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-----------------------------------------------------------------------------
Statistic identifier: St001595
-----------------------------------------------------------------------------
Collection: Skew partitions
-----------------------------------------------------------------------------
Description: The number of standard Young tableaux of the skew partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return StandardTableaux(la).cardinality()
-----------------------------------------------------------------------------
Statistic values:
[[1],[]] => 1
[[2],[]] => 1
[[1,1],[]] => 1
[[2,1],[1]] => 2
[[3],[]] => 1
[[2,1],[]] => 2
[[3,1],[1]] => 3
[[2,2],[1]] => 2
[[3,2],[2]] => 3
[[1,1,1],[]] => 1
[[2,2,1],[1,1]] => 3
[[2,1,1],[1]] => 3
[[3,2,1],[2,1]] => 6
[[4],[]] => 1
[[3,1],[]] => 3
[[4,1],[1]] => 4
[[2,2],[]] => 2
[[3,2],[1]] => 5
[[4,2],[2]] => 6
[[2,1,1],[]] => 3
[[3,2,1],[1,1]] => 8
[[3,1,1],[1]] => 6
[[4,2,1],[2,1]] => 12
[[3,3],[2]] => 3
[[4,3],[3]] => 4
[[2,2,1],[1]] => 5
[[3,3,1],[2,1]] => 8
[[3,2,1],[2]] => 8
[[4,3,1],[3,1]] => 12
[[2,2,2],[1,1]] => 3
[[3,3,2],[2,2]] => 6
[[3,2,2],[2,1]] => 8
[[4,3,2],[3,2]] => 12
[[1,1,1,1],[]] => 1
[[2,2,2,1],[1,1,1]] => 4
[[2,2,1,1],[1,1]] => 6
[[3,3,2,1],[2,2,1]] => 12
[[2,1,1,1],[1]] => 4
[[3,2,2,1],[2,1,1]] => 12
[[3,2,1,1],[2,1]] => 12
[[4,3,2,1],[3,2,1]] => 24
[[5],[]] => 1
[[4,1],[]] => 4
[[5,1],[1]] => 5
[[3,2],[]] => 5
[[4,2],[1]] => 9
[[5,2],[2]] => 10
[[3,1,1],[]] => 6
[[4,2,1],[1,1]] => 15
[[4,1,1],[1]] => 10
[[5,2,1],[2,1]] => 20
[[3,3],[1]] => 5
[[4,3],[2]] => 9
[[5,3],[3]] => 10
[[2,2,1],[]] => 5
[[3,3,1],[1,1]] => 10
[[3,2,1],[1]] => 16
[[4,3,1],[2,1]] => 25
[[4,2,1],[2]] => 20
[[5,3,1],[3,1]] => 30
[[3,2,2],[1,1]] => 11
[[4,3,2],[2,2]] => 20
[[4,2,2],[2,1]] => 20
[[5,3,2],[3,2]] => 30
[[2,1,1,1],[]] => 4
[[3,2,2,1],[1,1,1]] => 15
[[3,2,1,1],[1,1]] => 20
[[4,3,2,1],[2,2,1]] => 40
[[3,1,1,1],[1]] => 10
[[4,2,2,1],[2,1,1]] => 30
[[4,2,1,1],[2,1]] => 30
[[5,3,2,1],[3,2,1]] => 60
[[4,4],[3]] => 4
[[5,4],[4]] => 5
[[3,3,1],[2]] => 11
[[4,4,1],[3,1]] => 15
[[4,3,1],[3]] => 15
[[5,4,1],[4,1]] => 20
[[2,2,2],[1]] => 5
[[3,3,2],[2,1]] => 16
[[4,4,2],[3,2]] => 20
[[3,2,2],[2]] => 10
[[4,3,2],[3,1]] => 25
[[5,4,2],[4,2]] => 30
[[2,2,1,1],[1]] => 9
[[3,3,2,1],[2,1,1]] => 25
[[3,3,1,1],[2,1]] => 20
[[4,4,2,1],[3,2,1]] => 40
[[3,2,1,1],[2]] => 15
[[4,3,2,1],[3,1,1]] => 40
[[4,3,1,1],[3,1]] => 30
[[5,4,2,1],[4,2,1]] => 60
[[3,3,3],[2,2]] => 6
[[4,4,3],[3,3]] => 10
[[4,3,3],[3,2]] => 15
[[5,4,3],[4,3]] => 20
[[2,2,2,1],[1,1]] => 9
[[3,3,3,1],[2,2,1]] => 15
[[3,3,2,1],[2,2]] => 20
[[4,4,3,1],[3,3,1]] => 30
[[3,2,2,1],[2,1]] => 25
[[4,3,3,1],[3,2,1]] => 40
[[4,3,2,1],[3,2]] => 40
[[5,4,3,1],[4,3,1]] => 60
[[2,2,2,2],[1,1,1]] => 4
[[3,3,3,2],[2,2,2]] => 10
[[3,3,2,2],[2,2,1]] => 20
[[4,4,3,2],[3,3,2]] => 30
[[3,2,2,2],[2,1,1]] => 15
[[4,3,3,2],[3,2,2]] => 30
[[4,3,2,2],[3,2,1]] => 40
[[5,4,3,2],[4,3,2]] => 60
[[1,1,1,1,1],[]] => 1
[[2,2,2,2,1],[1,1,1,1]] => 5
[[2,2,2,1,1],[1,1,1]] => 10
[[3,3,3,2,1],[2,2,2,1]] => 20
[[2,2,1,1,1],[1,1]] => 10
[[3,3,2,2,1],[2,2,1,1]] => 30
[[3,3,2,1,1],[2,2,1]] => 30
[[4,4,3,2,1],[3,3,2,1]] => 60
[[2,1,1,1,1],[1]] => 5
[[3,2,2,2,1],[2,1,1,1]] => 20
[[3,2,2,1,1],[2,1,1]] => 30
[[4,3,3,2,1],[3,2,2,1]] => 60
[[3,2,1,1,1],[2,1]] => 20
[[4,3,2,2,1],[3,2,1,1]] => 60
[[4,3,2,1,1],[3,2,1]] => 60
[[5,4,3,2,1],[4,3,2,1]] => 120
[[6],[]] => 1
[[5,1],[]] => 5
[[6,1],[1]] => 6
[[4,2],[]] => 9
[[5,2],[1]] => 14
[[6,2],[2]] => 15
[[4,1,1],[]] => 10
[[5,2,1],[1,1]] => 24
[[5,1,1],[1]] => 15
[[6,2,1],[2,1]] => 30
[[3,3],[]] => 5
[[4,3],[1]] => 14
[[5,3],[2]] => 19
[[6,3],[3]] => 20
[[3,2,1],[]] => 16
[[4,3,1],[1,1]] => 30
[[4,2,1],[1]] => 35
[[5,3,1],[2,1]] => 54
[[5,2,1],[2]] => 40
[[6,3,1],[3,1]] => 60
[[4,2,2],[1,1]] => 26
[[5,3,2],[2,2]] => 45
[[5,2,2],[2,1]] => 40
[[6,3,2],[3,2]] => 60
[[3,1,1,1],[]] => 10
[[4,2,2,1],[1,1,1]] => 36
[[4,2,1,1],[1,1]] => 45
[[5,3,2,1],[2,2,1]] => 90
[[4,1,1,1],[1]] => 20
[[5,2,2,1],[2,1,1]] => 60
[[5,2,1,1],[2,1]] => 60
[[6,3,2,1],[3,2,1]] => 120
[[4,4],[2]] => 9
[[5,4],[3]] => 14
[[6,4],[4]] => 15
[[3,3,1],[1]] => 21
[[4,4,1],[2,1]] => 30
[[4,3,1],[2]] => 40
[[5,4,1],[3,1]] => 54
[[5,3,1],[3]] => 45
