Identifier
-
Mp00159:
Permutations
—Demazure product with inverse⟶
Permutations
Mp00223: Permutations —runsort⟶ Permutations
St000255: Permutations ⟶ ℤ
Values
=>
[1]=>[1]=>[1]=>1
[1,2]=>[1,2]=>[1,2]=>1
[2,1]=>[2,1]=>[1,2]=>1
[1,2,3]=>[1,2,3]=>[1,2,3]=>1
[1,3,2]=>[1,3,2]=>[1,3,2]=>2
[2,1,3]=>[2,1,3]=>[1,3,2]=>2
[2,3,1]=>[3,2,1]=>[1,2,3]=>1
[3,1,2]=>[3,2,1]=>[1,2,3]=>1
[3,2,1]=>[3,2,1]=>[1,2,3]=>1
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>1
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>3
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>2
[1,3,4,2]=>[1,4,3,2]=>[1,4,2,3]=>3
[1,4,2,3]=>[1,4,3,2]=>[1,4,2,3]=>3
[1,4,3,2]=>[1,4,3,2]=>[1,4,2,3]=>3
[2,1,3,4]=>[2,1,3,4]=>[1,3,4,2]=>3
[2,1,4,3]=>[2,1,4,3]=>[1,4,2,3]=>3
[2,3,1,4]=>[3,2,1,4]=>[1,4,2,3]=>3
[2,3,4,1]=>[4,2,3,1]=>[1,2,3,4]=>1
[2,4,1,3]=>[3,4,1,2]=>[1,2,3,4]=>1
[2,4,3,1]=>[4,3,2,1]=>[1,2,3,4]=>1
[3,1,2,4]=>[3,2,1,4]=>[1,4,2,3]=>3
[3,1,4,2]=>[4,2,3,1]=>[1,2,3,4]=>1
[3,2,1,4]=>[3,2,1,4]=>[1,4,2,3]=>3
[3,2,4,1]=>[4,2,3,1]=>[1,2,3,4]=>1
[3,4,1,2]=>[4,3,2,1]=>[1,2,3,4]=>1
[3,4,2,1]=>[4,3,2,1]=>[1,2,3,4]=>1
[4,1,2,3]=>[4,2,3,1]=>[1,2,3,4]=>1
[4,1,3,2]=>[4,2,3,1]=>[1,2,3,4]=>1
[4,2,1,3]=>[4,3,2,1]=>[1,2,3,4]=>1
[4,2,3,1]=>[4,3,2,1]=>[1,2,3,4]=>1
[4,3,1,2]=>[4,3,2,1]=>[1,2,3,4]=>1
[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>1
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>1
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>4
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>3
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,5,3,4]=>6
[1,2,5,3,4]=>[1,2,5,4,3]=>[1,2,5,3,4]=>6
[1,2,5,4,3]=>[1,2,5,4,3]=>[1,2,5,3,4]=>6
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>2
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>8
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,4,2,5,3]=>8
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,5,2,3,4]=>4
[1,3,5,2,4]=>[1,4,5,2,3]=>[1,4,5,2,3]=>6
[1,3,5,4,2]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,4,2,3,5]=>[1,4,3,2,5]=>[1,4,2,5,3]=>8
[1,4,2,5,3]=>[1,5,3,4,2]=>[1,5,2,3,4]=>4
[1,4,3,2,5]=>[1,4,3,2,5]=>[1,4,2,5,3]=>8
[1,4,3,5,2]=>[1,5,3,4,2]=>[1,5,2,3,4]=>4
[1,4,5,2,3]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,4,5,3,2]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,5,2,3,4]=>[1,5,3,4,2]=>[1,5,2,3,4]=>4
[1,5,2,4,3]=>[1,5,3,4,2]=>[1,5,2,3,4]=>4
[1,5,3,2,4]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,5,3,4,2]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,5,4,2,3]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[1,5,4,3,2]=>[1,5,4,3,2]=>[1,5,2,3,4]=>4
[2,1,3,4,5]=>[2,1,3,4,5]=>[1,3,4,5,2]=>4
[2,1,3,5,4]=>[2,1,3,5,4]=>[1,3,5,2,4]=>8
[2,1,4,3,5]=>[2,1,4,3,5]=>[1,4,2,3,5]=>3
[2,1,4,5,3]=>[2,1,5,4,3]=>[1,5,2,3,4]=>4
[2,1,5,3,4]=>[2,1,5,4,3]=>[1,5,2,3,4]=>4
[2,1,5,4,3]=>[2,1,5,4,3]=>[1,5,2,3,4]=>4
[2,3,1,4,5]=>[3,2,1,4,5]=>[1,4,5,2,3]=>6
[2,3,1,5,4]=>[3,2,1,5,4]=>[1,5,2,3,4]=>4
[2,3,4,1,5]=>[4,2,3,1,5]=>[1,5,2,3,4]=>4
[2,3,4,5,1]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[2,3,5,1,4]=>[4,2,5,1,3]=>[1,3,2,5,4]=>8
[2,3,5,4,1]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[2,4,1,3,5]=>[3,4,1,2,5]=>[1,2,5,3,4]=>6
[2,4,1,5,3]=>[3,5,1,4,2]=>[1,4,2,3,5]=>3
[2,4,3,1,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[2,4,3,5,1]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[2,4,5,1,3]=>[4,5,3,1,2]=>[1,2,3,4,5]=>1
[2,4,5,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[2,5,1,3,4]=>[3,5,1,4,2]=>[1,4,2,3,5]=>3
[2,5,1,4,3]=>[3,5,1,4,2]=>[1,4,2,3,5]=>3
[2,5,3,1,4]=>[4,5,3,1,2]=>[1,2,3,4,5]=>1
[2,5,3,4,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[2,5,4,1,3]=>[4,5,3,1,2]=>[1,2,3,4,5]=>1
[2,5,4,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,1,2,4,5]=>[3,2,1,4,5]=>[1,4,5,2,3]=>6
[3,1,2,5,4]=>[3,2,1,5,4]=>[1,5,2,3,4]=>4
[3,1,4,2,5]=>[4,2,3,1,5]=>[1,5,2,3,4]=>4
[3,1,4,5,2]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[3,1,5,2,4]=>[4,2,5,1,3]=>[1,3,2,5,4]=>8
[3,1,5,4,2]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[3,2,1,4,5]=>[3,2,1,4,5]=>[1,4,5,2,3]=>6
[3,2,1,5,4]=>[3,2,1,5,4]=>[1,5,2,3,4]=>4
[3,2,4,1,5]=>[4,2,3,1,5]=>[1,5,2,3,4]=>4
[3,2,4,5,1]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[3,2,5,1,4]=>[4,2,5,1,3]=>[1,3,2,5,4]=>8
[3,2,5,4,1]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[3,4,1,2,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[3,4,1,5,2]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[3,4,2,1,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[3,4,2,5,1]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[3,4,5,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,4,5,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,5,1,2,4]=>[4,5,3,1,2]=>[1,2,3,4,5]=>1
[3,5,1,4,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,5,2,1,4]=>[4,5,3,1,2]=>[1,2,3,4,5]=>1
[3,5,2,4,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,5,4,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[3,5,4,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,1,2,3,5]=>[4,2,3,1,5]=>[1,5,2,3,4]=>4
[4,1,2,5,3]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[4,1,3,2,5]=>[4,2,3,1,5]=>[1,5,2,3,4]=>4
[4,1,3,5,2]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[4,1,5,2,3]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[4,1,5,3,2]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[4,2,1,3,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[4,2,1,5,3]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[4,2,3,1,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[4,2,3,5,1]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[4,2,5,1,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,2,5,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,3,1,2,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[4,3,1,5,2]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[4,3,2,1,5]=>[4,3,2,1,5]=>[1,5,2,3,4]=>4
[4,3,2,5,1]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[4,3,5,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,3,5,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,1,2,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,1,3,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,2,1,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,2,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,3,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[4,5,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,1,2,3,4]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[5,1,2,4,3]=>[5,2,3,4,1]=>[1,2,3,4,5]=>1
[5,1,3,2,4]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[5,1,3,4,2]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[5,1,4,2,3]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[5,1,4,3,2]=>[5,2,4,3,1]=>[1,2,4,3,5]=>3
[5,2,1,3,4]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[5,2,1,4,3]=>[5,3,2,4,1]=>[1,2,4,3,5]=>3
[5,2,3,1,4]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,2,3,4,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,2,4,1,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,2,4,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,1,2,4]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,1,4,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,2,1,4]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,2,4,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,4,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,3,4,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,1,2,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,1,3,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,2,1,3]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,2,3,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,3,1,2]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>1
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>1
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>5
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>4
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>10
[1,2,3,6,4,5]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>10
[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>10
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>3
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>15
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>20
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>10
[1,2,4,6,3,5]=>[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>20
[1,2,4,6,5,3]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,5,3,4,6]=>[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>20
[1,2,5,3,6,4]=>[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>10
[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>20
[1,2,5,4,6,3]=>[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>10
[1,2,5,6,3,4]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,5,6,4,3]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,6,3,4,5]=>[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>10
[1,2,6,3,5,4]=>[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>10
[1,2,6,4,3,5]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,6,4,5,3]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,6,5,3,4]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>10
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>2
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>10
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>8
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>20
[1,3,2,6,4,5]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>20
[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>20
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>15
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>25
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>20
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,3,4,6,2,5]=>[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>11
[1,3,4,6,5,2]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,3,5,2,4,6]=>[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>6
[1,3,5,2,6,4]=>[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>38
[1,3,5,4,2,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,3,5,4,6,2]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,3,5,6,2,4]=>[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>10
[1,3,5,6,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,3,6,2,4,5]=>[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>38
[1,3,6,2,5,4]=>[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>38
[1,3,6,4,2,5]=>[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>10
[1,3,6,4,5,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,3,6,5,2,4]=>[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>10
[1,3,6,5,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,2,3,5,6]=>[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>15
[1,4,2,3,6,5]=>[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>25
[1,4,2,5,3,6]=>[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>20
[1,4,2,5,6,3]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,4,2,6,3,5]=>[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>11
[1,4,2,6,5,3]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>15
[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>25
[1,4,3,5,2,6]=>[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>20
[1,4,3,5,6,2]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,4,3,6,2,5]=>[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>11
[1,4,3,6,5,2]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,4,5,2,3,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,4,5,2,6,3]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,4,5,3,2,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,4,5,3,6,2]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,4,5,6,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,5,6,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,6,2,3,5]=>[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>10
[1,4,6,2,5,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,6,3,2,5]=>[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>10
[1,4,6,3,5,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,6,5,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,4,6,5,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,2,3,4,6]=>[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>20
[1,5,2,3,6,4]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,5,2,4,3,6]=>[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>20
[1,5,2,4,6,3]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,5,2,6,3,4]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,5,2,6,4,3]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,5,3,2,4,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,5,3,2,6,4]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,5,3,4,2,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,5,3,4,6,2]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,5,3,6,2,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,3,6,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,4,2,3,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,5,4,2,6,3]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>20
[1,5,4,3,6,2]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,5,4,6,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,4,6,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,2,3,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,2,4,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,3,2,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,3,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,4,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,5,6,4,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,2,3,4,5]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,6,2,3,5,4]=>[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>5
[1,6,2,4,3,5]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,6,2,4,5,3]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,6,2,5,3,4]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,6,2,5,4,3]=>[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>19
[1,6,3,2,4,5]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,6,3,2,5,4]=>[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>19
[1,6,3,4,2,5]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,3,4,5,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,3,5,2,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,3,5,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,2,3,5]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,2,5,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,3,2,5]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,3,5,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,5,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,4,5,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,2,3,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,2,4,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,3,2,4]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,3,4,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,4,2,3]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>5
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,3,4,5,6,2]=>5
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,3,4,6,2,5]=>15
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>8
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>15
[2,1,3,6,4,5]=>[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>15
[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>15
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>3
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,4,2,3,6,5]=>15
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>15
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>5
[2,1,4,6,3,5]=>[2,1,5,6,3,4]=>[1,5,6,2,3,4]=>10
[2,1,4,6,5,3]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,5,3,4,6]=>[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>15
[2,1,5,3,6,4]=>[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>5
[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>15
[2,1,5,4,6,3]=>[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>5
[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,5,6,4,3]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,6,3,4,5]=>[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>5
[2,1,6,3,5,4]=>[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>5
[2,1,6,4,3,5]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,6,4,5,3]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,6,5,3,4]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>5
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>10
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>15
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>4
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[2,3,1,6,4,5]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[2,3,1,6,5,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>10
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>5
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[2,3,4,6,1,5]=>[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>15
[2,3,4,6,5,1]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[2,3,5,1,4,6]=>[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>51
