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;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;
namespace AtCoderSolve
{
    class Solve
    {
        const int mod = 1000000007;
        const int INF = 2147483647;
        const long SINF = 9223372036854775807;

        static long N;
        static List<Queue<int>> A = new List<Queue<int>>();
        //static int[] H;
        //static string S, T;


        public static void Input()
        {
            var cin = new Scanner();
            N = int.Parse(Console.ReadLine());
            
            for(var i = 0; i < N; i++)
            {
                var input = cin.SplitReader();
                A.Add(new Queue<int>());
                for(var j = 0; j < input.Length; j++)
                {
                    A[i].Enqueue(input[j] - 1);
                }
            }
        }

        static void Main(string[] args)
        {
            Input();
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            
            bool[] c = new bool[N];

            for(var i = 0; i < N; i++)
            {
                c[i] = false;
            }

            long ans = 0;
            long game = (long)N * (N - 1) / 2;
            while (game > 0)
            {
                int shouka = 0;
                for(var i = 0; i < N; i++)
                {
                    if (!A[i].Any()|| c[i])
                    {
                        continue;
                    }
                    int aite = A[i].Peek();
                    if (!A[aite].Any()|| c[aite])
                    {
                        continue;
                    }

                    if (i == A[aite].Peek())
                    {
                        shouka++;
                        c[i] = true;
                        c[aite] = true;
                    }

                }
                if (shouka == 0)
                {
                    Console.WriteLine(-1);
                    return;
                }
                game -= shouka;
                

                for(var i = 0; i < N; i++)
                {
                    if (c[i]) {
                       int _ = A[i].Dequeue();
                    }
                }

                for(var i = 0; i < N; i++)
                {
                    c[i] = false;
                }
                ans++;
                //foreach(var x in A) { Console.WriteLine(x.Count()); }
            }


            Console.WriteLine(ans);
            //Console.Out.Flush();
        }

    }

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }

        public int[] MultiLineReader(int N)
        {
            int[] ret = new int[N];
            for(var i = 0; i < N; i++)
            {
                ret[i] = int.Parse(Console.ReadLine());
            }

            return ret;
        }
        public long[] MultiLineReaderL(int N)
        {
            long[] ret = new long[N];
            for (var i = 0; i < N; i++)
            {
                ret[i] = long.Parse(Console.ReadLine());
            }

            return ret;
        }

    }

    public class Graph
    {
        
    }
}