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)

#if true
//#if false
#define UTAKA_DEBUG
#endif

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Runtime.CompilerServices;

namespace UtakaApp
{
    public partial class Program
    {
        public const string ContestName = "abc139";
        public const string ProblemName = "E";

        public static void Main(string[] args)
        {
#if UTAKA_LOCAL
//#if false
            new TestCaseCheckerForAtCoder().TestProblems();
#else
            var console = new MyConsole();
            new Program().Solve(System.Console.In, console);
            console.Flush();
#endif
            var sw = new StreamWriter(System.Console.OpenStandardOutput()) {AutoFlush = false};
        }

        public void Solve(TextReader textReader, IConsole console)
        {
            var cin = new ConsoleInput(textReader, ' ');

            int N = cin.ReadInt;

            int[,] A = new int[N, N - 1];

            bool[,] isDone = new bool[N, N];

            bool[] todayFinished = new bool[N];

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

            int[] currentIndexes = new int[N];

            for (int i = 0; i < N; i++)
            {
                int[] tmpA = cin.ReadIntArray(N - 1);

                for (int j = 0; j < N - 1; j++)
                {
                    A[i, j] = tmpA[j] - 1;
                }
            }

            long countOfDays = 0;

            while (true)
            {
                bool found = false;

                Array.Clear(todayFinished, 0, todayFinished.Length);

                for (int p = N - 1; p >= 0; p--)
                {
                    if (todayFinished[p])
                    {
                        continue;
                    }

                    int currentInd = currentIndexes[p];

                    if (currentInd >= N - 1)
                    {
                        continue;
                    }

                    int enemyIndex = A[p, currentInd];

                    if (enemyIndex >= N - 1)
                    {
                        continue;
                    }

                    if (todayFinished[enemyIndex])
                    {
                        continue;
                    }

                    while (enemyIndex < N - 1 && isDone[p, enemyIndex])
                    {
                        currentIndexes[p]++;
                        enemyIndex = currentIndexes[p];
                    }

                    if (enemyIndex >= N - 1)
                    {
                        continue;
                    }

                    int counterpartIndex = currentIndexes[enemyIndex];

                    if (A[enemyIndex, counterpartIndex] == p)
                    {
                        isDone[p, enemyIndex] = true;
                        isDone[enemyIndex, p] = true;

                        currentIndexes[p]++;
                        currentIndexes[enemyIndex]++;

                        found = true;

                        todayFinished[p] = true;
                        todayFinished[enemyIndex] = true;
                    }
                }

                if (!found)
                {
                    bool success = true;

                    foreach (var currentIndex in currentIndexes)
                    {
                        if (currentIndex < N - 1)
                        {
                            success = false;
                        }
                    }

                    if (!success)
                    {
                        console.WriteLine((-1).ToString());
                        return;
                    }
                    else
                    {
                        break;
                    }
                }
                else
                {
                    countOfDays++;
                }
            }

            console.WriteLine(countOfDays.ToString());
        }
    }

    public partial class Program
    {
        public const int ModLarge = 1000000007;
    }

    public class ConsoleInput
    {
        private readonly TextReader _stream;
        private char _separator = ' ';
        private Queue<string> inputStream;

        public ConsoleInput(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 => _stream.ReadLine();
        public int ReadInt => int.Parse(Read);
        public long ReadLong => long.Parse(Read);
        public double ReadDouble => 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;
        }
    }

    public interface IConsole
    {
        void Flush();
        void Write(string str);
        void WriteLine(string str);
    }

    public class MyConsole : IConsole
    {
        public MyConsole()
        {
            var sw = new StreamWriter(System.Console.OpenStandardOutput()) {AutoFlush = false};
            System.Console.SetOut(sw);
        }

        public void Flush()
        {
            System.Console.Out.Flush();
        }

        public void Write(string str)
        {
            System.Console.Write(str);
        }

        public void WriteLine(string str)
        {
            System.Console.WriteLine(str);
        }
    }

#if UTAKA_LOCAL

    public class DebugConsole : IConsole
    {
        private StringBuilder mSb;

        public DebugConsole()
        {
            mSb = new StringBuilder();
        }

        public void Flush()
        {
            // 何もしない
        }

        public void Write(string str)
        {
            mSb.Append(str);
        }

        public void WriteLine(string str)
        {
            mSb.AppendLine(str);
        }

        public string GetAllOutput()
        {
            return mSb.ToString();
        }
    }

#endif

#if UTAKA_LOCAL

    public class TestCaseCheckerForAtCoder
    {
        private string DirectoryPath => $"../../../../{Program.ContestName}/{Program.ProblemName}";

        private string GetInputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.in";
            return $"{DirectoryPath}/in_{testCaseNumber}.txt";
        }

        private string GetOutputFilePath(int testCaseNumber)
        {
            //return $"{DirectoryPath}/sample-{testCaseNumber}.out";
            return $"{DirectoryPath}/out_{testCaseNumber}.txt";
        }

        public bool TestProblem(int testCaseNumber)
        {
            var inputFilePath = GetInputFilePath(testCaseNumber);
            var outputFilePath = GetOutputFilePath(testCaseNumber);

            TextReader inputStream = new StreamReader(inputFilePath);

            var debugConsoleWriter = new DebugConsole();

            new Program().Solve(inputStream, debugConsoleWriter);

            var output = debugConsoleWriter.GetAllOutput();

            TextReader outputStream = new StreamReader(outputFilePath);
            var outputAnswer = outputStream.ReadToEnd();

            Dbg.WriteLine(output);
            Dbg.WriteLine(outputAnswer);

            var isCorrect = output == outputAnswer;

            return isCorrect;
        }

        public void TestProblems()
        {
            var isSuccessAll = true;

            var testCaseNumber = 1;
            while (true)
            {
                var inputFileName = GetInputFilePath(testCaseNumber);
                if (!File.Exists(inputFileName))
                {
                    break;
                }

                System.Console.WriteLine($"TestCase {testCaseNumber} =====================================================");

                var result = TestProblem(testCaseNumber);

                if (result)
                {
                    System.Console.WriteLine($"Success");
                }
                else
                {
                    isSuccessAll = false;
                    System.Console.WriteLine($"Failure *****");
                }

                testCaseNumber++;
            }

            if (isSuccessAll)
            {
                System.Console.WriteLine($"!!!!!!!!! All Success !!!!!!!!!");
            }
        }
    }

#endif

#if UTAKA_LOCAL

    public static class Dbg
    {
        public static void WriteLine(string str)
        {
            System.Console.WriteLine(str);
        }

        public static void Write(string str)
        {
            System.Console.Write(str);
        }
    }
#else
    public static class Dbg
    {
        public static void WriteLine(string str)
        {
        }

        public static void Write(string str)
        {
        }
    }

#endif
}