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, MOD = int(input()), 10 ** 9 + 7

memo = [{} for _ in range(N+1)]

def ok(last4):
    for i in range(4):
        t = list(last4)

        if i >= 1:
            t[i-1], t[i] = t[i], t[i-1]

        if ''.join(t).count('AGC') >= 1:
            return False

    return True


def dfs(cur, last3):
    global N, MOD, memo

    if last3 in memo[cur]:
        return memo[cur][last3]

    if cur == N:
        return 1

    ret = 0
    for c in 'AGCT':
        if ok(last3 + c):
            ret = (ret + dfs(cur + 1, last3[1:] + c)) % MOD

    memo[cur][last3] = ret

    return ret


print(dfs(0, 'TTT'))
