export const NORM_2D = 1.0 / 47.0;
export const NORM_3D = 1.0 / 103.0;
export const NORM_4D = 1.0 / 30.0;
export const SQUISH_2D = (Math.sqrt(2 + 1) - 1) / 2;
export const SQUISH_3D = (Math.sqrt(3 + 1) - 1) / 3;
export const SQUISH_4D = (Math.sqrt(4 + 1) - 1) / 4;
export const STRETCH_2D = (1 / Math.sqrt(2 + 1) - 1) / 2;
export const STRETCH_3D = (1 / Math.sqrt(3 + 1) - 1) / 3;
export const STRETCH_4D = (1 / Math.sqrt(4 + 1) - 1) / 4;

export const base2D = [
  [1, 1, 0, 1, 0, 1, 0, 0, 0],
  [1, 1, 0, 1, 0, 1, 2, 1, 1]
];

export const base3D = [
  [0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1],
  [2, 1, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 3, 1, 1, 1],
  [1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1]
];

export const base4D = [
  [0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1],
  [3, 1, 1, 1, 0, 3, 1, 1, 0, 1, 3, 1, 0, 1, 1, 3, 0, 1, 1, 1, 4, 1, 1, 1, 1],
  [
    1,
    1,
    0,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    1,
    0,
    0,
    1,
    0,
    1,
    0,
    0,
    0,
    1,
    2,
    1,
    1,
    0,
    0,
    2,
    1,
    0,
    1,
    0,
    2,
    1,
    0,
    0,
    1,
    2,
    0,
    1,
    1,
    0,
    2,
    0,
    1,
    0,
    1,
    2,
    0,
    0,
    1,
    1
  ],
  [
    3,
    1,
    1,
    1,
    0,
    3,
    1,
    1,
    0,
    1,
    3,
    1,
    0,
    1,
    1,
    3,
    0,
    1,
    1,
    1,
    2,
    1,
    1,
    0,
    0,
    2,
    1,
    0,
    1,
    0,
    2,
    1,
    0,
    0,
    1,
    2,
    0,
    1,
    1,
    0,
    2,
    0,
    1,
    0,
    1,
    2,
    0,
    0,
    1,
    1
  ]
];

export const gradients2D = [
  5,
  2,
  2,
  5,
  -5,
  2,
  -2,
  5,
  5,
  -2,
  2,
  -5,
  -5,
  -2,
  -2,
  -5
];

export const gradients3D = [
  -11,
  4,
  4,
  -4,
  11,
  4,
  -4,
  4,
  11,
  11,
  4,
  4,
  4,
  11,
  4,
  4,
  4,
  11,
  -11,
  -4,
  4,
  -4,
  -11,
  4,
  -4,
  -4,
  11,
  11,
  -4,
  4,
  4,
  -11,
  4,
  4,
  -4,
  11,
  -11,
  4,
  -4,
  -4,
  11,
  -4,
  -4,
  4,
  -11,
  11,
  4,
  -4,
  4,
  11,
  -4,
  4,
  4,
  -11,
  -11,
  -4,
  -4,
  -4,
  -11,
  -4,
  -4,
  -4,
  -11,
  11,
  -4,
  -4,
  4,
  -11,
  -4,
  4,
  -4,
  -11
];

export const gradients4D = [
  3,
  1,
  1,
  1,
  1,
  3,
  1,
  1,
  1,
  1,
  3,
  1,
  1,
  1,
  1,
  3,
  -3,
  1,
  1,
  1,
  -1,
  3,
  1,
  1,
  -1,
  1,
  3,
  1,
  -1,
  1,
  1,
  3,
  3,
  -1,
  1,
  1,
  1,
  -3,
  1,
  1,
  1,
  -1,
  3,
  1,
  1,
  -1,
  1,
  3,
  -3,
  -1,
  1,
  1,
  -1,
  -3,
  1,
  1,
  -1,
  -1,
  3,
  1,
  -1,
  -1,
  1,
  3,
  3,
  1,
  -1,
  1,
  1,
