Identifier
-
Mp00090:
Permutations
—cycle-as-one-line notation⟶
Permutations
St000255: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>1
[1,2]=>[1,2]=>1
[2,1]=>[1,2]=>1
[1,2,3]=>[1,2,3]=>1
[1,3,2]=>[1,2,3]=>1
[2,1,3]=>[1,2,3]=>1
[2,3,1]=>[1,2,3]=>1
[3,1,2]=>[1,3,2]=>2
[3,2,1]=>[1,3,2]=>2
[1,2,3,4]=>[1,2,3,4]=>1
[1,2,4,3]=>[1,2,3,4]=>1
[1,3,2,4]=>[1,2,3,4]=>1
[1,3,4,2]=>[1,2,3,4]=>1
[1,4,2,3]=>[1,2,4,3]=>3
[1,4,3,2]=>[1,2,4,3]=>3
[2,1,3,4]=>[1,2,3,4]=>1
[2,1,4,3]=>[1,2,3,4]=>1
[2,3,1,4]=>[1,2,3,4]=>1
[2,3,4,1]=>[1,2,3,4]=>1
[2,4,1,3]=>[1,2,4,3]=>3
[2,4,3,1]=>[1,2,4,3]=>3
[3,1,2,4]=>[1,3,2,4]=>2
[3,1,4,2]=>[1,3,4,2]=>3
[3,2,1,4]=>[1,3,2,4]=>2
[3,2,4,1]=>[1,3,4,2]=>3
[3,4,1,2]=>[1,3,2,4]=>2
[3,4,2,1]=>[1,3,2,4]=>2
[4,1,2,3]=>[1,4,3,2]=>5
[4,1,3,2]=>[1,4,2,3]=>3
[4,2,1,3]=>[1,4,3,2]=>5
[4,2,3,1]=>[1,4,2,3]=>3
[4,3,1,2]=>[1,4,2,3]=>3
[4,3,2,1]=>[1,4,2,3]=>3
[1,2,3,4,5]=>[1,2,3,4,5]=>1
[1,2,3,5,4]=>[1,2,3,4,5]=>1
[1,2,4,3,5]=>[1,2,3,4,5]=>1
[1,2,4,5,3]=>[1,2,3,4,5]=>1
[1,2,5,3,4]=>[1,2,3,5,4]=>4
[1,2,5,4,3]=>[1,2,3,5,4]=>4
[1,3,2,4,5]=>[1,2,3,4,5]=>1
[1,3,2,5,4]=>[1,2,3,4,5]=>1
[1,3,4,2,5]=>[1,2,3,4,5]=>1
[1,3,4,5,2]=>[1,2,3,4,5]=>1
[1,3,5,2,4]=>[1,2,3,5,4]=>4
[1,3,5,4,2]=>[1,2,3,5,4]=>4
[1,4,2,3,5]=>[1,2,4,3,5]=>3
[1,4,2,5,3]=>[1,2,4,5,3]=>6
[1,4,3,2,5]=>[1,2,4,3,5]=>3
[1,4,3,5,2]=>[1,2,4,5,3]=>6
[1,4,5,2,3]=>[1,2,4,3,5]=>3
[1,4,5,3,2]=>[1,2,4,3,5]=>3
[1,5,2,3,4]=>[1,2,5,4,3]=>14
[1,5,2,4,3]=>[1,2,5,3,4]=>6
[1,5,3,2,4]=>[1,2,5,4,3]=>14
[1,5,3,4,2]=>[1,2,5,3,4]=>6
[1,5,4,2,3]=>[1,2,5,3,4]=>6
[1,5,4,3,2]=>[1,2,5,3,4]=>6
[2,1,3,4,5]=>[1,2,3,4,5]=>1
[2,1,3,5,4]=>[1,2,3,4,5]=>1
[2,1,4,3,5]=>[1,2,3,4,5]=>1
[2,1,4,5,3]=>[1,2,3,4,5]=>1
[2,1,5,3,4]=>[1,2,3,5,4]=>4
[2,1,5,4,3]=>[1,2,3,5,4]=>4
[2,3,1,4,5]=>[1,2,3,4,5]=>1
[2,3,1,5,4]=>[1,2,3,4,5]=>1
[2,3,4,1,5]=>[1,2,3,4,5]=>1
[2,3,4,5,1]=>[1,2,3,4,5]=>1
[2,3,5,1,4]=>[1,2,3,5,4]=>4
[2,3,5,4,1]=>[1,2,3,5,4]=>4
[2,4,1,3,5]=>[1,2,4,3,5]=>3
[2,4,1,5,3]=>[1,2,4,5,3]=>6
[2,4,3,1,5]=>[1,2,4,3,5]=>3
[2,4,3,5,1]=>[1,2,4,5,3]=>6
[2,4,5,1,3]=>[1,2,4,3,5]=>3
[2,4,5,3,1]=>[1,2,4,3,5]=>3
[2,5,1,3,4]=>[1,2,5,4,3]=>14
[2,5,1,4,3]=>[1,2,5,3,4]=>6
[2,5,3,1,4]=>[1,2,5,4,3]=>14
[2,5,3,4,1]=>[1,2,5,3,4]=>6
[2,5,4,1,3]=>[1,2,5,3,4]=>6
[2,5,4,3,1]=>[1,2,5,3,4]=>6
[3,1,2,4,5]=>[1,3,2,4,5]=>2
[3,1,2,5,4]=>[1,3,2,4,5]=>2
[3,1,4,2,5]=>[1,3,4,2,5]=>3
[3,1,4,5,2]=>[1,3,4,5,2]=>4
[3,1,5,2,4]=>[1,3,5,4,2]=>11
[3,1,5,4,2]=>[1,3,5,2,4]=>8
[3,2,1,4,5]=>[1,3,2,4,5]=>2
[3,2,1,5,4]=>[1,3,2,4,5]=>2
[3,2,4,1,5]=>[1,3,4,2,5]=>3
[3,2,4,5,1]=>[1,3,4,5,2]=>4
[3,2,5,1,4]=>[1,3,5,4,2]=>11
[3,2,5,4,1]=>[1,3,5,2,4]=>8
[3,4,1,2,5]=>[1,3,2,4,5]=>2
[3,4,1,5,2]=>[1,3,2,4,5]=>2
[3,4,2,1,5]=>[1,3,2,4,5]=>2
[3,4,2,5,1]=>[1,3,2,4,5]=>2
[3,4,5,1,2]=>[1,3,5,2,4]=>8
[3,4,5,2,1]=>[1,3,5,2,4]=>8
[3,5,1,2,4]=>[1,3,2,5,4]=>8
[3,5,1,4,2]=>[1,3,2,5,4]=>8
[3,5,2,1,4]=>[1,3,2,5,4]=>8
[3,5,2,4,1]=>[1,3,2,5,4]=>8
[3,5,4,1,2]=>[1,3,4,2,5]=>3
[3,5,4,2,1]=>[1,3,4,2,5]=>3
[4,1,2,3,5]=>[1,4,3,2,5]=>5
[4,1,2,5,3]=>[1,4,5,3,2]=>9
[4,1,3,2,5]=>[1,4,2,3,5]=>3
[4,1,3,5,2]=>[1,4,5,2,3]=>6
[4,1,5,2,3]=>[1,4,2,3,5]=>3
[4,1,5,3,2]=>[1,4,3,5,2]=>7
[4,2,1,3,5]=>[1,4,3,2,5]=>5
[4,2,1,5,3]=>[1,4,5,3,2]=>9
[4,2,3,1,5]=>[1,4,2,3,5]=>3
[4,2,3,5,1]=>[1,4,5,2,3]=>6
[4,2,5,1,3]=>[1,4,2,3,5]=>3
[4,2,5,3,1]=>[1,4,3,5,2]=>7
[4,3,1,2,5]=>[1,4,2,3,5]=>3
[4,3,1,5,2]=>[1,4,5,2,3]=>6
[4,3,2,1,5]=>[1,4,2,3,5]=>3
[4,3,2,5,1]=>[1,4,5,2,3]=>6
[4,3,5,1,2]=>[1,4,2,3,5]=>3
[4,3,5,2,1]=>[1,4,2,3,5]=>3
[4,5,1,2,3]=>[1,4,2,5,3]=>8
[4,5,1,3,2]=>[1,4,3,2,5]=>5
[4,5,2,1,3]=>[1,4,2,5,3]=>8
[4,5,2,3,1]=>[1,4,3,2,5]=>5
[4,5,3,1,2]=>[1,4,2,5,3]=>8
[4,5,3,2,1]=>[1,4,2,5,3]=>8
[5,1,2,3,4]=>[1,5,4,3,2]=>14
[5,1,2,4,3]=>[1,5,3,2,4]=>7
[5,1,3,2,4]=>[1,5,4,2,3]=>9
[5,1,3,4,2]=>[1,5,2,3,4]=>4
[5,1,4,2,3]=>[1,5,3,4,2]=>10
[5,1,4,3,2]=>[1,5,2,3,4]=>4
[5,2,1,3,4]=>[1,5,4,3,2]=>14
[5,2,1,4,3]=>[1,5,3,2,4]=>7
[5,2,3,1,4]=>[1,5,4,2,3]=>9
[5,2,3,4,1]=>[1,5,2,3,4]=>4
[5,2,4,1,3]=>[1,5,3,4,2]=>10
[5,2,4,3,1]=>[1,5,2,3,4]=>4
[5,3,1,2,4]=>[1,5,4,2,3]=>9
[5,3,1,4,2]=>[1,5,2,3,4]=>4
[5,3,2,1,4]=>[1,5,4,2,3]=>9
[5,3,2,4,1]=>[1,5,2,3,4]=>4
[5,3,4,1,2]=>[1,5,2,3,4]=>4
[5,3,4,2,1]=>[1,5,2,3,4]=>4
[5,4,1,2,3]=>[1,5,3,2,4]=>7
[5,4,1,3,2]=>[1,5,2,4,3]=>11
[5,4,2,1,3]=>[1,5,3,2,4]=>7
[5,4,2,3,1]=>[1,5,2,4,3]=>11
[5,4,3,1,2]=>[1,5,2,4,3]=>11
[5,4,3,2,1]=>[1,5,2,4,3]=>11
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>[1,2,3,4,5,6]=>1
[1,2,3,5,4,6]=>[1,2,3,4,5,6]=>1
[1,2,3,5,6,4]=>[1,2,3,4,5,6]=>1
[1,2,3,6,4,5]=>[1,2,3,4,6,5]=>5
[1,2,3,6,5,4]=>[1,2,3,4,6,5]=>5
[1,2,4,3,5,6]=>[1,2,3,4,5,6]=>1
[1,2,4,3,6,5]=>[1,2,3,4,5,6]=>1
[1,2,4,5,3,6]=>[1,2,3,4,5,6]=>1
[1,2,4,5,6,3]=>[1,2,3,4,5,6]=>1
[1,2,4,6,3,5]=>[1,2,3,4,6,5]=>5
[1,2,4,6,5,3]=>[1,2,3,4,6,5]=>5
[1,2,5,3,4,6]=>[1,2,3,5,4,6]=>4
[1,2,5,3,6,4]=>[1,2,3,5,6,4]=>10
[1,2,5,4,3,6]=>[1,2,3,5,4,6]=>4
[1,2,5,4,6,3]=>[1,2,3,5,6,4]=>10
[1,2,5,6,3,4]=>[1,2,3,5,4,6]=>4
[1,2,5,6,4,3]=>[1,2,3,5,4,6]=>4
[1,2,6,3,4,5]=>[1,2,3,6,5,4]=>30
[1,2,6,3,5,4]=>[1,2,3,6,4,5]=>10
[1,2,6,4,3,5]=>[1,2,3,6,5,4]=>30
[1,2,6,4,5,3]=>[1,2,3,6,4,5]=>10
[1,2,6,5,3,4]=>[1,2,3,6,4,5]=>10
[1,2,6,5,4,3]=>[1,2,3,6,4,5]=>10
[1,3,2,4,5,6]=>[1,2,3,4,5,6]=>1
[1,3,2,4,6,5]=>[1,2,3,4,5,6]=>1
[1,3,2,5,4,6]=>[1,2,3,4,5,6]=>1
[1,3,2,5,6,4]=>[1,2,3,4,5,6]=>1
[1,3,2,6,4,5]=>[1,2,3,4,6,5]=>5
[1,3,2,6,5,4]=>[1,2,3,4,6,5]=>5
[1,3,4,2,5,6]=>[1,2,3,4,5,6]=>1
[1,3,4,2,6,5]=>[1,2,3,4,5,6]=>1
[1,3,4,5,2,6]=>[1,2,3,4,5,6]=>1
[1,3,4,5,6,2]=>[1,2,3,4,5,6]=>1
[1,3,4,6,2,5]=>[1,2,3,4,6,5]=>5
[1,3,4,6,5,2]=>[1,2,3,4,6,5]=>5
[1,3,5,2,4,6]=>[1,2,3,5,4,6]=>4
[1,3,5,2,6,4]=>[1,2,3,5,6,4]=>10
[1,3,5,4,2,6]=>[1,2,3,5,4,6]=>4
[1,3,5,4,6,2]=>[1,2,3,5,6,4]=>10
[1,3,5,6,2,4]=>[1,2,3,5,4,6]=>4
