Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00326: Permutations —weak order rowmotion⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00326: Permutations —weak order rowmotion⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
Cc0005;cc-rep-0
[1,0]=>[1]=>[1]=>[1]
[1,0,1,0]=>[1,2]=>[2,1]=>[1,1]
[1,1,0,0]=>[2,1]=>[1,2]=>[2]
[1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]=>[1,1,1]
[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]=>[1,2]
[1,1,0,1,0,0]=>[2,3,1]=>[2,1,3]=>[1,2]
[1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]=>[3]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1]=>[2,1,1]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]=>[1,2,1]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,2,4,1]=>[1,2,1]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1]=>[3,1]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2]=>[1,1,2]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,2,1,3]=>[1,1,2]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[3,2,1,4]=>[1,1,2]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[2,1,3,4]=>[1,3]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3]=>[1,3]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[2,3,1,4]=>[2,2]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,1,2,4]=>[1,3]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[2,1,1,1]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[1,2,1,1]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,3,5,2,1]=>[1,2,1,1]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[3,1,1]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[1,1,2,1]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[2,2,1]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[1,1,2,1]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[4,3,2,5,1]=>[1,1,2,1]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,2,4,5,1]=>[1,3,1]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[1,3,1]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,4,2,5,1]=>[2,2,1]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,2,3,5,1]=>[1,3,1]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[4,1]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[1,1,1,2]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,2]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[1,2,2]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,3,5,1,2]=>[1,2,2]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[3,2]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[5,4,2,1,3]=>[1,1,1,2]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,5,2,1,3]=>[2,1,2]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,3,2,1,4]=>[1,1,1,2]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[1,1,1,2]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[3,2,1,4,5]=>[1,1,3]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,2,1,3,4]=>[1,1,3]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[3,4,2,1,5]=>[2,1,2]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,2,1,3,5]=>[1,1,3]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[2,1,3,4,5]=>[1,4]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[1,1,3]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[2,3]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,2,3,1,4]=>[1,2,2]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[4,2,3,1,5]=>[1,2,2]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[2,3,1,4,5]=>[2,3]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[5,3,1,2,4]=>[1,1,3]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[1,2,2]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[4,3,1,2,5]=>[1,1,3]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[3,1,2,4,5]=>[1,4]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[1,4]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[3,2]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[3,4,1,2,5]=>[2,3]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,1,2,3,5]=>[1,4]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[3,1,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,4,3,5,2,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[4,3,5,6,2,1]=>[1,3,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[1,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[4,5,3,6,2,1]=>[2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,3,4,6,2,1]=>[1,3,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[4,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[1,1,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[5,4,6,2,3,1]=>[1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[3,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,5,3,2,4,1]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[5,6,3,2,4,1]=>[2,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[4,3,2,5,6,1]=>[1,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[6,3,2,4,5,1]=>[1,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[4,5,3,2,6,1]=>[2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,3,2,4,6,1]=>[1,1,3,1]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[3,2,4,5,6,1]=>[1,4,1]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[1,1,3,1]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[2,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[5,3,4,2,6,1]=>[1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[3,4,2,5,6,1]=>[2,3,1]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[6,4,2,3,5,1]=>[1,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,3,5,2,6,1]=>[1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[5,4,2,3,6,1]=>[1,1,3,1]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,2,3,5,6,1]=>[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]=>[1,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[3,4,5,2,6,1]=>[3,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,5,2,3,6,1]=>[2,3,1]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,2,3,4,6,1]=>[1,4,1]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[5,1]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,1,2]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,4,6,3,1,2]=>[1,2,1,2]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[3,1,2]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[1,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[6,4,3,5,1,2]=>[1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[5,4,3,6,1,2]=>[1,1,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,5,6,1,2]=>[1,3,2]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[1,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,5,3,6,1,2]=>[2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,3,4,6,1,2]=>[1,3,2]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[4,2]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,6,4,2,1,3]=>[2,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[6,4,5,2,1,3]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,2,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,5,6,2,1,3]=