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 itertools
import functools
L = "ATGC"
MOD = 10 ** 9 + 7
@functools.lru_cache(maxsize = None)
def rec(s, k):
    if s.count("AGC"):
        return 0
    for i in range(3):
        t = list(s)
        t[i], t[i + 1] = t[i + 1], t[i]
        if ''.join(t).count("AGC"):
            return 0
    if k == 0:
        return 1
    ret = 0
    for x in L:
        ret = (ret + rec(x + s[:3], k - 1)) % MOD
    return ret

N = int(input())
if N == 3:
    print(61)
else:
    ret = 0
    for s in itertools.product(L, repeat = 4):
        ret = (ret + rec(''.join(s), N - 4)) % MOD
    print(ret)
