Identifier
-
Mp00138:
Dyck paths
—to noncrossing partition⟶
Set partitions
St000577: Set partitions ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0009;cc-rep
[1,0,1,0]=>{{1},{2}}=>1
[1,1,0,0]=>{{1,2}}=>0
[1,0,1,0,1,0]=>{{1},{2},{3}}=>3
[1,0,1,1,0,0]=>{{1},{2,3}}=>2
[1,1,0,0,1,0]=>{{1,2},{3}}=>1
[1,1,0,1,0,0]=>{{1,3},{2}}=>1
[1,1,1,0,0,0]=>{{1,2,3}}=>0
[1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4}}=>6
[1,0,1,0,1,1,0,0]=>{{1},{2},{3,4}}=>5
[1,0,1,1,0,0,1,0]=>{{1},{2,3},{4}}=>4
[1,0,1,1,0,1,0,0]=>{{1},{2,4},{3}}=>4
[1,0,1,1,1,0,0,0]=>{{1},{2,3,4}}=>3
[1,1,0,0,1,0,1,0]=>{{1,2},{3},{4}}=>3
[1,1,0,0,1,1,0,0]=>{{1,2},{3,4}}=>2
[1,1,0,1,0,0,1,0]=>{{1,3},{2},{4}}=>3
[1,1,0,1,0,1,0,0]=>{{1,4},{2},{3}}=>3
[1,1,0,1,1,0,0,0]=>{{1,3,4},{2}}=>2
[1,1,1,0,0,0,1,0]=>{{1,2,3},{4}}=>1
[1,1,1,0,0,1,0,0]=>{{1,4},{2,3}}=>1
[1,1,1,0,1,0,0,0]=>{{1,2,4},{3}}=>1
[1,1,1,1,0,0,0,0]=>{{1,2,3,4}}=>0
[1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5}}=>10
[1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4,5}}=>9
[1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5}}=>8
[1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3,5},{4}}=>8
[1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3,4,5}}=>7
[1,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4},{5}}=>7
[1,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5}}=>6
[1,0,1,1,0,1,0,0,1,0]=>{{1},{2,4},{3},{5}}=>7
[1,0,1,1,0,1,0,1,0,0]=>{{1},{2,5},{3},{4}}=>7
[1,0,1,1,0,1,1,0,0,0]=>{{1},{2,4,5},{3}}=>6
[1,0,1,1,1,0,0,0,1,0]=>{{1},{2,3,4},{5}}=>5
[1,0,1,1,1,0,0,1,0,0]=>{{1},{2,5},{3,4}}=>5
[1,0,1,1,1,0,1,0,0,0]=>{{1},{2,3,5},{4}}=>5
[1,0,1,1,1,1,0,0,0,0]=>{{1},{2,3,4,5}}=>4
[1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5}}=>6
[1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3},{4,5}}=>5
[1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5}}=>4
[1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,5},{4}}=>4
[1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4,5}}=>3
[1,1,0,1,0,0,1,0,1,0]=>{{1,3},{2},{4},{5}}=>6
[1,1,0,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5}}=>5
[1,1,0,1,0,1,0,0,1,0]=>{{1,4},{2},{3},{5}}=>6
[1,1,0,1,0,1,0,1,0,0]=>{{1,5},{2},{3},{4}}=>6
[1,1,0,1,0,1,1,0,0,0]=>{{1,4,5},{2},{3}}=>5
[1,1,0,1,1,0,0,0,1,0]=>{{1,3,4},{2},{5}}=>4
[1,1,0,1,1,0,0,1,0,0]=>{{1,5},{2},{3,4}}=>4
[1,1,0,1,1,0,1,0,0,0]=>{{1,3,5},{2},{4}}=>4
[1,1,0,1,1,1,0,0,0,0]=>{{1,3,4,5},{2}}=>3
[1,1,1,0,0,0,1,0,1,0]=>{{1,2,3},{4},{5}}=>3
[1,1,1,0,0,0,1,1,0,0]=>{{1,2,3},{4,5}}=>2
[1,1,1,0,0,1,0,0,1,0]=>{{1,4},{2,3},{5}}=>3
[1,1,1,0,0,1,0,1,0,0]=>{{1,5},{2,3},{4}}=>3
[1,1,1,0,0,1,1,0,0,0]=>{{1,4,5},{2,3}}=>2
[1,1,1,0,1,0,0,0,1,0]=>{{1,2,4},{3},{5}}=>3
[1,1,1,0,1,0,0,1,0,0]=>{{1,5},{2,4},{3}}=>3
[1,1,1,0,1,0,1,0,0,0]=>{{1,2,5},{3},{4}}=>3
[1,1,1,0,1,1,0,0,0,0]=>{{1,2,4,5},{3}}=>2
[1,1,1,1,0,0,0,0,1,0]=>{{1,2,3,4},{5}}=>1
[1,1,1,1,0,0,0,1,0,0]=>{{1,5},{2,3,4}}=>1
[1,1,1,1,0,0,1,0,0,0]=>{{1,2,5},{3,4}}=>1
[1,1,1,1,0,1,0,0,0,0]=>{{1,2,3,5},{4}}=>1
[1,1,1,1,1,0,0,0,0,0]=>{{1,2,3,4,5}}=>0
[1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6}}=>15
[1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5,6}}=>14
[1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4,5},{6}}=>13
[1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4,6},{5}}=>13
[1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4,5,6}}=>12
[1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6}}=>12
[1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3,4},{5,6}}=>11
[1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3,5},{4},{6}}=>12
[1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3,6},{4},{5}}=>12
[1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3,5,6},{4}}=>11
[1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3,4,5},{6}}=>10
[1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3,6},{4,5}}=>10
[1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3,4,6},{5}}=>10
[1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3,4,5,6}}=>9
[1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6}}=>11
[1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5,6}}=>10
[1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2,3},{4,5},{6}}=>9
[1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2,3},{4,6},{5}}=>9
[1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2,3},{4,5,6}}=>8
[1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6}}=>11
[1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2,4},{3},{5,6}}=>10
[1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2,5},{3},{4},{6}}=>11
[1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2,6},{3},{4},{5}}=>11
[1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2,5,6},{3},{4}}=>10
[1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2,4,5},{3},{6}}=>9
[1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2,6},{3},{4,5}}=>9
[1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2,4,6},{3},{5}}=>9
[1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2,4,5,6},{3}}=>8
[1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2,3,4},{5},{6}}=>8
[1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2,3,4},{5,6}}=>7
[1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2,5},{3,4},{6}}=>8
[1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2,6},{3,4},{5}}=>8
[1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2,5,6},{3,4}}=>7
[1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2,3,5},{4},{6}}=>8
[1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2,6},{3,5},{4}}=>8
[1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2,3,6},{4},{5}}=>8
[1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2,3,5,6},{4}}=>7
[1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2,3,4,5},{6}}=>6
[1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2,6},{3,4,5}}=>6
