- FindStat

edit this statistic or download as text // json

Identifier

St000078: Permutations ⟶ ℤ

Values

=>
                            
                            
                            
                            

                        []=>1
[1]=>1
[1,2]=>1
[2,1]=>1
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>1
[2,3,1]=>1
[3,1,2]=>1
[3,2,1]=>1
[1,2,3,4]=>1
[1,2,4,3]=>3
[1,3,2,4]=>2
[1,3,4,2]=>3
[1,4,2,3]=>3
[1,4,3,2]=>5
[2,1,3,4]=>1
[2,1,4,3]=>4
[2,3,1,4]=>1
[2,3,4,1]=>1
[2,4,1,3]=>2
[2,4,3,1]=>2
[3,1,2,4]=>1
[3,1,4,2]=>2
[3,2,1,4]=>1
[3,2,4,1]=>1
[3,4,1,2]=>1
[3,4,2,1]=>1
[4,1,2,3]=>1
[4,1,3,2]=>2
[4,2,1,3]=>1
[4,2,3,1]=>1
[4,3,1,2]=>1
[4,3,2,1]=>1
[1,2,3,4,5]=>1
[1,2,3,5,4]=>4
[1,2,4,3,5]=>3
[1,2,4,5,3]=>6
[1,2,5,3,4]=>6
[1,2,5,4,3]=>14
[1,3,2,4,5]=>2
[1,3,2,5,4]=>13
[1,3,4,2,5]=>3
[1,3,4,5,2]=>4
[1,3,5,2,4]=>8
[1,3,5,4,2]=>11
[1,4,2,3,5]=>3
[1,4,2,5,3]=>8
[1,4,3,2,5]=>5
[1,4,3,5,2]=>7
[1,4,5,2,3]=>6
[1,4,5,3,2]=>9
[1,5,2,3,4]=>4
[1,5,2,4,3]=>11
[1,5,3,2,4]=>7
[1,5,3,4,2]=>10
[1,5,4,2,3]=>9
[1,5,4,3,2]=>14
[2,1,3,4,5]=>1
[2,1,3,5,4]=>5
[2,1,4,3,5]=>4
[2,1,4,5,3]=>8
[2,1,5,3,4]=>8
[2,1,5,4,3]=>21
[2,3,1,4,5]=>1
[2,3,1,5,4]=>6
[2,3,4,1,5]=>1
[2,3,4,5,1]=>1
[2,3,5,1,4]=>3
[2,3,5,4,1]=>3
[2,4,1,3,5]=>2
[2,4,1,5,3]=>6
[2,4,3,1,5]=>2
[2,4,3,5,1]=>2
[2,4,5,1,3]=>3
[2,4,5,3,1]=>3
[2,5,1,3,4]=>3
[2,5,1,4,3]=>10
[2,5,3,1,4]=>3
[2,5,3,4,1]=>3
[2,5,4,1,3]=>5
[2,5,4,3,1]=>5
[3,1,2,4,5]=>1
[3,1,2,5,4]=>6
[3,1,4,2,5]=>2
[3,1,4,5,2]=>3
[3,1,5,2,4]=>6
[3,1,5,4,2]=>10
[3,2,1,4,5]=>1
[3,2,1,5,4]=>8
[3,2,4,1,5]=>1
[3,2,4,5,1]=>1
[3,2,5,1,4]=>4
[3,2,5,4,1]=>4
[3,4,1,2,5]=>1
[3,4,1,5,2]=>2
[3,4,2,1,5]=>1
[3,4,2,5,1]=>1
[3,4,5,1,2]=>1
[3,4,5,2,1]=>1
[3,5,1,2,4]=>2
[3,5,1,4,2]=>4
[3,5,2,1,4]=>2
[3,5,2,4,1]=>2
[3,5,4,1,2]=>2
[3,5,4,2,1]=>2
[4,1,2,3,5]=>1
[4,1,2,5,3]=>3
[4,1,3,2,5]=>2
[4,1,3,5,2]=>3
[4,1,5,2,3]=>3
[4,1,5,3,2]=>5
[4,2,1,3,5]=>1
[4,2,1,5,3]=>4
[4,2,3,1,5]=>1
[4,2,3,5,1]=>1
[4,2,5,1,3]=>2
[4,2,5,3,1]=>2
[4,3,1,2,5]=>1
[4,3,1,5,2]=>2
[4,3,2,1,5]=>1
[4,3,2,5,1]=>1
[4,3,5,1,2]=>1
[4,3,5,2,1]=>1
[4,5,1,2,3]=>1
[4,5,1,3,2]=>2
[4,5,2,1,3]=>1
[4,5,2,3,1]=>1
[4,5,3,1,2]=>1
[4,5,3,2,1]=>1
[5,1,2,3,4]=>1
[5,1,2,4,3]=>3
[5,1,3,2,4]=>2
[5,1,3,4,2]=>3
[5,1,4,2,3]=>3
[5,1,4,3,2]=>5
[5,2,1,3,4]=>1
[5,2,1,4,3]=>4
[5,2,3,1,4]=>1
[5,2,3,4,1]=>1
[5,2,4,1,3]=>2
[5,2,4,3,1]=>2
[5,3,1,2,4]=>1
[5,3,1,4,2]=>2
[5,3,2,1,4]=>1
[5,3,2,4,1]=>1
[5,3,4,1,2]=>1
[5,3,4,2,1]=>1
[5,4,1,2,3]=>1
[5,4,1,3,2]=>2
[5,4,2,1,3]=>1
[5,4,2,3,1]=>1
[5,4,3,1,2]=>1
[5,4,3,2,1]=>1
[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>10
[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>30
[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>29
[1,2,4,5,3,6]=>6
[1,2,4,5,6,3]=>10
[1,2,4,6,3,5]=>20
[1,2,4,6,5,3]=>35
[1,2,5,3,4,6]=>6
[1,2,5,3,6,4]=>20
[1,2,5,4,3,6]=>14
[1,2,5,4,6,3]=>25
[1,2,5,6,3,4]=>20
[1,2,5,6,4,3]=>40
[1,2,6,3,4,5]=>10
[1,2,6,3,5,4]=>35
[1,2,6,4,3,5]=>25
[1,2,6,4,5,3]=>46
[1,2,6,5,3,4]=>40
[1,2,6,5,4,3]=>84
[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>15
[1,3,2,5,4,6]=>13
[1,3,2,5,6,4]=>32
[1,3,2,6,4,5]=>32
[1,3,2,6,5,4]=>121
[1,3,4,2,5,6]=>3
[1,3,4,2,6,5]=>26
[1,3,4,5,2,6]=>4
[1,3,4,5,6,2]=>5
[1,3,4,6,2,5]=>15
[1,3,4,6,5,2]=>19
[1,3,5,2,4,6]=>8
[1,3,5,2,6,4]=>34
[1,3,5,4,2,6]=>11
[1,3,5,4,6,2]=>14
[1,3,5,6,2,4]=>20
[1,3,5,6,4,2]=>26
[1,3,6,2,4,5]=>15
[1,3,6,2,5,4]=>74
[1,3,6,4,2,5]=>21
[1,3,6,4,5,2]=>27
[1,3,6,5,2,4]=>44
[1,3,6,5,4,2]=>58
[1,4,2,3,5,6]=>3
[1,4,2,3,6,5]=>26
[1,4,2,5,3,6]=>8
[1,4,2,5,6,3]=>15
[1,4,2,6,3,5]=>34
[1,4,2,6,5,3]=>74
[1,4,3,2,5,6]=>5
[1,4,3,2,6,5]=>67
[1,4,3,5,2,6]=>7
[1,4,3,5,6,2]=>9
[1,4,3,6,2,5]=>40
[1,4,3,6,5,2]=>53
[1,4,5,2,3,6]=>6
[1,4,5,2,6,3]=>15
[1,4,5,3,2,6]=>9
[1,4,5,3,6,2]=>12
[1,4,5,6,2,3]=>10
[1,4,5,6,3,2]=>14
[1,4,6,2,3,5]=>15
[1,4,6,2,5,3]=>38
[1,4,6,3,2,5]=>23
[1,4,6,3,5,2]=>31
[1,4,6,5,2,3]=>26
[1,4,6,5,3,2]=>37
[1,5,2,3,4,6]=>4
[1,5,2,3,6,4]=>15
[1,5,2,4,3,6]=>11
[1,5,2,4,6,3]=>21
[1,5,2,6,3,4]=>20
[1,5,2,6,4,3]=>44
[1,5,3,2,4,6]=>7
[1,5,3,2,6,4]=>40
[1,5,3,4,2,6]=>10
[1,5,3,4,6,2]=>13
[1,5,3,6,2,4]=>24
[1,5,3,6,4,2]=>32
[1,5,4,2,3,6]=>9
[1,5,4,2,6,3]=>23
[1,5,4,3,2,6]=>14
[1,5,4,3,6,2]=>19
[1,5,4,6,2,3]=>16
[1,5,4,6,3,2]=>23
[1,5,6,2,3,4]=>10
[1,5,6,2,4,3]=>26
[1,5,6,3,2,4]=>16
[1,5,6,3,4,2]=>22
[1,5,6,4,2,3]=>19
[1,5,6,4,3,2]=>28
[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>19
[1,6,2,4,3,5]=>14
[1,6,2,4,5,3]=>27
[1,6,2,5,3,4]=>26
[1,6,2,5,4,3]=>58
[1,6,3,2,4,5]=>9
[1,6,3,2,5,4]=>53
[1,6,3,4,2,5]=>13
[1,6,3,4,5,2]=>17
[1,6,3,5,2,4]=>32
[1,6,3,5,4,2]=>43
[1,6,4,2,3,5]=>12
[1,6,4,2,5,3]=>31
[1,6,4,3,2,5]=>19
[1,6,4,3,5,2]=>26
[1,6,4,5,2,3]=>22
[1,6,4,5,3,2]=>32
[1,6,5,2,3,4]=>14
[1,6,5,2,4,3]=>37
[1,6,5,3,2,4]=>23
[1,6,5,3,4,2]=>32
[1,6,5,4,2,3]=>28
[1,6,5,4,3,2]=>42
[2,1,3,4,5,6]=>1
[2,1,3,4,6,5]=>6
[2,1,3,5,4,6]=>5
[2,1,3,5,6,4]=>13
[2,1,3,6,4,5]=>13
[2,1,3,6,5,4]=>42
[2,1,4,3,5,6]=>4
[2,1,4,3,6,5]=>41
[2,1,4,5,3,6]=>8
[2,1,4,5,6,3]=>13
[2,1,4,6,3,5]=>29
[2,1,4,6,5,3]=>51
[2,1,5,3,4,6]=>8
[2,1,5,3,6,4]=>29
[2,1,5,4,3,6]=>21
[2,1,5,4,6,3]=>38
[2,1,5,6,3,4]=>29
[2,1,5,6,4,3]=>60
[2,1,6,3,4,5]=>13
[2,1,6,3,5,4]=>51
[2,1,6,4,3,5]=>38
[2,1,6,4,5,3]=>71
[2,1,6,5,3,4]=>60
[2,1,6,5,4,3]=>135
[2,3,1,4,5,6]=>1
[2,3,1,4,6,5]=>7
[2,3,1,5,4,6]=>6
[2,3,1,5,6,4]=>15
[2,3,1,6,4,5]=>15
[2,3,1,6,5,4]=>56
[2,3,4,1,5,6]=>1
[2,3,4,1,6,5]=>8
[2,3,4,5,1,6]=>1
[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>4
[2,3,4,6,5,1]=>4
[2,3,5,1,4,6]=>3
[2,3,5,1,6,4]=>12
[2,3,5,4,1,6]=>3
[2,3,5,4,6,1]=>3
[2,3,5,6,1,4]=>6
[2,3,5,6,4,1]=>6
[2,3,6,1,4,5]=>6
[2,3,6,1,5,4]=>28
[2,3,6,4,1,5]=>6
[2,3,6,4,5,1]=>6
[2,3,6,5,1,4]=>14
[2,3,6,5,4,1]=>14
[2,4,1,3,5,6]=>2
[2,4,1,3,6,5]=>21
[2,4,1,5,3,6]=>6
[2,4,1,5,6,3]=>11
[2,4,1,6,3,5]=>24
[2,4,1,6,5,3]=>52
[2,4,3,1,5,6]=>2
[2,4,3,1,6,5]=>26
[2,4,3,5,1,6]=>2
[2,4,3,5,6,1]=>2
[2,4,3,6,1,5]=>13
[2,4,3,6,5,1]=>13
[2,4,5,1,3,6]=>3
[2,4,5,1,6,3]=>8
[2,4,5,3,1,6]=>3
[2,4,5,3,6,1]=>3
[2,4,5,6,1,3]=>4
[2,4,5,6,3,1]=>4
[2,4,6,1,3,5]=>8
[2,4,6,1,5,3]=>22
[2,4,6,3,1,5]=>8
[2,4,6,3,5,1]=>8
[2,4,6,5,1,3]=>11
[2,4,6,5,3,1]=>11
[2,5,1,3,4,6]=>3
[2,5,1,3,6,4]=>13
[2,5,1,4,3,6]=>10
[2,5,1,4,6,3]=>19
[2,5,1,6,3,4]=>17
[2,5,1,6,4,3]=>40
[2,5,3,1,4,6]=>3
[2,5,3,1,6,4]=>16
[2,5,3,4,1,6]=>3
[2,5,3,4,6,1]=>3
[2,5,3,6,1,4]=>8
[2,5,3,6,4,1]=>8
[2,5,4,1,3,6]=>5
[2,5,4,1,6,3]=>14
[2,5,4,3,1,6]=>5
[2,5,4,3,6,1]=>5
[2,5,4,6,1,3]=>7
[2,5,4,6,3,1]=>7
[2,5,6,1,3,4]=>6
[2,5,6,1,4,3]=>18
[2,5,6,3,1,4]=>6
[2,5,6,3,4,1]=>6
[2,5,6,4,1,3]=>9
[2,5,6,4,3,1]=>9
[2,6,1,3,4,5]=>4
[2,6,1,3,5,4]=>18
[2,6,1,4,3,5]=>14
[2,6,1,4,5,3]=>27
[2,6,1,5,3,4]=>25
[2,6,1,5,4,3]=>61
[2,6,3,1,4,5]=>4
[2,6,3,1,5,4]=>22
[2,6,3,4,1,5]=>4
[2,6,3,4,5,1]=>4
[2,6,3,5,1,4]=>11
[2,6,3,5,4,1]=>11
[2,6,4,1,3,5]=>7
[2,6,4,1,5,3]=>20
[2,6,4,3,1,5]=>7
[2,6,4,3,5,1]=>7
[2,6,4,5,1,3]=>10
[2,6,4,5,3,1]=>10
[2,6,5,1,3,4]=>9
[2,6,5,1,4,3]=>28
[2,6,5,3,1,4]=>9
[2,6,5,3,4,1]=>9
[2,6,5,4,1,3]=>14
[2,6,5,4,3,1]=>14
[3,1,2,4,5,6]=>1
[3,1,2,4,6,5]=>7
[3,1,2,5,4,6]=>6
[3,1,2,5,6,4]=>15
[3,1,2,6,4,5]=>15
[3,1,2,6,5,4]=>56
[3,1,4,2,5,6]=>2
[3,1,4,2,6,5]=>21
[3,1,4,5,2,6]=>3
[3,1,4,5,6,2]=>4
[3,1,4,6,2,5]=>13
[3,1,4,6,5,2]=>18
[3,1,5,2,4,6]=>6
[3,1,5,2,6,4]=>24
[3,1,5,4,2,6]=>10
[3,1,5,4,6,2]=>14
[3,1,5,6,2,4]=>17
[3,1,5,6,4,2]=>25
[3,1,6,2,4,5]=>11
[3,1,6,2,5,4]=>52
[3,1,6,4,2,5]=>19
[3,1,6,4,5,2]=>27
[3,1,6,5,2,4]=>40
[3,1,6,5,4,2]=>61
[3,2,1,4,5,6]=>1
[3,2,1,4,6,5]=>9
[3,2,1,5,4,6]=>8
[3,2,1,5,6,4]=>20
[3,2,1,6,4,5]=>20
[3,2,1,6,5,4]=>82
[3,2,4,1,5,6]=>1
[3,2,4,1,6,5]=>10
[3,2,4,5,1,6]=>1
[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>5
[3,2,4,6,5,1]=>5
[3,2,5,1,4,6]=>4
