Identifier
-
Mp00242:
Dyck paths
—Hessenberg poset⟶
Posets
St000908: Posets ⟶ ℤ
Values
=>
Cc0005;cc-rep-0
Cc0014;cc-rep
[1,0]=>([],1)=>1
[1,0,1,0]=>([(0,1)],2)=>1
[1,1,0,0]=>([],2)=>2
[1,0,1,0,1,0]=>([(0,2),(2,1)],3)=>1
[1,0,1,1,0,0]=>([(0,2),(1,2)],3)=>1
[1,1,0,0,1,0]=>([(0,1),(0,2)],3)=>1
[1,1,0,1,0,0]=>([(1,2)],3)=>2
[1,1,1,0,0,0]=>([],3)=>3
[1,0,1,0,1,0,1,0]=>([(0,3),(2,1),(3,2)],4)=>1
[1,0,1,0,1,1,0,0]=>([(0,3),(1,3),(3,2)],4)=>1
[1,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(2,3)],4)=>1
[1,0,1,1,0,1,0,0]=>([(0,3),(1,2),(2,3)],4)=>1
[1,0,1,1,1,0,0,0]=>([(0,3),(1,3),(2,3)],4)=>1
[1,1,0,0,1,0,1,0]=>([(0,3),(3,1),(3,2)],4)=>1
[1,1,0,0,1,1,0,0]=>([(0,2),(0,3),(1,2),(1,3)],4)=>2
[1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(3,1)],4)=>1
[1,1,0,1,0,1,0,0]=>([(0,3),(1,2),(1,3)],4)=>2
[1,1,0,1,1,0,0,0]=>([(1,3),(2,3)],4)=>2
[1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3)],4)=>1
[1,1,1,0,0,1,0,0]=>([(1,2),(1,3)],4)=>2
[1,1,1,0,1,0,0,0]=>([(2,3)],4)=>3
[1,1,1,1,0,0,0,0]=>([],4)=>4
[1,0,1,0,1,0,1,0,1,0]=>([(0,4),(2,3),(3,1),(4,2)],5)=>1
[1,0,1,0,1,0,1,1,0,0]=>([(0,4),(1,4),(2,3),(4,2)],5)=>1
[1,0,1,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>1
[1,0,1,0,1,1,0,1,0,0]=>([(0,4),(1,2),(2,4),(4,3)],5)=>1
[1,0,1,0,1,1,1,0,0,0]=>([(0,4),(1,4),(2,4),(4,3)],5)=>1
[1,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>1
[1,0,1,1,0,0,1,1,0,0]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>1
[1,0,1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>1
[1,0,1,1,0,1,0,1,0,0]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>1
[1,0,1,1,0,1,1,0,0,0]=>([(0,4),(1,3),(2,3),(3,4)],5)=>1
[1,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>1
[1,0,1,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>1
[1,0,1,1,1,0,1,0,0,0]=>([(0,4),(1,4),(2,3),(3,4)],5)=>1
[1,0,1,1,1,1,0,0,0,0]=>([(0,4),(1,4),(2,4),(3,4)],5)=>1
[1,1,0,0,1,0,1,0,1,0]=>([(0,3),(3,4),(4,1),(4,2)],5)=>1
[1,1,0,0,1,0,1,1,0,0]=>([(0,4),(1,4),(4,2),(4,3)],5)=>1
[1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>1
[1,1,0,0,1,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>2
[1,1,0,0,1,1,1,0,0,0]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>2
[1,1,0,1,0,0,1,0,1,0]=>([(0,4),(3,2),(4,1),(4,3)],5)=>1
[1,1,0,1,0,0,1,1,0,0]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>2
[1,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>1
[1,1,0,1,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>2
[1,1,0,1,0,1,1,0,0,0]=>([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>2
[1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>1
[1,1,0,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(3,4)],5)=>2
[1,1,0,1,1,0,1,0,0,0]=>([(0,4),(1,4),(2,3),(2,4)],5)=>2
[1,1,0,1,1,1,0,0,0,0]=>([(1,4),(2,4),(3,4)],5)=>2
[1,1,1,0,0,0,1,0,1,0]=>([(0,4),(4,1),(4,2),(4,3)],5)=>1
[1,1,1,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>2
[1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(4,1),(4,2)],5)=>1
[1,1,1,0,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>2
[1,1,1,0,0,1,1,0,0,0]=>([(1,3),(1,4),(2,3),(2,4)],5)=>3
[1,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(4,1)],5)=>1
[1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4)],5)=>2
[1,1,1,0,1,0,1,0,0,0]=>([(1,4),(2,3),(2,4)],5)=>3
[1,1,1,0,1,1,0,0,0,0]=>([(2,4),(3,4)],5)=>3
[1,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4)],5)=>1
[1,1,1,1,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4)],5)=>2
[1,1,1,1,0,0,1,0,0,0]=>([(2,3),(2,4)],5)=>3
[1,1,1,1,0,1,0,0,0,0]=>([(3,4)],5)=>4
[1,1,1,1,1,0,0,0,0,0]=>([],5)=>5
[1,0,1,0,1,0,1,0,1,0,1,0]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>1
[1,0,1,0,1,0,1,0,1,1,0,0]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>1
[1,0,1,0,1,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>1
[1,0,1,0,1,0,1,1,0,1,0,0]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>1
[1,0,1,0,1,0,1,1,1,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>1
[1,0,1,0,1,1,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>1
[1,0,1,0,1,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>1
[1,0,1,0,1,1,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>1
[1,0,1,0,1,1,0,1,0,1,0,0]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>1
[1,0,1,0,1,1,0,1,1,0,0,0]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>1
[1,0,1,0,1,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>1
[1,0,1,0,1,1,1,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>1
[1,0,1,0,1,1,1,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>1
[1,0,1,0,1,1,1,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>1
[1,0,1,1,0,0,1,0,1,0,1,0]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>1
[1,0,1,1,0,0,1,0,1,1,0,0]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>1
[1,0,1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>1
[1,0,1,1,0,0,1,1,0,1,0,0]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>1
[1,0,1,1,0,0,1,1,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>1
[1,0,1,1,0,1,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>1
[1,0,1,1,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>1
[1,0,1,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>1
[1,0,1,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>1
[1,0,1,1,0,1,0,1,1,0,0,0]=>([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>1
[1,0,1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>1
[1,0,1,1,0,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>1
[1,0,1,1,0,1,1,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>1
[1,0,1,1,0,1,1,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>1
[1,0,1,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>1
[1,0,1,1,1,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1
[1,0,1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>1
[1,0,1,1,1,0,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1
[1,0,1,1,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[1,0,1,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>1
[1,0,1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1
[1,0,1,1,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
[1,0,1,1,1,0,1,1,0,0,0,0]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>1
[1,0,1,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>1
