Identifier
-
Mp00064:
Permutations
—reverse⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St000546: Permutations ⟶ ℤ
Values
=>
Cc0010;cc-rep-2
[1]=>[1]=>[.,.]=>[1]=>0
[1,2]=>[2,1]=>[[.,.],.]=>[1,2]=>0
[2,1]=>[1,2]=>[.,[.,.]]=>[2,1]=>1
[1,2,3]=>[3,2,1]=>[[[.,.],.],.]=>[1,2,3]=>0
[1,3,2]=>[2,3,1]=>[[.,.],[.,.]]=>[3,1,2]=>1
[2,1,3]=>[3,1,2]=>[[.,[.,.]],.]=>[2,1,3]=>0
[2,3,1]=>[1,3,2]=>[.,[[.,.],.]]=>[2,3,1]=>1
[3,1,2]=>[2,1,3]=>[[.,.],[.,.]]=>[3,1,2]=>1
[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1]=>2
[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>0
[1,2,4,3]=>[3,4,2,1]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>1
[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>0
[1,3,4,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>1
[1,4,2,3]=>[3,2,4,1]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>1
[1,4,3,2]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>2
[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>0
[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>1
[2,3,1,4]=>[4,1,3,2]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>0
[2,3,4,1]=>[1,4,3,2]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>1
[2,4,1,3]=>[3,1,4,2]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>1
[2,4,3,1]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>2
[3,1,2,4]=>[4,2,1,3]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>0
[3,1,4,2]=>[2,4,1,3]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>1
[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>0
[3,2,4,1]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>1
[3,4,1,2]=>[2,1,4,3]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>1
[3,4,2,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>2
[4,1,2,3]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>1
[4,1,3,2]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>2
[4,2,1,3]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>1
[4,2,3,1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>2
[4,3,1,2]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>2
[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>3
[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>0
[1,2,3,5,4]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1
[1,2,4,3,5]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>0
[1,2,4,5,3]=>[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[1,2,5,3,4]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1
[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[1,3,2,4,5]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>0
[1,3,2,5,4]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[1,3,4,2,5]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>0
[1,3,4,5,2]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>1
[1,3,5,2,4]=>[4,2,5,3,1]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[1,3,5,4,2]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[1,4,2,3,5]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>0
[1,4,2,5,3]=>[3,5,2,4,1]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>0
[1,4,3,5,2]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1
[1,4,5,2,3]=>[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[1,4,5,3,2]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[1,5,2,3,4]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1
[1,5,2,4,3]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[1,5,3,2,4]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[1,5,3,4,2]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[1,5,4,2,3]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[1,5,4,3,2]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>3
[2,1,3,4,5]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>0
[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1
[2,1,4,3,5]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>0
[2,1,4,5,3]=>[3,5,4,1,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[2,1,5,3,4]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1
[2,1,5,4,3]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[2,3,1,4,5]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>0
[2,3,1,5,4]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1
[2,3,4,1,5]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>0
[2,3,4,5,1]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>1
[2,3,5,1,4]=>[4,1,5,3,2]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1
[2,3,5,4,1]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>2
[2,4,1,3,5]=>[5,3,1,4,2]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>0
[2,4,1,5,3]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[2,4,3,1,5]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>0
[2,4,3,5,1]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>1
[2,4,5,1,3]=>[3,1,5,4,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[2,4,5,3,1]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2
[2,5,1,3,4]=>[4,3,1,5,2]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1
[2,5,1,4,3]=>[3,4,1,5,2]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[2,5,3,1,4]=>[4,1,3,5,2]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1
[2,5,3,4,1]=>[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>2
[2,5,4,1,3]=>[3,1,4,5,2]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[2,5,4,3,1]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>3
[3,1,2,4,5]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>0
[3,1,2,5,4]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[3,1,4,2,5]=>[5,2,4,1,3]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>0
[3,1,4,5,2]=>[2,5,4,1,3]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>1
[3,1,5,2,4]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[3,1,5,4,2]=>[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[3,2,1,4,5]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>0
[3,2,1,5,4]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1
[3,2,4,1,5]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>0
[3,2,4,5,1]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>1
[3,2,5,1,4]=>[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1
[3,2,5,4,1]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>2
[3,4,1,2,5]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>0
[3,4,1,5,2]=>[2,5,1,4,3]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>1
[3,4,2,1,5]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>0
[3,4,2,5,1]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>1
[3,4,5,1,2]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>1
[3,4,5,2,1]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>2
[3,5,1,2,4]=>[4,2,1,5,3]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[3,5,1,4,2]=>[2,4,1,5,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[3,5,2,1,4]=>[4,1,2,5,3]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1
[3,5,2,4,1]=>[1,4,2,5,3]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>2
[3,5,4,1,2]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[3,5,4,2,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>3
[4,1,2,3,5]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>0
[4,1,2,5,3]=>[3,5,2,1,4]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[4,1,3,2,5]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>0
[4,1,3,5,2]=>[2,5,3,1,4]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1
[4,1,5,2,3]=>[3,2,5,1,4]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[4,1,5,3,2]=>[2,3,5,1,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[4,2,1,3,5]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>0
[4,2,1,5,3]=>[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[4,2,3,1,5]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>0
[4,2,3,5,1]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>1
[4,2,5,1,3]=>[3,1,5,2,4]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[4,2,5,3,1]=>[1,3,5,2,4]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2
[4,3,1,2,5]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>0
[4,3,1,5,2]=>[2,5,1,3,4]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1
[4,3,2,1,5]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>0
[4,3,2,5,1]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>1
[4,3,5,1,2]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>1
[4,3,5,2,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>2
[4,5,1,2,3]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>1
[4,5,1,3,2]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[4,5,2,1,3]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>1
[4,5,2,3,1]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>2
[4,5,3,1,2]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>2
[4,5,3,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>3
[5,1,2,3,4]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>1
[5,1,2,4,3]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[5,1,3,2,4]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[5,1,3,4,2]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[5,1,4,2,3]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[5,1,4,3,2]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>3
[5,2,1,3,4]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>1
[5,2,1,4,3]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[5,2,3,1,4]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>1
[5,2,3,4,1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>2
[5,2,4,1,3]=>[3,1,4,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[5,2,4,3,1]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>3
[5,3,1,2,4]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>1
[5,3,1,4,2]=>[2,4,1,3,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[5,3,2,1,4]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>1
[5,3,2,4,1]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>2
[5,3,4,1,2]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>2
[5,3,4,2,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>3
[5,4,1,2,3]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>2
[5,4,1,3,2]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>3
[5,4,2,1,3]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>2
[5,4,2,3,1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>3
[5,4,3,1,2]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>3
[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>4
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>0
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>0
[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,2,3,6,4,5]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>0
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[1,2,4,6,3,5]=>[5,3,6,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,2,5,3,4,6]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>0
[1,2,5,3,6,4]=>[4,6,3,5,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[1,2,5,6,3,4]=>[4,3,6,5,2,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[1,2,6,3,4,5]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1
[1,2,6,3,5,4]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,2,6,4,3,5]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,2,6,4,5,3]=>[3,5,4,6,2,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,2,6,5,3,4]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>0
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,3,2,6,4,5]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>0
[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>0
[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1
[1,3,4,6,2,5]=>[5,2,6,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[1,3,5,2,6,4]=>[4,6,2,5,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[1,3,5,6,2,4]=>[4,2,6,5,3,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[1,3,6,2,4,5]=>[5,4,2,6,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[1,3,6,2,5,4]=>[4,5,2,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,3,6,4,2,5]=>[5,2,4,6,3,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[1,3,6,4,5,2]=>[2,5,4,6,3,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[1,3,6,5,2,4]=>[4,2,5,6,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[1,4,2,3,5,6]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>0
[1,4,2,3,6,5]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[1,4,2,5,6,3]=>[3,6,5,2,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[1,4,2,6,3,5]=>[5,3,6,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,4,2,6,5,3]=>[3,5,6,2,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>0
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>0
[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1
[1,4,3,6,2,5]=>[5,2,6,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[1,4,5,2,6,3]=>[3,6,2,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>0
[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1
[1,4,5,6,2,3]=>[3,2,6,5,4,1]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>2
[1,4,6,2,3,5]=>[5,3,2,6,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,4,6,2,5,3]=>[3,5,2,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,4,6,3,2,5]=>[5,2,3,6,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[1,4,6,3,5,2]=>[2,5,3,6,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[1,4,6,5,2,3]=>[3,2,5,6,4,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[1,5,2,3,4,6]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>0
[1,5,2,3,6,4]=>[4,6,3,2,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,5,2,4,3,6]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[1,5,2,4,6,3]=>[3,6,4,2,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[1,5,2,6,3,4]=>[4,3,6,2,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,5,2,6,4,3]=>[3,4,6,2,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[1,5,3,2,4,6]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[1,5,3,2,6,4]=>[4,6,2,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[1,5,3,4,6,2]=>[2,6,4,3,5,1]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[1,5,3,6,2,4]=>[4,2,6,3,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,5,3,6,4,2]=>[2,4,6,3,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[1,5,4,2,3,6]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[1,5,4,2,6,3]=>[3,6,2,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>0
[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1
[1,5,4,6,2,3]=>[3,2,6,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[1,5,6,2,3,4]=>[4,3,2,6,5,1]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[1,5,6,2,4,3]=>[3,4,2,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[1,5,6,3,2,4]=>[4,2,3,6,5,1]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[1,5,6,3,4,2]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[1,5,6,4,2,3]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>3
[1,6,2,3,4,5]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1
[1,6,2,3,5,4]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,6,2,4,3,5]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,6,2,4,5,3]=>[3,5,4,2,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,6,2,5,3,4]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,6,2,5,4,3]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[1,6,3,2,4,5]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[1,6,3,2,5,4]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,6,3,4,2,5]=>[5,2,4,3,6,1]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[1,6,3,4,5,2]=>[2,5,4,3,6,1]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[1,6,3,5,2,4]=>[4,2,5,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,6,3,5,4,2]=>[2,4,5,3,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[1,6,4,2,3,5]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[1,6,4,2,5,3]=>[3,5,2,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,6,4,3,2,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[1,6,4,3,5,2]=>[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[1,6,4,5,2,3]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[1,6,4,5,3,2]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[1,6,5,2,3,4]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[1,6,5,2,4,3]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[1,6,5,3,2,4]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[1,6,5,3,4,2]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[1,6,5,4,2,3]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>4
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>0
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>0
[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,1,3,6,4,5]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>0
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[2,1,4,6,3,5]=>[5,3,6,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,1,5,3,4,6]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>0
[2,1,5,3,6,4]=>[4,6,3,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[2,1,5,6,3,4]=>[4,3,6,5,1,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[2,1,6,3,4,5]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1
[2,1,6,3,5,4]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,1,6,4,3,5]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,1,6,4,5,3]=>[3,5,4,6,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,1,6,5,3,4]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>0
[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1
[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>0
[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1
[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>0
[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1
[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>0
[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>1
[2,3,4,6,1,5]=>[5,1,6,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1
[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>2
[2,3,5,1,4,6]=>[6,4,1,5,3,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>0
[2,3,5,1,6,4]=>[4,6,1,5,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>0
[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>1
[2,3,5,6,1,4]=>[4,1,6,5,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1
[2,3,6,1,5,4]=>[4,5,1,6,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,3,6,4,1,5]=>[5,1,4,6,3,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1
[2,3,6,4,5,1]=>[1,5,4,6,3,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>2
[2,3,6,5,1,4]=>[4,1,5,6,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[2,4,1,3,5,6]=>[6,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>0
[2,4,1,3,6,5]=>[5,6,3,1,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,4,1,5,3,6]=>[6,3,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[2,4,1,5,6,3]=>[3,6,5,1,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,4,1,6,5,3]=>[3,5,6,1,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>0
[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>0
[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>1
[2,4,3,6,1,5]=>[5,1,6,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[2,4,5,1,3,6]=>[6,3,1,5,4,2]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[2,4,5,1,6,3]=>[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>0
[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>1
[2,4,5,6,1,3]=>[3,1,6,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>2
[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,4,6,1,5,3]=>[3,5,1,6,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,4,6,3,1,5]=>[5,1,3,6,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[2,4,6,3,5,1]=>[1,5,3,6,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[2,4,6,5,1,3]=>[3,1,5,6,4,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[2,5,1,3,4,6]=>[6,4,3,1,5,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>0
[2,5,1,3,6,4]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,5,1,4,3,6]=>[6,3,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[2,5,1,4,6,3]=>[3,6,4,1,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[2,5,1,6,3,4]=>[4,3,6,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,5,1,6,4,3]=>[3,4,6,1,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[2,5,3,1,4,6]=>[6,4,1,3,5,2]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>0
[2,5,3,1,6,4]=>[4,6,1,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,5,3,4,1,6]=>[6,1,4,3,5,2]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>0
[2,5,3,4,6,1]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>1
[2,5,3,6,1,4]=>[4,1,6,3,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,5,3,6,4,1]=>[1,4,6,3,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[2,5,4,1,3,6]=>[6,3,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[2,5,4,1,6,3]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>0
[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>1
[2,5,4,6,1,3]=>[3,1,6,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2
[2,5,6,1,3,4]=>[4,3,1,6,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[2,5,6,1,4,3]=>[3,4,1,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[2,5,6,3,1,4]=>[4,1,3,6,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[2,5,6,3,4,1]=>[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[2,5,6,4,1,3]=>[3,1,4,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>3
[2,6,1,3,4,5]=>[5,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1
[2,6,1,3,5,4]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,6,1,4,3,5]=>[5,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,6,1,4,5,3]=>[3,5,4,1,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,6,1,5,3,4]=>[4,3,5,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,6,1,5,4,3]=>[3,4,5,1,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[2,6,3,1,4,5]=>[5,4,1,3,6,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1
[2,6,3,1,5,4]=>[4,5,1,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1
[2,6,3,4,5,1]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>2
[2,6,3,5,1,4]=>[4,1,5,3,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,6,3,5,4,1]=>[1,4,5,3,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[2,6,4,1,3,5]=>[5,3,1,4,6,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[2,6,4,1,5,3]=>[3,5,1,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[2,6,4,3,5,1]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[2,6,4,5,1,3]=>[3,1,5,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[2,6,4,5,3,1]=>[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[2,6,5,1,3,4]=>[4,3,1,5,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[2,6,5,1,4,3]=>[3,4,1,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[2,6,5,3,1,4]=>[4,1,3,5,6,2]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[2,6,5,3,4,1]=>[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[2,6,5,4,1,3]=>[3,1,4,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>4
[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>0
[3,1,2,4,6,5]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[3,1,2,5,4,6]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,1,2,6,4,5]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[3,1,2,6,5,4]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,1,4,2,5,6]=>[6,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>0
[3,1,4,2,6,5]=>[5,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,1,4,5,2,6]=>[6,2,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>0
[3,1,4,5,6,2]=>[2,6,5,4,1,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1
[3,1,4,6,2,5]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,1,4,6,5,2]=>[2,5,6,4,1,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,1,5,2,4,6]=>[6,4,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,1,5,4,2,6]=>[6,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[3,1,5,4,6,2]=>[2,6,4,5,1,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[3,1,5,6,2,4]=>[4,2,6,5,1,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,1,5,6,4,2]=>[2,4,6,5,1,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[3,1,6,2,4,5]=>[5,4,2,6,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[3,1,6,2,5,4]=>[4,5,2,6,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,1,6,4,2,5]=>[5,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,1,6,4,5,2]=>[2,5,4,6,1,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,1,6,5,2,4]=>[4,2,5,6,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,1,6,5,4,2]=>[2,4,5,6,1,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>0
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>0
[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,2,1,6,4,5]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>0
[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1
[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>0
[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>1
[3,2,4,6,1,5]=>[5,1,6,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1
[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>2
[3,2,5,1,4,6]=>[6,4,1,5,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>0
[3,2,5,1,6,4]=>[4,6,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>0
[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>1
[3,2,5,6,1,4]=>[4,1,6,5,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[3,2,6,1,4,5]=>[5,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1
[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,2,6,4,1,5]=>[5,1,4,6,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1
[3,2,6,4,5,1]=>[1,5,4,6,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>2
[3,2,6,5,1,4]=>[4,1,5,6,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>0
[3,4,1,2,6,5]=>[5,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,4,1,5,2,6]=>[6,2,5,1,4,3]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>0
[3,4,1,5,6,2]=>[2,6,5,1,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1
[3,4,1,6,2,5]=>[5,2,6,1,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,4,1,6,5,2]=>[2,5,6,1,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>0
[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1
[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>0
[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>1
[3,4,2,6,1,5]=>[5,1,6,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1
[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>2
[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>0
[3,4,5,1,6,2]=>[2,6,1,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1
[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>0
[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>1
[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>1
[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>2
[3,4,6,1,2,5]=>[5,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,4,6,1,5,2]=>[2,5,1,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,4,6,2,1,5]=>[5,1,2,6,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1
[3,4,6,2,5,1]=>[1,5,2,6,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>2
[3,4,6,5,1,2]=>[2,1,5,6,4,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>3
[3,5,1,2,4,6]=>[6,4,2,1,5,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[3,5,1,2,6,4]=>[4,6,2,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,5,1,4,2,6]=>[6,2,4,1,5,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[3,5,1,4,6,2]=>[2,6,4,1,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,5,1,6,4,2]=>[2,4,6,1,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[3,5,2,1,4,6]=>[6,4,1,2,5,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>0
[3,5,2,1,6,4]=>[4,6,1,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,5,2,4,1,6]=>[6,1,4,2,5,3]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>0
[3,5,2,4,6,1]=>[1,6,4,2,5,3]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>1
[3,5,2,6,1,4]=>[4,1,6,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,5,2,6,4,1]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[3,5,4,1,2,6]=>[6,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[3,5,4,1,6,2]=>[2,6,1,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>0
[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>1
[3,5,4,6,1,2]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>2
[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[3,5,6,1,4,2]=>[2,4,1,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[3,5,6,2,1,4]=>[4,1,2,6,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[3,5,6,2,4,1]=>[1,4,2,6,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[3,5,6,4,1,2]=>[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>3
[3,6,1,2,4,5]=>[5,4,2,1,6,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[3,6,1,2,5,4]=>[4,5,2,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,6,1,4,2,5]=>[5,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,6,1,4,5,2]=>[2,5,4,1,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,6,1,5,2,4]=>[4,2,5,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,6,1,5,4,2]=>[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[3,6,2,1,4,5]=>[5,4,1,2,6,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1
[3,6,2,1,5,4]=>[4,5,1,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,6,2,4,1,5]=>[5,1,4,2,6,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1
[3,6,2,4,5,1]=>[1,5,4,2,6,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>2
[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,6,2,5,4,1]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[3,6,4,1,2,5]=>[5,2,1,4,6,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[3,6,4,1,5,2]=>[2,5,1,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,6,4,2,1,5]=>[5,1,2,4,6,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1
[3,6,4,2,5,1]=>[1,5,2,4,6,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>2
[3,6,4,5,1,2]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[3,6,4,5,2,1]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>3
[3,6,5,1,2,4]=>[4,2,1,5,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[3,6,5,1,4,2]=>[2,4,1,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[3,6,5,2,4,1]=>[1,4,2,5,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[3,6,5,4,1,2]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>4
[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>0
[4,1,2,3,6,5]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[4,1,2,5,3,6]=>[6,3,5,2,1,4]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,1,2,6,3,5]=>[5,3,6,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[4,1,2,6,5,3]=>[3,5,6,2,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,1,3,2,5,6]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>0
[4,1,3,2,6,5]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,1,3,5,2,6]=>[6,2,5,3,1,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>0
[4,1,3,5,6,2]=>[2,6,5,3,1,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1
[4,1,3,6,2,5]=>[5,2,6,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,1,3,6,5,2]=>[2,5,6,3,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,1,5,2,3,6]=>[6,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,1,5,3,2,6]=>[6,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>0
[4,1,5,3,6,2]=>[2,6,3,5,1,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1
[4,1,5,6,2,3]=>[3,2,6,5,1,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,1,5,6,3,2]=>[2,3,6,5,1,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>2
[4,1,6,2,3,5]=>[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[4,1,6,2,5,3]=>[3,5,2,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,1,6,3,2,5]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,1,6,3,5,2]=>[2,5,3,6,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,1,6,5,2,3]=>[3,2,5,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,1,6,5,3,2]=>[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>0
[4,2,1,3,6,5]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[4,2,1,5,3,6]=>[6,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[4,2,1,5,6,3]=>[3,6,5,1,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,2,1,6,3,5]=>[5,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>0
[4,2,3,1,6,5]=>[5,6,1,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>0
[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>1
[4,2,3,6,1,5]=>[5,1,6,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[4,2,3,6,5,1]=>[1,5,6,3,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[4,2,5,1,3,6]=>[6,3,1,5,2,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[4,2,5,1,6,3]=>[3,6,1,5,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,2,5,3,1,6]=>[6,1,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>0
[4,2,5,3,6,1]=>[1,6,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>1
[4,2,5,6,1,3]=>[3,1,6,5,2,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,2,5,6,3,1]=>[1,3,6,5,2,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>2
[4,2,6,1,3,5]=>[5,3,1,6,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,2,6,3,1,5]=>[5,1,3,6,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[4,2,6,3,5,1]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[4,2,6,5,1,3]=>[3,1,5,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,2,6,5,3,1]=>[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>0
[4,3,1,2,6,5]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,3,1,5,2,6]=>[6,2,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>0
[4,3,1,5,6,2]=>[2,6,5,1,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1
[4,3,1,6,2,5]=>[5,2,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,3,1,6,5,2]=>[2,5,6,1,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>0
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>0
[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>1
[4,3,2,6,1,5]=>[5,1,6,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>2
[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>0
[4,3,5,1,6,2]=>[2,6,1,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1
[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>0
[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>1
[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>1
[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>2
[4,3,6,1,2,5]=>[5,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,3,6,1,5,2]=>[2,5,1,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,3,6,2,1,5]=>[5,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[4,3,6,2,5,1]=>[1,5,2,6,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>2
[4,3,6,5,1,2]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>3
[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>0
[4,5,1,2,6,3]=>[3,6,2,1,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,5,1,3,2,6]=>[6,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>0
[4,5,1,3,6,2]=>[2,6,3,1,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1
[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,5,1,6,3,2]=>[2,3,6,1,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>2
[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>0
[4,5,2,1,6,3]=>[3,6,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>0
[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>1
[4,5,2,6,1,3]=>[3,1,6,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,5,2,6,3,1]=>[1,3,6,2,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>2
[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>0
[4,5,3,1,6,2]=>[2,6,1,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1
[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>0
[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>1
[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>1
[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>2
[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>1
[4,5,6,1,3,2]=>[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>2
[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>1
[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>2
[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>2
[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>3
