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(10**9)
from functools import lru_cache
mod=1000000007

def judge(last4):
    for i in range(4):
        t=list(last4)
        if i:
            t[i-1],t[i]=t[i],t[i-1]
        if ''.join(t).count('AGC'):
            return False
    return True

@lru_cache(maxsize=None)
def dfs(cur,last3):
    if cur==0:
        return 1
    ret=0
    for c in 'ACGT':
        if judge(last3+c):
            ret+=dfs(cur-1,last3[1:]+c)
            ret%=mod
    return ret

n=int(input())
print(dfs(n,'TTT'))