Identifier
Mp00119:
Dyck paths
—to 321-avoiding permutation (Krattenthaler)⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,1,0,0,0]=>[3,1,2]=>[3,1,2]=>[[.,[.,.]],.]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0]=>[1,4,2,3]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,1,1,0,0,0]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0]=>[3,1,2,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[1,1,1,0,0,1,0,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,1,0,1,0,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[1,1,1,1,0,0,0,0]=>[4,1,2,3]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,2,3]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,3]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,0,1,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4]=>[3,5,1,2,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,5,3]=>[4,1,5,2,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,3]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,8,4,5,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,8,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,3,7]=>[1,2,8,4,5,6,3,7]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,3,5,7,8]=>[1,2,6,4,3,5,7,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,6,7,5]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,4,7,3,5,6,8]=>[1,2,7,4,3,5,6,8]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,3,6,8,4,7]=>[1,2,5,8,3,6,4,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,7,4,6,8]=>[1,2,5,7,3,4,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>[1,2,5,8,3,4,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,8,3,4,6,7]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,8,5,3,4,7]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>[1,2,8,3,5,6,4,7]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,8,5,4,3,6]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[1,2,8,3,5,4,7,6]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,6,3,4,7,5,8]=>[1,2,6,3,7,4,5,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,3,4,7,8,5]=>[1,2,6,3,8,4,7,5]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[1,2,6,3,8,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,2,6,3,7,4,5,8]=>[1,2,6,7,4,3,5,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,8,4,3,7,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,8,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,2,6,7,3,4,5,8]=>[1,2,7,3,4,6,5,8]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,2,6,7,3,4,8,5]=>[1,2,7,3,8,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,3,8,4,5]=>[1,2,7,8,4,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[1,2,8,3,4,6,5,7]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,8,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,7,3,8,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,8,4,5,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[1,2,8,3,4,5,7,6]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,4,7]=>[1,3,2,8,5,6,4,7]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,8,4,5,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,2,6,7,8,4,5]=>[1,3,2,8,4,6,7,5]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,7,4,8,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,8,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,4,5,6]=>[1,3,2,8,4,5,7,6]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,2,7]=>[1,8,3,4,5,6,2,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,2,6]=>[1,8,3,4,5,2,7,6]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>[1,8,3,4,5,2,6,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,4,6,2,5,7,8]=>[1,6,3,4,2,5,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,2,5,8,7]=>[1,6,3,4,2,5,8,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,2,5,8]=>[1,7,3,4,2,6,5,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,2,5]=>[1,8,3,4,2,6,7,5]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,4,7,2,5,6,8]=>[1,7,3,4,2,5,6,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,2,5,8,6]=>[1,7,3,4,2,8,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,2,8,5,6]=>[1,7,3,4,8,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,2,6,7,8,4]=>[1,5,3,8,2,6,7,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>[1,5,3,8,2,6,4,7]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,7,2,4,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,8,2,4,6,7]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,6,2,8,4,7]=>[1,6,3,8,5,2,4,7]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,5,6,8,2,4,7]=>[1,8,3,2,5,6,4,7]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,8,5,4,2,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,2,4,7,5,8]=>[1,6,3,2,7,4,5,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,6,2,4,7,8,5]=>[1,6,3,2,8,4,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[1,6,3,2,8,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,6,2,7,4,5,8]=>[1,6,3,7,4,2,5,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[1,6,3,8,4,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,8,4,2,5,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,2,4,5,8]=>[1,7,3,2,4,6,5,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,6,7,2,4,8,5]=>[1,7,3,2,8,6,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,2,8,4,5]=>[1,7,3,8,4,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,2,4,5,6,8]=>[1,7,3,2,4,5,6,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,7,2,4,5,8,6]=>[1,7,3,2,4,8,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[1,7,3,2,8,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,8,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[1,8,3,2,4,5,7,6]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[.,[[.,[.,.]],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,2,3,6,8,5,7]=>[1,4,2,3,8,6,5,7]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[1,4,2,3,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,8,2,5,6,3,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,2,5,7,3,6,8]=>[1,4,7,2,5,3,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,6,3,5,7,8]=>[1,4,6,2,3,5,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,6,3,5,8,7]=>[1,4,6,2,3,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,2,6,7,3,5,8]=>[1,4,7,2,3,6,5,8]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]=>[1,4,7,2,8,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,8,2