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;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
namespace Collections
{
	class program
	{
    //static long MAX_LONG = 5000000000000000;
		static void Main(string[] args)
		{

			// 入力
			long N = long.Parse(Console.ReadLine());
      //int[] input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
			List<List<int>> senshu = new List<List<int>>();
			for(int i=0; i<N; i++)
			{
				int[] input = Console.ReadLine().Split().Select(p => int.Parse(p)).ToArray();
				List<int> a = new List<int>(input);
				senshu.Add(a);
			}

			int[] done = new int[N]; // 選手Nが何人目まで終わったかをチェックする

			int day = 0;
			while(true)
			{
				HashSet<int> nolonger = new HashSet<int>(); //一回試合したらもうできない

				bool isGamed = false; // 1日に１試合も組めない場合は-1
				int allDone = 0; //全員終わってたらOK
				for(int i=0; i<N; i++)
				{
					if(nolonger.Count >= N)
					{
						break; // 全員試合を組んだ
					}
					// 選手iと選手 senshu[i-1][done[i-1]]が試合をする
					int a = i+1; //青コーナー
					if(nolonger.Contains(a))
						continue;
					//Console.WriteLine("debug3 " + a + " " + done[i]);
					if(done[i] >= N - 1)
					{
						// 選手aはすでに全試合終わっているので試合は組めない
						allDone++;
						continue;
					}

					int b = senshu[i][done[i]]; // 赤コーナー
					if(nolonger.Contains(b))
						continue;

					if(done[b-1] >= N - 1)
					{
						continue; //選手bも同様
					}

					if(senshu[b-1][done[b-1]] != a)
					{
						// もしbの次の相手がaじゃなかったら、試合は組めない
						continue;
					}
					else
					{
						nolonger.Add(a);
						nolonger.Add(b);
						isGamed = true;
						done[a-1] += 1;
						done[b-1] += 1;
					}
				}

				if(isGamed)
				{
					day++;
				}
				else if(allDone < N)
				{
					// もしも１試合も組まれなかった場合は-1
					Console.WriteLine("-1");
					return;
				}
				else
				{
					break;
				}
			}

			Console.WriteLine(day + "");
    }
	}
}