#include<bits/stdc++.h>
using namespace std;
int n;
int f[210][4][4][4];

int main()
{
	cin >> n;
	for(int i=0;i<4;i++){
		for(int j=0;j<4;j++){
			for(int k=0;k<4;k++){
				if(i==0&&j==1&&k==2)continue;
				if(i==0&&j==2&&k==1)continue;
				if(i==1&&j==0&&k==2)continue;
				f[3][i][j][k]=1;
			}
		}
	}
	for(int a=4;a<=n;a++){
		for(int t=0;t<4;t++){
			for(int i=0;i<4;i++){
				for(int j=0;j<4;j++){
					for(int k=0;k<4;k++){
						// t i j k
						if(i==0&&j==1&&k==2)continue;
						if(i==0&&j==2&&k==1)continue;
						if(i==1&&j==0&&k==2)continue;
						if(t==0&&i==1&&k==2)continue;
						if(t==0&&j==1&&k==2)continue;
						f[a][i][j][k]+=f[a-1][t][i][j];
						f[a][i][j][k]%=1000000007;
					}
				}
			}
		}
	}
	int ans=0;
	for(int i=0;i<4;i++){
		for(int j=0;j<4;j++){
			for(int k=0;k<4;k++){
				ans+=f[n][i][j][k];
				ans%=1000000007;
			}
		}
	}
	cout<<ans<<endl;
}
### Prompt

Please provide a CPP coded solution 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;
int n;
int f[210][4][4][4];

int main()
{
	cin >> n;
	for(int i=0;i<4;i++){
		for(int j=0;j<4;j++){
			for(int k=0;k<4;k++){
				if(i==0&&j==1&&k==2)continue;
				if(i==0&&j==2&&k==1)continue;
				if(i==1&&j==0&&k==2)continue;
				f[3][i][j][k]=1;
			}
		}
	}
	for(int a=4;a<=n;a++){
		for(int t=0;t<4;t++){
			for(int i=0;i<4;i++){
				for(int j=0;j<4;j++){
					for(int k=0;k<4;k++){
						// t i j k
						if(i==0&&j==1&&k==2)continue;
						if(i==0&&j==2&&k==1)continue;
						if(i==1&&j==0&&k==2)continue;
						if(t==0&&i==1&&k==2)continue;
						if(t==0&&j==1&&k==2)continue;
						f[a][i][j][k]+=f[a-1][t][i][j];
						f[a][i][j][k]%=1000000007;
					}
				}
			}
		}
	}
	int ans=0;
	for(int i=0;i<4;i++){
		for(int j=0;j<4;j++){
			for(int k=0;k<4;k++){
				ans+=f[n][i][j][k];
				ans%=1000000007;
			}
		}
	}
	cout<<ans<<endl;
}
```