*****************************************************************************
*       www.FindStat.org - The Combinatorial Statistic Finder               *
*                                                                           *
*       Copyright (C) 2019 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.                   *
*****************************************************************************

-----------------------------------------------------------------------------
Statistic identifier: St000920

-----------------------------------------------------------------------------
Collection: Dyck paths

-----------------------------------------------------------------------------
Description: The logarithmic height of a Dyck path.

This is the floor of the binary logarithm of the usual height increased by one:
$$
\lfloor\log_2(1+height(D))\rfloor
$$

-----------------------------------------------------------------------------
References: [1]   Françon, J. Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique [[MathSciNet:0775838]]

-----------------------------------------------------------------------------
Code:
def statistic(D):
    return floor(log(1+D.height(), 2))


-----------------------------------------------------------------------------
Statistic values:

[]                                                => 0
[1,0]                                             => 1
[1,0,1,0]                                         => 1
[1,1,0,0]                                         => 1
[1,0,1,0,1,0]                                     => 1
[1,0,1,1,0,0]                                     => 1
[1,1,0,0,1,0]                                     => 1
[1,1,0,1,0,0]                                     => 1
[1,1,1,0,0,0]                                     => 2
[1,0,1,0,1,0,1,0]                                 => 1
[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]                                 => 1
[1,0,1,1,1,0,0,0]                                 => 2
[1,1,0,0,1,0,1,0]                                 => 1
[1,1,0,0,1,1,0,0]                                 => 1
[1,1,0,1,0,0,1,0]                                 => 1
[1,1,0,1,0,1,0,0]                                 => 1
[1,1,0,1,1,0,0,0]                                 => 2
[1,1,1,0,0,0,1,0]                                 => 2
[1,1,1,0,0,1,0,0]                                 => 2
[1,1,1,0,1,0,0,0]                                 => 2
[1,1,1,1,0,0,0,0]                                 => 2
[1,0,1,0,1,0,1,0,1,0]                             => 1
[1,0,1,0,1,0,1,1,0,0]                             => 1
[1,0,1,0,1,1,0,0,1,0]                             => 1
[1,0,1,0,1,1,0,1,0,0]                             => 1
[1,0,1,0,1,1,1,0,0,0]                             => 2
[1,0,1,1,0,0,1,0,1,0]                             => 1
[1,0,1,1,0,0,1,1,0,0]                             => 1
[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]                             => 2
[1,0,1,1,1,0,0,0,1,0]                             => 2
[1,0,1,1,1,0,0,1,0,0]                             => 2
[1,0,1,1,1,0,1,0,0,0]                             => 2
[1,0,1,1,1,1,0,0,0,0]                             => 2
[1,1,0,0,1,0,1,0,1,0]                             => 1
[1,1,0,0,1,0,1,1,0,0]                             => 1
[1,1,0,0,1,1,0,0,1,0]                             => 1
[1,1,0,0,1,1,0,1,0,0]                             => 1
[1,1,0,0,1,1,1,0,0,0]                             => 2
[1,1,0,1,0,0,1,0,1,0]                             => 1
[1,1,0,1,0,0,1,1,0,0]                             => 1
[1,1,0,1,0,1,0,0,1,0]                             => 1
[1,1,0,1,0,1,0,1,0,0]                             => 1
[1,1,0,1,0,1,1,0,0,0]                             => 2
[1,1,0,1,1,0,0,0,1,0]                             => 2
[1,1,0,1,1,0,0,1,0,0]                             => 2
[1,1,0,1,1,0,1,0,0,0]                             => 2
[1,1,0,1,1,1,0,0,0,0]                             => 2
[1,1,1,0,0,0,1,0,1,0]                             => 2
[1,1,1,0,0,0,1,1,0,0]                             => 2
[1,1,1,0,0,1,0,0,1,0]                             => 2
[1,1,1,0,0,1,0,1,0,0]                             => 2
[1,1,1,0,0,1,1,0,0,0]                             => 2
[1,1,1,0,1,0,0,0,1,0]                             => 2
[1,1,1,0,1,0,0,1,0,0]                             => 2
[1,1,1,0,1,0,1,0,0,0]                             => 2
[1,1,1,0,1,1,0,0,0,0]                             => 2
[1,1,1,1,0,0,0,0,1,0]                             => 2
[1,1,1,1,0,0,0,1,0,0]                             => 2
[1,1,1,1,0,0,1,0,0,0]                             => 2
[1,1,1,1,0,1,0,0,0,0]                             => 2
[1,1,1,1,1,0,0,0,0,0]                             => 2
[1,0,1,0,1,0,1,0,1,0,1,0]                         => 1
[1,0,1,0,1,0,1,0,1,1,0,0]                         => 1
[1,0,1,0,1,0,1,1,0,0,1,0]                         => 1
[1,0,1,0,1,0,1,1,0,1,0,0]                         => 1
[1,0,1,0,1,0,1,1,1,0,0,0]                         => 2
[1,0,1,0,1,1,0,0,1,0,1,0]                         => 1
[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]                         => 1
[1,0,1,0,1,1,0,1,0,1,0,0]                         => 1
[1,0,1,0,1,1,0,1,1,0,0,0]                         => 2
[1,0,1,0,1,1,1,0,0,0,1,0]                         => 2
[1,0,1,0,1,1,1,0,0,1,0,0]                         => 2
[1,0,1,0,1,1,1,0,1,0,0,0]                         => 2
[1,0,1,0,1,1,1,1,0,0,0,0]                         => 2
[1,0,1,1,0,0,1,0,1,0,1,0]                         => 1
[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]                         => 1
[1,0,1,1,0,0,1,1,1,0,0,0]                         => 2
[1,0,1,1,0,1,0,0,1,0,1,0]                         => 1
[1,0,1,1,0,1,0,0,1,1,0,0]                         => 1
[1,0,1,1,0,1,0,1,0,0,1,0]                         => 1
[1,0,1,1,0,1,0,1,0,1,0,0]                         => 1
[1,0,1,1,0,1,0,1,1,0,0,0]                         => 2
[1,0,1,1,0,1,1,0,0,0,1,0]                         => 2
[1,0,1,1,0,1,1,0,0,1,0,0]                         => 2
[1,0,1,1,0,1,1,0,1,0,0,0]                         => 2
[1,0,1,1,0,1,1,1,0,0,0,0]                         => 2
[1,0,1,1,1,0,0,0,1,0,1,0]                         => 2
[1,0,1,1,1,0,0,0,1,1,0,0]                         => 2
[1,0,1,1,1,0,0,1,0,0,1,0]                         => 2
[1,0,1,1,1,0,0,1,0,1,0,0]                         => 2
[1,0,1,1,1,0,0,1,1,0,0,0]                         => 2
[1,0,1,1,1,0,1,0,0,0,1,0]                         => 2
[1,0,1,1,1,0,1,0,0,1,0,0]                         => 2
[1,0,1,1,1,0,1,0,1,0,0,0]                         => 2
[1,0,1,1,1,0,1,1,0,0,0,0]                         => 2
[1,0,1,1,1,1,0,0,0,0,1,0]                         => 2
[1,0,1,1,1,1,0,0,0,1,0,0]                         => 2
[1,0,1,1,1,1,0,0,1,0,0,0]                         => 2
[1,0,1,1,1,1,0,1,0,0,0,0]                         => 2
[1,0,1,1,1,1,1,0,0,0,0,0]                         => 2
[1,1,0,0,1,0,1,0,1,0,1,0]                         => 1
[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]                         => 1
[1,1,0,0,1,0,1,1,1,0,0,0]                         => 2
[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
[1,1,0,0,1,1,0,1,0,0,1,0]                         => 1
[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]                         => 2
[1,1,0,0,1,1,1,0,0,0,1,0]                         => 2
[1,1,0,0,1,1,1,0,0,1,0,0]                         => 2
[1,1,0,0,1,1,1,0,1,0,0,0]                         => 2
[1,1,0,0,1,1,1,1,0,0,0,0]                         => 2
[1,1,0,1,0,0,1,0,1,0,1,0]                         => 1
[1,1,0,1,0,0,1,0,1,1,0,0]                         => 1
[1,1,0,1,0,0,1,1,0,0,1,0]                         => 1
[1,1,0,1,0,0,1,1,0,1,0,0]                         => 1
[1,1,0,1,0,0,1,1,1,0,0,0]                         => 2
[1,1,0,1,0,1,0,0,1,0,1,0]                         => 1
[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]                         => 1
[1,1,0,1,0,1,0,1,0,1,0,0]                         => 1
[1,1,0,1,0,1,0,1,1,0,0,0]                         => 2
[1,1,0,1,0,1,1,0,0,0,1,0]                         => 2
[1,1,0,1,0,1,1,0,0,1,0,0]                         => 2
[1,1,0,1,0,1,1,0,1,0,0,0]                         => 2
[1,1,0,1,0,1,1,1,0,0,0,0]                         => 2
[1,1,0,1,1,0,0,0,1,0,1,0]                         => 2
[1,1,0,1,1,0,0,0,1,1,0,0]                         => 2
[1,1,0,1,1,0,0,1,0,0,1,0]                         => 2
[1,1,0,1,1,0,0,1,0,1,0,0]                         => 2
[1,1,0,1,1,0,0,1,1,0,0,0]                         => 2
[1,1,0,1,1,0,1,0,0,0,1,0]                         => 2
[1,1,0,1,1,0,1,0,0,1,0,0]                         => 2
[1,1,0,1,1,0,1,0,1,0,0,0]                         => 2
[1,1,0,1,1,0,1,1,0,0,0,0]                         => 2
[1,1,0,1,1,1,0,0,0,0,1,0]                         => 2
[1,1,0,1,1,1,0,0,0,1,0,0]                         => 2
[1,1,0,1,1,1,0,0,1,0,0,0]                         => 2
[1,1,0,1,1,1,0,1,0,0,0,0]                         => 2
[1,1,0,1,1,1,1,0,0,0,0,0]                         => 2
[1,1,1,0,0,0,1,0,1,0,1,0]                         => 2
[1,1,1,0,0,0,1,0,1,1,0,0]                         => 2
[1,1,1,0,0,0,1,1,0,0,1,0]                         => 2
[1,1,1,0,0,0,1,1,0,1,0,0]                         => 2
[1,1,1,0,0,0,1,1,1,0,0,0]                         => 2
[1,1,1,0,0,1,0,0,1,0,1,0]                         => 2
[1,1,1,0,0,1,0,0,1,1,0,0]                         => 2
[1,1,1,0,0,1,0,1,0,0,1,0]                         => 2
[1,1,1,0,0,1,0,1,0,1,0,0]                         => 2
[1,1,1,0,0,1,0,1,1,0,0,0]                         => 2
[1,1,1,0,0,1,1,0,0,0,1,0]                         => 2
[1,1,1,0,0,1,1,0,0,1,0,0]                         => 2
[1,1,1,0,0,1,1,0,1,0,0,0]                         => 2
[1,1,1,0,0,1,1,1,0,0,0,0]                         => 2
[1,1,1,0,1,0,0,0,1,0,1,0]                         => 2
[1,1,1,0,1,0,0,0,1,1,0,0]                         => 2
[1,1,1,0,1,0,0,1,0,0,1,0]                         => 2
[1,1,1,0,1,0,0,1,0,1,0,0]                         => 2
[1,1,1,0,1,0,0,1,1,0,0,0]                         => 2
[1,1,1,0,1,0,1,0,0,0,1,0]                         => 2
[1,1,1,0,1,0,1,0,0,1,0,0]                         => 2
[1,1,1,0,1,0,1,0,1,0,0,0]                         => 2
[1,1,1,0,1,0,1,1,0,0,0,0]                         => 2
[1,1,1,0,1,1,0,0,0,0,1,0]                         => 2
[1,1,1,0,1,1,0,0,0,1,0,0]                         => 2
[1,1,1,0,1,1,0,0,1,0,0,0]                         => 2
[1,1,1,0,1,1,0,1,0,0,0,0]                         => 2
[1,1,1,0,1,1,1,0,0,0,0,0]                         => 2
[1,1,1,1,0,0,0,0,1,0,1,0]                         => 2
[1,1,1,1,0,0,0,0,1,1,0,0]                         => 2
[1,1,1,1,0,0,0,1,0,0,1,0]                         => 2
[1,1,1,1,0,0,0,1,0,1,0,0]                         => 2
[1,1,1,1,0,0,0,1,1,0,0,0]                         => 2
[1,1,1,1,0,0,1,0,0,0,1,0]                         => 2
[1,1,1,1,0,0,1,0,0,1,0,0]                         => 2
[1,1,1,1,0,0,1,0,1,0,0,0]                         => 2
[1,1,1,1,0,0,1,1,0,0,0,0]                         => 2
[1,1,1,1,0,1,0,0,0,0,1,0]                         => 2
[1,1,1,1,0,1,0,0,0,1,0,0]                         => 2
