#include<bits/stdc++.h>
using namespace std;
const int mod = 1e9 + 7;
int ans, dp[128][4][4][4];
bool check(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(check(b, c, d) || check(c, b, d) || check(b, d, c))
							continue;
						if(check(a, c, d) || check(a, b, d))
							continue;
						dp[i + 1][b][c][d] = (dp[i + 1][b][c][d] + dp[i][a][b][c]) % mod;
					}
	for(int a = 0; a < 4; a++)
		for(int b = 0; b < 4; b++)
			for(int c = 0; c < 4; c++){
				ans += dp[n][a][b][c];
				ans %= mod;
			}
	cout << ans;
}	
### 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 int mod = 1e9 + 7;
int ans, dp[128][4][4][4];
bool check(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(check(b, c, d) || check(c, b, d) || check(b, d, c))
							continue;
						if(check(a, c, d) || check(a, b, d))
							continue;
						dp[i + 1][b][c][d] = (dp[i + 1][b][c][d] + dp[i][a][b][c]) % mod;
					}
	for(int a = 0; a < 4; a++)
		for(int b = 0; b < 4; b++)
			for(int c = 0; c < 4; c++){
				ans += dp[n][a][b][c];
				ans %= mod;
			}
	cout << ans;
}	
```