[1,3,5,6,4,2]=>[1,2,3,5,4,6]=>4
[1,3,6,2,4,5]=>[1,2,3,6,5,4]=>30
[1,3,6,2,5,4]=>[1,2,3,6,4,5]=>10
[1,3,6,4,2,5]=>[1,2,3,6,5,4]=>30
[1,3,6,4,5,2]=>[1,2,3,6,4,5]=>10
[1,3,6,5,2,4]=>[1,2,3,6,4,5]=>10
[1,3,6,5,4,2]=>[1,2,3,6,4,5]=>10
[1,4,2,3,5,6]=>[1,2,4,3,5,6]=>3
[1,4,2,3,6,5]=>[1,2,4,3,5,6]=>3
[1,4,2,5,3,6]=>[1,2,4,5,3,6]=>6
[1,4,2,5,6,3]=>[1,2,4,5,6,3]=>10
[1,4,2,6,3,5]=>[1,2,4,6,5,3]=>35
[1,4,2,6,5,3]=>[1,2,4,6,3,5]=>20
[1,4,3,2,5,6]=>[1,2,4,3,5,6]=>3
[1,4,3,2,6,5]=>[1,2,4,3,5,6]=>3
[1,4,3,5,2,6]=>[1,2,4,5,3,6]=>6
[1,4,3,5,6,2]=>[1,2,4,5,6,3]=>10
[1,4,3,6,2,5]=>[1,2,4,6,5,3]=>35
[1,4,3,6,5,2]=>[1,2,4,6,3,5]=>20
[1,4,5,2,3,6]=>[1,2,4,3,5,6]=>3
[1,4,5,2,6,3]=>[1,2,4,3,5,6]=>3
[1,4,5,3,2,6]=>[1,2,4,3,5,6]=>3
[1,4,5,3,6,2]=>[1,2,4,3,5,6]=>3
[1,4,5,6,2,3]=>[1,2,4,6,3,5]=>20
[1,4,5,6,3,2]=>[1,2,4,6,3,5]=>20
[1,4,6,2,3,5]=>[1,2,4,3,6,5]=>15
[1,4,6,2,5,3]=>[1,2,4,3,6,5]=>15
[1,4,6,3,2,5]=>[1,2,4,3,6,5]=>15
[1,4,6,3,5,2]=>[1,2,4,3,6,5]=>15
[1,4,6,5,2,3]=>[1,2,4,5,3,6]=>6
[1,4,6,5,3,2]=>[1,2,4,5,3,6]=>6
[1,5,2,3,4,6]=>[1,2,5,4,3,6]=>14
[1,5,2,3,6,4]=>[1,2,5,6,4,3]=>40
[1,5,2,4,3,6]=>[1,2,5,3,4,6]=>6
[1,5,2,4,6,3]=>[1,2,5,6,3,4]=>20
[1,5,2,6,3,4]=>[1,2,5,3,4,6]=>6
[1,5,2,6,4,3]=>[1,2,5,4,6,3]=>25
[1,5,3,2,4,6]=>[1,2,5,4,3,6]=>14
[1,5,3,2,6,4]=>[1,2,5,6,4,3]=>40
[1,5,3,4,2,6]=>[1,2,5,3,4,6]=>6
[1,5,3,4,6,2]=>[1,2,5,6,3,4]=>20
[1,5,3,6,2,4]=>[1,2,5,3,4,6]=>6
[1,5,3,6,4,2]=>[1,2,5,4,6,3]=>25
[1,5,4,2,3,6]=>[1,2,5,3,4,6]=>6
[1,5,4,2,6,3]=>[1,2,5,6,3,4]=>20
[1,5,4,3,2,6]=>[1,2,5,3,4,6]=>6
[1,5,4,3,6,2]=>[1,2,5,6,3,4]=>20
[1,5,4,6,2,3]=>[1,2,5,3,4,6]=>6
[1,5,4,6,3,2]=>[1,2,5,3,4,6]=>6
[1,5,6,2,3,4]=>[1,2,5,3,6,4]=>20
[1,5,6,2,4,3]=>[1,2,5,4,3,6]=>14
[1,5,6,3,2,4]=>[1,2,5,3,6,4]=>20
[1,5,6,3,4,2]=>[1,2,5,4,3,6]=>14
[1,5,6,4,2,3]=>[1,2,5,3,6,4]=>20
[1,5,6,4,3,2]=>[1,2,5,3,6,4]=>20
[1,6,2,3,4,5]=>[1,2,6,5,4,3]=>84
[1,6,2,3,5,4]=>[1,2,6,4,3,5]=>25
[1,6,2,4,3,5]=>[1,2,6,5,3,4]=>40
[1,6,2,4,5,3]=>[1,2,6,3,4,5]=>10
[1,6,2,5,3,4]=>[1,2,6,4,5,3]=>46
[1,6,2,5,4,3]=>[1,2,6,3,4,5]=>10
[1,6,3,2,4,5]=>[1,2,6,5,4,3]=>84
[1,6,3,2,5,4]=>[1,2,6,4,3,5]=>25
[1,6,3,4,2,5]=>[1,2,6,5,3,4]=>40
[1,6,3,4,5,2]=>[1,2,6,3,4,5]=>10
[1,6,3,5,2,4]=>[1,2,6,4,5,3]=>46
[1,6,3,5,4,2]=>[1,2,6,3,4,5]=>10
[1,6,4,2,3,5]=>[1,2,6,5,3,4]=>40
[1,6,4,2,5,3]=>[1,2,6,3,4,5]=>10
[1,6,4,3,2,5]=>[1,2,6,5,3,4]=>40
[1,6,4,3,5,2]=>[1,2,6,3,4,5]=>10
[1,6,4,5,2,3]=>[1,2,6,3,4,5]=>10
[1,6,4,5,3,2]=>[1,2,6,3,4,5]=>10
[1,6,5,2,3,4]=>[1,2,6,4,3,5]=>25
[1,6,5,2,4,3]=>[1,2,6,3,5,4]=>35
[1,6,5,3,2,4]=>[1,2,6,4,3,5]=>25
[1,6,5,3,4,2]=>[1,2,6,3,5,4]=>35
[1,6,5,4,2,3]=>[1,2,6,3,5,4]=>35
[1,6,5,4,3,2]=>[1,2,6,3,5,4]=>35
[2,1,3,4,5,6]=>[1,2,3,4,5,6]=>1
[2,1,3,4,6,5]=>[1,2,3,4,5,6]=>1
[2,1,3,5,4,6]=>[1,2,3,4,5,6]=>1
[2,1,3,5,6,4]=>[1,2,3,4,5,6]=>1
[2,1,3,6,4,5]=>[1,2,3,4,6,5]=>5
[2,1,3,6,5,4]=>[1,2,3,4,6,5]=>5
[2,1,4,3,5,6]=>[1,2,3,4,5,6]=>1
[2,1,4,3,6,5]=>[1,2,3,4,5,6]=>1
[2,1,4,5,3,6]=>[1,2,3,4,5,6]=>1
[2,1,4,5,6,3]=>[1,2,3,4,5,6]=>1
[2,1,4,6,3,5]=>[1,2,3,4,6,5]=>5
[2,1,4,6,5,3]=>[1,2,3,4,6,5]=>5
[2,1,5,3,4,6]=>[1,2,3,5,4,6]=>4
[2,1,5,3,6,4]=>[1,2,3,5,6,4]=>10
[2,1,5,4,3,6]=>[1,2,3,5,4,6]=>4
[2,1,5,4,6,3]=>[1,2,3,5,6,4]=>10
[2,1,5,6,3,4]=>[1,2,3,5,4,6]=>4
[2,1,5,6,4,3]=>[1,2,3,5,4,6]=>4
[2,1,6,3,4,5]=>[1,2,3,6,5,4]=>30
[2,1,6,3,5,4]=>[1,2,3,6,4,5]=>10
[2,1,6,4,3,5]=>[1,2,3,6,5,4]=>30
[2,1,6,4,5,3]=>[1,2,3,6,4,5]=>10
[2,1,6,5,3,4]=>[1,2,3,6,4,5]=>10
[2,1,6,5,4,3]=>[1,2,3,6,4,5]=>10
[2,3,1,4,5,6]=>[1,2,3,4,5,6]=>1
[2,3,1,4,6,5]=>[1,2,3,4,5,6]=>1
[2,3,1,5,4,6]=>[1,2,3,4,5,6]=>1
[2,3,1,5,6,4]=>[1,2,3,4,5,6]=>1
[2,3,1,6,4,5]=>[1,2,3,4,6,5]=>5
[2,3,1,6,5,4]=>[1,2,3,4,6,5]=>5
[2,3,4,1,5,6]=>[1,2,3,4,5,6]=>1
[2,3,4,1,6,5]=>[1,2,3,4,5,6]=>1
[2,3,4,5,1,6]=>[1,2,3,4,5,6]=>1
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>1
[2,3,4,6,1,5]=>[1,2,3,4,6,5]=>5
[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>5
[2,3,5,1,4,6]=>[1,2,3,5,4,6]=>4
[2,3,5,1,6,4]=>[1,2,3,5,6,4]=>10
[2,3,5,4,1,6]=>[1,2,3,5,4,6]=>4
[2,3,5,4,6,1]=>[1,2,3,5,6,4]=>10
[2,3,5,6,1,4]=>[1,2,3,5,4,6]=>4
[2,3,5,6,4,1]=>[1,2,3,5,4,6]=>4
[2,3,6,1,4,5]=>[1,2,3,6,5,4]=>30
[2,3,6,1,5,4]=>[1,2,3,6,4,5]=>10
[2,3,6,4,1,5]=>[1,2,3,6,5,4]=>30
[2,3,6,4,5,1]=>[1,2,3,6,4,5]=>10
[2,3,6,5,1,4]=>[1,2,3,6,4,5]=>10
[2,3,6,5,4,1]=>[1,2,3,6,4,5]=>10
[2,4,1,3,5,6]=>[1,2,4,3,5,6]=>3
[2,4,1,3,6,5]=>[1,2,4,3,5,6]=>3
[2,4,1,5,3,6]=>[1,2,4,5,3,6]=>6
[2,4,1,5,6,3]=>[1,2,4,5,6,3]=>10
[2,4,1,6,3,5]=>[1,2,4,6,5,3]=>35
[2,4,1,6,5,3]=>[1,2,4,6,3,5]=>20
[2,4,3,1,5,6]=>[1,2,4,3,5,6]=>3
[2,4,3,1,6,5]=>[1,2,4,3,5,6]=>3
[2,4,3,5,1,6]=>[1,2,4,5,3,6]=>6
[2,4,3,5,6,1]=>[1,2,4,5,6,3]=>10
[2,4,3,6,1,5]=>[1,2,4,6,5,3]=>35
[2,4,3,6,5,1]=>[1,2,4,6,3,5]=>20
[2,4,5,1,3,6]=>[1,2,4,3,5,6]=>3
[2,4,5,1,6,3]=>[1,2,4,3,5,6]=>3
[2,4,5,3,1,6]=>[1,2,4,3,5,6]=>3
[2,4,5,3,6,1]=>[1,2,4,3,5,6]=>3
[2,4,5,6,1,3]=>[1,2,4,6,3,5]=>20
[2,4,5,6,3,1]=>[1,2,4,6,3,5]=>20
[2,4,6,1,3,5]=>[1,2,4,3,6,5]=>15
[2,4,6,1,5,3]=>[1,2,4,3,6,5]=>15
[2,4,6,3,1,5]=>[1,2,4,3,6,5]=>15
[2,4,6,3,5,1]=>[1,2,4,3,6,5]=>15
[2,4,6,5,1,3]=>[1,2,4,5,3,6]=>6
[2,4,6,5,3,1]=>[1,2,4,5,3,6]=>6
[2,5,1,3,4,6]=>[1,2,5,4,3,6]=>14
[2,5,1,3,6,4]=>[1,2,5,6,4,3]=>40
[2,5,1,4,3,6]=>[1,2,5,3,4,6]=>6
[2,5,1,4,6,3]=>[1,2,5,6,3,4]=>20
[2,5,1,6,3,4]=>[1,2,5,3,4,6]=>6
[2,5,1,6,4,3]=>[1,2,5,4,6,3]=>25
[2,5,3,1,4,6]=>[1,2,5,4,3,6]=>14
[2,5,3,1,6,4]=>[1,2,5,6,4,3]=>40
[2,5,3,4,1,6]=>[1,2,5,3,4,6]=>6
[2,5,3,4,6,1]=>[1,2,5,6,3,4]=>20
[2,5,3,6,1,4]=>[1,2,5,3,4,6]=>6
[2,5,3,6,4,1]=>[1,2,5,4,6,3]=>25
[2,5,4,1,3,6]=>[1,2,5,3,4,6]=>6
[2,5,4,1,6,3]=>[1,2,5,6,3,4]=>20
[2,5,4,3,1,6]=>[1,2,5,3,4,6]=>6
[2,5,4,3,6,1]=>[1,2,5,6,3,4]=>20
[2,5,4,6,1,3]=>[1,2,5,3,4,6]=>6
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>6