  3,
  -1,
  1,
  1,
  1,
  -3,
  1,
  1,
  1,
  -1,
  3,
  -3,
  1,
  -1,
  1,
  -1,
  3,
  -1,
  1,
  -1,
  1,
  -3,
  1,
  -1,
  1,
  -1,
  3,
  3,
  -1,
  -1,
  1,
  1,
  -3,
  -1,
  1,
  1,
  -1,
  -3,
  1,
  1,
  -1,
  -1,
  3,
  -3,
  -1,
  -1,
  1,
  -1,
  -3,
  -1,
  1,
  -1,
  -1,
  -3,
  1,
  -1,
  -1,
  -1,
  3,
  3,
  1,
  1,
  -1,
  1,
  3,
  1,
  -1,
  1,
  1,
  3,
  -1,
  1,
  1,
  1,
  -3,
  -3,
  1,
  1,
  -1,
  -1,
  3,
  1,
  -1,
  -1,
  1,
  3,
  -1,
  -1,
  1,
  1,
  -3,
  3,
  -1,
  1,
  -1,
  1,
  -3,
  1,
  -1,
  1,
  -1,
  3,
  -1,
  1,
  -1,
  1,
  -3,
  -3,
  -1,
  1,
  -1,
  -1,
  -3,
  1,
  -1,
  -1,
  -1,
  3,
  -1,
  -1,
  -1,
  1,
  -3,
  3,
  1,
  -1,
  -1,
  1,
  3,
  -1,
  -1,
  1,
  1,
  -3,
  -1,
  1,
  1,
  -1,
  -3,
  -3,
  1,
  -1,
  -1,
  -1,
  3,
  -1,
  -1,
  -1,
  1,
  -3,
  -1,
  -1,
  1,
  -1,
  -3,
  3,
  -1,
  -1,
  -1,
  1,
  -3,
  -1,
  -1,
  1,
  -1,
  -3,
  -1,
  1,
  -1,
  -1,
  -3,
  -3,
  -1,
  -1,
  -1,
  -1,
  -3,
  -1,
  -1,
  -1,
  -1,
  -3,
  -1,
  -1,
  -1,
  -1,
  -3
];

export const lookupPairs2D = [
  0,
  1,
  1,
  0,
  4,
  1,
  17,
  0,
  20,
  2,
  21,
  2,
  22,
  5,
  23,
  5,
  26,
  4,
  39,
  3,
  42,
  4,
  43,
  3
];

export const lookupPairs3D = [
  0,
  2,
  1,
  1,
  2,
  2,
  5,
  1,
  6,
  0,
  7,
  0,
  32,
  2,
  34,
  2,
  129,
  1,
  133,
  1,
  160,
  5,
  161,
  5,
  518,
  0,
  519,
  0,
  546,
  4,
  550,
  4,
  645,
  3,
  647,
  3,
  672,
  5,
  673,
  5,
  674,
  4,
  677,
  3,
  678,
  4,
  679,
  3,
  680,
  13,
  681,
  13,
  682,
  12,
  685,
  14,
  686,
  12,
  687,
  14,
  712,
  20,
  714,
  18,
  809,
  21,
  813,
  23,
  840,
  20,
  841,
  21,
  1198,
  19,
  1199,
  22,
  1226,
  18,
  1230,
  19,
  1325,
  23,
  1327,
  22,
  1352,
  15,
  1353,
  17,
  1354,
  15,
  1357,
  17,
  1358,
  16,
  1359,
  16,
  1360,
  11,
  1361,
  10,
  1362,
  11,
  1365,
  10,
  1366,
  9,
  1367,
  9,
  1392,
  11,
  1394,
  11,
  1489,
  10,
  1493,
  10,
  1520,
  8,
  1521,
  8,
  1878,
  9,
  1879,
  9,
  1906,
  7,
  1910,
  7,
  2005,
  6,
  2007,
  6,
  2032,
  8,
  2033,
  8,
  2034,
  7,
  2037,
  6,
  2038,
  7,
  2039,
  6
];

export const lookupPairs4D = [
  0,
  3,
  1,
  2,
  2,
  3,
  5,
  2,
  6,
  1,
  7,
  1,
  8,
  3,
  9,
  2,
  10,
  3,
  13,
  2,
  16,
  3,
  18,
  3,
  22,
  1,
  23,
  1,
  24,
  3,
  26,
  3,
  33,
  2,
  37,
  2,
  38,
  1,
  39,
  1,
  41,
  2,
  45,
  2,
  54,
  1,
  55,
  1,
  56,
  0,
  57,
  0,
  58,
  0,
  59,
  0,
  60,
  0,
  61,
  0,
  62,
  0,
  63,
  0,
  256,
  3,
  258,
  3,
  264,
  3,
  266,
  3,
  272,
  3,
