Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

2
1 2 1 2 2 1

Sample Output 1

2

Let us rearrange the five leftmost cards so that the integers written on the six cards will be 2\ 2\ 2\ 1\ 1\ 1 from left to right.

Then, remove the three leftmost cards, all of which have the same integer 2, gaining 1 point.

Now, the integers written on the remaining cards are 1\ 1\ 1.

Since these three cards have the same integer 1, we gain 1 more point.

In this way, we can gain 2 points - which is the maximum possible.

Sample Input 2

3
1 1 2 2 3 3 3 2 1

Sample Output 2

1

Sample Input 3

3
1 1 2 2 2 3 3 3 1

Sample Output 3

3

Solution in C (GCC 9.2.1) (judge verdict: Accepted)

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a;*c;f;*i;j;m;n;s;u;v;w;C[72000];D[2001][2001];M[2001];
main(){
  c=C;
  for(;++n,~scanf("%d",&w)||(w=0,n%3-1);a=u,u=v,v=w,w=a)
    if(n%3<1)
      if(n<4)M[v]=M[w]=D[v][w]=D[w][v]=m=1e7;
      else{
        for(s=0;s++<2e3;)for(j=3;a=u,u=v,v=w,w=a,j--;)
          u-v|v-w?
            *++c=u,*++c=s,*++c=v-w?:D[s][v]+1,
            *++c=u,*++c=v,*++c=D[w][w]+1,
            *++c=u,*++c=v,*++c=m,
            *++c=u,*++c=s,*++c=M[s]
          :++f;
        for(;c>C;)
          w=*c--,v=*c--,u=*c--,
          D[u][v]>w||(D[u][v]=D[v][u]=w),M[u]>w||(M[u]=w),M[v]>w||(M[v]=w),m=m>w?m:w;
      }
  printf("%d",m+=f/6e3-1e7);
}