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.Text;
using System.Linq;
namespace Practice
{
    class Program
    {
        static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }
        private const int MOD = 1000000007;
        private const int MAX = 100001;
        static long[] fac = new long[MAX];
        static long[] finv = new long[MAX];
        static long[] inv = new long[MAX];


        static void Solve()
        {
            int n = Input.NextInt();
            var lists = new List<Tuple<int, int>>[n];
            int m = n * (n - 1) / 2;
            var delay = new int[n];
            for(int i=0;i<n;++i)
            {
                var a = Input.NextInt(n - 1);
                var list = new List<Tuple<int, int>>(2*n);
                foreach(var ai in a)
                {
                    var elem = i < ai - 1 ? new Tuple<int, int>(i, ai - 1) : new Tuple<int, int>(ai - 1, i);
                    list.Add(elem);
                }
                lists[i] = list;
            }
            var dic = new Dictionary<Tuple<int, int>, int>();

            int pairTotal = 0;
            int day = 0;

            while(true)
            {
                dic.Clear();
                int pair = 0;
                for(int i=0;i<n;++i)
                {
                    var list = lists[i];
                    int dayThisChara = day - delay[i];
                    if (dayThisChara < list.Count)
                    {
                        var ai = list[dayThisChara];
                        if (!dic.ContainsKey(ai))
                        {
                            dic.Add(ai, i);
                        }
                        else
                        {
                            dic.Remove(ai);
                            pair++;
                            pairTotal++;
                        }
                    }
                }



                if( pair == 0)
                {
                    break;
                }

                // あふれたやつらは延期
                foreach(var kv in dic)
                {
                    int idx = kv.Value;
                    delay[idx]++;
                }
                day++;
            }

            int ans = 0;
            if( pairTotal < n * (n-1)/2)
            {
                ans = -1;
            }
            else
            {
                for(int i=0;i<n;++i)
                {
                    var list = lists[i];
                    ans = Math.Max(ans, list.Count + delay[i]);
                }
            }

            Console.WriteLine(ans);
        }


        #region よく使う便利関数


        static void COMinit()
        {
            fac[0] = fac[1] = 1;
            finv[0] = finv[1] = 1;
            inv[1] = 1;
            for (int i = 2; i < MAX; i++)
            {
                fac[i] = fac[i - 1] * i % MOD;
                inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD;
                finv[i] = finv[i - 1] * inv[i] % MOD;
            }
        }

        // 二項係数計算
        static long COM(long n, long k)
        {
            if (n < k) return 0;
            if (n < 0 || k < 0) return 0;
            return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD;
        }

        static class Input
        {
            static char[] separator = { ' ' };
            public static bool IsEof { get; set; }
            static Queue<string> q { get; set; }

            static Input()
            {
                IsEof = false;
                q = new Queue<string>();
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="items"></param>
            public static void SetText(IEnumerable<string> items)
            {
                foreach (var item in items)
                {
                    SetText(item);
                }
            }

            /// <summary>
            /// 入力予約
            /// </summary>
            /// <param name="s"></param>
            /// <returns></returns>
            public static bool SetText(string s)
            {
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                return true;
            }

            /// <summary>
            /// 内部queueに入力からの値をsplitして格納する
            /// </summary>
            /// <returns></returns>
            static bool read()
            {
                var s = Console.ReadLine();
                if (s == null) return false;

                foreach (var elem in s.Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries))
                {
                    q.Enqueue(elem);
                }

                if (!q.Any()) return read();

                return true;
            }

            /// <summary>
            /// 次のstringを一つ読み込む
            /// </summary>
            /// <returns></returns>
            public static string Next()
            {
                if (!q.Any())
                {
                    if (!read())
                    {
                        IsEof = true;
                        return "";
                    }
                }

                return q.Dequeue();
            }

            public static int NextInt() => int.Parse(Next());
            public static long NextLong() => long.Parse(Next());
            public static double NextDouble() => double.Parse(Next());

            public static List<string> Next(int n) => Enumerable.Range(0, n).Select(_ => Next()).ToList();
            public static List<int> NextInt(int n) => Next(n).Select(x => int.Parse(x)).ToList();
            public static List<long> NextLong(int n) => Next(n).Select(x => long.Parse(x)).ToList();
            public static List<double> NextDouble(int n) => Next(n).Select(x => double.Parse(x)).ToList();

            public static List<string> NextLine() => Console.ReadLine().Trim().Split(separator, StringSplitOptions.RemoveEmptyEntries).ToList();
            public static List<int> NextIntLine() => NextLine().Select(x => int.Parse(x)).ToList();
            public static List<long> NextLongLine() => NextLine().Select(x => long.Parse(x)).ToList();
            public static List<double> NextDoubleLine() => NextLine().Select(x => double.Parse(x)).ToList();
        }
        private static bool isPrime(long x)
        {
            if (x == 2) { return true; }
            if (x < 2 || x % 2 == 0) { return false; }
            long i = 3;
            while (i * i <= x)
            {
                if (x % i == 0) { return false; }
                i = i + 2;
            }
            return true;
        }
        private static long lcm(long x, long y)
        {
            return x / gcd(x, y) * y;
        }
        private static long gcd(long x, long y)
        {
            return y > 0 ? gcd(y, x % y) : x;
        }
        private static long pow(long x, long n)
        {
            if (n == 0) { return 1; }
            long res = pow(x * x % MOD, n / 2);
            if (n % 2 == 1)
            {
                res = res * x % MOD;
            }
            return res;
        }
        private static void Swap<T>(ref T x, ref T y)
        {
            T t = x;
            x = y;
            y = t;
        }

