You are given an integer N. Find the number of strings of length N that satisfy the following conditions, modulo 10^9+7:

* The string does not contain characters other than `A`, `C`, `G` and `T`.
* The string does not contain `AGC` as a substring.
* The condition above cannot be violated by swapping two adjacent characters once.

Constraints

* 3 \leq N \leq 100

Input

Input is given from Standard Input in the following format:


N


Output

Print the number of strings of length N that satisfy the following conditions, modulo 10^9+7.

Examples

Input

3


Output

61


Input

4


Output

230


Input

100


Output

388130742
import sys
input = sys.stdin.readline

def main():
    N = int(input())
    dp = [[0] * 4 if i != 3 else [1] * 4 for i in range(N+3)]
    MOD = int(1e9) + 7
    for i in range(4, N+3):
        sum_pre = sum(dp[i-1]) % MOD
        # A
        dp[i][0] = sum_pre
        # C
        dp[i][1] = (sum_pre - dp[i-2][0] - dp[i-2][2] - dp[i-3][0] * 3) % MOD
        # G
        dp[i][2] = (sum_pre - dp[i-2][0] + dp[i-3][2]) % MOD
        # T
        dp[i][3] = sum_pre
    print(sum(dp[-1]) % MOD)

if __name__ == "__main__":
    main()