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.Linq;
using System.Collections;
using System.Collections.Generic;
using static Library.Comfort;
using static Library.Math;
using static Library.Algorithm;
using static System.Math;

namespace AtCoderer
{
    public class App
    {
        public static void Solve()
        {
            int n = In();
            Queue<int>[] q = new Queue<int>[n];
            Queue<int> que = new Queue<int>();
            bool[] imut = new bool[n];
            for (int i = 0; i < n; i++)
            {
                q[i] = new Queue<int>();
                foreach (var v in Parse())
                {
                    q[i].Enqueue(v - 1);
                }
            }

            for (int i = 0; i < n; i++)
            {
                que.Enqueue(i);
            }
            int curr = 0;
            while (true)
            {
                curr++;
                while (que.Count != 0)
                {
                    var v = que.Dequeue();
                    if (!imut[v])
                    {
                        if (q[q[v].Peek()].Peek() == v)
                        {
                            imut[v] = true;
                            imut[q[v].Peek()] = true;
                        }
                    }
                }

                for (int i = 0; i < n; i++)
                {
                    if(imut[i])
                    {
                        q[i].Dequeue();
                        if(q[i].Count != 0)
                            que.Enqueue(i);
                        imut[i] = false;
                    }
                }

                if(que.Count == 0)
                {
                    if (q.All(x => x.Count == 0))
                        cout = curr;
                    else
                        cout = -1;
                    return;
                }
            }
        }
        public static void Main(string[] args)
        {
#if DEBUG
            while (true)
            {
                Solve();
            }
#else
            Solve();
#endif
        }
    }
}
namespace Library
{
    public static class Comfort
    {
        public const int mod = 1000000007;
        public class Point
        {
            public int a;
            public int b;
            public Point(int a, int b)
            {
                this.a = a;
                this.b = b;
            }
        }
        public static int[] OrderBy(this int[] IArr)
        {
            int[] arr = new int[IArr.Length];
            Array.Copy(IArr, arr, IArr.Length);
            Array.Sort(arr);
            return arr;
        }
        public static int Max(params int[] p) => p.Max();
        public static long Max(params long[] p) => p.Max();
        public static int Min(params int[] p) => p.Min();
        public static long Min(params long[] p) => p.Min();
        public static int In()
        {
            return int.Parse(Console.ReadLine());
        }
        public static int Inl()
        {
            return int.Parse(Console.ReadLine());
        }
        public static int[] Parsed;
        public static int[] Parse()
        {
            Parsed = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            return Parsed;
        }
        public static long[] Parsel()
        {
            return Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
        }
        public static void Parse(out int a, out int b)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
        }
        public static void Parse(out int a, out int b, out int c)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
        }
        public static void Parse(out int a, out int b, out int c, out int d)
        {
            var r = Console.ReadLine().Split().Select(v => int.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
            d = r[3];
        }
        public static void Parse(out long a, out long b)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
        }
        public static void Parse(out long a, out long b, out long c)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
        }
        public static void Parse(out long a, out long b, out long c, out long d)
        {
            var r = Console.ReadLine().Split().Select(v => long.Parse(v)).ToArray();
            a = r[0];
            b = r[1];
            c = r[2];
            d = r[3];
        }
        public static string ToString(this IEnumerable<char> v)
        {
            return string.Join("", v);
        }
        public static string Join<T>(this IEnumerable<T> v)
        {
            return string.Join(" ", v);
        }
        public static string Join<T>(this IEnumerable<T> v, char c)
        {
            return string.Join(c.ToString(), v);
        }
        public static string Join<T>(this IEnumerable<T> v, string s)
        {
            return string.Join(s, v);
        }
        public static object cout
        {
            set
            {
                Console.WriteLine(value);
            }
        }
        public static object dbg
        {
            set
            {
#if DEBUG
                Console.WriteLine(value);
#endif
            }
        }
        public static object dout
        {
            set
            {
                dbg = value;
            }
        }
    }
    public static class Math
    {
        public static bool IsNatural(this float v) => v - (int)v == 0;
        public static bool IsNatural(this double v) => v - (int)v == 0;
        public static long nCm(long n, long m)
        {
            if (m == 0) return 1;
            if (n == 0) return 0;
            return n * nCm(n - 1, m - 1) / m;
        }
        public static IEnumerable<int> Factor(int n)
        {
            int i = 2;
            int tmp = n;

