Identifier
Mp00061:
Permutations
—to increasing tree⟶
Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00130: Permutations —descent tops⟶ Binary words
Images
=>
Cc0010;cc-rep-1
[1]=>[.,.]=>[1]=>[1]=>
[1,2]=>[.,[.,.]]=>[2,1]=>[1,2]=>0
[2,1]=>[[.,.],.]=>[1,2]=>[2,1]=>1
[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1]=>[1,2,3]=>00
[1,3,2]=>[.,[[.,.],.]]=>[2,3,1]=>[1,3,2]=>01
[2,1,3]=>[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>10
[2,3,1]=>[[.,[.,.]],.]=>[2,1,3]=>[3,1,2]=>01
[3,1,2]=>[[.,.],[.,.]]=>[3,1,2]=>[2,1,3]=>10
[3,2,1]=>[[[.,.],.],.]=>[1,2,3]=>[3,2,1]=>11
[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]=>[1,2,3,4]=>000
[1,2,4,3]=>[.,[.,[[.,.],.]]]=>[3,4,2,1]=>[1,2,4,3]=>001
[1,3,2,4]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>010
[1,3,4,2]=>[.,[[.,[.,.]],.]]=>[3,2,4,1]=>[1,4,2,3]=>001
[1,4,2,3]=>[.,[[.,.],[.,.]]]=>[4,2,3,1]=>[1,3,2,4]=>010
[1,4,3,2]=>[.,[[[.,.],.],.]]=>[2,3,4,1]=>[1,4,3,2]=>011
[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>100
[2,1,4,3]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101
[2,3,1,4]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>010
[2,3,4,1]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]=>[4,1,2,3]=>001
[2,4,1,3]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>010
[2,4,3,1]=>[[.,[[.,.],.]],.]=>[2,3,1,4]=>[4,1,3,2]=>011
[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>100
[3,1,4,2]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101
[3,2,1,4]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>110
[3,2,4,1]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>101
[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[4,2,1,3]=>[3,1,2,4]=>010
[3,4,2,1]=>[[[.,[.,.]],.],.]=>[2,1,3,4]=>[4,3,1,2]=>011
[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[4,3,1,2]=>[2,1,3,4]=>100
[4,1,3,2]=>[[.,.],[[.,.],.]]=>[3,4,1,2]=>[2,1,4,3]=>101
[4,2,1,3]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>110
[4,2,3,1]=>[[[.,.],[.,.]],.]=>[3,1,2,4]=>[4,2,1,3]=>101
[4,3,1,2]=>[[[.,.],.],[.,.]]=>[4,1,2,3]=>[3,2,1,4]=>110
[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4]=>[4,3,2,1]=>111
[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]=>[1,2,3,4,5]=>0000
[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]=>[4,5,3,2,1]=>[1,2,3,5,4]=>0001
[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>0010
[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]=>[4,3,5,2,1]=>[1,2,5,3,4]=>0001
[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]=>[5,3,4,2,1]=>[1,2,4,3,5]=>0010
[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]=>[3,4,5,2,1]=>[1,2,5,4,3]=>0011
[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>0100
[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>0101
[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>0010
[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]=>[4,3,2,5,1]=>[1,5,2,3,4]=>0001
[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>0010
[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]=>[3,4,2,5,1]=>[1,5,2,4,3]=>0011
[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>0100
[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>0101
[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>0101
[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]=>[5,3,2,4,1]=>[1,4,2,3,5]=>0010
[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]=>[3,2,4,5,1]=>[1,5,4,2,3]=>0011
[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]=>[5,4,2,3,1]=>[1,3,2,4,5]=>0100
[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]=>[4,5,2,3,1]=>[1,3,2,5,4]=>0101
[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]=>[4,2,3,5,1]=>[1,5,3,2,4]=>0101
[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]]=>[5,2,3,4,1]=>[1,4,3,2,5]=>0110
[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]=>[2,3,4,5,1]=>[1,5,4,3,2]=>0111
[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000
[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1001
[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011
[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0010
[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]=>[5,1,2,3,4]=>0001
[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0010
[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]=>[3,4,2,1,5]=>[5,1,2,4,3]=>0011
[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>0110
[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>0101
[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0010
[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]=>[3,2,4,1,5]=>[5,1,4,2,3]=>0011
[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[2,5,3,1,4]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>0110
[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]=>[4,2,3,1,5]=>[5,1,3,2,4]=>0101
[2,5,4,1,3]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>0110
[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]=>[2,3,4,1,5]=>[5,1,4,3,2]=>0111
[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000
[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1001
[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011
[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>1001
[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>1011
[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0110
[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>0101
[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]=>[5,3,2,1,4]=>[4,1,2,3,5]=>0010
[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]=>[5,4,1,2,3]=>0011
[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0110
[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>0101
[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]=>[5,2,3,1,4]=>[4,1,3,2,5]=>0110
[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]=>[2,3,1,4,5]=>[5,4,1,3,2]=>0111
[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000
[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[4,1,3,5,2]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1001
[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011
[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[4,2,1,5,3]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>1001
[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>1011
[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110
[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>1101
[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>1011
[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[5,4,2,1,3]=>[3,1,2,4,5]=>0100
[4,5,1,3,2]=>[[.,[.,.]],[[.,.],.]]=>[4,5,2,1,3]=>[3,1,2,5,4]=>0101
[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0110
[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]=>[4,2,1,3,5]=>[5,3,1,2,4]=>0101
[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[5,2,1,3,4]=>[4,3,1,2,5]=>0110
[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]=>[5,4,3,1,2]=>0111
[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[5,4,3,1,2]=>[2,1,3,4,5]=>1000
[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]=>[4,5,3,1,2]=>[2,1,3,5,4]=>1001
[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]=>[4,3,5,1,2]=>[2,1,5,3,4]=>1001
[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]=>[5,3,4,1,2]=>[2,1,4,3,5]=>1010
[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]=>[3,4,5,1,2]=>[2,1,5,4,3]=>1011
[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[5,2,1,4,3]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[4,3,1,2,5]=>[5,2,1,3,4]=>1001
[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]=>[3,4,1,2,5]=>[5,2,1,4,3]=>1011
[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110
[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>1101
[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[5,3,1,2,4]=>[4,2,1,3,5]=>1010
[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]=>[3,1,2,4,5]=>[5,4,2,1,3]=>1011
[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[5,4,1,2,3]=>[3,2,1,4,5]=>1100
[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]=>[4,5,1,2,3]=>[3,2,1,5,4]=>1101
[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110
[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]=>[4,1,2,3,5]=>[5,3,2,1,4]=>1101
[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[5,1,2,3,4]=>[4,3,2,1,5]=>1110
[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]=>[5,4,3,2,1]=>1111
[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>00000
[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>00001
[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>00010
[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>00001
[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>00010
[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>00011
[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101
[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00010
[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>00001
[1,2,4,6,3,5]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00010
[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>00011
[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101
[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110
[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>00101
[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>00010
[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>00011
[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>00100
[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>00101
[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110
[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>00101
[1,2,6,5,3,4]=>[.,[.,[[[.,.],.],[.,.]]]]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>00110
[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>00111
[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000
[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001
[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01001
[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011
[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>00010
[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>00001
[1,3,4,6,2,5]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>00010
[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>00011
[1,3,5,2,4,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,3,5,2,6,4]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>00110
[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>00101
[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>00010
[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>00011
[1,3,6,2,4,5]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,3,6,2,5,4]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,3,6,4,2,5]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>00110
[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>00101
[1,3,6,5,2,4]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>00110
[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>00111
[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000
[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001
[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01001
[1,4,2,6,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,4,2,6,5,3]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011
[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01001
[1,4,3,6,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01011
[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,4,5,3,2,6]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>00110
[1,4,5,3,6,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>00101
[1,4,5,6,2,3]=>[.,[[.,[.,[.,.]]],[.,.]]]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>00010
[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>00011
[1,4,6,2,3,5]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,4,6,3,2,5]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>00110
[1,4,6,3,5,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>00101
[1,4,6,5,2,3]=>[.,[[.,[[.,.],.]],[.,.]]]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>00110
[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>00111
[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000
[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001
[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,5,2,4,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01001
[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011
[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,5,3,2,6,4]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01001
[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,5,3,6,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01011
[1,5,4,2,3,6]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01101
[1,5,4,6,2,3]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,5,4,6,3,2]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>01011
[1,5,6,2,3,4]=>[.,[[.,[.,.]],[.,[.,.]]]]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>00100
[1,5,6,2,4,3]=>[.,[[.,[.,.]],[[.,.],.]]]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>00101
[1,5,6,3,2,4]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>00110
[1,5,6,3,4,2]=>[.,[[[.,[.,.]],[.,.]],.]]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>00101
[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>00110
[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>00111
[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>01000
[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>01001
[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,6,2,4,5,3]=>[.,[[.,.],[[.,[.,.]],.]]]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>01001
[1,6,2,5,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>01010
[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>01011
[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,6,3,2,5,4]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,6,3,4,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>01001
[1,6,3,5,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>01011
[1,6,4,2,3,5]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,6,4,2,5,3]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,6,4,3,2,5]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01101
[1,6,4,5,2,3]=>[.,[[[.,.],[.,.]],[.,.]]]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>01010
[1,6,4,5,3,2]=>[.,[[[[.,.],[.,.]],.],.]]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>01011
[1,6,5,2,3,4]=>[.,[[[.,.],.],[.,[.,.]]]]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>01100
[1,6,5,2,4,3]=>[.,[[[.,.],.],[[.,.],.]]]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>01101
[1,6,5,3,2,4]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[1,6,5,3,4,2]=>[.,[[[[.,.],.],[.,.]],.]]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>01101
[1,6,5,4,2,3]=>[.,[[[[.,.],.],.],[.,.]]]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>01110
[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>01111
[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001
[2,1,3,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001
[2,1,4,6,3,5]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011
[2,1,5,3,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[2,1,5,3,6,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[2,1,5,6,4,3]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011
[2,1,6,3,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[2,1,6,3,5,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[2,1,6,4,3,5]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[2,1,6,5,3,4]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[2,3,1,6,4,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010
[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>00001
[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010
[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>00011
[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110
[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>00101
[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010
[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>00011
[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,3,6,1,5,4]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,3,6,4,1,5]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110
[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>00101
[2,3,6,5,1,4]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110
[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>00111
[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[2,4,1,3,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,4,1,6,5,3]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>01001
[2,4,3,6,1,5]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>01011
[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,4,5,1,6,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,4,5,3,1,6]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110
[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>00101
[2,4,5,6,1,3]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010
[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>00011
[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,4,6,1,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,4,6,3,1,5]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110
[2,4,6,3,5,1]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>00101
[2,4,6,5,1,3]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110
[2,4,6,5,3,1]=>[[.,[[.,[[.,.],.]],.]],.]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>00111
[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[2,5,1,4,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,5,1,4,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[2,5,1,6,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,5,1,6,4,3]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[2,5,3,1,4,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,5,3,1,6,4]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>01001
[2,5,3,6,1,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,5,3,6,4,1]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>01011
[2,5,4,1,3,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,5,4,1,6,3]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110
[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>01101
[2,5,4,6,1,3]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>01011
[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[2,5,6,1,4,3]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[2,5,6,3,1,4]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110
[2,5,6,3,4,1]=>[[.,[[.,[.,.]],[.,.]]],.]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>00101
[2,5,6,4,1,3]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110
[2,5,6,4,3,1]=>[[.,[[[.,[.,.]],.],.]],.]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>00111
[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[2,6,1,3,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[2,6,1,4,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,6,1,4,5,3]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[2,6,1,5,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[2,6,1,5,4,3]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[2,6,3,1,4,5]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,6,3,1,5,4]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,6,3,4,1,5]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>01001
[2,6,3,5,1,4]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,6,3,5,4,1]=>[[.,[[.,.],[[.,.],.]]],.]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>01011
[2,6,4,1,3,5]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,6,4,1,5,3]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,6,4,3,1,5]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110
[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>01101
[2,6,4,5,1,3]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>01011
[2,6,5,1,3,4]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[2,6,5,1,4,3]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[2,6,5,3,1,4]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110
[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>01101
[2,6,5,4,1,3]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110
[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>01111
[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[3,1,2,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001
[3,1,2,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[3,1,2,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[3,1,4,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001
[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[3,1,4,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011
[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[3,1,5,4,2,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[3,1,5,4,6,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[3,1,5,6,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[3,1,5,6,4,2]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011
[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[3,1,6,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[3,1,6,4,2,5]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[3,1,6,4,5,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[3,1,6,5,2,4]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[3,1,6,5,4,2]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[3,2,1,6,4,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>10001
[3,2,4,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>10011
[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[3,2,5,1,6,4]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[3,2,5,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[3,2,5,6,4,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>10011
[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[3,2,6,1,5,4]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[3,2,6,4,1,5]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[3,2,6,4,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[3,2,6,5,1,4]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[3,2,6,5,4,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>10111
[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[3,4,1,6,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,4,1,6,5,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[3,4,2,1,6,5]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,4,2,6,5,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110
[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00101
[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>00010
[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>00011
[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[3,4,6,1,5,2]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[3,4,6,2,1,5]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110
[3,4,6,2,5,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00101
[3,4,6,5,1,2]=>[[.,[.,[[.,.],.]]],[.,.]]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>00110
[3,4,6,5,2,1]=>[[[.,[.,[[.,.],.]]],.],.]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>00111
[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[3,5,1,2,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,5,1,4,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,5,1,6,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[3,5,2,1,4,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[3,5,2,1,6,4]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,5,2,4,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[3,5,2,6,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,5,2,6,4,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[3,5,4,1,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[3,5,4,1,6,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[3,5,4,2,1,6]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110
[3,5,4,2,6,1]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>01101
[3,5,4,6,1,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[3,5,4,6,2,1]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>01011
[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[3,5,6,1,4,2]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[3,5,6,2,1,4]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110
[3,5,6,2,4,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00101
[3,5,6,4,1,2]=>[[.,[[.,[.,.]],.]],[.,.]]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>00110
[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>00111
[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[3,6,1,2,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[3,6,1,4,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[3,6,1,5,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[3,6,1,5,4,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[3,6,2,1,4,5]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[3,6,2,1,5,4]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[3,6,2,4,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[3,6,2,5,4,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[3,6,4,1,2,5]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[3,6,4,1,5,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[3,6,4,2,1,5]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110
[3,6,4,2,5,1]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>01101
[3,6,4,5,1,2]=>[[.,[[.,.],[.,.]]],[.,.]]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>01010
[3,6,4,5,2,1]=>[[[.,[[.,.],[.,.]]],.],.]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>01011
[3,6,5,1,2,4]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[3,6,5,1,4,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[3,6,5,2,1,4]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110
[3,6,5,2,4,1]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>01101
[3,6,5,4,1,2]=>[[.,[[[.,.],.],.]],[.,.]]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>01110
[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>01111
[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001
[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[4,1,3,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[4,1,3,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[4,1,3,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001
[4,1,3,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[4,1,3,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011
[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[4,1,5,6,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[4,1,5,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011
[4,1,6,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[4,1,6,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[4,1,6,5,2,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[4,1,6,5,3,2]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[4,2,1,3,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[4,2,1,5,3,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[4,2,1,5,6,3]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[4,2,1,6,3,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[4,2,1,6,5,3]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>10001
[4,2,3,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>10011
[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[4,2,5,1,6,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[4,2,5,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[4,2,5,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[4,2,5,6,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[4,2,5,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>10011
[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[4,2,6,3,1,5]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[4,2,6,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[4,2,6,5,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[4,2,6,5,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>10111
[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[4,3,1,2,6,5]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[4,3,1,6,2,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[4,3,1,6,5,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[4,3,2,6,5,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[4,3,5,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[4,3,5,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>10011
[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[4,3,6,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[4,3,6,5,1,2]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[4,3,6,5,2,1]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>10111
[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[4,5,1,2,6,3]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[4,5,1,3,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[4,5,1,3,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[4,5,1,6,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[4,5,1,6,3,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[4,5,2,1,3,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[4,5,2,1,6,3]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[4,5,2,3,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[4,5,2,6,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,5,2,6,3,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[4,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110
[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>01101
[4,5,3,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>01011
[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>00100
[4,5,6,1,3,2]=>[[.,[.,[.,.]]],[[.,.],.]]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>00101
[4,5,6,2,1,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110
[4,5,6,2,3,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>00101
[4,5,6,3,1,2]=>[[[.,[.,[.,.]]],.],[.,.]]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>00110
[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>00111
[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[4,6,1,2,5,3]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[4,6,1,3,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[4,6,1,3,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[4,6,1,5,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[4,6,1,5,3,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[4,6,2,1,3,5]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[4,6,2,1,5,3]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[4,6,2,3,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,6,2,3,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[4,6,2,5,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,6,2,5,3,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[4,6,3,1,2,5]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[4,6,3,2,1,5]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110
[4,6,3,2,5,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>01101
[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[4,6,3,5,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>01011
[4,6,5,1,2,3]=>[[.,[[.,.],.]],[.,[.,.]]]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>01100
[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>01101
[4,6,5,2,1,3]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110
[4,6,5,2,3,1]=>[[[.,[[.,.],.]],[.,.]],.]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>01101
[4,6,5,3,1,2]=>[[[.,[[.,.],.]],.],[.,.]]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>01110
[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>01111
[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[5,1,2,4,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001
[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[5,1,3,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[5,1,3,4,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[5,1,3,4,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001
[5,1,3,6,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[5,1,3,6,4,2]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011
[5,1,4,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[5,1,4,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[5,1,4,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[5,1,4,6,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011
[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[5,1,6,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[5,1,6,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[5,1,6,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[5,1,6,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[5,2,1,3,6,4]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[5,2,1,4,3,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,2,1,4,6,3]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[5,2,1,6,3,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,2,1,6,4,3]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,2,3,1,6,4]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>10001
[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[5,2,3,6,4,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>10011
[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,2,4,1,6,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[5,2,4,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[5,2,4,6,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[5,2,4,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>10011
[5,2,6,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,2,6,1,4,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,2,6,3,1,4]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[5,2,6,3,4,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[5,2,6,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>10111
[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,3,1,4,6,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[5,3,1,6,2,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,3,1,6,4,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[5,3,2,1,6,4]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[5,3,2,6,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[5,3,2,6,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,3,4,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>10011
[5,3,6,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,3,6,1,4,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,3,6,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[5,3,6,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[5,3,6,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[5,3,6,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>10111
[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[5,4,1,2,6,3]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[5,4,1,3,2,6]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,4,1,3,6,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[5,4,1,6,3,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[5,4,2,1,6,3]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[5,4,2,6,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11101
[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11011
[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[5,4,6,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[5,4,6,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[5,4,6,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>10111
[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>01000
[5,6,1,2,4,3]=>[[.,[.,.]],[.,[[.,.],.]]]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>01001
[5,6,1,3,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[5,6,1,3,4,2]=>[[.,[.,.]],[[.,[.,.]],.]]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>01001
[5,6,1,4,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>01010
[5,6,1,4,3,2]=>[[.,[.,.]],[[[.,.],.],.]]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>01011
[5,6,2,1,3,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[5,6,2,1,4,3]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[5,6,2,3,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>01001
[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[5,6,2,4,3,1]=>[[[.,[.,.]],[[.,.],.]],.]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>01011
[5,6,3,1,2,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[5,6,3,1,4,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[5,6,3,2,1,4]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110
[5,6,3,2,4,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>01101
[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>01010
[5,6,3,4,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>01011
[5,6,4,1,2,3]=>[[[.,[.,.]],.],[.,[.,.]]]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>01100
[5,6,4,1,3,2]=>[[[.,[.,.]],.],[[.,.],.]]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>01101
[5,6,4,2,1,3]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110
[5,6,4,2,3,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>01101
[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>01110
[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>01111
[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>10000
[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>10001
[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>10001
[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>10010
[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>10011
[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>10001
[6,1,3,5,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[6,1,3,5,4,2]=>[[.,.],[[.,[[.,.],.]],.]]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>10011
[6,1,4,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[6,1,4,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[6,1,4,5,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>10010
[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>10011
[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>10100
[6,1,5,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>10101
[6,1,5,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>10101
[6,1,5,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>10110
[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>10111
[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,2,1,4,5,3]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[6,2,1,5,3,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,2,1,5,4,3]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,2,3,1,5,4]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>10001
[6,2,3,5,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>10011
[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,2,4,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,2,4,3,1,5]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[6,2,4,5,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[6,2,4,5,3,1]=>[[[.,.],[[.,[.,.]],.]],.]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>10011
[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,2,5,1,4,3]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,2,5,3,1,4]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[6,2,5,3,4,1]=>[[[.,.],[[.,.],[.,.]]],.]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>10101
[6,2,5,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>10111
[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[6,3,1,2,5,4]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[6,3,1,4,2,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,3,1,4,5,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[6,3,1,5,2,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,3,1,5,4,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,3,2,1,5,4]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,3,4,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>10010
[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>10011
[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,3,5,1,4,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[6,3,5,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>10110
[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>10111
[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[6,4,1,2,5,3]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[6,4,1,3,2,5]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,4,1,3,5,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,4,1,5,3,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,4,2,1,5,3]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[6,4,2,5,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,4,3,1,5,2]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11101
[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11011
[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>10100
[6,4,5,1,3,2]=>[[[.,.],[.,.]],[[.,.],.]]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>10101
[6,4,5,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>10101
[6,4,5,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>10110
[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>10111
[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>11000
[6,5,1,2,4,3]=>[[[.,.],.],[.,[[.,.],.]]]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>11001
[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,5,1,3,4,2]=>[[[.,.],.],[[.,[.,.]],.]]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>11001
[6,5,1,4,2,3]=>[[[.,.],.],[[.,.],[.,.]]]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>11010
[6,5,1,4,3,2]=>[[[.,.],.],[[[.,.],.],.]]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>11011
[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,5,2,1,4,3]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>11001
[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>11011
[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,5,3,1,4,2]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11101
[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>11010
[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>11011
[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>11100
[6,5,4,1,3,2]=>[[[[.,.],.],.],[[.,.],.]]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>11101
[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>11101
[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>11110
[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>11111
[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>000000
[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>000001
[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>000010
[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>000001
[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>000010
[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>000011
[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100
[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101
[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000010
[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>000001
[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000010
[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>000011
[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100
[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101
[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110
[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>000101
[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>000010
[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>000011
[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>000100
[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>000101
[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110
[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>000101
[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>000110
[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>000111
[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000
[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001
[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001001
[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011
[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>000010
[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>000001
[1,2,4,5,7,3,6]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>000010
[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>000011
[1,2,4,6,3,5,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,4,6,3,7,5]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>000110
[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>000101
[1,2,4,6,7,3,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>000010
[1,2,4,6,7,5,3]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>000011
[1,2,4,7,3,5,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,4,7,3,6,5]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,4,7,5,3,6]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>000110
[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>000101
[1,2,4,7,6,3,5]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>000110
[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>000111
[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000
[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001
[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,5,3,6,7,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001001
[1,2,5,3,7,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,5,3,7,6,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011
[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001001
[1,2,5,4,7,3,6]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001011
[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,5,6,4,3,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>000110
[1,2,5,6,4,7,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>000101
[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>000010
[1,2,5,6,7,4,3]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>000011
[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,5,7,4,3,6]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>000110
[1,2,5,7,4,6,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>000101
[1,2,5,7,6,3,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>000110
[1,2,5,7,6,4,3]=>[.,[.,[[[.,[[.,.],.]],.],.]]]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>000111
[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000
[1,2,6,3,4,7,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001
[1,2,6,3,5,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,6,3,5,7,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001001
[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,6,3,7,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011
[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,6,4,3,7,5]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001001
[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,6,4,7,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001011
[1,2,6,5,3,4,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,6,5,3,7,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110
[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001101
[1,2,6,5,7,3,4]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>001011
[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>000100
[1,2,6,7,3,5,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>000101
[1,2,6,7,4,3,5]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>000110
[1,2,6,7,4,5,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>000101
[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>000110
[1,2,6,7,5,4,3]=>[.,[.,[[[[.,[.,.]],.],.],.]]]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>000111
[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>001000
[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>001001
[1,2,7,3,5,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,7,3,5,6,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>001001
[1,2,7,3,6,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>001010
[1,2,7,3,6,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>001011
[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>001001
[1,2,7,4,6,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>001011
[1,2,7,5,3,4,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,7,5,3,6,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110
[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001101
[1,2,7,5,6,3,4]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>001010
[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>001011
[1,2,7,6,3,4,5]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>001100
[1,2,7,6,3,5,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>001101
[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110
[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>001101
[1,2,7,6,5,3,4]=>[.,[.,[[[[.,.],.],.],[.,.]]]]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>001110
[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>001111
[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001
[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001
[1,3,2,5,7,4,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011
[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,3,2,6,4,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,3,2,6,7,5,4]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011
[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,3,2,7,6,4,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,3,4,2,7,5,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010
[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>000001
[1,3,4,5,7,2,6]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010
[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>000011
[1,3,4,6,2,5,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,4,6,2,7,5]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110
[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>000101
[1,3,4,6,7,2,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010
[1,3,4,6,7,5,2]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>000011
[1,3,4,7,2,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,4,7,2,6,5]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,4,7,5,2,6]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110
[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>000101
[1,3,4,7,6,2,5]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110
[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>000111
[1,3,5,2,4,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,3,5,2,4,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,3,5,2,6,4,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,5,2,6,7,4]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,3,5,2,7,4,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,5,2,7,6,4]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>001001
[1,3,5,4,7,2,6]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>001011
[1,3,5,6,2,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,5,6,2,7,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,5,6,4,2,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110
[1,3,5,6,4,7,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>000101
[1,3,5,6,7,2,4]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010
[1,3,5,6,7,4,2]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>000011
[1,3,5,7,2,4,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,5,7,2,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,5,7,4,2,6]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110
[1,3,5,7,4,6,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>000101
[1,3,5,7,6,2,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110
[1,3,5,7,6,4,2]=>[.,[[.,[[.,[[.,.],.]],.]],.]]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>000111
[1,3,6,2,4,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,3,6,2,4,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,3,6,2,5,4,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,6,2,5,7,4]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,3,6,2,7,4,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,6,2,7,5,4]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,3,6,4,2,5,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,6,4,2,7,5]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,6,4,5,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,6,4,5,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>001001
[1,3,6,4,7,2,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,6,4,7,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>001011
[1,3,6,5,2,4,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,6,5,2,7,4]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110
[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>001101
[1,3,6,5,7,2,4]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,6,5,7,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>001011
[1,3,6,7,2,4,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,3,6,7,2,5,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,3,6,7,4,2,5]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110
[1,3,6,7,4,5,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>000101
[1,3,6,7,5,2,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110
[1,3,6,7,5,4,2]=>[.,[[.,[[[.,[.,.]],.],.]],.]]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>000111
[1,3,7,2,4,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,3,7,2,4,6,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,3,7,2,5,4,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,7,2,5,6,4]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,3,7,2,6,4,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,3,7,2,6,5,4]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,3,7,4,2,5,6]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,7,4,2,6,5]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,7,4,5,2,6]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>001001
[1,3,7,4,6,2,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,7,4,6,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>001011
[1,3,7,5,2,4,6]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,7,5,2,6,4]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,7,5,4,2,6]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110
[1,3,7,5,4,6,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>001101
[1,3,7,5,6,2,4]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,3,7,5,6,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>001011
[1,3,7,6,2,4,5]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,3,7,6,2,5,4]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,3,7,6,4,2,5]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110
[1,3,7,6,4,5,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>001101
[1,3,7,6,5,2,4]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110
[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>001111
[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,4,2,3,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001
[1,4,2,3,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,4,2,3,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,4,2,5,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,4,2,5,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,4,2,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001
[1,4,2,5,7,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,4,2,5,7,6,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011
[1,4,2,6,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,4,2,6,3,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,4,2,6,5,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,4,2,6,5,7,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,4,2,6,7,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,4,2,6,7,5,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011
[1,4,2,7,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,4,2,7,3,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,4,2,7,5,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,4,2,7,5,6,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,4,2,7,6,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,4,2,7,6,5,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>010001
[1,4,3,5,7,2,6]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>010011
[1,4,3,6,2,5,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,4,3,6,2,7,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,4,3,6,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,4,3,6,7,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>010011
[1,4,3,7,2,5,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,4,3,7,2,6,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,4,3,7,5,2,6]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,4,3,7,5,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,4,3,7,6,2,5]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,4,3,7,6,5,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>010111
[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,4,5,2,7,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,4,5,3,2,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,4,5,3,2,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,4,5,3,6,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,5,3,6,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,4,5,3,7,2,6]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,5,3,7,6,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,4,5,6,2,3,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,4,5,6,2,7,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,4,5,6,3,2,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110
[1,4,5,6,3,7,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>000101
[1,4,5,6,7,2,3]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>000010
[1,4,5,6,7,3,2]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>000011
[1,4,5,7,2,3,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,4,5,7,2,6,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,4,5,7,3,2,6]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110
[1,4,5,7,3,6,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>000101
[1,4,5,7,6,2,3]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>000110
[1,4,5,7,6,3,2]=>[.,[[[.,[.,[[.,.],.]]],.],.]]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>000111
[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,4,6,2,3,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,6,2,7,5,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,4,6,3,2,5,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,4,6,3,2,7,5]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,4,6,3,5,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,6,3,5,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,4,6,3,7,2,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,6,3,7,5,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,4,6,5,2,3,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,4,6,5,2,7,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,4,6,5,3,2,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110
[1,4,6,5,3,7,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>001101
[1,4,6,5,7,2,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,4,6,5,7,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>001011
[1,4,6,7,2,3,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,4,6,7,2,5,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,4,6,7,3,2,5]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110
[1,4,6,7,3,5,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>000101
[1,4,6,7,5,2,3]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>000110
[1,4,6,7,5,3,2]=>[.,[[[.,[[.,[.,.]],.]],.],.]]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>000111
[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,4,7,2,5,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,4,7,2,6,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,4,7,2,6,5,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,4,7,3,2,5,6]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,4,7,3,2,6,5]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,4,7,3,5,2,6]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,7,3,5,6,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,4,7,3,6,2,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,4,7,3,6,5,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,4,7,5,2,3,6]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,4,7,5,2,6,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,4,7,5,3,2,6]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110
[1,4,7,5,3,6,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>001101
[1,4,7,5,6,2,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>001010
[1,4,7,5,6,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>001011
[1,4,7,6,2,3,5]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,4,7,6,2,5,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,4,7,6,3,2,5]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110
[1,4,7,6,3,5,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>001101
[1,4,7,6,5,2,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>001110
[1,4,7,6,5,3,2]=>[.,[[[.,[[[.,.],.],.]],.],.]]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>001111
[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[1,5,2,3,6,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,5,2,3,6,7,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001
[1,5,2,3,7,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,5,2,3,7,6,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[1,5,2,4,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,5,2,4,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,5,2,4,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,5,2,4,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001
[1,5,2,4,7,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,5,2,4,7,6,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011
[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,5,2,6,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,5,2,6,4,7,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,5,2,6,7,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,5,2,6,7,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011
[1,5,2,7,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,5,2,7,3,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,5,2,7,4,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,5,2,7,4,6,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,5,2,7,6,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,5,2,7,6,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[1,5,3,2,4,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,5,3,2,4,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,5,3,2,6,4,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,5,3,2,6,7,4]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,5,3,2,7,4,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,5,3,2,7,6,4]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>010001
[1,5,3,4,7,2,6]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>010011
[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,5,3,6,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,5,3,6,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,5,3,6,7,2,4]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,5,3,6,7,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>010011
[1,5,3,7,2,4,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,5,3,7,4,2,6]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,5,3,7,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,5,3,7,6,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,5,3,7,6,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>010111
[1,5,4,2,3,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,5,4,2,3,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,5,4,2,6,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,5,4,2,6,7,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,5,4,2,7,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,5,4,2,7,6,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,5,4,3,7,2,6]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,5,4,6,2,3,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,5,4,6,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,5,4,6,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,5,4,6,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,5,4,6,7,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,5,4,6,7,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>010011
[1,5,4,7,2,3,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,5,4,7,2,6,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,5,4,7,3,2,6]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,5,4,7,3,6,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,5,4,7,6,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,5,4,7,6,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>010111
[1,5,6,2,3,4,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,5,6,2,3,7,4]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,5,6,2,4,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,5,6,2,4,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,5,6,2,7,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,5,6,2,7,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,5,6,3,2,4,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,5,6,3,2,7,4]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,5,6,3,4,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,6,3,4,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,5,6,3,7,2,4]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,6,3,7,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,5,6,4,3,2,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110
[1,5,6,4,3,7,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>001101
[1,5,6,4,7,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,6,4,7,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>001011
[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>000100
[1,5,6,7,2,4,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>000101
[1,5,6,7,3,2,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110
[1,5,6,7,3,4,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>000101
[1,5,6,7,4,2,3]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>000110
[1,5,6,7,4,3,2]=>[.,[[[[.,[.,[.,.]]],.],.],.]]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>000111
[1,5,7,2,3,4,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,5,7,2,3,6,4]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,5,7,2,4,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,5,7,2,4,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,5,7,2,6,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,5,7,2,6,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,5,7,3,2,4,6]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,5,7,3,2,6,4]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,5,7,3,4,2,6]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,7,3,4,6,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,5,7,3,6,2,4]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,7,3,6,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,5,7,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,5,7,4,3,2,6]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110
[1,5,7,4,3,6,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>001101
[1,5,7,4,6,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,5,7,4,6,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>001011
[1,5,7,6,2,3,4]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>001100
[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>001101
[1,5,7,6,3,2,4]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110
[1,5,7,6,3,4,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>001101
[1,5,7,6,4,2,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>001110
[1,5,7,6,4,3,2]=>[.,[[[[.,[[.,.],.]],.],.],.]]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>001111
[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[1,6,2,3,4,7,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[1,6,2,3,5,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,6,2,3,5,7,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001
[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,6,2,3,7,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[1,6,2,4,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,6,2,4,3,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,6,2,4,5,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,6,2,4,5,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001
[1,6,2,4,7,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,6,2,4,7,5,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011
[1,6,2,5,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,6,2,5,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,6,2,5,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,6,2,5,4,7,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,6,2,5,7,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,6,2,5,7,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011
[1,6,2,7,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,6,2,7,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,6,2,7,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,6,2,7,4,5,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,6,2,7,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,6,2,7,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[1,6,3,2,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,6,3,2,4,7,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,6,3,2,5,4,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,3,2,5,7,4]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,6,3,2,7,4,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,3,2,7,5,4]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,3,4,2,7,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>010001
[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,6,3,4,7,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>010011
[1,6,3,5,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,3,5,2,7,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,6,3,5,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,6,3,5,7,2,4]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,6,3,5,7,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>010011
[1,6,3,7,2,4,5]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,3,7,2,5,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,3,7,4,2,5]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,6,3,7,4,5,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,6,3,7,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>010111
[1,6,4,2,3,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,6,4,2,3,7,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,6,4,2,5,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,4,2,5,7,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,6,4,2,7,3,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,4,2,7,5,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,6,4,3,2,7,5]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,6,4,3,5,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,6,4,3,7,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,6,4,3,7,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,6,4,5,2,3,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,4,5,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,4,5,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,6,4,5,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,6,4,5,7,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,6,4,5,7,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>010011
[1,6,4,7,2,3,5]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,4,7,2,5,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,4,7,3,2,5]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,6,4,7,3,5,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,6,4,7,5,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,6,4,7,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>010111
[1,6,5,2,3,4,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,6,5,2,3,7,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,6,5,2,4,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,5,2,4,7,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,6,5,2,7,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,6,5,2,7,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,6,5,3,2,4,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,6,5,3,2,7,4]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,6,5,3,4,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,6,5,3,4,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,6,5,3,7,2,4]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,6,5,3,7,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,6,5,4,2,3,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,6,5,4,2,7,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011101
[1,6,5,4,7,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011011
[1,6,5,7,2,3,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,6,5,7,2,4,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,6,5,7,3,2,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,6,5,7,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,6,5,7,4,2,3]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,6,5,7,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>010111
[1,6,7,2,3,4,5]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>001000
[1,6,7,2,3,5,4]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>001001
[1,6,7,2,4,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,6,7,2,4,5,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>001001
[1,6,7,2,5,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>001010
[1,6,7,2,5,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>001011
[1,6,7,3,2,4,5]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,6,7,3,2,5,4]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,6,7,3,4,2,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,6,7,3,4,5,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>001001
[1,6,7,3,5,2,4]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,6,7,3,5,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>001011
[1,6,7,4,2,3,5]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,6,7,4,2,5,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,6,7,4,3,2,5]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110
[1,6,7,4,3,5,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>001101
[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>001010
[1,6,7,4,5,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>001011
[1,6,7,5,2,3,4]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>001100
[1,6,7,5,2,4,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>001101
[1,6,7,5,3,2,4]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110
[1,6,7,5,3,4,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>001101
[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>001110
[1,6,7,5,4,3,2]=>[.,[[[[[.,[.,.]],.],.],.],.]]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>001111
[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>010000
[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>010001
[1,7,2,3,5,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,7,2,3,5,6,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>010001
[1,7,2,3,6,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>010010
[1,7,2,3,6,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>010011
[1,7,2,4,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,7,2,4,3,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,7,2,4,5,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,7,2,4,5,6,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>010001
[1,7,2,4,6,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,7,2,4,6,5,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>010011
[1,7,2,5,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,7,2,5,3,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,7,2,5,4,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,7,2,5,4,6,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,7,2,5,6,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>010010
[1,7,2,5,6,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>010011
[1,7,2,6,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>010100
[1,7,2,6,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>010101
[1,7,2,6,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,7,2,6,4,5,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>010101
[1,7,2,6,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>010110
[1,7,2,6,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>010111
[1,7,3,2,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,7,3,2,4,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,7,3,2,5,4,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,3,2,5,6,4]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,7,3,2,6,4,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,3,2,6,5,4]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>010001
[1,7,3,4,6,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>010011
[1,7,3,5,2,4,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,3,5,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,3,5,4,2,6]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,7,3,5,6,2,4]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>010011
[1,7,3,6,2,4,5]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,3,6,2,5,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,3,6,4,2,5]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>010101
[1,7,3,6,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>010111
[1,7,4,2,3,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,7,4,2,3,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,7,4,2,5,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,4,2,5,6,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,7,4,2,6,3,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,4,2,6,5,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,4,3,2,6,5]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,4,3,5,2,6]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,7,4,3,6,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,7,4,5,2,3,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,4,5,2,6,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,4,5,3,2,6]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,7,4,5,3,6,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,7,4,5,6,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>010010
[1,7,4,5,6,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>010011
[1,7,4,6,2,3,5]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,4,6,2,5,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,4,6,3,2,5]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,7,4,6,3,5,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,7,4,6,5,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>010110
[1,7,4,6,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>010111
[1,7,5,2,3,4,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,7,5,2,3,6,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,7,5,2,4,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,5,2,4,6,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,7,5,2,6,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,5,2,6,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,7,5,3,2,4,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,5,3,2,6,4]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,5,3,4,2,6]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,5,3,4,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,7,5,3,6,2,4]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,5,3,6,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,7,5,4,2,3,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,5,4,2,6,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011101
[1,7,5,4,6,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011011
[1,7,5,6,2,3,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>010100
[1,7,5,6,2,4,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>010101
[1,7,5,6,3,2,4]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>010101
[1,7,5,6,4,2,3]=>[.,[[[[.,.],[.,.]],.],[.,.]]]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>010110
[1,7,5,6,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>010111
[1,7,6,2,3,4,5]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>011000
[1,7,6,2,3,5,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>011001
[1,7,6,2,4,3,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,6,2,4,5,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>011001
[1,7,6,2,5,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>011010
[1,7,6,2,5,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>011011
[1,7,6,3,2,4,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,6,3,2,5,4]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,6,3,4,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,6,3,4,5,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>011001
[1,7,6,3,5,2,4]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,6,3,5,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>011011
[1,7,6,4,2,3,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,6,4,2,5,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,7,6,4,3,5,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011101
[1,7,6,4,5,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>011010
[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>011011
[1,7,6,5,2,3,4]=>[.,[[[[.,.],.],.],[.,[.,.]]]]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>011100
[1,7,6,5,2,4,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>011101
[1,7,6,5,3,2,4]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,7,6,5,3,4,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>011101
[1,7,6,5,4,2,3]=>[.,[[[[[.,.],.],.],.],[.,.]]]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>011110
[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>011111
