#include<iostream>
using namespace std;
const int mod=1000000007;

long dp[101][4][4][4];

int main(){
	int n;
	cin >> n;
	dp[0][3][3][3]=1;
	for(int i=0;i<n;i++){
		for(int x=0;x<4;x++)
		for(int y=0;y<4;y++)
		for(int z=0;z<4;z++)
		for(int j=0;j<4;j++){
			if(y==0 && z==1 && j==2) continue;
			if(y==0 && z==2 && j==1) continue;
			if(y==1 && z==0 && j==2) continue;
			if(x==0 && y==1 && j==2) continue;
			if(x==0 && z==1 && j==2) continue;
			dp[i+1][y][z][j]+=dp[i][x][y][z];
			dp[i+1][y][z][j]%=mod;
		}
	}
	long ans=0;
	for(int x=0;x<4;x++)
	for(int y=0;y<4;y++)
	for(int z=0;z<4;z++){
		ans+=dp[n][x][y][z];
		ans%=mod;
	}
	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<iostream>
using namespace std;
const int mod=1000000007;

long dp[101][4][4][4];

int main(){
	int n;
	cin >> n;
	dp[0][3][3][3]=1;
	for(int i=0;i<n;i++){
		for(int x=0;x<4;x++)
		for(int y=0;y<4;y++)
		for(int z=0;z<4;z++)
		for(int j=0;j<4;j++){
			if(y==0 && z==1 && j==2) continue;
			if(y==0 && z==2 && j==1) continue;
			if(y==1 && z==0 && j==2) continue;
			if(x==0 && y==1 && j==2) continue;
			if(x==0 && z==1 && j==2) continue;
			dp[i+1][y][z][j]+=dp[i][x][y][z];
			dp[i+1][y][z][j]%=mod;
		}
	}
	long ans=0;
	for(int x=0;x<4;x++)
	for(int y=0;y<4;y++)
	for(int z=0;z<4;z++){
		ans+=dp[n][x][y][z];
		ans%=mod;
	}
	cout << ans << endl;
	return 0;
}

```