>[3,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,6,3,2,1,4]=>[2,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[4,3,2,1,5,6]=>[1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,3,2,1,4,5]=>[1,1,1,3]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[4,5,3,2,1,6]=>[2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,3,2,1,4,6]=>[1,1,1,3]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[3,2,1,4,5,6]=>[1,1,4]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[6,5,2,1,3,4]=>[1,1,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,6,2,1,3,4]=>[2,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,3,4,2,1,5]=>[1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>[1,2,1,2]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[3,4,2,1,5,6]=>[2,1,3]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[6,4,2,1,3,5]=>[1,1,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,3,5,2,1,6]=>[1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[5,4,2,1,3,6]=>[1,1,1,3]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[4,2,1,3,5,6]=>[1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,2,1,3,4,5]=>[1,1,4]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[3,4,5,2,1,6]=>[3,1,2]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[4,5,2,1,3,6]=>[2,1,3]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>[1,1,4]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[2,1,3,4,5,6]=>[1,5]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,1,1,3]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[2,1,3]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[5,4,6,1,2,3]=>[1,2,3]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[6,5,2,3,1,4]=>[1,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,6,2,3,1,4]=>[2,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,4,2,3,1,5]=>[1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[5,4,2,3,1,6]=>[1,1,2,2]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[4,2,3,1,5,6]=>[1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,2,3,1,4,5]=>[1,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>[2,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[5,2,3,1,4,6]=>[1,2,3]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[2,3,1,4,5,6]=>[2,4]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[6,5,3,1,2,4]=>[1,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,6,3,1,2,4]=>[2,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[6,3,2,4,1,5]=>[1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[5,3,2,4,1,6]=>[1,1,2,2]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[3,2,4,1,5,6]=>[1,2,3]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[6,4,3,1,2,5]=>[1,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[5,4,3,1,2,6]=>[1,1,1,3]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>[1,1,4]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[6,3,1,2,4,5]=>[1,1,4]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[3,2,4,5,1,6]=>[1,3,2]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[4,5,3,1,2,6]=>[2,1,3]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,3,1,2,4,6]=>[1,1,4]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[3,1,2,4,5,6]=>[1,5]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,1,4]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[2,4]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,2,3,4,1,5]=>[1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[5,2,3,4,1,6]=>[1,3,2]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[2,3,4,1,5,6]=>[3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[6,3,4,1,2,5]=>[1,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[2,2,2]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[5,3,4,1,2,6]=>[1,2,3]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>[2,4]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[6,4,1,2,3,5]=>[1,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,2,3,5,1,6]=>[1,3,2]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,3,5,1,2,6]=>[1,2,3]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[5,4,1,2,3,6]=>[1,1,4]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[4,1,2,3,5,6]=>[1,5]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,5]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[4,2]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[3,4,5,1,2,6]=>[3,3]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[4,5,1,2,3,6]=>[2,4]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,1,2,3,4,6]=>[1,5]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[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]=>[1,1,1,1,1,1,1]
[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]=>[2,1,1,1,1,1]
[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]=>[1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[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]=>[3,1,1,1,1]
[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]=>[1,1,2,1,1,1]
[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]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[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]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[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]=>[1,1,1,2,1,1]
[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]=>[2,1,2,1,1]
[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]=>[1,2,2,1,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]
[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]=>[3,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[7,4,3,5,6,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,4,3,5,7,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[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]=>[1,1,3,1,1]
[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]=>[2,3,1,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[7,4,5,3,6,2,1]=>[1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[6,4,5,3,7,2,1]=>[1,2,2,1,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[5,3,4,6,7,2,1]=>[1,4,1,1]
[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]=>[1,4,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[5,6,3,4,7,2,1]=>[2,3,1,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,3,4,5,7,2,1]=>[1,4,1,1]
[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]=>[5,1,1]
[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]=>[1,1,1,1,2,1]
[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]=>[2,1,1,2,1]
[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]=>[1,2,1,2,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]
[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]=>[3,1,2,1]
[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]=>[1,1,2,2,1]
[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]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[5,4,6,7,2,3,1]=>[1,3,2,1]
[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]=>[1,3,2,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[5,6,4,7,2,3,1]=>[2,2,2,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,4,5,7,2,3,1]=>[1,3,2,1]
