z1 := (1,2,3,4,6,8,11,16)(7,9,13,18)(10,14,20,25)(12,17,22,28,37,50,68,90)(19,
     24,31,42,58,79,106,144)(21,26,34,46,59,30,40,55)(23,29,39,53,73,97,130,
     175)(27,35,48,66,87,118,160,214)(32,43,60,36,49,67,88,120)(33,44,62,82,
     105,142,167,223)(38,51,70,93,123,166,222,304)(41,56,77,103,139,189,254,
     346)(45,63,83,111,151,201,273,373)(47,65,85,115,155,206,281,383)(52,71,
     95,127,172,230,315,420)(54,74,99,133,180,241,328,423)(57,78,104,141,69,
     91,75,100)(61,81,108,147,196,265,362,478)(64,84,113,152,140,190,256,349)
     (72,96,129,173,232,317,224,306)(76,101,136,184)(80,107,102,137,186,250,
     339,452)(86,116,157,209,286,210,287,390)(89,121,164,219,117,158,211,289)
     (92,124,168,125)(94,126,170,227,270,368,382,408)(98,131,177,237,323,433,
     551,680)(109,148,197,267,364,159,212,291)(110,149,199,269,367,439,558,
     688)(112,132,178,239,325,435,554,683)(114,153,204,277,226,309,412,527)
     (119,161,216,296,249,337,449,569)(122,165,221,303,162,191,257,234)(128,
     135,182,245,179,240,326,436)(134,181,243,330,220,301,406,517)(138,187,
     252,342,457,578,711,829)(143,193,260,355,188,253,344,459)(145,194,261,
     357,472,593,731,848)(146,195,263,360,475,597,732,850)(150,200,271,370,
     484,314,418,535)(154,205,279,381,495,615,534,663)(156,207,283,386,163,
     217,298,402)(169,225,308,410,524,375,489,608)(171,228,312,416,532,660,
     428,545)(174,233,319,426,229,313,288,391)(176,235,321,429,546,672,640,
     642)(183,246,333,443,562,693,814,746)(185,248,336,282,384,448,568,702)
     (192,258,352,466,264,203,275,376)(198,268,218,299,404,518,425,542)(202,
     274,295,399)(208,284,387,498,620,572,705,761)(213,292,242,329)(215,294,
     398,511,335,446,566,616)(231,316,422,539,310,413,528,655)(236,322,431,
     290,393,505,244,331)(238,324,354,468)(247,334,445,565,697,818,916,619)
     (251,340,454,575)(255,347,451,571,434,552,345,460)(259,353,467,586,721,
     837,744,598)(262,358,473,594)(266,363,359,369,440,548,675,380)(272,371,
     486,280)(276,377,491,611,742,858,851,859)(278,379,494,587,561,692,689,
     810)(285,388,499,622,749,866,954,1004)(293,396,508,633,389,500,624,752)
     (297,400,513,639,769,430,547,674)(300,405,520,646,773,884,963,925)(302,
     407,438,557,686,809,553,682)(305,372,487,607,479,482,603,350)(307,409,
     523,650,465,583,718,835)(311,414,530,657,612,743,860,950)(318,424,541,
     577,710,828,926,461)(320,427,544,669,798,751,684,808)(327,437,556,504,
     432,549,677,679)(332,441,559,651,779,803,804,483)(338,450,570,704,592,
     729,846,897)(341,455,540,666,442,560,691,812)(343,458,580,714,833,929,
     564,529)(348,463,581,715)(351,464,555,596,411,525,652,477)(356,470,590,
     726,842,937,856,949)(361,476,599,733)(365,480,601,735)(366,481,419,536)
     (374,397,509,634,764,880,961,1011)(378,492,613,456,576,709,826,923)(385,
     496,617,747,862,952,1002,1030)(392,503,627,756,873,957,1007,1034)(394,
     502,626,754)(395,506,630,760,878,914,980,869)(401,514,641,770,883,415,
     453,573)(403,516,643,604,737,676,802,488)(417,533,662,789,827,924,985,
     694)(421,538,665,792)(444,563,695,816)(447,567,700,821,920,983,863,763)
     (462,521,647,775,885,722,838,907)(469,588,723,801,584,719,771,849)(471,
     591,728,844,939,623,750,868)(474,595,522,648,776,602,736,854)(485,605,
     739,585,720,836,905,922)(490,609,740,857,661,787,895,971)(497,618,664,
     790)(501,625,753,870,865,936,574,706)(507,631,762,725,727,696,817,915)
     (510,635,765,649,777,888,962,874)(512,637,766,768,628,757,875,606)(515,
     519,644,772)(526,653,543,668,796,903,632,645)(531,658,785,892,953,1003,
     707,824)(537,600,734,852,659,786,893,969)(550,678,805,911,671,614,745,
     861)(579,712,831,670,799,621,748,864)(582,716,834,685)(589,724,840,934,
     990,1023,1043,1008)(610,741,797,904,968,1016,910,930)(629,758,876,959,
     879,960,917,981)(636,690,811,912,978,1006,1033,1031)(638,767,882,853,946,
     999,738,717)(654,781,698,783,708,825,887,823)(656,782,755,701,780,890,
     965,982)(667,794,902,975,855,948,791,898)(673,800,908,976,998,958,713,
     832)(681,806,899,793,900,973,1017,967)(687,807)(699,819,918,955)(703,822,
     820,919,921,984,928,931)(730,847,942,996)(759,877)(778,871,944,788,896,
     972,886,964)(784,891,966,1015,977,1019,1040,991)(795,813,913,979,1012,
     889,830,927)(815,867,906,901,974,1018,988,1020)(841,935,992,1025)(843,
     938,941,995,1027,1047,1057,1062)(845,940,994,1000,986,943,997,1028)(872,
     956,1005,1014)(881,951,1001,987)(894,970,1013,1038,1029,989,1021,1041)
     (932,945)(993,1026,1046,1048,1022,1042,1054,1037)(1009,1035,1051,1055)
     (1010,1036)(1024,1044,1050,1059,1063,1060,1064,1066)(1032,1049,1058,1045)
     (1039,1053)(1052,1061,1065,1056);