Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
St000369: Dyck paths ⟶ ℤ
Values
=>
Cc0002;cc-rep-0
Cc0005;cc-rep
[1]=>[1,0,1,0]=>0
[2]=>[1,1,0,0,1,0]=>0
[1,1]=>[1,0,1,1,0,0]=>1
[3]=>[1,1,1,0,0,0,1,0]=>1
[2,1]=>[1,0,1,0,1,0]=>0
[1,1,1]=>[1,0,1,1,1,0,0,0]=>2
[4]=>[1,1,1,1,0,0,0,0,1,0]=>2
[3,1]=>[1,1,0,1,0,0,1,0]=>0
[2,2]=>[1,1,0,0,1,1,0,0]=>1
[2,1,1]=>[1,0,1,1,0,1,0,0]=>2
[1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0]=>3
[5]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>3
[4,1]=>[1,1,1,0,1,0,0,0,1,0]=>2
[3,2]=>[1,1,0,0,1,0,1,0]=>0
[3,1,1]=>[1,0,1,1,0,0,1,0]=>1
[2,2,1]=>[1,0,1,0,1,1,0,0]=>2
[2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0]=>3
[1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>4
[6]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>4
[5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>3
[4,2]=>[1,1,1,0,0,1,0,0,1,0]=>1
[4,1,1]=>[1,1,0,1,1,0,0,0,1,0]=>2
[3,3]=>[1,1,1,0,0,0,1,1,0,0]=>2
[3,2,1]=>[1,0,1,0,1,0,1,0]=>0
[3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0]=>3
[2,2,2]=>[1,1,0,0,1,1,1,0,0,0]=>3
[2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0]=>4
[2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>4
[1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>5
[6,1]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>4
[5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>3
[5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>4
[4,3]=>[1,1,1,0,0,0,1,0,1,0]=>2
[4,2,1]=>[1,1,0,1,0,1,0,0,1,0]=>0
[4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0]=>3
[3,3,1]=>[1,1,0,1,0,0,1,1,0,0]=>1
[3,2,2]=>[1,1,0,0,1,1,0,1,0,0]=>2
[3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0]=>3
[3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>4
[2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0]=>4
[2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>5
[2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>5
[1,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>6
[6,2]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>4
[6,1,1]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>5
[5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>3
[5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>3
[5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>4
[4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>4
[4,3,1]=>[1,1,0,1,0,0,1,0,1,0]=>0
[4,2,2]=>[1,1,0,0,1,1,0,0,1,0]=>1
[4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0]=>2
[4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>5
[3,3,2]=>[1,1,0,0,1,0,1,1,0,0]=>2
[3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0]=>3
[3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0]=>4
[3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>4
[3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>5
[2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>5
[2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>6
[2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>6
[2,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>6
[6,3]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>5
[6,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>4
[6,1,1,1]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>6
[5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>4
[5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>2
[5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>3
[5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>4
[5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>5
[4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>3
[4,3,2]=>[1,1,0,0,1,0,1,0,1,0]=>0
[4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0]=>1
[4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0]=>2
[4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>4
[4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>6
[3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>4
[3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0]=>3
[3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>5
[3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>5
[3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>6
[3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>5
[3,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>6
[2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>6
[2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>7
[2,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>7
[6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>5
[6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>4
[6,2,2]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>5
[6,2,1,1]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>6
[6,1,1,1,1]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>6
[5,5]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>6
[5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>4
[5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>1
[5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>2
[5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>3
[5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>5
[5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>7
[4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>2
[4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>3
[4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>3
[4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0]=>0
[4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>4
[4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>4
[4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>5
[4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>5
[4,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>7
[3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>4
[3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>5
[3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>6
[3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>6
[3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>6
[3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>7
[3,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>6
[2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>7
[2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>8
[2,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>8
[6,5]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>6
[6,4,1]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>5
[6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>4
[6,3,1,1]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>5
[6,2,2,1]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>6
[6,2,1,1,1]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>6
[6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>7
[5,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>6
[5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>2
[5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>3
[5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>3
[5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>0
[5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>4
[5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>4
[5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>5
[5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>7
[5,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>8
[4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>4
[4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>1
[4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>5
[4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>2
[4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>3
[4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>4
[4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>5
[4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>6
[4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>6
[4,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>6
[3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>5
[3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>6
[3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>7
[3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>7
[3,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>7
[3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>7
[3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>8
[3,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>8
[2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>8
[2,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>9
[6,5,1]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>6
[6,4,2]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>4
[6,4,1,1]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>5
[6,3,3]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>5
[6,3,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>4
[6,3,1,1,1]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>6
[6,2,2,2]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>6
[6,2,2,1,1]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>7
[6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>7
[6,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>9
[5,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>5
[5,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>6
[5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>3
[5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>0
[5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>4
[5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>1
[5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>2
[5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>3