[1,0,1,1,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>1
[1,0,1,1,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1
[1,0,1,1,1,1,0,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>1
[1,0,1,1,1,1,1,0,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>1
[1,1,0,0,1,0,1,0,1,0,1,0]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>1
[1,1,0,0,1,0,1,0,1,1,0,0]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>1
[1,1,0,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>1
[1,1,0,0,1,0,1,1,0,1,0,0]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>1
[1,1,0,0,1,0,1,1,1,0,0,0]=>([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>1
[1,1,0,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>1
[1,1,0,0,1,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>2
[1,1,0,0,1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>1
[1,1,0,0,1,1,0,1,0,1,0,0]=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>2
[1,1,0,0,1,1,0,1,1,0,0,0]=>([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1
[1,1,0,0,1,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,0,1,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>2
[1,1,0,0,1,1,1,1,0,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>1
[1,1,0,1,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>1
[1,1,0,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>1
[1,1,0,1,0,0,1,1,0,1,0,0]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>2
[1,1,0,1,0,0,1,1,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>2
[1,1,0,1,0,1,0,0,1,0,1,0]=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>1
[1,1,0,1,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>2
[1,1,0,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>1
[1,1,0,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>2
[1,1,0,1,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>2
[1,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1
[1,1,0,1,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,1,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>2
[1,1,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>1
[1,1,0,1,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>2
[1,1,0,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>1
[1,1,0,1,1,0,0,1,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>2
[1,1,0,1,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>2
[1,1,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>1
[1,1,0,1,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>2
[1,1,0,1,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>2
[1,1,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>1
[1,1,0,1,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>2
[1,1,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>2
[1,1,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>2
[1,1,0,1,1,1,1,0,0,0,0,0]=>([(1,5),(2,5),(3,5),(4,5)],6)=>2
[1,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>1
[1,1,1,0,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>1
[1,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1
[1,1,1,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>2
[1,1,1,0,0,0,1,1,1,0,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,0,0,1,0,0,1,0,1,0]=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>1
[1,1,1,0,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>2
[1,1,1,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>1
[1,1,1,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>2
[1,1,1,0,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>2
[1,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>1
[1,1,1,0,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>2
[1,1,1,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,0,0,1,1,1,0,0,0,0]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3
[1,1,1,0,1,0,0,0,1,0,1,0]=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>1
[1,1,1,0,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>2
[1,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>1
[1,1,1,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>2
[1,1,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>1
[1,1,1,0,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>2
[1,1,1,0,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,0,1,0,1,1,0,0,0,0]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3
[1,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>1
[1,1,1,0,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>2
[1,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,0,1,1,0,1,0,0,0,0]=>([(1,5),(2,5),(3,4),(3,5)],6)=>3
[1,1,1,0,1,1,1,0,0,0,0,0]=>([(2,5),(3,5),(4,5)],6)=>3
[1,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>1
[1,1,1,1,0,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>2
[1,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>1
[1,1,1,1,0,0,0,1,0,1,0,0]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>2
[1,1,1,1,0,0,0,1,1,0,0,0]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>1
[1,1,1,1,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>2
[1,1,1,1,0,0,1,0,1,0,0,0]=>([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,1,0,0,1,1,0,0,0,0]=>([(2,4),(2,5),(3,4),(3,5)],6)=>4
[1,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>1
[1,1,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>2
[1,1,1,1,0,1,0,0,1,0,0,0]=>([(1,5),(2,3),(2,4),(2,5)],6)=>3
[1,1,1,1,0,1,0,1,0,0,0,0]=>([(2,5),(3,4),(3,5)],6)=>4
[1,1,1,1,0,1,1,0,0,0,0,0]=>([(3,5),(4,5)],6)=>4
[1,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>1
[1,1,1,1,1,0,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4),(1,5)],6)=>2
[1,1,1,1,1,0,0,0,1,0,0,0]=>([(2,3),(2,4),(2,5)],6)=>3
[1,1,1,1,1,0,0,1,0,0,0,0]=>([(3,4),(3,5)],6)=>4
[1,1,1,1,1,0,1,0,0,0,0,0]=>([(4,5)],6)=>5
[1,1,1,1,1,1,0,0,0,0,0,0]=>([],6)=>6
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)=>1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>1
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)=>1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)=>1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>1
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)=>1
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)=>1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)=>1