[[6,4,1],[4,1]] => 60
[[2,2,2],[]] => 5
[[3,3,2],[1,1]] => 21
[[4,4,2],[2,2]] => 30
[[3,2,2],[1]] => 21
[[4,3,2],[2,1]] => 61
[[5,4,2],[3,2]] => 75
[[4,2,2],[2]] => 30
[[5,3,2],[3,1]] => 75
[[6,4,2],[4,2]] => 90
[[2,2,1,1],[]] => 9
[[3,3,2,1],[1,1,1]] => 30
[[3,3,1,1],[1,1]] => 30
[[4,4,2,1],[2,2,1]] => 60
[[3,2,1,1],[1]] => 35
[[4,3,2,1],[2,1,1]] => 96
[[4,3,1,1],[2,1]] => 75
[[5,4,2,1],[3,2,1]] => 150
[[4,2,1,1],[2]] => 45
[[5,3,2,1],[3,1,1]] => 120
[[5,3,1,1],[3,1]] => 90
[[6,4,2,1],[4,2,1]] => 180
[[4,3,3],[2,2]] => 26
[[5,4,3],[3,3]] => 40
[[5,3,3],[3,2]] => 45
[[6,4,3],[4,3]] => 60
[[3,2,2,1],[1,1]] => 40
[[4,3,3,1],[2,2,1]] => 66
[[4,3,2,1],[2,2]] => 80
[[5,4,3,1],[3,3,1]] => 120
[[4,2,2,1],[2,1]] => 75
[[5,3,3,1],[3,2,1]] => 120
[[5,3,2,1],[3,2]] => 120
[[6,4,3,1],[4,3,1]] => 180
[[3,2,2,2],[1,1,1]] => 19
[[4,3,3,2],[2,2,2]] => 45
[[4,3,2,2],[2,2,1]] => 80
[[5,4,3,2],[3,3,2]] => 120
[[4,2,2,2],[2,1,1]] => 45
[[5,3,3,2],[3,2,2]] => 90
[[5,3,2,2],[3,2,1]] => 120
[[6,4,3,2],[4,3,2]] => 180
[[2,1,1,1,1],[]] => 5
[[3,2,2,2,1],[1,1,1,1]] => 24
[[3,2,2,1,1],[1,1,1]] => 45
[[4,3,3,2,1],[2,2,2,1]] => 90
[[3,2,1,1,1],[1,1]] => 40
[[4,3,2,2,1],[2,2,1,1]] => 120
[[4,3,2,1,1],[2,2,1]] => 120
[[5,4,3,2,1],[3,3,2,1]] => 240
[[3,1,1,1,1],[1]] => 15
[[4,2,2,2,1],[2,1,1,1]] => 60
[[4,2,2,1,1],[2,1,1]] => 90
[[5,3,3,2,1],[3,2,2,1]] => 180
[[4,2,1,1,1],[2,1]] => 60
[[5,3,2,2,1],[3,2,1,1]] => 180
[[5,3,2,1,1],[3,2,1]] => 180
[[6,4,3,2,1],[4,3,2,1]] => 360
[[5,5],[4]] => 5
[[6,5],[5]] => 6
[[4,4,1],[3]] => 19
[[5,5,1],[4,1]] => 24
[[5,4,1],[4]] => 24
[[6,5,1],[5,1]] => 30
[[3,3,2],[2]] => 21
[[4,4,2],[3,1]] => 40
[[5,5,2],[4,2]] => 45
[[4,3,2],[3]] => 30
[[5,4,2],[4,1]] => 54
[[6,5,2],[5,2]] => 60
[[3,3,1,1],[2]] => 26
[[4,4,2,1],[3,1,1]] => 66
[[4,4,1,1],[3,1]] => 45
[[5,5,2,1],[4,2,1]] => 90
[[4,3,1,1],[3]] => 36
[[5,4,2,1],[4,1,1]] => 90
[[5,4,1,1],[4,1]] => 60
[[6,5,2,1],[5,2,1]] => 120
[[3,3,3],[2,1]] => 16
[[4,4,3],[3,2]] => 35
[[5,5,3],[4,3]] => 40
[[4,3,3],[3,1]] => 30
[[5,4,3],[4,2]] => 54
[[6,5,3],[5,3]] => 60
[[2,2,2,1],[1]] => 14
[[3,3,3,1],[2,1,1]] => 30
[[3,3,2,1],[2,1]] => 61
[[4,4,3,1],[3,2,1]] => 96
[[4,4,2,1],[3,2]] => 80
[[5,5,3,1],[4,3,1]] => 120
[[3,2,2,1],[2]] => 30
[[4,3,3,1],[3,1,1]] => 60
[[4,3,2,1],[3,1]] => 96
[[5,4,3,1],[4,2,1]] => 150
[[5,4,2,1],[4,2]] => 120
[[6,5,3,1],[5,3,1]] => 180
[[3,3,2,2],[2,1,1]] => 40
[[4,4,3,2],[3,2,2]] => 75
[[4,4,2,2],[3,2,1]] => 80
[[5,5,3,2],[4,3,2]] => 120
[[4,3,2,2],[3,1,1]] => 66
[[5,4,3,2],[4,2,2]] => 120
[[5,4,2,2],[4,2,1]] => 120
[[6,5,3,2],[5,3,2]] => 180
[[2,2,1,1,1],[1]] => 14
[[3,3,2,2,1],[2,1,1,1]] => 54
[[3,3,2,1,1],[2,1,1]] => 75
[[4,4,3,2,1],[3,2,2,1]] => 150
[[3,3,1,1,1],[2,1]] => 40
[[4,4,2,2,1],[3,2,1,1]] => 120
[[4,4,2,1,1],[3,2,1]] => 120
[[5,5,3,2,1],[4,3,2,1]] => 240
[[3,2,1,1,1],[2]] => 24
[[4,3,2,2,1],[3,1,1,1]] => 90
[[4,3,2,1,1],[3,1,1]] => 120
[[5,4,3,2,1],[4,2,2,1]] => 240
[[4,3,1,1,1],[3,1]] => 60
[[5,4,2,2,1],[4,2,1,1]] => 180
[[5,4,2,1,1],[4,2,1]] => 180
[[6,5,3,2,1],[5,3,2,1]] => 360
[[4,4,4],[3,3]] => 10
[[5,5,4],[4,4]] => 15
[[5,4,4],[4,3]] => 24
[[6,5,4],[5,4]] => 30
[[3,3,3,1],[2,2]] => 26
[[4,4,4,1],[3,3,1]] => 36
[[4,4,3,1],[3,3]] => 45
[[5,5,4,1],[4,4,1]] => 60
[[4,3,3,1],[3,2]] => 66
[[5,4,4,1],[4,3,1]] => 90
[[5,4,3,1],[4,3]] => 90
[[6,5,4,1],[5,4,1]] => 120
[[2,2,2,2],[1,1]] => 9
[[3,3,3,2],[2,2,1]] => 35
[[4,4,4,2],[3,3,2]] => 45
[[3,3,2,2],[2,2]] => 30
[[4,4,3,2],[3,3,1]] => 75
[[5,5,4,2],[4,4,2]] => 90
[[3,2,2,2],[2,1]] => 30
[[4,3,3,2],[3,2,1]] => 96
[[5,4,4,2],[4,3,2]] => 120
[[4,3,2,2],[3,2]] => 60
[[5,4,3,2],[4,3,1]] => 150
[[6,5,4,2],[5,4,2]] => 180
[[2,2,2,1,1],[1,1]] => 19
[[3,3,3,2,1],[2,2,1,1]] => 54
[[3,3,3,1,1],[2,2,1]] => 45
[[4,4,4,2,1],[3,3,2,1]] => 90
[[3,3,2,1,1],[2,2]] => 45
[[4,4,3,2,1],[3,3,1,1]] => 120
[[4,4,3,1,1],[3,3,1]] => 90
[[5,5,4,2,1],[4,4,2,1]] => 180
[[3,2,2,1,1],[2,1]] => 54
[[4,3,3,2,1],[3,2,1,1]] => 150
[[4,3,3,1,1],[3,2,1]] => 120
[[5,4,4,2,1],[4,3,2,1]] => 240
[[4,3,2,1,1],[3,2]] => 90
[[5,4,3,2,1],[4,3,1,1]] => 240
[[5,4,3,1,1],[4,3,1]] => 180
[[6,5,4,2,1],[5,4,2,1]] => 360
[[3,3,3,3],[2,2,2]] => 10
[[4,4,4,3],[3,3,3]] => 20
[[4,4,3,3],[3,3,2]] => 45
[[5,5,4,3],[4,4,3]] => 60
[[4,3,3,3],[3,2,2]] => 36
[[5,4,4,3],[4,3,3]] => 60
