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 (1.15.1) (judge verdict: Wrong Answer)

//! ----------------------------------------------
//! Framework <https://github.com/vain0x/procon>
//!
//! See the bottom of file for solution.
//! ----------------------------------------------

#![allow(unused_imports)]
#![allow(non_snake_case)]

use std::cell::RefCell;
use std::cmp::{max, min, Ordering};
use std::collections::*;
use std::fmt::{Debug, Display, Formatter, Write as FmtWrite};
use std::io::{stderr, stdin, BufRead, Write};
use std::mem::{replace, swap};
use std::ops::*;
use std::rc::Rc;

/// Print values to standard error if debug mode.
#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), stderr());
            writeln!(err, "\x1B[33m{}\x1B[0m = {:?}", e, $e).unwrap()
        })*
    };
}

/// Read from standard input and parse each word.
/// - `read!(T, U, ..)` parses a line as a tuple of words.
/// - `read![[T]]` parses a line as an array of words.
/// - `read![..; N]` parses `N` lines, using `read!(..)` repeatedly.
#[allow(unused_macros)]
macro_rules! read {
    ([$t:ty] ; $n:expr) =>
        ((0..$n).map(|_| read!([$t])).collect::<Vec<_>>());
    ($($t:ty),+ ; $n:expr) =>
        ((0..$n).map(|_| read!($($t),+)).collect::<Vec<_>>());
    ([$t:ty]) =>
        (rl().split_whitespace().map(|w| w.parse().unwrap()).collect::<Vec<$t>>());
    ($($t:ty),*) => {{
        let buf = rl();
        let mut w = buf.split_whitespace();
        ($(w.next().unwrap().parse::<$t>().unwrap()),*)
    }};
}

/// Read a line from standard input.
#[allow(dead_code)]
fn rl() -> String {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();

    #[allow(deprecated)]
    buf.trim_right().to_owned()
}

// -----------------------------------------------
// Solution
// -----------------------------------------------

#[derive(Clone, Copy, Debug, PartialEq, Eq)]
enum State {
    White,
    Gray,
    Black,
}

use State::*;

struct Solver {
    A: Vec<Vec<usize>>,
    ord: Vec<Vec<usize>>,
    states: Vec<Vec<State>>,
    matches: Vec<(usize, usize)>,
    ok: bool,
}

impl Solver {
    fn new(A: Vec<Vec<usize>>) -> Solver {
        let N = A.len();

        let mut ord = vec![vec![0; N]; N];
        for u in 0..N {
            for ui in 0..N - 1 {
                let v = A[u][ui];
                ord[u][v] = ui;
            }
        }

        Solver {
            A: A,
            ord: ord,
            states: vec![vec![White; N]; N],
            matches: vec![],
            ok: true,
        }
    }

    // 選手 u が v と戦う順目
    fn ord(&self, u: usize, v: usize) -> usize {
        self.ord[u][v]
    }

    fn dfs(&mut self, u: usize, v: usize) {
        // 選手 u と v の試合を行いたい
        // 先に行わなければいけない試合をスケジュールする

        assert_ne!(u, v);

        if u > v {
            self.dfs(v, u);
            return;
        }

        if !self.ok {
            return;
        }

        let ui = self.ord(u, v);
        let vi = self.ord(v, u);

        match self.states[u][v] {
            White => {}
            Gray => {
                self.ok = false;
                return;
            }
            Black => return,
        }
        self.states[u][v] = Gray;

        // 先に済ませなければいけない試合をスケジュールする

        if ui >= 1 {
            let w = self.A[u][ui - 1];
            self.dfs(u, w);
        }

        if vi >= 1 {
            let w = self.A[v][vi - 1];
            self.dfs(v, w);
        }

        self.matches.push((u, v));
        debug!((u, v));

        self.states[u][v] = Black;
    }

    fn day_count(&self) -> usize {
        let N = self.A.len();

        let mut done = vec![true; N];
        let mut day_count = 0;

        for &(u, v) in &self.matches {
            if done[u] || done[v] {
                for i in 0..N {
                    done[i] = false;
                }
                day_count += 1;
                debug!(day_count);
            }

            done[u] = true;
            done[v] = true;
            debug!((u, v));
        }

        day_count
    }
}

fn main() {
    let N = read!(usize);
    let mut A = read![[usize]; N];

    let mut Q = BinaryHeap::new();

    for i in 0..N {
        for x in A[i].iter_mut() {
            *x -= 1;
        }

        Q.push((N - 1, i));
    }

    let mut solver = Solver::new(A);
    for u in 0..N {
        for v in u + 1..N {
            solver.dfs(u, v);
        }
    }

    if !solver.ok {
        println!("-1");
        return;
    }

    println!("{}", solver.day_count())
}