,3,6,7,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,2,6,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,7,3,5,6,8]=>[1,4,7,2,3,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,8,5,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,8,2,3,5,7,6]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,7,3,8]=>[1,5,7,4,2,6,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,8,4,2,6,3,7]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,4,5,2,7,3,6,8]=>[1,5,7,4,2,3,6,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,2,8,3,6,7]=>[1,5,8,4,2,3,6,7]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,6,2,3,7,8]=>[1,6,2,4,5,3,7,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,6,2,8,3,7]=>[1,6,8,4,5,2,3,7]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,2,3,8]=>[1,7,2,4,5,6,3,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,2,3]=>[1,8,2,4,5,6,7,3]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,4,5,7,2,3,6,8]=>[1,7,2,4,5,3,6,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,2,3,8,6]=>[1,7,2,4,5,8,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,7,2,8,3,6]=>[1,7,8,4,5,3,2,6]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,4,6,2,3,5,8,7]=>[1,6,2,4,3,5,8,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,4,6,2,3,7,5,8]=>[1,6,2,4,7,3,5,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,2,3,7,8,5]=>[1,6,2,4,8,3,7,5]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,4,6,2,7,3,5,8]=>[1,6,7,4,3,2,5,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,8,4,3,2,7,5]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,2,8,3,5,7]=>[1,6,8,4,3,2,5,7]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,2,3,5,8]=>[1,7,2,4,3,6,5,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,2,3,8,5]=>[1,7,2,4,8,6,3,5]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,8,4,3,6,2,5]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,2,3,5,8,6]=>[1,7,2,4,3,8,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,2,8,3,5,6]=>[1,7,8,4,3,5,2,6]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,2,3,6,4,7,8]=>[1,5,2,6,3,4,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,5,2,3,6,4,8,7]=>[1,5,2,6,3,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,2,3,6,7,4,8]=>[1,5,2,7,3,6,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,2,3,6,8,4,7]=>[1,5,2,8,3,6,4,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,5,2,3,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[1,5,2,7,3,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,2,3,7,8,4,6]=>[1,5,2,8,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,6,3,4,7,8]=>[1,5,6,3,2,4,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,8,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,2,6,7,3,4,8]=>[1,5,7,3,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,2,6,7,8,3,4]=>[1,5,8,3,2,6,7,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,7,3,4,6,8]=>[1,5,7,3,2,4,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[1,5,7,3,2,8,4,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,8,2,4,3,6]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,2,7,8,3,4,6]=>[1,5,8,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,8,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,5,6,2,3,7,4,8]=>[1,6,2,7,5,3,4,8]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[1,6,2,8,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[1,6,8,3,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,5,6,2,8,3,4,7]=>[1,6,8,3,5,2,4,7]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,2,3,8,4]=>[1,7,2,8,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,8,3,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[1,8,2,3,5,6,4,7]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,5,7,2,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,2,3,4,8,6]=>[1,7,2,3,5,8,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[1,7,2,8,5,4,3,6]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,8,3,5,4,2,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[1,8,2,3,5,4,6,7]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,6,2,3,4,7,5,8]=>[1,6,2,3,7,4,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,2,3,4,8,5,7]=>[1,6,2,3,8,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[1,6,2,7,8,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,2,3,7,8,4,5]=>[1,6,2,8,4,3,7,5]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,6,2,3,8,4,5,7]=>[1,6,2,8,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,7,3,4,5,8]=>[1,6,7,3,4,2,5,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,8,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,2,7,8,3,4,5]=>[1,6,8,3,4,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[1,6,8,3,4,2,5,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,2,3,4,5,8]=>[1,7,2,3,4,6,5,8]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,7,2,3,4,8,5]=>[1,7,2,3,8,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[1,7,2,8,4,6,3,5]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,8,2,3,4,6,7,5]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[1,8,2,3,4,6,5,7]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,8,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,2,3,4,8,5,6]=>[1,7,2,3,8,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,2,3,8,4,5,6]=>[1,7,2,8,4,5,3,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[1,7,8,3,4,5,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,4,6,8,5,7]=>[2,1,3,4,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,4,8,6]=>[2,1,3,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,4,6]=>[2,1,3,8,5,4,7,6]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,3,5,8,4,6,7]=>[2,1,3,8,5,4,6,7]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,4,5]=>[2,1,3,8,4,6,7,5]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,7,4,5,8,6]=>[2,1,3,7,4,8,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,3,7,8,4,5,6]=>[2,1,3,8,4,5,7,6]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,3,7,8,5]=>[2,1,6,4,8,3,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,3,5,8,6]=>[2,1,7,4,3,8,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,3,8,5,6]=>[2,1,7,4,8,5,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,5,7,6]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,4,7,8]=>[2,1,5,6,3,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,3,6,8,4,7]=>[2,1,5,8,3,6,4,7]