12,2,2,6,15,2,2,4,12,9,9,9,1,8,2,6,6,6,9,1,4,6,6,1,2,2,1,1,1,1],[1,7,28,7,28,
8,1,7,8,7,1,1],[1,21,28,7,7,21,28,8,21,7,7,8,7,7,1],[1,7,28,7,28,8,1,7,8,7,1,
1],[1,1,42,16,21,6,84,12,36,16,32,2,21,3,24,9,18,18,72,12,16,3,6,9,9,18,18,8,
12,24,1,9,9,12,3,1,1],[1,1,42,16,21,6,12,84,36,16,32,2,3,21,24,9,18,18,72,12,
16,3,6,9,9,18,18,8,12,24,1,9,9,12,3,1,1],[1,1,26,16,13,6,36,12,12,16,32,2,9,3,
8,9,6,18,24,12,16,1,6,9,3,6,6,8,12,8,1,3,3,4,1,1,1],[1,1,18,16,9,18,12,12,12,
16,2,3,3,15,12,6,18,12,12,16,3,6,3,9,6,6,6,12,12,8,12,1,3,3,6,6,4,8,3,1,1],[1,
1,18,16,9,18,12,12,12,16,2,3,3,15,12,6,18,12,12,16,3,6,3,9,6,6,6,12,12,8,12,1,
3,3,6,6,4,8,3,1,1],[1,1,26,16,13,6,12,36,12,16,32,2,3,9,8,9,6,18,24,12,16,1,6,
9,3,6,6,8,12,8,1,3,3,4,1,1,1],[1,1,26,16,13,6,28,28,12,16,32,7,7,8,8,3,4,6,12,
8,24,4,4,16,1,1,1,2,3,3,3,3,6,6,6,4,4,4,8,8,8,3,3,3,6,4,4,4,8,1,1],[1,1,18,4,
9,18,12,12,12,4,2,3,3,15,12,6,18,12,8,12,3,6,3,9,6,6,6,12,12,1,4,4,4,1,3,3,6,
6,3,2,4,3,1,1,1,1],[1,1,20,10,10,15,6,10,20,20,5,15,15,6,10,10,10,15,6,5,10,6,
5,1,1],[1,1,10,25,6,10,5,15,15,6,20,10,15,6,5,10,6,5,1,1],[1,1,18,8,32,9,6,12,
12,8,32,2,3,3,9,18,16,12,12,24,6,9,16,2,8,8,8,12,12,1,6,8,1,1,2,1],[1,1,14,28,
7,28,28,56,8,7,8,7,28,8,1,8,7,14,8,7,1,1,1,1],[1,1,42,28,21,28,28,42,28,56,8,
7,7,21,84,7,7,28,8,21,8,7,7,14,14,8,7,7,1,1],[1,1,28,21,28,8,7,7,21,28,8,21,8,
7,7,8,7,7,1],[1,1,28,21,28,8,7,7,21,28,8,21,8,7,7,8,7,7,1],[1,1,14,28,7,28,28,
56,8,7,8,7,28,8,1,8,7,14,8,7,1,1,1,1],[1,1,11,20,15,6,11,20,5,10,6,10,15,6,10,
6,5,5,5,5,6,10,6,5,1,1],[1,1,50,16,25,18,84,36,60,16,32,32,2,21,9,8,24,15,12,
30,42,24,12,120,12,16,16,16,3,1,3,6,6,9,15,9,15,6,18,30,30,12,12,8,12,24,8,16,
1,15,3,9,9,3,9,6,6,18,12,4,4,8,3,3,1,3,3,3,3,1,4,3,1,1,1,1],[1,1,50,16,25,18,
52,52,60,16,32,32,6,13,13,8,8,27,4,30,54,8,12,120,4,4,16,16,16,1,1,1,2,18,3,
27,9,9,6,18,18,30,12,12,4,4,4,8,8,8,8,8,16,3,9,3,9,9,9,3,6,6,6,4,4,4,4,4,4,4,
4,4,8,1,3,3,3,3,3,3,4,4,4,3,1,1],[1,1,50,16,25,18,36,84,60,16,32,32,2,9,21,24,
8,15,12,30,42,24,12,120,12,16,16,16,1,3,3,6,6,9,15,15,9,6,30,18,30,12,12,8,12,
24,8,16,1,9,3,3,15,9,9,6,6,18,12,4,4,8,3,1,3,3,3,3,3,1,4,3,1,1,1,1],[1,1,42,8,
32,21,6,12,84,36,8,32,32,96,2,3,21,24,9,18,18,72,16,12,12,16,24,48,3,6,9,9,18,
18,16,32,2,8,8,8,12,12,24,24,1,9,9,16,6,12,12,3,8,1,1,2,1,3,1,1],[1,1,18,8,32,
