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] + [0]*(n+3)
G=[1] + [0]*(n+3)
C=[1] + [0]*(n+3)
for i in range(1,n):
    t=(2*A[i-1]+G[i-1]+C[i-1])%mod
    A[i]=t
    G[i]=(t-A[i-2]+G[i-3])%mod
    C[i]=(t-A[i-2]-G[i-2]-3*A[i-3])%mod
print((2*A[n-1]+G[n-1]+C[n-1])%mod)