[[5,4,3,3],[4,3,2]] => 90
[[6,5,4,3],[5,4,3]] => 120
[[2,2,2,2,1],[1,1,1]] => 14
[[3,3,3,3,1],[2,2,2,1]] => 24
[[3,3,3,2,1],[2,2,2]] => 40
[[4,4,4,3,1],[3,3,3,1]] => 60
[[3,3,2,2,1],[2,2,1]] => 75
[[4,4,3,3,1],[3,3,2,1]] => 120
[[4,4,3,2,1],[3,3,2]] => 120
[[5,5,4,3,1],[4,4,3,1]] => 180
[[3,2,2,2,1],[2,1,1]] => 54
[[4,3,3,3,1],[3,2,2,1]] => 90
[[4,3,3,2,1],[3,2,2]] => 120
[[5,4,4,3,1],[4,3,3,1]] => 180
[[4,3,2,2,1],[3,2,1]] => 150
[[5,4,3,3,1],[4,3,2,1]] => 240
[[5,4,3,2,1],[4,3,2]] => 240
[[6,5,4,3,1],[5,4,3,1]] => 360
[[2,2,2,2,2],[1,1,1,1]] => 5
[[3,3,3,3,2],[2,2,2,2]] => 15
[[3,3,3,2,2],[2,2,2,1]] => 40
[[4,4,4,3,2],[3,3,3,2]] => 60
[[3,3,2,2,2],[2,2,1,1]] => 45
[[4,4,3,3,2],[3,3,2,2]] => 90
[[4,4,3,2,2],[3,3,2,1]] => 120
[[5,5,4,3,2],[4,4,3,2]] => 180
[[3,2,2,2,2],[2,1,1,1]] => 24
[[4,3,3,3,2],[3,2,2,2]] => 60
[[4,3,3,2,2],[3,2,2,1]] => 120
[[5,4,4,3,2],[4,3,3,2]] => 180
[[4,3,2,2,2],[3,2,1,1]] => 90
[[5,4,3,3,2],[4,3,2,2]] => 180
[[5,4,3,2,2],[4,3,2,1]] => 240
[[6,5,4,3,2],[5,4,3,2]] => 360
[[1,1,1,1,1,1],[]] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => 6
[[2,2,2,2,1,1],[1,1,1,1]] => 15
[[3,3,3,3,2,1],[2,2,2,2,1]] => 30
[[2,2,2,1,1,1],[1,1,1]] => 20
[[3,3,3,2,2,1],[2,2,2,1,1]] => 60
[[3,3,3,2,1,1],[2,2,2,1]] => 60
[[4,4,4,3,2,1],[3,3,3,2,1]] => 120
[[2,2,1,1,1,1],[1,1]] => 15
[[3,3,2,2,2,1],[2,2,1,1,1]] => 60
[[3,3,2,2,1,1],[2,2,1,1]] => 90
[[4,4,3,3,2,1],[3,3,2,2,1]] => 180
[[3,3,2,1,1,1],[2,2,1]] => 60
[[4,4,3,2,2,1],[3,3,2,1,1]] => 180
[[4,4,3,2,1,1],[3,3,2,1]] => 180
[[5,5,4,3,2,1],[4,4,3,2,1]] => 360
[[2,1,1,1,1,1],[1]] => 6
[[3,2,2,2,2,1],[2,1,1,1,1]] => 30
[[3,2,2,2,1,1],[2,1,1,1]] => 60
[[4,3,3,3,2,1],[3,2,2,2,1]] => 120
[[3,2,2,1,1,1],[2,1,1]] => 60
[[4,3,3,2,2,1],[3,2,2,1,1]] => 180
[[4,3,3,2,1,1],[3,2,2,1]] => 180
[[5,4,4,3,2,1],[4,3,3,2,1]] => 360
[[3,2,1,1,1,1],[2,1]] => 30
[[4,3,2,2,2,1],[3,2,1,1,1]] => 120
[[4,3,2,2,1,1],[3,2,1,1]] => 180
[[5,4,3,3,2,1],[4,3,2,2,1]] => 360
[[4,3,2,1,1,1],[3,2,1]] => 120
[[5,4,3,2,2,1],[4,3,2,1,1]] => 360
[[5,4,3,2,1,1],[4,3,2,1]] => 360
[[6,5,4,3,2,1],[5,4,3,2,1]] => 720
[[7],[]] => 1
[[6,1],[]] => 6
[[7,1],[1]] => 7
[[5,2],[]] => 14
[[6,2],[1]] => 20
[[7,2],[2]] => 21
[[5,1,1],[]] => 15
[[6,2,1],[1,1]] => 35
[[6,1,1],[1]] => 21
[[7,2,1],[2,1]] => 42
[[4,3],[]] => 14
[[5,3],[1]] => 28
[[6,3],[2]] => 34
[[7,3],[3]] => 35
[[4,2,1],[]] => 35
[[5,3,1],[1,1]] => 63
[[5,2,1],[1]] => 64
[[6,3,1],[2,1]] => 98
[[6,2,1],[2]] => 70
[[7,3,1],[3,1]] => 105
[[5,2,2],[1,1]] => 50
[[6,3,2],[2,2]] => 84
[[6,2,2],[2,1]] => 70
[[7,3,2],[3,2]] => 105
[[4,1,1,1],[]] => 20
[[5,2,2,1],[1,1,1]] => 70
[[5,2,1,1],[1,1]] => 84
[[6,3,2,1],[2,2,1]] => 168
[[5,1,1,1],[1]] => 35
[[6,2,2,1],[2,1,1]] => 105
[[6,2,1,1],[2,1]] => 105
[[7,3,2,1],[3,2,1]] => 210
[[4,4],[1]] => 14
[[5,4],[2]] => 28
[[6,4],[3]] => 34
[[7,4],[4]] => 35
[[3,3,1],[]] => 21
[[4,4,1],[1,1]] => 35
[[4,3,1],[1]] => 70
[[5,4,1],[2,1]] => 98
[[5,3,1],[2]] => 99
[[6,4,1],[3,1]] => 133
[[6,3,1],[3]] => 105
[[7,4,1],[4,1]] => 140
[[3,2,2],[]] => 21
[[4,3,2],[1,1]] => 77
[[5,4,2],[2,2]] => 105
[[4,2,2],[1]] => 56
[[5,3,2],[2,1]] => 155
[[6,4,2],[3,2]] => 189
[[5,2,2],[2]] => 70
[[6,3,2],[3,1]] => 175
[[7,4,2],[4,2]] => 210
[[3,2,1,1],[]] => 35
[[4,3,2,1],[1,1,1]] => 112
[[4,3,1,1],[1,1]] => 105
[[5,4,2,1],[2,2,1]] => 210
[[4,2,1,1],[1]] => 90
[[5,3,2,1],[2,1,1]] => 245
[[5,3,1,1],[2,1]] => 189
[[6,4,2,1],[3,2,1]] => 378
[[5,2,1,1],[2]] => 105
[[6,3,2,1],[3,1,1]] => 280
[[6,3,1,1],[3,1]] => 210
[[7,4,2,1],[4,2,1]] => 420
[[5,3,3],[2,2]] => 71
[[6,4,3],[3,3]] => 105
[[6,3,3],[3,2]] => 105
[[7,4,3],[4,3]] => 140
[[4,2,2,1],[1,1]] => 111
[[5,3,3,1],[2,2,1]] => 182
[[5,3,2,1],[2,2]] => 210
[[6,4,3,1],[3,3,1]] => 315
[[5,2,2,1],[2,1]] => 175
[[6,3,3,1],[3,2,1]] => 280
[[6,3,2,1],[3,2]] => 280
[[7,4,3,1],[4,3,1]] => 420
[[4,2,2,2],[1,1,1]] => 55
[[5,3,3,2],[2,2,2]] => 126
[[5,3,2,2],[2,2,1]] => 210
[[6,4,3,2],[3,3,2]] => 315
[[5,2,2,2],[2,1,1]] => 105
[[6,3,3,2],[3,2,2]] => 210
[[6,3,2,2],[3,2,1]] => 280
[[7,4,3,2],[4,3,2]] => 420
[[3,1,1,1,1],[]] => 15
[[4,2,2,2,1],[1,1,1,1]] => 70
[[4,2,2,1,1],[1,1,1]] => 126
[[5,3,3,2,1],[2,2,2,1]] => 252
[[4,2,1,1,1],[1,1]] => 105
[[5,3,2,2,1],[2,2,1,1]] => 315
[[5,3,2,1,1],[2,2,1]] => 315
[[6,4,3,2,1],[3,3,2,1]] => 630
[[4,1,1,1,1],[1]] => 35
