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
a,b,c,d,e,f,g=[0]*6+[1]
for i in [0]*int(input()):d,c,e,f,a,b,g=c,a,a-f,b,g,g-e,(g*4-(c+e+f+d*3))%(10**9+7)
print(g)