[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]=>[4,2,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[5,6,7,3,2,4,1]=>[3,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[7,4,3,2,5,6,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,4,3,2,5,7,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[7,6,3,2,4,5,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[6,7,3,2,4,5,1]=>[2,1,3,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[7,4,5,3,2,6,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[6,4,5,3,2,7,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[6,5,3,2,4,7,1]=>[1,1,1,3,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[5,3,2,4,6,7,1]=>[1,1,4,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[7,3,2,4,5,6,1]=>[1,1,4,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[5,6,3,2,4,7,1]=>[2,1,3,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,3,2,4,5,7,1]=>[1,1,4,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[3,2,4,5,6,7,1]=>[1,5,1]
[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]=>[1,1,1,3,1]
[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]=>[2,1,3,1]
[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]=>[1,2,3,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[6,5,7,2,3,4,1]=>[1,2,3,1]
[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]=>[3,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[7,6,3,4,2,5,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[6,7,3,4,2,5,1]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[7,5,3,4,2,6,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[6,5,3,4,2,7,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[5,3,4,2,6,7,1]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[7,3,4,2,5,6,1]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[5,6,3,4,2,7,1]=>[2,2,2,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[6,3,4,2,5,7,1]=>[1,2,3,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[3,4,2,5,6,7,1]=>[2,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[6,7,4,2,3,5,1]=>[2,1,3,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[6,4,3,5,2,7,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[5,4,2,3,6,7,1]=>[1,1,4,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[1,1,4,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[5,6,4,2,3,7,1]=>[2,1,3,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,4,2,3,5,7,1]=>[1,1,4,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[4,2,3,5,6,7,1]=>[1,5,1]
[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]=>[1,1,4,1]
[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]=>[2,4,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[6,3,4,5,2,7,1]=>[1,3,2,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[3,4,5,2,6,7,1]=>[3,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[7,4,5,2,3,6,1]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[6,4,5,2,3,7,1]=>[1,2,3,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[4,5,2,3,6,7,1]=>[2,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[7,5,2,3,4,6,1]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,3,4,6,2,7,1]=>[1,3,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,4,6,2,3,7,1]=>[1,2,3,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[6,5,2,3,4,7,1]=>[1,1,4,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[5,2,3,4,6,7,1]=>[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]=>[1,5,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[3,4,5,6,2,7,1]=>[4,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[4,5,6,2,3,7,1]=>[3,3,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[5,6,2,3,4,7,1]=>[2,4,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,2,3,4,5,7,1]=>[1,5,1]
[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]=>[6,1]
[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]=>[1,1,1,1,1,2]
[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]=>[2,1,1,1,2]
[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]=>[1,2,1,1,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]
[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]=>[3,1,1,2]
[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]=>[1,1,2,1,2]
[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]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[5,4,6,7,3,1,2]=>[1,3,1,2]
[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]=>[1,3,1,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[5,6,4,7,3,1,2]=>[2,2,1,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,4,5,7,3,1,2]=>[1,3,1,2]
[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]=>[4,1,2]
[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]=>[1,1,1,2,2]
[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]=>[2,1,2,2]
[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]=>[1,2,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,5,7,3,4,1,2]=>[1,2,2,2]
[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]=>[3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[5,4,3,6,7,1,2]=>[1,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[7,4,3,5,6,1,2]=>[1,1,3,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[5,6,4,3,7,1,2]=>[2,1,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,4,3,5,7,1,2]=>[1,1,3,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[4,3,5,6,7,1,2]=>[1,4,2]
[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]=>[1,1,3,2]
[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]=>[2,3,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[7,4,5,3,6,1,2]=>[1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[6,4,5,3,7,1,2]=>[1,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[4,5,3,6,7,1,2]=>[2,3,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[7,5,3,4,6,1,2]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,4,6,3,7,1,2]=>[1,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[6,5,3,4,7,1,2]=>[1,1,3,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[5,3,4,6,7,1,2]=>[1,4,2]
[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]=>[1,4,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[4,5,6,3,7,1,2]=>[3,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[5,6,3,4,7,1,2]=>[2,3,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,3,4,5,7,1,2]=>[1,4,2]
