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.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

namespace AtCorder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            new Program().Solve(new ConsoleInput(Console.In, ' '));
        }

        public void Solve(ConsoleInput cin)
        {
            var N = cin.ReadInt;
            var ans = 0L;
            var A = new int[N, N - 1];
            for (int i = 0; i < N; i++)
            {
                for (int j = 0; j < N - 1; j++)
                {
                    A[i, j] = cin.ReadInt;
                }
            }
            var nowIndex = new int[N];
            for (int i = 0; i < N; i++)
            {
                nowIndex[i] = 0;
            }
            var flag = false;
            var isBattle = new bool[N];
            while (true)
            {
                ans++;

                for (int i = 0; i < N; i++)
                {
                    isBattle[i] = true;
                }

                for (int i = 0; i < N; i++)
                {
                    if (nowIndex[i] == N - 1 || !isBattle[i])
                    {
                        continue;
                    }
                    var aite = A[i, nowIndex[i]];
                    if (!isBattle[aite - 1]) continue;
                    if (i + 1 == A[aite - 1, nowIndex[aite - 1]])
                    {
                        nowIndex[i]++;
                        nowIndex[aite - 1]++;
                        isBattle[i] = false;
                        isBattle[aite - 1] = false;
                        flag = true;
                    }

                }

                if (nowIndex.Sum() == (N - 1) * N)
                {
                    WriteLine(ans);
                    return;
                }
                if (!flag)
                {
                    WriteLine(-1);
                    return;
                }
            }
        }



        public long C(int X, int Y)
        {

            if (Y == 0 || Y == X)
            {
                return 1;
            }
            if (X < Y)
            {
                return 0;
            }
            var Pascal = new long[X + 1, X + 1];
            for (int i = 0; i <= X; i++)
            {
                Pascal[i, 0] = 1L;
                Pascal[i, i] = 1L;
            }
            for (int i = 2; i <= X; i++)
            {
                for (int j = 1; j < i; j++)
                {
                    Pascal[i, j] = Pascal[i - 1, j] + Pascal[i - 1, j - 1];
                }
            }
            return Pascal[X, Y];
        }

        public class ConsoleInput
        {
            private readonly System.IO.TextReader _stream;
            private char _separator = ' ';
            private Queue<string> inputStream;
            public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
            {
                this._separator = separator;
                this._stream = stream;
                inputStream = new Queue<string>();
            }
            public string Read
            {
                get
                {
                    if (inputStream.Count != 0) return inputStream.Dequeue();
                    string[] tmp = _stream.ReadLine().Split(_separator);
                    for (int i = 0; i < tmp.Length; ++i)
                        inputStream.Enqueue(tmp[i]);
                    return inputStream.Dequeue();
                }
            }
            public string ReadLine { get { return _stream.ReadLine(); } }
            public int ReadInt { get { return int.Parse(Read); } }
            public long ReadLong { get { return long.Parse(Read); } }
            public double ReadDouble { get { return double.Parse(Read); } }
            public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
            public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
            public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
        }
    }
}