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: Accepted)

// after YouTube explanation
use proconio::{input, fastout};
use std::cmp;

fn chmax(y: &mut i32, x: i32) {
    if *y < x { *y = x; }
}

fn upd(dp: &mut Vec<Vec<i32>>, n: usize, i: usize, j: usize, x: i32){
    chmax(&mut dp[i][j], x);
    chmax(&mut dp[j][i], x);
    chmax(&mut dp[i][n], x);
    chmax(&mut dp[n][i], x);
    chmax(&mut dp[n][j], x);
    chmax(&mut dp[j][n], x);
    chmax(&mut dp[n][n], x);
}

#[fastout]
fn main() {
    input! {
        n: usize,
        mut a: [usize; n*3],
    }
    for i in 0..a.len() {a[i] -= 1}
    let mut dp: Vec<Vec<i32>> = vec![vec![-1000000000;n+1];n+1];
    upd(&mut dp, n, a[0], a[1], 0);
    let mut base = 0;
    for aa in a[2..].chunks_exact(3) {
        let mut x = aa[0];
        let mut y = aa[1];
        let mut z = aa[2];
        if x==y && y==z {
            base += 1;
            continue;
        }
        let mut q = Vec::new();
        for _ in 0..3 {
            for ai in 0..(n+1) {
                let mut now = dp[ai][n];
                if y==z { now = cmp::max(now,dp[ai][y]+1)}
                q.push((ai,x,now));
            }
            let now = cmp::max(dp[n][n], dp[z][z]+1);
            q.push((x,y,now));
            let t = x; x = y; y = z; z = t;
        }
        for (x,y,now) in q {upd(&mut dp, n, x, y, now)}
    }
    let mut ans = dp[n][n];
    let l = a[n*3-1];
    ans = cmp::max(ans, dp[l][l]+1);
    ans += base;
    println!("{}", ans);
}