[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]=>[5,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,6,7,4,2,1,3]=>[3,1,1,2]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[6,7,4,5,2,1,3]=>[2,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[5,4,6,7,2,1,3]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[7,4,5,6,2,1,3]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,6,4,7,2,1,3]=>[2,2,1,2]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,4,5,7,2,1,3]=>[1,3,1,2]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[4,5,6,7,2,1,3]=>[4,1,2]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[5,6,7,3,2,1,4]=>[3,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,7,3,2,1,4,5]=>[2,1,1,3]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[7,4,5,3,2,1,6]=>[1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[6,4,5,3,2,1,7]=>[1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[5,6,3,2,1,4,7]=>[2,1,1,3]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[3,2,1,4,5,6,7]=>[1,1,5]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[6,7,5,2,1,3,4]=>[2,1,1,3]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[7,5,6,2,1,3,4]=>[1,2,1,3]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[6,5,7,2,1,3,4]=>[1,2,1,3]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[5,6,7,2,1,3,4]=>[3,1,3]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[7,6,3,4,2,1,5]=>[1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,7,3,4,2,1,5]=>[2,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[7,5,3,4,2,1,6]=>[1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[6,5,3,4,2,1,7]=>[1,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[5,3,4,2,1,6,7]=>[1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[7,3,4,2,1,5,6]=>[1,2,1,3]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[5,6,3,4,2,1,7]=>[2,2,1,2]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[6,3,4,2,1,5,7]=>[1,2,1,3]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[3,4,2,1,5,6,7]=>[2,1,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,7,4,2,1,3,5]=>[2,1,1,3]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[7,4,3,5,2,1,6]=>[1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>[1,1,2,1,2]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[5,6,4,2,1,3,7]=>[2,1,1,3]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[4,2,1,3,5,6,7]=>[1,1,5]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,7,2,1,3,4,5]=>[2,1,4]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[7,3,4,5,2,1,6]=>[1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>[1,3,1,2]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[3,4,5,2,1,6,7]=>[3,1,3]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[7,4,5,2,1,3,6]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[6,4,5,2,1,3,7]=>[1,2,1,3]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[4,5,2,1,3,6,7]=>[2,1,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,3,4,6,2,1,7]=>[1,3,1,2]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,4,6,2,1,3,7]=>[1,2,1,3]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[5,2,1,3,4,6,7]=>[1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[7,2,1,3,4,5,6]=>[1,1,5]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[3,4,5,6,2,1,7]=>[4,1,2]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[4,5,6,2,1,3,7]=>[3,1,3]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[5,6,2,1,3,4,7]=>[2,1,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>[1,1,5]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[2,1,3,4,5,6,7]=>[1,6]
[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]=>[1,1,1,1,3]
[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]=>[2,1,1,3]
[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]=>[1,2,1,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[6,5,7,4,1,2,3]=>[1,2,1,3]
[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]=>[3,1,3]
[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]=>[1,1,2,3]
[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]=>[2,2,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[7,5,4,6,1,2,3]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[6,5,4,7,1,2,3]=>[1,1,2,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[5,4,6,7,1,2,3]=>[1,3,3]
[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]=>[1,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[5,6,4,7,1,2,3]=>[2,2,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[6,4,5,7,1,2,3]=>[1,3,3]
[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]=>[4,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[7,6,5,2,3,1,4]=>[1,1,1,2,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[6,7,5,2,3,1,4]=>[2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[7,5,6,2,3,1,4]=>[1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[6,5,7,2,3,1,4]=>[1,2,2,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[5,6,7,2,3,1,4]=>[3,2,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[7,6,4,2,3,1,5]=>[1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,7,4,2,3,1,5]=>[2,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[7,5,4,2,3,1,6]=>[1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[6,5,4,2,3,1,7]=>[1,1,1,2,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[5,4,2,3,1,6,7]=>[1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[7,4,2,3,1,5,6]=>[1,1,2,3]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>[2,1,2,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[6,4,2,3,1,5,7]=>[1,1,2,3]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[4,2,3,1,5,6,7]=>[1,2,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[7,6,2,3,1,4,5]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,7,2,3,1,4,5]=>[2,2,3]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[7,4,5,2,3,1,6]=>[1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[6,4,5,2,3,1,7]=>[1,2,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[4,5,2,3,1,6,7]=>[2,2,3]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[7,5,2,3,1,4,6]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[5,4,6,2,3,1,7]=>[1,2,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[6,5,2,3,1,4,7]=>[1,1,2,3]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[5,2,3,1,4,6,7]=>[1,2,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[7,2,3,1,4,5,6]=>[1,2,4]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[4,5,6,2,3,1,7]=>[3,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>[2,2,3]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,2,3,1,4,5,7]=>[1,2,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[2,3,1,4,5,6,7]=>[2,5]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[6,7,5,3,1,2,4]=>[2,1,1,3]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[7,5,6,3,1,2,4]=>[1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[6,5,7,3,1,2,4]=>[1,2,1,3]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[5,6,7,3,1,2,4]=>[3,1,3]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[7,6,3,2,4,1,5]=>[1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,7,3,2,4,1,5]=>[2,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[7,5,3,2,4,1,6]=>[1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[6,5,3,2,4,1,7]=>[1,1,1,2,2]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[5,3,2,4,1,6,7]=>[1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[7,3,2,4,1,5,6]=>[1,1,2,3]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[5,6,3,2,4,1,7]=>[2,1,2,2]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[6,3,2,4,1,5,7]=>[1,1,2,3]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