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)=>1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>1
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>1
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>1
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)=>1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7)=>1
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)=>1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7)=>1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>1
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>1
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>1
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>1
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>1
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>1
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>1
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>1
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>1
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>1
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)=>1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>1
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)=>1
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)=>1
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)=>1
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)=>2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>1
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>1
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)=>2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>2
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)=>2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>1
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>2
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7)=>2
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)=>2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)=>2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)=>2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)=>2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>1
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)=>1
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7)=>2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)=>2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7)=>2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7)=>1
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)=>2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)=>1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)=>1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7)=>2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)=>1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)=>1
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>1
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)=>1
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)=>1
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)=>2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>1
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>1
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>3
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)=>3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)=>1
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)=>1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7)=>2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>1
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)=>3
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)=>1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)=>1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>3
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)=>1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)=>2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7)=>3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>3
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>([(2,6),(3,6),(4,6),(5,6)],7)=>3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)=>1
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>1
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>1
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)=>1
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>1
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7)=>1
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)=>1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)=>1
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)=>1
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>4
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)=>1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>4
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)=>1
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)=>2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>3
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>([(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>([(2,6),(3,6),(4,5),(4,6)],7)=>4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>([(3,6),(4,6),(5,6)],7)=>4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)=>1
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>([(3,5),(3,6),(4,5),(4,6)],7)=>5
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>1
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>([(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>([(2,6),(3,4),(3,5),(3,6)],7)=>4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>([(3,6),(4,5),(4,6)],7)=>5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>([(4,6),(5,6)],7)=>5
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)=>1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>([(2,3),(2,4),(2,5),(2,6)],7)=>3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>([(3,4),(3,5),(3,6)],7)=>4
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>([(4,5),(4,6)],7)=>5
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>([(5,6)],7)=>6
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>([],7)=>7
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Description
The length of the shortest maximal antichain in a poset.
Map
Hessenberg poset
Description
The Hessenberg poset of a Dyck path.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
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