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,7,4,6,8]=>[2,1,5,7,3,4,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,8,4,6,7]=>[2,1,5,8,3,4,6,7]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,3,4]=>[2,1,8,3,5,6,7,4]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,3,4,8,6]=>[2,1,7,3,5,8,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,3,4,8,5,7]=>[2,1,6,3,8,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,8,4,5,7]=>[2,1,6,8,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,3,4,8,5]=>[2,1,7,3,8,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,8,4,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,3,4,5,8,6]=>[2,1,7,3,4,8,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,3,4,8,5,6]=>[2,1,7,3,8,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,4,7]=>[3,2,1,8,5,6,4,7]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,1,5,7,4,6,8]=>[3,2,1,7,5,4,6,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,1,5,8,4,6,7]=>[3,2,1,8,5,4,6,7]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]=>[3,2,1,6,8,4,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,6,8,4,5,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,4,5,8]=>[3,2,1,7,4,6,5,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,6,7,5]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,7,4,5,6,8]=>[3,2,1,7,4,5,6,8]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,7,4,8,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,8,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,5,7,6]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,1,7]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,1,6,8]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,1,6]=>[8,2,3,4,5,1,7,6]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,4,6,1,8,5,7]=>[6,2,3,4,8,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,1,5,8]=>[7,2,3,4,1,6,5,8]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,1,5,6,8]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,1,5,8,6]=>[7,2,3,4,1,8,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,1,8,5,6]=>[7,2,3,4,8,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>[8,2,3,4,1,5,7,6]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,1,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[5,2,3,1,4,8,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,4,7,8]=>[5,2,3,6,1,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,1,6,7,4,8]=>[5,2,3,7,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,3,5,6,1,4,7,8]=>[6,2,3,1,5,4,7,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,5,6,7,1,4,8]=>[7,2,3,1,5,6,4,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[8,2,3,1,5,6,4,7]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,1,8,4,6]=>[7,2,3,8,5,4,1,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[8,2,3,1,5,4,7,6]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,1,4,5,7,8]=>[6,2,3,1,4,5,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,1,4,7,8,5]=>[6,2,3,1,8,4,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,1,7,4,5,8]=>[6,2,3,7,4,1,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,8,5]=>[6,2,3,7,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,8,4,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,1,8,4,5,7]=>[6,2,3,8,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,6,7,1,4,5,8]=>[7,2,3,1,4,6,5,8]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,1,4,8,5]=>[7,2,3,1,8,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,1,8,4,5]=>[7,2,3,8,4,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>[8,2,3,1,4,6,5,7]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,1,4,5,6,8]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[8,2,3,1,4,5,7,6]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,3,5,8,6,7]=>[4,2,1,3,5,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,3,7,5,8,6]=>[4,2,1,3,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,3,6,8,7]=>[4,2,5,1,3,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,1,5,6,7,3,8]=>[4,2,7,1,5,6,3,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,1,5,6,8,3,7]=>[4,2,8,1,5,6,3,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[2,4,1,5,7,8,3,6]=>[4,2,8,1,5,3,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,4,1,5,8,3,6,7]=>[4,2,8,1,5,3,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,6,3,5,7,8]=>[4,2,6,1,3,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,8,3,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[4,2,7,1,3,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,8,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,4,1,7,8,3,5,6]=>[4,2,8,1,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,8,1,3,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,7,3,8]=>[5,2,7,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,8,4,1,6,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,4,5,1,7,3,6,8]=>[5,2,7,4,1,3,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[5,2,8,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,1,8,3,6,7]=>[5,2,8,4,1,3,6,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,1,7,3,8]=>[6,2,7,4,5,1,3,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,1,8,3,7]=>[6,2,8,4,5,1,3,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,1,3,8]=>[7,2,1,4,5,6,3,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,1,3]=>[8,2,1,4,5,6,7,3]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,1,3,8,6]=>[7,2,1,4,5,8,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,7,1,8,3,6]=>[7,2,8,4,5,3,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>[6,2,8,4,3,1,7,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,8,4,3,1,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,8,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,4,7,1,3,5,6,8]=>[7,2,1,4,3,5,6,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,4,7,1,8,3,5,6]=>[7,2,8,4,3,5,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[8,2,1,4,3,5,7,6]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,4,7,8,6]=>[5,2,1,3,4,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,5,1,3,6,4,7,8]=>[5,2,1,6,3,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]=>[5,2,1,6,3,4,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,1,3,6,7,8,4]=>[5,2,1,8,3,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,1,3,6,8,4,7]=>[5,2,1,8,3,6,4,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,5,1,3,7