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
def ok(last4):
    ret = True
    if last4 in ["ATGC","AGGC","AGTC"]:
        ret = False
    elif True in [s in last4 for s in ["AGC","ACG","GAC"]]:
        ret = False
    return ret
N = int(input())
mod = 10**9+7
memo = [{} for i in range(N+1)]

def dfs(current, last3):
    if last3 in memo[current]:
        return memo[current][last3]
    if current == N:
        return 1
    ret = 0
    for c in "ATGC":
        if ok(last3+c):
            ret += dfs(current+1, last3[1:]+c)
            ret %= mod
    memo[current][last3] = ret
    return ret

print(dfs(0, "TTT"))