[2,5,6,1,3,4]=>[1,2,5,3,6,4]=>20
[2,5,6,1,4,3]=>[1,2,5,4,3,6]=>14
[2,5,6,3,1,4]=>[1,2,5,3,6,4]=>20
[2,5,6,3,4,1]=>[1,2,5,4,3,6]=>14
[2,5,6,4,1,3]=>[1,2,5,3,6,4]=>20
[2,5,6,4,3,1]=>[1,2,5,3,6,4]=>20
[2,6,1,3,4,5]=>[1,2,6,5,4,3]=>84
[2,6,1,3,5,4]=>[1,2,6,4,3,5]=>25
[2,6,1,4,3,5]=>[1,2,6,5,3,4]=>40
[2,6,1,4,5,3]=>[1,2,6,3,4,5]=>10
[2,6,1,5,3,4]=>[1,2,6,4,5,3]=>46
[2,6,1,5,4,3]=>[1,2,6,3,4,5]=>10
[2,6,3,1,4,5]=>[1,2,6,5,4,3]=>84
[2,6,3,1,5,4]=>[1,2,6,4,3,5]=>25
[2,6,3,4,1,5]=>[1,2,6,5,3,4]=>40
[2,6,3,4,5,1]=>[1,2,6,3,4,5]=>10
[2,6,3,5,1,4]=>[1,2,6,4,5,3]=>46
[2,6,3,5,4,1]=>[1,2,6,3,4,5]=>10
[2,6,4,1,3,5]=>[1,2,6,5,3,4]=>40
[2,6,4,1,5,3]=>[1,2,6,3,4,5]=>10
[2,6,4,3,1,5]=>[1,2,6,5,3,4]=>40
[2,6,4,3,5,1]=>[1,2,6,3,4,5]=>10
[2,6,4,5,1,3]=>[1,2,6,3,4,5]=>10
[2,6,4,5,3,1]=>[1,2,6,3,4,5]=>10
[2,6,5,1,3,4]=>[1,2,6,4,3,5]=>25
[2,6,5,1,4,3]=>[1,2,6,3,5,4]=>35
[2,6,5,3,1,4]=>[1,2,6,4,3,5]=>25
[2,6,5,3,4,1]=>[1,2,6,3,5,4]=>35
[2,6,5,4,1,3]=>[1,2,6,3,5,4]=>35
[2,6,5,4,3,1]=>[1,2,6,3,5,4]=>35
[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>2
[3,1,2,4,6,5]=>[1,3,2,4,5,6]=>2
[3,1,2,5,4,6]=>[1,3,2,4,5,6]=>2
[3,1,2,5,6,4]=>[1,3,2,4,5,6]=>2
[3,1,2,6,4,5]=>[1,3,2,4,6,5]=>10
[3,1,2,6,5,4]=>[1,3,2,4,6,5]=>10
[3,1,4,2,5,6]=>[1,3,4,2,5,6]=>3
[3,1,4,2,6,5]=>[1,3,4,2,5,6]=>3
[3,1,4,5,2,6]=>[1,3,4,5,2,6]=>4
[3,1,4,5,6,2]=>[1,3,4,5,6,2]=>5
[3,1,4,6,2,5]=>[1,3,4,6,5,2]=>19
[3,1,4,6,5,2]=>[1,3,4,6,2,5]=>15
[3,1,5,2,4,6]=>[1,3,5,4,2,6]=>11
[3,1,5,2,6,4]=>[1,3,5,6,4,2]=>26
[3,1,5,4,2,6]=>[1,3,5,2,4,6]=>8
[3,1,5,4,6,2]=>[1,3,5,6,2,4]=>20
[3,1,5,6,2,4]=>[1,3,5,2,4,6]=>8
[3,1,5,6,4,2]=>[1,3,5,4,6,2]=>14
[3,1,6,2,4,5]=>[1,3,6,5,4,2]=>58
[3,1,6,2,5,4]=>[1,3,6,4,2,5]=>21
[3,1,6,4,2,5]=>[1,3,6,5,2,4]=>44
[3,1,6,4,5,2]=>[1,3,6,2,4,5]=>15
[3,1,6,5,2,4]=>[1,3,6,4,5,2]=>27
[3,1,6,5,4,2]=>[1,3,6,2,4,5]=>15
[3,2,1,4,5,6]=>[1,3,2,4,5,6]=>2
[3,2,1,4,6,5]=>[1,3,2,4,5,6]=>2
[3,2,1,5,4,6]=>[1,3,2,4,5,6]=>2
[3,2,1,5,6,4]=>[1,3,2,4,5,6]=>2
[3,2,1,6,4,5]=>[1,3,2,4,6,5]=>10
[3,2,1,6,5,4]=>[1,3,2,4,6,5]=>10
[3,2,4,1,5,6]=>[1,3,4,2,5,6]=>3
[3,2,4,1,6,5]=>[1,3,4,2,5,6]=>3
[3,2,4,5,1,6]=>[1,3,4,5,2,6]=>4
[3,2,4,5,6,1]=>[1,3,4,5,6,2]=>5
[3,2,4,6,1,5]=>[1,3,4,6,5,2]=>19
[3,2,4,6,5,1]=>[1,3,4,6,2,5]=>15
[3,2,5,1,4,6]=>[1,3,5,4,2,6]=>11
[3,2,5,1,6,4]=>[1,3,5,6,4,2]=>26
[3,2,5,4,1,6]=>[1,3,5,2,4,6]=>8
[3,2,5,4,6,1]=>[1,3,5,6,2,4]=>20
[3,2,5,6,1,4]=>[1,3,5,2,4,6]=>8
[3,2,5,6,4,1]=>[1,3,5,4,6,2]=>14
[3,2,6,1,4,5]=>[1,3,6,5,4,2]=>58
[3,2,6,1,5,4]=>[1,3,6,4,2,5]=>21
[3,2,6,4,1,5]=>[1,3,6,5,2,4]=>44
[3,2,6,4,5,1]=>[1,3,6,2,4,5]=>15
[3,2,6,5,1,4]=>[1,3,6,4,5,2]=>27
[3,2,6,5,4,1]=>[1,3,6,2,4,5]=>15
[3,4,1,2,5,6]=>[1,3,2,4,5,6]=>2
[3,4,1,2,6,5]=>[1,3,2,4,5,6]=>2
[3,4,1,5,2,6]=>[1,3,2,4,5,6]=>2
[3,4,1,5,6,2]=>[1,3,2,4,5,6]=>2
[3,4,1,6,2,5]=>[1,3,2,4,6,5]=>10
[3,4,1,6,5,2]=>[1,3,2,4,6,5]=>10
[3,4,2,1,5,6]=>[1,3,2,4,5,6]=>2
[3,4,2,1,6,5]=>[1,3,2,4,5,6]=>2
[3,4,2,5,1,6]=>[1,3,2,4,5,6]=>2
[3,4,2,5,6,1]=>[1,3,2,4,5,6]=>2
[3,4,2,6,1,5]=>[1,3,2,4,6,5]=>10
[3,4,2,6,5,1]=>[1,3,2,4,6,5]=>10
[3,4,5,1,2,6]=>[1,3,5,2,4,6]=>8
[3,4,5,1,6,2]=>[1,3,5,6,2,4]=>20
[3,4,5,2,1,6]=>[1,3,5,2,4,6]=>8
[3,4,5,2,6,1]=>[1,3,5,6,2,4]=>20
[3,4,5,6,1,2]=>[1,3,5,2,4,6]=>8
[3,4,5,6,2,1]=>[1,3,5,2,4,6]=>8
[3,4,6,1,2,5]=>[1,3,6,5,2,4]=>44
[3,4,6,1,5,2]=>[1,3,6,2,4,5]=>15
[3,4,6,2,1,5]=>[1,3,6,5,2,4]=>44
[3,4,6,2,5,1]=>[1,3,6,2,4,5]=>15
[3,4,6,5,1,2]=>[1,3,6,2,4,5]=>15
[3,4,6,5,2,1]=>[1,3,6,2,4,5]=>15
[3,5,1,2,4,6]=>[1,3,2,5,4,6]=>8
[3,5,1,2,6,4]=>[1,3,2,5,6,4]=>20
[3,5,1,4,2,6]=>[1,3,2,5,4,6]=>8
[3,5,1,4,6,2]=>[1,3,2,5,6,4]=>20
[3,5,1,6,2,4]=>[1,3,2,5,4,6]=>8
[3,5,1,6,4,2]=>[1,3,2,5,4,6]=>8
[3,5,2,1,4,6]=>[1,3,2,5,4,6]=>8
[3,5,2,1,6,4]=>[1,3,2,5,6,4]=>20
[3,5,2,4,1,6]=>[1,3,2,5,4,6]=>8
[3,5,2,4,6,1]=>[1,3,2,5,6,4]=>20
[3,5,2,6,1,4]=>[1,3,2,5,4,6]=>8
[3,5,2,6,4,1]=>[1,3,2,5,4,6]=>8
[3,5,4,1,2,6]=>[1,3,4,2,5,6]=>3
[3,5,4,1,6,2]=>[1,3,4,2,5,6]=>3
[3,5,4,2,1,6]=>[1,3,4,2,5,6]=>3
[3,5,4,2,6,1]=>[1,3,4,2,5,6]=>3
[3,5,4,6,1,2]=>[1,3,4,6,2,5]=>15
[3,5,4,6,2,1]=>[1,3,4,6,2,5]=>15
[3,5,6,1,2,4]=>[1,3,6,4,2,5]=>21
[3,5,6,1,4,2]=>[1,3,6,2,5,4]=>51
[3,5,6,2,1,4]=>[1,3,6,4,2,5]=>21
[3,5,6,2,4,1]=>[1,3,6,2,5,4]=>51
[3,5,6,4,1,2]=>[1,3,6,2,5,4]=>51
[3,5,6,4,2,1]=>[1,3,6,2,5,4]=>51
[3,6,1,2,4,5]=>[1,3,2,6,5,4]=>60
[3,6,1,2,5,4]=>[1,3,2,6,4,5]=>20
[3,6,1,4,2,5]=>[1,3,2,6,5,4]=>60
[3,6,1,4,5,2]=>[1,3,2,6,4,5]=>20
[3,6,1,5,2,4]=>[1,3,2,6,4,5]=>20
[3,6,1,5,4,2]=>[1,3,2,6,4,5]=>20
[3,6,2,1,4,5]=>[1,3,2,6,5,4]=>60
[3,6,2,1,5,4]=>[1,3,2,6,4,5]=>20
[3,6,2,4,1,5]=>[1,3,2,6,5,4]=>60
[3,6,2,4,5,1]=>[1,3,2,6,4,5]=>20
[3,6,2,5,1,4]=>[1,3,2,6,4,5]=>20
[3,6,2,5,4,1]=>[1,3,2,6,4,5]=>20
[3,6,4,1,2,5]=>[1,3,4,2,6,5]=>15
[3,6,4,1,5,2]=>[1,3,4,2,6,5]=>15
[3,6,4,2,1,5]=>[1,3,4,2,6,5]=>15
[3,6,4,2,5,1]=>[1,3,4,2,6,5]=>15
[3,6,4,5,1,2]=>[1,3,4,5,2,6]=>4
[3,6,4,5,2,1]=>[1,3,4,5,2,6]=>4
[3,6,5,1,2,4]=>[1,3,5,2,6,4]=>25
[3,6,5,1,4,2]=>[1,3,5,4,2,6]=>11
[3,6,5,2,1,4]=>[1,3,5,2,6,4]=>25
[3,6,5,2,4,1]=>[1,3,5,4,2,6]=>11
[3,6,5,4,1,2]=>[1,3,5,2,6,4]=>25
[3,6,5,4,2,1]=>[1,3,5,2,6,4]=>25
[4,1,2,3,5,6]=>[1,4,3,2,5,6]=>5
[4,1,2,3,6,5]=>[1,4,3,2,5,6]=>5
[4,1,2,5,3,6]=>[1,4,5,3,2,6]=>9
[4,1,2,5,6,3]=>[1,4,5,6,3,2]=>14
[4,1,2,6,3,5]=>[1,4,6,5,3,2]=>37
[4,1,2,6,5,3]=>[1,4,6,3,2,5]=>23
[4,1,3,2,5,6]=>[1,4,2,3,5,6]=>3
[4,1,3,2,6,5]=>[1,4,2,3,5,6]=>3
[4,1,3,5,2,6]=>[1,4,5,2,3,6]=>6
[4,1,3,5,6,2]=>[1,4,5,6,2,3]=>10
[4,1,3,6,2,5]=>[1,4,6,5,2,3]=>26
[4,1,3,6,5,2]=>[1,4,6,2,3,5]=>15
[4,1,5,2,3,6]=>[1,4,2,3,5,6]=>3
[4,1,5,2,6,3]=>[1,4,2,3,5,6]=>3
[4,1,5,3,2,6]=>[1,4,3,5,2,6]=>7
[4,1,5,3,6,2]=>[1,4,3,5,6,2]=>9
[4,1,5,6,2,3]=>[1,4,6,3,5,2]=>31
[4,1,5,6,3,2]=>[1,4,6,2,3,5]=>15
[4,1,6,2,3,5]=>[1,4,2,3,6,5]=>15
[4,1,6,2,5,3]=>[1,4,2,3,6,5]=>15