[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[2,1,3,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[2,1,3,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[2,1,3,6,7,5,4]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[2,1,3,7,6,4,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[2,1,4,5,7,3,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[2,1,4,6,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,4,6,3,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[2,1,4,6,7,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[2,1,4,6,7,5,3]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[2,1,4,7,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,4,7,3,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,4,7,5,3,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[2,1,4,7,5,6,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[2,1,4,7,6,3,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[2,1,4,7,6,5,3]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[2,1,5,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[2,1,5,3,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[2,1,5,3,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,5,3,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[2,1,5,3,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,5,3,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[2,1,5,4,7,3,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,5,6,4,3,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[2,1,5,6,4,7,3]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[2,1,5,6,7,3,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[2,1,5,6,7,4,3]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,5,7,4,3,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[2,1,5,7,4,6,3]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[2,1,5,7,6,3,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[2,1,5,7,6,4,3]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[2,1,6,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[2,1,6,3,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[2,1,6,3,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,6,3,5,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[2,1,6,3,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,6,3,7,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,6,4,3,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,6,4,7,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[2,1,6,5,3,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,6,5,3,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[2,1,6,5,7,3,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,6,5,7,4,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[2,1,6,7,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[2,1,6,7,3,5,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[2,1,6,7,4,3,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[2,1,6,7,4,5,3]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[2,1,6,7,5,4,3]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[2,1,7,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[2,1,7,3,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[2,1,7,3,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,7,3,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[2,1,7,3,6,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[2,1,7,3,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[2,1,7,4,6,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[2,1,7,5,3,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,7,5,3,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,7,5,4,3,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[2,1,7,5,6,3,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[2,1,7,5,6,4,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[2,1,7,6,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[2,1,7,6,3,5,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[2,1,7,6,4,3,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[2,1,7,6,4,5,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[2,1,7,6,5,3,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[2,3,1,4,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[2,3,1,5,7,4,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[2,3,1,6,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,3,1,6,4,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,3,1,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,3,1,6,7,5,4]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[2,3,1,7,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,3,1,7,4,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,3,1,7,5,4,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,3,1,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,3,1,7,6,4,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,3,1,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,3,4,1,7,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>000001
[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>000011
[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>000101
[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>000011
[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,4,7,1,6,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,4,7,5,1,6]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>000101
[2,3,4,7,6,1,5]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>000111
[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,3,5,1,4,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,5,1,7,6,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>001001
[2,3,5,4,7,1,6]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>001011
[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,5,6,1,7,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,5,6,4,1,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>000101
[2,3,5,6,7,1,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>000011
[2,3,5,7,1,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,5,7,1,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,5,7,4,1,6]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[2,3,5,7,4,6,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>000101
[2,3,5,7,6,1,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>000111
[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,3,6,1,5,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,6,1,5,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,3,6,1,7,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,6,1,7,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,3,6,4,1,5,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,6,4,1,7,5]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>001001
[2,3,6,4,7,1,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,6,4,7,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>001011
[2,3,6,5,1,4,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,6,5,1,7,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>001101
[2,3,6,5,7,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>001011
[2,3,6,7,1,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,3,6,7,1,5,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,3,6,7,4,1,5]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[2,3,6,7,4,5,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>000101
[2,3,6,7,5,1,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>000111
[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,3,7,1,4,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,3,7,1,5,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,7,1,5,6,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,3,7,1,6,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,3,7,1,6,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,3,7,4,1,5,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,7,4,1,6,5]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,7,4,5,1,6]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>001001
[2,3,7,4,6,1,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,7,4,6,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>001011
[2,3,7,5,1,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,7,5,1,6,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,7,5,4,1,6]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>001101
[2,3,7,5,6,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>001011
[2,3,7,6,1,4,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,3,7,6,1,5,4]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,3,7,6,4,1,5]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>001101
[2,3,7,6,5,1,4]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>001111
[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[2,4,1,3,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[2,4,1,3,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,4,1,3,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[2,4,1,3,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,4,1,3,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,4,1,5,3,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,4,1,5,7,6,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,4,1,6,5,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,4,1,6,5,7,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,4,1,6,7,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,4,1,6,7,5,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,4,1,7,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,4,1,7,5,3,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,4,1,7,5,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,4,1,7,6,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,4,1,7,6,5,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,4,3,1,7,5,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>010001
[2,4,3,5,7,1,6]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>010011
[2,4,3,6,1,5,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,4,3,6,1,7,5]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,4,3,6,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,4,3,6,7,5,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>010011
[2,4,3,7,1,5,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,4,3,7,1,6,5]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,4,3,7,5,1,6]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,4,3,7,5,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,4,3,7,6,1,5]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,4,3,7,6,5,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>010111
[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,4,5,1,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,4,5,1,6,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,5,1,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,4,5,1,7,3,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,5,1,7,6,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,4,5,3,1,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,4,5,3,1,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,4,5,3,6,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,5,3,6,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,4,5,3,7,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,5,3,7,6,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,4,5,6,1,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,4,5,6,1,7,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,4,5,6,3,1,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>000101
[2,4,5,6,7,1,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>000011
[2,4,5,7,1,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,4,5,7,1,6,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,4,5,7,3,1,6]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[2,4,5,7,3,6,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>000101
[2,4,5,7,6,1,3]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>000111
[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,4,6,1,3,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,4,6,1,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,6,1,5,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,4,6,1,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,6,1,7,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,4,6,3,1,5,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,4,6,3,1,7,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,4,6,3,5,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,6,3,5,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,4,6,3,7,1,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,6,3,7,5,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,4,6,5,1,3,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,4,6,5,1,7,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,4,6,5,3,1,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[2,4,6,5,3,7,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>001101
[2,4,6,5,7,1,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>001011
[2,4,6,7,1,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,4,6,7,1,5,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,4,6,7,3,1,5]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[2,4,6,7,3,5,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>000101
[2,4,6,7,5,1,3]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>000111
[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,4,7,1,3,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,4,7,1,5,3,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,7,1,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,4,7,1,6,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,4,7,1,6,5,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,4,7,3,1,5,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,4,7,3,1,6,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,4,7,3,5,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,7,3,5,6,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,4,7,3,6,1,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,4,7,3,6,5,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,4,7,5,1,3,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,4,7,5,1,6,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,4,7,5,3,1,6]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[2,4,7,5,3,6,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>001101
[2,4,7,5,6,1,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[2,4,7,5,6,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>001011
[2,4,7,6,1,3,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,4,7,6,1,5,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,4,7,6,3,1,5]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[2,4,7,6,3,5,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>001101
[2,4,7,6,5,1,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>001111
[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[2,5,1,3,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,5,1,3,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[2,5,1,4,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,5,1,4,3,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,5,1,4,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,5,1,4,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[2,5,1,4,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,5,1,4,7,6,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[2,5,1,6,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,5,1,6,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,5,1,6,4,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,5,1,6,4,7,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,5,1,6,7,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,5,1,6,7,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[2,5,1,7,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,5,1,7,3,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,5,1,7,4,3,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,5,1,7,4,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,5,1,7,6,3,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,5,1,7,6,4,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[2,5,3,1,4,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,5,3,1,4,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,5,3,1,6,4,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,5,3,1,6,7,4]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,5,3,1,7,4,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,5,3,1,7,6,4]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,5,3,4,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>010001
[2,5,3,4,7,1,6]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>010011
[2,5,3,6,1,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,5,3,6,1,7,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,5,3,6,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,5,3,6,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,5,3,6,7,1,4]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,5,3,6,7,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>010011
[2,5,3,7,1,4,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,5,3,7,1,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,5,3,7,4,1,6]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,5,3,7,4,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,5,3,7,6,1,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,5,3,7,6,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>010111
[2,5,4,1,3,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,5,4,1,3,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,5,4,1,6,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,5,4,1,6,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,5,4,1,7,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,5,4,1,7,6,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,5,4,3,1,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,5,4,3,7,1,6]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,5,4,6,1,3,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,5,4,6,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,5,4,6,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,5,4,6,7,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>010011
[2,5,4,7,1,3,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,5,4,7,1,6,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,5,4,7,3,1,6]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,5,4,7,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,5,4,7,6,1,3]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,5,4,7,6,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>010111
[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,5,6,1,3,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,5,6,1,4,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,5,6,1,4,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,5,6,1,7,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,5,6,1,7,4,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,5,6,3,1,4,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,5,6,3,1,7,4]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,5,6,3,4,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,6,3,4,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,5,6,3,7,1,4]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,6,3,7,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,5,6,4,1,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,5,6,4,1,7,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,5,6,4,3,1,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[2,5,6,4,3,7,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>001101
[2,5,6,4,7,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,6,4,7,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>001011
[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[2,5,6,7,1,4,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[2,5,6,7,3,1,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[2,5,6,7,3,4,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>000101
[2,5,6,7,4,1,3]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>000111
[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,5,7,1,3,6,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,5,7,1,4,3,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,5,7,1,4,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,5,7,1,6,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,5,7,1,6,4,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,5,7,3,1,4,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,5,7,3,1,6,4]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,5,7,3,4,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,7,3,4,6,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,5,7,3,6,1,4]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,7,3,6,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,5,7,4,1,3,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,5,7,4,1,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,5,7,4,3,1,6]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[2,5,7,4,3,6,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>001101
[2,5,7,4,6,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,5,7,4,6,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>001011
[2,5,7,6,1,3,4]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[2,5,7,6,1,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[2,5,7,6,3,1,4]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[2,5,7,6,3,4,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>001101
[2,5,7,6,4,1,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>001111
[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[2,6,1,3,5,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,6,1,3,5,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[2,6,1,3,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,6,1,3,7,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[2,6,1,4,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,6,1,4,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,6,1,4,5,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,6,1,4,5,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[2,6,1,4,7,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,6,1,4,7,5,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[2,6,1,5,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,6,1,5,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,6,1,5,4,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,6,1,5,4,7,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,6,1,5,7,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,6,1,5,7,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[2,6,1,7,3,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,6,1,7,3,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,6,1,7,4,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,6,1,7,4,5,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,6,1,7,5,3,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,6,1,7,5,4,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[2,6,3,1,4,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,6,3,1,4,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,6,3,1,5,4,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,3,1,5,7,4]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,6,3,1,7,4,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,3,1,7,5,4]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,6,3,4,1,5,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,3,4,1,7,5]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,6,3,4,5,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>010001
[2,6,3,4,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,6,3,4,7,5,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>010011
[2,6,3,5,1,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,3,5,1,7,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,3,5,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,6,3,5,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,6,3,5,7,1,4]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,6,3,5,7,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>010011
[2,6,3,7,1,4,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,3,7,1,5,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,3,7,4,1,5]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,6,3,7,4,5,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,6,3,7,5,1,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,6,3,7,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>010111
[2,6,4,1,3,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,6,4,1,3,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,6,4,1,5,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,4,1,5,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,6,4,1,7,3,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,4,1,7,5,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,6,4,3,1,5,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,6,4,3,1,7,5]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,6,4,3,5,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,6,4,3,5,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,6,4,3,7,1,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,6,4,3,7,5,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,6,4,5,1,3,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,4,5,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,4,5,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,6,4,5,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,6,4,5,7,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,6,4,5,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>010011
[2,6,4,7,1,3,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,4,7,1,5,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,4,7,3,1,5]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,6,4,7,3,5,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,6,4,7,5,1,3]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,6,4,7,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>010111
[2,6,5,1,3,4,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,6,5,1,3,7,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,6,5,1,4,3,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,5,1,4,7,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,6,5,1,7,3,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,6,5,1,7,4,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,6,5,3,1,4,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,6,5,3,1,7,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,6,5,3,4,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,6,5,3,4,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,6,5,3,7,1,4]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,6,5,3,7,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,6,5,4,1,3,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,6,5,4,1,7,3]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>011101
[2,6,5,4,7,1,3]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,6,5,4,7,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>011011
[2,6,5,7,1,3,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,6,5,7,1,4,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,6,5,7,3,1,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,6,5,7,3,4,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,6,5,7,4,1,3]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>010111
[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[2,6,7,1,3,5,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[2,6,7,1,4,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,6,7,1,4,5,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[2,6,7,1,5,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[2,6,7,1,5,4,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[2,6,7,3,1,4,5]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,6,7,3,1,5,4]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,6,7,3,4,1,5]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,6,7,3,4,5,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>001001
[2,6,7,3,5,1,4]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,6,7,3,5,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>001011
[2,6,7,4,1,3,5]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,6,7,4,1,5,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,6,7,4,3,1,5]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[2,6,7,4,3,5,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>001101
[2,6,7,4,5,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[2,6,7,4,5,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>001011
[2,6,7,5,1,3,4]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[2,6,7,5,1,4,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[2,6,7,5,3,1,4]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[2,6,7,5,3,4,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>001101
[2,6,7,5,4,1,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>001111
[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[2,7,1,3,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[2,7,1,3,5,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,7,1,3,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[2,7,1,3,6,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[2,7,1,3,6,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[2,7,1,4,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,7,1,4,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,7,1,4,5,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,7,1,4,5,6,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[2,7,1,4,6,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,7,1,4,6,5,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[2,7,1,5,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,7,1,5,3,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,7,1,5,4,3,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,7,1,5,4,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,7,1,5,6,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[2,7,1,5,6,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[2,7,1,6,3,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[2,7,1,6,3,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[2,7,1,6,4,3,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,7,1,6,4,5,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[2,7,1,6,5,3,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[2,7,1,6,5,4,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[2,7,3,1,4,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,7,3,1,4,6,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,7,3,1,5,4,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,3,1,5,6,4]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,7,3,1,6,4,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,3,1,6,5,4]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,7,3,4,1,5,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,3,4,1,6,5]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,3,4,5,1,6]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>010001
[2,7,3,4,6,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,7,3,4,6,5,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>010011
[2,7,3,5,1,4,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,3,5,1,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,3,5,4,1,6]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,7,3,5,4,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,7,3,5,6,1,4]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,7,3,5,6,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>010011
[2,7,3,6,1,4,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,3,6,1,5,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,3,6,4,1,5]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,7,3,6,4,5,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>010101
[2,7,3,6,5,1,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,7,3,6,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>010111
[2,7,4,1,3,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,7,4,1,3,6,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,7,4,1,5,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,4,1,5,6,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,7,4,1,6,3,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,4,1,6,5,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,7,4,3,1,5,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,4,3,1,6,5]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,4,3,5,1,6]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,4,3,5,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,7,4,3,6,1,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,4,3,6,5,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,7,4,5,1,3,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,4,5,1,6,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,4,5,3,1,6]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,7,4,5,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,7,4,5,6,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>010011
[2,7,4,6,1,3,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,4,6,1,5,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,4,6,3,1,5]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,7,4,6,3,5,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,7,4,6,5,1,3]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>010111
[2,7,5,1,3,4,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,7,5,1,3,6,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,7,5,1,4,3,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,5,1,4,6,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,7,5,1,6,3,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,5,1,6,4,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,7,5,3,1,4,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,5,3,1,6,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,5,3,4,1,6]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,5,3,4,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,7,5,3,6,1,4]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,5,3,6,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,7,5,4,1,3,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,5,4,1,6,3]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,5,4,3,1,6]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[2,7,5,4,3,6,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>011101
[2,7,5,4,6,1,3]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,5,4,6,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>011011
[2,7,5,6,1,3,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[2,7,5,6,1,4,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[2,7,5,6,3,1,4]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,7,5,6,3,4,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>010101
[2,7,5,6,4,1,3]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[2,7,5,6,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>010111
[2,7,6,1,3,4,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[2,7,6,1,3,5,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[2,7,6,1,4,3,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,6,1,4,5,3]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[2,7,6,1,5,3,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[2,7,6,1,5,4,3]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[2,7,6,3,1,4,5]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,6,3,1,5,4]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,6,3,4,1,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,6,3,4,5,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>011001
[2,7,6,3,5,1,4]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,6,3,5,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>011011
[2,7,6,4,1,3,5]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,6,4,1,5,3]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,6,4,3,1,5]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[2,7,6,4,3,5,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>011101
[2,7,6,4,5,1,3]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>011011
[2,7,6,5,1,3,4]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[2,7,6,5,1,4,3]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[2,7,6,5,3,1,4]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[2,7,6,5,3,4,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>011101
[2,7,6,5,4,1,3]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>011111
[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[3,1,2,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[3,1,2,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[3,1,2,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[3,1,2,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[3,1,2,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[3,1,2,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[3,1,2,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[3,1,2,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[3,1,2,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[3,1,2,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[3,1,2,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[3,1,2,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[3,1,2,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[3,1,2,6,7,5,4]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[3,1,2,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[3,1,2,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[3,1,2,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[3,1,2,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[3,1,2,7,6,4,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[3,1,2,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[3,1,4,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[3,1,4,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,4,2,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[3,1,4,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,4,2,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,4,5,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[3,1,4,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,4,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[3,1,4,6,5,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[3,1,4,6,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[3,1,4,6,7,5,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,4,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,4,7,5,2,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[3,1,4,7,5,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[3,1,4,7,6,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[3,1,4,7,6,5,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[3,1,5,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,5,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[3,1,5,4,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,5,4,2,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,5,4,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,5,4,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[3,1,5,4,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,5,4,7,6,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[3,1,5,6,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,5,6,2,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,5,6,4,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[3,1,5,6,4,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[3,1,5,6,7,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[3,1,5,6,7,4,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[3,1,5,7,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,5,7,2,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,5,7,4,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[3,1,5,7,4,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[3,1,5,7,6,2,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[3,1,5,7,6,4,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[3,1,6,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,6,2,5,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[3,1,6,2,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,6,2,7,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[3,1,6,4,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,6,4,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,6,4,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,6,4,5,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[3,1,6,4,7,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,6,4,7,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[3,1,6,5,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,6,5,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,6,5,4,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[3,1,6,5,4,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[3,1,6,5,7,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,6,5,7,4,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[3,1,6,7,2,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[3,1,6,7,2,5,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[3,1,6,7,4,2,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[3,1,6,7,4,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[3,1,6,7,5,2,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[3,1,6,7,5,4,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[3,1,7,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[3,1,7,2,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,7,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[3,1,7,2,6,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[3,1,7,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[3,1,7,4,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,7,4,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,7,4,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,7,4,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[3,1,7,4,6,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,7,4,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[3,1,7,5,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,7,5,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,7,5,4,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[3,1,7,5,4,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[3,1,7,5,6,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[3,1,7,5,6,4,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[3,1,7,6,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[3,1,7,6,2,5,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[3,1,7,6,4,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[3,1,7,6,4,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[3,1,7,6,5,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[3,1,7,6,5,4,2]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[3,2,1,5,7,4,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[3,2,1,6,4,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[3,2,1,6,7,5,4]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[3,2,4,1,7,5,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001
[3,2,4,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011
[3,2,4,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,4,6,1,7,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[3,2,4,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[3,2,4,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011
[3,2,4,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,4,7,1,6,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,4,7,5,1,6]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[3,2,4,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[3,2,4,7,6,1,5]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[3,2,4,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111
[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[3,2,5,1,4,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[3,2,5,1,6,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,5,1,6,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[3,2,5,1,7,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,5,1,7,6,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[3,2,5,4,7,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[3,2,5,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,5,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,5,6,4,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[3,2,5,6,4,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[3,2,5,6,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[3,2,5,6,7,4,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011
[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,5,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,5,7,4,1,6]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[3,2,5,7,4,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[3,2,5,7,6,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[3,2,5,7,6,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111
[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[3,2,6,1,4,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[3,2,6,1,5,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,6,1,5,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[3,2,6,1,7,4,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,6,1,7,5,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[3,2,6,4,1,5,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,6,4,1,7,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,6,4,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,6,4,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[3,2,6,4,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,6,4,7,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[3,2,6,5,1,4,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,6,5,1,7,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,6,5,4,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[3,2,6,5,4,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[3,2,6,5,7,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,6,5,7,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[3,2,6,7,1,5,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[3,2,6,7,4,1,5]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[3,2,6,7,4,5,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[3,2,6,7,5,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[3,2,6,7,5,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111
[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[3,2,7,1,4,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[3,2,7,1,5,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,7,1,5,6,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[3,2,7,1,6,4,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[3,2,7,1,6,5,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[3,2,7,4,1,5,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,7,4,1,6,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,7,4,5,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,7,4,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[3,2,7,4,6,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,7,4,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[3,2,7,5,1,4,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,7,5,1,6,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,7,5,4,1,6]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[3,2,7,5,4,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[3,2,7,5,6,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[3,2,7,5,6,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[3,2,7,6,1,4,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[3,2,7,6,1,5,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[3,2,7,6,4,1,5]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[3,2,7,6,4,5,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[3,2,7,6,5,1,4]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[3,2,7,6,5,4,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111
[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,4,1,5,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[3,4,1,5,7,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,4,1,5,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[3,4,1,6,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,4,1,6,2,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,4,1,6,5,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,4,1,6,5,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,4,1,6,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,4,1,6,7,5,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[3,4,1,7,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,4,1,7,2,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,4,1,7,5,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,4,1,7,5,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,4,1,7,6,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,4,1,7,6,5,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[3,4,2,1,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[3,4,2,1,6,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,4,2,1,6,7,5]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[3,4,2,1,7,5,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,4,2,1,7,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,4,2,5,1,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,4,2,5,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,4,2,6,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,4,2,6,5,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,4,2,6,5,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,4,2,6,7,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,4,2,6,7,5,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,4,2,7,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,4,2,7,5,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,4,2,7,5,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,4,2,7,6,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,4,2,7,6,5,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,4,5,1,2,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,4,5,1,7,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,5,1,7,6,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,4,5,2,1,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,4,5,2,7,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,5,2,7,6,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[3,4,5,6,1,7,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101
[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>000010
[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>000011
[3,4,5,7,1,2,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[3,4,5,7,1,6,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[3,4,5,7,2,1,6]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[3,4,5,7,2,6,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101
[3,4,5,7,6,1,2]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>000110
[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>000111
[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,4,6,1,2,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,4,6,1,5,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,6,1,5,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,4,6,1,7,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,6,1,7,5,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,4,6,2,1,5,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,4,6,2,1,7,5]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,4,6,2,5,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,6,2,5,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,4,6,2,7,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,6,2,7,5,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,4,6,5,1,2,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[3,4,6,5,1,7,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[3,4,6,5,2,1,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101
[3,4,6,5,7,1,2]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[3,4,6,5,7,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>001011
[3,4,6,7,1,2,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[3,4,6,7,1,5,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[3,4,6,7,2,1,5]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[3,4,6,7,2,5,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101
[3,4,6,7,5,1,2]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>000110
[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>000111
[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,4,7,1,2,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,4,7,1,5,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,7,1,5,6,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,4,7,1,6,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,4,7,1,6,5,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,4,7,2,1,5,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,4,7,2,1,6,5]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,4,7,2,5,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,7,2,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,4,7,2,6,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,4,7,2,6,5,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,4,7,5,1,2,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[3,4,7,5,1,6,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[3,4,7,5,2,1,6]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[3,4,7,5,2,6,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101
[3,4,7,5,6,1,2]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>001010
[3,4,7,5,6,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>001011
[3,4,7,6,1,2,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[3,4,7,6,1,5,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[3,4,7,6,2,1,5]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[3,4,7,6,2,5,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101
[3,4,7,6,5,1,2]=>[[.,[.,[[[.,.],.],.]]],[.,.]]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>001110
[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>001111
[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[3,5,1,2,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[3,5,1,2,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,5,1,2,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[3,5,1,2,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,5,1,2,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[3,5,1,4,7,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,5,1,6,4,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,5,1,6,4,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,5,1,6,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,5,1,6,7,4,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,5,1,7,4,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,5,1,7,4,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,5,1,7,6,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,5,1,7,6,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[3,5,2,1,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[3,5,2,1,4,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[3,5,2,1,6,4,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,5,2,1,6,7,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[3,5,2,1,7,4,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,5,2,1,7,6,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,5,2,4,1,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,5,2,4,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,5,2,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[3,5,2,4,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,5,2,4,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[3,5,2,6,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,5,2,6,1,7,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,5,2,6,4,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,5,2,6,4,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,5,2,6,7,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,5,2,6,7,4,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[3,5,2,7,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,5,2,7,1,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,5,2,7,4,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,5,2,7,4,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,5,2,7,6,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,5,2,7,6,4,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[3,5,4,1,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,5,4,1,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,5,4,1,6,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,5,4,1,6,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,5,4,1,7,2,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,5,4,1,7,6,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,5,4,2,1,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,5,4,2,1,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,5,4,2,6,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,5,4,2,6,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,5,4,2,7,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,5,4,2,7,6,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,5,4,6,1,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,5,4,6,1,7,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,5,4,6,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,5,4,6,7,1,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[3,5,4,6,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>010011
[3,5,4,7,1,2,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,5,4,7,1,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,5,4,7,2,1,6]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,5,4,7,2,6,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,5,4,7,6,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[3,5,4,7,6,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>010111
[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,5,6,1,2,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,5,6,1,4,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,5,6,1,4,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,5,6,1,7,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,5,6,1,7,4,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,5,6,2,1,4,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,5,6,2,1,7,4]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,5,6,2,4,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,5,6,2,4,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,5,6,2,7,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,5,6,2,7,4,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,5,6,4,1,2,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[3,5,6,4,1,7,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[3,5,6,4,2,1,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[3,5,6,4,2,7,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101
[3,5,6,4,7,1,2]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[3,5,6,4,7,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>001011
[3,5,6,7,1,2,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[3,5,6,7,1,4,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[3,5,6,7,2,1,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[3,5,6,7,2,4,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101
[3,5,6,7,4,1,2]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>000110
[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>000111
[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,5,7,1,2,6,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,5,7,1,4,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,5,7,1,4,6,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,5,7,1,6,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,5,7,1,6,4,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,5,7,2,1,4,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,5,7,2,1,6,4]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,5,7,2,4,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,5,7,2,4,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,5,7,2,6,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,5,7,2,6,4,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,5,7,4,1,2,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[3,5,7,4,1,6,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[3,5,7,4,2,1,6]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[3,5,7,4,2,6,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101
[3,5,7,4,6,1,2]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[3,5,7,4,6,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>001011
[3,5,7,6,1,2,4]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[3,5,7,6,1,4,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[3,5,7,6,2,1,4]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[3,5,7,6,2,4,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101
[3,5,7,6,4,1,2]=>[[.,[[.,[[.,.],.]],.]],[.,.]]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>001110
[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>001111
[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[3,6,1,2,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[3,6,1,2,5,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,6,1,2,5,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[3,6,1,2,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,6,1,2,7,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[3,6,1,4,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,6,1,4,2,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,6,1,4,7,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[3,6,1,5,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,6,1,5,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,6,1,5,4,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,6,1,5,4,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,6,1,5,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,6,1,5,7,4,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[3,6,1,7,2,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,6,1,7,2,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,6,1,7,4,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,6,1,7,4,5,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,6,1,7,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[3,6,2,1,4,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[3,6,2,1,4,7,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[3,6,2,1,5,4,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,6,2,1,5,7,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[3,6,2,1,7,4,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,6,2,1,7,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[3,6,2,4,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,6,2,4,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,6,2,4,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[3,6,2,4,7,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,6,2,4,7,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,6,2,5,1,7,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,6,2,5,4,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,6,2,5,4,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,6,2,5,7,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,6,2,5,7,4,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[3,6,2,7,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,6,2,7,1,5,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,6,2,7,4,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,6,2,7,4,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,6,2,7,5,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,6,2,7,5,4,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[3,6,4,1,2,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,6,4,1,2,7,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,6,4,1,5,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,6,4,1,5,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,6,4,1,7,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,6,4,1,7,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,6,4,2,1,5,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,6,4,2,1,7,5]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,6,4,2,5,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,6,4,2,5,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,6,4,2,7,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,6,4,2,7,5,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,6,4,5,1,2,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,6,4,5,1,7,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,6,4,5,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,6,4,5,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,6,4,5,7,1,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[3,6,4,5,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>010011
[3,6,4,7,1,2,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,6,4,7,1,5,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,6,4,7,2,1,5]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,6,4,7,2,5,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,6,4,7,5,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[3,6,4,7,5,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>010111
[3,6,5,1,2,4,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,6,5,1,2,7,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,6,5,1,4,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,6,5,1,4,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,6,5,1,7,2,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,6,5,1,7,4,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,6,5,2,1,4,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,6,5,2,1,7,4]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,6,5,2,4,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,6,5,2,4,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,6,5,2,7,1,4]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,6,5,2,7,4,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,6,5,4,1,2,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[3,6,5,4,1,7,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[3,6,5,4,2,1,7]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[3,6,5,4,2,7,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101
[3,6,5,4,7,1,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[3,6,5,4,7,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>011011
[3,6,5,7,1,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,6,5,7,1,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,6,5,7,2,1,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,6,5,7,2,4,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,6,5,7,4,1,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[3,6,5,7,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>010111
[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[3,6,7,1,2,5,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[3,6,7,1,4,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,6,7,1,4,5,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[3,6,7,1,5,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[3,6,7,1,5,4,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[3,6,7,2,1,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[3,6,7,2,1,5,4]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[3,6,7,2,4,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,6,7,2,4,5,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[3,6,7,2,5,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[3,6,7,2,5,4,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[3,6,7,4,1,2,5]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[3,6,7,4,1,5,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[3,6,7,4,2,1,5]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[3,6,7,4,2,5,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101
[3,6,7,4,5,1,2]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>001010
[3,6,7,4,5,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>001011
[3,6,7,5,1,2,4]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[3,6,7,5,1,4,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[3,6,7,5,2,1,4]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[3,6,7,5,2,4,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101
[3,6,7,5,4,1,2]=>[[.,[[[.,[.,.]],.],.]],[.,.]]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>001110
[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>001111
[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[3,7,1,2,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[3,7,1,2,5,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,7,1,2,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[3,7,1,2,6,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[3,7,1,2,6,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[3,7,1,4,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,7,1,4,2,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,7,1,4,5,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[3,7,1,4,6,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,7,1,4,6,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[3,7,1,5,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,7,1,5,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,7,1,5,4,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,7,1,5,4,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,7,1,5,6,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[3,7,1,5,6,4,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[3,7,1,6,2,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[3,7,1,6,2,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[3,7,1,6,4,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,7,1,6,4,5,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[3,7,1,6,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[3,7,1,6,5,4,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[3,7,2,1,4,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[3,7,2,1,5,4,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,7,2,1,5,6,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[3,7,2,1,6,4,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[3,7,2,1,6,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[3,7,2,4,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,7,2,4,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,7,2,4,5,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[3,7,2,4,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,7,2,4,6,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,7,2,5,1,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,7,2,5,4,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,7,2,5,4,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,7,2,5,6,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[3,7,2,5,6,4,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[3,7,2,6,1,5,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[3,7,2,6,4,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,7,2,6,4,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[3,7,2,6,5,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[3,7,2,6,5,4,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[3,7,4,1,2,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,7,4,1,2,6,5]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,7,4,1,5,2,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,4,1,5,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,7,4,1,6,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,4,1,6,5,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,7,4,2,1,5,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,7,4,2,1,6,5]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,7,4,2,5,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,4,2,5,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,7,4,2,6,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,4,2,6,5,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,7,4,5,1,2,6]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,7,4,5,1,6,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,7,4,5,2,1,6]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,7,4,5,2,6,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,7,4,5,6,1,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>010010
[3,7,4,5,6,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>010011
[3,7,4,6,1,2,5]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,7,4,6,1,5,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,7,4,6,2,1,5]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,7,4,6,2,5,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,7,4,6,5,1,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>010110
[3,7,4,6,5,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>010111
[3,7,5,1,2,4,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,7,5,1,2,6,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,7,5,1,4,2,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,5,1,4,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,7,5,1,6,2,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,5,1,6,4,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,7,5,2,1,4,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,7,5,2,1,6,4]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,7,5,2,4,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,5,2,4,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,7,5,2,6,1,4]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,5,2,6,4,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,7,5,4,1,2,6]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[3,7,5,4,1,6,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[3,7,5,4,2,1,6]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[3,7,5,4,2,6,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101
[3,7,5,4,6,1,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[3,7,5,4,6,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>011011
[3,7,5,6,1,2,4]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[3,7,5,6,1,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[3,7,5,6,2,1,4]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[3,7,5,6,2,4,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[3,7,5,6,4,1,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>010110
[3,7,5,6,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>010111
[3,7,6,1,2,4,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[3,7,6,1,2,5,4]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[3,7,6,1,4,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,6,1,4,5,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[3,7,6,1,5,2,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[3,7,6,1,5,4,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[3,7,6,2,1,4,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[3,7,6,2,1,5,4]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[3,7,6,2,4,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,6,2,4,5,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[3,7,6,2,5,1,4]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[3,7,6,2,5,4,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[3,7,6,4,1,2,5]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[3,7,6,4,1,5,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[3,7,6,4,2,1,5]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[3,7,6,4,2,5,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101
[3,7,6,4,5,1,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>011010
[3,7,6,4,5,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>011011
[3,7,6,5,1,2,4]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[3,7,6,5,1,4,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[3,7,6,5,2,1,4]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[3,7,6,5,2,4,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101
[3,7,6,5,4,1,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>011110
[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>011111
[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[4,1,2,3,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[4,1,2,5,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[4,1,2,6,5,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[4,1,2,6,7,3,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[4,1,2,6,7,5,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[4,1,2,7,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[4,1,2,7,5,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[4,1,2,7,5,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[4,1,2,7,6,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[4,1,2,7,6,5,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[4,1,3,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[4,1,3,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,3,2,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[4,1,3,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,3,2,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[4,1,3,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,3,5,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,3,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[4,1,3,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[4,1,3,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[4,1,3,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[4,1,3,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,3,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,3,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[4,1,3,6,5,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[4,1,3,6,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[4,1,3,6,7,5,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[4,1,3,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,3,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,3,7,5,2,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[4,1,3,7,5,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[4,1,3,7,6,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[4,1,3,7,6,5,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,5,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[4,1,5,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,5,2,7,6,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,5,3,2,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,5,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,5,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[4,1,5,3,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,5,3,7,6,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[4,1,5,6,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,5,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,5,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[4,1,5,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[4,1,5,6,7,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[4,1,5,6,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[4,1,5,7,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,5,7,2,6,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,5,7,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[4,1,5,7,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[4,1,5,7,6,2,3]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[4,1,5,7,6,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[4,1,6,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[4,1,6,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[4,1,6,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,6,2,5,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[4,1,6,2,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,6,2,7,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[4,1,6,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,6,3,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,6,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,6,3,5,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[4,1,6,3,7,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,6,3,7,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[4,1,6,5,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,6,5,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,6,5,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[4,1,6,5,3,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[4,1,6,5,7,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,6,5,7,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[4,1,6,7,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[4,1,6,7,2,5,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[4,1,6,7,3,2,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[4,1,6,7,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[4,1,6,7,5,2,3]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[4,1,6,7,5,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[4,1,7,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[4,1,7,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[4,1,7,2,5,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,7,2,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[4,1,7,2,6,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[4,1,7,2,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[4,1,7,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,7,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,7,3,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,7,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[4,1,7,3,6,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,7,3,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[4,1,7,5,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,7,5,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,7,5,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[4,1,7,5,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[4,1,7,5,6,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[4,1,7,5,6,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[4,1,7,6,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[4,1,7,6,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[4,1,7,6,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[4,1,7,6,3,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[4,1,7,6,5,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[4,1,7,6,5,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[4,2,1,3,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[4,2,1,3,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[4,2,1,3,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[4,2,1,3,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[4,2,1,3,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[4,2,1,5,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,2,1,5,3,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,2,1,5,6,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,2,1,5,6,7,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[4,2,1,5,7,3,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,2,1,5,7,6,3]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[4,2,1,6,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,2,1,6,3,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,2,1,6,5,3,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,2,1,6,5,7,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[4,2,1,6,7,3,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,2,1,6,7,5,3]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[4,2,1,7,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,2,1,7,3,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,2,1,7,5,3,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,2,1,7,5,6,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[4,2,1,7,6,3,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,2,1,7,6,5,3]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,3,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001
[4,2,3,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011
[4,2,3,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,3,6,1,7,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[4,2,3,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[4,2,3,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011
[4,2,3,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,3,7,1,6,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,3,7,5,1,6]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[4,2,3,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[4,2,3,7,6,1,5]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[4,2,3,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111
[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,2,5,1,7,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,2,5,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,5,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,5,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,5,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[4,2,5,3,7,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,5,3,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[4,2,5,6,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,5,6,1,7,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,5,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[4,2,5,6,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[4,2,5,6,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[4,2,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011
