#include<bits/stdc++.h>
using namespace std;

int mod=1000000007;
int dp[110][5][5][5];

int main(){
  int N;
  cin >> N;
  dp[0][3][3][3]=1;
  for(int len=0;len<N;len++){
    for(int i=0;i<=3;i++){
      for(int j=0;j<=3;j++){
        for(int k=0;k<=3;k++){
          if(dp[len][i][j][k]==0){continue;}
          for(int a=0;a<=3;a++){
            if(a==2 && i==1 && j==0){continue;}
            if(a==2 && i==0 && j==1){continue;}
            if(a==1 && i==2 && j==0){continue;}
            if(a==2 && i==1 && k==0){continue;}
            if(a==2 && j==1 && k==0){continue;}
            dp[len+1][a][i][j]+=dp[len][i][j][k];
            dp[len+1][a][i][j]%=mod;
          }
        }
      }
    }
  }
  int ans=0;
  for(int i=0;i<=3;i++){
    for(int j=0;j<=3;j++){
      for(int k=0;k<=3;k++){
          ans+=dp[N][i][j][k];
          ans%=mod;
      }
    }
  }
  cout << ans << endl;
}
### Prompt

Please create a solution in Cpp to the following problem:

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

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;

int mod=1000000007;
int dp[110][5][5][5];

int main(){
  int N;
  cin >> N;
  dp[0][3][3][3]=1;
  for(int len=0;len<N;len++){
    for(int i=0;i<=3;i++){
      for(int j=0;j<=3;j++){
        for(int k=0;k<=3;k++){
          if(dp[len][i][j][k]==0){continue;}
          for(int a=0;a<=3;a++){
            if(a==2 && i==1 && j==0){continue;}
            if(a==2 && i==0 && j==1){continue;}
            if(a==1 && i==2 && j==0){continue;}
            if(a==2 && i==1 && k==0){continue;}
            if(a==2 && j==1 && k==0){continue;}
            dp[len+1][a][i][j]+=dp[len][i][j][k];
            dp[len+1][a][i][j]%=mod;
          }
        }
      }
    }
  }
  int ans=0;
  for(int i=0;i<=3;i++){
    for(int j=0;j<=3;j++){
      for(int k=0;k<=3;k++){
          ans+=dp[N][i][j][k];
          ans%=mod;
      }
    }
  }
  cout << ans << endl;
}
```