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
n = int(input())
dp = [[0]*4 for i in range(n+1)]
mod = 10**9+7

dp[0][0] = dp[0][1] = dp[0][2] = dp[0][3] = 1
dp[1][0] = dp[1][1] = dp[1][2] = dp[1][3] = 4

for i in range(2,n):
    for j in range(4):
        dp[i][j] = sum(dp[i-1])%mod
    dp[i][1] -= dp[i-2][0]
    dp[i][2] -= (dp[i-2][0] + dp[i-2][1])
    if i >= 3:
        dp[i][2] -= 3*dp[i-3][0]
        dp[i][1] += dp[i-3][1]
        

print(sum(dp[n-1])%mod)