4, 9, 3 }, { 10, 6, 1, 5 } } },
  { "5_{2}", { { 1, 5, 2, 4 }, { 3, 9, 4, 8 }, { 5, 1, 6, 10 }, { 7, 3, 8, 2 }, { 9, 7, 10, 6 } } }
};

static const struct {
  const char *name;
  int crossing_ar[6][4];
} rolfsen6[] = {
  { "6_{1}", { { 1, 7, 2, 6 }, { 3, 10, 4, 11 }, { 5, 3, 6, 2 }, { 7, 1, 8, 12 }, { 9, 4, 10, 5 }, { 11, 9, 12, 8 } } },
  { "6_{2}", { { 1, 8, 2, 9 }, { 3, 11, 4, 10 }, { 5, 1, 6, 12 }, { 7, 2, 8, 3 }, { 9, 7, 10, 6 }, { 11, 5, 12, 4 } } },
  { "6_{3}", { { 4, 2, 5, 1 }, { 8, 4, 9, 3 }, { 12, 9, 1, 10 }, { 10, 5, 11, 6 }, { 6, 11, 7, 12 }, { 2, 8, 3, 7 } } }
};

static const struct {
  const char *name;
  int crossing_ar[7][4];
} rolfsen7[] = {
  { "7_{1}", { { 1, 9, 2, 8 }, { 3, 11, 4, 10 }, { 5, 13, 6, 12 }, { 7, 1, 8, 14 }, { 9, 3, 10, 2 }, { 11, 5, 12, 4 }, { 13, 7, 14, 6 } } },
  { "7_{2}", { { 2, 10, 3, 9 }, { 4, 14, 5, 13 }, { 6, 12, 7, 11 }, { 8, 2, 9, 1 }, { 10, 8, 11, 7 }, { 12, 6, 13, 5 }, { 14, 4, 1, 3 } } },
  { "7_{3}", { { 1, 9, 2, 8 }, { 3, 11, 4, 10 }, { 5, 1, 6, 14 }, { 7, 13, 8, 12 }, { 9, 3, 10, 2 }, { 11, 5, 12, 4 }, { 13, 7, 14, 6 } } },
  { "7_{4}", { { 2, 10, 3, 9 }, { 4, 12, 5, 11 }, { 6, 14, 7, 13 }, { 8, 4, 9, 3 }, { 10, 2, 11, 1 }, { 12, 8, 13, 7 }, { 14, 6, 1, 5 } } },
  { "7_{5}", { { 2, 10, 3, 9 }, { 4, 2, 5, 1 }, { 6, 14, 7, 13 }, { 8, 12, 9, 11 }, { 10, 4, 11, 3 }, { 12, 6, 13, 5 }, { 14, 8, 1, 7 } } },
  { "7_{6}", { { 1, 13, 2, 12 }, { 3, 9, 4, 8 }, { 5, 1, 6, 14 }, { 7, 10, 8, 11 }, { 9, 3, 10, 2 }, { 11, 6, 12, 7 }, { 13, 5, 14, 4 } } },
  { "7_{7}", { { 1, 10, 2, 11 }, { 3, 13, 4, 12 }, { 5, 14, 6, 1 }, { 7, 5, 8, 4 }, { 9, 2, 10, 3 }, { 11, 9, 12, 8 }, { 13, 6, 14, 7 } } }
};

