Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,0,0,1,0]=>[3,1,2]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[3,2,6,4,7,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,5,4,7,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[3,2,6,4,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[3,2,6,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[3,2,7,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[3,2,5,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[5,2,4,6,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[3,2,5,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[3,2,6,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,4,7,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,4,7,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,4,7,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[3,2,5,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[5,2,4,6,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[2,1,6,5,7,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[3,2,6,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[6,2,4,5,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[3,2,4,6,7,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[4,2,3,6,7,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,5,7,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[2,6,3,4,7,1,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[2,5,3,4,7,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[2,5,3,4,1,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[2,6,3,4,5,7,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[2,5,3,6,1,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,4,1,6,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[2,5,3,7,1,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[2,6,3,7,5,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[3,4,1,7,5,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,4,3,7,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,4,3,7,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[2,4,3,7,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[2,5,3,6,1,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[3,4,1,6,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[5,4,3,6,1,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[2,4,3,5,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[2,3,1,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[3,6,1,5,7,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[2,6,3,5,7,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[3,4,1,5,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[2,4,3,6,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[2,3,1,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[2,3,1,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[2,5,6,4,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,3,6,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[5,3,6,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[2,5,7,4,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[2,6,7,4,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[4,3,7,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,3,7,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,3,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[2,5,6,4,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[4,3,6,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[5,3,6,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[4,3,5,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[2,3,5,4,1,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[2,4,5,1,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[2,4,6,1,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[2,4,6,1,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[2,4,7,1,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[4,6,5,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[2,6,5,4,7,1,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[4,3,5,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[6,3,5,4,7,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[4,3,6,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[2,3,6,4,7,1,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[2,4,6,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[2,4,5,1,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[4,3,5,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[2,4,5,1,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[4,3,5,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[2,4,5,1,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[2,6,4,7,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[5,3,4,7,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[6,3,4,7,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[5,3,6,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[2,3,6,7,5,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[2,5,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[2,5,4,7,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[2,5,4,6,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[5,3,4,6,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[2,5,4,6,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[2,3,5,6,1,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[2,6,4,5,7,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[2,3,6,5,7,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[2,3,5,6,1,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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.