9,42,12,12,36,8,32,2,3,3,27,36,18,18,36,16,12,12,48,24,96,9,6,9,9,18,18,18,36,
36,16,2,8,8,8,12,12,24,24,1,9,9,18,18,16,6,12,12,12,24,24,24,9,8,1,1,2,6,6,8,
3,3,6,1,1],[1,1,42,8,32,21,6,84,12,36,8,32,32,96,2,21,3,24,9,18,18,72,16,12,
12,16,24,48,3,6,9,9,18,18,16,32,2,8,8,8,12,12,24,24,1,9,9,16,6,12,12,3,8,1,1,
2,1,3,1,1],[1,1,20,20,45,36,20,20,15,15,45,10,36,60,60,45,10,36,15,15,10,15,
15,10,6,6,1],[1,1,11,20,45,6,11,20,5,45,45,10,6,50,45,60,6,45,10,6,5,5,5,5,45,
15,6,10,20,18,15,15,15,15,6,10,5,1,6,5,3,1,1],[1,1,66,8,32,33,42,84,84,108,8,
32,64,192,2,21,21,24,24,27,36,54,90,72,36,216,16,12,12,48,32,24,96,96,3,3,9,
18,6,27,27,27,27,18,54,54,54,36,36,16,64,2,8,8,8,12,12,24,24,24,24,24,24,96,1,
27,9,9,27,9,27,18,18,54,16,32,6,12,12,12,12,12,12,12,24,24,24,9,3,3,9,9,9,9,
16,8,1,1,2,6,6,12,12,9,8,1,1,3,3,3,3,6,1,3,3,1,1,1,1],[1,1,30,20,20,15,60,36,
20,20,40,120,15,45,60,45,90,10,36,80,20,60,60,60,15,15,45,90,90,10,40,36,15,
15,60,60,45,10,20,20,36,15,15,15,15,30,10,10,10,15,15,6,6,10,6,6,1,1],[1,1,98,
112,49,42,196,84,252,112,224,224,64,14,49,21,8,56,63,28,126,126,56,84,504,28,
84,112,112,112,64,7,1,7,14,42,21,63,21,63,42,42,126,126,84,84,64,56,28,84,28,
168,56,56,56,56,112,7,63,21,63,21,21,21,42,42,42,64,28,84,28,28,28,28,28,28,
28,56,56,8,7,21,7,21,21,21,21,7,28,28,28,8,21,8,8,7,7,7,7,8,8,8,7,7,1],[1,1,
98,112,49,42,84,196,252,112,224,224,64,14,21,49,56,8,63,28,126,126,56,84,504,
84,28,112,112,112,64,1,7,7,14,42,21,63,63,21,42,126,42,126,84,84,64,56,84,28,
28,56,56,168,56,56,112,7,21,21,21,63,63,21,42,42,42,64,84,28,28,28,28,28,28,
28,28,56,56,8,7,7,21,21,21,21,21,7,28,28,28,8,21,8,8,7,7,7,7,8,8,8,7,7,1],[1,
1,35,140,105,126,35,140,120,35,105,315,70,126,210,105,420,120,315,70,126,120,
35,35,35,35,105,105,105,70,126,120,105,105,105,105,105,35,70,21,42,35,21,15,
15,7,1],[1,1,210,56,560,105,210,420,420,1260,336,56,560,1120,3360,960,70,105,
105,120,120,315,420,630,630,840,1260,2520,280,336,420,420,560,560,840,1680,
1680,960,336,15,15,105,210,210,315,315,315,315,630,630,630,630,1260,1260,280,
1120,336,960,70,280,280,280,420,420,420,840,840,840,840,840,840,840,1680,336,
35,315,315,315,315,315,315,630,630,630,280,560,560,1008,960,210,420,420,420,
420,420,420,420,420,420,420,840,840,840,840,120,120,336,105,105,105,315,315,
315,315,280,280,280,280,35,35,70,210,210,420,420,420,120,120,56,168,336,315,
