Problem:
Score : 500 points

Problem Statement

N players will participate in a tennis tournament. We will call them Player 1, Player 2, \ldots, Player N.

The tournament is round-robin format, and there will be N(N-1)/2 matches in total.
Is it possible to schedule these matches so that all of the following conditions are satisfied? If the answer is yes, also find the minimum number of days required.

Each player plays at most one matches in a day.

Each player i (1 \leq i \leq N) plays one match against Player A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} in this order.

Constraints

3 \leq N \leq 1000

1 \leq A_{i, j} \leq N

A_{i, j} \neq i

A_{i, 1}, A_{i, 2}, \ldots, A_{i, N-1} are all different.

Input

Input is given from Standard Input in the following format:

N
A_{1, 1} A_{1, 2} \ldots A_{1, N-1}
A_{2, 1} A_{2, 2} \ldots A_{2, N-1}
:
A_{N, 1} A_{N, 2} \ldots A_{N, N-1}

Output

If it is possible to schedule all the matches so that all of the conditions are satisfied, print the minimum number of days required; if it is impossible, print -1.

Sample Input 1

3
2 3
1 3
1 2

Sample Output 1

3

All the conditions can be satisfied if the matches are scheduled for three days as follows:

Day 1: Player 1 vs Player 2

Day 2: Player 1 vs Player 3

Day 3: Player 2 vs Player 3

This is the minimum number of days required.

Sample Input 2

4
2 3 4
1 3 4
4 1 2
3 1 2

Sample Output 2

4

All the conditions can be satisfied if the matches are scheduled for four days as follows:

Day 1: Player 1 vs Player 2, Player 3 vs Player 4

Day 2: Player 1 vs Player 3

Day 3: Player 1 vs Player 4, Player 2 vs Player 3

Day 4: Player 2 vs Player 4

This is the minimum number of days required.

Sample Input 3

3
2 3
3 1
1 2

Sample Output 3

-1

Any scheduling of the matches violates some condition.

Solution in Rust (1.42.0) (judge verdict: Accepted)

//use itertools::Itertools;
use std::cmp;
use std::collections::BTreeMap;
use std::collections::BTreeSet;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::io::Read;
use std::usize::MAX;

macro_rules! input {(source = $s:expr, $($r:tt)*) => {let mut iter = $s.split_whitespace();let mut next = || { iter.next().unwrap() };input_inner!{next, $($r)*}};($($r:tt)*) => {let stdin = std::io::stdin();let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));let mut next = move || -> String{bytes.by_ref().map(|r|r.unwrap() as char).skip_while(|c|c.is_whitespace()).take_while(|c|!c.is_whitespace()).collect()};input_inner!{next, $($r)*}};}
macro_rules! input_inner {($next:expr) => {};($next:expr, ) => {};($next:expr, $var:ident : $t:tt $($r:tt)*) => {let $var = read_value!($next, $t);input_inner!{$next $($r)*}};}
macro_rules! read_value {($next:expr, ( $($t:tt),* )) => {( $(read_value!($next, $t)),* )};($next:expr, [ $t:tt ; $len:expr ]) => {(0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()};($next:expr, chars) => {read_value!($next, String).chars().collect::<Vec<char>>()};($next:expr, usize1) => {read_value!($next, usize) - 1};($next:expr, [ $t:tt ]) => {{let len = read_value!($next, usize);(0..len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()}};($next:expr, $t:ty) => {$next().parse::<$t>().expect("Parse error")};}

fn solve() {
    input! {
        n: usize,
        a: [[usize1;n-1];n]
    }
    let mut ans = 0;

    let mut adj_list: HashMap<(usize, usize), Vec<(usize, usize)>> = HashMap::new();
    let mut deg: HashMap<(usize, usize), usize> = HashMap::new();

    let mut edges = Vec::new();

    for i in 0..n {
        for j in i + 1..n {
            adj_list.entry((i, j)).or_insert_with(Vec::new);
            deg.entry((i, j)).or_insert(0);
        }
    }

    for i in 0..n {
        for now in 0..n - 2 {
            let next = now + 1;

            let now_node = (cmp::min(i, a[i][now]), cmp::max(i, a[i][now]));
            let next_node = (cmp::min(i, a[i][next]), cmp::max(i, a[i][next]));
            edges.push((next_node, now_node));

            let deg_count = deg.entry(next_node).or_insert(0);
            *deg_count += 1;

            adj_list
                .entry(now_node)
                .or_insert_with(Vec::new)
                .push(next_node);
        }
    }

    let mut isolated = VecDeque::new();

    for (&index, &deg_count) in &deg {
        if deg_count == 0 {
            isolated.push_front(index);
        }
    }

    //println!("{:?}", deg);

    let node_count = n * (n - 1) / 2;
    let mut topological_order = vec![];
    while isolated.len() != 0 {
        let next = isolated.pop_back().unwrap();
        topological_order.push(next);

        let next_adj_list = adj_list.get(&next).unwrap();
        for i in next_adj_list {
            //println!("{:?} {}", next, deg.get(i).unwrap());
            let count = deg.entry(*i).or_insert(0);
            *count -= 1;
            if *count == 0 {
                isolated.push_front(*i);
            }
        }
    }

    if node_count != topological_order.len() {
        println!("-1");
        return;
    }

    let mut dists: HashMap<(usize, usize), usize> = HashMap::new();
    for &i in &topological_order {
        let adj_nodes = adj_list.get(&i).unwrap();

        let main_dist_tmp = dists.entry(i).or_insert(1);
        let main_dist = *main_dist_tmp;

        let mut visited: HashMap<(usize, usize), bool> = HashMap::new();
        for j in adj_nodes {
            //println!("{:?} {:?}", i, j);
            let dist = dists.entry(*j).or_insert(main_dist + 1);
            *dist = cmp::max(main_dist + 1, 1);

            ans = cmp::max(ans, *dist);
        }
        //println!("{:?}", dists);
    }

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

fn main() {
    let thd = std::thread::Builder::new().stack_size(104_857_600);
    thd.spawn(|| solve()).unwrap().join().unwrap();

    /*
    // 入力を一括で読み込む場合
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut input = buf.split_whitespace();

    // inputに対しnext()で読み込んでいく
    let q: usize = input.next().unwrap().parse().unwrap();
    */
}

const LARGE_PRIME: u64 = 1_000_000_007;

// @〜でsnippet
fn topological_sort(n: usize, edges: &[(usize, usize)]) -> Vec<usize> {
    let mut result = vec![];
    let mut isolated = VecDeque::new();

    // to[x] = [a,b] x -> a, x -> b が存在
    let mut to = vec![vec![]; n + 1];

    // deg[x] = a -> x, b -> xのような辺の数
    let mut deg = vec![0; n + 1];
    for e in edges {
        to[e.0].push(e.1);
        deg[e.1] += 1;
    }

    for i in 1..n + 1 {
        if deg[i] == 0 {
            isolated.push_front(i);
        }
    }

    while isolated.len() != 0 {
        let next = isolated.pop_back().unwrap();
        result.push(next);
        for i in &to[next] {
            deg[*i] -= 1;
            if deg[*i] == 0 {
                isolated.push_front(*i);
            }
        }
    }

    result
}