[3,2,5,1,6,4]=>16
[3,2,5,4,1,6]=>4
[3,2,5,4,6,1]=>4
[3,2,5,6,1,4]=>8
[3,2,5,6,4,1]=>8
[3,2,6,1,4,5]=>8
[3,2,6,1,5,4]=>42
[3,2,6,4,1,5]=>8
[3,2,6,4,5,1]=>8
[3,2,6,5,1,4]=>21
[3,2,6,5,4,1]=>21
[3,4,1,2,5,6]=>1
[3,4,1,2,6,5]=>9
[3,4,1,5,2,6]=>2
[3,4,1,5,6,2]=>3
[3,4,1,6,2,5]=>9
[3,4,1,6,5,2]=>15
[3,4,2,1,5,6]=>1
[3,4,2,1,6,5]=>12
[3,4,2,5,1,6]=>1
[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>6
[3,4,2,6,5,1]=>6
[3,4,5,1,2,6]=>1
[3,4,5,1,6,2]=>2
[3,4,5,2,1,6]=>1
[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>1
[3,4,6,1,2,5]=>3
[3,4,6,1,5,2]=>6
[3,4,6,2,1,5]=>3
[3,4,6,2,5,1]=>3
[3,4,6,5,1,2]=>3
[3,4,6,5,2,1]=>3
[3,5,1,2,4,6]=>2
[3,5,1,2,6,4]=>9
[3,5,1,4,2,6]=>4
[3,5,1,4,6,2]=>6
[3,5,1,6,2,4]=>9
[3,5,1,6,4,2]=>15
[3,5,2,1,4,6]=>2
[3,5,2,1,6,4]=>12
[3,5,2,4,1,6]=>2
[3,5,2,4,6,1]=>2
[3,5,2,6,1,4]=>6
[3,5,2,6,4,1]=>6
[3,5,4,1,2,6]=>2
[3,5,4,1,6,2]=>4
[3,5,4,2,1,6]=>2
[3,5,4,2,6,1]=>2
[3,5,4,6,1,2]=>2
[3,5,4,6,2,1]=>2
[3,5,6,1,2,4]=>3
[3,5,6,1,4,2]=>6
[3,5,6,2,1,4]=>3
[3,5,6,2,4,1]=>3
[3,5,6,4,1,2]=>3
[3,5,6,4,2,1]=>3
[3,6,1,2,4,5]=>3
[3,6,1,2,5,4]=>15
[3,6,1,4,2,5]=>6
[3,6,1,4,5,2]=>9
[3,6,1,5,2,4]=>15
[3,6,1,5,4,2]=>25
[3,6,2,1,4,5]=>3
[3,6,2,1,5,4]=>20
[3,6,2,4,1,5]=>3
[3,6,2,4,5,1]=>3
[3,6,2,5,1,4]=>10
[3,6,2,5,4,1]=>10
[3,6,4,1,2,5]=>3
[3,6,4,1,5,2]=>6
[3,6,4,2,1,5]=>3
[3,6,4,2,5,1]=>3
[3,6,4,5,1,2]=>3
[3,6,4,5,2,1]=>3
[3,6,5,1,2,4]=>5
[3,6,5,1,4,2]=>10
[3,6,5,2,1,4]=>5
[3,6,5,2,4,1]=>5
[3,6,5,4,1,2]=>5
[3,6,5,4,2,1]=>5
[4,1,2,3,5,6]=>1
[4,1,2,3,6,5]=>8
[4,1,2,5,3,6]=>3
[4,1,2,5,6,3]=>6
[4,1,2,6,3,5]=>12
[4,1,2,6,5,3]=>28
[4,1,3,2,5,6]=>2
[4,1,3,2,6,5]=>26
[4,1,3,5,2,6]=>3
[4,1,3,5,6,2]=>4
[4,1,3,6,2,5]=>16
[4,1,3,6,5,2]=>22
[4,1,5,2,3,6]=>3
[4,1,5,2,6,3]=>8
[4,1,5,3,2,6]=>5
[4,1,5,3,6,2]=>7
[4,1,5,6,2,3]=>6
[4,1,5,6,3,2]=>9
[4,1,6,2,3,5]=>8
[4,1,6,2,5,3]=>22
[4,1,6,3,2,5]=>14
[4,1,6,3,5,2]=>20
[4,1,6,5,2,3]=>18
[4,1,6,5,3,2]=>28
[4,2,1,3,5,6]=>1
[4,2,1,3,6,5]=>10
[4,2,1,5,3,6]=>4
[4,2,1,5,6,3]=>8
[4,2,1,6,3,5]=>16
[4,2,1,6,5,3]=>42
[4,2,3,1,5,6]=>1
[4,2,3,1,6,5]=>12
[4,2,3,5,1,6]=>1
[4,2,3,5,6,1]=>1
[4,2,3,6,1,5]=>6
[4,2,3,6,5,1]=>6
[4,2,5,1,3,6]=>2
[4,2,5,1,6,3]=>6
[4,2,5,3,1,6]=>2
[4,2,5,3,6,1]=>2
[4,2,5,6,1,3]=>3
[4,2,5,6,3,1]=>3
[4,2,6,1,3,5]=>6
[4,2,6,1,5,3]=>20
[4,2,6,3,1,5]=>6
[4,2,6,3,5,1]=>6
[4,2,6,5,1,3]=>10
[4,2,6,5,3,1]=>10
[4,3,1,2,5,6]=>1
[4,3,1,2,6,5]=>12
[4,3,1,5,2,6]=>2
[4,3,1,5,6,2]=>3
[4,3,1,6,2,5]=>12
[4,3,1,6,5,2]=>20
[4,3,2,1,5,6]=>1
[4,3,2,1,6,5]=>16
[4,3,2,5,1,6]=>1
[4,3,2,5,6,1]=>1
[4,3,2,6,1,5]=>8
[4,3,2,6,5,1]=>8
[4,3,5,1,2,6]=>1
[4,3,5,1,6,2]=>2
[4,3,5,2,1,6]=>1
[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>1
[4,3,6,1,2,5]=>4
[4,3,6,1,5,2]=>8
[4,3,6,2,1,5]=>4
[4,3,6,2,5,1]=>4
[4,3,6,5,1,2]=>4
[4,3,6,5,2,1]=>4
[4,5,1,2,3,6]=>1
[4,5,1,2,6,3]=>3
[4,5,1,3,2,6]=>2
[4,5,1,3,6,2]=>3
[4,5,1,6,2,3]=>3
[4,5,1,6,3,2]=>5
[4,5,2,1,3,6]=>1
[4,5,2,1,6,3]=>4
[4,5,2,3,1,6]=>1
[4,5,2,3,6,1]=>1
[4,5,2,6,1,3]=>2
[4,5,2,6,3,1]=>2
[4,5,3,1,2,6]=>1
[4,5,3,1,6,2]=>2
[4,5,3,2,1,6]=>1
[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>1
[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>2
[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>1
[4,5,6,3,1,2]=>1
[4,5,6,3,2,1]=>1
[4,6,1,2,3,5]=>2
[4,6,1,2,5,3]=>6
[4,6,1,3,2,5]=>4
[4,6,1,3,5,2]=>6
[4,6,1,5,2,3]=>6
[4,6,1,5,3,2]=>10
[4,6,2,1,3,5]=>2
[4,6,2,1,5,3]=>8
[4,6,2,3,1,5]=>2
[4,6,2,3,5,1]=>2
[4,6,2,5,1,3]=>4
[4,6,2,5,3,1]=>4
[4,6,3,1,2,5]=>2
[4,6,3,1,5,2]=>4
[4,6,3,2,1,5]=>2
[4,6,3,2,5,1]=>2
[4,6,3,5,1,2]=>2
[4,6,3,5,2,1]=>2
[4,6,5,1,2,3]=>2
[4,6,5,1,3,2]=>4
[4,6,5,2,1,3]=>2
[4,6,5,2,3,1]=>2
[4,6,5,3,1,2]=>2
[4,6,5,3,2,1]=>2
[5,1,2,3,4,6]=>1
[5,1,2,3,6,4]=>4
[5,1,2,4,3,6]=>3
[5,1,2,4,6,3]=>6
[5,1,2,6,3,4]=>6
[5,1,2,6,4,3]=>14
[5,1,3,2,4,6]=>2
[5,1,3,2,6,4]=>13
[5,1,3,4,2,6]=>3
[5,1,3,4,6,2]=>4
[5,1,3,6,2,4]=>8
[5,1,3,6,4,2]=>11
[5,1,4,2,3,6]=>3
[5,1,4,2,6,3]=>8
[5,1,4,3,2,6]=>5
[5,1,4,3,6,2]=>7
[5,1,4,6,2,3]=>6
[5,1,4,6,3,2]=>9
[5,1,6,2,3,4]=>4
[5,1,6,2,4,3]=>11
[5,1,6,3,2,4]=>7
[5,1,6,3,4,2]=>10
[5,1,6,4,2,3]=>9
[5,1,6,4,3,2]=>14
[5,2,1,3,4,6]=>1
[5,2,1,3,6,4]=>5
[5,2,1,4,3,6]=>4
[5,2,1,4,6,3]=>8
[5,2,1,6,3,4]=>8
[5,2,1,6,4,3]=>21
[5,2,3,1,4,6]=>1
[5,2,3,1,6,4]=>6
[5,2,3,4,1,6]=>1
[5,2,3,4,6,1]=>1
[5,2,3,6,1,4]=>3
[5,2,3,6,4,1]=>3
[5,2,4,1,3,6]=>2
[5,2,4,1,6,3]=>6
[5,2,4,3,1,6]=>2
[5,2,4,3,6,1]=>2
[5,2,4,6,1,3]=>3
[5,2,4,6,3,1]=>3
[5,2,6,1,3,4]=>3
[5,2,6,1,4,3]=>10
[5,2,6,3,1,4]=>3
[5,2,6,3,4,1]=>3
[5,2,6,4,1,3]=>5
[5,2,6,4,3,1]=>5
[5,3,1,2,4,6]=>1
[5,3,1,2,6,4]=>6
[5,3,1,4,2,6]=>2
[5,3,1,4,6,2]=>3
[5,3,1,6,2,4]=>6
[5,3,1,6,4,2]=>10
[5,3,2,1,4,6]=>1
[5,3,2,1,6,4]=>8
[5,3,2,4,1,6]=>1
[5,3,2,4,6,1]=>1
[5,3,2,6,1,4]=>4
[5,3,2,6,4,1]=>4
[5,3,4,1,2,6]=>1
[5,3,4,1,6,2]=>2
[5,3,4,2,1,6]=>1
[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>1
[5,3,6,1,2,4]=>2
[5,3,6,1,4,2]=>4
[5,3,6,2,1,4]=>2
[5,3,6,2,4,1]=>2
[5,3,6,4,1,2]=>2
[5,3,6,4,2,1]=>2
[5,4,1,2,3,6]=>1
[5,4,1,2,6,3]=>3
[5,4,1,3,2,6]=>2
[5,4,1,3,6,2]=>3
[5,4,1,6,2,3]=>3
[5,4,1,6,3,2]=>5
[5,4,2,1,3,6]=>1
[5,4,2,1,6,3]=>4
[5,4,2,3,1,6]=>1
[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>2
[5,4,2,6,3,1]=>2
[5,4,3,1,2,6]=>1
[5,4,3,1,6,2]=>2
[5,4,3,2,1,6]=>1
[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>1
[5,4,3,6,2,1]=>1
[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>2
[5,4,6,2,1,3]=>1
[5,4,6,2,3,1]=>1
[5,4,6,3,1,2]=>1
[5,4,6,3,2,1]=>1
[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>3
[5,6,1,3,2,4]=>2
[5,6,1,3,4,2]=>3
[5,6,1,4,2,3]=>3
[5,6,1,4,3,2]=>5
[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>4
[5,6,2,3,1,4]=>1
[5,6,2,3,4,1]=>1
[5,6,2,4,1,3]=>2
[5,6,2,4,3,1]=>2
[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>2
[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>1
[5,6,3,4,1,2]=>1
[5,6,3,4,2,1]=>1
[5,6,4,1,2,3]=>1
[5,6,4,1,3,2]=>2
[5,6,4,2,1,3]=>1
[5,6,4,2,3,1]=>1
[5,6,4,3,1,2]=>1
[5,6,4,3,2,1]=>1
[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>4
[6,1,2,4,3,5]=>3
[6,1,2,4,5,3]=>6
[6,1,2,5,3,4]=>6
[6,1,2,5,4,3]=>14
[6,1,3,2,4,5]=>2
[6,1,3,2,5,4]=>13
[6,1,3,4,2,5]=>3
[6,1,3,4,5,2]=>4
[6,1,3,5,2,4]=>8
[6,1,3,5,4,2]=>11
[6,1,4,2,3,5]=>3
[6,1,4,2,5,3]=>8
[6,1,4,3,2,5]=>5
[6,1,4,3,5,2]=>7
[6,1,4,5,2,3]=>6
[6,1,4,5,3,2]=>9
[6,1,5,2,3,4]=>4
[6,1,5,2,4,3]=>11
[6,1,5,3,2,4]=>7
[6,1,5,3,4,2]=>10
[6,1,5,4,2,3]=>9
[6,1,5,4,3,2]=>14
[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>5
[6,2,1,4,3,5]=>4
[6,2,1,4,5,3]=>8
[6,2,1,5,3,4]=>8
[6,2,1,5,4,3]=>21
[6,2,3,1,4,5]=>1
[6,2,3,1,5,4]=>6
[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>1
[6,2,3,5,1,4]=>3
[6,2,3,5,4,1]=>3
[6,2,4,1,3,5]=>2
[6,2,4,1,5,3]=>6
[6,2,4,3,1,5]=>2
[6,2,4,3,5,1]=>2
[6,2,4,5,1,3]=>3
[6,2,4,5,3,1]=>3
[6,2,5,1,3,4]=>3
[6,2,5,1,4,3]=>10
[6,2,5,3,1,4]=>3
[6,2,5,3,4,1]=>3
[6,2,5,4,1,3]=>5
[6,2,5,4,3,1]=>5
[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>6
[6,3,1,4,2,5]=>2
[6,3,1,4,5,2]=>3
[6,3,1,5,2,4]=>6
[6,3,1,5,4,2]=>10
[6,3,2,1,4,5]=>1
[6,3,2,1,5,4]=>8
[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>1
[6,3,2,5,1,4]=>4
[6,3,2,5,4,1]=>4
[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>2
[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>1
[6,3,4,5,1,2]=>1
[6,3,4,5,2,1]=>1
[6,3,5,1,2,4]=>2
[6,3,5,1,4,2]=>4
[6,3,5,2,1,4]=>2
[6,3,5,2,4,1]=>2
[6,3,5,4,1,2]=>2
[6,3,5,4,2,1]=>2
[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>3
[6,4,1,3,2,5]=>2
[6,4,1,3,5,2]=>3
[6,4,1,5,2,3]=>3
[6,4,1,5,3,2]=>5
[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>4
[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>1
[6,4,2,5,1,3]=>2
[6,4,2,5,3,1]=>2
[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>2
