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: Accepted)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using static System.Math;

namespace Sample
{
    public class Program
    {
        public static void Main(string[] args)
        {
            using (var sc = new SetConsole()) { Solve(); }
        }

        public static void Solve()
        {
            var n = GetString().ToInt();
            var list = new List<List<int>>();
            for (int i = 0; i < n; i++) { list.Add(new List<int>(Enumerable.Repeat(0, n - 1))); }
            for (int i = 0; i < n; i++)
            {
                var a = GetArray<int>();
                for (int j = 0; j < a.Length; j++)
                {
                    list[i][j] = a[j] - 1;
                }
            }
            var q = new List<Tuple<int, int>>();
            Func<int, bool> check = player =>
            {
                if (!list[player].Any()) { return false; }

                int matchedPlayer = list[player].First();
                if (!list[matchedPlayer].Any()) { return false; }

                if (list[matchedPlayer].First() != player) { return false; }

                var pair = Tuple.Create(player, matchedPlayer);
                if (pair.Item2 < pair.Item1) { pair = Tuple.Create(pair.Item2, pair.Item1); }
                q.Add(pair);
                return true;
            };

            for (int i = 0; i < n; i++) { check(i); }

            var day = 0;
            while (q.Any())
            {
                day++;
                var prevQ = new List<Tuple<int, int>>();
                foreach (var item in q.Distinct())
                {
                    prevQ.Add(item);
                }
                q = new List<Tuple<int, int>>();
                foreach (var p in prevQ)
                {
                    // 試合を消す
                    var i = p.Item1;
                    var j = p.Item2;
                    list[i].RemoveAt(0);
                    list[j].RemoveAt(0);
                }
                foreach (var p in prevQ)
                {
                    check(p.Item1);
                    check(p.Item2);
                }
            }

            foreach (var item in list)
            {
                if (item.Any()) { CWrite(-1); return; }
            }
            CWrite(day);
        }

        static void CWrite<T>(T str) => Console.WriteLine(str);
        static string GetString() => Console.ReadLine();
        static T[] GetArray<T>()
        {
            var str = Console.ReadLine();
            if (str == null) { throw new ArgumentNullException("標準入力がnullです 解答がおかしいはずです"); }

            var t = typeof(T);
            if (t == typeof(string))
            {
                return (T[])(object)str.Split();
            }
            if (t == typeof(int))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            if (t == typeof(long))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            if (t == typeof(double))
            {
                return (T[])(object)str.ToNumArray<T>();
            }
            throw new NotSupportedException($"{t} is not supported.");
        }
    }



    class SetConsole : IDisposable
    {
        readonly StreamWriter sw = new StreamWriter(Console.OpenStandardOutput());
        public SetConsole()
        {
            sw.AutoFlush = false;
            Console.SetOut(sw);
        }
        public void Dispose()
        {
            Console.Out.Flush();
            sw.AutoFlush = true;
            Console.SetOut(sw);
        }
    }

    static class ExtentionsLibrary
    {
        public static T[] CopyArray<T>(this T[] array)
        {
            var newArray = new T[array.Length];
            Array.Copy(array, newArray, array.Length);
            return newArray;
        }
        public static T[,] CopyArray<T>(this T[,] array)
        {
            var firstDimentionLength = array.GetLength(0);
            var secondDimentionLength = array.GetLength(1);
            var newDArray = new T[firstDimentionLength, secondDimentionLength];
            Array.Copy(array, newDArray, firstDimentionLength * secondDimentionLength);
            return newDArray;
        }
        public static T[] ToNumArray<T>(this string str)
        {
            var t = typeof(T);
            if (t == typeof(int))
            {
                return (T[])(object)str.Split().Select(int.Parse).ToArray();
            }
            if (t == typeof(long))
            {
                return (T[])(object)str.Split().Select(long.Parse).ToArray();
            }
            if (t == typeof(double))
            {
                return (T[])(object)str.Split().Select(double.Parse).ToArray();
            }
            throw new NotSupportedException();
        }
        public static int ToInt(this string str) => int.Parse(str);
        public static int ToInt(this char chr) => int.Parse(chr.ToString());
        public static long ToLong(this string str) => long.Parse(str);
        public static DateTime ToDateTime(this string str) => DateTime.Parse(str);
    }
}