[4,1,6,3,2,5]=>[1,4,3,6,5,2]=>34
[4,1,6,3,5,2]=>[1,4,3,6,2,5]=>26
[4,1,6,5,2,3]=>[1,4,5,2,3,6]=>6
[4,1,6,5,3,2]=>[1,4,5,3,6,2]=>12
[4,2,1,3,5,6]=>[1,4,3,2,5,6]=>5
[4,2,1,3,6,5]=>[1,4,3,2,5,6]=>5
[4,2,1,5,3,6]=>[1,4,5,3,2,6]=>9
[4,2,1,5,6,3]=>[1,4,5,6,3,2]=>14
[4,2,1,6,3,5]=>[1,4,6,5,3,2]=>37
[4,2,1,6,5,3]=>[1,4,6,3,2,5]=>23
[4,2,3,1,5,6]=>[1,4,2,3,5,6]=>3
[4,2,3,1,6,5]=>[1,4,2,3,5,6]=>3
[4,2,3,5,1,6]=>[1,4,5,2,3,6]=>6
[4,2,3,5,6,1]=>[1,4,5,6,2,3]=>10
[4,2,3,6,1,5]=>[1,4,6,5,2,3]=>26
[4,2,3,6,5,1]=>[1,4,6,2,3,5]=>15
[4,2,5,1,3,6]=>[1,4,2,3,5,6]=>3
[4,2,5,1,6,3]=>[1,4,2,3,5,6]=>3
[4,2,5,3,1,6]=>[1,4,3,5,2,6]=>7
[4,2,5,3,6,1]=>[1,4,3,5,6,2]=>9
[4,2,5,6,1,3]=>[1,4,6,3,5,2]=>31
[4,2,5,6,3,1]=>[1,4,6,2,3,5]=>15
[4,2,6,1,3,5]=>[1,4,2,3,6,5]=>15
[4,2,6,1,5,3]=>[1,4,2,3,6,5]=>15
[4,2,6,3,1,5]=>[1,4,3,6,5,2]=>34
[4,2,6,3,5,1]=>[1,4,3,6,2,5]=>26
[4,2,6,5,1,3]=>[1,4,5,2,3,6]=>6
[4,2,6,5,3,1]=>[1,4,5,3,6,2]=>12
[4,3,1,2,5,6]=>[1,4,2,3,5,6]=>3
[4,3,1,2,6,5]=>[1,4,2,3,5,6]=>3
[4,3,1,5,2,6]=>[1,4,5,2,3,6]=>6
[4,3,1,5,6,2]=>[1,4,5,6,2,3]=>10
[4,3,1,6,2,5]=>[1,4,6,5,2,3]=>26
[4,3,1,6,5,2]=>[1,4,6,2,3,5]=>15
[4,3,2,1,5,6]=>[1,4,2,3,5,6]=>3
[4,3,2,1,6,5]=>[1,4,2,3,5,6]=>3
[4,3,2,5,1,6]=>[1,4,5,2,3,6]=>6
[4,3,2,5,6,1]=>[1,4,5,6,2,3]=>10
[4,3,2,6,1,5]=>[1,4,6,5,2,3]=>26
[4,3,2,6,5,1]=>[1,4,6,2,3,5]=>15
[4,3,5,1,2,6]=>[1,4,2,3,5,6]=>3
[4,3,5,1,6,2]=>[1,4,2,3,5,6]=>3
[4,3,5,2,1,6]=>[1,4,2,3,5,6]=>3
[4,3,5,2,6,1]=>[1,4,2,3,5,6]=>3
[4,3,5,6,1,2]=>[1,4,6,2,3,5]=>15
[4,3,5,6,2,1]=>[1,4,6,2,3,5]=>15
[4,3,6,1,2,5]=>[1,4,2,3,6,5]=>15
[4,3,6,1,5,2]=>[1,4,2,3,6,5]=>15
[4,3,6,2,1,5]=>[1,4,2,3,6,5]=>15
[4,3,6,2,5,1]=>[1,4,2,3,6,5]=>15
[4,3,6,5,1,2]=>[1,4,5,2,3,6]=>6
[4,3,6,5,2,1]=>[1,4,5,2,3,6]=>6
[4,5,1,2,3,6]=>[1,4,2,5,3,6]=>8
[4,5,1,2,6,3]=>[1,4,2,5,6,3]=>15
[4,5,1,3,2,6]=>[1,4,3,2,5,6]=>5
[4,5,1,3,6,2]=>[1,4,3,2,5,6]=>5
[4,5,1,6,2,3]=>[1,4,6,3,2,5]=>23
[4,5,1,6,3,2]=>[1,4,6,2,5,3]=>38
[4,5,2,1,3,6]=>[1,4,2,5,3,6]=>8
[4,5,2,1,6,3]=>[1,4,2,5,6,3]=>15
[4,5,2,3,1,6]=>[1,4,3,2,5,6]=>5
[4,5,2,3,6,1]=>[1,4,3,2,5,6]=>5
[4,5,2,6,1,3]=>[1,4,6,3,2,5]=>23
[4,5,2,6,3,1]=>[1,4,6,2,5,3]=>38
[4,5,3,1,2,6]=>[1,4,2,5,3,6]=>8
[4,5,3,1,6,2]=>[1,4,2,5,6,3]=>15
[4,5,3,2,1,6]=>[1,4,2,5,3,6]=>8
[4,5,3,2,6,1]=>[1,4,2,5,6,3]=>15
[4,5,3,6,1,2]=>[1,4,6,2,5,3]=>38
[4,5,3,6,2,1]=>[1,4,6,2,5,3]=>38
[4,5,6,1,2,3]=>[1,4,2,5,3,6]=>8
[4,5,6,1,3,2]=>[1,4,2,5,3,6]=>8
[4,5,6,2,1,3]=>[1,4,2,5,3,6]=>8
[4,5,6,2,3,1]=>[1,4,2,5,3,6]=>8
[4,5,6,3,1,2]=>[1,4,3,6,2,5]=>26
[4,5,6,3,2,1]=>[1,4,3,6,2,5]=>26
[4,6,1,2,3,5]=>[1,4,2,6,5,3]=>51
[4,6,1,2,5,3]=>[1,4,2,6,3,5]=>25
[4,6,1,3,2,5]=>[1,4,3,2,6,5]=>25
[4,6,1,3,5,2]=>[1,4,3,2,6,5]=>25
[4,6,1,5,2,3]=>[1,4,5,2,6,3]=>15
[4,6,1,5,3,2]=>[1,4,5,3,2,6]=>9
[4,6,2,1,3,5]=>[1,4,2,6,5,3]=>51
[4,6,2,1,5,3]=>[1,4,2,6,3,5]=>25
[4,6,2,3,1,5]=>[1,4,3,2,6,5]=>25
[4,6,2,3,5,1]=>[1,4,3,2,6,5]=>25
[4,6,2,5,1,3]=>[1,4,5,2,6,3]=>15
[4,6,2,5,3,1]=>[1,4,5,3,2,6]=>9
[4,6,3,1,2,5]=>[1,4,2,6,5,3]=>51
[4,6,3,1,5,2]=>[1,4,2,6,3,5]=>25
[4,6,3,2,1,5]=>[1,4,2,6,5,3]=>51
[4,6,3,2,5,1]=>[1,4,2,6,3,5]=>25
[4,6,3,5,1,2]=>[1,4,5,2,6,3]=>15
[4,6,3,5,2,1]=>[1,4,5,2,6,3]=>15
[4,6,5,1,2,3]=>[1,4,2,6,3,5]=>25
[4,6,5,1,3,2]=>[1,4,2,6,3,5]=>25
[4,6,5,2,1,3]=>[1,4,2,6,3,5]=>25
[4,6,5,2,3,1]=>[1,4,2,6,3,5]=>25
[4,6,5,3,1,2]=>[1,4,3,5,2,6]=>7
[4,6,5,3,2,1]=>[1,4,3,5,2,6]=>7
[5,1,2,3,4,6]=>[1,5,4,3,2,6]=>14
[5,1,2,3,6,4]=>[1,5,6,4,3,2]=>28
[5,1,2,4,3,6]=>[1,5,3,2,4,6]=>7
[5,1,2,4,6,3]=>[1,5,6,3,2,4]=>16
[5,1,2,6,3,4]=>[1,5,3,2,4,6]=>7
[5,1,2,6,4,3]=>[1,5,4,6,3,2]=>23
[5,1,3,2,4,6]=>[1,5,4,2,3,6]=>9
[5,1,3,2,6,4]=>[1,5,6,4,2,3]=>19
[5,1,3,4,2,6]=>[1,5,2,3,4,6]=>4
[5,1,3,4,6,2]=>[1,5,6,2,3,4]=>10
[5,1,3,6,2,4]=>[1,5,2,3,4,6]=>4
[5,1,3,6,4,2]=>[1,5,4,6,2,3]=>16
[5,1,4,2,3,6]=>[1,5,3,4,2,6]=>10
[5,1,4,2,6,3]=>[1,5,6,3,4,2]=>22
[5,1,4,3,2,6]=>[1,5,2,3,4,6]=>4
[5,1,4,3,6,2]=>[1,5,6,2,3,4]=>10
[5,1,4,6,2,3]=>[1,5,2,3,4,6]=>4
[5,1,4,6,3,2]=>[1,5,3,4,6,2]=>13
[5,1,6,2,3,4]=>[1,5,3,6,4,2]=>32
[5,1,6,2,4,3]=>[1,5,4,2,3,6]=>9
[5,1,6,3,2,4]=>[1,5,2,3,6,4]=>15
[5,1,6,3,4,2]=>[1,5,4,3,6,2]=>19
[5,1,6,4,2,3]=>[1,5,2,3,6,4]=>15
[5,1,6,4,3,2]=>[1,5,3,6,2,4]=>24
[5,2,1,3,4,6]=>[1,5,4,3,2,6]=>14
[5,2,1,3,6,4]=>[1,5,6,4,3,2]=>28
[5,2,1,4,3,6]=>[1,5,3,2,4,6]=>7
[5,2,1,4,6,3]=>[1,5,6,3,2,4]=>16
[5,2,1,6,3,4]=>[1,5,3,2,4,6]=>7
[5,2,1,6,4,3]=>[1,5,4,6,3,2]=>23
[5,2,3,1,4,6]=>[1,5,4,2,3,6]=>9
[5,2,3,1,6,4]=>[1,5,6,4,2,3]=>19
[5,2,3,4,1,6]=>[1,5,2,3,4,6]=>4
[5,2,3,4,6,1]=>[1,5,6,2,3,4]=>10
[5,2,3,6,1,4]=>[1,5,2,3,4,6]=>4
[5,2,3,6,4,1]=>[1,5,4,6,2,3]=>16
[5,2,4,1,3,6]=>[1,5,3,4,2,6]=>10
[5,2,4,1,6,3]=>[1,5,6,3,4,2]=>22
[5,2,4,3,1,6]=>[1,5,2,3,4,6]=>4
[5,2,4,3,6,1]=>[1,5,6,2,3,4]=>10
[5,2,4,6,1,3]=>[1,5,2,3,4,6]=>4
[5,2,4,6,3,1]=>[1,5,3,4,6,2]=>13
[5,2,6,1,3,4]=>[1,5,3,6,4,2]=>32
[5,2,6,1,4,3]=>[1,5,4,2,3,6]=>9
[5,2,6,3,1,4]=>[1,5,2,3,6,4]=>15
[5,2,6,3,4,1]=>[1,5,4,3,6,2]=>19
[5,2,6,4,1,3]=>[1,5,2,3,6,4]=>15
[5,2,6,4,3,1]=>[1,5,3,6,2,4]=>24
[5,3,1,2,4,6]=>[1,5,4,2,3,6]=>9
[5,3,1,2,6,4]=>[1,5,6,4,2,3]=>19
[5,3,1,4,2,6]=>[1,5,2,3,4,6]=>4
[5,3,1,4,6,2]=>[1,5,6,2,3,4]=>10
[5,3,1,6,2,4]=>[1,5,2,3,4,6]=>4
[5,3,1,6,4,2]=>[1,5,4,6,2,3]=>16
[5,3,2,1,4,6]=>[1,5,4,2,3,6]=>9
[5,3,2,1,6,4]=>[1,5,6,4,2,3]=>19
[5,3,2,4,1,6]=>[1,5,2,3,4,6]=>4
[5,3,2,4,6,1]=>[1,5,6,2,3,4]=>10
[5,3,2,6,1,4]=>[1,5,2,3,4,6]=>4
[5,3,2,6,4,1]=>[1,5,4,6,2,3]=>16
[5,3,4,1,2,6]=>[1,5,2,3,4,6]=>4
[5,3,4,1,6,2]=>[1,5,6,2,3,4]=>10
[5,3,4,2,1,6]=>[1,5,2,3,4,6]=>4
[5,3,4,2,6,1]=>[1,5,6,2,3,4]=>10
[5,3,4,6,1,2]=>[1,5,2,3,4,6]=>4
[5,3,4,6,2,1]=>[1,5,2,3,4,6]=>4
[5,3,6,1,2,4]=>[1,5,2,3,6,4]=>15
[5,3,6,1,4,2]=>[1,5,4,2,3,6]=>9
[5,3,6,2,1,4]=>[1,5,2,3,6,4]=>15
[5,3,6,2,4,1]=>[1,5,4,2,3,6]=>9
[5,3,6,4,1,2]=>[1,5,2,3,6,4]=>15
