Identifier
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00023: Dyck paths —to non-crossing permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
Images
=>
Cc0005;cc-rep-1
[1]=>[1,0]=>[1]=>[1] [1,1]=>[1,0,1,0]=>[1,2]=>[2,1] [2]=>[1,1,0,0]=>[2,1]=>[1,2] [1,1,1]=>[1,0,1,0,1,0]=>[1,2,3]=>[3,2,1] [1,2]=>[1,0,1,1,0,0]=>[1,3,2]=>[2,3,1] [2,1]=>[1,1,0,0,1,0]=>[2,1,3]=>[3,1,2] [3]=>[1,1,1,0,0,0]=>[3,2,1]=>[1,2,3] [1,1,1,1]=>[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1] [1,1,2]=>[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1] [1,2,1]=>[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1] [1,3]=>[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1] [2,1,1]=>[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2] [2,2]=>[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2] [3,1]=>[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3] [4]=>[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4] [1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1] [1,1,1,2]=>[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1] [1,1,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1] [1,1,3]=>[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1] [1,2,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1] [1,2,2]=>[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1] [1,3,1]=>[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1] [1,4]=>[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1] [2,1,1,1]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2] [2,1,2]=>[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2] [2,2,1]=>[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2] [2,3]=>[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2] [3,1,1]=>[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3] [3,2]=>[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3] [4,1]=>[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4] [5]=>[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5] [1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1] [1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1] [1,1,1,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1] [1,1,1,3]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1] [1,1,2,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1] [1,1,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1] [1,1,3,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1] [1,1,4]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1] [1,2,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1] [1,2,1,2]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1] [1,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1] [1,2,3]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1] [1,3,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1] [1,3,2]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1] [1,4,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1] [1,5]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1] [2,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2] [2,1,1,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2] [2,1,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2] [2,1,3]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2] [2,2,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2] [2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2] [2,3,1]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2] [2,4]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2] [3,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3] [3,1,2]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3] [3,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3] [3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3] [4,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4] [4,2]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4] [5,1]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5] [6]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6] [1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1] [1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1] [1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1] [1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1] [1,1,1,2,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1] [1,1,1,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1] [1,1,1,3,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1] [1,1,1,4]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1] [1,1,2,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1] [1,1,2,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1] [1,1,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1] [1,1,2,3]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1] [1,1,3,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1] [1,1,3,2]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1] [1,1,4,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1] [1,1,5]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1] [1,2,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1] [1,2,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1] [1,2,1,2,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1] [1,2,1,3]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1] [1,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1] [1,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1] [1,2,3,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1] [1,2,4]