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
def check(s):
    ban = ["AGC", "ACG", "GAC", "AGGC", "ATGC", "AGTC"]
    for b in ban:
        if b in s:
            return False
    return True

n = int(input())
dp = [Counter() for i in range(n+1)]
dp[0]["RAN"] = 1

for i in range(n):
    for key, value in dp[i].items():
        for c in "ACTG":
            if check(key+c):
                dp[i+1][key[1:]+c]+=value % mod

print (sum(dp[n].values())%mod)