[5,3,6,4,2,1]=>[1,5,2,3,6,4]=>15
[5,4,1,2,3,6]=>[1,5,3,2,4,6]=>7
[5,4,1,2,6,3]=>[1,5,6,3,2,4]=>16
[5,4,1,3,2,6]=>[1,5,2,4,3,6]=>11
[5,4,1,3,6,2]=>[1,5,6,2,4,3]=>26
[5,4,1,6,2,3]=>[1,5,2,4,6,3]=>21
[5,4,1,6,3,2]=>[1,5,3,2,4,6]=>7
[5,4,2,1,3,6]=>[1,5,3,2,4,6]=>7
[5,4,2,1,6,3]=>[1,5,6,3,2,4]=>16
[5,4,2,3,1,6]=>[1,5,2,4,3,6]=>11
[5,4,2,3,6,1]=>[1,5,6,2,4,3]=>26
[5,4,2,6,1,3]=>[1,5,2,4,6,3]=>21
[5,4,2,6,3,1]=>[1,5,3,2,4,6]=>7
[5,4,3,1,2,6]=>[1,5,2,4,3,6]=>11
[5,4,3,1,6,2]=>[1,5,6,2,4,3]=>26
[5,4,3,2,1,6]=>[1,5,2,4,3,6]=>11
[5,4,3,2,6,1]=>[1,5,6,2,4,3]=>26
[5,4,3,6,1,2]=>[1,5,2,4,6,3]=>21
[5,4,3,6,2,1]=>[1,5,2,4,6,3]=>21
[5,4,6,1,2,3]=>[1,5,2,4,3,6]=>11
[5,4,6,1,3,2]=>[1,5,3,6,2,4]=>24
[5,4,6,2,1,3]=>[1,5,2,4,3,6]=>11
[5,4,6,2,3,1]=>[1,5,3,6,2,4]=>24
[5,4,6,3,1,2]=>[1,5,2,4,3,6]=>11
[5,4,6,3,2,1]=>[1,5,2,4,3,6]=>11
[5,6,1,2,3,4]=>[1,5,3,2,6,4]=>26
[5,6,1,2,4,3]=>[1,5,4,2,6,3]=>23
[5,6,1,3,2,4]=>[1,5,2,6,4,3]=>44
[5,6,1,3,4,2]=>[1,5,4,3,2,6]=>14
[5,6,1,4,2,3]=>[1,5,2,6,3,4]=>20
[5,6,1,4,3,2]=>[1,5,3,2,6,4]=>26
[5,6,2,1,3,4]=>[1,5,3,2,6,4]=>26
[5,6,2,1,4,3]=>[1,5,4,2,6,3]=>23
[5,6,2,3,1,4]=>[1,5,2,6,4,3]=>44
[5,6,2,3,4,1]=>[1,5,4,3,2,6]=>14
[5,6,2,4,1,3]=>[1,5,2,6,3,4]=>20
[5,6,2,4,3,1]=>[1,5,3,2,6,4]=>26
[5,6,3,1,2,4]=>[1,5,2,6,4,3]=>44
[5,6,3,1,4,2]=>[1,5,4,2,6,3]=>23
[5,6,3,2,1,4]=>[1,5,2,6,4,3]=>44
[5,6,3,2,4,1]=>[1,5,4,2,6,3]=>23
[5,6,3,4,1,2]=>[1,5,2,6,3,4]=>20
[5,6,3,4,2,1]=>[1,5,2,6,3,4]=>20
[5,6,4,1,2,3]=>[1,5,2,6,3,4]=>20
[5,6,4,1,3,2]=>[1,5,3,4,2,6]=>10
[5,6,4,2,1,3]=>[1,5,2,6,3,4]=>20
[5,6,4,2,3,1]=>[1,5,3,4,2,6]=>10
[5,6,4,3,1,2]=>[1,5,2,6,3,4]=>20
[5,6,4,3,2,1]=>[1,5,2,6,3,4]=>20
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>42
[6,1,2,3,5,4]=>[1,6,4,3,2,5]=>19
[6,1,2,4,3,5]=>[1,6,5,3,2,4]=>23
[6,1,2,4,5,3]=>[1,6,3,2,4,5]=>9
[6,1,2,5,3,4]=>[1,6,4,5,3,2]=>32
[6,1,2,5,4,3]=>[1,6,3,2,4,5]=>9
[6,1,3,2,4,5]=>[1,6,5,4,2,3]=>28
[6,1,3,2,5,4]=>[1,6,4,2,3,5]=>12
[6,1,3,4,2,5]=>[1,6,5,2,3,4]=>14
[6,1,3,4,5,2]=>[1,6,2,3,4,5]=>5
[6,1,3,5,2,4]=>[1,6,4,5,2,3]=>22
[6,1,3,5,4,2]=>[1,6,2,3,4,5]=>5
[6,1,4,2,3,5]=>[1,6,5,3,4,2]=>32
[6,1,4,2,5,3]=>[1,6,3,4,2,5]=>13
[6,1,4,3,2,5]=>[1,6,5,2,3,4]=>14
[6,1,4,3,5,2]=>[1,6,2,3,4,5]=>5
[6,1,4,5,2,3]=>[1,6,3,4,5,2]=>17
[6,1,4,5,3,2]=>[1,6,2,3,4,5]=>5
[6,1,5,2,3,4]=>[1,6,4,2,3,5]=>12
[6,1,5,2,4,3]=>[1,6,3,5,4,2]=>43
[6,1,5,3,2,4]=>[1,6,4,3,5,2]=>26
[6,1,5,3,4,2]=>[1,6,2,3,5,4]=>19
[6,1,5,4,2,3]=>[1,6,3,5,2,4]=>32
[6,1,5,4,3,2]=>[1,6,2,3,5,4]=>19
[6,2,1,3,4,5]=>[1,6,5,4,3,2]=>42
[6,2,1,3,5,4]=>[1,6,4,3,2,5]=>19
[6,2,1,4,3,5]=>[1,6,5,3,2,4]=>23
[6,2,1,4,5,3]=>[1,6,3,2,4,5]=>9
[6,2,1,5,3,4]=>[1,6,4,5,3,2]=>32
[6,2,1,5,4,3]=>[1,6,3,2,4,5]=>9
[6,2,3,1,4,5]=>[1,6,5,4,2,3]=>28
[6,2,3,1,5,4]=>[1,6,4,2,3,5]=>12
[6,2,3,4,1,5]=>[1,6,5,2,3,4]=>14
[6,2,3,4,5,1]=>[1,6,2,3,4,5]=>5
[6,2,3,5,1,4]=>[1,6,4,5,2,3]=>22
[6,2,3,5,4,1]=>[1,6,2,3,4,5]=>5
[6,2,4,1,3,5]=>[1,6,5,3,4,2]=>32
[6,2,4,1,5,3]=>[1,6,3,4,2,5]=>13
[6,2,4,3,1,5]=>[1,6,5,2,3,4]=>14
[6,2,4,3,5,1]=>[1,6,2,3,4,5]=>5
[6,2,4,5,1,3]=>[1,6,3,4,5,2]=>17
[6,2,4,5,3,1]=>[1,6,2,3,4,5]=>5
[6,2,5,1,3,4]=>[1,6,4,2,3,5]=>12
[6,2,5,1,4,3]=>[1,6,3,5,4,2]=>43
[6,2,5,3,1,4]=>[1,6,4,3,5,2]=>26
[6,2,5,3,4,1]=>[1,6,2,3,5,4]=>19
[6,2,5,4,1,3]=>[1,6,3,5,2,4]=>32
[6,2,5,4,3,1]=>[1,6,2,3,5,4]=>19
[6,3,1,2,4,5]=>[1,6,5,4,2,3]=>28
[6,3,1,2,5,4]=>[1,6,4,2,3,5]=>12
[6,3,1,4,2,5]=>[1,6,5,2,3,4]=>14
[6,3,1,4,5,2]=>[1,6,2,3,4,5]=>5
[6,3,1,5,2,4]=>[1,6,4,5,2,3]=>22
[6,3,1,5,4,2]=>[1,6,2,3,4,5]=>5
[6,3,2,1,4,5]=>[1,6,5,4,2,3]=>28
[6,3,2,1,5,4]=>[1,6,4,2,3,5]=>12
[6,3,2,4,1,5]=>[1,6,5,2,3,4]=>14
[6,3,2,4,5,1]=>[1,6,2,3,4,5]=>5
[6,3,2,5,1,4]=>[1,6,4,5,2,3]=>22
[6,3,2,5,4,1]=>[1,6,2,3,4,5]=>5
[6,3,4,1,2,5]=>[1,6,5,2,3,4]=>14
[6,3,4,1,5,2]=>[1,6,2,3,4,5]=>5
[6,3,4,2,1,5]=>[1,6,5,2,3,4]=>14
[6,3,4,2,5,1]=>[1,6,2,3,4,5]=>5
[6,3,4,5,1,2]=>[1,6,2,3,4,5]=>5
[6,3,4,5,2,1]=>[1,6,2,3,4,5]=>5
[6,3,5,1,2,4]=>[1,6,4,2,3,5]=>12
[6,3,5,1,4,2]=>[1,6,2,3,5,4]=>19
[6,3,5,2,1,4]=>[1,6,4,2,3,5]=>12
[6,3,5,2,4,1]=>[1,6,2,3,5,4]=>19
[6,3,5,4,1,2]=>[1,6,2,3,5,4]=>19
[6,3,5,4,2,1]=>[1,6,2,3,5,4]=>19
[6,4,1,2,3,5]=>[1,6,5,3,2,4]=>23
[6,4,1,2,5,3]=>[1,6,3,2,4,5]=>9
[6,4,1,3,2,5]=>[1,6,5,2,4,3]=>37
[6,4,1,3,5,2]=>[1,6,2,4,3,5]=>14
[6,4,1,5,2,3]=>[1,6,3,2,4,5]=>9
[6,4,1,5,3,2]=>[1,6,2,4,5,3]=>27
[6,4,2,1,3,5]=>[1,6,5,3,2,4]=>23
[6,4,2,1,5,3]=>[1,6,3,2,4,5]=>9
[6,4,2,3,1,5]=>[1,6,5,2,4,3]=>37
[6,4,2,3,5,1]=>[1,6,2,4,3,5]=>14
[6,4,2,5,1,3]=>[1,6,3,2,4,5]=>9
[6,4,2,5,3,1]=>[1,6,2,4,5,3]=>27
[6,4,3,1,2,5]=>[1,6,5,2,4,3]=>37
[6,4,3,1,5,2]=>[1,6,2,4,3,5]=>14
[6,4,3,2,1,5]=>[1,6,5,2,4,3]=>37
[6,4,3,2,5,1]=>[1,6,2,4,3,5]=>14
[6,4,3,5,1,2]=>[1,6,2,4,5,3]=>27
[6,4,3,5,2,1]=>[1,6,2,4,5,3]=>27
[6,4,5,1,2,3]=>[1,6,3,5,2,4]=>32
[6,4,5,1,3,2]=>[1,6,2,4,3,5]=>14
[6,4,5,2,1,3]=>[1,6,3,5,2,4]=>32
[6,4,5,2,3,1]=>[1,6,2,4,3,5]=>14
[6,4,5,3,1,2]=>[1,6,2,4,3,5]=>14
[6,4,5,3,2,1]=>[1,6,2,4,3,5]=>14
[6,5,1,2,3,4]=>[1,6,4,2,5,3]=>31
[6,5,1,2,4,3]=>[1,6,3,2,5,4]=>34
[6,5,1,3,2,4]=>[1,6,4,3,2,5]=>19
[6,5,1,3,4,2]=>[1,6,2,5,4,3]=>58
[6,5,1,4,2,3]=>[1,6,3,2,5,4]=>34
[6,5,1,4,3,2]=>[1,6,2,5,3,4]=>26
[6,5,2,1,3,4]=>[1,6,4,2,5,3]=>31
[6,5,2,1,4,3]=>[1,6,3,2,5,4]=>34
[6,5,2,3,1,4]=>[1,6,4,3,2,5]=>19
[6,5,2,3,4,1]=>[1,6,2,5,4,3]=>58
[6,5,2,4,1,3]=>[1,6,3,2,5,4]=>34
[6,5,2,4,3,1]=>[1,6,2,5,3,4]=>26
[6,5,3,1,2,4]=>[1,6,4,2,5,3]=>31
[6,5,3,1,4,2]=>[1,6,2,5,4,3]=>58
[6,5,3,2,1,4]=>[1,6,4,2,5,3]=>31
[6,5,3,2,4,1]=>[1,6,2,5,4,3]=>58
[6,5,3,4,1,2]=>[1,6,2,5,3,4]=>26
[6,5,3,4,2,1]=>[1,6,2,5,3,4]=>26
[6,5,4,1,2,3]=>[1,6,3,4,2,5]=>13
[6,5,4,1,3,2]=>[1,6,2,5,3,4]=>26
[6,5,4,2,1,3]=>[1,6,3,4,2,5]=>13
[6,5,4,2,3,1]=>[1,6,2,5,3,4]=>26
[6,5,4,3,1,2]=>[1,6,2,5,3,4]=>26
[6,5,4,3,2,1]=>[1,6,2,5,3,4]=>26