,4,6,8]=>[5,2,1,7,3,4,6,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,1,3,7,4,8,6]=>[5,2,1,7,3,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,1,3,7,8,4,6]=>[5,2,1,8,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,1,3,8,4,6,7]=>[5,2,1,8,3,4,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,8,4,7]=>[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,1,6,7,3,4,8]=>[5,2,7,3,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,8,3,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[5,2,7,3,1,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,8,4,6]=>[5,2,7,8,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,1,7,8,3,4,6]=>[5,2,8,3,1,4,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,1,8,3,4,6,7]=>[5,2,8,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,5,6,1,3,7,8,4]=>[6,2,1,8,5,3,7,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,1,7,3,4,8]=>[6,2,7,3,5,1,4,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[6,2,8,3,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,1,8,3,4,7]=>[6,2,8,3,5,1,4,7]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,1,8,3,4]=>[7,2,8,3,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,5,7,1,3,4,8,6]=>[7,2,1,3,5,8,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,6,1,3,4,8,5,7]=>[6,2,1,3,8,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,1,3,7,8,4,5]=>[6,2,1,8,4,3,7,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[6,2,7,3,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,8,4,5]=>[6,2,7,8,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[6,2,8,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,6,7,1,3,4,8,5]=>[7,2,1,3,8,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[8,2,1,3,4,6,5,7]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,1,3,4,5,8,6]=>[7,2,1,3,4,8,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,1,3,4,8,5,6]=>[7,2,1,3,8,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,1,3,8,4,5,6]=>[7,2,1,8,4,5,3,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,8,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[8,2,1,3,4,5,7,6]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,1,2,4,7,5,8,6]=>[3,1,2,4,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,1,2,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,2,5,7,4,8,6]=>[3,1,2,7,5,8,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,2,6,4,7,8,5]=>[3,1,2,6,8,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,2,6,4,8,5,7]=>[3,1,2,6,8,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,2,6,7,4,8,5]=>[3,1,2,7,8,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,1,2,6,7,8,4,5]=>[3,1,2,8,4,6,7,5]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,2,7,4,5,8,6]=>[3,1,2,7,4,8,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,2,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,8,6,5,7]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,7,5,6,8]=>[3,4,1,2,7,5,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,1,4,5,6,8,2,7]=>[3,8,1,4,5,6,2,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6,8]=>[3,7,1,4,5,2,6,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,4,6,2,5,8,7]=>[3,6,1,4,2,5,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,4,6,7,2,5,8]=>[3,7,1,4,2,6,5,8]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,1,4,6,8,2,5,7]=>[3,8,1,4,2,6,5,7]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,4,7,2,5,8,6]=>[3,7,1,4,2,8,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,5,2,4,6,8,7]=>[3,5,1,2,4,6,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,8]=>[3,5,1,2,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,5,2,4,7,8,6]=>[3,5,1,2,4,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,5,2,4,8,6,7]=>[3,5,1,2,4,8,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]=>[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,2,6,8,4,7]=>[3,5,1,8,2,6,4,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,7,4,6,8]=>[3,5,1,7,2,4,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,8,2,4,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,8,2,4,6,7]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,8,5,2,4,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]=>[3,7,1,2,5,6,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,1,5,6,8,2,4,7]=>[3,8,1,2,5,6,4,7]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,1,5,7,8,2,4,6]=>[3,8,1,2,5,4,7,6]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[3,6,1,2,4,5,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,6,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,6,2,4,8,5,7]=>[3,6,1,2,8,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,8,4,5,7]=>[3,6,1,8,4,2,5,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[3,7,1,2,4,6,5,8]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,1,6,7,2,8,4,5]=>[3,7,1,8,4,6,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[3,8,1,2,4,6,5,7]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,7,2,4,5,6,8]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,7,2,4,5,8,6]=>[3,7,1,2,4,8,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[3,8,1,2,4,5,7,6]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,2,7,5,8,6]=>[4,1,3,2,7,8,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,8,6,7]=>[4,5,3,1,2,8,6,7]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,1,5,7,8,2,6]=>[4,8,3,1,5,2,7,6]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,6,2,5,7,8]=>[4,6,3,1,2,5,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,1,6,7,8,2,5]=>[4,8,3,1,2,6,7,5]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,1,6,8,2,5,7]=>[4,8,3,1,2,6,5,7]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,7,2,5,8,6]=>[4,7,3,1,2,8,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,8,5,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,1,2,6,8,7]=>[5,1,3,4,2,6,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,5,1,2,7,6,8]=>[5,1,3,4,2,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,7,2,8]=>[5,7,3,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,6,8,2,7]=>[5,8,3,4,1,6,2,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,8,6]=>[5,7,3,4,1,8,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,5,7,1,2,8,6]=>[7,1,3,4,5,8,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,1,8,2,6]=>[7,8,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[8,1,3,4,5,2,6,7]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