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1] [1,3,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1] [1,3,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1] [1,3,2,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1] [1,3,3]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1] [1,4,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1] [1,4,2]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1] [1,5,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1] [1,6]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1] [2,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2] [2,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2] [2,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2] [2,1,1,3]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2] [2,1,2,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2] [2,1,2,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2] [2,1,3,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2] [2,1,4]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2] [2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2] [2,2,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2] [2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2] [2,2,3]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2] [2,3,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2] [2,3,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2] [2,4,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2] [2,5]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2] [3,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3] [3,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3] [3,1,2,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3] [3,1,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3] [3,2,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3] [3,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3] [3,3,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3] [3,4]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3] [4,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4] [4,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4] [4,2,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4] [4,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4] [5,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5] [5,2]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5] [6,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6] [7]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7] [1,1,1,1,1,1,1,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1] [1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[7,8,6,5,4,3,2,1] [1,1,1,1,1,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[8,6,7,5,4,3,2,1] [1,1,1,1,1,3]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[6,7,8,5,4,3,2,1] [1,1,1,1,2,1,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[8,7,5,6,4,3,2,1] [1,1,1,1,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[7,8,5,6,4,3,2,1] [1,1,1,1,3,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[8,5,6,7,4,3,2,1] [1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[5,6,7,8,4,3,2,1] [1,1,1,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1] [1,1,1,2,1,2]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[7,8,6,4,5,3,2,1] [1,1,1,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[8,6,7,4,5,3,2,1] [1,1,1,2,3]=>[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[6,7,8,4,5,3,2,1] [1,1,1,3,1,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[8,7,4,5,6,3,2,1] [1,1,1,3,2]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[7,8,4,5,6,3,2,1] [1,1,1,4,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[8,4,5,6,7,3,2,1] [1,1,1,5]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[4,5,6,7,8,3,2,1] [1,1,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[8,7,6,5,3,4,2,1] [1,1,2,1,1,2]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[7,8,6,5,3,4,2,1] [1,1,2,1,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[8,6,7,5,3,4,2,1] [1,1,2,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[6,7,8,5,3,4,2,1] [1,1,2,2,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1] [1,1,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[7,8,5,6,3,4,2,1] [1,1,2,3,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,6,5,8]=>[8,5,6,7,3,4,2,1] [1,1,2,4]=>[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[5,6,7,8,3,4,2,1] [1,1,3,1,1,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[8,7,6,3,4,5,2,1] [1,1,3,1,2]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[7,8,6,3,4,5,2,1] [1,1,3,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,4,3,7,6,8]=>[8,6,7,3,4,5,2,1] [1,1,3,3]=>[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[6,7,8,3,4,5,2,1] [1,1,4,1,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1] [1,1,4,2]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,5,4,3,8,7]=>[7,8,3,4,5,6,2,1] [1,1,5,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[8,3,4,5,6,7,2,1] [1,1,6]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[3,4,5,6,7,8,2,1] [1,2,1,1,1,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[8,7,6,5,4,2,3,1] [1,2,1,1,1,2]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[7,8,6,5,4,2,3,1] [1,2,1,1,2,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1] [1,2,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[6,7,8,5,4,2,3,1] [1,2,1,2,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