[1,1,1,1,0,1,0,0,1,0,0,0]                         => 2
[1,1,1,1,0,1,0,1,0,0,0,0]                         => 2
[1,1,1,1,0,1,1,0,0,0,0,0]                         => 2
[1,1,1,1,1,0,0,0,0,0,1,0]                         => 2
[1,1,1,1,1,0,0,0,0,1,0,0]                         => 2
[1,1,1,1,1,0,0,0,1,0,0,0]                         => 2
[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]                         => 2
[1,1,1,1,1,1,0,0,0,0,0,0]                         => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]                     => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]                     => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]                     => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]                     => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]                     => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]                     => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]                     => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]                     => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]                     => 1
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]                     => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]                     => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]                     => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]                     => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]                     => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]                     => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]                     => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]                     => 1
[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]                     => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]                     => 1
[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]                     => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]                     => 1
[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]                     => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]                     => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]                     => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]                     => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]                     => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]                     => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]                     => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]                     => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]                     => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]                     => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]                     => 2
[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]                     => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]                     => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]                     => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]                     => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]                     => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]                     => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]                     => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]                     => 1
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]                     => 1
[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]                     => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]                     => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]                     => 1
[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]                     => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]                     => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]                     => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]                     => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]                     => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]                     => 1
[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]                     => 1
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]                     => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]                     => 1
[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]                     => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]                     => 1
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]                     => 2
[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]                     => 2
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]                     => 2
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]                     => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]                     => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]                     => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]                     => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]                     => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]                     => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]                     => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]                     => 2
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]                     => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]                     => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]                     => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]                     => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]                     => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]                     => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]                     => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]                     => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]                     => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]                     => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]                     => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]                     => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]                     => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]                     => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]                     => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]                     => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]                     => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]                     => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]                     => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]                     => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]                     => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]                     => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]                     => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]                     => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]                     => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]                     => 2
[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]                     => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]                     => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]                     => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]                     => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]                     => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]                     => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]                     => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]                     => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]                     => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]                     => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]                     => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]                     => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]                     => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]                     => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]                     => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]                     => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]                     => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]                     => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]                     => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]                     => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]                     => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]                     => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]                     => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]                     => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]                     => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]                     => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]                     => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]                     => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]                     => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]                     => 1
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]                     => 1
[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]                     => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]                     => 1
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]                     => 1
[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]                     => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]                     => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]                     => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]                     => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]                     => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]                     => 1
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]                     => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]                     => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]                     => 1
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]                     => 2
[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]                     => 1