[1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2,3,6},{4,5}}=>6
[1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2,3,4,6},{5}}=>6
[1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2,3,4,5,6}}=>5
[1,1,0,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6}}=>10
[1,1,0,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5,6}}=>9
[1,1,0,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4,5},{6}}=>8
[1,1,0,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4,6},{5}}=>8
[1,1,0,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4,5,6}}=>7
[1,1,0,0,1,1,0,0,1,0,1,0]=>{{1,2},{3,4},{5},{6}}=>7
[1,1,0,0,1,1,0,0,1,1,0,0]=>{{1,2},{3,4},{5,6}}=>6
[1,1,0,0,1,1,0,1,0,0,1,0]=>{{1,2},{3,5},{4},{6}}=>7
[1,1,0,0,1,1,0,1,0,1,0,0]=>{{1,2},{3,6},{4},{5}}=>7
[1,1,0,0,1,1,0,1,1,0,0,0]=>{{1,2},{3,5,6},{4}}=>6
[1,1,0,0,1,1,1,0,0,0,1,0]=>{{1,2},{3,4,5},{6}}=>5
[1,1,0,0,1,1,1,0,0,1,0,0]=>{{1,2},{3,6},{4,5}}=>5
[1,1,0,0,1,1,1,0,1,0,0,0]=>{{1,2},{3,4,6},{5}}=>5
[1,1,0,0,1,1,1,1,0,0,0,0]=>{{1,2},{3,4,5,6}}=>4
[1,1,0,1,0,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6}}=>10
[1,1,0,1,0,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5,6}}=>9
[1,1,0,1,0,0,1,1,0,0,1,0]=>{{1,3},{2},{4,5},{6}}=>8
[1,1,0,1,0,0,1,1,0,1,0,0]=>{{1,3},{2},{4,6},{5}}=>8
[1,1,0,1,0,0,1,1,1,0,0,0]=>{{1,3},{2},{4,5,6}}=>7
[1,1,0,1,0,1,0,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6}}=>10
[1,1,0,1,0,1,0,0,1,1,0,0]=>{{1,4},{2},{3},{5,6}}=>9
[1,1,0,1,0,1,0,1,0,0,1,0]=>{{1,5},{2},{3},{4},{6}}=>10
[1,1,0,1,0,1,0,1,0,1,0,0]=>{{1,6},{2},{3},{4},{5}}=>10
[1,1,0,1,0,1,0,1,1,0,0,0]=>{{1,5,6},{2},{3},{4}}=>9
[1,1,0,1,0,1,1,0,0,0,1,0]=>{{1,4,5},{2},{3},{6}}=>8
[1,1,0,1,0,1,1,0,0,1,0,0]=>{{1,6},{2},{3},{4,5}}=>8
[1,1,0,1,0,1,1,0,1,0,0,0]=>{{1,4,6},{2},{3},{5}}=>8
[1,1,0,1,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2},{3}}=>7
[1,1,0,1,1,0,0,0,1,0,1,0]=>{{1,3,4},{2},{5},{6}}=>7
[1,1,0,1,1,0,0,0,1,1,0,0]=>{{1,3,4},{2},{5,6}}=>6
[1,1,0,1,1,0,0,1,0,0,1,0]=>{{1,5},{2},{3,4},{6}}=>7
[1,1,0,1,1,0,0,1,0,1,0,0]=>{{1,6},{2},{3,4},{5}}=>7
[1,1,0,1,1,0,0,1,1,0,0,0]=>{{1,5,6},{2},{3,4}}=>6
[1,1,0,1,1,0,1,0,0,0,1,0]=>{{1,3,5},{2},{4},{6}}=>7
[1,1,0,1,1,0,1,0,0,1,0,0]=>{{1,6},{2},{3,5},{4}}=>7
[1,1,0,1,1,0,1,0,1,0,0,0]=>{{1,3,6},{2},{4},{5}}=>7
[1,1,0,1,1,0,1,1,0,0,0,0]=>{{1,3,5,6},{2},{4}}=>6
[1,1,0,1,1,1,0,0,0,0,1,0]=>{{1,3,4,5},{2},{6}}=>5
[1,1,0,1,1,1,0,0,0,1,0,0]=>{{1,6},{2},{3,4,5}}=>5
[1,1,0,1,1,1,0,0,1,0,0,0]=>{{1,3,6},{2},{4,5}}=>5
[1,1,0,1,1,1,0,1,0,0,0,0]=>{{1,3,4,6},{2},{5}}=>5
[1,1,0,1,1,1,1,0,0,0,0,0]=>{{1,3,4,5,6},{2}}=>4
[1,1,1,0,0,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6}}=>6
[1,1,1,0,0,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5,6}}=>5
[1,1,1,0,0,0,1,1,0,0,1,0]=>{{1,2,3},{4,5},{6}}=>4
[1,1,1,0,0,0,1,1,0,1,0,0]=>{{1,2,3},{4,6},{5}}=>4
[1,1,1,0,0,0,1,1,1,0,0,0]=>{{1,2,3},{4,5,6}}=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>{{1,4},{2,3},{5},{6}}=>6
[1,1,1,0,0,1,0,0,1,1,0,0]=>{{1,4},{2,3},{5,6}}=>5
[1,1,1,0,0,1,0,1,0,0,1,0]=>{{1,5},{2,3},{4},{6}}=>6
[1,1,1,0,0,1,0,1,0,1,0,0]=>{{1,6},{2,3},{4},{5}}=>6
[1,1,1,0,0,1,0,1,1,0,0,0]=>{{1,5,6},{2,3},{4}}=>5
[1,1,1,0,0,1,1,0,0,0,1,0]=>{{1,4,5},{2,3},{6}}=>4
[1,1,1,0,0,1,1,0,0,1,0,0]=>{{1,6},{2,3},{4,5}}=>4
[1,1,1,0,0,1,1,0,1,0,0,0]=>{{1,4,6},{2,3},{5}}=>4
[1,1,1,0,0,1,1,1,0,0,0,0]=>{{1,4,5,6},{2,3}}=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>{{1,2,4},{3},{5},{6}}=>6
[1,1,1,0,1,0,0,0,1,1,0,0]=>{{1,2,4},{3},{5,6}}=>5
[1,1,1,0,1,0,0,1,0,0,1,0]=>{{1,5},{2,4},{3},{6}}=>6
[1,1,1,0,1,0,0,1,0,1,0,0]=>{{1,6},{2,4},{3},{5}}=>6
[1,1,1,0,1,0,0,1,1,0,0,0]=>{{1,5,6},{2,4},{3}}=>5
[1,1,1,0,1,0,1,0,0,0,1,0]=>{{1,2,5},{3},{4},{6}}=>6
[1,1,1,0,1,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3},{4}}=>6
[1,1,1,0,1,0,1,0,1,0,0,0]=>{{1,2,6},{3},{4},{5}}=>6
[1,1,1,0,1,0,1,1,0,0,0,0]=>{{1,2,5,6},{3},{4}}=>5
[1,1,1,0,1,1,0,0,0,0,1,0]=>{{1,2,4,5},{3},{6}}=>4
[1,1,1,0,1,1,0,0,0,1,0,0]=>{{1,6},{2,4,5},{3}}=>4
[1,1,1,0,1,1,0,0,1,0,0,0]=>{{1,2,6},{3},{4,5}}=>4
[1,1,1,0,1,1,0,1,0,0,0,0]=>{{1,2,4,6},{3},{5}}=>4
[1,1,1,0,1,1,1,0,0,0,0,0]=>{{1,2,4,5,6},{3}}=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>{{1,2,3,4},{5},{6}}=>3
[1,1,1,1,0,0,0,0,1,1,0,0]=>{{1,2,3,4},{5,6}}=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>{{1,5},{2,3,4},{6}}=>3
[1,1,1,1,0,0,0,1,0,1,0,0]=>{{1,6},{2,3,4},{5}}=>3
[1,1,1,1,0,0,0,1,1,0,0,0]=>{{1,5,6},{2,3,4}}=>2
[1,1,1,1,0,0,1,0,0,0,1,0]=>{{1,2,5},{3,4},{6}}=>3
[1,1,1,1,0,0,1,0,0,1,0,0]=>{{1,6},{2,5},{3,4}}=>3
[1,1,1,1,0,0,1,0,1,0,0,0]=>{{1,2,6},{3,4},{5}}=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>{{1,2,5,6},{3,4}}=>2
[1,1,1,1,0,1,0,0,0,0,1,0]=>{{1,2,3,5},{4},{6}}=>3
[1,1,1,1,0,1,0,0,0,1,0,0]=>{{1,6},{2,3,5},{4}}=>3
[1,1,1,1,0,1,0,0,1,0,0,0]=>{{1,2,6},{3,5},{4}}=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>{{1,2,3,6},{4},{5}}=>3
[1,1,1,1,0,1,1,0,0,0,0,0]=>{{1,2,3,5,6},{4}}=>2
[1,1,1,1,1,0,0,0,0,0,1,0]=>{{1,2,3,4,5},{6}}=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>{{1,6},{2,3,4,5}}=>1
[1,1,1,1,1,0,0,0,1,0,0,0]=>{{1,2,6},{3,4,5}}=>1
[1,1,1,1,1,0,0,1,0,0,0,0]=>{{1,2,3,6},{4,5}}=>1
[1,1,1,1,1,0,1,0,0,0,0,0]=>{{1,2,3,4,6},{5}}=>1
[1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2,3,4,5,6}}=>0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>{{1},{2},{3},{4},{5},{6},{7}}=>21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>{{1},{2},{3},{4},{5},{6,7}}=>20
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>{{1},{2},{3},{4},{5,6},{7}}=>19
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>{{1},{2},{3},{4},{5,7},{6}}=>19
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>{{1},{2},{3},{4},{5,6,7}}=>18
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>{{1},{2},{3},{4,5},{6},{7}}=>18
