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.Collections.Generic;
using System.Linq;

namespace ABC139E
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = CIN.Long();
            long[][] A = new long[N + 1][];
            Dictionary<string, HashSet<string>> condition = new Dictionary<string, HashSet<string>>();
            for (int i = 1; i <= N; i++)
            {
                A[i] = CIN.LongArray();
                for (int j = 1; j < A[i].Length; j++)
                {
                    string game = toStr(A[i][j], i);
                    if (condition.ContainsKey(game))
                    {
                        condition[game].Add(toStr(A[i][j - 1], i));
                    }
                    else
                    {
                        condition.Add(game, new HashSet<string> {toStr(A[i][j - 1], i)});
                    }
                }
            }

            int[] indexes = new int[N + 1];
            HashSet<string> done = new HashSet<string>();
            bool[] turn = new bool[N + 1];

            long games = N * (N - 1) / 2;
            int ans = 0;
            while (done.Count < games)
            {
                bool cannot = true;
                turn = new bool[N + 1];
                for (int i = 1; i <= N; i++)
                {
                    if (indexes[i] == N - 1)
                    {
                        continue;
                    }
                    if (turn[i] || turn[A[i][indexes[i]]])
                    {
                        continue;
                    }

                    string game = toStr(i, A[i][indexes[i]]);
                    if (done.Contains(game))
                    {
                        continue;
                    }
                    if (condition.ContainsKey(game))
                    {
                        bool dame = false;

                        List<string> removeList = new List<string>();
                        foreach (string g in condition[game])
                        {
                            if (done.Contains(g))
                            {
                                removeList.Add(g);
                                continue;
                            }
                            dame = true;
                            break;
                        }

                        foreach (string re in removeList)
                        {
                            condition[game].Remove(re);
                        }
                        if (dame)
                        {
                            continue;
                        }
                    }

                    done.Add(game);
                    turn[i] = true;
                    turn[A[i][indexes[i]]] = true;
                    indexes[A[i][indexes[i]]]++;
                    indexes[i]++;
                    cannot = false;
                }

                if (cannot)
                {
                    Console.WriteLine(-1);
                    return;
                }

                ans++;
            }

            Console.WriteLine(ans);
        }

        static string toStr(long A, long B)
        {
            return "" + Math.Min(A, B) + "_" + Math.Max(A, B);
        }
    }

    internal static class CIN
    {
        public static string String()
        {
            return Console.ReadLine();
        }

        public static int Int()
        {
            return int.Parse(Console.ReadLine());
        }

        public static int[] IntArray()
        {
            return Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        }

        public static long Long()
        {
            return long.Parse(Console.ReadLine());
        }

        public static long[] LongArray()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        public static double[] DoubleArray()
        {
            return Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
        }
    }
}