280,280,120,120,120,35,35,105,105,105,105,105,210,168,168,35,120,120,120,120,
120,56,105,105,105,35,35,35,28,56,35,28,15,15,8,1]],
[1,2,2,3,3,4,4,4,4,4,5,6,6,6,6,7,8,8,8,8,8,8,8,8,8,8,8,8,9,10,12,12,12,12,12,
12,12,14,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,18,18,20,21,24,24,24,
24,24,24,24,24,24,24,24,24,24,24,24,30,32,32,32,32,32,32,32,32,32,32,36,36,36,
40,42,48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,56,56,60,64,64,64,64,64,64,
64,72,72,72,72,96,96,96,96,96,96,96,96,112,112,120,120,120,128,144,144,168,
168,168,192,192,192,192,192,192,192,192,240,240,288,336,336,336,336,336,360,
384,384,384,576,576,576,720,720,1152,1440,2688,2688,5040,40320],
[168,168,144,162,115,156,145,124,125,84,131,162,115,87,36,89,159,157,155,153,
149,132,126,108,113,104,82,52,134,131,124,125,116,115,101,73,73,89,131,166,
165,156,144,145,132,132,132,132,113,108,108,108,82,82,134,87,131,89,159,133,
133,133,124,125,126,92,104,91,93,101,101,99,73,131,163,132,132,132,132,132,
132,113,113,108,134,116,115,88,89,145,124,125,124,126,126,124,125,126,125,122,
101,102,103,104,153,149,131,156,157,155,132,132,132,132,134,134,133,134,163,
163,159,145,145,124,125,126,149,153,162,146,131,132,133,134,153,150,149,163,
163,157,155,157,155,156,145,146,147,163,149,150,151,152,153,162,155,156,157,
163,163,163,164,162,163,164,165,166,167,168],
[1,1,1,1,1,1,1,1,1,1,1,1,1,5,1,1,2,1,1,1,1,1,2,1,2,3,1,3,1,1,8,9,4,5,1,1,5,1,
1,1,1,2,3,2,1,2,2,2,2,3,3,3,7,7,1,5,11,16,17,2,17,17,8,9,23,32,26,31,8,12,4,9,
13,1,2,6,6,6,6,6,6,7,7,6,29,4,5,11,16,17,31,32,8,65,65,31,32,23,9,59,35,61,62,
26,20,21,11,6,18,19,19,18,22,22,55,55,17,29,75,75,17,59,59,63,64,65,21,20,129,
130,39,46,117,85,105,136,106,119,120,75,119,120,75,108,90,130,129,75,106,136,
151,152,105,129,119,144,120,120,148,119,161,154,148,161,165,166,167,168],
[(  1,231,218)(  2,162,216)(  3,234,223)(  4,171,228)(  5,174,230)
(  6,129,191)(  7,203,237)(  8,239,104)(  9,100,193)( 10,164,167)( 11,199,187)
( 12,238,133)( 13,211,229)( 14,188,201)( 15,102, 42)( 16,114,221)( 17,166,153)
( 18,103,115)( 19,170,202)( 20,181,214)( 21,224, 51)( 22,131, 60)( 23, 97,135)
( 24,106,233)( 25,204,232)( 26, 79, 90)( 27,236,145)( 28, 78, 50)( 29,138,222)
( 30,213, 77)( 31, 80,107)( 32,219, 70)( 33,150,130)( 34,125,165)( 35, 41, 58)
( 36,178, 93)( 37,172,235)( 38,173, 89)( 39,240,180)( 40, 73, 75)( 43,184,101)