[8,7,5,6,4,2,3,1] [1,2,1,2,2]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[7,8,5,6,4,2,3,1] [1,2,1,3,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[8,5,6,7,4,2,3,1] [1,2,1,4]=>[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[5,6,7,8,4,2,3,1] [1,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[8,7,6,4,5,2,3,1] [1,2,2,1,2]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,4,6,8,7]=>[7,8,6,4,5,2,3,1] [1,2,2,2,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1] [1,2,2,3]=>[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[6,7,8,4,5,2,3,1] [1,2,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[8,7,4,5,6,2,3,1] [1,2,3,2]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[7,8,4,5,6,2,3,1] [1,2,4,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[8,4,5,6,7,2,3,1] [1,2,5]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[4,5,6,7,8,2,3,1] [1,3,1,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[8,7,6,5,2,3,4,1] [1,3,1,1,2]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[7,8,6,5,2,3,4,1] [1,3,1,2,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[8,6,7,5,2,3,4,1] [1,3,1,3]=>[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[6,7,8,5,2,3,4,1] [1,3,2,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,4,3,2,6,5,7,8]=>[8,7,5,6,2,3,4,1] [1,3,2,2]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,3,2,6,5,8,7]=>[7,8,5,6,2,3,4,1] [1,3,3,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1] [1,3,4]=>[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[5,6,7,8,2,3,4,1] [1,4,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[8,7,6,2,3,4,5,1] [1,4,1,2]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,5,4,3,2,6,8,7]=>[7,8,6,2,3,4,5,1] [1,4,2,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[8,6,7,2,3,4,5,1] [1,4,3]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[6,7,8,2,3,4,5,1] [1,5,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[8,7,2,3,4,5,6,1] [1,5,2]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[7,8,2,3,4,5,6,1] [1,6,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1] [1,7]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,1] [2,1,1,1,1,1,1]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2] [2,1,1,1,1,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2] [2,1,1,1,2,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[8,6,7,5,4,3,1,2] [2,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[6,7,8,5,4,3,1,2] [2,1,1,2,1,1]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[8,7,5,6,4,3,1,2] [2,1,1,2,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[7,8,5,6,4,3,1,2] [2,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,7,6,5,8]=>[8,5,6,7,4,3,1,2] [2,1,1,4]=>[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[5,6,7,8,4,3,1,2] [2,1,2,1,1,1]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[8,7,6,4,5,3,1,2] [2,1,2,1,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2] [2,1,2,2,1]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6,8]=>[8,6,7,4,5,3,1,2] [2,1,2,3]=>[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[6,7,8,4,5,3,1,2] [2,1,3,1,1]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,6,5,4,7,8]=>[8,7,4,5,6,3,1,2] [2,1,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[7,8,4,5,6,3,1,2] [2,1,4,1]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,7,6,5,4,8]=>[8,4,5,6,7,3,1,2] [2,1,5]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[4,5,6,7,8,3,1,2] [2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[8,7,6,5,3,4,1,2] [2,2,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[7,8,6,5,3,4,1,2] [2,2,1,2,1]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,3,5,7,6,8]=>[8,6,7,5,3,4,1,2] [2,2,1,3]=>[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[6,7,8,5,3,4,1,2] [2,2,2,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[8,7,5,6,3,4,1,2] [2,2,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2] [2,2,3,1]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,7,6,5,8]=>[8,5,6,7,3,4,1,2] [2,2,4]=>[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2] [2,3,1,1,1]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[8,7,6,3,4,5,1,2] [2,3,1,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[7,8,6,3,4,5,1,2] [2,3,2,1]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,5,4,3,7,6,8]=>[8,6,7,3,4,5,1,2] [2,3,3]=>[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,5,4,3,8,7,6]=>[6,7,8,3,4,5,1,2] [2,4,1,1]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,6,5,4,3,7,8]=>[8,7,3,4,5,6,1,2] [2,4,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2] [2,5,1]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[8,3,4,5,6,7,1,2] [2,6]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2] [3,1,1,1,1,1]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3] [3,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[7,8,6,5,4,1,2,3] [3,1,1,2,1]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[8,6,7,5,4,1,2,3] [3,1,1,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3] [3,1,2,1,1]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,2,1,4,6,5,7,8]=>[8,7,5,6,4,1,2,3] [3,1,2,2]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,2,1,4,6,5,8,7]=>[7,8,5,6,4,1,2,3] [3,1,3,1]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[8,5,6,7,4,1,2,3] [3,1,4]=>[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[5,6,7,8,4,1,2,3] [3,2,1,1,1