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,7,5,6]=>[1,2,3,4,5,7,6]=>6
[1,2,3,4,7,6,5]=>[1,2,3,4,5,7,6]=>6
[1,2,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>1
[1,2,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>1
[1,2,3,5,7,4,6]=>[1,2,3,4,5,7,6]=>6
[1,2,3,5,7,6,4]=>[1,2,3,4,5,7,6]=>6
[1,2,3,6,4,5,7]=>[1,2,3,4,6,5,7]=>5
[1,2,3,6,5,4,7]=>[1,2,3,4,6,5,7]=>5
[1,2,3,6,7,4,5]=>[1,2,3,4,6,5,7]=>5
[1,2,3,6,7,5,4]=>[1,2,3,4,6,5,7]=>5
[1,2,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>1
[1,2,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>1
[1,2,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>1
[1,2,4,3,7,5,6]=>[1,2,3,4,5,7,6]=>6
[1,2,4,3,7,6,5]=>[1,2,3,4,5,7,6]=>6
[1,2,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>1
[1,2,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>1
[1,2,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>1
[1,2,4,5,7,3,6]=>[1,2,3,4,5,7,6]=>6
[1,2,4,5,7,6,3]=>[1,2,3,4,5,7,6]=>6
[1,2,4,6,3,5,7]=>[1,2,3,4,6,5,7]=>5
[1,2,4,6,5,3,7]=>[1,2,3,4,6,5,7]=>5
[1,2,4,6,7,3,5]=>[1,2,3,4,6,5,7]=>5
[1,2,4,6,7,5,3]=>[1,2,3,4,6,5,7]=>5
[1,2,6,7,3,4,5]=>[1,2,3,6,4,7,5]=>40
[1,2,6,7,4,3,5]=>[1,2,3,6,4,7,5]=>40
[1,2,6,7,5,3,4]=>[1,2,3,6,4,7,5]=>40
[1,2,6,7,5,4,3]=>[1,2,3,6,4,7,5]=>40
[1,3,2,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,3,2,4,5,7,6]=>[1,2,3,4,5,6,7]=>1
[1,3,2,4,6,5,7]=>[1,2,3,4,5,6,7]=>1
[1,3,2,4,6,7,5]=>[1,2,3,4,5,6,7]=>1
[1,3,2,4,7,5,6]=>[1,2,3,4,5,7,6]=>6
[1,3,2,4,7,6,5]=>[1,2,3,4,5,7,6]=>6
[1,3,2,5,4,6,7]=>[1,2,3,4,5,6,7]=>1
[1,3,2,5,4,7,6]=>[1,2,3,4,5,6,7]=>1
[1,3,2,5,6,4,7]=>[1,2,3,4,5,6,7]=>1
[1,3,2,5,6,7,4]=>[1,2,3,4,5,6,7]=>1
[1,3,2,5,7,4,6]=>[1,2,3,4,5,7,6]=>6
[1,3,2,5,7,6,4]=>[1,2,3,4,5,7,6]=>6
[1,3,2,6,4,5,7]=>[1,2,3,4,6,5,7]=>5
[1,3,2,6,5,4,7]=>[1,2,3,4,6,5,7]=>5
[1,3,2,6,7,4,5]=>[1,2,3,4,6,5,7]=>5
[1,3,2,6,7,5,4]=>[1,2,3,4,6,5,7]=>5
[1,3,4,2,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,3,4,2,5,7,6]=>[1,2,3,4,5,6,7]=>1
[1,3,4,2,6,5,7]=>[1,2,3,4,5,6,7]=>1
[1,3,4,2,6,7,5]=>[1,2,3,4,5,6,7]=>1
[1,3,4,2,7,5,6]=>[1,2,3,4,5,7,6]=>6
[1,3,4,2,7,6,5]=>[1,2,3,4,5,7,6]=>6
[1,3,4,5,2,6,7]=>[1,2,3,4,5,6,7]=>1
[1,3,4,5,2,7,6]=>[1,2,3,4,5,6,7]=>1
[1,3,4,5,6,2,7]=>[1,2,3,4,5,6,7]=>1
[1,3,4,5,6,7,2]=>[1,2,3,4,5,6,7]=>1
[1,3,4,5,7,2,6]=>[1,2,3,4,5,7,6]=>6
[1,3,4,5,7,6,2]=>[1,2,3,4,5,7,6]=>6
[1,3,4,6,2,5,7]=>[1,2,3,4,6,5,7]=>5
[1,3,4,6,5,2,7]=>[1,2,3,4,6,5,7]=>5
[1,3,4,6,7,2,5]=>[1,2,3,4,6,5,7]=>5
[1,3,4,6,7,5,2]=>[1,2,3,4,6,5,7]=>5
[1,3,6,7,2,4,5]=>[1,2,3,6,4,7,5]=>40
[1,3,6,7,4,2,5]=>[1,2,3,6,4,7,5]=>40
[1,3,6,7,5,2,4]=>[1,2,3,6,4,7,5]=>40
[1,3,6,7,5,4,2]=>[1,2,3,6,4,7,5]=>40
[1,6,2,7,4,3,5]=>[1,2,6,3,4,7,5]=>45
[1,6,2,7,5,3,4]=>[1,2,6,3,4,7,5]=>45
[1,6,3,7,4,2,5]=>[1,2,6,3,4,7,5]=>45
[1,6,3,7,5,2,4]=>[1,2,6,3,4,7,5]=>45
[1,6,4,7,2,3,5]=>[1,2,6,3,4,7,5]=>45
[1,6,4,7,3,2,5]=>[1,2,6,3,4,7,5]=>45
[1,6,4,7,5,2,3]=>[1,2,6,3,4,7,5]=>45
[1,6,4,7,5,3,2]=>[1,2,6,3,4,7,5]=>45
[2,1,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[2,1,3,4,5,7,6]=>[1,2,3,4,5,6,7]=>1
[2,1,3,4,6,5,7]=>[1,2,3,4,5,6,7]=>1
[2,1,3,4,6,7,5]=>[1,2,3,4,5,6,7]=>1
[2,1,3,4,7,5,6]=>[1,2,3,4,5,7,6]=>6
[2,1,3,4,7,6,5]=>[1,2,3,4,5,7,6]=>6
[2,1,3,5,4,6,7]=>[1,2,3,4,5,6,7]=>1
[2,1,3,5,4,7,6]=>[1,2,3,4,5,6,7]=>1
[2,1,3,5,6,4,7]=>[1,2,3,4,5,6,7]=>1
[2,1,3,5,6,7,4]=>[1,2,3,4,5,6,7]=>1
[2,1,3,5,7,4,6]=>[1,2,3,4,5,7,6]=>6
[2,1,3,5,7,6,4]=>[1,2,3,4,5,7,6]=>6
[2,1,3,6,4,5,7]=>[1,2,3,4,6,5,7]=>5
[2,1,3,6,5,4,7]=>[1,2,3,4,6,5,7]=>5
[2,1,3,6,7,4,5]=>[1,2,3,4,6,5,7]=>5
[2,1,3,6,7,5,4]=>[1,2,3,4,6,5,7]=>5
[2,1,4,3,5,6,7]=>[1,2,3,4,5,6,7]=>1
[2,1,4,3,5,7,6]=>[1,2,3,4,5,6,7]=>1
[2,1,4,3,6,5,7]=>[1,2,3,4,5,6,7]=>1
[2,1,4,3,6,7,5]=>[1,2,3,4,5,6,7]=>1
[2,1,4,3,7,5,6]=>[1,2,3,4,5,7,6]=>6
[2,1,4,3,7,6,5]=>[1,2,3,4,5,7,6]=>6
[2,1,4,5,3,6,7]=>[1,2,3,4,5,6,7]=>1
[2,1,4,5,3,7,6]=>[1,2,3,4,5,6,7]=>1
[2,1,4,5,6,3,7]=>[1,2,3,4,5,6,7]=>1
[2,1,4,5,6,7,3]=>[1,2,3,4,5,6,7]=>1
[2,1,4,5,7,3,6]=>[1,2,3,4,5,7,6]=>6
[2,1,4,5,7,6,3]=>[1,2,3,4,5,7,6]=>6
[2,1,4,6,3,5,7]=>[1,2,3,4,6,5,7]=>5
[2,1,4,6,5,3,7]=>[1,2,3,4,6,5,7]=>5
[2,1,4,6,7,3,5]=>[1,2,3,4,6,5,7]=>5
[2,1,4,6,7,5,3]=>[1,2,3,4,6,5,7]=>5
[2,1,6,7,3,4,5]=>[1,2,3,6,4,7,5]=>40
[2,1,6,7,4,3,5]=>[1,2,3,6,4,7,5]=>40
[2,1,6,7,5,3,4]=>[1,2,3,6,4,7,5]=>40
[2,1,6,7,5,4,3]=>[1,2,3,6,4,7,5]=>40
[2,3,1,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[2,3,1,4,5,7,6]=>[1,2,3,4,5,6,7]=>1
[2,3,1,4,6,5,7]=>[1,2,3,4,5,6,7]=>1
[2,3,1,4,6,7,5]=>[1,2,3,4,5,6,7]=>1
[2,3,1,4,7,5,6]=>[1,2,3,4,5,7,6]=>6
[2,3,1,4,7,6,5]=>[1,2,3,4,5,7,6]=>6
[2,3,1,5,4,6,7]=>[1,2,3,4,5,6,7]=>1
[2,3,1,5,4,7,6]=>[1,2,3,4,5,6,7]=>1
[2,3,1,5,6,4,7]=>[1,2,3,4,5,6,7]=>1
[2,3,1,5,6,7,4]=>[1,2,3,4,5,6,7]=>1
[2,3,1,5,7,4,6]=>[1,2,3,4,5,7,6]=>6
[2,3,1,5,7,6,4]=>[1,2,3,4,5,7,6]=>6
[2,3,1,6,4,5,7]=>[1,2,3,4,6,5,7]=>5
[2,3,1,6,5,4,7]=>[1,2,3,4,6,5,7]=>5
[2,3,1,6,7,4,5]=>[1,2,3,4,6,5,7]=>5
[2,3,1,6,7,5,4]=>[1,2,3,4,6,5,7]=>5
[2,3,4,1,5,6,7]=>[1,2,3,4,5,6,7]=>1
[2,3,4,1,5,7,6]=>[1,2,3,4,5,6,7]=>1
[2,3,4,1,6,5,7]=>[1,2,3,4,5,6,7]=>1
[2,3,4,1,6,7,5]=>[1,2,3,4,5,6,7]=>1
[2,3,4,1,7,5,6]=>[1,2,3,4,5,7,6]=>6
[2,3,4,1,7,6,5]=>[1,2,3,4,5,7,6]=>6
[2,3,4,5,1,6,7]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,1,7,6]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,6,1,7]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,7,1,6]=>[1,2,3,4,5,7,6]=>6
[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>6
[2,3,4,6,1,5,7]=>[1,2,3,4,6,5,7]=>5
[2,3,4,6,5,1,7]=>[1,2,3,4,6,5,7]=>5
[2,3,4,6,7,1,5]=>[1,2,3,4,6,5,7]=>5
[2,3,4,6,7,5,1]=>[1,2,3,4,6,5,7]=>5
[2,3,6,7,1,4,5]=>[1,2,3,6,4,7,5]=>40
[2,3,6,7,4,1,5]=>[1,2,3,6,4,7,5]=>40
[2,3,6,7,5,1,4]=>[1,2,3,6,4,7,5]=>40
[2,3,6,7,5,4,1]=>[1,2,3,6,4,7,5]=>40
