Identifier
Identifier
St000012:
Dyck paths
⟶ ℤ
(values match
St001295Gives the vector space dimension of the homomorphism space between J^2 and J^2.)
Values
[1,0]
=>
0
=>
0
[1,0,1,0]
=>
0
=>
0
[1,1,0,0]
=>
1
=>
1
[1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,1,0,0]
=>
1
=>
1
[1,1,0,0,1,0]
=>
1
=>
1
[1,1,0,1,0,0]
=>
2
=>
2
[1,1,1,0,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,0,1,1,0,0]
=>
1
=>
1
[1,0,1,1,0,0,1,0]
=>
1
=>
1
[1,0,1,1,0,1,0,0]
=>
2
=>
2
[1,0,1,1,1,0,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,0]
=>
1
=>
1
[1,1,0,0,1,1,0,0]
=>
2
=>
2
[1,1,0,1,0,0,1,0]
=>
2
=>
2
[1,1,0,1,0,1,0,0]
=>
3
=>
3
[1,1,0,1,1,0,0,0]
=>
4
=>
4
[1,1,1,0,0,0,1,0]
=>
3
=>
3
[1,1,1,0,0,1,0,0]
=>
4
=>
4
[1,1,1,0,1,0,0,0]
=>
5
=>
5
[1,1,1,1,0,0,0,0]
=>
6
=>
6
[1,0,1,0,1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,0,1,0,1,1,0,0]
=>
1
=>
1
[1,0,1,0,1,1,0,0,1,0]
=>
1
=>
1
[1,0,1,0,1,1,0,1,0,0]
=>
2
=>
2
[1,0,1,0,1,1,1,0,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,0,1,0]
=>
1
=>
1
[1,0,1,1,0,0,1,1,0,0]
=>
2
=>
2
[1,0,1,1,0,1,0,0,1,0]
=>
2
=>
2
[1,0,1,1,0,1,0,1,0,0]
=>
3
=>
3
[1,0,1,1,0,1,1,0,0,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,0]
=>
3
=>
3
[1,0,1,1,1,0,0,1,0,0]
=>
4
=>
4
[1,0,1,1,1,0,1,0,0,0]
=>
5
=>
5
[1,0,1,1,1,1,0,0,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,0,1,0]
=>
1
=>
1
[1,1,0,0,1,0,1,1,0,0]
=>
2
=>
2
[1,1,0,0,1,1,0,0,1,0]
=>
2
=>
2
[1,1,0,0,1,1,0,1,0,0]
=>
3
=>
3
[1,1,0,0,1,1,1,0,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,0,1,0]
=>
2
=>
2
[1,1,0,1,0,0,1,1,0,0]
=>
3
=>
3
[1,1,0,1,0,1,0,0,1,0]
=>
3
=>
3
[1,1,0,1,0,1,0,1,0,0]
=>
4
=>
4
[1,1,0,1,0,1,1,0,0,0]
=>
5
=>
5
[1,1,0,1,1,0,0,0,1,0]
=>
4
=>
4
[1,1,0,1,1,0,0,1,0,0]
=>
5
=>
5
[1,1,0,1,1,0,1,0,0,0]
=>
6
=>
6
[1,1,0,1,1,1,0,0,0,0]
=>
7
=>
7
[1,1,1,0,0,0,1,0,1,0]
=>
3
=>
3
[1,1,1,0,0,0,1,1,0,0]
=>
4
=>
4
[1,1,1,0,0,1,0,0,1,0]
=>
4
=>
4
[1,1,1,0,0,1,0,1,0,0]
=>
5
=>
5
[1,1,1,0,0,1,1,0,0,0]
=>
6
=>
6
[1,1,1,0,1,0,0,0,1,0]
=>
5
=>
5
[1,1,1,0,1,0,0,1,0,0]
=>
6
=>
6
[1,1,1,0,1,0,1,0,0,0]
=>
7
=>
7
[1,1,1,0,1,1,0,0,0,0]
=>
8
=>
8
[1,1,1,1,0,0,0,0,1,0]
=>
6
=>
6
[1,1,1,1,0,0,0,1,0,0]
=>
7
=>
7
[1,1,1,1,0,0,1,0,0,0]
=>
8
=>
8
[1,1,1,1,0,1,0,0,0,0]
=>
9
=>
9
[1,1,1,1,1,0,0,0,0,0]
=>
10
=>
10
[1,0,1,0,1,0,1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,0,1,0,1,0,1,1,0,0]
=>
1
=>
1
[1,0,1,0,1,0,1,1,0,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,1,0,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,1,0,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,1,0,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,1,0,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,1,0,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,1,1,1,0,0,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,1,0,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,1,0,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,1,0,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,1,0,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,1,1,0,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,1,0,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,1,0,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,1,1,1,0,0,0,0,0]
=>
10
=>
10
[1,1,0,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,1,0,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,1,0,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,1,0,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,1,0,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,1,0,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,1,0,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,1,0,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,1,0,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,1,0,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,1,0,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,1,0,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,1,0,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,1,0,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,1,0,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,1,0,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,1,0,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,1,0,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,1,1,0,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,1,1,0,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,1,1,0,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,1,1,0,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,1,1,0,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,1,1,0,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,1,1,0,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,1,1,0,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,1,1,0,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,1,1,0,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,1,1,0,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,1,1,0,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,1,1,0,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,1,1,0,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,1,1,0,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,1,1,0,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,1,1,0,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,1,1,0,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,1,1,0,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,1,1,0,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,1,1,0,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,1,1,0,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,1,1,0,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,1,1,0,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,1,1,0,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,1,1,0,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,1,1,0,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,1,1,0,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,1,1,1,0,0,0,0,1,0,1,0]
=>
6
=>
6
[1,1,1,1,0,0,0,0,1,1,0,0]
=>
7
=>
7
[1,1,1,1,0,0,0,1,0,0,1,0]
=>
7
=>
7
[1,1,1,1,0,0,0,1,0,1,0,0]
=>
8
=>
8
[1,1,1,1,0,0,0,1,1,0,0,0]
=>
9
=>
9
[1,1,1,1,0,0,1,0,0,0,1,0]
=>
8
=>
8
[1,1,1,1,0,0,1,0,0,1,0,0]
=>
9
=>
9
[1,1,1,1,0,0,1,0,1,0,0,0]
=>
10
=>
10
[1,1,1,1,0,0,1,1,0,0,0,0]
=>
11
=>
11
[1,1,1,1,0,1,0,0,0,0,1,0]
=>
9
=>
9
[1,1,1,1,0,1,0,0,0,1,0,0]
=>
10
=>
10
[1,1,1,1,0,1,0,0,1,0,0,0]
=>
11
=>
11
[1,1,1,1,0,1,0,1,0,0,0,0]
=>
12
=>
12
[1,1,1,1,0,1,1,0,0,0,0,0]
=>
13
=>
13
[1,1,1,1,1,0,0,0,0,0,1,0]
=>
10
=>
10
[1,1,1,1,1,0,0,0,0,1,0,0]
=>
11
=>
11
[1,1,1,1,1,0,0,0,1,0,0,0]
=>
12
=>
12
[1,1,1,1,1,0,0,1,0,0,0,0]
=>
13
=>
13
[1,1,1,1,1,0,1,0,0,0,0,0]
=>
14
=>
14
[1,1,1,1,1,1,0,0,0,0,0,0]
=>
15
=>
15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
1
=>
1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
6
=>
6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
10
=>
10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
6
=>
6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