[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]                     => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]                     => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]                     => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]                     => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]                     => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]                     => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]                     => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]                     => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]                     => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]                     => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]                     => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]                     => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]                     => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]                     => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]                     => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]                     => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]                     => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]                     => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]                     => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]                     => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]                     => 1
[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]                     => 1
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]                     => 2
[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]                     => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]                     => 1
[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]                     => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]                     => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]                     => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]                     => 2
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]                     => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]                     => 1
[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]                     => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]                     => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]                     => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]                     => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]                     => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]                     => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]                     => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]                     => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]                     => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]                     => 2
[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]                     => 2
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]                     => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]                     => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]                     => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]                     => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]                     => 2
[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]                     => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]                     => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]                     => 2
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]                     => 2
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]                     => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]                     => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]                     => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]                     => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]                     => 2
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]                     => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]                     => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]                     => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]                     => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]                     => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]                     => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]                     => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]                     => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]                     => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]                     => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]                     => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]                     => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]                     => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]                     => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]                     => 2
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]                     => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]                     => 2
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]                     => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]                     => 2
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]                     => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]                     => 2
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]                     => 2
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]                     => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]                     => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]                     => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]                     => 2
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]                     => 2
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]                     => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]                     => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]                     => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]                     => 2
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]                     => 2
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]                     => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]                     => 2
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]                     => 2
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]                     => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]                     => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]                     => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]                     => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]                     => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]                     => 2
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]                     => 2
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]                     => 2
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]                     => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]                     => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]                     => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]                     => 2
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]                     => 2
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]                     => 2
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]                     => 2
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]                     => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]                     => 2
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]                     => 2
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]                     => 2
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]                     => 2
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]                     => 2
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]                     => 2
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]                     => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]                     => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]                     => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]                     => 2
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]                     => 2
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]                     => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]                     => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]                     => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]                     => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]                     => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]                     => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]                     => 2
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]                     => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]                     => 2
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]                     => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]                     => 2
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]                     => 2
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]                     => 2
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]                     => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]                     => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]                     => 2
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]                     => 2
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]                     => 2
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]                     => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]                     => 2
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]                     => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]                     => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]                     => 2
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]                     => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]                     => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]                     => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]                     => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]                     => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]                     => 2