  274,
  3,
  280,
  3,
  282,
  3,
  2049,
  2,
  2053,
  2,
  2057,
  2,
  2061,
  2,
  2081,
  2,
  2085,
  2,
  2089,
  2,
  2093,
  2,
  2304,
  9,
  2305,
  9,
  2312,
  9,
  2313,
  9,
  16390,
  1,
  16391,
  1,
  16406,
  1,
  16407,
  1,
  16422,
  1,
  16423,
  1,
  16438,
  1,
  16439,
  1,
  16642,
  8,
  16646,
  8,
  16658,
  8,
  16662,
  8,
  18437,
  6,
  18439,
  6,
  18469,
  6,
  18471,
  6,
  18688,
  9,
  18689,
  9,
  18690,
  8,
  18693,
  6,
  18694,
  8,
  18695,
  6,
  18696,
  9,
  18697,
  9,
  18706,
  8,
  18710,
  8,
  18725,
  6,
  18727,
  6,
  131128,
  0,
  131129,
  0,
  131130,
  0,
  131131,
  0,
  131132,
  0,
  131133,
  0,
  131134,
  0,
  131135,
  0,
  131352,
  7,
  131354,
  7,
  131384,
  7,
  131386,
  7,
  133161,
  5,
  133165,
  5,
  133177,
  5,
  133181,
  5,
  133376,
  9,
  133377,
  9,
  133384,
  9,
  133385,
  9,
  133400,
  7,
  133402,
  7,
  133417,
  5,
  133421,
  5,
  133432,
  7,
  133433,
  5,
  133434,
  7,
  133437,
  5,
  147510,
  4,
  147511,
  4,
  147518,
  4,
  147519,
  4,
  147714,
  8,
  147718,
  8,
  147730,
  8,
  147734,
  8,
  147736,
  7,
  147738,
  7,
  147766,
  4,
  147767,
  4,
  147768,
  7,
  147770,
  7,
  147774,
  4,
  147775,
  4,
  149509,
  6,
  149511,
  6,
  149541,
  6,
  149543,
  6,
  149545,
  5,
  149549,
  5,
  149558,
  4,
  149559,
  4,
  149561,
  5,
  149565,
  5,
  149566,
  4,
  149567,
  4,
  149760,
  9,
  149761,
  9,
  149762,
  8,
  149765,
  6,
  149766,
  8,
  149767,
  6,
  149768,
  9,
  149769,
  9,
  149778,
  8,
  149782,
  8,
  149784,
  7,
  149786,
  7,
  149797,
  6,
  149799,
  6,
  149801,
  5,
  149805,
  5,
  149814,
  4,
  149815,
  4,
  149816,
  7,
  149817,
  5,
  149818,
  7,
  149821,
  5,
  149822,
  4,
  149823,
  4,
  149824,
  37,
  149825,
  37,
  149826,
  36,
  149829,
  34,
  149830,
  36,
  149831,
  34,
  149832,
  37,
  149833,
  37,
  149842,
  36,
  149846,
  36,
  149848,
  35,
  149850,
  35,
  149861,
  34,
  149863,
  34,
  149865,
  33,
  149869,
  33,
  149878,
  32,
  149879,
  32,
  149880,
  35,
  149881,
  33,
  149882,
  35,
  149885,
  33,
  149886,
  32,
  149887,
  32,
  150080,
  49,
  150082,
  48,
  150088,
  49,
  150098,
  48,
  150104,
  47,
  150106,
  47,
  151873,
  46,
  151877,
  45,
  151881,
  46,
  151909,
  45,
  151913,
  44,
  151917,
  44,
  152128,
  49,
  152129,
  46,
  152136,
  49,
  152137,
  46,
  166214,
  43,
  166215,
  42,
  166230,
  43,
  166247,
  42,
  166262,
  41,
  166263,
  41,
  166466,
  48,
  166470,
  43,
  166482,
  48,
  166486,
  43,
  168261,
  45,