[2,6,1,7,4,3,5]=>[1,2,6,3,4,7,5]=>45
[2,6,1,7,5,3,4]=>[1,2,6,3,4,7,5]=>45
[2,6,3,7,4,1,5]=>[1,2,6,3,4,7,5]=>45
[2,6,3,7,5,1,4]=>[1,2,6,3,4,7,5]=>45
[2,6,4,7,1,3,5]=>[1,2,6,3,4,7,5]=>45
[2,6,4,7,3,1,5]=>[1,2,6,3,4,7,5]=>45
[2,6,4,7,5,1,3]=>[1,2,6,3,4,7,5]=>45
[2,6,4,7,5,3,1]=>[1,2,6,3,4,7,5]=>45
[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>2
[3,1,2,4,5,7,6]=>[1,3,2,4,5,6,7]=>2
[3,1,2,4,6,5,7]=>[1,3,2,4,5,6,7]=>2
[3,1,2,4,6,7,5]=>[1,3,2,4,5,6,7]=>2
[3,1,2,5,4,6,7]=>[1,3,2,4,5,6,7]=>2
[3,1,2,5,4,7,6]=>[1,3,2,4,5,6,7]=>2
[3,1,2,5,6,4,7]=>[1,3,2,4,5,6,7]=>2
[3,1,2,5,6,7,4]=>[1,3,2,4,5,6,7]=>2
[3,1,7,2,4,5,6]=>[1,3,7,6,5,4,2]=>378
[3,1,7,4,5,6,2]=>[1,3,7,2,4,5,6]=>24
[3,1,7,4,6,5,2]=>[1,3,7,2,4,5,6]=>24
[3,1,7,5,4,6,2]=>[1,3,7,2,4,5,6]=>24
[3,1,7,5,6,4,2]=>[1,3,7,2,4,5,6]=>24
[3,2,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>2
[3,2,1,4,5,7,6]=>[1,3,2,4,5,6,7]=>2
[3,2,1,4,6,5,7]=>[1,3,2,4,5,6,7]=>2
[3,2,1,4,6,7,5]=>[1,3,2,4,5,6,7]=>2
[3,2,1,5,4,6,7]=>[1,3,2,4,5,6,7]=>2
[3,2,1,5,4,7,6]=>[1,3,2,4,5,6,7]=>2
[3,2,1,5,6,4,7]=>[1,3,2,4,5,6,7]=>2
[3,2,1,5,6,7,4]=>[1,3,2,4,5,6,7]=>2
[3,2,7,1,4,5,6]=>[1,3,7,6,5,4,2]=>378
[3,2,7,4,5,6,1]=>[1,3,7,2,4,5,6]=>24
[3,2,7,4,6,5,1]=>[1,3,7,2,4,5,6]=>24
[3,2,7,5,4,6,1]=>[1,3,7,2,4,5,6]=>24
[3,2,7,5,6,4,1]=>[1,3,7,2,4,5,6]=>24
[3,4,1,2,5,6,7]=>[1,3,2,4,5,6,7]=>2
[3,4,1,2,5,7,6]=>[1,3,2,4,5,6,7]=>2
[3,4,1,2,6,5,7]=>[1,3,2,4,5,6,7]=>2
[3,4,1,2,6,7,5]=>[1,3,2,4,5,6,7]=>2
[3,4,1,5,2,6,7]=>[1,3,2,4,5,6,7]=>2
[3,4,1,5,2,7,6]=>[1,3,2,4,5,6,7]=>2
[3,4,1,5,6,2,7]=>[1,3,2,4,5,6,7]=>2
[3,4,1,5,6,7,2]=>[1,3,2,4,5,6,7]=>2
[3,4,2,1,5,6,7]=>[1,3,2,4,5,6,7]=>2
[3,4,2,1,5,7,6]=>[1,3,2,4,5,6,7]=>2
[3,4,2,1,6,5,7]=>[1,3,2,4,5,6,7]=>2
[3,4,2,1,6,7,5]=>[1,3,2,4,5,6,7]=>2
[3,4,2,5,1,6,7]=>[1,3,2,4,5,6,7]=>2
[3,4,2,5,1,7,6]=>[1,3,2,4,5,6,7]=>2
[3,4,2,5,6,1,7]=>[1,3,2,4,5,6,7]=>2
[3,4,2,5,6,7,1]=>[1,3,2,4,5,6,7]=>2
[3,4,7,1,5,6,2]=>[1,3,7,2,4,5,6]=>24
[3,4,7,1,6,5,2]=>[1,3,7,2,4,5,6]=>24
[3,4,7,2,5,6,1]=>[1,3,7,2,4,5,6]=>24
[3,4,7,2,6,5,1]=>[1,3,7,2,4,5,6]=>24
[3,4,7,5,1,6,2]=>[1,3,7,2,4,5,6]=>24
[3,4,7,5,2,6,1]=>[1,3,7,2,4,5,6]=>24
[3,4,7,5,6,1,2]=>[1,3,7,2,4,5,6]=>24
[3,4,7,5,6,2,1]=>[1,3,7,2,4,5,6]=>24
[4,1,2,6,3,7,5]=>[1,4,6,7,5,3,2]=>97
[4,1,2,7,3,5,6]=>[1,4,7,6,5,3,2]=>211
[4,1,3,6,5,7,2]=>[1,4,6,7,2,3,5]=>45
[4,1,3,7,5,6,2]=>[1,4,7,2,3,5,6]=>27
[4,1,3,7,6,5,2]=>[1,4,7,2,3,5,6]=>27
[4,1,5,6,3,7,2]=>[1,4,6,7,2,3,5]=>45
[4,1,5,7,3,6,2]=>[1,4,7,2,3,5,6]=>27
[4,1,5,7,6,3,2]=>[1,4,7,2,3,5,6]=>27
[4,2,1,6,3,7,5]=>[1,4,6,7,5,3,2]=>97
[4,2,1,7,3,5,6]=>[1,4,7,6,5,3,2]=>211
[4,2,3,6,5,7,1]=>[1,4,6,7,2,3,5]=>45
[4,2,3,7,5,6,1]=>[1,4,7,2,3,5,6]=>27
[4,2,3,7,6,5,1]=>[1,4,7,2,3,5,6]=>27
[4,2,5,6,3,7,1]=>[1,4,6,7,2,3,5]=>45
[4,2,5,7,3,6,1]=>[1,4,7,2,3,5,6]=>27
[4,2,5,7,6,3,1]=>[1,4,7,2,3,5,6]=>27
[4,3,1,6,5,7,2]=>[1,4,6,7,2,3,5]=>45
[4,3,1,7,5,6,2]=>[1,4,7,2,3,5,6]=>27
[4,3,1,7,6,5,2]=>[1,4,7,2,3,5,6]=>27
[4,3,2,6,5,7,1]=>[1,4,6,7,2,3,5]=>45
[4,3,2,7,5,6,1]=>[1,4,7,2,3,5,6]=>27
[4,3,2,7,6,5,1]=>[1,4,7,2,3,5,6]=>27
[4,3,5,6,1,7,2]=>[1,4,6,7,2,3,5]=>45
[4,3,5,6,2,7,1]=>[1,4,6,7,2,3,5]=>45
[4,3,5,7,1,6,2]=>[1,4,7,2,3,5,6]=>27
[4,3,5,7,2,6,1]=>[1,4,7,2,3,5,6]=>27
[4,3,5,7,6,1,2]=>[1,4,7,2,3,5,6]=>27
[4,3,5,7,6,2,1]=>[1,4,7,2,3,5,6]=>27
[5,1,2,3,6,7,4]=>[1,5,6,7,4,3,2]=>48
[5,1,2,3,7,4,6]=>[1,5,7,6,4,3,2]=>124
[5,1,2,7,4,3,6]=>[1,5,4,7,6,3,2]=>125
[5,1,2,7,6,4,3]=>[1,5,6,4,7,3,2]=>43
[5,1,3,4,6,7,2]=>[1,5,6,7,2,3,4]=>20
[5,1,3,4,7,6,2]=>[1,5,7,2,3,4,6]=>24
[5,1,3,6,7,4,2]=>[1,5,7,2,3,4,6]=>24
[5,1,3,7,2,4,6]=>[1,5,2,3,4,7,6]=>24
[5,1,3,7,2,6,4]=>[1,5,2,3,4,7,6]=>24
[5,1,4,3,6,7,2]=>[1,5,6,7,2,3,4]=>20
[5,1,4,3,7,6,2]=>[1,5,7,2,3,4,6]=>24
[5,1,4,6,7,3,2]=>[1,5,7,2,3,4,6]=>24
[5,1,4,7,2,3,6]=>[1,5,2,3,4,7,6]=>24
[5,1,4,7,2,6,3]=>[1,5,2,3,4,7,6]=>24
[5,2,1,3,6,7,4]=>[1,5,6,7,4,3,2]=>48
[5,2,1,3,7,4,6]=>[1,5,7,6,4,3,2]=>124
[5,2,1,7,4,3,6]=>[1,5,4,7,6,3,2]=>125
[5,2,1,7,6,4,3]=>[1,5,6,4,7,3,2]=>43
[5,2,3,4,6,7,1]=>[1,5,6,7,2,3,4]=>20
[5,2,3,4,7,6,1]=>[1,5,7,2,3,4,6]=>24
[5,2,3,6,7,4,1]=>[1,5,7,2,3,4,6]=>24
[5,2,3,7,1,4,6]=>[1,5,2,3,4,7,6]=>24
[5,2,3,7,1,6,4]=>[1,5,2,3,4,7,6]=>24
[5,2,4,3,6,7,1]=>[1,5,6,7,2,3,4]=>20
[5,2,4,3,7,6,1]=>[1,5,7,2,3,4,6]=>24
[5,2,4,6,7,3,1]=>[1,5,7,2,3,4,6]=>24
[5,2,4,7,1,3,6]=>[1,5,2,3,4,7,6]=>24
[5,2,4,7,1,6,3]=>[1,5,2,3,4,7,6]=>24
[5,3,1,4,6,7,2]=>[1,5,6,7,2,3,4]=>20
[5,3,1,4,7,6,2]=>[1,5,7,2,3,4,6]=>24
[5,3,1,6,7,4,2]=>[1,5,7,2,3,4,6]=>24
[5,3,1,7,2,4,6]=>[1,5,2,3,4,7,6]=>24
[5,3,1,7,2,6,4]=>[1,5,2,3,4,7,6]=>24
[5,3,2,4,6,7,1]=>[1,5,6,7,2,3,4]=>20
[5,3,2,4,7,6,1]=>[1,5,7,2,3,4,6]=>24
[5,3,2,6,7,4,1]=>[1,5,7,2,3,4,6]=>24
[5,3,2,7,1,4,6]=>[1,5,2,3,4,7,6]=>24
[5,3,2,7,1,6,4]=>[1,5,2,3,4,7,6]=>24
[5,3,4,1,6,7,2]=>[1,5,6,7,2,3,4]=>20
[5,3,4,1,7,6,2]=>[1,5,7,2,3,4,6]=>24
[5,3,4,2,6,7,1]=>[1,5,6,7,2,3,4]=>20
[5,3,4,2,7,6,1]=>[1,5,7,2,3,4,6]=>24
[5,3,4,6,7,1,2]=>[1,5,7,2,3,4,6]=>24
[5,3,4,6,7,2,1]=>[1,5,7,2,3,4,6]=>24
[5,3,4,7,1,2,6]=>[1,5,2,3,4,7,6]=>24
[5,3,4,7,1,6,2]=>[1,5,2,3,4,7,6]=>24
[5,3,4,7,2,1,6]=>[1,5,2,3,4,7,6]=>24
[5,3,4,7,2,6,1]=>[1,5,2,3,4,7,6]=>24
[5,7,1,4,2,6,3]=>[1,5,2,7,3,4,6]=>56
[5,7,1,4,6,2,3]=>[1,5,6,2,7,3,4]=>45
[5,7,1,6,2,4,3]=>[1,5,2,7,3,4,6]=>56
[5,7,2,4,1,6,3]=>[1,5,2,7,3,4,6]=>56
[5,7,2,4,6,1,3]=>[1,5,6,2,7,3,4]=>45
[5,7,2,6,1,4,3]=>[1,5,2,7,3,4,6]=>56
[5,7,3,4,1,6,2]=>[1,5,2,7,3,4,6]=>56
[5,7,3,4,2,6,1]=>[1,5,2,7,3,4,6]=>56
[5,7,3,4,6,1,2]=>[1,5,6,2,7,3,4]=>45
[5,7,3,4,6,2,1]=>[1,5,6,2,7,3,4]=>45
[5,7,3,6,1,4,2]=>[1,5,2,7,3,4,6]=>56
[5,7,3,6,2,4,1]=>[1,5,2,7,3,4,6]=>56
[5,7,4,1,2,6,3]=>[1,5,2,7,3,4,6]=>56
[5,7,4,1,6,2,3]=>[1,5,6,2,7,3,4]=>45
[5,7,4,2,1,6,3]=>[1,5,2,7,3,4,6]=>56
[5,7,4,2,6,1,3]=>[1,5,6,2,7,3,4]=>45