[4,6,1,2,3,5]=>[5,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[4,6,1,2,5,3]=>[3,5,2,1,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,6,1,3,2,5]=>[5,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,6,1,3,5,2]=>[2,5,3,1,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,6,1,5,2,3]=>[3,2,5,1,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,6,1,5,3,2]=>[2,3,5,1,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[4,6,2,1,3,5]=>[5,3,1,2,6,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[4,6,2,1,5,3]=>[3,5,1,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,6,2,3,1,5]=>[5,1,3,2,6,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[4,6,2,3,5,1]=>[1,5,3,2,6,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,6,2,5,3,1]=>[1,3,5,2,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[4,6,3,1,2,5]=>[5,2,1,3,6,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[4,6,3,1,5,2]=>[2,5,1,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,6,3,2,1,5]=>[5,1,2,3,6,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[4,6,3,2,5,1]=>[1,5,2,3,6,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>2
[4,6,3,5,1,2]=>[2,1,5,3,6,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[4,6,3,5,2,1]=>[1,2,5,3,6,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>3
[4,6,5,1,2,3]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[4,6,5,1,3,2]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[4,6,5,2,3,1]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[4,6,5,3,1,2]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>4
[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>0
[5,1,2,3,6,4]=>[4,6,3,2,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[5,1,2,4,3,6]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[5,1,2,4,6,3]=>[3,6,4,2,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,1,2,6,3,4]=>[4,3,6,2,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[5,1,2,6,4,3]=>[3,4,6,2,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,1,3,2,4,6]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[5,1,3,2,6,4]=>[4,6,2,3,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,1,3,4,2,6]=>[6,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[5,1,3,6,2,4]=>[4,2,6,3,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,1,3,6,4,2]=>[2,4,6,3,1,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,1,4,2,3,6]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[5,1,4,2,6,3]=>[3,6,2,4,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,1,4,3,2,6]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>0
[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1
[5,1,4,6,2,3]=>[3,2,6,4,1,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,1,4,6,3,2]=>[2,3,6,4,1,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[5,1,6,2,3,4]=>[4,3,2,6,1,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[5,1,6,2,4,3]=>[3,4,2,6,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,1,6,3,2,4]=>[4,2,3,6,1,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,1,6,3,4,2]=>[2,4,3,6,1,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,1,6,4,2,3]=>[3,2,4,6,1,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,1,6,4,3,2]=>[2,3,4,6,1,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>3
[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>0
[5,2,1,3,6,4]=>[4,6,3,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[5,2,1,4,3,6]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[5,2,1,4,6,3]=>[3,6,4,1,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,2,1,6,3,4]=>[4,3,6,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[5,2,1,6,4,3]=>[3,4,6,1,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>0
[5,2,3,1,6,4]=>[4,6,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>0
[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>1
[5,2,3,6,1,4]=>[4,1,6,3,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[5,2,3,6,4,1]=>[1,4,6,3,2,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[5,2,4,1,3,6]=>[6,3,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[5,2,4,1,6,3]=>[3,6,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,2,4,3,1,6]=>[6,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>0
[5,2,4,3,6,1]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>1
[5,2,4,6,1,3]=>[3,1,6,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,2,4,6,3,1]=>[1,3,6,4,2,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2
[5,2,6,1,3,4]=>[4,3,1,6,2,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[5,2,6,1,4,3]=>[3,4,1,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,2,6,3,1,4]=>[4,1,3,6,2,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[5,2,6,3,4,1]=>[1,4,3,6,2,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[5,2,6,4,1,3]=>[3,1,4,6,2,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,2,6,4,3,1]=>[1,3,4,6,2,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>3
[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>0
[5,3,1,2,6,4]=>[4,6,2,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,3,1,4,2,6]=>[6,2,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[5,3,1,4,6,2]=>[2,6,4,1,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[5,3,1,6,2,4]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>0
[5,3,2,1,6,4]=>[4,6,1,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>0
[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>1
[5,3,2,6,1,4]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[5,3,2,6,4,1]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>0
[5,3,4,1,6,2]=>[2,6,1,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>0
[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>1
[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>1
[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>2
[5,3,6,1,2,4]=>[4,2,1,6,3,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,3,6,2,1,4]=>[4,1,2,6,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[5,3,6,2,4,1]=>[1,4,2,6,3,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[5,3,6,4,1,2]=>[2,1,4,6,3,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,3,6,4,2,1]=>[1,2,4,6,3,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>3
[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>0
[5,4,1,2,6,3]=>[3,6,2,1,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,4,1,3,2,6]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>0
[5,4,1,3,6,2]=>[2,6,3,1,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1
[5,4,1,6,2,3]=>[3,2,6,1,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>0
[5,4,2,1,6,3]=>[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>0
[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>1
[5,4,2,6,1,3]=>[3,1,6,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,4,2,6,3,1]=>[1,3,6,2,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2
[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>0
[5,4,3,1,6,2]=>[2,6,1,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>0
[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>1
[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>1
[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>2
[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>1
[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>1
[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>2
[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>2
[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>3
[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>1
[5,6,1,2,4,3]=>[3,4,2,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,6,1,3,2,4]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,6,1,3,4,2]=>[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,6,1,4,2,3]=>[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,6,1,4,3,2]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>3
[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>1
[5,6,2,1,4,3]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>1
[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>2
[5,6,2,4,1,3]=>[3,1,4,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,6,2,4,3,1]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>3
[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>1
[5,6,3,1,4,2]=>[2,4,1,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>1
[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>2
[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>2
[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>3
[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>2
[5,6,4,1,3,2]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>3
[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>2
[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>3
[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>3
[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>4
[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>1
[6,1,2,3,5,4]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[6,1,2,4,3,5]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[6,1,2,4,5,3]=>[3,5,4,2,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,1,2,5,3,4]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[6,1,2,5,4,3]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,1,3,2,4,5]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[6,1,3,2,5,4]=>[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,1,3,4,2,5]=>[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[6,1,3,4,5,2]=>[2,5,4,3,1,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[6,1,3,5,2,4]=>[4,2,5,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,1,3,5,4,2]=>[2,4,5,3,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,1,4,2,3,5]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[6,1,4,2,5,3]=>[3,5,2,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,1,4,3,2,5]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[6,1,4,3,5,2]=>[2,5,3,4,1,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[6,1,4,5,2,3]=>[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,1,4,5,3,2]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[6,1,5,2,3,4]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[6,1,5,2,4,3]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,1,5,3,2,4]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,1,5,3,4,2]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,1,5,4,2,3]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,1,5,4,3,2]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>4
[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>1
[6,2,1,3,5,4]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[6,2,1,4,3,5]=>[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[6,2,1,4,5,3]=>[3,5,4,1,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,2,1,5,3,4]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[6,2,1,5,4,3]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>1
[6,2,3,1,5,4]=>[4,5,1,3,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>1
[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>2
[6,2,3,5,1,4]=>[4,1,5,3,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[6,2,3,5,4,1]=>[1,4,5,3,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[6,2,4,1,3,5]=>[5,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[6,2,4,1,5,3]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,2,4,3,1,5]=>[5,1,3,4,2,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[6,2,4,5,1,3]=>[3,1,5,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,2,4,5,3,1]=>[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[6,2,5,1,3,4]=>[4,3,1,5,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[6,2,5,1,4,3]=>[3,4,1,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,2,5,3,1,4]=>[4,1,3,5,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[6,2,5,3,4,1]=>[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[6,2,5,4,1,3]=>[3,1,4,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,2,5,4,3,1]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>4
[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>1
[6,3,1,2,5,4]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,3,1,4,2,5]=>[5,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[6,3,1,4,5,2]=>[2,5,4,1,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[6,3,1,5,2,4]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,3,1,5,4,2]=>[2,4,5,1,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>1
[6,3,2,1,5,4]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>1
[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>2
[6,3,2,5,1,4]=>[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>1
[6,3,4,1,5,2]=>[2,5,1,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>1
[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>2
[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>2
[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>3
[6,3,5,1,2,4]=>[4,2,1,5,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,3,5,1,4,2]=>[2,4,1,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,3,5,2,1,4]=>[4,1,2,5,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[6,3,5,4,1,2]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,3,5,4,2,1]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>4
[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>1
[6,4,1,2,5,3]=>[3,5,2,1,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,4,1,3,2,5]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[6,4,1,3,5,2]=>[2,5,3,1,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[6,4,1,5,2,3]=>[3,2,5,1,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,4,1,5,3,2]=>[2,3,5,1,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>1
[6,4,2,1,5,3]=>[3,5,1,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>1
[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>2
[6,4,2,5,1,3]=>[3,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>1
[6,4,3,1,5,2]=>[2,5,1,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>1
[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>2
[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>2
[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>3
[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>2
[6,4,5,1,3,2]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>2
[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>3
[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>3
[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>4
[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>2
[6,5,1,2,4,3]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,5,1,3,2,4]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,5,1,3,4,2]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,5,1,4,2,3]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,5,1,4,3,2]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>4
[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>2
[6,5,2,1,4,3]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>2
[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>3
[6,5,2,4,1,3]=>[3,1,4,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,5,2,4,3,1]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>4
[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>2
[6,5,3,1,4,2]=>[2,4,1,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>2
[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>3
[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>3
[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>4
[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>3
[6,5,4,1,3,2]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>4
[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>3
[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>4
[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>4
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>5
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>0
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>0
[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>0
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,2,3,5,7,4,6]=>[6,4,7,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,3,6,4,5,7]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>0
[1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,3,7,5,4,6]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,3,7,6,4,5]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>0
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,2,4,3,7,5,6]=>[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,2,4,7,3,5,6]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,2,4,7,5,6,3]=>[3,6,5,7,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,2,5,3,4,6,7]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>0
[1,2,5,3,4,7,6]=>[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,5,3,6,4,7]=>[7,4,6,3,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,2,5,3,7,4,6]=>[6,4,7,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,5,3,7,6,4]=>[4,6,7,3,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[1,2,5,6,3,4,7]=>[7,4,3,6,5,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,2,5,7,3,4,6]=>[6,4,3,7,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,5,7,6,3,4]=>[4,3,6,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,6,3,4,5,7]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>0
[1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,6,4,5,7,3]=>[3,7,5,4,6,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,2,6,4,7,5,3]=>[3,5,7,4,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,7,3,5,4,6]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,7,3,5,6,4]=>[4,6,5,3,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,7,3,6,5,4]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,2,7,4,3,5,6]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,2,7,4,5,6,3]=>[3,6,5,4,7,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,2,7,4,6,5,3]=>[3,5,6,4,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,2,7,5,3,4,6]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,2,7,5,3,6,4]=>[4,6,3,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,7,5,6,3,4]=>[4,3,6,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,2,7,6,3,4,5]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,2,7,6,3,5,4]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,2,7,6,4,5,3]=>[3,5,4,6,7,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,2,7,6,5,3,4]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>0
[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[1,3,2,4,7,5,6]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[1,3,2,7,4,5,6]=>[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>0
[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,4,2,7,5,6]=>[6,5,7,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[1,3,4,6,2,7,5]=>[5,7,2,6,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,4,6,7,2,5]=>[5,2,7,6,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,4,7,2,5,6]=>[6,5,2,7,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,3,6,4,2,7,5]=>[5,7,2,4,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,6,4,7,2,5]=>[5,2,7,4,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[1,3,6,7,4,2,5]=>[5,2,4,7,6,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,3,7,2,4,5,6]=>[6,5,4,2,7,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[1,3,7,4,2,5,6]=>[6,5,2,4,7,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[1,3,7,5,6,4,2]=>[2,4,6,5,7,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>0
[1,4,2,3,5,7,6]=>[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,4,2,3,7,5,6]=>[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,4,2,5,6,3,7]=>[7,3,6,5,2,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[1,4,2,5,7,6,3]=>[3,6,7,5,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,2,6,5,7,3]=>[3,7,5,6,2,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,4,2,6,7,5,3]=>[3,5,7,6,2,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,4,2,7,3,5,6]=>[6,5,3,7,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,4,2,7,5,6,3]=>[3,6,5,7,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,2,7,6,5,3]=>[3,5,6,7,2,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,4,5,2,6,3,7]=>[7,3,6,2,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[1,4,5,2,7,6,3]=>[3,6,7,2,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,5,6,2,3,7]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,5,7,6,2,3]=>[3,2,6,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,6,2,5,7,3]=>[3,7,5,2,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,4,6,2,7,5,3]=>[3,5,7,2,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,4,6,5,2,7,3]=>[3,7,2,5,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,4,6,5,7,2,3]=>[3,2,7,5,6,4,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,4,6,7,5,2,3]=>[3,2,5,7,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,4,7,2,3,5,6]=>[6,5,3,2,7,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,4,7,2,5,6,3]=>[3,6,5,2,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,7,2,6,5,3]=>[3,5,6,2,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,4,7,5,2,6,3]=>[3,6,2,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,7,5,6,2,3]=>[3,2,6,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,4,7,6,2,5,3]=>[3,5,2,6,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,4,7,6,5,2,3]=>[3,2,5,6,7,4,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,5,2,3,4,6,7]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>0
[1,5,2,3,4,7,6]=>[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,5,2,3,6,4,7]=>[7,4,6,3,2,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,5,2,3,6,7,4]=>[4,7,6,3,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,2,3,7,4,6]=>[6,4,7,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,5,2,3,7,6,4]=>[4,6,7,3,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,2,4,6,7,3]=>[3,7,6,4,2,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[1,5,2,6,3,4,7]=>[7,4,3,6,2,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,2,6,7,3,4]=>[4,3,7,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,2,7,3,4,6]=>[6,4,3,7,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,2,7,6,3,4]=>[4,3,6,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,3,6,4,2,7]=>[7,2,4,6,3,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[1,5,3,7,6,4,2]=>[2,4,6,7,3,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,5,4,2,6,7,3]=>[3,7,6,2,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[1,5,4,6,2,7,3]=>[3,7,2,6,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[1,5,4,6,7,2,3]=>[3,2,7,6,4,5,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[1,5,6,2,3,4,7]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,6,3,4,2,7]=>[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[1,5,6,7,2,3,4]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[1,5,7,2,3,4,6]=>[6,4,3,2,7,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,7,3,6,4,2]=>[2,4,6,3,7,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,5,7,6,2,3,4]=>[4,3,2,6,7,5,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,5,7,6,3,4,2]=>[2,4,3,6,7,5,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,6,2,3,4,5,7]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>0
[1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,6,2,3,7,4,5]=>[5,4,7,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,6,2,4,5,7,3]=>[3,7,5,4,2,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,6,2,4,7,5,3]=>[3,5,7,4,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,6,2,7,4,5,3]=>[3,5,4,7,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,3,4,2,7,5]=>[5,7,2,4,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,6,3,4,7,2,5]=>[5,2,7,4,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,6,3,5,7,4,2]=>[2,4,7,5,3,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[1,6,3,7,4,2,5]=>[5,2,4,7,3,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,6,4,2,5,7,3]=>[3,7,5,2,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,4,5,2,7,3]=>[3,7,2,5,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,6,4,5,7,2,3]=>[3,2,7,5,4,6,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[1,6,4,7,2,5,3]=>[3,5,2,7,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,4,7,5,2,3]=>[3,2,5,7,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,5,3,7,4,2]=>[2,4,7,3,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[1,6,5,7,3,4,2]=>[2,4,3,7,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,7,3,4,2,5]=>[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[1,6,7,4,2,5,3]=>[3,5,2,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,6,7,4,5,2,3]=>[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,7,2,3,5,4,6]=>[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,7,2,3,5,6,4]=>[4,6,5,3,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,7,2,3,6,5,4]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,2,4,3,5,6]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,7,2,4,6,5,3]=>[3,5,6,4,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,2,5,3,4,6]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,2,5,6,3,4]=>[4,3,6,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,2,6,4,5,3]=>[3,5,4,6,2,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,2,6,5,3,4]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,2,6,5,4,3]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[1,7,3,2,4,5,6]=>[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[1,7,3,4,2,5,6]=>[6,5,2,4,3,7,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[1,7,3,5,6,4,2]=>[2,4,6,5,3,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,7,3,6,5,4,2]=>[2,4,5,6,3,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[1,7,4,2,3,5,6]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[1,7,4,2,5,6,3]=>[3,6,5,2,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,7,4,2,6,5,3]=>[3,5,6,2,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,4,5,2,6,3]=>[3,6,2,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,7,4,5,6,2,3]=>[3,2,6,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[1,7,4,6,2,5,3]=>[3,5,2,6,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,4,6,5,2,3]=>[3,2,5,6,4,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,5,2,3,4,6]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[1,7,5,2,3,6,4]=>[4,6,3,2,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,5,2,6,3,4]=>[4,3,6,2,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,5,3,6,4,2]=>[2,4,6,3,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,7,5,6,2,3,4]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[1,7,5,6,3,4,2]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[1,7,6,2,3,4,5]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[1,7,6,2,3,5,4]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,6,2,4,5,3]=>[3,5,4,2,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,6,2,5,3,4]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,6,2,5,4,3]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[1,7,6,3,5,4,2]=>[2,4,5,3,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[1,7,6,4,2,5,3]=>[3,5,2,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,6,4,5,2,3]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[1,7,6,5,2,3,4]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[1,7,6,5,2,4,3]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[1,7,6,5,3,4,2]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[1,7,6,5,4,2,3]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>0
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[2,1,3,4,7,5,6]=>[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[2,1,3,7,4,5,6]=>[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,1,4,3,7,5,6]=>[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,1,4,7,3,5,6]=>[6,5,3,7,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,1,7,3,4,5,6]=>[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[2,1,7,4,3,5,6]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>0
[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[2,3,1,7,4,5,6]=>[6,5,4,7,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>0
[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[2,3,4,1,7,5,6]=>[6,5,7,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>0
[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>0
[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>1
[2,3,4,5,7,1,6]=>[6,1,7,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>1
[2,3,4,7,1,5,6]=>[6,5,1,7,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[2,3,4,7,5,1,6]=>[6,1,5,7,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>1
[2,3,6,4,5,7,1]=>[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>1
[2,3,7,1,4,5,6]=>[6,5,4,1,7,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[2,3,7,4,5,1,6]=>[6,1,5,4,7,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[2,4,1,3,5,7,6]=>[6,7,5,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,4,1,3,7,5,6]=>[6,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,4,1,7,3,5,6]=>[6,5,3,7,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>1
[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>1
[2,4,7,1,3,5,6]=>[6,5,3,1,7,4,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,5,3,4,6,7,1]=>[1,7,6,4,3,5,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>1
[2,6,3,4,5,7,1]=>[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>1
[2,7,1,3,4,5,6]=>[6,5,4,3,1,7,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[2,7,1,4,3,5,6]=>[6,5,3,4,1,7,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[2,7,3,1,4,5,6]=>[6,5,4,1,3,7,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[2,7,3,4,1,5,6]=>[6,5,1,4,3,7,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[2,7,4,1,3,5,6]=>[6,5,3,1,4,7,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>0
[3,1,2,4,5,7,6]=>[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[3,1,2,4,7,5,6]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[3,1,2,7,4,5,6]=>[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[3,1,4,2,5,6,7]=>[7,6,5,2,4,1,3]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>0
[3,1,4,2,5,7,6]=>[6,7,5,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,1,4,2,6,7,5]=>[5,7,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,4,2,7,5,6]=>[6,5,7,2,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,1,4,5,6,7,2]=>[2,7,6,5,4,1,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[3,1,4,6,2,7,5]=>[5,7,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,4,6,7,2,5]=>[5,2,7,6,4,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,4,7,2,5,6]=>[6,5,2,7,4,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,1,5,6,4,2,7]=>[7,2,4,6,5,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[3,1,5,7,6,4,2]=>[2,4,6,7,5,1,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,6,4,7,2,5]=>[5,2,7,4,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,6,5,7,4,2]=>[2,4,7,5,6,1,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[3,1,6,7,4,2,5]=>[5,2,4,7,6,1,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,1,7,2,4,5,6]=>[6,5,4,2,7,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[3,1,7,4,2,5,6]=>[6,5,2,4,7,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,1,7,5,6,4,2]=>[2,4,6,5,7,1,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>0
[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[3,2,1,4,7,5,6]=>[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[3,2,1,7,4,5,6]=>[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[3,2,4,1,7,5,6]=>[6,5,7,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>1
[3,2,4,7,1,5,6]=>[6,5,1,7,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>1
[3,2,7,1,4,5,6]=>[6,5,4,1,7,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[3,2,7,4,1,5,6]=>[6,5,1,4,7,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>0
[3,4,1,2,5,7,6]=>[6,7,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,4,1,2,6,7,5]=>[5,7,6,2,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,1,2,7,5,6]=>[6,5,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,4,1,5,6,7,2]=>[2,7,6,5,1,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[3,4,1,6,2,7,5]=>[5,7,2,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,1,6,7,2,5]=>[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,1,7,2,5,6]=>[6,5,2,7,1,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>1
[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>0
[3,4,5,1,6,7,2]=>[2,7,6,1,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>1
[3,4,5,6,1,7,2]=>[2,7,1,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>1
[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>1
[3,4,6,1,2,7,5]=>[5,7,2,1,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,6,1,7,2,5]=>[5,2,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,6,2,5,1,7]=>[7,1,5,2,6,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>0
[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>0
[3,4,6,7,1,2,5]=>[5,2,1,7,6,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,4,7,1,2,5,6]=>[6,5,2,1,7,4,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,5,1,6,4,2,7]=>[7,2,4,6,1,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[3,5,1,7,6,4,2]=>[2,4,6,7,1,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,5,2,4,6,7,1]=>[1,7,6,4,2,5,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>1
[3,5,6,1,4,2,7]=>[7,2,4,1,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[3,5,6,4,1,2,7]=>[7,2,1,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[3,5,7,1,6,4,2]=>[2,4,6,1,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,5,7,6,1,4,2]=>[2,4,1,6,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,5,7,6,4,1,2]=>[2,1,4,6,7,5,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,6,1,4,2,7,5]=>[5,7,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,1,5,7,4,2]=>[2,4,7,5,1,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[3,6,1,7,4,2,5]=>[5,2,4,7,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,4,1,2,7,5]=>[5,7,2,1,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,4,1,7,2,5]=>[5,2,7,1,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,4,2,5,1,7]=>[7,1,5,2,4,6,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>0
[3,6,4,5,2,1,7]=>[7,1,2,5,4,6,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>0
[3,6,4,7,1,2,5]=>[5,2,1,7,4,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,5,1,7,4,2]=>[2,4,7,1,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>0
[3,6,5,7,1,4,2]=>[2,4,1,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[3,6,5,7,4,1,2]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[3,6,7,1,4,2,5]=>[5,2,4,1,7,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[3,7,1,2,4,5,6]=>[6,5,4,2,1,7,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[3,7,1,4,2,5,6]=>[6,5,2,4,1,7,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,7,1,5,6,4,2]=>[2,4,6,5,1,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,7,1,6,5,4,2]=>[2,4,5,6,1,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[3,7,2,1,4,5,6]=>[6,5,4,1,2,7,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[3,7,2,4,1,5,6]=>[6,5,1,4,2,7,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[3,7,4,1,2,5,6]=>[6,5,2,1,4,7,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[3,7,5,1,6,4,2]=>[2,4,6,1,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,7,5,6,1,4,2]=>[2,4,1,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,7,5,6,4,1,2]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[3,7,6,1,5,4,2]=>[2,4,5,1,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[3,7,6,5,1,4,2]=>[2,4,1,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[3,7,6,5,4,1,2]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>0