[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>1
[6,4,3,5,1,2]=>1
[6,4,3,5,2,1]=>1
[6,4,5,1,2,3]=>1
[6,4,5,1,3,2]=>2
[6,4,5,2,1,3]=>1
[6,4,5,2,3,1]=>1
[6,4,5,3,1,2]=>1
[6,4,5,3,2,1]=>1
[6,5,1,2,3,4]=>1
[6,5,1,2,4,3]=>3
[6,5,1,3,2,4]=>2
[6,5,1,3,4,2]=>3
[6,5,1,4,2,3]=>3
[6,5,1,4,3,2]=>5
[6,5,2,1,3,4]=>1
[6,5,2,1,4,3]=>4
[6,5,2,3,1,4]=>1
[6,5,2,3,4,1]=>1
[6,5,2,4,1,3]=>2
[6,5,2,4,3,1]=>2
[6,5,3,1,2,4]=>1
[6,5,3,1,4,2]=>2
[6,5,3,2,1,4]=>1
[6,5,3,2,4,1]=>1
[6,5,3,4,1,2]=>1
[6,5,3,4,2,1]=>1
[6,5,4,1,2,3]=>1
[6,5,4,1,3,2]=>2
[6,5,4,2,1,3]=>1
[6,5,4,2,3,1]=>1
[6,5,4,3,1,2]=>1
[6,5,4,3,2,1]=>1
[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>5
[1,2,3,4,6,7,5]=>15
[1,2,3,4,7,5,6]=>15
[1,2,3,4,7,6,5]=>55
[1,2,3,5,4,6,7]=>4
[1,2,3,5,4,7,6]=>54
[1,2,3,5,6,4,7]=>10
[1,2,3,5,6,7,4]=>20
[1,2,3,5,7,4,6]=>40
[1,2,3,5,7,6,4]=>85
[1,2,3,6,4,5,7]=>10
[1,2,3,6,4,7,5]=>40
[1,2,3,6,5,4,7]=>30
[1,2,3,6,5,7,4]=>65
[1,2,3,6,7,4,5]=>50
[1,2,3,6,7,5,4]=>125
[1,2,3,7,4,5,6]=>20
[1,2,3,7,4,6,5]=>85
[1,2,3,7,5,4,6]=>65
[1,2,3,7,5,6,4]=>146
[1,2,3,7,6,4,5]=>125
[1,2,3,7,6,5,4]=>330
[1,2,4,3,5,6,7]=>3
[1,2,4,3,5,7,6]=>32
[1,2,4,3,6,5,7]=>29
[1,2,4,3,6,7,5]=>84
[1,2,4,3,7,5,6]=>84
[1,2,4,3,7,6,5]=>439
[1,2,4,5,3,6,7]=>6
[1,2,4,5,3,7,6]=>71
[1,2,4,5,6,3,7]=>10
[1,2,4,5,6,7,3]=>15
[1,2,4,5,7,3,6]=>45
[1,2,4,5,7,6,3]=>69
[1,2,4,6,3,5,7]=>20
[1,2,4,6,3,7,5]=>115
[1,2,4,6,5,3,7]=>35
[1,2,4,6,5,7,3]=>54
[1,2,4,6,7,3,5]=>75
[1,2,4,6,7,5,3]=>120
[1,2,4,7,3,5,6]=>45
[1,2,4,7,3,6,5]=>310
[1,2,4,7,5,3,6]=>81
[1,2,4,7,5,6,3]=>127
[1,2,4,7,6,3,5]=>205
[1,2,4,7,6,5,3]=>335
[1,2,5,3,4,6,7]=>6
[1,2,5,3,4,7,6]=>71
[1,2,5,3,6,4,7]=>20
[1,2,5,3,6,7,4]=>45
[1,2,5,3,7,4,6]=>115
[1,2,5,3,7,6,4]=>310
[1,2,5,4,3,6,7]=>14
[1,2,5,4,3,7,6]=>294
[1,2,5,4,6,3,7]=>25
[1,2,5,4,6,7,3]=>39
[1,2,5,4,7,3,6]=>195
[1,2,5,4,7,6,3]=>320
[1,2,5,6,3,4,7]=>20
[1,2,5,6,3,7,4]=>60
[1,2,5,6,4,3,7]=>40
[1,2,5,6,4,7,3]=>66
[1,2,5,6,7,3,4]=>50
[1,2,5,6,7,4,3]=>90
[1,2,5,7,3,4,6]=>60
[1,2,5,7,3,6,4]=>184
[1,2,5,7,4,3,6]=>124
[1,2,5,7,4,6,3]=>208
[1,2,5,7,6,3,4]=>160
[1,2,5,7,6,4,3]=>295
[1,2,6,3,4,5,7]=>10
[1,2,6,3,4,7,5]=>45
[1,2,6,3,5,4,7]=>35
[1,2,6,3,5,7,4]=>81
[1,2,6,3,7,4,5]=>75
[1,2,6,3,7,5,4]=>205
[1,2,6,4,3,5,7]=>25
[1,2,6,4,3,7,5]=>195
[1,2,6,4,5,3,7]=>46
[1,2,6,4,5,7,3]=>73
[1,2,6,4,7,3,5]=>130
[1,2,6,4,7,5,3]=>215
[1,2,6,5,3,4,7]=>40
[1,2,6,5,3,7,4]=>124
[1,2,6,5,4,3,7]=>84
[1,2,6,5,4,7,3]=>142
[1,2,6,5,7,3,4]=>110
[1,2,6,5,7,4,3]=>205
[1,2,6,7,3,4,5]=>50
[1,2,6,7,3,5,4]=>160
[1,2,6,7,4,3,5]=>110
[1,2,6,7,4,5,3]=>190
[1,2,6,7,5,3,4]=>155
[1,2,6,7,5,4,3]=>300
[1,2,7,3,4,5,6]=>15
[1,2,7,3,4,6,5]=>69
[1,2,7,3,5,4,6]=>54
[1,2,7,3,5,6,4]=>127
[1,2,7,3,6,4,5]=>120
[1,2,7,3,6,5,4]=>335
[1,2,7,4,3,5,6]=>39
[1,2,7,4,3,6,5]=>320
[1,2,7,4,5,3,6]=>73
[1,2,7,4,5,6,3]=>117
[1,2,7,4,6,3,5]=>215
[1,2,7,4,6,5,3]=>360
[1,2,7,5,3,4,6]=>66
[1,2,7,5,3,6,4]=>208
[1,2,7,5,4,3,6]=>142
[1,2,7,5,4,6,3]=>243
[1,2,7,5,6,3,4]=>190
[1,2,7,5,6,4,3]=>360
[1,2,7,6,3,4,5]=>90
[1,2,7,6,3,5,4]=>295
[1,2,7,6,4,3,5]=>205
[1,2,7,6,4,5,3]=>360
[1,2,7,6,5,3,4]=>300
[1,2,7,6,5,4,3]=>594
[1,3,2,4,5,6,7]=>2
[1,3,2,4,5,7,6]=>17
[1,3,2,4,6,5,7]=>15
[1,3,2,4,6,7,5]=>47
[1,3,2,4,7,5,6]=>47
[1,3,2,4,7,6,5]=>200
[1,3,2,5,4,6,7]=>13
[1,3,2,5,4,7,6]=>198
[1,3,2,5,6,4,7]=>32
[1,3,2,5,6,7,4]=>61
[1,3,2,5,7,4,6]=>153
[1,3,2,5,7,6,4]=>328
[1,3,2,6,4,5,7]=>32
[1,3,2,6,4,7,5]=>153
[1,3,2,6,5,4,7]=>121
[1,3,2,6,5,7,4]=>267
[1,3,2,6,7,4,5]=>185
[1,3,2,6,7,5,4]=>496
[1,3,2,7,4,5,6]=>61
[1,3,2,7,4,6,5]=>328
[1,3,2,7,5,4,6]=>267
[1,3,2,7,5,6,4]=>610
[1,3,2,7,6,4,5]=>496
[1,3,2,7,6,5,4]=>1514
[1,3,4,2,5,6,7]=>3
[1,3,4,2,5,7,6]=>29
[1,3,4,2,6,5,7]=>26
[1,3,4,2,6,7,5]=>79
[1,3,4,2,7,5,6]=>77
[1,3,4,2,7,6,5]=>398
[1,3,4,5,2,6,7]=>4
[1,3,4,5,2,7,6]=>43
[1,3,4,5,6,2,7]=>5
[1,3,4,5,6,7,2]=>6
[1,3,4,5,7,2,6]=>24
[1,3,4,5,7,6,2]=>29
[1,3,4,6,2,5,7]=>15
[1,3,4,6,2,7,5]=>80
[1,3,4,6,5,2,7]=>19
[1,3,4,6,5,7,2]=>23
[1,3,4,6,7,2,5]=>45
[1,3,4,6,7,5,2]=>55
[1,3,4,7,2,5,6]=>36
[1,3,4,7,2,6,5]=>230
[1,3,4,7,5,2,6]=>46
[1,3,4,7,5,6,2]=>56
[1,3,4,7,6,2,5]=>130
[1,3,4,7,6,5,2]=>160
[1,3,5,2,4,6,7]=>8
[1,3,5,2,4,7,6]=>131
[1,3,5,2,6,4,7]=>34
[1,3,5,2,6,7,4]=>75
[1,3,5,2,7,4,6]=>172
[1,3,5,2,7,6,4]=>480
[1,3,5,4,2,6,7]=>11
[1,3,5,4,2,7,6]=>221
[1,3,5,4,6,2,7]=>14
[1,3,5,4,6,7,2]=>17
[1,3,5,4,7,2,6]=>125
[1,3,5,4,7,6,2]=>154
[1,3,5,6,2,4,7]=>20
[1,3,5,6,2,7,4]=>70
[1,3,5,6,4,2,7]=>26
[1,3,5,6,4,7,2]=>32
[1,3,5,6,7,2,4]=>40
[1,3,5,6,7,4,2]=>50
[1,3,5,7,2,4,6]=>64
[1,3,5,7,2,6,4]=>235
[1,3,5,7,4,2,6]=>84
[1,3,5,7,4,6,2]=>104
[1,3,5,7,6,2,4]=>135
[1,3,5,7,6,4,2]=>170
[1,3,6,2,4,5,7]=>15
[1,3,6,2,4,7,5]=>89
[1,3,6,2,5,4,7]=>74
[1,3,6,2,5,7,4]=>170
[1,3,6,2,7,4,5]=>144
[1,3,6,2,7,5,4]=>456
[1,3,6,4,2,5,7]=>21
[1,3,6,4,2,7,5]=>150
[1,3,6,4,5,2,7]=>27
[1,3,6,4,5,7,2]=>33
[1,3,6,4,7,2,5]=>85
[1,3,6,4,7,5,2]=>105
[1,3,6,5,2,4,7]=>44
[1,3,6,5,2,7,4]=>165
[1,3,6,5,4,2,7]=>58
[1,3,6,5,4,7,2]=>72
[1,3,6,5,7,2,4]=>95
[1,3,6,5,7,4,2]=>120
[1,3,6,7,2,4,5]=>60
[1,3,6,7,2,5,4]=>250
[1,3,6,7,4,2,5]=>80
[1,3,6,7,4,5,2]=>100
[1,3,6,7,5,2,4]=>145
[1,3,6,7,5,4,2]=>185
[1,3,7,2,4,5,6]=>24
[1,3,7,2,4,6,5]=>151
[1,3,7,2,5,4,6]=>127
[1,3,7,2,5,6,4]=>297
[1,3,7,2,6,4,5]=>266
[1,3,7,2,6,5,4]=>888
[1,3,7,4,2,5,6]=>34
[1,3,7,4,2,6,5]=>255
[1,3,7,4,5,2,6]=>44
[1,3,7,4,5,6,2]=>54
[1,3,7,4,6,2,5]=>145
[1,3,7,4,6,5,2]=>180
[1,3,7,5,2,4,6]=>76
[1,3,7,5,2,6,4]=>294
[1,3,7,5,4,2,6]=>101
[1,3,7,5,4,6,2]=>126
[1,3,7,5,6,2,4]=>170
[1,3,7,5,6,4,2]=>216
[1,3,7,6,2,4,5]=>115
[1,3,7,6,2,5,4]=>504
[1,3,7,6,4,2,5]=>155
[1,3,7,6,4,5,2]=>195
[1,3,7,6,5,2,4]=>294
[1,3,7,6,5,4,2]=>378
[1,4,2,3,5,6,7]=>3
[1,4,2,3,5,7,6]=>29
[1,4,2,3,6,5,7]=>26
[1,4,2,3,6,7,5]=>77
[1,4,2,3,7,5,6]=>79
[1,4,2,3,7,6,5]=>398
[1,4,2,5,3,6,7]=>8
[1,4,2,5,3,7,6]=>131
[1,4,2,5,6,3,7]=>15
[1,4,2,5,6,7,3]=>24
[1,4,2,5,7,3,6]=>89
[1,4,2,5,7,6,3]=>151
[1,4,2,6,3,5,7]=>34
[1,4,2,6,3,7,5]=>172
[1,4,2,6,5,3,7]=>74
[1,4,2,6,5,7,3]=>127
[1,4,2,6,7,3,5]=>144
[1,4,2,6,7,5,3]=>266
[1,4,2,7,3,5,6]=>75
[1,4,2,7,3,6,5]=>480
[1,4,2,7,5,3,6]=>170
[1,4,2,7,5,6,3]=>297
[1,4,2,7,6,3,5]=>456
[1,4,2,7,6,5,3]=>888
[1,4,3,2,5,6,7]=>5
[1,4,3,2,5,7,6]=>72
[1,4,3,2,6,5,7]=>67
[1,4,3,2,6,7,5]=>198
[1,4,3,2,7,5,6]=>198
[1,4,3,2,7,6,5]=>1186
[1,4,3,5,2,6,7]=>7
[1,4,3,5,2,7,6]=>109
[1,4,3,5,6,2,7]=>9
[1,4,3,5,6,7,2]=>11
[1,4,3,5,7,2,6]=>62
[1,4,3,5,7,6,2]=>77
[1,4,3,6,2,5,7]=>40
[1,4,3,6,2,7,5]=>212
[1,4,3,6,5,2,7]=>53
[1,4,3,6,5,7,2]=>66
[1,4,3,6,7,2,5]=>122
[1,4,3,6,7,5,2]=>154
[1,4,3,7,2,5,6]=>95
[1,4,3,7,2,6,5]=>743
[1,4,3,7,5,2,6]=>127
[1,4,3,7,5,6,2]=>159
[1,4,3,7,6,2,5]=>432
[1,4,3,7,6,5,2]=>553
[1,4,5,2,3,6,7]=>6
[1,4,5,2,3,7,6]=>74
[1,4,5,2,6,3,7]=>15
[1,4,5,2,6,7,3]=>27
[1,4,5,2,7,3,6]=>89
[1,4,5,2,7,6,3]=>183
[1,4,5,3,2,6,7]=>9
[1,4,5,3,2,7,6]=>162
[1,4,5,3,6,2,7]=>12
[1,4,5,3,6,7,2]=>15
[1,4,5,3,7,2,6]=>94
[1,4,5,3,7,6,2]=>120
[1,4,5,6,2,3,7]=>10
[1,4,5,6,2,7,3]=>24
[1,4,5,6,3,2,7]=>14
[1,4,5,6,3,7,2]=>18
[1,4,5,6,7,2,3]=>15
[1,4,5,6,7,3,2]=>20
[1,4,5,7,2,3,6]=>36
[1,4,5,7,2,6,3]=>87
[1,4,5,7,3,2,6]=>51
[1,4,5,7,3,6,2]=>66
[1,4,5,7,6,2,3]=>55
[1,4,5,7,6,3,2]=>74
[1,4,6,2,3,5,7]=>15
[1,4,6,2,3,7,5]=>89
[1,4,6,2,5,3,7]=>38
[1,4,6,2,5,7,3]=>69
[1,4,6,2,7,3,5]=>109
[1,4,6,2,7,5,3]=>227
[1,4,6,3,2,5,7]=>23
[1,4,6,3,2,7,5]=>202
[1,4,6,3,5,2,7]=>31
[1,4,6,3,5,7,2]=>39
[1,4,6,3,7,2,5]=>118
[1,4,6,3,7,5,2]=>152
[1,4,6,5,2,3,7]=>26
[1,4,6,5,2,7,3]=>63
[1,4,6,5,3,2,7]=>37
[1,4,6,5,3,7,2]=>48
[1,4,6,5,7,2,3]=>40
[1,4,6,5,7,3,2]=>54
[1,4,6,7,2,3,5]=>45
[1,4,6,7,2,5,3]=>110
[1,4,6,7,3,2,5]=>65
[1,4,6,7,3,5,2]=>85
[1,4,6,7,5,2,3]=>71
[1,4,6,7,5,3,2]=>97
[1,4,7,2,3,5,6]=>27
[1,4,7,2,3,6,5]=>183
[1,4,7,2,5,3,6]=>69
