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)

#[allow(unused_imports)]
use {
    proconio::{fastout, input, marker::*},
    std::cmp::*,
    std::collections::*,
    std::ops::*,
};

#[derive(Clone)]
struct Dp(BTreeMap<(usize, usize), usize>);
impl Dp {
    fn set(&mut self, a: usize, b: usize, x: usize) {
        if a < b {
            self.0
                .entry((a, b))
                .and_modify(|v| *v = max(*v, x))
                .or_insert(x);
        } else {
            self.0
                .entry((b, a))
                .and_modify(|v| *v = max(*v, x))
                .or_insert(x);
        }
    }
}

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [usize; 3*n]
    }
    let mut dp = Dp(BTreeMap::<_, _>::new());
    dp.set(a[0], a[1], 0);
    for (ai, aj, ak) in (0..n - 1).map(|i| (3 * i + 2, 3 * i + 3, 3 * i + 4)) {
        if a[ai] == a[aj] && a[aj] == a[ak] {
            for (_, v) in dp.0.iter_mut() {
                *v += 1;
            }
            continue;
        }

        if a[ai] == a[aj] || a[aj] == a[ak] || a[ak] == a[ai] {
            let (a1, a2) = if a[aj] == a[ak] {
                (a[ai], a[aj])
            } else if a[ai] == a[ak] {
                (a[aj], a[ak])
            } else {
                (a[ak], a[ai])
            };

            let mut next = dp.clone();
            for (&(b1, b2), &v) in dp.0.iter() {
                if b1 == b2 && b1 == a1 {
                    next.set(a2, a2, v + 1);
                }
                if b1 == a2 {
                    next.set(b2, a1, v + 1);
                }
                if b2 == a2 {
                    next.set(b1, a1, v + 1);
                }
                next.set(b1, a1, v);
                next.set(b1, a2, v);
                next.set(b2, a1, v);
                next.set(b2, a2, v);
            }
            dp = next;
            continue;
        }

        let mut next = dp.clone();
        let (a1, a2, a3) = (a[ai], a[aj], a[ak]);
        for (&(b1, b2), &v) in dp.0.iter() {
            if b1 == b2 {
                if b1 == a1 {
                    next.set(a2, a3, v + 1);
                }
                if b1 == a2 {
                    next.set(a1, a3, v + 1);
                }
                if b1 == a3 {
                    next.set(a1, a2, v + 1);
                }
            }
            next.set(b1, a1, v);
            next.set(b1, a2, v);
            next.set(b1, a3, v);
            next.set(b2, a1, v);
            next.set(b2, a2, v);
            next.set(b2, a3, v);
            next.set(a1, a2, v);
            next.set(a2, a3, v);
            next.set(a3, a1, v);
        }
        dp = next;
    }
    if let Some(v) = dp.0.get_mut(&(a[3 * n - 1], a[3 * n - 1])) {
        *v += 1;
    }
    let mut ans = 0;
    for &v in dp.0.values() {
        ans = max(ans, v);
    }
    println!("{}", ans);
}