Identifier
Values
[1,0,1,0] => [1] => 1
[1,0,1,0,1,0] => [2,1] => 2
[1,0,1,1,0,0] => [1,1] => 1
[1,1,0,0,1,0] => [2] => 1
[1,1,0,1,0,0] => [1] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => 12
[1,0,1,0,1,1,0,0] => [2,2,1] => 6
[1,0,1,1,0,0,1,0] => [3,1,1] => 4
[1,0,1,1,0,1,0,0] => [2,1,1] => 3
[1,0,1,1,1,0,0,0] => [1,1,1] => 1
[1,1,0,0,1,0,1,0] => [3,2] => 6
[1,1,0,0,1,1,0,0] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [3,1] => 3
[1,1,0,1,0,1,0,0] => [2,1] => 2
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 1
[1,1,1,0,0,1,0,0] => [2] => 1
[1,1,1,0,1,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => 20
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 252
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 32760
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 352
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 8
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 32760
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 462
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 660
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 260
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 20
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 6
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 5
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 4
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 252
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 9
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 462
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 195
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 6
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 352
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 195
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 260
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 12
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 6
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 5
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 4
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 3
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 8
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 6
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 20
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 6
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 2
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 4
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 3
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => 30
[1,0,1,0,1,0,1,1,1,0,0,0] => [3,3,3,2,1] => 16516800
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,2,2,2,1] => 1305103800
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => 885360
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 10
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,3,3,1,1] => 4444440
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => 6865460
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => 50581800
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 26400
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 560
[1,0,1,1,1,0,0,0,1,1,0,0] => [4,4,1,1,1] => 95940
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => 118815436
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 1848
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => 16744
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 308154
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 924
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 30
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 8
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 7
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => [3,3,3,2] => 12
[1,1,0,0,1,1,0,0,1,1,0,0] => [4,4,2,2] => 2970240
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => 373920
[1,1,0,0,1,1,1,0,0,0,1,0] => [5,2,2,2] => 95940
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => 9576
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 6188
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => [4,3,3,1] => 7120080
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => 24360
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => 20
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 252
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => 118815436
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 32760
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 352
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 8
[1,1,0,1,1,0,0,0,1,0,1,0] => [5,4,1,1] => 1305103800
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => 9576
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => 50581800
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 32760
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 462
>>> Load all 848 entries. <<<
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 308154
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 660
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 260
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 20
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 7
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 4
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => [5,4,3] => 16516800
[1,1,1,0,0,0,1,0,1,1,0,0] => [4,4,3] => 12
[1,1,1,0,0,0,1,1,0,0,1,0] => [5,3,3] => 4444440
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => 24360
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 9
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => 373920
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => 6865460
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 252
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 9
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 1848
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 462
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 195
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => 885360
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 6188
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 26400
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 352
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 195
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 924
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 260
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 12
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 5
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 10
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 8
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 560
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 8
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 30
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 20
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 4
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2,1] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => 5580
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1,1] => 11492910
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1,1] => 2046431520
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => 1148850
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 312
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1,1] => 1613040
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1,1] => 52360
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1,1] => 99795696
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => 1656
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1,1] => 11662560
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1,1] => 976530456
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => 64584
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 3696
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 42
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,3,3,3,2] => 15
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,3,2,2,2] => 1558378800
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [6,2,2,2,2] => 1613040
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [5,2,2,2,2] => 5012700
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [4,2,2,2,2] => 1247290
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,2,2,2,2] => 433440
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1] => 30
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2,1] => 16516800
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2,1] => 1305103800
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => 885360
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 10
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1,1] => 4444440
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => 6865460
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => 50581800
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 26400
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 560
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1,1] => 5012700
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1,1] => 95940
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => 118815436
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 1848
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1,1] => 976530456
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => 16744
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 308154
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 924
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 30
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 5
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,4,4,3] => 16
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [3,3,3,3] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [3,3,3,2] => 12
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [4,4,2,2] => 2970240
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => 373920
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [6,2,2,2] => 52360
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [5,2,2,2] => 95940
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => 9576
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 6188
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [4,3,3,1] => 7120080
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => 24360
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => 20
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [6,2,2,1] => 99795696
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => 118815436
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 32760
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 352
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [5,5,1,1] => 1247290
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [5,4,1,1] => 1305103800
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => 9576
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => 50581800
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 32760
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 462
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => 64584
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 308154
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 660
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 260
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 20
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,5,4] => 15
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [4,4,4] => 12
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [5,4,3] => 16516800
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [4,4,3] => 12
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [6,3,3] => 11492910
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [5,3,3] => 4444440
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => 24360
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 9
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,5,2] => 1558378800
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => 373920
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [6,3,2] => 2046431520
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => 6865460
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 252
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 9
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => 1656
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 1848
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 462
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 195
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,5,1] => 433440
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => 885360
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 6188
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => 1148850
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 26400
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 352
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 195
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 3696
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 924
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 260
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 12
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 6
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 5
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,5] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => 10
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => 5580
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 312
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 560
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 8
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 6
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 42
