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)

a;f;j;n;s;u;v;w;C[37000];D[3001][3001];M[3001];*c=C;main(m){for(;++n%3+scanf("%d",&w);u=v,w-=v=w)for(s=2;n%3?0:s++<6e3+2?u-v|v-w||!j?*++c=u,*++c=s/3,*++c=fmax(v-w?:D[s/3][v]+1,M[s/3]),*++c=v,*++c=w,*++c=j=j?fmax(D[u][u]+1,m):1e7:++f:c>C?w=*c,v=c[~s|-2],u=c[s%2-2],c-=s%2*3,D[u][v]>w||(D[u][v]=w),M[u]>w||(M[u]=w),m=m>w?m:w:0;u=v,v=w,w=a)a=u;printf("%d",m+=f/6e3-1e7);}