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 Rust (1.42.0) (judge verdict: Wrong Answer)

use proconio::{*, marker::*};

fn main() {
    input! {
        n: usize,
        a: [Usize1; 3*n],
    }

    let mut zero = vec![0; n];
    let mut one = vec![0; n];

    for i in 0..2 {
        zero[a[i]] += 1;
    }

    let mut ans = 0;
    for ii in 0..n-1 {
        for jj in (2+ii*3)..(2+ii*3+3) {
            one[a[jj]] += 1;
        }
        let mut tmp = (3, n);
        for k in 0..n {
            if zero[k] + one[k] >= 3 {
                if zero[k] < tmp.0 {
                    tmp = (zero[k], k);
                }
            }
        }
        if tmp.0 < 3 {
            ans += 1;
        }
        if tmp.0 == 0 {
            assert!(one[tmp.1] >= 3);
            one[tmp.1] -= 3;
            for i in 0..n {
                zero[i] += one[i];
            }
        }
        if tmp.0 == 1 {
            assert_eq!(zero[tmp.1], 1);
            zero[tmp.1] -= 1;
            one[tmp.1] -= 2;
            for i in 0..n {
                zero[i] = (zero[i]).min(1);
                zero[i] += one[i];
            }
        }
        if tmp.0 == 2 {
            assert_eq!(zero[tmp.1], 2);
            one[tmp.1] -= 1;
            for i in 0..n {
                zero[i] = one[i];
            }
        }
        if tmp.0 == 3 {
            for i in 0..n {
                zero[i] += one[i];
            }
        }
        for i in 0..n {
            one[i] = 0;
        }
    }


    one[a[3*n-1]] += 1;

    // println!("{:?}", zero);
    // println!("{:?}", one);
    let mut three = false;
    for i in 0..n {
        if zero[i] + one[i] >= 3 {
            three = true;
        }
    }
    if three {
        ans += 1;
    }

    println!("{}", ans);
}