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rdkit/Code/PgSQL/RDLib/DistMat.cpp
Greg Landrum 75a79b6327 initial import
2006-05-06 22:20:08 +00:00

2068 lines
135 KiB
C++
Raw Blame History

// $Id
//
// Copyright (C) 2005-2006 Rational Discovery LLC
//
// @@ All Rights Reserved @@
//
char numByteOnBits[]={
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
};
char byteByteDistMat[]={
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
4,5,5,6,5,6,6,7,5,6,6,7,6,7,7,8,3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,4,5,5,6,5,6,6,7,2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
2,3,3,4,3,4,4,5,3,4,4,5,4,5,5,6,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,
1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,5,0,1,1,2,1,2,2,3,1,2,2,3,2,3,3,4,
5,4,6,5,6,5,7,6,6,5,7,6,7,6,8,7,4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,5,4,6,5,6,5,7,6,3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
3,2,4,3,4,3,5,4,4,3,5,4,5,4,6,5,2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,
2,1,3,2,3,2,4,3,3,2,4,3,4,3,5,4,1,0,2,1,2,1,3,2,2,1,3,2,3,2,4,3,
5,6,4,5,6,7,5,6,6,7,5,6,7,8,6,7,4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,5,6,4,5,6,7,5,6,3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
3,4,2,3,4,5,3,4,4,5,3,4,5,6,4,5,2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,
2,3,1,2,3,4,2,3,3,4,2,3,4,5,3,4,1,2,0,1,2,3,1,2,2,3,1,2,3,4,2,3,
6,5,5,4,7,6,6,5,7,6,6,5,8,7,7,6,5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,6,5,5,4,7,6,6,5,4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
4,3,3,2,5,4,4,3,5,4,4,3,6,5,5,4,3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,
3,2,2,1,4,3,3,2,4,3,3,2,5,4,4,3,2,1,1,0,3,2,2,1,3,2,2,1,4,3,3,2,
5,6,6,7,4,5,5,6,6,7,7,8,5,6,6,7,4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,5,6,6,7,4,5,5,6,3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
3,4,4,5,2,3,3,4,4,5,5,6,3,4,4,5,2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,
2,3,3,4,1,2,2,3,3,4,4,5,2,3,3,4,1,2,2,3,0,1,1,2,2,3,3,4,1,2,2,3,
6,5,7,6,5,4,6,5,7,6,8,7,6,5,7,6,5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,6,5,7,6,5,4,6,5,4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
4,3,5,4,3,2,4,3,5,4,6,5,4,3,5,4,3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,
3,2,4,3,2,1,3,2,4,3,5,4,3,2,4,3,2,1,3,2,1,0,2,1,3,2,4,3,2,1,3,2,
6,7,5,6,5,6,4,5,7,8,6,7,6,7,5,6,5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,6,7,5,6,5,6,4,5,4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
4,5,3,4,3,4,2,3,5,6,4,5,4,5,3,4,3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,
3,4,2,3,2,3,1,2,4,5,3,4,3,4,2,3,2,3,1,2,1,2,0,1,3,4,2,3,2,3,1,2,
7,6,6,5,6,5,5,4,8,7,7,6,7,6,6,5,6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,7,6,6,5,6,5,5,4,5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
5,4,4,3,4,3,3,2,6,5,5,4,5,4,4,3,4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,
4,3,3,2,3,2,2,1,5,4,4,3,4,3,3,2,3,2,2,1,2,1,1,0,4,3,3,2,3,2,2,1,
5,6,6,7,6,7,7,8,4,5,5,6,5,6,6,7,4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
4,5,5,6,5,6,6,7,3,4,4,5,4,5,5,6,3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
3,4,4,5,4,5,5,6,2,3,3,4,3,4,4,5,2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,
2,3,3,4,3,4,4,5,1,2,2,3,2,3,3,4,1,2,2,3,2,3,3,4,0,1,1,2,1,2,2,3,
6,5,7,6,7,6,8,7,5,4,6,5,6,5,7,6,5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
5,4,6,5,6,5,7,6,4,3,5,4,5,4,6,5,4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
4,3,5,4,5,4,6,5,3,2,4,3,4,3,5,4,3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,
3,2,4,3,4,3,5,4,2,1,3,2,3,2,4,3,2,1,3,2,3,2,4,3,1,0,2,1,2,1,3,2,
6,7,5,6,7,8,6,7,5,6,4,5,6,7,5,6,5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
5,6,4,5,6,7,5,6,4,5,3,4,5,6,4,5,4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
4,5,3,4,5,6,4,5,3,4,2,3,4,5,3,4,3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,
3,4,2,3,4,5,3,4,2,3,1,2,3,4,2,3,2,3,1,2,3,4,2,3,1,2,0,1,2,3,1,2,
7,6,6,5,8,7,7,6,6,5,5,4,7,6,6,5,6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
6,5,5,4,7,6,6,5,5,4,4,3,6,5,5,4,5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
5,4,4,3,6,5,5,4,4,3,3,2,5,4,4,3,4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,
4,3,3,2,5,4,4,3,3,2,2,1,4,3,3,2,3,2,2,1,4,3,3,2,2,1,1,0,3,2,2,1,
6,7,7,8,5,6,6,7,5,6,6,7,4,5,5,6,5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
5,6,6,7,4,5,5,6,4,5,5,6,3,4,4,5,4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
4,5,5,6,3,4,4,5,3,4,4,5,2,3,3,4,3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,
3,4,4,5,2,3,3,4,2,3,3,4,1,2,2,3,2,3,3,4,1,2,2,3,1,2,2,3,0,1,1,2,
7,6,8,7,6,5,7,6,6,5,7,6,5,4,6,5,6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
6,5,7,6,5,4,6,5,5,4,6,5,4,3,5,4,5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
5,4,6,5,4,3,5,4,4,3,5,4,3,2,4,3,4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,
4,3,5,4,3,2,4,3,3,2,4,3,2,1,3,2,3,2,4,3,2,1,3,2,2,1,3,2,1,0,2,1,
7,8,6,7,6,7,5,6,6,7,5,6,5,6,4,5,6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
6,7,5,6,5,6,4,5,5,6,4,5,4,5,3,4,5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
5,6,4,5,4,5,3,4,4,5,3,4,3,4,2,3,4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,
4,5,3,4,3,4,2,3,3,4,2,3,2,3,1,2,3,4,2,3,2,3,1,2,2,3,1,2,1,2,0,1,
8,7,7,6,7,6,6,5,7,6,6,5,6,5,5,4,7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
7,6,6,5,6,5,5,4,6,5,5,4,5,4,4,3,6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
6,5,5,4,5,4,4,3,5,4,4,3,4,3,3,2,5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,
5,4,4,3,4,3,3,2,4,3,3,2,3,2,2,1,4,3,3,2,3,2,2,1,3,2,2,1,2,1,1,0,
};
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