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]                     => 2
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]                     => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]                     => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]                     => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]                     => 2
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]                     => 2
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]                     => 2
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]                     => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]                     => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]                     => 2
[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]                     => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]                     => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]                     => 2
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]                     => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]                     => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]                     => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]                     => 2
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]                     => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]                     => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]                     => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]                     => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]                     => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]                     => 2
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]                     => 2
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]                     => 2
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]                     => 2
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]                     => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]                     => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]                     => 2
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]                     => 2
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]                     => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]                     => 2
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]                     => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]                     => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]                     => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]                     => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]                     => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]                     => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]                     => 2
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]                     => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]                     => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]                     => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]                     => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]                     => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]                     => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]                     => 2
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]                     => 2
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]                     => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]                     => 2
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]                     => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]                     => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]                     => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]                     => 2
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]                     => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]                     => 2
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]                     => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]                     => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]                     => 2
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]                     => 2
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]                     => 2
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]                     => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]                     => 2
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]                     => 2
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]                     => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]                     => 2
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]                     => 2
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]                     => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]                     => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]                     => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]                     => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]                     => 2
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]                     => 2
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]                     => 2
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]                     => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]                     => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]                     => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]                     => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]                     => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]                     => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]                     => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]                     => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]                     => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]                     => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]                     => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]                     => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]                     => 2
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]                     => 2
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]                     => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]                     => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]                     => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]                     => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]                     => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]                     => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]                     => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]                     => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]                     => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]                     => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]                     => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]                     => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]                     => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]                     => 2
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]                     => 2
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]                     => 2
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]                     => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]                     => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]                     => 2
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]                     => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]                     => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]                     => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]                     => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]                     => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]                     => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]                     => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]                     => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]                     => 2
[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]                     => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]                     => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]                 => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]                 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]                 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]                 => 1
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]                 => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]                 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]                 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]                 => 1
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]                 => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]                 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]                 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]                 => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]                 => 1
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]                 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]                 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]                 => 1
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]                 => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]                 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]                 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]                 => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]                 => 1
[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]                 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]                 => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]                 => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]                 => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]                 => 1
[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]                 => 2