[2,3,5,1,6,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[2,3,5,4,1,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[2,3,5,4,6,1]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[2,3,5,6,1,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[2,3,5,6,4,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[2,3,6,1,4,5]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[2,3,6,1,5,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[2,3,6,4,1,5]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[2,3,6,4,5,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[2,3,6,5,1,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[2,3,6,5,4,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[2,4,1,3,5,6]=>[3,4,1,2,5,6]=>[1,2,5,6,3,4]=>20
[2,4,1,3,6,5]=>[3,4,1,2,6,5]=>[1,2,6,3,4,5]=>10
[2,4,1,5,3,6]=>[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>25
[2,4,1,5,6,3]=>[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>6
[2,4,1,6,3,5]=>[3,5,1,6,2,4]=>[1,6,2,4,3,5]=>14
[2,4,1,6,5,3]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,4,3,1,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[2,4,3,1,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[2,4,3,5,1,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[2,4,3,5,6,1]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[2,4,3,6,1,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[2,4,3,6,5,1]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[2,4,5,1,3,6]=>[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>10
[2,4,5,1,6,3]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[2,4,5,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[2,4,5,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[2,4,5,6,1,3]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[2,4,5,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[2,4,6,1,3,5]=>[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>1
[2,4,6,1,5,3]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,4,6,3,1,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[2,4,6,3,5,1]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[2,4,6,5,1,3]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,4,6,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,5,1,3,4,6]=>[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>25
[2,5,1,3,6,4]=>[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>6
[2,5,1,4,3,6]=>[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>25
[2,5,1,4,6,3]=>[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>6
[2,5,1,6,3,4]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,5,1,6,4,3]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,5,3,1,4,6]=>[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>10
[2,5,3,1,6,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[2,5,3,4,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[2,5,3,4,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[2,5,3,6,1,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[2,5,3,6,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[2,5,4,1,3,6]=>[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>10
[2,5,4,1,6,3]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[2,5,4,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[2,5,4,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[2,5,4,6,1,3]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[2,5,4,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[2,5,6,1,3,4]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,5,6,1,4,3]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,5,6,3,1,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,5,6,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,5,6,4,1,3]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,5,6,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,6,1,3,4,5]=>[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>6
[2,6,1,3,5,4]=>[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>6
[2,6,1,4,3,5]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,6,1,4,5,3]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,6,1,5,3,4]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,6,1,5,4,3]=>[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>15
[2,6,3,1,4,5]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[2,6,3,1,5,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[2,6,3,4,1,5]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[2,6,3,4,5,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[2,6,3,5,1,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[2,6,3,5,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[2,6,4,1,3,5]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,6,4,1,5,3]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,6,4,3,1,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,6,4,3,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,6,4,5,1,3]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,6,4,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,6,5,1,3,4]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,6,5,1,4,3]=>[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>10
[2,6,5,3,1,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,6,5,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[2,6,5,4,1,3]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[2,6,5,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,1,2,4,5,6]=>[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>10
[3,1,2,4,6,5]=>[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>15
[3,1,2,5,4,6]=>[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>4
[3,1,2,5,6,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,1,2,6,4,5]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,1,2,6,5,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,1,4,2,5,6]=>[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>10
[3,1,4,2,6,5]=>[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>5
[3,1,4,5,2,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[3,1,4,5,6,2]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[3,1,4,6,2,5]=>[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>15
[3,1,4,6,5,2]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[3,1,5,2,4,6]=>[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>51
[3,1,5,2,6,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,1,5,4,2,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[3,1,5,4,6,2]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[3,1,5,6,2,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,1,5,6,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,1,6,2,4,5]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,1,6,2,5,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,1,6,4,2,5]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,1,6,4,5,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,1,6,5,2,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,1,6,5,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>10
[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>15
[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>4
[3,2,1,5,6,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,2,1,6,4,5]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>5
[3,2,4,1,5,6]=>[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>10
[3,2,4,1,6,5]=>[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>5
[3,2,4,5,1,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[3,2,4,5,6,1]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[3,2,4,6,1,5]=>[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>15
[3,2,4,6,5,1]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[3,2,5,1,4,6]=>[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>51
[3,2,5,1,6,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,2,5,4,1,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[3,2,5,4,6,1]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[3,2,5,6,1,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,2,5,6,4,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,2,6,1,4,5]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,2,6,1,5,4]=>[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>20
[3,2,6,4,1,5]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,2,6,4,5,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,2,6,5,1,4]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[3,2,6,5,4,1]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[3,4,1,5,2,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[3,4,1,5,6,2]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[3,4,1,6,2,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[3,4,1,6,5,2]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[3,4,2,1,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[3,4,2,1,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[3,4,2,5,1,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[3,4,2,5,6,1]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[3,4,2,6,1,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[3,4,2,6,5,1]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,4,5,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,4,5,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,4,5,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,4,5,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,4,6,1,2,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[3,4,6,1,5,2]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[3,4,6,2,1,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[3,4,6,2,5,1]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[3,4,6,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,4,6,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,5,1,2,4,6]=>[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>10
[3,5,1,2,6,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,5,1,4,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,5,1,4,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,5,1,6,2,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,5,1,6,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,5,2,1,4,6]=>[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>10
[3,5,2,1,6,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,5,2,4,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,5,2,4,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,5,2,6,1,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,5,2,6,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,5,4,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,5,4,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,5,4,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[3,5,4,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[3,5,4,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,5,4,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,5,6,1,2,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,5,6,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,5,6,2,1,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,5,6,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,5,6,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,5,6,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,1,2,4,5]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,6,1,2,5,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,6,1,4,2,5]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,6,1,4,5,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,6,1,5,2,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,6,1,5,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,6,2,1,4,5]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,6,2,1,5,4]=>[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>4
[3,6,2,4,1,5]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,6,2,4,5,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,6,2,5,1,4]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[3,6,2,5,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[3,6,4,1,2,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,6,4,1,5,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,4,2,1,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,6,4,2,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,4,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,4,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,5,1,2,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,6,5,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,5,2,1,4]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[3,6,5,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,5,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[3,6,5,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,1,2,3,5,6]=>[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>10
[4,1,2,3,6,5]=>[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>5
[4,1,2,5,3,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[4,1,2,5,6,3]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[4,1,2,6,3,5]=>[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>15
[4,1,2,6,5,3]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[4,1,3,2,5,6]=>[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>10
[4,1,3,2,6,5]=>[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>5
[4,1,3,5,2,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[4,1,3,5,6,2]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[4,1,3,6,2,5]=>[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>15
[4,1,3,6,5,2]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[4,1,5,2,3,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[4,1,5,2,6,3]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[4,1,5,3,2,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[4,1,5,3,6,2]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[4,1,5,6,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,1,5,6,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,1,6,2,3,5]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[4,1,6,2,5,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,1,6,3,2,5]=>[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>20
[4,1,6,3,5,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,1,6,5,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,1,6,5,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[4,2,1,3,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[4,2,1,3,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[4,2,1,5,3,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[4,2,1,5,6,3]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[4,2,1,6,3,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[4,2,1,6,5,3]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[4,2,3,1,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[4,2,3,1,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[4,2,3,5,1,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[4,2,3,5,6,1]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[4,2,3,6,1,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[4,2,3,6,5,1]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[4,2,5,1,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,2,5,1,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,2,5,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,2,5,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,2,5,6,1,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,2,5,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,2,6,1,3,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[4,2,6,1,5,3]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[4,2,6,3,1,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[4,2,6,3,5,1]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[4,2,6,5,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,2,6,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,3,1,2,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[4,3,1,2,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[4,3,1,5,2,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[4,3,1,5,6,2]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[4,3,1,6,2,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[4,3,1,6,5,2]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>10
[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>5
[4,3,2,5,1,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[4,3,2,5,6,1]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[4,3,2,6,1,5]=>[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>25
[4,3,2,6,5,1]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[4,3,5,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,3,5,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,3,5,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,3,5,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,3,5,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,3,5,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,3,6,1,2,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[4,3,6,1,5,2]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[4,3,6,2,1,5]=>[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>10
