Avoid the Set {012, 210}

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 012, 210 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

9

4

69

Read the Editorial