static const struct {
  const char *name;
  int crossing_ar[8][4];
} rolfsen8[] = {
  { "8_{1}", { { 1, 9, 2, 8 }, { 3, 7, 4, 6 }, { 5, 12, 6, 13 }, { 7, 3, 8, 2 }, { 9, 1, 10, 16 }, { 11, 15, 12, 14 }, { 13, 4, 14, 5 }, { 15, 11, 16, 10 } } },
  { "8_{2}", { { 1, 10, 2, 11 }, { 3, 13, 4, 12 }, { 5, 15, 6, 14 }, { 7, 1, 8, 16 }, { 9, 2, 10, 3 }, { 11, 9, 12, 8 }, { 13, 5, 14, 4 }, { 15, 7, 16, 6 } } },
  { "8_{3}", { { 6, 2, 7, 1 }, { 14, 10, 15, 9 }, { 10, 5, 11, 6 }, { 12, 3, 13, 4 }, { 4, 11, 5, 12 }, { 2, 13, 3, 14 }, { 16, 8, 1, 7 }, { 8, 16, 9, 15 } } },
  { "8_{4}", { { 2, 11, 3, 12 }, { 4, 9, 5, 10 }, { 6, 16, 7, 15 }, { 8, 14, 9, 13 }, { 10, 1, 11, 2 }, { 12, 3, 13, 4 }, { 14, 8, 15, 7 }, { 16, 6, 1, 5 } } },
  { "8_{5}", { { 1, 7, 2, 6 }, { 3, 9, 4, 8 }, { 5, 12, 6, 13 }, { 7, 3, 8, 2 }, { 9, 15, 10, 14 }, { 11, 1, 12, 16 }, { 13, 4, 14, 5 }, { 15, 11, 16, 10 } } },
  { "8_{6}", { { 2, 9, 3, 10 }, { 4, 14, 5, 13 }, { 6, 16, 7, 15 }, { 8, 12, 9, 11 }, { 10, 1, 11, 2 }, { 12, 8, 13, 7 }, { 14, 6, 15, 5 }, { 16, 4, 1, 3 } } },
  { "8_{7}", { { 2, 9, 3, 10 }, { 4, 14, 5, 13 }, { 6, 15, 7, 16 }, { 8, 1, 9, 2 }, { 10, 5, 11, 6 }, { 12, 4, 13, 3 }, { 14, 12, 15, 11 }, { 16, 7, 1, 8 } } },
  { "8_{8}", { { 1, 7, 2, 6 }, { 3, 12, 4, 13 }, { 5, 9, 6, 8 }, { 7, 3, 8, 2 }, { 9, 16, 10, 1 }, { 11, 14, 12, 15 }, { 13, 4, 14, 5 }, { 15, 10, 16, 11 } } },
  { "8_{9}", { { 6, 2, 7, 1 }, { 14, 8, 15, 7 }, { 10, 3, 11, 4 }, { 2, 13, 3, 14 }, { 12, 5, 13, 6 }, { 4, 11, 5, 12 }, { 16, 10, 1, 9 }, { 8, 16, 9, 15 } } },
  { "8_{10}", { { 2, 14, 3, 13 }, { 4, 9, 5, 10 }, { 6, 11, 7, 12 }, { 8, 15, 9, 16 }, { 10, 5, 11, 6 }, { 12, 2, 13, 1 }, { 14, 7, 15, 8 }, { 16, 4, 1, 3 } } },
  { "8_{11}", { { 1, 10, 2, 11 }, { 3, 13, 4, 12 }, { 5, 15, 6, 14 }, { 7, 1, 8, 16 }, { 9, 2, 10, 3 }, { 11, 9, 12, 8 }, { 13, 7, 14, 6 }, { 15, 5, 16, 4 } } },
  { "8_{12}", { { 4, 2, 5, 1 }, { 10, 8, 11, 7 }, { 8, 3, 9, 4 }, { 2, 9, 3, 10 }, { 14, 6, 15, 5 }, { 16, 11, 1, 12 }, { 12, 15, 13, 16 }, { 6, 14, 7, 13 } } },
  { "8_{13}", { { 1, 9, 2, 8 }, { 3, 14, 4, 15 }, { 5, 12, 6, 13 }, { 7, 11, 8, 10 }, { 9, 3, 10, 2 }, { 11, 16, 12, 1 }, { 13, 4, 14, 5 }, { 15, 6, 16, 7 } } },
  { "8_{14}", { { 2, 12, 3, 11 }, { 4, 8, 5, 7 }, { 6, 15, 7, 16 }, { 8, 14, 9, 13 }, { 10, 2, 11, 1 }, { 12, 10, 13, 9 }, { 14, 4, 15, 3 }, { 16, 5, 1, 6 } } },
  { "8_{15}", { { 1, 7, 2, 6 }, { 3, 15, 4, 14 }, { 5, 9, 6, 8 }, { 7, 3, 8, 2 }, { 9, 13, 10, 12 }, { 11, 1, 12, 16 }, { 13, 5, 14, 4 }, { 15, 11, 16, 10 } } },
  { "8_{16}", { { 2, 7, 3, 8 }, { 4, 10, 5, 9 }, { 6, 1, 7, 2 }, { 8, 14, 9, 13 }, { 10, 15, 11, 16 }, { 12, 6, 13, 5 }, { 14, 3, 15, 4 }, { 16, 11, 1, 12 } } },
  { "8_{17}", { { 6, 2, 7, 1 }, { 14, 8, 15, 7 }, { 8, 3, 9, 4 }, { 2, 13, 3, 14 }, { 12, 5, 13, 6 }, { 4, 9, 5, 10 }, { 16, 12, 1, 11 }, { 10, 16, 11, 15 } } },
  { "8_{18}", { { 6, 2, 7, 1 }, { 8, 3, 9, 4 }, { 16, 11, 1, 12 }, { 2, 14, 3, 13 }, { 4, 15, 5, 16 }, { 10, 6, 11, 5 }, { 12, 7, 13, 8 }, { 14, 10, 15, 9 } } },
  { "8_{19}", { { 2, 14, 3, 13 }, { 5, 11, 6, 10 }, { 7, 15, 8, 14 }, { 9, 5, 10, 4 }, { 11, 7, 12, 6 }, { 12, 2, 13, 1 }, { 15, 9, 16, 8 }, { 16, 4, 1, 3 } } },
  { "8_{20}", { { 1, 7, 2, 6 }, { 4, 13, 5, 14 }, { 5, 9, 6, 8 }, { 7, 3, 8, 2 }, { 10, 15, 11, 16 }, { 12, 9, 13, 10 }, { 14, 3, 15, 4 }, { 16, 11, 1, 12 } } },
  { "8_{21}", { { 1, 7, 2, 6 }, { 4, 13, 5, 14 }, { 5, 9, 6, 8 }, { 7, 3, 8, 2 }, { 9, 13, 10, 12 }, { 11, 1, 12, 16 }, { 14, 3, 15, 4 }, { 15, 11, 16, 10 } } }
};