,4,6,1,2,5,7,8]=>[6,1,3,4,2,5,7,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,1,2,5,8,7]=>[6,1,3,4,2,5,8,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,1,2,7,5,8]=>[6,1,3,4,7,2,5,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,4,6,1,7,2,5,8]=>[6,7,3,4,2,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[6,8,3,4,2,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,4,6,7,1,8,2,5]=>[7,8,3,4,2,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[8,1,3,4,2,6,7,5]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[8,1,3,4,2,6,5,7]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,1,2,5,8,6]=>[7,1,3,4,2,8,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,8,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,5,1,2,6,4,7,8]=>[5,1,3,6,2,4,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]=>[5,1,3,6,2,4,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,1,2,6,7,4,8]=>[5,1,3,7,2,6,4,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,1,2,6,8,4,7]=>[5,1,3,8,2,6,4,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,1,2,7,4,6,8]=>[5,1,3,7,2,4,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,1,2,7,8,4,6]=>[5,1,3,8,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,5,1,2,8,4,6,7]=>[5,1,3,8,2,4,6,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,5,1,6,7,2,4,8]=>[5,7,3,2,1,6,4,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,1,6,7,8,2,4]=>[5,8,3,2,1,6,7,4]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,1,6,8,2,4,7]=>[5,8,3,2,1,6,4,7]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,5,1,7,2,4,6,8]=>[5,7,3,2,1,4,6,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,8,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,1,7,8,2,4,6]=>[5,8,3,2,1,4,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,1,2,7,4,8]=>[6,1,3,7,5,2,4,8]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,5,6,1,2,7,8,4]=>[6,1,3,8,5,2,7,4]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[6,1,3,8,5,2,4,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,1,7,2,4,8]=>[6,7,3,2,5,1,4,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[6,8,3,2,5,1,7,4]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,8,3,2,5,1,4,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,5,6,7,1,2,4,8]=>[7,1,3,2,5,6,4,8]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,1,8,2,4]=>[7,8,3,2,5,6,1,4]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[8,1,3,2,5,6,7,4]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,1,2,4,8,6]=>[7,1,3,2,5,8,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,1,2,7,4,5,8]=>[6,1,3,7,4,2,5,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,1,2,7,8,4,5]=>[6,1,3,8,4,2,7,5]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,6,1,7,2,4,5,8]=>[6,7,3,2,4,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[6,7,3,2,8,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,8,4,5]=>[6,7,3,8,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,1,2,4,8,5]=>[7,1,3,2,8,6,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[7,1,3,8,4,6,2,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,1,8,2,4,5]=>[7,8,3,2,4,6,1,5]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[8,1,3,2,4,6,7,5]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,1,2,4,5,8,6]=>[7,1,3,2,4,8,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,1,2,4,8,5,6]=>[7,1,3,2,8,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,1,2,8,4,5,6]=>[7,1,3,8,4,5,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[8,1,3,2,4,5,7,6]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,7,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,2,5,3,6,7,8]=>[4,1,5,2,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[4,1,5,2,3,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,2,5,3,7,8,6]=>[4,1,5,2,3,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,8,6,7]=>[4,1,5,2,3,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,2,5,6,7,8,3]=>[4,1,8,2,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[4,1,2,5,7,3,8,6]=>[4,1,7,2,5,8,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,2,6,3,5,7,8]=>[4,1,6,2,3,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,2,6,3,5,8,7]=>[4,1,6,2,3,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[4,1,6,2,7,3,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,2,6,3,8,5,7]=>[4,1,6,2,8,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,2,6,8,3,5,7]=>[4,1,8,2,3,6,5,7]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,7,3,5,6,8]=>[4,1,7,2,3,5,6,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,1,2,7,3,5,8,6]=>[4,1,7,2,3,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,2,7,3,8,5,6]=>[4,1,7,2,8,5,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,2,7,8,3,5,6]=>[4,1,8,2,3,5,7,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[4,5,2,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,2,3,7,6,8]=>[4,5,2,1,3,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,5,2,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,5,2,3,8,6,7]=>[4,5,2,1,3,8,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,2,6,7,3,8]=>[4,5,7,1,2,6,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,2,6,8,3,7]=>[4,5,8,1,2,6,3,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,2,7,8,3,6]=>[4,5,8,1,2,3,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,8,3,6,7]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,1,5,6,2,3,8,7]=>[4,6,2,1,5,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,1,5,6,7,2,8,3]=>[4,7,8,1,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,1,5,6,7,8,2,3]=>[4,8,2,1,5,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,1,5,6,8,2,3,7]=>[4,8,2,1,5,6,3,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>[4,7,2,1,5,3,6,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,1,5,7,2,8,3,6]=>[4,7,8,1,5,3,2,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[4,6,2,1,3,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,6,2,3,5,8,7]=>[4,6,2,1,3,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,6,2,3,7,5,8]=>[4,6,2,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,6,2,3,7,8,5]=>[4,6,2,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>[4,7,2,1,3,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,1,6,7,2,8,3,5]=>[4,7,8,1,3,6,2,5]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,1,6,7,8,2,3,5]=>[4,8,2,1,3,