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: Time Limit Exceeded)

#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn f(memo: &mut std::collections::BTreeMap<(usize,usize,usize), i64>, v: &mut [usize]) -> i64 {
  if v.len() == 3 {
     return if v[0] == v[1] && v[1] == v[2] { 1 } else { 0 };
  }
  if let Some(&x) = memo.get(&(v.len(), v[0], v[1])) {
    return x;
  }
  
  let mut res = 0;
  let v2 = (3..5).map(|i|v[i]).collect_vec();
  let v3 = (0..5).map(|i|v[i]).sorted().collect_vec();
  if v3[0] == v3[2] {
    v[3] = v3[3];
    v[4] = v3[4];
    res = f(memo, &mut v[3..]) + 1;
  } else if v3[1] == v3[3] {
    v[3] = v3[0];
    v[4] = v3[4];
    res = f(memo, &mut v[3..]) + 1;
  } else if v3[2] == v3[4] {
    v[3] = v3[0];
    v[4] = v3[1];
    res = f(memo, &mut v[3..]) + 1;
  } else {
    for i in (0..5).combinations(2) {
      v[3] = v3[i[0]];
      v[4] = v3[i[1]];
      res = std::cmp::max(res, f(memo, &mut v[3..]));
    }
  }
  v[3] = v2[0];
  v[4] = v2[1];
  memo.insert((v.len(), v[0], v[1]), res);
  res
}

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

  	let res = f(&mut std::collections::BTreeMap::new(), &mut a[..]);

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