static const struct {
  const char *name;
  int crossing_ar[9][4];
} rolfsen9[] = {
  { "9_{1}", { { 1, 11, 2, 10 }, { 3, 13, 4, 12 }, { 5, 15, 6, 14 }, { 7, 17, 8, 16 }, { 9, 1, 10, 18 }, { 11, 3, 12, 2 }, { 13, 5, 14, 4 }, { 15, 7, 16, 6 }, { 17, 9, 18, 8 } } },
  { "9_{2}", { { 2, 8, 3, 7 }, { 4, 14, 5, 13 }, { 6, 4, 7, 3 }, { 8, 2, 9, 1 }, { 10, 18, 11, 17 }, { 12, 16, 13, 15 }, { 14, 6, 15, 5 }, { 16, 12, 17, 11 }, { 18, 10, 1, 9 } } },
  { "9_{3}", { { 1, 11, 2, 10 }, { 3, 15, 4, 14 }, { 5, 13, 6, 12 }, { 7, 17, 8, 16 }, { 9, 1, 10, 18 }, { 11, 3, 12, 2 }, { 13, 5, 14, 4 }, { 15, 7, 16, 6 }, { 17, 9, 18, 8 } } },
  { "9_{4}", { { 2, 14, 3, 13 }, { 4, 12, 5, 11 }, { 6, 16, 7, 15 }, { 8, 18, 9, 17 }, { 10, 6, 11, 5 }, { 12, 4, 13, 3 }, { 14, 2, 15, 1 }, { 16, 8, 17, 7 }, { 18, 10, 1, 9 } } },
  { "9_{5}", { { 2, 14, 3, 13 }, { 4, 12, 5, 11 }, { 6, 16, 7, 15 }, { 8, 18, 9, 17 }, { 10, 6, 11, 5 }, { 12, 4, 13, 3 }, { 14, 2, 15, 1 }, { 16, 10, 17, 9 }, { 18, 8, 1, 7 } } },
  { "9_{6}", { { 1, 13, 2, 12 }, { 3, 7, 4, 6 }, { 5, 15, 6, 14 }, { 7, 3, 8, 2 }, { 9, 17, 10, 16 }, { 11, 1, 12, 18 }, { 13, 5, 14, 4 }, { 15, 9, 16, 8 }, { 17, 11, 18, 10 } } },
  { "9_{7}", { { 2, 10, 3, 9 }, { 4, 12, 5, 11 }, { 6, 16, 7, 15 }, { 8, 6, 9, 5 }, { 10, 4, 11, 3 }, { 12, 2, 13, 1 }, { 14, 18, 15, 17 }, { 16, 8, 17, 7 }, { 18, 14, 1, 13 } } },
  { "9_{8}", { { 1, 16, 2, 17 }, { 3, 14, 4, 15 }, { 5, 11, 6, 10 }, { 7, 1, 8, 18 }, { 9, 13, 10, 12 }, { 11, 7, 12, 6 }, { 13, 4, 14, 5 }, { 15, 2, 16, 3 }, { 17, 9, 18, 8 } } },
  { "9_{9}", { { 1, 13, 2, 12 }, { 3, 9, 4, 8 }, { 5, 15, 6, 14 }, { 7, 17, 8, 16 }, { 9, 3, 10, 2 }, { 11, 1, 12, 18 }, { 13, 5, 14, 4 }, { 15, 7, 16, 6 }, { 17, 11, 18, 10 } } },
  { "9_{10}", { { 1, 13, 2, 12 }, { 3, 11, 4, 10 }, { 5, 17, 6, 16 }, { 7, 15, 8, 14 }, { 9, 1, 10, 18 }, { 11, 3, 12, 2 }, { 13, 5, 14, 4 }, { 15, 7, 16, 6 }, { 17, 9, 18, 8 } } },
  { "9_{11}", { { 2, 7, 3, 8 }, { 4, 13, 5, 14 }, { 6, 15, 7, 16 }, { 8, 12, 9, 11 }, { 10, 17, 11, 18 }, { 12, 3, 13, 4 }, { 14, 5, 15, 6 }, { 16, 2, 17, 1 }, { 18, 9, 1, 10 } } },
  { "9_{12}", { { 2, 9, 3, 10 }, { 4, 16, 5, 15 }, { 6, 14, 7, 13 }, { 8, 3, 9, 4 }, { 10, 18, 11, 17 }, { 12, 8, 13, 7 }, { 14, 6, 15, 5 }, { 16, 2, 17, 1 }, { 18, 12, 1, 11 } } },
  { "9_{13}", { { 2, 12, 3, 11 }, { 4, 14, 5, 13 }, { 6, 16, 7, 15 }, { 8, 18, 9, 17 }, { 10, 6, 11, 5 }, { 12, 4, 13, 3 }, { 14, 2, 15, 1 }, { 16, 10, 17, 9 }, { 18, 8, 1, 7 } } },
  { "9_{14}", { { 1, 12, 2, 13 }, { 3, 10, 4, 11 }, { 5, 16, 6, 17 }, { 7, 1, 8, 18 }, { 9, 4, 10, 5 }, { 11, 2, 12, 3 }, { 13, 9, 14, 8 }, { 15, 6, 16, 7 }, { 17, 15, 18, 14 } } },
  { "9_{15}", { { 2, 9, 3, 10 }, { 4, 7, 5, 8 }, { 6, 15, 7, 16 }, { 8, 3, 9, 4 }, { 10, 14, 11, 13 }, { 12, 17, 13, 18 }, { 14, 5, 15, 6 }, { 16, 2, 17, 1 }, { 18, 11, 1, 12 } } },
  { "9_{16}", { { 1, 9, 2, 8 }, { 3, 11, 4, 10 }, { 5, 15, 6, 14 }, { 7, 5, 8, 4 }, { 9, 3, 10, 2 }, { 11, 17, 12, 16 }, { 13, 1, 14, 18 }, { 15, 7, 16, 6 }, { 17, 13, 18, 12 } } },
  { "9_{17}", { { 1, 9, 2, 8 }, { 3, 12, 4, 13 }, { 5, 16, 6, 17 }, { 7, 1, 8, 18 }, { 9, 3, 10, 2 }, { 11, 4, 12, 5 }, { 13, 11, 14, 10 }, { 15, 6, 16, 7 }, { 17, 15, 18, 14 } } },
  { "9_{18}", { { 2, 12, 3, 11 }, { 4, 2, 5, 1 }, { 6, 16, 7, 15 }, { 8, 14, 9, 13 }, { 10, 18, 11, 17 }, { 12, 4, 13, 3 }, { 14, 8, 15, 7 }, { 16, 10, 17, 9 }, { 18, 6, 1, 5 } } },
  { "9_{19}", { { 2, 14, 3, 13 }, { 4, 11, 5, 12 }, { 6, 4, 7, 3 }, { 8, 17, 9, 18 }, { 10, 5, 11, 6 }, { 12, 8, 13, 7 }, { 14, 2, 15, 1 }, { 16, 9, 17, 10 }, { 18, 16, 1, 15 } } },
  { "9_{20}", { { 1, 11, 2, 10 }, { 3, 16, 4, 17 }, { 5, 13, 6, 12 }, { 7, 3, 8, 2 }, { 9, 1, 10, 18 }, { 11, 15, 12, 14 }, { 13, 7, 14, 6 }, { 15, 4, 16, 5 }, { 17, 9, 18, 8 } } },
  { "9_{21}", { { 2, 7, 3, 8 }, { 4, 13, 5, 14 }, { 6, 15, 7, 16 }, { 8, 12, 9, 11 }, { 10, 17, 11, 18 }, { 12, 5, 13, 6 }, { 14, 3, 15, 4 }, { 16, 2, 17, 1 }, { 18, 9, 1, 10 } } },
  { "9_{22}", { { 1, 7, 2, 6 }, { 3, 8, 4, 9 }, { 5, 14, 6, 15 }, { 7, 11, 8, 10 }, { 9, 2, 10, 3 }, { 11, 17, 12, 16 }, { 13, 1, 14, 18 }, { 15, 4, 16, 5 }, { 17, 13, 18, 12 } } },
  { "9_{23}", { { 2, 16, 3, 15 }, { 4, 12, 5, 11 }, { 6, 4, 7, 3 }, { 8, 18, 9, 17 }, { 10, 14, 11, 13 }, { 12, 6, 13, 5 }, { 14, 8, 15, 7 }, { 16, 2, 17, 1 }, { 18, 10, 1, 9 } } },
  { "9_{24}", { { 1, 13, 2, 12 }, { 3, 7, 4, 6 }, { 5, 1, 6, 18 }, { 7, 14, 8, 15 }, { 9, 16, 10, 17 }, { 11, 3, 12, 2 }, { 13, 10, 14, 11 }, { 15, 8, 16, 9 }, { 17, 5, 18, 4 } } },
