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
N = int(input())
mod = 10 ** 9 + 7
dp = [{} for i in range(N)]
forbid = set(['AGC', 'GAC', 'ACG'])


def search(i, prefix):
    if prefix in forbid:
        return 0
    elif i == N:
        return 1
    elif prefix in dp[i]:
        return dp[i][prefix]

    ret = 0
    for c in 'ACGT':
        if prefix[0] == 'A' and (prefix[1] == 'G' or prefix[2] == 'G') and c == 'C':
            continue
        ret += search(i + 1, prefix[1:] + c)
    dp[i][prefix] = ret % mod
    return ret % mod


print(search(0, 'BBB'))