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>{{1},{2},{3},{4,5},{6,7}}=>17
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>{{1},{2},{3},{4,6},{5},{7}}=>18
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>{{1},{2},{3},{4,7},{5},{6}}=>18
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>{{1},{2},{3},{4,6,7},{5}}=>17
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>{{1},{2},{3},{4,5,6},{7}}=>16
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>{{1},{2},{3},{4,7},{5,6}}=>16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>{{1},{2},{3},{4,5,7},{6}}=>16
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>{{1},{2},{3},{4,5,6,7}}=>15
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>{{1},{2},{3,4},{5},{6},{7}}=>17
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>{{1},{2},{3,4},{5},{6,7}}=>16
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>{{1},{2},{3,4},{5,6},{7}}=>15
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>{{1},{2},{3,4},{5,7},{6}}=>15
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>{{1},{2},{3,4},{5,6,7}}=>14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>{{1},{2},{3,5},{4},{6},{7}}=>17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>{{1},{2},{3,5},{4},{6,7}}=>16
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>{{1},{2},{3,6},{4},{5},{7}}=>17
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>{{1},{2},{3,7},{4},{5},{6}}=>17
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4},{5}}=>16
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>{{1},{2},{3,5,6},{4},{7}}=>15
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>{{1},{2},{3,7},{4},{5,6}}=>15
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>{{1},{2},{3,5,7},{4},{6}}=>15
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>{{1},{2},{3,5,6,7},{4}}=>14
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>{{1},{2},{3,4,5},{6},{7}}=>14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>{{1},{2},{3,4,5},{6,7}}=>13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>{{1},{2},{3,6},{4,5},{7}}=>14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>{{1},{2},{3,7},{4,5},{6}}=>14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>{{1},{2},{3,6,7},{4,5}}=>13
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>{{1},{2},{3,4,6},{5},{7}}=>14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>{{1},{2},{3,7},{4,6},{5}}=>14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>{{1},{2},{3,4,7},{5},{6}}=>14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>{{1},{2},{3,4,6,7},{5}}=>13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>{{1},{2},{3,4,5,6},{7}}=>12
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>{{1},{2},{3,7},{4,5,6}}=>12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>{{1},{2},{3,4,7},{5,6}}=>12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>{{1},{2},{3,4,5,7},{6}}=>12
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7}}=>11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>{{1},{2,3},{4},{5},{6},{7}}=>16
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>{{1},{2,3},{4},{5},{6,7}}=>15
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>{{1},{2,3},{4},{5,6},{7}}=>14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>{{1},{2,3},{4},{5,7},{6}}=>14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>{{1},{2,3},{4},{5,6,7}}=>13
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>{{1},{2,3},{4,5},{6},{7}}=>13
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>{{1},{2,3},{4,5},{6,7}}=>12
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>{{1},{2,3},{4,6},{5},{7}}=>13
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>{{1},{2,3},{4,7},{5},{6}}=>13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>{{1},{2,3},{4,6,7},{5}}=>12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>{{1},{2,3},{4,5,6},{7}}=>11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>{{1},{2,3},{4,7},{5,6}}=>11
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>{{1},{2,3},{4,5,7},{6}}=>11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>{{1},{2,3},{4,5,6,7}}=>10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>{{1},{2,4},{3},{5},{6},{7}}=>16
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>{{1},{2,4},{3},{5},{6,7}}=>15
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>{{1},{2,4},{3},{5,6},{7}}=>14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>{{1},{2,4},{3},{5,7},{6}}=>14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>{{1},{2,4},{3},{5,6,7}}=>13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3},{4},{6},{7}}=>16
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3},{4},{6,7}}=>15
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3},{4},{5},{7}}=>16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3},{4},{5},{6}}=>16
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4},{5}}=>15
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3},{4},{7}}=>14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3},{4},{5,6}}=>14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3},{4},{6}}=>14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3},{4}}=>13
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>{{1},{2,4,5},{3},{6},{7}}=>13
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>{{1},{2,4,5},{3},{6,7}}=>12
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3},{4,5},{7}}=>13
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3},{4,5},{6}}=>13
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3},{4,5}}=>12
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>{{1},{2,4,6},{3},{5},{7}}=>13
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3},{4,6},{5}}=>13
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>{{1},{2,4,7},{3},{5},{6}}=>13
