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 = int(input())
mask = 0b111111
mod = 10**9+7
dp = [[0]*4**3 for _ in range(n+1)]
dp[0][63] = 1
for i in range(n):
  for bit in range(4**3):
    for x in range(4):
      nb = bit<<2&63|x
      f = nb == 6 or nb == 9 or nb == 33
      f |= bit&51 == 2 and x == 1
      f |= bit&60 == 8 and x == 1
      if f:
        continue
      dp[i+1][nb] += dp[i][bit]
      dp[i+1][nb] %= mod
print(sum(dp[-1])%mod)