            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;
        }
        public static int Gcd(int a, int b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static int GcdRecursive(int x, int y) => y == 0 ? x : GcdRecursive(y, x % y);
        public static long Gcd(long a, long b) => a > b ? GcdRecursive(a, b) : GcdRecursive(b, a);
        private static long GcdRecursive(long x, long y) => y == 0 ? x : GcdRecursive(y, x % y);
        public static long Lcm(int a, int b) => ((long)a) * b / Gcd(a, b);
    }
    public static class Algorithm
    {
        public static IEnumerable<KeyValuePair<T, int>> UniteNext<T>(this IEnumerable<T> arr) where T : IEquatable<T>
        {
            int cont = 0;
            T prev = arr.First();
            foreach (var v in arr)
            {
                if (v.Equals(prev))
                {
                    cont++;
                }
                else
                {
                    yield return new KeyValuePair<T, int>(prev, cont);
                    cont = 1;
                }
                prev = v;
            }
            yield return new KeyValuePair<T, int>(prev, cont);
        }
        public class EnumAll
        {
            bool Over = false;
            int UpperValue;
            int Dimension;
            public int[] Current { private set; get; }
            public EnumAll(int MaxValue, int Dimension)
            {
                this.Dimension = Dimension;
                UpperValue = MaxValue;
                Current = new int[Dimension];
                Current[0] = -1;
            }
            public bool Next()
            {
                if (Over)
                    return false;
                bool flag = false;
                for (int i = 0; i < Dimension; i++)
                {
                    if (++Current[i] >= UpperValue)
                        Current[i] = 0;
                    else
                    {
                        flag = true;
                        break;
                    }
                }
                if (!flag)
                {
                    Over = true;
                    return false;
                }
                return true;
            }
        }
        public class Graph
        {
            public int Count = -1;
            private HashSet<int>[] Joined;
            public static Graph GenerateComplete(int size)
            {
                throw new NotImplementedException();
            }
            public Graph(int size)
            {
                Joined = new HashSet<int>[size];
                for (int i = 0; i < Joined.Length; i++)
                    Joined[i] = new HashSet<int>();
                Count = size;
            }
            public int[] GetConnected(int index)
            {
                return Joined[index].ToArray();
            }
            public void AddEdge(int a, int b)
            {
                if (a == b)
                    dbg = "ループを追加することはできません A:" + a + " B:" + b;
                else
                {
                    if (!Joined[a].Add(b))
                        dbg = "多重辺を追加することはできません A:" + a + " B:" + b;
                    else
                        Joined[b].Add(a);
                }
            }
            public int[] ToTree(int Root)
            {
                var ar = new int[Count];
                for (int i = 0; i < ar.Length; i++)
                    ar[i] = -10000000;
                ar[Root] = -1;
                Queue<int> bfs = new Queue<int>();
                bfs.Enqueue(Root);
                while (bfs.Count != 0)
                {
                    var t = bfs.Dequeue();
                    foreach (var v in Joined[t])
                    {
                        bfs.Enqueue(v);
                        if (ar[v] == -10000000)
                            ar[v] = t;
                    }
                }
                return ar;
            }
        }
        public class UnionFind
        {
            private int[] Parent;
            private int GetRoot(int v)
            {
                if (Parent[v] < 0)
                    return v;
                else
                    return Parent[v] = GetRoot(Parent[v]);
            }
            public UnionFind(int size)
            {
                Parent = new int[size];
                for (int i = 0; i < size; i++)
                    Parent[i] = -1;
            }
            public bool AreGrouped(int a, int b)
            {
                return GetRoot(a) == GetRoot(b);
            }
            public void Connect(int a, int b)
            {
                a = GetRoot(a);
                b = GetRoot(b);
                if (a == b) return;
                if (Parent[b] < Parent[a])
                {
                    Parent[b] += Parent[a];
                    Parent[a] = b;
                }
                else
                {
                    Parent[a] += Parent[b];
                    Parent[b] = a;
                }
            }
            public int GetGroupSize(int a)
            {
                return -Parent[GetRoot(a)];
            }
        }
        public class PriorityQueue<T> where T : IComparable
        {
            List<T> buffer = new List<T>();
            static void PushHeap(List<T> array, T elem)
            {
                int n = array.Count;
                array.Add(elem);

                while (n != 0)
                {
                    int i = (n - 1) / 2;
                    if (array[n].CompareTo(array[i]) < 0)
                    {
                        T tmp = array[n]; array[n] = array[i]; array[i] = tmp;
                    }
                    n = i;
                }
            }
            static void PopHeap(List<T> array)
            {
                int n = array.Count - 1;
                array[0] = array[n];
                array.RemoveAt(array.Count - 1);

                for (int i = 0, j; (j = 2 * i + 1) < n;)
                {
                    if ((j != n - 1) && (array[j].CompareTo(array[j + 1]) > 0))
                        j++;
                    if (array[i].CompareTo(array[j]) > 0)
                    {
                        T tmp = array[j]; array[j] = array[i]; array[i] = tmp;
                    }
                    i = j;
                }
            }
            public int Count
            {
                get
                {
                    return buffer.Count;
                }
            }
            public void Push(T elem)
            {
                PushHeap(this.buffer, elem);
            }
            public T Peek()
            {
                return buffer[0];
            }

            public T Pop()
            {
                T a = buffer[0];
                PopHeap(this.buffer);
                return a;
            }
        }
        public class KMP
        {
            int[] Table;
            string a, b;
            int m = 0;
            int i = 0;
            public KMP(string a)
            {
                this.a = a;
                Table = new int[a.Length];
                int subindex = 0;

                Table[0] = -1;
                Table[1] = 0;

                for (int i = 2; i < a.Length;)
                {
                    if (a[i - 1] == a[subindex])
                    {
                        subindex++;
                        Table[i] = subindex;
                        i++;
                    }
                    else if (subindex > 0)
                        subindex = Table[subindex];
                    else
                    {
                        Table[i] = 0;
                        i++;
                    }
                }
            }
            public void SetSearchBase(string v)
            {
                b = v;
                m = 0;
                i = 0;
            }
            public int Search()
            {
                m++;
                i = 0;
                while (m + i < b.Length)
                {
                    if (a[i] == b[m + i])
                    {
                        i++;
                        if (i == a.Length)
                            return m;
                    }
                    else
                    {
                        m = m + i - Table[i];
                        if (i > 0)
                            i = Table[i];
                    }
                }
                return -1;
            }
        }
    }
}