]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[8,7,6,4,5,1,2,3] [3,2,1,2]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,2,1,5,4,6,8,7]=>[7,8,6,4,5,1,2,3] [3,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[8,6,7,4,5,1,2,3] [3,2,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,2,1,5,4,8,7,6]=>[6,7,8,4,5,1,2,3] [3,3,1,1]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[8,7,4,5,6,1,2,3] [3,3,2]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,2,1,6,5,4,8,7]=>[7,8,4,5,6,1,2,3] [3,4,1]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[8,4,5,6,7,1,2,3] [3,5]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[4,5,6,7,8,1,2,3] [4,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4] [4,1,1,2]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[7,8,6,5,1,2,3,4] [4,1,2,1]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[8,6,7,5,1,2,3,4] [4,1,3]=>[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[6,7,8,5,1,2,3,4] [4,2,1,1]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[8,7,5,6,1,2,3,4] [4,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4] [4,3,1]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[8,5,6,7,1,2,3,4] [4,4]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4] [5,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5] [5,1,2]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[7,8,6,1,2,3,4,5] [5,2,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[8,6,7,1,2,3,4,5] [5,3]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[6,7,8,1,2,3,4,5] [6,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6] [6,2]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6] [7,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7] [8]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8] [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]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,9,8,7]=>[7,8,9,6,5,4,3,2,1] [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]=>[1,2,3,4,5,7,6,8,9]=>[9,8,6,7,5,4,3,2,1] [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]=>[1,2,3,4,5,7,6,9,8]=>[8,9,6,7,5,4,3,2,1] [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]=>[1,2,3,4,5,8,7,6,9]=>[9,6,7,8,5,4,3,2,1] [1,1,1,1,1,4]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[6,7,8,9,5,4,3,2,1] [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]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,5,6,4,3,2,1] [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]=>[1,2,3,4,6,5,7,9,8]=>[8,9,7,5,6,4,3,2,1] [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]=>[1,2,3,4,6,5,8,7,9]=>[9,7,8,5,6,4,3,2,1] [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]=>[1,2,3,4,7,6,5,8,9]=>[9,8,5,6,7,4,3,2,1] [1,1,1,1,5]=>[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1] [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]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,6,4,5,3,2,1] [1,1,1,2,2,2]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[8,9,6,7,4,5,3,2,1] [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]=>[1,2,3,6,5,4,7,8,9]=>[9,8,7,4,5,6,3,2,1] [1,1,1,6]=>[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[4,5,6,7,8,9,3,2,1] [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]=>[1,2,4,3,5,6,7,8,9]=>[9,8,7,6,5,3,4,2,1] [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]=>[1,2,4,3,5,6,7,9,8]=>[8,9,7,6,5,3,4,2,1] [1,1,2,1,1,3]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,6,9,8,7]=>[7,8,9,6,5,3,4,2,1] [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]=>[1,2,4,3,6,5,7,8,9]=>[9,8,7,5,6,3,4,2,1] [1,1,2,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[9,7,8,5,6,3,4,2,1] [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]=>[1,2,5,4,3,6,7,8,9]=>[9,8,7,6,3,4,5,2,1] [1,1,4,3]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,6,5,4,3,9,8,7]=>[7,8,9,3,4,5,6,2,1] [1,1,5,2]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,7,6,5,4,3,9,8]=>[8,9,3,4,5,6,7,2,1] [1,1,6,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,8,7,6,5,4,3,9]=>[9,3,4,5,6,7,8,2,1] [1,1,7]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,2,1] [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]=>[1,3,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,3,1] [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]=>[1,3,2,4,5,6,7,9,8]=>[8,9,7,6,5,4,2,3,1] [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]=>[1,3,2,4,5,6,8,7,9]=>[9,7,8,6,5,4,2,3,1] [1,2,1,1,1,3]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>[7,8,9,6,5,4,2,3,1] [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]=>[1,3,2,4,5,7,6,8,9]=>[9,8,6,7,5,4,2,3,1] [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]=>[1,3,2,4,6,5,7,8,9]=>[9,8,7,5,6,4,2,3,1] [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]=>[1,3,2,5,4,6,7,8,9]=>[9,8,7,6,4,5,2,3,1] [1,2,2,2,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,8,9]=>[9,8,6,7,4,5,2,3,1] [1,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[8,9,6,7,4,5,2,3,1] [1,2,6]=>[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,9,8,7,6,5,4]=>[4,5,6,7,8,9,2,3,1] [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]=>[1,4,3,2,5,6,7,8,9]=>[9,8,7,6,5,2,3,4,1] [1,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8,9]=>[9,8,7,6,2,3,4,5,1] [1,4,4]=>[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2,9,8,7,6]=>[6,7,8,9,2,3,4,5,1] [1,5,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