( 44,175,160)( 45,149,197)( 46,105, 82)( 47,109, 72)( 48,185,126)( 49,200, 87)
( 52, 65, 84)( 53,143, 71)( 54,132, 81)( 55,140, 67)( 56,112,168)( 57, 96, 98)
( 59, 74,161)( 61,163,196)( 62,127,113)( 63,120,205)( 64,124,227)( 66,207,147)
( 68,169,111)( 69,206,137)( 76,141,136)( 83, 99, 88)( 85,155,212)( 86,177,118)
( 91,198,108)( 92,220,134)( 94,144, 95)(110,157,158)(116,122,119)(117,225,142)
(121,226,186)(123,190,146)(128,156,139)(148,189,194)(151,208,215)(152,192,183)
(154,209,159)(176,195,179)(182,217,210),(  1,201, 84,232,136,203,202)
(  2,191,227,134, 31, 52,103)(  3,167,109,235,168,171,222)(  4,113, 36, 81,
  83,123, 50)(  5,193,212,142, 46, 72, 79)(  6, 28,147,160,213,224,204)
(  7, 88, 53, 59, 62,152, 35)(  8,218, 33,240,176,150, 86)(  9, 41,118,196,
 184,219,172)( 10, 73,233,208, 17, 16, 77)( 11, 24,101, 14, 96,221,226)
( 12,223, 48,236,182,185, 66)( 13, 94,100,195, 39, 65,189)( 15,115,170,139,
 239, 30,209)( 18, 42, 45, 82,229,198,186)( 19, 78,199,159, 38,124,190)
( 20,119,129,217, 27, 47,154)( 21,135,158, 68, 67,102, 76)( 22, 90,138,110,
 238, 43,194)( 23, 95,237,133,173, 44,216)( 25,180,200,127,106, 87,210)
( 26, 60, 63,107,214,206,215)( 29, 58,166,148, 55,155,192)( 32,165,156, 49,
  89,131, 56)( 34,122,228,104,140, 61,230)( 37,145,169, 99,114,111,179)
( 40,105,157,116, 71,164,163)( 51,183,121, 74, 98,112,205)( 54, 75,141,197,
  70,146,151)( 57, 80,128,144, 93,188,175)( 64,149,125,174,161, 69,211)
( 85,120, 97,162,132, 91,181)( 92,187,207,234,143,225,126)(117,153,177,231,
 178,220,130)],
[[[[]]],[[[2,1,1,1],[1,1,2,-2,1,1,2,1],[3,1,4,1,3,1,4,1]]],[[[2,1,1,1,2,1,1,1,
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-1],[3,1,4,1,3,1,4,1]],[[2,1,1,-1,2,-1,1,-1,2,-1,1,-1,2,-2]],[[1,1,2,1],[1,-1,
2,2,1,1],[3,1,4,-1,3,1,4,-1]]],[[[1,-1],[1,1,2,1],[4,1,3,1,2,2,4,1,3,1,2,1,1,
1]],[[2,1,1,-1,2,-1,1,-1,2,-1,1,-1,2,-2]]],[[[1,-1],[1,1,2,1],[4,1,3,1,2,1,1,
1,4,1,3,1,2,2]],[[1,1,2,1,1,1,2,-1,1,1,2,1,1,-1,2,-1]]],[[[1,-1],[2,1,1,1,2,1,
3,-1,2,1,1,-1,2,1,3,1]],[[1,-1],[1,1,2,1],[3,1,2,1,4,2,3,1]]],[[[1,1,2,1],[2,
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1]]],[[[2,1,1,1,2,1],[3,1,1,1,3,-1]],[[1,-1,2,-1,1,-1,2,1,1,1]]],[[[1,-1,2,1,
1,1,2,-1]]],[[[2,1,1,1,2,-1,1,-1,2,-1,1,1,2,-1]],[[1,1,2,1],[3,1,1,1,2,1,3,
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