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
from functools import lru_cache


def check(s):
    bads = ["AGC", "ACG", "GAC"] + [b.format(_s) for b in ["AG{}C", "A{}GC"] for _s in "ACGT"]
    return not any(map(lambda x: x in s, bads))


def solve(string):
    n = int(string)

    @lru_cache(n * 4**3)
    def dfs(pos, last3):
        if pos == n:
            return 1
        ans = 0
        for _s in "ACGT":
            ans += dfs(pos + 1, last3[1:] + _s) if check(last3 + _s) else 0
        return ans % (10**9 + 7)

    return str(dfs(0, "TTT"))


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