[4,3,6,2,5,1]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[4,3,6,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,3,6,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,1,2,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,1,2,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,1,3,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,1,3,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,1,6,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,1,6,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,2,1,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,2,1,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,2,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,2,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,2,6,1,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,2,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,3,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,3,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,3,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[4,5,3,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[4,5,3,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,3,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,5,6,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,1,2,3,5]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[4,6,1,2,5,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,6,1,3,2,5]=>[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>1
[4,6,1,3,5,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,6,1,5,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,6,1,5,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[4,6,2,1,3,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[4,6,2,1,5,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,2,3,1,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[4,6,2,3,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,2,5,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,2,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,3,1,2,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[4,6,3,1,5,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,3,2,1,5]=>[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>1
[4,6,3,2,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,3,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,3,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[4,6,5,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,1,2,3,4,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[5,1,2,3,6,4]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[5,1,2,4,3,6]=>[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>5
[5,1,2,4,6,3]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[5,1,2,6,3,4]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[5,1,2,6,4,3]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[5,1,3,2,4,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[5,1,3,2,6,4]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[5,1,3,4,2,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[5,1,3,4,6,2]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[5,1,3,6,2,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,3,6,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,4,2,3,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[5,1,4,2,6,3]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[5,1,4,3,2,6]=>[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>14
[5,1,4,3,6,2]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[5,1,4,6,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,4,6,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,2,3,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,2,4,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,3,2,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,3,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,4,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,1,6,4,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[5,2,1,3,4,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[5,2,1,3,6,4]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[5,2,1,4,3,6]=>[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>14
[5,2,1,4,6,3]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[5,2,1,6,3,4]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[5,2,1,6,4,3]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[5,2,3,1,4,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,2,3,1,6,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,2,3,4,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,2,3,4,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,2,3,6,1,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,2,3,6,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,2,4,1,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,2,4,1,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,2,4,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,2,4,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,2,4,6,1,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,2,4,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,2,6,1,3,4]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[5,2,6,1,4,3]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[5,2,6,3,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,2,6,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,2,6,4,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,2,6,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,1,2,4,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,1,2,6,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,1,4,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,1,4,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,1,6,2,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,1,6,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,2,1,4,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,2,1,6,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,2,4,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,2,4,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,2,6,1,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,2,6,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,4,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,4,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,4,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,3,4,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,3,4,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,4,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,1,2,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,2,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,3,6,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,1,2,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,1,2,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,1,3,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,1,3,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,1,6,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,1,6,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,2,1,3,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,2,1,6,3]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,2,3,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,2,3,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,2,6,1,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,2,6,3,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,3,1,2,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,3,1,6,2]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>5
[5,4,3,2,6,1]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[5,4,3,6,1,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,3,6,2,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,4,6,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,2,3,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,2,4,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,3,2,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,3,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,4,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,1,4,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,1,3,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,1,4,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,3,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,4,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,2,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,1,2,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,2,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,3,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[5,6,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,1,2,3,4,5]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>1
[6,1,2,4,3,5]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[6,1,2,4,5,3]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[6,1,2,5,3,4]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[6,1,2,5,4,3]=>[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>4
[6,1,3,2,4,5]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[6,1,3,2,5,4]=>[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>3
[6,1,3,4,2,5]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,3,4,5,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,3,5,2,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,3,5,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,2,3,5]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,2,5,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,3,2,5]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,3,5,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,5,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,4,5,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,2,3,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,2,4,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,3,2,4]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,3,4,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,4,2,3]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,1,5,4,3,2]=>[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>6
[6,2,1,3,4,5]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[6,2,1,3,5,4]=>[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>6
[6,2,1,4,3,5]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[6,2,1,4,5,3]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[6,2,1,5,3,4]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[6,2,1,5,4,3]=>[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>6
[6,2,3,1,4,5]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,2,3,1,5,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,2,3,4,1,5]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,2,3,4,5,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,2,3,5,1,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,2,3,5,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,2,4,1,3,5]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[6,2,4,1,5,3]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[6,2,4,3,1,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,4,3,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,4,5,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,4,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,5,1,3,4]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[6,2,5,1,4,3]=>[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>1
[6,2,5,3,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,5,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,5,4,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,2,5,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,1,2,4,5]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,3,1,2,5,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,3,1,4,2,5]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,1,4,5,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,1,5,2,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,1,5,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,2,1,4,5]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,3,2,1,5,4]=>[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>6
[6,3,2,4,1,5]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,2,4,5,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,2,5,1,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,2,5,4,1]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,1,2,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,1,5,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,2,1,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,2,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,4,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,1,2,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,2,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,3,5,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,2,3,5]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,2,5,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,3,2,5]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,3,5,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,5,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,1,5,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,1,3,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,1,5,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,3,1,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,3,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,5,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,2,5,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,1,2,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,1,5,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,2,1,5]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,2,5,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,5,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,3,5,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,4,5,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,2,3,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,2,4,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,3,2,4]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,3,4,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,4,2,3]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,1,3,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,1,4,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,3,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,3,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,4,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,2,4,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,1,2,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,1,4,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,2,1,4]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,2,4,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,4,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,3,4,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,1,2,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,1,3,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,2,1,3]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,2,3,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,3,1,2]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>1
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>6
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>5
[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>40
[1,2,3,6,4,5,7]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>40
[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>40
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>2
[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,3,5,4,2,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,3,5,6,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,3,5,6,7,2,4]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,5,6,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,5,7,2,4,6]=>[1,5,6,7,2,3,4]=>[1,5,6,7,2,3,4]=>20
