S=4;
puzzle_input=[|
13, 4, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 11, 0, 14, 10|
9, 12, 14, 5, 7, 0, 0, 15, 0, 0, 0, 0, 0, 2, 1, 0|
2, 15, 0, 6, 16, 0, 10, 9, 0, 0, 0, 0, 0, 5, 3, 0|
0, 0, 1, 0, 5, 0, 14, 0, 0, 0, 0, 0, 9, 6, 0, 0|
0, 0, 0, 0, 10, 12, 0, 5, 0, 0, 13, 0, 0, 0, 6, 8|
0, 0, 0, 0, 8, 0, 9, 0, 2, 0, 0, 14, 16, 0, 0, 11|
0, 0, 0, 0, 0, 0, 6, 7, 9, 0, 0, 0, 5, 15, 13, 12|
0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 12, 2, 0, 0, 3|
16, 9, 15, 10, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 0, 0|
0, 13, 0, 3, 0, 11, 0, 0, 0, 4, 1, 16, 0, 0, 0, 0|
0, 0, 8, 12, 6, 7, 16, 0, 0, 5, 0, 0, 0, 0, 0, 0|
0, 2, 11, 0, 1, 0, 0, 0, 10, 13, 12, 0, 0, 0, 0, 0|
4, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 9|
3, 6, 0, 0, 0, 0, 0, 0, 12, 1, 11, 8, 14, 0, 0, 5|
0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 7, 10, 15, 11, 0, 4|
0, 11, 10, 1, 0, 0, 0, 0, 0, 0, 15, 9, 6, 0, 7, 0
|];