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>{{1},{2,4,6,7},{3},{5}}=>12
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>{{1},{2,4,5,6},{3},{7}}=>11
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3},{4,5,6}}=>11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>{{1},{2,4,7},{3},{5,6}}=>11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>{{1},{2,4,5,7},{3},{6}}=>11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>{{1},{2,4,5,6,7},{3}}=>10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>{{1},{2,3,4},{5},{6},{7}}=>12
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>{{1},{2,3,4},{5},{6,7}}=>11
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>{{1},{2,3,4},{5,6},{7}}=>10
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>{{1},{2,3,4},{5,7},{6}}=>10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>{{1},{2,3,4},{5,6,7}}=>9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>{{1},{2,5},{3,4},{6},{7}}=>12
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>{{1},{2,5},{3,4},{6,7}}=>11
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>{{1},{2,6},{3,4},{5},{7}}=>12
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>{{1},{2,7},{3,4},{5},{6}}=>12
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4},{5}}=>11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>{{1},{2,5,6},{3,4},{7}}=>10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>{{1},{2,7},{3,4},{5,6}}=>10
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>{{1},{2,5,7},{3,4},{6}}=>10
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>{{1},{2,5,6,7},{3,4}}=>9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>{{1},{2,3,5},{4},{6},{7}}=>12
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>{{1},{2,3,5},{4},{6,7}}=>11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>{{1},{2,6},{3,5},{4},{7}}=>12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>{{1},{2,7},{3,5},{4},{6}}=>12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,5},{4}}=>11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4},{5},{7}}=>12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4},{5}}=>12
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4},{5},{6}}=>12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4},{5}}=>11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>{{1},{2,3,5,6},{4},{7}}=>10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>{{1},{2,7},{3,5,6},{4}}=>10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4},{5,6}}=>10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>{{1},{2,3,5,7},{4},{6}}=>10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>{{1},{2,3,5,6,7},{4}}=>9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>{{1},{2,3,4,5},{6},{7}}=>9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>{{1},{2,3,4,5},{6,7}}=>8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>{{1},{2,6},{3,4,5},{7}}=>9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>{{1},{2,7},{3,4,5},{6}}=>9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>{{1},{2,6,7},{3,4,5}}=>8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>{{1},{2,3,6},{4,5},{7}}=>9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>{{1},{2,7},{3,6},{4,5}}=>9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>{{1},{2,3,7},{4,5},{6}}=>9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>{{1},{2,3,6,7},{4,5}}=>8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>{{1},{2,3,4,6},{5},{7}}=>9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>{{1},{2,7},{3,4,6},{5}}=>9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>{{1},{2,3,7},{4,6},{5}}=>9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5},{6}}=>9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>{{1},{2,3,4,6,7},{5}}=>8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6},{7}}=>7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>{{1},{2,7},{3,4,5,6}}=>7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>{{1},{2,3,7},{4,5,6}}=>7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>{{1},{2,3,4,7},{5,6}}=>7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>{{1},{2,3,4,5,7},{6}}=>7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7}}=>6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>{{1,2},{3},{4},{5},{6},{7}}=>15
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>{{1,2},{3},{4},{5},{6,7}}=>14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>{{1,2},{3},{4},{5,6},{7}}=>13
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>{{1,2},{3},{4},{5,7},{6}}=>13
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>{{1,2},{3},{4},{5,6,7}}=>12
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>{{1,2},{3},{4,5},{6},{7}}=>12
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>{{1,2},{3},{4,5},{6,7}}=>11
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>{{1,2},{3},{4,6},{5},{7}}=>12
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>{{1,2},{3},{4,7},{5},{6}}=>12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>{{1,2},{3},{4,6,7},{5}}=>11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>{{1,2},{3},{4,5,6},{7}}=>10
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>{{1,2},{3},{4,7},{5,6}}=>10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>{{1,2},{3},{4,5,7},{6}}=>10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>{{1,2},{3},{4,5,6,7}}=>9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>{{1,2},{3,4},{5},{6},{7}}=>11
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>{{1,2},{3,4},{5},{6,7}}=>10
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>{{1,2},{3,4},{5,6},{7}}=>9
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>{{1,2},{3,4},{5,7},{6}}=>9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>{{1,2},{3,4},{5,6,7}}=>8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>{{1,2},{3,5},{4},{6},{7}}=>11
