Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
Mp00029: Dyck paths —to binary tree: left tree, up step, right tree, down step⟶ Binary trees
Images
=>
Cc0005;cc-rep-1Cc0005;cc-rep-2Cc0010;cc-rep-3
[1]=>[1,0]=>[1,0]=>[.,.] [1,1]=>[1,0,1,0]=>[1,1,0,0]=>[.,[.,.]] [2]=>[1,1,0,0]=>[1,0,1,0]=>[[.,.],.] [1,1,1]=>[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[.,[.,[.,.]]] [1,2]=>[1,0,1,1,0,0]=>[1,0,1,1,0,0]=>[[.,.],[.,.]] [2,1]=>[1,1,0,0,1,0]=>[1,1,0,1,0,0]=>[.,[[.,.],.]] [3]=>[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[[[.,.],.],.] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[.,[.,[.,[.,.]]]] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,0,0]=>[[.,.],[.,[.,.]]] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,0,0]=>[.,[[.,.],[.,.]]] [1,3]=>[1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[[[.,.],.],[.,.]] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[1,1,1,0,1,0,0,0]=>[.,[.,[[.,.],.]]] [2,2]=>[1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,0]=>[[.,.],[[.,.],.]] [3,1]=>[1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,0,0]=>[.,[[[.,.],.],.]] [4]=>[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[[[[.,.],.],.],.] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[.,[.,[.,[.,[.,.]]]]] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[[.,.],[.,[.,[.,.]]]] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,0,0,0]=>[.,[[.,.],[.,[.,.]]]] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[[[.,.],.],[.,[.,.]]] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,0,0,0]=>[.,[.,[[.,.],[.,.]]]] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[[.,.],[[.,.],[.,.]]] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,0,0]=>[.,[[[.,.],.],[.,.]]] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[[[[.,.],.],.],[.,.]] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,0,0,0]=>[.,[.,[.,[[.,.],.]]]] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[[.,.],[.,[[.,.],.]]] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,0,0]=>[.,[[.,.],[[.,.],.]]] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[[[.,.],.],[[.,.],.]] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,0,0]=>[.,[.,[[[.,.],.],.]]] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[[.,.],[[[.,.],.],.]] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,0]=>[.,[[[[.,.],.],.],.]] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[[[[[.,.],.],.],.],.] [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,.]]]]] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,.]]]]] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[[[.,.],.],[.,[.,[.,.]]]] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,.]]]]] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[[.,.],[[.,.],[.,[.,.]]]] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[.,.],.],[.,[.,.]]]] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[.,.],.],.],[.,[.,.]]] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,.]]]]] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[.,.],[.,.]]]] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[.,.],[.,.]]]] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[[[.,.],.],[[.,.],[.,.]]] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[.,.],.],[.,.]]]] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[.,.],.],[.,.]]] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[.,.],.],.],[.,.]]] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[.,.],.],.],.],[.,.]] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],.]]]]] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[.,.],.]]]] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[.,.],.]]]] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[[[.,.],.],[.,[[.,.],.]]] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[.,.],.]]]] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[[.,.],[[.,.],[[.,.],.]]] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[.,.],.],[[.,.],.]]] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[.,.],.],.],[[.,.],.]] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[.,.],.],.]]]] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[.,.],.],.]]] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[.,.],.],.]]] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[[[.,.],.],[[[.,.],.],.]] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[.,.],.],.],.]]] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[.,.],.],.],.]] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[.,.],.],.],.],.]] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[.,.],.],.],.],.],.] [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,.]]]] [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,.]]]]] [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,.]]]]] [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,.]]]] [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,.]]]]] [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,.]]]] [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,.]]]] [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,.]]] [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]] [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,.]]]]] [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,.]]]]] [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,.]]]] [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,.]]]]] [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,.]]]] [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,.]]]] [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,.]]] [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,.]]]]] [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,.]]]] [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,.]]]] [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,.]]] [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,.]]]] [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,.]]] [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,.]]] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[.,.],.],.],.],.],[.,.]] [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],.]]]]] [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],.]]]]] [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],.]]]] [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],.]]]]] [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],.]]]] [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],.]]]] [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],.]]] [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],.]]]]] [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],.]]]] [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],.]]]] [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],.]]] [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],.]]]] [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],.]]] [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],.]]] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[.,.],.]] [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],.]]]]] [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],.]]]] [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],.]]]] [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],.]]] [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],.]]]] [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],.]]] [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],.]]] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[.,.],.],.]] [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],.]]]] [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],.]]] [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],.]]] [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[.,.],.],.],.]] [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],.]]] [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[.,.],.],.],.],.]] [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[.,.],.],.],.],.],.]] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[.,.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]] [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]] [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]] [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]] [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]] [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]] [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]] [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]] [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]] [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]] [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]] [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]] [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]] [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]] [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]] [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]] [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]] [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]] [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]] [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]] [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]] [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]] [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]] [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]] [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]] [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]] [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]] [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]] [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]] [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]] [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]] [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]] [1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]] [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]] [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]] [