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+const input = [3, 8, 1001, 8, 10, 8, 105, 1, 0, 0, 21, 46, 55, 68, 89, 110, 191, 272, 353, 434, 99999, 3, 9, 1002, 9, 3, 9, 1001, 9, 3, 9, 102, 4, 9, 9, 101, 4, 9, 9, 1002, 9, 5, 9, 4, 9, 99, 3, 9, 102, 3, 9, 9, 4, 9, 99, 3, 9, 1001, 9, 5, 9, 102, 4, 9, 9, 4, 9, 99, 3, 9, 1001, 9, 5, 9, 1002, 9, 2, 9, 1001, 9, 5, 9, 1002, 9, 3, 9, 4, 9, 99, 3, 9, 101, 3, 9, 9, 102, 3, 9, 9, 101, 3, 9, 9, 1002, 9, 4, 9, 4, 9, 99, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 1001, 9, 2, 9, 4, 9, 3, 9, 1001, 9, 2, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 1001, 9, 2, 9, 4, 9, 99, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 101, 1, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 99, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 101, 1, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 99, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 101, 1, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 1001, 9, 2, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 99, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 101, 1, 9, 9, 4, 9, 3, 9, 101, 2, 9, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 3, 9, 1002, 9, 2, 9, 4, 9, 3, 9, 1001, 9, 1, 9, 4, 9, 3, 9, 102, 2, 9, 9, 4, 9, 99];
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