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 collections, itertools
N = int(input())
mod = 10**9 + 7
dp = collections.defaultdict(int)
dp['TTTA'] = dp['TTTG'] = dp['TTTC'] = dp['TTTT'] = 1
for _ in range(N - 1):
    dp2 = collections.defaultdict(int)
    for p, q, r, s, t in itertools.product('AGCT', repeat=5):
        if 'AGC' in [q + s + t, s + r + t, r + s + t, q + r + t, r + t + s]:
            continue
        else:
            dp2[q + r + s + t] += dp[p + q + r + s]
    dp = dp2
print(sum(dp.values()) % mod)