[4,1,2,3,5,7,6]=>[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[4,1,2,3,7,5,6]=>[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[4,1,2,5,6,3,7]=>[7,3,6,5,2,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,1,2,5,7,6,3]=>[3,6,7,5,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,2,6,5,7,3]=>[3,7,5,6,2,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,1,2,6,7,5,3]=>[3,5,7,6,2,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,1,2,7,3,5,6]=>[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[4,1,2,7,5,6,3]=>[3,6,5,7,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,2,7,6,5,3]=>[3,5,6,7,2,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,1,5,2,6,3,7]=>[7,3,6,2,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,1,5,2,7,6,3]=>[3,6,7,2,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,5,6,2,3,7]=>[7,3,2,6,5,1,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,1,5,7,2,6,3]=>[3,6,2,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,5,7,6,2,3]=>[3,2,6,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,6,2,5,7,3]=>[3,7,5,2,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,1,6,2,7,5,3]=>[3,5,7,2,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,1,6,5,2,7,3]=>[3,7,2,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,1,6,5,7,2,3]=>[3,2,7,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,1,6,7,2,5,3]=>[3,5,2,7,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,1,6,7,5,2,3]=>[3,2,5,7,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,1,7,2,3,5,6]=>[6,5,3,2,7,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[4,1,7,2,5,6,3]=>[3,6,5,2,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,7,2,6,5,3]=>[3,5,6,2,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,1,7,5,2,6,3]=>[3,6,2,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,7,5,6,2,3]=>[3,2,6,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,1,7,6,2,5,3]=>[3,5,2,6,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,1,7,6,5,2,3]=>[3,2,5,6,7,1,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,2,1,3,5,7,6]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[4,2,1,3,7,5,6]=>[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[4,2,1,7,3,5,6]=>[6,5,3,7,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>1
[4,2,5,3,6,7,1]=>[1,7,6,3,5,2,4]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>1
[4,2,7,1,3,5,6]=>[6,5,3,1,7,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>0
[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>1
[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>0
[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>1
[4,3,6,2,5,1,7]=>[7,1,5,2,6,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>0
[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>0
[4,5,1,2,6,3,7]=>[7,3,6,2,1,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,5,1,2,7,6,3]=>[3,6,7,2,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,5,1,6,2,3,7]=>[7,3,2,6,1,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,5,1,7,2,6,3]=>[3,6,2,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,5,1,7,6,2,3]=>[3,2,6,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>1
[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>0
[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>0
[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>0
[4,5,7,1,2,6,3]=>[3,6,2,1,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,5,7,1,6,2,3]=>[3,2,6,1,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,5,7,6,1,2,3]=>[3,2,1,6,7,5,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,6,1,2,5,7,3]=>[3,7,5,2,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,1,2,7,5,3]=>[3,5,7,2,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,6,1,5,2,7,3]=>[3,7,2,5,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,1,5,7,2,3]=>[3,2,7,5,1,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,1,7,2,5,3]=>[3,5,2,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,6,3,2,5,1,7]=>[7,1,5,2,3,6,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>0
[4,6,3,5,2,1,7]=>[7,1,2,5,3,6,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>0
[4,6,5,1,2,7,3]=>[3,7,2,1,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,5,1,7,2,3]=>[3,2,7,1,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,5,7,1,2,3]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[4,6,7,1,2,5,3]=>[3,5,2,1,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,6,7,1,5,2,3]=>[3,2,5,1,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,6,7,5,1,2,3]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[4,7,1,2,3,5,6]=>[6,5,3,2,1,7,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[4,7,1,2,5,6,3]=>[3,6,5,2,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,1,2,6,5,3]=>[3,5,6,2,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,7,1,5,2,6,3]=>[3,6,2,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,1,5,6,2,3]=>[3,2,6,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,7,1,6,5,2,3]=>[3,2,5,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,7,2,1,3,5,6]=>[6,5,3,1,2,7,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,5,6,1,2,3]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[4,7,6,1,2,5,3]=>[3,5,2,1,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[4,7,6,5,1,2,3]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>0
[5,1,2,3,4,7,6]=>[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[5,1,2,3,6,4,7]=>[7,4,6,3,2,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[5,1,2,3,6,7,4]=>[4,7,6,3,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,2,3,7,4,6]=>[6,4,7,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[5,1,2,3,7,6,4]=>[4,6,7,3,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,1,2,6,3,4,7]=>[7,4,3,6,2,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[5,1,2,6,3,7,4]=>[4,7,3,6,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,2,6,7,3,4]=>[4,3,7,6,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,2,7,3,4,6]=>[6,4,3,7,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,2,7,6,3,4]=>[4,3,6,7,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,3,6,4,2,7]=>[7,2,4,6,3,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,1,3,7,6,4,2]=>[2,4,6,7,3,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,1,4,2,6,7,3]=>[3,7,6,2,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,1,4,6,2,7,3]=>[3,7,2,6,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,1,4,6,7,2,3]=>[3,2,7,6,4,1,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,1,6,2,3,4,7]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[5,1,6,2,3,7,4]=>[4,7,3,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,6,3,4,2,7]=>[7,2,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,1,6,7,2,3,4]=>[4,3,2,7,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,1,7,2,3,4,6]=>[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[5,1,7,2,3,6,4]=>[4,6,3,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,7,2,6,3,4]=>[4,3,6,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,7,3,6,4,2]=>[2,4,6,3,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,1,7,6,2,3,4]=>[4,3,2,6,7,1,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,1,7,6,3,4,2]=>[2,4,3,6,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>1
[5,3,1,6,4,2,7]=>[7,2,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,3,1,7,6,4,2]=>[2,4,6,7,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>1
[5,3,6,1,4,2,7]=>[7,2,4,1,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,3,6,4,1,2,7]=>[7,2,1,4,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,3,7,1,6,4,2]=>[2,4,6,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,3,7,6,1,4,2]=>[2,4,1,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,3,7,6,4,1,2]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,4,1,2,6,7,3]=>[3,7,6,2,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,4,1,6,2,7,3]=>[3,7,2,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,4,1,6,7,2,3]=>[3,2,7,6,1,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>0
[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>0
[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>0
[5,4,6,1,2,7,3]=>[3,7,2,1,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,4,6,1,7,2,3]=>[3,2,7,1,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>0
[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>1
[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>0
[5,6,1,2,3,7,4]=>[4,7,3,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,6,1,2,7,3,4]=>[4,3,7,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,6,1,3,4,2,7]=>[7,2,4,3,1,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,6,1,7,2,3,4]=>[4,3,2,7,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,6,3,1,4,2,7]=>[7,2,4,1,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>0
[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>0
[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>1
[5,7,1,2,3,4,6]=>[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,7,1,2,6,3,4]=>[4,3,6,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,7,1,3,6,4,2]=>[2,4,6,3,1,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,3,6,4,1,2]=>[2,1,4,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[5,7,6,1,3,4,2]=>[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,6,3,1,4,2]=>[2,4,1,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>0
[6,1,2,3,4,7,5]=>[5,7,4,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[6,1,2,3,7,4,5]=>[5,4,7,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[6,1,2,4,5,7,3]=>[3,7,5,4,2,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,1,2,4,7,5,3]=>[3,5,7,4,2,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,2,7,3,4,5]=>[5,4,3,7,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[6,1,2,7,4,5,3]=>[3,5,4,7,2,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,3,4,2,7,5]=>[5,7,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,1,3,4,7,2,5]=>[5,2,7,4,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,1,3,5,7,4,2]=>[2,4,7,5,3,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,1,3,7,4,2,5]=>[5,2,4,7,3,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,1,4,2,5,7,3]=>[3,7,5,2,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,1,4,2,7,5,3]=>[3,5,7,2,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,4,5,2,7,3]=>[3,7,2,5,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,1,4,5,7,2,3]=>[3,2,7,5,4,1,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,1,4,7,2,5,3]=>[3,5,2,7,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,4,7,5,2,3]=>[3,2,5,7,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,5,3,7,4,2]=>[2,4,7,3,5,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,1,5,7,3,4,2]=>[2,4,3,7,5,1,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[6,1,7,2,4,5,3]=>[3,5,4,2,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,7,3,4,2,5]=>[5,2,4,3,7,1,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,1,7,4,2,5,3]=>[3,5,2,4,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,1,7,4,5,2,3]=>[3,2,5,4,7,1,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>1
[6,3,1,4,2,7,5]=>[5,7,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,1,4,7,2,5]=>[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,1,5,7,4,2]=>[2,4,7,5,1,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,3,1,7,4,2,5]=>[5,2,4,7,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,4,1,2,7,5]=>[5,7,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,4,1,7,2,5]=>[5,2,7,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>0
[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>0
[6,3,4,7,1,2,5]=>[5,2,1,7,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,5,1,7,4,2]=>[2,4,7,1,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,3,5,4,2,1,7]=>[7,1,2,4,5,3,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>0
[6,3,5,7,1,4,2]=>[2,4,1,7,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,3,5,7,4,1,2]=>[2,1,4,7,5,3,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,3,7,1,4,2,5]=>[5,2,4,1,7,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,3,7,4,1,2,5]=>[5,2,1,4,7,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,4,1,2,5,7,3]=>[3,7,5,2,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,1,2,7,5,3]=>[3,5,7,2,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,4,1,5,2,7,3]=>[3,7,2,5,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,1,5,7,2,3]=>[3,2,7,5,1,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,1,7,2,5,3]=>[3,5,2,7,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,4,1,7,5,2,3]=>[3,2,5,7,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>0
[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>0
[6,4,5,1,2,7,3]=>[3,7,2,1,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,5,1,7,2,3]=>[3,2,7,1,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>1
[6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,4,7,1,5,2,3]=>[3,2,5,1,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,4,7,5,1,2,3]=>[3,2,1,5,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,5,1,3,7,4,2]=>[2,4,7,3,1,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,1,7,3,4,2]=>[2,4,3,7,1,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,3,1,7,4,2]=>[2,4,7,1,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>0
[6,5,3,7,1,4,2]=>[2,4,1,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,3,7,4,1,2]=>[2,1,4,7,3,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>0
[6,5,7,1,3,4,2]=>[2,4,3,1,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,7,3,1,4,2]=>[2,4,1,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>2
[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>1
[6,7,1,2,4,5,3]=>[3,5,4,2,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,7,1,3,4,2,5]=>[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,7,1,4,5,2,3]=>[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,7,3,1,4,2,5]=>[5,2,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>1
[6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,7,4,1,5,2,3]=>[3,2,5,1,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>2
[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>1
[7,1,2,3,4,6,5]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[7,1,2,3,5,4,6]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[7,1,2,3,5,6,4]=>[4,6,5,3,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,2,4,3,5,6]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[7,1,2,4,5,6,3]=>[3,6,5,4,2,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,1,2,4,6,5,3]=>[3,5,6,4,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,2,5,3,4,6]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[7,1,2,5,3,6,4]=>[4,6,3,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,2,5,6,3,4]=>[4,3,6,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[7,1,2,6,3,5,4]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,2,6,4,5,3]=>[3,5,4,6,2,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,2,6,5,3,4]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,1,3,2,4,5,6]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[7,1,3,4,2,5,6]=>[6,5,2,4,3,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[7,1,3,5,6,4,2]=>[2,4,6,5,3,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,1,4,2,3,5,6]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,1,4,5,6,2,3]=>[3,2,6,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,1,4,6,2,5,3]=>[3,5,2,6,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,4,6,5,2,3]=>[3,2,5,6,4,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,5,2,3,4,6]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,5,3,6,4,2]=>[2,4,6,3,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,1,5,6,2,3,4]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,1,5,6,3,4,2]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,6,2,5,4,3]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,1,6,3,5,4,2]=>[2,4,5,3,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,1,6,4,2,5,3]=>[3,5,2,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,6,4,5,2,3]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,1,6,5,2,3,4]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,1,6,5,2,4,3]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,1,6,5,3,4,2]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,1,6,5,4,2,3]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>1
[7,2,1,4,3,5,6]=>[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>1
[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>1
[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>1
[7,2,4,1,3,5,6]=>[6,5,3,1,4,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>1
[7,3,1,4,2,5,6]=>[6,5,2,4,1,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[7,3,1,5,6,4,2]=>[2,4,6,5,1,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>1
[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>1
[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>1
[7,3,5,1,6,4,2]=>[2,4,6,1,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,3,5,6,1,4,2]=>[2,4,1,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,3,5,6,4,1,2]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,3,6,1,5,4,2]=>[2,4,5,1,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,3,6,5,4,1,2]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>1
[7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,4,1,5,2,6,3]=>[3,6,2,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,1,5,6,2,3]=>[3,2,6,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>1
[7,4,5,1,2,6,3]=>[3,6,2,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>2
[7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,4,6,5,1,2,3]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>1
[7,5,1,2,3,6,4]=>[4,6,3,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,5,1,2,6,3,4]=>[4,3,6,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,5,1,3,6,4,2]=>[2,4,6,3,1,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,5,1,6,3,4,2]=>[2,4,3,6,1,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,3,1,6,4,2]=>[2,4,6,1,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,3,6,1,4,2]=>[2,4,1,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,3,6,4,1,2]=>[2,1,4,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>2
[7,5,6,1,3,4,2]=>[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,6,3,1,4,2]=>[2,4,1,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>3
[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>2
[7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,1,2,5,3,4]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,1,3,5,4,2]=>[2,4,5,3,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,1,4,2,5,3]=>[3,5,2,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,1,5,4,2,3]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[7,6,3,1,5,4,2]=>[2,4,5,1,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,3,5,1,4,2]=>[2,4,1,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,3,5,4,1,2]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>3
[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>3
[7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>4
[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>4
[7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>5
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>6
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>7
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>5
[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>5
[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>5
[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>3
[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>3
[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>5
[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>5
[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[7,8,3,2,4,5,6,1]=>[1,6,5,4,2,3,8,7]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>1
[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>1
[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>1
[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>1
[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>1
[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>1
[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>1
[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>1
[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>1
[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>1
[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>1
[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>0
[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>0
[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>0
[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>0
[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>0
[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>0
[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>0
[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>0
[7,5,4,3,6,2,1,8]=>[8,1,2,6,3,4,5,7]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>0
[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>0
[6,5,7,3,2,4,1,8]=>[8,1,4,2,3,7,5,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>0
[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>0
[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>0
[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>0
[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>0
[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>0
[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>0
[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>0
[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>0
[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>0
[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>0
[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>0
[5,7,8,6,4,3,2,1]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>5
[4,7,8,6,5,3,2,1]=>[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>5
[4,6,8,7,5,3,2,1]=>[1,2,3,5,7,8,6,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[3,7,8,6,5,4,2,1]=>[1,2,4,5,6,8,7,3]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>5
[3,6,8,7,5,4,2,1]=>[1,2,4,5,7,8,6,3]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[3,5,8,7,6,4,2,1]=>[1,2,4,6,7,8,5,3]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[3,4,6,7,8,5,2,1]=>[1,2,5,8,7,6,4,3]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[2,7,8,6,5,4,3,1]=>[1,3,4,5,6,8,7,2]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>5
[2,6,8,7,5,4,3,1]=>[1,3,4,5,7,8,6,2]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[2,5,8,7,6,4,3,1]=>[1,3,4,6,7,8,5,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[2,4,8,7,6,5,3,1]=>[1,3,5,6,7,8,4,2]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[3,2,6,5,8,7,4,1]=>[1,4,7,8,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[2,3,6,7,8,5,4,1]=>[1,4,5,8,7,6,3,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[2,3,5,6,8,7,4,1]=>[1,4,7,8,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[2,3,5,4,6,7,8,1]=>[1,8,7,6,4,5,3,2]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>1
[2,4,3,5,6,7,8,1]=>[1,8,7,6,5,3,4,2]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>1
[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[1,7,8,6,5,4,3,2]=>[2,3,4,5,6,8,7,1]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[1,6,8,7,5,4,3,2]=>[2,3,4,5,7,8,6,1]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[1,5,8,7,6,4,3,2]=>[2,3,4,6,7,8,5,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[1,4,8,7,6,5,3,2]=>[2,3,5,6,7,8,4,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,3,8,7,6,5,4,2]=>[2,4,5,6,7,8,3,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,3,5,8,7,6,4,2]=>[2,4,6,7,8,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,3,5,7,8,6,4,2]=>[2,4,6,8,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,3,5,6,7,8,4,2]=>[2,4,8,7,6,5,3,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[1,3,4,5,7,8,6,2]=>[2,6,8,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,3,4,5,6,7,8,2]=>[2,8,7,6,5,4,3,1]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[2,1,7,6,8,5,4,3]=>[3,4,5,8,6,7,1,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[1,2,8,7,6,5,4,3]=>[3,4,5,6,7,8,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[1,2,4,8,7,6,5,3]=>[3,5,6,7,8,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,4,6,8,7,5,3]=>[3,5,7,8,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,4,5,7,8,6,3]=>[3,6,8,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,4,6,7,5,8,3]=>[3,8,5,7,6,4,2,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[2,3,1,5,7,6,8,4]=>[4,8,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,1,3,6,5,7,8,4]=>[4,8,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,2,3,5,7,8,6,4]=>[4,6,8,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,3,5,6,8,7,4]=>[4,7,8,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,3,5,6,7,8,4]=>[4,8,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,2,3,4,6,8,7,5]=>[5,7,8,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,4,6,7,8,5]=>[5,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[2,1,5,4,3,7,8,6]=>[6,8,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,2,5,4,3,7,8,6]=>[6,8,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,3,4,5,7,8,6]=>[6,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[1,6,5,4,3,2,8,7]=>[7,8,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,3,4,1,5,6,8,7]=>[7,8,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[3,2,1,4,5,6,8,7]=>[7,8,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[2,3,1,4,5,6,8,7]=>[7,8,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[4,7,6,5,3,2,1,8]=>[8,1,2,3,5,6,7,4]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>0
[3,5,7,6,4,2,1,8]=>[8,1,2,4,6,7,5,3]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[4,3,7,6,5,2,1,8]=>[8,1,2,5,6,7,3,4]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>0
[3,4,7,6,5,2,1,8]=>[8,1,2,5,6,7,4,3]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>0
[2,6,7,5,4,3,1,8]=>[8,1,3,4,5,7,6,2]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>0
[2,3,5,6,7,4,1,8]=>[8,1,4,7,6,5,3,2]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[1,2,3,5,6,7,4,8]=>[8,4,7,6,5,3,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,2,3,4,6,7,5,8]=>[8,5,7,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[1,3,5,6,4,2,7,8]=>[8,7,2,4,6,5,3,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[1,2,4,5,6,3,7,8]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>0
[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>0
[1,3,4,2,5,6,7,8]=>[8,7,6,5,2,4,3,1]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>0
[1,2,3,4,8,6,7,5]=>[5,7,6,8,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,5,8,6,7,4]=>[4,7,6,8,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,3,8,5,6,7,4]=>[4,7,6,5,8,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,3,8,5,7,6,4]=>[4,6,7,5,8,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,4,8,6,7,5,3]=>[3,5,7,6,8,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,4,6,7,5,3]=>[3,5,7,6,4,8,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,4,7,6,5,3]=>[3,5,6,7,4,8,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,8,5,6,7,4,3]=>[3,4,7,6,5,8,2,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,3,8,5,7,6,4,2]=>[2,4,6,7,5,8,3,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,3,8,7,5,6,4,2]=>[2,4,6,5,7,8,3,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,3,5,7,6,4,2]=>[2,4,6,7,5,3,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,3,7,5,6,4,2]=>[2,4,6,5,7,3,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,3,7,6,5,4,2]=>[2,4,5,6,7,3,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,8,4,7,6,5,3,2]=>[2,3,5,6,7,4,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,8,7,4,6,5,3,2]=>[2,3,5,6,4,7,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,8,7,5,6,4,3,2]=>[2,3,4,6,5,7,8,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[2,3,1,7,5,6,8,4]=>[4,8,6,5,7,1,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,3,8,5,6,7,4,1]=>[1,4,7,6,5,8,3,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[2,5,3,4,6,7,8,1]=>[1,8,7,6,4,3,5,2]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>1
[2,8,4,7,6,5,3,1]=>[1,3,5,6,7,4,8,2]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[2,8,7,5,6,4,3,1]=>[1,3,4,6,5,7,8,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[3,2,8,6,5,7,4,1]=>[1,4,7,5,6,8,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[8,2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,2,7,4,6,5,3,1]=>[1,3,5,6,4,7,2,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,2,7,5,6,4,3,1]=>[1,3,4,6,5,7,2,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[7,3,4,6,5,2,1,8]=>[8,1,2,5,6,4,3,7]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>0
[7,3,6,4,5,2,1,8]=>[8,1,2,5,4,6,3,7]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>0
[8,3,7,5,6,4,2,1]=>[1,2,4,6,5,7,3,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[7,4,3,6,5,2,1,8]=>[8,1,2,5,6,3,4,7]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>0
[8,7,3,5,6,4,2,1]=>[1,2,4,6,5,3,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[2,4,1,3,6,5,8,7]=>[7,8,5,6,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,6,3,5,8,7]=>[7,8,5,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,6,1,3,5,8,7]=>[7,8,5,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,3,6,8,5,7]=>[7,5,8,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,6,3,8,5,7]=>[7,5,8,3,6,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,6,3,8,5,7]=>[7,5,8,3,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,6,1,3,8,5,7]=>[7,5,8,3,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,6,8,3,5,7]=>[7,5,3,8,6,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,6,8,3,5,7]=>[7,5,3,8,6,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,8,3,4,5,6,7]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[2,8,1,3,4,5,6,7]=>[7,6,5,4,3,1,8,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[2,1,3,8,4,5,6,7]=>[7,6,5,4,8,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[2,3,1,8,4,5,6,7]=>[7,6,5,4,8,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[2,3,8,1,4,5,6,7]=>[7,6,5,4,1,8,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[2,1,3,4,8,5,6,7]=>[7,6,5,8,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[2,3,1,4,8,5,6,7]=>[7,6,5,8,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[2,1,3,4,5,8,6,7]=>[7,6,8,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>1
[2,3,1,4,5,8,6,7]=>[7,6,8,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>1
[2,3,4,1,5,8,6,7]=>[7,6,8,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[3,1,4,2,5,6,7,8]=>[8,7,6,5,2,4,1,3]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>0
[3,1,4,5,6,7,8,2]=>[2,8,7,6,5,4,1,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[3,4,1,5,6,7,8,2]=>[2,8,7,6,5,1,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[3,4,5,1,6,7,8,2]=>[2,8,7,6,1,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[3,4,5,6,1,7,8,2]=>[2,8,7,1,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[3,4,5,6,7,1,8,2]=>[2,8,1,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>1
[3,1,8,2,4,5,6,7]=>[7,6,5,4,2,8,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[3,8,1,2,4,5,6,7]=>[7,6,5,4,2,1,8,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[3,1,2,8,4,5,6,7]=>[7,6,5,4,8,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[1,3,2,8,4,5,6,7]=>[7,6,5,4,8,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[3,1,2,4,8,5,6,7]=>[7,6,5,8,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[1,3,2,4,8,5,6,7]=>[7,6,5,8,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[3,1,2,4,5,8,6,7]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[1,3,2,4,5,8,6,7]=>[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[3,1,2,4,5,6,8,7]=>[7,8,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[4,1,5,2,6,3,7,8]=>[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[4,5,1,2,6,3,7,8]=>[8,7,3,6,2,1,5,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[4,1,5,6,2,3,7,8]=>[8,7,3,2,6,5,1,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[4,5,1,6,2,3,7,8]=>[8,7,3,2,6,1,5,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[4,1,2,5,6,3,7,8]=>[8,7,3,6,5,2,1,4]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[1,4,2,5,6,3,7,8]=>[8,7,3,6,5,2,4,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[1,4,5,2,6,3,7,8]=>[8,7,3,6,2,5,4,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>0
[4,8,1,2,3,5,6,7]=>[7,6,5,3,2,1,8,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,4,2,8,3,5,6,7]=>[7,6,5,3,8,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[4,1,2,3,8,5,6,7]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,4,2,3,8,5,6,7]=>[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,2,4,3,8,5,6,7]=>[7,6,5,8,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[4,1,2,3,5,8,6,7]=>[7,6,8,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,4,2,3,5,8,6,7]=>[7,6,8,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,2,4,3,5,8,6,7]=>[7,6,8,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[4,1,2,3,5,6,8,7]=>[7,8,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,4,2,3,5,6,8,7]=>[7,8,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,1,2,7,3,8,4]=>[4,8,3,7,2,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,6,7,2,3,8,4]=>[4,8,3,2,7,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,7,1,2,3,8,4]=>[4,8,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,6,2,7,8,3,4]=>[4,3,8,7,2,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,1,2,7,8,3,4]=>[4,3,8,7,2,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,6,7,2,8,3,4]=>[4,3,8,2,7,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,6,7,8,2,3,4]=>[4,3,2,8,7,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,1,7,8,2,3,4]=>[4,3,2,8,7,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,7,1,8,2,3,4]=>[4,3,2,8,1,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,6,2,7,3,4,8]=>[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,6,7,2,3,4,8]=>[8,4,3,2,7,6,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,6,1,7,2,3,4,8]=>[8,4,3,2,7,1,6,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,6,2,3,7,4,8]=>[8,4,7,3,2,6,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,2,6,3,7,4,8]=>[8,4,7,3,6,2,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,2,6,7,3,4,8]=>[8,4,3,7,6,2,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,5,6,7,2,3,4,8]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,6,2,3,7,8,4]=>[4,8,7,3,2,6,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,6,1,2,3,7,8,4]=>[4,8,7,3,2,1,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,2,6,3,7,8,4]=>[4,8,7,3,6,2,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,6,2,3,7,8,4]=>[4,8,7,3,2,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,2,6,7,3,8,4]=>[4,8,3,7,6,2,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,2,6,7,3,8,4]=>[4,8,3,7,6,2,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,6,7,2,3,8,4]=>[4,8,3,2,7,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,2,6,7,8,3,4]=>[4,3,8,7,6,2,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,2,6,7,8,3,4]=>[4,3,8,7,6,2,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,6,2,7,8,3,4]=>[4,3,8,7,2,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,6,7,2,8,3,4]=>[4,3,8,2,7,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,6,7,8,2,3,4]=>[4,3,2,8,7,6,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[5,1,2,3,6,7,4,8]=>[8,4,7,6,3,2,1,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,2,5,3,6,7,4,8]=>[8,4,7,6,3,5,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,2,5,6,3,7,4,8]=>[8,4,7,3,6,5,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[1,2,5,6,7,3,4,8]=>[8,4,3,7,6,5,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>0
[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,2,3,6,7,8,4]=>[4,8,7,6,3,2,5,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,2,5,3,6,7,8,4]=>[4,8,7,6,3,5,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,2,5,6,3,7,8,4]=>[4,8,7,3,6,5,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,2,5,6,7,3,8,4]=>[4,8,3,7,6,5,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,2,5,6,7,8,3,4]=>[4,3,8,7,6,5,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>1
