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
#賢く解くと...
n=int(input())
mod=10**9+7
memo=[{} for _ in range(n+1)]

def judge(last4):
    for i in range(4):
        t=list(last4)
        if i<3:
            t[i],t[i+1]=t[i+1],t[i]
        s=''.join(t)
        if 'AGC' in s:
            return False
    return True

def dfs(i,last3):
    if last3 in memo[i]:
        return memo[i][last3]
    if i==n:
        return 1
    res=0
    for c in 'ACGT':
        if judge(last3+c):
            res=(res+dfs(i+1,last3[1:]+c))%mod
    memo[i][last3]=res
    return res

print(dfs(0,'TTT'))