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[4,8,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,7,2,3,8,5,6]=>[4,7,2,1,8,5,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[4,8,2,1,3,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[4,8,2,1,3,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[5,1,2,4,3,6,8,7]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[5,1,6,4,2,3,8,7]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,5,1,2,6,7,3,8]=>[5,1,7,4,2,6,3,8]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,1,2,6,8,3,7]=>[5,1,8,4,2,6,3,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,1,2,7,3,6,8]=>[5,1,7,4,2,3,6,8]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,1,2,7,8,3,6]=>[5,1,8,4,2,3,7,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,1,2,8,3,6,7]=>[5,1,8,4,2,3,6,7]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,1,6,2,3,8,7]=>[5,6,2,4,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[5,6,8,4,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,8,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[4,5,1,6,7,2,3,8]=>[5,7,2,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,1,6,7,8,2,3]=>[5,8,2,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,1,6,8,2,3,7]=>[5,8,2,4,1,6,3,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,1,7,2,3,6,8]=>[5,7,2,4,1,3,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,1,7,8,2,3,6]=>[5,8,2,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,1,8,2,3,6,7]=>[5,8,2,4,1,3,6,7]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,6,1,2,7,3,8]=>[6,1,7,4,5,2,3,8]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,7,8,3]=>[6,1,8,4,5,2,7,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[6,1,8,4,5,2,3,7]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[6,8,2,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,8,2,4,5,1,3,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,1,8,2,3]=>[7,8,2,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[7,1,8,4,5,3,2,6]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[4,6,1,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[4,6,1,2,3,7,5,8]=>[6,1,2,4,7,3,5,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[4,6,1,2,3,7,8,5]=>[6,1,2,4,8,3,7,5]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,1,2,3,8,5,7]=>[6,1,2,4,8,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,1,2,7,3,8,5]=>[6,1,7,4,8,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,1,2,8,3,5,7]=>[6,1,8,4,3,2,5,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,1,7,2,3,5,8]=>[6,7,2,4,3,1,5,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,8,3,5]=>[6,7,8,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[6,8,2,4,3,1,5,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>[7,1,8,4,3,6,2,5]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,8,2,4,3,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,1,2,8,3,5,6]=>[7,1,8,4,3,5,2,6]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[7,8,2,4,3,5,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,1,2,3,5,6]=>[8,1,2,4,3,5,7,6]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,3,6,4,7,8]=>[5,1,2,6,3,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,1,2,3,6,4,8,7]=>[5,1,2,6,3,4,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[5,1,2,7,3,6,4,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,1,2,3,6,7,8,4]=>[5,1,2,8,3,6,7,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]=>[5,1,2,7,3,4,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,3,7,4,8,6]=>[5,1,2,7,3,8,4,6]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,3,8,4,6,7]=>[5,1,2,8,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,1,2,6,3,4,7,8]=>[5,1,6,3,2,4,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,1,2,6,3,4,8,7]=>[5,1,6,3,2,4,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,1,2,6,7,8,3,4]=>[5,1,8,3,2,6,7,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,1,2,6,8,3,4,7]=>[5,1,8,3,2,6,4,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[5,1,7,3,2,4,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[5,1,2,7,3,4,8,6]=>[5,1,7,3,2,8,4,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[5,1,2,7,3,8,4,6]=>[5,1,7,8,2,4,3,6]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,1,2,7,8,3,4,6]=>[5,1,8,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[5,1,8,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,1,6,2,3,7,4,8]=>[5,6,2,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,1,6,2,3,7,8,4]=>[5,6,2,8,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,2,7,8,3,4]=>[5,6,8,3,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,1,6,7,2,3,4,8]=>[5,7,2,3,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,1,6,7,2,3,8,4]=>[5,7,2,8,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,1,6,7,8,2,3,4]=>[5,8,2,3,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,1,6,8,2,3,4,7]=>[5,8,2,3,1,6,4,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,1,7,2,3,8,4,6]=>[5,7,2,8,1,4,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,8,3,4,6]=>[5,7,8,3,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,1,8,2,3,4,6,7]=>[5,8,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[5,6,1,2,3,7,8,4]=>[6,1,2,8,5,3,7,4]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,8,4,7]=>[6,1,2,8,5,3,4,7]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,1,2,7,3,8,4]=>[6,1,7,8,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,1,2,7,8,3,4]=>[6,1,8,3,5,2,7,4]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,8,3,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,1,7,8,2,3,4]=>[6,8,2,3,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,1,8,2,3,4,7]=>[6,8,2,3,5,1,4,7]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,1,2,3,8,4]=>[7,1,2,8,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[7,1,8,3,5,6,2,4]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,8,2,3,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,1,2,3,4,8,6]=>[7,1,2,3,5,8,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,1,2,8,3,4,6]=>[7,1,8,3,5,4,2,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,1,8,2,3,4,6]=>[7,8,2,3,5,4,1,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[6,1,2,3,7,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,1,2,3,4,7,8,5]=>[6,1,2,3,8,4,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,1,2,3,4,8,5,7]=>[6,1,2,3,8,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