Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[1,2]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[2,1]=>[2,1]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[2,3,1]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,2,4,1]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[[.,[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[.,[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[[[.,.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[.,[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[.,[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 312-avoiding permutation
Description
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.