  168263,
  42,
  168293,
  45,
  168295,
  42,
  168512,
  31,
  168513,
  28,
  168514,
  31,
  168517,
  28,
  168518,
  25,
  168519,
  25,
  280952,
  40,
  280953,
  39,
  280954,
  40,
  280957,
  39,
  280958,
  38,
  280959,
  38,
  281176,
  47,
  281178,
  47,
  281208,
  40,
  281210,
  40,
  282985,
  44,
  282989,
  44,
  283001,
  39,
  283005,
  39,
  283208,
  30,
  283209,
  27,
  283224,
  30,
  283241,
  27,
  283256,
  22,
  283257,
  22,
  297334,
  41,
  297335,
  41,
  297342,
  38,
  297343,
  38,
  297554,
  29,
  297558,
  24,
  297562,
  29,
  297590,
  24,
  297594,
  21,
  297598,
  21,
  299365,
  26,
  299367,
  23,
  299373,
  26,
  299383,
  23,
  299389,
  20,
  299391,
  20,
  299584,
  31,
  299585,
  28,
  299586,
  31,
  299589,
  28,
  299590,
  25,
  299591,
  25,
  299592,
  30,
  299593,
  27,
  299602,
  29,
  299606,
  24,
  299608,
  30,
  299610,
  29,
  299621,
  26,
  299623,
  23,
  299625,
  27,
  299629,
  26,
  299638,
  24,
  299639,
  23,
  299640,
  22,
  299641,
  22,
  299642,
  21,
  299645,
  20,
  299646,
  21,
  299647,
  20,
  299648,
  61,
  299649,
  60,
  299650,
  61,
  299653,
  60,
  299654,
  59,
  299655,
  59,
  299656,
  58,
  299657,
  57,
  299666,
  55,
  299670,
  54,
  299672,
  58,
  299674,
  55,
  299685,
  52,
  299687,
  51,
  299689,
  57,
  299693,
  52,
  299702,
  54,
  299703,
  51,
  299704,
  56,
  299705,
  56,
  299706,
  53,
  299709,
  50,
  299710,
  53,
  299711,
  50,
  299904,
  61,
  299906,
  61,
  299912,
  58,
  299922,
  55,
  299928,
  58,
  299930,
  55,
  301697,
  60,
  301701,
  60,
  301705,
  57,
  301733,
  52,
  301737,
  57,
  301741,
  52,
  301952,
  79,
  301953,
  79,
  301960,
  76,
  301961,
  76,
  316038,
  59,
  316039,
  59,
  316054,
  54,
  316071,
  51,
  316086,
  54,
  316087,
  51,
  316290,
  78,
  316294,
  78,
  316306,
  73,
  316310,
  73,
  318085,
  77,
  318087,
  77,
  318117,
  70,
  318119,
  70,
  318336,
  79,
  318337,
  79,
  318338,
  78,
  318341,
  77,
  318342,
  78,
  318343,
  77,
  430776,
  56,
  430777,
  56,
  430778,
  53,
  430781,
  50,
  430782,
  53,
  430783,
  50,
  431000,
  75,
  431002,
  72,
  431032,
  75,
  431034,
  72,
  432809,
  74,
  432813,
  69,
  432825,
  74,
  432829,
  69,
  433032,
  76,
  433033,
  76,
  433048,
  75,
  433065,
  74,
  433080,
  75,
  433081,
  74,
  447158,
  71,
  447159,
  68,
  447166,
  71,
  447167,
  68,
  447378,
  73,
  447382,
  73,
  447386,
  72,
  447414,
  71,
  447418,
  72,
  447422,
  71,
  449189,
  70,
  449191,
  70,
  449197,
  69,
  449207,