[3,2,4,1,5,6,7]=>[1,2,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,7,4,3,1,2,5]=>[2,1,1,3]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[7,4,3,2,5,1,6]=>[1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[6,4,3,2,5,1,7]=>[1,1,1,2,2]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[5,6,4,3,1,2,7]=>[2,1,1,3]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[4,3,1,2,5,6,7]=>[1,1,5]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,7,3,1,2,4,5]=>[2,1,4]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[7,3,2,4,5,1,6]=>[1,1,3,2]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[6,3,2,4,5,1,7]=>[1,1,3,2]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[3,2,4,5,1,6,7]=>[1,3,3]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[7,4,5,3,1,2,6]=>[1,2,1,3]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[6,4,5,3,1,2,7]=>[1,2,1,3]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[4,5,3,1,2,6,7]=>[2,1,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>[1,1,3,2]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,4,6,3,1,2,7]=>[1,2,1,3]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>[1,1,5]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[7,3,1,2,4,5,6]=>[1,1,5]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[3,2,4,5,6,1,7]=>[1,4,2]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[4,5,6,3,1,2,7]=>[3,1,3]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[5,6,3,1,2,4,7]=>[2,1,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,3,1,2,4,5,7]=>[1,1,5]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[3,1,2,4,5,6,7]=>[1,6]
[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]=>[1,1,1,4]
[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]=>[2,1,4]
[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]=>[1,2,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[6,5,7,1,2,3,4]=>[1,2,4]
[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]=>[3,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[7,6,2,3,4,1,5]=>[1,1,3,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,7,2,3,4,1,5]=>[2,3,2]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[7,5,2,3,4,1,6]=>[1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[6,5,2,3,4,1,7]=>[1,1,3,2]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[5,2,3,4,1,6,7]=>[1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[7,2,3,4,1,5,6]=>[1,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[5,6,2,3,4,1,7]=>[2,3,2]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[6,2,3,4,1,5,7]=>[1,3,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[2,3,4,1,5,6,7]=>[3,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[7,6,3,4,1,2,5]=>[1,1,2,3]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,7,3,4,1,2,5]=>[2,2,3]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[7,3,4,2,5,1,6]=>[1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[6,3,4,2,5,1,7]=>[1,2,2,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[3,4,2,5,1,6,7]=>[2,2,3]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[7,5,3,4,1,2,6]=>[1,1,2,3]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[5,3,4,2,6,1,7]=>[1,2,2,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[6,5,3,4,1,2,7]=>[1,1,2,3]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[5,3,4,1,2,6,7]=>[1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[7,3,4,1,2,5,6]=>[1,2,4]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[3,4,2,5,6,1,7]=>[2,3,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[5,6,3,4,1,2,7]=>[2,2,3]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[6,3,4,1,2,5,7]=>[1,2,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[3,4,1,2,5,6,7]=>[2,5]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,7,4,1,2,3,5]=>[2,1,4]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[7,4,2,3,5,1,6]=>[1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[6,4,2,3,5,1,7]=>[1,1,3,2]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[4,2,3,5,1,6,7]=>[1,3,3]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[7,4,3,5,1,2,6]=>[1,1,2,3]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[6,4,3,5,1,2,7]=>[1,1,2,3]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>[1,2,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[5,4,2,3,6,1,7]=>[1,1,3,2]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[5,4,3,6,1,2,7]=>[1,1,2,3]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[5,4,1,2,3,6,7]=>[1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[7,4,1,2,3,5,6]=>[1,1,5]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>[1,4,2]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[4,3,5,6,1,2,7]=>[1,3,3]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[5,6,4,1,2,3,7]=>[2,1,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,4,1,2,3,5,7]=>[1,1,5]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>[1,6]
[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]=>[1,1,5]
[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]=>[2,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[7,2,3,4,5,1,6]=>[1,4,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[6,2,3,4,5,1,7]=>[1,4,2]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[2,3,4,5,1,6,7]=>[4,3]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[7,3,4,5,1,2,6]=>[1,3,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[3,2,2]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[6,3,4,5,1,2,7]=>[1,3,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>[3,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[7,4,5,1,2,3,6]=>[1,2,4]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[4,5,2,3,6,1,7]=>[2,3,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[4,5,3,6,1,2,7]=>[2,2,3]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[6,4,5,1,2,3,7]=>[1,2,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[4,5,1,2,3,6,7]=>[2,5]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[7,5,1,2,3,4,6]=>[1,1,5]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,2,3,4,6,1,7]=>[1,4,2]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,3,4,6,1,2,7]=>[1,3,3]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,4,6,1,2,3,7]=>[1,2,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[6,5,1,2,3,4,7]=>[1,1,5]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[5,1,2,3,4,6,7]=>[1,6]
[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]=>[1,6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[5,2]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[3,4,5,6,1,2,7]=>[4,3]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[4,5,6,1,2,3,7]=>[3,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[5,6,1,2,3,4,7]=>[2,5]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,1,2,3,4,5,7]=>[1,6]
[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]=>[7]
Map
to 312-avoiding permutation
Description
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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