[5,7,4,3,1,6,2]=>[1,5,2,7,3,4,6]=>56
[5,7,4,3,2,6,1]=>[1,5,2,7,3,4,6]=>56
[5,7,4,3,6,1,2]=>[1,5,6,2,7,3,4]=>45
[5,7,4,3,6,2,1]=>[1,5,6,2,7,3,4]=>45
[5,7,4,6,1,2,3]=>[1,5,2,7,3,4,6]=>56
[5,7,4,6,1,3,2]=>[1,5,2,7,3,4,6]=>56
[5,7,4,6,2,1,3]=>[1,5,2,7,3,4,6]=>56
[5,7,4,6,2,3,1]=>[1,5,2,7,3,4,6]=>56
[6,1,2,3,4,7,5]=>[1,6,7,5,4,3,2]=>90
[6,1,2,3,7,5,4]=>[1,6,5,7,4,3,2]=>76
[6,1,2,7,4,5,3]=>[1,6,5,4,7,3,2]=>66
[6,1,3,4,5,7,2]=>[1,6,7,2,3,4,5]=>15
[6,1,3,5,4,7,2]=>[1,6,7,2,3,4,5]=>15
[6,1,3,7,4,2,5]=>[1,6,2,3,4,7,5]=>24
[6,1,3,7,5,2,4]=>[1,6,2,3,4,7,5]=>24
[6,1,4,3,5,7,2]=>[1,6,7,2,3,4,5]=>15
[6,1,4,5,3,7,2]=>[1,6,7,2,3,4,5]=>15
[6,1,4,7,3,2,5]=>[1,6,2,3,4,7,5]=>24
[6,1,4,7,5,2,3]=>[1,6,2,3,4,7,5]=>24
[6,1,7,3,4,5,2]=>[1,6,5,4,3,7,2]=>56
[6,1,7,3,5,2,4]=>[1,6,2,3,7,4,5]=>45
[6,1,7,4,5,2,3]=>[1,6,2,3,7,4,5]=>45
[6,1,7,5,3,2,4]=>[1,6,2,3,7,4,5]=>45
[6,1,7,5,4,2,3]=>[1,6,2,3,7,4,5]=>45
[6,2,1,3,4,7,5]=>[1,6,7,5,4,3,2]=>90
[6,2,1,3,7,5,4]=>[1,6,5,7,4,3,2]=>76
[6,2,1,7,4,5,3]=>[1,6,5,4,7,3,2]=>66
[6,2,3,4,5,7,1]=>[1,6,7,2,3,4,5]=>15
[6,2,3,5,4,7,1]=>[1,6,7,2,3,4,5]=>15
[6,2,3,7,4,1,5]=>[1,6,2,3,4,7,5]=>24
[6,2,3,7,5,1,4]=>[1,6,2,3,4,7,5]=>24
[6,2,4,3,5,7,1]=>[1,6,7,2,3,4,5]=>15
[6,2,4,5,3,7,1]=>[1,6,7,2,3,4,5]=>15
[6,2,4,7,3,1,5]=>[1,6,2,3,4,7,5]=>24
[6,2,4,7,5,1,3]=>[1,6,2,3,4,7,5]=>24
[6,2,7,3,4,5,1]=>[1,6,5,4,3,7,2]=>56
[6,2,7,3,5,1,4]=>[1,6,2,3,7,4,5]=>45
[6,2,7,4,5,1,3]=>[1,6,2,3,7,4,5]=>45
[6,2,7,5,3,1,4]=>[1,6,2,3,7,4,5]=>45
[6,2,7,5,4,1,3]=>[1,6,2,3,7,4,5]=>45
[6,3,1,4,5,7,2]=>[1,6,7,2,3,4,5]=>15
[6,3,1,5,4,7,2]=>[1,6,7,2,3,4,5]=>15
[6,3,1,7,4,2,5]=>[1,6,2,3,4,7,5]=>24
[6,3,1,7,5,2,4]=>[1,6,2,3,4,7,5]=>24
[6,3,2,4,5,7,1]=>[1,6,7,2,3,4,5]=>15
[6,3,2,5,4,7,1]=>[1,6,7,2,3,4,5]=>15
[6,3,2,7,4,1,5]=>[1,6,2,3,4,7,5]=>24
[6,3,2,7,5,1,4]=>[1,6,2,3,4,7,5]=>24
[6,3,4,1,5,7,2]=>[1,6,7,2,3,4,5]=>15
[6,3,4,2,5,7,1]=>[1,6,7,2,3,4,5]=>15
[6,3,4,5,1,7,2]=>[1,6,7,2,3,4,5]=>15
[6,3,4,5,2,7,1]=>[1,6,7,2,3,4,5]=>15
[6,3,4,7,1,2,5]=>[1,6,2,3,4,7,5]=>24
[6,3,4,7,2,1,5]=>[1,6,2,3,4,7,5]=>24
[6,3,4,7,5,1,2]=>[1,6,2,3,4,7,5]=>24
[6,3,4,7,5,2,1]=>[1,6,2,3,4,7,5]=>24
[6,3,7,1,5,2,4]=>[1,6,2,3,7,4,5]=>45
[6,3,7,2,5,1,4]=>[1,6,2,3,7,4,5]=>45
[6,3,7,4,5,1,2]=>[1,6,2,3,7,4,5]=>45
[6,3,7,4,5,2,1]=>[1,6,2,3,7,4,5]=>45
[6,3,7,5,1,2,4]=>[1,6,2,3,7,4,5]=>45
[6,3,7,5,2,1,4]=>[1,6,2,3,7,4,5]=>45
[6,3,7,5,4,1,2]=>[1,6,2,3,7,4,5]=>45
[6,3,7,5,4,2,1]=>[1,6,2,3,7,4,5]=>45
[6,7,1,4,5,2,3]=>[1,6,2,7,3,4,5]=>40
[6,7,1,5,4,2,3]=>[1,6,2,7,3,4,5]=>40
[6,7,2,4,5,1,3]=>[1,6,2,7,3,4,5]=>40
[6,7,2,5,4,1,3]=>[1,6,2,7,3,4,5]=>40
[6,7,3,4,5,1,2]=>[1,6,2,7,3,4,5]=>40
[6,7,3,4,5,2,1]=>[1,6,2,7,3,4,5]=>40
[6,7,3,5,4,1,2]=>[1,6,2,7,3,4,5]=>40
[6,7,3,5,4,2,1]=>[1,6,2,7,3,4,5]=>40
[6,7,4,1,5,2,3]=>[1,6,2,7,3,4,5]=>40
[6,7,4,2,5,1,3]=>[1,6,2,7,3,4,5]=>40
[6,7,4,3,5,1,2]=>[1,6,2,7,3,4,5]=>40
[6,7,4,3,5,2,1]=>[1,6,2,7,3,4,5]=>40
[6,7,4,5,1,2,3]=>[1,6,2,7,3,4,5]=>40
[6,7,4,5,2,1,3]=>[1,6,2,7,3,4,5]=>40
[6,7,4,5,3,1,2]=>[1,6,2,7,3,4,5]=>40
[6,7,4,5,3,2,1]=>[1,6,2,7,3,4,5]=>40
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>132
[7,1,2,5,3,4,6]=>[1,7,6,4,5,3,2]=>107
[7,1,2,5,6,3,4]=>[1,7,4,5,6,3,2]=>62
[7,1,2,6,3,5,4]=>[1,7,4,6,5,3,2]=>151
[7,1,2,6,4,3,5]=>[1,7,5,4,6,3,2]=>89
[7,1,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[7,1,3,4,6,5,2]=>[1,7,2,3,4,5,6]=>6
[7,1,3,5,4,6,2]=>[1,7,2,3,4,5,6]=>6
[7,1,3,5,6,4,2]=>[1,7,2,3,4,5,6]=>6
[7,1,4,3,5,6,2]=>[1,7,2,3,4,5,6]=>6
[7,1,4,3,6,5,2]=>[1,7,2,3,4,5,6]=>6
[7,1,4,5,3,6,2]=>[1,7,2,3,4,5,6]=>6
[7,1,4,5,6,3,2]=>[1,7,2,3,4,5,6]=>6
[7,1,5,2,6,4,3]=>[1,7,3,5,6,4,2]=>122
[7,1,6,2,4,5,3]=>[1,7,3,6,5,4,2]=>251
[7,1,6,3,2,5,4]=>[1,7,4,3,6,5,2]=>150
[7,1,6,3,4,2,5]=>[1,7,5,4,3,6,2]=>75
[7,1,6,5,3,2,4]=>[1,7,4,5,3,6,2]=>54
[7,2,1,3,4,5,6]=>[1,7,6,5,4,3,2]=>132
[7,2,1,5,3,4,6]=>[1,7,6,4,5,3,2]=>107
[7,2,1,5,6,3,4]=>[1,7,4,5,6,3,2]=>62
[7,2,1,6,3,5,4]=>[1,7,4,6,5,3,2]=>151
[7,2,1,6,4,3,5]=>[1,7,5,4,6,3,2]=>89
[7,2,3,4,5,6,1]=>[1,7,2,3,4,5,6]=>6
[7,2,3,4,6,5,1]=>[1,7,2,3,4,5,6]=>6
[7,2,3,5,4,6,1]=>[1,7,2,3,4,5,6]=>6
[7,2,3,5,6,4,1]=>[1,7,2,3,4,5,6]=>6
[7,2,4,3,5,6,1]=>[1,7,2,3,4,5,6]=>6
[7,2,4,3,6,5,1]=>[1,7,2,3,4,5,6]=>6
[7,2,4,5,3,6,1]=>[1,7,2,3,4,5,6]=>6
[7,2,4,5,6,3,1]=>[1,7,2,3,4,5,6]=>6
[7,2,5,1,6,4,3]=>[1,7,3,5,6,4,2]=>122
[7,2,6,1,4,5,3]=>[1,7,3,6,5,4,2]=>251
[7,2,6,3,1,5,4]=>[1,7,4,3,6,5,2]=>150
[7,2,6,3,4,1,5]=>[1,7,5,4,3,6,2]=>75
[7,2,6,5,3,1,4]=>[1,7,4,5,3,6,2]=>54
[7,3,1,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[7,3,1,4,6,5,2]=>[1,7,2,3,4,5,6]=>6
[7,3,1,5,4,6,2]=>[1,7,2,3,4,5,6]=>6
[7,3,1,5,6,4,2]=>[1,7,2,3,4,5,6]=>6
[7,3,2,4,5,6,1]=>[1,7,2,3,4,5,6]=>6
[7,3,2,4,6,5,1]=>[1,7,2,3,4,5,6]=>6
[7,3,2,5,4,6,1]=>[1,7,2,3,4,5,6]=>6
[7,3,2,5,6,4,1]=>[1,7,2,3,4,5,6]=>6
[7,3,4,1,5,6,2]=>[1,7,2,3,4,5,6]=>6
[7,3,4,1,6,5,2]=>[1,7,2,3,4,5,6]=>6
[7,3,4,2,5,6,1]=>[1,7,2,3,4,5,6]=>6
[7,3,4,2,6,5,1]=>[1,7,2,3,4,5,6]=>6
[7,3,4,5,1,6,2]=>[1,7,2,3,4,5,6]=>6
[7,3,4,5,2,6,1]=>[1,7,2,3,4,5,6]=>6
[7,3,4,5,6,1,2]=>[1,7,2,3,4,5,6]=>6
[7,3,4,5,6,2,1]=>[1,7,2,3,4,5,6]=>6
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Description
The number of reduced Kogan faces with the permutation as type.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
This is equivalent to finding the number of ways to represent the permutation $\pi \in S_{n+1}$ as a reduced subword of $s_n (s_{n-1} s_n) (s_{n-2} s_{n-1} s_n) \dotsm (s_1 \dotsm s_n)$, or the number of reduced pipe dreams for $\pi$.
Map
cycle-as-one-line notation
Description
Return the permutation obtained by concatenating the cycles of a permutation, each written with minimal element first, sorted by minimal element.
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