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
import re,functools as f
@f.lru_cache(None)
def d(n,b):return n<1or sum(d(n-1,b[1:]+s)for s in'ACGT'if not re.match('.AGC|.ACG|.GAC|A.GC|AG.C',b+s))%(10**9+7)
print(d(int(input()),'TTT'))