[1,4,7,2,5,6,3]=>126
[1,4,7,2,6,3,5]=>227
[1,4,7,2,6,5,3]=>477
[1,4,7,3,2,5,6]=>42
[1,4,7,3,2,6,5]=>426
[1,4,7,3,5,2,6]=>57
[1,4,7,3,5,6,2]=>72
[1,4,7,3,6,2,5]=>250
[1,4,7,3,6,5,2]=>324
[1,4,7,5,2,3,6]=>48
[1,4,7,5,2,6,3]=>117
[1,4,7,5,3,2,6]=>69
[1,4,7,5,3,6,2]=>90
[1,4,7,5,6,2,3]=>75
[1,4,7,5,6,3,2]=>102
[1,4,7,6,2,3,5]=>95
[1,4,7,6,2,5,3]=>234
[1,4,7,6,3,2,5]=>139
[1,4,7,6,3,5,2]=>183
[1,4,7,6,5,2,3]=>153
[1,4,7,6,5,3,2]=>211
[1,5,2,3,4,6,7]=>4
[1,5,2,3,4,7,6]=>43
[1,5,2,3,6,4,7]=>15
[1,5,2,3,6,7,4]=>36
[1,5,2,3,7,4,6]=>80
[1,5,2,3,7,6,4]=>230
[1,5,2,4,3,6,7]=>11
[1,5,2,4,3,7,6]=>221
[1,5,2,4,6,3,7]=>21
[1,5,2,4,6,7,3]=>34
[1,5,2,4,7,3,6]=>150
[1,5,2,4,7,6,3]=>255
[1,5,2,6,3,4,7]=>20
[1,5,2,6,3,7,4]=>64
[1,5,2,6,4,3,7]=>44
[1,5,2,6,4,7,3]=>76
[1,5,2,6,7,3,4]=>60
[1,5,2,6,7,4,3]=>115
[1,5,2,7,3,4,6]=>70
[1,5,2,7,3,6,4]=>235
[1,5,2,7,4,3,6]=>165
[1,5,2,7,4,6,3]=>294
[1,5,2,7,6,3,4]=>250
[1,5,2,7,6,4,3]=>504
[1,5,3,2,4,6,7]=>7
[1,5,3,2,4,7,6]=>109
[1,5,3,2,6,4,7]=>40
[1,5,3,2,6,7,4]=>95
[1,5,3,2,7,4,6]=>212
[1,5,3,2,7,6,4]=>743
[1,5,3,4,2,6,7]=>10
[1,5,3,4,2,7,6]=>184
[1,5,3,4,6,2,7]=>13
[1,5,3,4,6,7,2]=>16
[1,5,3,4,7,2,6]=>105
[1,5,3,4,7,6,2]=>131
[1,5,3,6,2,4,7]=>24
[1,5,3,6,2,7,4]=>95
[1,5,3,6,4,2,7]=>32
[1,5,3,6,4,7,2]=>40
[1,5,3,6,7,2,4]=>55
[1,5,3,6,7,4,2]=>70
[1,5,3,7,2,4,6]=>95
[1,5,3,7,2,6,4]=>434
[1,5,3,7,4,2,6]=>129
[1,5,3,7,4,6,2]=>163
[1,5,3,7,6,2,4]=>254
[1,5,3,7,6,4,2]=>328
[1,5,4,2,3,6,7]=>9
[1,5,4,2,3,7,6]=>162
[1,5,4,2,6,3,7]=>23
[1,5,4,2,6,7,3]=>42
[1,5,4,2,7,3,6]=>202
[1,5,4,2,7,6,3]=>426
[1,5,4,3,2,6,7]=>14
[1,5,4,3,2,7,6]=>381
[1,5,4,3,6,2,7]=>19
[1,5,4,3,6,7,2]=>24
[1,5,4,3,7,2,6]=>224
[1,5,4,3,7,6,2]=>291
[1,5,4,6,2,3,7]=>16
[1,5,4,6,2,7,3]=>39
[1,5,4,6,3,2,7]=>23
[1,5,4,6,3,7,2]=>30
[1,5,4,6,7,2,3]=>25
[1,5,4,6,7,3,2]=>34
[1,5,4,7,2,3,6]=>85
[1,5,4,7,2,6,3]=>210
[1,5,4,7,3,2,6]=>125
[1,5,4,7,3,6,2]=>165
[1,5,4,7,6,2,3]=>138
[1,5,4,7,6,3,2]=>191
[1,5,6,2,3,4,7]=>10
[1,5,6,2,3,7,4]=>36
[1,5,6,2,4,3,7]=>26
[1,5,6,2,4,7,3]=>48
[1,5,6,2,7,3,4]=>45
[1,5,6,2,7,4,3]=>95
[1,5,6,3,2,4,7]=>16
[1,5,6,3,2,7,4]=>85
[1,5,6,3,4,2,7]=>22
[1,5,6,3,4,7,2]=>28
[1,5,6,3,7,2,4]=>50
[1,5,6,3,7,4,2]=>65
[1,5,6,4,2,3,7]=>19
[1,5,6,4,2,7,3]=>47
[1,5,6,4,3,2,7]=>28
[1,5,6,4,3,7,2]=>37
[1,5,6,4,7,2,3]=>31
[1,5,6,4,7,3,2]=>43
[1,5,6,7,2,3,4]=>20
[1,5,6,7,2,4,3]=>50
[1,5,6,7,3,2,4]=>30
[1,5,6,7,3,4,2]=>40
[1,5,6,7,4,2,3]=>34
[1,5,6,7,4,3,2]=>48
[1,5,7,2,3,4,6]=>24
[1,5,7,2,3,6,4]=>87
[1,5,7,2,4,3,6]=>63
[1,5,7,2,4,6,3]=>117
[1,5,7,2,6,3,4]=>110
[1,5,7,2,6,4,3]=>234
[1,5,7,3,2,4,6]=>39
[1,5,7,3,2,6,4]=>210
[1,5,7,3,4,2,6]=>54
[1,5,7,3,4,6,2]=>69
[1,5,7,3,6,2,4]=>124
[1,5,7,3,6,4,2]=>162
[1,5,7,4,2,3,6]=>47
[1,5,7,4,2,6,3]=>117
[1,5,7,4,3,2,6]=>70
[1,5,7,4,3,6,2]=>93
[1,5,7,4,6,2,3]=>78
[1,5,7,4,6,3,2]=>109
[1,5,7,6,2,3,4]=>50
[1,5,7,6,2,4,3]=>126
[1,5,7,6,3,2,4]=>76
[1,5,7,6,3,4,2]=>102
[1,5,7,6,4,2,3]=>87
[1,5,7,6,4,3,2]=>124
[1,6,2,3,4,5,7]=>5
[1,6,2,3,4,7,5]=>24
[1,6,2,3,5,4,7]=>19
[1,6,2,3,5,7,4]=>46
[1,6,2,3,7,4,5]=>45
[1,6,2,3,7,5,4]=>130
[1,6,2,4,3,5,7]=>14
[1,6,2,4,3,7,5]=>125
[1,6,2,4,5,3,7]=>27
[1,6,2,4,5,7,3]=>44
[1,6,2,4,7,3,5]=>85
[1,6,2,4,7,5,3]=>145
[1,6,2,5,3,4,7]=>26
[1,6,2,5,3,7,4]=>84
[1,6,2,5,4,3,7]=>58
[1,6,2,5,4,7,3]=>101
[1,6,2,5,7,3,4]=>80
[1,6,2,5,7,4,3]=>155
[1,6,2,7,3,4,5]=>40
[1,6,2,7,3,5,4]=>135
[1,6,2,7,4,3,5]=>95
[1,6,2,7,4,5,3]=>170
[1,6,2,7,5,3,4]=>145
[1,6,2,7,5,4,3]=>294
[1,6,3,2,4,5,7]=>9
[1,6,3,2,4,7,5]=>62
[1,6,3,2,5,4,7]=>53
[1,6,3,2,5,7,4]=>127
[1,6,3,2,7,4,5]=>122
[1,6,3,2,7,5,4]=>432
[1,6,3,4,2,5,7]=>13
[1,6,3,4,2,7,5]=>105
[1,6,3,4,5,2,7]=>17
[1,6,3,4,5,7,2]=>21
[1,6,3,4,7,2,5]=>60
[1,6,3,4,7,5,2]=>75
[1,6,3,5,2,4,7]=>32
[1,6,3,5,2,7,4]=>129
[1,6,3,5,4,2,7]=>43
[1,6,3,5,4,7,2]=>54
[1,6,3,5,7,2,4]=>75
[1,6,3,5,7,4,2]=>96
[1,6,3,7,2,4,5]=>55
[1,6,3,7,2,5,4]=>254
[1,6,3,7,4,2,5]=>75
[1,6,3,7,4,5,2]=>95
[1,6,3,7,5,2,4]=>149
[1,6,3,7,5,4,2]=>193
[1,6,4,2,3,5,7]=>12
[1,6,4,2,3,7,5]=>94
[1,6,4,2,5,3,7]=>31
[1,6,4,2,5,7,3]=>57
[1,6,4,2,7,3,5]=>118
[1,6,4,2,7,5,3]=>250
[1,6,4,3,2,5,7]=>19
[1,6,4,3,2,7,5]=>224
[1,6,4,3,5,2,7]=>26
[1,6,4,3,5,7,2]=>33
[1,6,4,3,7,2,5]=>132
[1,6,4,3,7,5,2]=>172
[1,6,4,5,2,3,7]=>22
[1,6,4,5,2,7,3]=>54
[1,6,4,5,3,2,7]=>32
[1,6,4,5,3,7,2]=>42
[1,6,4,5,7,2,3]=>35
[1,6,4,5,7,3,2]=>48
[1,6,4,7,2,3,5]=>50
[1,6,4,7,2,5,3]=>124
[1,6,4,7,3,2,5]=>74
[1,6,4,7,3,5,2]=>98
[1,6,4,7,5,2,3]=>82
[1,6,4,7,5,3,2]=>114
[1,6,5,2,3,4,7]=>14
[1,6,5,2,3,7,4]=>51
[1,6,5,2,4,3,7]=>37
[1,6,5,2,4,7,3]=>69
[1,6,5,2,7,3,4]=>65
[1,6,5,2,7,4,3]=>139
[1,6,5,3,2,4,7]=>23
[1,6,5,3,2,7,4]=>125
[1,6,5,3,4,2,7]=>32
[1,6,5,3,4,7,2]=>41
[1,6,5,3,7,2,4]=>74
[1,6,5,3,7,4,2]=>97
[1,6,5,4,2,3,7]=>28
[1,6,5,4,2,7,3]=>70
[1,6,5,4,3,2,7]=>42
[1,6,5,4,3,7,2]=>56
[1,6,5,4,7,2,3]=>47
[1,6,5,4,7,3,2]=>66
[1,6,5,7,2,3,4]=>30
[1,6,5,7,2,4,3]=>76
[1,6,5,7,3,2,4]=>46
[1,6,5,7,3,4,2]=>62
[1,6,5,7,4,2,3]=>53
[1,6,5,7,4,3,2]=>76
[1,6,7,2,3,4,5]=>15
[1,6,7,2,3,5,4]=>55
[1,6,7,2,4,3,5]=>40
[1,6,7,2,4,5,3]=>75
[1,6,7,2,5,3,4]=>71
[1,6,7,2,5,4,3]=>153
[1,6,7,3,2,4,5]=>25
[1,6,7,3,2,5,4]=>138
[1,6,7,3,4,2,5]=>35
[1,6,7,3,4,5,2]=>45
[1,6,7,3,5,2,4]=>82
[1,6,7,3,5,4,2]=>108
[1,6,7,4,2,3,5]=>31
[1,6,7,4,2,5,3]=>78
[1,6,7,4,3,2,5]=>47
[1,6,7,4,3,5,2]=>63
[1,6,7,4,5,2,3]=>53
[1,6,7,4,5,3,2]=>75
[1,6,7,5,2,3,4]=>34
[1,6,7,5,2,4,3]=>87
[1,6,7,5,3,2,4]=>53
[1,6,7,5,3,4,2]=>72
[1,6,7,5,4,2,3]=>62
[1,6,7,5,4,3,2]=>90
[1,7,2,3,4,5,6]=>6
[1,7,2,3,4,6,5]=>29
[1,7,2,3,5,4,6]=>23
[1,7,2,3,5,6,4]=>56
[1,7,2,3,6,4,5]=>55
[1,7,2,3,6,5,4]=>160
[1,7,2,4,3,5,6]=>17
[1,7,2,4,3,6,5]=>154
[1,7,2,4,5,3,6]=>33
[1,7,2,4,5,6,3]=>54
[1,7,2,4,6,3,5]=>105
[1,7,2,4,6,5,3]=>180
[1,7,2,5,3,4,6]=>32
[1,7,2,5,3,6,4]=>104
[1,7,2,5,4,3,6]=>72
[1,7,2,5,4,6,3]=>126
[1,7,2,5,6,3,4]=>100
[1,7,2,5,6,4,3]=>195
[1,7,2,6,3,4,5]=>50
[1,7,2,6,3,5,4]=>170
[1,7,2,6,4,3,5]=>120
[1,7,2,6,4,5,3]=>216
[1,7,2,6,5,3,4]=>185
[1,7,2,6,5,4,3]=>378
[1,7,3,2,4,5,6]=>11
[1,7,3,2,4,6,5]=>77
[1,7,3,2,5,4,6]=>66
[1,7,3,2,5,6,4]=>159
[1,7,3,2,6,4,5]=>154
[1,7,3,2,6,5,4]=>553
[1,7,3,4,2,5,6]=>16
[1,7,3,4,2,6,5]=>131
[1,7,3,4,5,2,6]=>21
[1,7,3,4,5,6,2]=>26
[1,7,3,4,6,2,5]=>75
[1,7,3,4,6,5,2]=>94
[1,7,3,5,2,4,6]=>40
[1,7,3,5,2,6,4]=>163
[1,7,3,5,4,2,6]=>54
[1,7,3,5,4,6,2]=>68
[1,7,3,5,6,2,4]=>95
[1,7,3,5,6,4,2]=>122
[1,7,3,6,2,4,5]=>70
[1,7,3,6,2,5,4]=>328
[1,7,3,6,4,2,5]=>96
[1,7,3,6,4,5,2]=>122
[1,7,3,6,5,2,4]=>193
[1,7,3,6,5,4,2]=>251
[1,7,4,2,3,5,6]=>15
[1,7,4,2,3,6,5]=>120
[1,7,4,2,5,3,6]=>39
[1,7,4,2,5,6,3]=>72
[1,7,4,2,6,3,5]=>152
[1,7,4,2,6,5,3]=>324
[1,7,4,3,2,5,6]=>24
[1,7,4,3,2,6,5]=>291
[1,7,4,3,5,2,6]=>33
[1,7,4,3,5,6,2]=>42
[1,7,4,3,6,2,5]=>172
[1,7,4,3,6,5,2]=>225
[1,7,4,5,2,3,6]=>28
[1,7,4,5,2,6,3]=>69
[1,7,4,5,3,2,6]=>41
[1,7,4,5,3,6,2]=>54
[1,7,4,5,6,2,3]=>45
[1,7,4,5,6,3,2]=>62
[1,7,4,6,2,3,5]=>65
[1,7,4,6,2,5,3]=>162
[1,7,4,6,3,2,5]=>97
[1,7,4,6,3,5,2]=>129
[1,7,4,6,5,2,3]=>108
[1,7,4,6,5,3,2]=>151
[1,7,5,2,3,4,6]=>18
[1,7,5,2,3,6,4]=>66
[1,7,5,2,4,3,6]=>48
[1,7,5,2,4,6,3]=>90
[1,7,5,2,6,3,4]=>85
[1,7,5,2,6,4,3]=>183
[1,7,5,3,2,4,6]=>30
[1,7,5,3,2,6,4]=>165
[1,7,5,3,4,2,6]=>42
[1,7,5,3,4,6,2]=>54
[1,7,5,3,6,2,4]=>98
[1,7,5,3,6,4,2]=>129
[1,7,5,4,2,3,6]=>37
[1,7,5,4,2,6,3]=>93
[1,7,5,4,3,2,6]=>56
[1,7,5,4,3,6,2]=>75
[1,7,5,4,6,2,3]=>63
[1,7,5,4,6,3,2]=>89
[1,7,5,6,2,3,4]=>40
[1,7,5,6,2,4,3]=>102
[1,7,5,6,3,2,4]=>62
[1,7,5,6,3,4,2]=>84
[1,7,5,6,4,2,3]=>72
[1,7,5,6,4,3,2]=>104
[1,7,6,2,3,4,5]=>20
[1,7,6,2,3,5,4]=>74
[1,7,6,2,4,3,5]=>54
[1,7,6,2,4,5,3]=>102
[1,7,6,2,5,3,4]=>97
[1,7,6,2,5,4,3]=>211
[1,7,6,3,2,4,5]=>34
[1,7,6,3,2,5,4]=>191
[1,7,6,3,4,2,5]=>48
[1,7,6,3,4,5,2]=>62
[1,7,6,3,5,2,4]=>114
[1,7,6,3,5,4,2]=>151
