************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 The FindStatCrew <info@findstat.org>           *
*                                                                      *
*    This information is distributed in the hope that it will be       *
*    useful, but WITHOUT ANY WARRANTY; without even the implied        *
*    warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  *
************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00027

------------------------------------------------------------------------
Map name: to partition

------------------------------------------------------------------------
Domain: Dyck paths

------------------------------------------------------------------------
Codomain: Integer partitions

------------------------------------------------------------------------
Description: The cut-out partition of a Dyck path.

The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.

In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.

This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.

------------------------------------------------------------------------
References: 

------------------------------------------------------------------------
Code:

def mapping(elt):
    n = len(elt) // 2
    res = []
    for c in reversed(elt):
        if c == 0:
            n -= 1
        else:
            res.append(n)
    return Partition(res)


------------------------------------------------------------------------
Map images:

[1,0]                             => []
[1,0,1,0]                         => [1]
[1,1,0,0]                         => []
[1,0,1,0,1,0]                     => [2,1]
[1,0,1,1,0,0]                     => [1,1]
[1,1,0,0,1,0]                     => [2]
[1,1,0,1,0,0]                     => [1]
[1,1,1,0,0,0]                     => []
[1,0,1,0,1,0,1,0]                 => [3,2,1]
[1,0,1,0,1,1,0,0]                 => [2,2,1]
[1,0,1,1,0,0,1,0]                 => [3,1,1]
[1,0,1,1,0,1,0,0]                 => [2,1,1]
[1,0,1,1,1,0,0,0]                 => [1,1,1]
[1,1,0,0,1,0,1,0]                 => [3,2]
[1,1,0,0,1,1,0,0]                 => [2,2]
[1,1,0,1,0,0,1,0]                 => [3,1]
[1,1,0,1,0,1,0,0]                 => [2,1]
[1,1,0,1,1,0,0,0]                 => [1,1]
[1,1,1,0,0,0,1,0]                 => [3]
[1,1,1,0,0,1,0,0]                 => [2]
[1,1,1,0,1,0,0,0]                 => [1]
[1,1,1,1,0,0,0,0]                 => []
[1,0,1,0,1,0,1,0,1,0]             => [4,3,2,1]
[1,0,1,0,1,0,1,1,0,0]             => [3,3,2,1]
[1,0,1,0,1,1,0,0,1,0]             => [4,2,2,1]
[1,0,1,0,1,1,0,1,0,0]             => [3,2,2,1]
[1,0,1,0,1,1,1,0,0,0]             => [2,2,2,1]
[1,0,1,1,0,0,1,0,1,0]             => [4,3,1,1]
[1,0,1,1,0,0,1,1,0,0]             => [3,3,1,1]
[1,0,1,1,0,1,0,0,1,0]             => [4,2,1,1]
[1,0,1,1,0,1,0,1,0,0]             => [3,2,1,1]
[1,0,1,1,0,1,1,0,0,0]             => [2,2,1,1]
[1,0,1,1,1,0,0,0,1,0]             => [4,1,1,1]
[1,0,1,1,1,0,0,1,0,0]             => [3,1,1,1]
[1,0,1,1,1,0,1,0,0,0]             => [2,1,1,1]
[1,0,1,1,1,1,0,0,0,0]             => [1,1,1,1]
[1,1,0,0,1,0,1,0,1,0]             => [4,3,2]
[1,1,0,0,1,0,1,1,0,0]             => [3,3,2]
[1,1,0,0,1,1,0,0,1,0]             => [4,2,2]
[1,1,0,0,1,1,0,1,0,0]             => [3,2,2]
[1,1,0,0,1,1,1,0,0,0]             => [2,2,2]
[1,1,0,1,0,0,1,0,1,0]             => [4,3,1]
[1,1,0,1,0,0,1,1,0,0]             => [3,3,1]
[1,1,0,1,0,1,0,0,1,0]             => [4,2,1]
[1,1,0,1,0,1,0,1,0,0]             => [3,2,1]
[1,1,0,1,0,1,1,0,0,0]             => [2,2,1]
[1,1,0,1,1,0,0,0,1,0]             => [4,1,1]
[1,1,0,1,1,0,0,1,0,0]             => [3,1,1]
[1,1,0,1,1,0,1,0,0,0]             => [2,1,1]
[1,1,0,1,1,1,0,0,0,0]             => [1,1,1]
[1,1,1,0,0,0,1,0,1,0]             => [4,3]
[1,1,1,0,0,0,1,1,0,0]             => [3,3]
[1,1,1,0,0,1,0,0,1,0]             => [4,2]
[1,1,1,0,0,1,0,1,0,0]             => [3,2]
[1,1,1,0,0,1,1,0,0,0]             => [2,2]
[1,1,1,0,1,0,0,0,1,0]             => [4,1]
[1,1,1,0,1,0,0,1,0,0]             => [3,1]
[1,1,1,0,1,0,1,0,0,0]             => [2,1]
[1,1,1,0,1,1,0,0,0,0]             => [1,1]
[1,1,1,1,0,0,0,0,1,0]             => [4]
[1,1,1,1,0,0,0,1,0,0]             => [3]
[1,1,1,1,0,0,1,0,0,0]             => [2]
[1,1,1,1,0,1,0,0,0,0]             => [1]
[1,1,1,1,1,0,0,0,0,0]             => []
[1,0,1,0,1,0,1,0,1,0,1,0]         => [5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0]         => [4,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0]         => [5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0]         => [4,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0]         => [3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0]         => [5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0]         => [4,4,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0]         => [5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0]         => [4,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0]         => [3,3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0]         => [5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0]         => [4,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0]         => [3,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0]         => [2,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0]         => [5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0]         => [4,4,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0]         => [5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0]         => [4,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0]         => [3,3,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0]         => [5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0]         => [4,4,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0]         => [5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0]         => [4,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0]         => [3,3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0]         => [5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0]         => [4,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0]         => [3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0]         => [2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0]         => [5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0]         => [4,4,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0]         => [5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0]         => [4,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0]         => [3,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0]         => [5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0]         => [4,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0]         => [3,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0]         => [2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0]         => [5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0]         => [4,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0]         => [3,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0]         => [2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0]         => [1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0]         => [5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0]         => [4,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0]         => [5,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0]         => [4,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0]         => [3,3,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0]         => [5,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0]         => [4,4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0]         => [5,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0]         => [4,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0]         => [3,3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0]         => [5,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0]         => [4,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0]         => [3,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0]         => [2,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0]         => [5,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0]         => [4,4,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0]         => [5,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0]         => [4,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0]         => [3,3,3,1]
[1,1,0,1,0,1,0,0,1,0,1,0]         => [5,4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0]         => [4,4,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0]         => [5,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0]         => [4,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0]         => [3,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0]         => [5,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0]         => [4,2,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0]         => [3,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0]         => [2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0]         => [5,4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0]         => [4,4,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0]         => [5,3,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0]         => [4,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0]         => [3,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0]         => [5,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0]         => [4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0]         => [3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0]         => [2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0]         => [5,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0]         => [4,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0]         => [3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0]         => [2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0]         => [1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0]         => [5,4,3]
