#include<bits/stdc++.h>
using namespace std;
int n,a[6060],dp[2020][2020],mx[2020],gx[101010][3],sz,mmxx,al;
void ggxx(int x,int y,int vl)
{
	gx[sz][0]=x;
	gx[sz][1]=y;
	gx[sz][2]=vl;
	sz++;
}
void gggxxx(int x,int y,int vl)
{
	dp[x][y]=max(dp[x][y],vl);
	mx[x]=max(mx[x],vl);
	swap(x,y);
	dp[x][y]=max(dp[x][y],vl);
	mx[x]=max(mx[x],vl);
	mmxx=max(mmxx,vl);
}
void ggggxxxx()
{
	for(int i=0;i<sz;i++)
	{
		gggxxx(gx[i][0],gx[i][1],gx[i][2]);
	}
	sz=0;
}
int main()
{
	memset(dp,-0x3f3f3f,sizeof(dp));
	memset(mx,-0x3f3f3f,sizeof(mx));
	mmxx=-0x3f3f3f;
	cin>>n;
	for(int i=0;i<n*3;i++)
	{
		cin>>a[i];
		a[i]--;
	}
	gggxxx(a[0],a[1],0);
	for(int i=0;i<n-1;i++)
	{
		int x[3];
		x[0]=a[3*i+2];
		x[1]=a[3*i+3];
		x[2]=a[3*i+4];
		if(x[0]==x[1] && x[1]==x[2])
		{
			al++;
			continue;
		}
		for(int tt=0;tt<3;tt++)
		{
			ggxx(x[0],x[1],max(mmxx,dp[x[2]][x[2]]+1));
			for(int j=0;j<n;j++)
			{
				if(x[0]==x[1])
				{
					ggxx(j,x[2],dp[j][x[0]]+1);
				}
				ggxx(j,x[2],mx[j]);
			}
			swap(x[0],x[1]);
			swap(x[1],x[2]);
		}
		ggggxxxx();
	}
	cout<<max(mmxx,dp[a[3*n-1]][a[3*n-1]]+1)+al<<endl;
	return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

We have 3N cards arranged in a row from left to right, where each card has an integer between 1 and N (inclusive) written on it. The integer written on the i-th card from the left is A_i.

You will do the following operation N-1 times:

* Rearrange the five leftmost cards in any order you like, then remove the three leftmost cards. If the integers written on those three cards are all equal, you gain 1 point.



After these N-1 operations, if the integers written on the remaining three cards are all equal, you will gain 1 additional point.

Find the maximum number of points you can gain.

Constraints

* 1 \leq N \leq 2000
* 1 \leq A_i \leq N

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \cdots A_{3N}


Output

Print the maximum number of points you can gain.

Examples

Input

2
1 2 1 2 2 1


Output

2


Input

3
1 1 2 2 3 3 3 2 1


Output

1


Input

3
1 1 2 2 2 3 3 3 1


Output

3

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
int n,a[6060],dp[2020][2020],mx[2020],gx[101010][3],sz,mmxx,al;
void ggxx(int x,int y,int vl)
{
	gx[sz][0]=x;
	gx[sz][1]=y;
	gx[sz][2]=vl;
	sz++;
}
void gggxxx(int x,int y,int vl)
{
	dp[x][y]=max(dp[x][y],vl);
	mx[x]=max(mx[x],vl);
	swap(x,y);
	dp[x][y]=max(dp[x][y],vl);
	mx[x]=max(mx[x],vl);
	mmxx=max(mmxx,vl);
}
void ggggxxxx()
{
	for(int i=0;i<sz;i++)
	{
		gggxxx(gx[i][0],gx[i][1],gx[i][2]);
	}
	sz=0;
}
int main()
{
	memset(dp,-0x3f3f3f,sizeof(dp));
	memset(mx,-0x3f3f3f,sizeof(mx));
	mmxx=-0x3f3f3f;
	cin>>n;
	for(int i=0;i<n*3;i++)
	{
		cin>>a[i];
		a[i]--;
	}
	gggxxx(a[0],a[1],0);
	for(int i=0;i<n-1;i++)
	{
		int x[3];
		x[0]=a[3*i+2];
		x[1]=a[3*i+3];
		x[2]=a[3*i+4];
		if(x[0]==x[1] && x[1]==x[2])
		{
			al++;
			continue;
		}
		for(int tt=0;tt<3;tt++)
		{
			ggxx(x[0],x[1],max(mmxx,dp[x[2]][x[2]]+1));
			for(int j=0;j<n;j++)
			{
				if(x[0]==x[1])
				{
					ggxx(j,x[2],dp[j][x[0]]+1);
				}
				ggxx(j,x[2],mx[j]);
			}
			swap(x[0],x[1]);
			swap(x[1],x[2]);
		}
		ggggxxxx();
	}
	cout<<max(mmxx,dp[a[3*n-1]][a[3*n-1]]+1)+al<<endl;
	return 0;
}
```