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>{{1,2},{3,5},{4},{6,7}}=>10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>{{1,2},{3,6},{4},{5},{7}}=>11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>{{1,2},{3,7},{4},{5},{6}}=>11
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4},{5}}=>10
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>{{1,2},{3,5,6},{4},{7}}=>9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>{{1,2},{3,7},{4},{5,6}}=>9
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>{{1,2},{3,5,7},{4},{6}}=>9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>{{1,2},{3,5,6,7},{4}}=>8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>{{1,2},{3,4,5},{6},{7}}=>8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>{{1,2},{3,4,5},{6,7}}=>7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>{{1,2},{3,6},{4,5},{7}}=>8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>{{1,2},{3,7},{4,5},{6}}=>8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>{{1,2},{3,6,7},{4,5}}=>7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>{{1,2},{3,4,6},{5},{7}}=>8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>{{1,2},{3,7},{4,6},{5}}=>8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>{{1,2},{3,4,7},{5},{6}}=>8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>{{1,2},{3,4,6,7},{5}}=>7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>{{1,2},{3,4,5,6},{7}}=>6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>{{1,2},{3,7},{4,5,6}}=>6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>{{1,2},{3,4,7},{5,6}}=>6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>{{1,2},{3,4,5,7},{6}}=>6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>{{1,2},{3,4,5,6,7}}=>5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>{{1,3},{2},{4},{5},{6},{7}}=>15
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>{{1,3},{2},{4},{5},{6,7}}=>14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>{{1,3},{2},{4},{5,6},{7}}=>13
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>{{1,3},{2},{4},{5,7},{6}}=>13
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>{{1,3},{2},{4},{5,6,7}}=>12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>{{1,3},{2},{4,5},{6},{7}}=>12
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>{{1,3},{2},{4,5},{6,7}}=>11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>{{1,3},{2},{4,6},{5},{7}}=>12
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>{{1,3},{2},{4,7},{5},{6}}=>12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>{{1,3},{2},{4,6,7},{5}}=>11
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>{{1,3},{2},{4,5,6},{7}}=>10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>{{1,3},{2},{4,7},{5,6}}=>10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>{{1,3},{2},{4,5,7},{6}}=>10
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>{{1,3},{2},{4,5,6,7}}=>9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2},{3},{5},{6},{7}}=>15
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2},{3},{5},{6,7}}=>14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2},{3},{5,6},{7}}=>13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2},{3},{5,7},{6}}=>13
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2},{3},{5,6,7}}=>12
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3},{4},{6},{7}}=>15
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3},{4},{6,7}}=>14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3},{4},{5},{7}}=>15
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3},{4},{5},{6}}=>15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4},{5}}=>14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3},{4},{7}}=>13
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3},{4},{5,6}}=>13
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3},{4},{6}}=>13
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3},{4}}=>12
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2},{3},{6},{7}}=>12
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2},{3},{6,7}}=>11
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3},{4,5},{7}}=>12
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3},{4,5},{6}}=>12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3},{4,5}}=>11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2},{3},{5},{7}}=>12
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3},{4,6},{5}}=>12
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2},{3},{5},{6}}=>12
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2},{3},{5}}=>11
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2},{3},{7}}=>10
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3},{4,5,6}}=>10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2},{3},{5,6}}=>10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2},{3},{6}}=>10
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2},{3}}=>9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>{{1,3,4},{2},{5},{6},{7}}=>11
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>{{1,3,4},{2},{5},{6,7}}=>10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>{{1,3,4},{2},{5,6},{7}}=>9
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>{{1,3,4},{2},{5,7},{6}}=>9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>{{1,3,4},{2},{5,6,7}}=>8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2},{3,4},{6},{7}}=>11
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2},{3,4},{6,7}}=>10
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2},{3,4},{5},{7}}=>11
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2},{3,4},{5},{6}}=>11
