Problem:
Score : 400 points

Problem Statement

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.

Notes

A substring of a string T is a string obtained by removing zero or more characters from the beginning and the end of T.

For example, the substrings of ATCODER include TCO, AT, CODER, ATCODER and (the empty string), but not AC.

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.

Sample Input 1

3

Sample Output 1

61

There are 4^3 = 64 strings of length 3 that do not contain characters other than A, C, G and T. Among them, only AGC, ACG and GAC violate the condition, so the answer is 64 - 3 = 61.

Sample Input 2

4

Sample Output 2

230

Sample Input 3

100

Sample Output 3

388130742

Be sure to print the number of strings modulo 10^9+7.

Solution in Python (3.4.3) (judge verdict: Accepted)

# DPをつかった解放を全然思いつけなかった
# 解説動画がわかりやすい

mod = 1000000007
N = int(input())

dp = [ [[[0 for c3 in range(4)]  for c2 in range(4)]  for c1 in range(4)] for n in range(N+1)]

# 全部TのときはOK
dp[0][3][3][3] = 1

# 文字の数
for n in range(N):
  # 後ろから1文字目
  for c1 in range(4):
    # 後ろから2文字目
    for c2 in range(4):
      # 後ろから3文字目
      for c3 in range(4):
        # 該当するものがないとき
        if dp[n][c1][c2][c3] == 0: continue

        # 新しく追加する文字
        for a in range(4):
          # AGCに当てはまる文字
          if(c2 == 0 and c1 == 1 and a == 2): continue
          if(c2 == 0 and c1 == 2 and a == 1): continue
          if(c2 == 1 and c1 == 0 and a == 2): continue
          if(c3 == 0 and c1 == 1 and a == 2): continue
          if(c3 == 0 and c2 == 1 and a == 2): continue

          dp[n+1][a][c1][c2] += dp[n][c1][c2][c3]

ans = 0
# 後ろから1文字目
for c1 in range(4):
  # 後ろから2文字目
  for c2 in range(4):
    # 後ろから3文字目
    for c3 in range(4):
      ans += dp[N][c1][c2][c3]

print(ans % mod)