[1,5,2,3,4,6,7,8]=>[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>0
[1,2,5,3,4,6,7,8]=>[8,7,6,4,3,5,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>0
[6,1,7,2,8,3,4,5]=>[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,7,1,2,8,3,4,5]=>[5,4,3,8,2,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,7,8,2,3,4,5]=>[5,4,3,2,8,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,7,1,8,2,3,4,5]=>[5,4,3,2,8,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,7,2,3,8,4,5]=>[5,4,8,3,2,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,7,1,2,3,8,4,5]=>[5,4,8,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,2,7,3,8,4,5]=>[5,4,8,3,7,2,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,2,7,3,8,4,5]=>[5,4,8,3,7,2,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,7,2,3,8,4,5]=>[5,4,8,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,7,2,8,3,4,5]=>[5,4,3,8,2,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,7,8,2,3,4,5]=>[5,4,3,2,8,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,7,2,3,4,8,5]=>[5,8,4,3,2,7,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,7,1,2,3,4,8,5]=>[5,8,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,2,7,3,4,8,5]=>[5,8,4,3,7,2,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,2,7,3,4,8,5]=>[5,8,4,3,7,2,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,7,2,3,4,8,5]=>[5,8,4,3,2,7,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,2,3,7,4,8,5]=>[5,8,4,7,3,2,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,2,3,7,4,8,5]=>[5,8,4,7,3,2,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,6,3,7,4,8,5]=>[5,8,4,7,3,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,6,7,3,4,8,5]=>[5,8,4,3,7,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,2,3,7,8,4,5]=>[5,4,8,7,3,2,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,2,3,7,8,4,5]=>[5,4,8,7,3,2,6,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,6,3,7,8,4,5]=>[5,4,8,7,3,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,6,7,8,3,4,5]=>[5,4,3,8,7,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[6,1,7,2,3,4,5,8]=>[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[6,1,2,7,3,4,5,8]=>[8,5,4,3,7,2,1,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,6,2,7,3,4,5,8]=>[8,5,4,3,7,2,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,6,7,2,3,4,5,8]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[6,1,2,3,7,4,5,8]=>[8,5,4,7,3,2,1,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,6,3,7,4,5,8]=>[8,5,4,7,3,6,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,6,7,3,4,5,8]=>[8,5,4,3,7,6,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[6,1,2,3,4,7,5,8]=>[8,5,7,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,6,2,3,4,7,5,8]=>[8,5,7,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,6,3,4,7,5,8]=>[8,5,7,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,3,6,4,7,5,8]=>[8,5,7,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[1,2,3,6,7,4,5,8]=>[8,5,4,7,6,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>0
[6,1,2,3,4,7,8,5]=>[5,8,7,4,3,2,1,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,6,3,4,7,8,5]=>[5,8,7,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,3,6,4,7,8,5]=>[5,8,7,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,2,3,6,7,4,8,5]=>[5,8,4,7,6,3,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>1
[1,6,2,3,4,5,7,8]=>[8,7,5,4,3,2,6,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>0
[1,2,6,3,4,5,7,8]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>0
[1,2,3,6,4,5,7,8]=>[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>0
[7,1,8,2,3,4,5,6]=>[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[7,1,2,8,3,4,5,6]=>[6,5,4,3,8,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,2,8,3,4,5,6]=>[6,5,4,3,8,2,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,8,2,3,4,5,6]=>[6,5,4,3,2,8,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[7,1,2,3,8,4,5,6]=>[6,5,4,8,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,2,3,8,4,5,6]=>[6,5,4,8,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,7,3,8,4,5,6]=>[6,5,4,8,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,7,8,3,4,5,6]=>[6,5,4,3,8,7,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[7,1,2,3,4,8,5,6]=>[6,5,8,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,2,3,4,8,5,6]=>[6,5,8,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,7,3,4,8,5,6]=>[6,5,8,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,3,7,4,8,5,6]=>[6,5,8,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[7,1,2,3,4,5,8,6]=>[6,8,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,2,3,4,5,8,6]=>[6,8,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,7,3,4,5,8,6]=>[6,8,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,3,7,4,5,8,6]=>[6,8,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,3,4,7,5,8,6]=>[6,8,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,2,3,4,7,8,5,6]=>[6,5,8,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>1
[1,7,2,3,4,5,6,8]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[1,2,7,3,4,5,6,8]=>[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[1,2,3,7,4,5,6,8]=>[8,6,5,4,7,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[1,2,3,4,7,5,6,8]=>[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>0
[1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[1,2,3,8,4,5,6,7]=>[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>1
[2,1,7,5,4,8,3,6]=>[6,3,8,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,4,7,2,1,8,3,6]=>[6,3,8,1,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,4,7,2,6,5,3,1]=>[1,3,5,6,2,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[4,5,8,1,2,7,6,3]=>[3,6,7,2,1,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,6,8,1,7,2,5,3]=>[3,5,2,7,1,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,6,8,7,1,2,4,3]=>[3,4,2,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,5,7,6,2,4,3,1]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[3,8,1,7,6,5,4,2]=>[2,4,5,6,7,1,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[4,8,7,1,6,5,3,2]=>[2,3,5,6,1,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[5,8,7,6,1,4,3,2]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[6,8,7,5,4,1,3,2]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>1
[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]=>9
[3,2,8,1,4,5,6,7]=>[7,6,5,4,1,8,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[4,2,6,8,1,3,5,7]=>[7,5,3,1,8,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,4,8,1,3,5,7]=>[7,5,3,1,8,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[5,4,7,8,1,2,3,6]=>[6,3,2,1,8,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,2,4,6,1,3,5,7]=>[7,5,3,1,6,4,2,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[7,5,4,8,1,2,3,6]=>[6,3,2,1,8,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,6,2,4,1,3,5,7]=>[7,5,3,1,4,2,6,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[5,7,2,4,8,1,3,6]=>[6,3,1,8,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[4,3,2,6,8,1,5,7]=>[7,5,1,8,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,5,2,4,8,1,3,7]=>[7,3,1,8,4,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,4,2,7,8,1,3,6]=>[6,3,1,8,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,5,2,7,8,1,3,4]=>[4,3,1,8,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,7,2,4,6,1,3,5]=>[5,3,1,6,4,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,5,8,2,4,1,3,6]=>[6,3,1,4,2,8,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,4,7,2,6,1,3,5]=>[5,3,1,6,2,7,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,4,3,2,8,1,5,7]=>[7,5,1,8,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,5,4,2,8,1,3,7]=>[7,3,1,8,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,5,4,3,8,1,2,7]=>[7,2,1,8,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[7,5,4,2,8,1,3,6]=>[6,3,1,8,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,4,2,6,1,3,5]=>[5,3,1,6,2,4,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,7,6,2,4,1,3,5]=>[5,3,1,4,2,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[8,4,3,7,2,6,1,5]=>[5,1,6,2,7,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[6,5,4,3,2,8,1,7]=>[7,1,8,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[7,6,5,3,2,8,1,4]=>[4,1,8,2,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,7,4,3,2,6,1,5]=>[5,1,6,2,3,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[8,7,6,5,2,4,1,3]=>[3,1,4,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,1,2,3,4,7,5,6]=>[6,5,7,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,1,2,3,7,4,5,6]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,1,2,3,6,7,4,5]=>[5,4,7,6,3,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,2,6,3,7,4,5]=>[5,4,7,3,6,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,2,7,6,3,4,5]=>[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,1,2,5,6,7,3,4]=>[4,3,7,6,5,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,4,2,3,5,6,7]=>[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[8,1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[6,1,8,2,3,7,4,5]=>[5,4,7,3,2,8,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[5,1,4,2,7,3,8,6]=>[6,8,3,7,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,1,7,5,6,2,3,4]=>[4,3,2,6,5,7,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[2,6,1,5,3,7,8,4]=>[4,8,7,3,5,1,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,6,1,2,3,7,4,5]=>[5,4,7,3,2,1,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[5,4,1,2,7,3,8,6]=>[6,8,3,7,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,1,2,6,3,4,5]=>[5,4,3,6,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[5,8,1,2,6,7,3,4]=>[4,3,7,6,2,1,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[7,8,1,5,6,2,3,4]=>[4,3,2,6,5,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[2,6,4,1,3,8,5,7]=>[7,5,8,3,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,5,1,3,7,8,4]=>[4,8,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[7,8,5,1,6,2,3,4]=>[4,3,2,6,1,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[2,8,4,6,1,3,5,7]=>[7,5,3,1,6,4,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,3,7,5,6,1,8,4]=>[4,8,1,6,5,7,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,8,4,7,6,1,3,5]=>[5,3,1,6,7,4,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[8,1,2,3,4,5,6,9,7]=>[7,9,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[9,1,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[7,1,2,3,4,5,8,9,6]=>[6,9,8,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>1
[9,1,2,3,4,8,5,6,7]=>[7,6,5,8,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[6,1,2,3,4,7,8,9,5]=>[5,9,8,7,4,3,2,1,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>1
[8,1,2,3,9,4,5,6,7]=>[7,6,5,4,9,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[9,1,2,3,8,7,4,5,6]=>[6,5,4,7,8,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[9,1,2,8,3,4,5,6,7]=>[7,6,5,4,3,8,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[9,1,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[2,9,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,9,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>1
[9,3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,1]=>1
[3,5,1,6,4,2,8,7]=>[7,8,2,4,6,1,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[2,1,5,7,4,8,3,6]=>[6,3,8,4,7,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,6,7,8,3,1,4,2]=>[2,4,1,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,6,7,8,1,3,4,2]=>[2,4,3,1,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[4,5,7,1,2,8,6,3]=>[3,6,8,2,1,7,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,5,3,7,1,6,8,4]=>[4,8,6,1,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,5,4,1,2,8,3,6]=>[6,3,8,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,7,4,1,2,8,3,6]=>[6,3,8,2,1,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,8,6,7,1,2,3,4]=>[4,3,2,1,7,6,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,4,7,1,2,8,3,6]=>[6,3,8,2,1,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,6,8,7,1,2,3,4]=>[4,3,2,1,7,8,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,5,8,6,1,2,3,4]=>[4,3,2,1,6,8,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,5,7,6,1,2,3,4]=>[4,3,2,1,6,7,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,7,8,6,1,2,3,4]=>[4,3,2,1,6,8,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,8,7,6,1,2,3,4]=>[4,3,2,1,6,7,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,3,2,1,6,8,5,7]=>[7,5,8,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[4,3,2,1,8,6,5,7]=>[7,5,6,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,1,8,4,7,2,5,3]=>[3,5,2,7,4,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,6,8,4,7,2,5,3]=>[3,5,2,7,4,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,2,8,3,7,6,4]=>[4,6,7,3,8,2,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,1,2,8,3,7,6,4]=>[4,6,7,3,8,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,5,8,3,7,6,4]=>[4,6,7,3,8,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[2,4,1,3,8,7,6,5]=>[5,6,7,8,3,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,2,1,3,8,7,6,5]=>[5,6,7,8,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,4,8,1,7,2,5,3]=>[3,5,2,7,1,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,5,1,8,7,2,6,3]=>[3,6,2,7,8,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,1,5,8,7,2,6,3]=>[3,6,2,7,8,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,4,5,8,7,2,6,3]=>[3,6,2,7,8,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,2,5,1,4,3,8,7]=>[7,8,3,4,1,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,2,7,1,4,3,8,6]=>[6,8,3,4,1,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,2,5,1,4,3,8,6]=>[6,8,3,4,1,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,1,8,2,6,3,7,4]=>[4,7,3,6,2,8,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,5,2,6,3,7,4]=>[4,7,3,6,2,5,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,1,6,2,8,3,7,4]=>[4,7,3,8,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[2,1,8,4,7,3,6,5]=>[5,6,3,7,4,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[3,5,6,1,4,8,2,7]=>[7,2,8,4,1,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,6,7,3,1,8,4,2]=>[2,4,8,1,3,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,6,1,7,3,8,4,2]=>[2,4,8,3,7,1,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,1,6,7,3,8,4,2]=>[2,4,8,3,7,6,1,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[4,1,5,7,8,2,6,3]=>[3,6,2,8,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[3,5,6,7,8,4,1,2]=>[2,1,4,8,7,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,4,1,5,8,6,2,3]=>[3,2,6,8,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,5,4,2,1,3,7]=>[7,3,1,2,4,5,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,1,6,7,4,5,2,3]=>[3,2,5,4,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,2,7,8,5,6,3]=>[3,6,5,8,7,2,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,4,3,8,2,1,5,7]=>[7,5,1,2,8,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[1,5,8,3,7,6,4,2]=>[2,4,6,7,3,8,5,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,6,1,2,3,8,7,4]=>[4,7,8,3,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,7,1,2,8,3,6,4]=>[4,6,3,8,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,8,1,2,7,6,3,4]=>[4,3,6,7,2,1,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,8,2,1,7,6,3,5]=>[5,3,6,7,1,2,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,1,2,8,7,6,5,3]=>[3,5,6,7,8,2,1,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,1,7,6,5,4,2,3]=>[3,2,4,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[7,5,1,2,8,3,6,4]=>[4,6,3,8,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,5,1,2,7,3,6,4]=>[4,6,3,7,2,1,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,1,6,7,2,4,5,3]=>[3,5,4,2,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,2,8,7,5,6,3]=>[3,6,5,7,8,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,8,1,2,7,3,6,4]=>[4,6,3,7,2,1,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,1,8,7,2,4,5,3]=>[3,5,4,2,7,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,8,7,1,2,3,4,5]=>[5,4,3,2,1,7,8,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,7,6,2,4,5,3]=>[3,5,4,2,6,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,1,6,2,3,5,4]=>[4,5,3,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[2,1,5,4,7,3,8,6]=>[6,8,3,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,1,6,2,7,5,8,4]=>[4,8,5,7,2,6,1,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[4,1,6,2,7,5,8,3]=>[3,8,5,7,2,6,1,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[2,1,6,5,7,3,8,4]=>[4,8,3,7,5,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[1,3,6,7,5,8,2,4]=>[4,2,8,5,7,6,3,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[3,7,6,5,8,2,1,4]=>[4,1,2,8,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[3,6,8,5,7,2,4,1]=>[1,4,2,7,5,8,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[2,3,5,7,6,8,1,4]=>[4,1,8,6,7,5,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,1,6,5,7,8,3,4]=>[4,3,8,7,5,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,4,1,5,7,2,6,3]=>[3,6,2,7,5,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,6,1,8,7,2,5,3]=>[3,5,2,7,8,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[2,7,6,8,5,4,1,3]=>[3,1,4,5,8,6,7,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[8,7,6,3,5,1,4,2]=>[2,4,1,5,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,4,7,6,5,1,3,2]=>[2,3,1,5,6,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,7,1,5,6,4,3,2]=>[2,3,4,6,5,1,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[8,1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[2,8,7,4,1,6,3,5]=>[5,3,6,1,4,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[2,1,7,8,5,4,3,6]=>[6,3,4,5,8,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,6,3,7,1,8,4,2]=>[2,4,8,1,7,3,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,3,8,7,6,4,2,1]=>[1,2,4,6,7,8,3,5]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[7,5,3,1,8,6,4,2]=>[2,4,6,8,1,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[6,1,7,5,3,2,8,4]=>[4,8,2,3,5,7,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[7,6,5,3,2,1,8,4]=>[4,8,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[6,5,3,2,8,7,4,1]=>[1,4,7,8,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,2,6,3,8,7,4,1]=>[1,4,7,8,3,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[5,2,7,6,3,1,8,4]=>[4,8,1,3,6,7,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,5,2,1,7,3,8,4]=>[4,8,3,7,1,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,2,7,4,1,8,3,6]=>[6,3,8,1,4,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[4,8,1,5,7,2,6,3]=>[3,6,2,7,5,1,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,8,2,7,6,4,3,1]=>[1,3,4,6,7,2,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[6,2,8,7,5,4,3,1]=>[1,3,4,5,7,8,2,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[7,6,2,1,8,5,4,3]=>[3,4,5,8,1,2,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[6,1,7,2,8,5,4,3]=>[3,4,5,8,2,7,1,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[8,5,7,1,6,4,3,2]=>[2,3,4,6,1,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[6,8,1,7,5,4,3,2]=>[2,3,4,5,7,1,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[7,1,8,6,5,4,3,2]=>[2,3,4,5,6,8,1,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[1,8,6,7,2,3,4,5]=>[5,4,3,2,7,6,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,6,7,2,3,4,5]=>[5,4,3,2,7,6,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,4,2,1,3,8,5,7]=>[7,5,8,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,6,2,1,3,8,5,7]=>[7,5,8,3,1,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[8,6,1,7,2,3,4,5]=>[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,6,8,7,2,3,4,5]=>[5,4,3,2,7,8,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,8,1,7,2,3,4,5]=>[5,4,3,2,7,1,8,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,1,8,7,2,3,4,5]=>[5,4,3,2,7,8,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,7,6,2,3,4,5]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,8,7,6,2,3,4,5]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[6,5,2,7,1,8,3,4]=>[4,3,8,1,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[2,6,1,5,4,3,8,7]=>[7,8,3,4,5,1,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[2,1,4,8,3,7,6,5]=>[5,6,7,3,8,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,3,8,7,2,1,6,5]=>[5,6,1,2,7,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[6,5,2,1,4,3,8,7]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[2,1,8,7,4,3,6,5]=>[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,8,3,5,2,7,4,1]=>[1,4,7,2,5,3,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,5,2,6,3,8,1,4]=>[4,1,8,3,6,2,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[5,7,8,6,3,4,1,2]=>[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[2,8,7,6,1,4,3,5]=>[5,3,4,1,6,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,8,3,4,5,1,6,2]=>[2,6,1,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,8,1,6,5,4,3,2]=>[2,3,4,5,6,1,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[1,8,5,7,3,6,4,2]=>[2,4,6,3,7,5,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,6,7,3,8,4,1,2]=>[2,1,4,8,3,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[1,5,8,6,2,7,3,4]=>[4,3,7,2,6,8,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,1,6,3,4,2,8,7]=>[7,8,2,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,7,1,4,2,3,8,6]=>[6,8,3,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,8,7,6,3,4,1,2]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[3,8,7,6,5,4,1,2]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[6,3,7,5,8,1,2,4]=>[4,2,1,8,5,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[2,5,7,4,8,1,3,6]=>[6,3,1,8,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,4,1,7,8,2,3,6]=>[6,3,2,8,7,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,7,1,5,8,6,2,3]=>[3,2,6,8,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,4,7,5,1,2,3]=>[3,2,1,5,7,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,1,4,2,6,5,3]=>[3,5,6,2,4,1,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,1,9]=>0
[2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,1]=>1
[2,3,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,3,2]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,8,9,1,10]=>0
[2,3,4,5,6,7,1,8,9]=>[9,8,1,7,6,5,4,3,2]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]=>[2,3,4,5,6,7,1,8,9]=>0
[1,8,2,7,3,4,5,6]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,1,2,7,3,4,5,6]=>[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,8,7,3,4,5,6]=>[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[6,5,3,8,7,2,4,1]=>[1,4,2,7,8,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[1,8,2,4,3,5,6,7]=>[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,8,2,3,4,7,5,6]=>[6,5,7,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,8,2,6,3,7,4,5]=>[5,4,7,3,6,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,8,4,7,5,6]=>[6,5,7,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,6,2,8,3,7,4,5]=>[5,4,7,3,8,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[5,6,8,3,4,1,2,7]=>[7,2,1,4,3,8,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,7,8,4,1,2,3,6]=>[6,3,2,1,4,8,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,7,8,1,5,2,4,3]=>[3,4,2,5,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[6,7,8,1,5,4,2,3]=>[3,2,4,5,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[5,7,8,3,1,6,4,2]=>[2,4,6,1,3,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[4,6,3,8,2,1,5,7]=>[7,5,1,2,8,3,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[5,7,8,2,1,4,3,6]=>[6,3,4,1,2,8,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,7,8,1,2,5,4,3]=>[3,4,5,2,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[3,6,1,7,5,2,8,4]=>[4,8,2,5,7,1,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,6,1,8,7,2,4,3]=>[3,4,2,7,8,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[6,3,5,8,2,7,4,1]=>[1,4,7,2,8,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,2,4,7,1,8,3,6]=>[6,3,8,1,7,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,3,6,1,4,8,2,7]=>[7,2,8,4,1,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,8,7,5,6,3,4,2]=>[2,4,3,6,5,7,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,5,6,7,2,3,4]=>[4,3,2,7,6,5,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,2,1,5,7,3,8,4]=>[4,8,3,7,5,1,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[1,8,4,7,2,6,5,3]=>[3,5,6,2,7,4,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[3,5,7,8,6,1,4,2]=>[2,4,1,6,8,7,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,4,6,2,7,5,8,3]=>[3,8,5,7,2,6,4,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,8,4,2,6,7,5,3]=>[3,5,7,6,2,4,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,5,3,1,7,6,8,4]=>[4,8,6,7,1,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[4,6,1,2,7,5,8,3]=>[3,8,5,7,2,1,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[8,4,1,2,6,7,5,3]=>[3,5,7,6,2,1,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,3,5,1,7,6,8,4]=>[4,8,6,7,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[3,6,7,1,5,8,2,4]=>[4,2,8,5,1,7,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[8,4,1,6,7,5,2,3]=>[3,2,5,7,6,1,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,2,3,1,7,6,8,4]=>[4,8,6,7,1,3,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,1,4,2,7,5,8,3]=>[3,8,5,7,2,4,1,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,7,1,3,5,8,2,4]=>[4,2,8,5,3,1,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[4,7,8,5,6,1,2,3]=>[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,6,8,1,2,7,5,3]=>[3,5,7,2,1,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,5,7,1,6,2,3,4]=>[4,3,2,6,1,7,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,5,7,1,2,3,6,4]=>[4,6,3,2,1,7,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,8,5,7,1,6,2,3]=>[3,2,6,1,7,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,8,5,7,1,2,6,3]=>[3,6,2,1,7,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,5,4,2,1,3,8,7]=>[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,5,4,3,1,2,8,7]=>[7,8,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[6,5,4,1,3,2,8,7]=>[7,8,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,7,4,1,6,5,3,2]=>[2,3,5,6,1,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,7,4,1,6,5,2,3]=>[3,2,5,6,1,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,4,1,6,2,5,3]=>[3,5,2,6,1,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,6,5,2,1,4,3]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,7,4,3,6,2,1,5]=>[5,1,2,6,3,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[2,1,8,7,6,4,3,5]=>[5,3,4,6,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,7,4,2,6,5,3,1]=>[1,3,5,6,2,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,3,1,7,6,5,4,2]=>[2,4,5,6,7,1,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,6,5,3,1,4,2]=>[2,4,1,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,6,5,1,3,4,2]=>[2,4,3,1,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[8,7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[8,7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[8,7,6,5,1,2,4,3]=>[3,4,2,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[7,3,4,1,8,5,6,2]=>[2,6,5,8,1,4,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[2,6,1,5,7,8,3,4]=>[4,3,8,7,5,1,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,2,8,6,7,3,4,1]=>[1,4,3,7,6,8,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,5,6,2,7,3,4,1]=>[1,4,3,7,2,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[7,3,6,2,5,1,8,4]=>[4,8,1,5,2,6,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[6,2,5,1,7,3,8,4]=>[4,8,3,7,1,5,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,2,4,1,7,3,8,6]=>[6,8,3,7,1,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,1,7,4,8,5,6,2]=>[2,6,5,8,4,7,1,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,3,8,4,5,1,6,2]=>[2,6,1,5,4,8,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,8,5,6,1,3,4,2]=>[2,4,3,1,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,3,5,6,4,1,2]=>[2,1,4,6,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,5,6,7,8,1,4,2]=>[2,4,1,8,7,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,7,8,6,1,3,4,2]=>[2,4,3,1,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,2,5,6,3,8,1,4]=>[4,1,8,3,6,5,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,7,5,2,4,8,3,6]=>[6,3,8,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,8,1,2,3,4,7,5]=>[5,7,4,3,2,1,8,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,5,7,2,3,8,6,4]=>[4,6,8,3,2,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,8,2,3,6,7,4]=>[4,7,6,3,2,8,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[2,5,3,7,6,1,8,4]=>[4,8,1,6,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,4,2,7,5,8,6,3]=>[3,6,8,5,7,2,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,8,3,7,1,6,4,2]=>[2,4,6,1,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,2,7,5,3,8,6,4]=>[4,6,8,3,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,4,7,5,1,8,6,2]=>[2,6,8,1,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,5,8,7,6,1,2,3]=>[3,2,1,6,7,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,4,8,7,1,6,3,5]=>[5,3,6,1,7,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,5,8,7,2,6,3,4]=>[4,3,6,2,7,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,4,2,8,7,6,5,3]=>[3,5,6,7,8,2,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,2,8,7,1,6,3,5]=>[5,3,6,1,7,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,1,8,3,7,6,4,2]=>[2,4,6,7,3,8,1,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,2,8,3,7,6,4,5]=>[5,4,6,7,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,2,5,4,7,3,8,6]=>[6,8,3,7,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,5,4,2,8,3,6]=>[6,3,8,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,2,5,3,8,7,6,4]=>[4,6,7,8,3,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,5,2,8,6,3,7,4]=>[4,7,3,6,8,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,5,2,6,3,8,7,4]=>[4,7,8,3,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,8,5,2,6,3,7,4]=>[4,7,3,6,2,5,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,5,2,7,3,8,6,4]=>[4,6,8,3,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,8,5,3,7,6,4]=>[4,6,7,3,5,8,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,7,2,8,5,3,6,4]=>[4,6,3,5,8,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,8,7,5,3,6,4]=>[4,6,3,5,7,8,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[2,8,6,1,4,3,5,7]=>[7,5,3,4,1,6,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]=>0
[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]=>0
[1,2,3,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>1
[9,1,2,3,4,5,6,7,10,8]=>[8,10,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[1,8,2,3,4,5,6,9,7]=>[7,9,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[2,1,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>1
[2,10,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,10,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>1
[2,1,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]=>0
[1,2,8,3,7,4,5,6]=>[6,5,4,7,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[1,8,7,2,6,5,3,4]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,7,8,2,5,6,3,4]=>[4,3,6,5,2,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,5,7,3,1,6,4,2]=>[2,4,6,1,3,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,6,1,3,4,2,7,8]=>[8,7,2,4,3,1,6,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[8,7,1,2,3,6,5,4]=>[4,5,6,3,2,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[7,8,1,2,3,5,6,4]=>[4,6,5,3,2,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[3,5,6,1,7,8,4,2]=>[2,4,8,7,1,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[1,5,6,8,2,3,7,4]=>[4,7,3,2,8,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,1,7,8,2,3,6,4]=>[4,6,3,2,8,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,1,4,5,7,8,6,2]=>[2,6,8,7,5,4,1,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,8,2,3,4,5,7,6]=>[6,7,5,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,8,3,4,6,7,5]=>[5,7,6,4,3,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[5,7,1,2,8,6,3,4]=>[4,3,6,8,2,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,7,3,8,6,4,2]=>[2,4,6,8,3,7,5,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[6,1,7,8,2,5,4,3]=>[3,4,5,2,8,7,1,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[6,1,7,8,5,4,2,3]=>[3,2,4,5,8,7,1,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[6,3,8,5,2,7,4,1]=>[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[8,7,1,6,2,4,5,3]=>[3,5,4,2,6,1,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[6,5,4,3,1,8,2,7]=>[7,2,8,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[3,8,6,2,5,7,4,1]=>[1,4,7,5,2,6,8,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[8,7,5,2,6,4,3,1]=>[1,3,4,6,2,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[8,7,1,6,2,5,4,3]=>[3,4,5,2,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[8,6,1,7,4,2,5,3]=>[3,5,2,4,7,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,7,3,4,6,5]=>[5,6,4,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[5,4,2,7,1,8,3,6]=>[6,3,8,1,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,6,4,7,5,3,2,1]=>[1,2,3,5,7,4,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[5,2,6,8,7,3,4,1]=>[1,4,3,7,8,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,1,7,6,5,2,4,3]=>[3,4,2,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[1,2,8,7,6,3,4,5]=>[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[5,1,6,8,7,4,2,3]=>[3,2,4,7,8,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[6,8,4,7,5,3,2,1]=>[1,2,3,5,7,4,8,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[6,8,7,2,5,4,3,1]=>[1,3,4,5,2,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[1,8,7,6,5,4,2,3]=>[3,2,4,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[1,8,6,7,4,5,2,3]=>[3,2,5,4,7,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,7,4,8,5,6,1,2]=>[2,1,6,5,8,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,7,1,8,5,6,2,3]=>[3,2,6,5,8,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,1,7,4,5,2,3]=>[3,2,5,4,7,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,7,4,8,5,6,2,3]=>[3,2,6,5,8,4,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,5,6,2,7,3,4]=>[4,3,7,2,6,5,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,8,6,7,1,4,2,3]=>[3,2,4,1,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[4,8,6,7,1,5,2,3]=>[3,2,5,1,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,2,8,6,7,3,4]=>[4,3,7,6,8,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,8,4,7,1,5,2,3]=>[3,2,5,1,7,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,8,1,6,2,7,3,4]=>[4,3,7,2,6,1,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,8,1,5,2,6,3,4]=>[4,3,6,2,5,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]=>0
[1,2,3,4,5,6,8,9,7]=>[7,9,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,8,9,6]=>[6,9,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>1
[1,2,3,4,6,7,8,9,5]=>[5,9,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>1
[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]=>0
[1,2,3,4,5,6,9,8,7]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,2,3,4,5,6,7,9,10,8]=>[8,10,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,8,9,10,7]=>[7,10,9,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>1
[1,2,3,4,5,7,8,9,10,6]=>[6,10,9,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>1
[1,2,3,4,6,7,8,9,10,5]=>[5,10,9,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>1
[3,2,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,2,3]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,1]=>1
[6,4,8,1,7,5,2,3]=>[3,2,5,7,1,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,5,2,8,4,1,3,7]=>[7,3,1,4,8,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]=>8
[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>0