[1,7,6,4,2,3,5]=>43
[1,7,6,4,2,5,3]=>109
[1,7,6,4,3,2,5]=>66
[1,7,6,4,3,5,2]=>89
[1,7,6,4,5,2,3]=>75
[1,7,6,4,5,3,2]=>107
[1,7,6,5,2,3,4]=>48
[1,7,6,5,2,4,3]=>124
[1,7,6,5,3,2,4]=>76
[1,7,6,5,3,4,2]=>104
[1,7,6,5,4,2,3]=>90
[1,7,6,5,4,3,2]=>132
[2,1,3,4,5,6,7]=>1
[2,1,3,4,5,7,6]=>7
[2,1,3,4,6,5,7]=>6
[2,1,3,4,6,7,5]=>19
[2,1,3,4,7,5,6]=>19
[2,1,3,4,7,6,5]=>74
[2,1,3,5,4,6,7]=>5
[2,1,3,5,4,7,6]=>73
[2,1,3,5,6,4,7]=>13
[2,1,3,5,6,7,4]=>26
[2,1,3,5,7,4,6]=>55
[2,1,3,5,7,6,4]=>119
[2,1,3,6,4,5,7]=>13
[2,1,3,6,4,7,5]=>55
[2,1,3,6,5,4,7]=>42
[2,1,3,6,5,7,4]=>93
[2,1,3,6,7,4,5]=>71
[2,1,3,6,7,5,4]=>182
[2,1,3,7,4,5,6]=>26
[2,1,3,7,4,6,5]=>119
[2,1,3,7,5,4,6]=>93
[2,1,3,7,5,6,4]=>215
[2,1,3,7,6,4,5]=>182
[2,1,3,7,6,5,4]=>499
[2,1,4,3,5,6,7]=>4
[2,1,4,3,5,7,6]=>45
[2,1,4,3,6,5,7]=>41
[2,1,4,3,6,7,5]=>121
[2,1,4,3,7,5,6]=>121
[2,1,4,3,7,6,5]=>658
[2,1,4,5,3,6,7]=>8
[2,1,4,5,3,7,6]=>101
[2,1,4,5,6,3,7]=>13
[2,1,4,5,6,7,3]=>19
[2,1,4,5,7,3,6]=>64
[2,1,4,5,7,6,3]=>97
[2,1,4,6,3,5,7]=>29
[2,1,4,6,3,7,5]=>169
[2,1,4,6,5,3,7]=>51
[2,1,4,6,5,7,3]=>78
[2,1,4,6,7,3,5]=>111
[2,1,4,6,7,5,3]=>177
[2,1,4,7,3,5,6]=>67
[2,1,4,7,3,6,5]=>473
[2,1,4,7,5,3,6]=>122
[2,1,4,7,5,6,3]=>190
[2,1,4,7,6,3,5]=>317
[2,1,4,7,6,5,3]=>520
[2,1,5,3,4,6,7]=>8
[2,1,5,3,4,7,6]=>101
[2,1,5,3,6,4,7]=>29
[2,1,5,3,6,7,4]=>67
[2,1,5,3,7,4,6]=>169
[2,1,5,3,7,6,4]=>473
[2,1,5,4,3,6,7]=>21
[2,1,5,4,3,7,6]=>452
[2,1,5,4,6,3,7]=>38
[2,1,5,4,6,7,3]=>59
[2,1,5,4,7,3,6]=>304
[2,1,5,4,7,6,3]=>501
[2,1,5,6,3,4,7]=>29
[2,1,5,6,3,7,4]=>89
[2,1,5,6,4,3,7]=>60
[2,1,5,6,4,7,3]=>99
[2,1,5,6,7,3,4]=>73
[2,1,5,6,7,4,3]=>132
[2,1,5,7,3,4,6]=>89
[2,1,5,7,3,6,4]=>284
[2,1,5,7,4,3,6]=>195
[2,1,5,7,4,6,3]=>330
[2,1,5,7,6,3,4]=>247
[2,1,5,7,6,4,3]=>465
[2,1,6,3,4,5,7]=>13
[2,1,6,3,4,7,5]=>64
[2,1,6,3,5,4,7]=>51
[2,1,6,3,5,7,4]=>122
[2,1,6,3,7,4,5]=>111
[2,1,6,3,7,5,4]=>317
[2,1,6,4,3,5,7]=>38
[2,1,6,4,3,7,5]=>304
[2,1,6,4,5,3,7]=>71
[2,1,6,4,5,7,3]=>112
[2,1,6,4,7,3,5]=>206
[2,1,6,4,7,5,3]=>343
[2,1,6,5,3,4,7]=>60
[2,1,6,5,3,7,4]=>195
[2,1,6,5,4,3,7]=>135
[2,1,6,5,4,7,3]=>231
[2,1,6,5,7,3,4]=>174
[2,1,6,5,7,4,3]=>333
[2,1,6,7,3,4,5]=>73
[2,1,6,7,3,5,4]=>247
[2,1,6,7,4,3,5]=>174
[2,1,6,7,4,5,3]=>304
[2,1,6,7,5,3,4]=>240
[2,1,6,7,5,4,3]=>481
[2,1,7,3,4,5,6]=>19
[2,1,7,3,4,6,5]=>97
[2,1,7,3,5,4,6]=>78
[2,1,7,3,5,6,4]=>190
[2,1,7,3,6,4,5]=>177
[2,1,7,3,6,5,4]=>520
[2,1,7,4,3,5,6]=>59
[2,1,7,4,3,6,5]=>501
[2,1,7,4,5,3,6]=>112
[2,1,7,4,5,6,3]=>178
[2,1,7,4,6,3,5]=>343
[2,1,7,4,6,5,3]=>579
[2,1,7,5,3,4,6]=>99
[2,1,7,5,3,6,4]=>330
[2,1,7,5,4,3,6]=>231
[2,1,7,5,4,6,3]=>401
[2,1,7,5,6,3,4]=>304
[2,1,7,5,6,4,3]=>594
[2,1,7,6,3,4,5]=>132
[2,1,7,6,3,5,4]=>465
[2,1,7,6,4,3,5]=>333
[2,1,7,6,4,5,3]=>594
[2,1,7,6,5,3,4]=>481
[2,1,7,6,5,4,3]=>1000
[2,3,1,4,5,6,7]=>1
[2,3,1,4,5,7,6]=>8
[2,3,1,4,6,5,7]=>7
[2,3,1,4,6,7,5]=>22
[2,3,1,4,7,5,6]=>22
[2,3,1,4,7,6,5]=>93
[2,3,1,5,4,6,7]=>6
[2,3,1,5,4,7,6]=>92
[2,3,1,5,6,4,7]=>15
[2,3,1,5,6,7,4]=>29
[2,3,1,5,7,4,6]=>71
[2,3,1,5,7,6,4]=>154
[2,3,1,6,4,5,7]=>15
[2,3,1,6,4,7,5]=>71
[2,3,1,6,5,4,7]=>56
[2,3,1,6,5,7,4]=>125
[2,3,1,6,7,4,5]=>87
[2,3,1,6,7,5,4]=>232
[2,3,1,7,4,5,6]=>29
[2,3,1,7,4,6,5]=>153
[2,3,1,7,5,4,6]=>124
[2,3,1,7,5,6,4]=>287
[2,3,1,7,6,4,5]=>235
[2,3,1,7,6,5,4]=>709
[2,3,4,1,5,6,7]=>1
[2,3,4,1,5,7,6]=>9
[2,3,4,1,6,5,7]=>8
[2,3,4,1,6,7,5]=>24
[2,3,4,1,7,5,6]=>24
[2,3,4,1,7,6,5]=>118
[2,3,4,5,1,6,7]=>1
[2,3,4,5,1,7,6]=>10
[2,3,4,5,6,1,7]=>1
[2,3,4,5,6,7,1]=>1
[2,3,4,5,7,1,6]=>5
[2,3,4,5,7,6,1]=>5
[2,3,4,6,1,5,7]=>4
[2,3,4,6,1,7,5]=>20
[2,3,4,6,5,1,7]=>4
[2,3,4,6,5,7,1]=>4
[2,3,4,6,7,1,5]=>10
[2,3,4,6,7,5,1]=>10
[2,3,4,7,1,5,6]=>10
[2,3,4,7,1,6,5]=>60
[2,3,4,7,5,1,6]=>10
[2,3,4,7,5,6,1]=>10
[2,3,4,7,6,1,5]=>30
[2,3,4,7,6,5,1]=>30
[2,3,5,1,4,6,7]=>3
[2,3,5,1,4,7,6]=>49
[2,3,5,1,6,4,7]=>12
[2,3,5,1,6,7,4]=>26
[2,3,5,1,7,4,6]=>60
[2,3,5,1,7,6,4]=>160
[2,3,5,4,1,6,7]=>3
[2,3,5,4,1,7,6]=>58
[2,3,5,4,6,1,7]=>3
[2,3,5,4,6,7,1]=>3
[2,3,5,4,7,1,6]=>29
[2,3,5,4,7,6,1]=>29
[2,3,5,6,1,4,7]=>6
[2,3,5,6,1,7,4]=>20
[2,3,5,6,4,1,7]=>6
[2,3,5,6,4,7,1]=>6
[2,3,5,6,7,1,4]=>10
[2,3,5,6,7,4,1]=>10
[2,3,5,7,1,4,6]=>20
[2,3,5,7,1,6,4]=>70
[2,3,5,7,4,1,6]=>20
[2,3,5,7,4,6,1]=>20
[2,3,5,7,6,1,4]=>35
[2,3,5,7,6,4,1]=>35
[2,3,6,1,4,5,7]=>6
[2,3,6,1,4,7,5]=>34
[2,3,6,1,5,4,7]=>28
[2,3,6,1,5,7,4]=>64
[2,3,6,1,7,4,5]=>54
[2,3,6,1,7,5,4]=>168
[2,3,6,4,1,5,7]=>6
[2,3,6,4,1,7,5]=>40
[2,3,6,4,5,1,7]=>6
[2,3,6,4,5,7,1]=>6
[2,3,6,4,7,1,5]=>20
[2,3,6,4,7,5,1]=>20
[2,3,6,5,1,4,7]=>14
[2,3,6,5,1,7,4]=>50
[2,3,6,5,4,1,7]=>14
[2,3,6,5,4,7,1]=>14
[2,3,6,5,7,1,4]=>25
[2,3,6,5,7,4,1]=>25
[2,3,6,7,1,4,5]=>20
[2,3,6,7,1,5,4]=>80
[2,3,6,7,4,1,5]=>20
[2,3,6,7,4,5,1]=>20
[2,3,6,7,5,1,4]=>40
[2,3,6,7,5,4,1]=>40
[2,3,7,1,4,5,6]=>10
[2,3,7,1,4,6,5]=>60
[2,3,7,1,5,4,6]=>50
[2,3,7,1,5,6,4]=>117
[2,3,7,1,6,4,5]=>105
[2,3,7,1,6,5,4]=>346
[2,3,7,4,1,5,6]=>10
[2,3,7,4,1,6,5]=>70
[2,3,7,4,5,1,6]=>10
[2,3,7,4,5,6,1]=>10
[2,3,7,4,6,1,5]=>35
[2,3,7,4,6,5,1]=>35
[2,3,7,5,1,4,6]=>25
[2,3,7,5,1,6,4]=>92
[2,3,7,5,4,1,6]=>25
[2,3,7,5,4,6,1]=>25
[2,3,7,5,6,1,4]=>46
[2,3,7,5,6,4,1]=>46
[2,3,7,6,1,4,5]=>40
[2,3,7,6,1,5,4]=>168
[2,3,7,6,4,1,5]=>40
[2,3,7,6,4,5,1]=>40
[2,3,7,6,5,1,4]=>84
[2,3,7,6,5,4,1]=>84
[2,4,1,3,5,6,7]=>2
[2,4,1,3,5,7,6]=>23
[2,4,1,3,6,5,7]=>21
[2,4,1,3,6,7,5]=>64
[2,4,1,3,7,5,6]=>63
[2,4,1,3,7,6,5]=>346
[2,4,1,5,3,6,7]=>6
[2,4,1,5,3,7,6]=>93
[2,4,1,5,6,3,7]=>11
[2,4,1,5,6,7,3]=>17
[2,4,1,5,7,3,6]=>63
[2,4,1,5,7,6,3]=>103
[2,4,1,6,3,5,7]=>24
[2,4,1,6,3,7,5]=>133
[2,4,1,6,5,3,7]=>52
[2,4,1,6,5,7,3]=>86
[2,4,1,6,7,3,5]=>103
[2,4,1,6,7,5,3]=>183
[2,4,1,7,3,5,6]=>53
[2,4,1,7,3,6,5]=>378
[2,4,1,7,5,3,6]=>121
[2,4,1,7,5,6,3]=>204
[2,4,1,7,6,3,5]=>323
[2,4,1,7,6,5,3]=>609
[2,4,3,1,5,6,7]=>2
[2,4,3,1,5,7,6]=>28
[2,4,3,1,6,5,7]=>26
[2,4,3,1,6,7,5]=>77
[2,4,3,1,7,5,6]=>77
[2,4,3,1,7,6,5]=>463
[2,4,3,5,1,6,7]=>2
[2,4,3,5,1,7,6]=>30
[2,4,3,5,6,1,7]=>2
[2,4,3,5,6,7,1]=>2
[2,4,3,5,7,1,6]=>15
[2,4,3,5,7,6,1]=>15
[2,4,3,6,1,5,7]=>13
[2,4,3,6,1,7,5]=>64
[2,4,3,6,5,1,7]=>13
[2,4,3,6,5,7,1]=>13
[2,4,3,6,7,1,5]=>32
[2,4,3,6,7,5,1]=>32
[2,4,3,7,1,5,6]=>32
[2,4,3,7,1,6,5]=>242
[2,4,3,7,5,1,6]=>32
[2,4,3,7,5,6,1]=>32
[2,4,3,7,6,1,5]=>121
[2,4,3,7,6,5,1]=>121
[2,4,5,1,3,6,7]=>3
[2,4,5,1,3,7,6]=>41
[2,4,5,1,6,3,7]=>8
[2,4,5,1,6,7,3]=>14
[2,4,5,1,7,3,6]=>45
[2,4,5,1,7,6,3]=>91
[2,4,5,3,1,6,7]=>3
[2,4,5,3,1,7,6]=>52
[2,4,5,3,6,1,7]=>3
[2,4,5,3,6,7,1]=>3
[2,4,5,3,7,1,6]=>26
[2,4,5,3,7,6,1]=>26
[2,4,5,6,1,3,7]=>4
[2,4,5,6,1,7,3]=>10
[2,4,5,6,3,1,7]=>4
[2,4,5,6,3,7,1]=>4
[2,4,5,6,7,1,3]=>5
[2,4,5,6,7,3,1]=>5
[2,4,5,7,1,3,6]=>15
[2,4,5,7,1,6,3]=>38
[2,4,5,7,3,1,6]=>15
[2,4,5,7,3,6,1]=>15
[2,4,5,7,6,1,3]=>19
[2,4,5,7,6,3,1]=>19
[2,4,6,1,3,5,7]=>8
[2,4,6,1,3,7,5]=>54
[2,4,6,1,5,3,7]=>22
[2,4,6,1,5,7,3]=>39
[2,4,6,1,7,3,5]=>60
[2,4,6,1,7,5,3]=>124
[2,4,6,3,1,5,7]=>8
[2,4,6,3,1,7,5]=>68
[2,4,6,3,5,1,7]=>8
[2,4,6,3,5,7,1]=>8
[2,4,6,3,7,1,5]=>34
[2,4,6,3,7,5,1]=>34
[2,4,6,5,1,3,7]=>11
[2,4,6,5,1,7,3]=>28
[2,4,6,5,3,1,7]=>11
[2,4,6,5,3,7,1]=>11
[2,4,6,5,7,1,3]=>14
[2,4,6,5,7,3,1]=>14
[2,4,6,7,1,3,5]=>20
[2,4,6,7,1,5,3]=>52
[2,4,6,7,3,1,5]=>20
[2,4,6,7,3,5,1]=>20
[2,4,6,7,5,1,3]=>26
[2,4,6,7,5,3,1]=>26
[2,4,7,1,3,5,6]=>15
[2,4,7,1,3,6,5]=>118
[2,4,7,1,5,3,6]=>42
[2,4,7,1,5,6,3]=>75
[2,4,7,1,6,3,5]=>132
[2,4,7,1,6,5,3]=>276
[2,4,7,3,1,5,6]=>15
[2,4,7,3,1,6,5]=>148
[2,4,7,3,5,1,6]=>15
[2,4,7,3,5,6,1]=>15
[2,4,7,3,6,1,5]=>74
[2,4,7,3,6,5,1]=>74
[2,4,7,5,1,3,6]=>21
[2,4,7,5,1,6,3]=>54
[2,4,7,5,3,1,6]=>21
[2,4,7,5,3,6,1]=>21
[2,4,7,5,6,1,3]=>27
[2,4,7,5,6,3,1]=>27
[2,4,7,6,1,3,5]=>44
[2,4,7,6,1,5,3]=>116
[2,4,7,6,3,1,5]=>44
[2,4,7,6,3,5,1]=>44
[2,4,7,6,5,1,3]=>58
[2,4,7,6,5,3,1]=>58
[2,5,1,3,4,6,7]=>3