[5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>6
[5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>5
[5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>7
[5,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>8
[4,4,4]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>6
[4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>2
[4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>3
[4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>4
[4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>7
[4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>4
[4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>5
[4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>6
[4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>5
[4,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>6
[4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>7
[4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>8
[4,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>7
[3,3,3,3]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>7
[3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>6
[3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>8
[3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>8
[3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>9
[3,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>8
[3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>8
[3,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>9
[2,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>9
[2,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>10
[7,1,1,1,1,1,1]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>9
[6,5,2]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>6
[6,5,1,1]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>7
[6,4,3]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>4
[6,4,2,1]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>3
[6,4,1,1,1]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>5
[6,3,3,1]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>4
[6,3,2,2]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>5
[6,3,2,1,1]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>6
[6,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>7
[6,2,2,2,1]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>6
[6,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>8
[6,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>9
[5,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>5
[5,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>4
[5,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>6
[5,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>6
[5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>0
[5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>1
[5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>2
[5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>7
[5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>2
[5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>3
[5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>4
[5,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>5
[5,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>7
[5,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>7
[5,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>8
[5,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>8
[4,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>5
[4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>3
[4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>4
[4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>5
[4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>6
[4,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>8
[4,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>6
[4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>6
[4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>7
[4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>7
[4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>8
[4,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>6
[4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>8
[4,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>9
[3,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>7
[3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>8
[3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>9
[3,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>9
[3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>9
[3,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>10
[3,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>9
[3,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>10
[2,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>10
[7,2,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>9
[6,5,3]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>5
[6,5,2,1]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>6
[6,5,1,1,1]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>6
[6,4,4]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>6
[6,4,3,1]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,2]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>3
[6,4,2,1,1]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>4
[6,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>7
[6,3,3,2]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>4
[6,3,3,1,1]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>5
[6,3,2,2,1]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>6
[6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>7
[6,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>9
[6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>7
[6,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>8
[6,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>10
[5,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>7
[5,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>3
[5,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>4
[5,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>5
[5,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>8
[5,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>4
[5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>0
[5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>2
[5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>5
[5,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>8
[5,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>5
[5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>3
[5,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>6
[5,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>6
[5,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>7
[5,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>6
[5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>9
[5,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>9
[4,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>5
[4,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>6
[4,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>6
[4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>4
[4,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>7
[4,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>7
[4,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>8
[4,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>7
[4,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>7
[4,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>8
[4,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>9
[4,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>8
[4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>8
[4,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>9
[4,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>9
[4,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>10
[3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>8
[3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>9
[3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>10
[3,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>10
[3,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>10
[3,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>11
[3,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>10
[7,3,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>9
[7,2,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>10
[6,5,4]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>6
[6,5,3,1]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>4
[6,5,2,2]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>5
[6,5,2,1,1]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>6
[6,5,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>7
[6,4,4,1]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>5
[6,4,3,2]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>1
[6,4,3,1,1]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>2
[6,4,2,2,1]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>3
[6,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>6
[6,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>9
[6,3,3,3]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>6
[6,3,3,2,1]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>4
[6,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>7
[6,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>7
[6,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>8
[6,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>9
[6,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>8
[6,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>10
[5,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>6