  { "9_{25}", { { 2, 10, 3, 9 }, { 4, 17, 5, 18 }, { 6, 12, 7, 11 }, { 8, 4, 9, 3 }, { 10, 14, 11, 13 }, { 12, 8, 13, 7 }, { 14, 2, 15, 1 }, { 16, 5, 17, 6 }, { 18, 16, 1, 15 } } },
  { "9_{26}", { { 2, 10, 3, 9 }, { 4, 11, 5, 12 }, { 6, 17, 7, 18 }, { 8, 15, 9, 16 }, { 10, 14, 11, 13 }, { 12, 3, 13, 4 }, { 14, 2, 15, 1 }, { 16, 5, 17, 6 }, { 18, 7, 1, 8 } } },
  { "9_{27}", { { 2, 9, 3, 10 }, { 4, 7, 5, 8 }, { 6, 14, 7, 13 }, { 8, 15, 9, 16 }, { 10, 18, 11, 17 }, { 12, 3, 13, 4 }, { 14, 6, 15, 5 }, { 16, 2, 17, 1 }, { 18, 12, 1, 11 } } },
  { "9_{28}", { { 1, 16, 2, 17 }, { 3, 15, 4, 14 }, { 5, 3, 6, 2 }, { 7, 13, 8, 12 }, { 9, 7, 10, 6 }, { 11, 18, 12, 1 }, { 13, 9, 14, 8 }, { 15, 5, 16, 4 }, { 17, 10, 18, 11 } } },
  { "9_{29}", { { 2, 10, 3, 9 }, { 4, 17, 5, 18 }, { 6, 12, 7, 11 }, { 8, 4, 9, 3 }, { 10, 15, 11, 16 }, { 12, 6, 13, 5 }, { 14, 1, 15, 2 }, { 16, 7, 17, 8 }, { 18, 13, 1, 14 } } },
  { "9_{30}", { { 1, 9, 2, 8 }, { 3, 16, 4, 17 }, { 5, 1, 6, 18 }, { 7, 12, 8, 13 }, { 9, 3, 10, 2 }, { 11, 6, 12, 7 }, { 13, 10, 14, 11 }, { 15, 4, 16, 5 }, { 17, 15, 18, 14 } } },
  { "9_{31}", { { 1, 9, 2, 8 }, { 3, 10, 4, 11 }, { 5, 13, 6, 12 }, { 7, 1, 8, 18 }, { 9, 16, 10, 17 }, { 11, 15, 12, 14 }, { 13, 7, 14, 6 }, { 15, 4, 16, 5 }, { 17, 3, 18, 2 } } },
  { "9_{32}", { { 2, 8, 3, 7 }, { 4, 9, 5, 10 }, { 6, 13, 7, 14 }, { 8, 16, 9, 15 }, { 10, 5, 11, 6 }, { 12, 17, 13, 18 }, { 14, 3, 15, 4 }, { 16, 2, 17, 1 }, { 18, 11, 1, 12 } } },
  { "9_{33}", { { 1, 15, 2, 14 }, { 3, 16, 4, 17 }, { 5, 12, 6, 13 }, { 7, 5, 8, 4 }, { 9, 2, 10, 3 }, { 11, 6, 12, 7 }, { 13, 1, 14, 18 }, { 15, 11, 16, 10 }, { 17, 8, 18, 9 } } },
  { "9_{34}", { { 2, 13, 3, 14 }, { 4, 17, 5, 18 }, { 6, 16, 7, 15 }, { 8, 4, 9, 3 }, { 10, 5, 11, 6 }, { 12, 8, 13, 7 }, { 14, 1, 15, 2 }, { 16, 11, 17, 12 }, { 18, 10, 1, 9 } } },
  { "9_{35}", { { 2, 12, 3, 11 }, { 4, 16, 5, 15 }, { 6, 14, 7, 13 }, { 8, 18, 9, 17 }, { 10, 4, 11, 3 }, { 12, 2, 13, 1 }, { 14, 6, 15, 5 }, { 16, 10, 17, 9 }, { 18, 8, 1, 7 } } },
  { "9_{36}", { { 2, 15, 3, 16 }, { 4, 11, 5, 12 }, { 6, 4, 7, 3 }, { 8, 17, 9, 18 }, { 10, 5, 11, 6 }, { 12, 10, 13, 9 }, { 14, 1, 15, 2 }, { 16, 7, 17, 8 }, { 18, 13, 1, 14 } } },
  { "9_{37}", { { 1, 10, 2, 11 }, { 3, 14, 4, 15 }, { 5, 1, 6, 18 }, { 7, 17, 8, 16 }, { 9, 2, 10, 3 }, { 11, 9, 12, 8 }, { 13, 4, 14, 5 }, { 15, 13, 16, 12 }, { 17, 7, 18, 6 } } },
  { "9_{38}", { { 2, 14, 3, 13 }, { 4, 10, 5, 9 }, { 6, 16, 7, 15 }, { 8, 4, 9, 3 }, { 10, 18, 11, 17 }, { 12, 6, 13, 5 }, { 14, 2, 15, 1 }, { 16, 12, 17, 11 }, { 18, 8, 1, 7 } } },
  { "9_{39}", { { 1, 12, 2, 13 }, { 3, 17, 4, 16 }, { 5, 10, 6, 11 }, { 7, 18, 8, 1 }, { 9, 14, 10, 15 }, { 11, 2, 12, 3 }, { 13, 6, 14, 7 }, { 15, 5, 16, 4 }, { 17, 8, 18, 9 } } },
  { "9_{40}", { { 1, 15, 2, 14 }, { 3, 12, 4, 13 }, { 5, 11, 6, 10 }, { 7, 3, 8, 2 }, { 9, 18, 10, 1 }, { 11, 17, 12, 16 }, { 13, 9, 14, 8 }, { 15, 6, 16, 7 }, { 17, 5, 18, 4 } } },
  { "9_{41}", { { 1, 15, 2, 14 }, { 3, 12, 4, 13 }, { 5, 16, 6, 17 }, { 7, 3, 8, 2 }, { 9, 18, 10, 1 }, { 11, 4, 12, 5 }, { 13, 9, 14, 8 }, { 15, 6, 16, 7 }, { 17, 10, 18, 11 } } },
  { "9_{42}", { { 1, 4, 2, 5 }, { 5, 10, 6, 11 }, { 3, 9, 4, 8 }, { 9, 3, 10, 2 }, { 16, 12, 17, 11 }, { 14, 7, 15, 8 }, { 6, 15, 7, 16 }, { 18, 14, 1, 13 }, { 12, 18, 13, 17 } } },
  { "9_{43}", { { 1, 9, 2, 8 }, { 3, 16, 4, 17 }, { 5, 1, 6, 18 }, { 6, 12, 7, 11 }, { 9, 3, 10, 2 }, { 10, 14, 11, 13 }, { 12, 8, 13, 7 }, { 15, 4, 16, 5 }, { 17, 15, 18, 14 } } },
  { "9_{44}", { { 2, 9, 3, 10 }, { 3, 16, 4, 17 }, { 5, 1, 6, 18 }, { 6, 12, 7, 11 }, { 8, 1, 9, 2 }, { 10, 14, 11, 13 }, { 12, 8, 13, 7 }, { 15, 4, 16, 5 }, { 17, 15, 18, 14 } } },
  { "9_{45}", { { 2, 9, 3, 10 }, { 3, 16, 4, 17 }, { 5, 1, 6, 18 }, { 7, 12, 8, 13 }, { 8, 1, 9, 2 }, { 11, 6, 12, 7 }, { 13, 10, 14, 11 }, { 15, 4, 16, 5 }, { 17, 15, 18, 14 } } },
  { "9_{46}", { { 2, 10, 3, 9 }, { 3, 14, 4, 15 }, { 6, 17, 7, 18 }, { 8, 11, 9, 12 }, { 10, 2, 11, 1 }, { 13, 4, 14, 5 }, { 15, 13, 16, 12 }, { 16, 7, 17, 8 }, { 18, 5, 1, 6 } } },
  { "9_{47}", { { 1, 15, 2, 14 }, { 4, 17, 5, 18 }, { 6, 16, 7, 15 }, { 8, 4, 9, 3 }, { 10, 5, 11, 6 }, { 12, 8, 13, 7 }, { 13, 3, 14, 2 }, { 16, 11, 17, 12 }, { 18, 10, 1, 9 } } },
  { "9_{48}", { { 1, 10, 2, 11 }, { 3, 14, 4, 15 }, { 6, 17, 7, 18 }, { 9, 2, 10, 3 }, { 11, 9, 12, 8 }, { 13, 4, 14, 5 }, { 15, 13, 16, 12 }, { 16, 7, 17, 8 }, { 18, 5, 1, 6 } } },
  { "9_{49}", { { 1, 15, 2, 14 }, { 4, 12, 5, 11 }, { 6, 16, 7, 15 }, { 7, 3, 8, 2 }, { 10, 18, 11, 17 }, { 12, 4, 13, 3 }, { 13, 9, 14, 8 }, { 16, 6, 17, 5 }, { 18, 10, 1, 9 } } }
};