[4,2,5,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,5,7,1,6,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,5,7,3,1,6]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[4,2,5,7,3,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[4,2,5,7,6,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[4,2,5,7,6,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111
[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,2,6,1,3,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,6,1,7,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,2,6,3,1,5,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,6,3,1,7,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,6,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,6,3,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[4,2,6,3,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,6,3,7,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[4,2,6,5,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,6,5,1,7,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,6,5,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[4,2,6,5,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[4,2,6,5,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,6,5,7,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[4,2,6,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,2,6,7,1,5,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,2,6,7,3,1,5]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[4,2,6,7,3,5,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[4,2,6,7,5,1,3]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[4,2,6,7,5,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111
[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,2,7,1,3,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,2,7,1,6,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,2,7,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,2,7,3,1,5,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,7,3,1,6,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,7,3,5,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,7,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[4,2,7,3,6,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,7,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[4,2,7,5,1,3,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,7,5,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,7,5,3,1,6]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[4,2,7,5,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[4,2,7,5,6,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,2,7,5,6,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[4,2,7,6,1,3,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,2,7,6,1,5,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,2,7,6,3,1,5]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[4,2,7,6,3,5,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[4,2,7,6,5,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[4,2,7,6,5,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111
[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[4,3,1,2,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[4,3,1,2,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[4,3,1,2,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[4,3,1,2,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[4,3,1,2,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,3,1,5,2,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[4,3,1,5,7,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,3,1,5,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[4,3,1,6,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,3,1,6,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,3,1,6,5,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,3,1,6,5,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[4,3,1,6,7,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[4,3,1,6,7,5,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[4,3,1,7,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[4,3,1,7,2,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[4,3,1,7,5,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,3,1,7,5,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[4,3,1,7,6,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[4,3,1,7,6,5,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[4,3,2,5,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[4,3,2,5,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[4,3,2,6,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[4,3,2,6,5,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[4,3,2,6,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[4,3,2,6,7,5,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[4,3,2,7,1,6,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[4,3,2,7,5,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[4,3,2,7,5,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[4,3,2,7,6,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[4,3,2,7,6,5,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,3,5,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,3,5,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,5,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,3,5,1,7,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,5,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[4,3,5,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,5,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[4,3,5,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,3,5,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[4,3,5,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>100011
[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,3,5,7,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,3,5,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[4,3,5,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[4,3,5,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[4,3,5,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>100111
[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,3,6,1,2,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,3,6,1,5,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,6,1,5,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,3,6,1,7,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,6,1,7,5,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,3,6,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[4,3,6,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,6,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[4,3,6,2,7,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,6,2,7,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[4,3,6,5,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,3,6,5,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,3,6,5,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[4,3,6,5,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[4,3,6,5,7,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,3,6,5,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[4,3,6,7,1,5,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[4,3,6,7,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[4,3,6,7,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[4,3,6,7,5,1,2]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[4,3,6,7,5,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>100111
[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[4,3,7,1,2,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[4,3,7,1,5,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,7,1,5,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[4,3,7,1,6,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[4,3,7,1,6,5,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[4,3,7,2,1,6,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[4,3,7,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[4,3,7,2,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[4,3,7,5,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,3,7,5,1,6,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,3,7,5,2,1,6]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[4,3,7,5,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[4,3,7,5,6,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[4,3,7,5,6,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[4,3,7,6,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[4,3,7,6,1,5,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[4,3,7,6,2,1,5]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[4,3,7,6,2,5,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[4,3,7,6,5,1,2]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[4,3,7,6,5,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>101111
[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[4,5,1,2,3,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[4,5,1,2,6,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,5,1,2,6,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[4,5,1,2,7,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,5,1,2,7,6,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[4,5,1,3,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,5,1,3,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,5,1,3,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,5,1,3,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[4,5,1,3,7,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,5,1,3,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[4,5,1,6,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,5,1,6,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,5,1,6,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,5,1,6,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,5,1,6,7,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,5,1,6,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[4,5,1,7,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,5,1,7,2,6,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,5,1,7,3,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,5,1,7,3,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,5,1,7,6,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,5,1,7,6,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[4,5,2,1,3,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,5,2,1,3,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,5,2,1,6,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,5,2,1,6,7,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,5,2,1,7,3,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,5,2,1,7,6,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,5,2,3,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,5,2,3,1,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,5,2,3,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,5,2,3,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[4,5,2,3,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,5,2,3,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[4,5,2,6,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,5,2,6,1,7,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,5,2,6,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,5,2,6,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,5,2,6,7,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,5,2,6,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[4,5,2,7,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,5,2,7,1,6,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,5,2,7,3,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,5,2,7,3,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,5,2,7,6,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,5,2,7,6,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,5,3,1,7,2,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[4,5,3,2,1,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[4,5,3,2,7,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,5,3,2,7,6,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[4,5,3,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,5,3,6,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,5,3,6,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[4,5,3,7,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,5,3,7,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,5,3,7,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,5,3,7,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,5,3,7,6,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,5,3,7,6,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[4,5,6,1,3,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,5,6,1,3,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[4,5,6,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,5,6,1,7,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[4,5,6,2,1,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,5,6,2,1,7,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,5,6,2,3,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,6,2,3,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[4,5,6,2,7,1,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,6,2,7,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[4,5,6,3,1,2,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,5,6,3,1,7,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101
[4,5,6,3,7,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>001011
[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>000100
[4,5,6,7,1,3,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>000101
[4,5,6,7,2,1,3]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[4,5,6,7,2,3,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>000101
[4,5,6,7,3,1,2]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>000110
[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>000111
[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[4,5,7,1,3,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,5,7,1,3,6,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[4,5,7,1,6,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,5,7,1,6,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[4,5,7,2,1,3,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,5,7,2,1,6,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,5,7,2,3,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,7,2,3,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[4,5,7,2,6,1,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,7,2,6,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[4,5,7,3,1,2,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,5,7,3,1,6,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,5,7,3,2,1,6]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[4,5,7,3,2,6,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101
[4,5,7,3,6,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,5,7,3,6,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>001011
[4,5,7,6,1,2,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>001100
[4,5,7,6,1,3,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>001101
[4,5,7,6,2,1,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[4,5,7,6,2,3,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>001101
[4,5,7,6,3,1,2]=>[[[.,[.,[[.,.],.]]],.],[.,.]]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>001110
[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>001111
[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[4,6,1,2,3,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[4,6,1,2,5,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,6,1,2,5,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[4,6,1,2,7,3,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,6,1,2,7,5,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[4,6,1,3,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,6,1,3,2,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,6,1,3,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,6,1,3,5,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[4,6,1,3,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,6,1,3,7,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[4,6,1,5,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,6,1,5,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,6,1,5,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,6,1,5,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,6,1,5,7,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,6,1,5,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[4,6,1,7,2,3,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,6,1,7,2,5,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,6,1,7,3,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,6,1,7,3,5,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,6,1,7,5,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,6,1,7,5,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[4,6,2,1,3,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,6,2,1,3,7,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,6,2,1,5,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,6,2,1,5,7,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,6,2,1,7,3,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,6,2,1,7,5,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,6,2,3,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,6,2,3,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,6,2,3,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,6,2,3,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[4,6,2,3,7,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,6,2,3,7,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[4,6,2,5,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,6,2,5,1,7,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,6,2,5,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,6,2,5,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,6,2,5,7,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,6,2,5,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[4,6,2,7,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,6,2,7,1,5,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,6,2,7,3,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,6,2,7,3,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,6,2,7,5,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,6,2,7,5,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[4,6,3,1,2,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,6,3,1,2,7,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,6,3,1,7,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,6,3,2,1,5,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[4,6,3,2,1,7,5]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[4,6,3,2,5,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,6,3,2,5,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[4,6,3,2,7,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,6,3,2,7,5,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,6,3,5,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,6,3,5,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,6,3,5,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,6,3,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,6,3,5,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[4,6,3,7,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,6,3,7,1,5,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,6,3,7,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,6,3,7,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,6,3,7,5,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,6,3,7,5,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[4,6,5,1,2,3,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[4,6,5,1,2,7,3]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[4,6,5,1,3,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,6,5,1,3,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[4,6,5,1,7,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,6,5,1,7,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[4,6,5,2,1,3,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,6,5,2,1,7,3]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,6,5,2,3,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,6,5,2,3,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[4,6,5,2,7,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,6,5,2,7,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[4,6,5,3,1,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,6,5,3,1,7,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,6,5,3,2,1,7]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[4,6,5,3,2,7,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101
[4,6,5,3,7,1,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,6,5,3,7,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>011011
[4,6,5,7,1,2,3]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[4,6,5,7,1,3,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[4,6,5,7,2,1,3]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[4,6,5,7,2,3,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[4,6,5,7,3,1,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[4,6,5,7,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>010111
[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[4,6,7,1,2,5,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[4,6,7,1,3,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,6,7,1,3,5,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[4,6,7,1,5,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[4,6,7,2,1,3,5]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,6,7,2,1,5,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,6,7,2,3,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,6,7,2,3,5,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[4,6,7,2,5,1,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,6,7,2,5,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[4,6,7,3,1,2,5]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[4,6,7,3,1,5,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[4,6,7,3,2,1,5]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[4,6,7,3,2,5,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101
[4,6,7,3,5,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[4,6,7,3,5,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>001011
[4,6,7,5,1,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>001100
[4,6,7,5,1,3,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>001101
[4,6,7,5,2,1,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[4,6,7,5,2,3,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>001101
[4,6,7,5,3,1,2]=>[[[.,[[.,[.,.]],.]],.],[.,.]]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>001110
[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>001111
[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[4,7,1,2,3,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[4,7,1,2,5,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,7,1,2,5,6,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[4,7,1,2,6,3,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[4,7,1,2,6,5,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[4,7,1,3,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,7,1,3,2,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,7,1,3,5,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,7,1,3,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[4,7,1,3,6,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,7,1,3,6,5,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[4,7,1,5,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,7,1,5,2,6,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,7,1,5,3,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,7,1,5,3,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,7,1,5,6,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[4,7,1,5,6,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[4,7,1,6,2,3,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[4,7,1,6,2,5,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[4,7,1,6,3,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,7,1,6,3,5,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[4,7,1,6,5,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[4,7,1,6,5,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[4,7,2,1,3,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,7,2,1,3,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,7,2,1,5,3,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,7,2,1,5,6,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,7,2,1,6,3,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,7,2,1,6,5,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,7,2,3,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,7,2,3,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,7,2,3,5,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,7,2,3,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[4,7,2,3,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,7,2,3,6,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[4,7,2,5,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,7,2,5,1,6,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,7,2,5,3,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,7,2,5,3,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,7,2,5,6,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,7,2,5,6,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[4,7,2,6,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,7,2,6,1,5,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,7,2,6,3,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,7,2,6,3,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[4,7,2,6,5,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,7,2,6,5,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[4,7,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[4,7,3,1,2,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[4,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[4,7,3,1,6,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[4,7,3,1,6,5,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[4,7,3,2,1,5,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[4,7,3,2,1,6,5]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[4,7,3,2,5,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,7,3,2,5,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[4,7,3,2,6,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[4,7,3,2,6,5,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[4,7,3,5,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,7,3,5,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,7,3,5,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,7,3,5,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,7,3,5,6,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[4,7,3,5,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[4,7,3,6,1,5,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[4,7,3,6,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[4,7,3,6,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[4,7,3,6,5,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[4,7,3,6,5,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[4,7,5,1,2,3,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[4,7,5,1,2,6,3]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[4,7,5,1,3,2,6]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,7,5,1,3,6,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[4,7,5,1,6,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,7,5,1,6,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[4,7,5,2,1,3,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,7,5,2,1,6,3]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,7,5,2,3,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,5,2,3,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[4,7,5,2,6,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,5,2,6,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[4,7,5,3,1,2,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,7,5,3,1,6,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,7,5,3,2,1,6]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[4,7,5,3,2,6,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101
[4,7,5,3,6,1,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,5,3,6,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>011011
[4,7,5,6,1,2,3]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>010100
[4,7,5,6,1,3,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>010101
[4,7,5,6,2,1,3]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[4,7,5,6,2,3,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>010101
[4,7,5,6,3,1,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>010110
[4,7,5,6,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>010111
[4,7,6,1,2,3,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[4,7,6,1,2,5,3]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[4,7,6,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,7,6,1,3,5,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[4,7,6,1,5,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[4,7,6,1,5,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[4,7,6,2,1,3,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,7,6,2,1,5,3]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,7,6,2,3,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,6,2,3,5,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[4,7,6,2,5,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,6,2,5,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[4,7,6,3,1,2,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[4,7,6,3,1,5,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[4,7,6,3,2,1,5]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[4,7,6,3,2,5,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101
[4,7,6,3,5,1,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[4,7,6,3,5,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>011011
[4,7,6,5,1,2,3]=>[[.,[[[.,.],.],.]],[.,[.,.]]]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>011100
[4,7,6,5,1,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>011101
[4,7,6,5,2,1,3]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[4,7,6,5,2,3,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>011101
[4,7,6,5,3,1,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>011110
[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>011111
[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[5,1,2,4,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[5,1,2,4,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[5,1,2,4,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[5,1,2,4,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[5,1,2,4,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[5,1,2,6,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[5,1,2,6,4,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[5,1,2,6,7,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[5,1,2,6,7,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[5,1,2,7,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[5,1,2,7,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[5,1,2,7,6,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[5,1,2,7,6,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[5,1,3,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[5,1,3,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,3,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[5,1,3,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,3,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[5,1,3,4,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,3,4,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,3,4,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[5,1,3,4,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[5,1,3,4,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[5,1,3,4,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[5,1,3,6,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,3,6,2,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,3,6,4,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[5,1,3,6,4,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[5,1,3,6,7,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[5,1,3,6,7,4,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[5,1,3,7,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,3,7,2,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,3,7,4,2,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[5,1,3,7,4,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[5,1,3,7,6,2,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[5,1,3,7,6,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[5,1,4,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[5,1,4,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[5,1,4,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,4,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[5,1,4,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,4,2,7,6,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,4,3,2,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,4,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,4,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[5,1,4,3,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,4,3,7,6,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[5,1,4,6,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,4,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,4,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[5,1,4,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[5,1,4,6,7,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[5,1,4,6,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[5,1,4,7,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,4,7,2,6,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,4,7,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[5,1,4,7,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[5,1,4,7,6,2,3]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[5,1,4,7,6,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[5,1,6,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,6,2,4,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[5,1,6,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,6,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[5,1,6,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,6,3,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,6,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,6,3,4,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[5,1,6,3,7,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,6,3,7,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[5,1,6,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,6,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[5,1,6,4,3,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[5,1,6,4,7,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,6,4,7,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[5,1,6,7,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[5,1,6,7,2,4,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[5,1,6,7,3,2,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[5,1,6,7,3,4,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[5,1,6,7,4,2,3]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[5,1,6,7,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[5,1,7,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[5,1,7,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[5,1,7,2,4,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,7,2,4,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[5,1,7,2,6,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[5,1,7,2,6,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[5,1,7,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,7,3,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,7,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,7,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[5,1,7,3,6,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,7,3,6,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[5,1,7,4,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,7,4,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,7,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[5,1,7,4,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[5,1,7,4,6,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[5,1,7,4,6,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[5,1,7,6,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[5,1,7,6,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[5,1,7,6,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[5,1,7,6,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[5,1,7,6,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[5,1,7,6,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[5,2,1,3,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[5,2,1,3,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,2,1,3,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[5,2,1,3,7,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,2,1,3,7,6,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[5,2,1,4,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,2,1,4,3,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,2,1,4,6,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,2,1,4,6,7,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[5,2,1,4,7,3,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,2,1,4,7,6,3]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[5,2,1,6,3,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,2,1,6,3,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,2,1,6,4,3,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,2,1,6,4,7,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,2,1,6,7,3,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,2,1,6,7,4,3]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[5,2,1,7,3,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,2,1,7,3,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,2,1,7,4,3,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,2,1,7,4,6,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,2,1,7,6,3,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,2,1,7,6,4,3]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,2,3,1,4,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,2,3,1,6,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,3,1,6,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,2,3,1,7,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,3,1,7,6,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001
[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011
[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,3,6,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[5,2,3,6,4,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[5,2,3,6,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[5,2,3,6,7,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011
[5,2,3,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,3,7,4,1,6]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[5,2,3,7,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[5,2,3,7,6,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[5,2,3,7,6,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111
[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,2,4,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,2,4,1,6,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,4,1,6,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,2,4,1,7,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,4,1,7,6,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,4,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,4,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[5,2,4,3,7,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[5,2,4,6,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,4,6,1,7,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,4,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[5,2,4,6,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[5,2,4,6,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[5,2,4,6,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011
[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,4,7,1,6,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,4,7,3,1,6]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[5,2,4,7,3,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[5,2,4,7,6,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[5,2,4,7,6,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111
[5,2,6,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,2,6,1,3,7,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,2,6,1,4,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,6,1,4,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,2,6,1,7,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,6,1,7,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,2,6,3,1,4,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,6,3,1,7,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,6,3,4,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,6,3,4,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[5,2,6,3,7,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,6,3,7,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,6,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[5,2,6,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[5,2,6,4,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,6,4,7,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,2,6,7,1,4,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,2,6,7,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[5,2,6,7,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[5,2,6,7,4,1,3]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[5,2,6,7,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111
[5,2,7,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,2,7,1,3,6,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,2,7,1,4,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,7,1,4,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,2,7,1,6,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,2,7,1,6,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,2,7,3,1,4,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,7,3,1,6,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,7,3,4,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,7,3,4,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[5,2,7,3,6,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,7,3,6,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,7,4,3,1,6]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[5,2,7,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[5,2,7,4,6,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,2,7,4,6,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[5,2,7,6,1,3,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,2,7,6,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,2,7,6,3,1,4]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[5,2,7,6,3,4,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[5,2,7,6,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[5,2,7,6,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111
[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[5,3,1,2,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,3,1,2,6,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[5,3,1,2,7,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,3,1,2,7,6,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,3,1,4,2,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,3,1,4,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,3,1,4,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[5,3,1,4,7,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,3,1,4,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[5,3,1,6,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,3,1,6,2,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,3,1,6,4,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,3,1,6,4,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,3,1,6,7,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,3,1,6,7,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[5,3,1,7,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,3,1,7,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,3,1,7,4,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,3,1,7,4,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,3,1,7,6,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,3,1,7,6,4,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[5,3,2,1,4,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[5,3,2,1,6,4,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,3,2,1,6,7,4]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[5,3,2,1,7,4,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,3,2,1,7,6,4]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[5,3,2,4,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,3,2,4,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[5,3,2,6,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,3,2,6,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,3,2,6,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,3,2,6,4,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[5,3,2,6,7,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,3,2,6,7,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[5,3,2,7,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,3,2,7,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,3,2,7,4,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,3,2,7,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[5,3,2,7,6,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,3,2,7,6,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,3,4,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,3,4,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,4,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,3,4,1,7,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,4,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,3,4,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[5,3,4,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,4,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,3,4,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[5,3,4,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>100011
[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,3,4,7,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[5,3,4,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[5,3,4,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>100111
[5,3,6,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,3,6,1,2,7,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,3,6,1,4,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,6,1,4,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,3,6,1,7,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,6,1,7,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,3,6,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,3,6,2,1,7,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,3,6,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,6,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[5,3,6,2,7,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,6,2,7,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[5,3,6,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,3,6,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,3,6,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[5,3,6,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[5,3,6,4,7,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,3,6,4,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,3,6,7,1,4,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,3,6,7,2,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[5,3,6,7,2,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[5,3,6,7,4,1,2]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[5,3,6,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>100111
[5,3,7,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,3,7,1,2,6,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,3,7,1,4,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,7,1,4,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,3,7,1,6,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,3,7,1,6,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,3,7,2,1,4,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,3,7,2,1,6,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,3,7,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,7,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[5,3,7,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,3,7,2,6,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[5,3,7,4,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,3,7,4,1,6,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,3,7,4,2,1,6]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[5,3,7,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[5,3,7,4,6,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[5,3,7,4,6,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[5,3,7,6,1,2,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,3,7,6,1,4,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,3,7,6,2,1,4]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[5,3,7,6,2,4,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[5,3,7,6,4,1,2]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[5,3,7,6,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>101111
[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[5,4,1,2,3,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[5,4,1,2,6,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,4,1,2,6,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[5,4,1,2,7,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[5,4,1,2,7,6,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[5,4,1,3,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,4,1,3,2,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,4,1,3,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,4,1,3,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[5,4,1,3,7,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,4,1,3,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[5,4,1,6,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,4,1,6,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,4,1,6,3,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,4,1,6,7,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[5,4,1,6,7,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[5,4,1,7,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[5,4,1,7,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[5,4,1,7,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,4,1,7,3,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[5,4,1,7,6,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[5,4,1,7,6,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[5,4,2,1,3,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[5,4,2,1,6,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,4,2,1,6,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[5,4,2,1,7,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,4,2,1,7,6,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,4,2,3,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[5,4,2,3,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,4,2,3,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[5,4,2,6,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,4,2,6,1,7,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,4,2,6,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[5,4,2,6,7,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,4,2,6,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[5,4,2,7,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,4,2,7,1,6,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,4,2,7,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,4,2,7,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[5,4,2,7,6,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,4,2,7,6,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[5,4,3,1,2,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,4,3,1,6,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[5,4,3,1,7,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[5,4,3,1,7,6,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,4,3,6,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[5,4,3,6,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[5,4,3,7,1,6,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[5,4,3,7,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[5,4,3,7,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[5,4,3,7,6,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[5,4,3,7,6,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,4,6,1,2,7,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,4,6,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,4,6,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,4,6,1,7,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,4,6,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,4,6,2,1,7,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[5,4,6,2,7,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,6,2,7,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[5,4,6,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,4,6,3,1,7,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[5,4,6,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[5,4,6,7,1,3,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[5,4,6,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[5,4,6,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[5,4,6,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>100111
[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[5,4,7,1,2,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[5,4,7,1,3,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,4,7,1,3,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[5,4,7,1,6,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[5,4,7,1,6,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[5,4,7,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,4,7,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,4,7,2,3,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,7,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[5,4,7,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,7,2,6,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[5,4,7,3,1,2,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[5,4,7,3,1,6,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[5,4,7,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[5,4,7,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[5,4,7,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[5,4,7,6,1,2,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[5,4,7,6,1,3,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[5,4,7,6,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[5,4,7,6,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[5,4,7,6,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[5,4,7,6,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>101111
[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[5,6,1,2,3,7,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[5,6,1,2,4,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[5,6,1,2,4,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[5,6,1,2,7,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[5,6,1,2,7,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[5,6,1,3,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,6,1,3,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,6,1,3,4,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,6,1,3,4,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[5,6,1,3,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,6,1,3,7,4,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[5,6,1,4,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,6,1,4,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,6,1,4,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,6,1,4,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[5,6,1,4,7,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,6,1,4,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[5,6,1,7,2,3,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,6,1,7,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,6,1,7,3,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,6,1,7,3,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[5,6,1,7,4,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,6,1,7,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[5,6,2,1,3,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,6,2,1,3,7,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,6,2,1,4,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,2,1,4,7,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,6,2,1,7,3,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,2,1,7,4,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,6,2,3,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,2,3,1,7,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,2,3,4,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,6,2,3,4,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[5,6,2,3,7,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,6,2,3,7,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,2,4,1,7,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,2,4,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,6,2,4,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[5,6,2,4,7,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,6,2,4,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[5,6,2,7,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,2,7,1,4,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,2,7,3,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,6,2,7,3,4,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[5,6,2,7,4,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,6,2,7,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[5,6,3,1,2,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,6,3,1,2,7,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,6,3,1,4,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,3,1,4,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,6,3,1,7,2,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,3,1,7,4,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,6,3,2,1,4,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,6,3,2,1,7,4]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,6,3,2,4,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,6,3,2,4,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[5,6,3,2,7,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,6,3,2,7,4,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,3,4,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,6,3,4,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,6,3,4,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,3,7,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,3,7,2,1,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,6,3,7,2,4,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,6,3,7,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,6,3,7,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[5,6,4,1,2,3,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,6,4,1,2,7,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,6,4,1,3,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,4,1,3,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,6,4,1,7,2,3]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,6,4,1,7,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,6,4,2,1,3,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,6,4,2,1,7,3]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,6,4,2,3,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,6,4,2,3,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[5,6,4,2,7,1,3]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,6,4,2,7,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,6,4,3,1,7,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101
[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>011011
[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,6,4,7,1,3,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,6,4,7,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,6,4,7,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,6,4,7,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>010111
[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>001000
[5,6,7,1,2,4,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>001001
[5,6,7,1,3,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[5,6,7,1,3,4,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>001001
[5,6,7,1,4,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>001010
[5,6,7,1,4,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>001011
[5,6,7,2,1,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[5,6,7,2,1,4,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[5,6,7,2,3,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[5,6,7,2,3,4,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>001001
[5,6,7,2,4,1,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[5,6,7,2,4,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>001011
[5,6,7,3,1,2,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[5,6,7,3,1,4,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[5,6,7,3,2,1,4]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[5,6,7,3,2,4,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101
[5,6,7,3,4,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>001010
[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>001011
[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>001100
[5,6,7,4,1,3,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>001101
[5,6,7,4,2,1,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[5,6,7,4,2,3,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>001101
[5,6,7,4,3,1,2]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>001110
[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>001111
[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[5,7,1,2,3,6,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[5,7,1,2,4,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[5,7,1,2,4,6,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[5,7,1,2,6,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[5,7,1,2,6,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[5,7,1,3,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,7,1,3,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,7,1,3,4,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,7,1,3,4,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[5,7,1,3,6,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,7,1,3,6,4,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[5,7,1,4,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,7,1,4,2,6,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,7,1,4,3,2,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,7,1,4,3,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[5,7,1,4,6,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[5,7,1,4,6,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[5,7,1,6,2,3,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[5,7,1,6,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[5,7,1,6,3,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,7,1,6,3,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[5,7,1,6,4,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[5,7,1,6,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[5,7,2,1,3,4,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,7,2,1,3,6,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,7,2,1,4,3,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,2,1,4,6,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,7,2,1,6,3,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,2,1,6,4,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,7,2,3,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,2,3,1,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,2,3,4,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,7,2,3,4,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[5,7,2,3,6,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,7,2,3,6,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,2,4,1,6,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,2,4,3,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,7,2,4,3,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[5,7,2,4,6,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,7,2,4,6,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[5,7,2,6,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,2,6,1,4,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,2,6,3,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,7,2,6,3,4,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[5,7,2,6,4,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,7,2,6,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[5,7,3,1,2,4,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,7,3,1,2,6,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,7,3,1,4,2,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,3,1,4,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,7,3,1,6,2,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,3,1,6,4,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,7,3,2,1,4,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,7,3,2,1,6,4]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,7,3,2,4,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,7,3,2,4,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[5,7,3,2,6,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,7,3,2,6,4,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,3,4,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,7,3,4,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,7,3,4,6,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[5,7,3,4,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[5,7,3,6,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,3,6,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,3,6,2,1,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,7,3,6,2,4,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,7,3,6,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[5,7,3,6,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[5,7,4,1,2,3,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[5,7,4,1,2,6,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[5,7,4,1,3,2,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,4,1,3,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[5,7,4,1,6,2,3]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[5,7,4,1,6,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[5,7,4,2,1,3,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,7,4,2,1,6,3]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,7,4,2,3,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,7,4,2,3,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[5,7,4,2,6,1,3]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,7,4,2,6,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[5,7,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[5,7,4,3,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[5,7,4,3,2,1,6]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[5,7,4,3,2,6,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101
[5,7,4,3,6,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[5,7,4,3,6,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>011011
[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[5,7,4,6,1,3,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[5,7,4,6,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,7,4,6,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[5,7,4,6,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[5,7,4,6,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>010111
[5,7,6,1,2,3,4]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>011000
[5,7,6,1,2,4,3]=>[[.,[[.,.],.]],[.,[[.,.],.]]]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>011001
[5,7,6,1,3,2,4]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[5,7,6,1,3,4,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>011001
[5,7,6,1,4,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>011010
[5,7,6,1,4,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>011011
[5,7,6,2,1,3,4]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[5,7,6,2,1,4,3]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[5,7,6,2,3,1,4]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[5,7,6,2,3,4,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>011001
[5,7,6,2,4,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[5,7,6,2,4,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>011011
[5,7,6,3,1,2,4]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[5,7,6,3,1,4,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[5,7,6,3,2,1,4]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[5,7,6,3,2,4,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101
[5,7,6,3,4,1,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>011010
[5,7,6,3,4,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>011011
[5,7,6,4,1,2,3]=>[[[.,[[.,.],.]],.],[.,[.,.]]]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>011100
[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>011101
[5,7,6,4,2,1,3]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[5,7,6,4,2,3,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>011101
[5,7,6,4,3,1,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>011110
[5,7,6,4,3,2,1]=>[[[[[.,[[.,.],.]],.],.],.],.]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>011111
[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[6,1,2,3,5,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[6,1,2,4,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[6,1,2,4,5,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[6,1,2,4,7,3,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[6,1,2,4,7,5,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[6,1,2,5,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[6,1,2,5,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[6,1,2,5,4,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[6,1,2,5,7,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[6,1,2,5,7,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[6,1,2,7,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[6,1,2,7,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[6,1,2,7,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[6,1,2,7,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[6,1,2,7,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[6,1,3,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[6,1,3,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,3,2,5,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[6,1,3,2,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,3,2,7,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[6,1,3,4,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,3,4,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,3,4,5,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[6,1,3,4,5,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[6,1,3,4,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[6,1,3,4,7,5,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[6,1,3,5,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,3,5,2,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,3,5,4,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[6,1,3,5,4,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[6,1,3,5,7,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[6,1,3,5,7,4,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[6,1,3,7,2,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,3,7,2,5,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,3,7,4,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[6,1,3,7,4,5,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[6,1,3,7,5,2,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[6,1,3,7,5,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[6,1,4,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[6,1,4,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[6,1,4,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,4,2,5,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[6,1,4,2,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,4,2,7,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[6,1,4,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,4,3,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,4,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,4,3,5,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[6,1,4,3,7,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,4,3,7,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[6,1,4,5,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,4,5,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,4,5,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[6,1,4,5,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[6,1,4,5,7,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[6,1,4,5,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[6,1,4,7,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,4,7,2,5,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,4,7,3,2,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[6,1,4,7,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[6,1,4,7,5,2,3]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[6,1,4,7,5,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[6,1,5,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[6,1,5,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[6,1,5,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,5,2,4,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[6,1,5,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,5,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[6,1,5,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,5,3,2,7,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,5,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,5,3,4,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[6,1,5,3,7,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,5,3,7,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[6,1,5,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,5,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[6,1,5,4,3,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[6,1,5,4,7,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,5,4,7,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[6,1,5,7,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[6,1,5,7,2,4,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[6,1,5,7,3,2,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[6,1,5,7,3,4,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[6,1,5,7,4,2,3]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[6,1,5,7,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[6,1,7,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[6,1,7,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[6,1,7,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,7,2,4,5,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[6,1,7,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[6,1,7,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[6,1,7,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,7,3,2,5,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,7,3,4,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,7,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[6,1,7,3,5,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,7,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[6,1,7,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,7,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,7,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[6,1,7,4,3,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[6,1,7,4,5,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[6,1,7,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[6,1,7,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[6,1,7,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[6,1,7,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[6,1,7,5,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[6,1,7,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[6,2,1,3,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[6,2,1,3,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,2,1,3,5,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[6,2,1,3,7,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,2,1,3,7,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[6,2,1,4,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,2,1,4,3,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,2,1,4,5,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,2,1,4,5,7,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[6,2,1,4,7,3,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,2,1,4,7,5,3]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[6,2,1,5,3,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,2,1,5,3,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,2,1,5,4,3,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,2,1,5,4,7,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,2,1,5,7,3,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,2,1,5,7,4,3]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[6,2,1,7,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,2,1,7,3,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,2,1,7,4,3,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,2,1,7,4,5,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,2,1,7,5,3,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,2,1,7,5,4,3]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,2,3,1,4,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,2,3,1,5,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,3,1,5,7,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,2,3,1,7,4,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,3,1,7,5,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,3,4,1,7,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001
[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[6,2,3,4,7,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011
[6,2,3,5,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,3,5,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[6,2,3,5,4,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[6,2,3,5,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[6,2,3,5,7,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011
[6,2,3,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,3,7,1,5,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,3,7,4,1,5]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[6,2,3,7,4,5,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[6,2,3,7,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111
[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,2,4,1,3,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,2,4,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,4,1,5,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,2,4,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,4,1,7,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,2,4,3,1,5,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,4,3,1,7,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,4,3,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[6,2,4,3,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,4,3,7,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[6,2,4,5,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,4,5,1,7,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,4,5,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[6,2,4,5,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[6,2,4,5,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[6,2,4,5,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011
[6,2,4,7,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,4,7,1,5,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,4,7,3,1,5]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[6,2,4,7,3,5,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[6,2,4,7,5,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[6,2,4,7,5,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111
[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,2,5,1,3,7,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,2,5,1,4,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,5,1,4,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,2,5,1,7,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,5,1,7,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,2,5,3,1,4,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,5,3,1,7,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,5,3,4,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,5,3,4,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[6,2,5,3,7,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,5,3,7,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[6,2,5,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,5,4,1,7,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[6,2,5,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[6,2,5,4,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,5,4,7,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,2,5,7,1,4,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,2,5,7,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[6,2,5,7,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[6,2,5,7,4,1,3]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[6,2,5,7,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111
[6,2,7,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,2,7,1,3,5,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,2,7,1,4,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,7,1,4,5,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,2,7,1,5,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,2,7,1,5,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,2,7,3,1,4,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,7,3,1,5,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,7,3,4,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,7,3,4,5,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[6,2,7,3,5,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,7,3,5,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[6,2,7,4,1,3,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,7,4,1,5,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,7,4,3,1,5]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[6,2,7,4,3,5,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,2,7,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[6,2,7,5,1,3,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,2,7,5,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,2,7,5,3,1,4]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[6,2,7,5,3,4,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[6,2,7,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[6,2,7,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111
