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 itertools import product

n = int(input())
i = 3
ans = 61
dpm = {
    "".join(k): 1
    for k in product("ACGT", repeat=3)
}
for k in ("AGC", "ACG", "GAC"):
    dpm[k] = 0

MOD = 1000000007

while i < n:
    ndpm = {k: 0 for k in dpm}
    for k in dpm:
        for c in "ACGT":
            ns = k + c
            if ns[-3:] in ("AGC", "ACG", "GAC") or \
                    (ns[0] == "A" and ns[-2:] == "GC") or \
                    (ns[0:2] == "AG" and ns[-1] == "C"):
                continue
            ndpm[ns[-3:]] += dpm[k] % MOD
    dpm = ndpm
    i += 1

print(sum(dpm.values()) % MOD)