static const struct {
  const char *name;
  int crossing_ar[10][4];
} rolfsen10[] = {
  { "10_{1}", { { 2, 11, 3, 12 }, { 4, 20, 5, 19 }, { 6, 18, 7, 17 }, { 8, 16, 9, 15 }, { 10, 14, 11, 13 }, { 12, 1, 13, 2 }, { 14, 10, 15, 9 }, { 16, 8, 17, 7 }, { 18, 6, 19, 5 }, { 20, 4, 1, 3 } } },
  { "10_{2}", { { 1, 13, 2, 12 }, { 3, 14, 4, 15 }, { 5, 3, 6, 2 }, { 7, 17, 8, 16 }, { 9, 19, 10, 18 }, { 11, 1, 12, 20 }, { 13, 4, 14, 5 }, { 15, 7, 16, 6 }, { 17, 9, 18, 8 }, { 19, 11, 20, 10 } } },
  { "10_{3}", { { 2, 10, 3, 9 }, { 4, 17, 5, 18 }, { 6, 15, 7, 16 }, { 8, 4, 9, 3 }, { 10, 2, 11, 1 }, { 12, 20, 13, 19 }, { 14, 7, 15, 8 }, { 16, 5, 17, 6 }, { 18, 14, 19, 13 }, { 20, 12, 1, 11 } } },
  { "10_{4}", { { 2, 13, 3, 14 }, { 4, 11, 5, 12 }, { 6, 20, 7, 19 }, { 8, 18, 9, 17 }, { 10, 16, 11, 15 }, { 12, 1, 13, 2 }, { 14, 3, 15, 4 }, { 16, 10, 17, 9 }, { 18, 8, 19, 7 }, { 20, 6, 1, 5 } } },
  { "10_{5}", { { 2, 13, 3, 14 }, { 4, 17, 5, 18 }, { 6, 16, 7, 15 }, { 8, 6, 9, 5 }, { 10, 19, 11, 20 }, { 12, 1, 13, 2 }, { 14, 3, 15, 4 }, { 16, 8, 17, 7 }, { 18, 9, 19, 10 }, { 20, 11, 1, 12 } } },
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  { "10_{160}", { { 1, 13, 2, 12 }, { 4, 18, 5, 17 }, { 6, 14, 7, 13 }, { 8, 4, 9, 3 }, { 10, 15, 11, 16 }, { 11, 1, 12, 20 }, { 14, 6, 15, 5 }, { 16, 9, 17, 10 }, { 18, 8, 19, 7 }, { 19, 3, 20, 2 } } },
  { "10_{161}", { { 1, 13, 2, 12 }, { 4, 18, 5, 17 }, { 6, 14, 7, 13 }, { 8, 4, 9, 3 }, { 9, 17, 10, 16 }, { 11, 1, 12, 20 }, { 14, 6, 15, 5 }, { 15, 11, 16, 10 }, { 18, 8, 19, 7 }, { 19, 3, 20, 2 } } },
  { "10_{162}", { { 2, 9, 3, 10 }, { 5, 12, 6, 13 }, { 6, 18, 7, 17 }, { 8, 16, 9, 15 }, { 10, 19, 11, 20 }, { 11, 4, 12, 5 }, { 14, 1, 15, 2 }, { 16, 8, 17, 7 }, { 18, 4, 19, 3 }, { 20, 13, 1, 14 } } },
  { "10_{163}", { { 1, 8, 2, 9 }, { 3, 11, 4, 10 }, { 6, 14, 7, 13 }, { 9, 17, 10, 16 }, { 11, 18, 12, 19 }, { 12, 8, 13, 7 }, { 14, 6, 15, 5 }, { 15, 1, 16, 20 }, { 17, 2, 18, 3 }, { 19, 5, 20, 4 } } },
  { "10_{164}", { { 2, 12, 3, 11 }, { 3, 16, 4, 17 }, { 6, 14, 7, 13 }, { 8, 15, 9, 16 }, { 9, 5, 10, 4 }, { 12, 2, 13, 1 }, { 14, 19, 15, 20 }, { 17, 10, 18, 11 }, { 18, 5, 19, 6 }, { 20, 8, 1, 7 } } },
  { "10_{165}", { { 1, 8, 2, 9 }, { 3, 12, 4, 13 }, { 4, 17, 5, 18 }, { 7, 2, 8, 3 }, { 9, 14, 10, 15 }, { 11, 17, 12, 16 }, { 13, 6, 14, 7 }, { 15, 20, 16, 1 }, { 18, 5, 19, 6 }, { 19, 11, 20, 10 } } }
};