[1,3,5,7,4,6,2]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,3,5,7,6,2,4]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,5,7,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,6,4,5,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,3,6,4,7,2,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,6,4,7,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,6,5,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,3,6,5,7,2,4]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,6,5,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,6,7,4,2,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,6,7,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,6,7,5,2,4]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,6,7,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,4,5,2,6]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,4,5,6,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,4,6,2,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,4,6,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,5,4,2,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,5,4,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,5,6,2,4]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,5,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,6,4,2,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,6,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,3,7,6,5,2,4]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,3,7,6,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,2,5,3,7,6]=>[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,4,2,5,6,3,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,2,5,6,7,3]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,4,3,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,4,3,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,3,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,2,3,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,4,5,3,2,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,4,5,6,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,5,6,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,5,6,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,6,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,7,2,6,3]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,7,3,6,2]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,7,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,5,7,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,2,5,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,6,2,7,3,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,6,2,7,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,3,5,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,6,3,7,2,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,6,3,7,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,5,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,6,5,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,4,6,5,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,5,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,7,2,3,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,6,7,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,7,3,2,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,6,7,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,7,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,6,7,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,2,5,3,6]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,2,5,6,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,2,6,3,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,2,6,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,3,5,2,6]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,3,5,6,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,3,6,2,5]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,3,6,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,5,2,3,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,5,2,6,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,5,3,2,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,5,3,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,5,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,5,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,6,2,3,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,6,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,6,3,2,5]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,4,7,6,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,6,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,4,7,6,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,2,3,4,7,6]=>[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,2,3,6,4,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,2,3,6,7,4]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,5,2,4,3,7,6]=>[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,2,4,6,3,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,2,4,6,7,3]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,2,4,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,3,4,2,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,3,6,2,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,3,6,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,3,6,7,2,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,6,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,7,2,6,4]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,7,4,6,2]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,7,6,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,3,7,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,2,3,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>56
[1,5,4,6,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,4,6,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,4,6,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,6,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,7,2,6,3]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,7,3,6,2]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,7,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,4,7,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,2,3,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,2,4,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,2,7,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,2,7,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,3,2,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,3,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,3,7,2,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,3,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,4,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,4,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,5,6,4,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,4,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,6,7,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,2,3,4,6]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,2,3,6,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,2,4,3,6]=>[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,2,4,6,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,2,6,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,2,6,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,3,2,4,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,3,2,6,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,3,4,2,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,3,4,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,3,6,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,3,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,4,2,3,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,4,2,6,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,4,3,2,6]=>[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>15
[1,5,7,4,3,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,4,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,4,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,5,7,6,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,2,3,4,5,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,2,3,4,7,5]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,6,2,3,5,4,7]=>[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,2,3,5,7,4]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,4,2,5,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,3,4,5,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,3,4,7,2,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,4,7,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,5,2,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,3,5,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,3,5,7,2,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,5,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,2,4,5]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,2,5,4]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,4,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,5,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,3,7,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,2,3,5,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,2,5,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,2,7,3,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,2,7,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,3,2,5,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,3,5,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,3,7,2,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,3,7,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,5,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,5,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,4,5,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,5,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,2,3,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,3,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,4,7,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,2,3,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,2,4,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,2,7,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,2,7,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,3,2,4,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,3,4,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,3,7,2,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,3,7,4,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,4,2,3,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>40
[1,6,5,4,7,2,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,4,7,3,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,5,7,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,3,4,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,3,5,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,4,3,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,4,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,5,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,2,5,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,2,4,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,2,5,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,4,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,5,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,3,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,2,3,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,3,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,4,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,6,7,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,2,3,4,5,6]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,7,2,3,4,6,5]=>[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,4,5,2,6]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,4,5,6,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,4,6,2,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,4,6,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,2,4,6]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,2,6,4]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,4,2,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,4,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,6,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,5,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,2,4,5]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,2,5,4]=>[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,4,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,5,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,3,6,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,2,5,3,6]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,2,5,6,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,2,6,3,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,2,6,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,3,5,2,6]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,3,5,6,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,3,6,2,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,3,6,5,2]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,2,3,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,2,6,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,3,2,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,3,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,5,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,2,3,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,3,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,4,6,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,3,4,6]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,3,6,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,4,3,6]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,4,6,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,6,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,2,6,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,2,4,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,2,6,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,4,2,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,4,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,6,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,3,6,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,2,3,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,2,6,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,3,2,6]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,3,6,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,6,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,4,6,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,5,6,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,3,4,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,3,5,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,4,3,5]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,4,5,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,5,3,4]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,2,5,4,3]=>[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,2,4,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,2,5,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,4,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,4,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,5,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,3,5,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,2,3,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,2,5,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,3,2,5]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,3,5,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,5,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,4,5,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,2,3,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,2,4,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,3,2,4]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,3,4,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,4,2,3]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>6
[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,5,7,6,4]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,6,4,7,5]=>[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,6,5,7,4]=>[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,6,7,4,5]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,6,7,5,4]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,4,5,6]=>[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,4,6,5]=>[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,5,4,6]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,5,6,4]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,6,4,5]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>24
[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,4,6,5,3,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,4,6,7,3,5]=>[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>15
[2,1,4,6,7,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,4,7,5,3,6]=>[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>15
[2,1,4,7,5,6,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,4,7,6,3,5]=>[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>15
[2,1,4,7,6,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,3,6,4,7]=>[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,5,3,6,7,4]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,4,6,3,7]=>[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,5,4,6,7,3]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,6,3,4,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,5,6,4,3,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,5,6,7,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,6,7,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,7,3,4,6]=>[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>15
[2,1,5,7,3,6,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,7,4,3,6]=>[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>15
[2,1,5,7,4,6,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,7,6,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,5,7,6,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,3,4,5,7]=>[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,3,4,7,5]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,3,5,4,7]=>[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,3,5,7,4]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,4,3,5,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,4,5,3,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,4,7,3,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,4,7,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,5,3,4,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>45
[2,1,6,5,7,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,5,7,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,3,4,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,3,5,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,4,3,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,4,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,5,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,6,7,5,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,3,4,5,6]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,3,4,6,5]=>[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,4,5,3,6]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,4,5,6,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,4,6,3,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,4,6,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,3,4,6]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,3,6,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,4,3,6]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,4,6,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,6,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,5,6,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,3,4,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,3,5,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,4,3,5]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,4,5,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,5,3,4]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>6
