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 defaultdict

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

nglist = [
    "?AGC", "AGC?",
    "A?GC", "AG?C",
    "GAC?", "?GAC",
    "ACG?", "?ACG"
]
ng = {}
for t in "AGCT":
    for n in nglist:
        ng[n.replace('?', t)] = 1

dp = {"TTT": 1}

for i in range(N):
    ans = 0
    _dp = defaultdict(int)
    for k, v in dp.items():
        for t in "AGCT":
            s = k+t
            if s not in ng:
                _dp[s[1:]] += v
                ans = (ans+v) % MOD
    dp = _dp
    if i == (N-1):
        print(ans)
