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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main {

    public static class Player {

        public int[] enemies;
        public int current;
        public boolean isMatched;

        public Player( int n ){
            enemies = new int[ n - 1 ];
            current = 0;
            isMatched = true;
        }

    }

    public static boolean check( Player[] players , int n ){
        for( int i = 0 ; i < n ; i++ ){
            if( players[i].current !=  n - 2 ){
                return false;
            }
        }
        return true;
    }

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        int n = Integer.parseInt( in.nextLine() );
        Player[] players  = new Player[n];
        for( int i = 0 ; i < n ; i++ ){
            String[] params = in.nextLine().split(" ");
            players[i] = new Player(n);
            int[] as = new int[n-1];
            for( int j = 0 ; j < n - 1 ; j++ ){
                as[j] = Integer.parseInt(params[j]) - 1;
            }
            players[i].enemies = as;
        }

        int count = 0;
        // 日単位のループ
        while (true ){

            // 今日の対戦状況を初期化
            for( int i = 0 ; i < n ; i++ ){
                players[i].isMatched = false;
            }

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

                // 既に対戦が終了していた場合はcontinue
                if( players[i].current == n - 1 ){
                    continue;
                }

                // 対戦相手配列index
                int enemyIndex = players[i].enemies[players[i].current];

                // 既にどちらかが対戦済みなら次の対戦相手のチェックへ
                if( players[i].isMatched || players[enemyIndex].isMatched ){
                    continue;
                }

                // 対戦相手とマッチングしたらマッチしたこと、次の対戦相手の情報へ
                if( i == players[enemyIndex].enemies[players[enemyIndex].current] ){
                    players[i].isMatched = true;
                    players[enemyIndex].isMatched = true;
                    players[i].current++;
                    players[enemyIndex].current++;
                }
            }

            count++;

            // 全てのメンバーが最後まで試合できていれば終了
            boolean isEnd = true;
            for( int i = 0 ; i < n ; i++ ){
                if( players[i].current != n - 1 ){
                    isEnd = false;
                    break;
                }
            }
            if( isEnd ){
                System.out.println( count );
                return;
            }

            // 当日全てのメンバーがマッチできなければ-1
            boolean isMatched = false;
            for( int i = 0 ; i < n ; i++ ){
                // 当日すべてのメンバーがマッチできなければ-1
                if( players[i].isMatched ){
                    isMatched = true;
                    break;
                }
            }
            if( !isMatched ){
                System.out.println( -1 );
                return;
            }

        }


    }

}

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