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 sys
sys.setrecursionlimit(1000)

n = int(input())
mod = 1000000007
memo = {}
def doit(n, a, b, c):
    if n == 0:
        return 1
    key = (n, a, b, c)
    if not key in memo:
        ret = (doit(n - 1, b, c, 'A') + doit(n - 1, b, c, 'T')) % mod
        if (b != 'A' or c != 'C'):
            ret = (ret + doit(n - 1, b, c, 'G')) % mod
        if (b != 'A' or c != 'G') and (b != 'G' or c != 'A') and (a != 'A' or c != 'G')  and (a != 'A' or b != 'G'):
            ret = (ret + doit(n - 1, b, c, 'C')) % mod
        memo[key] = ret
    return memo[key]
print(doit(n, '', '', ''))