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

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}

int64_t dp[101][4][4][4];

bool ng(int a, int b, int c){
    return (a==1 && b==2 && c==3);
}

int main(){
    int N;
    cin >> N;
    dp[0][0][0][0] = 1;
    for(int i=0; i<N; i++) for(int a=0; a<4; a++) for(int b=0; b<4; b++) for(int c=0; c<4; c++) for(int d=0; d<4; d++){
        if(ng(a, b, c) || ng(a, c, d) || ng(a, b, d) || ng(b, c, d)) continue;
        if(ng(c, b, d) || ng(b, d, c)) continue;
        add(dp[i+1][b][c][d], dp[i][a][b][c]);
    }
    int64_t ans = 0;
    for(int a=0; a<4; a++) for(int b=0; b<4; b++) for(int c=0; c<4; c++) add(ans, dp[N][a][b][c]);
    cout << ans << endl;
    return 0;
}
### Prompt

Develop a solution in CPP to the problem described below:

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;

const int64_t MOD = 1e9+7;
void add(int64_t& a, int64_t b){
    a = (a+b) % MOD;
}

int64_t dp[101][4][4][4];

bool ng(int a, int b, int c){
    return (a==1 && b==2 && c==3);
}

int main(){
    int N;
    cin >> N;
    dp[0][0][0][0] = 1;
    for(int i=0; i<N; i++) for(int a=0; a<4; a++) for(int b=0; b<4; b++) for(int c=0; c<4; c++) for(int d=0; d<4; d++){
        if(ng(a, b, c) || ng(a, c, d) || ng(a, b, d) || ng(b, c, d)) continue;
        if(ng(c, b, d) || ng(b, d, c)) continue;
        add(dp[i+1][b][c][d], dp[i][a][b][c]);
    }
    int64_t ans = 0;
    for(int a=0; a<4; a++) for(int b=0; b<4; b++) for(int c=0; c<4; c++) add(ans, dp[N][a][b][c]);
    cout << ans << endl;
    return 0;
}
```