Identifier
Values
[1] => [1,0,1,0] => 2
[2] => [1,1,0,0,1,0] => 3
[1,1] => [1,0,1,1,0,0] => 3
[3] => [1,1,1,0,0,0,1,0] => 4
[2,1] => [1,0,1,0,1,0] => 5
[1,1,1] => [1,0,1,1,1,0,0,0] => 4
[4] => [1,1,1,1,0,0,0,0,1,0] => 5
[3,1] => [1,1,0,1,0,0,1,0] => 7
[2,2] => [1,1,0,0,1,1,0,0] => 6
[2,1,1] => [1,0,1,1,0,1,0,0] => 7
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 5
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[4,1] => [1,1,1,0,1,0,0,0,1,0] => 9
[3,2] => [1,1,0,0,1,0,1,0] => 9
[3,1,1] => [1,0,1,1,0,0,1,0] => 10
[2,2,1] => [1,0,1,0,1,1,0,0] => 9
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 9
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 11
[4,2] => [1,1,1,0,0,1,0,0,1,0] => 12
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 13
[3,3] => [1,1,1,0,0,0,1,1,0,0] => 10
[3,2,1] => [1,0,1,0,1,0,1,0] => 14
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 13
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 10
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 12
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 13
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 15
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 16
[4,3] => [1,1,1,0,0,0,1,0,1,0] => 14
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 19
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 16
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 16
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 19
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 16
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 14
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 15
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 13
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 19
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 18
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 24
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 21
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 23
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 22
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 26
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 21
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 22
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 23
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 24
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 19
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 18
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 18
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 22
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 29
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 25
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 30
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 28
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 33
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 25
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 28
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 33
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 25
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 28
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 28
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 25
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 30
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 29
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 22
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 21
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 25
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 37
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 34
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 40
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 31
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 34
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 37
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 42
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 41
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 42
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 31
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 31
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 35
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 30
>>> Load all 632 entries. <<<
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 41
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 35
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 42
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 40
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 29
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 30
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 31
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 37
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 34
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 34
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 37
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 34
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 25
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 26
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 43
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 46
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 52
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 50
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 51
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 37
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 36
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 43
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 48
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 56
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 54
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 54
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 51
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 36
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 47
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 46
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 47
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 56
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 50
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 48
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 52
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 47
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 43
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 46
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 40
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 36
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 43
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 44
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 30
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 47
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 55
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 61
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 50
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 70
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 67
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 55
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 66
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 62
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 43
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 46
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 51
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 66
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 62
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 63
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 75
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 66
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 67
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 60
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 53
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 63
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 55
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 53
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 62
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 66
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 70
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 59
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 51
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 61
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 62
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 50
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 46
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 55
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 55
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 47
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 52
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 50
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 61
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 67
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 62
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 85
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 79
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 78
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 79
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 94
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 82
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 76
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 82
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 73
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 52
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 71
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 66
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 50
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 76
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 89
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 76
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 89
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 94
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 78
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 66
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 79
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 80
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 55
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 79
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 65
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 55
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 76
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 78
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 71
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 85
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 84
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 67
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 74
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 50
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 52
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 62
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 60
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 61
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 67
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 49
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 58
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 86
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 70
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 95
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 87
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 65
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 99
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 97
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 115
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 97
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 91
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 106
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 112
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 118
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 97
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 81
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 97
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 98
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 55
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 83
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 81
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 96
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 81
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 80
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 112
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 90
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 75
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 106
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 96
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 115
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 113
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 87
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 96
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 65
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 75
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 65
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 91
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 81
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 97
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 95
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 80
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 83
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 99
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 94
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 95
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 104
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 70
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 83
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 55
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 65
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 70
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 76
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 64
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 76
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 62
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 116
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 116
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 75
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 113
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 109
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 129
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 107
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 105
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 118
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 136
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 139
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 145
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 115
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 95
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 132
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 134
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 121
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 145
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 142
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 107
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 118
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 89
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 99
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 114
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 116
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 121
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 96
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 96
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 110
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 95
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 132
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 116
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 139
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 135
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 110
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 114
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 136
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 128
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 129
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 141
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 91
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 108
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 69
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 95
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 95
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 96
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 99
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 118
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 110
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 109
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 119
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 89
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 105
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 113
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 122
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 100
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 119
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 89
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 75
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 80
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 74
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 88
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 82
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 140
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 171
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 140
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 123
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 136
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 156
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 157
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 163
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 127
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 127
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 145
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 125
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 174
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 173
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 151
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 181
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 175
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 140
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 145
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 173
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 162
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 163
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 178
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 112
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 133
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 108
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 123
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 105
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 146
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 145
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 126
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 151
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 146
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 103
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 142
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 140
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 142
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 146
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 174
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 160
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 157
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 171
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 123
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 145
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 156
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 168
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 136
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 162
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 116
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 103
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 105
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 125
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 115
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 108
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 127
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 136
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 146
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 115
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 137
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 123
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 130
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 120
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 143
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 129
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 80
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 95
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 96
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 158
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 215
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 196
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 215
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 133
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 158
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 133
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 151
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 171
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 145
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 202
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 199
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 171
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 205
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 197
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 137
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 189
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 185
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 188
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 193
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 230
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 210
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 205
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 223
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 157
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 185
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 199
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 214
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 172
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 205
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 143
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 117
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 161
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 157
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 158
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 162
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 193
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 176
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 171
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 186
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 156
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 158
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 188
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 170
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 161
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 189
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 202
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 216
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 166
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 198
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 171
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 180
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 166
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 198
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 176
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 117
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 137
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 145
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 155
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 151
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 158
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 145
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 173
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 149
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 132
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 157
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 157
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 83
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 98
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 105
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 429
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 345
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 255
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 359
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 255
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 303
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 227
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 219
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 359
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 252
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 295
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 220
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 314
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 225
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 268
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 233
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 345
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 241
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 281
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 209
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 295
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 211
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 251
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 303
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 214
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 251
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 268
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 219
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 297
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 207
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 241
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 179
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 252
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 180
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 214
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 255
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 180
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 211
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 225
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 255
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 179
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 209
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 220
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 227
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1430
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1001
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1166
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 869
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1220
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 875
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1040
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 785
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 530
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 770
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 605
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 440
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 275
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 875
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 715
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 575
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 479
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 356
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 335
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 110
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 861
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 754
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 690
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 645
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 443
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 842
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 519
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 449
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 381
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 286
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 323
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 170
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1166
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 821
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 717
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 737
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 648
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 220
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 561
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 387
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 770
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 489
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 435
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 602
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 276
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 491
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 379
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 476
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 356
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 286
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 267
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 208
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 170
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1001
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 704
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 821
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 614
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 407
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 861
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 558
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 513
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 261
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 138
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 471
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 179
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 623
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 387
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 216
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 262
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 869
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 614
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 538
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 180
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Description
The number of Dyck paths that are weakly above a Dyck path.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.