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]                 => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]                 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]                 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]                 => 1
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]                 => 2
[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]                 => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]                 => 2
[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]                 => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]                 => 2
[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]                 => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]                 => 2
[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]                 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]                 => 2
[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]                 => 2
[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]                 => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]                 => 2
[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]                 => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]                 => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]                 => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]                 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]                 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]                 => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]                 => 1
[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]                 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]                 => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]                 => 1
[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]                 => 1
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]                 => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]                 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]                 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]                 => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]                 => 1
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]                 => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]                 => 1
[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]                 => 2
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]                 => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]                 => 1
[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]                 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]                 => 1
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]                 => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]                 => 1
[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]                 => 2
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]                 => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]                 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]                 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]                 => 1
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]                 => 2
[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]                 => 2
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]                 => 2
[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]                 => 2
[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]                 => 2
[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]                 => 2
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]                 => 2
[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]                 => 2
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]                 => 2
[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]                 => 2
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]                 => 2
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]                 => 2
[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]                 => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]                 => 2
[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]                 => 2
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]                 => 2
[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]                 => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]                 => 2
[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]                 => 2
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]                 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]                 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]                 => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]                 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]                 => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]                 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]                 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]                 => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]                 => 1
[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]                 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]                 => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]                 => 1
[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]                 => 1
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]                 => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]                 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]                 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]                 => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]                 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]                 => 1
[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]                 => 1
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]                 => 2
[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]                 => 1
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]                 => 1
[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]                 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]                 => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]                 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]                 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]                 => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]                 => 1
[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]                 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]                 => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]                 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]                 => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]                 => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]                 => 1
[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]                 => 2
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]                 => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]                 => 1
[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]                 => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]                 => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]                 => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]                 => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]                 => 1
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]                 => 1
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]                 => 2
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]                 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]                 => 1
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]                 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]                 => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]                 => 1
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]                 => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]                 => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]                 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]                 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]                 => 1
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]                 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]                 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]                 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]                 => 1
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]                 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]                 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]                 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]                 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]                 => 2
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]                 => 2
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]                 => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]                 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]                 => 2
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]                 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]                 => 2
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]                 => 2
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]                 => 2
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]                 => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]                 => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]                 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]                 => 2
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]                 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]                 => 2
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]                 => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]                 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]                 => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]                 => 2
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]                 => 2
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]                 => 2
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]                 => 2
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]                 => 2
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]                 => 2
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]                 => 2
