Identifier
Values
[1] => [1,0,1,0] => 1
[2] => [1,1,0,0,1,0] => 2
[1,1] => [1,0,1,1,0,0] => 2
[3] => [1,1,1,0,0,0,1,0] => 3
[2,1] => [1,0,1,0,1,0] => 4
[1,1,1] => [1,0,1,1,1,0,0,0] => 3
[4] => [1,1,1,1,0,0,0,0,1,0] => 4
[3,1] => [1,1,0,1,0,0,1,0] => 6
[2,2] => [1,1,0,0,1,1,0,0] => 5
[2,1,1] => [1,0,1,1,0,1,0,0] => 6
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 4
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[4,1] => [1,1,1,0,1,0,0,0,1,0] => 8
[3,2] => [1,1,0,0,1,0,1,0] => 8
[3,1,1] => [1,0,1,1,0,0,1,0] => 9
[2,2,1] => [1,0,1,0,1,1,0,0] => 8
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 8
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 10
[4,2] => [1,1,1,0,0,1,0,0,1,0] => 11
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 12
[3,3] => [1,1,1,0,0,0,1,1,0,0] => 9
[3,2,1] => [1,0,1,0,1,0,1,0] => 13
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 12
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 9
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 11
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 12
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 14
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 15
[4,3] => [1,1,1,0,0,0,1,0,1,0] => 13
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 18
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 16
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 15
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 15
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 18
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 15
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 13
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 14
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 17
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 18
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 17
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 23
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 20
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 22
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 21
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 25
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 20
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 21
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 22
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 23
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 18
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 14
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 17
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 17
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 14
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 21
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 28
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 24
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 29
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 27
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 32
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 25
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 24
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 27
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 31
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 31
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 32
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 24
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 27
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 27
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 24
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 29
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 28
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 21
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 19
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 21
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 20
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 24
[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 36
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 33
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 39
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 30
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 20
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 33
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 36
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 41
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 40
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 41
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 30
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 30
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 34
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 29
>>> Load all 632 entries. <<<
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 41
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 40
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 34
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 41
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 39
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 28
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 29
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 30
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 36
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 33
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 33
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 36
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 33
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 20
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 24
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 25
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 26
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 42
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 45
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 51
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 49
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 50
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 36
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 35
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => 42
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 47
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => 39
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => 55
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => 53
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => 44
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 53
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 50
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 35
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => 33
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => 46
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 44
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => 45
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => 46
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => 55
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 49
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => 47
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 51
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 46
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => 33
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => 39
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => 42
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 45
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 39
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 35
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 42
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 43
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 26
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 29
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 46
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 54
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 60
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 49
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 69
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 66
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 54
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 65
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 61
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 42
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 45
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 50
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 47
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 65
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 61
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 61
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 62
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 74
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 65
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 61
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 66
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 59
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 34
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 52
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 52
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 62
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 54
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 52
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 61
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 65
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 69
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 58
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 50
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 60
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 61
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 34
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 47
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 49
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 45
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 54
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 54
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 46
[3,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 51
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 27
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 32
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 49
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 60
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 66
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 61
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 84
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 78
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 77
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 78
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 93
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 81
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 75
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 81
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 72
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 51
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 70
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 65
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 49
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => 75
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => 74
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => 88
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 75
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => 71
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 83
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => 88
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 93
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 77
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 65
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 78
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 79
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 54
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 61
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => 71
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => 74
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 78
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 64
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 54
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => 75
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 77
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 70
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 84
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 83
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 66
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 73
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 49
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 51
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 61
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 59
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 60
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 66
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 48
[3,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 57
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 34
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 85
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 69
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 94
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 86
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 64
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 98
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 96
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 114
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 96
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 90
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 105
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 111
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 117
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 96
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 80
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 96
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 97
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 54
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 82
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 80
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 95
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 80
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 79
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => 89
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 103
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 106
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 111
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 89
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 74
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 103
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 105
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 95
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 114
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 112
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 86
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 95
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 64
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 74
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 64
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => 89
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 90
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 80
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 96
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 94
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 79
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 82
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 98
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 93
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 94
[4,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 103
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 69
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 82
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 54
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 64
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 69
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 75
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 63
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 75
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 61
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 115
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 115
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 74
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 112
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 108
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 128
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 106
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 104
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 117
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 135
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 138
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 144
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 114
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 94
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 131
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 133
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 120
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 144
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 141
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 106
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 117
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 88
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 98
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 113
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 115
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 120
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 95
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 95
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 109
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 94
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 131
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 131
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 115
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 138
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 134
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 109
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 113
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 135
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 127
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 128
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 140
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 90
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 107
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 68
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 94
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 94
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 95
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 98
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 117
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 109
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 108
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 118
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 88
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 104
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 112
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 121
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 99
[4,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 118
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 88
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 74
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 79
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 73
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 87
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 81
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 139
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 170
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 139
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 122
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 135
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 155
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 156
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 162
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 126
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 126
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 144
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 124
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 173
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 172
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 150
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 180
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 174
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 139
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 144
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 172
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 161
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 162
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 177
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 111
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 132
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 107
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 122
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 104
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 145
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 144
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 125
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 150
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 145
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 102
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 141
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 139
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 141
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 145
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 173
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 159
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 156
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 170
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 122
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 144
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 155
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 167
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 135
[5,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 161
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 115
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 102
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 104
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 124
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 114
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 107
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 126
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 135
[4,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 145
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 114
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 136
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 122
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 129
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 119
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 142
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 128
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 79
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 94
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 95
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 157
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 214
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 195
[7,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 214
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 132
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 157
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 132
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 150
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 170
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 144
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 201
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 198
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 170
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 204
[6,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 196
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 136
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 188
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 184
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 187
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 192
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 229
[6,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 209
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 204
[6,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 222
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 156
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 184
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 198
[6,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 213
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 171
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 204
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 142
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 116
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 160
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 156
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 157
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 161
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 192
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 175
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 170
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 185
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 155
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 157
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 187
[5,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 169
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 160
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 188
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 201
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 215
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 165
[5,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 197
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 170
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 179
[5,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 165
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 197
[5,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 175
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 116
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 136
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 144
[4,4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 154
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 150
[4,4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 157
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 144
[4,4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 172
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 148
[4,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 131
[4,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 156
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 156
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 82
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 97
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 104
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 428
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 296
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 344
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 254
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 164
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 358
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 254
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 302
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 226
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 218
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 358
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 251
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 294
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 219
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 313
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 224
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 267
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 232
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 344
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 240
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 280
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 208
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 294
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 210
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 250
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 302
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 213
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 250
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 267
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 218
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 296
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 206
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 240
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 178
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 251
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 179
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 213
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 254
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 179
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 210
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 224
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 254
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 178
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 208
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 219
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 226
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 164
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1429
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1000
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1165
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 868
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 571
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1219
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 874
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1039
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 784
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 529
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 769
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 604
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 439
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 274
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 874
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 714
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 574
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 478
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 355
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 334
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 109
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 860
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 753
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 689
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 644
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 442
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 841
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 518
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 448
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 380
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 285
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 322
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 169
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1165
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 820
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 716
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 736
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 647
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 219
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 560
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 386
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 769
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 488
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 434
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 601
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 275
[7,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 490
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 378
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 475
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 355
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 285
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 266
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 207
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 169
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1000
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 703
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 820
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 613
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 406
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 860
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 557
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 512
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 260
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 137
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 470
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 178
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 622
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 386
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 215
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 261
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 868
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 613
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 537
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 179
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Description
The number of Dyck paths that are weakly above the Dyck path, except for the path itself.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.