unsigned
rolfsen_crossing_knots (unsigned n)
{
  assert (n <= 10);
  switch (n)
    {
    case 0: // ??? really?
    case 1:
    case 2:
      return 0;
      
    case 3:
      return sizeof rolfsen3 / sizeof rolfsen3[0];
    case 4:
      return sizeof rolfsen4 / sizeof rolfsen4[0];
    case 5:
      return sizeof rolfsen5 / sizeof rolfsen5[0];
    case 6:
      return sizeof rolfsen6 / sizeof rolfsen6[0];
    case 7:
      return sizeof rolfsen7 / sizeof rolfsen7[0];
    case 8:
      return sizeof rolfsen8 / sizeof rolfsen8[0];
    case 9:
      return sizeof rolfsen9 / sizeof rolfsen9[0];
    case 10:
      return sizeof rolfsen10 / sizeof rolfsen10[0];
    default: abort ();
    }
}

planar_diagram
rolfsen_knot (unsigned n, unsigned k)
{
  assert (n <= 10);
  assert (k >= 1);
  assert (k <= rolfsen_crossing_knots (n));
  k --;
  switch (n)
    {
    case 3:
      return planar_diagram (rolfsen3[k].name, 3, rolfsen3[k].crossing_ar);
    case 4:
      return planar_diagram (rolfsen4[k].name, 4, rolfsen4[k].crossing_ar);
    case 5:
      return planar_diagram (rolfsen5[k].name, 5, rolfsen5[k].crossing_ar);
    case 6:
      return planar_diagram (rolfsen6[k].name, 6, rolfsen6[k].crossing_ar);
    case 7:
      return planar_diagram (rolfsen7[k].name, 7, rolfsen7[k].crossing_ar);
    case 8:
      return planar_diagram (rolfsen8[k].name, 8, rolfsen8[k].crossing_ar);
    case 9:
      return planar_diagram (rolfsen9[k].name, 9, rolfsen9[k].crossing_ar);
    case 10:
      return planar_diagram (rolfsen10[k].name, 10, rolfsen10[k].crossing_ar);
    default: abort ();
    }
}

unsigned htw_alternating[16] = {
  0, 0, 1, 1, 2, 3, 7, 18, 41, 123, 367, 1288, 4878, 19536, 85263, 379799
};

unsigned htw_nonalternating[16] = {
  0, 0, 0, 0, 0, 0, 0, 3, 8, 42, 185, 888, 5110, 27436, 168030, 1008906
};

unsigned
htw_knots (unsigned n, bool alternating)
{
  assert (between (1, n, 16));
  if (alternating)
    return htw_alternating[n - 1];
  else
    return htw_nonalternating[n - 1];
}

unsigned
htw_knots (unsigned n)
{
  assert (between (1, n, 16));
  return htw_alternating[n - 1] + htw_nonalternating[n - 1];
}

dt_code
htw_knot (unsigned n, bool alternating, unsigned k)
{
  assert (between (1, n, 16));
  assert (between (1, k, htw_knots (n, alternating)));

  const char *file;
  long off;
  if (alternating)
    {
      unsigned before = 0;
      for (unsigned i = 0; i < n - 1; i ++)
	before += htw_alternating[i];
      off = 8 * (before + k - 1);
      
      file = HOME "/alternating";
    }
  else
    {
      unsigned before = 0;
      for (unsigned i = 0; i < n - 1; i ++)
	before += htw_nonalternating[i];
      off = 10 * (before + k - 1);
      
      file = HOME "/nonalternating";
    }
  FILE *fp = fopen (file, "r");
  if (fp == 0)
    {
      stderror ("fopen: %s", file);
      exit (EXIT_FAILURE);
    }
  
  if (fseek (fp, off, SEEK_SET) != 0)
    {
      stderror ("fseek");
      exit (EXIT_FAILURE);
    }
  
  unsigned char buf[10];
  size_t count = (n + 1) / 2;
  if (!alternating)
    count += 2;
  if (fread (buf, 1, count, fp) != count)
    {
      stderror ("fread");
      exit (EXIT_FAILURE);
    }
  
  fclose (fp);
  fp = 0;
  
