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,g,a_,a__,ac,ga,al=[0]*6+[1]
for i in range(int(input())):
    a__,a_,ac,ga,a,g,al=a_,a,a-ga,g,al,al-ac,(al*4-(a_+ac+ga+a__*3))%(pow(10,9)+7)
print(al)