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]] [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]] [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]] [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]] [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]] [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]] [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]] [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]] [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]] [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]] [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]] [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]] [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]] [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]] [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]] [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,.]] [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]] [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]] [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]] [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]] [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]] [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]] [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]] [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]] [2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]] [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]] [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]] [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]] [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]] [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]] [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]] [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]] [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]] [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]] [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]] [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]] [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]] [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]] [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]] [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]] [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]] [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]] [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]] [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]] [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],.]] [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]] [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]] [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]] [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]] [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]] [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]] [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]] [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]] [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]] [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]] [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]] [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]] [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]] [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]] [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]] [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],.]] [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]] [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]] [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]] [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]] [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]] [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]] [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]] [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],.]] [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]] [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]] [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]] [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],.]] [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]] [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],.]] [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],.]] [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[.,.],.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,2,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]] [1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]] [1,1,1,1,2,3]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]] [1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] [1,1,1,2,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]] [1,1,1,2,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]] [1,1,1,2,4]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]] [1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]] [1,1,1,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]] [1,1,1,4,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]] [1,1,1,5,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]] [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]] [1,1,2,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]] [1,1,2,1,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]] [1,1,2,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]] [1,1,2,4,1]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[[.,.],[.,[.,.]]]]] [1,1,2,5]=>[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]] [1,1,3,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]] [1,1,4,1,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]] [1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[.,[.,.]]]] [1,1,5,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]] [1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]] [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]] [1,2,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] [1,2,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [1,2,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]] [1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]] [1,2,1,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]] [1,2,1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]] [1,2,1,5]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[[.,.],[.,.]]]] [1,2,2,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]] [1,2,2,1,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]] [1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]] [1,2,4,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[.,.],[.,.]]]]] [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]] [1,3,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] [1,3,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]] [1,3,1,4]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[.,.],.],[.,.]]]] [1,3,5]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]] [1,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]] [1,4,1,3]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[.,.],.],.],[.,.]]]] [1,4,2,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[[.,.],[[[[.,.],.],.],[.,.]]]]] [1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]] [1,5,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]] [1,5,1,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[[.,.],.],.],.],[.,.]]]] [1,5,2,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[[.,.],[[[[[.,.],.],.],.],[.,.]]]] [1,5,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]] [1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]] [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]] [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]] [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]] [2,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [2,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [2,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]] [2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]] [2,1,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]] [2,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]] [2,1,1,2,3]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[[.,.],[.,[.,[[.,.],.]]]]] [2,1,1,4,1]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[[.,.],.]]]]] [2,1,1,5]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]] [2,1,2,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]] [2,1,2,1,3]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[[.,.],[.,[[.,.],.]]]]] [2,1,3,3]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[[[.,.],.],[[[.,.],.],[.,[[.,.],.]]]] [2,1,6]=>[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]] [2,2,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]] [2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]] [2,2,1,4]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[.,.],[[.,.],.]]]] [2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]] [2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [2,2,3,1,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[[.,.],[[.,.],.]]]]] [2,2,5]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]] [2,3,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]] [2,3,4]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]] [2,4,1,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[[.,.],.]]]]] [2,4,3]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]] [2,5,1,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[.,.],.],.],.],[[.,.],.]]]] [2,5,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[.,.],.],.],.],[[.,.],.]]] [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]] [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]] [3,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] [3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]] [3,1,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]] [3,1,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[[[.,.],.],.]]]]] [3,1,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]] [3,1,2,