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 static System.Console;
using static System.Math;
using System.IO;
using System.Collections.Generic;
namespace I_am_the_green_coder{
    
    class Inonoa{
        static bool[,] moumita;
        static long[,] maxlens;
        static List<long[]>[,] sakis;
        static long ans = 1;
        static void Main(){
            long n = ILongs()[0];
            long[][] a = ILongLongs(n);
            moumita = new bool[n,n];
            sakis = new List<long[]>[n,n];
            maxlens = new long[n,n];
            
            for(int i=0;i<n;i++){
                for(int j=0;j<n;j++){
                    sakis[i,j] = new List<long[]>();
                    maxlens[i,j] = -1;
                }
            }

            for(int i=0;i<n;i++){
                for(int j=0;j<n-2;j++){
                    sakis[Min(i,a[i][j]-1),Max(i,a[i][j]-1)].Add(new long[2]{Min(i,a[i][j+1]-1),Max(i,a[i][j+1]-1)});
                    //WriteLine("{0},{1}を追加",Min(i,a[i][j+1]-1),Max(i,a[i][j+1]-1));
                }
            }

            for(int i=0;i<n;i++){
                sakis[0,0].Add(new long[2]{Min(i,a[i][0]-1),Max(i,a[i][0]-1)});
            }
            
            long an = Dfs(0,0) - 1;
            if(an>=n*n)WriteLine(-1);
            else WriteLine(an);

        }

        static long Dfs(long x, long y){
            //1つ先の試合群のdfsの値のmaxに1足してreturn
            //試合群それぞれの計算結果はメモする
            //閉路も考慮せよ
            
            //WriteLine("{0},{1}",x,y);
            
            moumita[x,y] = true;
            long ans = 1;
            
            foreach(long[] saki in sakis[x,y]){
                if(moumita[saki[0],saki[1]])return moumita.Length*2;
                if(maxlens[saki[0],saki[1]]>0){
                    if(ans<=maxlens[saki[0],saki[1]])ans = maxlens[saki[0],saki[1]] + 1;
                }else{
                    long sakidfs = Dfs(saki[0],saki[1]);
                    if(ans<=sakidfs)ans = sakidfs + 1;
                }
            }
            
            maxlens[x,y] = ans;
            
            moumita[x,y] = false;
            
            return ans;
        }

        static readonly long MOD = 1000000007;

        ///<summary>a_1, a_2, a_3, ...みたいなの</summary>
        static long[] ILongs(){
            string[] s = ReadLine().Split();
            long[] re = new long[s.Length];
            for(long i=0;i<s.Length;i++){
                re[i] = long.Parse(s[i]);
            }
            return re;
        }

        ///<summary>xooxoxoxxoxo...みたいなの</summary>
        static char[] IChars(){
            return ReadLine().ToCharArray();
        }

        ///<summary>n m とかをちょっとはやくかくだけ</summary>
        static string[] IStrings(){
            return ReadLine().Split();
        }

        ///<summary>n行の入力を取ったり</summary>
        static long[][] ILongLongs(long n){
            long[][] re = new long[n][];
            for(long i=0;i<n;i++){
                string[] s = ReadLine().Split();
                re[i] = new long[s.Length];
                for(long j=0;j<s.Length;j++){
                    re[i][j] = long.Parse(s[j]);
                }
            }
            return re;
        }

        ///<summary>n行の文字列を取ったり</summary>
        static char[][] ICharsChars(long n){
            char[][] re = new char[n][];
            for(long i=0;i<n;i++){
                re[i] = ReadLine().ToCharArray();
            }
            return re;
        }
    }
}