[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[6,3,1,2,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,3,1,2,5,7,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[6,3,1,2,7,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,3,1,2,7,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[6,3,1,4,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,3,1,4,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,3,1,4,5,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,3,1,4,5,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[6,3,1,4,7,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,3,1,4,7,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[6,3,1,5,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,3,1,5,2,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,3,1,5,4,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,3,1,5,4,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,3,1,5,7,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,3,1,5,7,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[6,3,1,7,2,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,3,1,7,2,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,3,1,7,4,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,3,1,7,4,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,3,1,7,5,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,3,1,7,5,4,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,3,2,1,4,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,3,2,1,5,4,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,3,2,1,5,7,4]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,3,2,1,7,4,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,3,2,1,7,5,4]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,3,2,4,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[6,3,2,4,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,3,2,4,7,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,3,2,5,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,3,2,5,4,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,3,2,5,7,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,3,2,5,7,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[6,3,2,7,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,3,2,7,1,5,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,3,2,7,4,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,3,2,7,4,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,3,2,7,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,3,2,7,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,3,4,1,2,7,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,3,4,1,5,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,4,1,5,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,3,4,1,7,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,4,1,7,5,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,3,4,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,3,4,2,7,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,4,2,7,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,3,4,5,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,3,4,5,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>100011
[6,3,4,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,3,4,7,1,5,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,3,4,7,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[6,3,4,7,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[6,3,4,7,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[6,3,4,7,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>100111
[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,3,5,1,2,7,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,3,5,1,4,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,5,1,4,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,3,5,1,7,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,5,1,7,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,3,5,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,3,5,2,1,7,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,5,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,3,5,2,7,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,5,2,7,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,3,5,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,3,5,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,3,5,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[6,3,5,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[6,3,5,4,7,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,3,5,4,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,3,5,7,1,4,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,3,5,7,2,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[6,3,5,7,2,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[6,3,5,7,4,1,2]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[6,3,5,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>100111
[6,3,7,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,3,7,1,2,5,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,3,7,1,4,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,7,1,4,5,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,3,7,1,5,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,3,7,1,5,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,3,7,2,1,4,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,3,7,2,1,5,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,3,7,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,7,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,3,7,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,3,7,2,5,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,3,7,4,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,3,7,4,1,5,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,3,7,4,2,1,5]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[6,3,7,4,2,5,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[6,3,7,4,5,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[6,3,7,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[6,3,7,5,1,2,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,3,7,5,1,4,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,3,7,5,2,1,4]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[6,3,7,5,2,4,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[6,3,7,5,4,1,2]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[6,3,7,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>101111
[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[6,4,1,2,3,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[6,4,1,2,5,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,4,1,2,5,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[6,4,1,2,7,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,4,1,2,7,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[6,4,1,3,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,4,1,3,2,7,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,4,1,3,5,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,4,1,3,5,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[6,4,1,3,7,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,4,1,3,7,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[6,4,1,5,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,4,1,5,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,4,1,5,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,4,1,5,3,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,4,1,5,7,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,4,1,5,7,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[6,4,1,7,2,3,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,4,1,7,2,5,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,4,1,7,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,4,1,7,3,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,4,1,7,5,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,4,1,7,5,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,4,2,1,3,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,4,2,1,5,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,4,2,1,5,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,4,2,1,7,3,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,4,2,1,7,5,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,4,2,3,1,7,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,4,2,3,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[6,4,2,3,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,4,2,3,7,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[6,4,2,5,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,4,2,5,1,7,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,4,2,5,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,4,2,5,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,4,2,5,7,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,4,2,5,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[6,4,2,7,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,4,2,7,1,5,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,4,2,7,3,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,4,2,7,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,4,2,7,5,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,4,2,7,5,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,4,3,1,2,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,4,3,1,5,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,4,3,1,5,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,4,3,1,7,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,4,3,1,7,5,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[6,4,3,2,1,7,5]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[6,4,3,2,7,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,4,3,2,7,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,4,3,5,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[6,4,3,5,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[6,4,3,7,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,4,3,7,1,5,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,4,3,7,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,4,3,7,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[6,4,3,7,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,4,3,7,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,4,5,1,2,7,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,4,5,1,3,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,4,5,1,3,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,4,5,1,7,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,4,5,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,4,5,2,1,7,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,4,5,2,7,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,5,2,7,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,4,5,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,4,5,3,1,7,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[6,4,5,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[6,4,5,7,1,3,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[6,4,5,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[6,4,5,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[6,4,5,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>100111
[6,4,7,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,4,7,1,2,5,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,4,7,1,3,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,4,7,1,3,5,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,4,7,1,5,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,4,7,1,5,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,4,7,2,1,3,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,4,7,2,1,5,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,4,7,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,7,2,3,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,4,7,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,7,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,4,7,3,1,2,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,4,7,3,1,5,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,4,7,3,2,1,5]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[6,4,7,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[6,4,7,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,4,7,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[6,4,7,5,1,2,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[6,4,7,5,1,3,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[6,4,7,5,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[6,4,7,5,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[6,4,7,5,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[6,4,7,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>101111
[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[6,5,1,2,3,7,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[6,5,1,2,4,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,5,1,2,4,7,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[6,5,1,2,7,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[6,5,1,2,7,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[6,5,1,3,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,5,1,3,2,7,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,5,1,3,4,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,5,1,3,4,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[6,5,1,3,7,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,5,1,3,7,4,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[6,5,1,4,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,5,1,4,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,5,1,4,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,5,1,4,3,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,5,1,4,7,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[6,5,1,4,7,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[6,5,1,7,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[6,5,1,7,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[6,5,1,7,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,5,1,7,3,4,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[6,5,1,7,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[6,5,1,7,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,5,2,1,3,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,5,2,1,4,3,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,2,1,4,7,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,5,2,1,7,3,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,2,1,7,4,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,2,3,1,7,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[6,5,2,3,7,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,5,2,3,7,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,2,4,1,7,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,2,4,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,5,2,4,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,5,2,4,7,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,5,2,4,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[6,5,2,7,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,2,7,1,4,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,2,7,3,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,5,2,7,3,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[6,5,2,7,4,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,5,2,7,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,5,3,1,2,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,5,3,1,4,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,3,1,4,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,5,3,1,7,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,3,1,7,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[6,5,3,2,1,7,4]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,5,3,2,4,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[6,5,3,2,7,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,5,3,2,7,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,3,4,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[6,5,3,7,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,3,7,1,4,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,3,7,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,5,3,7,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[6,5,3,7,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[6,5,3,7,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[6,5,4,1,2,7,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[6,5,4,1,3,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,4,1,3,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[6,5,4,1,7,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[6,5,4,1,7,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[6,5,4,2,1,7,3]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[6,5,4,2,7,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,5,4,2,7,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101
[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111011
[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[6,5,4,7,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[6,5,4,7,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,5,4,7,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[6,5,4,7,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>110111
[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[6,5,7,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[6,5,7,1,3,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,5,7,1,3,4,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[6,5,7,1,4,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[6,5,7,1,4,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[6,5,7,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,5,7,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,5,7,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,5,7,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,5,7,2,4,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[6,5,7,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,5,7,3,1,4,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,5,7,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[6,5,7,3,2,4,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[6,5,7,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[6,5,7,4,1,3,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[6,5,7,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>101111
[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>010000
[6,7,1,2,3,5,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>010001
[6,7,1,2,4,3,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[6,7,1,2,4,5,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>010001
[6,7,1,2,5,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>010010
[6,7,1,2,5,4,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>010011
[6,7,1,3,2,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[6,7,1,3,2,5,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[6,7,1,3,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[6,7,1,3,4,5,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>010001
[6,7,1,3,5,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[6,7,1,3,5,4,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>010011
[6,7,1,4,2,3,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[6,7,1,4,2,5,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[6,7,1,4,3,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[6,7,1,4,3,5,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[6,7,1,4,5,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>010010
[6,7,1,4,5,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>010011
[6,7,1,5,2,3,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>010100
[6,7,1,5,2,4,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>010101
[6,7,1,5,3,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[6,7,1,5,3,4,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>010101
[6,7,1,5,4,2,3]=>[[.,[.,.]],[[[.,.],.],[.,.]]]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>010110
[6,7,1,5,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>010111
[6,7,2,1,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[6,7,2,1,3,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[6,7,2,1,4,3,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,2,1,4,5,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[6,7,2,1,5,3,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,2,1,5,4,3]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[6,7,2,3,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,2,3,1,5,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,2,3,4,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[6,7,2,3,4,5,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>010001
[6,7,2,3,5,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[6,7,2,3,5,4,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>010011
[6,7,2,4,1,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,2,4,1,5,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,2,4,3,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[6,7,2,4,3,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[6,7,2,4,5,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[6,7,2,4,5,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>010011
[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,2,5,1,4,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,2,5,3,1,4]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[6,7,2,5,3,4,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>010101
[6,7,2,5,4,1,3]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[6,7,2,5,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>010111
[6,7,3,1,2,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[6,7,3,1,2,5,4]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[6,7,3,1,4,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,3,1,4,5,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[6,7,3,1,5,2,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,3,1,5,4,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[6,7,3,2,1,4,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,3,2,1,5,4]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,3,2,4,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,3,2,4,5,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[6,7,3,2,5,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,3,2,5,4,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,3,4,1,5,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,3,4,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[6,7,3,4,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>010010
[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>010011
[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,3,5,1,4,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,3,5,2,1,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[6,7,3,5,2,4,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>010110
[6,7,3,5,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>010111
[6,7,4,1,2,3,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[6,7,4,1,2,5,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[6,7,4,1,3,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,4,1,3,5,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[6,7,4,1,5,2,3]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,4,1,5,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[6,7,4,2,1,3,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,4,2,1,5,3]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,4,2,3,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,4,2,3,5,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[6,7,4,2,5,1,3]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,4,2,5,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,4,3,1,5,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,4,3,2,1,5]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[6,7,4,3,2,5,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101
[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,4,3,5,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>011011
[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>010100
[6,7,4,5,1,3,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>010101
[6,7,4,5,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[6,7,4,5,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>010101
[6,7,4,5,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>010110
[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>010111
[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>011000
[6,7,5,1,2,4,3]=>[[[.,[.,.]],.],[.,[[.,.],.]]]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>011001
[6,7,5,1,3,2,4]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,5,1,3,4,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>011001
[6,7,5,1,4,2,3]=>[[[.,[.,.]],.],[[.,.],[.,.]]]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>011010
[6,7,5,1,4,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>011011
[6,7,5,2,1,3,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,5,2,1,4,3]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,5,2,3,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,5,2,3,4,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>011001
[6,7,5,2,4,1,3]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,5,2,4,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>011011
[6,7,5,3,1,2,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,5,3,1,4,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,5,3,2,1,4]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[6,7,5,3,2,4,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101
[6,7,5,3,4,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>011010
[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>011011
[6,7,5,4,1,2,3]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>011100
[6,7,5,4,1,3,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>011101
[6,7,5,4,2,1,3]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[6,7,5,4,2,3,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>011101
[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>011110
[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>011111
[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>100000
[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>100001
[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>100001
[7,1,2,3,6,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>100010
[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>100011
[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[7,1,2,4,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[7,1,2,4,5,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>100001
[7,1,2,4,6,3,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[7,1,2,4,6,5,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>100011
[7,1,2,5,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[7,1,2,5,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[7,1,2,5,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[7,1,2,5,6,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>100010
[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>100011
[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>100100
[7,1,2,6,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>100101
[7,1,2,6,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>100101
[7,1,2,6,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>100110
[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>100111
[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[7,1,3,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[7,1,3,2,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,3,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[7,1,3,2,6,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,3,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[7,1,3,4,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,3,4,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,3,4,5,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[7,1,3,4,5,6,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>100001
[7,1,3,4,6,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[7,1,3,4,6,5,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>100011
[7,1,3,5,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,3,5,2,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,3,5,4,2,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[7,1,3,5,4,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[7,1,3,5,6,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[7,1,3,5,6,4,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>100011
[7,1,3,6,2,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,3,6,2,5,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,3,6,4,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[7,1,3,6,4,5,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>100101
[7,1,3,6,5,2,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[7,1,3,6,5,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>100111
[7,1,4,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[7,1,4,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[7,1,4,2,5,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,4,2,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[7,1,4,2,6,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,4,2,6,5,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[7,1,4,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,4,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,4,3,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,4,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[7,1,4,3,6,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,4,3,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[7,1,4,5,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,4,5,2,6,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,4,5,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[7,1,4,5,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[7,1,4,5,6,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>100010
[7,1,4,5,6,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>100011
[7,1,4,6,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,4,6,2,5,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,4,6,3,2,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[7,1,4,6,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[7,1,4,6,5,2,3]=>[[.,.],[[.,[[.,.],.]],[.,.]]]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>100110
[7,1,4,6,5,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>100111
[7,1,5,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[7,1,5,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[7,1,5,2,4,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,5,2,4,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[7,1,5,2,6,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,5,2,6,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[7,1,5,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,5,3,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,5,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,5,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[7,1,5,3,6,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,5,3,6,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[7,1,5,4,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,5,4,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,5,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[7,1,5,4,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[7,1,5,4,6,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,5,4,6,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[7,1,5,6,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>100100
[7,1,5,6,2,4,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>100101
[7,1,5,6,3,2,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[7,1,5,6,3,4,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>100101
[7,1,5,6,4,2,3]=>[[.,.],[[[.,[.,.]],.],[.,.]]]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>100110
[7,1,5,6,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>100111
[7,1,6,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>101000
[7,1,6,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>101001
[7,1,6,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,6,2,4,5,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>101001
[7,1,6,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>101010
[7,1,6,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>101011
[7,1,6,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,6,3,2,5,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,6,3,4,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,6,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>101001
[7,1,6,3,5,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,6,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>101011
[7,1,6,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,6,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,6,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[7,1,6,4,3,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[7,1,6,4,5,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>101010
[7,1,6,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>101011
[7,1,6,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>101100
[7,1,6,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>101101
[7,1,6,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[7,1,6,5,3,4,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>101101
[7,1,6,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>101110
[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>101111
[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[7,2,1,3,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[7,2,1,3,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,2,1,3,5,6,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[7,2,1,3,6,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,2,1,3,6,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[7,2,1,4,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,2,1,4,3,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,2,1,4,5,3,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,2,1,4,5,6,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[7,2,1,4,6,3,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,2,1,4,6,5,3]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[7,2,1,5,3,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,2,1,5,3,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,2,1,5,4,3,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,2,1,5,4,6,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,2,1,5,6,3,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,2,1,5,6,4,3]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[7,2,1,6,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,2,1,6,3,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,2,1,6,4,3,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,2,1,6,4,5,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,2,1,6,5,3,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,2,1,6,5,4,3]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,2,3,1,4,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,2,3,1,5,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,3,1,5,6,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,2,3,1,6,4,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,3,1,6,5,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>100001
[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>100011
[7,2,3,5,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,3,5,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,3,5,4,1,6]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[7,2,3,5,6,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>100011
[7,2,3,6,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,3,6,1,5,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,3,6,4,1,5]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>100101
[7,2,3,6,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>100111
[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,2,4,1,3,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,2,4,1,5,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,4,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,2,4,1,6,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,4,1,6,5,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,2,4,3,1,5,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,4,3,1,6,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,4,3,5,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[7,2,4,3,6,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[7,2,4,5,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,4,5,1,6,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,4,5,3,1,6]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[7,2,4,5,3,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[7,2,4,5,6,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[7,2,4,5,6,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>100011
[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,4,6,1,5,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,4,6,3,1,5]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[7,2,4,6,3,5,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[7,2,4,6,5,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[7,2,4,6,5,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>100111
[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,2,5,1,3,6,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,2,5,1,4,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,5,1,4,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,2,5,1,6,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,5,1,6,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,2,5,3,1,4,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,5,3,1,6,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,5,3,4,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,5,3,4,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[7,2,5,3,6,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,5,3,6,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[7,2,5,4,1,3,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,5,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,5,4,3,1,6]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[7,2,5,4,6,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,5,4,6,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,2,5,6,1,4,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,2,5,6,3,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>100101
[7,2,5,6,4,1,3]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[7,2,5,6,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>100111
[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,2,6,1,3,5,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,2,6,1,4,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,6,1,4,5,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,2,6,1,5,3,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,2,6,1,5,4,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,2,6,3,1,4,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,6,3,1,5,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,6,3,4,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,6,3,4,5,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>101001
[7,2,6,3,5,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,6,3,5,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>101011
[7,2,6,4,1,3,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,6,4,1,5,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,6,4,3,1,5]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[7,2,6,4,3,5,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[7,2,6,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>101011
[7,2,6,5,1,3,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,2,6,5,1,4,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,2,6,5,3,1,4]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[7,2,6,5,3,4,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>101101
[7,2,6,5,4,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>101111
[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[7,3,1,2,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[7,3,1,2,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,3,1,2,5,6,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[7,3,1,2,6,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,3,1,2,6,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[7,3,1,4,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,3,1,4,2,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,3,1,4,5,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,3,1,4,5,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[7,3,1,4,6,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,3,1,4,6,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[7,3,1,5,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,3,1,5,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,3,1,5,4,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,3,1,5,4,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,3,1,5,6,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,3,1,5,6,4,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[7,3,1,6,2,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,3,1,6,2,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,3,1,6,4,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,3,1,6,4,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,3,1,6,5,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,3,1,6,5,4,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,3,2,1,4,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,3,2,1,5,4,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,3,2,1,5,6,4]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,3,2,1,6,4,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,3,2,1,6,5,4]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,3,2,4,1,6,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[7,3,2,4,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,3,2,5,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,3,2,5,4,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,3,2,5,6,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,3,2,5,6,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,3,2,6,1,5,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,3,2,6,4,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,3,2,6,4,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,3,2,6,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,3,4,1,2,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,3,4,1,5,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,4,1,5,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,3,4,1,6,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,4,1,6,5,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,3,4,2,1,6,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,3,4,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,4,2,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,3,4,5,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,3,4,5,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>100010
[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>100011
[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,3,4,6,1,5,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,3,4,6,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[7,3,4,6,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>100110
[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>100111
[7,3,5,1,2,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,3,5,1,2,6,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,3,5,1,4,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,5,1,4,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,3,5,1,6,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,5,1,6,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,3,5,2,1,4,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,3,5,2,1,6,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,3,5,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,5,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,3,5,2,6,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,5,2,6,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,3,5,4,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,3,5,4,1,6,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,3,5,4,2,1,6]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[7,3,5,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[7,3,5,4,6,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,3,5,4,6,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,3,5,6,1,4,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,3,5,6,2,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[7,3,5,6,2,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[7,3,5,6,4,1,2]=>[[[.,.],[[.,[.,.]],.]],[.,.]]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>100110
[7,3,5,6,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>100111
[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,3,6,1,2,5,4]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,3,6,1,4,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,6,1,4,5,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,3,6,1,5,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,3,6,1,5,4,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,3,6,2,1,4,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,3,6,2,1,5,4]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,3,6,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,3,6,2,5,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,3,6,4,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,3,6,4,1,5,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,3,6,4,2,1,5]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[7,3,6,4,2,5,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[7,3,6,4,5,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>101010
[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>101011
[7,3,6,5,1,2,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,3,6,5,1,4,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,3,6,5,2,1,4]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[7,3,6,5,2,4,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[7,3,6,5,4,1,2]=>[[[.,.],[[[.,.],.],.]],[.,.]]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>101110
[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>101111
[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[7,4,1,2,3,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,4,1,2,5,6,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[7,4,1,2,6,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,4,1,2,6,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[7,4,1,3,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,4,1,3,2,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,4,1,3,5,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,4,1,3,5,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[7,4,1,3,6,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,4,1,3,6,5,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[7,4,1,5,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,4,1,5,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,4,1,5,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,4,1,5,3,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,4,1,5,6,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,4,1,5,6,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[7,4,1,6,2,3,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,4,1,6,2,5,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,4,1,6,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,4,1,6,3,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,4,1,6,5,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,4,1,6,5,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,4,2,1,3,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,4,2,1,5,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,4,2,1,5,6,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,4,2,1,6,3,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,4,2,1,6,5,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,4,2,3,1,6,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[7,4,2,3,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,4,2,3,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[7,4,2,5,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,4,2,5,1,6,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,4,2,5,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,4,2,5,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,4,2,5,6,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,4,2,5,6,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[7,4,2,6,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,4,2,6,1,5,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,4,2,6,3,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,4,2,6,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,4,2,6,5,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,4,2,6,5,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,4,3,1,2,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,4,3,1,5,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,4,3,1,5,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,4,3,1,6,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,4,3,1,6,5,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,4,3,5,1,6,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,4,3,5,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[7,4,3,6,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,4,3,6,1,5,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,4,3,6,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,4,3,6,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,4,3,6,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,4,3,6,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,4,5,1,2,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,4,5,1,3,2,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,4,5,1,3,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,4,5,1,6,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,4,5,1,6,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,4,5,2,1,6,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,4,5,2,6,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,5,2,6,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,4,5,3,1,2,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,4,5,3,1,6,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[7,4,5,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>100100
[7,4,5,6,1,3,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>100101
[7,4,5,6,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[7,4,5,6,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>100101
[7,4,5,6,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>100110
[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>100111
[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,4,6,1,2,5,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,4,6,1,3,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,4,6,1,3,5,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,4,6,1,5,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,4,6,1,5,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,4,6,2,1,3,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,4,6,2,1,5,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,4,6,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,6,2,3,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,4,6,2,5,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,6,2,5,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,4,6,3,1,2,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,4,6,3,1,5,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,4,6,3,2,1,5]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[7,4,6,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[7,4,6,5,1,2,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>101100
[7,4,6,5,1,3,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>101101
[7,4,6,5,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[7,4,6,5,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>101101
[7,4,6,5,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>101110
[7,4,6,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>101111
[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[7,5,1,2,3,6,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[7,5,1,2,4,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,5,1,2,4,6,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[7,5,1,2,6,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,5,1,2,6,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[7,5,1,3,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,5,1,3,2,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,5,1,3,4,2,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,5,1,3,4,6,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[7,5,1,3,6,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,5,1,3,6,4,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[7,5,1,4,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,5,1,4,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,5,1,4,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,5,1,4,3,6,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,5,1,4,6,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,5,1,4,6,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[7,5,1,6,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,5,1,6,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,5,1,6,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,5,1,6,3,4,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,5,1,6,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,5,1,6,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,5,2,1,3,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,5,2,1,4,3,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,2,1,4,6,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,5,2,1,6,3,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,2,1,6,4,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,2,3,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[7,5,2,3,6,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,5,2,3,6,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,2,4,1,6,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,2,4,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,5,2,4,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,5,2,4,6,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,5,2,4,6,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[7,5,2,6,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,2,6,1,4,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,2,6,3,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,5,2,6,3,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,5,2,6,4,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,5,2,6,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,5,3,1,2,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,5,3,1,4,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,3,1,4,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,5,3,1,6,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,3,1,6,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,5,3,2,1,6,4]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,5,3,2,6,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,5,3,2,6,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,3,4,1,6,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,5,3,4,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[7,5,3,6,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,3,6,1,4,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,3,6,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,5,3,6,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,5,3,6,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,5,3,6,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,5,4,1,2,6,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,5,4,1,3,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,4,1,3,6,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,5,4,1,6,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,5,4,1,6,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,5,4,2,1,6,3]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,5,4,2,6,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,5,4,2,6,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,5,4,3,1,6,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101
[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111011
[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,5,4,6,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,5,4,6,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,5,4,6,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,5,4,6,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>110111
[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>101000
[7,5,6,1,2,4,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>101001
[7,5,6,1,3,2,4]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,5,6,1,3,4,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>101001
[7,5,6,1,4,2,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>101010
[7,5,6,1,4,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>101011
[7,5,6,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,5,6,2,1,4,3]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,5,6,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,5,6,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>101001
[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,5,6,2,4,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>101011
[7,5,6,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,5,6,3,1,4,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,5,6,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[7,5,6,3,2,4,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>101010
[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>101011
[7,5,6,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>101100
[7,5,6,4,1,3,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>101101
[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>101101
[7,5,6,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>101110
[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>101111
[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>110000
[7,6,1,2,3,5,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>110001
[7,6,1,2,4,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,6,1,2,4,5,3]=>[[[.,.],.],[.,[[.,[.,.]],.]]]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>110001
[7,6,1,2,5,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>110010
[7,6,1,2,5,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>110011
[7,6,1,3,2,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,6,1,3,2,5,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,6,1,3,4,2,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,6,1,3,4,5,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>110001
[7,6,1,3,5,2,4]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,6,1,3,5,4,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>110011
[7,6,1,4,2,3,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,6,1,4,2,5,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,6,1,4,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,6,1,4,3,5,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,6,1,4,5,2,3]=>[[[.,.],.],[[.,[.,.]],[.,.]]]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>110010
[7,6,1,4,5,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>110011
[7,6,1,5,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>110100
[7,6,1,5,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>110101
[7,6,1,5,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,6,1,5,3,4,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>110101
[7,6,1,5,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>110110
[7,6,1,5,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>110111
[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,6,2,1,3,5,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,6,2,1,4,3,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,2,1,4,5,3]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,6,2,1,5,3,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,2,1,5,4,3]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,2,3,1,5,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>110001
[7,6,2,3,5,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,6,2,3,5,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>110011
[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,2,4,1,5,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,2,4,3,1,5]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,6,2,4,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,6,2,4,5,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,6,2,4,5,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>110011
[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,2,5,1,4,3]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,2,5,3,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,6,2,5,3,4,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>110101
[7,6,2,5,4,1,3]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,6,2,5,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>110111
[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,6,3,1,2,5,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,6,3,1,4,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,3,1,4,5,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,6,3,1,5,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,3,1,5,4,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,3,2,1,5,4]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,3,2,5,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,3,4,1,5,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,6,3,4,5,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>110010
[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>110011
[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,3,5,1,4,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,3,5,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,6,3,5,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,6,3,5,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>110110
[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>110111
[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,6,4,1,2,5,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,6,4,1,3,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,4,1,3,5,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,6,4,1,5,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,4,1,5,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,4,2,1,5,3]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,6,4,2,5,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,4,2,5,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,4,3,1,5,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101
[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111011
[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>110100
[7,6,4,5,1,3,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>110101
[7,6,4,5,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,6,4,5,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>110101
[7,6,4,5,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>110110
[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>110111
[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>111000
[7,6,5,1,2,4,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>111001
[7,6,5,1,3,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,5,1,3,4,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>111001
[7,6,5,1,4,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>111010
[7,6,5,1,4,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>111011
[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,5,2,1,4,3]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>111001
[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,5,2,4,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>111011
[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101
[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>111010
[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>111011
[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>111100
[7,6,5,4,1,3,2]=>[[[[[.,.],.],.],.],[[.,.],.]]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>111101
[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>111101
[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>111110
[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>111111
[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>1111111
[7,8,6,5,4,3,2,1]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>0111111
[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>1011111
[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>1011111
[6,7,8,5,4,3,2,1]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>0011111
[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1101111
[7,8,5,6,4,3,2,1]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>0101111
[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1101111
[8,5,6,7,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1001111
[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>1101111
[6,7,5,8,4,3,2,1]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>0101111
[7,5,6,8,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1001111
[6,5,7,8,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>1001111
[5,6,7,8,4,3,2,1]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>0001111
[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1110111
[7,8,6,4,5,3,2,1]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>0110111
[8,6,7,4,5,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1010111
[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1110111
[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111
[8,5,6,4,7,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1010111
[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111
[8,4,5,6,7,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1000111
[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>1110111
[6,7,5,4,8,3,2,1]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>0110111
[7,5,6,4,8,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1010111
[6,5,7,4,8,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>1010111
[5,6,7,4,8,3,2,1]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>0010111
[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111
[6,7,4,5,8,3,2,1]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>0100111
[7,5,4,6,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111
[7,4,5,6,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1000111
[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>1100111
[5,6,4,7,8,3,2,1]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>0100111
[6,4,5,7,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1000111
[5,4,6,7,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>1000111
[4,5,6,7,8,3,2,1]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>0000111
[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011
[7,8,6,5,3,4,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0111011
[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[7,8,5,6,3,4,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>0101011
[8,5,6,7,3,4,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[7,6,5,8,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[6,7,5,8,3,4,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>0101011
[6,5,7,8,3,4,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[5,6,7,8,3,4,2,1]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>0001011
[8,7,6,4,3,5,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011
[7,8,6,4,3,5,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0111011
[6,7,8,4,3,5,2,1]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>0011011
[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[8,6,7,3,4,5,2,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[6,5,3,1,2,4,7,8]=>[8,7,4,2,1,3,5,6]=>1010011
[7,6,8,3,4,5,2,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[6,5,3,1,2,4,7,8]=>[8,7,4,2,1,3,5,6]=>1010011
[6,7,8,3,4,5,2,1]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>0010011
[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011
[7,8,5,4,3,6,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0111011
[8,7,5,3,4,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[8,7,4,3,5,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011
[8,5,4,6,3,7,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[8,6,4,3,5,7,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[8,4,3,5,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[8,3,4,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011
[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>1111011
[6,7,5,4,3,8,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>0111011
[5,6,7,4,3,8,2,1]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>0011011
[7,6,4,5,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[6,7,4,5,3,8,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>0101011
[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[7,4,5,6,3,8,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[6,5,4,7,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>1101011
[6,4,5,7,3,8,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[5,4,6,7,3,8,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[4,5,6,7,3,8,2,1]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>0001011
[7,6,5,3,4,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[7,6,4,3,5,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[7,5,4,3,6,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[7,3,4,5,6,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011
[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>1110011
[6,5,3,4,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[6,3,4,5,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011
[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>1100011
[5,3,4,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011
[4,3,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>1000011
[3,4,5,6,7,8,2,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>0000011
[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101
[7,8,6,5,4,2,3,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>0111101
[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[8,7,5,6,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[8,6,5,7,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[7,6,5,8,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[7,5,6,8,4,2,3,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[5,6,7,8,4,2,3,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0001101
[8,7,6,4,5,2,3,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,6,8,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[8,7,4,5,6,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[8,5,6,4,7,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[8,6,4,5,7,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[7,5,6,4,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[6,5,7,4,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,6,4,5,8,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[4,5,6,7,8,2,3,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>0000101
[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101
[7,8,6,5,3,2,4,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>0111101
[8,6,7,5,3,2,4,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[7,6,8,5,3,2,4,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[6,7,8,5,3,2,4,1]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>0011101
[8,7,5,6,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[8,5,6,7,3,2,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[5,6,7,8,3,2,4,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0001101
[8,7,6,5,2,3,4,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[7,6,8,5,2,3,4,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[6,7,8,5,2,3,4,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>0011001
[8,7,5,6,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[7,8,5,6,2,3,4,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[8,6,5,7,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[7,6,5,8,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[6,7,5,8,2,3,4,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[6,5,7,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[5,6,7,8,2,3,4,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>0001001
[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101
[7,6,8,4,3,2,5,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,8,6,3,4,2,5,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[8,6,4,3,1,2,5,7]=>0110101
[8,6,7,3,4,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,6,8,3,4,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[6,7,8,4,2,3,5,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>0011001
[8,7,6,3,2,4,5,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,6,7,3,2,4,5,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[6,7,8,3,2,4,5,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>0011001
[8,7,6,2,3,4,5,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[7,6,8,2,3,4,5,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[6,7,8,2,3,4,5,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0010001
[7,8,5,4,3,2,6,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>0111101
[8,7,5,3,4,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,8,5,3,4,2,6,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[8,6,4,3,1,2,5,7]=>0110101
[8,7,4,3,5,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,8,4,3,5,2,6,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[7,5,2,1,3,4,6,8]=>[8,6,4,3,1,2,5,7]=>0110101
[8,7,5,4,2,3,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,7,5,3,2,4,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,7,4,3,2,5,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[7,8,3,4,2,5,6,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[8,7,2,3,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[7,8,2,3,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001
[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101
[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[8,5,6,3,4,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[8,4,5,3,6,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[8,6,5,4,2,3,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,5,6,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[8,6,5,3,2,4,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,6,4,2,3,5,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[8,6,2,3,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[8,4,5,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[8,3,4,5,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[8,5,4,2,3,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[8,3,4,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[8,4,2,3,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>1111101
[6,7,5,4,3,2,8,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>0111101
[6,5,7,4,3,2,8,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>1101101
[7,4,5,6,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[6,4,5,7,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[4,5,6,7,3,2,8,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>0001101
[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,5,6,3,4,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[6,5,7,3,4,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,6,4,3,5,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,4,5,3,6,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,5,3,4,6,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[6,4,5,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[5,4,6,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[6,4,3,5,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[3,4,5,6,7,2,8,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>0000101
[7,6,5,4,2,3,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[7,5,6,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[6,5,7,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[5,6,7,4,2,3,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>0011001
[7,6,4,5,2,3,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[6,7,4,5,2,3,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[7,4,5,6,2,3,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[6,5,4,7,2,3,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[5,6,4,7,2,3,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[5,4,6,7,2,3,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[4,5,6,7,2,3,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>0001001
[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[6,5,7,3,2,4,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[7,6,5,2,3,4,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,5,6,2,3,4,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[5,6,7,2,3,4,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0010001
[7,6,4,2,3,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,6,3,2,4,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,6,2,3,4,5,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[6,7,2,3,4,5,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001
[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[7,5,4,2,3,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,4,5,2,3,6,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[7,5,3,2,4,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,5,2,3,4,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[7,4,3,2,5,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[7,3,2,4,5,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>1111001
[4,5,6,3,2,7,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>0011001
[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[6,3,4,5,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[4,3,5,6,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>1001001
[3,4,5,6,2,7,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>0001001
[6,5,4,2,3,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[6,4,5,2,3,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[4,5,6,2,3,7,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0010001
[6,5,3,2,4,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[6,5,2,3,4,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>1110001
[5,3,4,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[4,3,5,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[3,4,5,2,6,7,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0010001
[5,4,2,3,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[4,5,2,3,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001
[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[4,3,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>1100001
[3,4,2,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001
[4,2,3,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>1000001
[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>0000001
[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[8,6,7,5,4,3,1,2]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[7,6,8,5,4,3,1,2]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[6,7,8,5,4,3,1,2]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110
[8,7,5,6,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[8,6,5,7,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,6,5,8,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,5,6,8,4,3,1,2]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[6,5,7,8,4,3,1,2]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[5,6,7,8,4,3,1,2]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0001110
[8,7,6,4,5,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[8,6,7,4,5,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[8,7,5,4,6,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[8,5,6,4,7,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[8,6,4,5,7,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[8,5,4,6,7,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[7,6,5,4,8,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[7,5,6,4,8,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[6,5,7,4,8,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[7,6,4,5,8,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[6,5,4,7,8,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[4,5,6,7,8,3,1,2]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>0000110
[8,7,6,5,3,4,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[8,7,5,6,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[8,6,5,7,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,6,5,8,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,7,5,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,6,7,8,3,4,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[8,7,6,3,4,5,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[8,7,4,5,3,6,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,8,4,5,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[8,7,4,3,5,6,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,8,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[8,7,3,4,5,6,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[8,6,5,4,3,7,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,5,4,3,6,7,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,5,3,4,6,7,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[8,4,3,5,6,7,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[8,3,4,5,6,7,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[7,6,5,4,3,8,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[6,7,4,5,3,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,6,4,7,3,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[4,5,6,7,3,8,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[7,6,5,3,4,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,6,4,3,5,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,6,3,4,5,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[7,5,4,3,6,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,5,3,4,6,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[7,3,4,5,6,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[6,5,4,3,7,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[5,6,4,3,7,8,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[4,5,6,3,7,8,1,2]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[6,4,3,5,7,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[6,3,4,5,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[5,4,3,6,7,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[5,3,4,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[4,3,5,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[7,8,6,5,4,2,1,3]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[8,6,7,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[6,7,8,5,4,2,1,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110
