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)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	let n: usize = s.next().unwrap().parse().unwrap();
	let a: Vec<usize> = s.take(3 * n).map(|a| a.parse().unwrap()).collect();

	if n == 1 {
		let mut a = a;
		a.sort();
		a.dedup();
		if a.len() == 1 {
			println!("1");
		} else {
			println!("0");
		}
		return;
	}

	let mut ans = 0;
	let mut last = 0;
	let mut i = 5;
	for _ in 0..n - 1 {
		let mut a: Vec<_> = a[0..i].iter().collect();
		a.sort();
		let mut cnt = vec![0; 2000];
		for a in a {
			cnt[a - 1] += 1;
		}
		let mut l = 0;
		for &c in cnt.iter() {
			l += c / 3;
		}
		if l > last {
			ans += 1;
			last = l;
		}
		i += 3;
	}
	if ans == n - 1 {
		let mut a = a;
		a.sort();
		let mut cnt = vec![0; 2000];
		for a in a {
			cnt[a - 1] += 1;
		}
		let mut l = 0;
		for &c in cnt.iter() {
			l += c / 3;
		}
		if l == n {
			ans += 1;
		}
	}
	println!("{}", ans);
}