10
=>
10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
11
=>
11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
14
=>
14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
15
=>
15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=>
8
=>
8
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=>
4
=>
4
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]
=>
5
=>
5
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=>
5
=>
5
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]
=>
6
=>
6
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]
=>
7
=>
7
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=>
5
=>
5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=>
6
=>
6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=>
6
=>
6
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=>
7
=>
7
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=>
8
=>
8
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
=>
7
=>
7
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=>
8
=>
8
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=>
9
=>
9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=>
10
=>
10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=>
6
=>
6
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]
=>
7
=>
7
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=>
7
=>
7
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=>
8
=>
8
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=>
9
=>
9
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=>
8
=>
8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=>
9
=>
9
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=>
10
=>
10
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=>
11
=>
11
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=>
9
=>
9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=>
10
=>
10
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=>
11
=>
11
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=>
12
=>
12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=>
13
=>
13
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=>
7
=>
7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=>
8
=>
8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
=>
8
=>
8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=>
9
=>
9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=>
10
=>
10
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=>
9
=>
9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=>
10
=>
10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=>
11
=>
11
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=>
12
=>
12
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
=>
10
=>
10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=>
11
=>
11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=>
12
=>
12
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=>
13
=>
13
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=>
14
=>
14
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=>
11
=>
11
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=>
12
=>
12
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=>
13
=>
13
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=>
14
=>
14
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=>
15
=>
15
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=>
16
=>
16
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=>
3
=>
3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=>
4
=>
4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]
=>
4
=>
4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]
=>
5
=>
5
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=>
6
=>
6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]
=>
4
=>
4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=>
5
=>
5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]
=>
5
=>
5
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]
=>
6
=>
6
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]
=>
7
=>
7
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=>
6
=>
6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=>
7
=>
7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=>
8
=>
8
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=>
9
=>
9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=>
4
=>
4
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=>
5
=>
5
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]
=>
5
=>
5
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]
=>
6
=>
6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=>
7
=>
7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=>
5
=>
5
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=>
6
=>
6
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=>
6
=>
6
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=>
7
=>
7
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=>
8
=>
8
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
=>
7
=>
7
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=>
8
=>
8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=>
9
=>
9
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=>
10
=>
10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=>
6
=>
6
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]
=>
7
=>
7
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
=>
7
=>
7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=>
8
=>
8
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=>
9
=>
9
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
=>
8
=>
8
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=>
9
=>
9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=>
10
=>
10
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=>
11
=>
11
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=>
9
=>
9
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=>
10
=>
10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=>
11
=>
11
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=>
12
=>
12
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=>
13
=>
13
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=>
5
=>
5
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]
=>
6
=>
6
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]
=>
6
=>
6
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=>
7
=>
7
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=>
8
=>
8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=>
6
=>
6
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=>
7
=>
7
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=>
7
=>
7
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=>
8
=>
8
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=>
9
=>
9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
=>
8
=>
8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=>
9
=>
9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=>
10
=>
10
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=>
11
=>
11
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=>
