#include <iostream>
#include <cstdio>
using namespace std;

int n, M=1e9+7, d[105][5][5][5];

int f(int p, int a, int b, int c) {
	int re=0;
	if(p==n) return 1;
	if(d[p][a][b][c]) return d[p][a][b][c];
  	for(int d=0; d<4; d++){
		if(b==0 && c==1 && d==2) continue;
		if(b==0 && c==2 && d==1) continue;
		if(b==1 && c==0 && d==2) continue;
		if(a==0 && c==1 && d==2) continue;
		if(a==0 && b==1 && d==2) continue;
		re += f(p+1, b, c, d);
		re %= M;
    }
	return d[p][a][b][c] = re;
}

int main() {
	cin >> n;
 	cout << f(0, 4, 4, 4);
	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 <cstdio>
using namespace std;

int n, M=1e9+7, d[105][5][5][5];

int f(int p, int a, int b, int c) {
	int re=0;
	if(p==n) return 1;
	if(d[p][a][b][c]) return d[p][a][b][c];
  	for(int d=0; d<4; d++){
		if(b==0 && c==1 && d==2) continue;
		if(b==0 && c==2 && d==1) continue;
		if(b==1 && c==0 && d==2) continue;
		if(a==0 && c==1 && d==2) continue;
		if(a==0 && b==1 && d==2) continue;
		re += f(p+1, b, c, d);
		re %= M;
    }
	return d[p][a][b][c] = re;
}

int main() {
	cin >> n;
 	cout << f(0, 4, 4, 4);
	return 0;
}
```