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 = 1000000007
ng3 = ("AGC", "ACG", "GAC")
ng4 = ("AAGC", "ACGC", "AGGC", "ATGC", "AGAC", "AGCC", "AGGC", "AGTC")


def isok(s):
    if s[-3:] in ng3:
        return False
    if s[-4:] in ng4:
        return False
    return True


N = int(input())
dp = [Counter() for _ in range(N + 1)]
dp[0] = {"": 1}
for n in range(1, N + 1):
    for s, v in dp[n-1].items():
        for c in "ACGT":
            if isok(s + c):
                dp[n][s[-3:] + c] += v
print(sum(dp[N].values()) % mod)