[2,5,1,3,4,7,6]=>38
[2,5,1,3,6,4,7]=>13
[2,5,1,3,6,7,4]=>32
[2,5,1,3,7,4,6]=>73
[2,5,1,3,7,6,4]=>220
[2,5,1,4,3,6,7]=>10
[2,5,1,4,3,7,6]=>213
[2,5,1,4,6,3,7]=>19
[2,5,1,4,6,7,3]=>30
[2,5,1,4,7,3,6]=>147
[2,5,1,4,7,6,3]=>249
[2,5,1,6,3,4,7]=>17
[2,5,1,6,3,7,4]=>57
[2,5,1,6,4,3,7]=>40
[2,5,1,6,4,7,3]=>69
[2,5,1,6,7,3,4]=>52
[2,5,1,6,7,4,3]=>101
[2,5,1,7,3,4,6]=>57
[2,5,1,7,3,6,4]=>204
[2,5,1,7,4,3,6]=>147
[2,5,1,7,4,6,3]=>261
[2,5,1,7,6,3,4]=>208
[2,5,1,7,6,4,3]=>430
[2,5,3,1,4,6,7]=>3
[2,5,3,1,4,7,6]=>45
[2,5,3,1,6,4,7]=>16
[2,5,3,1,6,7,4]=>38
[2,5,3,1,7,4,6]=>87
[2,5,3,1,7,6,4]=>300
[2,5,3,4,1,6,7]=>3
[2,5,3,4,1,7,6]=>52
[2,5,3,4,6,1,7]=>3
[2,5,3,4,6,7,1]=>3
[2,5,3,4,7,1,6]=>26
[2,5,3,4,7,6,1]=>26
[2,5,3,6,1,4,7]=>8
[2,5,3,6,1,7,4]=>30
[2,5,3,6,4,1,7]=>8
[2,5,3,6,4,7,1]=>8
[2,5,3,6,7,1,4]=>15
[2,5,3,6,7,4,1]=>15
[2,5,3,7,1,4,6]=>34
[2,5,3,7,1,6,4]=>148
[2,5,3,7,4,1,6]=>34
[2,5,3,7,4,6,1]=>34
[2,5,3,7,6,1,4]=>74
[2,5,3,7,6,4,1]=>74
[2,5,4,1,3,6,7]=>5
[2,5,4,1,3,7,6]=>107
[2,5,4,1,6,3,7]=>14
[2,5,4,1,6,7,3]=>25
[2,5,4,1,7,3,6]=>120
[2,5,4,1,7,6,3]=>252
[2,5,4,3,1,6,7]=>5
[2,5,4,3,1,7,6]=>134
[2,5,4,3,6,1,7]=>5
[2,5,4,3,6,7,1]=>5
[2,5,4,3,7,1,6]=>67
[2,5,4,3,7,6,1]=>67
[2,5,4,6,1,3,7]=>7
[2,5,4,6,1,7,3]=>18
[2,5,4,6,3,1,7]=>7
[2,5,4,6,3,7,1]=>7
[2,5,4,6,7,1,3]=>9
[2,5,4,6,7,3,1]=>9
[2,5,4,7,1,3,6]=>40
[2,5,4,7,1,6,3]=>106
[2,5,4,7,3,1,6]=>40
[2,5,4,7,3,6,1]=>40
[2,5,4,7,6,1,3]=>53
[2,5,4,7,6,3,1]=>53
[2,5,6,1,3,4,7]=>6
[2,5,6,1,3,7,4]=>24
[2,5,6,1,4,3,7]=>18
[2,5,6,1,4,7,3]=>33
[2,5,6,1,7,3,4]=>29
[2,5,6,1,7,4,3]=>64
[2,5,6,3,1,4,7]=>6
[2,5,6,3,1,7,4]=>30
[2,5,6,3,4,1,7]=>6
[2,5,6,3,4,7,1]=>6
[2,5,6,3,7,1,4]=>15
[2,5,6,3,7,4,1]=>15
[2,5,6,4,1,3,7]=>9
[2,5,6,4,1,7,3]=>24
[2,5,6,4,3,1,7]=>9
[2,5,6,4,3,7,1]=>9
[2,5,6,4,7,1,3]=>12
[2,5,6,4,7,3,1]=>12
[2,5,6,7,1,3,4]=>10
[2,5,6,7,1,4,3]=>28
[2,5,6,7,3,1,4]=>10
[2,5,6,7,3,4,1]=>10
[2,5,6,7,4,1,3]=>14
[2,5,6,7,4,3,1]=>14
[2,5,7,1,3,4,6]=>15
[2,5,7,1,3,6,4]=>61
[2,5,7,1,4,3,6]=>46
[2,5,7,1,4,6,3]=>85
[2,5,7,1,6,3,4]=>75
[2,5,7,1,6,4,3]=>168
[2,5,7,3,1,4,6]=>15
[2,5,7,3,1,6,4]=>76
[2,5,7,3,4,1,6]=>15
[2,5,7,3,4,6,1]=>15
[2,5,7,3,6,1,4]=>38
[2,5,7,3,6,4,1]=>38
[2,5,7,4,1,3,6]=>23
[2,5,7,4,1,6,3]=>62
[2,5,7,4,3,1,6]=>23
[2,5,7,4,3,6,1]=>23
[2,5,7,4,6,1,3]=>31
[2,5,7,4,6,3,1]=>31
[2,5,7,6,1,3,4]=>26
[2,5,7,6,1,4,3]=>74
[2,5,7,6,3,1,4]=>26
[2,5,7,6,3,4,1]=>26
[2,5,7,6,4,1,3]=>37
[2,5,7,6,4,3,1]=>37
[2,6,1,3,4,5,7]=>4
[2,6,1,3,4,7,5]=>22
[2,6,1,3,5,4,7]=>18
[2,6,1,3,5,7,4]=>45
[2,6,1,3,7,4,5]=>43
[2,6,1,3,7,5,4]=>131
[2,6,1,4,3,5,7]=>14
[2,6,1,4,3,7,5]=>127
[2,6,1,4,5,3,7]=>27
[2,6,1,4,5,7,3]=>43
[2,6,1,4,7,3,5]=>88
[2,6,1,4,7,5,3]=>150
[2,6,1,5,3,4,7]=>25
[2,6,1,5,3,7,4]=>86
[2,6,1,5,4,3,7]=>61
[2,6,1,5,4,7,3]=>107
[2,6,1,5,7,3,4]=>81
[2,6,1,5,7,4,3]=>161
[2,6,1,7,3,4,5]=>36
[2,6,1,7,3,5,4]=>132
[2,6,1,7,4,3,5]=>96
[2,6,1,7,4,5,3]=>173
[2,6,1,7,5,3,4]=>141
[2,6,1,7,5,4,3]=>300
[2,6,3,1,4,5,7]=>4
[2,6,3,1,4,7,5]=>26
[2,6,3,1,5,4,7]=>22
[2,6,3,1,5,7,4]=>53
[2,6,3,1,7,4,5]=>51
[2,6,3,1,7,5,4]=>178
[2,6,3,4,1,5,7]=>4
[2,6,3,4,1,7,5]=>30
[2,6,3,4,5,1,7]=>4
[2,6,3,4,5,7,1]=>4
[2,6,3,4,7,1,5]=>15
[2,6,3,4,7,5,1]=>15
[2,6,3,5,1,4,7]=>11
[2,6,3,5,1,7,4]=>42
[2,6,3,5,4,1,7]=>11
[2,6,3,5,4,7,1]=>11
[2,6,3,5,7,1,4]=>21
[2,6,3,5,7,4,1]=>21
[2,6,3,7,1,4,5]=>20
[2,6,3,7,1,5,4]=>88
[2,6,3,7,4,1,5]=>20
[2,6,3,7,4,5,1]=>20
[2,6,3,7,5,1,4]=>44
[2,6,3,7,5,4,1]=>44
[2,6,4,1,3,5,7]=>7
[2,6,4,1,3,7,5]=>64
[2,6,4,1,5,3,7]=>20
[2,6,4,1,5,7,3]=>36
[2,6,4,1,7,3,5]=>72
[2,6,4,1,7,5,3]=>152
[2,6,4,3,1,5,7]=>7
[2,6,4,3,1,7,5]=>80
[2,6,4,3,5,1,7]=>7
[2,6,4,3,5,7,1]=>7
[2,6,4,3,7,1,5]=>40
[2,6,4,3,7,5,1]=>40
[2,6,4,5,1,3,7]=>10
[2,6,4,5,1,7,3]=>26
[2,6,4,5,3,1,7]=>10
[2,6,4,5,3,7,1]=>10
[2,6,4,5,7,1,3]=>13
[2,6,4,5,7,3,1]=>13
[2,6,4,7,1,3,5]=>24
[2,6,4,7,1,5,3]=>64
[2,6,4,7,3,1,5]=>24
[2,6,4,7,3,5,1]=>24
[2,6,4,7,5,1,3]=>32
[2,6,4,7,5,3,1]=>32
[2,6,5,1,3,4,7]=>9
[2,6,5,1,3,7,4]=>37
[2,6,5,1,4,3,7]=>28
[2,6,5,1,4,7,3]=>52
[2,6,5,1,7,3,4]=>46
[2,6,5,1,7,4,3]=>104
[2,6,5,3,1,4,7]=>9
[2,6,5,3,1,7,4]=>46
[2,6,5,3,4,1,7]=>9
[2,6,5,3,4,7,1]=>9
[2,6,5,3,7,1,4]=>23
[2,6,5,3,7,4,1]=>23
[2,6,5,4,1,3,7]=>14
[2,6,5,4,1,7,3]=>38
[2,6,5,4,3,1,7]=>14
[2,6,5,4,3,7,1]=>14
[2,6,5,4,7,1,3]=>19
[2,6,5,4,7,3,1]=>19
[2,6,5,7,1,3,4]=>16
[2,6,5,7,1,4,3]=>46
[2,6,5,7,3,1,4]=>16
[2,6,5,7,3,4,1]=>16
[2,6,5,7,4,1,3]=>23
[2,6,5,7,4,3,1]=>23
[2,6,7,1,3,4,5]=>10
[2,6,7,1,3,5,4]=>42
[2,6,7,1,4,3,5]=>32
[2,6,7,1,4,5,3]=>60
[2,6,7,1,5,3,4]=>54
[2,6,7,1,5,4,3]=>125
[2,6,7,3,1,4,5]=>10
[2,6,7,3,1,5,4]=>52
[2,6,7,3,4,1,5]=>10
[2,6,7,3,4,5,1]=>10
[2,6,7,3,5,1,4]=>26
[2,6,7,3,5,4,1]=>26
[2,6,7,4,1,3,5]=>16
[2,6,7,4,1,5,3]=>44
[2,6,7,4,3,1,5]=>16
[2,6,7,4,3,5,1]=>16
[2,6,7,4,5,1,3]=>22
[2,6,7,4,5,3,1]=>22
[2,6,7,5,1,3,4]=>19
[2,6,7,5,1,4,3]=>56
[2,6,7,5,3,1,4]=>19
[2,6,7,5,3,4,1]=>19
[2,6,7,5,4,1,3]=>28
[2,6,7,5,4,3,1]=>28
[2,7,1,3,4,5,6]=>5
[2,7,1,3,4,6,5]=>28
[2,7,1,3,5,4,6]=>23
[2,7,1,3,5,6,4]=>58
[2,7,1,3,6,4,5]=>56
[2,7,1,3,6,5,4]=>173
[2,7,1,4,3,5,6]=>18
[2,7,1,4,3,6,5]=>168
[2,7,1,4,5,3,6]=>35
[2,7,1,4,5,6,3]=>56
[2,7,1,4,6,3,5]=>117
[2,7,1,4,6,5,3]=>201
[2,7,1,5,3,4,6]=>33
[2,7,1,5,3,6,4]=>115
[2,7,1,5,4,3,6]=>82
[2,7,1,5,4,6,3]=>145
[2,7,1,5,6,3,4]=>110
[2,7,1,5,6,4,3]=>221
[2,7,1,6,3,4,5]=>49
[2,7,1,6,3,5,4]=>183
[2,7,1,6,4,3,5]=>134
[2,7,1,6,4,5,3]=>244
[2,7,1,6,5,3,4]=>201
[2,7,1,6,5,4,3]=>435
[2,7,3,1,4,5,6]=>5
[2,7,3,1,4,6,5]=>33
[2,7,3,1,5,4,6]=>28
[2,7,3,1,5,6,4]=>68
[2,7,3,1,6,4,5]=>66
[2,7,3,1,6,5,4]=>234
[2,7,3,4,1,5,6]=>5
[2,7,3,4,1,6,5]=>38
[2,7,3,4,5,1,6]=>5
[2,7,3,4,5,6,1]=>5
[2,7,3,4,6,1,5]=>19
[2,7,3,4,6,5,1]=>19
[2,7,3,5,1,4,6]=>14
[2,7,3,5,1,6,4]=>54
[2,7,3,5,4,1,6]=>14
[2,7,3,5,4,6,1]=>14
[2,7,3,5,6,1,4]=>27
[2,7,3,5,6,4,1]=>27
[2,7,3,6,1,4,5]=>26
[2,7,3,6,1,5,4]=>116
[2,7,3,6,4,1,5]=>26
[2,7,3,6,4,5,1]=>26
[2,7,3,6,5,1,4]=>58
[2,7,3,6,5,4,1]=>58
[2,7,4,1,3,5,6]=>9
[2,7,4,1,3,6,5]=>85
[2,7,4,1,5,3,6]=>26
[2,7,4,1,5,6,3]=>47
[2,7,4,1,6,3,5]=>96
[2,7,4,1,6,5,3]=>204
[2,7,4,3,1,5,6]=>9
[2,7,4,3,1,6,5]=>106
[2,7,4,3,5,1,6]=>9
[2,7,4,3,5,6,1]=>9
[2,7,4,3,6,1,5]=>53
[2,7,4,3,6,5,1]=>53
[2,7,4,5,1,3,6]=>13
[2,7,4,5,1,6,3]=>34
[2,7,4,5,3,1,6]=>13
[2,7,4,5,3,6,1]=>13
[2,7,4,5,6,1,3]=>17
[2,7,4,5,6,3,1]=>17
[2,7,4,6,1,3,5]=>32
[2,7,4,6,1,5,3]=>86
[2,7,4,6,3,1,5]=>32
[2,7,4,6,3,5,1]=>32
[2,7,4,6,5,1,3]=>43
[2,7,4,6,5,3,1]=>43
[2,7,5,1,3,4,6]=>12
[2,7,5,1,3,6,4]=>50
[2,7,5,1,4,3,6]=>38
[2,7,5,1,4,6,3]=>71
[2,7,5,1,6,3,4]=>63
[2,7,5,1,6,4,3]=>144
[2,7,5,3,1,4,6]=>12
[2,7,5,3,1,6,4]=>62
[2,7,5,3,4,1,6]=>12
[2,7,5,3,4,6,1]=>12
[2,7,5,3,6,1,4]=>31
[2,7,5,3,6,4,1]=>31
[2,7,5,4,1,3,6]=>19
[2,7,5,4,1,6,3]=>52
[2,7,5,4,3,1,6]=>19
[2,7,5,4,3,6,1]=>19
[2,7,5,4,6,1,3]=>26
[2,7,5,4,6,3,1]=>26
[2,7,5,6,1,3,4]=>22
[2,7,5,6,1,4,3]=>64
[2,7,5,6,3,1,4]=>22
[2,7,5,6,3,4,1]=>22
[2,7,5,6,4,1,3]=>32
[2,7,5,6,4,3,1]=>32
[2,7,6,1,3,4,5]=>14
[2,7,6,1,3,5,4]=>60
[2,7,6,1,4,3,5]=>46
[2,7,6,1,4,5,3]=>87
[2,7,6,1,5,3,4]=>79
[2,7,6,1,5,4,3]=>186
[2,7,6,3,1,4,5]=>14
[2,7,6,3,1,5,4]=>74
[2,7,6,3,4,1,5]=>14
[2,7,6,3,4,5,1]=>14
[2,7,6,3,5,1,4]=>37
[2,7,6,3,5,4,1]=>37
[2,7,6,4,1,3,5]=>23
[2,7,6,4,1,5,3]=>64
[2,7,6,4,3,1,5]=>23
[2,7,6,4,3,5,1]=>23
[2,7,6,4,5,1,3]=>32
[2,7,6,4,5,3,1]=>32
[2,7,6,5,1,3,4]=>28
[2,7,6,5,1,4,3]=>84
[2,7,6,5,3,1,4]=>28
[2,7,6,5,3,4,1]=>28
[2,7,6,5,4,1,3]=>42
[2,7,6,5,4,3,1]=>42
[3,1,2,4,5,6,7]=>1
[3,1,2,4,5,7,6]=>8
[3,1,2,4,6,5,7]=>7
[3,1,2,4,6,7,5]=>22
[3,1,2,4,7,5,6]=>22
[3,1,2,4,7,6,5]=>93
[3,1,2,5,4,6,7]=>6
[3,1,2,5,4,7,6]=>92
[3,1,2,5,6,4,7]=>15
[3,1,2,5,6,7,4]=>29
[3,1,2,5,7,4,6]=>71
[3,1,2,5,7,6,4]=>153
[3,1,2,6,4,5,7]=>15
[3,1,2,6,4,7,5]=>71
[3,1,2,6,5,4,7]=>56
[3,1,2,6,5,7,4]=>124