  68,
  449213,
  69,
  449215,
  68,
  449408,
  67,
  449409,
  67,
  449410,
  66,
  449413,
  64,
  449414,
  66,
  449415,
  64,
  449416,
  67,
  449417,
  67,
  449426,
  66,
  449430,
  66,
  449432,
  65,
  449434,
  65,
  449445,
  64,
  449447,
  64,
  449449,
  63,
  449453,
  63,
  449462,
  62,
  449463,
  62,
  449464,
  65,
  449465,
  63,
  449466,
  65,
  449469,
  63,
  449470,
  62,
  449471,
  62,
  449472,
  19,
  449473,
  19,
  449474,
  18,
  449477,
  16,
  449478,
  18,
  449479,
  16,
  449480,
  19,
  449481,
  19,
  449490,
  18,
  449494,
  18,
  449496,
  17,
  449498,
  17,
  449509,
  16,
  449511,
  16,
  449513,
  15,
  449517,
  15,
  449526,
  14,
  449527,
  14,
  449528,
  17,
  449529,
  15,
  449530,
  17,
  449533,
  15,
  449534,
  14,
  449535,
  14,
  449728,
  19,
  449729,
  19,
  449730,
  18,
  449734,
  18,
  449736,
  19,
  449737,
  19,
  449746,
  18,
  449750,
  18,
  449752,
  17,
  449754,
  17,
  449784,
  17,
  449786,
  17,
  451520,
  19,
  451521,
  19,
  451525,
  16,
  451527,
  16,
  451528,
  19,
  451529,
  19,
  451557,
  16,
  451559,
  16,
  451561,
  15,
  451565,
  15,
  451577,
  15,
  451581,
  15,
  451776,
  19,
  451777,
  19,
  451784,
  19,
  451785,
  19,
  465858,
  18,
  465861,
  16,
  465862,
  18,
  465863,
  16,
  465874,
  18,
  465878,
  18,
  465893,
  16,
  465895,
  16,
  465910,
  14,
  465911,
  14,
  465918,
  14,
  465919,
  14,
  466114,
  18,
  466118,
  18,
  466130,
  18,
  466134,
  18,
  467909,
  16,
  467911,
  16,
  467941,
  16,
  467943,
  16,
  468160,
  13,
  468161,
  13,
  468162,
  13,
  468163,
  13,
  468164,
  13,
  468165,
  13,
  468166,
  13,
  468167,
  13,
  580568,
  17,
  580570,
  17,
  580585,
  15,
  580589,
  15,
  580598,
  14,
  580599,
  14,
  580600,
  17,
  580601,
  15,
  580602,
  17,
  580605,
  15,
  580606,
  14,
  580607,
  14,
  580824,
  17,
  580826,
  17,
  580856,
  17,
  580858,
  17,
  582633,
  15,
  582637,
  15,
  582649,
  15,
  582653,
  15,
  582856,
  12,
  582857,
  12,
  582872,
  12,
  582873,
  12,
  582888,
  12,
  582889,
  12,
  582904,
  12,
  582905,
  12,
  596982,
  14,
  596983,
  14,
  596990,
  14,
  596991,
  14,
  597202,
  11,
  597206,
  11,
  597210,
  11,
  597214,
  11,
  597234,
  11,
  597238,
  11,
  597242,
  11,
  597246,
  11,
  599013,
  10,
  599015,
  10,
  599021,
  10,
  599023,
  10,
  599029,
  10,
  599031,
  10,
  599037,
  10,
  599039,
  10,
  599232,
  13,
  599233,
  13,
  599234,
  13,
  599235,
  13,
  599236,
  13,
  599237,
  13,
  599238,
  13,
  599239,
  13,