[[5,2,2,2,1],[2,1,1,1]] => 140
[[5,2,2,1,1],[2,1,1]] => 210
[[6,3,3,2,1],[3,2,2,1]] => 420
[[5,2,1,1,1],[2,1]] => 140
[[6,3,2,2,1],[3,2,1,1]] => 420
[[6,3,2,1,1],[3,2,1]] => 420
[[7,4,3,2,1],[4,3,2,1]] => 840
[[5,5],[3]] => 14
[[6,5],[4]] => 20
[[7,5],[5]] => 21
[[4,4,1],[2]] => 49
[[5,5,1],[3,1]] => 63
[[5,4,1],[3]] => 78
[[6,5,1],[4,1]] => 98
[[6,4,1],[4]] => 84
[[7,5,1],[5,1]] => 105
[[3,3,2],[1]] => 42
[[4,4,2],[2,1]] => 91
[[5,5,2],[3,2]] => 105
[[4,3,2],[2]] => 91
[[5,4,2],[3,1]] => 169
[[6,5,2],[4,2]] => 189
[[5,3,2],[3]] => 105
[[6,4,2],[4,1]] => 189
[[7,5,2],[5,2]] => 210
[[3,3,1,1],[1]] => 56
[[4,4,2,1],[2,1,1]] => 147
[[4,4,1,1],[2,1]] => 105
[[5,5,2,1],[3,2,1]] => 210
[[4,3,1,1],[2]] => 111
[[5,4,2,1],[3,1,1]] => 280
[[5,4,1,1],[3,1]] => 189
[[6,5,2,1],[4,2,1]] => 378
[[5,3,1,1],[3]] => 126
[[6,4,2,1],[4,1,1]] => 315
[[6,4,1,1],[4,1]] => 210
[[7,5,2,1],[5,2,1]] => 420
[[3,3,3],[1,1]] => 21
[[4,4,3],[2,2]] => 56
[[5,5,3],[3,3]] => 70
[[4,3,3],[2,1]] => 77
[[5,4,3],[3,2]] => 155
[[6,5,3],[4,3]] => 175
[[5,3,3],[3,1]] => 105
[[6,4,3],[4,2]] => 189
[[7,5,3],[5,3]] => 210
[[2,2,2,1],[]] => 14
[[3,3,3,1],[1,1,1]] => 35
[[3,3,2,1],[1,1]] => 91
[[4,4,3,1],[2,2,1]] => 147
[[4,4,2,1],[2,2]] => 140
[[5,5,3,1],[3,3,1]] => 210
[[3,2,2,1],[1]] => 70
[[4,3,3,1],[2,1,1]] => 147
[[4,3,2,1],[2,1]] => 272
[[5,4,3,1],[3,2,1]] => 427
[[5,4,2,1],[3,2]] => 350
[[6,5,3,1],[4,3,1]] => 525
[[4,2,2,1],[2]] => 105
[[5,3,3,1],[3,1,1]] => 210
[[5,3,2,1],[3,1]] => 336
[[6,4,3,1],[4,2,1]] => 525
[[6,4,2,1],[4,2]] => 420
[[7,5,3,1],[5,3,1]] => 630
[[3,3,2,2],[1,1,1]] => 49
[[4,4,3,2],[2,2,2]] => 105
[[4,4,2,2],[2,2,1]] => 140
[[5,5,3,2],[3,3,2]] => 210
[[4,3,2,2],[2,1,1]] => 181
[[5,4,3,2],[3,2,2]] => 336
[[5,4,2,2],[3,2,1]] => 350
[[6,5,3,2],[4,3,2]] => 525
[[5,3,2,2],[3,1,1]] => 231
[[6,4,3,2],[4,2,2]] => 420
[[6,4,2,2],[4,2,1]] => 420
[[7,5,3,2],[5,3,2]] => 630
[[2,2,1,1,1],[]] => 14
[[3,3,2,2,1],[1,1,1,1]] => 63
[[3,3,2,1,1],[1,1,1]] => 105
[[4,4,3,2,1],[2,2,2,1]] => 210
[[3,3,1,1,1],[1,1]] => 70
[[4,4,2,2,1],[2,2,1,1]] => 210
[[4,4,2,1,1],[2,2,1]] => 210
[[5,5,3,2,1],[3,3,2,1]] => 420
[[3,2,1,1,1],[1]] => 64
[[4,3,2,2,1],[2,1,1,1]] => 245
[[4,3,2,1,1],[2,1,1]] => 336
[[5,4,3,2,1],[3,2,2,1]] => 672
[[4,3,1,1,1],[2,1]] => 175
[[5,4,2,2,1],[3,2,1,1]] => 525
[[5,4,2,1,1],[3,2,1]] => 525
[[6,5,3,2,1],[4,3,2,1]] => 1050
[[4,2,1,1,1],[2]] => 84
[[5,3,2,2,1],[3,1,1,1]] => 315
[[5,3,2,1,1],[3,1,1]] => 420
[[6,4,3,2,1],[4,2,2,1]] => 840
[[5,3,1,1,1],[3,1]] => 210
[[6,4,2,2,1],[4,2,1,1]] => 630
[[6,4,2,1,1],[4,2,1]] => 630
[[7,5,3,2,1],[5,3,2,1]] => 1260
[[5,4,4],[3,3]] => 50
[[6,5,4],[4,4]] => 70
[[6,4,4],[4,3]] => 84
[[7,5,4],[5,4]] => 105
[[4,3,3,1],[2,2]] => 132
[[5,4,4,1],[3,3,1]] => 182
[[5,4,3,1],[3,3]] => 210
[[6,5,4,1],[4,4,1]] => 280
[[5,3,3,1],[3,2]] => 231
[[6,4,4,1],[4,3,1]] => 315
[[6,4,3,1],[4,3]] => 315
[[7,5,4,1],[5,4,1]] => 420
[[3,2,2,2],[1,1]] => 49
[[4,3,3,2],[2,2,1]] => 181
[[5,4,4,2],[3,3,2]] => 231
[[4,3,2,2],[2,2]] => 140
[[5,4,3,2],[3,3,1]] => 350
[[6,5,4,2],[4,4,2]] => 420
[[4,2,2,2],[2,1]] => 105
[[5,3,3,2],[3,2,1]] => 336
[[6,4,4,2],[4,3,2]] => 420
[[5,3,2,2],[3,2]] => 210
[[6,4,3,2],[4,3,1]] => 525
[[7,5,4,2],[5,4,2]] => 630
[[3,2,2,1,1],[1,1]] => 99
[[4,3,3,2,1],[2,2,1,1]] => 280
[[4,3,3,1,1],[2,2,1]] => 231
[[5,4,4,2,1],[3,3,2,1]] => 462
[[4,3,2,1,1],[2,2]] => 210
[[5,4,3,2,1],[3,3,1,1]] => 560
[[5,4,3,1,1],[3,3,1]] => 420
[[6,5,4,2,1],[4,4,2,1]] => 840
[[4,2,2,1,1],[2,1]] => 189
[[5,3,3,2,1],[3,2,1,1]] => 525
[[5,3,3,1,1],[3,2,1]] => 420
[[6,4,4,2,1],[4,3,2,1]] => 840
[[5,3,2,1,1],[3,2]] => 315
[[6,4,3,2,1],[4,3,1,1]] => 840
[[6,4,3,1,1],[4,3,1]] => 630
[[7,5,4,2,1],[5,4,2,1]] => 1260
[[4,3,3,3],[2,2,2]] => 55
[[5,4,4,3],[3,3,3]] => 105
[[5,4,3,3],[3,3,2]] => 210
[[6,5,4,3],[4,4,3]] => 280
[[5,3,3,3],[3,2,2]] => 126
[[6,4,4,3],[4,3,3]] => 210
[[6,4,3,3],[4,3,2]] => 315
[[7,5,4,3],[5,4,3]] => 420
[[3,2,2,2,1],[1,1,1]] => 78
[[4,3,3,3,1],[2,2,2,1]] => 133
[[4,3,3,2,1],[2,2,2]] => 210
[[5,4,4,3,1],[3,3,3,1]] => 315
[[4,3,2,2,1],[2,2,1]] => 350
[[5,4,3,3,1],[3,3,2,1]] => 560
[[5,4,3,2,1],[3,3,2]] => 560
[[6,5,4,3,1],[4,4,3,1]] => 840
[[4,2,2,2,1],[2,1,1]] => 189
[[5,3,3,3,1],[3,2,2,1]] => 315
[[5,3,3,2,1],[3,2,2]] => 420
[[6,4,4,3,1],[4,3,3,1]] => 630