7
=>
7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=>
8
=>
8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=>
8
=>
8
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=>
9
=>
9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=>
10
=>
10
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=>
9
=>
9
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=>
10
=>
10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=>
11
=>
11
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=>
12
=>
12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=>
10
=>
10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=>
11
=>
11
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=>
12
=>
12
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=>
13
=>
13
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=>
14
=>
14
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=>
8
=>
8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=>
9
=>
9
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=>
9
=>
9
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=>
10
=>
10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=>
11
=>
11
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=>
10
=>
10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=>
11
=>
11
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=>
12
=>
12
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=>
13
=>
13
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=>
11
=>
11
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=>
12
=>
12
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=>
13
=>
13
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=>
14
=>
14
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=>
15
=>
15
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=>
12
=>
12
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=>
13
=>
13
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=>
14
=>
14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=>
15
=>
15
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=>
16
=>
16
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=>
17
=>
17
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=>
6
=>
6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=>
7
=>
7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=>
7
=>
7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]
=>
8
=>
8
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=>
9
=>
9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=>
7
=>
7
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]
=>
8
=>
8
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=>
8
=>
8
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=>
9
=>
9
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=>
10
=>
10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]
=>
9
=>
9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]
=>
10
=>
10
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]
=>
11
=>
11
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=>
12
=>
12
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=>
8
=>
8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]
=>
9
=>
9
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=>
9
=>
9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=>
10
=>
10
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=>
11
=>
11
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=>
10
=>
10
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=>
11
=>
11
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=>
12
=>
12
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=>
13
=>
13
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=>
11
=>
11
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=>
12
=>
12
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=>
13
=>
13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=>
14
=>
14
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=>
15
=>
15
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=>
9
=>
9
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=>
10
=>
10
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=>
10
=>
10
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=>
11
=>
11
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=>
12
=>
12
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=>
11
=>
11
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=>
12
=>
12
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=>
13
=>
13
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=>
14
=>
14
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=>
12
=>
12
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=>
13
=>
13
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=>
14
=>
14
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=>
15
=>
15
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=>
16
=>
16
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=>
13
=>
13
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=>
14
=>
14
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=>
15
=>
15
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=>
16
=>
16
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=>
17
=>
17
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=>
18
=>
18
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=>
10
=>
10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=>
11
=>
11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]
=>
11
=>
11
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=>
12
=>
12
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=>
13
=>
13
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]
=>
12
=>
12
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=>
13
=>
13
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=>
14
=>
14
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=>
15
=>
15
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=>
13
=>
13
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=>
14
=>
14
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]
=>
15
=>
15
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=>
16
=>
16
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=>
17
=>
17
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=>
14
=>
14
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=>
15
=>
15
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=>
16
=>
16
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=>
17
=>
17
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=>
18
=>
18
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=>
19
=>
19
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=>
15
=>
15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=>
16
=>
16
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=>
17
=>
17
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=>
18
=>
18
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=>
19
=>
19
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=>
20
=>
20
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=>