[5,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>2
[5,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>3
[5,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>4
[5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>7
[5,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>10
[5,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>3
[5,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>4
[5,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>4
[5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>0
[5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>5
[5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>5
[5,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>6
[5,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>6
[5,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>5
[5,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>6
[5,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>7
[5,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>7
[5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>8
[5,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>8
[5,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>10
[5,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>11
[4,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>7
[4,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>5
[4,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>8
[4,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>6
[4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>7
[4,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>8
[4,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>8
[4,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>9
[4,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>9
[4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>8
[4,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>9
[4,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>10
[4,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>10
[4,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>9
[4,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>10
[4,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>10
[3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>9
[3,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>11
[3,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>11
[3,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>12
[3,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>11
[7,4,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>10
[7,3,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>9
[7,2,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>11
[6,5,4,1]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>6
[6,5,3,2]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>2
[6,5,3,1,1]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>3
[6,5,2,2,1]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>4
[6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>7
[6,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>10
[6,4,4,2]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>3
[6,4,4,1,1]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>4
[6,4,3,3]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>4
[6,4,3,2,1]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>0
[6,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>5
[6,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>5
[6,4,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>6
[6,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>8
[6,3,3,3,1]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>5
[6,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>6
[6,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>7
[6,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>9
[6,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>8
[6,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>10
[6,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>10
[6,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>11
[5,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>4
[5,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>5
[5,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>5
[5,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>1
[5,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>6
[5,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>6
[5,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>7
[5,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>9
[5,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>6
[5,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>2
[5,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>7
[5,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>3
[5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>4
[5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[5,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>6
[5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>8
[5,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>7
[5,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>7
[5,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>8
[5,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>9
[5,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>8
[5,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>9
[5,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>10
[5,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>11
[4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>6
[4,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>7
[4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>8
[4,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>10
[4,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>8
[4,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>9
[4,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>10
[4,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>9
[4,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>10
[4,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>11
[4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>9
[4,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>11
[4,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>11
[4,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>12
[4,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>10
[3,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>11
[3,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>12
[3,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>12
[7,5,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>10
[7,4,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>9
[7,3,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>10
[7,3,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>11
[7,2,2,2,2,2]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>10
[7,2,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>11
[6,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>11
[6,5,4,2]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>3
[6,5,4,1,1]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>4
[6,5,3,3]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>4
[6,5,3,2,1]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>0
[6,5,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>5
[6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>5
[6,5,2,2,1,1]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>6
[6,5,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>10
[6,4,4,3]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>5
[6,4,4,2,1]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>1
[6,4,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>6
[6,4,3,3,1]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>2
[6,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>3
[6,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>4
[6,4,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>7
[6,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>7
[6,4,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>8
[6,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>6
[6,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>7
[6,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>8
[6,3,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>9
[6,3,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>10
[6,3,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>11
[6,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>12
[5,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>6
[5,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>2
[5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>7
[5,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>3
[5,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>4
[5,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>5
[5,5,3,1,1,1,1]=>[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>8
[5,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>8
[5,5,2,2,1,1,1]=>[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>9
[5,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>4
[5,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>5
[5,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>6
[5,4,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>9
[5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>6
[5,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>7
[5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[5,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>6
[5,4,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>9