[[5,3,2,2,1],[3,2,1]] => 525
[[6,4,3,3,1],[4,3,2,1]] => 840
[[6,4,3,2,1],[4,3,2]] => 840
[[7,5,4,3,1],[5,4,3,1]] => 1260
[[3,2,2,2,2],[1,1,1,1]] => 29
[[4,3,3,3,2],[2,2,2,2]] => 84
[[4,3,3,2,2],[2,2,2,1]] => 210
[[5,4,4,3,2],[3,3,3,2]] => 315
[[4,3,2,2,2],[2,2,1,1]] => 210
[[5,4,3,3,2],[3,3,2,2]] => 420
[[5,4,3,2,2],[3,3,2,1]] => 560
[[6,5,4,3,2],[4,4,3,2]] => 840
[[4,2,2,2,2],[2,1,1,1]] => 84
[[5,3,3,3,2],[3,2,2,2]] => 210
[[5,3,3,2,2],[3,2,2,1]] => 420
[[6,4,4,3,2],[4,3,3,2]] => 630
[[5,3,2,2,2],[3,2,1,1]] => 315
[[6,4,3,3,2],[4,3,2,2]] => 630
[[6,4,3,2,2],[4,3,2,1]] => 840
[[7,5,4,3,2],[5,4,3,2]] => 1260
[[2,1,1,1,1,1],[]] => 6
[[3,2,2,2,2,1],[1,1,1,1,1]] => 35
[[3,2,2,2,1,1],[1,1,1,1]] => 84
[[4,3,3,3,2,1],[2,2,2,2,1]] => 168
[[3,2,2,1,1,1],[1,1,1]] => 105
[[4,3,3,2,2,1],[2,2,2,1,1]] => 315
[[4,3,3,2,1,1],[2,2,2,1]] => 315
[[5,4,4,3,2,1],[3,3,3,2,1]] => 630
[[3,2,1,1,1,1],[1,1]] => 70
[[4,3,2,2,2,1],[2,2,1,1,1]] => 280
[[4,3,2,2,1,1],[2,2,1,1]] => 420
[[5,4,3,3,2,1],[3,3,2,2,1]] => 840
[[4,3,2,1,1,1],[2,2,1]] => 280
[[5,4,3,2,2,1],[3,3,2,1,1]] => 840
[[5,4,3,2,1,1],[3,3,2,1]] => 840
[[6,5,4,3,2,1],[4,4,3,2,1]] => 1680
[[3,1,1,1,1,1],[1]] => 21
[[4,2,2,2,2,1],[2,1,1,1,1]] => 105
[[4,2,2,2,1,1],[2,1,1,1]] => 210
[[5,3,3,3,2,1],[3,2,2,2,1]] => 420
[[4,2,2,1,1,1],[2,1,1]] => 210
[[5,3,3,2,2,1],[3,2,2,1,1]] => 630
[[5,3,3,2,1,1],[3,2,2,1]] => 630
[[6,4,4,3,2,1],[4,3,3,2,1]] => 1260
[[4,2,1,1,1,1],[2,1]] => 105
[[5,3,2,2,2,1],[3,2,1,1,1]] => 420
[[5,3,2,2,1,1],[3,2,1,1]] => 630
[[6,4,3,3,2,1],[4,3,2,2,1]] => 1260
[[5,3,2,1,1,1],[3,2,1]] => 420
[[6,4,3,2,2,1],[4,3,2,1,1]] => 1260
[[6,4,3,2,1,1],[4,3,2,1]] => 1260
[[7,5,4,3,2,1],[5,4,3,2,1]] => 2520
[[6,6],[5]] => 6
[[7,6],[6]] => 7
[[5,5,1],[4]] => 29
[[6,6,1],[5,1]] => 35
[[6,5,1],[5]] => 35
[[7,6,1],[6,1]] => 42
[[4,4,2],[3]] => 49
[[5,5,2],[4,1]] => 78
[[6,6,2],[5,2]] => 84
[[5,4,2],[4]] => 63
[[6,5,2],[5,1]] => 98
[[7,6,2],[6,2]] => 105
[[4,4,1,1],[3]] => 55
[[5,5,2,1],[4,1,1]] => 133
[[5,5,1,1],[4,1]] => 84
[[6,6,2,1],[5,2,1]] => 168
[[5,4,1,1],[4]] => 70
[[6,5,2,1],[5,1,1]] => 168
[[6,5,1,1],[5,1]] => 105
[[7,6,2,1],[6,2,1]] => 210
[[3,3,3],[2]] => 21
[[4,4,3],[3,1]] => 70
[[5,5,3],[4,2]] => 99
[[6,6,3],[5,3]] => 105
[[4,3,3],[3]] => 35
[[5,4,3],[4,1]] => 98
[[6,5,3],[5,2]] => 133
[[7,6,3],[6,3]] => 140
[[3,3,2,1],[2]] => 77
[[4,4,3,1],[3,1,1]] => 147
[[4,4,2,1],[3,1]] => 181
[[5,5,3,1],[4,2,1]] => 280
[[5,5,2,1],[4,2]] => 210
[[6,6,3,1],[5,3,1]] => 315
[[4,3,2,1],[3]] => 112
[[5,4,3,1],[4,1,1]] => 210
[[5,4,2,1],[4,1]] => 245
[[6,5,3,1],[5,2,1]] => 378
[[6,5,2,1],[5,2]] => 280
[[7,6,3,1],[6,3,1]] => 420
[[4,4,2,2],[3,1,1]] => 132
[[5,5,3,2],[4,2,2]] => 231
[[5,5,2,2],[4,2,1]] => 210
[[6,6,3,2],[5,3,2]] => 315
[[5,4,2,2],[4,1,1]] => 182
[[6,5,3,2],[5,2,2]] => 315
[[6,5,2,2],[5,2,1]] => 280
[[7,6,3,2],[6,3,2]] => 420
[[3,3,1,1,1],[2]] => 50
[[4,4,2,2,1],[3,1,1,1]] => 182
[[4,4,2,1,1],[3,1,1]] => 231
[[5,5,3,2,1],[4,2,2,1]] => 462
[[4,4,1,1,1],[3,1]] => 105
[[5,5,2,2,1],[4,2,1,1]] => 315
[[5,5,2,1,1],[4,2,1]] => 315
[[6,6,3,2,1],[5,3,2,1]] => 630
[[4,3,1,1,1],[3]] => 70
[[5,4,2,2,1],[4,1,1,1]] => 252
[[5,4,2,1,1],[4,1,1]] => 315
[[6,5,3,2,1],[5,2,2,1]] => 630
[[5,4,1,1,1],[4,1]] => 140
[[6,5,2,2,1],[5,2,1,1]] => 420
[[6,5,2,1,1],[5,2,1]] => 420
[[7,6,3,2,1],[6,3,2,1]] => 840
[[4,4,4],[3,2]] => 35
[[5,5,4],[4,3]] => 64
[[6,6,4],[5,4]] => 70
[[5,4,4],[4,2]] => 63
[[6,5,4],[5,3]] => 98
[[7,6,4],[6,4]] => 105
[[3,3,3,1],[2,1]] => 77
[[4,4,4,1],[3,2,1]] => 112
[[4,4,3,1],[3,2]] => 181
[[5,5,4,1],[4,3,1]] => 245
[[5,5,3,1],[4,3]] => 210
[[6,6,4,1],[5,4,1]] => 280
[[4,3,3,1],[3,1]] => 147
[[5,4,4,1],[4,2,1]] => 210
[[5,4,3,1],[4,2]] => 280
[[6,5,4,1],[5,3,1]] => 378
[[6,5,3,1],[5,3]] => 315
[[7,6,4,1],[6,4,1]] => 420
[[2,2,2,2],[1]] => 14
[[3,3,3,2],[2,1,1]] => 70
[[4,4,4,2],[3,2,2]] => 105
[[3,3,2,2],[2,1]] => 91
[[4,4,3,2],[3,2,1]] => 272
[[5,5,4,2],[4,3,2]] => 336
[[4,4,2,2],[3,2]] => 140
[[5,5,3,2],[4,3,1]] => 350
[[6,6,4,2],[5,4,2]] => 420
[[3,2,2,2],[2]] => 35
[[4,3,3,2],[3,1,1]] => 147
[[5,4,4,2],[4,2,2]] => 210
[[4,3,2,2],[3,1]] => 147
[[5,4,3,2],[4,2,1]] => 427
[[6,5,4,2],[5,3,2]] => 525
[[5,4,2,2],[4,2]] => 210
[[6,5,3,2],[5,3,1]] => 525
[[7,6,4,2],[6,4,2]] => 630
[[2,2,2,1,1],[1]] => 28