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[2,3,1,4,7,5,6]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[2,3,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>24
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,5,7,4,6]=>[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>15
[2,3,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,6,4,5,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[2,3,1,6,4,7,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[2,3,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,4,5,6]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,4,6,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,5,4,6]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,6,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,3,4,1,7,5,6]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,3,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[2,3,4,5,7,1,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[2,3,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[2,3,4,6,1,7,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[2,3,4,7,1,5,6]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[2,3,4,7,1,6,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[2,3,5,1,6,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[2,3,5,1,7,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,5,6,1,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[2,3,6,1,4,7,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[2,3,6,1,5,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[2,3,6,1,7,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,6,1,7,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,6,4,1,7,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[2,3,6,5,1,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,1,4,5,6]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[2,3,7,1,4,6,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[2,3,7,1,5,4,6]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,1,5,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,1,6,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,1,6,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,4,1,5,6]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[2,3,7,4,1,6,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[2,4,1,6,7,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,4,1,7,5,6,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,4,1,7,6,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,4,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[2,4,3,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[2,4,3,1,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,4,3,1,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,4,3,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[2,4,3,6,1,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[2,4,3,7,1,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[2,4,3,7,1,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[2,4,5,1,6,3,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[2,4,5,1,7,6,3]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,4,5,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[2,4,5,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[2,4,5,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[2,4,5,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,4,5,6,7,1,3]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,4,5,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,4,6,1,7,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,4,6,3,1,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[2,4,6,3,5,1,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[2,4,6,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,4,6,7,1,3,5]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[2,4,6,7,3,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[2,4,6,7,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,4,6,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,4,7,1,5,6,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,4,7,1,6,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,4,7,3,1,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[2,4,7,3,1,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[2,4,7,5,1,3,6]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[2,4,7,5,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[2,4,7,5,6,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,4,7,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,4,7,6,1,3,5]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[2,4,7,6,3,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[2,4,7,6,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,4,7,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,1,6,7,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,1,6,7,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,1,7,3,6,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,1,7,4,6,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,1,7,6,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,1,7,6,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,5,3,1,6,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[2,5,3,1,7,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,5,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[2,5,3,4,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[2,5,3,4,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[2,5,3,6,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,5,3,6,7,1,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,3,6,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,4,1,6,3,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[2,5,4,1,7,6,3]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,5,4,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[2,5,4,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[2,5,4,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[2,5,4,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,5,4,6,7,1,3]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,4,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,6,1,7,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,6,1,7,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,6,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,5,6,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,5,6,7,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,6,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,6,7,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,6,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,1,3,6,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,7,1,4,6,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,7,1,6,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,7,1,6,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,5,7,3,1,4,6]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[2,5,7,3,4,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,3,6,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,7,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,4,1,3,6]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[2,5,7,4,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,4,6,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,7,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,6,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,7,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,5,7,6,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,5,7,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,1,4,7,3,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,4,7,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,5,7,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,5,7,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,3,4,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,3,5,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,4,3,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,4,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,5,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,1,7,5,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,6,3,1,4,5,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[2,6,3,1,5,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[2,6,3,1,7,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,6,3,1,7,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,6,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,3,4,7,1,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,3,4,7,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,3,5,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,3,5,7,1,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,3,5,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,4,1,7,3,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,4,1,7,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,4,3,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,4,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,4,7,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,4,7,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,4,7,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,4,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,5,1,7,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,5,1,7,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,5,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,5,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[2,6,5,7,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,5,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,5,7,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,5,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,1,3,4,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,1,3,5,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,1,4,3,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,1,4,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,1,5,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,1,5,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,6,7,3,4,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,3,5,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,4,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,4,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,5,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,6,7,5,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,6,7,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,1,4,5,3,6]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,4,5,6,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,4,6,3,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,4,6,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,3,4,6]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,3,6,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,4,3,6]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,4,6,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,6,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,5,6,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,3,4,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,3,5,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,4,3,5]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,4,5,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,5,3,4]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,1,6,5,4,3]=>[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>45
[2,7,3,1,5,4,6]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,7,3,1,5,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,7,3,1,6,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,7,3,1,6,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[2,7,3,4,5,1,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,3,4,6,1,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,4,1,5,3,6]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,4,1,5,6,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,4,1,6,3,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,4,1,6,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,4,5,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,4,5,6,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,4,6,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,4,6,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,1,3,4,6]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,1,3,6,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,1,4,3,6]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,1,4,6,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,1,6,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,1,6,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,5,3,4,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,3,6,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,4,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,4,6,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,6,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,5,6,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,1,3,4,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,1,3,5,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,1,4,3,5]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,1,4,5,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,1,5,3,4]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,1,5,4,3]=>[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>24
[2,7,6,3,4,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,3,5,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,4,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,4,5,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,5,3,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[2,7,6,5,4,1,3]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[2,7,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,1,2,4,6,7,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,1,2,4,7,5,6]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,1,2,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,1,2,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>24
[3,1,2,5,6,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,1,2,5,6,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,5,7,4,6]=>[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>15
[3,1,2,5,7,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,6,4,5,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,1,2,6,4,7,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,1,2,6,5,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,6,7,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,6,7,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,4,5,6]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,4,6,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,5,4,6]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,5,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,6,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,2,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,1,4,2,5,6,7]=>[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[3,1,4,2,5,7,6]=>[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[3,1,4,2,6,7,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,1,4,2,7,5,6]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,1,4,2,7,6,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,1,4,5,2,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,1,4,5,2,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,1,4,5,6,2,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[3,1,4,5,6,7,2]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[3,1,4,5,7,2,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[3,1,4,5,7,6,2]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[3,1,4,6,2,7,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,1,4,7,2,5,6]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,1,4,7,2,6,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,1,5,2,6,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,1,5,2,7,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,5,6,2,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,1,6,2,4,7,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,1,6,2,5,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,1,6,2,7,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,6,2,7,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,6,4,2,7,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,1,6,5,2,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,2,4,5,6]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,1,7,2,4,6,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,1,7,2,5,4,6]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,2,5,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,2,6,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,2,6,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,4,2,5,6]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,1,7,4,2,6,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,2,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,2,1,4,7,5,6]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>27