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4},{5}}=>10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2},{3,4},{7}}=>9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2},{3,4},{5,6}}=>9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2},{3,4},{6}}=>9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2},{3,4}}=>8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>{{1,3,5},{2},{4},{6},{7}}=>11
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>{{1,3,5},{2},{4},{6,7}}=>10
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2},{3,5},{4},{7}}=>11
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2},{3,5},{4},{6}}=>11
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,5},{4}}=>10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4},{5},{7}}=>11
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4},{5}}=>11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4},{5},{6}}=>11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4},{5}}=>10
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>{{1,3,5,6},{2},{4},{7}}=>9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2},{3,5,6},{4}}=>9
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4},{5,6}}=>9
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>{{1,3,5,7},{2},{4},{6}}=>9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>{{1,3,5,6,7},{2},{4}}=>8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>{{1,3,4,5},{2},{6},{7}}=>8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>{{1,3,4,5},{2},{6,7}}=>7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2},{3,4,5},{7}}=>8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2},{3,4,5},{6}}=>8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2},{3,4,5}}=>7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>{{1,3,6},{2},{4,5},{7}}=>8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2},{3,6},{4,5}}=>8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>{{1,3,7},{2},{4,5},{6}}=>8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>{{1,3,6,7},{2},{4,5}}=>7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>{{1,3,4,6},{2},{5},{7}}=>8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2},{3,4,6},{5}}=>8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>{{1,3,7},{2},{4,6},{5}}=>8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5},{6}}=>8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>{{1,3,4,6,7},{2},{5}}=>7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>{{1,3,4,5,6},{2},{7}}=>6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2},{3,4,5,6}}=>6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>{{1,3,7},{2},{4,5,6}}=>6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>{{1,3,4,7},{2},{5,6}}=>6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>{{1,3,4,5,7},{2},{6}}=>6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,3,4,5,6,7},{2}}=>5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>{{1,2,3},{4},{5},{6},{7}}=>10
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>{{1,2,3},{4},{5},{6,7}}=>9
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>{{1,2,3},{4},{5,6},{7}}=>8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>{{1,2,3},{4},{5,7},{6}}=>8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>{{1,2,3},{4},{5,6,7}}=>7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>{{1,2,3},{4,5},{6},{7}}=>7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>{{1,2,3},{4,5},{6,7}}=>6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>{{1,2,3},{4,6},{5},{7}}=>7
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>{{1,2,3},{4,7},{5},{6}}=>7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>{{1,2,3},{4,6,7},{5}}=>6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>{{1,2,3},{4,5,6},{7}}=>5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>{{1,2,3},{4,7},{5,6}}=>5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>{{1,2,3},{4,5,7},{6}}=>5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>{{1,2,3},{4,5,6,7}}=>4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>{{1,4},{2,3},{5},{6},{7}}=>10
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>{{1,4},{2,3},{5},{6,7}}=>9
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>{{1,4},{2,3},{5,6},{7}}=>8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>{{1,4},{2,3},{5,7},{6}}=>8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>{{1,4},{2,3},{5,6,7}}=>7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>{{1,5},{2,3},{4},{6},{7}}=>10
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>{{1,5},{2,3},{4},{6,7}}=>9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>{{1,6},{2,3},{4},{5},{7}}=>10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>{{1,7},{2,3},{4},{5},{6}}=>10
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4},{5}}=>9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3},{4},{7}}=>8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>{{1,7},{2,3},{4},{5,6}}=>8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3},{4},{6}}=>8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3},{4}}=>7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>{{1,4,5},{2,3},{6},{7}}=>7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>{{1,4,5},{2,3},{6,7}}=>6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>{{1,6},{2,3},{4,5},{7}}=>7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>{{1,7},{2,3},{4,5},{6}}=>7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,3},{4,5}}=>6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>{{1,4,6},{2,3},{5},{7}}=>7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>{{1,7},{2,3},{4,6},{5}}=>7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>{{1,4,7},{2,3},{5},{6}}=>7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>{{1,4,6,7},{2,3},{5}}=>6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>{{1,4,5,6},{2,3},{7}}=>5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>{{1,7},{2,3},{4,5,6}}=>5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>{{1,4,7},{2,3},{5,6}}=>5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>{{1,4,5,7},{2,3},{6}}=>5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>{{1,4,5,6,7},{2,3}}=>4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>{{1,2,4},{3},{5},{6},{7}}=>10