,1,2,3,7,4,8,5]=>[6,1,2,7,8,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,1,2,3,8,4,5,7]=>[6,1,2,8,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[6,1,7,3,4,2,5,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,1,2,7,3,4,8,5]=>[6,1,7,3,8,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,1,2,7,3,8,4,5]=>[6,1,7,8,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,1,2,7,8,3,4,5]=>[6,1,8,3,4,2,7,5]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[6,1,8,3,4,2,5,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,7,2,3,4,5,8]=>[6,7,2,3,4,1,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,1,7,2,3,4,8,5]=>[6,7,2,3,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,8,3,4,5]=>[6,7,8,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[6,8,2,3,4,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[6,8,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,1,2,8,3,4,5]=>[7,1,8,3,4,6,2,5]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[7,8,2,3,4,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[8,1,2,3,4,6,5,7]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,8,6]=>[7,1,2,3,4,8,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,8,5,6]=>[7,1,2,3,8,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,8,4,5,6]=>[7,1,2,8,4,5,3,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[7,1,8,3,4,5,2,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[7,8,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[1,9,2,3,4,5,6,8,7]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,1,2,3,4,5,6,7,10]=>[9,1,2,3,4,5,6,8,7,10]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,1,2,3,4,5,7,9]=>[8,1,2,3,4,6,5,7,9]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[1,9,2,3,4,5,7,6,8]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,9,8]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,9,7]=>[1,8,2,3,4,5,9,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[1,9,3,2,4,5,6,7,8]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,7,9]=>[1,8,2,3,4,5,6,7,9]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,9,1,3,4,5,6,7,8,10]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,1,2,3,4,5,6,7,10,9]=>[8,1,2,3,4,5,6,7,10,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,10,3,4,5,6,7,8,9]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,2,3,4,5,6,7,8,10]=>[1,9,2,3,4,5,6,7,8,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,1,8]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,1,9,7]=>[8,2,3,4,5,6,9,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,9,1,5,6,7,8]=>[9,2,3,4,1,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[4,2,6,1,8,3,9,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,8,1,9,3]=>[8,2,9,4,5,6,7,1,3]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,6,1,7,3,8,4,9,5]=>[6,2,7,8,9,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,1,4,8,9,2,5,6,7]=>[3,9,1,4,2,5,6,8,7]=>[[.,[.,.]],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,8,2,4,5,6,9,7]=>[3,8,1,2,4,5,9,6,7]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,9,2,4,5,6,7,8]=>[3,9,1,2,4,5,6,7,8]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,7,8,9,2]=>[6,9,3,4,5,1,7,8,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[9,1,3,2,4,5,6,7,8]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,9,7]=>[4,1,6,2,8,3,9,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,1,2,8,9,3,5,6,7]=>[4,1,9,2,3,5,6,8,7]=>[[.,[.,[.,.]]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,9,3]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,1,2,3,4,6,7,8]=>[9,1,2,3,5,4,6,7,8]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,1,2,3,4,7,8,9,5]=>[6,1,2,3,9,4,7,8,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[6,8,1,2,3,4,5,9,7]=>[8,1,2,3,4,6,9,5,7]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,1,2,3,4,5,8,9,6]=>[7,1,2,3,4,9,5,8,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,9,3,4,5,6]=>[7,8,9,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,7,6,8]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,9,7]=>[8,1,2,3,4,5,9,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[8,1,2,9,4,5,6,3,7]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,1,9,2,3,4,5,6,7]=>[8,9,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,4,7,8,9,5]=>[1,2,3,6,9,4,7,8,5]=>[.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,3,6,7,8,9,4]=>[1,2,5,9,3,6,7,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,6,8,7]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,4,8,5,6,9,7]=>[1,2,3,4,8,5,9,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,11,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,9,5,6,8,7]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,4,5,9,10,6,7,8]=>[1,2,3,4,5,10,6,7,9,8]=>[.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>[3,12,1,4,5,6,7,8,9,10,11,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,4,7,5,6,9,8]=>[1,2,3,4,7,5,6,9,8]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,7,8]=>[1,3,2,4,5,6,9,7,8]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,3,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7,9]=>[1,4,2,3,6,5,8,7,9]=>[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,2,3,4,5,6,8,9]=>[1,7,2,3,4,5,6,8,9]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,2,3,4,5,6,9,8]=>[1,7,2,3,4,5,6,9,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,9,7,8]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5,8,6,7,9]=>[2,1,3,4,5,8,6,7,9]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5,9,6,7,8]=>[2,1,3,4,5,9,6,7,8]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,9,7,8]=>[2,1,4,3,6,5,9,7,8]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>[2,1,8,3,4,5,6,7,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,2,4,5,6,7,9,8]=>[3,1,2,4,5,6,7,9,8]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,2,4,5,6,9,7,8]=>[3,1,2,4,5,6,9,7,8]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>[3,1,2,4,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>[3,1,2,9,4,5,6,7,8]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,5,9,6,7,8]=>[4,1,2,3,5,9,6,7,8]=>[[.,[.,[.,.]]