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())
mod = 10**9+7
A = [1]+(N+3)*[0]
G = [1]+(N+3)*[0]
C = [1]+(N+3)*[0]

for n in range(1,N):
  T = (2*A[n-1]+G[n-1]+C[n-1])%mod
  A[n] = T
  G[n] = (T-A[n-2]+G[n-3])%mod
  C[n] = (T-A[n-2]-G[n-2]-3*A[n-3])%mod

print((2*A[N-1]+G[N-1]+C[N-1])%mod)