[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>24
[3,2,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,2,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,5,7,4,6]=>[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>15
[3,2,1,5,7,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,6,4,5,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,2,1,6,4,7,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>24
[3,2,1,6,5,7,4]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,6,7,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,4,5,6]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,4,6,5]=>[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,5,4,6]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,5,6,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,6,4,5]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>6
[3,2,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[3,2,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[3,2,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,2,4,1,7,5,6]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,2,4,1,7,6,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,2,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,2,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,2,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[3,2,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[3,2,4,5,7,1,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[3,2,4,5,7,6,1]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[3,2,4,6,1,7,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,2,4,7,1,5,6]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,2,4,7,1,6,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[3,2,5,1,6,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,2,5,1,7,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,5,6,1,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,2,6,1,4,7,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,2,6,1,5,7,4]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,2,6,1,7,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,6,1,7,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,6,4,1,7,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,2,6,5,1,7,4]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,1,4,5,6]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,2,7,1,4,6,5]=>[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>45
[3,2,7,1,5,4,6]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,1,5,6,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,1,6,4,5]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,1,6,5,4]=>[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,4,1,5,6]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,2,7,4,1,6,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[3,4,1,2,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[3,4,1,2,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,1,2,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,1,2,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,1,6,2,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,1,7,2,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,1,7,2,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[3,4,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[3,4,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,2,1,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[3,4,2,6,1,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,2,7,1,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,2,7,1,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,4,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,4,5,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,4,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,4,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,4,5,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,6,1,2,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,6,1,5,2,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,6,2,1,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,6,2,5,1,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,6,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,6,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,4,6,7,1,5,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,6,7,2,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,6,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,1,2,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,7,1,2,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,7,2,1,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,7,2,1,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[3,4,7,5,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,5,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,6,1,5,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,6,2,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,4,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,1,2,6,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,5,1,2,7,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,5,1,4,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,5,1,4,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,5,1,4,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,5,1,6,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,1,6,7,2,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,1,6,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,2,1,6,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,5,2,1,7,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,5,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,5,2,4,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,5,2,4,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,5,2,6,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,2,6,7,1,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,2,6,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,5,4,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,5,4,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,5,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[3,5,4,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[3,5,4,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[3,5,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,6,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,6,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,6,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,6,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,5,6,7,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,6,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,6,7,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,6,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,6,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,6,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,1,2,4,6]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[3,5,7,1,4,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,1,6,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,7,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,2,1,4,6]=>[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>1
[3,5,7,2,4,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,2,6,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,7,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,4,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,4,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,5,7,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,1,2,4,5,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,6,1,2,5,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,6,1,2,7,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,6,1,2,7,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,6,1,4,5,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,1,4,7,2,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,1,4,7,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,1,5,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,1,5,7,2,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,1,5,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,2,1,4,5,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,6,2,1,5,4,7]=>[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>56
[3,6,2,1,7,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,6,2,1,7,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,6,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,2,4,7,1,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,2,4,7,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,2,5,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,2,5,7,1,4]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,2,5,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,4,1,5,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,4,7,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,4,7,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,4,7,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,4,7,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,4,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,4,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,5,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,5,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,5,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,5,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[3,6,5,7,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,5,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,5,7,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,5,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,5,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,5,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,1,4,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,1,5,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,2,4,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,2,5,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,6,7,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,1,2,5,4,6]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,1,2,5,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,1,2,6,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,1,2,6,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,1,4,5,2,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,1,4,6,2,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,2,1,5,4,6]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,2,1,5,6,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,2,1,6,4,5]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,2,1,6,5,4]=>[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>24
[3,7,2,4,5,1,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,2,4,6,1,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,1,4,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,1,6,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,2,4,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,2,6,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,1,4,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,1,5,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,2,4,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,2,5,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,1,2,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,2,1,4]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[3,7,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,1,2,3,5,6,7]=>[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,1,2,3,5,7,6]=>[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,1,2,3,6,7,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,2,3,7,5,6]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,2,3,7,6,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,2,5,3,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,1,2,5,3,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,1,2,5,6,3,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[4,1,2,5,6,7,3]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[4,1,2,5,7,3,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[4,1,2,5,7,6,3]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[4,1,2,6,3,7,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,2,7,3,5,6]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,2,7,3,6,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,3,2,5,6,7]=>[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,1,3,2,5,7,6]=>[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,1,3,2,6,7,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,3,2,7,5,6]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,3,2,7,6,5]=>[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,1,3,5,2,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,1,3,5,2,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,1,3,5,6,2,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[4,1,3,5,6,7,2]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[4,1,3,5,7,2,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[4,1,3,5,7,6,2]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[4,1,3,6,2,7,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,3,7,2,5,6]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,3,7,2,6,5]=>[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>45
[4,1,6,2,3,7,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,1,6,3,2,7,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,1,7,2,3,5,6]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,1,7,2,3,6,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,1,7,3,2,5,6]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,1,7,3,2,6,5]=>[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>40
[4,2,1,3,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,2,1,3,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,2,1,3,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,1,3,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,1,3,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,1,6,3,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,1,7,3,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,1,7,3,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,3,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,2,3,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,2,3,1,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,3,1,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,3,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,2,3,6,1,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,3,7,1,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,3,7,1,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,2,5,1,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,2,5,1,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,2,5,1,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,2,5,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,2,5,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,2,5,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,2,5,6,1,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,5,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,5,6,7,1,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,5,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,6,1,3,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,6,1,5,3,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,6,3,1,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,6,3,5,1,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,6,5,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,6,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,2,6,7,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,6,7,3,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,6,7,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,6,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,1,3,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,7,1,3,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,7,3,1,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,7,3,1,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,2,7,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,5,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,6,3,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,2,7,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,3,1,2,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,3,1,2,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,1,2,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,1,2,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,1,6,2,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,1,7,2,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,1,7,2,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>20
[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>24
[4,3,2,1,6,7,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,2,1,7,5,6]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>6
[4,3,2,6,1,7,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,2,7,1,5,6]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,2,7,1,6,5]=>[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>40