21
=>
21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
0
=>
0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
1
=>
1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
6
=>
6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
6
=>
6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
7
=>
7
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
8
=>
8
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
9
=>
9
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
10
=>
10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
6
=>
6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
7
=>
7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
7
=>
7
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
8
=>
8
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
8
=>
8
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
9
=>
9
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
10
=>
10
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
11
=>
11
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
9
=>
9
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
10
=>
10
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
11
=>
11
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
12
=>
12
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
13
=>
13
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
10
=>
10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
11
=>
11
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
12
=>
12
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
13
=>
13
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
14
=>
14
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
15
=>
15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]
=>
2
=>
2
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]
=>
3
=>
3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]
=>
5
=>
5
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]
=>
6
=>
6
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]
=>
7
=>
7
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]
=>
13
=>
13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]
=>
7
=>
7
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]
=>
8
=>
8
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]
=>
8
=>
8
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]
=>
9
=>
9
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]
=>
10
=>
10
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]
=>
11
=>
11
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]
=>
12
=>
12
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]
=>
13
=>
13
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]
=>
14
=>
14
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]
=>
11
=>
11
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]
=>
12
=>
12
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]
=>
13
=>
13
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]
=>
14
=>
14
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]
=>
15
=>
15
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=>
16
=>
16
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]
=>
3
=>
3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]
=>
4
=>
4
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]
=>
5
=>
5
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]
=>
6
=>
6
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]
=>
7
=>
7
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]
=>
10
=>
10
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]
=>
12
=>
12
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]
=>
14
=>
14
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]
=>
8
=>
8
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]
=>
9
=>
9
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]
=>
10
=>
10
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]
=>
11
=>
11
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]
=>
12
=>
12
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]
=>
11
=>
11
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]
=>
12
=>
12
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]
=>
13
=>
13
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]
=>
14
=>
14
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]
=>
15
=>
15
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]
=>
12
=>
12
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]
=>
13
=>
13
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]
=>
14
=>
14
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]
=>
15
=>
15
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]
=>
16
=>
16
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]
=>
17
=>
17
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]
=>
6
=>
6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]
=>
7
=>
7
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]
=>
8
=>
8
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]
=>
9
=>
9
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]
=>
10
=>
10
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]
=>
11
=>
11
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]
=>
14
=>
14
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]
=>
15
=>
15
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]
=>
9
=>
9
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]
=>
10
=>
10
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]
=>
10
=>
10
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]
=>
11
=>
11
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]
=>
11
=>
11
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]
=>
12
=>
12
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]
=>
14
=>
14
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]
=>
12
=>
12
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]
=>
13
=>
13
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]
=>
14
=>
14
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]
=>
15
=>
15
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]
=>
16
=>
16
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]
=>
13
=>
13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]
=>
14
=>
14
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]
=>
15
=>
15
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]
=>
16
=>
16
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]
=>
17
=>
17
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]
=>
18
=>
18
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]
=>
10
=>
10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]
=>
11
=>
11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]
=>
11
=>
11
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]
=>
12
=>
12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]
=>
13
=>
13
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]
=>
12
=>
12
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]
=>
13
=>
13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]
=>
14
=>
14