  int even_labels_ar[16];
  for (unsigned i = 0; i < n; i ++)
    {
      unsigned j = buf[i / 2];
      j = is_even (i)
	? j >> 4
	: j & 0xf;
      if (j == 0)
	j = 16;
      j *= 2;
      even_labels_ar[i] = j;
    }
  
  if (!alternating)
    {
      unsigned signs = buf[count - 2] << 8 | buf[count - 1];
      for (unsigned i = 0; i < n; i ++)
	{
	  if (!unsigned_bittest (signs, 16 - i))
	    even_labels_ar[i] *= -1;
	}
    }
  
  char buf2[100];
  sprintf (buf2, "%d%c%d", n, alternating ? 'a' : 'n', k);
  
  return dt_code (std::string (buf2), n, even_labels_ar);
}

dt_code
htw_knot (unsigned n, unsigned k)
{
  assert (between (1, n, 16));
  assert (k >= 1);
  
  unsigned na = htw_knots (n, 1);
  if (k <= na)
    return htw_knot (n, 1, k);
  else
    return htw_knot (n, 0, k - na);
}

unsigned mt_alternating[14] = {
  0, 0, 0, 1, 3, 8, 14, 39, 96, 297, 915, 3308, 12417, 51347,
};

unsigned mt_nonalternating[14] = {
  0, 0, 0, 0, 0, 1, 2, 11, 36, 155, 644, 3144, 16454, 91616,
};

unsigned
mt_links (unsigned n, bool alternating)
{
  assert (between (1, n, 14));
  if (alternating)
    return mt_alternating[n - 1];
  else
    return mt_nonalternating[n - 1];
}

unsigned
mt_links (unsigned n)
{
  assert (between (1, n, 14));
  return mt_alternating[n - 1] + mt_nonalternating[n - 1];
}

dt_code
mt_link (unsigned n, bool alternating, unsigned k)
{
  assert (between (1, n, 14));
  assert (between (1, k, mt_links (n, alternating)));
  
  char buf[1000];
  
  sprintf (buf, HOME "/mtlinks/hyperbolic_data_%02d%c", n, alternating ? 'a' : 'n');
  FILE *fp = fopen (buf, "r");
  if (fp == 0)
    {
      stderror ("fopen: %s", buf);
      exit (EXIT_FAILURE);
    }
  
  char *p;
  
  for (unsigned i = 1; i <= k; i ++)
    {
      if (fgets (buf, 1000, fp) == 0)
	{
	  stderror ("fgets: %s", buf);
	  exit (EXIT_FAILURE);
	}
      assert (alpha_to_int (buf[0]) == (int)n);
    }
  
  fclose (fp);
  
  char buf2[1000];
  sprintf (buf2, "L%d%c%d", n, alternating ? 'a' : 'n', k);
  
  return dt_code (buf2, buf);
}

dt_code
mt_link (unsigned n, unsigned k)
{
  assert (between (1, n, 16));
  assert (k >= 1);
  
  unsigned na = mt_links (n, 1);
  if (k <= na)
    return mt_link (n, 1, k);
  else
    return mt_link (n, 0, k - na);
}

planar_diagram
torus_knot (unsigned n_strands, unsigned n_shifts)
{
  basedvector<basedvector<int, 1>, 1> crossings ((n_strands - 1) * n_shifts);
  for (unsigned i = 1; i <= crossings.size (); i ++)
    crossings[i].resize (4);
  
  basedvector<unsigned, 1> start_strands (n_strands),
    strands (n_strands), 
    new_strands (n_strands);
  
  unsigned n_crossings = 0;
  unsigned n_edges = 0;
  
  for (unsigned i = 1; i <= n_strands; i ++)
    strands[i] = start_strands[i] = ++ n_edges;
  
  for (unsigned i = 1; i <= n_shifts; i ++)
    {
      if (i == n_shifts)
	new_strands = start_strands;
      else
	{
	  for (unsigned j = 1; j <= n_strands; j ++)
	    new_strands[j] = ++ n_edges;
	}
      
      unsigned p = strands[1];
      for (unsigned j = 1; j < n_strands; j ++)
	{
	  unsigned c = ++ n_crossings;
	  unsigned newp;
	  if (j == n_strands - 1)
	    newp = new_strands[n_strands];
	  else
	    newp = ++ n_edges;
	  
	  crossings[c][1] = strands[j + 1];
	  crossings[c][2] = newp;
	  crossings[c][3] = new_strands[j];
	  crossings[c][4] = p;
	  
	  p = newp;
	}
      
      basedvector<unsigned, 1> tmp = new_strands;
      new_strands = strands;
      strands = tmp;
    }
  
  assert (n_crossings == crossings.size ());
  assert (n_edges == n_crossings * 2);
  
  char buf[1000];
  sprintf (buf, "T(%d,%d)", n_strands, n_shifts);
  
  return planar_diagram (std::string (buf), crossings);
}

knot_diagram
braid (unsigned n_strands, unsigned n_twists, int twists_ar[])
{
  basedvector<int, 1> twists (n_twists);
  for (unsigned i = 1; i <= n_twists; i ++)
    twists[i] = twists_ar[i - 1];
  return braid (n_strands, twists);
}

knot_diagram
braid (unsigned n_strands, const basedvector<int, 1> &twists)
{
  unsigned e = 0;
  
  basedvector<unsigned, 1> final_strands (n_strands);
  basedvector<unsigned, 1> strands (n_strands);
  for (unsigned i = 1; i <= n_strands; i ++)
    {
      ++ e;
      final_strands[i] = strands[i] = e;
    }
  
  basedvector<unsigned, 1> last_twist (n_strands);
  for (unsigned i = 1; i <= n_strands; i ++)
    last_twist[i] = 0;
  for (unsigned i = 1; i <= twists.size (); i ++)
    {
      unsigned t = abs (twists[i]);
      last_twist[t] = i;
      last_twist[t + 1] = i;
    }
  
  unsigned n_crossings = twists.size ();
  for (unsigned i = 1; i <= n_strands; i ++)
    {
      if (last_twist[i] == 0)
	n_crossings ++;
    }
  