[4,3,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,3,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,3,5,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,3,5,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,3,5,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,3,5,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,3,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,5,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,5,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,6,1,2,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,6,1,5,2,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,6,2,1,7,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,6,2,5,1,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,6,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,6,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,3,6,7,1,5,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,6,7,2,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,6,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,6,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,1,2,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,7,1,2,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,7,2,1,5,6]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,7,2,1,6,5]=>[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>24
[4,3,7,5,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,5,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,6,1,5,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,6,2,5,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,3,7,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,1,2,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,1,2,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,1,3,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,1,3,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,1,3,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,1,6,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,1,6,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,1,6,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,1,6,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,2,1,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,2,1,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,2,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,2,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,2,6,1,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,2,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,2,6,7,1,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,2,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,3,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,3,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[4,5,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[4,5,3,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[4,5,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,1,2,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,1,3,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,2,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,2,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,3,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,3,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,5,7,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,1,2,5,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,1,2,7,3,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,1,2,7,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,1,3,5,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,1,3,7,2,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,1,3,7,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,1,5,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,1,5,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,1,5,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,1,5,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,2,1,5,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,2,5,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,2,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,2,7,1,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,2,7,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,2,7,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,2,7,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,2,7,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,2,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,3,1,5,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,3,7,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,3,7,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,3,7,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,3,7,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,3,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,3,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[4,6,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,2,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,3,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,1,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,6,7,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,1,2,5,3,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,1,2,6,3,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,1,3,5,2,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,1,3,6,2,5]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,1,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,1,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,2,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,3,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,1,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,2,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,3,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,1,3,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,3,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,1,2,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,2,1,5]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[4,7,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,1,2,3,4,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,1,2,3,4,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,1,2,3,6,4,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[5,1,2,3,6,7,4]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[5,1,2,3,7,4,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[5,1,2,3,7,6,4]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[5,1,2,4,3,6,7]=>[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,1,2,4,3,7,6]=>[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,1,2,4,6,3,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[5,1,2,4,6,7,3]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[5,1,2,4,7,3,6]=>[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>24
[5,1,2,4,7,6,3]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[5,2,3,1,4,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,2,3,1,4,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,2,3,1,7,4,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,2,3,4,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,2,3,4,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,2,3,4,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,2,3,6,1,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,3,6,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,3,6,7,1,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,3,6,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,4,1,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,2,4,1,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,2,4,1,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,2,4,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,2,4,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,2,4,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,2,4,6,1,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,4,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,4,6,7,1,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,4,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,1,3,4,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,1,4,3,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,3,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,4,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,2,6,7,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,7,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,7,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,7,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,6,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,3,4,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,4,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,2,7,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,1,2,4,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,1,2,4,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,1,2,7,4,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,1,4,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,1,4,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,1,4,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,1,6,2,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,1,6,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,1,6,7,2,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,1,6,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,2,1,4,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,2,1,4,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,2,1,7,4,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,2,4,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,2,4,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,2,4,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,2,6,1,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,2,6,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,2,6,7,1,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,2,6,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,4,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,4,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,4,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,4,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,3,4,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,3,4,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,3,4,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,4,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,4,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,4,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,1,2,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,2,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,3,6,7,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,7,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,6,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,1,4,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,2,4,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,4,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,4,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,3,7,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,1,2,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,1,2,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,1,2,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,1,3,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,1,3,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,1,3,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,1,6,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,1,6,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,1,6,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,1,6,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,2,1,3,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,2,1,3,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,2,1,7,3,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,2,3,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,2,3,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,2,3,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,2,6,1,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,2,6,3,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,2,6,7,1,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,2,6,7,3,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,3,1,2,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,3,1,2,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,3,1,7,2,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>15
[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>6
[5,4,3,2,7,1,6]=>[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>56
[5,4,3,6,1,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,3,6,2,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,3,6,7,1,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,3,6,7,2,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,4,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,6,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,1,2,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,1,3,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,2,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,2,3,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,3,1,6,2]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,3,2,6,1]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,4,7,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,2,4,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,2,7,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,2,7,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,3,2,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,3,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,3,7,2,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,3,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,4,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,4,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,1,4,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,1,4,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,1,4,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,4,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,2,7,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,7,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,7,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,7,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,2,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,3,7,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,7,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,3,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[5,6,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,6,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,3,4,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,4,3,6]=>[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,1,4,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,4,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,1,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,2,4,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,4,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,1,4,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,4,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,2,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,3,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,1,3,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,3,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,1,2,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,2,1,6]=>[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[5,7,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,1,2,3,4,5,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[6,1,2,3,4,7,5]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[6,1,2,3,5,4,7]=>[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>6