[3,1,2,6,7,4,5]=>87
[3,1,2,6,7,5,4]=>235
[3,1,2,7,4,5,6]=>29
[3,1,2,7,4,6,5]=>154
[3,1,2,7,5,4,6]=>125
[3,1,2,7,5,6,4]=>287
[3,1,2,7,6,4,5]=>232
[3,1,2,7,6,5,4]=>709
[3,1,4,2,5,6,7]=>2
[3,1,4,2,5,7,6]=>23
[3,1,4,2,6,5,7]=>21
[3,1,4,2,6,7,5]=>63
[3,1,4,2,7,5,6]=>64
[3,1,4,2,7,6,5]=>346
[3,1,4,5,2,6,7]=>3
[3,1,4,5,2,7,6]=>38
[3,1,4,5,6,2,7]=>4
[3,1,4,5,6,7,2]=>5
[3,1,4,5,7,2,6]=>22
[3,1,4,5,7,6,2]=>28
[3,1,4,6,2,5,7]=>13
[3,1,4,6,2,7,5]=>73
[3,1,4,6,5,2,7]=>18
[3,1,4,6,5,7,2]=>23
[3,1,4,6,7,2,5]=>43
[3,1,4,6,7,5,2]=>56
[3,1,4,7,2,5,6]=>32
[3,1,4,7,2,6,5]=>220
[3,1,4,7,5,2,6]=>45
[3,1,4,7,5,6,2]=>58
[3,1,4,7,6,2,5]=>131
[3,1,4,7,6,5,2]=>173
[3,1,5,2,4,6,7]=>6
[3,1,5,2,4,7,6]=>93
[3,1,5,2,6,4,7]=>24
[3,1,5,2,6,7,4]=>53
[3,1,5,2,7,4,6]=>133
[3,1,5,2,7,6,4]=>378
[3,1,5,4,2,6,7]=>10
[3,1,5,4,2,7,6]=>213
[3,1,5,4,6,2,7]=>14
[3,1,5,4,6,7,2]=>18
[3,1,5,4,7,2,6]=>127
[3,1,5,4,7,6,2]=>168
[3,1,5,6,2,4,7]=>17
[3,1,5,6,2,7,4]=>57
[3,1,5,6,4,2,7]=>25
[3,1,5,6,4,7,2]=>33
[3,1,5,6,7,2,4]=>36
[3,1,5,6,7,4,2]=>49
[3,1,5,7,2,4,6]=>57
[3,1,5,7,2,6,4]=>204
[3,1,5,7,4,2,6]=>86
[3,1,5,7,4,6,2]=>115
[3,1,5,7,6,2,4]=>132
[3,1,5,7,6,4,2]=>183
[3,1,6,2,4,5,7]=>11
[3,1,6,2,4,7,5]=>63
[3,1,6,2,5,4,7]=>52
[3,1,6,2,5,7,4]=>121
[3,1,6,2,7,4,5]=>103
[3,1,6,2,7,5,4]=>323
[3,1,6,4,2,5,7]=>19
[3,1,6,4,2,7,5]=>147
[3,1,6,4,5,2,7]=>27
[3,1,6,4,5,7,2]=>35
[3,1,6,4,7,2,5]=>88
[3,1,6,4,7,5,2]=>117
[3,1,6,5,2,4,7]=>40
[3,1,6,5,2,7,4]=>147
[3,1,6,5,4,2,7]=>61
[3,1,6,5,4,7,2]=>82
[3,1,6,5,7,2,4]=>96
[3,1,6,5,7,4,2]=>134
[3,1,6,7,2,4,5]=>52
[3,1,6,7,2,5,4]=>208
[3,1,6,7,4,2,5]=>81
[3,1,6,7,4,5,2]=>110
[3,1,6,7,5,2,4]=>141
[3,1,6,7,5,4,2]=>201
[3,1,7,2,4,5,6]=>17
[3,1,7,2,4,6,5]=>103
[3,1,7,2,5,4,6]=>86
[3,1,7,2,5,6,4]=>204
[3,1,7,2,6,4,5]=>183
[3,1,7,2,6,5,4]=>609
[3,1,7,4,2,5,6]=>30
[3,1,7,4,2,6,5]=>249
[3,1,7,4,5,2,6]=>43
[3,1,7,4,5,6,2]=>56
[3,1,7,4,6,2,5]=>150
[3,1,7,4,6,5,2]=>201
[3,1,7,5,2,4,6]=>69
[3,1,7,5,2,6,4]=>261
[3,1,7,5,4,2,6]=>107
[3,1,7,5,4,6,2]=>145
[3,1,7,5,6,2,4]=>173
[3,1,7,5,6,4,2]=>244
[3,1,7,6,2,4,5]=>101
[3,1,7,6,2,5,4]=>430
[3,1,7,6,4,2,5]=>161
[3,1,7,6,4,5,2]=>221
[3,1,7,6,5,2,4]=>300
[3,1,7,6,5,4,2]=>435
[3,2,1,4,5,6,7]=>1
[3,2,1,4,5,7,6]=>10
[3,2,1,4,6,5,7]=>9
[3,2,1,4,6,7,5]=>29
[3,2,1,4,7,5,6]=>29
[3,2,1,4,7,6,5]=>131
[3,2,1,5,4,6,7]=>8
[3,2,1,5,4,7,6]=>130
[3,2,1,5,6,4,7]=>20
[3,2,1,5,6,7,4]=>38
[3,2,1,5,7,4,6]=>102
[3,2,1,5,7,6,4]=>222
[3,2,1,6,4,5,7]=>20
[3,2,1,6,4,7,5]=>102
[3,2,1,6,5,4,7]=>82
[3,2,1,6,5,7,4]=>184
[3,2,1,6,7,4,5]=>126
[3,2,1,6,7,5,4]=>345
[3,2,1,7,4,5,6]=>38
[3,2,1,7,4,6,5]=>222
[3,2,1,7,5,4,6]=>184
[3,2,1,7,5,6,4]=>428
[3,2,1,7,6,4,5]=>345
[3,2,1,7,6,5,4]=>1101
[3,2,4,1,5,6,7]=>1
[3,2,4,1,5,7,6]=>11
[3,2,4,1,6,5,7]=>10
[3,2,4,1,6,7,5]=>31
[3,2,4,1,7,5,6]=>31
[3,2,4,1,7,6,5]=>165
[3,2,4,5,1,6,7]=>1
[3,2,4,5,1,7,6]=>12
[3,2,4,5,6,1,7]=>1
[3,2,4,5,6,7,1]=>1
[3,2,4,5,7,1,6]=>6
[3,2,4,5,7,6,1]=>6
[3,2,4,6,1,5,7]=>5
[3,2,4,6,1,7,5]=>26
[3,2,4,6,5,1,7]=>5
[3,2,4,6,5,7,1]=>5
[3,2,4,6,7,1,5]=>13
[3,2,4,6,7,5,1]=>13
[3,2,4,7,1,5,6]=>13
[3,2,4,7,1,6,5]=>84
[3,2,4,7,5,1,6]=>13
[3,2,4,7,5,6,1]=>13
[3,2,4,7,6,1,5]=>42
[3,2,4,7,6,5,1]=>42
[3,2,5,1,4,6,7]=>4
[3,2,5,1,4,7,6]=>70
[3,2,5,1,6,4,7]=>16
[3,2,5,1,6,7,4]=>34
[3,2,5,1,7,4,6]=>87
[3,2,5,1,7,6,4]=>233
[3,2,5,4,1,6,7]=>4
[3,2,5,4,1,7,6]=>82
[3,2,5,4,6,1,7]=>4
[3,2,5,4,6,7,1]=>4
[3,2,5,4,7,1,6]=>41
[3,2,5,4,7,6,1]=>41
[3,2,5,6,1,4,7]=>8
[3,2,5,6,1,7,4]=>26
[3,2,5,6,4,1,7]=>8
[3,2,5,6,4,7,1]=>8
[3,2,5,6,7,1,4]=>13
[3,2,5,6,7,4,1]=>13
[3,2,5,7,1,4,6]=>29
[3,2,5,7,1,6,4]=>102
[3,2,5,7,4,1,6]=>29
[3,2,5,7,4,6,1]=>29
[3,2,5,7,6,1,4]=>51
[3,2,5,7,6,4,1]=>51
[3,2,6,1,4,5,7]=>8
[3,2,6,1,4,7,5]=>50
[3,2,6,1,5,4,7]=>42
[3,2,6,1,5,7,4]=>97
[3,2,6,1,7,4,5]=>79
[3,2,6,1,7,5,4]=>251
[3,2,6,4,1,5,7]=>8
[3,2,6,4,1,7,5]=>58
[3,2,6,4,5,1,7]=>8
[3,2,6,4,5,7,1]=>8
[3,2,6,4,7,1,5]=>29
[3,2,6,4,7,5,1]=>29
[3,2,6,5,1,4,7]=>21
[3,2,6,5,1,7,4]=>76
[3,2,6,5,4,1,7]=>21
[3,2,6,5,4,7,1]=>21
[3,2,6,5,7,1,4]=>38
[3,2,6,5,7,4,1]=>38
[3,2,6,7,1,4,5]=>29
[3,2,6,7,1,5,4]=>120
[3,2,6,7,4,1,5]=>29
[3,2,6,7,4,5,1]=>29
[3,2,6,7,5,1,4]=>60
[3,2,6,7,5,4,1]=>60
[3,2,7,1,4,5,6]=>13
[3,2,7,1,4,6,5]=>89
[3,2,7,1,5,4,6]=>76
[3,2,7,1,5,6,4]=>180
[3,2,7,1,6,4,5]=>158
[3,2,7,1,6,5,4]=>549
[3,2,7,4,1,5,6]=>13
[3,2,7,4,1,6,5]=>102
[3,2,7,4,5,1,6]=>13
[3,2,7,4,5,6,1]=>13
[3,2,7,4,6,1,5]=>51
[3,2,7,4,6,5,1]=>51
[3,2,7,5,1,4,6]=>38
[3,2,7,5,1,6,4]=>142
[3,2,7,5,4,1,6]=>38
[3,2,7,5,4,6,1]=>38
[3,2,7,5,6,1,4]=>71
[3,2,7,5,6,4,1]=>71
[3,2,7,6,1,4,5]=>60
[3,2,7,6,1,5,4]=>270
[3,2,7,6,4,1,5]=>60
[3,2,7,6,4,5,1]=>60
[3,2,7,6,5,1,4]=>135
[3,2,7,6,5,4,1]=>135
[3,4,1,2,5,6,7]=>1
[3,4,1,2,5,7,6]=>10
[3,4,1,2,6,5,7]=>9
[3,4,1,2,6,7,5]=>27
[3,4,1,2,7,5,6]=>27
[3,4,1,2,7,6,5]=>148
[3,4,1,5,2,6,7]=>2
[3,4,1,5,2,7,6]=>29
[3,4,1,5,6,2,7]=>3
[3,4,1,5,6,7,2]=>4
[3,4,1,5,7,2,6]=>18
[3,4,1,5,7,6,2]=>25
[3,4,1,6,2,5,7]=>9
[3,4,1,6,2,7,5]=>48
[3,4,1,6,5,2,7]=>15
[3,4,1,6,5,7,2]=>21
[3,4,1,6,7,2,5]=>33
[3,4,1,6,7,5,2]=>48
[3,4,1,7,2,5,6]=>21
[3,4,1,7,2,6,5]=>145
[3,4,1,7,5,2,6]=>36
[3,4,1,7,5,6,2]=>51
[3,4,1,7,6,2,5]=>109
[3,4,1,7,6,5,2]=>165
[3,4,2,1,5,6,7]=>1
[3,4,2,1,5,7,6]=>13
[3,4,2,1,6,5,7]=>12
[3,4,2,1,6,7,5]=>36
[3,4,2,1,7,5,6]=>36
[3,4,2,1,7,6,5]=>213
[3,4,2,5,1,6,7]=>1
[3,4,2,5,1,7,6]=>14
[3,4,2,5,6,1,7]=>1
[3,4,2,5,6,7,1]=>1
[3,4,2,5,7,1,6]=>7
[3,4,2,5,7,6,1]=>7
[3,4,2,6,1,5,7]=>6
[3,4,2,6,1,7,5]=>30
[3,4,2,6,5,1,7]=>6
[3,4,2,6,5,7,1]=>6
[3,4,2,6,7,1,5]=>15
[3,4,2,6,7,5,1]=>15
[3,4,2,7,1,5,6]=>15
[3,4,2,7,1,6,5]=>112
[3,4,2,7,5,1,6]=>15
[3,4,2,7,5,6,1]=>15
[3,4,2,7,6,1,5]=>56
[3,4,2,7,6,5,1]=>56
[3,4,5,1,2,6,7]=>1
[3,4,5,1,2,7,6]=>12
[3,4,5,1,6,2,7]=>2
[3,4,5,1,6,7,2]=>3
[3,4,5,1,7,2,6]=>12
[3,4,5,1,7,6,2]=>20
[3,4,5,2,1,6,7]=>1
[3,4,5,2,1,7,6]=>16
[3,4,5,2,6,1,7]=>1
[3,4,5,2,6,7,1]=>1
[3,4,5,2,7,1,6]=>8
[3,4,5,2,7,6,1]=>8
[3,4,5,6,1,2,7]=>1
[3,4,5,6,1,7,2]=>2
[3,4,5,6,2,1,7]=>1
[3,4,5,6,2,7,1]=>1
[3,4,5,6,7,1,2]=>1
[3,4,5,6,7,2,1]=>1
[3,4,5,7,1,2,6]=>4
[3,4,5,7,1,6,2]=>8
[3,4,5,7,2,1,6]=>4
[3,4,5,7,2,6,1]=>4
[3,4,5,7,6,1,2]=>4
[3,4,5,7,6,2,1]=>4
[3,4,6,1,2,5,7]=>3
[3,4,6,1,2,7,5]=>18
[3,4,6,1,5,2,7]=>6
[3,4,6,1,5,7,2]=>9
[3,4,6,1,7,2,5]=>18
[3,4,6,1,7,5,2]=>30
[3,4,6,2,1,5,7]=>3
[3,4,6,2,1,7,5]=>24
[3,4,6,2,5,1,7]=>3
[3,4,6,2,5,7,1]=>3
[3,4,6,2,7,1,5]=>12
[3,4,6,2,7,5,1]=>12
[3,4,6,5,1,2,7]=>3
[3,4,6,5,1,7,2]=>6
[3,4,6,5,2,1,7]=>3
[3,4,6,5,2,7,1]=>3
[3,4,6,5,7,1,2]=>3
[3,4,6,5,7,2,1]=>3
[3,4,6,7,1,2,5]=>6
[3,4,6,7,1,5,2]=>12
[3,4,6,7,2,1,5]=>6
[3,4,6,7,2,5,1]=>6
[3,4,6,7,5,1,2]=>6
[3,4,6,7,5,2,1]=>6
[3,4,7,1,2,5,6]=>6
[3,4,7,1,2,6,5]=>42
[3,4,7,1,5,2,6]=>12
[3,4,7,1,5,6,2]=>18
[3,4,7,1,6,2,5]=>42
[3,4,7,1,6,5,2]=>70
[3,4,7,2,1,5,6]=>6
[3,4,7,2,1,6,5]=>56
[3,4,7,2,5,1,6]=>6
[3,4,7,2,5,6,1]=>6
[3,4,7,2,6,1,5]=>28
[3,4,7,2,6,5,1]=>28
[3,4,7,5,1,2,6]=>6
[3,4,7,5,1,6,2]=>12
[3,4,7,5,2,1,6]=>6
[3,4,7,5,2,6,1]=>6
[3,4,7,5,6,1,2]=>6
[3,4,7,5,6,2,1]=>6
[3,4,7,6,1,2,5]=>14
[3,4,7,6,1,5,2]=>28
[3,4,7,6,2,1,5]=>14
[3,4,7,6,2,5,1]=>14
[3,4,7,6,5,1,2]=>14
[3,4,7,6,5,2,1]=>14
[3,5,1,2,4,6,7]=>2
[3,5,1,2,4,7,6]=>29
[3,5,1,2,6,4,7]=>9
[3,5,1,2,6,7,4]=>21
[3,5,1,2,7,4,6]=>48
[3,5,1,2,7,6,4]=>145
[3,5,1,4,2,6,7]=>4
[3,5,1,4,2,7,6]=>89
[3,5,1,4,6,2,7]=>6
[3,5,1,4,6,7,2]=>8
[3,5,1,4,7,2,6]=>55
[3,5,1,4,7,6,2]=>76
[3,5,1,6,2,4,7]=>9
[3,5,1,6,2,7,4]=>32
[3,5,1,6,4,2,7]=>15
[3,5,1,6,4,7,2]=>21
[3,5,1,6,7,2,4]=>23
[3,5,1,6,7,4,2]=>34
[3,5,1,7,2,4,6]=>32
[3,5,1,7,2,6,4]=>121
[3,5,1,7,4,2,6]=>56
[3,5,1,7,4,6,2]=>80
[3,5,1,7,6,2,4]=>96
[3,5,1,7,6,4,2]=>148
[3,5,2,1,4,6,7]=>2
[3,5,2,1,4,7,6]=>37
[3,5,2,1,6,4,7]=>12
[3,5,2,1,6,7,4]=>28
[3,5,2,1,7,4,6]=>64
[3,5,2,1,7,6,4]=>213
[3,5,2,4,1,6,7]=>2
[3,5,2,4,1,7,6]=>42
