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