  599240,
  12,
  599241,
  12,
  599250,
  11,
  599254,
  11,
  599256,
  12,
  599257,
  12,
  599258,
  11,
  599262,
  11,
  599269,
  10,
  599271,
  10,
  599272,
  12,
  599273,
  12,
  599277,
  10,
  599279,
  10,
  599282,
  11,
  599285,
  10,
  599286,
  11,
  599287,
  10,
  599288,
  12,
  599289,
  12,
  599290,
  11,
  599293,
  10,
  599294,
  11,
  599295,
  10
];

export const p2D = [
  0,
  0,
  1,
  -1,
  0,
  0,
  -1,
  1,
  0,
  2,
  1,
  1,
  1,
  2,
  2,
  0,
  1,
  2,
  0,
  2,
  1,
  0,
  0,
  0
];

export const p3D = [
  0,
  0,
  1,
  -1,
  0,
  0,
  1,
  0,
  -1,
  0,
  0,
  -1,
  1,
  0,
  0,
  0,
  1,
  -1,
  0,
  0,
  -1,
  0,
  1,
  0,
  0,
  -1,
  1,
  0,
  2,
  1,
  1,
  0,
  1,
  1,
  1,
  -1,
  0,
  2,
  1,
  0,
  1,
  1,
  1,
  -1,
  1,
  0,
  2,
  0,
  1,
  1,
  1,
  -1,
  1,
  1,
  1,
  3,
  2,
  1,
  0,
  3,
  1,
  2,
  0,
  1,
  3,
  2,
  0,
  1,
  3,
  1,
  0,
  2,
  1,
  3,
  0,
  2,
  1,
  3,
  0,
  1,
  2,
  1,
  1,
  1,
  0,
  0,
  2,
  2,
  0,
  0,
  1,
  1,
  0,
  1,
  0,
  2,
  0,
  2,
  0,
  1,
  1,
  0,
  0,
  1,
  2,
  0,
  0,
  2,
  2,
  0,
  0,
  0,
  0,
  1,
  1,
  -1,
  1,
  2,
  0,
  0,
  0,
  0,
  1,
  -1,
  1,
  1,
  2,
  0,
  0,
  0,
  0,
  1,
  1,
  1,
  -1,
  2,
  3,
  1,
  1,
  1,
  2,
  0,
  0,
  2,
  2,
  3,
  1,
  1,
  1,
  2,
  2,
  0,
  0,
  2,
  3,
  1,
  1,
  1,
  2,
  0,
  2,
  0,
  2,
  1,
  1,
  -1,
  1,
  2,
  0,
  0,
  2,
  2,
  1,
  1,
  -1,
  1,
  2,
  2,
  0,
  0,
  2,
  1,
  -1,
  1,
  1,
  2,
  0,
  0,
  2,
  2,
  1,
  -1,
  1,
  1,
  2,
  0,
  2,
  0,
  2,
  1,
  1,
  1,
  -1,
  2,
  2,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  2,
  0,
  2,
  0
];

export const p4D = [
  0,
  0,
  1,
  -1,
  0,
  0,
  0,
  1,
  0,
  -1,
  0,
  0,
  1,
  0,
  0,
  -1,
  0,
  0,
  -1,
  1,
  0,
  0,
  0,
  0,
  1,
  -1,
  0,
  0,
  0,
  1,
  0,
  -1,
  0,
  0,
  -1,
  0,
  1,
  0,
  0,
  0,
  -1,
  1,
  0,
  0,
  0,
  0,
  1,
  -1,
  0,
  0,
  -1,
  0,
  0,
  1,
  0,
  0,
  -1,
  0,
  1,
  0,
  0,
  0,
  -1,
  1,
  0,
  2,
  1,
  1,
  0,
  0,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  0,
  2,
  1,
  0,
  1,
  0,
  1,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  0,
  2,
  0,
  1,
  1,
  0,
  1,
  -1,
  1,
  1,
  0,
  1,
  0,
  1,
  1,
  -1,
  0,
  2,
  1,
  0,
  0,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  0,
  2,
  0,
  1,
  0,
  1,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  1,
  0,
  2,
  0,
  0,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  1,
  1,
  4,
  2,
  1,
  1,
  0,
  4,
  1,
  2,
  1,
  0,
  4,
  1,
  1,
  2,
  0,