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[[.,.],[.,[[[.,.],.],.]]]]] [3,1,3,1,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[[[.,.],.],.]]]]] [3,1,4,1]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[[[.,.],.],.]]]] [3,1,5]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]] [3,2,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]] [3,2,1,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[[.,.],[[[.,.],.],.]]]]] [3,3,1,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[[[.,.],.],.]]]]] [3,4,1,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[[[.,.],.],.]]]] [3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]] [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]] [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] [4,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]] [4,1,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]] [4,2,1,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]] [4,2,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]] [4,2,3]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]] [4,3,1,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[[.,.],.],[[[[.,.],.],.],.]]]] [4,4,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[.,.],.],.],.]]] [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]] [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] [5,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]] [5,1,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[[.,.],[.,[[[[[.,.],.],.],.],.]]]] [5,1,3]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]] [5,2,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]] [5,2,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]] [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]] [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]] [6,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]] [6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]] [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]] [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]] [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]] [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]] [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.] [1,1,1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]] [1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,1,3,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,1,4,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]] [1,1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]] [1,1,1,1,2,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]] [1,1,1,1,3,1,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]] [1,1,1,1,4,1,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]] [1,1,1,1,5,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]] [1,1,1,1,6]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]] [1,1,1,2,1,1,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]] [1,1,1,2,1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]] [1,1,1,4,1,1,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]]] [1,1,1,6,1]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]] [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]] [1,1,2,1,1,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]] [1,1,3,1,1,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]] [1,1,3,5]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,[.,.]]]] [1,1,5,1,1,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[.,[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]] [1,1,5,3]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,[.,.]]]] [1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]] [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]] [1,2,1,1,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] [1,2,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] [1,2,1,1,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]] [1,2,1,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]] [1,2,1,6]=>[1,0,1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],[.,.]]]] [1,2,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]] [1,2,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]] [1,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]] [1,2,7]=>[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]] [1,3,1,1,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]] [1,3,1,1,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]] [1,3,1,5]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],[.,.]]]] [1,3,2,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]] [1,3,6]=>[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]] [1,4,1,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]]] [1,4,1,4]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],[.,.]]]] [1,4,5]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]] [1,5,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],[.,.]]]]]] [1,5,1,3]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],[.,.]]]] [1,5,4]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]] [1,6,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]] [1,6,1,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],[.,.]]]] [1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]] [1,7,2]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]] [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]] [2,1,1,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]] [2,1,1,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [2,1,1,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]] [2,1,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]] [2,1,1,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]] [2,1,1,1,1,4]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]] [2,1,1,1,2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]]] [2,1,1,1,5]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]] [2,1,1,6]=>[1,1,0,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[.,[[.,.],.]]]] [2,1,2,1,1,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]] [2,1,7]=>[1,1,0,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]] [2,2,1,1,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]] [2,2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] [2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]] [2,2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[.,[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]] [2,2,6]=>[1,1,0,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]] [2,3,1,1,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]]] [2,6,1,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[.,[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]] [2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]] [2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]] [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]] [3,1,1,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]] [3,1,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]] [3,1,6]=>[1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[[[[[[.,.],.],.],.],.],[.,[[[.,.],.],.]]] [3,2,1,1,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]] [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]] [4,1,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]] [4,1,1,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]] [4,5,1]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]] [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]] [5,1,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]] [5,1,1,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[[.,.],[.,[.,[.,[[[[[.,.],.],.],.],.]]]]] [5,1,4]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[[.,.],.],.],[.,[[[[[.,.],.],.],.],.]]] [5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]] [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]] [6,1,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]] [6,1,1,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[[.,.],[.,[.,[[[[[[.,.],.],.],.],.],.]]]] [6,1,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[[.,.],.],[.,[[[[[[.,.],.],.],.],.],.]]] [6,2,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]] [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]] [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]] [7,1,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,1,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[[.,.],[.,[[[[[[[.,.],.],.],.],.],.],.]]] [7,2,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]] [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]] [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]] [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]] [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]] [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.] [1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]] [1,8,1,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]] [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]] [2,2,2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]] [1,2,2,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]] [1,8,2]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]] [1,2,1,1,1,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]] [1,1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
inverse zeta map
Description
The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.
Map
to binary tree: left tree, up step, right tree, down step
Description
Return the binary tree corresponding to the Dyck path under the transformation left tree - up step - right tree - down step.
A Dyck path $D$ of semilength $n$ with $n > 1$ may be uniquely decomposed into $L 1 R 0$ for Dyck paths $L,R$ of respective semilengths $n_1,n_2$ with $n_1+n_2 = n-1$.
This map sends $D$ to the binary tree $T$ consisting of a root node with a left child according to $L$ and a right child according to $R$ and then recursively proceeds.
The base case of the unique Dyck path of semilength $1$ is sent to a single node.
This map may also be described as the unique map sending the Tamari orders on Dyck paths to the Tamari order on binary trees.