[8,7,5,6,4,2,1,3]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,6,5,8,4,2,1,3]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,5,6,8,4,2,1,3]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[6,5,7,8,4,2,1,3]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[5,6,7,8,4,2,1,3]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0001110
[8,7,6,4,5,2,1,3]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[7,6,5,4,8,2,1,3]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[6,7,5,4,8,2,1,3]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[6,5,7,4,8,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[7,6,4,5,8,2,1,3]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[7,5,4,6,8,2,1,3]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[4,5,6,7,8,2,1,3]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>0000110
[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,6,5,4,1,2,3]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[7,6,8,5,4,1,2,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[8,6,5,7,4,1,2,3]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,5,8,4,1,2,3]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,7,6,4,5,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,7,4,5,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[8,7,5,4,6,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,8,5,4,6,1,2,3]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,7,4,5,6,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,8,4,5,6,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[8,5,6,4,7,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,6,4,5,7,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,4,5,6,7,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[7,6,5,4,8,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,7,5,4,8,1,2,3]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[7,5,6,4,8,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,5,7,4,8,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[7,6,4,5,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,5,4,6,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,4,5,6,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[6,5,4,7,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,6,4,7,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,4,5,7,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[5,4,6,7,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[4,5,6,7,8,1,2,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[7,8,6,5,3,2,1,4]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[8,6,7,5,3,2,1,4]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[7,6,8,5,3,2,1,4]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[6,7,8,5,3,2,1,4]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110
[8,7,5,6,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[8,6,5,7,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[8,5,6,7,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,5,6,8,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[6,5,7,8,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[5,6,7,8,3,2,1,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0001110
[8,7,6,5,2,3,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,8,6,5,2,3,1,4]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[8,7,5,6,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,8,5,6,2,3,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[8,6,5,7,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,6,5,8,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,7,5,8,2,3,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,6,7,8,2,3,1,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,6,5,3,1,2,4]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,6,7,5,3,1,2,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,6,8,5,3,1,2,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[8,7,5,6,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,6,5,7,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,5,8,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,6,5,2,1,3,4]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[7,6,8,5,2,1,3,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[6,7,8,5,2,1,3,4]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[8,7,5,6,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,6,5,7,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,5,8,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,6,5,1,2,3,4]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,6,7,5,1,2,3,4]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[7,6,8,5,1,2,3,4]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[8,7,5,6,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[8,6,5,7,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,5,6,7,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,6,5,8,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,7,5,8,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,5,6,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,5,7,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[7,8,6,4,3,2,1,5]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[8,6,7,4,3,2,1,5]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[7,6,8,4,3,2,1,5]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[6,7,8,4,3,2,1,5]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110
[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[7,8,6,3,4,2,1,5]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[8,7,6,4,2,3,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,6,2,3,4,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[6,7,8,2,3,4,1,5]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[6,7,8,4,3,1,2,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[8,7,6,3,4,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,8,6,3,4,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,6,7,3,4,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,7,8,3,4,1,2,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,6,4,2,1,3,5]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,6,7,4,2,1,3,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[6,7,8,4,2,1,3,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,6,4,1,2,3,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[7,6,8,4,1,2,3,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,6,3,2,1,4,5]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,6,7,3,2,1,4,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,6,8,3,2,1,4,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[6,7,8,3,2,1,4,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[8,7,6,2,3,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,8,6,2,3,1,4,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,6,7,2,3,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,6,8,2,3,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,7,8,2,3,1,4,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,6,3,1,2,4,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,6,7,3,1,2,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[7,6,8,3,1,2,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,7,8,3,1,2,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,6,2,1,3,4,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,6,7,2,1,3,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,7,8,2,1,3,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,8,6,1,2,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[8,6,7,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,6,8,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[7,8,5,4,3,2,1,6]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[8,7,4,5,3,2,1,6]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[8,7,3,4,5,2,1,6]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[8,7,4,5,2,3,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,8,4,5,2,3,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,8,5,2,3,4,1,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[8,7,4,3,2,5,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,8,4,3,2,5,1,6]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[8,7,3,4,2,5,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,8,3,4,2,5,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[8,7,2,3,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[7,8,2,3,4,5,1,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,7,5,3,4,1,2,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,3,4,5,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,8,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,5,4,2,1,3,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,7,5,4,1,2,3,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,5,4,1,2,3,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[7,8,4,5,1,2,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,5,3,2,1,4,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,7,5,3,1,2,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,5,2,1,3,4,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,8,5,1,2,3,4,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,8,4,3,2,1,5,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,8,4,2,3,1,5,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,8,3,2,4,1,5,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,7,2,3,4,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,8,2,3,4,1,5,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,4,3,1,2,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,7,3,4,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[8,7,4,2,1,3,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,4,2,1,3,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,7,4,1,2,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,8,3,2,1,4,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[8,7,2,3,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,8,2,3,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,8,2,1,3,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[8,7,1,2,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[8,5,6,4,3,2,1,7]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[8,6,4,5,3,2,1,7]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[8,4,5,6,3,2,1,7]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[8,5,6,3,4,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[8,4,5,3,6,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[8,4,3,5,6,2,1,7]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[8,6,5,4,2,3,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,6,5,3,2,4,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,6,5,2,3,4,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,6,4,2,3,5,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,6,3,2,4,5,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,5,4,3,2,6,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,4,3,5,2,6,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,5,4,2,3,6,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,5,3,2,4,6,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,5,2,3,4,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[8,3,2,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[8,6,5,4,3,1,2,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[8,6,4,5,3,1,2,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,6,5,3,4,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,6,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,4,3,6,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,3,4,6,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,4,3,5,6,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,3,4,5,6,1,2,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[8,5,6,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[8,6,5,4,1,2,3,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,5,6,4,1,2,3,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[8,6,4,5,1,2,3,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,4,5,6,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[8,5,6,3,2,1,4,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[8,6,5,2,3,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,6,2,3,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,6,3,1,2,4,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[8,6,5,2,1,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,5,6,2,1,3,4,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,5,6,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,6,4,2,3,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,2,3,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,6,4,3,1,2,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,6,3,4,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[8,4,5,3,2,1,6,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[8,4,3,5,2,1,6,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[8,4,5,2,3,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,2,3,4,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,4,2,3,5,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[8,5,3,4,1,2,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,3,4,5,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,5,4,1,2,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,4,5,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,5,3,1,2,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,5,2,1,3,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[8,3,4,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[8,4,2,3,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,3,4,1,2,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[8,2,3,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>1111110
[6,7,5,4,3,2,1,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>0111110
[7,5,6,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[6,5,7,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>1011110
[5,6,7,4,3,2,1,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>0011110
[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[7,4,5,6,3,2,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>1101110
[5,4,6,7,3,2,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>1001110
[4,5,6,7,3,2,1,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>0001110
[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[6,7,5,3,4,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[7,5,6,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[6,5,7,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[6,7,4,3,5,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[7,5,4,3,6,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[5,6,4,3,7,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>0110110
[5,4,6,3,7,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[3,4,5,6,7,2,1,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>0000110
[7,6,5,4,2,3,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[6,7,5,4,2,3,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[7,6,4,5,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,7,4,5,2,3,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,5,4,6,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,5,4,7,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[5,6,4,7,2,3,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[4,5,6,7,2,3,1,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,6,5,2,3,4,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[6,7,5,2,3,4,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[5,6,7,2,3,4,1,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[6,7,4,3,2,5,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[6,7,3,4,2,5,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,6,4,2,3,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[6,7,4,2,3,5,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[6,7,3,2,4,5,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[7,6,2,3,4,5,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[6,7,2,3,4,5,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[7,4,2,3,5,6,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[5,6,4,3,2,7,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[5,6,3,4,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[4,5,3,6,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[3,4,5,6,2,7,1,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[6,5,3,2,4,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[6,4,2,3,5,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[4,5,2,3,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[4,3,2,5,6,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>1100010
[3,4,2,5,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[4,2,3,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>1000010
[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[7,6,5,4,3,1,2,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[6,7,5,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[7,5,6,4,3,1,2,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,6,4,5,3,1,2,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,5,3,4,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,5,7,3,4,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,5,4,3,7,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[5,6,3,4,7,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,3,4,5,7,1,2,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[4,3,5,6,7,1,2,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[3,4,5,6,7,1,2,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[7,6,5,4,2,1,3,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[6,5,7,4,2,1,3,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,6,4,5,2,1,3,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,5,4,6,2,1,3,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[7,4,5,6,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,6,4,7,1,2,3,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,4,6,7,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,5,6,7,1,2,3,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,6,5,2,3,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,7,5,2,3,1,4,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[7,5,6,2,3,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,5,7,2,3,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,6,7,2,3,1,4,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[5,6,7,3,1,2,4,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,5,6,2,1,3,4,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[5,6,7,2,1,3,4,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[6,7,5,1,2,3,4,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[7,5,6,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,5,7,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[6,7,4,3,2,1,5,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[7,6,3,4,2,1,5,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,6,4,2,3,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,7,4,2,3,1,5,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,6,2,3,4,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,7,2,3,4,1,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,6,4,3,1,2,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[6,7,3,2,1,4,5,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[7,6,2,3,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,7,2,3,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,7,3,1,2,4,5,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[7,4,5,3,2,1,6,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,4,3,5,2,1,6,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,5,4,2,3,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,3,2,4,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,2,3,4,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,4,2,3,5,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[7,5,4,3,1,2,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,4,5,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,5,2,3,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,4,3,1,2,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,3,4,1,2,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[7,2,3,1,4,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>1111100
[5,6,4,3,2,1,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[5,4,6,3,2,1,7,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[4,5,6,3,2,1,7,8]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[5,4,6,2,3,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,6,3,2,4,1,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[6,5,2,3,4,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,6,2,3,4,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[4,5,3,2,6,1,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[4,3,5,2,6,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[3,4,5,2,6,1,7,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[4,3,2,5,6,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[3,4,2,5,6,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,2,3,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[3,2,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[5,6,4,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[5,4,6,3,1,2,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,4,3,5,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[4,3,5,6,1,2,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,4,5,6,1,2,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[6,5,4,2,1,3,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[5,6,4,2,1,3,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[6,4,5,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[5,4,6,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[4,5,6,2,1,3,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[6,5,4,1,2,3,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[5,6,3,2,1,4,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[5,6,2,1,3,4,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[6,3,4,2,1,5,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[6,2,3,1,4,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,3,1,2,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>1111000
[4,5,3,2,1,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>0111000
[5,3,4,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[4,3,5,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[3,4,5,2,1,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[5,4,2,3,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[4,5,2,3,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,3,2,5,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[3,4,2,5,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,2,3,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[4,3,5,1,2,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[3,4,5,1,2,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[4,5,2,1,3,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[5,2,3,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>1110000
[3,4,2,1,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[4,3,1,2,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>1100000
[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>1000000
[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>0000000
[6,8,7,5,4,3,2,1]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>0111111
[5,8,7,6,4,3,2,1]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>0111111
[5,7,8,6,4,3,2,1]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>0011111
[6,5,8,7,4,3,2,1]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>1011111
[5,6,8,7,4,3,2,1]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>0011111
[5,7,6,8,4,3,2,1]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>0101111
[4,8,7,6,5,3,2,1]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>0111111
[4,7,8,6,5,3,2,1]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>0011111
[4,6,8,7,5,3,2,1]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>0011111
[4,7,6,8,5,3,2,1]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>0101111
[4,5,8,7,6,3,2,1]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>0011111
[4,5,6,8,7,3,2,1]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>0001111
[5,7,6,4,8,3,2,1]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>0110111
[4,7,6,5,8,3,2,1]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>0110111
[4,6,7,5,8,3,2,1]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>0010111
[5,4,7,6,8,3,2,1]=>[[[[[.,.],[[.,.],[.,.]]],.],.],.]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>1010111
[4,5,7,6,8,3,2,1]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>0010111
[4,6,5,7,8,3,2,1]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>0100111
[3,8,7,6,5,4,2,1]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>0111111
[3,6,8,7,5,4,2,1]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]=>[3,4,2,5,6,1,7,8]=>[8,7,1,6,5,2,4,3]=>0011111
[3,7,6,8,5,4,2,1]=>[[[.,[[[[.,.],[.,.]],.],.]],.],.]=>[4,2,3,5,6,1,7,8]=>[8,7,1,6,5,3,2,4]=>0101111
[3,5,8,7,6,4,2,1]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>0011111
[3,5,7,8,6,4,2,1]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>0001111
[3,5,6,8,7,4,2,1]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>0001111
[3,7,6,5,8,4,2,1]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>0110111
[3,5,6,7,8,4,2,1]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>0000111
[4,3,8,7,6,5,2,1]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>1011111
[4,3,6,7,8,5,2,1]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>1000111
[3,4,6,7,8,5,2,1]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>0000111
[5,4,3,8,7,6,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1101111
[5,4,3,7,8,6,2,1]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>1100111
[4,5,3,7,8,6,2,1]=>[[[[.,[.,.]],[[.,[.,.]],.]],.],.]=>[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>0100111
[3,5,4,7,8,6,2,1]=>[[[.,[[.,.],[[.,[.,.]],.]]],.],.]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>0100111
[4,3,5,7,8,6,2,1]=>[[[[.,.],[.,[[.,[.,.]],.]]],.],.]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>1000111
[3,4,5,7,8,6,2,1]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>0000111
[6,5,4,3,8,7,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>1110111
[4,5,6,3,8,7,2,1]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>0010111
[4,3,6,5,8,7,2,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1010111
[5,4,3,6,8,7,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1100111
[4,5,3,6,8,7,2,1]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>0100111
[4,3,5,6,8,7,2,1]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>1000111
[3,4,5,6,8,7,2,1]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>0000111
[5,7,6,4,3,8,2,1]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>0111011
[3,5,6,7,4,8,2,1]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]=>[6,4,3,2,5,1,7,8]=>[8,7,1,5,2,3,4,6]=>0001011
[4,3,7,6,5,8,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>1011011
[3,4,7,6,5,8,2,1]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>0011011
[3,4,6,7,5,8,2,1]=>[[[.,[.,[[.,[.,.]],[.,.]]]],.],.]=>[6,4,3,5,2,1,7,8]=>[8,7,1,2,5,3,4,6]=>0001011
[3,5,4,7,6,8,2,1]=>[[[.,[[.,.],[[.,.],[.,.]]]],.],.]=>[6,4,5,2,3,1,7,8]=>[8,7,1,3,2,5,4,6]=>0101011
[3,5,6,4,7,8,2,1]=>[[[.,[[.,[.,.]],[.,[.,.]]]],.],.]=>[6,5,3,2,4,1,7,8]=>[8,7,1,4,2,3,5,6]=>0010011
[4,3,6,5,7,8,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>1010011
[3,4,6,5,7,8,2,1]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>0010011
[3,5,4,6,7,8,2,1]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]=>[6,5,4,2,3,1,7,8]=>[8,7,1,3,2,4,5,6]=>0100011
[2,8,7,6,5,4,3,1]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>0111111
[2,7,8,6,5,4,3,1]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]=>[3,2,4,5,6,7,1,8]=>[8,1,7,6,5,4,2,3]=>0011111
[2,6,8,7,5,4,3,1]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>0011111
[2,7,6,8,5,4,3,1]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>0101111
[2,6,7,8,5,4,3,1]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>0001111
[2,5,8,7,6,4,3,1]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]=>[3,4,5,2,6,7,1,8]=>[8,1,7,6,2,5,4,3]=>0011111
[2,6,7,5,8,4,3,1]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]=>[5,3,2,4,6,7,1,8]=>[8,1,7,6,4,2,3,5]=>0010111
[2,5,6,7,8,4,3,1]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>0000111
[2,4,8,7,6,5,3,1]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>0011111
[2,4,6,8,7,5,3,1]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>0001111
[2,4,6,7,8,5,3,1]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>0000111
[2,5,4,8,7,6,3,1]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>0101111
[2,5,4,7,8,6,3,1]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]=>[5,4,6,2,3,7,1,8]=>[8,1,7,3,2,6,4,5]=>0100111
[2,4,5,7,8,6,3,1]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>0000111
[2,6,5,4,8,7,3,1]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>0110111
[2,5,6,4,8,7,3,1]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>0010111
[2,4,6,5,8,7,3,1]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>0010111
[2,7,6,5,4,8,3,1]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[8,1,7,5,4,3,2,6]=>0111011
[2,4,6,7,5,8,3,1]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>0001011
[2,5,4,7,6,8,3,1]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]=>[6,4,5,2,3,7,1,8]=>[8,1,7,3,2,5,4,6]=>0101011
[2,5,6,4,7,8,3,1]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>0010011
[2,4,6,5,7,8,3,1]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]=>[6,5,3,4,2,7,1,8]=>[8,1,7,2,4,3,5,6]=>0010011
[2,5,4,6,7,8,3,1]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[8,1,7,3,2,4,5,6]=>0100011
[2,4,5,6,7,8,3,1]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>0000011
[3,2,8,7,6,5,4,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1011111
[3,2,6,8,7,5,4,1]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>1001111
[3,2,6,7,5,8,4,1]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]=>[6,4,3,5,7,1,2,8]=>[8,2,1,7,5,3,4,6]=>1001011
[3,2,5,7,6,8,4,1]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[8,2,1,7,3,5,4,6]=>1001011
[3,2,5,6,7,8,4,1]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>1000011
[2,3,8,7,6,5,4,1]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>0011111
[2,3,6,7,8,5,4,1]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>0000111
[2,3,5,8,7,6,4,1]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>0001111
[2,3,5,7,8,6,4,1]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>0000111
[2,3,6,5,8,7,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>0010111
[2,3,5,6,8,7,4,1]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>0000111
[2,3,7,6,5,8,4,1]=>[[.,[.,[[[[.,.],.],[.,.]],.]]],.]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>0011011
[2,3,5,7,6,8,4,1]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]=>[6,4,5,3,7,2,1,8]=>[8,1,2,7,3,5,4,6]=>0001011
[2,3,5,6,7,8,4,1]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>0000011
[4,3,2,8,7,6,5,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>1101111
[4,3,2,7,8,6,5,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>1100111
[4,3,2,6,8,7,5,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>1100111
[3,4,2,8,7,6,5,1]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>0101111
[3,4,2,7,8,6,5,1]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>0100111
[2,4,3,8,7,6,5,1]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[8,1,3,2,7,6,5,4]=>0101111
[2,4,3,6,8,7,5,1]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>0100111
[3,2,4,8,7,6,5,1]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[8,2,1,3,7,6,5,4]=>1001111
[3,2,4,7,8,6,5,1]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]=>[5,4,6,7,3,1,2,8]=>[8,2,1,3,7,6,4,5]=>1000111
[2,3,4,8,7,6,5,1]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>0001111
[2,3,4,7,6,8,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>0001011
[2,3,4,6,7,8,5,1]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>0000011
[5,4,3,2,8,7,6,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1110111
[5,4,3,2,7,8,6,1]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>1110011
[4,5,3,2,8,7,6,1]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>0110111
[4,3,5,2,8,7,6,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1010111
[3,4,5,2,7,8,6,1]=>[[[.,[.,[.,.]]],[[.,[.,.]],.]],.]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>0010011
[2,5,4,3,8,7,6,1]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>0110111
[2,5,4,3,7,8,6,1]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>0110011
[2,4,5,3,8,7,6,1]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>0010111
[2,4,5,3,7,8,6,1]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]=>[6,5,7,3,2,4,1,8]=>[8,1,4,2,3,7,5,6]=>0010011
[3,2,5,4,7,8,6,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[8,2,1,4,3,7,5,6]=>1010011
[4,3,2,5,8,7,6,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>1100111
[4,3,2,5,7,8,6,1]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[8,3,2,1,4,7,5,6]=>1100011
[3,4,2,5,8,7,6,1]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>0100111
[3,4,2,5,7,8,6,1]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>0100011
[3,2,4,5,7,8,6,1]=>[[[.,.],[.,[.,[[.,[.,.]],.]]]],.]=>[6,5,7,4,3,1,2,8]=>[8,2,1,3,4,7,5,6]=>1000011
[2,3,4,5,8,7,6,1]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>0000111
[2,3,4,5,7,8,6,1]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>0000011
[6,5,4,3,2,8,7,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111011
[4,6,5,3,2,8,7,1]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[8,5,4,1,3,2,7,6]=>0111011
[5,4,6,3,2,8,7,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[8,5,4,2,1,3,7,6]=>1011011
[3,5,6,4,2,8,7,1]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>0011011
[4,3,6,5,2,8,7,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011
[5,4,3,6,2,8,7,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[4,5,3,6,2,8,7,1]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>0101011
[2,6,5,4,3,8,7,1]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[8,1,5,4,3,2,7,6]=>0111011
[2,4,6,5,3,8,7,1]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[8,1,5,2,4,3,7,6]=>0011011
[3,2,6,5,4,8,7,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>1011011
[2,3,5,6,4,8,7,1]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]=>[6,7,4,3,5,2,1,8]=>[8,1,2,5,3,4,7,6]=>0001011
[4,3,2,6,5,8,7,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[3,4,2,6,5,8,7,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[2,4,3,6,5,8,7,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0101011
[2,3,4,6,5,8,7,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>0001011
[5,4,3,2,6,8,7,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1110011
[2,4,5,3,6,8,7,1]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]=>[6,7,5,3,2,4,1,8]=>[8,1,4,2,3,5,7,6]=>0010011
[3,2,5,4,6,8,7,1]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]=>[6,7,5,3,4,1,2,8]=>[8,2,1,4,3,5,7,6]=>1010011
[4,3,2,5,6,8,7,1]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,1,2,3,8]=>[8,3,2,1,4,5,7,6]=>1100011
[3,4,2,5,6,8,7,1]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>0100011
[2,4,3,5,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>0100011
[3,2,4,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>1000011
[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]=>[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>0000011
[5,7,6,4,3,2,8,1]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>0111101
[4,7,6,5,3,2,8,1]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>0111101
[4,6,5,7,3,2,8,1]=>[[[[.,[[.,.],[.,.]]],.],[.,.]],.]=>[7,4,2,3,1,5,6,8]=>[8,6,5,1,3,2,4,7]=>0101101
[3,5,7,6,4,2,8,1]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]=>[7,3,4,2,5,1,6,8]=>[8,6,1,5,2,4,3,7]=>0011101
[3,5,6,7,4,2,8,1]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>0001101
[4,3,7,6,5,2,8,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1011101
[3,4,7,6,5,2,8,1]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>0011101
[3,4,6,7,5,2,8,1]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>0001101
[5,4,3,7,6,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1101101
[3,4,5,7,6,2,8,1]=>[[[.,[.,[.,[[.,.],.]]]],[.,.]],.]=>[7,4,5,3,2,1,6,8]=>[8,6,1,2,3,5,4,7]=>0001101
[4,6,5,3,7,2,8,1]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]=>[7,5,2,3,1,4,6,8]=>[8,6,4,1,3,2,5,7]=>0110101
[3,6,5,4,7,2,8,1]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>0110101
[3,5,6,4,7,2,8,1]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>0010101
[4,3,6,5,7,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[3,4,6,5,7,2,8,1]=>[[[.,[.,[[.,.],[.,.]]]],[.,.]],.]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>0010101
[3,5,4,6,7,2,8,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>0100101
[2,7,6,5,4,3,8,1]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]=>[7,2,3,4,5,6,1,8]=>[8,1,6,5,4,3,2,7]=>0111101
[2,5,6,7,4,3,8,1]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]=>[7,4,3,2,5,6,1,8]=>[8,1,6,5,2,3,4,7]=>0001101
[2,4,6,7,5,3,8,1]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>0001101
[2,5,4,7,6,3,8,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0101101
[2,4,6,5,7,3,8,1]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>0010101
[2,5,4,6,7,3,8,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>0100101
[2,4,5,6,7,3,8,1]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>0000101
[3,2,6,7,5,4,8,1]=>[[[.,.],[[[.,[.,.]],.],[.,.]]],.]=>[7,4,3,5,6,1,2,8]=>[8,2,1,6,5,3,4,7]=>1001101
[3,2,6,5,7,4,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[3,2,5,6,7,4,8,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>1000101
[2,3,7,6,5,4,8,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>0011101
[2,3,5,6,7,4,8,1]=>[[.,[.,[[.,[.,[.,.]]],[.,.]]]],.]=>[7,5,4,3,6,2,1,8]=>[8,1,2,6,3,4,5,7]=>0000101
[4,3,2,7,6,5,8,1]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>1101101
[4,3,2,6,7,5,8,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101
[3,4,2,7,6,5,8,1]=>[[[.,[.,.]],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>0101101
[3,4,2,6,7,5,8,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>0100101
[2,4,3,7,6,5,8,1]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>0101101
[3,2,4,7,6,5,8,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1001101
[2,3,4,7,6,5,8,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>0001101
[2,3,4,6,7,5,8,1]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]=>[7,5,4,6,3,2,1,8]=>[8,1,2,3,6,4,5,7]=>0000101
[5,4,3,2,7,6,8,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101
[3,5,4,2,7,6,8,1]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>0110101
[4,3,5,2,7,6,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[3,2,5,4,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[2,3,5,4,7,6,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>0010101
[4,3,2,5,7,6,8,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>1100101
[3,4,2,5,7,6,8,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>0100101
[3,2,4,5,7,6,8,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>1000101
[2,3,4,5,7,6,8,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[8,1,2,3,4,6,5,7]=>0000101
[3,5,6,4,2,7,8,1]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>0011001
[3,4,6,5,2,7,8,1]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]=>[7,6,3,4,2,1,5,8]=>[8,5,1,2,4,3,6,7]=>0011001
[3,5,4,6,2,7,8,1]=>[[[.,[[.,.],[.,.]]],[.,[.,.]]],.]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>0101001
[2,6,5,4,3,7,8,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>0111001
[2,5,6,4,3,7,8,1]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]=>[7,6,3,2,4,5,1,8]=>[8,1,5,4,2,3,6,7]=>0011001
[2,4,5,6,3,7,8,1]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]=>[7,6,4,3,2,5,1,8]=>[8,1,5,2,3,4,6,7]=>0001001
[2,3,6,5,4,7,8,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>0011001
[2,3,5,6,4,7,8,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>0001001
[4,3,2,6,5,7,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[3,4,2,6,5,7,8,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>0101001
[2,4,3,6,5,7,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001
[2,3,4,6,5,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>0001001
[3,5,4,2,6,7,8,1]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>0110001
[2,4,5,3,6,7,8,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>0010001
[2,3,5,4,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>0010001
[2,4,3,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>0100001
[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>0111111
[1,7,8,6,5,4,3,2]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]=>[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>0011111
[1,6,8,7,5,4,3,2]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>0011111
[1,7,6,8,5,4,3,2]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]=>[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>0101111
[1,6,7,8,5,4,3,2]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>0001111
[1,5,8,7,6,4,3,2]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>0011111
[1,6,5,8,7,4,3,2]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>0101111
[1,7,6,5,8,4,3,2]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>0110111
[1,6,7,5,8,4,3,2]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>0010111
[1,5,7,6,8,4,3,2]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>0010111
[1,5,6,7,8,4,3,2]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>0000111
[1,4,8,7,6,5,3,2]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>0011111
[1,4,7,8,6,5,3,2]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>0001111
[1,4,6,8,7,5,3,2]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>0001111
[1,4,6,7,8,5,3,2]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>0000111
[1,5,4,7,8,6,3,2]=>[.,[[[[.,.],[[.,[.,.]],.]],.],.]]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>0100111
[1,4,5,8,7,6,3,2]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>0001111
[1,7,6,5,4,8,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111011
[1,4,7,6,5,8,3,2]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]=>[6,3,4,5,2,7,8,1]=>[1,8,7,2,5,4,3,6]=>0011011
[1,4,6,7,5,8,3,2]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>0001011
[1,6,5,4,7,8,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0110011
[1,5,4,6,7,8,3,2]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>0100011
[1,4,5,6,7,8,3,2]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>0000011
[1,3,8,7,6,5,4,2]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>0011111
[1,3,6,8,7,5,4,2]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>0001111
[1,3,6,7,8,5,4,2]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>0000111
[1,3,5,8,7,6,4,2]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>0001111
[1,3,5,7,8,6,4,2]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>0000111
[1,3,5,6,8,7,4,2]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]=>[5,6,4,3,7,2,8,1]=>[1,8,2,7,3,4,6,5]=>0000111
[1,3,6,7,5,8,4,2]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>0001011
[1,3,6,5,7,8,4,2]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>0010011
[1,3,5,6,7,8,4,2]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>0000011
[1,4,3,8,7,6,5,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>0101111
[1,4,3,7,8,6,5,2]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>0100111
[1,4,3,7,6,8,5,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,8,3,2,7,5,4,6]=>0101011
[1,3,4,8,7,6,5,2]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>0001111
[1,3,4,7,6,8,5,2]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>0001011
[1,5,4,3,8,7,6,2]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>0110111
[1,4,5,3,8,7,6,2]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>0010111
[1,4,5,3,7,8,6,2]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>0010011
[1,3,5,4,8,7,6,2]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]=>[5,6,7,3,4,2,8,1]=>[1,8,2,4,3,7,6,5]=>0010111
[1,4,3,5,7,8,6,2]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>0100011
[1,3,4,5,8,7,6,2]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>0000111
[1,3,4,5,7,8,6,2]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]=>[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>0000011
[1,6,5,4,3,8,7,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111011
[1,5,6,4,3,8,7,2]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>0011011
[1,4,5,6,3,8,7,2]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[1,8,5,2,3,4,7,6]=>0001011
[1,4,3,6,5,8,7,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0101011
[1,5,4,3,6,8,7,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>0110011
[1,4,5,3,6,8,7,2]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0010011
[1,3,4,5,6,8,7,2]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]=>[6,7,5,4,3,2,8,1]=>[1,8,2,3,4,5,7,6]=>0000011
[1,7,6,5,4,3,8,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[1,8,6,5,4,3,2,7]=>0111101
[1,6,7,5,4,3,8,2]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[1,8,6,5,4,2,3,7]=>0011101
[1,6,5,7,4,3,8,2]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,8,6,5,3,2,4,7]=>0101101
[1,4,6,7,5,3,8,2]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]=>[7,4,3,5,2,6,8,1]=>[1,8,6,2,5,3,4,7]=>0001101
[1,5,6,4,7,3,8,2]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>0010101
[1,4,6,5,7,3,8,2]=>[.,[[[.,[[.,.],[.,.]]],[.,.]],.]]=>[7,5,3,4,2,6,8,1]=>[1,8,6,2,4,3,5,7]=>0010101
[1,5,4,6,7,3,8,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0100101
[1,4,5,6,7,3,8,2]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>0000101
[1,3,6,5,7,4,8,2]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]=>[7,5,3,4,6,2,8,1]=>[1,8,2,6,4,3,5,7]=>0010101
[1,3,5,6,7,4,8,2]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>0000101
[1,3,4,6,7,5,8,2]=>[.,[[.,[.,[[.,[.,.]],[.,.]]]],.]]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>0000101
[1,3,5,4,7,6,8,2]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>0010101
[1,3,4,5,7,6,8,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[1,8,2,3,4,6,5,7]=>0000101
[1,5,4,6,3,7,8,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001
[1,4,3,6,5,7,8,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0101001
[1,3,4,6,5,7,8,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>0001001
[1,5,4,3,6,7,8,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0110001
[1,4,5,3,6,7,8,2]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]=>[7,6,5,3,2,4,8,1]=>[1,8,4,2,3,5,6,7]=>0010001
[1,4,3,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0100001
[1,3,4,5,6,7,8,2]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>0000001
[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>1011111
[2,1,7,8,6,5,4,3]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>1001111
[2,1,6,8,7,5,4,3]=>[[.,.],[[[[.,[[.,.],.]],.],.],.]]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>1001111
[2,1,7,6,8,5,4,3]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>1010111
[2,1,6,7,8,5,4,3]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>1000111
[2,1,5,8,7,6,4,3]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]=>[4,5,6,3,7,8,1,2]=>[2,1,8,7,3,6,5,4]=>1001111
[2,1,5,7,8,6,4,3]=>[[.,.],[[[.,[[.,[.,.]],.]],.],.]]=>[5,4,6,3,7,8,1,2]=>[2,1,8,7,3,6,4,5]=>1000111
[2,1,6,5,8,7,4,3]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1010111
[2,1,5,6,8,7,4,3]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>1000111
[2,1,7,6,5,8,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011011
[2,1,6,7,5,8,4,3]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>1001011
[2,1,5,7,6,8,4,3]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>1001011
[2,1,6,5,7,8,4,3]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>1010011
[2,1,5,6,7,8,4,3]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>1000011
[2,1,4,8,7,6,5,3]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>1001111
[2,1,4,7,8,6,5,3]=>[[.,.],[[.,[[[.,[.,.]],.],.]],.]]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>1000111
[2,1,4,6,8,7,5,3]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>1000111
[2,1,4,6,7,8,5,3]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>1000011
[2,1,5,4,8,7,6,3]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[2,1,8,4,3,7,6,5]=>1010111
[2,1,5,4,7,8,6,3]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>1010011
[2,1,4,5,8,7,6,3]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>1000111
[2,1,4,5,7,8,6,3]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,3,8,1,2]=>[2,1,8,3,4,7,5,6]=>1000011
[2,1,6,5,4,8,7,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>1011011
[2,1,5,6,4,8,7,3]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,8,5,3,4,7,6]=>1001011
[2,1,4,6,5,8,7,3]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>1001011
[2,1,5,4,6,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1010011
[2,1,7,6,5,4,8,3]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>1011101
[2,1,5,7,6,4,8,3]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[2,1,8,6,3,5,4,7]=>1001101
[2,1,6,5,7,4,8,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[2,1,4,6,7,5,8,3]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1000101
[2,1,5,4,7,6,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,5,6,4,7,8,3]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[2,1,8,5,3,4,6,7]=>1001001
[2,1,4,5,6,7,8,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>1000001
[1,2,8,7,6,5,4,3]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>0011111
[1,2,7,8,6,5,4,3]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]=>[4,3,5,6,7,8,2,1]=>[1,2,8,7,6,5,3,4]=>0001111
[1,2,6,7,8,5,4,3]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>0000111
[1,2,5,8,7,6,4,3]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>0001111
[1,2,6,5,8,7,4,3]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]=>[5,6,3,4,7,8,2,1]=>[1,2,8,7,4,3,6,5]=>0010111
[1,2,5,6,8,7,4,3]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>0000111
[1,2,7,6,5,8,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011011
[1,2,5,7,6,8,4,3]=>[.,[.,[[[.,[[.,.],[.,.]]],.],.]]]=>[6,4,5,3,7,8,2,1]=>[1,2,8,7,3,5,4,6]=>0001011
[1,2,5,6,7,8,4,3]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>0000011
[1,2,4,8,7,6,5,3]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>0001111
[1,2,4,7,8,6,5,3]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>0000111
[1,2,4,6,8,7,5,3]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]=>[5,6,4,7,3,8,2,1]=>[1,2,8,3,7,4,6,5]=>0000111
[1,2,4,6,7,8,5,3]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>0000011
[1,2,5,4,8,7,6,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>0010111
[1,2,5,4,7,8,6,3]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>0010011
[1,2,4,5,8,7,6,3]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]=>[5,6,7,4,3,8,2,1]=>[1,2,8,3,4,7,6,5]=>0000111
[1,2,4,6,5,8,7,3]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>0001011
[1,2,5,4,6,8,7,3]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]=>[6,7,5,3,4,8,2,1]=>[1,2,8,4,3,5,7,6]=>0010011
[1,2,4,5,6,8,7,3]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]=>[6,7,5,4,3,8,2,1]=>[1,2,8,3,4,5,7,6]=>0000011
[1,2,7,6,5,4,8,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[1,2,8,6,5,4,3,7]=>0011101
[1,2,5,6,7,4,8,3]=>[.,[.,[[[.,[.,[.,.]]],[.,.]],.]]]=>[7,5,4,3,6,8,2,1]=>[1,2,8,6,3,4,5,7]=>0000101
[1,2,4,7,6,5,8,3]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,2,8,3,6,5,4,7]=>0001101
[1,2,5,4,7,6,8,3]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]=>[7,5,6,3,4,8,2,1]=>[1,2,8,4,3,6,5,7]=>0010101
[1,2,6,5,4,7,8,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011001
[1,2,5,4,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0010001
[1,2,4,5,6,7,8,3]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>0000001
[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>1101111
[3,2,1,7,8,6,5,4]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1100111
[3,2,1,6,8,7,5,4]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>1100111
[3,2,1,7,6,8,5,4]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>1101011
[3,2,1,6,7,8,5,4]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>1100011
[3,2,1,5,8,7,6,4]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>1100111
[3,2,1,5,7,8,6,4]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>1100011
[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101011
[3,2,1,5,6,8,7,4]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>1100011
[3,2,1,7,6,5,8,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[3,2,1,6,7,5,8,4]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1100101
[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[3,2,1,8,4,6,5,7]=>1100101
[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101001
[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1100001
[2,3,1,8,7,6,5,4]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111
[2,3,1,6,8,7,5,4]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,2,1,3]=>[3,1,2,8,7,4,6,5]=>0100111
[2,3,1,7,6,8,5,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>0101011
[2,3,1,6,7,8,5,4]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>0100011
[2,3,1,5,7,8,6,4]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,2,1,3]=>[3,1,2,8,4,7,5,6]=>0100011
[2,3,1,6,5,8,7,4]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>0101011
[2,3,1,7,6,5,8,4]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>0101101
[2,3,1,6,7,5,8,4]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>0100001
[1,3,2,8,7,6,5,4]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>0101111
[1,3,2,6,8,7,5,4]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[1,3,2,8,7,4,6,5]=>0100111
[1,3,2,7,6,8,5,4]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[1,3,2,8,7,5,4,6]=>0101011
[1,3,2,6,7,8,5,4]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>0100011
[1,3,2,5,7,8,6,4]=>[.,[[.,.],[[.,[[.,[.,.]],.]],.]]]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>0100011
[1,3,2,6,5,8,7,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[1,3,2,8,5,4,7,6]=>0101011
[1,3,2,5,6,8,7,4]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,2,3,1]=>[1,3,2,8,4,5,7,6]=>0100011
[1,3,2,7,6,5,8,4]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>0101101
[1,3,2,6,7,5,8,4]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,2,3,1]=>[1,3,2,8,6,4,5,7]=>0100101
[1,3,2,6,5,7,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>0101001
[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>0100001
[2,1,3,8,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>1001111
[2,1,3,7,8,6,5,4]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>1000111
[2,1,3,6,8,7,5,4]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>1000111
[2,1,3,6,5,8,7,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011
[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1000001
[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>0001111
[1,2,3,7,8,6,5,4]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>0000111
[1,2,3,6,8,7,5,4]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>0000111
[1,2,3,7,6,8,5,4]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>0001011
[1,2,3,6,7,8,5,4]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>0000011
[1,2,3,5,8,7,6,4]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>0000111
[1,2,3,5,7,8,6,4]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>0000011
[1,2,3,6,5,8,7,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>0001011
[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>0000011
[1,2,3,7,6,5,8,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>0001101
[1,2,3,6,7,5,8,4]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>0000101
[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>0000101
[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001001
[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>0000001
[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[4,3,2,1,7,8,6,5]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110011
[4,3,2,1,6,8,7,5]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110011
[4,3,2,1,7,6,8,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101
[4,3,2,1,6,7,8,5]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110001
[3,4,2,1,8,7,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>0110111
[3,4,2,1,7,8,6,5]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>0110011
[3,4,2,1,6,8,7,5]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>0110011
[3,4,2,1,7,6,8,5]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101
[3,4,2,1,6,7,8,5]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>0110001
[2,4,3,1,8,7,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>0110111
[2,4,3,1,7,8,6,5]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[2,4,3,1,6,8,7,5]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>0110011
[2,4,3,1,7,6,8,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101
[2,4,3,1,6,7,8,5]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>0110001
[3,2,4,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[3,2,4,1,7,8,6,5]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1010011
[3,2,4,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1010011
[3,2,4,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,2,4,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[2,3,4,1,8,7,6,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111
[2,3,4,1,7,8,6,5]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>0010011
[2,3,4,1,6,8,7,5]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011
[2,3,4,1,7,6,8,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[1,4,3,2,8,7,6,5]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>0110111
[1,4,3,2,7,6,8,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110101
[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>0110001
[1,3,4,2,8,7,6,5]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>0010111
[1,3,4,2,7,8,6,5]=>[.,[[.,[.,.]],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>0010011
[1,3,4,2,6,8,7,5]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>0010011
[1,3,4,2,7,6,8,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0010101
[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>0010001
[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[2,1,4,3,7,8,6,5]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010011
[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011
[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[1,2,4,3,8,7,6,5]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>0010111
[1,2,4,3,7,8,6,5]=>[.,[.,[[.,.],[[[.,[.,.]],.],.]]]]=>[6,5,7,8,3,4,2,1]=>[1,2,4,3,8,7,5,6]=>0010011
[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010101
[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>0010001
[3,2,1,4,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111
[3,2,1,4,7,8,6,5]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100011
[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>1100011
[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100001
[2,3,1,4,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0100111
[2,3,1,4,7,8,6,5]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>0100011
[2,3,1,4,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[1,3,2,4,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>0100111
[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>0100011
[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100101
[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100001
[2,1,3,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111
[2,1,3,4,7,8,6,5]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>1000011
[2,1,3,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001
[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>0000111
[1,2,3,4,7,8,6,5]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>0000011
[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>0000011
[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>0000101
[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>0000001
[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011
[5,4,3,2,1,7,8,6]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111001
[4,5,3,2,1,8,7,6]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011
[3,5,4,2,1,8,7,6]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>0111011
[3,5,4,2,1,7,8,6]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[5,4,1,3,2,8,6,7]=>0111001
[4,3,5,2,1,8,7,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[3,4,5,2,1,8,7,6]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[2,5,4,3,1,8,7,6]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>0111011
[2,4,5,3,1,8,7,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[2,4,5,3,1,7,8,6]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>0011001
[3,2,5,4,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[3,2,5,4,1,7,8,6]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1011001
[2,3,5,4,1,8,7,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>0011011
[4,3,2,5,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[4,3,2,5,1,7,8,6]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001
[3,4,2,5,1,8,7,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[3,4,2,5,1,7,8,6]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[2,4,3,5,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011
[2,4,3,5,1,7,8,6]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[3,2,4,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[2,3,4,5,1,8,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>0001011
[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[1,5,4,3,2,8,7,6]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]=>[6,7,8,2,3,4,5,1]=>[1,5,4,3,2,8,7,6]=>0111011
[1,4,5,3,2,8,7,6]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]=>[6,7,8,3,2,4,5,1]=>[1,5,4,2,3,8,7,6]=>0011011
[1,4,5,3,2,7,8,6]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>0011001
[1,3,5,4,2,7,8,6]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>0011001
[1,3,4,5,2,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>0001011
[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0001001
[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]=>[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>0011011
[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>0011001
[1,2,4,5,3,8,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>0001011
[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>0001001
[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>0101011
[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>0101001
[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]=>[6,7,8,4,5,3,1,2]=>[2,1,3,5,4,8,7,6]=>1001011
[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>0001011
[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>0001001
[4,3,2,1,5,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011
[4,3,2,1,5,7,8,6]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110001
[3,2,4,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[3,2,4,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001
[2,3,4,1,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>0110011
[1,4,3,2,5,7,8,6]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>0110001
[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0010001
[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]=>[6,7,8,5,3,4,2,1]=>[1,2,4,3,5,8,7,6]=>0010011
[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010001
[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100001
[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,2,3,1]=>[1,3,2,4,5,8,7,6]=>0100011
[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100001
[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[2,1,3,4,5,8,7,6]=>1000011
[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000001
[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>0000011
[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>0000001
[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[5,6,4,3,2,1,8,7]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>0111101
[4,6,5,3,2,1,8,7]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>0111101
[5,4,6,3,2,1,8,7]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101
[4,5,6,3,2,1,8,7]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[3,6,5,4,2,1,8,7]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]=>[7,8,2,3,4,1,5,6]=>[6,5,1,4,3,2,8,7]=>0111101
[3,5,6,4,2,1,8,7]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>0011101
[4,3,6,5,2,1,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[3,4,6,5,2,1,8,7]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>0011101
[5,4,3,6,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[4,5,3,6,2,1,8,7]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[4,3,5,6,2,1,8,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[3,4,5,6,2,1,8,7]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0001101
[2,6,5,4,3,1,8,7]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>0111101
[2,5,6,4,3,1,8,7]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>0011101
[2,4,6,5,3,1,8,7]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>0011101
[3,2,6,5,4,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1011101
[3,2,5,6,4,1,8,7]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[6,2,1,5,3,4,8,7]=>1001101
[2,3,6,5,4,1,8,7]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,2,5,4,3,8,7]=>0011101
[4,3,2,6,5,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[3,4,2,6,5,1,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[2,4,3,6,5,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>0101101
[5,4,3,2,6,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[4,3,5,2,6,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[2,4,5,3,6,1,8,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>0010101
[3,2,5,4,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,3,2,5,6,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[3,4,2,5,6,1,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[2,4,3,5,6,1,8,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>0100101
[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101
[1,6,5,4,3,2,8,7]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[1,6,5,4,3,2,8,7]=>0111101
[1,5,6,4,3,2,8,7]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[1,6,5,4,2,3,8,7]=>0011101
[1,5,4,6,3,2,8,7]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>0101101
[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0000101
[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[2,1,5,6,4,3,8,7]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101
[2,1,4,6,5,3,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101
[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0000101
[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,2,3,1]=>[1,3,2,6,5,4,8,7]=>0101101
[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>1001101
[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>0001101
[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0000101
[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[3,4,2,1,6,5,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[2,4,3,1,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[3,2,4,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101
[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>0000101
[5,4,3,2,1,6,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001
[2,5,4,3,1,6,8,7]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,1,4,3,2,6,8,7]=>0111001
[3,2,5,4,1,6,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[2,3,5,4,1,6,8,7]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001
[2,3,4,5,1,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[1,4,5,3,2,6,8,7]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]=>[7,8,6,3,2,4,5,1]=>[1,5,4,2,3,6,8,7]=>0011001
[1,3,5,4,2,6,8,7]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]=>[7,8,6,3,4,2,5,1]=>[1,5,2,4,3,6,8,7]=>0011001
[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[2,1,4,5,3,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]=>[7,8,6,3,4,5,2,1]=>[1,2,5,4,3,6,8,7]=>0011001
[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>0001001
[4,3,2,1,5,6,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[3,2,4,1,5,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[2,3,4,1,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[1,3,4,2,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001
[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[2,3,1,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>0000001
[5,7,6,4,3,2,1,8]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>0111110
[4,7,6,5,3,2,1,8]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>0111110
[5,4,7,6,3,2,1,8]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>1011110
[4,5,7,6,3,2,1,8]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>0011110
[4,6,5,7,3,2,1,8]=>[[[[.,[[.,.],[.,.]]],.],.],[.,.]]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>0101110
[3,5,7,6,4,2,1,8]=>[[[.,[[.,[[.,.],.]],.]],.],[.,.]]=>[8,3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3,8]=>0011110
[4,3,7,6,5,2,1,8]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3,8]=>1011110
[3,4,7,6,5,2,1,8]=>[[[.,[.,[[[.,.],.],.]]],.],[.,.]]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>0011110
[5,4,3,7,6,2,1,8]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>1101110
[3,6,5,4,7,2,1,8]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>0110110
[3,5,6,4,7,2,1,8]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>0010110
[2,7,6,5,4,3,1,8]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2,8]=>0111110
[2,6,7,5,4,3,1,8]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3,8]=>0011110
[2,5,7,6,4,3,1,8]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3,8]=>0011110
[2,4,6,7,5,3,1,8]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>0001110
[2,5,6,4,7,3,1,8]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>0010110
[2,4,5,6,7,3,1,8]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>0000110
[3,2,7,6,5,4,1,8]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3,8]=>1011110
[3,2,6,7,5,4,1,8]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>1001110
[3,2,5,7,6,4,1,8]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1001110
[2,3,7,6,5,4,1,8]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>0011110
[2,3,6,7,5,4,1,8]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>0001110
[2,3,5,7,6,4,1,8]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]=>[8,4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4,8]=>0001110
[2,3,6,5,7,4,1,8]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>0010110
[2,3,5,6,7,4,1,8]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]=>[8,5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5,8]=>0000110
[4,3,2,6,7,5,1,8]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[3,4,2,6,7,5,1,8]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>0100110
[2,3,4,7,6,5,1,8]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>0001110
[2,3,4,6,7,5,1,8]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]=>[8,5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5,8]=>0000110
[5,4,3,2,7,6,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[4,5,3,2,7,6,1,8]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110
[3,5,4,2,7,6,1,8]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0110110
[3,2,5,4,7,6,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[4,3,2,5,7,6,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[3,4,2,5,7,6,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[2,3,4,5,7,6,1,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5,8]=>0000110
[3,5,6,4,2,7,1,8]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>0011010
[3,4,6,5,2,7,1,8]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>0011010
[3,5,4,6,2,7,1,8]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>0101010
[2,5,4,6,3,7,1,8]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010
[3,2,6,5,4,7,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[2,3,5,6,4,7,1,8]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]=>[8,6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6,8]=>0001010
[3,4,2,6,5,7,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[2,4,3,6,5,7,1,8]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>0101010
[2,3,4,6,5,7,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>0001010
[2,3,5,4,6,7,1,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>0010010
[2,4,3,5,6,7,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>0100010
[1,7,6,5,4,3,2,8]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>0111110
[1,6,7,5,4,3,2,8]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]=>[8,3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3,8]=>0011110
[1,6,5,7,4,3,2,8]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4,8]=>0101110
[1,5,6,4,7,3,2,8]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>0010110
[1,5,4,6,7,3,2,8]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]=>[8,5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5,8]=>0100110
[1,3,5,7,6,4,2,8]=>[.,[[.,[[.,[[.,.],.]],.]],[.,.]]]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>0001110
[1,3,6,5,7,4,2,8]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]=>[8,5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5,8]=>0010110
[1,3,5,6,7,4,2,8]=>[.,[[.,[[.,[.,[.,.]]],.]],[.,.]]]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>0000110
[1,3,4,6,7,5,2,8]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]=>[8,5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5,8]=>0000110
[1,3,5,4,7,6,2,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>0010110
[1,4,3,5,7,6,2,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>0100110
[1,3,4,5,7,6,2,8]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]=>[8,5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5,8]=>0000110
[1,5,4,6,3,7,2,8]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>0101010
[1,4,5,6,3,7,2,8]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]=>[8,6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6,8]=>0001010
[1,3,6,5,4,7,2,8]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>0011010
[1,3,5,6,4,7,2,8]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>0001010
[1,4,3,6,5,7,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>0101010
[1,3,4,6,5,7,2,8]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]=>[8,6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6,8]=>0001010
[1,5,4,3,6,7,2,8]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>0110010
[1,4,5,3,6,7,2,8]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]=>[8,6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6,8]=>0010010
[1,4,3,5,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010
[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010
[2,1,7,6,5,4,3,8]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[2,1,6,7,5,4,3,8]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[2,1,5,6,7,4,3,8]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1000110
[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[1,2,7,6,5,4,3,8]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]=>[8,3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3,8]=>0011110
[1,2,5,6,7,4,3,8]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]=>[8,5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5,8]=>0000110
[1,2,4,6,7,5,3,8]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]=>[8,5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5,8]=>0000110
[1,2,5,6,4,7,3,8]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]=>[8,6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6,8]=>0001010
[1,2,4,6,5,7,3,8]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]=>[8,6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6,8]=>0001010
[1,2,5,4,6,7,3,8]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]=>[8,6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6,8]=>0010010
[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0000010
[3,2,1,7,6,5,4,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[2,3,1,6,7,5,4,8]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[2,3,1,6,5,7,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[1,3,2,7,6,5,4,8]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]=>[8,4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4,8]=>0101110
[1,3,2,6,7,5,4,8]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]=>[8,5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5,8]=>0100110
[1,3,2,5,7,6,4,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>0100110
[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>0101010
[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,2,3,7,6,5,4,8]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>0001110
[1,2,3,6,7,5,4,8]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]=>[8,5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5,8]=>0000110
[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>0000110
[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>0001010
[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0000010
[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[4,3,2,1,6,7,5,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[3,2,4,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[3,2,4,1,6,7,5,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[2,3,4,1,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110
[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>0010010
[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>0100110
[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>0000110
[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000010
[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[4,5,3,2,1,7,6,8]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[3,2,5,4,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[3,4,2,5,1,7,6,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[2,4,3,5,1,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[1,5,4,3,2,7,6,8]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]=>[8,6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6,8]=>0111010
[1,4,5,3,2,7,6,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>0011010
[1,3,5,4,2,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0011010
[1,4,3,5,2,7,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0101010
[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[2,1,5,4,3,7,6,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[4,3,2,1,5,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[3,2,4,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>0110010
[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[2,3,1,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>0000010
[3,6,5,4,2,1,7,8]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]=>[8,7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7,8]=>0111100
[2,4,5,6,3,1,7,8]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]=>[8,7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7,8]=>0001100
[2,3,5,6,4,1,7,8]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]=>[8,7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7,8]=>0001100
[4,3,2,6,5,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[2,3,4,6,5,1,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>0001100
[3,5,4,2,6,1,7,8]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[1,6,5,4,3,2,7,8]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]=>[8,7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7,8]=>0111100
[1,5,4,6,3,2,7,8]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>0101100
[1,3,5,6,4,2,7,8]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]=>[8,7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7,8]=>0001100
[1,4,3,6,5,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>0101100
[1,5,4,3,6,2,7,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0110100
[1,4,5,3,6,2,7,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0010100
[1,4,3,5,6,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0100100
[1,3,4,5,6,2,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[1,2,6,5,4,3,7,8]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>0011100
[1,2,4,6,5,3,7,8]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]=>[8,7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7,8]=>0001100
[1,2,4,5,6,3,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>0101100
[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]=>[8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8]=>0001100
[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[4,3,2,1,6,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[3,2,4,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[2,3,4,1,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100
[3,5,4,2,1,6,7,8]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>0111000
[2,5,4,3,1,6,7,8]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[2,4,5,3,1,6,7,8]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000
[3,2,5,4,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[2,3,5,4,1,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[2,4,3,5,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[1,5,4,3,2,6,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>0111000
[1,4,5,3,2,6,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>0011000
[1,4,3,5,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0101000
[1,3,4,5,2,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[2,1,4,5,3,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>0011000
[1,2,4,5,3,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000
[2,4,3,1,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>0110000
[1,3,4,2,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>0000101
[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>0000101
[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]=>[8,6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6,8]=>0001010
[1,2,3,7,5,6,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001001
[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>0001001
[1,2,3,8,5,7,6,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>0001011
[1,2,3,8,6,5,7,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>0001101
[1,2,3,8,6,7,5,4]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>0001011
[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010101
[1,2,4,5,8,6,7,3]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]=>[7,5,6,4,3,8,2,1]=>[1,2,8,3,4,6,5,7]=>0000101
[1,2,4,7,5,6,8,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>0001001
[1,2,4,8,5,6,7,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>0001001
[1,2,4,8,6,5,7,3]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]=>[7,4,5,6,3,8,2,1]=>[1,2,8,3,6,5,4,7]=>0001101
[1,2,6,4,5,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0010001
[1,2,7,4,5,6,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0010001