  1,
  4,
  2,
  1,
  0,
  1,
  4,
  1,
  2,
  0,
  1,
  4,
  1,
  1,
  0,
  2,
  1,
  4,
  2,
  0,
  1,
  1,
  4,
  1,
  0,
  2,
  1,
  4,
  1,
  0,
  1,
  2,
  1,
  4,
  0,
  2,
  1,
  1,
  4,
  0,
  1,
  2,
  1,
  4,
  0,
  1,
  1,
  2,
  1,
  2,
  1,
  1,
  0,
  0,
  3,
  2,
  1,
  0,
  0,
  3,
  1,
  2,
  0,
  0,
  1,
  2,
  1,
  0,
  1,
  0,
  3,
  2,
  0,
  1,
  0,
  3,
  1,
  0,
  2,
  0,
  1,
  2,
  0,
  1,
  1,
  0,
  3,
  0,
  2,
  1,
  0,
  3,
  0,
  1,
  2,
  0,
  1,
  2,
  1,
  0,
  0,
  1,
  3,
  2,
  0,
  0,
  1,
  3,
  1,
  0,
  0,
  2,
  1,
  2,
  0,
  1,
  0,
  1,
  3,
  0,
  2,
  0,
  1,
  3,
  0,
  1,
  0,
  2,
  1,
  2,
  0,
  0,
  1,
  1,
  3,
  0,
  0,
  2,
  1,
  3,
  0,
  0,
  1,
  2,
  2,
  3,
  1,
  1,
  1,
  0,
  2,
  1,
  1,
  1,
  -1,
  2,
  2,
  0,
  0,
  0,
  2,
  3,
  1,
  1,
  0,
  1,
  2,
  1,
  1,
  -1,
  1,
  2,
  2,
  0,
  0,
  0,
  2,
  3,
  1,
  0,
  1,
  1,
  2,
  1,
  -1,
  1,
  1,
  2,
  2,
  0,
  0,
  0,
  2,
  3,
  1,
  1,
  1,
  0,
  2,
  1,
  1,
  1,
  -1,
  2,
  0,
  2,
  0,
  0,
  2,
  3,
  1,
  1,
  0,
  1,
  2,
  1,
  1,
  -1,
  1,
  2,
  0,
  2,
  0,
  0,
  2,
  3,
  0,
  1,
  1,
  1,
  2,
  -1,
  1,
  1,
  1,
  2,
  0,
  2,
  0,
  0,
  2,
  3,
  1,
  1,
  1,
  0,
  2,
  1,
  1,
  1,
  -1,
  2,
  0,
  0,
  2,
  0,
  2,
  3,
  1,
  0,
  1,
  1,
  2,
  1,
  -1,
  1,
  1,
  2,
  0,
  0,
  2,
  0,
  2,
  3,
  0,
  1,
  1,
  1,
  2,
  -1,
  1,
  1,
  1,
  2,
  0,
  0,
  2,
  0,
  2,
  3,
  1,
  1,
  0,
  1,
  2,
  1,
  1,
  -1,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  3,
  1,
  0,
  1,
  1,
  2,
  1,
  -1,
  1,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  3,
  0,
  1,
  1,
  1,
  2,
  -1,
  1,
  1,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  -1,
  1,
  1,
  0,
  1,
  0,
  1,
  1,
  -1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  1,
  0,
  0,
  0,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  2,
  0,
  2,
  0,
  0,
  2,
  1,
  -1,
  1,
  1,
  0,
  1,
  0,
  1,
  1,
  -1,
  2,
  0,
  2,
  0,
  0,
  2,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  1,
  2,
  0,
  2,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  2,
  0,
  0,
  2,
  0,
  2,
  1,
  -1,
  1,
  1,
  0,
  1,
  0,
  1,
  1,
  -1,
  2,
  0,
  0,
  2,
  0,
  2,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  1,
  2,
  0,
  0,
  2,
  0,
  2,
  1,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  1,
  -1,
  1,
  0,
  1,
  1,
  0,
  1,
  -1,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  1,
  -1,
  0,
  1,
  1,
  1,
  0,
  -1,
  1,
  1,
  2,
  0,
  0,
  0,
  2,
  3,
  1,
  1,