[6,1,2,3,5,7,4]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[6,1,2,3,7,4,5]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[6,1,2,3,7,5,4]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[6,2,3,4,1,5,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,3,4,5,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,3,4,7,1,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,3,4,7,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,3,5,1,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,3,5,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,3,5,7,1,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,3,5,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,1,3,5,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,1,5,3,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,3,1,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,3,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,5,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,4,7,1,3,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,7,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,7,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,7,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,7,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,4,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,1,3,4,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,1,4,3,7]=>[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,3,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,4,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,2,5,7,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,7,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,7,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,7,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,5,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,2,7,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,1,4,2,5,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,1,4,5,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,1,4,7,2,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,1,4,7,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,1,5,2,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,1,5,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,1,5,7,2,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,1,5,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,2,4,1,5,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,2,4,5,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,2,4,7,1,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,2,4,7,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,2,5,1,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,2,5,4,1,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,2,5,7,1,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,2,5,7,4,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,1,2,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,1,5,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,2,1,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,2,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,4,7,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,7,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,7,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,7,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,4,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,1,2,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,2,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,3,5,7,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,7,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,5,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,3,7,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,2,3,5,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,2,5,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,2,7,3,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,2,7,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,3,2,5,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,3,5,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,3,7,2,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,3,7,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,5,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,5,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,1,5,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,1,5,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,1,3,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,1,5,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,3,1,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,3,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,5,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,5,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,2,7,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,7,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,7,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,7,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,7,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,2,7,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,1,2,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,1,5,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,2,1,5,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,2,5,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,5,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,5,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,3,7,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,7,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,7,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,7,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,7,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,3,7,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,4,5,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,5,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,4,7,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,2,3,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,2,4,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,2,7,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,2,7,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,3,2,4,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,3,4,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,3,7,2,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,3,7,4,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,4,2,3,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,4,3,2,7]=>[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,1,4,7,2,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,1,4,7,3,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,1,3,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,1,4,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,3,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,3,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,4,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,4,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,2,7,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,7,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,7,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,7,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,7,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,2,7,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,1,2,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,1,4,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,2,1,4,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,2,4,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,4,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,4,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,3,7,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,7,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,7,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,7,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,7,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,3,7,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,1,2,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,1,3,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,2,1,3,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,2,3,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,3,1,2,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>6
[6,5,4,7,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,7,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,7,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,7,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,7,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,4,7,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,5,7,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[6,7,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,1,2,3,4,5,6]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>1
[7,1,2,3,5,4,6]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[7,1,2,3,5,6,4]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[7,1,2,3,6,4,5]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[7,1,2,3,6,5,4]=>[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>5
[7,2,3,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,3,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,3,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,3,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,1,3,6]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,1,3,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,4,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,1,4,6]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,1,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,1,3,6]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,1,6,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,5,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,1,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,1,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,1,3,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,1,5,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,1,3,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,1,4,3]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,2,6,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,1,4,5,2,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,1,4,5,6,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,1,4,6,2,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,1,4,6,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,2,4,5,1,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,2,4,5,6,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,2,4,6,1,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,2,4,6,5,1]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,4,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,2,4,6]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,2,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,1,4,6]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,1,6,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,5,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,2,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,2,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,1,4,5]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,1,5,4]=>[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,3,6,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,2,5,3,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,2,5,6,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,2,6,3,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,2,6,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,3,5,2,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,3,5,6,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,3,6,2,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,1,3,6,5,2]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,1,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,5,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,2,6,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,5,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,3,6,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,5,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,4,6,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,3,4,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,3,6,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,4,3,6]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,4,6,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,6,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,1,2,6,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,1,4,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,1,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,4,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,3,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,1,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,4,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,2,6,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,2,4,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,2,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,4,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,4,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,6,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,1,6,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,1,4,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,1,6,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,4,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,4,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,6,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,2,6,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,4,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,3,6,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,2,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,2,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,3,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,3,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,6,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,1,6,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,1,3,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,1,6,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,3,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,3,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,6,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,2,6,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,1,2,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,1,6,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,2,1,6]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,2,6,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,6,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,3,6,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,4,6,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,5,6,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,3,4,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,3,5,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,4,3,5]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,4,5,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,5,3,4]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,1,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,1,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,3,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,4,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,2,5,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,2,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,2,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,4,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,4,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,5,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,1,5,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,1,4,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,1,5,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,4,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,4,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,5,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,2,5,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,4,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,3,5,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,2,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,2,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,3,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,3,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,5,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,1,5,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,1,3,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,1,5,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,3,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,3,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,5,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,2,5,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,1,2,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,1,5,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,2,1,5]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,2,5,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,5,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,3,5,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,4,5,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,2,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,2,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,3,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,3,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,4,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,1,4,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,1,3,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,1,4,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,3,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,3,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,4,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,2,4,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,1,2,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,1,4,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,2,1,4]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,2,4,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,4,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,3,4,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,1,2,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,1,3,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,2,1,3]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,2,3,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,3,1,2]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>1
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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
Demazure product with inverse
Description
This map sends a permutation $\pi$ to $\pi^{-1} \star \pi$ where $\star$ denotes the Demazure product on permutations.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
This map is a surjection onto the set of involutions, i.e., the set of permutations $\pi$ for which $\pi = \pi^{-1}$.
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
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