[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>0
[1,2,8,4,3,5,6,7]=>[7,6,5,3,4,8,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[1,8,3,2,4,5,6,7]=>[7,6,5,4,2,3,8,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[1,7,5,4,2,8,3,6]=>[6,3,8,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,1,4,7,2,8,3,6]=>[6,3,8,2,7,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,1,4,2,7,8,3,6]=>[6,3,8,7,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,2,3,7,8,5,6,4]=>[4,6,5,8,7,3,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,3,8,7,5,6,4]=>[4,6,5,7,8,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[10,1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[10,1,2,3,4,5,9,6,7,8]=>[8,7,6,9,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[9,1,2,3,4,10,5,6,7,8]=>[8,7,6,5,10,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[10,1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[10,1,2,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[9,1,10,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,10,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[11,1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>1
[8,1,2,3,4,5,6,9,10,7]=>[7,10,9,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>1
[8,4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,4,3,2,1,8,5,7]=>[7,5,8,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[8,4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[6,4,3,2,1,5,8,7]=>[7,8,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[5,6,3,4,1,2,8,7]=>[7,8,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[2,5,1,4,3,7,8,6]=>[6,8,7,3,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,2,1,4,3,7,8,6]=>[6,8,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,3,6,4,1,2,7,8]=>[8,7,2,1,4,6,3,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[6,2,5,1,3,7,8,4]=>[4,8,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[2,5,8,6,7,3,4,1]=>[1,4,3,7,6,8,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[1,8,4,6,2,7,5,3]=>[3,5,7,2,6,4,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,5,6,7,2,4,3]=>[3,4,2,7,6,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,8,5,6,7,4,2,3]=>[3,2,4,7,6,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,5,1,6,7,4,2,3]=>[3,2,4,7,6,1,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[3,8,5,1,7,6,4,2]=>[2,4,6,7,1,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[3,7,5,1,8,6,4,2]=>[2,4,6,8,1,5,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[4,8,3,2,6,1,5,7]=>[7,5,1,6,2,3,8,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[1,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[1,10,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]=>0
[8,3,7,5,6,1,4,2]=>[2,4,1,6,5,7,3,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,5,7,3,6,1,4,2]=>[2,4,1,6,3,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,1,7,5,6,3,4,2]=>[2,4,3,6,5,7,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,2,7,1,4,3,6,5]=>[5,6,3,4,1,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,1,7,2,6,4,5,3]=>[3,5,4,6,2,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,4,7,1,6,2,5,3]=>[3,5,2,6,1,7,4,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,1,7,4,6,2,5,3]=>[3,5,2,6,4,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,5,7,1,6,3,4,2]=>[2,4,3,6,1,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,6,8,5,4,3,2,7]=>[7,2,3,4,5,8,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[3,2,1,4,8,5,6,7]=>[7,6,5,8,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[1,5,2,7,8,4,3,6]=>[6,3,4,8,7,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,1,2,7,4,8,3,6]=>[6,3,8,4,7,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,8,1,4,3,7,6,5]=>[5,6,7,3,4,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,2,8,1,7,3,6,5]=>[5,6,3,7,1,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[2,8,1,7,4,3,6,5]=>[5,6,3,4,7,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,2,8,1,7,6,3,5]=>[5,3,6,7,1,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[2,8,1,7,6,4,3,5]=>[5,3,4,6,7,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,6,2,7,3,4,1,8]=>[8,1,4,3,7,2,6,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[9,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>1
[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>1
[4,2,3,5,6,7,8,9,1]=>[1,9,8,7,6,5,3,2,4]=>[.,[[[[[[[.,.],[.,.]],.],.],.],.],.]]=>[4,2,3,5,6,7,8,9,1]=>1
[3,4,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,4,3]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]=>[3,4,2,5,6,7,8,9,1]=>1
[3,2,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,2,3]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]=>[3,2,4,5,6,7,8,9,10,1]=>1
[2,3,4,5,6,7,8,9,10,11,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,9,10,11,1]=>1
[8,7,2,4,1,6,3,5]=>[5,3,6,1,4,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,8,7,3,6,1,4,2]=>[2,4,1,6,3,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,1,4,7,2,6,5,3]=>[3,5,6,2,7,4,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[6,7,1,2,8,5,4,3]=>[3,4,5,8,2,1,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[8,4,1,7,2,6,5,3]=>[3,5,6,2,7,1,4,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,4,8,7,2,6,5,3]=>[3,5,6,2,7,8,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,8,3,7,6,5,4]=>[4,5,6,7,3,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[6,7,1,8,2,5,4,3]=>[3,4,5,2,8,1,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[4,8,1,7,2,6,5,3]=>[3,5,6,2,7,1,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,8,2,3,7,6,5,4]=>[4,5,6,7,3,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,1,4,5,7,6,2,3]=>[3,2,6,7,5,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,1,2,5,7,3,6,4]=>[4,6,3,7,5,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,1,5,2,7,3,6,4]=>[4,6,3,7,2,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[4,2,8,7,1,3,6,5]=>[5,6,3,1,7,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,1,2,5,8,3,6,4]=>[4,6,3,8,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,2,5,7,3,6,4]=>[4,6,3,7,5,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,1,6,2,8,7,5,3]=>[3,5,7,8,2,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,6,1,5,7,3,8,4]=>[4,8,3,7,5,1,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[3,1,6,7,5,8,2,4]=>[4,2,8,5,7,6,1,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,2,8,5,6,3,7,4]=>[4,7,3,6,5,8,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,5,1,8,4,3,2,7]=>[7,2,3,4,8,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[3,5,6,4,1,8,2,7]=>[7,2,8,1,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,6,5,8,4,3,2,7]=>[7,2,3,4,8,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[6,8,5,1,4,3,2,7]=>[7,2,3,4,1,5,8,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,2,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[1,2,3,4,5,8,6,9,7]=>[7,9,6,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[1,2,3,4,7,5,8,9,6]=>[6,9,8,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>1
[1,2,3,6,4,7,8,9,5]=>[5,9,8,7,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>1
[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>1
[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>1
[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>1
[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>3
[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>1
[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>4
[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>5
[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>6
[10,9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[4,3,6,2,8,1,5,7]=>[7,5,1,8,2,6,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,8,4,3,2,1,5,7]=>[7,5,1,2,3,4,8,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[2,5,4,1,3,7,8,6]=>[6,8,7,3,1,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,8,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,8,7]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]=>[7,8,6,5,4,3,2,1,9]=>0
[8,9,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]=>[8,9,7,6,5,4,3,2,1,10]=>0
[7,6,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,6,7]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]=>[7,6,8,5,4,3,2,1,9]=>0
[7,3,5,1,8,6,4,2]=>[2,4,6,8,1,5,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,4,1,5,8,2,6,3]=>[3,6,2,8,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,5,7,2,6,3,4]=>[4,3,6,2,7,5,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,8,1,7,2,6,3,4]=>[4,3,6,2,7,1,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,8,2,7,5,6,3,4]=>[4,3,6,5,7,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[2,8,1,7,4,6,3,5]=>[5,3,6,4,7,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[2,8,4,7,1,6,3,5]=>[5,3,6,1,7,4,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,8,2,7,1,6,3,5]=>[5,3,6,1,7,2,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,8,1,7,5,6,2,3]=>[3,2,6,5,7,1,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,8,4,7,5,6,2,3]=>[3,2,6,5,7,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,5,1,8,6,2,3,4]=>[4,3,2,6,8,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,1,8,4,5,2,6,3]=>[3,6,2,5,4,8,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,1,7,4,2,5,3]=>[3,5,2,4,7,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,7,8,2,6,3,4]=>[4,3,6,2,8,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[2,6,3,7,8,5,4,1]=>[1,4,5,8,7,3,6,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[5,3,1,6,4,2,7,8]=>[8,7,2,4,6,1,3,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[4,6,1,7,5,2,8,3]=>[3,8,2,5,7,1,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[2,7,1,5,4,3,8,6]=>[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,2,1,4,3,6,5]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>0
[1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>0
[1,8,9,2,3,4,5,6,7]=>[7,6,5,4,3,2,9,8,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[1,10,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,8,2,9,3,4,5,6,7]=>[7,6,5,4,3,9,2,8,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[1,9,10,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,10,9,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[1,11,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>1
[1,4,7,2,5,8,6,3]=>[3,6,8,5,2,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,3,8,4,5,6,1,2]=>[2,1,6,5,4,8,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,8,5,2,7,3,6,4]=>[4,6,3,7,2,5,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,8,3,6,1,4,2,7]=>[7,2,4,1,6,3,8,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,1,3,2,7,5,8,4]=>[4,8,5,7,2,3,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[7,5,8,4,1,2,3,6]=>[6,3,2,1,4,8,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,8,5,4,3,1,2,7]=>[7,2,1,3,4,5,8,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,1,2,5,6,3,7,4]=>[4,7,3,6,5,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,8,2,5,7,6,3,4]=>[4,3,6,7,5,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,1,8,6,2,7,3,4]=>[4,3,7,2,6,8,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[3,4,7,8,5,6,1,2]=>[2,1,6,5,8,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,8,1,2,5,6,3,4]=>[4,3,6,5,2,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,8,7,2,3,6,4]=>[4,6,3,2,7,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,7,8,5,4,3,6]=>[6,3,4,5,8,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,2,1,3,6,5,8,7]=>[7,8,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[1,6,4,7,5,8,2,3]=>[3,2,8,5,7,4,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,1,7,5,3,8,2,4]=>[4,2,8,3,5,7,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,8,1,4,7,2,5,3]=>[3,5,2,7,4,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,5,1,4,3,8,2,7]=>[7,2,8,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,4,2,1,7,3,6,5]=>[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,8,6,7,5,2,3]=>[3,2,5,7,6,8,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,1,8,7,4,6,3,5]=>[5,3,6,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,2,4,1,3,6,5,7]=>[7,5,6,3,1,4,2,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,4,1,3,8,5,7]=>[7,5,8,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,4,1,3,5,8,7]=>[7,8,5,3,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,6,1,3,5,8,7]=>[7,8,5,3,1,6,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,6,4,3,5,8,7]=>[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,4,2,1,3,5,8,7]=>[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[8,4,2,1,6,3,5,7]=>[7,5,3,6,1,2,4,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,4,2,1,8,3,5,7]=>[7,5,3,8,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,1,4,3,8,5,7]=>[7,5,8,3,4,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,8,1,4,3,6,5,7]=>[7,5,6,3,4,1,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,8,2,1,3,6,5,7]=>[7,5,6,3,1,2,8,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,8,2,1,6,3,5,7]=>[7,5,3,6,1,2,8,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,8,1,4,6,3,5,7]=>[7,5,3,6,4,1,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,8,4,6,3,5,7]=>[7,5,3,6,4,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,6,4,8,3,5,7]=>[7,5,3,8,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,1,4,8,3,5,7]=>[7,5,3,8,4,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,4,1,8,3,5,7]=>[7,5,3,8,1,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,4,8,1,3,5,7]=>[7,5,3,1,8,4,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,6,2,8,1,3,5,7]=>[7,5,3,1,8,2,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,4,1,8,3,5,7]=>[7,5,3,8,1,4,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[8,2,4,1,6,3,5,7]=>[7,5,3,6,1,4,2,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,1,4,8,3,5,7]=>[7,5,3,8,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,1,6,8,3,5,7]=>[7,5,3,8,6,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,1,3,6,8,5,7]=>[7,5,8,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,3,8,6,5,7]=>[7,5,6,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,3,8,6,5,7]=>[7,5,6,8,3,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,1,3,8,6,5,7]=>[7,5,6,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,1,8,3,6,5,7]=>[7,5,6,3,8,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,1,8,6,3,5,7]=>[7,5,3,6,8,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,2,8,1,4,3,5,7]=>[7,5,3,4,1,8,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,8,1,3,6,5,7]=>[7,5,6,3,1,8,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,8,1,3,6,5,7]=>[7,5,6,3,1,8,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,1,8,3,6,5,7]=>[7,5,6,3,8,1,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,4,8,3,6,5,7]=>[7,5,6,3,8,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,4,8,1,6,3,5,7]=>[7,5,3,6,1,8,4,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,2,8,6,1,3,5,7]=>[7,5,3,1,6,8,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[6,4,8,2,1,3,5,7]=>[7,5,3,1,2,8,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[4,6,8,2,1,3,5,7]=>[7,5,3,1,2,8,6,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,8,4,1,3,5,7]=>[7,5,3,1,4,8,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,6,1,8,4,3,5,7]=>[7,5,3,4,8,1,6,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,1,8,6,4,3,5,7]=>[7,5,3,4,6,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[2,8,6,4,1,3,5,7]=>[7,5,3,1,4,6,8,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>1
[8,2,4,1,7,3,6,5]=>[5,6,3,7,1,4,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,4,8,7,1,5,2,3]=>[3,2,5,1,7,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,7,4,5,6,3]=>[3,6,5,4,7,8,2,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,1,6,2,7,4,5,3]=>[3,5,4,7,2,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,5,2,6,7,4,3]=>[3,4,7,6,2,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[2,8,5,7,6,4,3,1]=>[1,3,4,6,7,5,8,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[8,7,6,1,5,3,4,2]=>[2,4,3,5,1,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,1,6,4,5,3,2]=>[2,3,5,4,6,1,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,1,7,5,6,4,3,2]=>[2,3,4,6,5,7,1,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[1,8,6,7,5,4,3,2]=>[2,3,4,5,7,6,8,1]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[8,7,2,6,4,1,3,5]=>[5,3,1,4,6,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,1,7,4,5,8,2,3]=>[3,2,8,5,4,7,1,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,7,3,5,1,8,2,4]=>[4,2,8,1,5,3,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[4,8,7,2,6,5,3,1]=>[1,3,5,6,2,7,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[4,8,7,3,2,1,6,5]=>[5,6,1,2,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[4,8,7,3,2,6,1,5]=>[5,1,6,2,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[4,8,7,3,6,2,1,5]=>[5,1,2,6,3,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[5,8,7,6,3,4,2,1]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[5,8,7,6,3,1,4,2]=>[2,4,1,3,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,8,7,6,2,4,3,1]=>[1,3,4,2,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[5,8,7,6,4,2,3,1]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[5,8,7,6,4,1,3,2]=>[2,3,1,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[5,8,7,6,4,3,1,2]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[1,5,6,7,8,3,4,2]=>[2,4,3,8,7,6,5,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,3,6,1,7,8,4,2]=>[2,4,8,7,1,6,3,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,1,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>0
[2,4,8,1,3,7,6,5]=>[5,6,7,3,1,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,3,1,6,4,2,8,7]=>[7,8,2,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,1,6,2,8,7,4,3]=>[3,4,7,8,2,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[4,1,5,8,2,7,6,3]=>[3,6,7,2,8,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,1,2,5,8,7,6,3]=>[3,6,7,8,5,2,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,4,2,5,8,7,6,3]=>[3,6,7,8,5,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,8,2,5,4,1,3,6]=>[6,3,1,4,5,2,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,2,6,3,4,8,7,5]=>[5,7,8,4,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[3,7,6,5,2,1,8,4]=>[4,8,1,2,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[2,7,5,4,1,3,8,6]=>[6,8,3,1,4,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,5,2,1,8,4,3,7]=>[7,3,4,8,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,6,3,2,8,1,5,7]=>[7,5,1,8,2,3,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[7,1,8,5,3,6,4,2]=>[2,4,6,3,5,8,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[8,7,3,1,6,5,4,2]=>[2,4,5,6,1,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,2,6,1,5,4,3]=>[3,4,5,1,6,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[2,6,5,8,4,1,3,7]=>[7,3,1,4,8,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,5,4,8,3,2,1,7]=>[7,1,2,3,8,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[4,3,6,8,2,1,5,7]=>[7,5,1,2,8,6,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,5,2,1,7,8,3,4]=>[4,3,8,7,1,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[6,3,7,4,8,5,2,1]=>[1,2,5,8,4,7,3,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[5,7,3,8,1,6,4,2]=>[2,4,6,1,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[8,2,7,6,5,1,4,3]=>[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[4,3,8,7,6,2,1,5]=>[5,1,2,6,7,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[2,4,8,7,6,1,3,5]=>[5,3,1,6,7,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,5,8,6,4,3,2,1]=>[1,2,3,4,6,8,5,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>5
[3,8,7,6,5,1,4,2]=>[2,4,1,5,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[2,8,7,6,5,4,1,3]=>[3,1,4,5,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>0
[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]=>0
[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]=>0
[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]=>0
[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]=>0
[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]=>0
[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]=>0
[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]=>0
[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>0
[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]=>0
[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]=>0
[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]=>0
[5,1,7,4,8,2,3,6]=>[6,3,2,8,4,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,2,3,5,8,6,4]=>[4,6,8,5,3,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,1,2,3,8,5,6,4]=>[4,6,5,8,3,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,1,2,3,7,5,6,4]=>[4,6,5,7,3,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,1,2,3,8,7,4,5]=>[5,4,7,8,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[5,1,2,3,7,8,6,4]=>[4,6,8,7,3,2,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,2,3,8,7,6,4]=>[4,6,7,8,3,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,1,2,3,8,6,7,4]=>[4,7,6,8,3,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,1,2,3,6,8,7,4]=>[4,7,8,6,3,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[2,4,8,1,7,3,6,5]=>[5,6,3,7,1,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,5,8,2,7,6,3,4]=>[4,3,6,7,2,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,1,8,2,7,6,3,4]=>[4,3,6,7,2,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,2,8,7,6,5,3,1]=>[1,3,5,6,7,8,2,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[4,1,8,7,6,5,3,2]=>[2,3,5,6,7,8,1,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[5,8,3,7,6,1,4,2]=>[2,4,1,6,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[4,5,8,1,7,2,6,3]=>[3,6,2,7,1,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,2,7,1,4,6,3,5]=>[5,3,6,4,1,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,6,8,2,7,5,3]=>[3,5,7,2,8,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,4,5,7,2,6,3]=>[3,6,2,7,5,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,6,5,7,1,3,8,4]=>[4,8,3,1,7,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,3,7,8,6,4,1,2]=>[2,1,4,6,8,7,3,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[8,1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[7,1,5,8,2,6,3,4]=>[4,3,6,2,8,5,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,1,2,4,8,7,5,3]=>[3,5,7,8,4,2,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,6,7,4,5,3]=>[3,5,4,7,6,2,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,7,4,6,5,3]=>[3,5,6,4,7,2,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[7,8,5,6,3,1,4,2]=>[2,4,1,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,5,3,1,6,4,2]=>[2,4,6,1,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,5,3,6,1,4,2]=>[2,4,1,6,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,5,3,6,4,1,2]=>[2,1,4,6,3,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,3,8,1,6,4,2]=>[2,4,6,1,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,3,8,6,1,4,2]=>[2,4,1,6,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,3,8,6,4,1,2]=>[2,1,4,6,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,3,6,4,1,2]=>[2,1,4,6,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,3,1,6,4,2]=>[2,4,6,1,3,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,6,3,1,4,2]=>[2,4,1,3,6,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,6,3,4,1,2]=>[2,1,4,3,6,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,2,5,8,3,6,7,4]=>[4,7,6,3,8,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[4,6,3,2,1,8,5,7]=>[7,5,8,1,2,3,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[4,7,3,6,5,2,1,8]=>[8,1,2,5,6,3,7,4]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>0
[5,3,7,6,4,2,1,8]=>[8,1,2,4,6,7,3,5]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[1,6,8,7,4,2,5,3]=>[3,5,2,4,7,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,5,3,2,7,4,1,8]=>[8,1,4,7,2,3,5,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[5,2,6,3,7,4,1,8]=>[8,1,4,7,3,6,2,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[5,1,2,7,8,3,6,4]=>[4,6,3,8,7,2,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,1,8,2,4,5,6,3]=>[3,6,5,4,2,8,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,6,1,2,4,5,3]=>[3,5,4,2,1,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,2,4,1,7,6,3,5]=>[5,3,6,7,1,4,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,5,7,3,6,4,1,2]=>[2,1,4,6,3,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,1,8,6,5,4,3,7]=>[7,3,4,5,6,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,2,7,5,4,3,8,6]=>[6,8,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,8,7,6,5,2,4,3]=>[3,4,2,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[1,6,2,4,8,7,5,3]=>[3,5,7,8,4,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,6,5,7,2,4,1,8]=>[8,1,4,2,7,5,6,3]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[8,7,6,4,1,5,2,3]=>[3,2,5,1,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,5,7,2,4,8,3,6]=>[6,3,8,4,2,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,7,5,2,8,4,3,6]=>[6,3,4,8,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,6,1,4,2,7,5,3]=>[3,5,7,2,4,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,6,4,2,7,5,3]=>[3,5,7,2,4,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,8,1,4,2,7,5,3]=>[3,5,7,2,4,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,6,4,2,7,5,3]=>[3,5,7,2,4,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,7,5,6,3,8,1,4]=>[4,1,8,3,6,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[5,7,2,6,3,8,1,4]=>[4,1,8,3,6,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[4,7,1,8,2,5,6,3]=>[3,6,5,2,8,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,8,1,5,2,4,3,6]=>[6,3,4,2,5,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,7,2,8,5,6,3,4]=>[4,3,6,5,8,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,6,2,3,8,7,4,5]=>[5,4,7,8,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,8,5,4,3,2,1,7]=>[7,1,2,3,4,5,8,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[1,8,5,2,3,7,6,4]=>[4,6,7,3,2,5,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,7,1,2,4,3,8,6]=>[6,8,3,4,2,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,8,7,5,6,1,2,3]=>[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,3,8,2,7,6,1,5]=>[5,1,6,7,2,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[7,6,3,5,8,2,1,4]=>[4,1,2,8,5,3,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[5,6,1,8,2,7,3,4]=>[4,3,7,2,8,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,8,4,5,1,6,2,3]=>[3,2,6,1,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,6,3,4,1,8,2,7]=>[7,2,8,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,7,5,8,2,6,3,4]=>[4,3,6,2,8,5,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,7,1,5,3,8,2,4]=>[4,2,8,3,5,1,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[2,7,5,8,1,4,3,6]=>[6,3,4,1,8,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,6,7,1,4,2,5,3]=>[3,5,2,4,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,1,5,2,6,3,4]=>[4,3,6,2,5,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,7,1,5,2,3,6,4]=>[4,6,3,2,5,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,7,2,1,4,6,3,5]=>[5,3,6,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,4,2,1,7,6,3,5]=>[5,3,6,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,4,2,1,3,7,6,5]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,1,6,4,7,2,5,3]=>[3,5,2,7,4,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,8,3,6,4,1,2,7]=>[7,2,1,4,6,3,8,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,4,7,5,1,6,2,3]=>[3,2,6,1,5,7,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,4,7,5,1,2,6,3]=>[3,6,2,1,5,7,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,8,1,3,7,6,4,2]=>[2,4,6,7,3,1,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[6,3,7,1,5,2,8,4]=>[4,8,2,5,1,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[8,6,7,1,5,4,3,2]=>[2,3,4,5,1,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[2,1,6,8,5,4,3,7]=>[7,3,4,5,8,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,2,3,8,4,5,7,6]=>[6,7,5,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,8,3,4,5,7,6]=>[6,7,5,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,3,8,4,6,7,5]=>[5,7,6,4,8,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,7,8,2,5,3,6,4]=>[4,6,3,5,2,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,2,7,8,3,6,4]=>[4,6,3,8,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,2,3,4,6,7,5]=>[5,7,6,4,3,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,7,3,1,5,2,8,4]=>[4,8,2,5,1,3,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,7,4,5,1,2,8,3]=>[3,8,2,1,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,4,7,5,1,2,8,3]=>[3,8,2,1,5,7,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[4,6,7,5,8,1,2,3]=>[3,2,1,8,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[4,7,5,8,6,1,2,3]=>[3,2,1,6,8,5,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,8,5,7,6,1,2,3]=>[3,2,1,6,7,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,8,6,7,5,1,2,3]=>[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,5,7,8,6,1,2,3]=>[3,2,1,6,8,7,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,6,8,7,5,1,2,3]=>[3,2,1,5,7,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,8,7,6,5,1,2,3]=>[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,6,3,8,7,4,5]=>[5,4,7,8,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,8,3,6,4,7,5]=>[5,7,4,6,3,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,8,6,4,7,5]=>[5,7,4,6,8,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,6,4,8,7,5]=>[5,7,8,4,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,8,6,3,7,4,5]=>[5,4,7,3,6,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,8,4,7,6,5]=>[5,6,7,4,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,2,6,3,8,4,7,5]=>[5,7,4,8,3,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,8,6,3,4,7,5]=>[5,7,4,3,6,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,8,7,4,6,5]=>[5,6,4,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,2,3,8,7,6,4,5]=>[5,4,6,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[3,8,5,7,1,6,4,2]=>[2,4,6,1,7,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,8,6,7,2,3,4,1]=>[1,4,3,2,7,6,8,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[5,8,6,7,1,2,4,3]=>[3,4,2,1,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[4,8,6,7,1,2,5,3]=>[3,5,2,1,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,7,5,2,8,6,3]=>[3,6,8,2,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,8,6,7,4,1,2,3]=>[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,6,8,4,7,5,2,3]=>[3,2,5,7,4,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,7,5,8,6,2,3]=>[3,2,6,8,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,6,5,4,3,2,7]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[4,7,1,2,8,5,6,3]=>[3,6,5,8,2,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,4,7,2,8,5,6,3]=>[3,6,5,8,2,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,1,2,5,8,6,3,4]=>[4,3,6,8,5,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,7,2,5,8,6,3,4]=>[4,3,6,8,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,1,4,2,8,5,6,3]=>[3,6,5,8,2,4,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,2,6,8,5,4,1,3]=>[3,1,4,5,8,6,2,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[2,7,1,6,8,5,4,3]=>[3,4,5,8,6,1,7,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[7,2,1,6,8,5,4,3]=>[3,4,5,8,6,1,2,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[8,1,5,6,7,2,4,3]=>[3,4,2,7,6,5,1,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[5,6,3,8,1,4,2,7]=>[7,2,4,1,8,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,7,2,4,5,6,3]=>[3,6,5,4,2,7,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,5,2,1,3,7,8,4]=>[4,8,7,3,1,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,7,2,3,6,1,8,4]=>[4,8,1,6,3,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,1,4,2,8,7,5,3]=>[3,5,7,8,2,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,1,6,3,4,2,7,8]=>[8,7,2,4,3,6,1,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[4,8,7,6,3,2,1,5]=>[5,1,2,3,6,7,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[6,7,2,8,3,5,4,1]=>[1,4,5,3,8,2,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[6,5,4,3,8,2,1,7]=>[7,1,2,8,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[3,2,6,8,5,7,4,1]=>[1,4,7,5,8,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,5,2,3,1,6,8,4]=>[4,8,6,1,3,2,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,5,7,4,1,8,3,6]=>[6,3,8,1,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,4,3,7,6,2,1,5]=>[5,1,2,6,7,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[8,6,7,5,2,4,3,1]=>[1,3,4,2,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[8,2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,6,7,5,1,4,3,2]=>[2,3,4,1,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[7,8,6,5,4,1,3,2]=>[2,3,1,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[4,3,2,6,1,5,8,7]=>[7,8,5,1,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[2,8,1,6,5,4,3,7]=>[7,3,4,5,6,1,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,1,8,2,5,3,6,4]=>[4,6,3,5,2,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,7,2,1,6,5,4,3]=>[3,4,5,6,1,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[2,1,7,5,4,3,8,6]=>[6,8,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,5,4,8,2,1,3,6]=>[6,3,1,2,8,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,3,6,5,1,4,2]=>[2,4,1,5,6,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[5,1,2,6,8,3,7,4]=>[4,7,3,8,6,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,7,1,8,6,2,3,4]=>[4,3,2,6,8,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,2,7,8,6,3,4]=>[4,3,6,8,7,2,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,7,8,6,3,4,2]=>[2,4,3,6,8,7,1,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,1,3,7,8,6,4,2]=>[2,4,6,8,7,3,1,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[6,3,7,5,1,8,2,4]=>[4,2,8,1,5,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,6,7,5,3,8,2,4]=>[4,2,8,3,5,7,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,7,4,1,5,2,8,3]=>[3,8,2,5,1,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,6,7,4,5,2,8,3]=>[3,8,2,5,4,7,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,6,3,7,5,8,2,4]=>[4,2,8,5,7,3,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,3,1,7,5,8,2,4]=>[4,2,8,5,7,1,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,6,1,3,7,8,4,2]=>[2,4,8,7,3,1,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,6,1,7,8,3,4,2]=>[2,4,3,8,7,1,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,4,5,8,1,2,6,3]=>[3,6,2,1,8,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,8,3,5,6,7,4]=>[4,7,6,5,3,8,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[3,4,5,7,1,8,6,2]=>[2,6,8,1,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[3,4,7,8,1,5,6,2]=>[2,6,5,1,8,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[3,5,6,8,4,1,2,7]=>[7,2,1,4,8,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[3,7,2,8,4,5,6,1]=>[1,6,5,4,8,2,7,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[3,7,8,2,4,5,6,1]=>[1,6,5,4,2,8,7,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[3,8,2,1,4,5,6,7]=>[7,6,5,4,1,2,8,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[5,1,6,3,8,4,2,7]=>[7,2,4,8,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,1,2,7,8,5,4,3]=>[3,4,5,8,7,2,1,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[6,7,2,3,8,5,4,1]=>[1,4,5,8,3,2,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[7,1,2,8,4,5,6,3]=>[3,6,5,4,8,2,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,1,8,3,4,5,6,2]=>[2,6,5,4,3,8,1,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,3,2,6,5,1,8,4]=>[4,8,1,5,6,2,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[1,8,7,6,5,2,3,4]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,9,8,7,6,5,4,2,3]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[8,2,7,4,6,1,3,5]=>[5,3,1,6,4,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,2,7,8,5,6,3]=>[3,6,5,8,7,2,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,6,4,8,7,5,3]=>[3,5,7,8,4,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,7,8,5,6,3,4]=>[4,3,6,5,8,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,6,8,2,7,3,4]=>[4,3,7,2,8,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,5,7,8,2,3,6,4]=>[4,6,3,2,8,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,6,8,7,2,3,4]=>[4,3,2,7,8,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,7,8,5,3,6,4]=>[4,6,3,5,8,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,5,8,7,3,6,4]=>[4,6,3,7,8,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,5,7,8,6,2,3,4]=>[4,3,2,6,8,7,5,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,5,8,7,6,3,4]=>[4,3,6,7,8,5,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,1,2,7,8,4,3,6]=>[6,3,4,8,7,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,6,1,5,4,8,3,7]=>[7,3,8,4,5,1,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,6,3,1,4,8,2,7]=>[7,2,8,4,1,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,1,6,2,8,7,3,4]=>[4,3,7,8,2,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,3,8,6,7,4,5]=>[5,4,7,6,8,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,8,7,4,5,6]=>[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,2,3,4,5,9,6,7,8]=>[8,7,6,9,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[1,2,3,4,9,5,6,7,8]=>[8,7,6,5,9,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[1,2,3,9,4,5,6,7,8]=>[8,7,6,5,4,9,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[1,2,9,3,4,5,6,7,8]=>[8,7,6,5,4,3,9,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[9,1,2,3,4,5,6,7,8]=>1
