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_dict = [{} for i in range(N+1)]
def ok(last4):
    if re.match(r".*AGC|.*ACG|A.GC|AG.C|.*GAC", last4):
        return True
    else:
        return False

def dfs(ind, last3):
    if last3 in memo_dict[ind]:
        return memo_dict[ind][last3]
    if ind == N:
        return 1
    cnt = 0
    for c in "ATGC":
        if not ok(last3 + c):
            cnt += dfs(ind + 1, last3[1:] + c)
            cnt %= (1e9+7)
    memo_dict[ind][last3] = cnt
    return cnt
print(int(dfs(0,"TTT")))