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

s = "ATGC"
t = ["AGC", "ACG", "GAC"]
d = [defaultdict(int), {x+y+z: 1 for x in s for y in s for z in s if x+y+z not in t}]
# d = [{"": 1}, defaultdict(int)]

# print(d[0])
for i in range(4, n+1):
    a = i%2
    b = (i-1)%2

    d[a] = defaultdict(int)
    for k in d[b]:
        for c in s:
            if "AGC" not in [k[1:]+c, k[0]+k[2]+c, k[2]+k[1]+c, k[1]+c+k[2], k[0]+k[1]+c]:
                d[a][k[1:]+c] += d[b][k]
                d[a][k[1:]+c] %= MOD

print(sum(d[n%2].values()) % MOD)