[[3,3,3,2,1],[2,1,1,1]] => 98
[[3,3,3,1,1],[2,1,1]] => 105
[[4,4,4,2,1],[3,2,2,1]] => 210
[[3,3,2,1,1],[2,1]] => 155
[[4,4,3,2,1],[3,2,1,1]] => 427
[[4,4,3,1,1],[3,2,1]] => 336
[[5,5,4,2,1],[4,3,2,1]] => 672
[[4,4,2,1,1],[3,2]] => 210
[[5,5,3,2,1],[4,3,1,1]] => 560
[[5,5,3,1,1],[4,3,1]] => 420
[[6,6,4,2,1],[5,4,2,1]] => 840
[[3,2,2,1,1],[2]] => 63
[[4,3,3,2,1],[3,1,1,1]] => 210
[[4,3,3,1,1],[3,1,1]] => 210
[[5,4,4,2,1],[4,2,2,1]] => 420
[[4,3,2,1,1],[3,1]] => 245
[[5,4,3,2,1],[4,2,1,1]] => 672
[[5,4,3,1,1],[4,2,1]] => 525
[[6,5,4,2,1],[5,3,2,1]] => 1050
[[5,4,2,1,1],[4,2]] => 315
[[6,5,3,2,1],[5,3,1,1]] => 840
[[6,5,3,1,1],[5,3,1]] => 630
[[7,6,4,2,1],[6,4,2,1]] => 1260
[[4,4,3,3],[3,2,2]] => 111
[[5,5,4,3],[4,3,3]] => 175
[[5,5,3,3],[4,3,2]] => 210
[[6,6,4,3],[5,4,3]] => 280
[[5,4,3,3],[4,2,2]] => 182
[[6,5,4,3],[5,3,3]] => 280
[[6,5,3,3],[5,3,2]] => 315
[[7,6,4,3],[6,4,3]] => 420
[[3,3,2,2,1],[2,1,1]] => 169
[[4,4,3,3,1],[3,2,2,1]] => 280
[[4,4,3,2,1],[3,2,2]] => 350
[[5,5,4,3,1],[4,3,3,1]] => 525
[[4,4,2,2,1],[3,2,1]] => 350
[[5,5,3,3,1],[4,3,2,1]] => 560
[[5,5,3,2,1],[4,3,2]] => 560
[[6,6,4,3,1],[5,4,3,1]] => 840
[[4,3,2,2,1],[3,1,1]] => 280
[[5,4,3,3,1],[4,2,2,1]] => 462
[[5,4,3,2,1],[4,2,2]] => 560
[[6,5,4,3,1],[5,3,3,1]] => 840
[[5,4,2,2,1],[4,2,1]] => 525
[[6,5,3,3,1],[5,3,2,1]] => 840
[[6,5,3,2,1],[5,3,2]] => 840
[[7,6,4,3,1],[6,4,3,1]] => 1260
[[3,3,2,2,2],[2,1,1,1]] => 78
[[4,4,3,3,2],[3,2,2,2]] => 189
[[4,4,3,2,2],[3,2,2,1]] => 350
[[5,5,4,3,2],[4,3,3,2]] => 525
[[4,4,2,2,2],[3,2,1,1]] => 210
[[5,5,3,3,2],[4,3,2,2]] => 420
[[5,5,3,2,2],[4,3,2,1]] => 560
[[6,6,4,3,2],[5,4,3,2]] => 840
[[4,3,2,2,2],[3,1,1,1]] => 133
[[5,4,3,3,2],[4,2,2,2]] => 315
[[5,4,3,2,2],[4,2,2,1]] => 560
[[6,5,4,3,2],[5,3,3,2]] => 840
[[5,4,2,2,2],[4,2,1,1]] => 315
[[6,5,3,3,2],[5,3,2,2]] => 630
[[6,5,3,2,2],[5,3,2,1]] => 840
[[7,6,4,3,2],[6,4,3,2]] => 1260
[[2,2,1,1,1,1],[1]] => 20
[[3,3,2,2,2,1],[2,1,1,1,1]] => 98
[[3,3,2,2,1,1],[2,1,1,1]] => 189
[[4,4,3,3,2,1],[3,2,2,2,1]] => 378
[[3,3,2,1,1,1],[2,1,1]] => 175
[[4,4,3,2,2,1],[3,2,2,1,1]] => 525
[[4,4,3,2,1,1],[3,2,2,1]] => 525
[[5,5,4,3,2,1],[4,3,3,2,1]] => 1050
[[3,3,1,1,1,1],[2,1]] => 70
[[4,4,2,2,2,1],[3,2,1,1,1]] => 280
[[4,4,2,2,1,1],[3,2,1,1]] => 420
[[5,5,3,3,2,1],[4,3,2,2,1]] => 840
[[4,4,2,1,1,1],[3,2,1]] => 280
[[5,5,3,2,2,1],[4,3,2,1,1]] => 840
[[5,5,3,2,1,1],[4,3,2,1]] => 840
[[6,6,4,3,2,1],[5,4,3,2,1]] => 1680
[[3,2,1,1,1,1],[2]] => 35
[[4,3,2,2,2,1],[3,1,1,1,1]] => 168
[[4,3,2,2,1,1],[3,1,1,1]] => 315
[[5,4,3,3,2,1],[4,2,2,2,1]] => 630
[[4,3,2,1,1,1],[3,1,1]] => 280
[[5,4,3,2,2,1],[4,2,2,1,1]] => 840
[[5,4,3,2,1,1],[4,2,2,1]] => 840
[[6,5,4,3,2,1],[5,3,3,2,1]] => 1680
[[4,3,1,1,1,1],[3,1]] => 105
[[5,4,2,2,2,1],[4,2,1,1,1]] => 420
[[5,4,2,2,1,1],[4,2,1,1]] => 630
[[6,5,3,3,2,1],[5,3,2,2,1]] => 1260
[[5,4,2,1,1,1],[4,2,1]] => 420
[[6,5,3,2,2,1],[5,3,2,1,1]] => 1260
[[6,5,3,2,1,1],[5,3,2,1]] => 1260
[[7,6,4,3,2,1],[6,4,3,2,1]] => 2520
[[5,5,5],[4,4]] => 15
[[6,6,5],[5,5]] => 21
[[6,5,5],[5,4]] => 35
[[7,6,5],[6,5]] => 42
[[4,4,4,1],[3,3]] => 55
[[5,5,5,1],[4,4,1]] => 70
[[5,5,4,1],[4,4]] => 84
[[6,6,5,1],[5,5,1]] => 105
[[5,4,4,1],[4,3]] => 133
[[6,5,5,1],[5,4,1]] => 168
[[6,5,4,1],[5,4]] => 168
[[7,6,5,1],[6,5,1]] => 210
[[3,3,3,2],[2,2]] => 56
[[4,4,4,2],[3,3,1]] => 111
[[5,5,5,2],[4,4,2]] => 126
[[4,4,3,2],[3,3]] => 105
[[5,5,4,2],[4,4,1]] => 189
[[6,6,5,2],[5,5,2]] => 210
[[4,3,3,2],[3,2]] => 147
[[5,4,4,2],[4,3,1]] => 280
[[6,5,5,2],[5,4,2]] => 315
[[5,4,3,2],[4,3]] => 210
[[6,5,4,2],[5,4,1]] => 378
[[7,6,5,2],[6,5,2]] => 420
[[3,3,3,1,1],[2,2]] => 71
[[4,4,4,2,1],[3,3,1,1]] => 182
[[4,4,4,1,1],[3,3,1]] => 126
[[5,5,5,2,1],[4,4,2,1]] => 252
[[4,4,3,1,1],[3,3]] => 126
[[5,5,4,2,1],[4,4,1,1]] => 315
[[5,5,4,1,1],[4,4,1]] => 210
[[6,6,5,2,1],[5,5,2,1]] => 420
[[4,3,3,1,1],[3,2]] => 182
[[5,4,4,2,1],[4,3,1,1]] => 462
[[5,4,4,1,1],[4,3,1]] => 315
[[6,5,5,2,1],[5,4,2,1]] => 630
[[5,4,3,1,1],[4,3]] => 252
[[6,5,4,2,1],[5,4,1,1]] => 630
[[6,5,4,1,1],[5,4,1]] => 420
[[7,6,5,2,1],[6,5,2,1]] => 840
[[3,3,3,3],[2,2,1]] => 35
[[4,4,4,3],[3,3,2]] => 90
[[5,5,5,3],[4,4,3]] => 105
[[4,4,3,3],[3,3,1]] => 105
[[5,5,4,3],[4,4,2]] => 189
[[6,6,5,3],[5,5,3]] => 210
[[4,3,3,3],[3,2,1]] => 112
[[5,4,4,3],[4,3,2]] => 245
[[6,5,5,3],[5,4,3]] => 280