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>{{1,2,4},{3},{5},{6,7}}=>9
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>{{1,2,4},{3},{5,6},{7}}=>8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>{{1,2,4},{3},{5,7},{6}}=>8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>{{1,2,4},{3},{5,6,7}}=>7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,4},{3},{6},{7}}=>10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,4},{3},{6,7}}=>9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,4},{3},{5},{7}}=>10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,4},{3},{5},{6}}=>10
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,4},{3},{5}}=>9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,4},{3},{7}}=>8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,4},{3},{5,6}}=>8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,4},{3},{6}}=>8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,4},{3}}=>7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3},{4},{6},{7}}=>10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3},{4},{6,7}}=>9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3},{4},{7}}=>10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3},{4},{6}}=>10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3},{4}}=>9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4},{5},{7}}=>10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4},{5}}=>10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4},{5},{6}}=>10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4},{5}}=>9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3},{4},{7}}=>8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3},{4}}=>8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4},{5,6}}=>8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3},{4},{6}}=>8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3},{4}}=>7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>{{1,2,4,5},{3},{6},{7}}=>7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>{{1,2,4,5},{3},{6,7}}=>6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,4,5},{3},{7}}=>7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,4,5},{3},{6}}=>7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,4,5},{3}}=>6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3},{4,5},{7}}=>7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3},{4,5}}=>7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3},{4,5},{6}}=>7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3},{4,5}}=>6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>{{1,2,4,6},{3},{5},{7}}=>7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,4,6},{3},{5}}=>7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3},{4,6},{5}}=>7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5},{6}}=>7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>{{1,2,4,6,7},{3},{5}}=>6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>{{1,2,4,5,6},{3},{7}}=>5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,4,5,6},{3}}=>5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3},{4,5,6}}=>5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>{{1,2,4,7},{3},{5,6}}=>5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>{{1,2,4,5,7},{3},{6}}=>5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,4,5,6,7},{3}}=>4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>{{1,2,3,4},{5},{6},{7}}=>6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>{{1,2,3,4},{5},{6,7}}=>5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>{{1,2,3,4},{5,6},{7}}=>4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>{{1,2,3,4},{5,7},{6}}=>4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>{{1,2,3,4},{5,6,7}}=>3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>{{1,5},{2,3,4},{6},{7}}=>6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>{{1,5},{2,3,4},{6,7}}=>5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>{{1,6},{2,3,4},{5},{7}}=>6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>{{1,7},{2,3,4},{5},{6}}=>6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>{{1,6,7},{2,3,4},{5}}=>5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>{{1,5,6},{2,3,4},{7}}=>4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>{{1,7},{2,3,4},{5,6}}=>4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>{{1,5,7},{2,3,4},{6}}=>4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>{{1,5,6,7},{2,3,4}}=>3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>{{1,2,5},{3,4},{6},{7}}=>6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>{{1,2,5},{3,4},{6,7}}=>5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>{{1,6},{2,5},{3,4},{7}}=>6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>{{1,7},{2,5},{3,4},{6}}=>6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>{{1,6,7},{2,5},{3,4}}=>5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>{{1,2,6},{3,4},{5},{7}}=>6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4},{5}}=>6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>{{1,2,7},{3,4},{5},{6}}=>6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4},{5}}=>5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>{{1,2,5,6},{3,4},{7}}=>4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>{{1,7},{2,5,6},{3,4}}=>4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>{{1,2,7},{3,4},{5,6}}=>4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>{{1,2,5,7},{3,4},{6}}=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