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 Counter

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

dp = [Counter() for i in range(N+1)]
dp[0]["TTT"] = 1


def ok(last4):
    bad = ["AGC", "ACG", "GAC", "AGGC", "ATGC", "AGTC"]
    for b in bad:
        if b in last4:
            return False
    return True

for i in range(N):
    for key, value in dp[i].items():
        for c in "AGCT":
            if ok(key+c):
                dp[i+1][key[1:]+c] += value % MOD

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

