Identifier
Mp00120:
Dyck paths
—Lalanne-Kreweras involution⟶
Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-3
[1,0]=>[1,0]=>[1]=>[.,.]
[1,0,1,0]=>[1,1,0,0]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[1,0,1,0]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,1,0,0,1,0]=>[3,1,2]=>[[.,[.,.]],.]
[1,1,0,0,1,0]=>[1,0,1,1,0,0]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[1,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]]
[1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[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]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]
[1,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,1,2,3,6,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,1,2,7]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,1,2,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,1,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,1,2,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,1,2,6,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,6,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,1,4,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,1,3,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,1,3,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,1,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,1,3,5,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,1,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,1,3,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,1,6,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,1,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,10,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,4,3,2,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[8,9,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,9,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,1,2,7,8,9]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,1,2,4]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[6,7,5,4,3,2,1,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[6,7,5,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,7,1,2,8,9]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,1,2,8,9,10]=>[[[[[[.,[.,.]],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,1,2,3,9]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[10,7,8,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,7,8,9,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,2,3,8,9,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,1,4,5,6,7,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,2,3,1,4,9]=>[[[[[[.,.],[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,1,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,9,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,1,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,4,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[8,7,6,3,4,2,1,5,9]=>[[[[[[.,.],.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,2,1,4,5]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[7,6,5,3,2,1,4,8,9]=>[[[[[[.,.],.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,2,1,4,9]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,5,6,7,8,2,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,3,5,6,7,2,1]=>[[[[[[.,.],.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,5,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,5,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,3,2,1,5,6]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,3,2,1,9]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,2,1,5,9]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,6,7,3,2,1]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,3,9,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,6,3,7,2,1]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,1,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[8,5,6,4,3,2,1,7,9]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,3,2,1,6,7]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,6,3,2,1,9]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,2,1,6,9]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,7,3,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,9,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,7,9,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,7,8,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,7,1,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8,6,7,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8,6,5,7,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,8,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[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]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[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]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,10,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,1,2,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,1,2,3,4,7]=>[[[[[.,[.,[.,[.,.]]]],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,1,2,6,7,8,9]=>[[[[.,[.,.]],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,1,2,3,4,5,10]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9,10]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,5,7,8,9,10,11,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,6,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,1,2,3]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[8,9,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[9,8,3,4,5,6,7,1,2]=>[[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,2,3,1]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,1,2,3]=>[[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[10,9,3,4,5,6,7,8,1,2]=>[[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,3,4,1,2]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,1,2]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,3,4,5,6,7,8,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,1,3,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,6,5,4,3,2,1,8,9]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,3,6,7,8,9,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,3,2,1,6]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,1,2,7,8,9,10]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,2,3,7,8,9,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,9,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,9,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,4,9,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,8,10,7,6,5,4,3,2,1,11]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[9,6,7,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[9,10,6,7,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,9,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,8,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,7,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,2,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,2,1,3,9]=>[[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,1,2,3,5]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,1,2,3,4,6]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[11,9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[8,5,6,7,4,3,2,1,9]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,8,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,9,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,3,2,1,5,10]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,5,1,2]=>[[[[[[[.,[.,.]],.],[.,.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,2,1,8]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,10,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,1,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,10,1,11]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1,2,4,6,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,1,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,3,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[5,6,7,4,8,9,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[8,3,1,2,4,5,6,7,9]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,1,2,3,5,6,7]=>[[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,7,8,9,10,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,8,9,6,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7,6,8,9,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,8,9,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,8,9,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,6,9,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,9,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,7,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[5,3,4,6,7,8,9,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,10,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,3,4,5,6,8,1,2,9]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,6,7,8,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,1,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,6,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,4,3,2,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,2,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[10,8,6,5,4,3,2,1,7,9]=>[[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,2,3,1,4,6,8,10]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,1,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[8,9,4,5,6,3,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,8,5,6,3,4,1,2,9]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[10,7,8,5,6,3,4,1,2,9]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[7,8,5,6,3,4,1,2,9,10]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,7,10,6,5,4,3,2,1,11]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[8,9,4,5,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],[.,.]]
Map
Lalanne-Kreweras involution
Description
The Lalanne-Kreweras involution on Dyck paths.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Label the upsteps from left to right and record the labels on the first up step of each double rise. Do the same for the downsteps. Then form the Dyck path whose ascent lengths and descent lengths are the consecutives differences of the labels.
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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.