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())
MOD = 10**9+7
D = [[[[0]*4 for _ in range(4)] for _ in range(4)] for _ in range(N+3)]
D[0][3][3][3] = 1
for n in range(1,N+1):
    for i, j, k, l in product(range(4), repeat=4):
        if (i,j,l)==(2,1,0) or (i,k,l) == (2,1,0) or (i,j,k) == (1,2,0) or (i,j,k) == (2,0,1) or (i,j,k) == (2,1,0): continue
        D[n][i][j][k] += D[n-1][j][k][l]%MOD
res = 0
for i, j, k in product(range(4),repeat=3):
    res += D[N][i][j][k]
    res %= MOD
print(res)