  0,
  0,
  0,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  1,
  0,
  1,
  0,
  0,
  2,
  0,
  2,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  1,
  0,
  0,
  1,
  0,
  2,
  0,
  0,
  2,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  1,
  1,
  0,
  0,
  0,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  3,
  1,
  0,
  1,
  0,
  0,
  2,
  0,
  2,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  3,
  1,
  0,
  0,
  0,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  1,
  1,
  -1,
  1,
  3,
  1,
  1,
  0,
  0,
  0,
  2,
  2,
  0,
  0,
  0,
  2,
  1,
  -1,
  1,
  1,
  3,
  1,
  0,
  0,
  1,
  0,
  2,
  0,
  0,
  2,
  0,
  2,
  1,
  -1,
  1,
  1,
  3,
  1,
  0,
  0,
  0,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  1,
  -1,
  1,
  1,
  3,
  1,
  0,
  1,
  0,
  0,
  2,
  0,
  2,
  0,
  0,
  2,
  -1,
  1,
  1,
  1,
  3,
  1,
  0,
  0,
  1,
  0,
  2,
  0,
  0,
  2,
  0,
  2,
  -1,
  1,
  1,
  1,
  3,
  1,
  0,
  0,
  0,
  1,
  2,
  0,
  0,
  0,
  2,
  2,
  -1,
  1,
  1,
  1,
  3,
  3,
  2,
  1,
  0,
  0,
  3,
  1,
  2,
  0,
  0,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  2,
  0,
  1,
  0,
  3,
  1,
  0,
  2,
  0,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  0,
  2,
  1,
  0,
  3,
  0,
  1,
  2,
  0,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  2,
  0,
  0,
  1,
  3,
  1,
  0,
  0,
  2,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  0,
  2,
  0,
  1,
  3,
  0,
  1,
  0,
  2,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  0,
  0,
  2,
  1,
  3,
  0,
  0,
  1,
  2,
  4,
  1,
  1,
  1,
  1,
  3,
  3,
  2,
  1,
  0,
  0,
  3,
  1,
  2,
  0,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  3,
  2,
  0,
  1,
  0,
  3,
  1,
  0,
  2,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  3,
  0,
  2,
  1,
  0,
  3,
  0,
  1,
  2,
  0,
  2,
  1,
  1,
  1,
  -1,
  3,
  3,
  2,
  1,
  0,
  0,
  3,
  1,
  2,
  0,
  0,
  2,
  1,
  1,
  -1,
  1,
  3,
  3,
  2,
  0,
  0,
  1,
  3,
  1,
  0,
  0,
  2,
  2,
  1,
  1,
  -1,
  1,
  3,
  3,
  0,
  2,
  0,
  1,
  3,
  0,
  1,
  0,
  2,
  2,
  1,
  1,
  -1,
  1,
  3,
  3,
  2,
  0,
  1,
  0,
  3,
  1,
  0,
  2,
  0,
  2,
  1,
  -1,
  1,
  1,
  3,
  3,
  2,
  0,
  0,
  1,
  3,
  1,
  0,
  0,
  2,
  2,
  1,
  -1,
  1,
  1,
  3,
  3,
  0,
  0,
  2,
  1,
  3,
  0,
  0,
  1,
  2,
  2,
  1,
  -1,
  1,
  1,
  3,
  3,
  0,
  2,
  1,
  0,
  3,
  0,
  1,
  2,
  0,
  2,
  -1,
  1,
  1,
  1,
  3,
  3,
  0,
  2,
  0,
  1,
  3,
  0,
  1,
  0,
  2,
  2,
  -1,
  1,
  1,
  1,
  3,
  3,
  0,
  0,
  2,
  1,
  3,
  0,
  0,
  1,
  2,
  2,
  -1,
  1,
  1,
  1
];