[1,2,3,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,2,3,4,5,6,10,7,8,9]=>[9,8,7,10,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,2,3,4,5,10,6,7,8,9]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,2,3,4,10,5,6,7,8,9]=>[9,8,7,6,5,10,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,2,3,10,4,5,6,7,8,9]=>[9,8,7,6,5,4,10,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[1,9,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,9,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[1,2,10,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,10,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[10,1,2,3,4,5,6,7,8,9]=>1
[8,6,7,3,5,4,2,1]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[8,5,7,3,6,4,2,1]=>[1,2,4,6,3,7,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[8,1,7,4,6,5,3,2]=>[2,3,5,6,4,7,1,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,1,7,3,6,5,4,2]=>[2,4,5,6,3,7,1,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,5,7,2,6,4,3,1]=>[1,3,4,6,2,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[8,6,7,2,5,4,3,1]=>[1,3,4,5,2,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[8,4,7,1,6,5,3,2]=>[2,3,5,6,1,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,3,7,1,6,5,4,2]=>[2,4,5,6,1,7,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,2,7,1,6,5,4,3]=>[3,4,5,6,1,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,1,7,2,6,5,4,3]=>[3,4,5,6,2,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[8,1,7,6,5,3,4,2]=>[2,4,3,5,6,7,1,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,4,7,6,5,2,3,1]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,5,7,6,4,2,3,1]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[8,6,7,5,4,1,3,2]=>[2,3,1,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[8,5,7,6,4,1,3,2]=>[2,3,1,4,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[8,3,7,6,5,1,4,2]=>[2,4,1,5,6,7,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,6,4,5,1,3,2]=>[2,3,1,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[8,7,6,2,5,1,4,3]=>[3,4,1,5,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[7,8,2,5,1,4,3,6]=>[6,3,4,1,5,2,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,8,2,5,1,4,3,7]=>[7,3,4,1,5,2,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[2,5,3,7,6,8,1,4]=>[4,1,8,6,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,6,5,8,1,4,3,7]=>[7,3,4,1,8,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[3,7,2,6,5,8,1,4]=>[4,1,8,5,6,2,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[6,3,5,8,7,2,4,1]=>[1,4,2,7,8,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,1,5,8,4,2,3,6]=>[6,3,2,4,8,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,5,4,8,2,3,6]=>[6,3,2,8,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,8,5,4,2,3,6]=>[6,3,2,4,5,8,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[3,7,4,8,5,1,6,2]=>[2,6,1,5,8,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[2,5,3,6,8,7,4,1]=>[1,4,7,8,6,3,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[5,1,7,2,4,3,8,6]=>[6,8,3,4,2,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,1,7,4,2,3,8,6]=>[6,8,3,2,4,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,6,1,7,5,8,2,3]=>[3,2,8,5,7,1,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,2,5,7,3,8,6,4]=>[4,6,8,3,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[2,5,7,3,6,8,1,4]=>[4,1,8,6,3,7,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[8,6,1,7,2,4,5,3]=>[3,5,4,2,7,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,5,7,2,3,6,4]=>[4,6,3,2,7,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,7,5,8,2,3,6,4]=>[4,6,3,2,8,5,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,7,8,3,4,5,6,2]=>[2,6,5,4,3,8,7,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,5,8,7,2,3,6,4]=>[4,6,3,2,7,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,3,4,5,10,9,8,7,6]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>4
[1,8,2,7,6,5,4,3]=>[3,4,5,6,7,2,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[6,8,7,1,4,2,5,3]=>[3,5,2,4,1,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,1,3,7,5,2,8,4]=>[4,8,2,5,7,3,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,6,1,8,2,7,4,3]=>[3,4,7,2,8,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,8,7,2,6,5,4,3]=>[3,4,5,6,2,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[2,8,7,1,6,5,4,3]=>[3,4,5,6,1,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[3,8,7,1,6,5,4,2]=>[2,4,5,6,1,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,3,7,5,1,6,4,2]=>[2,4,6,1,5,7,3,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,4,8,6,2,7,5,3]=>[3,5,7,2,6,8,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,7,5,1,2,8,6,3]=>[3,6,8,2,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[4,8,5,1,2,7,6,3]=>[3,6,7,2,1,5,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,6,8,1,2,7,4,3]=>[3,4,7,2,1,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,6,1,7,4,5,2,3]=>[3,2,5,4,7,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,7,2,5,3,6,4]=>[4,6,3,5,2,7,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,1,5,2,8,3,6,4]=>[4,6,3,8,2,5,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,7,2,8,3,6,4]=>[4,6,3,8,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,1,8,2,7,3,6,4]=>[4,6,3,7,2,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,1,5,2,4,3,8,6]=>[6,8,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[3,6,7,1,2,5,8,4]=>[4,8,5,2,1,7,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,1,4,7,8,2,3,6]=>[6,3,2,8,7,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,6,8,5,2,1,4,3]=>[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[1,3,6,7,5,2,8,4]=>[4,8,2,5,7,6,3,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,3,6,7,2,5,8,4]=>[4,8,5,2,7,6,3,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[7,3,4,5,8,6,1,2]=>[2,1,6,8,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,3,4,5,8,1,6,2]=>[2,6,1,8,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,8,6,1,7,5,2,3]=>[3,2,5,7,1,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,7,3,1,5,6,8,4]=>[4,8,6,5,1,3,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[3,2,1,8,4,5,6,7]=>[7,6,5,4,8,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[1,8,7,2,4,5,6,3]=>[3,6,5,4,2,7,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,8,2,7,6,4,5,3]=>[3,5,4,6,7,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[2,8,7,6,5,1,4,3]=>[3,4,1,5,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[1,8,6,7,4,2,5,3]=>[3,5,2,4,7,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,5,7,8,4,1,3,6]=>[6,3,1,4,8,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,4,7,2,8,1,3,6]=>[6,3,1,8,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,4,7,5,1,8,2,3]=>[3,2,8,1,5,7,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[3,6,1,7,5,8,2,4]=>[4,2,8,5,7,1,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[3,5,6,4,1,2,8,7]=>[7,8,2,1,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,7,1,6,5,2,4,3]=>[3,4,2,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[3,7,1,8,4,5,6,2]=>[2,6,5,4,8,1,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[2,6,5,4,8,1,3,7]=>[7,3,1,8,4,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[9,10,7,8,5,6,3,1,4,2]=>[2,4,1,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[9,10,7,8,5,3,6,1,4,2]=>[2,4,1,6,3,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[9,10,7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[9,7,10,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,10,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[5,3,8,7,6,1,4,2]=>[2,4,1,6,7,8,3,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,8,1,7,6,5,4,3]=>[3,4,5,6,7,1,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[5,1,8,7,6,4,3,2]=>[2,3,4,6,7,8,1,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[5,7,4,2,8,1,3,6]=>[6,3,1,8,2,4,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,5,2,7,1,3,8,4]=>[4,8,3,1,7,2,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>1
[6,1,8,2,3,4,7,5]=>[5,7,4,3,2,8,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[7,3,1,4,8,5,6,2]=>[2,6,5,8,4,1,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,3,1,6,7,8,4,2]=>[2,4,8,7,6,1,3,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[5,3,8,7,6,4,1,2]=>[2,1,4,6,7,8,3,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,8,7,6,1,5,4,3]=>[3,4,5,1,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[6,1,8,7,5,4,3,2]=>[2,3,4,5,7,8,1,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[3,1,8,7,6,5,4,2]=>[2,4,5,6,7,8,1,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[4,8,1,7,6,5,3,2]=>[2,3,5,6,7,1,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[5,3,1,8,7,6,4,2]=>[2,4,6,7,8,1,3,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[9,7,5,3,1,10,8,6,4,2]=>[2,4,6,8,10,1,3,5,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[1,6,4,2,7,5,8,3]=>[3,8,5,7,2,4,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[7,8,1,4,2,5,6,3]=>[3,6,5,2,4,1,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,8,5,7,3,6,4]=>[4,6,3,7,5,8,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,1,2,4,5,8,6,3]=>[3,6,8,5,4,2,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,7,3,5,8,6,4]=>[4,6,8,5,3,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,8,1,7,5,6,4,2]=>[2,4,6,5,7,1,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[6,8,4,1,7,2,5,3]=>[3,5,2,7,1,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,3,8,1,4,5,6,2]=>[2,6,5,4,1,8,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,7,4,6,3,2,1,5]=>[5,1,2,3,6,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[9,8,7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[8,7,6,2,5,4,1,3]=>[3,1,4,5,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[6,5,8,4,3,2,1,7]=>[7,1,2,3,4,8,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>1
[8,4,7,6,3,2,1,5]=>[5,1,2,3,6,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,5,8,6,2,3,7,4]=>[4,7,3,2,6,8,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,4,7,6,2,5,3,1]=>[1,3,5,2,6,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[4,8,7,6,1,5,3,2]=>[2,3,5,1,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[2,7,6,1,8,5,4,3]=>[3,4,5,8,1,6,7,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[1,8,2,6,3,4,7,5]=>[5,7,4,3,6,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,5,1,7,6,3,4,2]=>[2,4,3,6,7,1,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[6,1,2,8,3,4,7,5]=>[5,7,4,3,8,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,6,4,7,1,5,2,3]=>[3,2,5,1,7,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,4,6,1,5,2,3]=>[3,2,5,1,6,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,8,7,6,1,5,2,3]=>[3,2,5,1,6,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,4,7,6,1,5,2,3]=>[3,2,5,1,6,7,4,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,4,6,7,1,5,2,3]=>[3,2,5,1,7,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,5,6,7,1,4,2,3]=>[3,2,4,1,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[5,6,8,7,1,4,2,3]=>[3,2,4,1,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[4,6,8,7,1,5,2,3]=>[3,2,5,1,7,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,7,8,5,1,4,2,3]=>[3,2,4,1,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[8,7,5,6,1,4,3,2]=>[2,3,4,1,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[8,5,7,6,1,4,3,2]=>[2,3,4,1,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[6,8,7,5,1,4,3,2]=>[2,3,4,1,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[7,8,6,5,1,4,3,2]=>[2,3,4,1,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[1,8,2,5,6,7,4,3]=>[3,4,7,6,5,2,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,2,8,5,6,7,3,4]=>[4,3,7,6,5,8,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,7,6,1,4,5,2,3]=>[3,2,5,4,1,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,4,5,1,6,2,3]=>[3,2,6,1,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,7,5,3,1,2,8,4]=>[4,8,2,1,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[4,2,1,8,3,7,6,5]=>[5,6,7,3,8,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,2,5,3,6,8,1,4]=>[4,1,8,6,3,5,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,8,7,2,3,6,5,4]=>[4,5,6,3,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,3,5,7,1,6,4,2]=>[2,4,6,1,7,5,3,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,3,8,5,1,6,4,2]=>[2,4,6,1,5,8,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[8,7,4,6,1,2,5,3]=>[3,5,2,1,6,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,6,7,4,1,2,5,3]=>[3,5,2,1,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,1,8,2,5,6,3,4]=>[4,3,6,5,2,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,8,7,1,5,6,4,2]=>[2,4,6,5,1,7,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,8,1,2,5,3,6,4]=>[4,6,3,5,2,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,3,6,7,8,4,2]=>[2,4,8,7,6,3,5,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[6,3,2,8,5,7,4,1]=>[1,4,7,5,8,2,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,2,3,7,6,1,8,4]=>[4,8,1,6,7,3,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,5,6,8,7,3,4,1]=>[1,4,3,7,8,6,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,6,2,5,4,1,3,7]=>[7,3,1,4,5,2,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[2,5,7,6,3,1,8,4]=>[4,8,1,3,6,7,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,3,7,5,8,6,4,2]=>[2,4,6,8,5,7,3,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,2,4,7,8,5,6,1]=>[1,6,5,8,7,4,2,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[4,6,8,3,2,1,5,7]=>[7,5,1,2,3,8,6,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[8,7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[3,6,1,2,7,5,8,4]=>[4,8,5,7,2,1,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[3,7,6,2,5,8,1,4]=>[4,1,8,5,2,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,5,2,3,6,7,4,1]=>[1,4,7,6,3,2,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[5,6,1,2,8,7,4,3]=>[3,4,7,8,2,1,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[2,7,6,8,1,5,4,3]=>[3,4,5,1,8,6,7,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[5,8,7,1,6,4,3,2]=>[2,3,4,6,1,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[4,1,6,7,5,8,2,3]=>[3,2,8,5,7,6,1,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[5,8,7,6,1,3,4,2]=>[2,4,3,1,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,1,2,8,3,5,6,4]=>[4,6,5,3,8,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,1,4,5,8,6,2,3]=>[3,2,6,8,5,4,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,1,5,6,2,3,7,4]=>[4,7,3,2,6,5,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,8,6,1,7,2,4,3]=>[3,4,2,7,1,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[7,1,2,8,5,6,3,4]=>[4,3,6,5,8,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,2,3,8,6,7,4,1]=>[1,4,7,6,8,3,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[7,6,2,8,5,1,4,3]=>[3,4,1,5,8,2,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[1,8,4,2,7,6,5,3]=>[3,5,6,7,2,4,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[5,7,4,8,2,1,3,6]=>[6,3,1,2,8,4,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,4,7,5,8,1,2,3]=>[3,2,1,8,5,7,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[4,7,1,2,5,8,6,3]=>[3,6,8,5,2,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,4,1,2,7,5,3]=>[3,5,7,2,1,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,1,7,5,4,3,2]=>[2,3,4,5,7,1,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[5,1,8,7,3,6,4,2]=>[2,4,6,3,7,8,1,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,4,8,5,1,6,2,3]=>[3,2,6,1,5,8,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,1,5,8,6,2,3,4]=>[4,3,2,6,8,5,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,1,8,2,7,3,4,5]=>[5,4,3,7,2,8,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,8,7,6,4,5,3,2]=>[2,3,5,4,6,7,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,8,7,3,6,5,4,2]=>[2,4,5,6,3,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[5,8,1,6,3,4,2,7]=>[7,2,4,3,6,1,8,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,4,7,3,6,2,1,8]=>[8,1,2,6,3,7,4,5]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>0
[8,6,5,3,7,2,4,1]=>[1,4,2,7,3,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,5,8,3,7,2,4,1]=>[1,4,2,7,3,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,2,7,1,8,4,3,6]=>[6,3,4,8,1,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,7,3,1,5,8,2,4]=>[4,2,8,5,1,3,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,3,8,2,5,7,4,1]=>[1,4,7,5,2,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[1,7,8,2,4,5,6,3]=>[3,6,5,4,2,8,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,6,1,3,4,2,8,7]=>[7,8,2,4,3,1,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,7,1,2,4,5,8,3]=>[3,8,5,4,2,1,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,8,2,3,5,6,7,4]=>[4,7,6,5,3,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,7,1,2,4,5,6,3]=>[3,6,5,4,2,1,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,8,1,2,4,5,6,3]=>[3,6,5,4,2,1,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,1,2,4,3,7,8,6]=>[6,8,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,8,3,2,7,6,1,5]=>[5,1,6,7,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[4,3,2,8,1,7,6,5]=>[5,6,7,1,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,2,6,4,7,5,8,3]=>[3,8,5,7,4,6,2,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,8,2,5,6,3,7,4]=>[4,7,3,6,5,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,2,7,5,8,3,6,4]=>[4,6,3,8,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,5,8,1,4,3,2,7]=>[7,2,3,4,1,8,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[5,7,6,8,2,3,1,4]=>[4,1,3,2,8,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,5,7,2,8,4,3,6]=>[6,3,4,8,2,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,3,2,6,1,8,5,7]=>[7,5,8,1,6,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,1,2,3,4,8,7,5]=>[5,7,8,4,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,8,2,3,4,7,6,5]=>[5,6,7,4,3,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,6,2,3,4,8,7,5]=>[5,7,8,4,3,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[4,8,1,5,2,7,6,3]=>[3,6,7,2,5,1,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,8,7,6,4,1,3,5]=>[5,3,1,4,6,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,8,7,6,2,1,3,5]=>[5,3,1,2,6,7,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,6,8,4,2,7,5,3]=>[3,5,7,2,4,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,8,2,3,7,6,4]=>[4,6,7,3,2,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,6,4,8,7,2,5,3]=>[3,5,2,7,8,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,6,4,8,2,7,5,3]=>[3,5,7,2,8,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,4,5,8,2,7,6,3]=>[3,6,7,2,8,5,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,2,7,6,5,4,1,3]=>[3,1,4,5,6,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[7,2,8,6,5,4,3,1]=>[1,3,4,5,6,8,2,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>5
[4,8,7,6,5,3,1,2]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[7,8,6,1,5,4,3,2]=>[2,3,4,5,1,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>5
[7,3,8,6,5,4,2,1]=>[1,2,4,5,6,8,3,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>5
[7,5,4,1,8,2,3,6]=>[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,5,7,2,8,1,3,4]=>[4,3,1,8,2,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[7,5,4,2,1,8,3,6]=>[6,3,8,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,5,7,2,1,8,3,4]=>[4,3,8,1,2,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[3,7,8,5,6,4,1,2]=>[2,1,4,6,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,8,5,6,1,4,2]=>[2,4,1,6,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,8,5,6,3,4,2]=>[2,4,3,6,5,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,5,8,6,3,4,2]=>[2,4,3,6,8,5,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,5,8,6,1,4,2]=>[2,4,1,6,8,5,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,5,8,6,4,1,2]=>[2,1,4,6,8,5,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,3,8,6,4,1,2]=>[2,1,4,6,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,8,5,6,4,1,2]=>[2,1,4,6,5,8,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,5,8,6,4,1,2]=>[2,1,4,6,8,5,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,5,7,8,6,4,1,2]=>[2,1,4,6,8,7,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,5,7,8,6,3,4,2]=>[2,4,3,6,8,7,5,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,5,7,8,3,6,4,2]=>[2,4,6,3,8,7,5,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,5,7,8,1,6,4,2]=>[2,4,6,1,8,7,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,5,8,6,1,4,2]=>[2,4,1,6,8,5,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,8,5,6,1,4,2]=>[2,4,1,6,5,8,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,1,5,6,3,4,2]=>[2,4,3,6,5,1,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,8,5,6,3,4,2]=>[2,4,3,6,5,8,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,5,8,6,3,4,2]=>[2,4,3,6,8,5,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,1,7,8,3,6,4,2]=>[2,4,6,3,8,7,1,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,1,7,8,5,6,4,2]=>[2,4,6,5,8,7,1,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,3,7,8,5,6,4,2]=>[2,4,6,5,8,7,3,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,1,7,5,8,6,4,2]=>[2,4,6,8,5,7,1,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,1,7,3,8,6,4,2]=>[2,4,6,8,3,7,1,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,5,3,8,6,4,2]=>[2,4,6,8,3,5,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,5,8,3,6,4,2]=>[2,4,6,3,8,5,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,3,5,1,6,4,2]=>[2,4,6,1,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,5,8,1,6,4,2]=>[2,4,6,1,8,5,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,3,7,1,8,6,4,2]=>[2,4,6,8,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,5,7,1,8,6,4,2]=>[2,4,6,8,1,7,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,5,3,8,6,4,2]=>[2,4,6,8,3,5,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,3,1,8,6,4,2]=>[2,4,6,8,1,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,3,8,6,1,4,2]=>[2,4,1,6,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,5,8,1,6,4,2]=>[2,4,6,1,8,5,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,5,8,3,6,4,2]=>[2,4,6,3,8,5,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,8,5,3,6,4,2]=>[2,4,6,3,5,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,8,5,1,6,4,2]=>[2,4,6,1,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,8,6,3,1,4,2]=>[2,4,1,3,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,6,1,3,4,2]=>[2,4,3,1,6,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,8,1,6,3,4,2]=>[2,4,3,6,1,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,8,3,5,6,4,2]=>[2,4,6,5,3,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,3,8,5,6,4,2]=>[2,4,6,5,8,3,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,1,8,5,6,4,2]=>[2,4,6,5,8,1,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,1,8,3,6,4,2]=>[2,4,6,3,8,1,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,1,8,6,3,4,2]=>[2,4,3,6,8,1,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,1,8,6,3,4,2]=>[2,4,3,6,8,1,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,5,1,6,3,4,2]=>[2,4,3,6,1,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,8,1,3,6,4,2]=>[2,4,6,3,1,8,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,1,8,3,6,4,2]=>[2,4,6,3,8,1,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,1,3,8,6,4,2]=>[2,4,6,8,3,1,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,7,1,3,8,6,4,2]=>[2,4,6,8,3,1,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,7,1,5,8,6,4,2]=>[2,4,6,8,5,1,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,7,3,5,8,6,4,2]=>[2,4,6,8,5,3,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[1,5,3,7,8,6,4,2]=>[2,4,6,8,7,3,5,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,5,1,7,8,6,4,2]=>[2,4,6,8,7,1,5,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[5,3,1,7,8,6,4,2]=>[2,4,6,8,7,1,3,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,1,5,8,6,4,2]=>[2,4,6,8,5,1,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,1,8,5,6,4,2]=>[2,4,6,5,8,1,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,3,8,1,5,6,4,2]=>[2,4,6,5,1,8,3,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,8,1,3,5,6,4,2]=>[2,4,6,5,3,1,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,8,3,5,6,4,2]=>[2,4,6,5,3,8,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,3,8,5,6,4,2]=>[2,4,6,5,8,3,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,1,3,5,8,6,4,2]=>[2,4,6,8,5,3,1,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[3,1,5,7,8,6,4,2]=>[2,4,6,8,7,5,1,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>3
[7,5,6,2,8,3,1,4]=>[4,1,3,8,2,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,4,8,1,2,5,6,3]=>[3,6,5,2,1,8,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,3,5,7,6,1,8,4]=>[4,8,1,6,7,5,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,5,1,4,7,3,8,6]=>[6,8,3,7,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,6,4,2,8,7,5,3]=>[3,5,7,8,2,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,6,1,2,8,7,5,3]=>[3,5,7,8,2,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,4,1,2,8,7,5,3]=>[3,5,7,8,2,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,3,7,4,5,8,6,2]=>[2,6,8,5,4,7,3,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,6,5,2,1,4,3,7]=>[7,3,4,1,2,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,8,2,7,3,6,5,4]=>[4,5,6,3,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>6
[5,8,1,7,3,6,4,2]=>[2,4,6,3,7,1,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,2,3,4,8,7,5,6]=>[6,5,7,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,8,4,2,3,5,6,7]=>[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[8,7,1,4,2,5,6,3]=>[3,6,5,2,4,1,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,1,8,5,6,2,3,4]=>[4,3,2,6,5,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[4,1,8,6,2,7,5,3]=>[3,5,7,2,6,8,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,4,1,2,6,5,3]=>[3,5,6,2,1,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[5,7,1,8,2,6,3,4]=>[4,3,6,2,8,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,6,2,8,4,7,5,3]=>[3,5,7,4,8,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,1,8,2,3,6,4]=>[4,6,3,2,8,1,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,1,8,2,3,5,6,4]=>[4,6,5,3,2,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,7,5,1,6,2,3,4]=>[4,3,2,6,1,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,8,6,1,7,2,5,3]=>[3,5,2,7,1,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,4,1,2,5,6,3]=>[3,6,5,2,1,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,8,7,2,3,6,4,5]=>[5,4,6,3,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,8,7,2,6,3,4,5]=>[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,8,2,7,6,3,4,5]=>[5,4,3,6,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,5,2,8,6,7,4,3]=>[3,4,7,6,8,2,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,4,1,2,7,5,6,3]=>[3,6,5,7,2,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,1,4,2,6,7,5,3]=>[3,5,7,6,2,4,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,7,3,6,4,5]=>[5,4,6,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,1,7,2,6,3,4,5]=>[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,1,7,2,3,6,4,5]=>[5,4,6,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,7,1,2,3,6,4,5]=>[5,4,6,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,4,2,7,6,1,3,5]=>[5,3,1,6,7,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,8,5,2,1,4,3,6]=>[6,3,4,1,2,5,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,8,5,4,1,3,2,7]=>[7,2,3,1,4,5,8,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[7,3,5,6,4,2,1,8]=>[8,1,2,4,6,5,3,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[4,8,6,7,5,3,2,1]=>[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[5,6,3,1,7,8,4,2]=>[2,4,8,7,1,3,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,5,1,2,3,8,6,4]=>[4,6,8,3,2,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,7,5,8,1,3,2,4]=>[4,2,3,1,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[2,5,7,1,4,3,8,6]=>[6,8,3,4,1,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,2,8,1,5,4,3,6]=>[6,3,4,5,1,8,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,7,8,2,5,4,3,6]=>[6,3,4,5,2,8,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,3,6,1,5,4,2]=>[2,4,5,1,6,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,8,5,6,3,4,2,7]=>[7,2,4,3,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[4,5,1,8,7,6,2,3]=>[3,2,6,7,8,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,2,6,8,3,7,4,1]=>[1,4,7,3,8,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[6,1,4,8,7,2,5,3]=>[3,5,2,7,8,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,6,7,4,8,5,2,1]=>[1,2,5,8,4,7,6,3]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[1,5,8,2,7,3,6,4]=>[4,6,3,7,2,8,5,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,8,5,3,7,2,4,1]=>[1,4,2,7,3,5,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,3,4,7,8,5,2,1]=>[1,2,5,8,7,4,3,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[6,1,2,7,4,5,8,3]=>[3,8,5,4,7,2,1,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[2,6,7,3,8,5,4,1]=>[1,4,5,8,3,7,6,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[1,4,5,7,8,2,6,3]=>[3,6,2,8,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[3,4,5,7,8,6,1,2]=>[2,1,6,8,7,5,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,6,8,2,3,4,7,5]=>[5,7,4,3,2,8,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,6,8,2,3,7,4,5]=>[5,4,7,3,2,8,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[7,8,1,4,5,2,6,3]=>[3,6,2,5,4,1,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,5,6,3,8,7,4]=>[4,7,8,3,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,4,8,1,5,6,2,3]=>[3,2,6,5,1,8,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,7,3,8,4,5,2,1]=>[1,2,5,4,8,3,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[2,6,7,8,5,3,4,1]=>[1,4,3,5,8,7,6,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[1,7,2,8,4,5,6,3]=>[3,6,5,4,8,2,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[3,1,2,6,7,5,8,4]=>[4,8,5,7,6,2,1,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[3,7,4,5,1,8,6,2]=>[2,6,8,1,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,7,4,2,1,6,3,5]=>[5,3,6,1,2,4,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,5,3,8,7,6,4,2]=>[2,4,6,7,8,3,5,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,2,8,7,5,6,3,4]=>[4,3,6,5,7,8,2,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,8,2,4,7,6,5,3]=>[3,5,6,7,4,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,1,8,5,2,7,6,3]=>[3,6,7,2,5,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[3,6,5,8,7,2,4,1]=>[1,4,2,7,8,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[1,8,2,5,3,6,7,4]=>[4,7,6,3,5,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,5,8,1,2,6,3,4]=>[4,3,6,2,1,8,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,2,5,8,4,1,3,7]=>[7,3,1,4,8,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,1,2,8,3,7,4,5]=>[5,4,7,3,8,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,2,5,7,8,1,3,4]=>[4,3,1,8,7,5,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,1,4,2,3,7,8,6]=>[6,8,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,8,7,6,2,5,4,3]=>[3,4,5,2,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[1,10,9,8,7,6,5,4,2,3]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[1,2,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[1,2,3,9,8,7,6,5,4]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[1,2,3,4,5,9,8,7,6]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[1,2,10,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[1,2,3,10,9,8,7,6,5,4]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>6
[1,2,3,4,10,9,8,7,6,5]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>5
[1,2,3,4,5,6,10,9,8,7]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>3
