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
N,m=int(input()),10**9+7

from collections import defaultdict

memo=[defaultdict(int) for i in range(N+1)]

def ok(last4):
    if 'AGC' in last4:
        return False
    for i in range(3):
        t=list(last4)
        t[i],t[i+1]=t[i+1],t[i]
        if 'AGC' in ''.join(t):
            return False
    return True

memo[0]['TTT']=1
for i in range(1,N+1):
    for last3 in memo[i-1].keys():
        v = memo[i-1][last3]%m
        tmp=0
        for c in ['A','G','T','C']:
            if ok(last3+c):
                memo[i][last3[1:]+c]+=v

print(sum(memo[N].values())%m)