[5,4,2,2,2,1,1]=>[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>10
[5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>9
[5,3,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>10
[5,3,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>10
[5,3,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>11
[5,3,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>10
[4,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>7
[4,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>8
[4,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>9
[4,4,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>10
[4,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>10
[4,4,3,3,1,1,1]=>[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>11
[4,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>11
[4,4,3,2,2,1,1]=>[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>12
[4,4,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>11
[4,3,3,3,2,2]=>[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>11
[4,3,3,3,2,1,1]=>[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>12
[4,3,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>12
[3,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>11
[3,3,3,3,3,1,1]=>[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>12
[3,3,3,3,2,2,1]=>[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>13
[6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>8
[6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[5,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>7
[6,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>6
[5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[6,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>7
[6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>2
[5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>6
[6,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>5
[5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>8
[6,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>4
[5,5,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>7
[6,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>6
[6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>6
[6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>1
[5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>5
[6,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>4
[5,4,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>7
[6,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>3
[5,5,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>6
[6,4,3,3,1,1]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>5
[6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>2
[5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>5
[6,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>4
[6,5,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>3
[6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>5
[6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>3
[5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[6,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>2
[5,5,3,3,2]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>5
[6,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>4
[6,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>1
[5,5,4,2,2]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>4
[6,4,4,2,2]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>3
[6,5,3,2,2]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>2
[6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>0
[5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>3
[6,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>2
[6,5,3,3,1]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>1
[6,5,4,2,1]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>0
[6,5,4,3]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>4
[7,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[6,6,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>6
[7,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>5
[6,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>10
[5,5,5,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>10
[7,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>4
[6,6,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>9
[7,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>8
[6,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>12
[5,5,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>13
[7,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>9
[6,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>12
[5,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>12
[4,4,4,4,3,2,1]=>[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>12
[6,6,5,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>8
[6,5,4,3,3,2,1]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>12
[6,5,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>12
[6,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>12
[5,4,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>12
[6,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>13
[3,3,3,3,3,2,1]=>[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>12
[6,6,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>7
[6,5,5,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>10
[6,5,4,4,2,2,1]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>11
[6,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>10
[5,5,4,3,2,2,1]=>[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>13
[7,6,5,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>7
[6,5,4,2,2,2,1]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>10
[6,5,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>10
[6,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>10
[5,4,3,2,2,2,1]=>[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>10
[6,5,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>12
[7,2,2,2,2,2,1]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>11
[7,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>1
[6,6,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>6
[6,5,5,4,3,1,1]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>9
[6,6,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>6
[6,5,5,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>8
[4,4,4,4,2,1,1]=>[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>12
[6,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>6
[5,5,4,3,2,1,1]=>[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>10
[7,6,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>6
[6,5,5,4,1,1,1]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>10
[6,5,4,3,1,1,1]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>6
[7,6,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>9
[5,5,5,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>10
[7,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>7
[6,5,4,2,1,1,1]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>6
[7,6,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>10
[7,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>9
[6,4,3,2,1,1,1]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>6
[6,5,4,1,1,1,1]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>9
[6,6,2,1,1,1,1]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>11
[7,6,1,1,1,1,1]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>10
[7,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>0
[6,6,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>5
[7,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>4
[6,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>8
[5,5,5,4,3,2]=>[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>9
[7,6,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>3
[6,5,4,4,3,2]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>9
[6,5,4,3,3,2]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>8
[5,4,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>11
[4,3,3,3,3,2]=>[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>11
[6,5,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>5
[4,4,4,3,2,2]=>[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>11
[7,6,5,2,2,2]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>6
[6,5,4,2,2,2]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>6
[5,4,3,2,2,2]=>[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>9
[6,6,2,2,2,2]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>10
[7,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>0
[6,6,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>4
[6,5,5,4,3,1]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>6
[4,4,4,4,3,1]=>[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>10
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Description
The dinv deficit of a Dyck path.
For a Dyck path $D$ of semilength $n$, this is defined as
$$\binom{n}{2} - \operatorname{area}(D) - \operatorname{dinv}(D).$$
In other words, this is the number of boxes in the partition traced out by $D$ for which the leg-length minus the arm-length is not in $\{0,1\}$.
See also St000376The bounce deficit of a Dyck path. for the bounce deficit.
For a Dyck path $D$ of semilength $n$, this is defined as
$$\binom{n}{2} - \operatorname{area}(D) - \operatorname{dinv}(D).$$
In other words, this is the number of boxes in the partition traced out by $D$ for which the leg-length minus the arm-length is not in $\{0,1\}$.
See also St000376The bounce deficit of a Dyck path. for the bounce deficit.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
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