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)

// https://atcoder.jp/contests/abc176/tasks/abc176_f
//
#![allow(unused_imports)]
use std::io::*;
use std::io::Write;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

// Input macros.
// Original by tanakh: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };

    ($iter:expr, mut $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, switch) => {
        {
            let ty = read_value!($iter, i32);
            if ty == 1 {
                vec![ty, read_value!($iter, i32), read_value!($iter, i32)]
            } else if ty == 2 {
                vec![ty, read_value!($iter, i32)]
            } else {
                vec![ty, read_value!($iter, i32)]
            }
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! read_line {
    ($t:tt) => {
        {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            s.trim_right().parse::<$t>().unwrap()
        }
    }
}

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ===

const INF: i32 = 100000;

// ====

struct DpWtihRowColMax {
    dp: Vec<Vec<i32>>,
    // dp[a][*]
    row_max: Vec<i32>,
    // dp[*][a]
    col_max: Vec<i32>
}

impl DpWtihRowColMax {
    fn new(n: usize) -> Self {
        Self {
            dp: dvec![-INF; n, n],
            row_max: vec![-INF; n],
            col_max: vec![-INF; n]
        }
    }

    fn set(&mut self, row: usize, col: usize, v: i32) {
        if self.dp[row][col] < v {
            self.dp[row][col] = v;
            self.row_max[row] = max(self.row_max[row], v);
        }
    }
}

fn main() {
    input! {
        n: usize, a: [usize1; 3*n]
    };

    let mut add_all = 0;
    let mut dpdp =  DpWtihRowColMax::new(n);
    dpdp.set(a[0], a[1], 0);
    dpdp.set(a[1], a[0], 0);
    for i in 0..n-1 {
        let mut upd = vec![];
        let v = [a[i*3+2], a[i*3+3], a[i*3+4]];
        if v[0] == v[1] && v[1] == v[2] {
            add_all += 1; // ?
            continue;
        }
        for j in 0..3 {
            let other = (0..3).filter(|&k| j != k).map(|k| v[k]).collect::<Vec<_>>();
            let mut amax = 0;
            for a in 0..n {
                amax = max(amax, dpdp.row_max[a]);
            }
            upd.push((other[0], other[1], max(amax, dpdp.dp[v[j]][v[j]] + 1)));
            upd.push((other[1], other[0], max(amax, dpdp.dp[v[j]][v[j]] + 1)));

            if other[0] == other[1] {
                for a in 0..n {
                    upd.push((a, v[j], dpdp.dp[other[0]][a]+1));
                    upd.push((v[j], a, dpdp.dp[other[0]][a]+1));
                }
            }
            for a in 0..n {
                let best = dpdp.row_max[a];
                if best >= 0 {
                    upd.push((a, v[j], best));
                    upd.push((v[j], a, best));
                }
            }
        }

        for (row, col, new_value) in upd {
            dpdp.set(row, col, new_value);
        }
    }

    let mut ans = 0;
    for i in 0..n {
        for j in 0..n {
            let pl = ifv!(i == a[3*n-1] && j == a[3*n-1], 1, 0);
            ans = max(ans, dpdp.dp[i][j]+pl);
        }
    }
    println!("{}", ans + add_all);
}