#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<string>
#include<map>
#define mod 1000000007
#define rep(i,N) for(int i=0;i<N;i++)
using namespace std;

int dp[101][4][4][4];
int main(){
    int N;
    cin>>N;
    dp[0][3][3][3]=1;
    rep(len,N)rep(c1,4)rep(c2,4)rep(c3,4){
        //....c3 c2 c1 a
        if(dp[len][c1][c2][c3]==0)continue;
        rep(a,4){
            if(c2==0&&c1==1&&a==2)continue;
            if(c2==1&&c1==0&&a==2)continue;
            if(c2==0&&c1==2&&a==1)continue;
            if(c3==0&&c1==1&&a==2)continue;
            if(c3==0&&c2==1&&a==2)continue;
            dp[len+1][a][c1][c2]+=dp[len][c1][c2][c3];
            dp[len+1][a][c1][c2]%=mod;
        }
    }
    int ans=0;
    rep(c1,4)rep(c2,4)rep(c3,4){
        ans+=dp[N][c1][c2][c3];
        ans%=mod;
    }
    cout<<ans<<endl;
    
    return 0;
}
### Prompt

Your challenge is to write a Cpp solution 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<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<string>
#include<map>
#define mod 1000000007
#define rep(i,N) for(int i=0;i<N;i++)
using namespace std;

int dp[101][4][4][4];
int main(){
    int N;
    cin>>N;
    dp[0][3][3][3]=1;
    rep(len,N)rep(c1,4)rep(c2,4)rep(c3,4){
        //....c3 c2 c1 a
        if(dp[len][c1][c2][c3]==0)continue;
        rep(a,4){
            if(c2==0&&c1==1&&a==2)continue;
            if(c2==1&&c1==0&&a==2)continue;
            if(c2==0&&c1==2&&a==1)continue;
            if(c3==0&&c1==1&&a==2)continue;
            if(c3==0&&c2==1&&a==2)continue;
            dp[len+1][a][c1][c2]+=dp[len][c1][c2][c3];
            dp[len+1][a][c1][c2]%=mod;
        }
    }
    int ans=0;
    rep(c1,4)rep(c2,4)rep(c3,4){
        ans+=dp[N][c1][c2][c3];
        ans%=mod;
    }
    cout<<ans<<endl;
    
    return 0;
}
```