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 30
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 20
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 4
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 14
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 1709400
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1] => 110880
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1] => 12307680
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1] => 384300
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 2394
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1] => 3558100
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1] => 414348
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1] => 981054360
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1] => 5490
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1] => 163361088
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1] => 42762720
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1] => 3502620
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1656
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 56
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1] => 11
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => 9
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2] => 51207660
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2] => 61372584
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2] => 9785880
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2] => 17054400
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2] => 12
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1] => 12
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => 5580
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1] => 11492910
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1] => 2046431520
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => 1148850
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 312
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1] => 51207660
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1] => 1613040
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1] => 52360
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1] => 99795696
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => 1656
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1] => 11662560
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1] => 976530456
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => 64584
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 3696
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 42
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1] => 11
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1] => 10
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 6
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3] => 15
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2] => 15
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2] => 1558378800
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2] => 3558100
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2] => 1613040
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2] => 5012700
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2] => 1247290
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2] => 433440
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1] => 30
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1] => 16516800
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1] => 1305103800
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => 885360
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 10
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1] => 4444440
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => 6865460
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => 50581800
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 26400
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 560
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1] => 61372584
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1] => 5012700
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1] => 95940
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => 118815436
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 1848
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1] => 42762720
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1] => 976530456
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => 16744
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 308154
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 924
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 30
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4] => 16
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3] => 16
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3] => 12
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2] => 12
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2] => 2970240
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => 373920
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2] => 414348
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2] => 52360
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2] => 95940
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => 9576
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 6188
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 8
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1] => 7120080
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => 24360
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => 20
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1] => 981054360
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1] => 99795696
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => 118815436
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 32760
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 352
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 8
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1] => 9785880
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1] => 1247290
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1] => 1305103800
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => 9576
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => 50581800
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 32760
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 462
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1] => 3502620
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => 64584
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 308154
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 660
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 260
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 20
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 8
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 7
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 6
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [5,5,5] => 15
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [5,5,4] => 15
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [4,4,4] => 12
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [5,4,3] => 16516800
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0] => [4,4,3] => 12
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [7,3,3] => 12307680
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [6,3,3] => 11492910
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0] => [5,3,3] => 4444440
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => 24360
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 9
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [5,5,2] => 1558378800
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => 373920
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [6,3,2] => 2046431520
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => 6865460
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 252
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [7,2,2] => 5490
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => 1656
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 1848
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 462
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 195
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,6,1] => 17054400
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0] => [5,5,1] => 433440
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => 885360
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 6188
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [7,3,1] => 384300
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => 1148850
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 26400
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 352
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 195
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => 1656
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 3696
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 924
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 260
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 12
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 6
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 6
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 5
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,6] => 14
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [6,6] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,5] => 1709400
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [6,5] => 12
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => 10
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,4] => 110880
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => 5580
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 10
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => 2394
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 312
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 560
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 8
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 6
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 56
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 42
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 30
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 20
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 5
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 4
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 1
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 8
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 8
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => 9
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => 72
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 72
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 9
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0] => [11] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1] => 10
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,2] => 90
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1] => 10
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,3] => 520
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1] => 10980
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 10980
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1] => 10
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1] => 520
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1] => 90
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1] => 10
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0] => [11,1] => 11
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2] => 110
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,1] => 11
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,3] => 6732
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1] => 8580
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1] => 11
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,4] => 597080
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1] => 3138564
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0] => [8,2,2] => 4290
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,1] => 6108960
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1] => 11
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1,1,1] => 11
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1,1,1,1,1] => 6108960
[1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1] => 11
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1] => 4290
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1,1] => 3138564
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1] => 8580
[1,0,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1,1,1] => 11
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1] => 597080
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1] => 6732
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1,1,1] => 110
[1,0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1,1,1] => 11
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0] => [10,2,1] => 25608
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,1,0] => [9,4] => 233244
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,1,0] => [9,2,1,1] => 30921660
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,5] => 521664
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [4,2,1,1,1,1,1,1,1] => 30921660
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1,1,1] => 12
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [3,3,1,1,1,1,1,1,1] => 12804