[1,1,1,0,0,0,1,0,1,1,0,0]         => [4,4,3]
[1,1,1,0,0,0,1,1,0,0,1,0]         => [5,3,3]
[1,1,1,0,0,0,1,1,0,1,0,0]         => [4,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0]         => [3,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0]         => [5,4,2]
[1,1,1,0,0,1,0,0,1,1,0,0]         => [4,4,2]
[1,1,1,0,0,1,0,1,0,0,1,0]         => [5,3,2]
[1,1,1,0,0,1,0,1,0,1,0,0]         => [4,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0]         => [3,3,2]
[1,1,1,0,0,1,1,0,0,0,1,0]         => [5,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0]         => [4,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0]         => [3,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0]         => [2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,0]         => [5,4,1]
[1,1,1,0,1,0,0,0,1,1,0,0]         => [4,4,1]
[1,1,1,0,1,0,0,1,0,0,1,0]         => [5,3,1]
[1,1,1,0,1,0,0,1,0,1,0,0]         => [4,3,1]
[1,1,1,0,1,0,0,1,1,0,0,0]         => [3,3,1]
[1,1,1,0,1,0,1,0,0,0,1,0]         => [5,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0]         => [4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0]         => [3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0]         => [2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0]         => [5,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0]         => [4,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0]         => [3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0]         => [2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0]         => [1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0]         => [5,4]
[1,1,1,1,0,0,0,0,1,1,0,0]         => [4,4]
[1,1,1,1,0,0,0,1,0,0,1,0]         => [5,3]
[1,1,1,1,0,0,0,1,0,1,0,0]         => [4,3]
[1,1,1,1,0,0,0,1,1,0,0,0]         => [3,3]
[1,1,1,1,0,0,1,0,0,0,1,0]         => [5,2]
[1,1,1,1,0,0,1,0,0,1,0,0]         => [4,2]
[1,1,1,1,0,0,1,0,1,0,0,0]         => [3,2]
[1,1,1,1,0,0,1,1,0,0,0,0]         => [2,2]
[1,1,1,1,0,1,0,0,0,0,1,0]         => [5,1]
[1,1,1,1,0,1,0,0,0,1,0,0]         => [4,1]
[1,1,1,1,0,1,0,0,1,0,0,0]         => [3,1]
[1,1,1,1,0,1,0,1,0,0,0,0]         => [2,1]
[1,1,1,1,0,1,1,0,0,0,0,0]         => [1,1]
[1,1,1,1,1,0,0,0,0,0,1,0]         => [5]
[1,1,1,1,1,0,0,0,0,1,0,0]         => [4]
[1,1,1,1,1,0,0,0,1,0,0,0]         => [3]
[1,1,1,1,1,0,0,1,0,0,0,0]         => [2]
[1,1,1,1,1,0,1,0,0,0,0,0]         => [1]
[1,1,1,1,1,1,0,0,0,0,0,0]         => []
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => [6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => [5,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]     => [6,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => [5,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]     => [4,4,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]     => [6,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]     => [5,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]     => [6,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]     => [5,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]     => [4,4,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]     => [6,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]     => [5,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]     => [4,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]     => [3,3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]     => [6,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]     => [5,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]     => [6,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]     => [5,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]     => [4,4,4,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]     => [6,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]     => [5,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]     => [6,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]     => [5,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]     => [4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]     => [6,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]     => [5,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]     => [4,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]     => [3,3,3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]     => [6,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]     => [5,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]     => [6,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]     => [5,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]     => [4,4,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]     => [6,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]     => [5,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]     => [4,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]     => [3,3,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]     => [6,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]     => [5,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]     => [4,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]     => [3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]     => [2,2,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]     => [6,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]     => [5,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]     => [6,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]     => [5,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]     => [4,4,4,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]     => [6,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]     => [5,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]     => [6,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]     => [5,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]     => [4,4,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]     => [6,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]     => [5,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]     => [4,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]     => [3,3,3,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]     => [6,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]     => [5,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]     => [6,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]     => [5,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]     => [4,4,4,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]     => [6,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]     => [5,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]     => [6,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]     => [5,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]     => [4,4,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]     => [6,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]     => [5,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]     => [4,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]     => [3,3,3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]     => [6,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]     => [5,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]     => [6,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]     => [5,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]     => [4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]     => [6,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]     => [5,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]     => [4,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]     => [3,3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]     => [6,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]     => [5,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]     => [4,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]     => [3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]     => [2,2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]     => [6,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]     => [5,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]     => [6,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]     => [5,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]     => [4,4,4,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]     => [6,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]     => [5,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]     => [6,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]     => [5,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]     => [4,4,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]     => [6,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]     => [5,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]     => [4,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]     => [3,3,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]     => [6,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]     => [5,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]     => [6,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]     => [5,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]     => [4,4,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]     => [6,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]     => [5,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]     => [4,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]     => [3,3,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]     => [6,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]     => [5,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]     => [4,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]     => [3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]     => [2,2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]     => [6,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]     => [5,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]     => [6,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]     => [5,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]     => [4,4,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]     => [6,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]     => [5,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]     => [4,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]     => [3,3,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]     => [6,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]     => [5,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]     => [4,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]     => [3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]     => [2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]     => [6,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]     => [5,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]     => [4,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]     => [3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]     => [2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]     => [1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]     => [6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]     => [5,5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]     => [6,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]     => [5,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]     => [4,4,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]     => [6,5,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]     => [5,5,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]     => [6,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]     => [5,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]     => [4,4,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]     => [6,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]     => [5,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]     => [4,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]     => [3,3,3,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]     => [6,5,4,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]     => [5,5,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]     => [6,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]     => [5,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]     => [4,4,4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]     => [6,5,3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]     => [5,5,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]     => [6,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]     => [5,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]     => [4,4,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]     => [6,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]     => [5,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]     => [4,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]     => [3,3,3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]     => [6,5,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]     => [5,5,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]     => [6,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]     => [5,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]     => [4,4,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]     => [6,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]     => [5,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]     => [4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]     => [3,3,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]     => [6,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]     => [5,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]     => [4,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]     => [3,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]     => [2,2,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]     => [6,5,4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]     => [5,5,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]     => [6,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]     => [5,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]     => [4,4,4,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]     => [6,5,3,3,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]     => [5,5,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]     => [6,4,3,3,1]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]     => [5,4,3,3,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]     => [4,4,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]     => [6,3,3,3,1]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]     => [5,3,3,3,1]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]     => [4,3,3,3,1]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]     => [3,3,3,3,1]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]     => [6,5,4,2,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]     => [5,5,4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]     => [6,4,4,2,1]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]     => [5,4,4,2,1]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]     => [4,4,4,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]     => [6,5,3,2,1]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]     => [5,5,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]     => [6,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]     => [5,4,3,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]     => [4,4,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]     => [6,3,3,2,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]     => [5,3,3,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]     => [4,3,3,2,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]     => [3,3,3,2,1]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]     => [6,5,2,2,1]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]     => [5,5,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]     => [6,4,2,2,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]     => [5,4,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]     => [4,4,2,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]     => [6,3,2,2,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]     => [5,3,2,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]     => [4,3,2,2,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]     => [3,3,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]     => [6,2,2,2,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]     => [5,2,2,2,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]     => [4,2,2,2,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]     => [3,2,2,2,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]     => [2,2,2,2,1]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]     => [6,5,4,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]     => [5,5,4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]     => [6,4,4,1,1]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]     => [5,4,4,1,1]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]     => [4,4,4,1,1]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]     => [6,5,3,1,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]     => [5,5,3,1,1]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]     => [6,4,3,1,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]     => [5,4,3,1,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]     => [4,4,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]     => [6,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]     => [5,3,3,1,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]     => [4,3,3,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]     => [3,3,3,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]     => [6,5,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]     => [5,5,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]     => [6,4,2,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]     => [5,4,2,1,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]     => [4,4,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]     => [6,3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]     => [5,3,2,1,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]     => [4,3,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]     => [3,3,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]     => [6,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]     => [5,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]     => [4,2,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]     => [3,2,2,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]     => [2,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]     => [6,5,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]     => [5,5,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]     => [6,4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]     => [5,4,1,1,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]     => [4,4,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]     => [6,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]     => [5,3,1,1,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]     => [4,3,1,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]     => [3,3,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]     => [6,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]     => [5,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]     => [4,2,1,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]     => [3,2,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]     => [2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]     => [6,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]     => [5,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]     => [4,1,1,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]     => [3,1,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]     => [2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]     => [1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]     => [6,5,4,3]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]     => [5,5,4,3]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]     => [6,4,4,3]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]     => [5,4,4,3]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]     => [4,4,4,3]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]     => [6,5,3,3]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]     => [5,5,3,3]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]     => [6,4,3,3]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]     => [5,4,3,3]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]     => [4,4,3,3]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]     => [6,3,3,3]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]     => [5,3,3,3]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]     => [4,3,3,3]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]     => [3,3,3,3]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]     => [6,5,4,2]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]     => [5,5,4,2]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]     => [6,4,4,2]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]     => [5,4,4,2]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]     => [4,4,4,2]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]     => [6,5,3,2]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]     => [5,5,3,2]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]     => [6,4,3,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]     => [5,4,3,2]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]     => [4,4,3,2]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]     => [6,3,3,2]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]     => [5,3,3,2]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]     => [4,3,3,2]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]     => [3,3,3,2]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]     => [6,5,2,2]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]     => [5,5,2,2]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]     => [6,4,2,2]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]     => [5,4,2,2]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]     => [4,4,2,2]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]     => [6,3,2,2]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]     => [5,3,2,2]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]     => [4,3,2,2]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]     => [3,3,2,2]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]     => [6,2,2,2]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]     => [5,2,2,2]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]     => [4,2,2,2]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]     => [3,2,2,2]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]     => [2,2,2,2]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]     => [6,5,4,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]     => [5,5,4,1]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]     => [6,4,4,1]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]     => [5,4,4,1]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]     => [4,4,4,1]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]     => [6,5,3,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]     => [5,5,3,1]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]     => [6,4,3,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]     => [5,4,3,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]     => [4,4,3,1]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]     => [6,3,3,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]     => [5,3,3,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]     => [4,3,3,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]     => [3,3,3,1]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]     => [6,5,2,1]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]     => [5,5,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]     => [6,4,2,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]     => [5,4,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]     => [4,4,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]     => [6,3,2,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]     => [5,3,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]     => [4,3,2,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]     => [3,3,2,1]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]     => [6,2,2,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]     => [5,2,2,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]     => [4,2,2,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]     => [3,2,2,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]     => [2,2,2,1]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]     => [6,5,1,1]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]     => [5,5,1,1]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]     => [6,4,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]     => [5,4,1,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]     => [4,4,1,1]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]     => [6,3,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]     => [5,3,1,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]     => [4,3,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]     => [3,3,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]     => [6,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]     => [5,2,1,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]     => [4,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]     => [3,2,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]     => [2,2,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]     => [6,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]     => [5,1,1,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]     => [4,1,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]     => [3,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]     => [2,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]     => [1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]     => [6,5,4]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]     => [5,5,4]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]     => [6,4,4]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]     => [5,4,4]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]     => [4,4,4]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]     => [6,5,3]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]     => [5,5,3]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]     => [6,4,3]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]     => [5,4,3]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]     => [4,4,3]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]     => [6,3,3]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]     => [5,3,3]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]     => [4,3,3]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]     => [3,3,3]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]     => [6,5,2]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]     => [5,5,2]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]     => [6,4,2]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]     => [5,4,2]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]     => [4,4,2]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]     => [6,3,2]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]     => [5,3,2]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]     => [4,3,2]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]     => [3,3,2]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]     => [6,2,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]     => [5,2,2]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]     => [4,2,2]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]     => [3,2,2]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]     => [2,2,2]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]     => [6,5,1]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]     => [5,5,1]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]     => [6,4,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]     => [5,4,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]     => [4,4,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]     => [6,3,1]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]     => [5,3,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]     => [4,3,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]     => [3,3,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]     => [6,2,1]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]     => [5,2,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]     => [4,2,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]     => [3,2,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]     => [2,2,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]     => [6,1,1]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]     => [5,1,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]     => [4,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]     => [3,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]     => [2,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]     => [1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]     => [6,5]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]     => [5,5]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]     => [6,4]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]     => [5,4]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]     => [4,4]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]     => [6,3]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]     => [5,3]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]     => [4,3]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]     => [3,3]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]     => [6,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]     => [5,2]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]     => [4,2]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]     => [3,2]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]     => [2,2]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]     => [6,1]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]     => [5,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]     => [4,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]     => [3,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]     => [2,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]     => [1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]     => [6]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]     => [5]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]     => [4]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]     => [3]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]     => [2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]     => [1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]     => []
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,6,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,5,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,4,3,3,2,1]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,6,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,5,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2,1]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,2,2,1]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2,1]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2,1]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2,1]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,1,1]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,6,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,5,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,4,3,3,1,1]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,6,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,5,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,1,1]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,2,1,1]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,1,1]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,1,1]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,1,1]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,1,1]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,1,1,1]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,1,1,1]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,1,1,1]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,1,1,1]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,1,1,1]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,6,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,5,5,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,6,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,5,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,4,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,4,4,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,6,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,5,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,4,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,3,1,1,1,1]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,6,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,5,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,4,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,6,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,5,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,2]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,6,5,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,5,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,5,3,3,2]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,5,5,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,6,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,5,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,4,3,3,2]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,4,4,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,6,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,5,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,3,3,2]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,4,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,3,3,3,2]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,3,3,3,3,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,2]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,6,5,4,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,5,4,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,5,4,2,2]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,5,5,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,6,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,5,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,4,4,2,2]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,4,4,4,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,6,5,3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,5,3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,5,3,2,2]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,5,5,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,6,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,5,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,4,3,2,2]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,4,4,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,6,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,5,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,3,2,2]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,4,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,3,3,2,2]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,3,3,3,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,6,5,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,5,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,5,2,2,2]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,5,5,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,6,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,5,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,4,2,2,2]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,4,4,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,6,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,5,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,4,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,3,2,2,2]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,3,3,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,6,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,5,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,2,2,2]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,4,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,2,2,2]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2,2,2]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,2,2]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2,2]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,6,5,4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,5,4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,5,4,3,1]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,5,5,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,6,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,5,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,4,4,3,1]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,4,4,4,3,1]

-----------------------------------------------------------------------------
Created: Jan 19, 2020 at 07:29 by FindStatCrew

-----------------------------------------------------------------------------
Last Updated: Jan 19, 2020 at 07:29 by Martin Rubey