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>[4,1,2,3,6,5,8,7,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,1,2,3,9,5,6,7,8]=>[4,1,2,3,9,5,6,7,8]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,1,2,3,4,7,6,8,9]=>[5,1,2,3,4,7,6,8,9]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,1,2,3,4,9,6,7,8]=>[5,1,2,3,4,9,6,7,8]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,1,2,3,4,5,9,7,8]=>[6,1,2,3,4,5,9,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,10,8,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>[1,4,2,3,6,5,8,7,10,9]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,7,10,8,9]=>[2,1,3,4,5,6,7,10,8,9]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,10,7,8,9]=>[2,1,4,3,6,5,10,7,8,9]=>[[.,.],[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,3,4,5,10,7,8,9]=>[2,1,6,3,4,5,10,7,8,9]=>[[.,.],[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,3,4,5,6,7,10,9]=>[2,1,8,3,4,5,6,7,10,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,10,4,5,6,7,8,9]=>[3,1,2,10,4,5,6,7,8,9]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7,10,9]=>[4,1,2,3,6,5,8,7,10,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,3,6,5,10,7,8,9]=>[4,1,2,3,6,5,10,7,8,9]=>[[.,[.,[.,.]]],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,8,5,6,7,10,9]=>[4,1,2,3,8,5,6,7,10,9]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,10,5,6,7,8,9]=>[4,1,2,3,10,5,6,7,8,9]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[5,1,2,3,4,10,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,1,2,3,4,5,10,7,8,9]=>[6,1,2,3,4,5,10,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,1,2,3,4,5,6,10,8,9]=>[7,1,2,3,4,5,6,10,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[10,2,3,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[9,10,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,10,8]=>[9,1,2,3,4,5,6,10,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[10,1,2,3,4,5,6,7,11,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,10,1,2,3,4,5,7,8,9]=>[10,1,2,3,4,6,5,7,8,9]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[10,1,2,3,5,4,6,7,8,9]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,6,7,8,2,9]=>[3,8,1,4,5,6,7,2,9]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[10,2,3,4,5,6,7,1,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,1,2,3,4,5,8,9,7]=>[6,1,2,3,4,5,9,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,1,2,3,4,10,5,6,7,8]=>[9,1,2,3,10,5,6,7,4,8]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,9,8]=>[4,2,6,1,7,3,5,9,8]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,9,8]=>[4,2,5,1,3,7,6,9,8]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,5,8,9]=>[4,2,6,1,7,3,5,8,9]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,8,5,9,7,10]=>[4,2,6,1,8,3,9,5,7,10]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,9,7]=>[4,2,5,1,3,8,9,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,6,3,7,5,9,8,10]=>[4,2,6,1,7,3,5,9,8,10]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,9,8]=>[3,2,1,6,7,4,5,9,8]=>[[[.,.],.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,9,8,10]=>[4,2,5,1,3,7,6,9,8,10]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[10,2,3,1,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,10,1,5,6,7,8,9]=>[10,2,3,4,1,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,10,1,6,7,8,9]=>[10,2,3,4,5,1,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[11,2,3,4,5,6,7,8,9,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[11,1,3,4,5,6,7,8,9,10,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[10,2,1,3,4,5,6,7,9,8]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[7,9,1,2,3,4,5,6,10,8]=>[9,1,2,3,4,5,7,10,6,8]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[1,2,9,4,3,5,6,7,8]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,9,5,4,6,7,8]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,9,6,5,7,8]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,9,7,6,8]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0]=>[10,1,2,11,3,4,5,6,7,8,9]=>[10,1,11,3,4,5,6,7,8,2,9]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,10,2,4,5,6,7,8,9]=>[3,10,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[8,1,9,2,10,3,4,5,6,7]=>[8,9,10,3,4,5,6,1,2,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,4,6,8,5,7,9]=>[1,2,3,4,8,6,5,7,9]=>[.,[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,11,2]=>[10,11,3,4,5,6,7,8,9,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,3,6,7,8,9]=>[4,2,5,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,9,8]=>[3,5,1,2,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,7,4,6,9,8]=>[3,1,2,7,5,4,6,9,8]=>[[.,[.,.]],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,9,8]=>[1,5,3,2,4,7,6,9,8]=>[.,[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,2,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,7,8,5,6,9]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,2,3,4,5,6,7,10,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,1,2,3,4,5,6,9,10,7]=>[8,1,2,3,4,5,10,6,9,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,5,7,9,10,1,2,4,6,8]=>[10,1,3,2,5,4,7,6,9,8]=>[[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,12,1,2]=>[12,1,3,4,5,6,7,8,9,10,11,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[12,2,3,4,5,6,7,8,9,10,1,11]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,12,11]=>[10,1,2,3,4,5,6,7,8,9,12,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,7,1,8,2,9,3,10,4]=>[7,8,9,10,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,2,7,3,8,4,9,5,10]=>[1,6,7,8,9,2,3,4,5,10]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,2,7,3,8,4,9,5,10,6]=>[1,2,7,8,9,10,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,1,2,3,9,10,4,6,7,8]=>[5,1,2,10,3,4,6,7,9,8]=>[[.,[.,[.,[.,.]]]],[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,3,4,5,6]=>[2,1,10,3,4,5,7,8,9,6]=>[[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,1,2,6,5,9,10,7,8]=>[4,1,3,2,6,5,10,7,9,8]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
Map
to 321-avoiding permutation (Krattenthaler)
Description
Krattenthaler's bijection to 321-avoiding permutations.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Draw the path of semilength $n$ in an $n\times n$ square matrix, starting at the upper left corner, with right and down steps, and staying below the diagonal. Then the permutation matrix is obtained by placing ones into the cells corresponding to the peaks of the path and placing ones into the remaining columns from left to right, such that the row indices of the cells increase.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.