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
import re
n = int(input())
memo = [{} for _ in range(n)]
MOD = 10**9 + 7

def check(string):
    if re.match(".*(AGC|GAC|ACG|A.?GC|AG.?C).*", string):
        return False
    return True


def dfs(string="", depth=0): # return ok count
    if depth == n:
        return 1

    if string in memo[depth]:
        return memo[depth][string]

    cnt = 0
    for i in "AGCT":
        next_string = string + i
        if check(next_string):
            cnt += dfs(string[-3:] + i, depth + 1)
            cnt %= MOD
    memo[depth][string] = cnt
    return cnt

print(dfs())