[[5,4,3,3],[4,3,1]] => 210
[[6,5,4,3],[5,4,2]] => 378
[[7,6,5,3],[6,5,3]] => 420
[[2,2,2,2,1],[1,1]] => 28
[[3,3,3,3,1],[2,2,1,1]] => 63
[[3,3,3,2,1],[2,2,1]] => 155
[[4,4,4,3,1],[3,3,2,1]] => 245
[[4,4,4,2,1],[3,3,2]] => 210
[[5,5,5,3,1],[4,4,3,1]] => 315
[[3,3,2,2,1],[2,2]] => 105
[[4,4,3,3,1],[3,3,1,1]] => 210
[[4,4,3,2,1],[3,3,1]] => 336
[[5,5,4,3,1],[4,4,2,1]] => 525
[[5,5,4,2,1],[4,4,2]] => 420
[[6,6,5,3,1],[5,5,3,1]] => 630
[[3,2,2,2,1],[2,1]] => 98
[[4,3,3,3,1],[3,2,1,1]] => 210
[[4,3,3,2,1],[3,2,1]] => 427
[[5,4,4,3,1],[4,3,2,1]] => 672
[[5,4,4,2,1],[4,3,2]] => 560
[[6,5,5,3,1],[5,4,3,1]] => 840
[[4,3,2,2,1],[3,2]] => 210
[[5,4,3,3,1],[4,3,1,1]] => 420
[[5,4,3,2,1],[4,3,1]] => 672
[[6,5,4,3,1],[5,4,2,1]] => 1050
[[6,5,4,2,1],[5,4,2]] => 840
[[7,6,5,3,1],[6,5,3,1]] => 1260
[[3,3,3,2,2],[2,2,1,1]] => 99
[[4,4,4,3,2],[3,3,2,2]] => 189
[[4,4,4,2,2],[3,3,2,1]] => 210
[[5,5,5,3,2],[4,4,3,2]] => 315
[[4,4,3,2,2],[3,3,1,1]] => 231
[[5,5,4,3,2],[4,4,2,2]] => 420
[[5,5,4,2,2],[4,4,2,1]] => 420
[[6,6,5,3,2],[5,5,3,2]] => 630
[[4,3,3,2,2],[3,2,1,1]] => 280
[[5,4,4,3,2],[4,3,2,2]] => 525
[[5,4,4,2,2],[4,3,2,1]] => 560
[[6,5,5,3,2],[5,4,3,2]] => 840
[[5,4,3,2,2],[4,3,1,1]] => 462
[[6,5,4,3,2],[5,4,2,2]] => 840
[[6,5,4,2,2],[5,4,2,1]] => 840
[[7,6,5,3,2],[6,5,3,2]] => 1260
[[2,2,2,1,1,1],[1,1]] => 34
[[3,3,3,2,2,1],[2,2,1,1,1]] => 133
[[3,3,3,2,1,1],[2,2,1,1]] => 189
[[4,4,4,3,2,1],[3,3,2,2,1]] => 378
[[3,3,3,1,1,1],[2,2,1]] => 105
[[4,4,4,2,2,1],[3,3,2,1,1]] => 315
[[4,4,4,2,1,1],[3,3,2,1]] => 315
[[5,5,5,3,2,1],[4,4,3,2,1]] => 630
[[3,3,2,1,1,1],[2,2]] => 84
[[4,4,3,2,2,1],[3,3,1,1,1]] => 315
[[4,4,3,2,1,1],[3,3,1,1]] => 420
[[5,5,4,3,2,1],[4,4,2,2,1]] => 840
[[4,4,3,1,1,1],[3,3,1]] => 210
[[5,5,4,2,2,1],[4,4,2,1,1]] => 630
[[5,5,4,2,1,1],[4,4,2,1]] => 630
[[6,6,5,3,2,1],[5,5,3,2,1]] => 1260
[[3,2,2,1,1,1],[2,1]] => 98
[[4,3,3,2,2,1],[3,2,1,1,1]] => 378
[[4,3,3,2,1,1],[3,2,1,1]] => 525
[[5,4,4,3,2,1],[4,3,2,2,1]] => 1050
[[4,3,3,1,1,1],[3,2,1]] => 280
[[5,4,4,2,2,1],[4,3,2,1,1]] => 840
[[5,4,4,2,1,1],[4,3,2,1]] => 840
[[6,5,5,3,2,1],[5,4,3,2,1]] => 1680
[[4,3,2,1,1,1],[3,2]] => 168
[[5,4,3,2,2,1],[4,3,1,1,1]] => 630
[[5,4,3,2,1,1],[4,3,1,1]] => 840
[[6,5,4,3,2,1],[5,4,2,2,1]] => 1680
[[5,4,3,1,1,1],[4,3,1]] => 420
[[6,5,4,2,2,1],[5,4,2,1,1]] => 1260
[[6,5,4,2,1,1],[5,4,2,1]] => 1260
[[7,6,5,3,2,1],[6,5,3,2,1]] => 2520
[[4,4,4,4],[3,3,3]] => 20
[[5,5,5,4],[4,4,4]] => 35
[[5,5,4,4],[4,4,3]] => 84
[[6,6,5,4],[5,5,4]] => 105
[[5,4,4,4],[4,3,3]] => 70
[[6,5,5,4],[5,4,4]] => 105
[[6,5,4,4],[5,4,3]] => 168
[[7,6,5,4],[6,5,4]] => 210
[[3,3,3,3,1],[2,2,2]] => 50
[[4,4,4,4,1],[3,3,3,1]] => 70
[[4,4,4,3,1],[3,3,3]] => 105
[[5,5,5,4,1],[4,4,4,1]] => 140
[[4,4,3,3,1],[3,3,2]] => 231
[[5,5,4,4,1],[4,4,3,1]] => 315
[[5,5,4,3,1],[4,4,3]] => 315
[[6,6,5,4,1],[5,5,4,1]] => 420
[[4,3,3,3,1],[3,2,2]] => 182
[[5,4,4,4,1],[4,3,3,1]] => 252
[[5,4,4,3,1],[4,3,3]] => 315
[[6,5,5,4,1],[5,4,4,1]] => 420
[[5,4,3,3,1],[4,3,2]] => 462
[[6,5,4,4,1],[5,4,3,1]] => 630
[[6,5,4,3,1],[5,4,3]] => 630
[[7,6,5,4,1],[6,5,4,1]] => 840
[[2,2,2,2,2],[1,1,1]] => 14
[[3,3,3,3,2],[2,2,2,1]] => 64
[[4,4,4,4,2],[3,3,3,2]] => 84
[[3,3,3,2,2],[2,2,2]] => 70
[[4,4,4,3,2],[3,3,3,1]] => 175
[[5,5,5,4,2],[4,4,4,2]] => 210
[[3,3,2,2,2],[2,2,1]] => 105
[[4,4,3,3,2],[3,3,2,1]] => 336
[[5,5,4,4,2],[4,4,3,2]] => 420
[[4,4,3,2,2],[3,3,2]] => 210
[[5,5,4,3,2],[4,4,3,1]] => 525
[[6,6,5,4,2],[5,5,4,2]] => 630
[[3,2,2,2,2],[2,1,1]] => 63
[[4,3,3,3,2],[3,2,2,1]] => 245
[[5,4,4,4,2],[4,3,3,2]] => 315
[[4,3,3,2,2],[3,2,2]] => 210
[[5,4,4,3,2],[4,3,3,1]] => 525
[[6,5,5,4,2],[5,4,4,2]] => 630
[[4,3,2,2,2],[3,2,1]] => 210
[[5,4,3,3,2],[4,3,2,1]] => 672
[[6,5,4,4,2],[5,4,3,2]] => 840
[[5,4,3,2,2],[4,3,2]] => 420
[[6,5,4,3,2],[5,4,3,1]] => 1050
[[7,6,5,4,2],[6,5,4,2]] => 1260
[[2,2,2,2,1,1],[1,1,1]] => 34
[[3,3,3,3,2,1],[2,2,2,1,1]] => 98
[[3,3,3,3,1,1],[2,2,2,1]] => 84
[[4,4,4,4,2,1],[3,3,3,2,1]] => 168
[[3,3,3,2,1,1],[2,2,2]] => 105
[[4,4,4,3,2,1],[3,3,3,1,1]] => 280
[[4,4,4,3,1,1],[3,3,3,1]] => 210
[[5,5,5,4,2,1],[4,4,4,2,1]] => 420
[[3,3,2,2,1,1],[2,2,1]] => 189
[[4,4,3,3,2,1],[3,3,2,1,1]] => 525
[[4,4,3,3,1,1],[3,3,2,1]] => 420
[[5,5,4,4,2,1],[4,4,3,2,1]] => 840
[[4,4,3,2,1,1],[3,3,2]] => 315
[[5,5,4,3,2,1],[4,4,3,1,1]] => 840