  basedvector<basedvector<unsigned, 1>, 1> crossings (n_crossings);
  for (unsigned i = 1; i <= n_crossings; i ++)
    crossings[i] = basedvector<unsigned, 1> (4);
  
  unsigned c = twists.size ();
  for (unsigned i = 1; i <= n_strands; i ++)
    {
      if (last_twist[i] == 0)
	{
	  ++ c;
	  unsigned e1 = strands[i];
	  unsigned e2 = ++ e;
	  
	  strands[i] = final_strands[i] = 0;
	  
	  crossings[c][1] = edge_from_ept (e1);
	  crossings[c][2] = edge_to_ept (e2);
	  crossings[c][3] = edge_from_ept (e2);
	  crossings[c][4] = edge_to_ept (e1);
	}
    }
  assert (c == n_crossings);
  
  for (unsigned i = 1; i <= twists.size (); i ++)
    {
      unsigned t = abs (twists[i]);
      unsigned e1 = strands[t],
	e4 = strands[t + 1];
      unsigned e2, e3;
      if (last_twist[t] == i)
	{
	  assert (final_strands[t] != 0);
	  e2 = final_strands[t];
	  strands[t] = final_strands[t] = 0;
	}
      else
	{
	  e ++;
	  e2 = e;
	  strands[t] = e;
	}
      if (last_twist[t + 1] == i)
	{
	  assert (final_strands[t + 1] != 0);
	  e3 = final_strands[t + 1];
	  strands[t + 1] = final_strands[t + 1] = 0;
	}
      else
	{
	  e ++;
	  e3 = e;
	  strands[t + 1] = e;
	}
      
      if (twists[i] > 0)
	{
	  crossings[i][1] = edge_to_ept (e1);
	  crossings[i][2] = edge_from_ept (e2);
	  crossings[i][3] = edge_from_ept (e3);
	  crossings[i][4] = edge_to_ept (e4);
	}
      else
	{
	  crossings[i][1] = edge_from_ept (e2);
	  crossings[i][2] = edge_from_ept (e3);
	  crossings[i][3] = edge_to_ept (e4);
	  crossings[i][4] = edge_to_ept (e1);
	}
    }
  
  assert (e == n_crossings * 2);
#ifndef NDEBUG
  for (unsigned i = 1; i <= n_strands; i ++)
    {
      assert (strands[i] == 0);
      assert (final_strands[i] == 0);
    }
#endif
  
  return knot_diagram ("abraid", crossings);
}

basedvector<basedvector<unsigned, 1>, 1> 
mutant_knot_groups (unsigned n)
{
  assert (11 <= n && n <= 15);
  
  char buf[1000];
  sprintf (buf, HOME "/mutant_knot_groups/dat%d", n);
  
  FILE *fp = fopen (buf, "r");
  if (fp == 0)
    {
      stderror ("fopen: %s", buf);
      exit (EXIT_FAILURE);
    }
  
  basedvector<basedvector<unsigned, 1>, 1> r;
  while (fgets (buf, sizeof buf, fp) != 0)
    {
      const char *p = buf;
      
      basedvector<unsigned, 1> g;
      
      unsigned i;
      int k;
      while (sscanf (p, "%d%n", &i, &k) == 1)
	{
	  g.append (i);
	  p += k;
	}
      
      assert (*p == '\n');
      assert (g.size () > 0);
      r.append (g);
    }
  
  return r;
}

knot_diagram
knot_desc::diagram () const
{
  switch (t)
    {
    case ROLFSEN:
      return knot_diagram (rolfsen_knot (i, j));
      
    case HTW:
      return knot_diagram (htw_knot (i, j));
    case HTW_ALT:
      return knot_diagram (htw_knot (i, 1, j));
    case HTW_NONALT:
      return knot_diagram (htw_knot (i, 0, j));

    case MT:
      return knot_diagram (mt_link (i, j));
    case MT_ALT:
      return knot_diagram (mt_link (i, 1, j));
    case MT_NONALT:
      return knot_diagram (mt_link (i, 0, j));
      
    case TORUS:
      return knot_diagram (torus_knot (i, j));
      
    default: abort ();
    }
}
  
std::string
knot_desc::name () const
{
  char buf[1000];

#if 0
  sprintf (buf, "knot_desc(%d, %d, %d)", (int)t, i, j);
  return buf;
#endif
  
  switch (t)
    {
    case ROLFSEN:
      sprintf (buf, "%d_%d", i, j);
      break;
      
    case HTW:
      {
	unsigned na = htw_knots (i, 1);
	if (j <= na)
	  sprintf (buf, "%da%d", i, j);
	else
	  sprintf (buf, "%dn%d", i, j - na);
      }
      break;
      
    case HTW_ALT:
      sprintf (buf, "%da%d", i, j);
      break;

    case HTW_NONALT:
      sprintf (buf, "%dn%d", i, j);
      break;

    case MT:
      {
	unsigned na = mt_links (i, 1);
	if (j <= na)
	  sprintf (buf, "L%da%d", i, j);
	else
	  sprintf (buf, "L%dn%d", i, j - na);
      }
      break;
      
    case MT_ALT:
      sprintf (buf, "L%da%d", i, j);
      break;

    case MT_NONALT:
      sprintf (buf, "L%dn%d", i, j);
      break;
      
    case TORUS:
      sprintf (buf, "T(%d, %d)", i, j);
      break;
      
    default: abort ();
    }
  
  return buf;
}

unsigned
knot_desc::table_crossing_knots () const
{
  switch (t)
    {
    case ROLFSEN:
      return rolfsen_crossing_knots (i);
      
    case HTW:
      return htw_knots (i);
    case HTW_ALT:
      return htw_knots (i, 1);
    case HTW_NONALT:
      return htw_knots (i, 0);

    case MT:
      return mt_links (i);
    case MT_ALT:
      return mt_links (i, 1);
    case MT_NONALT:
      return mt_links (i, 0);
      
    default: abort ();
    }
}

knot_desc::knot_desc (reader &r)
{
  int x;
  read (r, x);
  t = (table)x;
  
  read (r, i);
  read (r, j);
}

void
knot_desc::write_self (writer &w) const
{
  write (w, (int)t);
  write (w, i);
  write (w, j);
}