[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>0010001
[1,2,8,4,6,7,5,3]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>0010011
[1,2,8,4,7,6,5,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>0010111
[1,2,7,5,4,6,8,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011001
[1,2,8,5,4,6,7,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>0011001
[1,2,8,5,6,4,7,3]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]=>[7,5,3,4,6,8,2,1]=>[1,2,8,6,4,3,5,7]=>0010101
[1,2,8,6,5,4,7,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]=>[7,3,4,5,6,8,2,1]=>[1,2,8,6,5,4,3,7]=>0011101
[1,2,8,6,5,7,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011011
[1,2,8,7,5,6,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>0011011
[1,3,2,7,5,6,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>0101001
[1,3,2,8,5,7,6,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[1,3,2,8,5,4,7,6]=>0101011
[1,3,2,8,6,5,7,4]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>0101101
[1,3,2,8,6,7,5,4]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,2,3,1]=>[1,3,2,8,7,5,4,6]=>0101011
[1,3,4,2,8,6,7,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0010101
[1,3,4,5,8,6,7,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]=>[7,5,6,4,3,2,8,1]=>[1,8,2,3,4,6,5,7]=>0000101
[1,3,4,8,5,6,7,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>0001001
[1,3,6,4,5,2,8,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]=>[7,8,5,3,4,2,6,1]=>[1,6,2,4,3,5,8,7]=>0010101
[1,3,6,4,5,7,8,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0010001
[1,3,7,4,5,6,2,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]=>[8,6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6,8]=>0010010
[1,3,7,4,5,6,8,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0010001
[1,3,8,4,5,6,7,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>0010001
[1,3,8,4,6,5,7,2]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>0010101
[1,3,8,4,6,7,5,2]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>0010011
[1,3,8,5,6,7,4,2]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>0010011
[1,3,8,5,7,6,4,2]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]=>[5,6,3,4,7,2,8,1]=>[1,8,2,7,4,3,6,5]=>0010111
[1,3,8,6,5,7,4,2]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>0011011
[1,3,8,7,5,6,4,2]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>0011011
[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110101
[1,4,3,8,5,6,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0101001
[1,4,3,8,5,7,6,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0101011
[1,4,3,8,6,7,5,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,8,3,2,7,5,4,6]=>0101011
[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0101000
[1,5,3,4,2,7,8,6]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>0101001
[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0101011
[1,5,3,4,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010
[1,5,3,4,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0100001
[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0100100
[1,6,3,4,5,8,7,2]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]=>[6,7,5,4,2,3,8,1]=>[1,8,3,2,4,5,7,6]=>0100011
[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010
[1,7,3,4,5,6,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0100001
[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>0100001
[1,8,3,4,6,7,5,2]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>0100011
[1,6,3,5,4,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>0101100
[1,6,3,5,4,8,7,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0101011
[1,7,3,5,4,6,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]=>[8,6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6,8]=>0101010
[1,8,3,5,4,6,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>0101001
[1,8,3,5,4,7,6,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>0101011
[1,8,3,5,6,4,7,2]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>0100101
[1,8,3,7,5,6,4,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,2,3,8,1]=>[1,8,3,2,7,5,4,6]=>0101011
[1,8,3,7,6,5,4,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>0101111
[1,6,4,3,5,2,7,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0110100
[1,6,4,3,5,8,7,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>0110011
[1,8,4,3,5,6,7,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0110001
[1,8,4,3,5,7,6,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>0110011
[1,8,4,3,6,7,5,2]=>[.,[[[[.,.],.],[[.,[.,.]],.]],.]]=>[6,5,7,2,3,4,8,1]=>[1,8,4,3,2,7,5,6]=>0110011
[1,6,4,5,3,2,7,8]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]=>[8,7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7,8]=>0101100
[1,6,4,5,3,2,8,7]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>0101101
[1,6,4,5,3,8,7,2]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0101011
[1,7,4,5,3,6,8,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001
[1,8,4,5,3,6,7,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001
[1,7,4,5,6,3,8,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0100101
[1,8,4,5,6,3,7,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0100101
[1,8,4,5,6,7,3,2]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>0100011
[1,7,4,6,5,3,2,8]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]=>[8,4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4,8]=>0101110
[1,8,4,6,5,3,7,2]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[1,8,6,3,2,5,4,7]=>0101101
[1,8,4,6,5,7,3,2]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>0101011
[1,7,5,4,3,6,8,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111001
[1,8,5,4,3,6,7,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111001
[1,8,5,4,3,7,6,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111011
[1,8,5,4,6,7,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0110011
[1,8,5,4,7,6,3,2]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[1,8,7,4,3,2,6,5]=>0110111
[1,8,6,4,5,7,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0110011
[1,8,7,4,5,6,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>0110011
[1,8,7,4,6,5,3,2]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]=>[5,6,2,3,4,7,8,1]=>[1,8,7,4,3,2,6,5]=>0110111
[1,8,6,5,4,3,7,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[1,8,6,5,4,3,2,7]=>0111101
[1,8,6,5,4,7,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111011
[1,8,7,5,4,6,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>0111011
[1,8,7,5,6,4,3,2]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>0110111
[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[2,1,3,5,8,6,7,4]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[2,1,3,8,4,6,5,7]=>1000101
[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>1001001
[2,1,3,8,5,7,6,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011
[2,1,3,8,6,5,7,4]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>1001101
[2,1,3,8,6,7,5,4]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>1001011
[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[2,1,4,8,5,7,6,3]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>1001011
[2,1,4,8,6,7,5,3]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>1001011
[2,1,5,4,8,6,7,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,6,4,5,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1010011
[2,1,8,4,5,7,6,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>1010011
[2,1,7,4,6,5,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,8,4,6,5,7,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,8,4,6,7,5,3]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]=>[6,5,7,3,4,8,1,2]=>[2,1,8,4,3,7,5,6]=>1010011
[2,1,8,4,7,6,5,3]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]=>[5,6,7,3,4,8,1,2]=>[2,1,8,4,3,7,6,5]=>1010111
[2,1,8,5,4,6,7,3]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>1011001
[2,1,8,5,4,7,6,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>1011011
[2,1,7,5,6,4,8,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[2,1,8,5,6,4,7,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[2,1,8,5,6,7,4,3]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]=>[6,5,3,4,7,8,1,2]=>[2,1,8,7,4,3,5,6]=>1010011
[2,1,8,5,7,6,4,3]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1010111
[2,1,8,6,5,4,7,3]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>1011101
[2,1,8,6,5,7,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011011
[2,1,8,7,5,6,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>1011011
[2,3,1,7,5,6,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[2,3,1,8,6,7,5,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>0101011
[2,3,4,1,8,6,7,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[2,3,4,5,8,6,7,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]=>[7,5,6,4,3,2,1,8]=>[8,1,2,3,4,6,5,7]=>0000101
[2,3,4,7,5,6,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>0001010
[2,3,4,7,5,6,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>0001001
[2,3,4,8,5,6,7,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>0001001
[2,3,4,8,5,7,6,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>0001011
[2,3,4,8,6,5,7,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>0001101
[2,3,4,8,6,7,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>0001011
[2,3,5,4,8,6,7,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>0010101
[2,3,6,4,5,1,7,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>0010100
[2,3,6,4,5,1,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>0010101
[2,3,6,4,5,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>0010001
[2,3,6,4,5,8,7,1]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>0010011
[2,3,7,4,5,6,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>0010001
[2,3,8,4,5,6,7,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>0010001
[2,3,7,4,6,5,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>0010101
[2,3,7,5,4,6,8,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>0011001
[2,3,8,5,4,6,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>0011001
[2,3,7,5,6,4,1,8]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]=>[8,5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5,8]=>0010110
[2,3,8,5,7,6,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>0010111
[2,3,8,6,5,4,7,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>0011101
[2,4,3,5,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>0100101
[2,4,3,7,5,6,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001
[2,4,3,8,5,6,7,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001
[2,4,3,8,5,7,6,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0101011
[2,4,3,8,6,5,7,1]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>0101101
[2,5,3,4,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,5,3,4,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011
[2,5,3,4,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>0100001
[2,5,3,4,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>0100011
[2,5,3,4,7,6,8,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>0100101
[2,5,3,4,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>0100101
[2,6,3,4,5,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>0100001
[2,6,3,4,5,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>0100011
[2,7,3,4,5,6,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>0100010
[2,8,3,4,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>0100001
[2,8,3,4,5,7,6,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>0100011
[2,6,3,5,4,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>0101101
[2,6,3,5,4,8,7,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0101011
[2,7,3,5,4,6,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001
[2,8,3,5,4,7,6,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>0101011
[2,8,3,5,7,6,4,1]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>0100111
[2,8,3,7,5,6,4,1]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]=>[6,4,5,7,2,3,1,8]=>[8,1,3,2,7,5,4,6]=>0101011
[2,8,3,7,6,5,4,1]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]=>[4,5,6,7,2,3,1,8]=>[8,1,3,2,7,6,5,4]=>0101111
[2,5,4,3,8,6,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>0110101
[2,6,4,3,5,8,7,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>0110011
[2,7,4,3,5,6,8,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0110001
[2,8,4,3,5,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0110001
[2,8,4,3,5,7,6,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>0110011
[2,7,4,3,6,5,8,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>0110101
[2,8,4,3,6,5,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]=>[7,5,6,2,3,4,1,8]=>[8,1,4,3,2,6,5,7]=>0110101
[2,8,4,3,6,7,5,1]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]=>[6,5,7,2,3,4,1,8]=>[8,1,4,3,2,7,5,6]=>0110011
[2,8,4,3,7,6,5,1]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>0110111
[2,8,4,5,3,6,7,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>0101001
[2,7,4,5,6,3,8,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>0100101
[2,8,4,5,6,3,7,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>0100101
[2,8,4,5,6,7,3,1]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]=>[6,5,4,2,3,7,1,8]=>[8,1,7,3,2,4,5,6]=>0100011
[2,7,4,6,5,3,1,8]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4,8]=>0101110
[2,7,4,6,5,3,8,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0101101
[2,8,4,6,5,3,7,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0101101
[2,8,4,7,6,5,3,1]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>0101111
[2,7,5,4,3,6,8,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>0111001
[2,8,5,4,3,6,7,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>0111001
[2,8,5,4,3,7,6,1]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]=>[6,7,2,3,4,5,1,8]=>[8,1,5,4,3,2,7,6]=>0111011
[2,8,5,4,7,6,3,1]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>0110111
[2,8,7,4,6,5,3,1]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>0110111
[2,8,7,5,4,6,3,1]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]=>[6,2,3,4,5,7,1,8]=>[8,1,7,5,4,3,2,6]=>0111011
[2,8,7,5,6,4,3,1]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>0110111
[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[3,2,1,5,8,6,7,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[3,2,1,8,4,6,5,7]=>1100101
[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[3,2,1,7,5,6,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101001
[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101001
[3,2,1,8,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101011
[3,2,1,8,6,5,7,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[3,2,1,8,6,7,5,4]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>1101011
[3,2,4,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,2,4,5,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>1000101
[3,2,5,4,8,6,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[3,2,6,4,5,1,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[3,2,6,4,5,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[3,2,7,4,5,6,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[3,2,7,4,6,5,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[3,2,7,4,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[3,2,8,4,6,5,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[3,2,7,5,4,6,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[3,2,8,5,4,7,6,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>1011011
[3,2,7,5,6,4,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[3,2,8,5,6,4,7,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[3,2,8,5,7,6,4,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>1010111
[3,2,8,6,5,7,4,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1011011
[3,2,8,7,5,6,4,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1011011
[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[4,2,3,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001
[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,3,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[4,2,3,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1010011
[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[4,2,3,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,2,3,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[4,2,3,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[4,2,3,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>1000011
[4,2,3,7,6,5,8,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1001101
[4,2,3,8,7,6,5,1]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[8,2,1,3,7,6,5,4]=>1001111
[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[5,2,3,4,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>1000101
[6,2,3,4,5,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>1000011
[8,2,3,4,5,7,6,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>1000011
[6,2,3,5,4,7,1,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6,8]=>1001010
[7,2,3,5,4,6,1,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6,8]=>1001010
[8,2,3,5,7,6,4,1]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]=>[5,6,4,7,3,1,2,8]=>[8,2,1,3,7,4,6,5]=>1000111
[8,2,3,6,5,4,7,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>1001101
[8,2,3,7,6,5,4,1]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]=>[4,5,6,7,3,1,2,8]=>[8,2,1,3,7,6,5,4]=>1001111
[5,2,4,3,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[5,2,4,3,1,6,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[5,2,4,3,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[5,2,4,3,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[5,2,4,3,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,4,3,6,7,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[5,2,4,3,7,6,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[5,2,4,3,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[5,2,4,3,8,7,6,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[8,2,1,4,3,7,6,5]=>1010111
[6,2,4,3,5,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[7,2,4,3,6,5,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[7,2,4,3,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[8,2,4,3,6,5,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[8,2,4,3,6,7,5,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]=>[6,5,7,3,4,1,2,8]=>[8,2,1,4,3,7,5,6]=>1010011
[8,2,4,3,7,6,5,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[8,2,1,4,3,7,6,5]=>1010111
[8,2,4,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]=>[6,5,4,3,7,1,2,8]=>[8,2,1,7,3,4,5,6]=>1000011
[7,2,4,6,5,3,1,8]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1001110
[8,2,4,7,5,6,3,1]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]=>[6,4,5,3,7,1,2,8]=>[8,2,1,7,3,5,4,6]=>1001011
[6,2,5,4,3,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1011101
[6,2,5,4,3,7,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[7,2,5,4,3,6,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[8,2,5,4,3,7,6,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>1011011
[7,2,5,4,6,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[8,2,5,4,7,6,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>1010111
[7,2,6,4,5,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[8,2,6,4,5,3,7,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[8,2,6,4,5,7,3,1]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[8,2,1,7,4,3,5,6]=>1010011
[8,2,7,4,5,6,3,1]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]=>[6,5,3,4,7,1,2,8]=>[8,2,1,7,4,3,5,6]=>1010011
[8,2,7,4,6,5,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>1010111
[7,2,6,5,4,3,1,8]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]=>[8,3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3,8]=>1011110
[8,2,6,5,4,7,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1011011
[8,2,7,5,4,6,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>1011011
[8,2,7,5,6,4,3,1]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]=>[5,3,4,6,7,1,2,8]=>[8,2,1,7,6,4,3,5]=>1010111
[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1011111
[4,3,2,1,8,6,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101
[4,3,2,7,5,6,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[4,3,2,8,5,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[4,3,2,8,5,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[5,3,2,4,1,6,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[5,3,2,4,1,7,6,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[5,3,2,4,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,3,2,4,7,6,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[8,3,2,4,6,5,7,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>1100101
[8,3,2,4,6,7,5,1]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,1,2,3,8]=>[8,3,2,1,4,7,5,6]=>1100011
[8,3,2,4,7,6,5,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>1100111
[6,3,2,5,4,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[6,3,2,5,4,7,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[6,3,2,5,4,7,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[6,3,2,5,4,8,7,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[7,3,2,5,4,6,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[8,3,2,5,4,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[7,3,2,5,6,4,8,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101
[8,3,2,5,6,4,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101
[8,3,2,5,6,7,4,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,1,2,3,8]=>[8,3,2,1,7,4,5,6]=>1100011
[8,3,2,5,7,6,4,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>1100111
[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>1101111
[5,3,4,2,1,8,7,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[5,3,4,2,6,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,3,4,2,7,6,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[5,3,4,2,8,6,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[6,3,4,2,5,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[7,3,4,2,6,5,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[8,3,4,2,6,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[6,3,4,5,2,1,8,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[8,3,4,5,7,6,2,1]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>1000111
[8,3,4,7,6,5,2,1]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]=>[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>1001111
[6,3,5,4,2,1,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[6,3,5,4,2,7,8,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1011001
[6,3,5,4,2,8,7,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011
[8,3,5,4,2,6,7,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1011001
[8,3,5,4,2,7,6,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011
[7,3,5,4,6,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[8,3,5,4,6,7,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>1010011
[8,3,5,4,7,6,2,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1010111
[7,3,6,4,5,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[8,3,6,4,5,2,7,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[8,3,7,4,5,6,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>1010011
[8,3,7,4,6,5,2,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>1010111
[7,3,6,5,4,2,1,8]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]=>[8,3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3,8]=>1011110
[7,3,6,5,4,2,8,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1011101
[8,3,6,5,4,7,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>1011011
[8,3,7,5,4,6,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>1011011
[8,3,7,6,5,4,2,1]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>1011111
[5,4,3,2,8,6,7,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101
[6,4,3,2,5,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[6,4,3,2,5,8,7,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1110011
[8,4,3,2,5,7,6,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1110011
[7,4,3,2,6,5,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[7,4,3,2,6,5,8,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101
[8,4,3,2,6,5,7,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101
[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1110111
[6,4,3,5,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[8,4,3,5,2,7,6,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[8,4,3,5,7,6,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1100111
[7,4,3,6,5,2,1,8]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>1101110
[7,4,3,6,5,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1101101
[8,4,3,7,5,6,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>1101011
[8,4,3,7,6,5,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1101111
[6,5,3,4,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[8,5,3,4,2,7,6,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[8,5,3,4,7,6,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1100111
[8,7,3,4,6,5,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>1100111
[7,6,3,5,4,2,1,8]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>1101110
[7,6,3,5,4,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1101101
[8,6,3,5,4,2,7,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1101101
[8,6,3,5,4,7,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>1101011
[8,7,3,5,4,6,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>1101011
[8,7,3,5,6,4,2,1]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>1100111
[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>1101111
[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111011
[8,5,4,3,7,6,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>1110111
[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>1110111
[8,7,4,6,5,3,2,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>1101111
[2,4,1,3,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,1,4,6,3,5,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[2,4,1,6,3,5,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,4,6,1,3,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,4,1,3,6,8,5,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,4,6,1,3,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,4,6,1,8,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,4,6,8,1,3,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,1,4,6,3,5,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,4,6,1,3,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,4,1,6,3,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,4,6,1,3,7,5,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,4,6,7,1,3,5,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,4,1,3,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[2,1,4,6,7,3,8,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[2,4,1,6,7,3,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[2,4,6,1,7,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,4,6,7,1,3,8,5]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[2,1,4,6,7,8,3,5]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[2,4,1,6,7,8,3,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,4,6,7,8,1,3,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,4,3,7,5,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,4,1,3,7,5,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,1,4,7,3,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,4,1,3,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,4,1,7,3,8,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,4,7,1,8,3,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,4,7,8,1,3,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,4,1,5,3,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,4,5,1,3,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,4,5,1,7,3,6,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,4,1,3,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[2,4,5,1,3,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[2,1,4,5,7,3,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[2,4,1,5,7,3,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[2,4,5,1,7,3,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,4,5,1,7,8,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,4,5,7,8,1,3,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[2,1,4,8,3,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,4,8,1,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,4,1,5,3,8,6,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,4,5,1,8,3,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,4,1,5,3,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,4,1,5,6,3,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[2,4,5,1,6,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,4,5,6,1,3,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[2,1,4,5,6,8,3,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[2,4,1,5,6,8,3,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,4,5,1,6,8,3,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,4,5,6,8,1,3,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[2,4,5,1,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,4,5,1,6,3,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,4,5,6,1,3,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,4,1,5,6,7,3,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,4,5,6,7,1,3,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,4,1,5,6,7,8,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>0100001
[2,4,5,1,6,7,8,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[2,4,5,6,1,7,8,3]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[2,4,5,6,7,1,8,3]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101
[2,4,5,6,7,8,1,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[2,1,5,3,6,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,5,1,3,6,4,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[2,5,1,6,3,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,5,6,1,3,4,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,5,6,1,3,8,4,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,5,6,8,1,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,5,1,6,3,7,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,5,6,1,3,7,4,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,1,5,3,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[2,5,1,3,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[2,5,6,1,3,7,8,4]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[2,1,5,6,7,3,8,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[2,5,1,6,7,3,8,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[2,5,6,7,1,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[2,1,5,6,7,8,3,4]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[2,5,1,6,7,8,3,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,5,6,1,7,8,3,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,5,6,7,8,1,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,5,3,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,1,5,7,3,4,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[2,5,1,7,3,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,5,7,1,3,4,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,5,1,3,7,8,4,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,5,7,1,8,3,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,5,7,8,1,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,1,5,7,3,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,3,5,1,4,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,3,5,7,1,4,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,3,5,1,7,4,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,3,1,5,7,8,4,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,3,5,7,8,1,4,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,5,3,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[2,1,5,8,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,3,5,1,4,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,1,3,5,8,4,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,3,5,8,1,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,1,5,3,4,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[2,3,5,1,6,4,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,3,1,5,6,8,4,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,3,5,1,6,8,4,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,3,5,6,8,1,4,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,5,3,4,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[2,3,5,1,4,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,3,5,6,1,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,3,5,6,7,1,4,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,3,5,1,6,7,8,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[2,3,5,6,1,7,8,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[2,3,5,6,7,8,1,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[2,1,6,3,7,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,6,1,3,7,4,8,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,1,6,7,3,4,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[2,6,1,7,3,4,8,5]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,6,7,1,3,4,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,6,1,3,7,8,4,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,6,1,7,3,8,4,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,6,7,1,8,3,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,6,7,8,1,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,6,1,3,4,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[2,3,1,6,4,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,1,6,3,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[2,3,6,1,4,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[2,1,3,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[2,3,1,6,7,8,4,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[2,3,6,1,7,8,4,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,3,6,7,8,1,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,6,3,8,4,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[2,1,6,8,3,4,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,6,8,1,3,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,6,1,3,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[2,3,1,6,4,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,3,6,1,8,4,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,1,6,3,4,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[2,6,1,3,4,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[2,1,3,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[2,3,6,1,4,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,3,4,1,6,8,5,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,3,4,6,8,1,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[2,1,3,6,4,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[2,3,6,1,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,3,4,6,1,5,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,3,4,6,7,1,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,3,4,6,1,7,8,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[2,3,4,6,7,8,1,5]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[2,1,7,3,8,4,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[2,1,7,8,3,4,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[2,7,8,1,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,3,1,7,4,8,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,1,3,7,8,4,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[2,3,7,8,1,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,1,7,3,4,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[2,3,1,7,4,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[2,1,3,4,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[2,3,4,1,7,5,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,3,4,7,1,5,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[2,3,1,4,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,3,4,1,7,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,3,4,7,8,1,5,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,1,7,3,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,1,3,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[2,3,4,1,7,5,6,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,3,4,7,1,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,3,4,5,7,1,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,3,4,5,7,1,8,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101
[2,3,4,5,7,8,1,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[2,1,8,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[2,1,3,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[2,3,4,1,8,5,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[2,1,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[2,3,1,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[2,3,4,1,5,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>0000010
[3,1,4,2,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,1,4,6,2,5,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[3,4,1,6,2,5,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[3,4,6,1,2,5,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,4,1,2,6,8,5,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,4,1,6,2,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,4,6,8,1,2,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,4,1,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,4,1,6,2,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,4,6,1,2,7,5,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,4,6,7,1,2,5,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,4,2,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[3,4,1,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[3,4,6,1,2,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[3,1,4,6,7,2,8,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[3,4,1,6,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[3,4,6,1,7,2,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[3,4,6,7,1,2,8,5]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[3,1,4,6,7,8,2,5]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[3,4,1,6,7,8,2,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[3,4,6,1,7,8,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,4,6,7,8,1,2,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[3,1,4,2,7,5,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,4,1,2,7,5,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[3,4,7,1,2,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,4,7,1,8,2,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,4,7,8,1,2,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,4,2,7,5,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[3,4,1,5,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,4,5,7,1,2,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,4,2,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[3,4,1,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[3,4,5,1,2,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[3,1,4,5,7,2,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[3,4,1,5,7,2,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[3,4,5,7,1,2,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[3,1,4,5,7,8,2,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[3,4,1,5,7,8,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[3,4,5,1,7,8,2,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,4,5,7,8,1,2,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[3,1,4,2,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,4,8,1,2,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[3,4,1,5,2,8,6,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,4,5,1,2,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,4,5,8,1,2,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[3,4,5,1,2,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,1,4,5,6,2,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[3,4,1,5,6,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[3,4,5,1,6,2,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[3,4,5,6,1,2,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[3,1,4,5,6,8,2,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[3,4,1,5,6,8,2,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[3,4,5,6,8,1,2,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[3,1,4,5,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,4,5,1,6,2,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,1,4,5,6,7,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[3,4,5,1,6,7,2,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,1,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>1000001
[3,4,1,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>0100001
[3,4,5,1,6,7,8,2]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[3,4,5,6,1,7,8,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[3,4,5,6,7,1,8,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101
[3,1,5,2,6,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,5,1,2,6,4,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,1,5,6,2,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[3,5,6,1,2,4,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,5,1,2,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,5,6,1,2,8,4,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,5,6,1,8,2,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,5,6,8,1,2,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,5,6,2,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,5,6,1,2,4,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[3,5,1,2,6,7,4,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,5,1,6,2,7,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,5,6,1,2,7,4,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,5,6,1,7,2,4,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,5,6,7,1,2,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,5,2,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[3,5,1,2,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[3,5,6,1,2,7,8,4]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[3,1,5,6,7,2,8,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[3,5,1,6,7,2,8,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[3,5,6,1,7,2,8,4]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[3,5,6,7,1,2,8,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[3,1,5,6,7,8,2,4]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[3,5,1,6,7,8,2,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[3,5,6,1,7,8,2,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,5,6,7,8,1,2,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>0000100
[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,5,1,2,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,1,5,7,2,4,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[3,5,7,1,2,4,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,5,1,2,7,8,4,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,5,7,8,1,2,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,5,2,7,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,5,7,2,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,5,7,1,2,4,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[3,5,1,2,4,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,5,2,4,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[3,1,2,5,7,4,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,3,2,5,7,4,6,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,3,5,2,7,4,6,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,3,5,7,2,4,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,5,1,2,4,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[3,1,2,5,7,4,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,3,5,2,7,4,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,3,5,7,2,4,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,3,2,5,7,8,4,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,3,5,2,7,8,4,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,5,7,2,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,3,5,7,8,2,4,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,5,8,2,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,5,1,2,4,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,2,5,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,3,5,2,4,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[3,1,2,5,8,4,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,3,2,5,8,4,6,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,3,5,2,8,4,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,3,5,8,2,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,5,1,2,4,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[3,1,2,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,3,5,2,4,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[1,3,5,2,6,4,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,3,5,6,2,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,3,5,2,6,8,4,7]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,5,6,2,8,4,7]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,3,5,6,8,2,4,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[1,3,5,2,4,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[1,3,5,6,2,4,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[1,3,5,2,6,7,4,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,5,6,2,7,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,3,5,6,7,2,4,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,2,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1000001
[1,3,5,6,7,2,8,4]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0000101
[1,3,5,6,7,8,2,4]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010
[3,1,6,2,7,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,6,1,2,7,4,8,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,6,1,7,2,4,8,5]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[3,6,7,1,2,4,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[3,6,1,2,7,8,4,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[3,6,1,7,2,8,4,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,6,7,1,2,8,4,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,6,7,8,1,2,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[3,1,6,7,2,4,5,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,6,1,2,4,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,2,6,4,7,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,3,6,2,7,4,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[3,6,1,2,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[3,1,2,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,3,6,2,7,4,8,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,3,6,7,2,4,8,5]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,3,2,6,7,8,4,5]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,3,6,2,7,8,4,5]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,6,7,8,2,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,6,8,2,4,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,6,8,1,2,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[3,6,1,2,4,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,2,6,4,8,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,3,6,2,4,8,5,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[3,1,2,6,8,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,3,2,6,8,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[3,1,6,2,4,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[3,6,1,2,4,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[3,1,2,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,3,6,2,4,5,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[3,1,2,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,3,4,6,2,5,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,3,4,6,8,2,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,6,1,2,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[1,3,2,6,4,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,3,6,2,4,5,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[1,3,4,6,2,5,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,1,2,4,6,7,5,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,3,4,6,2,7,5,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,3,4,6,7,2,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,2,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001
[1,3,4,6,7,2,8,5]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0000101
[3,1,7,2,8,4,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,7,8,2,4,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,7,8,1,2,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[3,7,1,2,4,8,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,3,2,7,4,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,3,7,2,4,8,5,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[3,1,2,7,8,4,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,3,7,2,8,4,5,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,3,7,8,2,4,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,1,7,2,4,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[3,7,1,2,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[1,3,7,2,4,5,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[3,1,2,4,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,3,2,4,7,5,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,3,4,2,7,5,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,3,4,7,2,5,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[3,1,2,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,3,4,2,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,3,4,7,8,2,5,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,7,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[3,1,2,7,4,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,3,2,7,4,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,3,7,2,4,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[3,1,2,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,3,4,7,2,5,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,1,2,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,3,4,5,7,2,6,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,2,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000001
[1,3,4,5,7,8,2,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010
[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[3,8,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[3,1,2,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,3,2,8,4,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,3,8,2,4,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[3,1,2,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,3,4,2,8,5,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,3,4,8,2,5,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[3,1,2,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,3,2,4,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,3,4,2,5,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[1,3,4,5,2,8,6,7]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,3,4,5,8,2,6,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[3,1,2,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,3,4,5,6,8,2,7]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010
[4,1,5,2,6,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,5,1,2,6,3,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[4,1,5,6,2,3,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[4,5,1,6,2,3,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[4,5,1,2,6,8,3,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[4,5,6,1,2,8,3,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[4,5,6,1,8,2,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[4,5,6,8,1,2,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[4,1,5,2,6,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,1,5,6,2,3,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[4,5,1,2,6,7,3,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[4,5,1,6,2,7,3,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,5,6,1,2,7,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[4,5,6,1,7,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[4,1,5,2,6,7,8,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[4,5,1,2,6,7,8,3]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[4,5,6,1,2,7,8,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[4,1,5,6,7,2,8,3]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[4,5,1,6,7,2,8,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[4,5,6,1,7,2,8,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[4,5,6,7,1,2,8,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[4,1,5,6,7,8,2,3]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[4,5,1,6,7,8,2,3]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[4,5,6,1,7,8,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[4,1,5,2,7,3,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,5,1,2,7,3,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[4,5,1,7,2,3,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[4,5,1,2,7,8,3,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[4,5,1,7,2,8,3,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[4,5,7,8,1,2,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[4,1,5,2,7,3,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,5,1,2,3,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,4,2,5,3,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[4,1,2,5,7,3,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,4,5,2,7,3,6,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,4,5,7,2,3,6,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[4,1,5,2,3,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[1,4,5,2,3,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0010001
[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,4,5,2,7,3,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,4,5,7,2,3,8,6]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,4,2,5,7,8,3,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,4,5,2,7,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,4,5,7,8,2,3,6]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[4,1,5,2,8,3,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[4,5,1,2,3,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,4,2,5,3,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,5,2,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,4,2,5,8,3,6,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,4,5,2,8,3,6,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[4,1,2,5,6,3,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,4,5,2,6,3,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,4,2,5,6,8,3,7]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,4,5,2,6,8,3,7]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,4,5,6,8,2,3,7]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[4,1,5,2,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[4,1,2,5,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,4,2,5,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[4,1,2,5,6,3,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,4,5,2,6,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,4,5,6,2,3,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[1,4,2,5,6,7,3,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,4,5,2,6,7,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,4,5,6,2,7,3,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,4,5,6,7,2,3,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[4,1,2,5,6,7,8,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>1000001
[1,4,2,5,6,7,8,3]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>0100001
[1,4,5,2,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>0010001
[1,4,5,6,2,7,8,3]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0001001
[1,4,5,6,7,2,8,3]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]=>[7,8,5,4,3,2,6,1]=>[1,6,2,3,4,5,8,7]=>0000101
[1,4,5,6,7,8,2,3]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>0000010
[4,1,6,2,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,6,7,2,3,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[4,6,7,1,2,3,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[4,6,1,2,7,8,3,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[4,6,1,7,2,8,3,5]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,6,7,1,2,8,3,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[4,6,7,8,1,2,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>0001000
[4,1,6,2,7,3,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,1,6,7,2,3,5,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[4,6,7,1,2,3,5,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[4,6,1,2,3,7,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,4,2,6,3,7,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[4,1,2,6,7,3,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,4,2,6,7,3,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,4,6,7,2,3,5,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[4,1,6,2,3,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[1,4,6,2,3,7,8,5]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0010001
[4,1,2,6,7,3,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,4,6,2,7,3,8,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,4,2,6,7,8,3,5]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,4,6,2,7,8,3,5]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,4,6,7,2,8,3,5]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,4,6,7,8,2,3,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[4,1,6,2,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,1,6,8,2,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[4,6,8,1,2,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[4,6,1,2,3,8,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,4,2,6,3,8,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,6,2,3,8,5,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[1,4,2,6,8,3,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,4,6,2,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,4,6,8,2,3,5,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[4,1,6,2,3,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[4,6,1,2,3,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[4,1,2,6,3,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,4,6,2,3,5,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[4,1,2,3,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,4,2,3,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,2,4,6,3,5,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0001001
[4,1,2,3,6,8,5,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,4,6,3,8,5,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,4,6,8,3,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[4,1,6,2,3,5,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[4,6,1,2,3,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[1,4,2,6,3,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,4,6,2,3,5,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[4,1,2,3,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,4,2,3,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,4,6,3,5,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[4,1,2,3,6,7,5,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,4,6,3,7,5,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[4,1,2,3,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001
[1,4,2,3,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100001
[4,1,7,2,8,3,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[4,1,7,8,2,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[4,7,8,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[4,7,1,2,3,8,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,4,2,7,3,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[4,1,2,7,8,3,5,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,4,2,7,8,3,5,6]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,4,7,2,8,3,5,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,4,7,8,2,3,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[4,1,7,2,3,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[4,7,1,2,3,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,4,7,2,3,5,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[4,1,2,3,7,5,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,4,2,3,7,5,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,2,4,3,7,5,8,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101
[1,2,4,7,3,5,8,6]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0001001
[4,1,2,3,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>0010010
[1,2,4,7,3,8,5,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,4,7,8,3,5,6]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[4,1,7,2,3,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[4,7,1,2,3,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[4,1,2,7,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,4,2,7,3,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,4,7,2,3,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[4,1,2,3,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,4,2,3,7,5,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,4,3,7,5,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,4,7,3,5,6,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[4,1,2,3,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,4,2,3,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,4,5,7,3,6,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[4,1,2,3,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000001
[1,4,2,3,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100001
[1,2,4,5,7,3,8,6]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0000101
[1,2,4,5,7,8,3,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0000010
[4,1,8,2,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[4,8,1,2,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,4,2,8,3,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,4,8,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[4,1,2,3,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,4,2,3,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,4,8,3,5,6,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[4,1,2,3,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,4,2,3,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,4,3,5,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,4,5,3,8,6,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,4,5,8,3,6,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[4,1,2,3,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,4,2,3,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[1,2,4,5,6,8,3,7]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0000010
[1,4,2,3,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[5,1,6,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,6,1,2,7,3,8,4]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[5,1,6,7,2,3,8,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[5,6,1,7,2,3,8,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[5,6,7,1,2,3,8,4]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[5,6,1,2,7,8,3,4]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[5,6,7,1,2,8,3,4]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[5,6,7,1,8,2,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[5,1,6,2,7,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[1,5,2,6,3,7,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[5,1,2,6,7,3,4,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,5,2,6,7,3,4,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[5,1,6,2,3,7,8,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[5,6,1,2,3,7,8,4]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>0100001
[1,5,2,6,3,7,8,4]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>0101001
[1,5,6,2,3,7,8,4]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>0010001
[5,1,2,6,7,3,8,4]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[1,5,6,7,2,3,8,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>0001001
[1,5,2,6,7,8,3,4]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[1,5,6,2,7,8,3,4]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[1,5,6,7,2,8,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>0001010
[1,5,6,7,8,2,3,4]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>0000100
[5,1,6,2,8,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[5,6,8,1,2,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[5,6,1,2,3,8,4,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,5,2,6,3,8,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,6,2,3,8,4,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[5,1,2,6,8,3,4,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,5,2,6,8,3,4,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,5,6,2,8,3,4,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,5,6,8,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[5,1,6,2,3,4,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[5,6,1,2,3,4,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[5,1,2,6,3,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,5,6,2,3,4,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[1,5,2,3,6,4,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,2,5,3,6,4,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101
[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0001001
[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,5,6,3,8,4,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,5,6,8,3,4,7]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[5,1,6,2,3,4,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[5,1,2,6,3,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,5,2,6,3,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,5,6,2,3,4,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[5,1,2,3,6,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,5,2,3,6,4,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,5,3,6,4,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[5,1,2,3,6,7,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,5,6,3,7,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001
[1,5,2,3,6,7,8,4]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>0100001
[1,2,5,3,6,7,8,4]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>0010001
[1,2,5,6,3,7,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>0001001
[1,2,5,6,7,3,8,4]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]=>[7,8,5,4,3,6,2,1]=>[1,2,6,3,4,5,8,7]=>0000101
[1,2,5,6,7,8,3,4]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]=>[8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8]=>0000010
[5,1,7,2,8,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[5,1,7,8,2,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[5,7,8,1,2,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>0010000
[5,7,1,2,3,8,4,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,5,2,7,3,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,7,2,3,8,4,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[5,1,2,7,8,3,4,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,5,2,7,8,3,4,6]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,5,7,2,8,3,4,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,5,7,8,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[5,1,7,2,3,4,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[5,7,1,2,3,4,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[5,1,2,7,3,4,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,5,7,2,3,4,8,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,5,2,3,7,4,8,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,2,5,3,7,4,8,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101
[1,2,5,7,3,4,8,6]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0001001
[5,1,2,3,7,8,4,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,5,3,7,8,4,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>0010010
[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,5,7,8,3,4,6]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[5,7,1,2,3,4,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[5,1,2,7,3,4,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,5,2,7,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,5,2,3,7,4,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,5,3,7,4,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,5,7,3,4,6,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[1,5,2,3,4,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,5,3,4,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,3,5,7,4,6,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[5,1,2,3,4,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000001
[1,5,2,3,4,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100001
[1,2,5,3,4,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010001
[1,2,3,5,7,4,8,6]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0000101
[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0000010
[5,1,8,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[5,8,1,2,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[5,1,2,8,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,5,2,8,3,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,5,8,2,3,4,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,5,2,3,8,4,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,5,3,8,4,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,5,8,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[5,1,2,3,4,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,5,2,3,4,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,5,3,4,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,3,5,4,8,6,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,2,3,5,8,4,6,7]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[5,1,2,3,4,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,5,2,3,4,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[1,2,5,3,4,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001
[1,2,3,5,6,8,4,7]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0000010
[1,5,2,3,4,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,5,3,4,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[6,1,7,2,8,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[6,1,7,8,2,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[6,7,1,2,3,8,4,5]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[1,6,2,7,3,8,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,7,2,3,8,4,5]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>0010010
[6,1,2,7,8,3,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[1,6,2,7,8,3,4,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[1,6,7,2,8,3,4,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[1,6,7,8,2,3,4,5]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>0001000
[6,1,7,2,3,4,8,5]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[6,7,1,2,3,4,8,5]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[6,1,2,7,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[1,6,7,2,3,4,8,5]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>0010001
[6,1,2,3,7,4,8,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[1,6,2,3,7,4,8,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,2,3,1]=>[1,3,2,4,6,5,8,7]=>0100101
[1,2,6,3,7,4,8,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>0010101
[1,2,6,7,3,4,8,5]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>0001001
[6,1,2,3,7,8,4,5]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[1,2,6,3,7,8,4,5]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6,8]=>0010010
[1,2,6,7,3,8,4,5]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>0001010
[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>0000100
[6,1,7,2,3,4,5,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[6,1,2,7,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,6,2,7,3,4,5,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,6,7,2,3,4,5,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[6,1,2,3,7,4,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,6,2,3,7,4,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,6,3,7,4,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,6,7,3,4,5,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,6,2,3,4,7,5,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,6,3,4,7,5,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,3,6,4,7,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>1000001
[1,6,2,3,4,7,8,5]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>0100001
[1,2,6,3,4,7,8,5]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>0010001
[1,2,3,6,4,7,8,5]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>0001001
[1,2,3,6,7,4,8,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>0000101
[1,2,3,6,7,8,4,5]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>0000010
[6,1,8,2,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[6,8,1,2,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>0100000
[6,1,2,8,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,6,2,8,3,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,6,8,2,3,4,5,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[6,1,2,3,8,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,6,2,3,8,4,5,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,6,3,8,4,5,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,6,8,3,4,5,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,6,2,3,4,8,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,6,3,4,8,5,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,3,6,4,8,5,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,2,3,6,8,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[6,1,2,3,4,5,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,6,2,3,4,5,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[1,2,6,3,4,5,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001
[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>0001001
[1,2,3,4,6,8,5,7]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000010
[1,6,2,3,4,5,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,6,3,4,5,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000
[7,1,8,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[7,1,2,8,3,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[1,7,2,8,3,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,7,8,2,3,4,5,6]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>0010000
[7,1,2,3,8,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[1,7,2,3,8,4,5,6]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>0100100
[1,2,7,3,8,4,5,6]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>0010100
[1,2,7,8,3,4,5,6]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>0001000
[7,1,2,3,4,8,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[1,7,2,3,4,8,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,2,7,3,4,8,5,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>0010010
[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,2,3,7,8,4,5,6]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>0000100
[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>1000001
[1,7,2,3,4,5,8,6]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>0100001
[1,2,7,3,4,5,8,6]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>0010001
[1,2,3,7,4,5,8,6]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>0001001
[1,2,3,4,7,5,8,6]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>0000101
[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>0000010
[1,7,2,3,4,5,6,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,7,3,4,5,6,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000
[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100
[1,8,2,3,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>0100000
[1,2,8,3,4,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>0010000
[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>0001000
[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>0000100
[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>0000010
[5,3,2,6,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[7,3,2,5,4,8,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[8,4,5,2,3,7,6,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>1010011
[6,4,5,2,3,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[4,6,5,1,3,2,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[7,5,4,3,2,8,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,6,4,3,7,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[7,6,4,3,8,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[6,7,4,3,8,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[5,7,4,3,1,8,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[3,7,1,5,4,8,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[3,8,1,5,4,7,6,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>0101011
[4,8,5,1,3,7,6,2]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>0110011
[5,8,4,3,1,7,6,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011
[6,8,4,3,7,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[7,8,4,3,6,5,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110
[6,8,5,7,3,1,4,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[4,8,6,1,7,3,5,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101
[3,8,1,6,7,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[2,1,8,6,7,4,5,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[3,7,1,6,8,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[5,7,6,8,1,3,2,4]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[6,4,7,2,8,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,6,2,7,3,5,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[8,3,2,6,7,4,5,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101
[7,3,2,6,8,4,1,5]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[6,3,2,7,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,3,2,7,1,8,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[4,3,2,1,7,8,5,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[3,4,1,2,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0100111
[5,3,2,8,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[6,3,2,8,7,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[8,4,7,2,6,5,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1010111
[6,4,8,2,7,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,4,8,2,1,7,6,3]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[4,5,8,1,2,7,6,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[2,1,6,8,7,3,5,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101
[4,6,8,1,7,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001
[6,5,8,7,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011
[4,7,8,1,6,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[2,1,7,8,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[3,8,1,7,6,5,4,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111
[4,8,7,1,6,5,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>0110111
[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]=>[6,7,8,2,3,4,1,5]=>[5,1,4,3,2,8,7,6]=>0111011
[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>0111101
[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>101010101
[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>111111101
[9,7,6,5,4,3,2,10,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[10,8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8,10]=>111111010
[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[10,9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9,10]=>000010000
[3,5,1,7,2,9,4,10,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[10,8,9,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,9,8,10]=>010101010
[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>111110111
[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]=>[5,6,7,8,9,10,1,2,3,4]=>[4,3,2,1,10,9,8,7,6,5]=>111011111
[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]=>[3,4,5,6,7,8,9,10,1,2]=>[2,1,10,9,8,7,6,5,4,3]=>101111111
[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>011111110
[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]=>111111111
[3,2,5,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[4,2,6,1,3,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,3,6,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,2,4,1,3,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,3,5,1,2,4,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,3,7,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,4,7,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,2,7,1,3,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,3,7,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,4,7,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,3,5,1,2,4,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,3,6,1,2,4,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,4,6,1,2,3,5,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[3,2,8,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[4,2,8,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[5,4,8,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,2,8,1,3,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,3,8,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,4,8,1,2,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[6,5,8,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,2,8,1,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,3,8,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,4,8,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[7,5,8,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,2,4,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,3,5,1,2,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,3,6,1,2,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,3,7,1,2,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,4,7,1,2,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[8,5,7,1,2,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>1010000
[3,2,5,7,1,4,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,2,5,7,1,3,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,2,4,7,1,3,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,2,6,7,1,3,5,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,3,6,7,1,2,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,2,5,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,2,5,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,2,5,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,3,5,8,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,2,4,8,1,3,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,2,6,8,1,4,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[4,2,6,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,2,4,8,1,3,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,3,4,8,1,2,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,2,5,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,3,5,8,1,2,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,4,5,8,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,2,7,8,1,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,3,7,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[5,4,7,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,2,7,8,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,3,7,8,1,2,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[6,4,7,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,2,4,8,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,3,4,8,1,2,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,3,5,8,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,4,5,8,1,2,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[7,4,6,8,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,3,4,6,1,2,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,3,5,6,1,2,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,2,4,7,1,3,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,2,5,7,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,3,5,7,1,2,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,2,6,7,1,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[8,4,6,7,1,2,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>1001000