[1,0,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1,1,1] => 25608
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1] => 521664
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1] => 233244
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1,1,1,1] => 2580
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,5] => 92678040
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1] => 13
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1] => 13
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [7,7] => 14
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1,1] => 13
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1,1,1,1] => 13
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1,1] => 190164
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 14
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1] => 92678040
[1,0,1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,1,1,1,1,1,1] => 59280
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,1,0] => [9,3,3] => 282898980
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,2,2] => 1316224
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,7] => 16
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1,1,1,1,1,1] => 14
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1,1,1,1,1] => 14
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [4,4,1,1,1,1,1,1,1] => 1316224
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 16
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1,1,1,1] => 6126120
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,1,1,1,1,1,1] => 15
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [8,8] => 16
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1,1] => 15
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0] => [7,7,1,1] => 1006335330
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 14
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1,1] => 1709400
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1,1,1] => 384300
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => 2394
[1,1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1,1] => 3558100
[1,1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1,1] => 414348
[1,1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1,1] => 981054360
[1,1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1,1,1] => 5490
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1,1,1] => 163361088
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1,1,1] => 42762720
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1656
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 56
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1,1] => 12
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1,1] => 11
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => 9
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 7
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2,2] => 17054400
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 12
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 12
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => 5580
[1,1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1,1,1] => 2046431520
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 312
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [5,5,1,1,1,1] => 1613040
[1,1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1,1] => 52360
[1,1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1,1] => 99795696
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1,1,1,1] => 11662560
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 3696
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 42
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1,1] => 11
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 8
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 7
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 6
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,3,3,3,3] => 15
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,2,2,2] => 1613040
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,2,2,2] => 1247290
[1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,2] => 433440
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1] => 30
[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,3,3,2,1] => 16516800
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => 885360
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 10
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 26400
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 560
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1,1,1] => 95940
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => 118815436
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 1848
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,1,1] => 42762720
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => 16744
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 924
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 30
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1,1] => 10
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => 9
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 5
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0] => [4,4,4,4] => 16
[1,1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0,0] => [4,4,4,3] => 16
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0] => [4,4,2,2] => 2970240
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => 373920
[1,1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,2,2] => 95940
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3,1] => 7120080
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => 24360
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => 20
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 252
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 32760
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 352
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 8
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 32760
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 462
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 660
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 260
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 20
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 8
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 7
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 6
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 5
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0] => [5,5,5] => 15
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0] => [4,4,4] => 12
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3] => 16516800
[1,1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0,0] => [4,4,3] => 12
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0,0] => [6,3,3] => 11492910
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => 24360
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 9
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => 373920
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => 6865460
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 252
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 9
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0,0] => [7,2,2] => 5490
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 462
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 195
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0] => [6,6,1] => 17054400
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => 885360
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 6188
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => 1148850
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 26400
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 352
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 195
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => 1656
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 3696
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 924
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 260
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 12
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 6
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 8
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 7
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 5
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0] => [7,6] => 14
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0] => [6,6] => 12
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0] => [7,5] => 1709400
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => 10
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 8
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => 2394
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 8
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 56
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 20
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 7
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 5
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 4
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 6
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 6
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => 9
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0] => [8,2,1] => 10980
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 10980
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => 9
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2,1] => 16
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 6
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 9
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0] => [4,4,4] => 12
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0] => [4,4,4,4] => 16
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 8
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => 9
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => 9
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => 72
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [5,4,3,2,1] => 30
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 252
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0] => [6,6] => 12
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 6
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => 7
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => 8
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => 9
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => 20
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 12
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => 1656
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => 1656
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0,0] => [8,2,1] => 10980
[1,1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1,1] => 10980
[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,1] => 14
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0] => [7,7] => 14
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2,2] => 14
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1,1,1] => 10
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1,1] => 10
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,1,1,1,1] => 10
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,1,1,1] => 10
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1] => 10
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 20
[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,1] => 12
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => 885360
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 352
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 6
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,2,2,2] => 12
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 7
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 6
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 5
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 4
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 4
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 5
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0] => [8,7] => 16
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => 3
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 352
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 1
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1,1] => 14
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1,1,1,1,1] => 13
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 4
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 20
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 260
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 2
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [5,4,3,2,1] => 30
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 6
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 8
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 7
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 6
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 5
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 4
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => 10
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 8
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 26400
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 8
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 9
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searching the database for the individual values of this statistic
Description
The order of promotion on the set of standard tableaux of given shape.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.