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]
=>
15
=>
15
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]
=>
13
=>
13
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]
=>
14
=>
14
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]
=>
15
=>
15
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]
=>
16
=>
16
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]
=>
17
=>
17
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]
=>
14
=>
14
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]
=>
15
=>
15
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]
=>
16
=>
16
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]
=>
17
=>
17
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]
=>
18
=>
18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]
=>
19
=>
19
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]
=>
15
=>
15
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=>
16
=>
16
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]
=>
17
=>
17
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]
=>
18
=>
18
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]
=>
19
=>
19
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
=>
20
=>
20
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
=>
21
=>
21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]
=>
1
=>
1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]
=>
2
=>
2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]
=>
7
=>
7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]
=>
8
=>
8
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]
=>
4
=>
4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]
=>
6
=>
6
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]
=>
7
=>
7
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]
=>
8
=>
8
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]
=>
9
=>
9
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]
=>
7
=>
7
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]
=>
8
=>
8
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]
=>
9
=>
9
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]
=>
10
=>
10
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]
=>
11
=>
11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]
=>
3
=>
3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]
=>
6
=>
6
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]
=>
7
=>
7
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]
=>
7
=>
7
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]
=>
8
=>
8
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]
=>
8
=>
8
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]
=>
9
=>
9
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]
=>
11
=>
11
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]
=>
12
=>
12
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]
=>
4
=>
4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]
=>
5
=>
5
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]
=>
6
=>
6
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]
=>
7
=>
7
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]
=>
8
=>
8
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]
=>
11
=>
11
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]
=>
9
=>
9
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]
=>
11
=>
11
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]
=>
12
=>
12
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]
=>
13
=>
13
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]
=>
7
=>
7
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]
=>
8
=>
8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]
=>
8
=>
8
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]
=>
9
=>
9
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]
=>
9
=>
9
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]
=>
10
=>
10
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]
=>
11
=>
11
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]
=>
12
=>
12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]
=>
10
=>
10
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]
=>
11
=>
11
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]
=>
12
=>
12
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]
=>
13
=>
13
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]
=>
14
=>
14
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]
=>
11
=>
11
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]
=>
12
=>
12
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]
=>
13
=>
13
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]
=>
14
=>
14
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]
=>
15
=>
15
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]
=>
16
=>
16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]
=>
2
=>
2
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]
=>
3
=>
3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]
=>
3
=>
3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]
=>
5
=>
5
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]
=>
3
=>
3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]
=>
4
=>
4
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]
=>
4
=>
4
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]
=>
5
=>
5
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]
=>
6
=>
6
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]
=>
5
=>
5
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]
=>
6
=>
6
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]
=>
7
=>
7
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]
=>
8
=>
8
Description
The area of a Dyck path.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences $(a_1,\ldots,a_n)$ such that $a_1 = 0, a_{k+1} \leq a_k + 1$.
2. The generating function $\mathbf{D}_n(q) = \sum_{D \in \mathfrak{D}_n} q^{\operatorname{area}(D)}$ satisfy the recurrence $$\mathbf{D}_{n+1}(q) = \sum q^k \mathbf{D}_k(q) \mathbf{D}_{n-k}(q).$$
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of $q,t$-Catalan numbers.
This is the number of complete squares in the integer lattice which are below the path and above the x-axis. The 'half-squares' directly above the axis do not contribute to this statistic.
1. Dyck paths are bijection with area sequences $(a_1,\ldots,a_n)$ such that $a_1 = 0, a_{k+1} \leq a_k + 1$.
2. The generating function $\mathbf{D}_n(q) = \sum_{D \in \mathfrak{D}_n} q^{\operatorname{area}(D)}$ satisfy the recurrence $$\mathbf{D}_{n+1}(q) = \sum q^k \mathbf{D}_k(q) \mathbf{D}_{n-k}(q).$$
3. The area is equidistributed with St000005The bounce statistic of a Dyck path. and St000006The dinv of a Dyck path.. Pairs of these statistics play an important role in the theory of $q,t$-Catalan numbers.
References
[1] Haglund, J. The $q$,$t$-Catalan numbers and the space of diagonal harmonics MathSciNet:2371044
Code
def statistic(x):
return x.area()
Created
Sep 27, 2011 at 19:29 by Chris Berg
Updated
Jun 17, 2019 at 17:03 by Christian Stump
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