[3,6,2,5,1,4,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,6,2,5,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,6,3,5,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,6,2,4,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[3,7,2,5,1,4,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,7,3,5,1,2,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[3,7,2,6,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,7,3,6,1,2,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,7,2,6,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,7,2,5,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,8,2,5,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,2,4,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,3,6,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,4,6,1,2,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,8,3,5,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[3,8,2,7,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,8,2,7,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,8,3,7,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,2,7,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,3,7,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,8,4,7,1,2,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,8,2,7,1,3,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,8,3,7,1,2,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[6,8,5,7,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,8,2,4,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,8,2,5,1,3,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,8,3,5,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[7,8,4,6,1,2,3,5]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[4,3,2,6,1,5,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,3,2,6,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,4,2,6,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,3,2,5,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,5,2,4,1,3,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[4,3,2,7,1,5,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,3,2,7,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,3,2,7,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,4,2,7,1,3,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,4,3,7,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,5,2,7,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,5,3,7,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,3,2,5,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,4,2,5,1,3,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,4,2,6,1,3,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,4,3,6,1,2,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,5,2,6,1,3,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,5,3,6,1,2,4,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[4,3,2,8,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[5,3,2,8,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,3,2,8,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,4,2,8,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,4,3,8,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,5,2,8,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[6,5,3,8,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,3,2,8,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,4,2,8,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,4,3,8,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,5,3,8,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,5,4,8,1,2,3,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[7,6,2,8,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,3,2,5,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,4,2,5,1,3,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,4,2,6,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,5,3,6,1,2,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,6,2,4,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,6,2,5,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,4,2,7,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,4,3,7,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,5,2,7,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,5,3,7,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,6,3,7,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,2,4,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,2,5,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,3,5,1,2,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,2,6,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,3,6,1,2,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[8,7,4,6,1,2,3,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7,8]=>1101000
[3,6,2,5,8,1,4,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,6,3,5,8,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,6,2,4,8,1,3,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,7,2,5,8,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,7,3,5,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,7,2,4,8,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,7,3,4,8,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,7,3,6,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,7,2,6,8,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,7,4,6,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[3,8,2,5,7,1,4,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,8,3,5,7,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,8,2,4,7,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[3,8,2,6,7,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,8,2,6,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,8,3,6,7,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[6,8,2,5,7,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,2,4,6,1,3,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,3,4,6,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,2,5,6,1,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[7,8,3,5,6,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,3,2,6,8,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,3,2,6,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,4,2,6,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,4,3,6,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,3,2,5,8,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,4,3,5,8,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,5,2,4,8,1,3,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[4,3,2,7,8,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,3,2,7,8,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,4,2,7,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,4,3,7,8,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,4,2,7,8,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[6,4,3,7,8,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,4,2,5,8,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,4,3,5,8,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,5,2,6,8,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,5,3,6,8,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[7,6,2,4,8,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,3,2,5,7,1,4,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,4,2,5,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,5,2,4,7,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,3,2,6,7,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,5,2,6,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,5,3,6,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,6,2,4,7,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,6,2,5,7,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,6,3,5,7,1,2,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,7,2,4,6,1,3,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,7,3,4,6,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[8,7,2,5,6,1,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[4,3,7,2,6,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,7,2,6,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,3,7,2,5,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,7,2,5,1,3,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,7,3,5,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[4,3,8,2,6,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,3,8,2,6,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,8,2,6,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,8,3,6,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,3,8,2,5,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,8,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,8,3,5,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,5,8,2,4,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,5,8,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[4,3,8,2,7,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,3,8,2,7,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,8,2,7,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,8,3,7,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,3,8,2,7,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[6,4,8,2,7,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,3,8,2,5,1,4,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,4,8,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,5,8,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,5,8,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,5,8,4,6,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,6,8,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,6,8,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,6,2,5,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,6,2,4,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,7,3,5,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,7,2,4,1,3,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,3,7,2,6,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,7,2,6,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,7,3,6,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,7,2,6,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,6,7,2,4,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,6,7,2,5,1,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,6,7,3,5,1,2,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,4,3,2,7,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,5,3,2,7,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,5,4,2,7,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,3,2,6,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,4,2,6,1,3,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,5,3,2,8,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[6,5,4,3,8,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,3,2,8,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,5,4,2,8,1,3,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,6,3,2,8,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,6,4,3,8,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[7,6,5,2,8,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,3,2,6,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,4,2,6,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,5,2,4,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,5,3,2,7,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,3,2,7,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,6,4,3,7,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,3,2,5,1,4,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,4,2,6,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,4,3,6,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,5,2,6,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,5,3,6,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,6,2,4,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,6,2,5,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[8,7,6,3,5,1,2,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>1110100
[4,8,3,7,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,8,3,7,2,6,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,8,4,7,2,6,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,8,4,7,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[6,8,3,7,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[6,8,4,7,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[6,8,4,7,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[6,8,5,7,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[6,8,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,3,6,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,4,6,2,5,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,4,6,3,5,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,5,6,2,4,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,4,3,8,2,7,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,5,3,8,2,7,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,5,4,8,3,7,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,4,3,8,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,5,3,8,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,5,4,8,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,6,3,8,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,6,4,8,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[7,6,5,8,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,5,3,7,2,6,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,5,4,7,2,6,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,5,4,7,3,6,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,6,3,7,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,6,4,7,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,6,4,7,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,6,5,7,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,7,4,6,2,5,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,7,4,6,3,5,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,7,5,6,2,4,1,3]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[7,6,5,4,2,8,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,5,3,2,6,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,5,4,2,6,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,6,4,2,5,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,7,6,5,2,4,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>1111010
[8,1,2,3,4,7,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>1000010
[8,1,2,3,6,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[8,1,2,3,7,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>1000100
[7,1,2,3,6,4,8,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[8,1,2,3,6,7,4,5]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>1000010
[8,1,2,5,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[7,1,2,5,3,4,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[8,1,2,6,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[7,1,2,6,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>1001001
[4,1,2,7,6,3,8,5]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>1001101
[8,1,2,5,6,3,4,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[8,1,2,5,7,3,4,6]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[7,1,2,5,6,3,8,4]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[3,1,8,2,6,4,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,8,2,7,4,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[3,1,7,2,6,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,4,2,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[7,1,4,2,3,5,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[6,1,4,2,3,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[8,1,5,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[7,1,5,2,3,4,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[8,1,7,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>1010000
[6,1,5,2,3,7,8,4]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[5,1,4,2,8,3,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[5,1,4,2,7,3,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,4,2,6,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[8,1,4,2,7,3,5,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[7,1,4,2,6,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,5,2,6,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[8,1,5,2,7,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[7,1,8,2,6,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[7,1,5,2,6,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,4,2,6,7,8,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[3,1,8,5,2,4,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[3,1,7,5,2,4,8,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[3,1,8,6,2,4,5,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[3,1,7,6,2,4,8,5]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[3,1,6,5,2,8,4,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[3,1,8,5,2,7,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[3,1,8,6,2,7,4,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[8,1,4,5,2,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[7,1,4,5,2,3,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[8,1,4,6,2,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[7,1,4,8,2,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[7,1,4,6,2,3,8,5]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[8,1,6,5,2,3,4,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[7,1,8,5,2,3,4,6]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[7,1,8,6,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[7,1,6,5,2,3,8,4]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[8,1,6,5,2,7,3,4]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[3,1,4,7,6,2,8,5]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101
[3,1,8,5,6,2,4,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[3,1,8,5,7,2,4,6]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[3,1,7,5,6,2,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,1,7,5,6,2,3,4]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[7,1,4,5,6,2,8,3]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[8,1,4,5,6,7,2,3]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>1000010
[2,8,1,3,4,7,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[2,7,1,3,6,4,8,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[2,8,1,3,6,7,4,5]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[2,4,1,8,3,7,5,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,7,1,5,3,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,7,1,6,3,4,8,5]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[2,6,1,5,3,8,4,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,8,1,5,3,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,7,1,5,6,3,8,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[2,4,1,8,6,7,3,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[2,8,1,5,6,7,3,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[7,3,1,2,4,5,8,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[6,3,1,2,4,8,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[8,3,1,2,4,7,5,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[6,3,1,2,4,7,8,5]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100001
[5,3,1,2,8,7,4,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[5,3,1,2,6,7,8,4]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100001
[7,4,1,2,3,5,8,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[6,4,1,2,3,8,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[8,4,1,2,3,7,5,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[6,4,1,2,3,7,8,5]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]=>[7,6,8,5,4,1,2,3]=>[3,2,1,4,5,8,6,7]=>1100001
[7,6,1,2,3,4,8,5]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[5,8,1,2,3,7,4,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6,8]=>0100010
[8,6,1,2,3,7,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[5,7,1,2,6,3,8,4]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[5,4,1,2,8,7,3,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[5,8,1,2,6,7,3,4]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[5,4,1,2,6,7,8,3]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100001
[4,3,1,8,2,5,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[4,3,1,6,2,8,5,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[4,3,1,8,2,7,5,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,3,1,5,2,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[8,3,1,6,2,4,5,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[7,3,1,8,2,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[6,3,1,5,2,8,4,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,3,1,5,2,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,3,1,6,2,7,4,5]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,4,1,5,2,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[8,4,1,6,2,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[7,4,1,8,2,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[8,7,1,5,2,3,4,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[8,7,1,6,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[6,7,1,5,2,3,8,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[6,4,1,5,2,8,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,4,1,5,2,7,3,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,4,1,6,2,7,3,5]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[6,8,1,5,2,7,3,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,3,1,5,8,2,6,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[4,3,1,8,6,2,5,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[4,3,1,8,7,2,5,6]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[4,3,1,7,6,2,8,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[8,3,1,5,6,2,4,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[8,3,1,5,7,2,4,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[8,3,1,7,6,2,4,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[8,4,1,5,6,2,3,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[8,4,1,5,7,2,3,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[8,4,1,7,6,2,3,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[4,3,1,5,6,8,2,7]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[4,3,1,5,8,7,2,6]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[4,3,1,8,6,7,2,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[8,3,1,5,6,7,2,4]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[8,4,1,5,6,7,2,3]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[4,3,1,5,6,7,8,2]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1100001
[2,3,8,1,4,7,5,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,3,8,1,6,4,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,3,8,1,7,4,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,3,7,1,6,4,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,3,5,1,8,7,4,6]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[2,3,8,1,6,7,4,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[2,8,4,1,3,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[2,6,4,1,3,8,5,7]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[2,8,4,1,3,7,5,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[2,8,5,1,3,4,6,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[2,8,7,1,3,4,5,6]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[2,6,5,1,3,8,4,7]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[2,8,5,1,3,7,4,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[2,6,8,1,3,7,4,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[2,5,4,1,7,3,8,6]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[2,7,4,1,6,3,8,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[2,7,8,1,6,3,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[2,7,5,1,6,3,8,4]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[2,5,4,1,6,7,8,3]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>0110001
[7,3,4,1,2,5,8,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[6,3,4,1,2,8,5,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[8,3,4,1,2,7,5,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,3,4,1,2,7,8,5]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001
[7,3,5,1,2,4,8,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[6,3,7,1,2,4,8,5]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[6,3,5,1,2,8,4,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[8,3,5,1,2,7,4,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,3,8,1,2,7,4,5]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,3,5,1,2,7,8,4]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001
[7,5,4,1,2,3,8,6]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[6,8,4,1,2,3,5,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[6,7,4,1,2,3,8,5]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[6,8,5,1,2,3,4,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>0110000
[6,7,5,1,2,3,8,4]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[6,5,4,1,2,8,3,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[8,5,4,1,2,7,3,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[6,8,4,1,2,7,3,5]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[6,8,5,1,2,7,3,4]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[6,5,4,1,2,7,8,3]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110001
[5,3,4,1,8,2,6,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[5,3,4,1,7,2,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,3,4,1,6,2,5,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[8,3,4,1,7,2,5,6]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,3,4,1,6,2,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,3,5,1,6,2,4,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[8,3,5,1,7,2,4,6]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,3,8,1,6,2,4,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,3,5,1,6,2,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,5,4,1,6,2,3,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[8,5,4,1,7,2,3,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[7,8,4,1,6,2,3,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[7,8,5,1,6,2,3,4]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[7,5,4,1,6,2,8,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[5,3,4,1,6,8,2,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[5,3,4,1,8,7,2,6]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[8,3,4,1,6,7,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[8,3,5,1,6,7,2,4]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[8,5,4,1,6,7,2,3]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[5,3,4,1,6,7,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[2,3,8,5,1,4,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[2,3,7,5,1,4,8,6]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001
[2,3,8,6,1,4,5,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[2,3,7,6,1,4,8,5]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001
[2,3,6,5,1,8,4,7]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>0011010
[2,3,8,5,1,7,4,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>0011010
[2,3,8,6,1,7,4,5]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>0011010
[2,8,4,5,1,3,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,7,4,5,1,3,8,6]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0101001
[2,8,4,6,1,3,5,7]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,7,4,8,1,3,5,6]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,7,4,6,1,3,8,5]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0101001
[2,8,6,5,1,3,4,7]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[2,7,8,5,1,3,4,6]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000
[2,7,8,6,1,3,4,5]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000
[2,7,6,5,1,3,8,4]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,1,4,3,2,6,8,7]=>0111001
[2,6,4,5,1,8,3,7]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[2,8,4,5,1,7,3,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[2,8,4,6,1,7,3,5]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[2,6,4,5,1,7,8,3]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[8,3,6,5,1,2,4,7]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[7,3,8,5,1,2,4,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[7,3,8,6,1,2,4,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[7,3,6,5,1,2,8,4]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[7,6,4,5,1,2,8,3]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[8,3,6,5,1,7,2,4]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[8,6,4,5,1,7,2,3]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[2,3,4,8,6,1,5,7]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>0001100
[2,3,4,8,7,1,5,6]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>0001100
[2,3,8,5,6,1,4,7]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>0010100
[2,3,8,5,7,1,4,6]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>0010100
[2,3,7,5,6,1,8,4]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>0010101
[2,7,4,5,6,1,8,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>0100101
[8,3,4,5,7,1,2,6]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[8,3,7,5,6,1,2,4]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[2,3,4,5,8,7,1,6]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]=>[8,5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5,8]=>0000110
[2,3,4,8,6,7,1,5]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>0001010
[2,3,8,5,6,7,1,4]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>0010010
[2,8,4,5,6,7,1,3]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>0100010
[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>10000000
[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>10000001
[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7,9]=>10000010
[9,1,2,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]=>[9,7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7,9]=>10000010
[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]=>[8,7,9,6,5,4,3,1,2]=>[2,1,3,4,5,6,9,7,8]=>10000001
[3,1,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]=>[8,7,6,5,4,3,9,1,2]=>[2,1,9,3,4,5,6,7,8]=>10000001
[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>01000000
[2,8,1,3,4,5,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,9,8]=>01000001
[9,3,1,2,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[9,4,1,2,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[5,9,1,2,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>01000000
[5,8,1,2,3,4,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]=>[8,9,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,9,8]=>01000001
[9,6,1,2,3,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[9,7,1,2,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>11000000
[8,9,1,2,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>01000000
[2,3,9,1,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9]=>00100000
[2,9,4,1,3,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>01100000
[2,9,5,1,3,4,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>01100000
[2,6,9,1,3,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9]=>00100000
[2,9,7,1,3,4,5,6,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>01100000
[2,9,8,1,3,4,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>01100000
[9,5,4,1,2,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>11100000
[9,7,4,1,2,3,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>11100000
[9,8,4,1,2,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>11100000
[6,7,9,1,2,3,4,5,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9]=>00100000
[6,9,8,1,2,3,4,5,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>01100000
[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9]=>00010000
[2,3,7,9,1,4,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9]=>00010000
[2,7,8,9,1,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9]=>00010000
[9,8,6,5,1,2,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>11110000
[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9]=>00001000
[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9]=>00000100
[2,3,4,5,6,8,1,9,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]=>[8,9,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,9,8]=>00000101
[2,3,4,5,6,7,9,1,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,4,5,6,9,8,1,7]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]=>[9,6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6,9]=>00000110
[9,3,4,5,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[9,7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7,9]=>10000010
[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>00000001
[3,5,2,6,1,4,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[3,5,2,6,4,1,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[3,5,2,7,4,8,1,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[3,5,2,7,4,8,6,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[4,5,7,2,3,8,1,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[4,5,6,1,3,2,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[4,5,7,3,2,8,6,1]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>0011011
[4,6,7,3,8,1,2,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[4,5,7,1,3,8,2,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,5,1,7,4,8,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[2,1,5,7,4,8,6,3]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,8,5,3,4,7,6]=>1001011
[3,5,1,7,4,8,6,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>0101011
[4,5,7,1,3,8,6,2]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011
[4,5,7,3,1,8,6,2]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[4,6,7,3,8,5,2,1]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>0010111
[5,6,7,8,3,1,4,2]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0001101
[5,6,7,8,1,3,4,2]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[4,6,7,1,8,3,5,2]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[3,6,1,7,8,4,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[2,1,6,7,8,4,3,5]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1000110
[3,6,1,7,8,4,2,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[4,6,7,1,8,3,2,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[4,6,7,2,8,1,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[3,6,2,7,8,4,5,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>0100101
[3,6,2,7,8,4,1,5]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>0100110
[3,6,2,7,8,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[3,5,2,7,1,8,4,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[3,4,1,2,7,8,6,5]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>0100011
[3,5,2,7,1,8,6,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[3,6,2,7,8,1,5,4]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[3,6,2,7,8,5,1,4]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>0100110
[3,6,2,7,8,5,4,1]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>0100111
[4,5,7,2,1,8,6,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[4,5,7,1,2,8,6,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[2,1,6,7,8,3,5,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[3,6,1,7,8,2,5,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[4,6,7,1,8,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[5,6,7,8,1,2,4,3]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[5,6,7,8,2,1,4,3]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0001101
[5,6,7,8,2,4,1,3]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[4,6,7,1,8,5,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[3,6,1,7,8,5,2,4]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[2,1,6,7,8,5,3,4]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1000110
[3,6,1,7,8,5,4,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>0100111
[4,6,7,1,8,5,3,2]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111
[5,6,7,8,1,4,3,2]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>0001011
[5,6,7,8,4,1,3,2]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>0001101
[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>000011111
[3,6,7,4,5,8,1,2]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6,8]=>0010010
[2,6,7,4,5,1,8,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>0010101
[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0010100
[1,5,4,7,6,2,3,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>0101100
[2,5,4,7,6,1,8,3]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>0101101
[3,5,4,7,6,8,1,2]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6,8]=>0101010
[4,5,3,7,8,6,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5,8]=>0100110
[6,3,8,4,5,7,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[5,3,4,8,6,7,1,2]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]=>[8,6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6,8]=>1001010
[3,2,5,6,1,8,7,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[7,8,2,4,5,1,6,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[6,1,8,4,5,2,3,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[6,1,8,3,2,5,4,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[7,8,1,3,2,5,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[7,8,2,3,1,5,6,4]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[6,2,8,3,1,5,7,4]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1011001
[6,3,8,2,1,7,5,4]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[7,8,3,2,1,6,5,4]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011
[7,8,4,2,6,1,5,3]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[5,4,2,8,7,1,6,3]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[4,5,2,7,8,1,6,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[2,5,3,7,1,6,8,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0101010
[1,6,7,3,2,5,4,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>0011010
[2,6,7,3,1,5,8,4]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>0011001
[3,6,7,2,1,8,5,4]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[7,8,5,6,2,1,4,3]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[6,5,8,7,1,2,3,4]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[5,4,1,8,7,2,3,6]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[6,4,8,1,7,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,8,3,1,2,6,4,5]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[5,3,1,8,2,7,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[4,3,1,2,8,7,5,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[6,2,8,1,3,4,7,5]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[7,8,2,1,3,4,6,5]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[7,3,1,5,2,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,4,5,1,2,7,3,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[7,4,5,1,2,8,3,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,4,5,1,2,3,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[5,4,6,1,2,3,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[2,1,6,5,3,4,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[3,6,1,5,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[5,6,4,1,2,3,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[6,5,4,1,2,3,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[7,5,4,1,2,8,3,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[8,6,4,1,7,2,3,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[7,6,4,1,8,2,3,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[6,7,4,1,8,2,3,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[5,7,4,1,2,8,3,6]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[4,7,5,1,2,8,3,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[3,7,1,5,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[2,1,7,5,3,8,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[2,1,8,5,3,7,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[3,8,1,5,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,8,5,1,2,7,3,6]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[5,8,4,1,2,7,3,6]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[6,8,4,1,7,2,3,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[8,7,4,1,6,2,3,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[5,8,6,7,1,2,3,4]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,1,8,6,7,3,4,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[2,1,7,6,8,3,4,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[5,7,6,8,1,2,3,4]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[5,4,7,1,2,8,3,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,4,7,1,8,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,4,6,1,8,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[8,4,6,1,7,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[8,3,1,6,7,2,4,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,3,1,6,8,2,4,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[6,3,1,7,8,2,4,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[5,3,1,7,2,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[6,3,1,8,7,2,4,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[7,3,1,8,6,2,4,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[8,4,7,1,6,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,4,8,1,6,2,3,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[5,4,8,1,2,7,3,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[4,5,8,1,2,7,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[3,5,1,8,2,7,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[4,6,8,1,7,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[5,6,8,7,1,2,3,4]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[7,5,8,6,1,2,3,4]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[8,5,7,6,1,2,3,4]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[5,7,8,6,1,2,3,4]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000
[4,7,8,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[5,8,7,6,1,2,3,4]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[6,8,7,5,1,2,3,4]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>0111000
[6,4,7,2,5,1,8,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,4,2,7,6,1,3,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[5,4,2,7,6,1,8,3]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[5,4,3,7,6,8,1,2]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[5,4,3,7,8,6,1,2]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[5,4,3,8,6,7,1,2]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[5,4,3,6,8,7,1,2]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[5,4,2,6,7,1,8,3]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[5,4,2,6,7,1,3,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[5,3,2,6,1,7,4,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[5,3,2,6,1,7,8,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001
[5,3,2,6,1,8,7,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,4,2,6,8,1,7,3]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[5,4,2,8,6,1,7,3]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[6,4,8,2,5,1,7,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[7,8,4,2,5,1,6,3]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[7,8,4,2,5,1,3,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[5,4,2,8,6,1,3,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[5,3,2,6,1,8,4,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[4,3,2,1,6,8,5,7]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[4,3,2,1,8,6,5,7]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[5,3,2,8,1,6,4,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[7,8,3,2,1,5,4,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[7,8,3,2,1,5,6,4]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]=>[7,6,8,2,1,3,4,5]=>[5,4,3,1,2,8,6,7]=>0111001
[5,3,2,8,1,6,7,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001
[5,4,2,7,8,1,6,3]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[5,3,2,7,1,8,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,3,2,7,1,6,8,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001
[5,3,2,7,1,6,4,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,3,7,2,1,8,5,4]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[6,4,7,2,8,1,5,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[6,5,7,8,2,1,4,3]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[6,3,7,2,1,4,5,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[5,3,2,7,1,4,8,6]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[5,4,2,8,7,1,3,6]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[7,8,4,2,6,1,3,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[7,8,3,2,1,6,4,5]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[5,3,2,8,1,7,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[4,3,2,1,8,7,5,6]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[4,3,2,1,7,5,8,6]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[4,3,2,1,7,5,6,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[4,3,2,1,8,5,7,6]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[5,3,2,8,1,4,7,6]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[6,3,8,2,1,4,5,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[4,3,2,1,8,5,6,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[4,3,2,1,5,8,6,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[7,8,5,6,1,2,4,3]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[7,8,4,1,6,2,5,3]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[7,8,1,4,6,2,5,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[6,1,8,4,7,2,5,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[1,6,8,4,7,2,5,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>0010101
[7,8,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[7,8,2,4,6,1,5,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[7,8,2,1,3,6,5,4]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>0110011
[6,1,8,2,3,7,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[1,6,8,2,3,7,5,4]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>0010011
[6,2,8,1,3,7,5,4]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[6,2,8,4,7,1,5,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[6,3,8,4,7,5,1,2]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[2,6,8,4,7,1,5,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>0010101
[2,6,8,3,1,7,5,4]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[2,6,8,1,3,7,5,4]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[1,2,5,8,3,7,6,4]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]=>[6,7,8,4,3,5,2,1]=>[1,2,5,3,4,8,7,6]=>0001011
[2,4,1,3,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0100111
[2,5,3,8,1,7,6,4]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011
[4,2,1,3,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111
[4,1,2,3,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111
[4,3,1,2,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>1100111
[6,3,8,1,2,7,5,4]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[1,5,3,8,2,7,6,4]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0101011
[6,4,8,1,7,2,5,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,5,8,7,1,2,4,3]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[5,6,8,7,3,4,1,2]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>0011010
[5,6,8,7,2,1,4,3]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>0011101
[3,6,8,1,2,7,5,4]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[4,5,2,8,7,1,6,3]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[3,5,2,8,1,7,6,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[3,1,2,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>1000111
[3,4,5,8,7,6,1,2]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>0001110
[4,1,3,2,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,3,2,6,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,3,2,5,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[7,1,3,2,5,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,3,2,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,4,2,5,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[7,1,4,2,5,3,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,4,2,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,4,2,6,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,6,3,5,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,6,2,5,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,6,2,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,2,5,1,4,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,6,1,4,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,7,1,4,3,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,8,1,4,3,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,8,1,4,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,7,1,4,3,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,2,6,1,4,3,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,2,5,1,4,3,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,1,7,2,5,3,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,7,2,5,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,7,3,5,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,8,3,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,8,2,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,8,2,5,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,2,5,1,4,3,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,2,6,1,4,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,1,4,3,8,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,1,4,3,7,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,1,5,3,7,2,6,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[7,1,5,3,8,2,6,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,2,6,1,5,3,7,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,1,8,2,6,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,8,2,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,8,2,6,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,8,3,6,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,7,3,6,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,7,2,6,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,7,2,6,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[7,2,6,1,5,3,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,7,1,5,3,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,8,1,5,3,7,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,1,5,2,6,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,5,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,4,2,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,4,2,6,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,1,3,2,6,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[7,1,3,2,6,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,3,2,7,4,8,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,3,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,3,2,7,5,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,4,3,8,5,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,4,2,8,5,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,3,2,8,5,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,3,2,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,3,2,8,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,4,7,1,3,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,4,8,1,3,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,3,8,1,4,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,3,7,1,4,2,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,1,4,2,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,4,2,8,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,5,2,8,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,5,2,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,5,3,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[2,1,6,3,8,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,6,2,8,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[4,1,6,2,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[5,1,6,2,8,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[6,1,5,2,8,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[8,3,7,1,5,2,6,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,3,8,1,5,2,6,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,7,3,8,1,5,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[6,2,8,3,7,1,5,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[8,3,7,2,6,1,5,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,1,8,3,7,2,6,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,8,3,7,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,8,4,7,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,8,4,7,3,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,7,4,8,3,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,7,4,8,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,7,3,8,2,6,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[5,1,7,3,8,2,6,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[7,3,8,2,6,1,5,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,2,6,3,7,1,5,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[7,2,6,3,8,1,5,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[3,4,2,6,8,1,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[5,3,6,2,8,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[5,7,3,8,2,4,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[5,7,3,8,2,4,6,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[7,4,2,5,8,3,6,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>1100101
[7,4,2,5,8,3,1,6]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[4,5,2,6,3,8,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[5,3,1,6,8,2,4,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[5,6,2,8,1,3,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[3,5,6,1,4,8,2,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[4,5,1,6,3,8,2,7]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[7,4,5,3,8,2,1,6]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[7,4,5,3,8,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[4,7,1,5,8,3,2,6]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[4,5,1,7,8,3,6,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[7,4,1,5,8,3,6,2]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1100101
[6,7,4,3,8,1,5,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[6,7,4,8,3,1,5,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[6,7,4,8,3,5,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>0101011
[5,6,7,3,8,4,2,1]=>[[[[.,[.,[.,.]]],[[.,.],.]],.],.]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>0010111
[5,6,7,3,1,8,4,2]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[5,6,1,7,3,8,4,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>0101011
[5,1,6,7,3,8,4,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,8,5,3,4,7,6]=>1001011
[6,4,7,1,8,3,5,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[6,7,8,3,1,4,5,2]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0011001
[6,7,2,8,4,5,1,3]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[5,1,6,7,3,2,8,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101
[5,6,7,3,2,1,8,4]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[5,6,7,3,2,8,4,1]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>0011011
[5,6,2,7,3,8,4,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[5,6,2,7,3,1,8,4]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[5,6,2,1,7,3,8,4]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[6,1,7,4,2,8,3,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[6,7,2,1,8,3,4,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[7,5,8,2,1,3,4,6]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[5,7,3,1,8,2,4,6]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[4,7,1,5,2,8,3,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[7,4,2,5,1,8,3,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,7,4,2,1,8,3,5]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[6,7,4,2,8,3,1,5]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110
[6,7,4,2,8,3,5,1]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>0110101
[3,7,8,1,4,6,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[3,4,7,8,2,6,1,5]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[5,7,3,8,2,6,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[3,6,7,8,5,2,4,1]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]=>[7,4,3,2,5,1,6,8]=>[8,6,1,5,2,3,4,7]=>0001101
[6,4,7,8,2,1,5,3]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[4,1,5,7,8,2,6,3]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[5,1,6,2,7,8,4,3]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010011
[5,6,2,1,7,8,4,3]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>0110011
[5,6,2,7,1,8,4,3]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[5,6,2,7,8,4,3,1]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>0100111
[5,6,7,2,1,8,4,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[6,4,7,1,8,2,5,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,6,7,1,8,5,2,4]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[4,6,7,8,1,5,3,2]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>0001011
[5,1,6,7,8,4,3,2]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>1000111
[5,6,1,7,8,4,3,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,2,1,3]=>[3,1,2,8,7,6,4,5]=>0100111
[5,6,7,1,8,4,3,2]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111
[8,6,1,3,4,2,5,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[8,3,2,5,1,6,4,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[8,5,3,6,2,4,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[5,3,2,7,4,1,8,6]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[7,5,3,8,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[7,2,4,5,8,3,6,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>1000101
[2,4,5,3,7,1,8,6]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]=>[7,8,5,3,2,4,1,6]=>[6,1,4,2,3,5,8,7]=>0010101
[8,2,4,5,6,1,3,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[8,2,5,1,3,6,4,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[8,5,3,6,4,1,2,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[8,4,1,5,6,3,2,7]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[8,1,4,5,6,3,2,7]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1000110
[4,5,3,7,2,1,8,6]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[7,4,5,8,3,2,6,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[7,4,3,1,2,5,6,8]=>[8,6,5,2,1,3,4,7]=>1001101
[4,5,3,7,1,8,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[4,1,5,3,7,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[7,5,3,8,4,1,6,2]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[1,6,4,7,8,3,5,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>0100101
[6,4,7,8,3,5,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>1001011
[3,5,6,7,8,4,1,2]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>0000110
[3,1,5,6,7,8,4,2]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>1000011
[4,6,1,7,8,3,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[3,6,7,1,4,8,5,2]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011
[6,2,4,1,7,8,5,3]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1010011
[2,6,7,1,4,8,3,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[4,3,6,7,8,1,2,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>1000100
[1,5,3,6,7,8,2,4]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010
[3,5,6,7,8,2,1,4]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>0000110
[3,5,6,7,8,2,4,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>0000101
[5,2,7,1,3,8,4,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[5,3,1,7,8,2,4,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[4,5,2,7,8,1,3,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[4,2,6,7,8,3,5,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>1000101
[3,6,2,7,4,8,5,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[3,6,2,7,4,8,1,5]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[1,7,3,4,2,5,8,6]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>0101001
[4,7,2,1,3,5,8,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[7,8,1,3,4,2,6,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[7,8,3,4,2,1,6,5]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[6,3,2,7,1,8,5,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[3,6,2,7,1,8,5,4]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[6,7,3,8,2,5,4,1]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>0101011
[6,4,7,8,5,2,3,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>1001101
[2,6,4,7,8,1,5,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>0100101
[4,6,2,7,8,1,5,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[7,4,1,5,8,6,2,3]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[7,5,3,8,6,1,2,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,2,7,1,3,8,5,4]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[4,6,1,7,8,5,2,3]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>0100110
[5,1,2,6,7,8,4,3]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>1000011
[5,2,6,7,8,4,3,1]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>1000111
[2,5,6,7,8,4,1,3]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>0000110
[1,5,2,6,7,8,4,3]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,2,3,1]=>[1,3,2,8,7,4,5,6]=>0100011
[2,6,7,1,3,8,5,4]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[6,7,8,2,1,5,4,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[6,7,3,8,5,1,4,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[4,5,2,3,7,6,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[6,4,3,7,2,5,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,4,3,6,5,1,2,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[1,5,6,3,4,8,7,2]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0010011
[4,6,2,7,3,5,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[5,7,6,2,4,3,1,8]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0110110
[8,7,5,4,1,3,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[6,8,5,4,2,1,3,7]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>0111100
[5,8,6,2,4,1,3,7]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[3,2,8,6,5,1,4,7]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1011100
[4,1,2,6,5,8,7,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011
[5,1,6,2,4,8,7,3]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011
[6,1,5,4,2,8,7,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[7,1,5,4,8,2,6,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[1,8,6,7,4,5,3,2]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>0101011
[7,1,6,8,4,2,5,3]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101
[5,1,7,2,8,4,6,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[4,1,2,7,8,5,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>1000101
[3,2,1,7,8,5,6,4]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>1100101
[3,2,8,7,1,5,4,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[4,8,2,7,1,5,3,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,8,7,1,2,4,3,5]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>0110010
[7,8,6,1,4,2,3,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[8,7,6,1,4,3,2,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[1,7,6,8,4,3,5,2]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]=>[7,4,2,3,5,6,8,1]=>[1,8,6,5,3,2,4,7]=>0101101
[8,6,7,1,3,4,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[7,6,8,1,3,2,4,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[5,7,8,2,1,3,4,6]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[4,7,2,8,1,3,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,6,8,2,3,1,4,7]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[6,5,8,3,2,1,4,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,5,8,3,1,2,4,6]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[1,5,7,3,8,4,6,2]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[1,8,4,2,3,6,5,7]=>0010101
[1,4,3,7,8,5,6,2]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>0100101
[8,4,3,7,1,5,2,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,4,3,8,2,1,5,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[4,5,2,3,8,1,6,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[3,2,5,4,8,1,6,7]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[4,5,2,3,1,8,7,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[6,4,3,1,2,8,7,5]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011
[7,4,3,1,8,2,6,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[8,4,3,1,7,6,2,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[1,5,8,3,7,6,4,2]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>0010111
[8,5,1,3,7,6,2,4]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[4,6,2,1,3,8,7,5]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>0110011
[3,2,6,1,4,8,7,5]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[3,2,7,1,8,4,6,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,7,2,1,8,3,6,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[5,7,1,2,8,3,6,4]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[6,7,1,8,2,3,5,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[7,6,1,8,3,2,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[8,6,1,7,3,5,2,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[1,7,8,6,5,3,4,2]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]=>[7,3,2,4,5,6,8,1]=>[1,8,6,5,4,2,3,7]=>0011101
[8,7,1,6,5,3,2,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[6,8,1,7,2,5,3,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[3,2,8,1,7,6,4,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[4,1,2,8,7,6,5,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>1001111
[5,1,8,2,7,6,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[6,1,8,7,2,5,4,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[7,1,8,6,5,2,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[8,1,7,6,5,4,2,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[3,1,2,6,5,8,7,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011
[3,1,6,2,4,8,7,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[3,1,5,2,4,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[1,6,5,3,4,8,7,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>0110011
[6,1,5,2,4,8,7,3]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011
[6,5,1,2,3,8,7,4]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[6,4,1,2,3,8,7,5]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[5,4,1,2,3,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>1100011
[6,4,1,7,2,3,5,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[6,4,1,8,2,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[7,1,5,2,8,4,6,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[8,1,5,2,7,4,6,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[8,4,1,7,2,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[7,4,1,6,2,3,5,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[1,8,6,7,3,4,5,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001
[1,7,6,8,3,4,5,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]=>[7,6,4,2,3,5,8,1]=>[1,8,5,3,2,4,6,7]=>0101001
[4,7,1,2,8,3,6,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[3,1,7,2,8,4,6,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,2,7,8,5,6,4]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>1000101
[4,1,2,8,7,5,6,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>1001101
[3,1,2,8,7,5,6,4]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>1001101
[3,1,8,2,7,4,6,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>1010101
[3,1,8,7,2,4,5,6]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[3,1,7,6,2,4,5,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[4,8,1,2,7,3,6,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[5,8,1,2,7,3,6,4]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[5,1,8,2,7,4,6,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[1,5,8,3,7,4,6,2]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[1,8,4,2,3,6,5,7]=>0010101
[6,8,1,7,2,3,5,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[6,8,7,1,2,3,4,5]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[5,8,7,1,2,3,4,6]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[5,8,6,1,2,3,4,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[5,7,6,1,2,3,4,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>0110000
[7,8,1,6,2,3,5,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[1,7,8,6,3,4,5,2]=>[.,[[[[.,[.,.]],.],[.,[.,.]]],.]]=>[7,6,3,2,4,5,8,1]=>[1,8,5,4,2,3,6,7]=>0011001
[1,8,7,6,3,4,5,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111001
[3,2,5,1,6,4,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,2,5,4,7,1,8,6]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,5,3,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[4,2,5,3,7,1,8,6]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,5,3,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,5,1,6,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,1,5,4,6,2,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,5,3,6,2,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,3,5,1,6,2,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,3,5,2,7,1,8,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[4,3,6,2,7,5,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[4,3,6,2,7,1,8,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[4,3,6,1,7,2,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,3,5,1,7,2,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,1,5,4,7,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,5,4,7,3,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,5,4,7,6,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[4,1,5,3,7,6,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[4,3,5,1,7,6,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,3,6,1,7,5,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,3,6,5,7,1,8,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,3,6,4,7,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[5,3,6,4,7,1,8,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,3,6,1,7,4,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[5,1,6,3,7,4,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[4,1,6,3,7,5,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[3,1,6,4,7,5,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,6,4,7,5,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,1,6,4,7,3,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,6,4,7,2,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,6,3,7,2,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[5,1,6,3,7,2,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[5,3,6,1,7,2,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,3,6,2,7,1,8,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,3,6,2,7,4,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[5,2,6,3,7,4,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[5,2,6,3,7,1,8,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,6,1,7,3,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,5,1,7,3,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,6,1,7,3,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,6,3,7,1,8,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,6,3,7,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[3,2,6,4,7,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[3,2,6,4,7,1,8,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[3,2,6,1,7,4,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,2,5,1,7,4,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,2,4,1,7,5,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,1,4,2,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[3,2,5,1,7,6,8,4]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,2,6,1,7,5,8,4]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,2,6,5,7,1,8,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,6,5,7,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[4,2,6,5,7,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,2,6,1,7,5,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,2,5,1,7,6,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,1,5,2,7,6,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[3,1,5,2,7,6,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[2,1,5,3,7,6,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[2,1,6,3,7,5,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[3,1,6,2,7,5,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[4,1,6,2,7,5,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[5,1,6,2,7,4,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[5,2,6,1,7,4,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[5,2,6,4,7,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,6,4,7,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[5,4,6,2,7,3,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[5,4,6,2,7,1,8,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,4,6,1,7,2,8,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,1,6,4,7,2,8,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,6,5,7,2,8,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,6,5,7,2,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,6,5,7,3,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,6,5,7,4,8,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[4,1,6,5,7,3,8,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[5,1,6,4,7,3,8,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[5,4,6,1,7,3,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[5,4,6,3,7,1,8,2]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,6,3,5,2,4,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[3,7,5,2,4,1,8,6]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,1,3,2,5,8,7]=>0110101
[8,3,7,5,2,4,6,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1011001
[8,2,4,5,7,3,6,1]=>[[[.,.],[[.,[.,[.,.]]],[.,.]]],.]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>1000101
[2,4,5,7,3,1,8,6]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>0001101
[8,2,4,6,5,3,1,7]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>1001110
[8,2,5,4,6,1,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[8,6,3,5,1,4,2,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[8,6,1,4,5,3,2,7]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[8,1,5,6,4,3,2,7]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[5,7,4,3,2,1,8,6]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>0111101
[8,5,7,4,3,2,6,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>1011101
[4,6,8,3,2,7,5,1]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]=>[6,7,3,2,1,4,5,8]=>[8,5,4,1,2,3,7,6]=>0011011
[4,7,6,3,2,8,1,5]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>0111010
[1,4,6,7,3,2,8,5]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]=>[7,8,4,3,2,5,6,1]=>[1,6,5,2,3,4,8,7]=>0001101
[1,7,4,5,3,2,8,6]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>0101101
[3,7,5,1,4,2,8,6]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[8,5,7,4,2,1,6,3]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101
[8,3,7,5,1,4,6,2]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1011001
[8,4,1,7,5,3,6,2]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[4,6,3,8,7,1,5,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[1,7,4,8,6,3,5,2]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[1,8,6,3,2,5,4,7]=>0101101
[3,6,5,8,7,4,1,2]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]=>[8,4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4,8]=>0101110
[3,1,5,8,6,7,4,2]=>[[.,.],[[[.,[[.,.],[.,.]]],.],.]]=>[6,4,5,3,7,8,1,2]=>[2,1,8,7,3,5,4,6]=>1001011
[4,8,1,6,7,3,5,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[3,6,4,1,8,7,5,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>0110111
[8,2,6,1,4,7,5,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>1010011
[2,7,6,8,1,4,3,5]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[3,7,1,6,4,8,2,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[1,7,3,5,6,8,2,4]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>0100010
[1,3,6,7,5,8,2,4]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>0001010
[3,7,6,5,8,2,1,4]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>0110110
[3,6,8,5,7,2,4,1]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>0010101
[2,3,5,7,6,8,1,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>0001010
[3,8,2,4,6,7,5,1]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>0100011
[3,7,2,6,4,8,1,5]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[3,2,6,1,4,7,8,5]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,1,2,4]=>[4,2,1,3,5,8,6,7]=>1010001
[8,7,6,1,3,4,2,5]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[8,5,7,3,2,1,6,4]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101
[8,3,6,7,2,1,5,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[3,7,8,6,2,1,5,4]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>0011101
[8,7,6,3,5,2,4,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[2,7,4,8,1,6,5,3]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011
[4,6,8,2,1,7,5,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[8,5,3,7,1,6,2,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[8,3,6,1,7,5,2,4]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[8,1,2,5,6,7,4,3]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]=>[6,5,4,7,8,3,1,2]=>[2,1,3,8,7,4,5,6]=>1000011
[2,1,7,8,5,6,4,3]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>1001011
[8,2,5,7,6,4,3,1]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>1001111
[2,7,6,8,5,4,1,3]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]=>[8,4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4,8]=>0101110
[1,7,2,5,8,6,4,3]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,2,3,1]=>[1,3,2,8,7,4,6,5]=>0100111
[1,7,4,8,2,6,5,3]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0101011
[3,7,8,1,6,5,2,4]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[8,7,6,3,5,1,4,2]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[8,4,7,6,5,1,3,2]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1011101
[8,7,1,5,6,4,3,2]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1100111
[8,1,6,7,5,4,3,2]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>1001111
[6,5,3,1,2,4,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[4,6,3,5,1,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[8,5,3,7,2,1,4,6]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[6,8,1,4,5,7,3,2]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,2,1,3]=>[3,1,2,8,7,4,5,6]=>0100011
[8,7,2,4,5,1,3,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[3,6,2,4,5,1,8,7]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[2,6,1,4,5,3,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[6,1,2,4,5,3,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]=>[7,8,5,4,6,3,1,2]=>[2,1,3,6,4,5,8,7]=>1000101
[5,4,3,6,1,2,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[3,1,6,4,5,2,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,3,7,4,5,1,2,6]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[5,8,7,4,2,6,3,1]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]=>[6,7,2,3,1,4,5,8]=>[8,5,4,1,3,2,7,6]=>0111011
[8,1,7,4,2,6,3,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[3,7,8,4,5,1,2,6]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>0010100
[5,6,3,8,1,7,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[7,6,1,4,5,8,3,2]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>1100011
[3,7,6,4,5,8,2,1]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]=>[6,5,2,3,4,1,7,8]=>[8,7,1,4,3,2,5,6]=>0110011
[8,5,7,4,1,6,3,2]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[2,4,8,3,5,6,7,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>0010001
[3,8,4,2,5,6,7,1]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>0110001
[8,4,1,3,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>1100001
[6,5,3,8,4,1,7,2]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[2,1,5,8,4,6,7,3]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]=>[7,6,4,3,5,8,1,2]=>[2,1,8,5,3,4,6,7]=>1001001
[6,4,3,8,2,1,7,5]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[8,3,1,2,5,6,7,4]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>1100001
[3,1,8,2,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[2,3,8,1,5,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[4,3,8,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[7,6,5,3,1,2,4,8]=>[8,4,2,1,3,5,6,7]=>1010001
[4,8,2,3,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>0100001
[3,8,2,1,5,6,7,4]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>0110001
[2,8,1,3,5,6,7,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[8,1,2,3,5,6,7,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>1000001
[7,8,2,4,3,6,1,5]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[6,8,3,2,4,1,7,5]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[2,1,8,3,4,6,7,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>1010001
[2,1,7,8,5,4,3,6]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[5,7,3,8,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[2,7,8,4,5,3,1,6]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>0010110
[8,7,1,4,3,6,2,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[5,7,8,4,3,6,2,1]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>0011011
[5,6,3,8,4,2,7,1]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>0101101
[4,8,3,6,2,1,7,5]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[8,6,3,1,4,2,7,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[7,5,3,8,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[2,4,3,1,8,5,7,6]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[4,1,3,2,6,8,7,5]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011
[7,5,3,6,2,8,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,6,3,5,1,2,7,4]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[5,8,3,2,6,1,7,4]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[4,5,3,8,6,2,7,1]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>0101101
[5,8,2,4,7,6,1,3]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[8,7,5,4,1,6,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[2,7,6,4,5,8,1,3]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0110010
[5,7,3,6,1,8,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,8,3,5,2,1,7,4]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[7,8,5,4,2,6,1,3]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[8,6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6,8]=>0111010
[8,1,4,2,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[2,8,4,1,5,6,7,3]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>0110001
[4,8,1,2,5,6,7,3]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>0100001
[3,4,8,1,5,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[3,4,2,8,5,6,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>0101001
[4,1,2,8,5,6,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>1001001
[8,4,2,1,5,6,7,3]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110001
