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
def solve(string):
    n = int(string)
    dp = [[0] * 4 for _ in range(n)]
    dp[0] = [1] * 4
    for i in range(1, n):
        base = sum(dp[i - 1])
        for j in range(4):
            dp[i][j] = base
        # "AGC", "ACG", "GAC"
        if i >= 2:
            dp[i][1] -= dp[i - 2][0] + dp[i - 2][2]
            dp[i][2] -= dp[i - 2][0]
        # "AG{}C", "A{}GC"
        if i >= 3:
            dp[i][1] -= dp[i - 3][0] * 3
            dp[i][2] += dp[i - 3][2]

    return str(sum(dp[n - 1]) % (10**9 + 7))


if __name__ == '__main__':
    print(solve(input()))
