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 collections import defaultdict
N = int(input())
dp = [defaultdict(int) for _ in range(N+1)]
MOD = 10**9 + 7
dp[0]['TTT'] = 1


def ok(last4):
    for i in range(4):
        l = list(last4)
        if i >= 1:
            l[i-1], l[i] = l[i], l[i-1]
        if 'AGC' in ''.join(l):
            return False
    return True


for n in range(N):
    for s, cnt in dp[n].items():
        for c in 'AGCT':
            ns = s+c
            if ok(ns):
                dp[n+1][ns[-3:]] = (dp[n+1][ns[-3:]]+cnt) % MOD

print(sum(dp[N].values()) % MOD)