[7,5,2,4,8,6,1,3]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[6,5,3,2,8,1,7,4]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[2,1,5,3,8,6,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[6,4,3,5,8,1,7,2]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[7,3,5,4,8,6,1,2]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[8,3,4,1,5,6,7,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[4,3,1,8,5,6,7,2]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>1101001
[6,5,3,7,2,8,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[6,3,7,4,5,8,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>1010011
[6,7,2,4,5,8,3,1]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>0100011
[5,1,7,4,8,6,3,2]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>1010111
[2,5,7,4,8,6,3,1]=>[[.,[[[.,[.,.]],[[.,.],.]],.]],.]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>0010111
[5,6,3,7,1,8,4,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[3,8,7,4,5,2,1,6]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>0110110
[3,7,5,4,8,6,2,1]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]=>[5,6,2,3,4,1,7,8]=>[8,7,1,4,3,2,6,5]=>0110111
[5,6,3,1,8,2,7,4]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[4,6,3,8,1,2,7,5]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[3,2,5,1,6,8,4,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[3,6,2,5,4,8,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[3,5,2,4,7,1,8,6]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[4,2,6,5,3,8,1,7]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[5,4,2,1,6,8,3,7]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[6,3,5,1,4,8,2,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[4,6,1,5,3,8,2,7]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[5,4,3,2,7,1,8,6]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[5,4,3,8,2,7,6,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[4,3,6,2,8,7,5,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>1010111
[4,3,7,6,2,1,8,5]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[6,4,3,1,7,2,8,5]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[7,5,4,3,1,8,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[1,4,7,5,8,3,2,6]=>[.,[[[.,[[.,.],[.,.]]],.],[.,.]]]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>0010110
[7,1,3,5,8,4,2,6]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>1000110
[2,8,5,7,4,6,1,3]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010
[1,5,4,8,7,3,6,2]=>[.,[[[[.,.],[[.,.],.]],[.,.]],.]]=>[7,4,5,2,3,6,8,1]=>[1,8,6,3,2,5,4,7]=>0101101
[6,4,3,8,1,7,5,2]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[4,3,7,1,8,6,5,2]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[5,3,8,7,6,4,2,1]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>1011111
[7,5,3,1,8,6,4,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[1,8,6,5,3,7,4,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111011
[4,6,1,8,7,3,5,2]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>0101101
[6,8,7,3,1,4,5,2]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]=>[7,6,8,2,3,1,4,5]=>[5,4,1,3,2,8,6,7]=>0111001
[6,2,8,7,4,5,1,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[7,6,2,8,4,1,3,5]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[7,3,1,6,8,4,2,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[6,1,7,5,3,2,8,4]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[7,6,5,3,2,1,8,4]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[6,5,3,2,8,7,4,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1110111
[5,2,6,3,8,7,4,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]=>[5,6,7,3,4,1,2,8]=>[8,2,1,4,3,7,6,5]=>1010111
[5,2,7,6,3,1,8,4]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1011101
[6,5,2,1,7,3,8,4]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[5,2,7,4,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[4,7,2,6,3,1,8,5]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[2,4,8,6,3,7,5,1]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]=>[6,7,3,4,2,5,1,8]=>[8,1,5,2,4,3,7,6]=>0011011
[3,8,6,2,4,7,5,1]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>0110011
[7,3,6,2,4,1,8,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,3,7,1,4,6,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[3,8,2,5,7,1,6,4]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[8,3,6,2,7,1,5,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[7,8,3,6,2,1,5,4]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[8,7,3,6,2,5,4,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[4,7,8,2,1,6,5,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[4,2,6,8,1,7,5,3]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[5,4,8,2,7,1,6,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[4,8,1,5,7,2,6,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[5,8,3,7,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[5,8,7,2,6,1,3,4]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[8,6,2,7,5,1,3,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[3,6,8,1,7,5,2,4]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[6,5,2,8,1,7,4,3]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,2,7,1,8,6,4,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[5,8,2,7,6,4,3,1]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>0101111
[6,2,8,7,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>1011111
[7,6,2,1,8,5,4,3]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[6,1,7,2,8,5,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[8,7,4,6,1,5,3,2]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[8,5,7,1,6,4,3,2]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[6,8,1,7,5,4,3,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111
[7,1,8,6,5,4,3,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>1011111
[5,4,2,3,7,6,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[6,4,2,7,3,5,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[7,4,2,6,3,5,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[8,4,2,6,3,1,5,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[3,2,7,6,4,5,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[4,7,2,6,3,5,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[5,7,6,2,3,4,1,8]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010
[1,6,5,2,3,8,4,7]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>0110010
[6,8,5,2,3,1,4,7]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[5,8,6,2,3,1,4,7]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[3,2,8,6,4,1,5,7]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1011100
[3,2,1,6,4,8,5,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[7,1,5,2,8,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[1,8,6,7,2,3,4,5]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0101000
[8,1,6,7,2,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[7,1,6,8,2,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7,8]=>1001000
[3,2,1,7,8,4,5,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[3,2,8,7,1,4,5,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[5,8,7,2,1,3,4,6]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]=>[8,7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7,8]=>0111000
[1,7,6,8,2,3,4,5]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>0101000
[6,5,8,2,3,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,5,7,2,1,3,4,6]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[8,7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7,8]=>1011000
[6,4,2,8,3,1,5,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[5,4,2,3,8,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7,8]=>1100100
[3,2,5,4,1,8,6,7]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[4,5,2,3,1,8,6,7]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[5,4,2,3,1,8,6,7]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,4,2,1,3,8,5,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[7,4,2,1,8,3,5,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[8,4,2,1,7,3,5,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[1,4,2,8,7,3,5,6]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>0101100
[1,5,8,2,7,3,4,6]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7,8]=>0010100
[6,5,1,2,3,8,4,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[4,6,2,1,3,8,5,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[3,2,6,1,4,8,5,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[3,2,7,1,8,4,5,6]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[4,7,2,1,8,3,5,6]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[7,6,1,8,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[8,6,1,7,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[1,6,8,7,2,3,4,5]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>0011000
[1,7,8,6,2,3,4,5]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>0011000
[4,8,2,1,7,3,5,6]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[3,2,8,1,7,4,5,6]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[3,2,1,8,7,4,5,6]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[5,1,8,2,7,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[6,1,8,7,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[8,1,7,6,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[1,8,7,6,2,3,4,5]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>0111000
[6,3,5,1,2,4,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[6,3,7,5,1,8,4,2]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[6,5,2,7,1,8,3,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[8,5,2,7,4,1,3,6]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,4,3,5,1,2,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[3,1,4,6,5,2,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101
[5,7,4,6,2,8,3,1]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>0101011
[2,1,8,5,7,3,4,6]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[8,6,3,5,1,7,4,2]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,8,2,4,6,7,3,1]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>0100011
[7,5,4,8,1,6,3,2]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[5,1,4,6,8,2,7,3]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[2,5,4,6,7,1,8,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>0100101
[2,4,6,3,7,5,8,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]=>[7,5,6,3,2,4,1,8]=>[8,1,4,2,3,6,5,7]=>0010101
[4,1,6,3,8,5,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[3,7,4,2,8,6,5,1]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]=>[5,6,7,2,3,1,4,8]=>[8,4,1,3,2,7,6,5]=>0110111
[7,4,1,3,5,8,6,2]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>1100011
[6,5,8,4,1,7,3,2]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]=>[6,7,8,3,1,2,4,5]=>[5,4,2,1,3,8,7,6]=>1011011
[8,5,3,7,4,1,6,2]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[7,4,3,8,2,1,6,5]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[6,3,7,4,1,8,2,5]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[8,3,1,2,5,7,6,4]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>1100011
[3,1,8,2,7,6,5,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[2,3,8,1,6,7,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>0010011
[4,3,7,2,6,8,5,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[6,5,7,3,1,2,4,8]=>[8,4,2,1,3,7,5,6]=>1010011
[4,7,2,3,8,5,6,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>0100101
[3,8,2,1,7,5,6,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101
[2,8,1,3,6,5,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[2,7,8,5,4,3,1,6]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3,8]=>0011110
[8,7,1,6,3,4,2,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[3,8,6,7,2,4,1,5]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>0101010
[5,3,8,7,4,2,6,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1011101
[4,3,8,7,2,1,6,5]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[8,3,6,1,4,2,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[2,3,4,1,8,5,7,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[4,1,3,2,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[5,3,6,1,8,7,2,4]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[7,8,5,6,1,4,2,3]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[5,8,3,6,1,7,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,7,3,5,2,1,8,4]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[7,1,4,2,5,6,8,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>1010001
[2,7,4,1,6,5,8,3]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101
[4,1,2,5,8,6,7,3]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]=>[7,5,6,4,8,3,1,2]=>[2,1,3,8,4,6,5,7]=>1000101
[6,4,2,1,5,8,7,3]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110011
[8,5,2,4,6,1,7,3]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[7,5,3,2,6,8,1,4]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[2,1,5,3,6,8,7,4]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>1010011
[7,3,5,4,6,1,8,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[6,3,4,1,5,7,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[4,3,1,5,7,6,8,2]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]=>[7,5,6,4,8,1,2,3]=>[3,2,1,8,4,6,5,7]=>1100101
[4,5,2,6,3,1,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[6,5,2,1,4,3,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[8,5,2,7,4,1,6,3]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[8,3,7,5,2,1,6,4]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[6,3,7,5,2,8,4,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>1011011
[3,1,6,5,4,2,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[5,6,3,2,4,1,8,7]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[3,6,2,4,1,5,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[2,6,1,3,5,4,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>0100101
[6,7,2,3,4,8,5,1]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]=>[6,7,5,4,2,1,3,8]=>[8,3,1,2,4,5,7,6]=>0100011
[8,7,2,3,4,1,6,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[5,1,7,3,8,4,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[2,5,7,3,8,6,4,1]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>0010111
[7,6,1,3,5,8,4,2]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>1100011
[3,6,7,4,1,8,5,2]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[5,6,3,7,4,8,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[2,1,6,7,4,8,5,3]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]=>[6,7,4,3,5,8,1,2]=>[2,1,8,5,3,4,7,6]=>1001011
[2,1,8,7,4,3,6,5]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[5,8,3,7,4,2,6,1]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>0101101
[3,8,7,4,1,2,6,5]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]=>[7,8,6,2,3,4,1,5]=>[5,1,4,3,2,6,8,7]=>0111001
[7,8,1,3,5,2,6,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[5,8,7,3,2,6,1,4]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>0111010
[8,1,6,3,2,5,4,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[2,8,4,1,6,3,7,5]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[3,8,4,2,5,7,1,6]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010
[6,8,3,5,2,7,4,1]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]=>[6,7,4,2,1,3,5,8]=>[8,5,3,1,2,4,7,6]=>0101011
[2,1,5,3,8,7,6,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>1010111
[6,5,3,2,8,7,1,4]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[7,5,2,4,8,1,6,3]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[3,4,2,8,5,7,6,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[2,4,1,8,7,6,5,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111
[8,4,2,1,7,5,3,6]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[4,3,1,8,6,7,5,2]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>1101011
[5,7,1,6,8,2,4,3]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[8,6,2,5,1,7,4,3]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[4,6,2,5,8,3,7,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>0100101
[7,5,2,6,3,8,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[4,1,2,3,6,8,7,5]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>1000011
[7,5,2,8,3,4,6,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[4,7,2,8,1,5,3,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[8,7,2,1,4,5,6,3]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>1110001
[3,6,8,7,1,5,4,2]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>0011011
[5,7,8,6,3,4,1,2]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>0011010
[7,1,8,5,4,3,6,2]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>1011101
[2,7,8,4,5,3,6,1]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>0010101
[5,7,3,8,1,4,6,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[6,5,3,8,4,1,2,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[2,4,8,3,5,6,1,7]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]=>[8,6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6,8]=>0010010
[3,4,8,1,7,2,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,1,8,2,4,7,6,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>1010011
[2,3,8,1,4,6,7,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[4,3,8,2,5,1,7,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[6,3,8,4,2,5,7,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1011001
[7,4,3,8,2,5,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[2,1,4,8,3,5,7,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>1001001
[6,8,2,4,3,5,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[4,8,2,3,5,1,6,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>0100100
[3,8,2,1,4,6,5,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6,8]=>0110010
[2,8,1,3,4,5,7,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[2,8,4,1,6,5,7,3]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101
[2,8,5,6,7,4,3,1]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>0100111
[7,5,8,6,1,4,2,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[3,5,7,6,1,4,2,8]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>0011010
[3,5,7,2,4,1,6,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[7,5,8,2,4,1,6,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[2,8,5,3,4,7,6,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]=>[6,7,5,2,3,4,1,8]=>[8,1,4,3,2,5,7,6]=>0110011
[2,8,5,3,4,7,1,6]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0110010
[2,8,5,3,4,6,1,7]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0110010
[2,8,5,3,4,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0110001
[3,5,7,2,4,6,1,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[6,5,2,7,3,1,4,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,5,2,8,3,1,7,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[6,5,2,8,3,1,4,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[7,5,8,2,4,6,3,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[6,5,7,3,1,2,4,8]=>[8,4,2,1,3,7,5,6]=>1010011
[7,5,8,6,1,4,3,2]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[3,5,6,2,1,8,7,4]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[3,5,7,2,4,6,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>0010001
[6,5,2,7,3,1,8,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[4,1,2,3,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[6,5,2,7,3,4,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[5,1,2,6,4,8,7,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>1001011
[5,1,2,8,6,4,7,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>1001101
[5,1,6,8,7,3,4,2]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]=>[7,4,5,3,6,8,1,2]=>[2,1,8,6,3,5,4,7]=>1001101
[6,5,2,8,3,7,4,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[4,1,2,3,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[4,1,2,3,8,5,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>1000101
[6,1,2,8,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>1001001
[6,5,8,2,4,3,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[7,5,2,8,3,4,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[6,5,2,8,3,7,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[6,5,2,7,3,4,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[5,1,6,7,4,3,2,8]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[7,1,6,8,4,3,2,5]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>1001110
[5,7,8,6,3,4,2,1]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]=>[6,3,2,4,1,5,7,8]=>[8,7,5,1,4,2,3,6]=>0011011
[4,1,8,3,6,5,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[4,1,8,3,6,2,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,4,8,6,2,7,5]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>1001101
[4,1,6,7,8,3,2,5]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]=>[8,5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5,8]=>1000110
[4,5,2,6,3,7,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[4,5,2,7,3,8,1,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[3,5,6,2,4,8,1,7]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[3,6,5,2,8,1,7,4]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,1,3,2,5,8,7]=>0110101
[6,1,2,5,8,4,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>1000101
[7,1,6,5,8,3,4,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[7,5,2,6,3,8,4,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,1,2,3,8]=>[8,3,2,1,5,4,7,6]=>1101011
[4,1,2,3,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]=>[6,7,8,5,4,3,1,2]=>[2,1,3,4,5,8,7,6]=>1000011
[4,1,2,3,7,8,6,5]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>1000011
[4,5,2,7,3,8,6,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[4,1,2,6,8,5,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>1000101
[4,1,2,5,6,8,7,3]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]=>[6,7,5,4,8,3,1,2]=>[2,1,3,8,4,5,7,6]=>1000011
[4,5,2,6,3,7,8,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>0101001
[7,8,5,6,1,4,3,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[7,8,4,2,1,5,3,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]=>[8,6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6,8]=>0111010
[2,4,8,1,5,7,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[4,3,8,1,7,2,5,6]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[6,3,1,4,7,2,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,8,3,4,5,1,6,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[7,8,3,5,4,2,1,6]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4,8]=>0101110
[7,8,1,6,5,4,3,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>0101111
[2,1,8,7,5,4,3,6]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[1,3,8,2,6,4,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[5,3,7,1,6,4,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[6,1,2,5,8,7,4,3]=>[[.,.],[.,[[[.,[[.,.],.]],.],.]]]=>[5,6,4,7,8,3,1,2]=>[2,1,3,8,7,4,6,5]=>1000111
[6,3,1,8,4,2,7,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[6,4,2,1,5,3,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[6,4,3,7,5,8,1,2]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[4,3,8,7,5,6,1,2]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>1011010
[2,4,7,1,5,3,6,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[3,8,1,7,6,4,5,2]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>0101101
[1,8,5,7,3,6,4,2]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0101011
[2,7,5,8,3,6,1,4]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010
[1,5,6,8,2,4,7,3]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>0001001
[4,5,6,7,2,8,1,3]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[4,5,7,6,1,8,3,2]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>0011011
[1,5,8,6,2,7,3,4]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0011010
[1,6,5,8,3,2,7,4]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>0101101
[4,6,5,7,1,2,8,3]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0101001
[5,1,6,3,4,2,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[5,7,1,4,2,3,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[5,7,6,4,3,8,1,2]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>0111010
[6,2,4,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,1,4,2,7,6,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[1,6,2,4,7,8,3,5]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>0100010
[5,7,2,4,1,6,3,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,7,5,8,1,4,3,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[2,1,8,7,6,5,3,4]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[4,3,7,5,6,8,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[4,8,6,3,5,7,1,2]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010
[5,3,7,8,2,1,6,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[5,2,8,7,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[3,6,7,8,5,1,4,2]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>0001101
[3,7,8,5,1,2,4,6]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>0011000
[4,1,8,6,2,3,5,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[3,8,7,6,5,4,1,2]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]=>[8,2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2,8]=>0111110
[2,7,8,6,5,4,1,3]=>[[.,[[[[.,[.,.]],.],.],.]],[.,.]]=>[8,3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3,8]=>0011110
[6,4,2,7,1,3,8,5]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[7,4,2,5,1,3,8,6]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[8,5,3,6,1,7,2,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[4,3,7,1,2,5,8,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[3,6,2,7,1,4,8,5]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[6,3,7,4,1,2,8,5]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[4,7,1,5,2,3,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>0101001
[7,6,4,2,3,8,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,6,4,2,3,7,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[4,7,6,3,8,1,2,5]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[5,7,4,2,3,8,1,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[5,8,2,6,3,7,1,4]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[3,8,6,2,4,7,1,5]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010
[4,8,6,2,7,1,3,5]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[2,6,5,8,1,3,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>0101000
[2,5,7,4,8,1,3,6]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>0010100
[3,5,7,1,4,8,2,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[5,4,7,3,8,1,2,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[7,4,6,3,8,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,6,3,7,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>1010100
[8,4,1,6,7,2,3,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,4,1,6,8,2,3,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[6,5,3,7,1,8,2,4]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[5,3,6,4,7,8,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[6,3,7,4,8,5,1,2]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>1010110
[7,5,1,2,8,6,3,4]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[7,6,1,8,5,2,3,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[8,6,1,7,5,2,3,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[5,7,2,8,1,6,3,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[3,6,8,2,7,1,4,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[2,4,8,7,1,3,5,6]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[4,3,8,7,1,2,5,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[5,3,8,7,1,2,4,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[8,3,7,6,1,2,4,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[8,4,7,6,1,2,3,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[3,5,8,7,1,2,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[2,5,8,7,1,3,4,6]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[2,8,7,6,1,3,4,5]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[3,8,7,6,1,2,4,5]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[4,8,7,6,1,2,3,5]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>0111000
[5,6,3,1,4,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[7,5,3,8,2,1,6,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[2,1,7,8,5,3,6,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101
[5,7,3,8,1,2,6,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[8,7,1,4,5,3,2,6]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[2,7,8,4,1,6,5,3]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[7,1,8,4,2,6,5,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[7,5,1,4,8,6,3,2]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>1100111
[6,5,3,1,8,4,7,2]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101
[8,6,3,1,2,5,7,4]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110001
[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,4,5,6,8,9,1,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,4,5,7,8,9,1,6]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,4,6,7,8,9,1,5]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,5,6,7,8,9,1,4]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,4,5,6,7,8,9,1,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[3,4,5,6,7,8,9,1,2]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>00000010
[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>000000001
[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9]=>00000100
[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,4,5,6,7,9,10,1,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,4,5,6,8,9,10,1,7]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,4,5,7,8,9,10,1,6]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,4,6,7,8,9,10,1,5]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[2,3,5,6,7,8,9,10,1,4]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[1,4,5,6,7,8,9,2,3]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]=>[9,7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7,9]=>00000010
[2,4,5,6,7,8,9,10,1,3]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>000000010
[3,6,4,5,7,2,8,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>0100101
[5,3,2,7,4,6,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>1101001
[7,5,3,6,2,4,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[8,5,3,6,2,7,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[8,2,6,3,4,7,1,5]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[5,4,7,6,2,3,8,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>1011001
[6,7,3,5,2,4,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>0101001
[3,7,6,2,4,5,8,1]=>[[[.,[[.,.],.]],[.,[.,[.,.]]]],.]=>[7,6,5,2,3,1,4,8]=>[8,4,1,3,2,5,6,7]=>0110001
[2,7,6,3,4,5,8,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>0110001
[8,6,5,2,3,7,1,4]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,5,2,1,7,3,4,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[7,5,2,1,8,3,4,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[5,6,2,3,1,8,4,7]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,8,3,5,2,7,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[7,8,5,2,3,6,1,4]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[6,8,2,1,7,3,4,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[1,8,6,3,7,2,4,5]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]=>[8,7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7,8]=>0110100
[1,8,2,7,3,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[4,2,8,3,7,1,5,6]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[8,1,2,7,3,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>1001000
[3,6,2,7,1,8,4,5]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[6,3,7,1,2,8,4,5]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[7,2,6,1,8,3,4,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[3,2,1,5,8,4,6,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[4,3,5,1,6,8,2,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[6,5,3,4,8,7,1,2]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[5,3,2,8,7,1,4,6]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[5,3,1,8,7,2,4,6]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[8,5,3,7,6,1,2,4]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,1,8,3,7,2,4,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[6,3,8,1,7,2,4,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[3,7,8,2,4,6,1,5]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[6,7,3,8,2,5,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[2,3,8,7,1,4,5,6]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>0011000
[7,2,8,6,1,3,4,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[2,1,8,7,3,4,5,6]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[8,2,7,6,1,3,4,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]=>[8,7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7,8]=>1011000
[1,2,8,7,3,4,5,6]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>0011000
[1,3,8,7,2,4,5,6]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>0011000
[1,7,8,3,6,2,4,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>0010100
[5,4,8,7,6,1,2,3]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>1011100
[7,8,6,2,5,1,3,4]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[8,1,6,7,3,2,5,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>1001101
[8,1,5,3,7,2,4,6]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[8,1,5,3,6,2,4,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]=>[8,7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7,8]=>1010100
[7,5,1,3,6,2,4,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,5,8,3,6,2,4,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,4,8,3,2,6,5,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]=>[6,7,3,1,2,4,5,8]=>[8,5,4,2,1,3,7,6]=>1011011
[7,4,1,3,2,6,5,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[8,1,4,3,2,6,5,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[8,1,4,3,2,7,5,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>1011010
[8,1,4,3,2,7,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[8,1,5,3,6,2,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,1,4,3,2,5,7,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>1011001
[8,1,4,3,2,5,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]=>[8,7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7,8]=>1011000
[7,4,1,3,2,5,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]=>[8,7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7,8]=>1101000
[7,4,8,3,2,5,6,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[6,4,3,8,2,5,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[6,4,3,1,2,5,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[7,5,1,4,6,8,2,3]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[7,5,8,3,6,2,1,4]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>1010110
[6,4,3,8,2,5,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[6,4,3,7,2,5,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>1101001
[5,4,3,2,8,6,1,7]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[5,4,3,2,8,7,1,6]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[6,5,3,8,7,2,1,4]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]=>[8,4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4,8]=>1101110
[6,5,4,8,7,1,2,3]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,5,4,1,7,8,2,3]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[6,5,3,1,7,2,8,4]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[6,4,3,1,2,7,8,5]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>1110001
[5,4,3,2,1,8,6,7]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[6,5,3,1,8,2,7,4]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[6,5,4,1,8,7,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[7,5,1,4,8,6,2,3]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[7,4,1,3,2,8,5,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[6,4,3,1,2,8,5,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[6,4,3,1,2,7,5,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[6,4,3,8,2,7,5,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[6,5,3,8,7,2,4,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]=>[7,4,5,1,2,3,6,8]=>[8,6,3,2,1,5,4,7]=>1101101
[6,5,3,1,7,2,4,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[6,5,3,1,8,2,4,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[7,5,1,3,8,2,4,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,6,1,8,3,2,4,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>1101100
[7,6,1,8,4,5,2,3]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[7,6,8,1,4,5,2,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[7,6,8,1,3,2,5,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,5,3,7,8,2,4,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>1100101
[6,4,3,7,2,8,5,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]=>[6,7,4,1,2,3,5,8]=>[8,5,3,2,1,4,7,6]=>1101011
[6,4,3,7,2,1,5,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>1101100
[7,4,8,3,2,1,5,6]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>1011100
[7,4,8,3,2,1,6,5]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101
[6,5,4,8,1,7,2,3]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,5,3,8,1,2,7,4]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[5,4,3,2,8,1,7,6]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[6,4,3,7,2,1,8,5]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[6,5,3,7,1,2,8,4]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[6,5,4,7,1,8,2,3]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[6,5,3,7,8,2,1,4]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>1100110
[6,4,3,7,2,8,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[5,4,3,2,7,8,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[5,4,3,2,6,8,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[5,6,2,1,3,4,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>0110001
[7,8,1,2,5,4,6,3]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[8,4,1,3,7,6,2,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[6,5,2,1,8,7,4,3]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[4,7,2,8,1,3,6,5]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[3,4,7,1,8,2,6,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[1,8,2,4,3,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,7,2,4,3,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,6,2,4,3,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,5,2,4,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,6,2,5,3,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,7,2,5,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,8,2,5,3,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,8,2,6,3,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,7,2,6,3,4,5,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>0101000
[1,8,2,7,3,5,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,8,3,5,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,8,3,5,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,2,8,3,6,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,2,8,3,6,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,3,2,8,4,6,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,2,3,7,4,6,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,3,2,7,4,6,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,2,7,3,6,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,2,7,3,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,7,3,5,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,6,3,5,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,6,3,5,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,5,3,6,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,5,3,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,5,3,7,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,2,4,3,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,4,3,7,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,4,3,6,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,4,3,6,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,3,4,6,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,7,2,3,4,6,5,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,8,2,3,4,7,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>0100010
[1,8,2,4,3,7,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,4,3,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,4,3,8,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,2,4,3,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,5,3,8,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,5,3,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,5,3,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,6,3,7,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,6,3,8,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>0001010
[1,3,2,8,4,7,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,4,2,8,3,7,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,5,2,8,3,7,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,6,2,8,3,7,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,7,2,8,3,6,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[1,8,2,7,3,6,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>0101010
[4,6,3,7,2,5,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[4,6,3,7,5,2,1,8]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4,8]=>0101110
[4,6,3,8,5,1,7,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[5,6,8,3,4,1,2,7]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[5,6,8,4,3,1,7,2]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[5,6,8,4,3,1,2,7]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[5,7,8,4,1,6,3,2]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[5,7,8,4,1,3,6,2]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0011001
[5,6,8,4,2,1,7,3]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[4,6,2,8,5,1,7,3]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[3,2,6,8,5,1,7,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[6,2,1,5,3,4,8,7]=>1001101
[5,6,8,2,4,1,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[5,6,8,4,2,1,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[5,7,8,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[6,7,8,1,5,2,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[6,7,8,1,5,2,4,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[6,7,8,1,5,3,2,4]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[6,7,8,1,3,5,2,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[4,7,2,8,1,6,3,5]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[3,2,7,8,1,6,5,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[4,7,2,8,1,6,5,3]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[5,7,8,2,1,6,4,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[6,7,8,1,3,5,4,2]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011
[6,7,8,1,5,3,4,2]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[6,7,8,1,5,4,3,2]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111
[6,7,8,1,5,4,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[6,7,8,1,4,5,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[6,7,8,1,4,5,3,2]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>0010011
[6,7,8,1,4,3,5,2]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[6,7,8,1,3,4,5,2]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>0010001
[5,7,8,2,1,4,6,3]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0011001
[4,7,2,8,1,5,6,3]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[3,2,6,8,4,1,7,5]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]=>[7,8,4,3,5,1,2,6]=>[6,2,1,5,3,4,8,7]=>1001101
[4,6,2,8,3,1,7,5]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[5,6,8,3,2,1,7,4]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[5,7,8,3,1,4,6,2]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>0011001
[5,7,8,3,1,6,4,2]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[4,7,3,8,1,6,2,5]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[4,7,3,8,1,6,5,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[4,7,3,8,1,5,6,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[4,6,3,8,2,1,7,5]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[4,5,3,2,8,1,7,6]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[4,5,2,3,8,1,7,6]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>0100101
[3,2,5,4,8,1,7,6]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[4,5,3,2,8,1,6,7]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>0110100
[4,7,3,8,1,5,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[4,7,3,8,1,2,6,5]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[4,7,3,8,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>0101000
[5,7,8,3,1,2,4,6]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>0011000
[5,6,8,3,2,1,4,7]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[8,7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7,8]=>0011100
[6,7,8,1,3,4,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[6,7,8,1,4,3,2,5]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>0010110
[6,7,8,1,4,2,5,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[6,7,8,1,4,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[6,7,8,1,2,5,3,4]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[6,7,8,1,2,5,4,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[6,7,8,1,2,4,5,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>0010001
[6,7,8,1,3,2,5,4]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[6,7,8,1,3,2,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>0010100
[6,7,8,1,2,4,3,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>0010010
[6,7,8,1,2,3,5,4]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>0010001
[7,2,8,5,1,6,4,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[1,3,7,5,2,6,4,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>0011010
[7,2,8,5,4,1,6,3]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>1011101
[2,8,5,4,3,1,7,6]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]=>[7,8,2,3,4,5,1,6]=>[6,1,5,4,3,2,8,7]=>0111101
[2,8,4,5,6,1,7,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>0100101
[2,8,4,5,3,7,1,6]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010
[2,8,4,3,5,6,1,7]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>0110010
[7,2,8,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]=>[8,6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6,8]=>1010010
[1,6,3,7,5,2,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]=>[8,7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7,8]=>0101100
[6,3,2,8,5,1,4,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[7,4,8,2,5,6,3,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]=>[6,5,7,3,1,2,4,8]=>[8,4,2,1,3,7,5,6]=>1010011
[6,4,8,5,1,3,7,2]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1011001
[6,3,7,5,2,1,8,4]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>1011101
[4,3,7,5,1,2,8,6]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]=>[7,8,6,3,4,1,2,5]=>[5,2,1,4,3,6,8,7]=>1011001
[4,3,7,1,5,6,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>1010001
[3,4,1,2,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[3,4,2,1,7,5,8,6]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[3,6,5,7,1,4,8,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[6,5,2,7,4,1,8,3]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[3,5,2,6,4,8,7,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]=>[6,7,4,5,2,1,3,8]=>[8,3,1,2,5,4,7,6]=>0101011
[5,3,1,8,6,4,7,2]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[6,5,8,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[7,6,3,1,2,4,5,8]=>[8,5,4,2,1,3,6,7]=>1011001
[1,6,5,7,3,4,2,8]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>0101010
[1,5,2,7,4,6,3,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]=>[8,6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6,8]=>0101010
[5,2,1,8,7,6,3,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[2,3,4,8,6,5,1,7]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>0001110
[1,5,4,6,2,7,3,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0101010
[5,3,6,4,1,8,7,2]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[5,3,6,1,4,8,2,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[7,3,5,6,8,4,2,1]=>[[[[.,.],[[.,[.,[.,.]]],.]],.],.]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>1000111
[6,3,5,1,8,2,7,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[2,6,1,5,8,4,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>0100101
[5,7,1,6,3,8,4,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,2,1,3]=>[3,1,2,8,5,4,7,6]=>0101011
[3,2,4,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[3,1,4,2,7,8,6,5]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>1010011
[3,6,4,7,8,2,5,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>0100101
[3,1,4,6,8,5,7,2]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1000101
[2,5,4,6,1,7,8,3]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>0101001
[7,2,1,4,3,6,5,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>1101010
[7,3,4,1,2,6,5,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[7,4,3,2,1,6,5,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[7,6,3,2,5,4,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[6,7,3,2,5,4,8,1]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]=>[7,5,6,2,1,3,4,8]=>[8,4,3,1,2,6,5,7]=>0110101
[1,8,4,5,2,3,7,6]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>0101001
[7,3,5,1,6,2,4,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[7,2,1,5,6,3,4,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[7,2,1,6,5,4,3,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[7,3,6,1,5,4,2,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[7,4,6,5,1,3,2,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[1,8,5,4,3,2,7,6]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]=>[7,8,2,3,4,5,6,1]=>[1,6,5,4,3,2,8,7]=>0111101
[1,8,6,4,3,7,2,5]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]=>[8,6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6,8]=>0111010
[6,5,7,4,3,1,8,2]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>1011101
[6,4,7,5,1,3,8,2]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>1011001
[6,3,7,1,5,4,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[6,2,1,7,5,4,8,3]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[2,3,8,1,5,4,7,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>0010101
[2,4,8,5,1,3,7,6]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>0011001
[2,5,8,4,3,1,7,6]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]=>[7,8,3,2,4,5,1,6]=>[6,1,5,4,2,3,8,7]=>0011101
[2,6,8,4,3,7,1,5]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]=>[8,6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6,8]=>0011010
[1,8,7,4,3,6,5,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>0111011
[2,7,8,5,6,3,4,1]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>0010101
[2,6,8,5,7,3,1,4]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>0010110
[2,5,8,6,7,1,3,4]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>0010100
[2,4,8,6,1,7,3,5]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]=>[8,6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6,8]=>0011010
[3,2,1,8,6,7,4,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[5,2,1,7,6,8,4,3]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>1101011
[5,3,7,1,6,8,4,2]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>1010011
[5,4,7,6,1,8,3,2]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>1011011
[4,5,7,6,8,1,3,2]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>0010101
[4,6,7,5,8,3,1,2]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>0010110
[1,8,5,6,7,2,3,4]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]=>[8,7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7,8]=>0100100
[4,7,5,6,8,2,3,1]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]=>[7,5,4,2,3,1,6,8]=>[8,6,1,3,2,4,5,7]=>0100101
[5,3,6,1,7,8,2,4]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[5,2,1,6,7,8,3,4]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[6,3,5,1,7,2,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,5,4,7,2,1,8,3]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[5,6,4,7,2,8,1,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>0101010
[1,8,4,6,2,7,3,5]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]=>[8,6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6,8]=>0101010
[5,6,3,2,7,8,1,4]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[8,6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6,8]=>0110010
[6,5,3,2,7,1,8,4]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[6,4,3,2,1,7,8,5]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111001
[5,3,4,1,2,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>1010011
[4,6,3,2,8,7,1,5]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110
[4,7,3,2,8,6,5,1]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>0110111
[1,8,3,2,7,6,5,4]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>0110111
[1,8,4,7,2,6,5,3]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>0101011
[3,7,4,8,2,6,5,1]=>[[[.,[[.,.],[.,.]]],[[.,.],.]],.]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>0101011
[3,6,4,8,2,7,1,5]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]=>[8,6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6,8]=>0101010
[3,4,5,8,1,2,7,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>0001001
[4,3,5,1,8,2,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,1,6,8,7,3,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[4,3,6,1,8,7,2,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>1010110
[3,5,6,8,7,1,2,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>0001100
[1,8,6,7,5,4,2,3]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]=>[8,4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4,8]=>0101110
[3,4,7,8,1,6,5,2]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>0001011
[4,2,1,7,8,6,5,3]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>1100111
[2,3,8,1,7,6,5,4]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>0010111
[2,4,8,7,1,6,5,3]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]=>[6,7,8,3,4,2,1,5]=>[5,1,2,4,3,8,7,6]=>0011011
[2,5,8,7,6,1,4,3]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]=>[7,8,3,4,5,2,1,6]=>[6,1,2,5,4,3,8,7]=>0011101
[2,6,8,7,5,4,1,3]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]=>[8,3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3,8]=>0011110
[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>10101010101
[7,4,6,1,8,3,5,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[8,3,5,1,7,4,6,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[8,3,4,1,7,5,6,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,8,3,1,7,5,6,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101
[4,6,2,1,7,5,8,3]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101
[1,4,6,2,7,5,8,3]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0010101
[7,5,2,1,6,8,4,3]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110011
[6,8,4,3,1,7,5,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011
[3,6,8,4,1,7,5,2]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[3,6,7,5,1,8,4,2]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]=>[6,7,8,3,2,4,1,5]=>[5,1,4,2,3,8,7,6]=>0011011
[7,5,6,1,8,3,4,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,4,6,5,7,1,8,2]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>0010101
[4,7,5,6,1,8,3,2]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>0101011
[6,7,5,1,8,4,3,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>0110111
[6,8,4,1,7,5,3,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>0110111
[6,7,5,3,1,8,4,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]=>[6,7,8,2,1,3,4,5]=>[5,4,3,1,2,8,7,6]=>0111011
[8,4,2,1,6,7,5,3]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>1110011
[1,5,3,2,7,6,8,4]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,2,3,4,1]=>[1,4,3,2,8,6,5,7]=>0110101
[5,3,2,1,7,6,8,4]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101
[2,5,3,1,7,6,8,4]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>0110101
[2,8,4,1,6,7,5,3]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[2,7,5,1,6,8,4,3]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[2,4,6,1,7,5,8,3]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[4,7,1,6,5,8,2,3]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[4,8,2,6,5,7,1,3]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[4,6,1,2,7,5,8,3]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[7,5,1,2,6,8,4,3]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100011
[8,4,1,2,6,7,5,3]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>1100011
[5,3,1,2,7,6,8,4]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[1,2,5,3,7,6,8,4]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>0010101
[4,3,1,2,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[3,5,1,2,7,6,8,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[2,3,5,1,7,6,8,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>0010101
[7,6,1,5,8,3,2,4]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[3,6,7,1,5,8,2,4]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[7,1,6,5,8,2,4,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[7,5,1,6,8,4,2,3]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[8,4,1,6,7,5,2,3]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[5,2,3,1,7,6,8,4]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,5,2,1,7,6,8,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>0110101
[1,3,5,2,7,6,8,4]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,2,4,1]=>[1,4,2,3,8,6,5,7]=>0010101
[7,6,2,1,5,8,3,4]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[8,3,1,5,7,6,2,4]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[6,2,4,1,7,5,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[6,2,5,1,7,4,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[7,1,6,4,8,2,5,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[8,2,6,4,7,1,5,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[6,1,5,2,7,4,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[7,6,2,5,8,3,1,4]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[1,8,3,5,7,6,2,4]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]=>[8,5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5,8]=>0100110
[1,5,2,3,7,6,8,4]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100101
[5,2,1,3,7,6,8,4]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[7,5,2,6,8,4,1,3]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[8,4,2,6,7,5,1,3]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]=>[8,5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5,8]=>1100110
[6,1,4,2,7,5,8,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[8,2,6,5,7,1,4,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[3,6,8,2,5,7,1,4]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[8,3,2,5,7,6,1,4]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>1100110
[5,1,3,2,7,6,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[4,1,3,2,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[4,2,1,3,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,1,2,3]=>[3,2,1,4,8,6,5,7]=>1100101
[1,4,2,3,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,2,3,1]=>[1,3,2,4,8,6,5,7]=>0100101
[2,4,1,3,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[2,5,1,3,7,6,8,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>0100101
[6,8,2,3,5,7,1,4]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[6,7,1,3,5,8,2,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[5,1,2,3,7,6,8,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[3,1,2,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]=>[7,5,6,8,4,3,1,2]=>[2,1,3,4,8,6,5,7]=>1000101
[8,1,3,5,6,2,7,4]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[8,1,3,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>1010001
[2,7,8,3,4,5,6,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>0010001
[2,6,3,8,4,5,7,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>0101001
[6,3,2,1,4,5,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>1110001
[7,4,1,5,6,8,2,3]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>1100010
[4,7,8,5,6,1,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>0010100
[3,7,8,5,6,2,1,4]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>0010110
[3,7,8,4,2,6,1,5]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>0011010
[3,7,8,2,4,5,1,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[3,6,2,8,4,5,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6,8]=>0101010
[2,3,6,7,4,5,8,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>0001001
[3,5,2,4,8,6,1,7]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[3,5,4,2,8,7,1,6]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0110110
[6,4,5,1,7,8,2,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6,8]=>1010010
[7,4,1,2,3,8,5,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]=>[8,6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6,8]=>1100010
[6,2,4,1,3,7,5,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[2,6,4,8,3,7,5,1]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>0101011
[2,6,5,8,7,3,4,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>0101101
[6,2,5,1,7,3,4,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[6,5,2,1,8,3,4,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[2,5,6,7,8,3,4,1]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>0000101
[4,7,8,2,3,1,5,6]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>0010100
[4,7,8,3,2,1,6,5]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>0011101
[5,6,4,8,1,7,2,3]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[5,6,3,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[4,2,5,3,7,1,6,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>1010100
[4,3,6,7,2,1,8,5]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[3,4,6,7,2,8,1,5]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>0001010
[3,4,5,2,7,8,1,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>0010010
[3,4,2,5,6,8,1,7]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[5,2,7,8,6,4,1,3]=>[[[.,.],[[[.,[.,.]],.],.]],[.,.]]=>[8,4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4,8]=>1001110
[5,1,2,7,8,6,4,3]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]=>[5,4,6,7,8,3,1,2]=>[2,1,3,8,7,6,4,5]=>1000111
[4,7,1,2,8,6,5,3]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>0100111
[4,6,8,1,2,7,5,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>0010011
[6,8,7,3,5,1,2,4]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]=>[8,7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7,8]=>0110100
[7,8,1,6,3,5,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>0101010
[7,8,3,6,5,2,1,4]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4,8]=>0101110
[4,7,2,8,6,1,5,3]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[4,2,7,1,8,6,5,3]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>1010111
[7,8,2,3,6,5,1,4]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>0100110
[8,5,7,1,6,2,3,4]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>1010100
[8,5,7,1,2,6,3,4]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[6,8,2,7,1,3,5,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[6,8,7,2,5,3,1,4]=>[[[.,[[.,.],.]],[[.,.],.]],[.,.]]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>0110110
[1,6,8,3,7,4,5,2]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]=>[7,5,6,3,2,4,8,1]=>[1,8,4,2,3,6,5,7]=>0010101
[1,6,8,3,4,7,5,2]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]=>[6,7,5,3,2,4,8,1]=>[1,8,4,2,3,5,7,6]=>0010011
[6,2,4,8,1,7,5,3]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>1001011
[6,8,7,2,3,5,1,4]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>0110010
[6,8,2,1,7,3,5,4]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[8,5,7,1,2,3,6,4]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]=>[7,8,6,5,3,1,2,4]=>[4,2,1,3,5,6,8,7]=>1010001
[8,7,6,2,1,4,3,5]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,5,7,2,3,1,6,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,8,4,2,7,1,6,3]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>0110101
[1,8,7,5,3,4,6,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111001
[8,2,5,4,7,1,6,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[8,5,2,7,3,1,6,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[8,7,6,2,4,3,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[8,7,6,1,2,4,3,5]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>1110010
[8,7,6,1,4,2,3,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[8,7,6,4,1,3,2,5]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[5,8,4,7,2,1,6,3]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[1,8,7,5,4,3,6,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]=>[7,2,3,4,5,6,8,1]=>[1,8,6,5,4,3,2,7]=>0111101
[1,6,8,4,3,7,5,2]=>[.,[[[[.,[.,.]],.],[[.,.],.]],.]]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>0011011
[6,8,7,3,2,5,1,4]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>0111010
[8,5,7,1,3,2,6,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,8,4,7,1,2,6,3]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>0101001
[5,8,4,1,7,2,6,3]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>0110101
[5,8,4,7,1,6,2,3]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6,8]=>0101010
[8,1,2,6,5,7,4,3]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>1001011
[4,8,5,7,1,6,2,3]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]=>[8,6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6,8]=>0101010
[4,8,5,7,1,2,6,3]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>0101001
[4,8,5,1,7,2,6,3]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>0110101
[8,5,3,1,7,2,6,4]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[8,5,3,7,1,2,6,4]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[6,8,1,3,7,2,5,4]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]=>[7,8,5,4,6,2,1,3]=>[3,1,2,6,4,5,8,7]=>0100101
[4,6,2,8,1,7,5,3]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>0101011
[1,6,4,8,3,7,5,2]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>0101011
[8,5,3,7,2,1,6,4]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>1101101
[8,7,6,3,1,4,2,5]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,7,6,1,3,2,4,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>1110100
[8,5,3,2,7,1,6,4]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[4,8,5,2,7,1,6,3]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]=>[7,8,5,2,3,1,4,6]=>[6,4,1,3,2,5,8,7]=>0110101
[1,8,7,4,3,5,6,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>0111001
[1,8,7,3,4,5,6,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>0110001
[8,5,2,3,7,1,6,4]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>1100101
[6,3,1,5,4,2,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[8,5,4,2,1,7,3,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,5,4,2,1,7,6,3]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011
[6,5,4,2,1,3,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001
[6,5,4,2,3,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[6,3,2,5,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]=>[7,8,6,4,1,2,3,5]=>[5,3,2,1,4,6,8,7]=>1101001
[6,5,4,3,1,2,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001
[6,5,4,1,3,2,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[8,5,4,1,2,7,6,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>1110011
[8,7,4,1,6,3,2,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[8,7,4,1,6,3,5,2]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>1110101
[8,7,4,1,6,5,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[8,5,4,1,3,7,6,2]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>1110011
[8,5,4,3,1,7,6,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011
[8,3,2,5,1,7,6,4]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]=>[6,7,8,4,1,2,3,5]=>[5,3,2,1,4,8,7,6]=>1101011
[2,1,8,5,3,7,6,4]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>1011011
[8,3,2,5,1,7,4,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>1101010
[8,5,4,3,1,7,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,5,4,1,3,7,2,6]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>1110010
[8,7,4,1,6,5,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>1110110
[8,7,4,1,6,2,5,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>1110101
[8,7,6,5,2,1,4,3]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[8,7,4,3,6,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>1110110
[2,1,8,7,6,4,3,5]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>1011110
[2,1,8,7,6,4,5,3]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>1011101
[8,3,2,7,6,4,5,1]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>1101101
[8,7,4,3,6,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>1110101
[8,7,6,5,2,4,3,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>1111011
[8,5,4,2,3,7,6,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>1110011
[8,7,4,2,6,5,3,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>1110111
[8,7,4,2,6,3,5,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>1110101
[8,7,4,2,6,3,1,5]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[8,3,1,7,6,4,2,5]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[8,3,1,7,6,4,5,2]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>1101101
[8,3,1,7,6,5,4,2]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>1101111
[8,3,1,5,4,7,6,2]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>1101011
[8,3,1,5,4,7,2,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>1101010
[8,3,1,7,6,5,2,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>1101110
[8,3,1,7,6,2,5,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[8,7,4,2,6,1,5,3]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[8,7,4,2,6,5,1,3]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[8,5,4,2,3,7,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>1110010
[8,3,2,5,4,7,1,6]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]=>[8,6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6,8]=>1101010
[8,7,4,3,6,5,1,2]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>1110110
[8,7,6,5,3,1,4,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[8,7,6,5,1,3,2,4]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,7,6,5,1,3,4,2]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>1111001
[8,7,6,5,1,4,3,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>1111011
[8,7,6,5,4,1,3,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>1111101
[8,7,4,3,6,1,5,2]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>1110101
[8,3,2,7,6,1,5,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,1,2,3,6]=>[6,3,2,1,5,4,8,7]=>1101101
[2,1,8,7,6,3,5,4]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>1011101
[8,3,2,7,6,1,4,5]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[8,7,6,5,1,4,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>1111010
[8,7,6,5,1,2,4,3]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>1111001
[7,3,5,1,8,4,6,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[7,3,4,1,8,5,6,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,5,6,2,1,8,7,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>0011011
[1,6,5,2,7,4,3,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110
[7,4,3,1,8,6,5,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[7,6,5,1,8,4,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[7,6,4,1,8,5,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[6,4,2,1,8,7,5,3]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[1,6,4,2,7,5,3,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110
[1,5,3,2,7,6,4,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>0110110
[5,3,2,1,8,7,6,4]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>1110111
[2,5,3,1,7,8,6,4]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[2,6,4,1,7,8,5,3]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[2,6,5,1,7,8,4,3]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>0110011
[4,5,7,1,6,8,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[6,5,1,2,8,4,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[6,4,1,2,8,5,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[5,3,1,2,8,6,4,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[4,3,1,2,8,6,5,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[6,1,2,5,8,3,4,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[2,6,1,5,7,8,3,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[7,4,1,6,8,5,2,3]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[5,2,3,1,8,6,7,4]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[3,5,2,1,6,8,7,4]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>0110011
[1,6,2,5,7,3,4,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[6,2,1,5,8,7,3,4]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[7,3,1,5,8,6,2,4]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[6,2,4,1,8,5,7,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[6,2,5,1,8,4,7,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[7,3,1,4,8,6,2,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[6,2,1,4,8,7,3,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[1,6,2,4,7,3,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>0100100
[5,2,1,3,8,7,4,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[7,4,1,3,8,5,2,6]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[7,5,1,3,8,4,2,6]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]=>[8,5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5,8]=>1100110
[3,6,7,1,4,8,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>0010010
[7,6,1,4,8,3,2,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>1100110
[4,2,1,3,8,7,5,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>1100110
[2,6,1,4,7,8,3,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>0100010
[6,1,2,4,8,3,5,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>1000100
[5,2,3,1,6,4,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[7,4,5,2,3,1,8,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,6,7,3,5,2,4,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,3,5,2,4,1,8,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[6,3,5,2,4,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,2,4,1,6,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,1,6,3,5,2,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[6,3,4,1,5,2,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,6,3,4,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,7,3,4,1,8,6]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,8,6,7,3,4,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[6,2,8,5,7,3,4,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[6,2,7,3,4,1,8,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[7,3,4,1,5,2,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,1,7,3,5,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,7,4,5,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,7,4,5,3,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,8,6,7,4,5,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[4,1,8,6,7,3,5,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[8,6,7,3,4,1,5,2]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,5,7,3,4,1,6,2]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[8,5,6,2,7,3,4,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[8,4,7,3,5,1,6,2]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,1,8,4,7,3,6,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[4,1,8,5,7,3,6,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[3,1,8,5,7,4,6,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[2,1,8,5,7,4,6,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]=>[7,5,3,4,6,8,1,2]=>[2,1,8,6,4,3,5,7]=>1010101
[2,1,7,4,6,3,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,7,4,6,2,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,7,3,6,2,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[5,1,7,3,6,2,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[6,2,7,3,5,1,8,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[6,2,8,4,7,3,5,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>1010101
[8,4,7,3,6,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,3,6,2,5,1,8,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[6,2,5,1,7,3,8,4]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,4,1,7,3,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[6,2,4,1,7,3,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[8,5,7,3,6,2,4,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[8,5,7,4,6,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>1010101
[7,4,6,2,3,1,8,5]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[6,2,3,1,7,4,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,2,3,1,7,4,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[4,2,3,1,7,5,8,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[3,1,4,2,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[6,2,3,1,8,5,7,4]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[8,5,6,2,3,1,7,4]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[7,4,8,5,6,2,3,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[7,3,8,5,6,2,4,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[8,5,6,2,4,1,7,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[5,2,4,1,8,6,7,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[4,1,5,2,8,6,7,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[3,1,5,2,8,6,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[2,1,6,3,8,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[3,1,6,2,8,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[4,1,6,2,8,5,7,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[5,1,6,2,8,4,7,3]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>1010101
[8,4,6,2,5,1,7,3]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]=>[7,8,5,3,1,2,4,6]=>[6,4,2,1,3,5,8,7]=>1010101
[7,3,8,4,6,2,5,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>1010101
[6,2,7,3,8,4,5,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>1010101
[8,4,5,1,6,2,7,3]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>1010101
[5,1,8,4,6,2,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[4,1,8,5,6,2,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[3,1,8,5,6,2,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,8,5,6,3,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[2,1,7,4,8,5,6,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[3,1,7,4,8,5,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[4,1,7,3,8,5,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>1010101
[7,3,8,4,5,1,6,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[8,4,5,1,7,3,6,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>1010101
[7,3,6,2,8,4,5,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>1010101
[7,8,5,6,1,3,4,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[1,3,8,4,7,2,5,6]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]=>[8,7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7,8]=>0010100
[4,6,1,2,5,7,3,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]=>[8,6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6,8]=>0100010
[1,4,8,2,5,7,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>0010010
[7,8,2,4,5,6,1,3]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>0100010
[7,8,1,5,4,6,3,2]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]=>[6,4,5,7,8,2,1,3]=>[3,1,2,8,7,5,4,6]=>0101011
[7,8,2,1,6,3,4,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]=>[8,7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7,8]=>0110100
[7,8,4,5,3,1,6,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>0101101
[1,5,8,4,3,2,7,6]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]=>[7,8,3,2,4,5,6,1]=>[1,6,5,4,2,3,8,7]=>0011101
[2,6,4,8,3,7,1,5]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]=>[8,6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6,8]=>0101010
[1,4,6,8,3,7,5,2]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]=>[6,7,4,3,2,5,8,1]=>[1,8,5,2,3,4,7,6]=>0001011
[2,5,8,1,4,7,6,3]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>0010011
[5,6,2,1,4,7,8,3]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>0110001
[4,6,2,5,3,1,8,7]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]=>[7,8,4,5,2,1,3,6]=>[6,3,1,2,5,4,8,7]=>0101101
[7,5,3,6,2,4,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>1101010
[5,7,3,6,1,4,8,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,2,1,3,5]=>[5,3,1,2,4,8,6,7]=>0101001
[5,3,6,7,2,1,8,4]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]=>[7,8,4,3,1,2,5,6]=>[6,5,2,1,3,4,8,7]=>1001101
[6,3,1,2,4,5,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>1100001
[1,4,7,2,5,3,8,6]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>0010101
[1,6,7,5,8,2,4,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]=>[7,8,5,3,2,4,6,1]=>[1,6,4,2,3,5,8,7]=>0010101
[3,5,6,7,8,1,4,2]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>0000101
[5,2,7,6,1,4,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>1011010
[3,1,8,5,4,6,7,2]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>1011001
[5,7,8,6,3,2,1,4]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>0011110
[5,7,8,6,1,3,4,2]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]=>[7,6,8,3,2,4,1,5]=>[5,1,4,2,3,8,6,7]=>0011001
[7,6,5,8,1,3,4,2]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>1101001
[7,1,3,4,8,2,6,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>1000101
[2,6,3,4,5,8,1,7]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>0100010
[7,2,1,4,8,3,5,6]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>1100100
[5,7,6,4,1,8,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>0111011
[6,7,1,5,2,8,3,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]=>[8,6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6,8]=>0101010
[6,1,5,2,8,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>1010100
[6,7,5,3,8,4,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>0110110
[7,1,5,3,4,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>1010101
[7,5,2,4,3,1,6,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[7,4,6,1,2,5,3,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>1010010
[7,4,2,6,5,1,3,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>1101100
[6,8,1,2,3,4,7,5]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>0100001
[5,8,2,3,7,6,4,1]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>0100111
[2,1,4,7,8,5,6,3]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>1000101
[2,5,7,8,1,4,6,3]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>0001001
[5,2,8,4,6,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]=>[7,8,5,3,4,1,2,6]=>[6,2,1,4,3,5,8,7]=>1010101
[5,2,1,8,6,3,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]=>[7,8,4,5,6,1,2,3]=>[3,2,1,6,5,4,8,7]=>1101101
[4,2,8,5,7,6,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>1010111
[1,4,2,7,5,8,6,3]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]=>[6,7,4,5,8,2,3,1]=>[1,3,2,8,5,4,7,6]=>0101011
[4,1,8,6,7,5,3,2]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>1010111
[5,3,8,7,6,2,4,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>1011101
[5,8,4,7,6,2,1,3]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]=>[8,4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4,8]=>0101110
[5,8,7,4,3,6,1,2]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]=>[8,6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6,8]=>