[1,2,3,4,5,6,7,10,9,8]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[1,7,8,4,5,6,2,3]=>[3,2,6,5,4,8,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,1,4,6,2,7,5,3]=>[3,5,7,2,6,4,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,5,1,6,7,8,4,2]=>[2,4,8,7,6,1,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[6,1,4,8,7,5,2,3]=>[3,2,5,7,8,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,6,4,8,7,5,2,3]=>[3,2,5,7,8,4,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,7,2,5,4,8,3,6]=>[6,3,8,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,2,5,4,8,3,6]=>[6,3,8,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,7,1,5,4,8,3,6]=>[6,3,8,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,2,1,5,4,8,3,6]=>[6,3,8,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,2,7,5,4,8,3,6]=>[6,3,8,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,6,4,1,7,2,5,3]=>[3,5,2,7,1,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,3,6,5,2,1,8,4]=>[4,8,1,2,5,6,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[7,4,5,8,6,1,2,3]=>[3,2,1,6,8,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,1,8,7,6,2,3,4]=>[4,3,2,6,7,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,5,1,7,6,2,3,4]=>[4,3,2,6,7,1,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,5,1,6,2,7,3,4]=>[4,3,7,2,6,1,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[4,6,1,8,7,5,2,3]=>[3,2,5,7,8,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,4,6,1,7,5,2,3]=>[3,2,5,7,1,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,4,7,1,2,5,3]=>[3,5,2,1,7,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,4,8,7,1,2,5,3]=>[3,5,2,1,7,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,4,1,8,2,3,6]=>[6,3,2,8,1,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,6,8,7,4,1,2,3]=>[3,2,1,4,7,8,6,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[2,6,5,1,7,8,3,4]=>[4,3,8,7,1,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[6,1,5,4,3,2,8,7]=>[7,8,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,4,1,5,7,6,2,3]=>[3,2,6,7,5,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,5,4,2,7,8,3,6]=>[6,3,8,7,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,8,7,2,1,6,3,5]=>[5,3,6,1,2,7,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,7,6,4,1,2,5,3]=>[3,5,2,1,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[5,7,2,3,6,8,1,4]=>[4,1,8,6,3,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,5,2,8,4,1,3,6]=>[6,3,1,4,8,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[2,6,5,1,4,8,3,7]=>[7,3,8,4,1,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,4,1,2,7,8,3,6]=>[6,3,8,7,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,4,3,2,7,1,6,5]=>[5,6,1,7,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[4,8,7,6,5,2,3,1]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[6,8,1,2,7,4,5,3]=>[3,5,4,7,2,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,4,8,7,5,1,2,3]=>[3,2,1,5,7,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,8,7,6,1,2,5,3]=>[3,5,2,1,6,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[5,1,2,4,7,8,3,6]=>[6,3,8,7,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,5,8,4,3,1,2,7]=>[7,2,1,3,4,8,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[3,6,8,5,2,7,4,1]=>[1,4,7,2,5,8,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[2,1,6,5,4,8,3,7]=>[7,3,8,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,7,1,8,5,2,6,3]=>[3,6,2,5,8,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,1,3,6,4,2,8,7]=>[7,8,2,4,6,3,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,8,3,7,5,4,2,1]=>[1,2,4,5,7,3,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[7,1,2,4,8,5,6,3]=>[3,6,5,8,4,2,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[9,1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[10,1,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[9,8,1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[5,7,4,1,2,3,8,6]=>[6,8,3,2,1,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,5,1,8,2,7,6,3]=>[3,6,7,2,8,1,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,6,8,1,7,5,2,3]=>[3,2,5,7,1,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,5,1,4,3,2,8,7]=>[7,8,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[2,3,8,4,1,5,6,7]=>[7,6,5,1,4,8,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[1,5,6,3,4,8,2,7]=>[7,2,8,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,7,8,2,3,5,4,1]=>[1,4,5,3,2,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[5,8,6,2,3,7,4,1]=>[1,4,7,3,2,6,8,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[4,8,1,6,7,2,5,3]=>[3,5,2,7,6,1,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,2,1,7,4,3,6,5]=>[5,6,3,4,7,1,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,4,5,1,7,2,6,3]=>[3,6,2,7,1,5,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,5,6,8,7,4,2,3]=>[3,2,4,7,8,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,4,8,5,7,6,2,3]=>[3,2,6,7,5,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,7,2,8,5,3,4,1]=>[1,4,3,5,8,2,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[4,1,8,6,7,5,2,3]=>[3,2,5,7,6,8,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,7,1,8,5,4,2,3]=>[3,2,4,5,8,1,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[4,3,2,8,7,6,1,5]=>[5,1,6,7,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,7,4,2,5,8,6,3]=>[3,6,8,5,2,4,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,1,5,7,8,4,3,6]=>[6,3,4,8,7,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,8,7,5,6,2,3,4]=>[4,3,2,6,5,7,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,8,5,7,6,2,3,4]=>[4,3,2,6,7,5,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,1,7,2,3,8,6,4]=>[4,6,8,3,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,6,7,1,5,2,8,4]=>[4,8,2,5,1,7,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,2,1,7,4,8,3,6]=>[6,3,8,4,7,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,3,1,8,6,4,2,7]=>[7,2,4,6,8,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,8,1,4,7,5,2,3]=>[3,2,5,7,4,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,4,7,5,8,6,1,2]=>[2,1,6,8,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,3,6,1,4,2,7,8]=>[8,7,2,4,1,6,3,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[3,7,6,5,2,8,1,4]=>[4,1,8,2,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[9,1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[10,1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[8,2,7,6,1,5,4,3]=>[3,4,5,1,6,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[8,4,1,7,6,5,3,2]=>[2,3,5,6,7,1,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,2,3,6,8,7,4,5]=>[5,4,7,8,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,2,3,6,8,4,7,5]=>[5,7,4,8,6,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[3,6,7,8,4,5,2,1]=>[1,2,5,4,8,7,6,3]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[6,3,7,8,4,5,2,1]=>[1,2,5,4,8,7,3,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>3
[1,8,2,7,4,5,6,3]=>[3,6,5,4,7,2,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,6,1,2,7,4,5,3]=>[3,5,4,7,2,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,7,6,5,3,4]=>[4,3,5,6,7,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,1,7,4,2,6,5,3]=>[3,5,6,2,4,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,1,4,5,2,6,3]=>[3,6,2,5,4,1,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[7,5,1,8,2,6,3,4]=>[4,3,6,2,8,1,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[4,8,3,2,1,7,6,5]=>[5,6,7,1,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[8,1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>1
[9,7,10,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,10,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[9,7,10,5,8,6,3,4,1,2]=>[2,1,4,3,6,8,5,10,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[9,7,10,5,8,3,6,4,1,2]=>[2,1,4,6,3,8,5,10,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>4
[7,6,8,2,5,1,4,3]=>[3,4,1,5,2,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[5,1,7,2,4,8,3,6]=>[6,3,8,4,2,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,6,5,7,1,8,3,4]=>[4,3,8,1,7,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[8,4,7,3,2,6,1,5]=>[5,1,6,2,3,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,9,2,8,7,6,5,4,3]=>[3,4,5,6,7,8,2,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[1,8,7,4,2,6,5,3]=>[3,5,6,2,4,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[2,7,5,4,8,1,3,6]=>[6,3,1,8,4,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,5,6,4,8,1,2,7]=>[7,2,1,8,4,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[3,6,1,7,2,5,8,4]=>[4,8,5,2,7,1,6,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,1,3,8,7,6,4,2]=>[2,4,6,7,8,3,1,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,4,6,7,2,5,3]=>[3,5,2,7,6,4,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,5,3,8,2,7,4,1]=>[1,4,7,2,8,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[8,3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[5,2,8,6,3,7,4,1]=>[1,4,7,3,6,8,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[1,8,2,7,5,3,6,4]=>[4,6,3,5,7,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,4,1,5,2,8,6,3]=>[3,6,8,2,5,1,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,2,6,4,7,5,3]=>[3,5,7,4,6,2,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,3,5,2,7,4,1]=>[1,4,7,2,5,3,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,3,5,2,7,4,1,8]=>[8,1,4,7,2,5,3,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[8,1,4,2,5,7,6,3]=>[3,6,7,5,2,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,7,1,3,6,5,4,2]=>[2,4,5,6,3,1,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,8,7,6,5,3,4,2]=>[2,4,3,5,6,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[3,8,5,7,6,1,4,2]=>[2,4,1,6,7,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,7,2,4,6,5,3,1]=>[1,3,5,6,4,2,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,7,6,1,4,5,3,2]=>[2,3,5,4,1,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[4,5,8,1,7,6,2,3]=>[3,2,6,7,1,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,3,6,2,1,8,5,7]=>[7,5,8,1,2,6,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,4,8,3,2,1,5,7]=>[7,5,1,2,3,8,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[5,1,2,8,3,6,7,4]=>[4,7,6,3,8,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,8,2,7,4,6,5,3]=>[3,5,6,4,7,2,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,1,2,3,4,6,5]=>[5,6,4,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[1,6,7,8,9,2,3,4,5]=>[5,4,3,2,9,8,7,6,1]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]=>[6,7,8,9,1,2,3,4,5]=>1
[8,1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,1,7,2,4,6,5,3]=>[3,5,6,4,2,7,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[7,5,8,2,1,4,3,6]=>[6,3,4,1,2,8,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,7,8,2,3,5,6,4]=>[4,6,5,3,2,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,5,2,4,7,8,3,6]=>[6,3,8,7,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,7,1,5,8,4,3,6]=>[6,3,4,8,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[4,8,1,6,2,7,5,3]=>[3,5,7,2,6,1,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,1,8,4,2,7,5,3]=>[3,5,7,2,4,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,2,1,4,7,8,3,6]=>[6,3,8,7,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,5,3,6,8,4,2,7]=>[7,2,4,8,6,3,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,8,7,2,5,3,6,4]=>[4,6,3,5,2,7,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[2,8,1,4,7,3,6,5]=>[5,6,3,7,4,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[3,5,6,1,4,2,8,7]=>[7,8,2,4,1,6,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,1,6,8,2,3,7,4]=>[4,7,3,2,8,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,7,2,5,3,8,6,4]=>[4,6,8,3,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,8,7,5,6,1,4,2]=>[2,4,1,6,5,7,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[4,1,8,7,5,6,2,3]=>[3,2,6,5,7,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,3,2,5,8,7,4,1]=>[1,4,7,8,5,2,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,5,8,7,3,2,4,1]=>[1,4,2,3,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[1,8,4,2,5,7,6,3]=>[3,6,7,5,2,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,4,6,2,8,7,5,3]=>[3,5,7,8,2,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,4,8,1,2,3,6]=>[6,3,2,1,8,4,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,1,5,6,2,3,4]=>[4,3,2,6,5,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,7,8,1,2,6,3,4]=>[4,3,6,2,1,8,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,1,5,7,6,2,3,4]=>[4,3,2,6,7,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,4,1,7,5,2,8,3]=>[3,8,2,5,7,1,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[7,8,6,5,2,4,3,1]=>[1,3,4,2,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>5
[5,3,6,7,8,1,4,2]=>[2,4,1,8,7,6,3,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[2,5,4,7,8,1,3,6]=>[6,3,1,8,7,4,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,4,6,1,7,2,5,3]=>[3,5,2,7,1,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,8,3,1,7,6,4,2]=>[2,4,6,7,1,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,3,1,4,5,8,6,2]=>[2,6,8,5,4,1,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,2,7,3,6,1,8,4]=>[4,8,1,6,3,7,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,4,2,8,5,7,6,3]=>[3,6,7,5,8,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,6,5,4,1,3,2,7]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[4,8,7,6,5,1,3,2]=>[2,3,1,5,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[4,8,7,5,1,6,2,3]=>[3,2,6,1,5,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,1,6,3,4,8,2,7]=>[7,2,8,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,3,8,7,5,4,2,1]=>[1,2,4,5,7,8,3,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[7,2,1,5,8,4,3,6]=>[6,3,4,8,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,1,5,4,3,8,2,7]=>[7,2,8,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,8,7,2,3,4,5,6]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[1,8,2,3,7,4,5,6]=>[6,5,4,7,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,7,5,6,1,3,4,2]=>[2,4,3,1,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[3,6,5,8,2,7,4,1]=>[1,4,7,2,8,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[8,7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[7,2,5,4,1,3,8,6]=>[6,8,3,1,4,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,1,4,8,5,6,2,3]=>[3,2,6,5,8,4,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,3,1,9,4,5,6,7,8]=>[8,7,6,5,4,9,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>1
[3,9,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,9,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[1,8,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>0
[3,1,5,8,7,6,4,2]=>[2,4,6,7,8,5,1,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,7,5,3,6,4,2]=>[2,4,6,3,5,7,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,2,5,6,7,3,4]=>[4,3,7,6,5,2,8,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,1,8,2,9,3,10,4,5,6]=>[6,5,4,10,3,9,2,8,1,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>1
[1,5,2,7,4,8,3,6]=>[6,3,8,4,7,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,6,5,4,3,8,2,7]=>[7,2,8,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[4,1,8,7,5,2,6,3]=>[3,6,2,5,7,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,4,8,1,7,6,3,5]=>[5,3,6,7,1,8,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,3,5,7,2,4,1,8]=>[8,1,4,2,7,5,3,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[3,8,6,5,2,7,4,1]=>[1,4,7,2,5,6,8,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[2,1,6,5,3,7,8,4]=>[4,8,7,3,5,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>1
[2,3,1,4,5,6,7,9,8]=>[8,9,7,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>1
[1,3,2,4,5,6,7,9,8]=>[8,9,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>1
[8,7,4,6,5,2,3,1]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[8,4,6,7,5,1,2,3]=>[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,1,5,4,3,2,7]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,6,5,4,8,3,2,7]=>[7,2,3,8,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[8,6,5,1,4,3,2,7]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[6,1,7,3,5,2,8,4]=>[4,8,2,5,3,7,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[5,2,3,7,1,6,8,4]=>[4,8,6,1,7,3,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[8,7,5,3,1,6,4,2]=>[2,4,6,1,3,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,8,3,7,6,4,1,2]=>[2,1,4,6,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[6,8,3,5,7,2,4,1]=>[1,4,2,7,5,3,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[3,5,8,6,1,4,2,7]=>[7,2,4,1,6,8,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[2,4,1,8,7,3,6,5]=>[5,6,3,7,8,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[2,8,6,1,5,4,3,7]=>[7,3,4,5,1,6,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[3,5,1,6,8,4,2,7]=>[7,2,4,8,6,1,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,1,6,8,2,7,3,4]=>[4,3,7,2,8,6,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,8,1,3,4,5,6,2]=>[2,6,5,4,3,1,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,8,2,6,7,3,4,5]=>[5,4,3,7,6,2,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[3,1,4,2,5,6,7,8,9]=>[9,8,7,6,5,2,4,1,3]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>0
[4,7,5,1,8,2,6,3]=>[3,6,2,8,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,4,6,1,2,7,5,3]=>[3,5,7,2,1,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,7,4,1,5,8,6,2]=>[2,6,8,5,1,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,8,6,1,2,7,4,3]=>[3,4,7,2,1,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[6,8,1,2,4,7,5,3]=>[3,5,7,4,2,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,5,6,1,2,7,4,3]=>[3,4,7,2,1,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,6,7,8,5,2,4,3]=>[3,4,2,5,8,7,6,1]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>3
[1,9,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>0
[3,7,8,4,5,1,6,2]=>[2,6,1,5,4,8,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[6,3,1,7,2,5,8,4]=>[4,8,5,2,7,1,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,2,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>0
[1,2,3,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>0
[6,7,5,3,8,1,2,4]=>[4,2,1,8,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,7,2,3,5,8,6,4]=>[4,6,8,5,3,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,2,3,7,5,6,4]=>[4,6,5,7,3,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,8,3,6,7,4,5]=>[5,4,7,6,3,8,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[10,9,8,7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[10,9,1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>5
[7,8,4,1,5,6,2,3]=>[3,2,6,5,1,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,6,5,4,1,8,3,7]=>[7,3,8,1,4,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,2,5,1,4,8,3,7]=>[7,3,8,4,1,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,5,4,1,3,8,2,7]=>[7,2,8,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,8,4,7,6,5,2,3]=>[3,2,5,6,7,4,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,1,6,4,7,5,2,3]=>[3,2,5,7,4,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,2,1,4,3,8,6]=>[6,8,3,4,1,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,4,8,6,5,3,2,1]=>[1,2,3,5,6,8,4,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>5
[7,8,3,4,1,5,6,2]=>[2,6,5,1,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,5,2,6,7,3,4,1]=>[1,4,3,7,6,2,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[7,6,3,2,5,8,1,4]=>[4,1,8,5,2,3,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[1,9,2,8,3,7,4,6,5]=>[5,6,4,7,3,8,2,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[1,10,2,9,3,8,4,7,5,6]=>[6,5,7,4,8,3,9,2,10,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,1,2,3,4,5,6]=>4
[8,7,2,6,5,1,4,3]=>[3,4,1,5,6,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[4,8,2,7,6,5,3,1]=>[1,3,5,6,7,2,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[4,8,3,7,2,1,6,5]=>[5,6,1,2,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,8,6,2,3,7,4,5]=>[5,4,7,3,2,6,8,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,5,6,3,4,2,7,8]=>[8,7,2,4,3,6,5,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[1,5,3,6,4,2,7,8]=>[8,7,2,4,6,3,5,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[2,5,7,4,1,3,8,6]=>[6,8,3,1,4,7,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,2,6,5,4,1,3,7]=>[7,3,1,4,5,6,2,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,2,8,5,1,4,3,6]=>[6,3,4,1,5,8,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,1,6,5,2,3,4]=>[4,3,2,5,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,5,1,2,7,6,3,4]=>[4,3,6,7,2,1,5,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,4,1,8,2,7,5,3]=>[3,5,7,2,8,1,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,7,1,5,8,2,6,3]=>[3,6,2,8,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,3,8,4,1,5,6,2]=>[2,6,5,1,4,8,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[3,7,6,2,1,5,8,4]=>[4,8,5,1,2,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[4,3,8,2,1,7,6,5]=>[5,6,7,1,2,8,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[2,3,5,7,1,6,8,4]=>[4,8,6,1,7,5,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[4,8,2,1,3,7,6,5]=>[5,6,7,3,1,2,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,2,8,1,3,7,6,5]=>[5,6,7,3,1,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,2,8,5,3,6,7,4]=>[4,7,6,3,5,8,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,8,4,1,5,2,6,3]=>[3,6,2,5,1,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,1,2,5,3,6,7,4]=>[4,7,6,3,5,2,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,7,6,5,2,3,4]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,8,7,6,4,5,2,3]=>[3,2,5,4,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,8,7,1,5,2,6,3]=>[3,6,2,5,1,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,8,7,6,4,2,5,3]=>[3,5,2,4,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[8,1,7,6,4,5,3,2]=>[2,3,5,4,6,7,1,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[1,9,2,3,4,5,8,6,7]=>[7,6,8,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,2,8,3,4,7,5,6]=>[6,5,7,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>2
[8,1,2,3,7,6,4,5]=>[5,4,6,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,7,6,4,2,5,3,1]=>[1,3,5,2,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[2,6,5,1,4,3,8,7]=>[7,8,3,4,1,5,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,7,5,6,3,1,4,2]=>[2,4,1,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,8,7,1,4,3,6,5]=>[5,6,3,4,1,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[4,8,7,1,2,6,5,3]=>[3,5,6,2,1,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,5,3,6,4,1,2]=>[2,1,4,6,3,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,9,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,10,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[1,8,7,4,6,2,5,3]=>[3,5,2,6,4,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,3,5,6,1,4,2]=>[2,4,1,6,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,6,4,1,7,5,2,3]=>[3,2,5,7,1,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,4,1,2,7,5,3]=>[3,5,7,2,1,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,6,2,7,4,5,3]=>[3,5,4,7,2,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,4,1,8,2,5,6,3]=>[3,6,5,2,8,1,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,3,7,1,5,6,8,4]=>[4,8,6,5,1,7,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,3,4,8,1,5,6,2]=>[2,6,5,1,8,4,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,8,4,5,1,2,6,3]=>[3,6,2,1,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,3,2,8,7,1,6,5]=>[5,6,1,7,8,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[4,8,3,2,7,1,6,5]=>[5,6,1,7,2,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,6,7,4,2,5,8,3]=>[3,8,5,2,4,7,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,6,7,5,8,3,2,4]=>[4,2,3,8,5,7,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,7,5,3,1,8,2,4]=>[4,2,8,1,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[8,7,5,3,6,1,4,2]=>[2,4,1,6,3,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,7,5,6,8,3,1,4]=>[4,1,3,8,6,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,7,5,6,3,1,8,4]=>[4,8,1,3,6,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,7,5,3,6,8,1,4]=>[4,1,8,6,3,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,7,5,3,6,1,8,4]=>[4,8,1,6,3,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[2,7,5,3,1,6,8,4]=>[4,8,6,1,3,5,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[5,7,6,2,8,3,1,4]=>[4,1,3,8,2,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[8,4,5,1,7,6,2,3]=>[3,2,6,7,1,5,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,5,7,8,4,2,3,6]=>[6,3,2,4,8,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,5,7,8,2,4,3,6]=>[6,3,4,2,8,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,8,1,7,2,4,5,3]=>[3,5,4,2,7,1,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,5,6,1,4,2,7,8]=>[8,7,2,4,1,6,5,3]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[7,5,4,2,1,3,8,6]=>[6,8,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[4,1,8,2,6,7,5,3]=>[3,5,7,6,2,8,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,6,2,3,4,7,5]=>[5,7,4,3,2,6,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,1,2,8,7,3,4,5]=>[5,4,3,7,8,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[4,8,1,7,6,2,5,3]=>[3,5,2,6,7,1,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,1,8,7,6,5,2,3]=>[3,2,5,6,7,8,1,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,5,1,7,6,4,3,2]=>[2,3,4,6,7,1,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[3,8,7,6,1,5,4,2]=>[2,4,5,1,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,5,8,6,2,7,4,3]=>[3,4,7,2,6,8,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,6,1,2,7,3,4,5]=>[5,4,3,7,2,1,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[4,1,2,6,8,7,5,3]=>[3,5,7,8,6,2,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,6,8,7,5,2,3]=>[3,2,5,7,8,6,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,4,8,5,6,1,2,3]=>[3,2,1,6,5,8,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,7,8,1,2,5,6,3]=>[3,6,5,2,1,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,1,4,7,2,5,8,3]=>[3,8,5,2,7,4,1,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,4,8,7,5,2,6,3]=>[3,6,2,5,7,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,4,2,7,1,6,3,5]=>[5,3,6,1,7,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,7,6,1,3,5,4,2]=>[2,4,5,3,1,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[8,7,6,1,5,4,2,3]=>[3,2,4,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[8,7,6,1,2,5,3,4]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[8,1,7,5,3,6,4,2]=>[2,4,6,3,5,7,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[4,7,5,1,8,6,2,3]=>[3,2,6,8,1,5,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,6,2,7,5,4,3,1]=>[1,3,4,5,7,2,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[1,7,8,5,6,2,3,4]=>[4,3,2,6,5,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,3,5,6,1,4,2,7]=>[7,2,4,1,6,5,3,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,2,3,4,5,6,9,10,7,8]=>[8,7,10,9,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>1
[8,6,4,7,5,1,2,3]=>[3,2,1,5,7,4,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,5,3,1,7,6,4,2]=>[2,4,6,7,1,3,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[6,8,7,3,5,4,2,1]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[1,6,8,2,7,4,5,3]=>[3,5,4,7,2,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,2,1,8,4,3,6]=>[6,3,4,8,1,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,1,8,5,7,6,4,2]=>[2,4,6,7,5,8,1,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[2,8,4,1,3,7,6,5]=>[5,6,7,3,1,4,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[2,8,6,7,5,4,3,1]=>[1,3,4,5,7,6,8,2]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[8,6,7,4,1,5,2,3]=>[3,2,5,1,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,7,8,1,5,6,2,3]=>[3,2,6,5,1,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,1,8,2,3,7,6,4]=>[4,6,7,3,2,8,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,2,6,8,4,7,5,3]=>[3,5,7,4,8,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,5,6,2,7,4,3]=>[3,4,7,2,6,5,8,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,4,1,7,2,5,6,3]=>[3,6,5,2,7,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[3,2,7,6,5,8,1,4]=>[4,1,8,5,6,7,2,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[1,2,3,4,5,6,7,8,11,9,10]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[11,1,2,3,4,5,6,7,8,9,10]=>1
[3,5,8,7,6,4,1,2]=>[2,1,4,6,7,8,5,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[4,1,8,5,7,6,2,3]=>[3,2,6,7,5,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[3,2,1,4,5,8,6,7]=>[7,6,8,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>1
[8,1,2,6,7,3,4,5]=>[5,4,3,7,6,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[9,1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[6,8,7,1,5,4,3,2]=>[2,3,4,5,1,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[8,7,4,6,5,1,3,2]=>[2,3,1,5,6,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[9,8,7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[9,8,7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[9,8,7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>7
[10,9,1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,7,1,6,5,4,3,2]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,7,6,1,5,4,3,2]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,7,6,5,1,4,3,2]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[10,9,8,7,6,5,4,1,3,2]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[10,9,8,7,6,5,4,3,1,2]=>8
[1,7,2,8,5,4,3,6]=>[6,3,4,5,8,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,1,3,7,2,5,8,4]=>[4,8,5,2,7,3,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[8,1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[2,6,8,1,5,4,3,7]=>[7,3,4,5,1,8,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,4,7,8,2,1,3,6]=>[6,3,1,2,8,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[2,4,1,8,7,6,3,5]=>[5,3,6,7,8,1,4,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,8,3,1,4,5,6,2]=>[2,6,5,4,1,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,4,8,2,6,7,5,3]=>[3,5,7,6,2,8,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,8,7,2,5,6,3]=>[3,6,5,2,7,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,5,6,3,7,4,1,8]=>[8,1,4,7,3,6,5,2]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[5,2,1,7,8,4,3,6]=>[6,3,4,8,7,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,7,8,2,4,1,3,6]=>[6,3,1,4,2,8,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[2,8,4,1,7,3,6,5]=>[5,6,3,7,1,4,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,7,5,2,8,6,3]=>[3,6,8,2,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,4,7,5,8,6,3]=>[3,6,8,5,7,4,2,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,5,7,4,3,8,6]=>[6,8,3,4,7,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,4,2,6,8,7,5,3]=>[3,5,7,8,6,2,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,7,4,2,3,8,6]=>[6,8,3,2,4,7,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,6,1,4,7,5,2,3]=>[3,2,5,7,4,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,7,1,4,6,5,3,2]=>[2,3,5,6,4,1,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[6,8,7,5,4,3,1,2]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>5
[7,3,6,2,5,8,1,4]=>[4,1,8,5,2,6,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,5,1,6,7,2,3,4]=>[4,3,2,7,6,1,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,6,2,7,3,4,5]=>[5,4,3,7,2,6,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,2,7,4,5,6,3]=>[3,6,5,4,7,2,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,5,4,8,1,3,2,7]=>[7,2,3,1,8,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[6,5,1,4,8,3,2,7]=>[7,2,3,8,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[7,6,5,3,8,2,1,4]=>[4,1,2,8,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,7,6,3,1,5,4,2]=>[2,4,5,1,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[2,5,1,4,7,8,3,6]=>[6,3,8,7,4,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,5,1,6,4,2,7,8]=>[8,7,2,4,6,1,5,3]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[2,1,6,3,5,7,8,4]=>[4,8,7,5,3,6,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[6,8,7,1,4,5,2,3]=>[3,2,5,4,1,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,6,8,7,2,4,5,3]=>[3,5,4,2,7,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,8,7,1,2,4,5,3]=>[3,5,4,2,1,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,6,1,8,5,4,3,7]=>[7,3,4,5,8,1,6,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,1,7,4,5,6,2,3]=>[3,2,6,5,4,7,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,5,4,2,1,8,3,7]=>[7,3,8,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,5,1,2,4,8,3,6]=>[6,3,8,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,8,2,5,4,1,3,7]=>[7,3,1,4,5,2,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,1,3,4,5,8,6,2]=>[2,6,8,5,4,3,1,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,7,6,3,5,2,1,8]=>[8,1,2,5,3,6,7,4]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>0
[1,7,4,5,2,8,6,3]=>[3,6,8,2,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,1,2,3,8,4,7,5]=>[5,7,4,8,3,2,1,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,1,6,7,4,2,5,3]=>[3,5,2,4,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,1,4,7,2,5,3]=>[3,5,2,7,4,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,7,1,4,5,2,3]=>[3,2,5,4,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,4,5,1,2,8,6,3]=>[3,6,8,2,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,7,2,8,4,1,3,6]=>[6,3,1,4,8,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,4,7,5,8,1,6,2]=>[2,6,1,8,5,7,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,8,4,7,5,2,6,3]=>[3,6,2,5,7,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,6,2,8,3,4,7,5]=>[5,7,4,3,8,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[5,7,1,4,8,2,3,6]=>[6,3,2,8,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,5,1,8,4,2,3,6]=>[6,3,2,4,8,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,9,8,2,3,4,5,6,7]=>[7,6,5,4,3,2,8,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,10,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[1,2,6,8,7,3,4,5]=>[5,4,3,7,8,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,3,7,8,4,5,6,2]=>[2,6,5,4,8,7,3,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,1,4,7,6,5,2,3]=>[3,2,5,6,7,4,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[6,1,8,7,4,5,2,3]=>[3,2,5,4,7,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,6,7,2,5,8,3]=>[3,8,5,2,7,6,1,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,5,8,2,3,6,7,4]=>[4,7,6,3,2,8,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[3,1,5,6,8,4,2,7]=>[7,2,4,8,6,5,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[7,2,5,4,8,1,3,6]=>[6,3,1,8,4,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,4,8,7,6,5,2,3]=>[3,2,5,6,7,8,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,4,2,7,6,5,3,1]=>[1,3,5,6,7,2,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>5
[6,8,7,5,2,4,3,1]=>[1,3,4,2,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[2,8,3,4,1,5,6,7]=>[7,6,5,1,4,3,8,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>1
[5,8,6,3,1,4,2,7]=>[7,2,4,1,3,6,8,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[4,8,1,6,7,5,2,3]=>[3,2,5,7,6,1,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[6,8,4,1,7,5,2,3]=>[3,2,5,7,1,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,4,6,7,5,2,3]=>[3,2,5,7,6,4,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,4,1,6,7,2,5,3]=>[3,5,2,7,6,1,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,4,6,7,2,5,3]=>[3,5,2,7,6,4,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,6,4,7,5,3]=>[3,5,7,4,6,2,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,4,1,6,2,7,5,3]=>[3,5,7,2,6,1,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,8,6,1,2,7,5,3]=>[3,5,7,2,1,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,6,2,4,7,5,3]=>[3,5,7,4,2,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,6,1,2,4,7,5,3]=>[3,5,7,4,2,1,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,4,7,3,6,2,1,5]=>[5,1,2,6,3,7,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[10,1,9,2,8,3,7,4,6,5]=>[5,6,4,7,3,8,2,9,1,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[10,9,8,7,6,1,2,3,4,5]=>5
[5,4,7,1,2,3,8,6]=>[6,8,3,2,1,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,2,5,6,8,7,3,4]=>[4,3,7,8,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,3,7,1,2,5,8,4]=>[4,8,5,2,1,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,8,3,2,5,7,4,1]=>[1,4,7,5,2,3,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,1,2,8,6,7,4,3]=>[3,4,7,6,8,2,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[1,2,5,4,7,8,3,6]=>[6,3,8,7,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,7,6,3,5,4,1,2]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[7,8,1,5,2,3,6,4]=>[4,6,3,2,5,1,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,6,3,1,4,2,7,8]=>[8,7,2,4,1,3,6,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[5,2,3,6,7,4,1,8]=>[8,1,4,7,6,3,2,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[8,3,6,5,2,7,4,1]=>[1,4,7,2,5,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,4,8,5,1,2,6,3]=>[3,6,2,1,5,8,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,1,6,5,4,2,3]=>[3,2,4,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[5,6,8,1,2,3,7,4]=>[4,7,3,2,1,8,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,7,8,4,2,1,3,6]=>[6,3,1,2,4,8,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,2,3,4,5,8,9,6,7]=>[7,6,9,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]=>[8,9,1,2,3,4,5,6,7]=>1
[3,6,8,2,5,7,4,1]=>[1,4,7,5,2,8,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,4,1,7,2,5,8,3]=>[3,8,5,2,7,1,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,3,8,5,7,2,4,1]=>[1,4,2,7,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[2,5,1,7,4,8,3,6]=>[6,3,8,4,7,1,5,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,1,7,4,2,8,3,6]=>[6,3,8,2,4,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,1,3,4,5,6,9,7,8]=>[8,7,9,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[9,2,1,3,4,5,6,7,8]=>1
[2,1,3,4,5,6,7,10,8,9]=>[9,8,10,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>1