,6,5,4,3,2,7,8,9]=>[9,8,7,2,3,4,5,6,1] [1,6,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,6,5,4,3,2,8,9]=>[9,8,2,3,4,5,6,7,1] [1,6,2]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,7,6,5,4,3,2,9,8]=>[8,9,2,3,4,5,6,7,1] [1,7,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[9,2,3,4,5,6,7,8,1] [1,8]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,1] [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]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2] [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]=>[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2] [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]=>[2,1,3,4,5,6,8,7,9]=>[9,7,8,6,5,4,3,1,2] [2,1,1,1,1,3]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,8,7]=>[7,8,9,6,5,4,3,1,2] [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]=>[2,1,3,4,5,7,6,8,9]=>[9,8,6,7,5,4,3,1,2] [2,1,1,1,3,1]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5,8,7,6,9]=>[9,6,7,8,5,4,3,1,2] [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]=>[2,1,3,4,6,5,7,8,9]=>[9,8,7,5,6,4,3,1,2] [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]=>[2,1,3,5,4,6,7,8,9]=>[9,8,7,6,4,5,3,1,2] [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]=>[2,1,4,3,5,6,7,8,9]=>[9,8,7,6,5,3,4,1,2] [2,2,1,1,1,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,7,9,8]=>[8,9,7,6,5,3,4,1,2] [2,2,2,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9]=>[9,8,7,5,6,3,4,1,2] [2,2,2,1,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,6,5,7,9,8]=>[8,9,7,5,6,3,4,1,2] [2,2,2,2,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[9,7,8,5,6,3,4,1,2] [2,6,1]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[9,3,4,5,6,7,8,1,2] [2,7]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,1,2] [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]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3] [3,1,1,1,1,2]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,7,9,8]=>[8,9,7,6,5,4,1,2,3] [3,2,2,2]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>[8,9,6,7,4,5,1,2,3] [3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4,9,8,7]=>[7,8,9,4,5,6,1,2,3] [3,5,1]=>[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,1,8,7,6,5,4,9]=>[9,4,5,6,7,8,1,2,3] [3,6]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[4,5,6,7,8,9,1,2,3] [4,1,1,1,1,1]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4] [4,5]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[5,6,7,8,9,1,2,3,4] [5,1,1,1,1]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5] [5,3,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,4,3,2,1,8,7,6,9]=>[9,6,7,8,1,2,3,4,5] [5,4]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[6,7,8,9,1,2,3,4,5] [6,1,1,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6] [6,2,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>[9,7,8,1,2,3,4,5,6] [6,3]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[7,8,9,1,2,3,4,5,6] [7,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7] [7,2]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[8,9,1,2,3,4,5,6,7] [8,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8] [9]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9] [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]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1] [1,1,1,1,1,1,1,1,2]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,7,10,9,8]=>[8,9,10,7,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,8,7,9,10]=>[10,9,7,8,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,8,7,10,9]=>[9,10,7,8,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,9,8,7,10]=>[10,7,8,9,6,5,4,3,2,1] [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]=>[1,2,3,4,5,6,10,9,8,7]=>[7,8,9,10,6,5,4,3,2,1] [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]=>[1,2,3,4,5,7,6,8,9,10]=>[10,9,8,6,7,5,4,3,2,1] [1,1,1,1,1,2,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8,10]=>[10,8,9,6,7,5,4,3,2,1] [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]=>[1,2,3,4,5,10,9,8,7,6]=>[6,7,8,9,10,5,4,3,2,1] [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]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1] [1,1,1,1,2,2,2]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[9,10,7,8,5,6,4,3,2,1] [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]=>[1,2,3,4,10,9,8,7,6,5]=>[5,6,7,8,9,10,4,3,2,1] [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]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,7,6,4,5,3,2,1] [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]=>[1,2,3,5,4,6,7,8,10,9]=>[9,10,8,7,6,4,5,3,2,1] [1,1,1,2,2,1,1,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,7,6,8,9,10]=>[10,9,8,6,7,4,5,3,2,1] [1,1,1,2,2,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,3,2,1] [1,1,1,7]=>[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[4,5,6,7,8,9,10,3,2,1] [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]=>[1,2,4,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,4,2,1] [1,1,2,2,1,1,1,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,6,5,7,8,9,10]=>[10,9,8,7,5,6,3,4,2,1] [1,1,2,2,2,2]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,2,1] [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]=>[1,2,7,6,5,4,3,8,9,10]=>[10,9,8,3,4,5,6,7,2,1] [1,1,6,2]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,8,7,6,5,4,3,10,9]=>[9,10,3,4,5,6,7,8,2,1] [1,1,7,1]