Identifier
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ 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]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.] [1,0,1,1,0,0]=>[2,3,1]=>[3,1,2]=>[[.,.],[.,.]] [1,1,0,0,1,0]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]] [1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]] [1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]] [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.] [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]] [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[4,1,3,2]=>[[.,.],[[.,.],.]] [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[[[.,.],.],[.,.]] [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]] [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]] [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]] [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]] [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]] [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]] [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]] [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]] [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]] [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]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.] [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]] [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]] [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]] [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]] [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]] [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]] [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]] [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]] [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]] [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]] [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]] [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]] [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]] [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]] [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]] [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]] [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]] [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]] [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]] [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]] [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]] [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]] [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]] [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]] [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]] [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]] [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]] [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]] [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]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]] [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>[[[.,.],.],[[[.,.],.],.]] [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>[[[[.,.],.],.],[[.,.],.]] [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]] [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>[[[.,.],.],[.,[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>[[[.,.],.],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]] [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]] [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>[[[.,.],.],[[[.,.],.],.]] [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]] [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]] [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]] [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]] [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]] [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]] [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]] [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]] [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>[[[.,.],.],[.,[[.,.],.]]] [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]] [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]] [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]] [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]] [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]] [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]] [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]] [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]] [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]] [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]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.] [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]] [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]] [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]] [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]] [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]] [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]] [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]] [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]] [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]] [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>[.,[[[[.,.],.],.],[[.,.],.]]] [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]] [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]] [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]] [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>[[[.,.],.],[.,[[[.,.],.],.]]] [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]] [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]] [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [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]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.
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.