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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;

namespace E
{
  class Program
  {
    static void Main(string[] args)
    {
      Console.WriteLine(Run(args));
    }
    private static int Run(string[] args)
    {
      var N = int.Parse(Console.ReadLine());

      var gameCards = new Dictionary<string, GameCard>();

      // root
      var rootGameCard = new GameCard("00");

      for (int player = 1; player <= N; player++)
      {
        var preGameCard = rootGameCard;
        var list = Console.ReadLine().Split(' ');
        foreach (var vsPlayer in list)
        {
          var key = player < int.Parse(vsPlayer)
            ? string.Join(string.Empty, player.ToString(), vsPlayer)
            : string.Join(string.Empty, vsPlayer, player.ToString());
          if (!gameCards.ContainsKey(key))
          {
            gameCards.Add(key, new GameCard(key));
          }
          var gameCard = gameCards[key];
          if (!preGameCard.NextGames.ContainsKey(key))
          {
            preGameCard.NextGames.Add(key, gameCard);
          }
          // gameCard.PreGames.TryAdd(preGameCard.Key, preGameCard);
          // if (!gameCard.PreGames.ContainsKey(preGameCard.Key))
          // {
          //   gameCard.PreGames.Add(preGameCard.Key, preGameCard);
          // }

          preGameCard = gameCards[key];
        }
      }
      return GetGameDaysCount(new List<GameCard>(), rootGameCard, 0);
    }

    private static int GetGameDaysCount(List<GameCard> cache, GameCard gameCard, int days)
    {
      var ret = days++;
      cache.Add(gameCard);
      foreach (var nextGameCard in gameCard.NextGames.Values)
      {
        // 循環してたら即終わり
        if (cache.Any(x => x.Key.Equals(nextGameCard.Key)))
        {
          return -1;
        }
        var tmp = GetGameDaysCount(new List<GameCard>(cache), nextGameCard, days);
        // 最大深度のやつを採用
        if (tmp >= ret || tmp == -1)
        {
          ret = tmp;
        }
      }
      return ret;
    }
  }

  public class GameCard
  {
    public string Key { get; private set; }
    public Dictionary<string, GameCard> PreGames { get; set; }
    public Dictionary<string, GameCard> NextGames { get; set; }

    public GameCard(string key)
    {
      this.Key = key;
      this.PreGames = new Dictionary<string, GameCard>();
      this.NextGames = new Dictionary<string, GameCard>();
    }
  }
}