=>[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,9,8,7,6,5,4,3,10]=>[10,3,4,5,6,7,8,9,2,1] [1,1,8]=>[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,10,2,1] [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]=>[1,3,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,3,1] [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]=>[1,3,2,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,2,3,1] [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]=>[1,3,2,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,2,3,1] [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]=>[1,3,2,5,4,6,7,8,9,10]=>[10,9,8,7,6,4,5,2,3,1] [1,2,2,2,1,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,7,6,8,9,10]=>[10,9,8,6,7,4,5,2,3,1] [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]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1] [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]=>[1,4,3,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,3,4,1] [1,7,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,8,7,6,5,4,3,2,9,10]=>[10,9,2,3,4,5,6,7,8,1] [1,8,1]=>[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[10,2,3,4,5,6,7,8,9,1] [1,9]=>[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,10,1] [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]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2] [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]=>[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2] [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]=>[2,1,3,4,5,6,7,9,8,10]=>[10,8,9,7,6,5,4,3,1,2] [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]=>[2,1,3,4,5,6,8,7,9,10]=>[10,9,7,8,6,5,4,3,1,2] [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]=>[2,1,3,5,4,6,7,8,9,10]=>[10,9,8,7,6,4,5,3,1,2] [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]=>[2,1,4,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,4,1,2] [2,2,2,1,1,1,1]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8,9,10]=>[10,9,8,7,5,6,3,4,1,2] [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]=>[2,1,4,3,6,5,8,7,9,10]=>[10,9,7,8,5,6,3,4,1,2] [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]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2] [2,2,2,4]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,10,9,8,7]=>[7,8,9,10,5,6,3,4,1,2] [2,4,4]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[7,8,9,10,3,4,5,6,1,2] [2,6,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[9,10,3,4,5,6,7,8,1,2] [2,7,1]=>[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,9,8,7,6,5,4,3,10]=>[10,3,4,5,6,7,8,9,1,2] [2,8]=>[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[3,4,5,6,7,8,9,10,1,2] [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]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3] [3,2,2,2,1]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,1,2,3] [3,6,1]=>[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,2,1,9,8,7,6,5,4,10]=>[10,4,5,6,7,8,9,1,2,3] [3,7]=>[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[4,5,6,7,8,9,10,1,2,3] [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]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4] [4,2,2,2]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[9,10,7,8,5,6,1,2,3,4] [4,2,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[7,8,9,10,5,6,1,2,3,4] [4,3,3]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5,10,9,8]=>[8,9,10,5,6,7,1,2,3,4] [4,4,2]=>[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[9,10,5,6,7,8,1,2,3,4] [4,6]=>[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[5,6,7,8,9,10,1,2,3,4] [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]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5] [5,4,1]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[5,4,3,2,1,9,8,7,6,10]=>[10,6,7,8,9,1,2,3,4,5] [5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[6,7,8,9,10,1,2,3,4,5] [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]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6] [6,3,1]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[6,5,4,3,2,1,9,8,7,10]=>[10,7,8,9,1,2,3,4,5,6] [6,4]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[7,8,9,10,1,2,3,4,5,6] [7,1,1,1]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7] [7,3]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[8,9,10,1,2,3,4,5,6,7] [8,1,1]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8] [8,2]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[9,10,1,2,3,4,5,6,7,8] [9,1]=>[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9] [10]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10] [1,10]=>[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,3,4,5,6,7,8,9,10,11,1] [10,1]=>[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,10] [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]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2] [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]=>[1,3,2,5,4,7,6,9,8,11,10,12]=>[12,10,11,8,9,6,7,4,5,2,3,1] [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]=>[1,3,2,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,2,3,1] [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]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,11,9,8,7,6,5,4,3,2,1] [1,2,2,2,2,2]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[10,11,8,9,6,7,4,5,2,3,1]
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.