[6,1,5,8,4,3,2,7]=>[7,2,3,4,8,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,4,8,2,7,6,5,3]=>[3,5,6,7,2,8,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,3,7,8,9,4,5,6]=>[6,5,4,9,8,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]=>[7,8,9,1,2,3,4,5,6]=>1
[1,2,3,4,8,9,10,5,6,7]=>[7,6,5,10,9,8,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]=>[8,9,10,1,2,3,4,5,6,7]=>1
[1,2,7,8,9,10,3,4,5,6]=>[6,5,4,3,10,9,8,7,2,1]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>1
[1,2,6,8,3,4,7,5]=>[5,7,4,3,8,6,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[1,8,2,7,3,5,6,4]=>[4,6,5,3,7,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,6,3,7,2,5,8,4]=>[4,8,5,2,7,3,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,5,4,7,2,8,3,6]=>[6,3,8,2,7,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,6,7,1,5,2,8,3]=>[3,8,2,5,1,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,8,4,5,7,6,2,3]=>[3,2,6,7,5,4,8,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,2,7,4,8,1,3,6]=>[6,3,1,8,4,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,6,4,1,5,3,2]=>[2,3,5,1,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>5
[5,8,2,6,3,7,4,1]=>[1,4,7,3,6,2,8,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,2,5,6,3,7,4,1]=>[1,4,7,3,6,5,2,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,5,3,6,1,4,2,7]=>[7,2,4,1,6,3,5,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,5,6,1,3,4,2,7]=>[7,2,4,3,1,6,5,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,5,6,3,4,2,7]=>[7,2,4,3,6,5,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[3,8,5,6,1,4,2,7]=>[7,2,4,1,6,5,8,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,1,3,8,6,4,2,7]=>[7,2,4,6,8,3,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[5,3,8,1,6,4,2,7]=>[7,2,4,6,1,8,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,5,8,3,6,4,2,7]=>[7,2,4,6,3,8,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[6,8,5,7,3,2,4,1]=>[1,4,2,3,7,5,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[6,8,7,5,4,2,3,1]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>5
[7,2,3,5,1,6,8,4]=>[4,8,6,1,5,3,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,5,2,1,4,8,3,7]=>[7,3,8,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[2,1,6,5,8,4,3,7]=>[7,3,4,8,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[6,2,1,5,4,3,8,7]=>[7,8,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,5,4,2,3,7,8,6]=>[6,8,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,5,8,3,2,7,4,1]=>[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,8,5,1,2,4,3,6]=>[6,3,4,2,1,5,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,6,1,3,5,7,8,4]=>[4,8,7,5,3,1,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[3,8,5,7,6,4,1,2]=>[2,1,4,6,7,5,8,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,5,7,6,3,4,2]=>[2,4,3,6,7,5,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,5,6,3,7,8,4,2]=>[2,4,8,7,3,6,5,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,2,1,8,5,4,3,6]=>[6,3,4,5,8,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,6,8,2,3,7,4,1]=>[1,4,7,3,2,8,6,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[8,4,5,7,1,2,6,3]=>[3,6,2,1,7,5,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,4,5,7,8,6,2,3]=>[3,2,6,8,7,5,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,2,5,3,6,1,8,4]=>[4,8,1,6,3,5,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,5,2,8,3,6,7,4]=>[4,7,6,3,8,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[4,5,1,2,7,8,6,3]=>[3,6,8,7,2,1,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,6,7,5,1,2,8,3]=>[3,8,2,1,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[5,6,1,8,2,3,7,4]=>[4,7,3,2,8,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[1,8,3,5,6,4,2,7]=>[7,2,4,6,5,3,8,1]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[4,8,7,1,6,5,2,3]=>[3,2,5,6,1,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,5,8,7,6,3,4,2]=>[2,4,3,6,7,8,5,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,7,4,5,8,6,2,3]=>[3,2,6,8,5,4,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,2,4,1,3,6,5]=>[5,6,3,1,4,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,2,7,8,4,5,6,3]=>[3,6,5,4,8,7,2,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,2,5,6,8,3,7,4]=>[4,7,3,8,6,5,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,1,7,2,8,6,3,4]=>[4,3,6,8,2,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[7,5,1,4,8,2,3,6]=>[6,3,2,8,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,4,2,6,7,5,8,3]=>[3,8,5,7,6,2,4,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[3,8,2,6,5,7,4,1]=>[1,4,7,5,6,2,8,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,6,2,8,5,4,1,3]=>[3,1,4,5,8,2,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[1,8,2,6,7,4,5,3]=>[3,5,4,7,6,2,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,3,4,7,6,5]=>[5,6,7,4,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[8,6,3,2,5,7,4,1]=>[1,4,7,5,2,3,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,3,2,6,1,5,8,4]=>[4,8,5,1,6,2,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[4,1,8,2,5,7,6,3]=>[3,6,7,5,2,8,1,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,4,1,7,2,8,3,6]=>[6,3,8,2,7,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,5,2,4,1,8,3,6]=>[6,3,8,1,4,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,1,2,5,4,3,8,6]=>[6,8,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[3,5,1,6,4,8,2,7]=>[7,2,8,4,6,1,5,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,2,7,5,6,3,4]=>[4,3,6,5,7,2,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[6,4,8,7,5,3,2,1]=>[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[1,8,4,6,7,5,2,3]=>[3,2,5,7,6,4,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,4,7,2,1,3,6,5]=>[5,6,3,1,2,7,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,8,7,2,5,6,3]=>[3,6,5,2,7,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,7,2,8,3,5,6,4]=>[4,6,5,3,8,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,6,4,7,5,2,3]=>[3,2,5,7,4,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,6,4,7,5,3]=>[3,5,7,4,6,8,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,7,5,4,8,2,3,6]=>[6,3,2,8,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,2,7,4,1,3,8,6]=>[6,8,3,1,4,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,7,1,2,5,6,3,4]=>[4,3,6,5,2,1,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[8,1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[3,1,2,4,5,6,7,9,8]=>[8,9,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[4,7,8,5,1,6,2,3]=>[3,2,6,1,5,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,5,2,3,8,6,7,4]=>[4,7,6,8,3,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,5,2,4,1,3,8,7]=>[7,8,3,1,4,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,6,3,2,5,1,8,4]=>[4,8,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,7,4,5,1,2,6,3]=>[3,6,2,1,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,4,1,7,5,2,6,3]=>[3,6,2,5,7,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,5,2,6,8,3,7,4]=>[4,7,3,8,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,4,7,5,6,2,3]=>[3,2,6,5,7,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,7,4,6,5,1,2,3]=>[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[2,7,1,8,5,4,3,6]=>[6,3,4,5,8,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,1,2,8,5,4,3,6]=>[6,3,4,5,8,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,2,1,8,5,4,3,7]=>[7,3,4,5,8,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,8,2,6,7,3,4,1]=>[1,4,3,7,6,2,8,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[1,2,5,7,8,3,6,4]=>[4,6,3,8,7,5,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,5,4,8,2,1,3,7]=>[7,3,1,2,8,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,3,6,2,1,5,8,7]=>[7,8,5,1,2,6,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[6,2,1,5,4,8,3,7]=>[7,3,8,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,5,7,6,3,4,2,1]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>5
[3,1,5,6,4,2,8,7]=>[7,8,2,4,6,5,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[2,1,8,4,7,6,3,5]=>[5,3,6,7,4,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,4,7,1,2,6,5,3]=>[3,5,6,2,1,7,4,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,3,4,7,5,8,6,2]=>[2,6,8,5,7,4,3,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[6,1,4,8,2,7,5,3]=>[3,5,7,2,8,4,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,3,4,5,1,8,6,2]=>[2,6,8,1,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,5,8,7,1,6,2,3]=>[3,2,6,1,7,8,5,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,8,2,4,6,7,5,3]=>[3,5,7,6,4,2,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,5,8,1,6,2,3,4]=>[4,3,2,6,1,8,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,8,5,3,2,7,4,1]=>[1,4,7,2,3,5,8,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[1,3,6,2,7,5,8,4]=>[4,8,5,7,2,6,3,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[4,1,7,8,5,2,6,3]=>[3,6,2,5,8,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[3,1,5,6,4,8,2,7]=>[7,2,8,4,6,5,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,2,3,6,4,7,5]=>[5,7,4,6,3,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,1,8,5,4,3,2,7]=>[7,2,3,4,5,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[5,3,6,4,1,8,2,7]=>[7,2,8,1,4,6,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,5,6,2,7,3,4]=>[4,3,7,2,6,5,1,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,4,8,2,7,5,6,3]=>[3,6,5,7,2,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,8,3,7,6,2,1,5]=>[5,1,2,6,7,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>3
[1,8,7,6,2,3,5,4]=>[4,5,3,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[8,7,5,1,6,4,3,2]=>[2,3,4,6,1,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[7,3,1,8,4,5,6,2]=>[2,6,5,4,8,1,3,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,1,2,6,8,7,4,3]=>[3,4,7,8,6,2,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[8,1,5,7,3,6,4,2]=>[2,4,6,3,7,5,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,2,5,8,1,4,3,6]=>[6,3,4,1,8,5,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,7,5,8,6,2,3,4]=>[4,3,2,6,8,5,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,1,7,3,5,8,2,4]=>[4,2,8,5,3,7,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[8,1,4,2,7,6,5,3]=>[3,5,6,7,2,4,1,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[5,3,1,6,4,8,2,7]=>[7,2,8,4,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,4,2,7,5,6,3]=>[3,6,5,7,2,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[5,7,1,4,2,8,3,6]=>[6,3,8,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,7,2,4,1,8,3,6]=>[6,3,8,1,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[2,8,1,4,7,6,3,5]=>[5,3,6,7,4,1,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,8,1,2,6,3,7,4]=>[4,7,3,6,2,1,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[1,7,5,2,3,8,6,4]=>[4,6,8,3,2,5,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,7,6,2,3,8,1,4]=>[4,1,8,3,2,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,5,3,7,2,4,1,8]=>[8,1,4,2,7,3,5,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[1,8,2,3,5,7,6,4]=>[4,6,7,5,3,2,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[7,6,8,2,1,5,4,3]=>[3,4,5,1,2,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[5,1,7,8,4,2,3,6]=>[6,3,2,4,8,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[2,5,3,8,6,7,4,1]=>[1,4,7,6,8,3,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[4,2,8,7,6,1,3,5]=>[5,3,1,6,7,8,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,2,8,5,4,1,3,6]=>[6,3,1,4,5,8,2,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,2,6,5,1,4,3,7]=>[7,3,4,1,5,6,2,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[8,6,2,5,1,4,3,7]=>[7,3,4,1,5,2,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,8,1,7,6,2,3,4]=>[4,3,2,6,7,1,8,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,4,8,6,7,2,5,3]=>[3,5,2,7,6,8,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,1,2,8,6,7,3,4]=>[4,3,7,6,8,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,6,8,5,2,4,1,3]=>[3,1,4,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>3
[5,1,2,8,6,3,7,4]=>[4,7,3,6,8,2,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,1,7,4,5,2,8,3]=>[3,8,2,5,4,7,1,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[5,2,7,1,4,8,3,6]=>[6,3,8,4,1,7,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,8,7,4,1,5,2,3]=>[3,2,5,1,4,7,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[7,8,5,1,2,3,6,4]=>[4,6,3,2,1,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,6,5,2,7,4,1,8]=>[8,1,4,7,2,5,6,3]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[1,4,7,5,8,6,2,3]=>[3,2,6,8,5,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,5,7,6,3,4,1,2]=>[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,5,8,7,3,6,4,2]=>[2,4,6,3,7,8,5,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[7,5,8,1,2,3,6,4]=>[4,6,3,2,1,8,5,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,2,8,7,4,6,5,3]=>[3,5,6,4,7,8,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,7,2,3,8,5,6,4]=>[4,6,5,8,3,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,4,2,5,7,8,6,3]=>[3,6,8,7,5,2,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,5,3,7,6,4,2]=>[2,4,6,7,3,5,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,2,7,4,1,6,3,5]=>[5,3,6,1,4,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[8,4,1,7,5,6,2,3]=>[3,2,6,5,7,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[4,2,1,8,7,3,6,5]=>[5,6,3,7,8,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[1,4,8,5,2,7,6,3]=>[3,6,7,2,5,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,6,2,8,7,4,5,3]=>[3,5,4,7,8,2,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,5,6,2,8,3,7,4]=>[4,7,3,8,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[3,7,5,6,4,2,1,8]=>[8,1,2,4,6,5,7,3]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[1,4,6,7,5,8,2,3]=>[3,2,8,5,7,6,4,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[4,3,2,8,6,1,5,7]=>[7,5,1,6,8,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[7,5,2,4,1,3,8,6]=>[6,8,3,1,4,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,3,1,2,7,5,8,4]=>[4,8,5,7,2,1,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,7,2,4,5,8,6,3]=>[3,6,8,5,4,2,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,4,6,8,7,2,5,3]=>[3,5,2,7,8,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,7,6,4,5,3]=>[3,5,4,6,7,8,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,2,6,8,7,4,5,3]=>[3,5,4,7,8,6,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,2,8,6,7,4,5,3]=>[3,5,4,7,6,8,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,8,1,4,2,3,6]=>[6,3,2,4,1,8,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,7,1,4,5,2,8,3]=>[3,8,2,5,4,1,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[5,7,2,6,3,1,8,4]=>[4,8,1,3,6,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[6,7,5,1,3,2,8,4]=>[4,8,2,3,1,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[3,7,4,5,8,6,1,2]=>[2,1,6,8,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,2,4,7,8,1,3,6]=>[6,3,1,8,7,4,2,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[3,1,4,7,5,8,6,2]=>[2,6,8,5,7,4,1,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,2,7,4,8,5,6,3]=>[3,6,5,8,4,7,2,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[9,1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[10,1,2,3,4,5,6,9,8,7]=>[7,8,9,6,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>3
[4,6,7,5,1,8,2,3]=>[3,2,8,1,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,3,7,5,1,2,8,4]=>[4,8,2,1,5,7,3,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,2,3,4,5,9,8,6,7]=>[7,6,8,9,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,2,3,4,9,8,7,5,6]=>[6,5,7,8,9,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[1,2,3,9,8,7,6,4,5]=>[5,4,6,7,8,9,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[5,7,1,2,4,8,3,6]=>[6,3,8,4,2,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[5,7,8,1,2,3,6,4]=>[4,6,3,2,1,8,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[5,8,6,1,7,2,3,4]=>[4,3,2,7,1,6,8,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,7,2,3,4,6,5]=>[5,6,4,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[5,8,7,3,6,4,1,2]=>[2,1,4,6,3,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,1,7,6,2,5,4,3]=>[3,4,5,2,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>5
[2,6,5,7,8,1,3,4]=>[4,3,1,8,7,5,6,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[1,8,7,6,2,4,5,3]=>[3,5,4,2,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[7,2,5,3,1,6,8,4]=>[4,8,6,1,3,5,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[4,7,8,5,1,2,6,3]=>[3,6,2,1,5,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,1,5,8,2,4,3,6]=>[6,3,4,2,8,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,4,7,2,1,6,3,5]=>[5,3,6,1,2,7,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[9,8,1,7,2,3,4,5,6]=>[6,5,4,3,2,7,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[8,7,3,5,6,4,1,2]=>[2,1,4,6,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[4,6,1,7,2,5,8,3]=>[3,8,5,2,7,1,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[5,3,1,6,8,4,2,7]=>[7,2,4,8,6,1,3,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[8,1,4,5,7,2,6,3]=>[3,6,2,7,5,4,1,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,1,5,7,2,6,3,4]=>[4,3,6,2,7,5,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[5,6,3,7,8,1,4,2]=>[2,4,1,8,7,3,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,5,3,6,4,2,1,8]=>[8,1,2,4,6,3,5,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[1,5,2,6,8,7,3,4]=>[4,3,7,8,6,2,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[9,1,8,2,7,3,6,4,5]=>[5,4,6,3,7,2,8,1,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[2,5,6,7,3,4,1,8]=>[8,1,4,3,7,6,5,2]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>0
[6,1,7,5,8,3,2,4]=>[4,2,3,8,5,7,1,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[7,4,5,1,8,6,2,3]=>[3,2,6,8,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,5,6,2,8,7,3,4]=>[4,3,7,8,2,6,5,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[6,8,4,7,1,2,5,3]=>[3,5,2,1,7,4,8,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,8,7,6,3,5,4,2]=>[2,4,5,3,6,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,8,5,7,6,4,3,2]=>[2,3,4,6,7,5,8,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[1,6,8,2,7,3,4,5]=>[5,4,3,7,2,8,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[6,8,1,5,4,3,2,7]=>[7,2,3,4,5,1,8,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>1
[1,8,6,7,2,4,5,3]=>[3,5,4,2,7,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,7,4,5,8,1,6,2]=>[2,6,1,8,5,4,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[5,6,1,2,8,7,3,4]=>[4,3,7,8,2,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[8,1,7,5,2,6,3,4]=>[4,3,6,2,5,7,1,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,3,8,6,2,1,5,7]=>[7,5,1,2,6,8,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[2,7,5,1,4,3,8,6]=>[6,8,3,4,1,5,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[7,5,8,1,2,4,3,6]=>[6,3,4,2,1,8,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,9,8,7,6,5,2,3,4]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[2,8,4,7,1,3,6,5]=>[5,6,3,1,7,4,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[7,5,8,4,2,1,3,6]=>[6,3,1,2,4,8,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,6,1,3,4,8,2,7]=>[7,2,8,4,3,1,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[7,8,4,6,5,3,2,1]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>5
[1,6,7,2,8,3,9,4,10,5]=>[5,10,4,9,3,8,2,7,6,1]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>1
[1,8,2,7,6,3,5,4]=>[4,5,3,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,5,2,6,8,7,4,3]=>[3,4,7,8,6,2,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[5,4,2,1,7,3,8,6]=>[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[1,5,6,7,3,8,4,2]=>[2,4,8,3,7,6,5,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[6,4,7,1,5,2,8,3]=>[3,8,2,5,1,7,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[4,5,1,7,2,8,6,3]=>[3,6,8,2,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,6,4,7,2,5,3]=>[3,5,2,7,4,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,5,1,7,8,2,6,3]=>[3,6,2,8,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,6,7,3,5,8,2,4]=>[4,2,8,5,3,7,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[6,4,1,7,5,8,2,3]=>[3,2,8,5,7,1,4,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[6,1,8,4,7,5,2,3]=>[3,2,5,7,4,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,6,1,8,7,2,3,4]=>[4,3,2,7,8,1,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[2,5,8,6,3,7,4,1]=>[1,4,7,3,6,8,5,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[1,8,7,5,2,6,3,4]=>[4,3,6,2,5,7,8,1]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[4,8,7,2,6,1,3,5]=>[5,3,1,6,2,7,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[5,4,1,2,3,7,8,6]=>[6,8,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[6,8,7,4,5,3,2,1]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>5
[1,6,8,7,4,5,2,3]=>[3,2,5,4,7,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,1,2,3,7,4,6,5]=>[5,6,4,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>3
[7,2,3,5,6,1,8,4]=>[4,8,1,6,5,3,2,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[3,1,2,4,5,6,9,7,8]=>[8,7,9,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[2,5,7,6,3,8,1,4]=>[4,1,8,3,6,7,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[1,3,4,2,5,6,7,8,9]=>[9,8,7,6,5,2,4,3,1]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]=>[3,4,1,2,5,6,7,8,9]=>0
[7,3,2,6,5,8,1,4]=>[4,1,8,5,6,2,3,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[5,1,6,8,7,2,4,3]=>[3,4,2,7,8,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[7,1,5,4,2,3,8,6]=>[6,8,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[3,1,8,7,5,6,4,2]=>[2,4,6,5,7,8,1,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,1,8,7,6,3,4,2]=>[2,4,3,6,7,8,1,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,8,7,2,6,4,5,3]=>[3,5,4,6,2,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,8,4,7,6,2,5,3]=>[3,5,2,6,7,4,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[8,7,3,5,1,6,4,2]=>[2,4,6,1,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,4,8,7,6,2,5,3]=>[3,5,2,6,7,8,4,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,7,4,2,8,5,6,3]=>[3,6,5,8,2,4,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,6,3,5,2,1,8,4]=>[4,8,1,2,5,3,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[5,1,8,6,2,7,4,3]=>[3,4,7,2,6,8,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[3,4,1,5,7,8,6,2]=>[2,6,8,7,5,1,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[7,5,6,2,3,1,8,4]=>[4,8,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,5,2,3,6,1,8,4]=>[4,8,1,6,3,2,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[5,4,7,2,1,3,8,6]=>[6,8,3,1,2,7,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[5,6,3,1,8,4,2,7]=>[7,2,4,8,1,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[7,3,2,8,4,5,6,1]=>[1,6,5,4,8,2,3,7]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[3,2,7,6,5,1,8,4]=>[4,8,1,5,6,7,2,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[6,8,5,2,1,4,3,7]=>[7,3,4,1,2,5,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,2,7,5,8,6,3,4]=>[4,3,6,8,5,7,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[6,3,2,5,7,4,1,8]=>[8,1,4,7,5,2,3,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[5,4,2,7,1,3,8,6]=>[6,8,3,1,7,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,1,5,6,2,7,4,3]=>[3,4,7,2,6,5,1,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[6,2,1,5,3,7,8,4]=>[4,8,7,3,5,1,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[7,8,1,2,5,4,3,6]=>[6,3,4,5,2,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[8,1,7,2,6,5,3,4]=>[4,3,5,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,4,7,8,5,2,6,3]=>[3,6,2,5,8,7,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,1,5,7,2,8,6,3]=>[3,6,8,2,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[2,8,6,5,4,1,3,7]=>[7,3,1,4,5,6,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,8,7,2,1,3,6,5]=>[5,6,3,1,2,7,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[3,7,2,1,6,5,8,4]=>[4,8,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[5,1,3,6,8,4,2,7]=>[7,2,4,8,6,3,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>1
[4,5,1,7,8,6,2,3]=>[3,2,6,8,7,1,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[6,8,7,5,3,4,2,1]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[7,5,2,1,8,4,3,6]=>[6,3,4,8,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[8,3,7,6,5,4,1,2]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>5
[1,4,6,8,7,5,2,3]=>[3,2,5,7,8,6,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,7,2,4,5,8,6,1]=>[1,6,8,5,4,2,7,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[3,7,6,2,5,1,8,4]=>[4,8,1,5,2,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[5,1,7,8,2,6,3,4]=>[4,3,6,2,8,7,1,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,6,2,4,7,5,3]=>[3,5,7,4,2,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[5,7,3,6,4,2,1,8]=>[8,1,2,4,6,3,7,5]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>0
[7,4,6,5,3,2,1,8]=>[8,1,2,3,5,6,4,7]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>0
[4,1,2,5,7,8,6,3]=>[3,6,8,7,5,2,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[7,8,2,6,5,4,3,1]=>[1,3,4,5,6,2,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>5
[1,7,2,4,8,5,6,3]=>[3,6,5,8,4,2,7,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,2,6,1,4,3,5]=>[5,3,4,1,6,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>3
[6,2,1,3,5,7,8,4]=>[4,8,7,5,3,1,2,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>1
[5,4,7,1,8,2,3,6]=>[6,3,2,8,1,7,4,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[4,8,3,2,1,6,5,7]=>[7,5,6,1,2,3,8,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>1
[1,6,7,5,3,2,8,4]=>[4,8,2,3,5,7,6,1]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>1
[1,6,2,8,7,3,4,5]=>[5,4,3,7,8,2,6,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[4,8,7,1,6,2,5,3]=>[3,5,2,6,1,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[7,8,1,4,5,6,2,3]=>[3,2,6,5,4,1,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[8,7,1,3,5,6,4,2]=>[2,4,6,5,3,1,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[8,1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>5
[3,5,8,7,6,1,4,2]=>[2,4,1,6,7,8,5,3]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[3,5,6,7,1,8,4,2]=>[2,4,8,1,7,6,5,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[7,4,5,1,8,2,6,3]=>[3,6,2,8,1,5,4,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[4,8,7,1,5,6,2,3]=>[3,2,6,5,1,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[2,6,7,8,3,5,4,1]=>[1,4,5,3,8,7,6,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>3
[6,5,2,4,1,8,3,7]=>[7,3,8,1,4,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[5,7,2,4,1,3,8,6]=>[6,8,3,1,4,2,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,2,5,4,1,8,3,7]=>[7,3,8,1,4,5,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[1,3,2,4,5,6,9,7,8]=>[8,7,9,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[9,3,1,2,4,5,6,7,8]=>1
[2,3,1,4,5,6,9,7,8]=>[8,7,9,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]=>[9,2,3,1,4,5,6,7,8]=>1
[2,1,5,4,7,8,3,6]=>[6,3,8,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>1
[6,8,2,1,5,4,3,7]=>[7,3,4,5,1,2,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[7,5,1,4,2,8,3,6]=>[6,3,8,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[7,1,8,5,2,6,3,4]=>[4,3,6,2,5,8,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[3,7,8,4,5,6,1,2]=>[2,1,6,5,4,8,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[1,2,3,4,9,5,8,6,7]=>[7,6,8,5,9,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[9,8,1,2,3,4,5,6,7]=>2
[1,10,2,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,2,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[10,1,9,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[10,9,1,2,3,4,5,6,7,8]=>2
[5,1,3,6,4,2,7,8]=>[8,7,2,4,6,3,1,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>0
[8,6,3,7,5,4,2,1]=>[1,2,4,5,7,3,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>5
[3,1,7,8,4,5,6,2]=>[2,6,5,4,8,7,1,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[4,7,1,5,2,8,6,3]=>[3,6,8,2,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,4,2,8,6,7,5,3]=>[3,5,7,6,8,2,4,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[2,5,7,3,6,1,8,4]=>[4,8,1,6,3,7,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[8,7,6,2,1,5,4,3]=>[3,4,5,1,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>5
[9,1,8,7,6,5,4,2,3]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[1,7,2,5,8,3,6,4]=>[4,6,3,8,5,2,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,7,3,5,6,4,2]=>[2,4,6,5,3,7,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[5,6,8,1,2,7,3,4]=>[4,3,7,2,1,8,6,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[7,5,2,6,8,3,1,4]=>[4,1,3,8,6,2,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,6,3,2,1,5,8,4]=>[4,8,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>1
[8,6,5,3,2,7,4,1]=>[1,4,7,2,3,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[5,7,2,6,8,3,1,4]=>[4,1,3,8,6,2,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[3,2,7,4,5,8,6,1]=>[1,6,8,5,4,7,2,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>2
[6,1,8,2,4,7,5,3]=>[3,5,7,4,2,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,4,5,2,7,8,6,3]=>[3,6,8,7,2,5,4,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[5,1,2,8,7,3,6,4]=>[4,6,3,7,8,2,1,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>3
[1,6,7,4,5,8,2,3]=>[3,2,8,5,4,7,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[1,5,6,8,7,2,4,3]=>[3,4,2,7,8,6,5,1]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>3
[2,7,3,5,6,8,1,4]=>[4,1,8,6,5,3,7,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[7,1,4,8,2,5,6,3]=>[3,6,5,2,8,4,1,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,9,8,7,6,2,3,4,5]=>[5,4,3,2,6,7,8,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[1,10,9,8,7,6,5,2,3,4]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>6
[1,5,4,7,8,2,3,6]=>[6,3,2,8,7,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[9,8,7,6,1,2,3,5,4]=>[4,5,3,2,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[9,8,7,6,5,1,4,2,3]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[9,8,7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[8,6,7,1,2,4,5,3]=>[3,5,4,2,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[4,1,7,8,5,6,2,3]=>[3,2,6,5,8,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,4,8,2,5,7,6,3]=>[3,6,7,5,2,8,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[8,4,7,5,6,1,2,3]=>[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[1,4,2,8,7,5,6,3]=>[3,6,5,7,8,2,4,1]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>3
[6,8,5,2,4,1,3,7]=>[7,3,1,4,2,5,8,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>1
[4,6,8,7,1,2,5,3]=>[3,5,2,1,7,8,6,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[1,7,3,4,5,8,6,2]=>[2,6,8,5,4,3,7,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>2
[8,7,1,5,6,3,4,2]=>[2,4,3,6,5,1,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>4
[1,2,3,6,7,8,9,4,10,5]=>[5,10,4,9,8,7,6,3,2,1]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]=>[6,7,8,9,10,1,2,3,4,5]=>1
[5,1,8,6,2,3,7,4]=>[4,7,3,2,6,8,1,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[4,1,2,8,6,7,5,3]=>[3,5,7,6,8,2,1,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[3,6,2,8,5,7,4,1]=>[1,4,7,5,8,2,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[7,1,2,8,5,3,6,4]=>[4,6,3,5,8,2,1,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[8,1,2,6,3,4,7,5]=>[5,7,4,3,6,2,1,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>2
[8,5,2,7,6,4,3,1]=>[1,3,4,6,7,2,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>5
[5,6,8,2,7,3,4,1]=>[1,4,3,7,2,8,6,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>3
[10,1,2,3,4,9,8,5,6,7]=>[7,6,5,8,9,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>3
[9,1,2,8,7,6,5,4,3]=>[3,4,5,6,7,8,2,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[1,8,2,7,6,5,3,4]=>[4,3,5,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[1,8,7,4,6,5,2,3]=>[3,2,5,6,4,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[4,1,7,5,8,2,6,3]=>[3,6,2,8,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>2
[1,8,7,2,4,6,5,3]=>[3,5,6,4,2,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>4
[1,7,8,5,2,3,6,4]=>[4,6,3,2,5,8,7,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>2
[1,8,7,6,2,5,3,4]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>4
[9,8,7,1,6,2,3,4,5]=>[5,4,3,2,6,1,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>4
[9,8,7,6,1,5,2,3,4]=>[4,3,2,5,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[1,6,4,7,5,2,8,3]=>[3,8,2,5,7,4,6,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>1
[9,8,7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[10,9,8,7,1,6,2,5,3,4]=>[4,3,5,2,6,1,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[10,9,8,7,6,5,1,2,3,4]=>6
[7,8,3,6,5,4,2,1]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>5
[10,9,8,7,6,1,5,2,4,3]=>[3,4,2,5,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[9,8,7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[10,9,8,7,6,1,2,5,4,3]=>[3,4,5,2,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[10,9,8,7,6,5,4,1,2,3]=>7
[1,2,8,3,4,5,6,7,9]=>[9,7,6,5,4,3,8,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[8,1,2,3,4,5,6,7,9]=>0
[1,2,7,3,4,5,6,8,9]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>0
[1,2,3,7,4,5,6,8,9]=>[9,8,6,5,4,7,3,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[7,1,2,3,4,5,6,8,9]=>0
[1,2,9,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,9,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[9,1,2,3,4,5,6,7,8,10]=>0
[3,6,2,5,7,4,1,8]=>[8,1,4,7,5,2,6,3]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>0
[5,6,3,7,8,4,1,2]=>[2,1,4,8,7,3,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>2
[8,3,6,2,5,7,4,1]=>[1,4,7,5,2,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>3
[9,8,1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[9,8,7,1,2,6,5,4,3]=>[3,4,5,6,2,1,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>6
[9,8,1,7,2,6,3,5,4]=>[4,5,3,6,2,7,1,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[9,1,2,3,4,8,7,5,6]=>[6,5,7,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[1,5,2,4,3,7,8,6]=>[6,8,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>1
[1,6,8,2,4,7,5,3]=>[3,5,7,4,2,8,6,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>3
[8,5,6,1,2,3,7,4]=>[4,7,3,2,1,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>2
[5,2,3,7,6,8,1,4]=>[4,1,8,6,7,3,2,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>1
[9,1,8,2,7,3,6,5,4]=>[4,5,6,3,7,2,8,1,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>5
[9,1,2,3,4,8,5,7,6]=>[6,7,5,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[9,8,7,1,2,3,4,5,6]=>3
[10,1,2,3,4,5,9,8,6,7]=>[7,6,8,9,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[10,9,8,1,2,3,4,5,6,7]=>3
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Description
The number of global descents of a permutation.
The global descents are the integers in the set
C(π)={i∈[n−1]:∀1≤j≤i<k≤n:π(j)>π(k)}.
In particular, if i∈C(π) then i is a descent.
For the number of global ascents, see St000234The number of global ascents of a permutation..
The global descents are the integers in the set
C(π)={i∈[n−1]:∀1≤j≤i<k≤n:π(j)>π(k)}.
In particular, if i∈C(π) then i is a descent.
For the number of global ascents, see St000234The number of global ascents of a permutation..
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 132-avoiding permutation
Description
Return a 132-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the maximal element of the Sylvester class.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
The reverse of a permutation σ of length n is given by τ with τ(i)=σ(n+1−i).
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