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1S=4;
2puzzle_input=[|
313, 4, 0, 16, 0, 2, 0, 0, 0, 0, 0, 0, 11, 0, 14, 10|
49, 12, 14, 5, 7, 0, 0, 15, 0, 0, 0, 0, 0, 2, 1, 0|
52, 15, 0, 6, 16, 0, 10, 9, 0, 0, 0, 0, 0, 5, 3, 0|
60, 0, 1, 0, 5, 0, 14, 0, 0, 0, 0, 0, 9, 6, 0, 0|
70, 0, 0, 0, 10, 12, 0, 5, 0, 0, 13, 0, 0, 0, 6, 8|
80, 0, 0, 0, 8, 0, 9, 0, 2, 0, 0, 14, 16, 0, 0, 11|
90, 0, 0, 0, 0, 0, 6, 7, 9, 0, 0, 0, 5, 15, 13, 12|
100, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 12, 2, 0, 0, 3|
1116, 9, 15, 10, 0, 0, 0, 4, 0, 6, 0, 2, 0, 0, 0, 0|
120, 13, 0, 3, 0, 11, 0, 0, 0, 4, 1, 16, 0, 0, 0, 0|
130, 0, 8, 12, 6, 7, 16, 0, 0, 5, 0, 0, 0, 0, 0, 0|
140, 2, 11, 0, 1, 0, 0, 0, 10, 13, 12, 0, 0, 0, 0, 0|
154, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 9|
163, 6, 0, 0, 0, 0, 0, 0, 12, 1, 11, 8, 14, 0, 0, 5|
170, 14, 0, 0, 0, 0, 0, 0, 0, 0, 7, 10, 15, 11, 0, 4|
180, 11, 10, 1, 0, 0, 0, 0, 0, 0, 15, 9, 6, 0, 7, 0
19|];