[[5,5,4,3,1,1],[4,4,3,1]] => 630
[[6,6,5,4,2,1],[5,5,4,2,1]] => 1260
[[3,2,2,2,1,1],[2,1,1]] => 133
[[4,3,3,3,2,1],[3,2,2,1,1]] => 378
[[4,3,3,3,1,1],[3,2,2,1]] => 315
[[5,4,4,4,2,1],[4,3,3,2,1]] => 630
[[4,3,3,2,1,1],[3,2,2]] => 315
[[5,4,4,3,2,1],[4,3,3,1,1]] => 840
[[5,4,4,3,1,1],[4,3,3,1]] => 630
[[6,5,5,4,2,1],[5,4,4,2,1]] => 1260
[[4,3,2,2,1,1],[3,2,1]] => 378
[[5,4,3,3,2,1],[4,3,2,1,1]] => 1050
[[5,4,3,3,1,1],[4,3,2,1]] => 840
[[6,5,4,4,2,1],[5,4,3,2,1]] => 1680
[[5,4,3,2,1,1],[4,3,2]] => 630
[[6,5,4,3,2,1],[5,4,3,1,1]] => 1680
[[6,5,4,3,1,1],[5,4,3,1]] => 1260
[[7,6,5,4,2,1],[6,5,4,2,1]] => 2520
[[3,3,3,3,3],[2,2,2,2]] => 15
[[4,4,4,4,3],[3,3,3,3]] => 35
[[4,4,4,3,3],[3,3,3,2]] => 105
[[5,5,5,4,3],[4,4,4,3]] => 140
[[4,4,3,3,3],[3,3,2,2]] => 126
[[5,5,4,4,3],[4,4,3,3]] => 210
[[5,5,4,3,3],[4,4,3,2]] => 315
[[6,6,5,4,3],[5,5,4,3]] => 420
[[4,3,3,3,3],[3,2,2,2]] => 70
[[5,4,4,4,3],[4,3,3,3]] => 140
[[5,4,4,3,3],[4,3,3,2]] => 315
[[6,5,5,4,3],[5,4,4,3]] => 420
[[5,4,3,3,3],[4,3,2,2]] => 252
[[6,5,4,4,3],[5,4,3,3]] => 420
[[6,5,4,3,3],[5,4,3,2]] => 630
[[7,6,5,4,3],[6,5,4,3]] => 840
[[2,2,2,2,2,1],[1,1,1,1]] => 20
[[3,3,3,3,3,1],[2,2,2,2,1]] => 35
[[3,3,3,3,2,1],[2,2,2,2]] => 70
[[4,4,4,4,3,1],[3,3,3,3,1]] => 105
[[3,3,3,2,2,1],[2,2,2,1]] => 175
[[4,4,4,3,3,1],[3,3,3,2,1]] => 280
[[4,4,4,3,2,1],[3,3,3,2]] => 280
[[5,5,5,4,3,1],[4,4,4,3,1]] => 420
[[3,3,2,2,2,1],[2,2,1,1]] => 189
[[4,4,3,3,3,1],[3,3,2,2,1]] => 315
[[4,4,3,3,2,1],[3,3,2,2]] => 420
[[5,5,4,4,3,1],[4,4,3,3,1]] => 630
[[4,4,3,2,2,1],[3,3,2,1]] => 525
[[5,5,4,3,3,1],[4,4,3,2,1]] => 840
[[5,5,4,3,2,1],[4,4,3,2]] => 840
[[6,6,5,4,3,1],[5,5,4,3,1]] => 1260
[[3,2,2,2,2,1],[2,1,1,1]] => 98
[[4,3,3,3,3,1],[3,2,2,2,1]] => 168
[[4,3,3,3,2,1],[3,2,2,2]] => 280
[[5,4,4,4,3,1],[4,3,3,3,1]] => 420
[[4,3,3,2,2,1],[3,2,2,1]] => 525
[[5,4,4,3,3,1],[4,3,3,2,1]] => 840
[[5,4,4,3,2,1],[4,3,3,2]] => 840
[[6,5,5,4,3,1],[5,4,4,3,1]] => 1260
[[4,3,2,2,2,1],[3,2,1,1]] => 378
[[5,4,3,3,3,1],[4,3,2,2,1]] => 630
[[5,4,3,3,2,1],[4,3,2,2]] => 840
[[6,5,4,4,3,1],[5,4,3,3,1]] => 1260
[[5,4,3,2,2,1],[4,3,2,1]] => 1050
[[6,5,4,3,3,1],[5,4,3,2,1]] => 1680
[[6,5,4,3,2,1],[5,4,3,2]] => 1680
[[7,6,5,4,3,1],[6,5,4,3,1]] => 2520
[[2,2,2,2,2,2],[1,1,1,1,1]] => 6
[[3,3,3,3,3,2],[2,2,2,2,2]] => 21
[[3,3,3,3,2,2],[2,2,2,2,1]] => 70
[[4,4,4,4,3,2],[3,3,3,3,2]] => 105
[[3,3,3,2,2,2],[2,2,2,1,1]] => 105
[[4,4,4,3,3,2],[3,3,3,2,2]] => 210
[[4,4,4,3,2,2],[3,3,3,2,1]] => 280
[[5,5,5,4,3,2],[4,4,4,3,2]] => 420
[[3,3,2,2,2,2],[2,2,1,1,1]] => 84
[[4,4,3,3,3,2],[3,3,2,2,2]] => 210
[[4,4,3,3,2,2],[3,3,2,2,1]] => 420
[[5,5,4,4,3,2],[4,4,3,3,2]] => 630
[[4,4,3,2,2,2],[3,3,2,1,1]] => 315
[[5,5,4,3,3,2],[4,4,3,2,2]] => 630
[[5,5,4,3,2,2],[4,4,3,2,1]] => 840
[[6,6,5,4,3,2],[5,5,4,3,2]] => 1260
[[3,2,2,2,2,2],[2,1,1,1,1]] => 35
[[4,3,3,3,3,2],[3,2,2,2,2]] => 105
[[4,3,3,3,2,2],[3,2,2,2,1]] => 280
[[5,4,4,4,3,2],[4,3,3,3,2]] => 420
[[4,3,3,2,2,2],[3,2,2,1,1]] => 315
[[5,4,4,3,3,2],[4,3,3,2,2]] => 630
[[5,4,4,3,2,2],[4,3,3,2,1]] => 840
[[6,5,5,4,3,2],[5,4,4,3,2]] => 1260
[[4,3,2,2,2,2],[3,2,1,1,1]] => 168
[[5,4,3,3,3,2],[4,3,2,2,2]] => 420
[[5,4,3,3,2,2],[4,3,2,2,1]] => 840
[[6,5,4,4,3,2],[5,4,3,3,2]] => 1260
[[5,4,3,2,2,2],[4,3,2,1,1]] => 630
[[6,5,4,3,3,2],[5,4,3,2,2]] => 1260
[[6,5,4,3,2,2],[5,4,3,2,1]] => 1680
[[7,6,5,4,3,2],[6,5,4,3,2]] => 2520
[[1,1,1,1,1,1,1],[]] => 1
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 7
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => 21
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 42
[[2,2,2,2,1,1,1],[1,1,1,1]] => 35
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 105
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => 105
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 210
[[2,2,2,1,1,1,1],[1,1,1]] => 35
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 140
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => 210
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 420
[[3,3,3,2,1,1,1],[2,2,2,1]] => 140
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 420
-----------------------------------------------------------------------------
Created: Sep 22, 2020 at 09:47 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 22, 2020 at 09:47 by Martin Rubey