        /// <summary>
        /// 指定した値以上の先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値以上の先頭のインデクス</returns>
        public static int LowerBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) < 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int LowerBound<T>(IReadOnlyList<T> arr, T value) where T : IComparable
        {
            return LowerBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }

        /// <summary>
        /// 指定した値より大きい先頭のインデクスを返す
        /// </summary>
        /// <typeparam name="T">比較する値の型</typeparam>
        /// <param name="arr">対象の配列（※ソート済みであること）</param>
        /// <param name="start">開始インデクス [inclusive]</param>
        /// <param name="end">終了インデクス [exclusive]</param>
        /// <param name="value">検索する値</param>
        /// <param name="comparer">比較関数(インターフェイス)</param>
        /// <returns>指定した値より大きい先頭のインデクス</returns>
        public static int UpperBound<T>(IReadOnlyList<T> arr, int start, int end, T value, IComparer<T> comparer)
        {
            int low = start;
            int high = end;
            int mid;
            while (low < high)
            {
                mid = ((high - low) >> 1) + low;
                if (comparer.Compare(arr[mid], value) <= 0)
                    low = mid + 1;
                else
                    high = mid;
            }
            return low;
        }

        //引数省略のオーバーロード
        public static int UpperBound<T>(IReadOnlyList<T> arr, T value)
        {
            return UpperBound(arr, 0, arr.Count, value, Comparer<T>.Default);
        }
        #endregion
    }

    public class DisjointSet
    {
        private int[] rank;
        private int[] p;
        private int[] size;
        public DisjointSet(int n)
        {
            rank = new int[n];
            p = new int[n];
            size = new int[n];
            for (int i = 0; i < n; ++i)
            {
                MakeSet(i);
            }
        }
        public void MakeSet(int x)
        {
            p[x] = x;
            rank[x] = 0;
            size[x] = 1;
        }
        public bool IsSame(int x, int y)
        {
            return FindSet(x) == FindSet(y);
        }
        public void Unite(int x, int y)
        {
            Link(FindSet(x), FindSet(y));
        }
        public void Link(int x, int y)
        {
            if (rank[x] > rank[y])
            {
                p[y] = x;
                size[x] += size[y];
                size[y] = 0;
            }
            else
            {
                p[x] = y;
                size[y] += size[x];
                size[x] = 0;
                if (rank[x] == rank[y])
                {
                    rank[y]++;
                }
            }
        }
        public int FindSet(int x)
        {
            if (x != p[x])
            {
                p[x] = FindSet(p[x]);
            }
            return p[x];
        }
        public int Size(int x)
        {
            int root = FindSet(x);
            return size[root];
        }
    }
    public class PriorityQueue<T> where T : IComparable
    {
        private IComparer<T> _comparer = null;
        private int _type = 0;

        private T[] _heap;
        private int _sz = 0;

        private int _count = 0;

        /// <summary>
        /// Priority Queue with custom comparer
        /// </summary>
        public PriorityQueue(int maxSize, IComparer<T> comparer)
        {
            _heap = new T[maxSize];
            _comparer = comparer;
        }

        /// <summary>
        /// Priority queue
        /// </summary>
        /// <param name="maxSize">max size</param>
        /// <param name="type">0: asc, 1:desc</param>
        public PriorityQueue(int maxSize, int type = 0)
        {
            _heap = new T[maxSize];
            _type = type;
        }

        private int Compare(T x, T y)
        {
            if (_comparer != null) return _comparer.Compare(x, y);
            return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
        }

        public void Push(T x)
        {
            _count++;

            //node number
            var i = _sz++;

            while (i > 0)
            {
                //parent node number
                var p = (i - 1) / 2;

                if (Compare(_heap[p], x) <= 0) break;

                _heap[i] = _heap[p];
                i = p;
            }

            _heap[i] = x;
        }

        public T Pop()
        {
            _count--;

            T ret = _heap[0];
            T x = _heap[--_sz];

            int i = 0;
            while (i * 2 + 1 < _sz)
            {
                //children
                int a = i * 2 + 1;
                int b = i * 2 + 2;

                if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

                if (Compare(_heap[a], x) >= 0) break;

                _heap[i] = _heap[a];
                i = a;
            }

            _heap[i] = x;

            return ret;
        }

        public int Count()
        {
            return _count;
        }

        public T Peek()
        {
            return _heap[0];
        }

        public bool Contains(T x)
        {
            for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
            return false;
        }

        public void Clear()
        {
            while (this.Count() > 0) this.Pop();
        }

        public IEnumerator<T> GetEnumerator()
        {
            var ret = new List<T>();

            while (this.Count() > 0)
            {
                ret.Add(this.Pop());
            }

            foreach (var r in ret)
            {
                this.Push(r);
                yield return r;
            }
        }

        public T[] ToArray()
        {
            T[] array = new T[_sz];
            int i = 0;

            foreach (var r in this)
            {
                array[i++] = r;
            }

            return array;
        }
    }
}