>{{1,2,5,6,7},{3,4}}=>3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>{{1,2,3,5},{4},{6},{7}}=>6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>{{1,2,3,5},{4},{6,7}}=>5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,5},{4},{7}}=>6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,5},{4},{6}}=>6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,5},{4}}=>5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,5},{4},{7}}=>6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,5},{4}}=>6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,5},{4},{6}}=>6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,5},{4}}=>5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4},{5},{7}}=>6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4},{5}}=>6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4},{5}}=>6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5},{6}}=>6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4},{5}}=>5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>{{1,2,3,5,6},{4},{7}}=>4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,5,6},{4}}=>4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,5,6},{4}}=>4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4},{5,6}}=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>{{1,2,3,5,7},{4},{6}}=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,5,6,7},{4}}=>3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>{{1,2,3,4,5},{6},{7}}=>3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5},{6,7}}=>2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>{{1,6},{2,3,4,5},{7}}=>3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>{{1,7},{2,3,4,5},{6}}=>3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>{{1,6,7},{2,3,4,5}}=>2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>{{1,2,6},{3,4,5},{7}}=>3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>{{1,7},{2,6},{3,4,5}}=>3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>{{1,2,7},{3,4,5},{6}}=>3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>{{1,2,6,7},{3,4,5}}=>2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>{{1,2,3,6},{4,5},{7}}=>3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>{{1,7},{2,3,6},{4,5}}=>3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>{{1,2,7},{3,6},{4,5}}=>3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>{{1,2,3,7},{4,5},{6}}=>3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>{{1,2,3,6,7},{4,5}}=>2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>{{1,2,3,4,6},{5},{7}}=>3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,6},{5}}=>3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,6},{5}}=>3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,6},{5}}=>3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5},{6}}=>3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,6,7},{5}}=>2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6},{7}}=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>{{1,7},{2,3,4,5,6}}=>1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>{{1,2,7},{3,4,5,6}}=>1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>{{1,2,3,7},{4,5,6}}=>1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>{{1,2,3,4,7},{5,6}}=>1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,7},{6}}=>1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7}}=>0
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2},{3,4,5,6,7,8}}=>13
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,4,5,6,7,8},{3}}=>12
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,5,6,7,8},{4}}=>11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,6,7,8},{5}}=>10
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,7,8},{6}}=>9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>{{1},{2,3,4,5,6,7},{8}}=>13
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,8},{7}}=>8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1},{2,3,4,5,6,7,8}}=>7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>{{1,2},{3,4,5,6,7,8}}=>7
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2},{3}}=>11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>{{1,3,5,6,7,8},{2},{4}}=>10
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,3,4,5,6,7,8},{2}}=>6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>{{1,4,5,6,7,8},{2,3}}=>6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,4,5,6,7,8},{3}}=>5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>{{1,2,5,6,7,8},{3,4}}=>5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,5,6,7,8},{4}}=>4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>{{1,2,3,6,7,8},{4,5}}=>4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,6,7,8},{5}}=>3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>{{1,2,3,4,5,6},{7,8}}=>7
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>{{1,2,3,4,7,8},{5,6}}=>3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,7,8},{6}}=>2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>{{1,2,3,4,5,6,7},{8}}=>7
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>{{1,8},{2,3,4,5,6,7}}=>6
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>{{1,2,3,4,5,8},{6,7}}=>2
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,8},{7}}=>1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>{{1,2,3,4,5,6,7,8}}=>0
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Description
The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element.
This is the number of pairs $i\lt j$ in different blocks such that $i$ is the maximal element of a block.
This is the number of pairs $i\lt j$ in different blocks such that $i$ is the maximal element of a block.
Map
to noncrossing partition
Description
Biane's map to noncrossing set partitions.
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