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
MOD = 10**9 + 7

N = int(input())

STT = [
    [1,0,2,0],[1,3,4,5],[6,0,2,0],[1,0,10,0],[6,10,7,8],
    [1,0,9,0],[1,10,4,5],[6,10,2,0],[1,10,2,0],[6,10,2,0]
]

dp = [[0]*(11) for _ in range(N+1)]
dp[0][0] = 1
for i in range(N):
    for st in range(10):
        for ch in range(4):
            dp[i+1][STT[st][ch]] += dp[i][st]
            dp[i+1][STT[st][ch]] %= MOD

print(sum(dp[-1][:-1]) % MOD)