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]                 => 2
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]                 => 2
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]                 => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]                 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]                 => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]                 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]                 => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]                 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]                 => 2
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]                 => 2
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]                 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]                 => 2
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]                 => 2
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]                 => 2
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]                 => 2
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]                 => 2
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]                 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]                 => 2
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]                 => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]                 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]                 => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]                 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]                 => 2
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]                 => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]                 => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]                 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]                 => 3
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]                 => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]                 => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]             => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]             => 3
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]             => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]             => 3
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]             => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]             => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]             => 2
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]             => 2
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]             => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]             => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]             => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]             => 3
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]             => 2
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]             => 3
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]             => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]             => 2
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]             => 2
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]             => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]             => 2
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]             => 2
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]             => 2
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]             => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]             => 2
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]             => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]             => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]             => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]             => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]             => 3
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]             => 2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]             => 3
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]             => 3
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]             => 3
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]             => 3
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]             => 3
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]             => 2
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]             => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]             => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]             => 2
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]             => 3
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]             => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]             => 2
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]             => 3
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]             => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]             => 2
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]             => 3
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]             => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]             => 2
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]             => 2
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]             => 2
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]             => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]             => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]             => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]             => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]             => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]             => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]             => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]             => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]             => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]             => 2
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]             => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]             => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]             => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]             => 2
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]             => 2
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]             => 2
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]             => 2
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]             => 2
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]             => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]             => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]             => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]             => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]             => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]             => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]             => 1
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]             => 2
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]             => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]             => 2
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]             => 2
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]             => 1
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]             => 1
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]             => 2
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]             => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]             => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]             => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]             => 1
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]             => 1
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]             => 2
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]             => 2
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]             => 2
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]             => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]             => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]             => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]             => 2
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]             => 1
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]             => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]             => 2
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]             => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]             => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]             => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]             => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]             => 1
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]             => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]             => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]             => 2
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]             => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]             => 2
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]             => 2
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,1,0,0]             => 2
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]             => 2
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]             => 2
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]             => 2
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]             => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]             => 2
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]             => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]             => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]             => 2
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]             => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]             => 2
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]             => 2
[1,1,0,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]             => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]             => 2
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]             => 2
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]             => 2
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]             => 2
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]             => 2
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]             => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]             => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]             => 2
