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Problems > Strings with an Even Number of Zeros

Strings with an Even Number of Zeros

Difficulty: 1800 4000 ms 128 MB

combinatorics matrix-exponentiation

Count the strings of length N over {0, 1, 2} that contain an EVEN number of 0s, modulo 109+7.

Input: one integer N.

Output: the count modulo 109+7.

Constraints:

  • 1 ≤ N ≤ 1018

Sample Tests

Input 1
1
Output 1
2
Input 2
2
Output 2
5
Input 3
3
Output 3
14

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