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 re


def ok(last4):
    pattern = '.?AGC.?|.?GAC.?|.?ACG.?|A.GC|AG.C'
    res = re.match(pattern, last4)
    return res is None


def dfs(cur, last3, n, m, mod):
    if last3 in m[cur]:
        return m[cur][last3]
    if cur == n:
        return 1
    ret = 0
    for c in 'ACGT':
        if ok(last3 + c):
            ret = (ret + dfs(cur + 1, last3[1:] + c, n, m, mod)) % mod

    m[cur][last3] = ret
    return ret


def main():
    n = int(input())
    mod = 10 ** 9 + 7

    m = [{} for _ in range(n + 1)]
    ans = dfs(0, 'TTT', n, m, mod)

    print(ans)


if __name__ == '__main__':
    main()
