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
from collections import defaultdict
from functools import reduce

def main():
  m = 10 ** 9 + 7
  n = int(input())
  current = defaultdict(int)
  current['TTT'] = 1
  for i in range(n):
    wip = defaultdict(int)

    for c in 'AGCT':
      for k, v in current.items():
        if k + c in ['ATGC', 'AGTC', 'AGGC']:
          continue
        z = k[1:]+c
        if z in ['AGC', 'ACG', 'GAC']:
          continue
        wip[z] = (wip[z] + v) % m

    current = wip
  
  print(reduce(lambda acc, x: (acc + x) % m, wip.values()))

main()