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-----------------------------------------------------------------------------
Statistic identifier: St001932
-----------------------------------------------------------------------------
Collection: Dyck paths
-----------------------------------------------------------------------------
Description: The number of pairs of singleton blocks in the noncrossing set partition corresponding to a Dyck path, that can be merged to create another noncrossing set partition.
Let $D$ be a Dyck path, and let $P$ be the noncrossing set partition obtained by applying [[Mp00138]]. For each pair of singleton blocks $\{a\}, \{b\}$, let $P'$ be the set partition obtained from $P$ by merging the two blocks. This statistic enumerates the number of (unordered) pairs of singleton blocks such that $P'$ is noncrossing.
-----------------------------------------------------------------------------
References: [1] Rouyer, J., Ninet, A. Two New Integer Sequences Related to Crossroads and Catalan Numbers [[arXiv:2311.07181]]
-----------------------------------------------------------------------------
Code:
def statistic(D):
P = SetPartition(D.to_noncrossing_partition())
S = [b for b in P if len(b) == 1]
return sum(1 for b, c in Subsets(S, 2)
if SetPartition([p for p in P if p != b and p != c]
+ [b.union(c)]).is_noncrossing())
-----------------------------------------------------------------------------
Statistic values:
[1,0] => 0
[1,0,1,0] => 1
[1,1,0,0] => 0
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 0
[1,1,0,0,1,0] => 0
[1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => 0
[1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 4
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 0
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 0
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 0
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Created: Nov 15, 2023 at 00:03 by Martin Rubey
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Last Updated: Nov 15, 2023 at 00:03 by Martin Rubey