[3,5,2,4,6,1,7]=>2
[3,5,2,4,6,7,1]=>2
[3,5,2,4,7,1,6]=>21
[3,5,2,4,7,6,1]=>21
[3,5,2,6,1,4,7]=>6
[3,5,2,6,1,7,4]=>22
[3,5,2,6,4,1,7]=>6
[3,5,2,6,4,7,1]=>6
[3,5,2,6,7,1,4]=>11
[3,5,2,6,7,4,1]=>11
[3,5,2,7,1,4,6]=>24
[3,5,2,7,1,6,4]=>104
[3,5,2,7,4,1,6]=>24
[3,5,2,7,4,6,1]=>24
[3,5,2,7,6,1,4]=>52
[3,5,2,7,6,4,1]=>52
[3,5,4,1,2,6,7]=>2
[3,5,4,1,2,7,6]=>39
[3,5,4,1,6,2,7]=>4
[3,5,4,1,6,7,2]=>6
[3,5,4,1,7,2,6]=>39
[3,5,4,1,7,6,2]=>65
[3,5,4,2,1,6,7]=>2
[3,5,4,2,1,7,6]=>52
[3,5,4,2,6,1,7]=>2
[3,5,4,2,6,7,1]=>2
[3,5,4,2,7,1,6]=>26
[3,5,4,2,7,6,1]=>26
[3,5,4,6,1,2,7]=>2
[3,5,4,6,1,7,2]=>4
[3,5,4,6,2,1,7]=>2
[3,5,4,6,2,7,1]=>2
[3,5,4,6,7,1,2]=>2
[3,5,4,6,7,2,1]=>2
[3,5,4,7,1,2,6]=>13
[3,5,4,7,1,6,2]=>26
[3,5,4,7,2,1,6]=>13
[3,5,4,7,2,6,1]=>13
[3,5,4,7,6,1,2]=>13
[3,5,4,7,6,2,1]=>13
[3,5,6,1,2,4,7]=>3
[3,5,6,1,2,7,4]=>12
[3,5,6,1,4,2,7]=>6
[3,5,6,1,4,7,2]=>9
[3,5,6,1,7,2,4]=>12
[3,5,6,1,7,4,2]=>20
[3,5,6,2,1,4,7]=>3
[3,5,6,2,1,7,4]=>16
[3,5,6,2,4,1,7]=>3
[3,5,6,2,4,7,1]=>3
[3,5,6,2,7,1,4]=>8
[3,5,6,2,7,4,1]=>8
[3,5,6,4,1,2,7]=>3
[3,5,6,4,1,7,2]=>6
[3,5,6,4,2,1,7]=>3
[3,5,6,4,2,7,1]=>3
[3,5,6,4,7,1,2]=>3
[3,5,6,4,7,2,1]=>3
[3,5,6,7,1,2,4]=>4
[3,5,6,7,1,4,2]=>8
[3,5,6,7,2,1,4]=>4
[3,5,6,7,2,4,1]=>4
[3,5,6,7,4,1,2]=>4
[3,5,6,7,4,2,1]=>4
[3,5,7,1,2,4,6]=>8
[3,5,7,1,2,6,4]=>33
[3,5,7,1,4,2,6]=>16
[3,5,7,1,4,6,2]=>24
[3,5,7,1,6,2,4]=>33
[3,5,7,1,6,4,2]=>55
[3,5,7,2,1,4,6]=>8
[3,5,7,2,1,6,4]=>44
[3,5,7,2,4,1,6]=>8
[3,5,7,2,4,6,1]=>8
[3,5,7,2,6,1,4]=>22
[3,5,7,2,6,4,1]=>22
[3,5,7,4,1,2,6]=>8
[3,5,7,4,1,6,2]=>16
[3,5,7,4,2,1,6]=>8
[3,5,7,4,2,6,1]=>8
[3,5,7,4,6,1,2]=>8
[3,5,7,4,6,2,1]=>8
[3,5,7,6,1,2,4]=>11
[3,5,7,6,1,4,2]=>22
[3,5,7,6,2,1,4]=>11
[3,5,7,6,2,4,1]=>11
[3,5,7,6,4,1,2]=>11
[3,5,7,6,4,2,1]=>11
[3,6,1,2,4,5,7]=>3
[3,6,1,2,4,7,5]=>18
[3,6,1,2,5,4,7]=>15
[3,6,1,2,5,7,4]=>36
[3,6,1,2,7,4,5]=>33
[3,6,1,2,7,5,4]=>109
[3,6,1,4,2,5,7]=>6
[3,6,1,4,2,7,5]=>55
[3,6,1,4,5,2,7]=>9
[3,6,1,4,5,7,2]=>12
[3,6,1,4,7,2,5]=>34
[3,6,1,4,7,5,2]=>47
[3,6,1,5,2,4,7]=>15
[3,6,1,5,2,7,4]=>56
[3,6,1,5,4,2,7]=>25
[3,6,1,5,4,7,2]=>35
[3,6,1,5,7,2,4]=>40
[3,6,1,5,7,4,2]=>59
[3,6,1,7,2,4,5]=>23
[3,6,1,7,2,5,4]=>96
[3,6,1,7,4,2,5]=>40
[3,6,1,7,4,5,2]=>57
[3,6,1,7,5,2,4]=>75
[3,6,1,7,5,4,2]=>115
[3,6,2,1,4,5,7]=>3
[3,6,2,1,4,7,5]=>23
[3,6,2,1,5,4,7]=>20
[3,6,2,1,5,7,4]=>48
[3,6,2,1,7,4,5]=>44
[3,6,2,1,7,5,4]=>160
[3,6,2,4,1,5,7]=>3
[3,6,2,4,1,7,5]=>26
[3,6,2,4,5,1,7]=>3
[3,6,2,4,5,7,1]=>3
[3,6,2,4,7,1,5]=>13
[3,6,2,4,7,5,1]=>13
[3,6,2,5,1,4,7]=>10
[3,6,2,5,1,7,4]=>38
[3,6,2,5,4,1,7]=>10
[3,6,2,5,4,7,1]=>10
[3,6,2,5,7,1,4]=>19
[3,6,2,5,7,4,1]=>19
[3,6,2,7,1,4,5]=>17
[3,6,2,7,1,5,4]=>80
[3,6,2,7,4,1,5]=>17
[3,6,2,7,4,5,1]=>17
[3,6,2,7,5,1,4]=>40
[3,6,2,7,5,4,1]=>40
[3,6,4,1,2,5,7]=>3
[3,6,4,1,2,7,5]=>24
[3,6,4,1,5,2,7]=>6
[3,6,4,1,5,7,2]=>9
[3,6,4,1,7,2,5]=>24
[3,6,4,1,7,5,2]=>40
[3,6,4,2,1,5,7]=>3
[3,6,4,2,1,7,5]=>32
[3,6,4,2,5,1,7]=>3
[3,6,4,2,5,7,1]=>3
[3,6,4,2,7,1,5]=>16
[3,6,4,2,7,5,1]=>16
[3,6,4,5,1,2,7]=>3
[3,6,4,5,1,7,2]=>6
[3,6,4,5,2,1,7]=>3
[3,6,4,5,2,7,1]=>3
[3,6,4,5,7,1,2]=>3
[3,6,4,5,7,2,1]=>3
[3,6,4,7,1,2,5]=>8
[3,6,4,7,1,5,2]=>16
[3,6,4,7,2,1,5]=>8
[3,6,4,7,2,5,1]=>8
[3,6,4,7,5,1,2]=>8
[3,6,4,7,5,2,1]=>8
[3,6,5,1,2,4,7]=>5
[3,6,5,1,2,7,4]=>21
[3,6,5,1,4,2,7]=>10
[3,6,5,1,4,7,2]=>15
[3,6,5,1,7,2,4]=>21
[3,6,5,1,7,4,2]=>35
[3,6,5,2,1,4,7]=>5
[3,6,5,2,1,7,4]=>28
[3,6,5,2,4,1,7]=>5
[3,6,5,2,4,7,1]=>5
[3,6,5,2,7,1,4]=>14
[3,6,5,2,7,4,1]=>14
[3,6,5,4,1,2,7]=>5
[3,6,5,4,1,7,2]=>10
[3,6,5,4,2,1,7]=>5
[3,6,5,4,2,7,1]=>5
[3,6,5,4,7,1,2]=>5
[3,6,5,4,7,2,1]=>5
[3,6,5,7,1,2,4]=>7
[3,6,5,7,1,4,2]=>14
[3,6,5,7,2,1,4]=>7
[3,6,5,7,2,4,1]=>7
[3,6,5,7,4,1,2]=>7
[3,6,5,7,4,2,1]=>7
[3,6,7,1,2,4,5]=>6
[3,6,7,1,2,5,4]=>27
[3,6,7,1,4,2,5]=>12
[3,6,7,1,4,5,2]=>18
[3,6,7,1,5,2,4]=>27
[3,6,7,1,5,4,2]=>45
[3,6,7,2,1,4,5]=>6
[3,6,7,2,1,5,4]=>36
[3,6,7,2,4,1,5]=>6
[3,6,7,2,4,5,1]=>6
[3,6,7,2,5,1,4]=>18
[3,6,7,2,5,4,1]=>18
[3,6,7,4,1,2,5]=>6
[3,6,7,4,1,5,2]=>12
[3,6,7,4,2,1,5]=>6
[3,6,7,4,2,5,1]=>6
[3,6,7,4,5,1,2]=>6
[3,6,7,4,5,2,1]=>6
[3,6,7,5,1,2,4]=>9
[3,6,7,5,1,4,2]=>18
[3,6,7,5,2,1,4]=>9
[3,6,7,5,2,4,1]=>9
[3,6,7,5,4,1,2]=>9
[3,6,7,5,4,2,1]=>9
[3,7,1,2,4,5,6]=>4
[3,7,1,2,4,6,5]=>25
[3,7,1,2,5,4,6]=>21
[3,7,1,2,5,6,4]=>51
[3,7,1,2,6,4,5]=>48
[3,7,1,2,6,5,4]=>165
[3,7,1,4,2,5,6]=>8
[3,7,1,4,2,6,5]=>76
[3,7,1,4,5,2,6]=>12
[3,7,1,4,5,6,2]=>16
[3,7,1,4,6,2,5]=>47
[3,7,1,4,6,5,2]=>65
[3,7,1,5,2,4,6]=>21
[3,7,1,5,2,6,4]=>80
[3,7,1,5,4,2,6]=>35
[3,7,1,5,4,6,2]=>49
[3,7,1,5,6,2,4]=>57
[3,7,1,5,6,4,2]=>84
[3,7,1,6,2,4,5]=>34
[3,7,1,6,2,5,4]=>148
[3,7,1,6,4,2,5]=>59
[3,7,1,6,4,5,2]=>84
[3,7,1,6,5,2,4]=>115
[3,7,1,6,5,4,2]=>176
[3,7,2,1,4,5,6]=>4
[3,7,2,1,4,6,5]=>32
[3,7,2,1,5,4,6]=>28
[3,7,2,1,5,6,4]=>68
[3,7,2,1,6,4,5]=>64
[3,7,2,1,6,5,4]=>242
[3,7,2,4,1,5,6]=>4
[3,7,2,4,1,6,5]=>36
[3,7,2,4,5,1,6]=>4
[3,7,2,4,5,6,1]=>4
[3,7,2,4,6,1,5]=>18
[3,7,2,4,6,5,1]=>18
[3,7,2,5,1,4,6]=>14
[3,7,2,5,1,6,4]=>54
[3,7,2,5,4,1,6]=>14
[3,7,2,5,4,6,1]=>14
[3,7,2,5,6,1,4]=>27
[3,7,2,5,6,4,1]=>27
[3,7,2,6,1,4,5]=>25
[3,7,2,6,1,5,4]=>122
[3,7,2,6,4,1,5]=>25
[3,7,2,6,4,5,1]=>25
[3,7,2,6,5,1,4]=>61
[3,7,2,6,5,4,1]=>61
[3,7,4,1,2,5,6]=>4
[3,7,4,1,2,6,5]=>33
[3,7,4,1,5,2,6]=>8
[3,7,4,1,5,6,2]=>12
[3,7,4,1,6,2,5]=>33
[3,7,4,1,6,5,2]=>55
[3,7,4,2,1,5,6]=>4
[3,7,4,2,1,6,5]=>44
[3,7,4,2,5,1,6]=>4
[3,7,4,2,5,6,1]=>4
[3,7,4,2,6,1,5]=>22
[3,7,4,2,6,5,1]=>22
[3,7,4,5,1,2,6]=>4
[3,7,4,5,1,6,2]=>8
[3,7,4,5,2,1,6]=>4
[3,7,4,5,2,6,1]=>4
[3,7,4,5,6,1,2]=>4
[3,7,4,5,6,2,1]=>4
[3,7,4,6,1,2,5]=>11
[3,7,4,6,1,5,2]=>22
[3,7,4,6,2,1,5]=>11
[3,7,4,6,2,5,1]=>11
[3,7,4,6,5,1,2]=>11
[3,7,4,6,5,2,1]=>11
[3,7,5,1,2,4,6]=>7
[3,7,5,1,2,6,4]=>30
[3,7,5,1,4,2,6]=>14
[3,7,5,1,4,6,2]=>21
[3,7,5,1,6,2,4]=>30
[3,7,5,1,6,4,2]=>50
[3,7,5,2,1,4,6]=>7
[3,7,5,2,1,6,4]=>40
[3,7,5,2,4,1,6]=>7
[3,7,5,2,4,6,1]=>7
[3,7,5,2,6,1,4]=>20
[3,7,5,2,6,4,1]=>20
[3,7,5,4,1,2,6]=>7
[3,7,5,4,1,6,2]=>14
[3,7,5,4,2,1,6]=>7
[3,7,5,4,2,6,1]=>7
[3,7,5,4,6,1,2]=>7
[3,7,5,4,6,2,1]=>7
[3,7,5,6,1,2,4]=>10
[3,7,5,6,1,4,2]=>20
[3,7,5,6,2,1,4]=>10
[3,7,5,6,2,4,1]=>10
[3,7,5,6,4,1,2]=>10
[3,7,5,6,4,2,1]=>10
[3,7,6,1,2,4,5]=>9
[3,7,6,1,2,5,4]=>42
[3,7,6,1,4,2,5]=>18
[3,7,6,1,4,5,2]=>27
[3,7,6,1,5,2,4]=>42
[3,7,6,1,5,4,2]=>70
[3,7,6,2,1,4,5]=>9
[3,7,6,2,1,5,4]=>56
[3,7,6,2,4,1,5]=>9
[3,7,6,2,4,5,1]=>9
[3,7,6,2,5,1,4]=>28
[3,7,6,2,5,4,1]=>28
[3,7,6,4,1,2,5]=>9
[3,7,6,4,1,5,2]=>18
[3,7,6,4,2,1,5]=>9
[3,7,6,4,2,5,1]=>9
[3,7,6,4,5,1,2]=>9
[3,7,6,4,5,2,1]=>9
[3,7,6,5,1,2,4]=>14
[3,7,6,5,1,4,2]=>28
[3,7,6,5,2,1,4]=>14
[3,7,6,5,2,4,1]=>14
[3,7,6,5,4,1,2]=>14
[3,7,6,5,4,2,1]=>14
[4,2,5,1,3,6,7]=>2
[4,3,2,1,5,6,7]=>1
[4,5,6,1,2,3,7]=>1
[5,2,6,7,1,3,4]=>6
[5,3,2,6,1,4,7]=>4
[5,4,3,2,1,6,7]=>1
[5,6,3,4,1,2,7]=>1
[6,4,3,2,7,1,5]=>8
[6,4,7,2,5,1,3]=>4
                    

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Description

The number of alternating sign matrices whose left key is the permutation.
The left key of an alternating sign matrix was defined by Lascoux
in [2] and is obtained by successively removing all the `-1`'s until what remains is a permutation matrix. This notion corresponds to the notion of left key for semistandard tableaux.

References

[1] Aval, J.-C. Keys and alternating sign matrices MathSciNet:2465402
[2] A. Lascoux. Chern and Yang through ice, http://phalanstere.univ-mlv.fr/~al/ARTICLES/ChernYang.ps.gz

Code

def statistic(self):
    count = 0
    for a in AlternatingSignMatrices(len(list(self))):
        if a.left_key_as_permutation() == self:
            count = count + 1
    return count

Created

Jun 11, 2013 at 20:43 by Jessica Striker

Updated

Apr 27, 2018 at 14:43 by Christian Stump