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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

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

class Program
{
    #region Reader
    static string ReadStr => Console.ReadLine();
    static string[] ReadStrs => Console.ReadLine().Split(' ');
    static int ReadInt => Convert.ToInt32(Console.ReadLine().Trim());
    static int[] ReadInts => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt32(s)).ToArray();
    static long ReadLong => Convert.ToInt64(Console.ReadLine().Trim());
    static long[] ReadLongs => Console.ReadLine().Trim().Split(' ').Select(s => Convert.ToInt64(s)).ToArray();
    #endregion
    #region Method
    const int mod = 1000000007;
    public static int Mod(int a, int mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    public static long Mod(long a, long mod = mod) { return a % mod >= 0 ? a % mod : a % mod + mod; }
    #endregion





    /// <summary>
    /// 最大公約数
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <returns></returns>
    public static long Gcd(long a, long b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }



    public static Dictionary<int, int> PrimeFactors(int n)
    {
        int i = 2;
        int tmp = n;
        Dictionary<int, int> d = new Dictionary<int, int>();

        while (i * i <= n) //※1
        {
            if (tmp % i == 0)
            {
                tmp /= i;
                if (d.ContainsKey(i)) d[i]++;
                else d.Add(i, 1);
            }
            else
            {
                i++;
            }
        }
        if (tmp != 1)
        {
            if (d.ContainsKey(tmp)) d[tmp]++;
            else d.Add(tmp, 1);
        }
        return d;
    }


    #region Mod
    public static long GetInv(long a, long mod = 1000000007)
    {
        return PowerMod(a, mod - 2, mod);
    }
    public static long Combination(long a, long b, long mod = 1000000007)
    {
        if (b < 0 || b > a) return 0;
        if (b > a / 2) b = a - b;
        long numerator = Factorial(a, mod);
        long denominator = (Factorial(b, mod) * Factorial(a - b, mod)) % mod;

        return (numerator * GetInv(denominator, mod)) % mod;
    }
    public static long Factorial(long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return 1;
        long ans = n;
        for (int i = 2; i < n; i++)
        {
            ans = (ans * i) % mod;
        }

        return ans;
    }
    private static long PowerMod(long a, long n, long mod = 1000000007)
    {
        if (n == 0) return 1;
        if (n == 1) return a;

        long p = PowerMod(a, n / 2, mod);
        if (n % 2 == 1) return ((p * p) % mod * a) % mod;
        else return (p * p) % mod;
    }
    #endregion


    static List<long> Divisor(long N)
    {
        List<long> ans = new List<long>();
        int max = (int)Math.Sqrt(N);
        for (int i = 1; i < max; i++)
        {
            if (N % i == 0)
            {
                ans.Add(i);
                ans.Add(N / i);
            }
        }

        if (N % max == 0)
        {
            if (N / max == max) ans.Add(max);
            else
            {
                ans.Add(max);
                ans.Add(N / max);
            }
        }
        return ans;
    }


    class Segtree<T>
    {
        int n;
        T[] tree;
        Func<T, T, T> f;
        T exnum;
        public Segtree(int m, Func<T, T, T> f, T ex)
        {
            this.f = f;
            this.exnum = ex;
            n = 1;
            while (n < m) n <<= 1;

            tree = new T[(n << 1) - 1];
            for (int i = 0; i < tree.Length; i++) tree[i] = ex;
        }
        public Segtree(int m, T ini, Func<T, T, T> f, T ex) : this(m, f, ex)
        {
            for (int i = 0; i < m; ++i) tree[i + n - 1] = ini;
            all_update();
        }
        public void assign_without_update(int j, T x)
        {
            tree[j + n - 1] = x;
        }
        public void update(int j, T x)
        {
            int i = j + n - 1;
            tree[i] = x;
            while (i > 0)
            {
                i = (i - 1) >> 1;
                tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
            }
        }
        public void all_update()
        {
            for (int i = n - 2; i >= 0; i--)
                tree[i] = f(tree[(i << 1) + 1], tree[(i << 1) + 2]);
        }
        public T look(int i) { return tree[i + n - 1]; }

        // [s, t)
        public T run(int s, int t) { return query(s, t, 0, 0, n); }
        T query(int s, int t, int k, int l, int r)
        {
            if (r <= s || t <= l) return exnum;
            if (s <= l && r <= t) return tree[k];

            return f(query(s, t, (k << 1) + 1, l, (l + r) >> 1), query(s, t, (k + 1) << 1, (l + r) >> 1, r));
        }
    }

    struct ModInt
    {
        const int MOD = 998244353;// 1000000007;
        long value;
        static List<ModInt> fact = new List<ModInt> { 1 };
        public ModInt(long value) => this.value = value;
        public static implicit operator ModInt(long a) => new ModInt(a % MOD + (a < 0 ? MOD : 0));
        public static explicit operator int(ModInt a) => (int)a.value;
        public static ModInt operator +(ModInt a, ModInt b) => a.value + b.value;
        public static ModInt operator -(ModInt a, ModInt b) => a.value - b.value;
        public static ModInt operator *(ModInt a, ModInt b) => a.value * b.value;
        public static ModInt operator /(ModInt a, ModInt b) => a * Inv(b);
        public static ModInt Pow(ModInt a, int n) { if (n == 0) return 1; if (n == 1) return a; var p = Pow(a, n / 2); return p * p * Pow(a, n % 2); }
        public static ModInt Inv(ModInt a) => Pow(a, MOD - 2);
        public static ModInt Fact(int n) { for (int i = fact.Count; i <= n; i++) fact.Add(fact[^1] * i); return fact[n]; }
        public static ModInt Npr(int n, int r) => Fact(n) / Fact(n - r);
        public static ModInt Ncr(int n, int r) => Fact(n) / Fact(n - r) / Fact(r);
        public static ModInt Nhr(int n, int r) => Fact(n + r - 1) / Fact(n - 1) / Fact(r);
    }

    static void Main()
    {
        int N = ReadInt;
        Queue<int>[] queues = new Queue<int>[N];

        for (int i = 0; i < N; i++)
        {
            int[] v = ReadInts;

            queues[i] = new Queue<int>();

            for (int j = 0; j < N-1; j++)
            {
                queues[i].Enqueue(v[j]-1);
            }
        }


        int count = 0;
        while (true)
        {
            bool[] done = new bool[N];
            int c = 0;
            for (int player = 0; player < N; player++)
            {
                if (queues[player].Count == 0) continue;
                int opponent = queues[player].Peek();
                if (done[player] || done[opponent]) continue;
                if (player < opponent && queues[opponent].Peek() == player)
                {
                    queues[player].Dequeue();
                    queues[opponent].Dequeue();

                    done[player] = true;
                    done[opponent] = true;
                    c++;
                }

            }
            if (c == 0) break;
            if (count > 1000000) break;
            count++;
        }

        foreach (var item in queues)
        {
            if (item.Count != 0)
            {
                WriteLine(-1);
                return;
            }
        }
        WriteLine(count);
    }


}