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]             => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]             => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]             => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]             => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]             => 1
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]             => 1
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]             => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]             => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]             => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]             => 2
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]             => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]             => 2
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]             => 2
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]             => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]             => 2
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]             => 1
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]             => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]             => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]             => 2
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]             => 2
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]             => 2
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]             => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]         => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]         => 3
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]         => 3
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]         => 3
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]         => 3
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]         => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]         => 3
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]         => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]         => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0]         => 3
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]         => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]         => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]         => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]         => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]         => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]         => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]         => 1
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]         => 2
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]         => 2
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]         => 2
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]         => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]         => 1
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]         => 1
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]         => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]         => 1
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]         => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]         => 1
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]         => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 2
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]         => 3
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 2
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]         => 2
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]         => 2
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]         => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]         => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]         => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]         => 3
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]         => 3
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]         => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]         => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]         => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]         => 2
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]         => 2
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]         => 3
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]         => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]         => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]         => 3
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]         => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]         => 1
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]         => 2
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]         => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]         => 2
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]         => 2
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]         => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]         => 3
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0,0]         => 3
[1,1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]         => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]         => 2
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]         => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]         => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]         => 2
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0]         => 2
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0]         => 2
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]         => 2
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]         => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]         => 2
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]         => 2
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]         => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]         => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]         => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]         => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]         => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]         => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]         => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0]         => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]         => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]         => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]         => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]         => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]         => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]         => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]         => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]         => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]         => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]         => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]         => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]         => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]         => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]         => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]         => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]         => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]         => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]         => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]         => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]         => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]         => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0]         => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0]         => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0]         => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0]         => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0]         => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0]         => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0]         => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0]         => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0]         => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0]         => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0]         => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0]         => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0]         => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]         => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]         => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]         => 3
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]         => 3
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0,0]         => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]         => 3
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]         => 3
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]         => 3
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]         => 2
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]         => 2
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]     => 3
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]     => 3
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]     => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]     => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]     => 1
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]     => 2
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]     => 2
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]     => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]     => 3
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]     => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]     => 3
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]     => 3
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0]     => 3
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]     => 3
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]     => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]     => 2
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]     => 2
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]     => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]     => 3
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]     => 3
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]     => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]     => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]     => 3
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]     => 3
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0] => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => 3

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Created: Jul 29, 2017 at 15:23 by Martin Rubey

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Last Updated: Jun 17, 2021 at 10:55 by Martin Rubey