Avoid the Set {00, 12}

Difficulty: 2400 4000 ms 128 MB

combinatorics aho-corasick matrix-exponentiation

Count the strings of length N over {0, 1, 2} that contain none of 00, 12 as a substring, modulo 10⁹+7.

Input: one integer N.

Output: the count mod 10⁹+7.

Constraints:

• 1 ≤ N ≤ 10¹⁸

Sample Tests

1

3

2

7

4

36

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