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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class E
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public void Solve()
	{
		int N = GetInt();
		int[,] A = new int[N, N - 1];
		for(int i = 0; i < N; i++)
			for(int j = 0; j < N - 1; j++)
				A[i, j] = GetInt() - 1;

		var dict = new Dictionary<int, int>();
		int cnt = 0;
		for(int i = 0; i < N; i++)
		{
			for(int j = i + 1; j < N; j++)
			{
				dict[i * N + j] = cnt;
				cnt++;
			}
		}

		var adj = Enumerable.Range(0, cnt).Select(_ => new List<int>()).ToArray();
		for(int i = 0; i < N; i++)
		{
			for(int j = 0; j < N - 2; j++)
			{
				int v = dict[Math.Min(i, A[i, j]) * N + Math.Max(i, A[i, j])];
				int u = dict[Math.Min(i, A[i, j + 1]) * N + Math.Max(i, A[i, j + 1])];
				adj[v].Add(u);
			}
		}
		
		var tpl = tplSort(adj);
		if(tpl.Count != cnt)
		{
			Console.WriteLine(-1);
			return;
		}

		long[] dp = new long[cnt];
		for(int v = 0; v < cnt; v++)
			foreach(int u in adj[v])
				dp[u] = Math.Max(dp[u], dp[v] + 1);

		Console.WriteLine(dp.Max() + 1);
	}

	private List<int> tplSort(List<int>[] adj)
	{
		int N = adj.Length;
		int[] deg = new int[N];
		for(int v = 0; v < N; v++)
		{
			foreach(int u in adj[v])
				deg[u]++;
		}

		var res = new List<int>();
		var queue = new Queue<int>();
		for(int v = 0; v < N; v++)
			if(deg[v] == 0)
				queue.Enqueue(v);
		
		while(queue.Count > 0)
		{
			int v = queue.Dequeue();
			res.Add(v);
			foreach(int u in adj[v])
			{
				deg[u]--;
				if(deg[u] == 0)
					queue.Enqueue(u);
			}
		}

		return res;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}