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
n = int(input())
cs = 'ATGC'
ng = [
  'AGC',
  'GAC',
  'ACG',
  'AGGC',
  'ATGC',
  'ACGC',
  'AGAC',
  'AGTC'
]

mod = 10**9 + 7
d = defaultdict(int)
for c1 in cs:
  for c2 in cs:
    for c3 in cs:
      s = c1 + c2 + c3
      if s not in ng:
        d[s] += 1
for i in range(3, n):
  nd = defaultdict(int)
  for key in d.keys():
    for c in cs:
      cn = key[1:3] + c
      cn4 = key + c
      if cn not in ng and cn4 not in ng:
        nd[cn] = (nd[cn] + d[key]) % mod
  d = nd
print(sum([d[key] for key in d]) % mod)
      
